Finite Group Databasebeta

← C22×#513587 #72320953

Subgroups — C22×#513587 #72320953

Order 2048.

819848 conjugacy classes of subgroups.

The subgroup lattice has 1296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13809C212yesmaximal, complemented
2C22×#13749C211yesmaximal, characteristic, complemented
3C22×#13782C213yesmaximal, complemented
4C22×#13814C216yesmaximal, complemented
5C2×#513587C2196yesmaximal, direct product factor
6C22×#13784C213yesmaximal, complemented
7C25×#95C211yesmaximal, characteristic, complemented
8C23×#2275C211yesmaximal, characteristic, complemented
9C22×D4×#95C212yesmaximal, complemented
10C22×#13813C216yesmaximal, complemented
11C22×C4×#379C213yesmaximal, complemented
12C23×C4×#120C213yesmaximal
13C27×C4C2213yes—
14C24×#120C2211yescharacteristic
15C24×C4×D4C2213yes—
16C24×C4×D4C2216yes—
17C22×C4×#120C41192yescomplemented
18C22×C4×#120C221144yes—
19C23×#386C2216yes—
20C23×#386C2213yes—
21C23×#385C2216yes—
22C23×#385C2213yes—
23C23×#379C2213yes—
24C22×#2275—232no—
25C22×#2275C22148yescomplemented
26C23×C4×C4⋊C4C2213yescomplemented
27C23×C4×C22⋊C4C2213yes—
28C23×C4×C22⋊C4C2213yes—
29C23×C4×C22⋊C4C22112yes—
30C23×C4×C22⋊C4C2216yes—
31C23×C4×C22⋊C4C2213yes—
32C23×C4×C22⋊C4C2213yescomplemented
33C23×#376C2211yescharacteristic, complemented
34C24×#95—232no—
35C24×#95C2216yes—
36C24×#95C2212yes—
37C24×#95C2213yes—
38C24×#95C2211yescharacteristic
39C24×#95C22148yescomplemented
40C24×#95C2211yescharacteristic, complemented
41#513587C2211024yesdirect product factor
42C2×#13814C221288yescomplemented
43C2×#13813C221288yescomplemented
44C2×#13809C22196yescomplemented
45C2×D4×#95C22196yescomplemented
46C2×#13784C221144yescomplemented
47C2×#13782C221144yescomplemented
48C2×C4×#379C221144yescomplemented
49C22×#1437C2216yescomplemented
50C22×#1436C22112yescomplemented
51C22×#1436C2216yescomplemented
52C22×C4⋊#95C2216yescomplemented
53C22×#1434C2216yescomplemented
54C22×#1434C2216yescomplemented
55C22×C22⋊#95C2216yes—
56C22×C22⋊#95C2216yes—
57C22×C22⋊#95C2216yes—
58C22×C22⋊#95C2216yescomplemented
59C2×#13749C22148yescomplemented
60C22×C4×#95C2216yescomplemented
61C22×C4×#95C2212yescomplemented
62C28C2311yescharacteristic
63C25×D4C2311yescharacteristic
64C25×D4C2312yes—
65C26×C4—248no—
66C26×C4—248no—
67C26×C4—496no—
68C26×C4C2×C4196yescomplemented
69C26×C4C2316yes—
70C26×C4C2316yes—
71C26×C4C2313yes—
72C26×C4C2313yes—
73C26×C4C23172yes—
74C26×C4C2313yes—
75C23×#120C2×C4196yes—
76C23×#120C23124yes—
77C23×C4×D4—248no—
78C23×C4×D4—248no—
79C23×C4×D4—496no—
80C23×C4×D4C2×C4196yescomplemented
81C23×C4×D4C2×C41192yescomplemented
82C23×C4×D4C23172yes—
83C23×C4×D4C231144yes—
84C24×C4⋊C4C2313yes—
85C24×C4⋊C4C2316yes—
86C24×C22⋊C4C2313yes—
87C24×C22⋊C4C2316yes—
88C24×C22⋊C4C2313yes—
89C24×C22⋊C4C2316yes—
90C24×C22⋊C4C2313yes—
91C24×C22⋊C4C2316yes—
92C24×C22⋊C4C2311yescharacteristic
93C24×C22⋊C4C2312yes—
94C24×C42C2313yes—
95C24×C42C2316yes—
96C24×C42C2316yes—
97C24×C42C2316yes—
98C2×C4×#120C2×C414608yescomplemented
99C2×C4×#120C231768yes—
100C22×#386C2×C41192yescomplemented
101C22×#386C2×C4196yescomplemented
102C22×#386C23172yes—
103C22×#386C231144yes—
104C22×#385C2×C41192yescomplemented
105C22×#385C2×C4196yescomplemented
106C22×#385C23172yes—
107C22×#385C231144yes—
108C22×#379C2×C4196yescomplemented
109C22×#379C23172yes—
110C2×#2275—2768no—
111C2×#2275C231256yescomplemented
112C22×C4×C4⋊C4—248no—
113C22×C4×C4⋊C4C23172yescomplemented
114C22×C4×C22⋊C4—248no—
115C22×C4×C22⋊C4—248no—
116C22×C4×C22⋊C4—248no—
117C22×C4×C22⋊C4—496no—
118C22×C4×C22⋊C4C2×C41192yescomplemented
119C22×C4×C22⋊C4C2×C4196yescomplemented
120C22×C4×C22⋊C4C23172yes—
121C22×C4×C22⋊C4C23172yes—
122C22×C4×C22⋊C4C231288yes—
123C22×C4×C22⋊C4C23172yes—
124C22×C4×C22⋊C4C231144yes—
125C22×C4×C22⋊C4C23172yescomplemented
126C22×#376—216no—
127C22×#376C23124yescomplemented
128C23×#95—232no—
129C23×#95—296no—
130C23×#95—216no—
131C23×#95—2768no—
132C23×#95—248no—
133C23×#95D4132yescomplemented
134C23×#95C2316yes—
135C23×#95C2313yes—
136C23×#95C2313yes—
137C23×#95C2316yes—
138C23×#95C2316yes—
139C23×#95C23172yes—
140C23×#95C23148yes—
141C23×#95C231144yes—
142C23×#95C23112yes—
143C23×#95C23112yes—
144C23×#95C2316yes—
145C23×#95C2316yes—
146C23×#95C2316yes—
147C23×#95C2311yescharacteristic
148C23×#95C2313yes—
149C23×#95C23124yes—
150C23×#95C231256yescomplemented
151C23×#95C23124yescomplemented
152#13814C2311536yescomplemented
153#13813C2311536yescomplemented
154#13809C231512yescomplemented
155D4×#95C231512yescomplemented
156#13784C231768yescomplemented
157#13782C231768yescomplemented
158C4×#379C231768yescomplemented
159C2×#1437C231144yescomplemented
160C2×#1436C231288yescomplemented
161C2×#1436C231144yescomplemented
162C2×C4⋊#95C231144yescomplemented
163C2×#1434C231144yescomplemented
164C2×#1434C231144yescomplemented
165C2×C22⋊#95C231144yes—
166C2×C22⋊#95C231144yes—
167C2×C22⋊#95C231144yes—
168C2×C22⋊#95C231144yescomplemented
169#13749C231256yescomplemented
170C2×C4×#95C23148yescomplemented
171C2×C4×#95C231144yescomplemented
172C27—28no—
173C27—224no—
174C27—248no—
175C27—216no—
176C27C22×C4148yes—
177C27C24112yes—
178C27C2411yescharacteristic
179C27C2411yescharacteristic
180C27C2412yes—
181C24×D4—28no—
182C24×D4—224no—
183C24×D4—248no—
184C24×D4—216no—
185C24×D4C22×C4148yes—
186C24×D4C22×C4196yes—
187C24×D4C24112yes—
188C24×D4C24124yes—
189C25×C4—224no—
190C25×C4—224no—
191C25×C4—296no—
192C25×C4—296no—
193C25×C4—21536no—
194C25×C4—248no—
195C25×C4—248no—
196C25×C4—2576no—
197C25×C4—248no—
198C25×C4—248no—
199C25×C4—2576no—
200C25×C4—224no—
201C25×C4—224no—
202C25×C4—41536no—
203C25×C4—448no—
204C25×C4—448no—
205C25×C4—448no—
206C25×C4—448no—
207C25×C4—41152no—
208C25×C4—448no—
209C25×C4—41536no—
210C25×C4—41536no—
211C25×C4C22×C4196yes—
212C25×C4C22×C4196yes—
213C25×C4C22×C4148yes—
214C25×C4C22×C4148yes—
215C25×C4C22×C411152yescomplemented
216C25×C4C22×C4148yescomplemented
217C25×C4C2×D4148yes—
218C25×C4#41148yes—
219C25×C4C2416yes—
220C25×C4C2413yes—
221C25×C4C2413yes—
222C25×C4C2416yes—
223C25×C4C24172yes—
224C25×C4C24172yes—
225C25×C4C2411yescharacteristic
226C25×C4C2412yes—
227C25×C4C2413yes—
228C25×C4C2413yes—
229C25×C4C24136yes—
230C25×C4C241192yes—
231C25×C4C24136yes—
232C25×C4C24136yes—
233C22×#120C4211024yescomplemented
234C22×#120C22×C411152yes—
235C22×#120C24164yes—
236C22×C4×D4—21536no—
237C22×C4×D4—2576no—
238C22×C4×D4—2576no—
239C22×C4×D4—41536no—
240C22×C4×D4—41152no—
241C22×C4×D4C22×C411152yescomplemented
242C22×C4×D4C22×C412304yescomplemented
243C22×C4×D4C241192yes—
244C22×C4×D4C241384yes—
245C23×C4⋊C4—224no—
246C23×C4⋊C4—224no—
247C23×C4⋊C4—448no—
248C23×C4⋊C4C22×C4148yescomplemented
249C23×C4⋊C4C22×C4196yescomplemented
250C23×C4⋊C4C24136yes—
251C23×C4⋊C4C24172yes—
252C23×C22⋊C4—224no—
253C23×C22⋊C4—224no—
254C23×C22⋊C4—248no—
255C23×C22⋊C4—296no—
256C23×C22⋊C4—248no—
257C23×C22⋊C4—248no—
258C23×C22⋊C4—224no—
259C23×C22⋊C4—224no—
260C23×C22⋊C4—448no—
261C23×C22⋊C4C22×C4148yes—
262C23×C22⋊C4C22×C4196yes—
263C23×C22⋊C4C22×C4148yes—
264C23×C22⋊C4C22×C4196yes—
265C23×C22⋊C4C22×C4148yes—
266C23×C22⋊C4C22×C4196yes—
267C23×C22⋊C4C22×C4148yescomplemented
268C23×C22⋊C4C22×C4196yescomplemented
269C23×C22⋊C4C24136yes—
270C23×C22⋊C4C24172yes—
271C23×C22⋊C4C24136yes—
272C23×C22⋊C4C24172yes—
273C23×C22⋊C4C24136yes—
274C23×C22⋊C4C24172yes—
275C23×C22⋊C4C24112yes—
276C23×C22⋊C4C24124yes—
277C23×C42—224no—
278C23×C42—248no—
279C23×C42—224no—
280C23×C42—248no—
281C23×C42—448no—
282C23×C42—448no—
283C23×C42—448no—
284C23×C42C22×C4148yescomplemented
285C23×C42C22×C4196yescomplemented
286C23×C42C24136yes—
287C23×C42C24172yes—
288C23×C42C24172yes—
289C23×C42C24172yes—
290C4×#120C22×C4112288yescomplemented
291C2×#386C22×C412304yescomplemented
292C2×#386C22×C411152yescomplemented
293C2×#386C241192yes—
294C2×#386C241384yes—
295C2×#385C22×C412304yescomplemented
296C2×#385C22×C411152yescomplemented
297C2×#385C241192yes—
298C2×#385C241384yes—
299C2×#379C22×C411152yescomplemented
300C2×#379C241192yes—
301#2275—22048no—
302C2×C4×C4⋊C4—2576no—
303C2×C4×C4⋊C4C241192yescomplemented
304C2×C4×C22⋊C4—2576no—
305C2×C4×C22⋊C4—2576no—
306C2×C4×C22⋊C4—2576no—
307C2×C4×C22⋊C4—41152no—
308C2×C4×C22⋊C4C22×C412304yescomplemented
309C2×C4×C22⋊C4C22×C411152yescomplemented
310C2×C4×C22⋊C4C241192yes—
311C2×C4×C22⋊C4C241192yes—
312C2×C4×C22⋊C4C241768yes—
313C2×C4×C22⋊C4C241192yes—
314C2×C4×C22⋊C4C241384yes—
315C2×C4×C22⋊C4C241192yescomplemented
316C2×#376—2192no—
317C2×#376C24164yescomplemented
318C22×#95—2384no—
319C22×#95—21152no—
320C22×#95—2192no—
321C22×#95—22048no—
322C22×#95—248no—
323C22×#95—248no—
324C22×#95—2576no—
325C22×#95—224no—
326C22×#95—224no—
327C22×#95—248no—
328C22×#95—448no—
329C22×#95—448no—
330C22×#95C22×C4196yescomplemented
331C22×#95C22×C4196yescomplemented
332C22×#95C22×C4196yescomplemented
333C22×#95C2×D4116yes—
334C22×#95C2×D4148yes—
335C22×#95C2×D41384yescomplemented
336C22×#95C24172yes—
337C22×#95C24136yes—
338C22×#95C24136yes—
339C22×#95C24172yes—
340C22×#95C24172yes—
341C22×#95C241192yes—
342C22×#95C241128yes—
343C22×#95C241384yes—
344C22×#95C241144yes—
345C22×#95C241144yes—
346C22×#95C24172yes—
347C22×#95C24172yes—
348C22×#95C24172yes—
349C22×#95C24112yes—
350C22×#95C24136yes—
351C22×#95C24164yes—
352C22×#95C24164yescomplemented
353#1437C241384yescomplemented
354#1436C241768yescomplemented
355#1436C241384yescomplemented
356C4⋊#95C241384yescomplemented
357#1434C241384yescomplemented
358#1434C241384yescomplemented
359C22⋊#95C241384yes—
360C22⋊#95C241384yes—
361C22⋊#95C241384yes—
362C22⋊#95C241384yescomplemented
363C4×#95C241128yescomplemented
364C4×#95C241384yescomplemented
365C26—2384no—
366C26—2768no—
367C26—2128no—
368C26—2768no—
369C26—2384no—
370C26—2384no—
371C26—2768no—
372C26—2768no—
373C26—248no—
374C26—28no—
375C26—2144no—
376C26—224no—
377C26—2288no—
378C26—224no—
379C26—224no—
380C26—296no—
381C26—28no—
382C26—28no—
383C26—24no—
384C26—212no—
385C26—224no—
386C26—28no—
387C26C2×C421256yes—
388C26C23×C41288yes—
389C26C23×C4124yes—
390C26C23×C4124yes—
391C26C23×C4148yes—
392C26C22×D418yes—
393C26C2×#41124yes—
394C26H(5,𝔽2)148yes—
395C262−1+4116yes—
396C26C25116yes—
397C26C2516yes—
398C26C2516yes—
399C26C25112yes—
400C26C2511yescharacteristic
401C23×D4—2384no—
402C23×D4—2384no—
403C23×D4—2768no—
404C23×D4—2768no—
405C23×D4—248no—
406C23×D4—2144no—
407C23×D4—2288no—
408C23×D4—296no—
409C23×D4C2×C421256yes—
410C23×D4C2×C421512yes—
411C23×D4C23×C41288yes—
412C23×D4C23×C41576yes—
413C23×D4C25116yes—
414C23×D4C25132yes—
415C24×C4—24no—
416C24×C4—212no—
417C24×C4—248no—
418C24×C4—248no—
419C24×C4—224no—
420C24×C4—28no—
421C24×C4—2384no—
422C24×C4—2768no—
423C24×C4—2768no—
424C24×C4—2144no—
425C24×C4—224no—
426C24×C4—212no—
427C24×C4—212no—
428C24×C4—2144no—
429C24×C4—224no—
430C24×C4—212no—
431C24×C4—212no—
432C24×C4—248no—
433C24×C4—248no—
434C24×C4—2576no—
435C24×C4—248no—
436C24×C4—2576no—
437C24×C4—248no—
438C24×C4—248no—
439C24×C4—224no—
440C24×C4—224no—
441C24×C4—224no—
442C24×C4—224no—
443C24×C4—2768no—
444C24×C4—2768no—
445C24×C4—29216no—
446C24×C4—2288no—
447C24×C4—2288no—
448C24×C4—2768no—
449C24×C4—2288no—
450C24×C4—2288no—
451C24×C4—2768no—
452C24×C4—2384no—
453C24×C4—2144no—
454C24×C4—2144no—
455C24×C4—4384no—
456C24×C4—4384no—
457C24×C4—4384no—
458C24×C4—4384no—
459C24×C4—49216no—
460C24×C4—4384no—
461C24×C4—4384no—
462C24×C4—4288no—
463C24×C4—4288no—
464C24×C4—4288no—
465C24×C4—4288no—
466C24×C4—41536no—
467C24×C4—4384no—
468C24×C4—4288no—
469C24×C4—4768no—
470C24×C4—4768no—
471C24×C4—4768no—
472C24×C4—4768no—
473C24×C4—424576no—
474C24×C4—49216no—
475C24×C4—49216no—
476C24×C4—4384no—
477C24×C4—4384no—
478C24×C4—8192no—
479C24×C4—8192no—
480C24×C4C4×D41768yescomplemented
481C24×C4C23×C4148yes—
482C24×C4C23×C4124yes—
483C24×C4C23×C4124yes—
484C24×C4C23×C4148yes—
485C24×C4C23×C41576yes—
486C24×C4C23×C41576yes—
487C24×C4C23×C4124yes—
488C24×C4C23×C4124yes—
489C24×C4C23×C4124yes—
490C24×C4C23×C4148yes—
491C24×C4C23×C41288yes—
492C24×C4C23×C41288yes—
493C24×C4C23×C411536yescomplemented
494C24×C4C23×C41288yescomplemented
495C24×C4C22×D4124yes—
496C24×C4C22×D4124yes—
497C24×C4C22×D41288yes—
498C24×C4C2×#41124yes—
499C24×C4C2×#41124yes—
500C24×C4C2×#411288yes—
501C24×C4C25136yes—
502C24×C4C25118yes—
503C24×C4C25118yes—
504C24×C4C25136yes—
505C24×C4C25196yes—
506C24×C4C25196yes—
507C24×C4C2516yes—
508C24×C4C25112yes—
509C24×C4C25118yes—
510C24×C4C25118yes—
511C24×C4C25148yes—
512C24×C4C25148yes—
513C24×C4C25148yes—
514C2×#120C2×C4216144yescomplemented
515C2×#120C23×C411536yes—
516C2×C4×D4—29216no—
517C2×C4×D4—2768no—
518C2×C4×D4—2768no—
519C2×C4×D4—49216no—
520C2×C4×D4—41536no—
521C2×C4×D4C23×C411536yescomplemented
522C2×C4×D4C23×C413072yescomplemented
523C22×C4⋊C4—2384no—
524C22×C4⋊C4—2144no—
525C22×C4⋊C4—2144no—
526C22×C4⋊C4—4384no—
527C22×C4⋊C4—4288no—
528C22×C4⋊C4C23×C41288yescomplemented
529C22×C4⋊C4C23×C41576yescomplemented
530C22×C4⋊C4C25148yes—
531C22×C4⋊C4C25196yes—
532C22×C22⋊C4—2384no—
533C22×C22⋊C4—2384no—
534C22×C22⋊C4—2768no—
535C22×C22⋊C4—2768no—
536C22×C22⋊C4—2144no—
537C22×C22⋊C4—2144no—
538C22×C22⋊C4—2288no—
539C22×C22⋊C4—2576no—
540C22×C22⋊C4—2288no—
541C22×C22⋊C4—2288no—
542C22×C22⋊C4—2384no—
543C22×C22⋊C4—2144no—
544C22×C22⋊C4—2144no—
545C22×C22⋊C4—4384no—
546C22×C22⋊C4—4288no—
547C22×C22⋊C4C2×C421256yes—
548C22×C22⋊C4C2×C421512yes—
549C22×C22⋊C4C23×C41288yes—
550C22×C22⋊C4C23×C41576yes—
551C22×C22⋊C4C23×C41288yes—
552C22×C22⋊C4C23×C41576yes—
553C22×C22⋊C4C23×C41288yes—
554C22×C22⋊C4C23×C41576yes—
555C22×C22⋊C4C23×C41288yescomplemented
556C22×C22⋊C4C23×C41576yescomplemented
557C22×C22⋊C4C25148yes—
558C22×C22⋊C4C25196yes—
559C22×C22⋊C4C25148yes—
560C22×C22⋊C4C25196yes—
561C22×C22⋊C4C25148yes—
562C22×C22⋊C4C25196yes—
563C22×C22⋊C4C25116yes—
564C22×C22⋊C4C25132yes—
565C22×C42—2384no—
566C22×C42—2144no—
567C22×C42—2144no—
568C22×C42—2288no—
569C22×C42—2288no—
570C22×C42—4384no—
571C22×C42—4288no—
572C22×C42—4288no—
573C22×C42—4288no—
574C22×C42—8192no—
575C22×C42—8192no—
576C22×C42C23×C41288yescomplemented
577C22×C42C23×C41576yescomplemented
578C22×C42C25148yes—
579C22×C42C25196yes—
580C22×C42C25196yes—
581C22×C42C25196yes—
582#386C23×C413072yescomplemented
583#386C23×C411536yescomplemented
584#385C23×C413072yescomplemented
585#385C23×C411536yescomplemented
586#379C23×C411536yescomplemented
587C4×C4⋊C4—2768no—
588C4×C22⋊C4—2768no—
589C4×C22⋊C4—2768no—
590C4×C22⋊C4—2768no—
591C4×C22⋊C4—41536no—
592C4×C22⋊C4C23×C413072yescomplemented
593C4×C22⋊C4C23×C411536yescomplemented
594#376—2256no—
595C2×#95—2288no—
596C2×#95—2288no—
597C2×#95—2768no—
598C2×#95—2144no—
599C2×#95—2144no—
600C2×#95—2288no—
601C2×#95—2512no—
602C2×#95—21536no—
603C2×#95—2256no—
604C2×#95—4288no—
605C2×#95—4288no—
606C2×#95C23×C41576yescomplemented
607C2×#95C23×C41576yescomplemented
608C2×#95C23×C41576yescomplemented
609C2×#95C22×D4196yes—
610C2×#95C22×D41288yes—
611C2×#95C22×D41512yescomplemented
612C2×#95C25196yes—
613C2×#95C25148yes—
614C2×#95C25148yes—
615C2×#95C25196yes—
616C2×#95C25196yes—
617C2×#95C251192yes—
618C2×#95C251192yes—
619C2×#95C25196yes—
620C2×#95C25196yes—
621C2×#95C25196yes—
622C2×#95C25116yes—
623C2×#95C25148yes—
624C25—21152no—
625C25—22304no—
626C25—26144no—
627C25—22304no—
628C25—2384no—
629C25—26144no—
630C25—212288no—
631C25—232no—
632C25—224no—
633C25—296no—
634C25—272no—
635C25—2192no—
636C25—272no—
637C25—272no—
638C25—264no—
639C25—224no—
640C25—224no—
641C25—21152no—
642C25—2192no—
643C25—21152no—
644C25—2192no—
645C25—22304no—
646C25—2192no—
647C25—2192no—
648C25—22304no—
649C25—2192no—
650C25—2192no—
651C25—296no—
652C25—2192no—
653C25—232no—
654C25—264no—
655C25—2192no—
656C25—2384no—
657C25—2192no—
658C25—2192no—
659C25—2192no—
660C25—22048no—
661C25—24096no—
662C25—212no—
663C25—236no—
664C25—272no—
665C25—224no—
666C25—296no—
667C25—296no—
668C25—2192no—
669C25—2192no—
670C25—448no—
671C25—416no—
672C25—496no—
673C25—496no—
674C25C22×C421768yes—
675C25C22×C42164yes—
676C25C22×C42164yes—
677C25C22×C421128yes—
678C25C2×C4×D41192yes—
679C25C4×#411192yes—
680C25#5181384yes—
681C25#5201384yes—
682C25C24×C4172yes—
683C25C24×C41192yes—
684C25C24×C4172yes—
685C25C24×C41144yes—
686C25C24×C4112yes—
687C25C23×D4124yes—
688C25C23×D414yes—
689C25C22×#41172yes—
690C25C22×#41112yes—
691C25C2×H(5,𝔽2)1144yes—
692C25C2×H(5,𝔽2)124yes—
693C25C2×2−1+4148yes—
694C25C2×2−1+418yes—
695C25C2614yes—
696C25C2614yes—
697C25C2618yes—
698C25C2613yes—
699C22×D4—232no—
700C22×D4—296no—
701C22×D4—2192no—
702C22×D4—264no—
703C22×D4—21152no—
704C22×D4—21152no—
705C22×D4—22304no—
706C22×D4—22304no—
707C22×D4—22048no—
708C22×D4—24096no—
709C22×D4C22×C421768yes—
710C22×D4C22×C4211536yes—
711C22×D4C24×C41192yes—
712C22×D4C24×C41384yes—
713C23×C4—212no—
714C23×C4—236no—
715C23×C4—272no—
716C23×C4—2144no—
717C23×C4—2144no—
718C23×C4—224no—
719C23×C4—296no—
720C23×C4—296no—
721C23×C4—2192no—
722C23×C4—2192no—
723C23×C4—2192no—
724C23×C4—2192no—
725C23×C4—2192no—
726C23×C4—2192no—
727C23×C4—2192no—
728C23×C4—2192no—
729C23×C4—236no—
730C23×C4—236no—
731C23×C4—296no—
732C23×C4—272no—
733C23×C4—236no—
734C23×C4—236no—
735C23×C4—2144no—
736C23×C4—296no—
737C23×C4—272no—
738C23×C4—2144no—
739C23×C4—2144no—
740C23×C4—272no—
741C23×C4—272no—
742C23×C4—2144no—
743C23×C4—2384no—
744C23×C4—2144no—
745C23×C4—2384no—
746C23×C4—272no—
747C23×C4—272no—
748C23×C4—296no—
749C23×C4—296no—
750C23×C4—21152no—
751C23×C4—2192no—
752C23×C4—2192no—
753C23×C4—2192no—
754C23×C4—2192no—
755C23×C4—2192no—
756C23×C4—22304no—
757C23×C4—22304no—
758C23×C4—2192no—
759C23×C4—2192no—
760C23×C4—2192no—
761C23×C4—2192no—
762C23×C4—2192no—
763C23×C4—2192no—
764C23×C4—2192no—
765C23×C4—22304no—
766C23×C4—22304no—
767C23×C4—26144no—
768C23×C4—296no—
769C23×C4—296no—
770C23×C4—21152no—
771C23×C4—43072no—
772C23×C4—41152no—
773C23×C4—41152no—
774C23×C4—41152no—
775C23×C4—41152no—
776C23×C4—46144no—
777C23×C4—41152no—
778C23×C4—41152no—
779C23×C4—4192no—
780C23×C4—4192no—
781C23×C4—4192no—
782C23×C4—4192no—
783C23×C4—41152no—
784C23×C4—4192no—
785C23×C4—42304no—
786C23×C4—42304no—
787C23×C4—42304no—
788C23×C4—42304no—
789C23×C4—46144no—
790C23×C4—46144no—
791C23×C4—473728no—
792C23×C4—46144no—
793C23×C4—46144no—
794C23×C4—41152no—
795C23×C4—41152no—
796C23×C4—43072no—
797C23×C4—4192no—
798C23×C4—496no—
799C23×C4—448no—
800C23×C4—448no—
801C23×C4—4192no—
802C23×C4—496no—
803C23×C4—4192no—
804C23×C4—496no—
805C23×C4—4192no—
806C23×C4—8576no—
807C23×C4—8576no—
808C23×C4—81536no—
809C23×C4C22×C42164yes—
810C23×C4C22×C421128yes—
811C23×C4C2×C4×D41192yes—
812C23×C4C2×C4×D41192yes—
813C23×C4C2×C4×D412304yescomplemented
814C23×C4C24×C4172yes—
815C23×C4C24×C41144yes—
816C23×C4C24×C4172yes—
817C23×C4C24×C41144yes—
818C23×C4C24×C41384yes—
819C23×C4C24×C41384yes—
820C23×C4C24×C4172yes—
821C23×C4C24×C41144yes—
822C23×C4C24×C4172yes—
823C23×C4C24×C4172yes—
824C23×C4C24×C41192yes—
825C23×C4C24×C41192yes—
826C23×C4C24×C41192yescomplemented
827C23×C4C23×D4172yes—
828C23×C4C23×D4172yes—
829C23×C4C23×D41192yes—
830C23×C4C22×#41172yes—
831C23×C4C22×#41172yes—
832C23×C4C22×#411192yes—
833C23×C4C26112yes—
834C23×C4C26124yes—
835C23×C4C26112yes—
836C23×C4C26124yes—
837C23×C4C2614yes—
838C23×C4C2618yes—
839C23×C4C26112yes—
840C23×C4C26112yes—
841#120C22×C4214096yescomplemented
842C4×D4—26144no—
843C4×D4—46144no—
844C2×C4⋊C4—296no—
845C2×C4⋊C4—296no—
846C2×C4⋊C4—21152no—
847C2×C4⋊C4—41152no—
848C2×C4⋊C4—4192no—
849C2×C4⋊C4C24×C41192yescomplemented
850C2×C4⋊C4C24×C41384yescomplemented
851C2×C22⋊C4—296no—
852C2×C22⋊C4—296no—
853C2×C22⋊C4—2192no—
854C2×C22⋊C4—2384no—
855C2×C22⋊C4—2192no—
856C2×C22⋊C4—2192no—
857C2×C22⋊C4—21152no—
858C2×C22⋊C4—21152no—
859C2×C22⋊C4—22304no—
860C2×C22⋊C4—22304no—
861C2×C22⋊C4—296no—
862C2×C22⋊C4—296no—
863C2×C22⋊C4—21152no—
864C2×C22⋊C4—41152no—
865C2×C22⋊C4—4192no—
866C2×C22⋊C4C22×C421768yes—
867C2×C22⋊C4C22×C4211536yes—
868C2×C22⋊C4C24×C41192yes—
869C2×C22⋊C4C24×C41384yes—
870C2×C22⋊C4C24×C41192yes—
871C2×C22⋊C4C24×C41384yes—
872C2×C22⋊C4C24×C41192yes—
873C2×C22⋊C4C24×C41384yes—
874C2×C22⋊C4C24×C41192yescomplemented
875C2×C22⋊C4C24×C41384yescomplemented
876C2×C42—296no—
877C2×C42—296no—
878C2×C42—21152no—
879C2×C42—2192no—
880C2×C42—2192no—
881C2×C42—41152no—
882C2×C42—4192no—
883C2×C42—4192no—
884C2×C42—4192no—
885C2×C42—8576no—
886C2×C42—8576no—
887C2×C42C24×C41192yescomplemented
888C2×C42C24×C41384yescomplemented
889#95—2192no—
890#95—2192no—
891#95—296no—
892#95—296no—
893#95—2192no—
894#95—4192no—
895#95—4192no—
896#95C24×C41384yescomplemented
897#95C24×C41384yescomplemented
898#95C24×C41384yescomplemented
899#95C23×D4164yes—
900#95C23×D41192yes—
901C24—2384no—
902C24—2768no—
903C24—29216no—
904C24—218432no—
905C24—29216no—
906C24—232768no—
907C24—2768no—
908C24—2128no—
909C24—2144no—
910C24—2288no—
911C24—2288no—
912C24—2576no—
913C24—2288no—
914C24—2288no—
915C24—2288no—
916C24—248no—
917C24—296no—
918C24—28no—
919C24—224no—
920C24—224no—
921C24—224no—
922C24—28no—
923C24—28no—
924C24—2768no—
925C24—21536no—
926C24—2768no—
927C24—21536no—
928C24—21536no—
929C24—21536no—
930C24—21536no—
931C24—2384no—
932C24—2288no—
933C24—2384no—
934C24—2288no—
935C24—2768no—
936C24—2288no—
937C24—2288no—
938C24—2768no—
939C24—2288no—
940C24—2288no—
941C24—23072no—
942C24—2512no—
943C24—2512no—
944C24—2512no—
945C24—26144no—
946C24—24no—
947C24—212no—
948C24—224no—
949C24—28no—
950C24—2144no—
951C24—2144no—
952C24—2288no—
953C24—2288no—
954C24—2256no—
955C24—2512no—
956C24—472no—
957C24—4144no—
958C24—4144no—
959C24—424no—
960C24—4384no—
961C24—4384no—
962C24—4768no—
963C24C42×D41512yes—
964C24#227511024yescomplemented
965C24C23×C421256yes—
966C24C23×C42196yes—
967C24C23×C42196yes—
968C24C23×C421192yes—
969C24C23×C42116yes—
970C24C22×C4×D41288yes—
971C24C22×C4×D4148yes—
972C24C2×C4×#411288yes—
973C24C2×C4×#41148yes—
974C24C2×#5181576yes—
975C24C2×#518196yes—
976C24C2×#5201576yes—
977C24C2×#520196yes—
978C24#3484148yes—
979C24#3486116yes—
980C24#3490196yes—
981C24#3492196yes—
982C24C25×C4124yes—
983C24C25×C4124yes—
984C24C25×C4148yes—
985C24C25×C4118yes—
986C24C24×D418yes—
987C24C24×D416yes—
988C24C23×#41124yes—
989C24C23×#41118yes—
990C24C22×H(5,𝔽2)148yes—
991C24C22×H(5,𝔽2)136yes—
992C24C22×2−1+4116yes—
993C24C22×2−1+4112yes—
994C24C2711yescharacteristic
995C2×D4—2384no—
996C2×D4—2384no—
997C2×D4—2768no—
998C2×D4—2768no—
999C2×D4—23072no—
1000C2×D4—26144no—
1001C2×D4C23×C421256yes—
1002C2×D4C23×C421512yes—
1003C22×C4—2288no—
1004C22×C4—2288no—
1005C22×C4—2288no—
1006C22×C4—2288no—
1007C22×C4—24no—
1008C22×C4—212no—
1009C22×C4—224no—
1010C22×C4—248no—
1011C22×C4—248no—
1012C22×C4—28no—
1013C22×C4—2768no—
1014C22×C4—2768no—
1015C22×C4—2144no—
1016C22×C4—2144no—
1017C22×C4—2288no—
1018C22×C4—2288no—
1019C22×C4—2288no—
1020C22×C4—2288no—
1021C22×C4—2256no—
1022C22×C4—2512no—
1023C22×C4—224no—
1024C22×C4—212no—
1025C22×C4—212no—
1026C22×C4—248no—
1027C22×C4—212no—
1028C22×C4—212no—
1029C22×C4—224no—
1030C22×C4—224no—
1031C22×C4—224no—
1032C22×C4—248no—
1033C22×C4—248no—
1034C22×C4—248no—
1035C22×C4—248no—
1036C22×C4—224no—
1037C22×C4—224no—
1038C22×C4—2144no—
1039C22×C4—2144no—
1040C22×C4—2384no—
1041C22×C4—2288no—
1042C22×C4—2288no—
1043C22×C4—2288no—
1044C22×C4—2288no—
1045C22×C4—2288no—
1046C22×C4—2768no—
1047C22×C4—2768no—
1048C22×C4—2288no—
1049C22×C4—2288no—
1050C22×C4—2288no—
1051C22×C4—2768no—
1052C22×C4—2768no—
1053C22×C4—2384no—
1054C22×C4—44608no—
1055C22×C4—4384no—
1056C22×C4—4384no—
1057C22×C4—4384no—
1058C22×C4—4384no—
1059C22×C4—4384no—
1060C22×C4—4384no—
1061C22×C4—4384no—
1062C22×C4—4768no—
1063C22×C4—4768no—
1064C22×C4—4768no—
1065C22×C4—4768no—
1066C22×C4—49216no—
1067C22×C4—49216no—
1068C22×C4—424576no—
1069C22×C4—4384no—
1070C22×C4—4384no—
1071C22×C4—44608no—
1072C22×C4—472no—
1073C22×C4—4144no—
1074C22×C4—4288no—
1075C22×C4—4288no—
1076C22×C4—4288no—
1077C22×C4—4144no—
1078C22×C4—4288no—
1079C22×C4—4144no—
1080C22×C4—472no—
1081C22×C4—4768no—
1082C22×C4—4384no—
1083C22×C4—4384no—
1084C22×C4—4768no—
1085C22×C4—8192no—
1086C22×C4—8192no—
1087C22×C4—82304no—
1088C22×C4C23×C42196yes—
1089C22×C4C23×C421192yes—
1090C22×C4C22×C4×D41288yes—
1091C22×C4C22×C4×D41288yes—
1092C22×C4C22×C4×D41768yescomplemented
1093C22×C4C25×C4124yes—
1094C22×C4C25×C4148yes—
1095C22×C4C25×C4148yes—
1096C22×C4C25×C4124yes—
1097C22×C4C25×C4124yes—
1098C22×C4C25×C4148yes—
1099C22×C4C25×C4124yes—
1100C22×C4C25×C4124yes—
1101C22×C4C24×D4124yes—
1102C22×C4C24×D4124yes—
1103C22×C4C23×#41124yes—
1104C22×C4C23×#41124yes—
1105C4⋊C4—2384no—
1106C4⋊C4—4384no—
1107C22⋊C4—2384no—
1108C22⋊C4—2384no—
1109C22⋊C4—2768no—
1110C22⋊C4—2768no—
1111C22⋊C4—2384no—
1112C22⋊C4—4384no—
1113C22⋊C4C23×C421256yes—
1114C22⋊C4C23×C421512yes—
1115C42—2384no—
1116C42—4384no—
1117C42—8192no—
1118C42—8192no—
1119C23—21536no—
1120C23—23072no—
1121C23—224576no—
1122C23—21536no—
1123C23—21152no—
1124C23—21152no—
1125C23—21152no—
1126C23—248no—
1127C23—248no—
1128C23—248no—
1129C23—248no—
1130C23—2576no—
1131C23—21152no—
1132C23—248no—
1133C23—248no—
1134C23—22048no—
1135C23—24096no—
1136C23—224no—
1137C23—248no—
1138C23—248no—
1139C23—296no—
1140C23—248no—
1141C23—248no—
1142C23—248no—
1143C23—28no—
1144C23—216no—
1145C23—2512no—
1146C23—2384no—
1147C23—2384no—
1148C23—2384no—
1149C23—21024no—
1150C23—2576no—
1151C23—21152no—
1152C23—224no—
1153C23—224no—
1154C23—248no—
1155C23—248no—
1156C23—2192no—
1157C23—2384no—
1158C23—4576no—
1159C23—4288no—
1160C23—41024no—
1161C23—412no—
1162C23—424no—
1163C23—424no—
1164C23—44no—
1165C23—4288no—
1166C23C2×C42×D41384yes—
1167C23C2×C42×D4164yes—
1168C23C2×#22751128yes—
1169C23C2×#22751768yescomplemented
1170C23#341981192yes—
1171C23#342001192yes—
1172C23#342181384yes—
1173C23C24×C42116yes—
1174C23C24×C42116yes—
1175C23C24×C42132yes—
1176C23C24×C42112yes—
1177C23C23×C4×D4148yes—
1178C23C23×C4×D4136yes—
1179C23C22×C4×#41148yes—
1180C23C22×C4×#41136yes—
1181C23C22×#518196yes—
1182C23C22×#518172yes—
1183C23C22×#520196yes—
1184C23C22×#520172yes—
1185C23C2×#3484136yes—
1186C23C2×#3490172yes—
1187C23C2×#3492172yes—
1188C23C2×#3486112yes—
1189C23C26×C413yes—
1190C23C25×D411yescharacteristic
1191C23C24×#4113yes—
1192C23C23×H(5,𝔽2)16yes—
1193C23C23×2−1+412yes—
1194D4—2512no—
1195D4—21024no—
1196C2×C4—224no—
1197C2×C4—224no—
1198C2×C4—248no—
1199C2×C4—248no—
1200C2×C4—248no—
1201C2×C4—248no—
1202C2×C4—248no—
1203C2×C4—248no—
1204C2×C4—248no—
1205C2×C4—248no—
1206C2×C4—2192no—
1207C2×C4—2384no—
1208C2×C4—2576no—
1209C2×C4—2576no—
1210C2×C4—224no—
1211C2×C4—224no—
1212C2×C4—248no—
1213C2×C4—248no—
1214C2×C4—248no—
1215C2×C4—248no—
1216C2×C4—248no—
1217C2×C4—248no—
1218C2×C4—248no—
1219C2×C4—248no—
1220C2×C4—4768no—
1221C2×C4—41536no—
1222C2×C4—41536no—
1223C2×C4—4768no—
1224C2×C4—4576no—
1225C2×C4—4288no—
1226C2×C4—412no—
1227C2×C4—424no—
1228C2×C4—448no—
1229C2×C4—448no—
1230C2×C4—448no—
1231C2×C4—424no—
1232C2×C4—448no—
1233C2×C4—424no—
1234C2×C4—412no—
1235C2×C4—4576no—
1236C2×C4—4288no—
1237C2×C4—8384no—
1238C2×C4C24×C42116yes—
1239C2×C4C24×C42132yes—
1240C2×C4C23×C4×D4148yes—
1241C2×C4C23×C4×D4148yes—
1242C22—22048no—
1243C22—232no—
1244C22—248no—
1245C22—296no—
1246C22—232no—
1247C22—232no—
1248C22—296no—
1249C22—296no—
1250C22—296no—
1251C22—2768no—
1252C22—21536no—
1253C22—248no—
1254C22—296no—
1255C22—216no—
1256C22—232no—
1257C22—424no—
1258C22—448no—
1259C22—4384no—
1260C22—424no—
1261C22#5135871256yesdirect product factor
1262C22C22×C42×D4132yes—
1263C22C22×C42×D4124yes—
1264C22C22×#2275148yes—
1265C22C22×#2275164yescomplemented
1266C22C2×#34198172yes—
1267C22C2×#342181144yes—
1268C22C2×#34200172yes—
1269C22C25×C4211yescharacteristic
1270C22C24×C4×D413yes—
1271C22C23×C4×#4113yes—
1272C22C23×#51816yes—
1273C22C23×#52016yes—
1274C22C22×#348413yes—
1275C22C22×#349016yes—
1276C22C22×#349216yes—
1277C22C22×#348611yescharacteristic
1278C4—216no—
1279C4—248no—
1280C4—248no—
1281C4—232no—
1282C4—448no—
1283C4—424no—
1284C4—448no—
1285C4—424no—
1286C2—232no—
1287C2—264no—
1288C2—416no—
1289C2C22×#3419813yes—
1290C2C23×C42×D411yescharacteristic
1291C2C23×#227512yes—
1292C2C22×#3420013yes—
1293C2C2×#513587148yesdirect product factor
1294C2C22×#3421816yes—
subgroupG/H
center, socleC26C25
commutatorC22C25×C42
Frattini, cosocleC24C27
prime radicalC24×#120C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C26 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#13809C2semidirect
2. C22×#13749C2semidirect
3. C22×#13782C2semidirect
4. C22×#13814C2semidirect
5. C2×#513587C2direct (N × H)
6. C22×#13784C2semidirect
7. C25×#95C2semidirect
8. C23×#2275C2semidirect
9. C22×D4×#95C2semidirect
10. C22×#13813C2semidirect
11. C22×C4×#379C2semidirect
17. C22×C4×#120C4semidirect
25. C22×#2275C22semidirect
26. C23×C4×C4⋊C4C22semidirect
32. C23×C4×C22⋊C4C22semidirect
33. C23×#376C22semidirect
39. C24×#95C22semidirect
40. C24×#95C22semidirect
41. #513587C22direct (N × H)
42. C2×#13814C22semidirect
43. C2×#13813C22semidirect
44. C2×#13809C22semidirect
45. C2×D4×#95C22semidirect
46. C2×#13784C22semidirect
47. C2×#13782C22semidirect
48. C2×C4×#379C22semidirect
49. C22×#1437C22semidirect
50. C22×#1436C22semidirect
51. C22×#1436C22semidirect
52. C22×C4⋊#95C22semidirect
53. C22×#1434C22semidirect
54. C22×#1434C22semidirect
58. C22×C22⋊#95C22semidirect
59. C2×#13749C22semidirect
60. C22×C4×#95C22semidirect
61. C22×C4×#95C22semidirect
68. C26×C4C2×C4semidirect
80. C23×C4×D4C2×C4semidirect
81. C23×C4×D4C2×C4semidirect
98. C2×C4×#120C2×C4semidirect
100. C22×#386C2×C4semidirect
101. C22×#386C2×C4semidirect
104. C22×#385C2×C4semidirect
105. C22×#385C2×C4semidirect
108. C22×#379C2×C4semidirect
111. C2×#2275C23semidirect
113. C22×C4×C4⋊C4C23semidirect
118. C22×C4×C22⋊C4C2×C4semidirect
119. C22×C4×C22⋊C4C2×C4semidirect
125. C22×C4×C22⋊C4C23semidirect
127. C22×#376C23semidirect
133. C23×#95D4semidirect
150. C23×#95C23semidirect
151. C23×#95C23semidirect
152. #13814C23semidirect
153. #13813C23semidirect
154. #13809C23semidirect
155. D4×#95C23semidirect
156. #13784C23semidirect
157. #13782C23semidirect
158. C4×#379C23semidirect
159. C2×#1437C23semidirect
160. C2×#1436C23semidirect
161. C2×#1436C23semidirect
162. C2×C4⋊#95C23semidirect
163. C2×#1434C23semidirect
164. C2×#1434C23semidirect
168. C2×C22⋊#95C23semidirect
169. #13749C23semidirect
170. C2×C4×#95C23semidirect
171. C2×C4×#95C23semidirect
215. C25×C4C22×C4semidirect
216. C25×C4C22×C4semidirect
233. C22×#120C42semidirect
241. C22×C4×D4C22×C4semidirect
242. C22×C4×D4C22×C4semidirect
248. C23×C4⋊C4C22×C4semidirect
249. C23×C4⋊C4C22×C4semidirect
267. C23×C22⋊C4C22×C4semidirect
268. C23×C22⋊C4C22×C4semidirect
284. C23×C42C22×C4semidirect
285. C23×C42C22×C4semidirect
290. C4×#120C22×C4semidirect
291. C2×#386C22×C4semidirect
292. C2×#386C22×C4semidirect
295. C2×#385C22×C4semidirect
296. C2×#385C22×C4semidirect
299. C2×#379C22×C4semidirect
303. C2×C4×C4⋊C4C24semidirect
308. C2×C4×C22⋊C4C22×C4semidirect
309. C2×C4×C22⋊C4C22×C4semidirect
315. C2×C4×C22⋊C4C24semidirect
317. C2×#376C24semidirect
330. C22×#95C22×C4semidirect
331. C22×#95C22×C4semidirect
332. C22×#95C22×C4semidirect
335. C22×#95C2×D4semidirect
352. C22×#95C24semidirect
353. #1437C24semidirect
354. #1436C24semidirect
355. #1436C24semidirect
356. C4⋊#95C24semidirect
357. #1434C24semidirect
358. #1434C24semidirect
362. C22⋊#95C24semidirect
363. C4×#95C24semidirect
364. C4×#95C24semidirect
480. C24×C4C4×D4semidirect
493. C24×C4C23×C4semidirect
494. C24×C4C23×C4semidirect
514. C2×#120C2×C42semidirect
521. C2×C4×D4C23×C4semidirect
522. C2×C4×D4C23×C4semidirect
528. C22×C4⋊C4C23×C4semidirect
529. C22×C4⋊C4C23×C4semidirect
555. C22×C22⋊C4C23×C4semidirect
556. C22×C22⋊C4C23×C4semidirect
576. C22×C42C23×C4semidirect
577. C22×C42C23×C4semidirect
582. #386C23×C4semidirect
583. #386C23×C4semidirect
584. #385C23×C4semidirect
585. #385C23×C4semidirect
586. #379C23×C4semidirect
592. C4×C22⋊C4C23×C4semidirect
593. C4×C22⋊C4C23×C4semidirect
606. C2×#95C23×C4semidirect
607. C2×#95C23×C4semidirect
608. C2×#95C23×C4semidirect
611. C2×#95C22×D4semidirect
813. C23×C4C2×C4×D4semidirect
826. C23×C4C24×C4semidirect
841. #120C22×C42semidirect
849. C2×C4⋊C4C24×C4semidirect
850. C2×C4⋊C4C24×C4semidirect
874. C2×C22⋊C4C24×C4semidirect
875. C2×C22⋊C4C24×C4semidirect
887. C2×C42C24×C4semidirect
888. C2×C42C24×C4semidirect
896. #95C24×C4semidirect
897. #95C24×C4semidirect
898. #95C24×C4semidirect
964. C24#2275semidirect
1092. C22×C4C22×C4×D4semidirect
1169. C23C2×#2275semidirect
1261. C22#513587direct (N × H)
1265. C22C22×#2275semidirect
1293. C2C2×#513587direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#138092
C22×#137492
C22×#137822
C22×#138142
C2×#5135872
C22×#137842
C25×#952
C23×#22752
C22×D4×#952
C22×#138132
C22×C4×#3792
C23×C4×#1202