Finite Group Databasebeta

← C2×#7625442 #72314943

Subgroups — C2×#7625442 #72314943

Order 1024.

310709 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×#41C211yesmaximal, characteristic
2C22×#3428C212yesmaximal, complemented
3#7625442C2164yesmaximal, direct product factor
4C2×#34175C2116yesmaximal, complemented
5C2×#34174C212yesmaximal, complemented
6C2×#34173C212yesmaximal, complemented
7C2×#34172C216yesmaximal, complemented
8C2×#34171C216yesmaximal, complemented
9C2×C22⋊C4×#41C2116yesmaximal, complemented
10C2×#34044C216yesmaximal, complemented
11C22×#2280C216yesmaximal, complemented
12C24×#41—264no—
13C24×#41C4164yescomplemented
14C24×#41C2213yes—
15C24×#41C2218yes—
16C24×#41C2213yes—
17C24×#41C2211yescharacteristic
18C24×#41C2218yes—
19C24×#41C22132yes—
20C24×#41C2211yescharacteristic
21C25×Q8C2211yescharacteristic
22C25×D4C2213yes—
23C26×C4C2213yes—
24C2×#3428—264no—
25C2×#3428C22164yescomplemented
26C22×#520C22116yescomplemented
27C22×#519C2214yescomplemented
28C22×#518C22112yescomplemented
29C22×C4×#41C22116yescomplemented
30C23×#117C22112yescomplemented
31#34175C221512yescomplemented
32#34174C22164yescomplemented
33#34173C22164yescomplemented
34#34172C221192yescomplemented
35#34171C221192yescomplemented
36C22⋊C4×#41C221512yescomplemented
37C2×#2341C22132yescomplemented
38C2×Q8×C22⋊C4C22132yescomplemented
39C2×#2339C22196yescomplemented
40C2×D4×C22⋊C4C22196yescomplemented
41#34044C221192yescomplemented
42C2×#2311C22148yescomplemented
43C2×#2310C22112yescomplemented
44C2×#2309C22112yescomplemented
45C2×#2308C22124yescomplemented
46C2×#2297C22148yescomplemented
47C2×#2280C2214yes—
48C2×#2280C22112yes—
49C2×#2280C22112yescomplemented
50C2×#2280C22112yescomplemented
51C2×#2280C22124yescomplemented
52C2×#2280C22124yescomplemented
53C2×#2280C221192yescomplemented
54C22×#381C22112yescomplemented
55C22×#380C22124yescomplemented
56C22×#379C22112yes—
57C22×C4×C22⋊C4C22124yescomplemented
58C27C2313yes—
59C23×#41—22048no—
60C23×#41—2256no—
61C23×#41—2256no—
62C23×#41—21024no—
63C23×#41—232no—
64C23×#41—296no—
65C23×#41—296no—
66C23×#41C2×C4132yes—
67C23×#41C2×C41256yescomplemented
68C23×#41C2×C41256yescomplemented
69C23×#41C2×C4132yescomplemented
70C23×#41C2×C4196yescomplemented
71C23×#41C2×C4196yescomplemented
72C23×#41C2×C411024yescomplemented
73C23×#41D4164yes—
74C23×#41C23124yes—
75C23×#41C2318yes—
76C23×#41C23112yes—
77C23×#41C23112yes—
78C23×#41C231128yes—
79C23×#41C23148yes—
80C23×#41C23116yes—
81C23×#41C231128yes—
82C23×#41C23148yes—
83C23×#41C2314yes—
84C23×#41C2314yes—
85C23×#41C23116yes—
86C24×Q8—232no—
87C24×Q8C2×C4132yescomplemented
88C24×Q8C2318yes—
89C24×Q8C2313yes—
90C24×Q8C23116yes—
91C24×Q8C2311yescharacteristic
92C24×D4—296no—
93C24×D4C2×C4196yescomplemented
94C24×D4C23124yes—
95C24×D4C2316yes—
96C24×D4C2313yes—
97C24×D4C23148yes—
98C24×D4C2313yes—
99C25×C4—296no—
100C25×C4C2×C4196yescomplemented
101C25×C4C2311yescharacteristic
102C25×C4C2313yes—
103C25×C4C23112yes—
104C25×C4C23112yes—
105C25×C4C2313yes—
106C25×C4C2313yes—
107C25×C4C2313yes—
108C25×C4C23148yes—
109C25×C4C2313yes—
110#3428—21024no—
111C2×#520—2256no—
112C2×#520C231256yescomplemented
113C2×#519—264no—
114C2×#519C23164yescomplemented
115C2×#518—2192no—
116C2×#518C231192yescomplemented
117C2×C4×#41—2256no—
118C2×C4×#41C231256yescomplemented
119C22×C4×Q8C23132yescomplemented
120C22×C4×D4C23196yescomplemented
121C22×#117—2192no—
122C22×#117C2318yes—
123C22×#117C23124yes—
124C22×#117C23124yescomplemented
125C22×#117C23124yescomplemented
126C22×#117C231192yescomplemented
127C23×C4⋊C4C23124yescomplemented
128C23×C22⋊C4C23124yes—
129C23×C22⋊C4C23148yes—
130C23×C42C23124yescomplemented
131#2341C231512yescomplemented
132Q8×C22⋊C4C231512yescomplemented
133#2339C2311536yescomplemented
134D4×C22⋊C4C2311536yescomplemented
135#2311C231768yescomplemented
136#2310C231192yescomplemented
137#2309C231192yescomplemented
138#2308C231384yescomplemented
139#2297C231768yescomplemented
140C2×#391C23196yescomplemented
141C2×#390C23196yescomplemented
142C2×#386C231192yescomplemented
143#2280C231192yes—
144#2280C23164yes—
145#2280C231192yescomplemented
146#2280C231192yescomplemented
147#2280C231384yescomplemented
148#2280C231384yescomplemented
149C2×#381C2318yes—
150C2×#381C23124yes—
151C2×#381C23148yescomplemented
152C2×#381C231192yescomplemented
153C2×#380C23148yes—
154C2×#380C23116yes—
155C2×#380C23148yescomplemented
156C2×#380C23148yescomplemented
157C2×#380C231384yescomplemented
158C2×#379C23148yes—
159C2×#379C231192yes—
160C2×#379C2318yes—
161C2×#379C23124yes—
162C2×C4×C22⋊C4C23148yes—
163C2×C4×C22⋊C4C23116yes—
164C2×C4×C22⋊C4C23148yescomplemented
165C2×C4×C22⋊C4C23148yescomplemented
166C2×C4×C22⋊C4C231384yescomplemented
167C22×#95C23148yescomplemented
168C26—248no—
169C26—448no—
170C26C22×C4148yes—
171C26C2411yescharacteristic
172C26C24112yes—
173C26C2413yes—
174C26C24124yes—
175C26C2413yes—
176C22×#41—24096no—
177C22×#41—24096no—
178C22×#41—216384no—
179C22×#41—22048no—
180C22×#41—22048no—
181C22×#41—2512no—
182C22×#41—2128no—
183C22×#41—2256no—
184C22×#41—21536no—
185C22×#41—2384no—
186C22×#41—2768no—
187C22×#41—21536no—
188C22×#41—2192no—
189C22×#41—2192no—
190C22×#41—2768no—
191C22×#41C22⋊C411024yescomplemented
192C22×#41C22×C41128yes—
193C22×#41C22×C41384yes—
194C22×#41C22×C41192yes—
195C22×#41C22×C41192yes—
196C22×#41C22×C4164yes—
197C22×#41C22×C4164yes—
198C22×#41C22×C41256yes—
199C22×#41C22×C412048yescomplemented
200C22×#41C22×C412048yescomplemented
201C22×#41C22×C41256yescomplemented
202C22×#41C22×C41768yescomplemented
203C22×#41C22×C41768yescomplemented
204C22×#41C2×D41128yes—
205C22×#41C2×D41128yes—
206C22×#41C2×D41512yes—
207C22×#41C24196yes—
208C22×#41C241192yes—
209C22×#41C24164yes—
210C22×#41C24196yes—
211C22×#41C24132yes—
212C22×#41C24132yes—
213C23×Q8—2512no—
214C23×Q8—2128no—
215C23×Q8—2256no—
216C23×Q8—248no—
217C23×Q8C22×C41128yes—
218C23×Q8C22×C4148yes—
219C23×Q8C22×C4116yes—
220C23×Q8C22×C41256yescomplemented
221C23×Q8C2×D4132yes—
222C23×Q8C24124yes—
223C23×Q8C24164yes—
224C23×Q8C24112yes—
225C23×Q8C2414yes—
226C23×Q8C2418yes—
227C23×D4—296no—
228C23×D4—21536no—
229C23×D4—2384no—
230C23×D4—2768no—
231C23×D4—248no—
232C23×D4C22×C4196yes—
233C23×D4C22×C41384yes—
234C23×D4C22×C4148yes—
235C23×D4C22×C4148yes—
236C23×D4C22×C41768yescomplemented
237C23×D4C2×D4196yes—
238C23×D4C24148yes—
239C23×D4C24124yes—
240C23×D4C241192yes—
241C23×D4C24124yes—
242C23×D4C24112yes—
243C23×D4C24112yes—
244C23×D4C24124yes—
245C24×C4—248no—
246C24×C4—21536no—
247C24×C4—216no—
248C24×C4—248no—
249C24×C4—248no—
250C24×C4—248no—
251C24×C4—2192no—
252C24×C4—2192no—
253C24×C4—2768no—
254C24×C4C22×C4116yes—
255C24×C4C22×C4148yes—
256C24×C4C22×C4148yes—
257C24×C4C22×C41192yes—
258C24×C4C22×C41192yes—
259C24×C4C22×C4148yes—
260C24×C4C22×C4148yes—
261C24×C4C22×C4148yes—
262C24×C4C22×C41768yescomplemented
263C24×C4C2×D4196yes—
264C24×C4C2412yes—
265C24×C4C2411yescharacteristic
266C24×C4C2418yes—
267C24×C4C24112yes—
268C24×C4C2413yes—
269C24×C4C24124yes—
270C24×C4C24112yes—
271C24×C4C24112yes—
272C24×C4C24196yes—
273C24×C4C2416yes—
274C24×C4C24196yes—
275C24×C4C24124yes—
276C24×C4C24124yes—
277C24×C4C24124yes—
278C24×C4C2412yes—
279C24×C4C2416yes—
280C24×C4C24148yes—
281C24×C4C2413yes—
282C24×C4C2416yes—
283C24×C4C24124yes—
284C24×C4C2411yescharacteristic
285C24×C4C2416yes—
286#520—22048no—
287#519—2512no—
288#518—21536no—
289C4×#41—22048no—
290C2×C4×Q8—2256no—
291C2×C4×Q8C241256yescomplemented
292C2×C4×D4—2768no—
293C2×C4×D4C241768yescomplemented
294C2×#117—264no—
295C2×#117—2192no—
296C2×#117—2192no—
297C2×#117—2192no—
298C2×#117—21536no—
299C2×#117C241192yes—
300C2×#117C24164yes—
301C2×#117C241192yescomplemented
302C2×#117C241192yescomplemented
303C22×C4⋊C4—2192no—
304C22×C4⋊C4C24116yes—
305C22×C4⋊C4C24148yes—
306C22×C4⋊C4C241192yescomplemented
307C22×C22⋊C4—2192no—
308C22×C22⋊C4—4192no—
309C22×C22⋊C4C241192yes—
310C22×C22⋊C4C24116yes—
311C22×C22⋊C4C24132yes—
312C22×C22⋊C4C24148yes—
313C22×C22⋊C4C241384yes—
314C22×C22⋊C4C24196yes—
315C22×C42—2192no—
316C22×C42C24148yes—
317C22×C42C24116yes—
318C22×C42C241192yescomplemented
319#391C241768yescomplemented
320#390C241768yescomplemented
321#386C2411536yescomplemented
322#381C241192yes—
323#381C24164yes—
324#381C241384yescomplemented
325#380C241384yes—
326#380C241128yes—
327#380C241384yescomplemented
328#380C241384yescomplemented
329#379C241192yes—
330#379C241384yes—
331#379C24164yes—
332C4×C22⋊C4C241384yes—
333C4×C22⋊C4C241128yes—
334C4×C22⋊C4C241384yescomplemented
335C4×C22⋊C4C241384yescomplemented
336C2×#95C24132yes—
337C2×#95C24196yes—
338C2×#95C241384yescomplemented
339C25—28no—
340C25—216no—
341C25—2384no—
342C25—296no—
343C25—2192no—
344C25—224no—
345C25—296no—
346C25—4384no—
347C25—424no—
348C25—448no—
349C25—4192no—
350C25—424no—
351C25—4768no—
352C25C23×C418yes—
353C25C23×C4196yes—
354C25C23×C4124yes—
355C25C23×C41192yes—
356C25C23×C4124yes—
357C25C22×D4148yes—
358C25C2516yes—
359C25C2514yes—
360C25C25148yes—
361C25C2511yescharacteristic
362C25C2516yes—
363C25C2512yes—
364C25C25112yes—
365C25C25112yes—
366C2×#41—216384no—
367C2×#41—216384no—
368C2×#41—21024no—
369C2×#41—22048no—
370C2×#41—2512no—
371C2×#41—23072no—
372C2×#41—26144no—
373C2×#41—21536no—
374C2×#41—21536no—
375C2×#41—21536no—
376C2×#41—26144no—
377C2×#41—2768no—
378C2×#41—2768no—
379C2×#41C2×C22⋊C411024yescomplemented
380C2×#41C2×C22⋊C411024yescomplemented
381C2×#41C2×C22⋊C414096yescomplemented
382C2×#41C23×C41512yes—
383C2×#41C23×C411536yes—
384C2×#41C23×C41768yes—
385C2×#41C23×C41768yes—
386C2×#41C23×C41256yes—
387C2×#41C23×C41256yes—
388C2×#41C22×D41512yes—
389C2×#41C22×D41512yes—
390C22×Q8—21024no—
391C22×Q8—22048no—
392C22×Q8—2512no—
393C22×Q8—2384no—
394C22×Q8—296no—
395C22×Q8—2192no—
396C22×Q8C2×C22⋊C41256yescomplemented
397C22×Q8C23×C4196yes—
398C22×Q8C23×C41512yes—
399C22×Q8C23×C41192yes—
400C22×Q8C23×C4132yes—
401C22×Q8C23×C4164yes—
402C22×Q8C22×D4164yes—
403C22×Q8C22×D41128yes—
404C22×Q8C25148yes—
405C22×Q8C25116yes—
406C22×D4—2768no—
407C22×D4—2192no—
408C22×D4—2384no—
409C22×D4—23072no—
410C22×D4—26144no—
411C22×D4—21536no—
412C22×D4—2384no—
413C22×D4—296no—
414C22×D4—2192no—
415C22×D4C2×C22⋊C41768yescomplemented
416C22×D4C23×C41192yes—
417C22×D4C23×C4196yes—
418C22×D4C23×C41384yes—
419C22×D4C23×C411536yes—
420C22×D4C23×C41192yes—
421C22×D4C23×C4196yes—
422C22×D4C23×C41192yes—
423C22×D4C22×D41192yes—
424C22×D4C22×D41384yes—
425C22×D4C25196yes—
426C22×D4C25148yes—
427C22×D4C25148yes—
428C23×C4—2384no—
429C23×C4—28no—
430C23×C4—224no—
431C23×C4—296no—
432C23×C4—2192no—
433C23×C4—2128no—
434C23×C4—2384no—
435C23×C4—2384no—
436C23×C4—2384no—
437C23×C4—21536no—
438C23×C4—21536no—
439C23×C4—26144no—
440C23×C4—216no—
441C23×C4—216no—
442C23×C4—264no—
443C23×C4—296no—
444C23×C4—2192no—
445C23×C4—296no—
446C23×C4—2192no—
447C23×C4—248no—
448C23×C4—248no—
449C23×C4—2192no—
450C23×C4—2768no—
451C23×C4—2768no—
452C23×C4—2192no—
453C23×C4—4192no—
454C23×C4C2×C22⋊C41768yescomplemented
455C23×C4C23×C418yes—
456C23×C4C23×C4116yes—
457C23×C4C23×C4116yes—
458C23×C4C23×C4124yes—
459C23×C4C23×C4196yes—
460C23×C4C23×C4196yes—
461C23×C4C23×C4196yes—
462C23×C4C23×C4148yes—
463C23×C4C23×C4148yes—
464C23×C4C23×C4164yes—
465C23×C4C23×C41192yes—
466C23×C4C23×C41192yes—
467C23×C4C23×C41768yes—
468C23×C4C23×C41768yes—
469C23×C4C23×C41192yes—
470C23×C4C23×C41192yes—
471C23×C4C23×C418yes—
472C23×C4C23×C4124yes—
473C23×C4C23×C4148yes—
474C23×C4C23×C4148yes—
475C23×C4C23×C41192yes—
476C23×C4C22×D4196yes—
477C23×C4C22×D4116yes—
478C23×C4C22×D4148yes—
479C23×C4C22×D4196yes—
480C23×C4C22×D41384yes—
481C23×C4C25132yes—
482C23×C4C2512yes—
483C23×C4C2518yes—
484C23×C4C2518yes—
485C23×C4C2514yes—
486C23×C4C2516yes—
487C23×C4C25148yes—
488C23×C4C25112yes—
489C23×C4C25148yes—
490C23×C4C25124yes—
491C23×C4C25148yes—
492C23×C4C25124yes—
493C23×C4C251192yes—
494C23×C4C2511yescharacteristic
495C23×C4C2516yes—
496C23×C4C25124yes—
497C23×C4C2514yes—
498C23×C4C25112yes—
499C23×C4C25124yes—
500C23×C4C2511yescharacteristic
501C4×Q8—21024no—
502C4×D4—23072no—
503#117—2256no—
504#117—2768no—
505#117—2768no—
506#117—2768no—
507C2×C4⋊C4—264no—
508C2×C4⋊C4—2192no—
509C2×C4⋊C4—2768no—
510C2×C4⋊C4C25164yes—
511C2×C4⋊C4C251192yes—
512C2×C22⋊C4—264no—
513C2×C22⋊C4—2192no—
514C2×C22⋊C4—2768no—
515C2×C22⋊C4—2128no—
516C2×C22⋊C4—4768no—
517C2×C22⋊C4—4192no—
518C2×C22⋊C4C25164yes—
519C2×C22⋊C4C251128yes—
520C2×C22⋊C4C251192yes—
521C2×C22⋊C4C251384yes—
522C2×C42—264no—
523C2×C42—2192no—
524C2×C42—2768no—
525C2×C42C25164yes—
526C2×C42C251192yes—
527#95C251128yes—
528#95C251384yes—
529C24—2128no—
530C24—216no—
531C24—28no—
532C24—248no—
533C24—232no—
534C24—28no—
535C24—28no—
536C24—232no—
537C24—264no—
538C24—2192no—
539C24—248no—
540C24—224no—
541C24—2192no—
542C24—248no—
543C24—2384no—
544C24—2768no—
545C24—296no—
546C24—2384no—
547C24—496no—
548C24—4192no—
549C24—496no—
550C24—4768no—
551C24—4192no—
552C24—448no—
553C24—496no—
554C24—448no—
555C24—4768no—
556C24—43072no—
557C24—41536no—
558C24—4192no—
559C24C22×C22⋊C41192yes—
560C24C24×C4116yes—
561C24C24×C4124yes—
562C24C24×C41192yes—
563C24C24×C414yes—
564C24C24×C4124yes—
565C24C24×C418yes—
566C24C24×C4148yes—
567C24C24×C4148yes—
568C24C23×D418yes—
569C24C23×D4148yes—
570C24C23×D4196yes—
571C24#585116yes—
572C24C26112yes—
573C24C2612yes—
574C24C26112yes—
575C24C2614yes—
576C24C2611yescharacteristic
577#41—22048no—
578#41—26144no—
579#41—23072no—
580#41—23072no—
581#41C22×C22⋊C412048yescomplemented
582#41C22×C22⋊C412048yescomplemented
583C2×Q8—22048no—
584C2×Q8—2192no—
585C2×Q8—2384no—
586C2×Q8—2768no—
587C2×Q8C22×C22⋊C41256yes—
588C2×Q8C22×C22⋊C41512yescomplemented
589C2×Q8C24×C41192yes—
590C2×Q8C24×C4164yes—
591C2×Q8C23×D41128yes—
592C2×D4—2384no—
593C2×D4—2768no—
594C2×D4—21536no—
595C2×D4—26144no—
596C2×D4—2192no—
597C2×D4—2384no—
598C2×D4—2768no—
599C2×D4C22×C22⋊C41768yes—
600C2×D4C22×C22⋊C411536yescomplemented
601C2×D4C24×C41384yes—
602C2×D4C24×C41192yes—
603C2×D4C24×C41192yes—
604C2×D4C23×D41384yes—
605C22×C4—216no—
606C22×C4—28no—
607C22×C4—248no—
608C22×C4—224no—
609C22×C4—2192no—
610C22×C4—232no—
611C22×C4—296no—
612C22×C4—2384no—
613C22×C4—2768no—
614C22×C4—232no—
615C22×C4—232no—
616C22×C4—2192no—
617C22×C4—2192no—
618C22×C4—296no—
619C22×C4—296no—
620C22×C4—264no—
621C22×C4—264no—
622C22×C4—2256no—
623C22×C4—2384no—
624C22×C4—2768no—
625C22×C4—2384no—
626C22×C4—2768no—
627C22×C4—2192no—
628C22×C4—2192no—
629C22×C4—2768no—
630C22×C4—23072no—
631C22×C4—23072no—
632C22×C4—264no—
633C22×C4—2128no—
634C22×C4—2384no—
635C22×C4—4384no—
636C22×C4—8384no—
637C22×C4C22×C22⋊C4164yes—
638C22×C4C22×C22⋊C41192yes—
639C22×C4C22×C22⋊C41384yes—
640C22×C4C22×C22⋊C41384yes—
641C22×C4C22×C22⋊C411536yescomplemented
642C22×C4C24×C4116yes—
643C22×C4C24×C418yes—
644C22×C4C24×C4132yes—
645C22×C4C24×C4132yes—
646C22×C4C24×C4148yes—
647C22×C4C24×C4124yes—
648C22×C4C24×C41192yes—
649C22×C4C24×C41192yes—
650C22×C4C24×C41192yes—
651C22×C4C24×C4196yes—
652C22×C4C24×C4196yes—
653C22×C4C24×C414yes—
654C22×C4C24×C4116yes—
655C22×C4C24×C414yes—
656C22×C4C24×C4124yes—
657C22×C4C24×C4148yes—
658C22×C4C24×C4196yes—
659C22×C4C24×C4196yes—
660C22×C4C23×D418yes—
661C22×C4C23×D4148yes—
662C22×C4C23×D41192yes—
663C22×C4C23×D418yes—
664C22×C4C23×D41192yes—
665C22×C4C23×D4132yes—
666C22×C4C23×D4196yes—
667C22×C4C26164yes—
668C22×C4C2614yes—
669C22×C4C26112yes—
670C22×C4C2612yes—
671C22×C4C26112yes—
672C22×C4C2612yes—
673C4⋊C4—2128no—
674C4⋊C4—2384no—
675C22⋊C4—2128no—
676C22⋊C4—2384no—
677C22⋊C4—2256no—
678C22⋊C4—4384no—
679C42—2128no—
680C42—2384no—
681C23—2128no—
682C23—2256no—
683C23—2192no—
684C23—232no—
685C23—264no—
686C23—28no—
687C23—248no—
688C23—28no—
689C23—28no—
690C23—232no—
691C23—216no—
692C23—216no—
693C23—216no—
694C23—296no—
695C23—264no—
696C23—224no—
697C23—248no—
698C23—2384no—
699C23—296no—
700C23—248no—
701C23—296no—
702C23—2384no—
703C23—4384no—
704C23—496no—
705C23—4192no—
706C23—496no—
707C23—4192no—
708C23—4768no—
709C23—41536no—
710C23—43072no—
711C23—4192no—
712C23—4384no—
713C23—496no—
714C23C23×C22⋊C4116yes—
715C23C23×C22⋊C4196yes—
716C23C23×C22⋊C41192yes—
717C23#3428132yescomplemented
718C23C25×C4124yes—
719C23C25×C414yes—
720C23C25×C4124yes—
721C23C25×C418yes—
722C23C25×C412yes—
723C23C24×D418yes—
724C23C24×D4148yes—
725C23C24×D414yes—
726C23C2×#585116yes—
727C23C2×#58518yes—
728C23C2711yescharacteristic
729Q8—2384no—
730Q8C23×C22⋊C41256yes—
731D4—2768no—
732D4—2384no—
733D4C23×C22⋊C41768yes—
734C2×C4—28no—
735C2×C4—224no—
736C2×C4—232no—
737C2×C4—216no—
738C2×C4—296no—
739C2×C4—248no—
740C2×C4—2384no—
741C2×C4—264no—
742C2×C4—264no—
743C2×C4—2384no—
744C2×C4—2384no—
745C2×C4—2192no—
746C2×C4—2192no—
747C2×C4—264no—
748C2×C4—2128no—
749C2×C4—4128no—
750C2×C4—8384no—
751C2×C4C23×C22⋊C4116yes—
752C2×C4C23×C22⋊C4116yes—
753C2×C4C23×C22⋊C4164yes—
754C2×C4C23×C22⋊C4196yes—
755C2×C4C23×C22⋊C41192yes—
756C2×C4C23×C22⋊C41384yes—
757C2×C4C23×C22⋊C41384yes—
758C2×C4C25×C418yes—
759C2×C4C25×C4124yes—
760C2×C4C25×C414yes—
761C2×C4C25×C414yes—
762C2×C4C25×C4124yes—
763C2×C4C24×D418yes—
764C2×C4C24×D4148yes—
765C2×C4C24×D418yes—
766C22—2128no—
767C22—28no—
768C22—28no—
769C22—28no—
770C22—248no—
771C22—296no—
772C22—216no—
773C22—232no—
774C22—232no—
775C22—264no—
776C22—2192no—
777C22—224no—
778C22—248no—
779C22—4192no—
780C22—4768no—
781C22—4192no—
782C22—448no—
783C22—496no—
784C22C24×C22⋊C418yes—
785C22C24×C22⋊C4148yes—
786C22C24×C22⋊C414yes—
787C22C2×#342818yes—
788C22C2×#3428116yescomplemented
789C22#62811116yes—
790C22C26×C411yescharacteristic
791C22C25×D412yes—
792C22C22×#58514yes—
793C4—28no—
794C4—224no—
795C4—464no—
796C4C24×C22⋊C418yes—
797C4C24×C22⋊C418yes—
798C4C24×C22⋊C4148yes—
799C2—28no—
800C2—216no—
801C2—248no—
802C2—424no—
803C2#762544218yesdirect product factor
804C2C25×C22⋊C411yescharacteristic
805C2C22×#342812yes—
806C2C2×#6281114yes—
subgroupG/H
center, socleC23×C4C25
commutatorC22C26×C4
Frattini, cosocleC23C27
prime radicalC25×#41C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#3428C2semidirect
3. #7625442C2direct (N × H)
4. C2×#34175C2semidirect
5. C2×#34174C2semidirect
6. C2×#34173C2semidirect
7. C2×#34172C2semidirect
8. C2×#34171C2semidirect
9. C2×C22⋊C4×#41C2semidirect
10. C2×#34044C2semidirect
11. C22×#2280C2semidirect
13. C24×#41C4semidirect
25. C2×#3428C22semidirect
26. C22×#520C22semidirect
27. C22×#519C22semidirect
28. C22×#518C22semidirect
29. C22×C4×#41C22semidirect
30. C23×#117C22semidirect
31. #34175C22semidirect
32. #34174C22semidirect
33. #34173C22semidirect
34. #34172C22semidirect
35. #34171C22semidirect
36. C22⋊C4×#41C22semidirect
37. C2×#2341C22semidirect
38. C2×Q8×C22⋊C4C22semidirect
39. C2×#2339C22semidirect
40. C2×D4×C22⋊C4C22semidirect
41. #34044C22semidirect
42. C2×#2311C22semidirect
43. C2×#2310C22semidirect
44. C2×#2309C22semidirect
45. C2×#2308C22semidirect
46. C2×#2297C22semidirect
49. C2×#2280C22semidirect
50. C2×#2280C22semidirect
51. C2×#2280C22semidirect
52. C2×#2280C22semidirect
53. C2×#2280C22semidirect
54. C22×#381C22semidirect
55. C22×#380C22semidirect
57. C22×C4×C22⋊C4C22semidirect
67. C23×#41C2×C4semidirect
68. C23×#41C2×C4semidirect
69. C23×#41C2×C4semidirect
70. C23×#41C2×C4semidirect
71. C23×#41C2×C4semidirect
72. C23×#41C2×C4semidirect
87. C24×Q8C2×C4semidirect
93. C24×D4C2×C4semidirect
100. C25×C4C2×C4semidirect
112. C2×#520C23semidirect
114. C2×#519C23semidirect
116. C2×#518C23semidirect
118. C2×C4×#41C23semidirect
119. C22×C4×Q8C23semidirect
120. C22×C4×D4C23semidirect
124. C22×#117C23semidirect
125. C22×#117C23semidirect
126. C22×#117C23semidirect
127. C23×C4⋊C4C23semidirect
130. C23×C42C23semidirect
131. #2341C23semidirect
132. Q8×C22⋊C4C23semidirect
133. #2339C23semidirect
134. D4×C22⋊C4C23semidirect
135. #2311C23semidirect
136. #2310C23semidirect
137. #2309C23semidirect
138. #2308C23semidirect
139. #2297C23semidirect
140. C2×#391C23semidirect
141. C2×#390C23semidirect
142. C2×#386C23semidirect
145. #2280C23semidirect
146. #2280C23semidirect
147. #2280C23semidirect
148. #2280C23semidirect
151. C2×#381C23semidirect
152. C2×#381C23semidirect
155. C2×#380C23semidirect
156. C2×#380C23semidirect
157. C2×#380C23semidirect
164. C2×C4×C22⋊C4C23semidirect
165. C2×C4×C22⋊C4C23semidirect
166. C2×C4×C22⋊C4C23semidirect
167. C22×#95C23semidirect
191. C22×#41C22⋊C4semidirect
199. C22×#41C22×C4semidirect
200. C22×#41C22×C4semidirect
201. C22×#41C22×C4semidirect
202. C22×#41C22×C4semidirect
203. C22×#41C22×C4semidirect
220. C23×Q8C22×C4semidirect
236. C23×D4C22×C4semidirect
262. C24×C4C22×C4semidirect
291. C2×C4×Q8C24semidirect
293. C2×C4×D4C24semidirect
301. C2×#117C24semidirect
302. C2×#117C24semidirect
306. C22×C4⋊C4C24semidirect
318. C22×C42C24semidirect
319. #391C24semidirect
320. #390C24semidirect
321. #386C24semidirect
324. #381C24semidirect
327. #380C24semidirect
328. #380C24semidirect
334. C4×C22⋊C4C24semidirect
335. C4×C22⋊C4C24semidirect
338. C2×#95C24semidirect
379. C2×#41C2×C22⋊C4semidirect
380. C2×#41C2×C22⋊C4semidirect
381. C2×#41C2×C22⋊C4semidirect
396. C22×Q8C2×C22⋊C4semidirect
415. C22×D4C2×C22⋊C4semidirect
454. C23×C4C2×C22⋊C4semidirect
581. #41C22×C22⋊C4semidirect
582. #41C22×C22⋊C4semidirect
588. C2×Q8C22×C22⋊C4semidirect
600. C2×D4C22×C22⋊C4semidirect
641. C22×C4C22×C22⋊C4semidirect
717. C23#3428semidirect
788. C22C2×#3428semidirect
803. C2#7625442direct (N × H)

Maximal subgroups

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

subgroupindex
C25×#412
C22×#34282
#76254422
C2×#341752
C2×#341742
C2×#341732
C2×#341722
C2×#341712
C2×C22⋊C4×#412
C2×#340442
C22×#22802