Finite Group Databasebeta

← #4930581

Subgroups — #4930581

Order 512.

5769 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#518C211yesmaximal, characteristic, complemented
2C2×#2601C211yesmaximal, characteristic, complemented
3C2×#2603C211yesmaximal, characteristic, complemented
4C2×#2636C211yesmaximal, characteristic, complemented
5#14906C211yesmaximal, characteristic, complemented
6#14905C211yesmaximal, characteristic, complemented
7#14860C211yesmaximal, characteristic, complemented
8#14801C211yesmaximal, characteristic, complemented
9#14796C211yesmaximal, characteristic, complemented
10#14795C211yesmaximal, characteristic, complemented
11#14733C212yesmaximal, complemented
12#14732C212yesmaximal, complemented
13#14726C212yesmaximal, complemented
14#14725C212yesmaximal, complemented
15#14724C211yesmaximal, characteristic, complemented
16#14715C211yesmaximal, characteristic
17#14187C212yesmaximal, complemented
18#14185C212yesmaximal, complemented
19#13995C212yesmaximal, complemented
20#13971C212yesmaximal, complemented
21#13957C211yesmaximal, characteristic, complemented
22#13905C211yesmaximal, characteristic, complemented
23#13847C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#126C2211yescharacteristic, complemented
26C22×#120C2212yes—
27C2×#518—28no—
28C2×#518—28no—
29C2×#518—28no—
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2212yes—
32C22×C4×D4C2212yes—
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36C22×#117C2211yescharacteristic
37C22×#117C2211yescharacteristic
38C23×C22⋊C4C2212yes—
39C23×C22⋊C4C2212yes—
40#2636—28no—
41#2603—28no—
42#2601—28no—
43C2×#400C2211yescharacteristic, complemented
44C2×#399C2211yescharacteristic, complemented
45C2×#398C2211yescharacteristic, complemented
46C2×#398C2211yescharacteristic, complemented
47C2×#397C2211yescharacteristic, complemented
48C2×#396C2211yescharacteristic
49C2×#396C2212yescomplemented
50C2×#396C2211yescharacteristic, complemented
51C2×#394C2211yescharacteristic
52C2×#394C2211yescharacteristic
53C2×#394C2211yescharacteristic
54C2×#394C2212yes—
55C2×#394C2212yescomplemented
56C2×#392C2211yescharacteristic
57C2×#392C2211yescharacteristic
58C2×#392C2212yes—
59C2×#390C2211yescharacteristic
60C2×#390C2212yescomplemented
61C2×#389C2211yescharacteristic, complemented
62C2×#388C2211yescharacteristic
63C2×#388C2212yescomplemented
64C2×#388C2211yescharacteristic, complemented
65C2×#388C2211yescharacteristic, complemented
66C2×#387C2211yescharacteristic, complemented
67C2×#386C2211yescharacteristic
68C2×#386C2212yescomplemented
69C2×#386C2212yescomplemented
70C2×#386C2212yescomplemented
71C2×#386C2212yescomplemented
72C2×#385C2211yescharacteristic
73C2×#385C2212yescomplemented
74C2×#385C2212yescomplemented
75C2×#385C2212yescomplemented
76C2×#385C2212yescomplemented
77C2×#382C2211yescharacteristic, complemented
78C2×#380C2212yescomplemented
79C2×#380C2212yescomplemented
80C2×#379C2212yes—
81C2×#379C2212yes—
82C2×#379C2212yes—
83C2×C4×C4⋊C4C2211yescharacteristic, complemented
84C2×C4×C22⋊C4C2212yescomplemented
85C2×C4×C22⋊C4C2212yescomplemented
86C2×#376C2211yescharacteristic, complemented
87#1445C2211yescharacteristic, complemented
88#1445C2211yescharacteristic, complemented
89#1445C2211yescharacteristic, complemented
90#1445C2211yescharacteristic, complemented
91#1441C2212yescomplemented
92#1440C2212yes—
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1438C2211yescharacteristic
105#1438C2211yescharacteristic
106#1438C2211yescharacteristic
107#1438C2212yes—
108#1438C2211yescharacteristic
109#1438C2212yes—
110#1438C2212yes—
111#1438C2212yescomplemented
112#1438C2212yescomplemented
113#1437C2212yes—
114#1437C2212yescomplemented
115#1437C2212yescomplemented
116#1437C2212yescomplemented
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119#1436C2212yescomplemented
120#1436C2212yescomplemented
121#1434C2211yescharacteristic, complemented
122#1434C2211yescharacteristic, complemented
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C22⋊#95C2212yescomplemented
128C22⋊#95C2212yescomplemented
129C26C2312yes—
130C23×D4—28no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—28no—
134C23×D4—24no—
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C24×C4C2311yescharacteristic
142C24×C4C2312yes—
143C24×C4C2312yes—
144C24×C4C2312yes—
145C24×C4C2312yes—
146C2×#126—24no—
147C2×#126—24no—
148C2×#126—24no—
149C2×#120—28no—
150C2×#120—44no—
151C2×#120—44no—
152#518—2128no—
153C2×C4×D4—24no—
154C2×C4×D4—24no—
155C2×C4×D4—28no—
156C2×C4×D4—28no—
157C2×C4×D4—24no—
158C2×C4×D4—24no—
159C2×C4×D4—28no—
160C2×C4×D4—28no—
161C2×C4×D4—28no—
162C2×C4×D4—28no—
163C2×C4×D4—24no—
164C2×C4×D4—24no—
165C2×C4×D4—24no—
166C2×C4×D4—24no—
167C2×C4×D4—24no—
168C2×C4×D4—24no—
169C2×C4×D4D418yescomplemented
170C2×C4×D4D418yescomplemented
171C2×#117—24no—
172C2×#117—24no—
173C2×#117—24no—
174C2×#117—24no—
175C2×#117—24no—
176C2×#117D418yescomplemented
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C22⋊C4—28no—
193C22×C22⋊C4—28no—
194C22×C22⋊C4—28no—
195C22×C22⋊C4—28no—
196C22×C22⋊C4—28no—
197C22×C22⋊C4—28no—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C42C2312yes—
233C22×C42C2312yes—
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238#400—24no—
239#399—24no—
240#398—24no—
241#398—24no—
242#397—24no—
243#396—24no—
244#396—24no—
245#396—28no—
246#394—24no—
247#394—24no—
248#394—28no—
249#394—24no—
250#394—28no—
251#392—24no—
252#392—24no—
253#392—28no—
254#390—24no—
255#390—28no—
256#389—24no—
257#388—24no—
258#388—24no—
259#388—28no—
260#388—24no—
261#387—24no—
262#386—24no—
263#386—28no—
264#386—28no—
265#386—44no—
266#386—44no—
267#385—24no—
268#385—28no—
269#385—28no—
270#385—44no—
271#385—44no—
272#382—24no—
273#380—44no—
274#380—44no—
275#379—28no—
276#379—44no—
277#379—44no—
278C4×C4⋊C4—24no—
279C4×C22⋊C4—44no—
280C4×C22⋊C4—44no—
281#376—24no—
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2312yes—
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2311yescharacteristic
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C25—24no—
315C25—24no—
316C25—24no—
317C25—24no—
318C25—24no—
319C25—24no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25#4118yes—
329C25C2411yescharacteristic
330C25C2411yescharacteristic
331C25C2412yes—
332C25C2412yes—
333C22×D4—232no—
334C22×D4—264no—
335C22×D4—264no—
336C22×D4—232no—
337C22×D4—232no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—22no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—22no—
361C22×D4—24no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—41no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4C2×D414yes—
372C22×D4C2×D414yes—
373C22×D4#4118yes—
374C23×C4—24no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4C2×D414yes—
405C23×C4C2×D418yes—
406C23×C4C2×D418yes—
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2412yes—
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2412yes—
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426#126—416no—
427#120—432no—
428C4×D4—264no—
429C4×D4—264no—
430C4×D4—232no—
431C4×D4—232no—
432C4×D4—232no—
433C4×D4—232no—
434#117—232no—
435#117—232no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—41no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4C2×D414yes—
476C2×C4⋊C4C2×D414yes—
477C2×C4⋊C4C2×D414yes—
478C2×C4⋊C4C2×D414yes—
479C2×C22⋊C4—264no—
480C2×C22⋊C4—264no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4C2×D414yes—
576C2×C22⋊C4C2×D414yes—
577C2×C22⋊C4C2×D418yes—
578C2×C22⋊C4C2×D418yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—24no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—24no—
585C2×C42—24no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—42no—
589C2×C42—42no—
590C2×C42—42no—
591C2×C42C2×D414yes—
592C2×C42C2×D414yes—
593C2×C42C2×D414yes—
594C2×C42C2×D414yes—
595#95—24no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—24no—
601#95—22no—
602#95—22no—
603#95—24no—
604#95—22no—
605#95—24no—
606#95—24no—
607#95—22no—
608#95—24no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—24no—
614#95—24no—
615#95—24no—
616#95—24no—
617#95—24no—
618#95—24no—
619#95—24no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95—42no—
627C24—216no—
628C24—216no—
629C24—216no—
630C24—216no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—21no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—21no—
664C24—216no—
665C24—216no—
666C24—216no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—22no—
671C24—22no—
672C24—21no—
673C24—22no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—22no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24C22×D412yes—
707C24C22×D414yes—
708C24C22×D414yes—
709C24C2×#4114yes—
710C24C2×#4114yes—
711C24C2×#4114yes—
712C24C2×#4114yes—
713C24C2×#4114yes—
714C24C2511yescharacteristic
715C2×D4—216no—
716C2×D4—2256no—
717C2×D4—216no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—216no—
723C2×D4—216no—
724C2×D4—216no—
725C2×D4—216no—
726C2×D4—216no—
727C2×D4—216no—
728C2×D4—216no—
729C2×D4—216no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—216no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—44no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—84no—
744C2×D4—84no—
745C2×D4—82no—
746C2×D4—84no—
747C2×D4—84no—
748C2×D4—84no—
749C2×D4—84no—
750C2×D4—84no—
751C2×D4—84no—
752C22×C4—216no—
753C22×C4—216no—
754C22×C4—28no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—216no—
805C22×C4—216no—
806C22×C4—216no—
807C22×C4—216no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—84no—
861C22×C4—84no—
862C22×C4—84no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4—84no—
866C22×C4—84no—
867C22×C4—84no—
868C22×C4—84no—
869C22×C4—84no—
870C22×C4—84no—
871C22×C4—84no—
872C22×C4—84no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4C22×D414yes—
881C22×C4C22×D414yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C22×D412yes—
888C22×C4C22×D412yes—
889C22×C4C22×D412yes—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C22×D412yes—
893C22×C4C22×D412yes—
894C22×C4C2×#4114yes—
895C22×C4H(5,𝔽2)14yes—
896C22×C4H(5,𝔽2)12yes—
897C22×C4H(5,𝔽2)12yes—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—84no—
910C4⋊C4—84no—
911C4⋊C4—84no—
912C4⋊C4—82no—
913C22⋊C4—216no—
914C22⋊C4—216no—
915C22⋊C4—216no—
916C22⋊C4—216no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—216no—
920C22⋊C4—216no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—82no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—82no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C42—216no—
948C42—28no—
949C42—48no—
950C42—82no—
951C42—82no—
952C42#120116yescomplemented
953C23—264no—
954C23—22no—
955C23—24no—
956C23—24no—
957C23—22no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—22no—
972C23—24no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23—24no—
987C23—22no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—41no—
1019C23—41no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—41no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—41no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—41no—
1045C23—41no—
1046C23—42no—
1047C23—41no—
1048C23—42no—
1049C23—41no—
1050C23—41no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—41no—
1055C23—42no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—816no—
1068C23—816no—
1069C23—816no—
1070C23—816no—
1071C23—816no—
1072C23—816no—
1073C23—816no—
1074C23—816no—
1075C23—816no—
1076C23—816no—
1077C23—816no—
1078C23—816no—
1079C23—816no—
1080C23—816no—
1081C23#52514yes—
1082C23#52518yes—
1083C23#52518yes—
1084C23C23×D411yescharacteristic
1085C23C23×D411yescharacteristic
1086C23C23×D411yescharacteristic
1087C23C22×#4112yes—
1088C23C22×#4112yes—
1089C23C2×H(5,𝔽2)11yescharacteristic
1090C23C2×H(5,𝔽2)12yes—
1091C23C2×H(5,𝔽2)11yescharacteristic
1092C23#58511yescharacteristic
1093C23#58512yes—
1094C23#58511yescharacteristic
1095D4—232no—
1096D4—232no—
1097D4—264no—
1098D4—88no—
1099D4—816no—
1100D4—816no—
1101C2×C4—232no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—816no—
1212C2×C4—816no—
1213C2×C4—816no—
1214C2×C4—816no—
1215C2×C4C2×#12014yes—
1216C2×C4C2×#12014yes—
1217C2×C4C2×#12014yes—
1218C2×C4#52514yes—
1219C22—24no—
1220C22—28no—
1221C22—28no—
1222C22—28no—
1223C22—28no—
1224C22—24no—
1225C22—24no—
1226C22—28no—
1227C22—28no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—42no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—42no—
1252C22—42no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—42no—
1260C22—864no—
1261C22—81no—
1262C22—82no—
1263C22—82no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—82no—
1268C22—81no—
1269C22—81no—
1270C22—82no—
1271C22—81no—
1272C22C22×#12011yescharacteristic
1273C22C2×#52512yes—
1274C22C2×#52511yescharacteristic
1275C22C2×#52511yescharacteristic
1276C22C2×#52512yes—
1277C22#348811yescharacteristic
1278C22#348811yescharacteristic
1279C22#348812yes—
1280C22#349012yes—
1281C22#349112yes—
1282C22#349612yes—
1283C22#349611yescharacteristic
1284C22#349611yescharacteristic
1285C22#349811yescharacteristic
1286C22#349811yescharacteristic
1287C22#350011yescharacteristic
1288C22#350011yescharacteristic
1289C22#350512yes—
1290C22#350512yes—
1291C22#351312yes—
1292C22#351412yes—
1293C22#351912yes—
1294C22#352112yes—
1295C4—24no—
1296C4—24no—
1297C4—24no—
1298C4—24no—
1299C4—42no—
1300C4—42no—
1301C4—44no—
1302C4—42no—
1303C4—44no—
1304C4—44no—
1305C4—42no—
1306C4—81no—
1307C4—82no—
1308C4—82no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—82no—
1314C2—48no—
1315C2—48no—
1316C2—44no—
1317C2—161no—
1318C2#3536112yes—
1319C2#3536212yes—
1320C2#3551311yescharacteristic
1321C2#3551311yescharacteristic
1322C2#3568311yescharacteristic
1323C2#3575311yescharacteristic
1324C2#3576212yes—
1325C2#3577712yes—
1326C2#3599511yescharacteristic
1327C2#3607511yescharacteristic
1328C2#3661411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14715C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#518C2semidirect
2. C2×#2601C2semidirect
3. C2×#2603C2semidirect
4. C2×#2636C2semidirect
5. #14906C2semidirect
6. #14905C2semidirect
7. #14860C2semidirect
8. #14801C2semidirect
9. #14796C2semidirect
10. #14795C2semidirect
11. #14733C2semidirect
12. #14732C2semidirect
13. #14726C2semidirect
14. #14725C2semidirect
15. #14724C2semidirect
17. #14187C2semidirect
18. #14185C2semidirect
19. #13995C2semidirect
20. #13971C2semidirect
21. #13957C2semidirect
22. #13905C2semidirect
23. #13847C2semidirect
25. C22×#126C22semidirect
43. C2×#400C22semidirect
44. C2×#399C22semidirect
45. C2×#398C22semidirect
46. C2×#398C22semidirect
47. C2×#397C22semidirect
49. C2×#396C22semidirect
50. C2×#396C22semidirect
55. C2×#394C22semidirect
60. C2×#390C22semidirect
61. C2×#389C22semidirect
63. C2×#388C22semidirect
64. C2×#388C22semidirect
65. C2×#388C22semidirect
66. C2×#387C22semidirect
68. C2×#386C22semidirect
69. C2×#386C22semidirect
70. C2×#386C22semidirect
71. C2×#386C22semidirect
73. C2×#385C22semidirect
74. C2×#385C22semidirect
75. C2×#385C22semidirect
76. C2×#385C22semidirect
77. C2×#382C22semidirect
78. C2×#380C22semidirect
79. C2×#380C22semidirect
83. C2×C4×C4⋊C4C22semidirect
84. C2×C4×C22⋊C4C22semidirect
85. C2×C4×C22⋊C4C22semidirect
86. C2×#376C22semidirect
87. #1445C22semidirect
88. #1445C22semidirect
89. #1445C22semidirect
90. #1445C22semidirect
91. #1441C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
114. #1437C22semidirect
115. #1437C22semidirect
116. #1437C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. #1436C22semidirect
120. #1436C22semidirect
121. #1434C22semidirect
122. #1434C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
127. C22⋊#95C22semidirect
128. C22⋊#95C22semidirect
169. C2×C4×D4D4semidirect
170. C2×C4×D4D4semidirect
176. C2×#117D4semidirect
952. C42#120semidirect

Maximal subgroups

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

subgroupindex
C22×#5182
C2×#26012
C2×#26032
C2×#26362
#149062
#149052
#148602
#148012
#147962
#147952
#147332
#147322
#147262
#147252
#147242
#147152
#141872
#141852
#139952
#139712
#139572
#139052
#138472