Finite Group Databasebeta

← #649476

Subgroups — #649476

Order 512.

5178 conjugacy classes of subgroups.

The subgroup lattice has 1363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#532C211yesmaximal, characteristic
2C2×#2448C211yesmaximal, characteristic, complemented
3C2×#2446C211yesmaximal, characteristic, complemented
4C2×#2341C211yesmaximal, characteristic, complemented
5#15674C212yesmaximal, complemented
6#15340C212yesmaximal, complemented
7#15338C212yesmaximal, complemented
8#15338C212yesmaximal, complemented
9#15226C211yesmaximal, characteristic, complemented
10#15217C211yesmaximal, characteristic, complemented
11#15140C211yesmaximal, characteristic, complemented
12#15127C211yesmaximal, characteristic, complemented
13#14825C212yesmaximal, complemented
14#14824C212yesmaximal, complemented
15#14697C211yesmaximal, characteristic, complemented
16#14173C212yesmaximal, complemented
17#14173C212yesmaximal, complemented
18#14026C211yesmaximal, characteristic, complemented
19#14024C211yesmaximal, characteristic, complemented
20#13937C211yesmaximal, characteristic, complemented
21#13937C211yesmaximal, characteristic, complemented
22#13937C211yesmaximal, characteristic, complemented
23C4×#385C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C23×#41C2211yescharacteristic
26C2×#532—28no—
27C2×#532—28no—
28C2×#532—28no—
29C22×C4⋊Q8C2211yescharacteristic
30C22×#127C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C22×#124C2211yescharacteristic
33C22×#121C2212yes—
34C22×#121C2212yes—
35C22×C4×Q8C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×C4×D4C2212yes—
38C22×C4×D4C2212yes—
39C23×C42C2211yescharacteristic
40#2448—28no—
41#2446—28no—
42C2×#400C2212yes—
43C2×#399C2212yes—
44C2×#398C2212yes—
45C2×#397C2212yes—
46C2×#394C2212yes—
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2212yes—
50#2341—28no—
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#390C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#390C2212yes—
62C2×#390C2212yes—
63C2×#390C2211yescharacteristic
64C2×#390C2211yescharacteristic
65C2×#390C2211yescharacteristic
66C2×#390C2211yescharacteristic
67C2×#389C2211yescharacteristic
68C2×#389C2211yescharacteristic
69C2×#388C2212yes—
70C2×#388C2212yes—
71C2×#387C2212yes—
72C2×#387C2212yes—
73C2×#385C2211yescharacteristic
74C2×#385C2211yescharacteristic
75C2×#385C2212yes—
76C2×#380C2211yescharacteristic
77C2×#380C2212yes—
78C2×#380C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80C2×C4×C4⋊C4C2211yescharacteristic
81C2×C4×C22⋊C4C2212yes—
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2211yescharacteristic
84#1441C2212yes—
85#1441C2212yes—
86#1440C2212yes—
87#1440C2212yes—
88#1440C2212yes—
89#1440C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1438C2212yes—
97#1438C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1437C2212yes—
107#1437C2212yes—
108#1436C2212yes—
109#1436C2211yescharacteristic
110#1436C2211yescharacteristic
111#1436C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114#1436C2211yescharacteristic
115#1436C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2212yes—
126C22⋊#95C2211yescharacteristic
127C4×#95C2211yescharacteristic
128C4×#95C2211yescharacteristic
129C22×#41—24no—
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—24no—
133C22×#41—24no—
134C22×#41—24no—
135C22×#41—24no—
136C22×#41—24no—
137C22×#41—24no—
138C22×#41—42no—
139C22×#41—42no—
140C22×#41—42no—
141C22×#41—42no—
142C22×#41D418yes—
143C23×Q8C2311yescharacteristic
144C23×Q8C2311yescharacteristic
145C23×D4C2311yescharacteristic
146C23×D4C2311yescharacteristic
147C23×D4C2312yes—
148C23×D4C2312yes—
149C23×D4C2312yes—
150C23×D4C2312yes—
151C24×C4C2312yes—
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2312yes—
155C24×C4C2311yescharacteristic
156#532—2128no—
157C2×C4⋊Q8—24no—
158C2×C4⋊Q8—24no—
159C2×C4⋊Q8D418yes—
160C2×#127—24no—
161C2×#127—24no—
162C2×#127—24no—
163C2×#124—24no—
164C2×#124—24no—
165C2×#124—24no—
166C2×#124—24no—
167C2×#124—24no—
168C2×#124D418yes—
169C2×#121—28no—
170C2×#121—28no—
171C2×#121—28no—
172C2×#121—28no—
173C2×#121—28no—
174C2×#121—28no—
175C2×C4×Q8—24no—
176C2×C4×Q8—24no—
177C2×C4×Q8—24no—
178C2×C4×Q8—24no—
179C2×C4×Q8—42no—
180C2×C4×Q8—42no—
181C2×C4×D4—28no—
182C2×C4×D4—28no—
183C2×C4×D4—28no—
184C2×C4×D4—28no—
185C2×C4×D4—28no—
186C2×C4×D4—28no—
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C42—24no—
228C22×C42—24no—
229C22×C42—24no—
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2312yes—
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2312yes—
240#400—28no—
241#399—28no—
242#398—28no—
243#397—28no—
244#394—28no—
245#394—28no—
246#394—44no—
247#394—44no—
248#391—24no—
249#391—24no—
250#391—24no—
251#391—24no—
252#391—42no—
253#391—42no—
254#390—24no—
255#390—24no—
256#390—28no—
257#390—28no—
258#390—24no—
259#390—24no—
260#390—42no—
261#390—42no—
262#390—42no—
263#390—42no—
264#389—24no—
265#389—24no—
266#388—28no—
267#388—28no—
268#387—28no—
269#387—28no—
270#385—24no—
271#385—24no—
272#385—44no—
273#380—28no—
274#380—24no—
275#380—24no—
276C4×C4⋊C4—24no—
277C4×C4⋊C4—24no—
278C4×C22⋊C4—28no—
279C4×C22⋊C4—24no—
280C4×C22⋊C4—24no—
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2312yes—
302C2×#95C2311yescharacteristic
303C2×#95C2312yes—
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2312yes—
308C2×#95C2311yescharacteristic
309C2×#95C2311yescharacteristic
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2311yescharacteristic
317C25C2412yes—
318C25C2412yes—
319C25C2411yescharacteristic
320C2×#41—232no—
321C2×#41—232no—
322C2×#41—232no—
323C2×#41—416no—
324C2×#41—416no—
325C2×#41—416no—
326C2×#41—416no—
327C2×#41—416no—
328C2×#41—416no—
329C2×#41—416no—
330C2×#41—416no—
331C2×#41—416no—
332C2×#41—416no—
333C2×#41—416no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—22no—
342C22×Q8—22no—
343C22×Q8—22no—
344C22×Q8C2×D414yes—
345C22×Q8C2×D414yes—
346C22×Q8C2×D414yes—
347C22×Q8C2×D414yes—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—24no—
372C22×D4—24no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—24no—
378C22×D4—24no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4C2×D414yes—
388C22×D4C2×D414yes—
389C22×D4C2×D418yes—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—41no—
414C23×C4—41no—
415C23×C4—41no—
416C23×C4—41no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4C2×D418yes—
422C23×C4C2×D414yes—
423C23×C4#4114yes—
424C23×C4#4114yes—
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2412yes—
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2412yes—
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C4⋊Q8—232no—
446#127—232no—
447#124—232no—
448#124—232no—
449#121—264no—
450#121—264no—
451C4×Q8—416no—
452C4×Q8—416no—
453C4×D4—264no—
454C4×D4—264no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—41no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4—42no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4C2×D418yes—
495C2×C4⋊C4C2×D418yes—
496C2×C4⋊C4#4114yescomplemented
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—41no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—41no—
540C2×C22⋊C4—41no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
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⋊C4C2×D418yes—
574C2×C22⋊C4C2×D418yes—
575C2×C42—232no—
576C2×C42—22no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—22no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—24no—
587C2×C42—24no—
588C2×C42—22no—
589C2×C42—22no—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—24no—
593C2×C42—24no—
594C2×C42—22no—
595C2×C42—22no—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—42no—
603C2×C42—42no—
604C2×C42C2×D414yes—
605C2×C42C2×D414yes—
606#95—22no—
607#95—24no—
608#95—22no—
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—24no—
621#95—24no—
622#95—24no—
623#95—22no—
624#95—22no—
625#95—24no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—24no—
630#95—24no—
631#95—22no—
632#95—22no—
633#95—42no—
634#95—41no—
635#95—41no—
636#95—42no—
637#95—42no—
638#95—42no—
639#95—42no—
640#95—42no—
641#95#4114yescomplemented
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24C22×D414yes—
683C24C22×D414yes—
684C24C22×D412yes—
685C24C2×#4112yes—
686C24C2×#4112yes—
687C24C2511yescharacteristic
688#41—4128no—
689#41—4128no—
690C2×Q8—28no—
691C2×Q8—28no—
692C2×Q8—28no—
693C2×Q8—28no—
694C2×Q8—28no—
695C2×Q8—28no—
696C2×Q8—28no—
697C2×Q8—28no—
698C2×Q8—28no—
699C2×Q8—44no—
700C2×Q8—44no—
701C2×Q8—44no—
702C2×Q8—44no—
703C2×Q8#120116yes—
704C2×D4—216no—
705C2×D4—216no—
706C2×D4—216no—
707C2×D4—216no—
708C2×D4—216no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—48no—
745C2×D4—48no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—216no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—216no—
814C22×C4—216no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—21no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—21no—
870C22×C4—22no—
871C22×C4—48no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—48no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—48no—
887C22×C4—48no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4#123116yes—
895C22×C4C22×D414yes—
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D414yes—
899C22×C4C22×D414yes—
900C22×C4C22×D414yes—
901C22×C4C22×D412yes—
902C22×C4C22×D412yes—
903C22×C4C22×D412yes—
904C22×C4C22×D412yes—
905C22×C4C22×D412yes—
906C22×C4C22×D412yes—
907C22×C4C2×#4112yes—
908C22×C4C2×#4112yes—
909C22×C4C2×#4112yes—
910C22×C4C2×#4112yes—
911C22×C4C2×#4112yes—
912C22×C4C2×#4112yes—
913C22×C4C2×#4112yes—
914C22×C4C2×#4112yes—
915C22×C4C2×#4112yes—
916C22×C4C2×#4112yes—
917C22×C4H(5,𝔽2)12yes—
918C22×C4H(5,𝔽2)12yes—
919C22×C4H(5,𝔽2)12yes—
920C22×C42−1+412yes—
921C4⋊C4—216no—
922C4⋊C4—216no—
923C4⋊C4—28no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—48no—
934C4⋊C4—84no—
935C22⋊C4—28no—
936C22⋊C4—216no—
937C22⋊C4—216no—
938C22⋊C4—216no—
939C22⋊C4—216no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—84no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C22⋊C4—84no—
958C22⋊C4—84no—
959C22⋊C4—84no—
960C22⋊C4—84no—
961C42—28no—
962C42—28no—
963C42—28no—
964C42—28no—
965C42—48no—
966C42—48no—
967C42—44no—
968C42—44no—
969C42—44no—
970C42—44no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
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—24no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
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—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23C2×#12314yes—
1076C23C23×D411yescharacteristic
1077C23C23×D411yescharacteristic
1078C23C23×D411yescharacteristic
1079C23C22×#4111yescharacteristic
1080C23C22×#4111yescharacteristic
1081C23C22×#4111yescharacteristic
1082C23C22×#4111yescharacteristic
1083C23C2×H(5,𝔽2)11yescharacteristic
1084C23C2×H(5,𝔽2)11yescharacteristic
1085C23C2×H(5,𝔽2)11yescharacteristic
1086C23C2×2−1+411yescharacteristic
1087C23#58511yescharacteristic
1088C23#58511yescharacteristic
1089C23#58511yescharacteristic
1090C23#58511yescharacteristic
1091Q8—232no—
1092Q8—416no—
1093D4—432no—
1094D4—432no—
1095D4—432no—
1096D4—432no—
1097D4—416no—
1098D4—416no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—232no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—432no—
1146C2×C4—416no—
1147C2×C4—416no—
1148C2×C4—432no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—42no—
1202C2×C4—41no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—42no—
1221C2×C4—41no—
1222C2×C4—42no—
1223C2×C4—41no—
1224C2×C4—42no—
1225C2×C4—41no—
1226C2×C4—42no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—41no—
1233C2×C4C2×#12018yes—
1234C2×C4C2×#12014yes—
1235C2×C4C2×#12314yes—
1236C2×C4C2×#12314yes—
1237C2×C4#53414yes—
1238C2×C4#54614yes—
1239C2×C4#54614yes—
1240C2×C4#54614yes—
1241C2×C4#54614yes—
1242C2×C4#54814yes—
1243C2×C4#55014yes—
1244C22—24no—
1245C22—24no—
1246C22—24no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—82no—
1274C22—82no—
1275C22—82no—
1276C22—82no—
1277C22—82no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22C22×#12011yescharacteristic
1290C22C22×#12311yescharacteristic
1291C22#344411yescharacteristic
1292C22C2×#53411yescharacteristic
1293C22#345511yescharacteristic
1294C22C2×#54611yescharacteristic
1295C22C2×#54611yescharacteristic
1296C22C2×#54611yescharacteristic
1297C22C2×#54611yescharacteristic
1298C22C2×#54811yescharacteristic
1299C22C2×#55011yescharacteristic
1300C22D4×#4111yescharacteristic
1301C22D4×#4111yescharacteristic
1302C22D4×#4111yescharacteristic
1303C22D4×#4111yescharacteristic
1304C22#348011yescharacteristic
1305C22#348011yescharacteristic
1306C22#348711yescharacteristic
1307C22#348711yescharacteristic
1308C22#348811yescharacteristic
1309C22#348811yescharacteristic
1310C22#348911yescharacteristic
1311C22#348911yescharacteristic
1312C22#350611yescharacteristic
1313C22#350711yescharacteristic
1314C22#350811yescharacteristic
1315C22#351111yescharacteristic
1316C22#351111yescharacteristic
1317C22#351211yescharacteristic
1318C22#351411yescharacteristic
1319C22#351711yescharacteristic
1320C22#354611yescharacteristic
1321C22#355411yescharacteristic
1322C22#356211yescharacteristic
1323C22#356211yescharacteristic
1324C4—24no—
1325C4—24no—
1326C4—24no—
1327C4—28no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—44no—
1334C4—42no—
1335C4—82no—
1336C4—81no—
1337C4—81no—
1338C4—82no—
1339C4—81no—
1340C4—82no—
1341C4—82no—
1342C4—81no—
1343C4#240518yes—
1344C2—44no—
1345C2—84no—
1346C2—84no—
1347C2C2×#240511yescharacteristic
1348C2#3474411yescharacteristic
1349C2#3551711yescharacteristic
1350C2#3614111yescharacteristic
1351C2#3615011yescharacteristic
1352C2#3642811yescharacteristic
1353C2#3642911yescharacteristic
1354C2#3769911yescharacteristic
1355C2#3770111yescharacteristic
1356C2#3986411yescharacteristic
1357C2#3986511yescharacteristic
1358C2#5904911yescharacteristic
1359C2#5907811yescharacteristic
1360C2#5914511yescharacteristic
1361C2#5914611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#532C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2448C2semidirect
3. C2×#2446C2semidirect
4. C2×#2341C2semidirect
5. #15674C2semidirect
6. #15340C2semidirect
7. #15338C2semidirect
8. #15338C2semidirect
9. #15226C2semidirect
10. #15217C2semidirect
11. #15140C2semidirect
12. #15127C2semidirect
13. #14825C2semidirect
14. #14824C2semidirect
15. #14697C2semidirect
16. #14173C2semidirect
17. #14173C2semidirect
18. #14026C2semidirect
19. #14024C2semidirect
20. #13937C2semidirect
21. #13937C2semidirect
22. #13937C2semidirect
23. C4×#385C2semidirect
496. C2×C4⋊C4#41semidirect
641. #95#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5322
C2×#24482
C2×#24462
C2×#23412
#156742
#153402
#153382
#152262
#152172
#151402
#151272
#148252
#148242
#146972
#141732
#140262
#140242
#139372
C4×#3852