Finite Group Databasebeta

← #7632738

Subgroups — #7632738

Order 512.

8496 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3500C211yesmaximal, characteristic
2C2×C4×2−1+4C211yesmaximal, characteristic, complemented
3#36578C212yesmaximal, complemented
4#36483C212yesmaximal, complemented
5#36216C216yesmaximal, complemented
6#36216C216yesmaximal, complemented
7#35987C216yesmaximal, complemented
8#35976C216yesmaximal, complemented
9#35801C212yesmaximal, complemented
10#35801C212yesmaximal, complemented
11#35679C213yesmaximal, complemented
12#35673C213yesmaximal, complemented
13#35531C213yesmaximal, complemented
14#35517C213yesmaximal, complemented
15#35254C213yesmaximal, complemented
16#35182C213yesmaximal, complemented
17#34744C213yesmaximal, complemented
18C2×#2448C213yesmaximal, complemented
19#34259C211yesmaximal, characteristic, complemented
20#34258C211yesmaximal, characteristic, complemented
21#34258C211yesmaximal, characteristic, complemented
22#34250C211yesmaximal, characteristic, complemented
23C4⋊C4×#41C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25C22×H(5,𝔽2)C2211yescharacteristic
26#3500—216no—
27C2×#548C2212yes—
28C2×#548C2212yes—
29C2×#546C2216yes—
30C2×#546C2216yes—
31C2×#536C2213yes—
32C2×#535C2213yes—
33C2×#532C2213yes—
34C22×#124C2213yes—
35C4×2−1+4—216no—
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#520C2216yescomplemented
39C2×#520C2213yescomplemented
40C2×#519C2213yescomplemented
41C2×#519C2212yescomplemented
42C2×C4×#41C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C2×C4×#41C2216yescomplemented
46C2×C4×#41C2213yescomplemented
47C22×C4×Q8C2213yescomplemented
48C22×C4×Q8C2212yescomplemented
49#2854C2216yescomplemented
50#2854C2216yescomplemented
51#2853C22112yescomplemented
52#2624C2216yescomplemented
53#2624C2216yescomplemented
54#2623C22112yescomplemented
55#2504C2216yescomplemented
56#2501C2216yescomplemented
57#2500C2216yescomplemented
58#2500C2216yescomplemented
59#2498C22112yescomplemented
60#2498C22112yescomplemented
61#2487C2216yescomplemented
62#2486C2216yescomplemented
63#2485C2216yescomplemented
64#2485C2216yescomplemented
65#2482C22112yescomplemented
66#2482C22112yescomplemented
67#2448C2216yescomplemented
68#2448C2216yescomplemented
69#2448C2213yescomplemented
70#2448C2216yescomplemented
71#2448C2216yescomplemented
72#2448C2216yescomplemented
73#2448C2216yescomplemented
74#2448C2216yescomplemented
75#2448C2216yescomplemented
76#2448C2216yescomplemented
77#2448C2216yescomplemented
78#2448C2216yescomplemented
79#2448C2216yescomplemented
80#2448C2213yescomplemented
81#2448C2216yescomplemented
82#2447C2211yescharacteristic, complemented
83#2447C2213yescomplemented
84#2446C2213yescomplemented
85#2446C2216yescomplemented
86#2446C2213yescomplemented
87#2445C2213yescomplemented
88#2445C2216yescomplemented
89#2445C2213yescomplemented
90#2444C2216yescomplemented
91#2444C22112yescomplemented
92#2444C2216yescomplemented
93#2443C2216yescomplemented
94#2443C22112yescomplemented
95#2443C2216yescomplemented
96#2423C2216yescomplemented
97#2423C2216yescomplemented
98#2423C2216yescomplemented
99#2423C2216yescomplemented
100#2421C2216yescomplemented
101#2421C2216yescomplemented
102#2421C2216yescomplemented
103#2421C2216yescomplemented
104#2418C22112yescomplemented
105#2418C22112yescomplemented
106#2418C22112yescomplemented
107#2418C22112yescomplemented
108#2395C2216yescomplemented
109#2395C2216yescomplemented
110C2×#399C2216yescomplemented
111C2×#397C2216yescomplemented
112#2351C2211yescharacteristic, complemented
113#2351C2211yescharacteristic, complemented
114#2351C2212yescomplemented
115Q8×C4⋊C4C2211yescharacteristic, complemented
116Q8×C4⋊C4C2211yescharacteristic, complemented
117Q8×C4⋊C4C2212yescomplemented
118#2349C2213yescomplemented
119#2349C2213yescomplemented
120#2349C2216yescomplemented
121D4×C4⋊C4C2213yescomplemented
122D4×C4⋊C4C2213yescomplemented
123D4×C4⋊C4C2216yescomplemented
124#2341C2212yes—
125#2341C2212yes—
126#2341C2212yes—
127#2341C2212yes—
128Q8×C22⋊C4C2212yescomplemented
129Q8×C22⋊C4C2212yescomplemented
130#2339C2216yescomplemented
131#2339C2216yescomplemented
132D4×C22⋊C4C2216yes—
133D4×C22⋊C4C2216yes—
134D4×C22⋊C4C2216yes—
135D4×C22⋊C4C2216yes—
136#2317C2213yescomplemented
137#2316C2213yescomplemented
138#2311C2213yes—
139#2311C2213yes—
140#2311C2213yescomplemented
141#2310C2213yescomplemented
142#2309C2213yes—
143#2309C2213yes—
144C4×#123C2216yescomplemented
145C4×#123C2216yescomplemented
146#2297C2213yes—
147#2297C2213yes—
148#2297C2213yescomplemented
149#2296C2213yescomplemented
150#2296C2213yescomplemented
151#2296C2213yescomplemented
152C2×#391C2213yescomplemented
153C2×#390C2213yes—
154C2×#390C2213yes—
155C2×#389C2213yescomplemented
156C2×#388C2216yescomplemented
157C2×#388C2216yescomplemented
158#2285C2213yescomplemented
159C2×C4×C4⋊C4C2213yescomplemented
160C2×2−1+4—28no—
161C2×2−1+4—28no—
162C2×2−1+4D4116yes—
163C2×H(5,𝔽2)—28no—
164C2×H(5,𝔽2)—28no—
165C2×H(5,𝔽2)—28no—
166C22×#41C2313yes—
167C22×#41C2312yes—
168C22×#41C2313yes—
169C22×#41C2316yes—
170C22×#41C2311yescharacteristic
171C23×Q8C2313yes—
172C23×Q8C2312yes—
173C23×D4C2313yes—
174C23×D4C2316yes—
175#548—216no—
176#548—216no—
177#546—248no—
178#546—248no—
179#536—224no—
180#535—224no—
181#532—224no—
182C2×C4⋊Q8C2313yes—
183C2×#127C2313yes—
184C2×#124—224no—
185C2×#124C2313yes—
186C2×#124C2316yes—
187C2×#124C2316yes—
188C2×#124C2316yes—
189C2×#124C2311yescharacteristic
190C2×#123C23112yes—
191C2×#123C2316yes—
192C2×#123C2316yes—
193C2×#123C23112yes—
194C2×C22⋊Q8C2316yes—
195C2×C22⋊Q8C2316yes—
196C2×#121C2316yes—
197C2×#121C2316yes—
198C2×#121C2316yes—
199C2×#121C2316yes—
200C2×#120C23112yes—
201#520—28no—
202#520—224no—
203#520—248no—
204#520—28no—
205#519—224no—
206#519—216no—
207C4×#41—28no—
208C4×#41—28no—
209C4×#41—224no—
210C4×#41—248no—
211C4×#41—28no—
212C2×C4×Q8—224no—
213C2×C4×Q8—216no—
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2316yes—
223C2×C4×Q8C2313yes—
224C2×C4×Q8C2316yes—
225C2×C4×Q8C2316yes—
226C2×C4×Q8C2316yes—
227C2×C4×Q8C2316yes—
228C2×C4×Q8C2313yes—
229C2×C4×D4C2313yes—
230C2×C4×D4C2316yes—
231C2×C4×D4C2313yes—
232C2×C4×D4C2313yes—
233C2×C4×D4C2313yes—
234C2×C4×D4C2316yes—
235C2×C4×D4C2313yes—
236C2×C4×D4C2313yes—
237C2×C4×D4C2316yes—
238C2×C4×D4C2316yes—
239C2×C4×D4C2316yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C23112yes—
242C2×C4×D4C2316yes—
243C2×C4×D4C2313yes—
244C2×#117C2313yes—
245C2×#117C2313yes—
246C2×#117C2313yes—
247C2×#117C2313yes—
248C2×#117C2313yes—
249C2×#117C2316yes—
250C2×#117C23112yes—
251C2×#117C2316yes—
252C22×C4⋊C4C2313yes—
253C22×C4⋊C4C2313yes—
254C22×C4⋊C4C2316yes—
255C22×C4⋊C4C2316yes—
256C22×C4⋊C4C2313yes—
257C22×C4⋊C4C2313yes—
258C22×C4⋊C4C2316yes—
259C22×C22⋊C4C2316yes—
260C22×C22⋊C4C2316yes—
261C22×C22⋊C4C2316yes—
262C22×C22⋊C4C2316yes—
263C22×C22⋊C4C2316yes—
264C22×C22⋊C4C2316yes—
265C22×C42C2316yes—
266C22×C42C2316yes—
267C22×C42C2313yes—
268C22×C42C2313yes—
269C22×C42C2313yes—
270#400C2316yes—
271#400C23112yes—
272#400C2316yes—
273#399C23112yes—
274#399C23112yes—
275#399C23112yes—
276#399C2316yes—
277#399C23112yes—
278#399C23112yes—
279#399C2316yes—
280#398C2316yes—
281#398C23112yes—
282#398C2316yes—
283#397C23112yes—
284#397C23112yes—
285#397C23112yes—
286#397C2316yes—
287#397C23112yes—
288#397C23112yes—
289#397C2312yes—
290#397C2312yes—
291#397C2316yes—
292#397C2316yes—
293#397C2316yes—
294#394C2316yes—
295#394C2316yes—
296#394C23112yes—
297#394C23112yes—
298#394C2316yes—
299#394C2316yes—
300#391C2313yes—
301#391C2316yes—
302#391C2316yes—
303#391C2316yes—
304#391C2313yes—
305#391C2313yes—
306#391C2316yes—
307#391C2316yes—
308#391C2311yescharacteristic
309#391C2311yescharacteristic
310#391C2313yes—
311#390C2313yes—
312#390C2313yes—
313#390C2316yes—
314#390C2316yes—
315#390C2316yes—
316#390C2316yes—
317#390C2316yes—
318#390C2316yes—
319#390C2313yes—
320#390C2316yes—
321#390C2316yes—
322#390C2316yes—
323#390C2316yes—
324#390C2311yescharacteristic
325#390C2313yes—
326#390C2313yes—
327#389C2313yes—
328#389C2316yes—
329#389C2316yes—
330#389C2316yes—
331#389C2313yes—
332#389C2313yes—
333#389C2313yes—
334#389C2313yes—
335#389C2313yes—
336#389C2316yes—
337#389C2313yes—
338#389C2313yes—
339#389C2313yes—
340#389C2316yes—
341#389C2313yes—
342#389C2313yes—
343#389C2311yescharacteristic
344#388C23112yes—
345#388C23112yes—
346#388C23112yes—
347#388C23112yes—
348#388C23112yes—
349#388C23112yes—
350#388C23112yes—
351#388C23112yes—
352#388C2316yes—
353#388C23112yes—
354#388C2316yes—
355#388C2316yes—
356#388C23112yes—
357#388C2316yes—
358#387C2316yes—
359#387C2316yes—
360#387C23112yes—
361#387C23112yes—
362#387C2316yes—
363#387C2316yes—
364#386C23112yes—
365#386C23112yes—
366#386C23112yes—
367#386C2316yes—
368#386C2316yes—
369#386C2316yes—
370#386C2316yes—
371#386C2316yes—
372#386C2316yes—
373#386C2316yes—
374#386C23112yes—
375#386C2316yes—
376#385C23112yes—
377#385C2316yes—
378#385C2316yes—
379#385C2316yes—
380#385C2316yes—
381#385C2316yes—
382#385C2316yes—
383#385C2316yes—
384#385C2312yes—
385#384C2316yes—
386#384C2313yes—
387#384C2313yes—
388#382C2316yes—
389#382C2313yes—
390#382C2313yes—
391#381C23112yes—
392#381C2316yes—
393#381C2312yes—
394#380C2316yes—
395#380C2316yes—
396#380C2316yes—
397#380C2316yes—
398#380C2316yes—
399#380C2316yes—
400#380C23112yes—
401#380C2316yes—
402#380C2316yes—
403#379C23112yes—
404#379C23112yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2313yes—
407C4×C4⋊C4C2316yes—
408C4×C4⋊C4C2316yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2313yes—
411C4×C4⋊C4C2313yes—
412C4×C4⋊C4C2313yes—
413C4×C4⋊C4C2316yes—
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2313yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2316yes—
422C2×#95C2316yes—
423C2×#95C2316yes—
424C2×#95C2313yes—
425C2×#95C2316yes—
426C2×#95C2313yes—
427C25C2416yes—
4282−1+4—2128no—
429H(5,𝔽2)—464no—
430C2×#41—28no—
431C2×#41—28no—
432C2×#41—28no—
433C2×#41—224no—
434C2×#41—224no—
435C2×#41—212no—
436C2×#41—212no—
437C2×#41—212no—
438C2×#41—212no—
439C2×#41—212no—
440C2×#41C2×D4124yes—
441C2×#41C2×D4148yes—
442C2×#41C2×D418yes—
443C2×#41#4118yes—
444C2×#41#4118yes—
445C22×Q8—28no—
446C22×Q8—28no—
447C22×Q8—212no—
448C22×Q8—212no—
449C22×Q8C2×D4124yes—
450C22×Q8C2×D4116yes—
451C22×Q8C2411yescharacteristic
452C22×Q8C2416yes—
453C22×Q8C2413yes—
454C22×Q8C2411yescharacteristic
455C22×D4—224no—
456C22×D4—224no—
457C22×D4—224no—
458C22×D4—212no—
459C22×D4—212no—
460C22×D4—212no—
461C22×D4C2416yes—
462C22×D4C2416yes—
463C22×D4C2413yes—
464C22×D4C2416yes—
465C22×D4C2411yescharacteristic
466C22×D4C2416yes—
467C22×D4C2416yes—
468C22×D4C2413yes—
469C23×C4C2416yes—
470C23×C4C2413yes—
471C23×C4C2413yes—
472C23×C4C2412yes—
473C23×C4C2416yes—
474C23×C4C2416yes—
475C23×C4C2416yes—
476C23×C4C2413yes—
477C23×C4C2413yes—
478C23×C4C2416yes—
479C23×C4C2413yes—
480C23×C4C2413yes—
481C23×C4C2416yes—
482C23×C4C2413yes—
483C4⋊Q8—212no—
484#127—212no—
485#124—212no—
486#124—224no—
487#124—224no—
488#124—224no—
489#124—24no—
490#123—248no—
491#123—412no—
492#123—412no—
493#123—812no—
494C22⋊Q8—224no—
495C22⋊Q8—224no—
496#121—224no—
497#121—224no—
498#121—224no—
499#121—224no—
500#120—248no—
501C4×Q8—224no—
502C4×Q8—212no—
503C4×Q8—24no—
504C4×Q8—224no—
505C4×Q8—224no—
506C4×Q8—224no—
507C4×Q8—28no—
508C4×Q8—224no—
509C4×Q8—212no—
510C4×Q8—24no—
511C4×Q8—24no—
512C4×Q8—24no—
513C4×Q8—24no—
514C4×Q8—24no—
515C4×Q8—28no—
516C4×D4—224no—
517C4×D4—24no—
518C4×D4—212no—
519C4×D4—248no—
520C4×D4—224no—
521C4×D4—212no—
522C4×D4—212no—
523C4×D4—224no—
524C4×D4—212no—
525C4×D4—212no—
526C4×D4—212no—
527C4×D4—212no—
528C4×D4—224no—
529C4×D4—224no—
530C4×D4—224no—
531#117—248no—
532#117—224no—
533#117—224no—
534#117—212no—
535#117—212no—
536#117—212no—
537#117—212no—
538#117—212no—
539C2×C4⋊C4—224no—
540C2×C4⋊C4—224no—
541C2×C4⋊C4—212no—
542C2×C4⋊C4—212no—
543C2×C4⋊C4—46no—
544C2×C4⋊C4—46no—
545C2×C4⋊C4—86no—
546C2×C4⋊C4C2411yescharacteristic
547C2×C4⋊C4C2411yescharacteristic
548C2×C4⋊C4C2416yes—
549C2×C4⋊C4C2413yes—
550C2×C4⋊C4C2413yes—
551C2×C4⋊C4C2416yes—
552C2×C4⋊C4C24112yes—
553C2×C4⋊C4C2413yes—
554C2×C4⋊C4C2416yes—
555C2×C4⋊C4C2413yes—
556C2×C4⋊C4C2413yes—
557C2×C4⋊C4C2413yes—
558C2×C4⋊C4C2411yescharacteristic
559C2×C4⋊C4C2416yes—
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2413yes—
562C2×C4⋊C4C2413yes—
563C2×C4⋊C4C2413yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2416yes—
568C2×C4⋊C4C24112yes—
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2416yes—
578C2×C22⋊C4—224no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—412no—
581C2×C22⋊C4—412no—
582C2×C22⋊C4—86no—
583C2×C22⋊C4—86no—
584C2×C22⋊C4C2416yes—
585C2×C22⋊C4C2416yes—
586C2×C22⋊C4C2416yes—
587C2×C22⋊C4C2416yes—
588C2×C22⋊C4C24112yes—
589C2×C22⋊C4C24112yes—
590C2×C22⋊C4C2416yes—
591C2×C22⋊C4C2416yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C24112yes—
603C2×C22⋊C4C24112yes—
604C2×C22⋊C4C24112yes—
605C2×C22⋊C4C24112yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2412yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C42—224no—
614C2×C42—224no—
615C2×C42—212no—
616C2×C42—212no—
617C2×C42—212no—
618C2×C42C2416yes—
619C2×C42C2413yes—
620C2×C42C2413yes—
621C2×C42C2416yes—
622C2×C42C24112yes—
623C2×C42C2413yes—
624C2×C42C2413yes—
625C2×C42C2416yes—
626C2×C42C2413yes—
627C2×C42C2413yes—
628C2×C42C2413yes—
629C2×C42C2411yescharacteristic
630C2×C42C2416yes—
631C2×C42C2413yes—
632C2×C42C2413yes—
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635#95C2411yescharacteristic
636#95C2411yescharacteristic
637#95C2416yes—
638#95C2416yes—
639#95C2416yes—
640#95C2413yes—
641#95C2413yes—
642#95C2413yes—
643#95C2413yes—
644#95C2413yes—
645#95C2413yes—
646#95C24112yes—
647#95C24112yes—
648#95C24112yes—
649#95C2412yes—
650#95C2412yes—
651#95C2412yes—
652#95C2412yes—
653#95C2416yes—
654#95C2416yes—
655#95C2416yes—
656#95C2416yes—
657#95C2416yes—
658#95C2416yes—
659#95C2412yes—
660#95C2416yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664C24—212no—
665C24—212no—
666C24—212no—
667C24—46no—
668C24—46no—
669C24—46no—
670C24—46no—
671C24C2516yes—
672C24C2512yes—
673C24C2513yes—
674#41—2192no—
675#41—296no—
676#41—432no—
677#41—448no—
678#41#123164yescomplemented
679C2×Q8—264no—
680C2×Q8—296no—
681C2×Q8—22no—
682C2×Q8—26no—
683C2×Q8—212no—
684C2×Q8—212no—
685C2×Q8—26no—
686C2×Q8—22no—
687C2×Q8—22no—
688C2×Q8C22×D4124yes—
689C2×Q8C22×D4112yes—
690C2×Q8C22×D414yes—
691C2×Q8C2×#4114yes—
692C2×Q8C2×#4114yes—
693C2×D4—212no—
694C2×D4—212no—
695C2×D4—212no—
696C2×D4—212no—
697C2×D4—212no—
698C2×D4—212no—
699C2×D4—212no—
700C2×D4—212no—
701C2×D4—26no—
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—26no—
705C2×D4—212no—
706C2×D4—212no—
707C2×D4—26no—
708C2×D4—46no—
709C2×D4—46no—
710C2×D4—46no—
711C2×D4—46no—
712C2×D4—496no—
713C2×D4—448no—
714C2×D4C22×D4124yes—
715C2×D4C22×D414yes—
716C2×D4C22×D4112yes—
717C2×D4C2×#41112yes—
718C2×D4C2×#41112yes—
719C22×C4—212no—
720C22×C4—212no—
721C22×C4—212no—
722C22×C4—212no—
723C22×C4—24no—
724C22×C4—26no—
725C22×C4—26no—
726C22×C4—26no—
727C22×C4—26no—
728C22×C4—212no—
729C22×C4—212no—
730C22×C4—26no—
731C22×C4—26no—
732C22×C4—212no—
733C22×C4—212no—
734C22×C4—212no—
735C22×C4—212no—
736C22×C4—26no—
737C22×C4—26no—
738C22×C4—24no—
739C22×C4—43no—
740C22×C4—42no—
741C22×C4—43no—
742C22×C4—46no—
743C22×C4—46no—
744C22×C4—43no—
745C22×C4—43no—
746C22×C4—46no—
747C22×C4—46no—
748C22×C4—43no—
749C22×C4—43no—
750C22×C4—43no—
751C22×C4—43no—
752C22×C4—46no—
753C22×C4—46no—
754C22×C4—43no—
755C22×C4—43no—
756C22×C4C22×D4124yes—
757C22×C4C22×D4124yes—
758C22×C4C22×D4112yes—
759C22×C4C2×#41112yes—
760C22×C4C2×#41112yes—
761C22×C4C2511yescharacteristic
762C22×C4C2512yes—
763C22×C4C2512yes—
764C22×C4C2513yes—
765C22×C4C2513yes—
766C22×C4C2516yes—
767C22×C4C2511yescharacteristic
768C22×C4C2513yes—
769C22×C4C2513yes—
770C22×C4C2512yes—
771C22×C4C2511yescharacteristic
772C22×C4C2516yes—
773C22×C4C2513yes—
774C22×C4C2511yescharacteristic
775C22×C4C2513yes—
776C22×C4C2516yes—
777C22×C4C2511yescharacteristic
778C22×C4C2511yescharacteristic
779C22×C4C2511yescharacteristic
780C22×C4C2513yes—
781C4⋊C4—212no—
782C4⋊C4—224no—
783C4⋊C4—26no—
784C4⋊C4—26no—
785C4⋊C4—212no—
786C4⋊C4—212no—
787C4⋊C4—22no—
788C4⋊C4—26no—
789C4⋊C4—26no—
790C4⋊C4—26no—
791C4⋊C4—212no—
792C4⋊C4—212no—
793C4⋊C4—26no—
794C4⋊C4—212no—
795C4⋊C4—22no—
796C4⋊C4—26no—
797C4⋊C4—26no—
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—26no—
801C4⋊C4—26no—
802C4⋊C4—43no—
803C4⋊C4—43no—
804C4⋊C4—43no—
805C4⋊C4—43no—
806C4⋊C4—46no—
807C4⋊C4—412no—
808C4⋊C4—42no—
809C4⋊C4—46no—
810C4⋊C4—46no—
811C4⋊C4—46no—
812C4⋊C4—46no—
813C22⋊C4—24no—
814C22⋊C4—212no—
815C22⋊C4—212no—
816C22⋊C4—212no—
817C22⋊C4—212no—
818C22⋊C4—24no—
819C22⋊C4—24no—
820C22⋊C4—212no—
821C22⋊C4—212no—
822C22⋊C4—212no—
823C22⋊C4—212no—
824C22⋊C4—224no—
825C22⋊C4—224no—
826C22⋊C4—212no—
827C22⋊C4—212no—
828C22⋊C4—24no—
829C22⋊C4—412no—
830C22⋊C4—412no—
831C22⋊C4—46no—
832C22⋊C4—46no—
833C22⋊C4—412no—
834C22⋊C4—412no—
835C22⋊C4—46no—
836C22⋊C4—42no—
837C22⋊C4—46no—
838C22⋊C4—46no—
839C22⋊C4—46no—
840C22⋊C4—46no—
841C22⋊C4—46no—
842C42—212no—
843C42—22no—
844C42—26no—
845C42—22no—
846C42—224no—
847C42—212no—
848C42—26no—
849C42—212no—
850C42—26no—
851C42—26no—
852C42—26no—
853C42—26no—
854C42—22no—
855C42—26no—
856C42—26no—
857C42—26no—
858C42—212no—
859C23—23no—
860C23—23no—
861C23—23no—
862C23—23no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—26no—
870C23—26no—
871C23—26no—
872C23—26no—
873C23—26no—
874C23—26no—
875C23—26no—
876C23—424no—
877C23—812no—
878C23—812no—
879C23—812no—
880C23—812no—
881C23—812no—
882C23—812no—
883C23C23×D414yes—
884C23C23×D416yes—
885C23C22×#4116yes—
886C23C22×#4116yes—
887C23C2611yescharacteristic
888Q8—248no—
889Q8—224no—
890Q8—44no—
891Q8C2×#123116yes—
892D4—248no—
893D4—28no—
894D4—424no—
895D4—424no—
896D4—412no—
897D4—812no—
898D4—812no—
899D4C2×#123148yes—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—26no—
903C2×C4—26no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—248no—
907C2×C4—248no—
908C2×C4—23no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—26no—
913C2×C4—23no—
914C2×C4—21no—
915C2×C4—23no—
916C2×C4—23no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—23no—
921C2×C4—23no—
922C2×C4—26no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—26no—
927C2×C4—26no—
928C2×C4—23no—
929C2×C4—23no—
930C2×C4—23no—
931C2×C4—22no—
932C2×C4—23no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—23no—
937C2×C4—23no—
938C2×C4—23no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—26no—
942C2×C4—23no—
943C2×C4—26no—
944C2×C4—21no—
945C2×C4—23no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—23no—
949C2×C4—23no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—23no—
953C2×C4—412no—
954C2×C4—48no—
955C2×C4—412no—
956C2×C4—424no—
957C2×C4—86no—
958C2×C4—812no—
959C2×C4—86no—
960C2×C4—812no—
961C2×C4—86no—
962C2×C4—812no—
963C2×C4—86no—
964C2×C4C2×#123148yes—
965C2×C4C23×D4112yes—
966C2×C4C23×D412yes—
967C2×C4C23×D416yes—
968C2×C4C22×#4112yes—
969C2×C4C22×#4116yes—
970C2×C4C22×#4116yes—
971C2×C4C22×#4112yes—
972C2×C4#58512yes—
973C2×C4#58512yes—
974C22—26no—
975C22—26no—
976C22—26no—
977C22—26no—
978C22—26no—
979C22—26no—
980C22—24no—
981C22—24no—
982C22—24no—
983C22—42no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—46no—
988C22—46no—
989C22—46no—
990C22—46no—
991C22—46no—
992C22—46no—
993C22—46no—
994C22—1624no—
995C22C22×#123112yes—
996C22C24×D411yescharacteristic
997C22C23×#4111yescharacteristic
998C22C23×#4111yescharacteristic
999C22C2×#58511yescharacteristic
1000C22C2×#58511yescharacteristic
1001C22H(7,𝔽2)11yescharacteristic
1002C222−1+611yescharacteristic
1003C4—22no—
1004C4—22no—
1005C4—212no—
1006C4—42no—
1007C4—43no—
1008C4—42no—
1009C4—41no—
1010C4—43no—
1011C4—41no—
1012C4—46no—
1013C4—43no—
1014C4—41no—
1015C4—43no—
1016C4—46no—
1017C4—43no—
1018C4—43no—
1019C4—41no—
1020C4—42no—
1021C4C22×#123112yes—
1022C4C22×#12314yes—
1023C2—212no—
1024C2—44no—
1025C2—86no—
1026C2C23×#12311yescharacteristic
1027C2#6281011yescharacteristic
1028C2#6285711yescharacteristic
1029C2#6299511yescharacteristic
1030C2#6300211yescharacteristic
1031C2#6300311yescharacteristic
1032C2#6301011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3500C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×2−1+4C2semidirect
3. #36578C2semidirect
4. #36483C2semidirect
5. #36216C2semidirect
6. #36216C2semidirect
7. #35987C2semidirect
8. #35976C2semidirect
9. #35801C2semidirect
10. #35801C2semidirect
11. #35679C2semidirect
12. #35673C2semidirect
13. #35531C2semidirect
14. #35517C2semidirect
15. #35254C2semidirect
16. #35182C2semidirect
17. #34744C2semidirect
18. C2×#2448C2semidirect
19. #34259C2semidirect
20. #34258C2semidirect
21. #34258C2semidirect
22. #34250C2semidirect
23. C4⋊C4×#41C2semidirect
38. C2×#520C22semidirect
39. C2×#520C22semidirect
40. C2×#519C22semidirect
41. C2×#519C22semidirect
45. C2×C4×#41C22semidirect
46. C2×C4×#41C22semidirect
47. C22×C4×Q8C22semidirect
48. C22×C4×Q8C22semidirect
49. #2854C22semidirect
50. #2854C22semidirect
51. #2853C22semidirect
52. #2624C22semidirect
53. #2624C22semidirect
54. #2623C22semidirect
55. #2504C22semidirect
56. #2501C22semidirect
57. #2500C22semidirect
58. #2500C22semidirect
59. #2498C22semidirect
60. #2498C22semidirect
61. #2487C22semidirect
62. #2486C22semidirect
63. #2485C22semidirect
64. #2485C22semidirect
65. #2482C22semidirect
66. #2482C22semidirect
67. #2448C22semidirect
68. #2448C22semidirect
69. #2448C22semidirect
70. #2448C22semidirect
71. #2448C22semidirect
72. #2448C22semidirect
73. #2448C22semidirect
74. #2448C22semidirect
75. #2448C22semidirect
76. #2448C22semidirect
77. #2448C22semidirect
78. #2448C22semidirect
79. #2448C22semidirect
80. #2448C22semidirect
81. #2448C22semidirect
82. #2447C22semidirect
83. #2447C22semidirect
84. #2446C22semidirect
85. #2446C22semidirect
86. #2446C22semidirect
87. #2445C22semidirect
88. #2445C22semidirect
89. #2445C22semidirect
90. #2444C22semidirect
91. #2444C22semidirect
92. #2444C22semidirect
93. #2443C22semidirect
94. #2443C22semidirect
95. #2443C22semidirect
96. #2423C22semidirect
97. #2423C22semidirect
98. #2423C22semidirect
99. #2423C22semidirect
100. #2421C22semidirect
101. #2421C22semidirect
102. #2421C22semidirect
103. #2421C22semidirect
104. #2418C22semidirect
105. #2418C22semidirect
106. #2418C22semidirect
107. #2418C22semidirect
108. #2395C22semidirect
109. #2395C22semidirect
110. C2×#399C22semidirect
111. C2×#397C22semidirect
112. #2351C22semidirect
113. #2351C22semidirect
114. #2351C22semidirect
115. Q8×C4⋊C4C22semidirect
116. Q8×C4⋊C4C22semidirect
117. Q8×C4⋊C4C22semidirect
118. #2349C22semidirect
119. #2349C22semidirect
120. #2349C22semidirect
121. D4×C4⋊C4C22semidirect
122. D4×C4⋊C4C22semidirect
123. D4×C4⋊C4C22semidirect
128. Q8×C22⋊C4C22semidirect
129. Q8×C22⋊C4C22semidirect
130. #2339C22semidirect
131. #2339C22semidirect
136. #2317C22semidirect
137. #2316C22semidirect
140. #2311C22semidirect
141. #2310C22semidirect
144. C4×#123C22semidirect
145. C4×#123C22semidirect
148. #2297C22semidirect
149. #2296C22semidirect
150. #2296C22semidirect
151. #2296C22semidirect
152. C2×#391C22semidirect
155. C2×#389C22semidirect
156. C2×#388C22semidirect
157. C2×#388C22semidirect
158. #2285C22semidirect
159. C2×C4×C4⋊C4C22semidirect
678. #41#123semidirect

Maximal subgroups

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

subgroupindex
C2×#35002
C2×C4×2−1+42
#365782
#364832
#362162
#359872
#359762
#358012
#356792
#356732
#355312
#355172
#352542
#351822
#347442
C2×#24482
#342592
#342582
#342502
C4⋊C4×#412