Finite Group Databasebeta

← #7674202

Subgroups — #7674202

Order 512.

7800 conjugacy classes of subgroups.

The subgroup lattice has 971 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic, complemented
2C22×#536C211yesmaximal, characteristic, complemented
3#45323C218yesmaximal, complemented
4#45240C218yesmaximal, complemented
5#39417C218yesmaximal, complemented
6#37843C218yesmaximal, complemented
7#37841C218yesmaximal, complemented
8#37749C218yesmaximal, complemented
9#35679C211yesmaximal, characteristic, complemented
10#35677C211yesmaximal, characteristic, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35667C211yesmaximal, characteristic, complemented
13#35338C211yesmaximal, characteristic, complemented
14#35327C211yesmaximal, characteristic, complemented
15#35242C211yesmaximal, characteristic, complemented
16#35149C211yesmaximal, characteristic
17#34634C211yesmaximal, characteristic, complemented
18#34209C211yesmaximal, characteristic, complemented
19#34174C211yesmaximal, characteristic, complemented
20#34173C211yesmaximal, characteristic, complemented
21#34065C211yesmaximal, characteristic, complemented
22C23×#41C2211yescharacteristic
23C24×Q8C2211yescharacteristic
24#3509—216no—
25C2×#557C2214yescomplemented
26C2×#556C2214yescomplemented
27C2×#552C2218yes—
28C2×#541C2214yescomplemented
29C2×#536—216no—
30C2×#536C2218yes—
31C2×#536C2211yescharacteristic
32C2×#536C2211yescharacteristic
33C2×#536C2214yes—
34C2×#536C2214yes—
35C2×#536C2211yescharacteristic
36C2×#535C2211yescharacteristic
37C2×#533C2211yescharacteristic
38C2×#533C2214yescomplemented
39C22×C4⋊Q8C2211yescharacteristic
40C22×C4⋊Q8C2211yescharacteristic
41C22×#124C2211yescharacteristic
42C22×#124C2211yescharacteristic
43C2×#525C2211yescharacteristic
44C22×#123C2214yes—
45C22×C22⋊Q8C2214yes—
46C2×#519C2211yescharacteristic
47C2×#519C2211yescharacteristic
48C2×#519C2211yescharacteristic
49C2×#519C2211yescharacteristic
50C2×C4×#41C2211yescharacteristic
51C22×#117C2211yescharacteristic
52#2861C2214yescomplemented
53#2850C2214yescomplemented
54#2849C2214yes—
55#2849C2214yes—
56#2707C22116yescomplemented
57#2705C22116yescomplemented
58#2704C22116yescomplemented
59#2702C22116yescomplemented
60#2696C22116yescomplemented
61#2694C22116yescomplemented
62#2692C22116yescomplemented
63#2690C22116yescomplemented
64#2640C2214yescomplemented
65#2629C2214yescomplemented
66#2628C2214yescomplemented
67#2627C2214yes—
68#2626C2214yes—
69#2620C2214yescomplemented
70#2614C2214yes—
71#2613C2214yes—
72#2592C2218yescomplemented
73#2561C2218yes—
74#2560C22116yescomplemented
75#2558C22116yescomplemented
76#2556C22116yescomplemented
77#2554C22116yescomplemented
78#2548C2214yescomplemented
79#2546C2214yescomplemented
80#2545C2214yescomplemented
81#2545C2214yescomplemented
82#2545C2214yescomplemented
83#2544C2214yescomplemented
84#2534C2218yes—
85#2484C2218yes—
86#2482C2218yes—
87#2477C22116yescomplemented
88#2471C22116yescomplemented
89#2465C22116yescomplemented
90#2458C22116yescomplemented
91#2448C2218yescomplemented
92#2448C2218yescomplemented
93#2446C2218yescomplemented
94#2446C2218yescomplemented
95#2436C2214yescomplemented
96#2434C2214yescomplemented
97#2432C2214yes—
98#2431C2214yes—
99#2429C2218yescomplemented
100#2426C2218yescomplemented
101#2413C2218yes—
102#2411C2218yes—
103#2409C2218yescomplemented
104#2407C2218yes—
105#2396C2218yescomplemented
106#2365C2218yescomplemented
107#2344C2218yes—
108#2341C2218yes—
109#2341C2218yes—
110Q8×C22⋊C4C2218yescomplemented
111Q8×C22⋊C4C2218yescomplemented
112#2327C2214yescomplemented
113#2324C2214yescomplemented
114#2323C2214yescomplemented
115#2322C2214yes—
116#2321C2214yes—
117#2310C2211yescharacteristic
118#2310C2211yescharacteristic
119#2310C2211yescharacteristic
120#2310C2211yescharacteristic
121#2310C2211yescharacteristic
122#2310C2214yes—
123#2309C2211yescharacteristic
124#2309C2211yescharacteristic
125#2309C2211yescharacteristic
126#2309C2214yes—
127C4×C4⋊Q8C2214yescomplemented
128#2297C2211yescharacteristic
129#2296C2211yescharacteristic
130#2296C2211yescharacteristic
131#2296C2211yescharacteristic
132#2293C2214yescomplemented
133#2290C2214yescomplemented
134#2285C2211yescharacteristic
135#2280C2211yescharacteristic
136#2280C2211yescharacteristic
137#2280C2211yescharacteristic
138#2280C2214yes—
139#2280C2214yes—
140C4×#117C2211yescharacteristic
141C22×#41—28no—
142C22×#41—28no—
143C22×#41—44no—
144C22×#41C2311yescharacteristic
145C22×#41C2314yes—
146C22×#41C2314yes—
147C23×Q8—28no—
148C23×Q8—28no—
149C23×Q8—44no—
150C23×Q8C2311yescharacteristic
151C23×Q8C2312yes—
152C23×Q8C2314yes—
153C23×Q8C2314yes—
154C23×Q8C2311yescharacteristic
155C23×Q8C2311yescharacteristic
156C23×D4C2311yescharacteristic
157C23×D4C2312yes—
158C24×C4C2312yes—
159C24×C4C2312yes—
160C24×C4C2311yescharacteristic
161#557—232no—
162#556—232no—
163#552—264no—
164#541—232no—
165#536—28no—
166#536—28no—
167#536—232no—
168#536—232no—
169#536—264no—
170#536—44no—
171#535—44no—
172#533—232no—
173#533—28no—
174C2×C4⋊Q8—28no—
175C2×C4⋊Q8D4116yescomplemented
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2312yes—
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2312yes—
183C2×C4⋊Q8C2312yes—
184C2×C4⋊Q8C2314yes—
185C2×#127C2312yes—
186C2×#126C2318yes—
187C2×#126C2318yes—
188C2×#125C2312yes—
189C2×#125C2318yes—
190C2×#125C2318yes—
191C2×#125C2318yes—
192C2×#124—28no—
193C2×#124—28no—
194C2×#124C2314yes—
195C2×#124C2312yes—
196C2×#124C2312yes—
197C2×#124C2314yes—
198C2×#124C2314yes—
199C2×#124C2312yes—
200C2×#124C2312yes—
201C2×#124C2312yes—
202C2×#124C2312yes—
203#525—28no—
204C2×#123—232no—
205C2×#123C2312yes—
206C2×#123C2314yes—
207C2×#123C2314yes—
208C2×#123C23116yes—
209C2×#123C23116yes—
210C2×#123C2314yes—
211C2×C22⋊Q8—232no—
212C2×C22⋊Q8C23116yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C23116yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2314yes—
220C2×#121C2312yes—
221C2×#121C2314yes—
222C2×#120C2312yes—
223C2×#120C2314yes—
224#519—28no—
225#519—28no—
226#519—44no—
227#519—44no—
228C4×#41—28no—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2318yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2314yes—
243C2×#117—28no—
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2314yes—
251C2×#117C2311yescharacteristic
252C2×#117C2314yes—
253C2×#117C2314yes—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2318yes—
258C2×#117C2314yes—
259C2×#117C2314yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C22⋊C4C2314yes—
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2314yes—
266C22×C42C2312yes—
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269#400C2318yes—
270#400C23116yes—
271#399C2318yes—
272#399C23116yes—
273#398C2318yes—
274#398C2318yes—
275#398C23116yes—
276#398C23116yes—
277#397C23116yes—
278#397C23116yes—
279#396C23116yes—
280#396C2318yes—
281#396C2318yes—
282#396C23116yes—
283#396C23116yes—
284#395C23116yes—
285#395C2318yes—
286#394C23116yes—
287#394C23116yes—
288#394C23116yes—
289#393C23116yes—
290#393C23116yes—
291#393C2318yes—
292#392C23116yes—
293#391C23116yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#391C2314yes—
298#391C2314yes—
299#391C2314yes—
300#391C2314yes—
301#391C23116yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2312yes—
306#390C23116yes—
307#390C2314yes—
308#390C2314yes—
309#390C2314yes—
310#390C2314yes—
311#390C23116yes—
312#390C2314yes—
313#390C23116yes—
314#390C2314yes—
315#390C2318yes—
316#390C2312yes—
317#389C23116yes—
318#389C2318yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C23116yes—
323#388C2318yes—
324#388C23116yes—
325#388C23116yes—
326#388C23116yes—
327#388C2318yes—
328#388C2318yes—
329#388C23116yes—
330#388C23116yes—
331#388C23116yes—
332#388C23116yes—
333#387C23116yes—
334#387C2318yes—
335#387C23116yes—
336#387C23116yes—
337#387C23116yes—
338#386C23116yes—
339#386C2314yes—
340#386C2318yes—
341#386C23116yes—
342#386C23116yes—
343#385C2314yes—
344#385C2318yes—
345#385C23116yes—
346#385C23116yes—
347#385C2314yes—
348#385C2314yes—
349#384C2312yes—
350#382C2312yes—
351#381C2314yes—
352#381C2314yes—
353#381C2312yes—
354#381C2312yes—
355#381C2314yes—
356#381C2314yes—
357#381C2314yes—
358#381C2312yes—
359#380C2314yes—
360#380C2314yes—
361#380C23116yes—
362#380C2314yes—
363#380C23116yes—
364#380C2314yes—
365#379C2314yes—
366#379C2314yes—
367#379C2312yes—
368#379C2312yes—
369#379C2314yes—
370#379C2312yes—
371C4×C4⋊C4C23116yes—
372C4×C4⋊C4C2314yes—
373C4×C4⋊C4C2314yes—
374C4×C4⋊C4C2314yes—
375C4×C4⋊C4C2314yes—
376C4×C4⋊C4C2314yes—
377C4×C22⋊C4C23116yes—
378C4×C22⋊C4C2314yes—
379C4×C22⋊C4C2314yes—
380C4×C22⋊C4C2314yes—
381C4×C22⋊C4C23116yes—
382C4×C22⋊C4C2314yes—
383C4×C22⋊C4C2314yes—
384#376C2312yes—
385C43C2312yes—
386C25C2412yes—
387C25C2411yescharacteristic
388C2×#41—216no—
389C2×#41—216no—
390C2×#41—24no—
391C2×#41—24no—
392C2×#41—216no—
393C2×#41—216no—
394C2×#41—24no—
395C2×#41—48no—
396C2×#41—48no—
397C2×#41—464no—
398C22×Q8—216no—
399C22×Q8—216no—
400C22×Q8—28no—
401C22×Q8—24no—
402C22×Q8—24no—
403C22×Q8—24no—
404C22×Q8—28no—
405C22×Q8—216no—
406C22×Q8—216no—
407C22×Q8—24no—
408C22×Q8—24no—
409C22×Q8—24no—
410C22×Q8—24no—
411C22×Q8—44no—
412C22×Q8—48no—
413C22×Q8—48no—
414C22×Q8—464no—
415C22×Q8C2×D418yes—
416C22×Q8C2×D418yes—
417C22×Q8C2411yescharacteristic
418C22×Q8C2412yes—
419C22×Q8C2412yes—
420C22×Q8C2418yes—
421C22×Q8C2412yes—
422C22×Q8C2412yes—
423C22×Q8C2412yes—
424C22×Q8C2412yes—
425C22×Q8C2414yes—
426C22×D4—28no—
427C22×D4—28no—
428C22×D4—24no—
429C22×D4—24no—
430C22×D4—24no—
431C22×D4—44no—
432C22×D4C2412yes—
433C22×D4C2411yescharacteristic
434C22×D4C2412yes—
435C22×D4C2412yes—
436C22×D4C2418yes—
437C22×D4C2414yes—
438C22×D4C2418yes—
439C23×C4—24no—
440C23×C4—24no—
441C23×C4—28no—
442C23×C4—28no—
443C23×C4—28no—
444C23×C4—28no—
445C23×C4—44no—
446C23×C4—44no—
447C23×C4#4118yes—
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2418yes—
451C23×C4C2418yes—
452C23×C4C2412yes—
453C23×C4C2412yes—
454C23×C4C2411yescharacteristic
455C23×C4C2412yes—
456C23×C4C2412yes—
457C23×C4C2412yes—
458C23×C4C2414yes—
459C23×C4C2412yes—
460C23×C4C2411yescharacteristic
461C4⋊Q8—216no—
462C4⋊Q8—216no—
463C4⋊Q8—28no—
464C4⋊Q8—28no—
465C4⋊Q8—28no—
466C4⋊Q8—44no—
467C4⋊Q8C2×D4116yes—
468C4⋊Q8C2×D4116yes—
469C4⋊Q8C2×D4132yes—
470#127—44no—
471#126—232no—
472#126—232no—
473#125—232no—
474#125—232no—
475#125—232no—
476#125—28no—
477#124—216no—
478#124—216no—
479#124—28no—
480#124—28no—
481#124—28no—
482#124—28no—
483#124—216no—
484#124—44no—
485#124—44no—
486#123—216no—
487#123—216no—
488#123—28no—
489#123—264no—
490#123—264no—
491#123—48no—
492C22⋊Q8—216no—
493C22⋊Q8—216no—
494C22⋊Q8—216no—
495C22⋊Q8—28no—
496C22⋊Q8—264no—
497C22⋊Q8—264no—
498C22⋊Q8—232no—
499C22⋊Q8—48no—
500#121—28no—
501#121—48no—
502#120—28no—
503#120—48no—
504C4×Q8—216no—
505C4×Q8—216no—
506C4×Q8—216no—
507C4×Q8—216no—
508C4×Q8—232no—
509C4×Q8—28no—
510C4×Q8—216no—
511C4×Q8—48no—
512C4×Q8—48no—
513C4×Q8—48no—
514C4×Q8—48no—
515C4×D4—216no—
516C4×D4—216no—
517C4×D4—28no—
518#117—24no—
519#117—24no—
520#117—24no—
521#117—216no—
522#117—216no—
523#117—24no—
524#117—24no—
525#117—24no—
526#117—24no—
527#117—232no—
528#117—28no—
529#117—28no—
530#117—216no—
531#117—28no—
532#117—48no—
533#117—48no—
534C2×C4⋊C4—28no—
535C2×C4⋊C4—216no—
536C2×C4⋊C4C2×D4132yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C24116yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C22⋊C4—28no—
566C2×C22⋊C4—216no—
567C2×C22⋊C4—216no—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C24116yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2412yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C24116yes—
591C2×C22⋊C4C24116yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C24116yes—
594C2×C42—24no—
595C2×C42—28no—
596C2×C42C2×D418yes—
597C2×C42C2412yes—
598C2×C42C2418yes—
599C2×C42C2418yes—
600C2×C42C2412yes—
601C2×C42C2412yes—
602C2×C42C2412yes—
603C2×C42C2412yes—
604C2×C42C2412yes—
605C2×C42C2412yes—
606C2×C42C2412yes—
607C2×C42C2412yes—
608C2×C42C2414yes—
609C2×C42C2418yes—
610C2×C42C2418yes—
611C2×C42C2418yes—
612C2×C42C2411yescharacteristic
613C2×C42C2412yes—
614C2×C42C2411yescharacteristic
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C24116yes—
620#95C24116yes—
621#95C2418yes—
622#95C2418yes—
623#95C24116yes—
624#95C24116yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C24116yes—
629C24—22no—
630C24—22no—
631C24—24no—
632C24—24no—
633C24—24no—
634C24—44no—
635C24—48no—
636C24C2×#4114yes—
637C24C2514yes—
638C24C2512yes—
639C24C2512yes—
640C24C2511yescharacteristic
641#41—464no—
642#41—464no—
643#41—416no—
644C2×Q8—232no—
645C2×Q8—232no—
646C2×Q8—28no—
647C2×Q8—22no—
648C2×Q8—216no—
649C2×Q8—24no—
650C2×Q8—24no—
651C2×Q8—24no—
652C2×Q8—24no—
653C2×Q8—24no—
654C2×Q8—24no—
655C2×Q8—22no—
656C2×Q8—216no—
657C2×Q8—24no—
658C2×Q8—24no—
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—24no—
662C2×Q8—24no—
663C2×Q8—24no—
664C2×Q8—22no—
665C2×Q8—24no—
666C2×Q8—48no—
667C2×Q8—48no—
668C2×Q8—432no—
669C2×Q8—464no—
670C2×Q8—464no—
671C2×Q8—416no—
672C2×Q8C22×D418yes—
673C2×Q8C22×D418yes—
674C2×Q8C22×D418yes—
675C2×Q8C22×D418yes—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—216no—
679C2×D4—24no—
680C2×D4—28no—
681C2×D4—22no—
682C2×D4—216no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—22no—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—22no—
690C2×D4—24no—
691C2×D4—48no—
692C2×D4—432no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—416no—
696C2×D4—416no—
697C22×C4—22no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—22no—
703C22×C4—232no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—216no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—28no—
714C22×C4—24no—
715C22×C4—216no—
716C22×C4—216no—
717C22×C4—24no—
718C22×C4—216no—
719C22×C4—24no—
720C22×C4—48no—
721C22×C4—48no—
722C22×C4—44no—
723C22×C4—48no—
724C22×C4—44no—
725C22×C4—432no—
726C22×C4—432no—
727C22×C4C22×D418yes—
728C22×C4C22×D418yes—
729C22×C4C22×D418yes—
730C22×C4C22×D414yes—
731C22×C4C2×#4118yes—
732C22×C4C2×#4118yes—
733C22×C4C2×#4114yes—
734C22×C4C2×#4114yes—
735C22×C4H(5,𝔽2)14yes—
736C22×C4C2514yes—
737C22×C4C2514yes—
738C22×C4C2514yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2514yes—
742C22×C4C2514yes—
743C22×C4C2514yes—
744C22×C4C2514yes—
745C22×C4C2512yes—
746C22×C4C2512yes—
747C22×C4C2514yes—
748C22×C4C2514yes—
749C22×C4C2512yes—
750C22×C4C2512yes—
751C22×C4C2511yescharacteristic
752C22×C4C2511yescharacteristic
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—232no—
756C4⋊C4—28no—
757C4⋊C4—24no—
758C4⋊C4—28no—
759C4⋊C4—24no—
760C4⋊C4—24no—
761C4⋊C4—216no—
762C4⋊C4—216no—
763C4⋊C4—216no—
764C4⋊C4—216no—
765C4⋊C4—28no—
766C4⋊C4—28no—
767C4⋊C4—24no—
768C4⋊C4—28no—
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—24no—
772C4⋊C4—48no—
773C4⋊C4—48no—
774C4⋊C4—48no—
775C4⋊C4—48no—
776C4⋊C4—48no—
777C4⋊C4—48no—
778C4⋊C4—48no—
779C4⋊C4C22×D4132yes—
780C4⋊C4C22×D4132yes—
781C22⋊C4—24no—
782C22⋊C4—24no—
783C22⋊C4—24no—
784C22⋊C4—24no—
785C22⋊C4—28no—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—24no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—232no—
792C22⋊C4—216no—
793C22⋊C4—216no—
794C22⋊C4—28no—
795C22⋊C4—216no—
796C22⋊C4—216no—
797C22⋊C4—28no—
798C22⋊C4—48no—
799C22⋊C4—416no—
800C22⋊C4—48no—
801C22⋊C4—416no—
802C22⋊C4—416no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C42—24no—
808C42—24no—
809C42—24no—
810C42—28no—
811C42—216no—
812C42—216no—
813C42—24no—
814C42—24no—
815C42—24no—
816C42—24no—
817C42—24no—
818C42—24no—
819C42—48no—
820C42—48no—
821C42—48no—
822C42C22×D414yes—
823C42C22×D414yes—
824C42C22×D418yes—
825C23—24no—
826C23—22no—
827C23—22no—
828C23—24no—
829C23—24no—
830C23—28no—
831C23—22no—
832C23—24no—
833C23—22no—
834C23—24no—
835C23—22no—
836C23—24no—
837C23—216no—
838C23—28no—
839C23—48no—
840C23—48no—
841C23—48no—
842C23—416no—
843C23—48no—
844C23—88no—
845C23—88no—
846C23C23×D412yes—
847C23C22×#4114yes—
848C23C22×#4112yes—
849C23C2×H(5,𝔽2)12yes—
850C23C2611yescharacteristic
851Q8—216no—
852Q8—216no—
853Q8—216no—
854Q8—216no—
855Q8—432no—
856Q8—416no—
857Q8—48no—
858Q8—48no—
859Q8—44no—
860D4—432no—
861D4—48no—
862D4—48no—
863D4—48no—
864D4—44no—
865D4—88no—
866D4—168no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—28no—
876C2×C4—216no—
877C2×C4—216no—
878C2×C4—216no—
879C2×C4—216no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—22no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—22no—
893C2×C4—24no—
894C2×C4—28no—
895C2×C4—28no—
896C2×C4—28no—
897C2×C4—28no—
898C2×C4—28no—
899C2×C4—28no—
900C2×C4—24no—
901C2×C4—28no—
902C2×C4—24no—
903C2×C4—48no—
904C2×C4—432no—
905C2×C4—432no—
906C2×C4—416no—
907C2×C4—48no—
908C2×C4—48no—
909C2×C4—48no—
910C2×C4#546116yes—
911C2×C4C23×D414yes—
912C2×C4C23×D418yes—
913C2×C4C23×D418yes—
914C2×C4C23×D414yes—
915C2×C4C23×D412yes—
916C2×C4C23×D412yes—
917C2×C4C22×#4114yes—
918C2×C4C22×#4112yes—
919C2×C4C22×#4112yes—
920C2×C4C2×H(5,𝔽2)12yes—
921C2×C4C2×H(5,𝔽2)12yes—
922C22—24no—
923C22—24no—
924C22—24no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—416no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—48no—
933C22—44no—
934C22—48no—
935C22—44no—
936C22—48no—
937C22—44no—
938C22—42no—
939C22—816no—
940C22C2×#54614yes—
941C22C24×D411yescharacteristic
942C22C23×#4111yescharacteristic
943C22C22×H(5,𝔽2)11yescharacteristic
944C222−1+614yes—
945C4—24no—
946C4—24no—
947C4—24no—
948C4—28no—
949C4—28no—
950C4—44no—
951C4—44no—
952C4—44no—
953C4—44no—
954C4—44no—
955C4—44no—
956C4—44no—
957C4—44no—
958C4—44no—
959C4—42no—
960C4C2×#54614yes—
961C4C2×#54614yes—
962C2—24no—
963C2—44no—
964C2—82no—
965C2—84no—
966C2C22×#54611yescharacteristic
967C2#6284812yes—
968C2#6286012yes—
969C2#6288712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35149C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3509C2semidirect
2. C22×#536C2semidirect
3. #45323C2semidirect
4. #45240C2semidirect
5. #39417C2semidirect
6. #37843C2semidirect
7. #37841C2semidirect
8. #37749C2semidirect
9. #35679C2semidirect
10. #35677C2semidirect
11. #35674C2semidirect
12. #35667C2semidirect
13. #35338C2semidirect
14. #35327C2semidirect
15. #35242C2semidirect
17. #34634C2semidirect
18. #34209C2semidirect
19. #34174C2semidirect
20. #34173C2semidirect
21. #34065C2semidirect
25. C2×#557C22semidirect
26. C2×#556C22semidirect
28. C2×#541C22semidirect
38. C2×#533C22semidirect
52. #2861C22semidirect
53. #2850C22semidirect
56. #2707C22semidirect
57. #2705C22semidirect
58. #2704C22semidirect
59. #2702C22semidirect
60. #2696C22semidirect
61. #2694C22semidirect
62. #2692C22semidirect
63. #2690C22semidirect
64. #2640C22semidirect
65. #2629C22semidirect
66. #2628C22semidirect
69. #2620C22semidirect
72. #2592C22semidirect
74. #2560C22semidirect
75. #2558C22semidirect
76. #2556C22semidirect
77. #2554C22semidirect
78. #2548C22semidirect
79. #2546C22semidirect
80. #2545C22semidirect
81. #2545C22semidirect
82. #2545C22semidirect
83. #2544C22semidirect
87. #2477C22semidirect
88. #2471C22semidirect
89. #2465C22semidirect
90. #2458C22semidirect
91. #2448C22semidirect
92. #2448C22semidirect
93. #2446C22semidirect
94. #2446C22semidirect
95. #2436C22semidirect
96. #2434C22semidirect
99. #2429C22semidirect
100. #2426C22semidirect
103. #2409C22semidirect
105. #2396C22semidirect
106. #2365C22semidirect
110. Q8×C22⋊C4C22semidirect
111. Q8×C22⋊C4C22semidirect
112. #2327C22semidirect
113. #2324C22semidirect
114. #2323C22semidirect
127. C4×C4⋊Q8C22semidirect
132. #2293C22semidirect
133. #2290C22semidirect
175. C2×C4⋊Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
C22×#5362
#453232
#452402
#394172
#378432
#378412
#377492
#356792
#356772
#356742
#356672
#353382
#353272
#352422
#351492
#346342
#342092
#341742
#341732
#340652