Finite Group Databasebeta

← #7629010

Subgroups — #7629010

Order 512.

9950 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#532C211yesmaximal, characteristic, complemented
2C2×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
3#35600C218yesmaximal, complemented
4#35574C212yesmaximal, complemented
5#35563C212yesmaximal, complemented
6#35554C211yesmaximal, characteristic, complemented
7#35540C211yesmaximal, characteristic, complemented
8#35527C211yesmaximal, characteristic, complemented
9#35524C218yesmaximal, complemented
10#35512C211yesmaximal, characteristic, complemented
11#35451C214yesmaximal, complemented
12#35355C214yesmaximal, complemented
13#34956C214yesmaximal, complemented
14#34736C214yesmaximal, complemented
15#34715C218yesmaximal, complemented
16#34681C218yesmaximal, complemented
17C4×#535C212yesmaximal, complemented
18#34058C211yesmaximal, characteristic, complemented
19C4×#525C212yesmaximal, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C23×#41C2212yescomplemented
22C2×#535C2212yes—
23C2×#532—216no—
24C2×#532C2218yescomplemented
25C2×#532C2218yescomplemented
26C22×C4⋊Q8C2211yescharacteristic, complemented
27C22×#127C2211yescharacteristic
28C22×#124C2212yescomplemented
29C2×#525C2212yes—
30C2×#525C2218yescomplemented
31C22×#121C2211yescharacteristic
32C22×#121C2212yescomplemented
33C22×#121C2211yescharacteristic, complemented
34C4×H(5,𝔽2)—216no—
35C2×#520C2212yes—
36C2×#520C2214yescomplemented
37C2×#518C2214yes—
38C2×#518C2211yescharacteristic
39C2×#518C2214yescomplemented
40C2×C4×#41C2212yes—
41C2×C4×#41C2214yescomplemented
42C22×C4×D4C2214yes—
43C22×C4×D4C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic, complemented
45C22×C4×D4C2214yescomplemented
46C22×C4×D4C2212yescomplemented
47C23×C42C2211yescharacteristic, complemented
48#2600C22116yescomplemented
49#2579C2218yescomplemented
50#2579C2218yescomplemented
51#2534C2218yescomplemented
52#2534C2218yescomplemented
53#2483C2214yescomplemented
54#2476C22116yescomplemented
55#2474C22116yescomplemented
56#2472C22116yescomplemented
57#2464C22116yescomplemented
58#2461C22116yescomplemented
59#2459C22116yescomplemented
60#2456C22116yescomplemented
61#2452C2218yescomplemented
62#2451C2218yescomplemented
63#2445C2218yescomplemented
64#2445C2218yescomplemented
65#2440C2218yescomplemented
66#2439C2218yescomplemented
67#2433C2218yescomplemented
68#2431C2218yescomplemented
69#2428C2218yescomplemented
70#2426C2218yescomplemented
71#2424C22116yescomplemented
72#2422C2218yescomplemented
73#2420C2218yescomplemented
74#2416C2218yescomplemented
75#2414C2218yescomplemented
76#2409C2218yescomplemented
77#2408C2218yescomplemented
78#2408C2218yescomplemented
79#2407C2218yescomplemented
80#2407C22116yescomplemented
81#2406C2218yescomplemented
82#2405C2214yes—
83#2405C2214yescomplemented
84#2405C2214yescomplemented
85#2405C2214yescomplemented
86#2404C2218yescomplemented
87#2403C2214yes—
88#2403C2214yes—
89#2403C2214yes—
90#2392C22116yescomplemented
91#2388C22116yescomplemented
92#2328C2214yescomplemented
93#2326C2214yescomplemented
94#2324C2218yescomplemented
95#2321C2218yescomplemented
96#2319C2218yescomplemented
97#2317C2212yescomplemented
98#2316C2212yescomplemented
99#2312C2214yescomplemented
100#2311C2212yes—
101#2309C2211yescharacteristic
102#2309C2211yescharacteristic
103#2309C2212yescomplemented
104C4×#127C2214yescomplemented
105C4×#124C2214yescomplemented
106C4×C22⋊Q8C2214yescomplemented
107C4×C22⋊Q8C2214yescomplemented
108C4×#123C2214yescomplemented
109C4×#123C2214yescomplemented
110C4×#123C2218yescomplemented
111C4×#121C2218yescomplemented
112C4×#121C2214yescomplemented
113C4×#121C2214yescomplemented
114C4×#120C2214yescomplemented
115C4×#120C2218yescomplemented
116C4×#120C2218yescomplemented
117C4×#120C2214yescomplemented
118#2297C2212yes—
119#2297C2218yescomplemented
120#2296C2212yescomplemented
121#2293C2218yescomplemented
122#2290C2218yescomplemented
123#2280C2214yescomplemented
124#2280C2212yescomplemented
125C42×D4C2218yescomplemented
126C4×#117C2212yescomplemented
127C2×H(5,𝔽2)—216no—
128C2×H(5,𝔽2)—28no—
129C22×#41—216no—
130C22×#41—416no—
131C22×#41C2314yes—
132C22×#41C2318yes—
133C22×#41C2312yes—
134C22×#41C2318yes—
135C23×Q8C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2314yes—
138C23×D4C2314yes—
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2312yes—
142C23×D4C2312yes—
143C23×D4C2312yes—
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2312yes—
147C24×C4C2311yescharacteristic
148C24×C4C2314yes—
149C24×C4C2312yes—
150#535—216no—
151#532—264no—
152#532—264no—
153C2×C4⋊Q8—28no—
154C2×C4⋊Q8C2318yes—
155C2×#127—28no—
156C2×#127C2314yes—
157C2×#127C2318yes—
158C2×#124—216no—
159C2×#124C2314yes—
160C2×#124C23116yes—
161#525—216no—
162#525—432no—
163C2×#123C2314yes—
164C2×#123C2318yes—
165C2×#123C2318yes—
166C2×#123C2318yes—
167C2×C22⋊Q8C2314yes—
168C2×C22⋊Q8C23116yes—
169C2×#121—28no—
170C2×#121—28no—
171C2×#121—216no—
172C2×#121C2318yes—
173C2×#121C2318yes—
174C2×#121C2314yes—
175C2×#121C2318yes—
176C2×#121C23116yes—
177C2×#121C23116yes—
178C2×#120C2318yes—
179C2×#120C2314yes—
180C2×#120C2318yes—
181C2×#120C2318yes—
182C2×#120C2318yes—
183#520—232no—
184#520—216no—
185#518—28no—
186#518—232no—
187#518—232no—
188C4×#41—232no—
189C4×#41—216no—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2314yes—
193C2×C4×D4—232no—
194C2×C4×D4—216no—
195C2×C4×D4—232no—
196C2×C4×D4—28no—
197C2×C4×D4D4116yescomplemented
198C2×C4×D4C2312yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2318yes—
202C2×C4×D4C2318yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2318yes—
206C2×C4×D4C2318yes—
207C2×C4×D4C2318yes—
208C2×C4×D4C2318yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2318yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2318yes—
215C2×C4×D4C2318yes—
216C2×C4×D4C23116yes—
217C2×C4×D4C2318yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×#117C2312yes—
221C2×#117C2312yes—
222C2×#117C2312yes—
223C2×#117C2314yes—
224C2×#117C2318yes—
225C2×#117C2314yes—
226C2×#117C2318yes—
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2314yes—
230C22×C4⋊C4C2314yes—
231C22×C4⋊C4C2311yescharacteristic
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2314yes—
234C22×C22⋊C4C2314yes—
235C22×C22⋊C4C2318yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C42—28no—
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2314yes—
244C22×C42C2314yes—
245C22×C42C2314yes—
246C22×C42C2314yes—
247C22×C42C2311yescharacteristic
248#398C23116yes—
249#397C23116yes—
250#396C23116yes—
251#396C23116yes—
252#395C23116yes—
253#394C23116yes—
254#394C23116yes—
255#394C23116yes—
256#394C23116yes—
257#394C23116yes—
258#394C23116yes—
259#393C23116yes—
260#392C23116yes—
261#392C23116yes—
262#392C23116yes—
263#392C23116yes—
264#391C2314yes—
265#391C23116yes—
266#391C2314yes—
267#390C2314yes—
268#390C2314yes—
269#390C23116yes—
270#390C2318yes—
271#390C2318yes—
272#390C2318yes—
273#390C2314yes—
274#390C23116yes—
275#390C2314yes—
276#389C2318yes—
277#389C2318yes—
278#389C2318yes—
279#389C2314yes—
280#389C2314yes—
281#388C23116yes—
282#388C23116yes—
283#388C23116yes—
284#388C23116yes—
285#388C2318yes—
286#388C23116yes—
287#388C2318yes—
288#387C2318yes—
289#387C23116yes—
290#387C2318yes—
291#386C2318yes—
292#386C23116yes—
293#386C2314yes—
294#386C2318yes—
295#386C2318yes—
296#386C23116yes—
297#386C23116yes—
298#386C2314yes—
299#386C2318yes—
300#386C2318yes—
301#386C2318yes—
302#386C2318yes—
303#386C2318yes—
304#386C2318yes—
305#385C2318yes—
306#385C2314yes—
307#385C23116yes—
308#385C23116yes—
309#385C2318yes—
310#385C2318yes—
311#385C2314yes—
312#385C2318yes—
313#385C2318yes—
314#384C2314yes—
315#382C2314yes—
316#381C2318yes—
317#381C2318yes—
318#381C2314yes—
319#380C2318yes—
320#380C2318yes—
321#380C2318yes—
322#380C2314yes—
323#380C2314yes—
324#379C2314yes—
325#379C2314yes—
326#379C2318yes—
327#379C2318yes—
328#379C2314yes—
329C4×C4⋊C4C2314yes—
330C4×C4⋊C4C2318yes—
331C4×C4⋊C4C2318yes—
332C4×C4⋊C4C2318yes—
333C4×C4⋊C4C2314yes—
334C4×C22⋊C4C2314yes—
335C4×C22⋊C4C2318yes—
336C4×C22⋊C4C2318yes—
337C4×C22⋊C4C23116yes—
338C4×C22⋊C4C2318yes—
339C4×C22⋊C4C2318yes—
340C4×C22⋊C4C2318yes—
341C4×C22⋊C4C2318yes—
342C4×C22⋊C4C2318yes—
343C4×C22⋊C4C2314yes—
344#376C2314yes—
345C43C2314yes—
346C25C2411yescharacteristic
347C25C2414yes—
348C25C2412yes—
349C25C2412yes—
350H(5,𝔽2)—2128no—
351C2×#41—216no—
352C2×#41—216no—
353C2×#41—28no—
354C2×#41—232no—
355C2×#41—232no—
356C2×#41—28no—
357C2×#41—216no—
358C2×#41—232no—
359C2×#41—416no—
360C2×#41—416no—
361C2×#41—416no—
362C2×#41—4128no—
363C2×#41#41116yescomplemented
364C22×Q8—28no—
365C22×Q8—48no—
366C22×Q8C2418yes—
367C22×Q8C2412yes—
368C22×D4—216no—
369C22×D4—216no—
370C22×D4—232no—
371C22×D4—216no—
372C22×D4—28no—
373C22×D4—28no—
374C22×D4—28no—
375C22×D4—24no—
376C22×D4—28no—
377C22×D4—28no—
378C22×D4—28no—
379C22×D4—216no—
380C22×D4—48no—
381C22×D4—48no—
382C22×D4—48no—
383C22×D4—48no—
384C22×D4C2×D418yes—
385C22×D4C2418yes—
386C22×D4C2414yes—
387C22×D4C2418yes—
388C22×D4C2418yes—
389C22×D4C2418yes—
390C22×D4C2418yes—
391C22×D4C2418yes—
392C22×D4C2414yes—
393C22×D4C2414yes—
394C22×D4C2412yes—
395C22×D4C24116yes—
396C23×C4—24no—
397C23×C4—28no—
398C23×C4—28no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—28no—
402C23×C4—216no—
403C23×C4—44no—
404C23×C4—48no—
405C23×C4—48no—
406C23×C4—416no—
407C23×C4C2×D4116yes—
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2414yes—
411C23×C4C2414yes—
412C23×C4C2411yescharacteristic
413C23×C4C2412yes—
414C23×C4C2414yes—
415C23×C4C2414yes—
416C23×C4C2414yes—
417C23×C4C2414yes—
418C23×C4C2411yescharacteristic
419C23×C4C2414yes—
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2414yes—
423C23×C4C2414yes—
424C23×C4C2418yes—
425C23×C4C2414yes—
426C23×C4C2414yes—
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2414yes—
430C23×C4C2411yescharacteristic
431C4⋊Q8—232no—
432#127—232no—
433#127—216no—
434#124—216no—
435#124—264no—
436#123—216no—
437#123—416no—
438#123—416no—
439#123—416no—
440C22⋊Q8—216no—
441C22⋊Q8—432no—
442#121—232no—
443#121—216no—
444#121—232no—
445#121—232no—
446#121—264no—
447#121—432no—
448#120—216no—
449#120—232no—
450#120—416no—
451#120—416no—
452#120—416no—
453C4×Q8—216no—
454C4×Q8—28no—
455C4×Q8—28no—
456C4×D4—216no—
457C4×D4—216no—
458C4×D4—216no—
459C4×D4—232no—
460C4×D4—232no—
461C4×D4—232no—
462C4×D4—232no—
463C4×D4—232no—
464C4×D4—216no—
465C4×D4—232no—
466C4×D4—232no—
467C4×D4—216no—
468C4×D4—232no—
469C4×D4—232no—
470C4×D4—28no—
471C4×D4—216no—
472C4×D4—216no—
473C4×D4—28no—
474C4×D4—432no—
475C4×D4—416no—
476C4×D4C2×D4132yes—
477C4×D4C2×D4132yes—
478#117—28no—
479#117—28no—
480#117—28no—
481#117—216no—
482#117—232no—
483#117—216no—
484#117—416no—
485C2×C4⋊C4—216no—
486C2×C4⋊C4—28no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—216no—
489C2×C4⋊C4C2×D418yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2418yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2412yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C24116yes—
503C2×C4⋊C4C24116yes—
504C2×C4⋊C4C2414yes—
505C2×C22⋊C4—216no—
506C2×C22⋊C4—28no—
507C2×C22⋊C4—216no—
508C2×C22⋊C4—28no—
509C2×C22⋊C4—28no—
510C2×C22⋊C4—232no—
511C2×C22⋊C4C2×D4116yes—
512C2×C22⋊C4C2414yes—
513C2×C22⋊C4C2414yes—
514C2×C22⋊C4C2414yes—
515C2×C22⋊C4C2418yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2414yes—
521C2×C22⋊C4C2414yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C2418yes—
525C2×C22⋊C4C2418yes—
526C2×C22⋊C4C2418yes—
527C2×C22⋊C4C24116yes—
528C2×C22⋊C4C2418yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C24116yes—
531C2×C22⋊C4C24116yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C24116yes—
536C2×C22⋊C4C2418yes—
537C2×C42—24no—
538C2×C42—216no—
539C2×C42—24no—
540C2×C42—24no—
541C2×C42—216no—
542C2×C42—216no—
543C2×C42—216no—
544C2×C42C2×D418yes—
545C2×C42C2414yes—
546C2×C42C2414yes—
547C2×C42C2418yes—
548C2×C42C2414yes—
549C2×C42C2414yes—
550C2×C42C2412yes—
551C2×C42C2414yes—
552C2×C42C2414yes—
553C2×C42C2418yes—
554C2×C42C2412yes—
555C2×C42C2414yes—
556C2×C42C2418yes—
557C2×C42C2412yes—
558C2×C42C2412yes—
559#95C2418yes—
560#95C2418yes—
561#95C2418yes—
562#95C2418yes—
563#95C2418yes—
564#95C2418yes—
565#95C2418yes—
566#95C2418yes—
567#95C24116yes—
568#95C24116yes—
569#95C24116yes—
570C24—22no—
571C24—24no—
572C24—28no—
573C24—216no—
574C24—28no—
575C24—24no—
576C24—24no—
577C24—28no—
578C24—42no—
579C24—44no—
580C24—44no—
581C24—44no—
582C24—44no—
583C24—48no—
584C24—48no—
585C24C22×D418yes—
586C24C2514yes—
587C24C2514yes—
588C24C2514yes—
589C24C2512yes—
590C24C2511yescharacteristic
591#41—2128no—
592#41—264no—
593#41—4128no—
594#41—4128no—
595C2×Q8—24no—
596C2×Q8—216no—
597C2×Q8—24no—
598C2×Q8—216no—
599C2×Q8—48no—
600C2×Q8—432no—
601C2×Q8C2×#4118yescomplemented
602C2×D4—2128no—
603C2×D4—2128no—
604C2×D4—216no—
605C2×D4—28no—
606C2×D4—216no—
607C2×D4—28no—
608C2×D4—216no—
609C2×D4—216no—
610C2×D4—216no—
611C2×D4—216no—
612C2×D4—216no—
613C2×D4—216no—
614C2×D4—216no—
615C2×D4—232no—
616C2×D4—232no—
617C2×D4—24no—
618C2×D4—28no—
619C2×D4—216no—
620C2×D4—216no—
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—24no—
624C2×D4—28no—
625C2×D4—28no—
626C2×D4—216no—
627C2×D4—216no—
628C2×D4—48no—
629C2×D4—48no—
630C2×D4—48no—
631C2×D4—48no—
632C2×D4—48no—
633C2×D4—432no—
634C2×D4—432no—
635C2×D4—416no—
636C2×D4—416no—
637C2×D4—432no—
638C2×D4—432no—
639C2×D4—416no—
640C2×D4C22×D4116yes—
641C2×D4C2×#41116yes—
642C2×D4C2×#4118yescomplemented
643C22×C4—232no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—28no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—28no—
651C22×C4—216no—
652C22×C4—28no—
653C22×C4—216no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—22no—
660C22×C4—24no—
661C22×C4—24no—
662C22×C4—28no—
663C22×C4—28no—
664C22×C4—28no—
665C22×C4—28no—
666C22×C4—28no—
667C22×C4—28no—
668C22×C4—28no—
669C22×C4—28no—
670C22×C4—28no—
671C22×C4—216no—
672C22×C4—216no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—216no—
676C22×C4—432no—
677C22×C4—42no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—48no—
682C22×C4—48no—
683C22×C4—48no—
684C22×C4—416no—
685C22×C4—48no—
686C22×C4—48no—
687C22×C4—416no—
688C22×C4—432no—
689C22×C4—416no—
690C22×C4—832no—
691C22×C4C22×D414yes—
692C22×C4C22×D4116yes—
693C22×C4C22×D414yes—
694C22×C4C22×D418yes—
695C22×C4C22×D4116yes—
696C22×C4C22×D414yes—
697C22×C4C2×#4118yes—
698C22×C4C2×#41116yescomplemented
699C22×C4H(5,𝔽2)18yescomplemented
700C22×C4C2518yes—
701C22×C4C2512yes—
702C22×C4C2514yes—
703C22×C4C2518yes—
704C22×C4C2514yes—
705C22×C4C2514yes—
706C22×C4C2511yescharacteristic
707C22×C4C2512yes—
708C22×C4C2514yes—
709C22×C4C2514yes—
710C22×C4C2512yes—
711C22×C4C2512yes—
712C22×C4C2512yes—
713C22×C4C2511yescharacteristic
714C4⋊C4—28no—
715C4⋊C4—216no—
716C4⋊C4—24no—
717C4⋊C4—216no—
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—24no—
721C4⋊C4—28no—
722C4⋊C4—28no—
723C4⋊C4—216no—
724C4⋊C4—216no—
725C4⋊C4—216no—
726C4⋊C4—416no—
727C4⋊C4—416no—
728C4⋊C4C22×D4116yes—
729C22⋊C4—216no—
730C22⋊C4—28no—
731C22⋊C4—216no—
732C22⋊C4—28no—
733C22⋊C4—28no—
734C22⋊C4—216no—
735C22⋊C4—216no—
736C22⋊C4—28no—
737C22⋊C4—216no—
738C22⋊C4—28no—
739C22⋊C4—216no—
740C22⋊C4—216no—
741C22⋊C4—216no—
742C22⋊C4—232no—
743C22⋊C4—216no—
744C22⋊C4—216no—
745C22⋊C4—48no—
746C22⋊C4—48no—
747C22⋊C4—48no—
748C22⋊C4—416no—
749C22⋊C4—416no—
750C22⋊C4—48no—
751C22⋊C4—48no—
752C22⋊C4—416no—
753C22⋊C4C22×D4132yes—
754C42—24no—
755C42—24no—
756C42—28no—
757C42—28no—
758C42—28no—
759C42—216no—
760C42—28no—
761C42—28no—
762C42—28no—
763C42—28no—
764C42—216no—
765C42—48no—
766C42C22×D418yes—
767C42C22×D418yes—
768C23—22no—
769C23—22no—
770C23—28no—
771C23—232no—
772C23—24no—
773C23—22no—
774C23—24no—
775C23—28no—
776C23—24no—
777C23—28no—
778C23—28no—
779C23—22no—
780C23—28no—
781C23—24no—
782C23—28no—
783C23—216no—
784C23—24no—
785C23—28no—
786C23—28no—
787C23—28no—
788C23—48no—
789C23—48no—
790C23—416no—
791C23—44no—
792C23—48no—
793C23—48no—
794C23—44no—
795C23—48no—
796C23—88no—
797C23—816no—
798C23—816no—
799C23—832no—
800C23—88no—
801C23C23×D418yes—
802C23C23×D412yes—
803C23C22×#4118yes—
804C23C22×#4114yes—
805C23C2×H(5,𝔽2)14yes—
806C23C2611yescharacteristic
807Q8—216no—
808Q8—432no—
809D4—264no—
810D4—232no—
811D4—232no—
812D4—216no—
813D4—432no—
814D4—432no—
815D4—432no—
816D4—432no—
817D4—432no—
818D4—416no—
819D4—832no—
820C2×C4—28no—
821C2×C4—216no—
822C2×C4—28no—
823C2×C4—232no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—232no—
834C2×C4—28no—
835C2×C4—216no—
836C2×C4—232no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—28no—
842C2×C4—28no—
843C2×C4—24no—
844C2×C4—28no—
845C2×C4—28no—
846C2×C4—28no—
847C2×C4—28no—
848C2×C4—28no—
849C2×C4—28no—
850C2×C4—28no—
851C2×C4—44no—
852C2×C4—48no—
853C2×C4—416no—
854C2×C4—416no—
855C2×C4—416no—
856C2×C4—48no—
857C2×C4—44no—
858C2×C4—416no—
859C2×C4—416no—
860C2×C4—416no—
861C2×C4—88no—
862C2×C4—816no—
863C2×C4—88no—
864C2×C4—88no—
865C2×C4#525116yescomplemented
866C2×C4C23×D414yes—
867C2×C4C23×D412yes—
868C2×C4C23×D418yes—
869C2×C4C23×D414yes—
870C2×C4C23×D412yes—
871C2×C4C22×#4118yes—
872C2×C4C22×#4114yes—
873C2×C4C22×#4114yes—
874C2×C4C2×H(5,𝔽2)14yes—
875C2×C4C2×H(5,𝔽2)14yes—
876C2×C4#58514yes—
877C22—22no—
878C22—28no—
879C22—22no—
880C22—24no—
881C22—28no—
882C22—28no—
883C22—216no—
884C22—28no—
885C22—28no—
886C22—28no—
887C22—416no—
888C22—44no—
889C22—44no—
890C22—48no—
891C22—416no—
892C22—42no—
893C22—44no—
894C22—42no—
895C22—44no—
896C22—416no—
897C22—44no—
898C22—44no—
899C22—816no—
900C22—816no—
901C22—832no—
902C22C2×#52514yes—
903C22C24×D411yescharacteristic
904C22C23×#4112yes—
905C22C22×H(5,𝔽2)12yes—
906C22C2×#58512yes—
907C4—22no—
908C4—24no—
909C4—28no—
910C4—24no—
911C4—24no—
912C4—28no—
913C4—44no—
914C4—44no—
915C4—48no—
916C4—48no—
917C4—44no—
918C4—42no—
919C4C2×#52518yes—
920C4#348414yes—
921C2—24no—
922C2—44no—
923C2—48no—
924C2—48no—
925C2—84no—
926C2C22×#52511yescharacteristic
927C2C2×#348411yescharacteristic
928C2#6280014yes—
929C2#6281111yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#532C2semidirect
2. C2×C4×H(5,𝔽2)C2semidirect
3. #35600C2semidirect
4. #35574C2semidirect
5. #35563C2semidirect
6. #35554C2semidirect
7. #35540C2semidirect
8. #35527C2semidirect
9. #35524C2semidirect
10. #35512C2semidirect
11. #35451C2semidirect
12. #35355C2semidirect
13. #34956C2semidirect
14. #34736C2semidirect
15. #34715C2semidirect
16. #34681C2semidirect
17. C4×#535C2semidirect
18. #34058C2semidirect
19. C4×#525C2semidirect
21. C23×#41C22semidirect
24. C2×#532C22semidirect
25. C2×#532C22semidirect
26. C22×C4⋊Q8C22semidirect
28. C22×#124C22semidirect
30. C2×#525C22semidirect
32. C22×#121C22semidirect
33. C22×#121C22semidirect
36. C2×#520C22semidirect
39. C2×#518C22semidirect
41. C2×C4×#41C22semidirect
44. C22×C4×D4C22semidirect
45. C22×C4×D4C22semidirect
46. C22×C4×D4C22semidirect
47. C23×C42C22semidirect
48. #2600C22semidirect
49. #2579C22semidirect
50. #2579C22semidirect
51. #2534C22semidirect
52. #2534C22semidirect
53. #2483C22semidirect
54. #2476C22semidirect
55. #2474C22semidirect
56. #2472C22semidirect
57. #2464C22semidirect
58. #2461C22semidirect
59. #2459C22semidirect
60. #2456C22semidirect
61. #2452C22semidirect
62. #2451C22semidirect
63. #2445C22semidirect
64. #2445C22semidirect
65. #2440C22semidirect
66. #2439C22semidirect
67. #2433C22semidirect
68. #2431C22semidirect
69. #2428C22semidirect
70. #2426C22semidirect
71. #2424C22semidirect
72. #2422C22semidirect
73. #2420C22semidirect
74. #2416C22semidirect
75. #2414C22semidirect
76. #2409C22semidirect
77. #2408C22semidirect
78. #2408C22semidirect
79. #2407C22semidirect
80. #2407C22semidirect
81. #2406C22semidirect
83. #2405C22semidirect
84. #2405C22semidirect
85. #2405C22semidirect
86. #2404C22semidirect
90. #2392C22semidirect
91. #2388C22semidirect
92. #2328C22semidirect
93. #2326C22semidirect
94. #2324C22semidirect
95. #2321C22semidirect
96. #2319C22semidirect
97. #2317C22semidirect
98. #2316C22semidirect
99. #2312C22semidirect
103. #2309C22semidirect
104. C4×#127C22semidirect
105. C4×#124C22semidirect
106. C4×C22⋊Q8C22semidirect
107. C4×C22⋊Q8C22semidirect
108. C4×#123C22semidirect
109. C4×#123C22semidirect
110. C4×#123C22semidirect
111. C4×#121C22semidirect
112. C4×#121C22semidirect
113. C4×#121C22semidirect
114. C4×#120C22semidirect
115. C4×#120C22semidirect
116. C4×#120C22semidirect
117. C4×#120C22semidirect
119. #2297C22semidirect
120. #2296C22semidirect
121. #2293C22semidirect
122. #2290C22semidirect
123. #2280C22semidirect
124. #2280C22semidirect
125. C42×D4C22semidirect
126. C4×#117C22semidirect
197. C2×C4×D4D4semidirect
363. C2×#41#41semidirect
601. C2×Q8C2×#41semidirect
642. C2×D4C2×#41semidirect
698. C22×C4C2×#41semidirect
699. C22×C4H(5,𝔽2)semidirect
865. C2×C4#525semidirect

Maximal subgroups

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

subgroupindex
C22×#5322
C2×C4×H(5,𝔽2)2
#356002
#355742
#355632
#355542
#355402
#355272
#355242
#355122
#354512
#353552
#349562
#347362
#347152
#346812
C4×#5352
#340582
C4×#5252