Finite Group Databasebeta

← #7666983

Subgroups — #7666983

Order 512.

8400 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3481C212yesmaximal, complemented
2#59843C214yesmaximal, complemented
3#59836C214yesmaximal, complemented
4#59827C211yesmaximal, characteristic, complemented
5#59823C212yesmaximal, complemented
6#59816C211yesmaximal, characteristic, complemented
7#59812C218yesmaximal, complemented
8#59660C212yesmaximal, complemented
9#59420C212yesmaximal, complemented
10#59213C214yesmaximal, complemented
11#59035C214yesmaximal, complemented
12#52163C214yesmaximal, complemented
13#34976C212yesmaximal, complemented
14#34935C214yesmaximal, complemented
15#34932C214yesmaximal, complemented
16#34700C218yesmaximal, complemented
17C4×D42C214yesmaximal, complemented
18C4×#532C211yesmaximal, characteristic, complemented
19C4×#532C212yesmaximal, complemented
20#3481—232no—
21C2×#559C2212yes—
22C2×#554C2214yescomplemented
23C2×#553C2218yescomplemented
24C2×#551C2218yescomplemented
25C2×#546C2218yescomplemented
26C2×D42C2212yes—
27C2×D42C2214yes—
28C2×#532C2212yes—
29C2×#532C2211yescharacteristic
30C2×#529C2218yescomplemented
31C2×#525C2218yescomplemented
32C2×C4×#41C2214yescomplemented
33C2×C4×#41C2212yescomplemented
34C22×C4×D4C2218yescomplemented
35C22×C4×D4C2214yescomplemented
36#2732C2218yescomplemented
37#2728C2218yescomplemented
38#2724C2214yescomplemented
39#2708C22116yescomplemented
40#2697C2218yescomplemented
41#2679C2214yes—
42#2668C22116yescomplemented
43#2609C2218yescomplemented
44#2582C2212yescomplemented
45#2553C22116yescomplemented
46#2552C2214yescomplemented
47#2547C2214yescomplemented
48#2542C2214yescomplemented
49#2538C2214yescomplemented
50#2538C2218yescomplemented
51#2537C2212yes—
52#2537C2214yes—
53#2537C2218yescomplemented
54#2536C2218yescomplemented
55#2535C2218yescomplemented
56#2534C2218yescomplemented
57#2534C2218yescomplemented
58#2496C2218yescomplemented
59#2489C2218yescomplemented
60#2486C2214yescomplemented
61#2486C2214yescomplemented
62#2485C2218yescomplemented
63#2480C22116yescomplemented
64#2468C22116yescomplemented
65#2457C22116yescomplemented
66#2454C2218yescomplemented
67#2447C2218yescomplemented
68#2442C2218yescomplemented
69#2435C2218yescomplemented
70#2427C2218yescomplemented
71#2427C2218yescomplemented
72#2422C2218yescomplemented
73#2420C2218yescomplemented
74#2418C22116yescomplemented
75#2417C2218yescomplemented
76#2408C2214yes—
77#2408C2218yes—
78#2408C2214yescomplemented
79#2407C2218yescomplemented
80#2395C22116yescomplemented
81#2392C2218yescomplemented
82#2392C2218yescomplemented
83#2366C2214yes—
84#2361C2218yescomplemented
85#2361C2218yescomplemented
86#2358C22116yescomplemented
87D4×C4⋊C4C2214yescomplemented
88D4×C4⋊C4C2214yescomplemented
89D4×C22⋊C4C2218yescomplemented
90D4×C22⋊C4C2218yescomplemented
91C4×C4⋊Q8C2211yescharacteristic, complemented
92C4×C4⋊Q8C2212yescomplemented
93C4×C4⋊Q8C2211yescharacteristic, complemented
94C4×C4⋊Q8C2212yescomplemented
95C4×#127C2211yescharacteristic
96C4×#127C2212yes—
97C4×#127C2212yes—
98C4×#127C2211yescharacteristic
99C4×#124C2214yescomplemented
100C4×#124C2214yescomplemented
101C4×#124C2212yescomplemented
102C4×#124C2212yescomplemented
103C4×C22⋊Q8C2218yescomplemented
104C4×#121C2214yescomplemented
105C4×#121C2214yescomplemented
106C4×#121C2218yescomplemented
107C4×#121C2218yescomplemented
108C4×#121C2214yescomplemented
109C4×#121C2214yescomplemented
110C4×#121C2214yescomplemented
111C4×#121C2214yescomplemented
112C4×#120C22116yescomplemented
113#2297C2214yescomplemented
114#2297C2212yescomplemented
115#2293C2214yescomplemented
116#2293C2214yescomplemented
117#2293C2214yescomplemented
118#2285C2212yescomplemented
119#2285C2214yescomplemented
120#2285C2211yescharacteristic, complemented
121#2280C2218yescomplemented
122C42×D4C2214yescomplemented
123C42×D4C2214yescomplemented
124C42×D4C2214yescomplemented
125C2×C43C2211yescharacteristic, complemented
126C22×#41C2314yes—
127C22×#41C2312yes—
128C23×D4C2314yes—
129C23×D4C2318yes—
130C24×C4C2318yes—
131#559—216no—
132#554—232no—
133#553—264no—
134#551—264no—
135#546—264no—
136D42—216no—
137D42—232no—
138#532—216no—
139#532D4116yescomplemented
140C2×C4⋊Q8C2312yes—
141C2×C4⋊Q8C2311yescharacteristic
142C2×#127C2311yescharacteristic
143C2×#127C2312yes—
144#529—264no—
145C2×#126C23116yes—
146C2×#125C2318yes—
147C2×#124C2318yes—
148C2×#124C2314yes—
149C2×#124C2312yes—
150#525—264no—
151C2×#123C2318yes—
152C2×#123C2318yes—
153C2×#123C23116yes—
154C2×C22⋊Q8C23116yes—
155C2×C22⋊Q8C2318yes—
156C2×C22⋊Q8C2318yes—
157C2×#121C2318yes—
158C2×#121C2318yes—
159C2×#121C2318yes—
160C2×#121C2314yes—
161C2×#121C23116yes—
162C2×#121C2314yes—
163C2×#121C2314yes—
164C2×#120C23116yes—
165C2×#120C2318yes—
166C2×#120C2318yes—
167C4×#41—232no—
168C4×#41—48no—
169C2×C4×Q8C2314yes—
170C2×C4×Q8C2314yes—
171C2×C4×Q8C2312yes—
172C2×C4×Q8C2312yes—
173C2×C4×D4—264no—
174C2×C4×D4—416no—
175C2×C4×D4C2314yes—
176C2×C4×D4C2314yes—
177C2×C4×D4C2314yes—
178C2×C4×D4C2314yes—
179C2×C4×D4C2314yes—
180C2×C4×D4C2314yes—
181C2×C4×D4C2318yes—
182C2×C4×D4C23116yes—
183C2×C4×D4C2318yes—
184C2×C4×D4C2318yes—
185C2×C4×D4C23116yes—
186C2×C4×D4C2318yes—
187C2×C4×D4C2314yes—
188C2×C4×D4C2314yes—
189C2×C4×D4C2312yes—
190C2×C4×D4C2312yes—
191C2×C4×D4C2314yes—
192C2×C4×D4C2314yes—
193C2×C4×D4C2318yes—
194C2×C4×D4C2318yes—
195C2×C4×D4C2318yes—
196C2×C4×D4C2314yes—
197C2×C4×D4C2314yes—
198C2×C4×D4C2314yes—
199C2×#117C2318yes—
200C2×#117C2318yes—
201C2×#117C2314yes—
202C2×#117C2312yes—
203C2×#117C2314yes—
204C22×C4⋊C4C2318yes—
205C22×C4⋊C4C2314yes—
206C22×C22⋊C4C23116yes—
207C22×C22⋊C4C2318yes—
208C22×C42C2318yes—
209C22×C42C2314yes—
210C22×C42C2311yescharacteristic
211C22×C42C2312yes—
212C22×C42C2312yes—
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215#400C23116yes—
216#399C23116yes—
217#398C2318yes—
218#398C2318yes—
219#398C23116yes—
220#397C2318yes—
221#397C2318yes—
222#397C23116yes—
223#397C23116yes—
224#397C23116yes—
225#396C23116yes—
226#396C23116yes—
227#394C2318yes—
228#394C23116yes—
229#394C2318yes—
230#394C23116yes—
231#394C23116yes—
232#394C23116yes—
233#392C2318yes—
234#392C2318yes—
235#391C2314yes—
236#391C2314yes—
237#391C2312yes—
238#391C2312yes—
239#391C2318yes—
240#390C2314yes—
241#390C2314yes—
242#390C2314yes—
243#390C2314yes—
244#390C2314yes—
245#390C2314yes—
246#390C2314yes—
247#390C2312yes—
248#390C2314yes—
249#390C2312yes—
250#390C2318yes—
251#390C2318yes—
252#389C2314yes—
253#389C2314yes—
254#389C2314yes—
255#389C2314yes—
256#389C2314yes—
257#389C2314yes—
258#389C2318yes—
259#389C2318yes—
260#389C2318yes—
261#388C23116yes—
262#388C23116yes—
263#388C2318yes—
264#388C2318yes—
265#388C2318yes—
266#388C2318yes—
267#388C2318yes—
268#388C2318yes—
269#387C23116yes—
270#386C23116yes—
271#386C23116yes—
272#386C23116yes—
273#386C23116yes—
274#386C23116yes—
275#386C2318yes—
276#386C2318yes—
277#386C2318yes—
278#385C23116yes—
279#385C23116yes—
280#385C23116yes—
281#385C23116yes—
282#384C2311yescharacteristic
283#384C2312yes—
284#384C2312yes—
285#384C2311yescharacteristic
286#384C2318yes—
287#382C2312yes—
288#382C2314yes—
289#382C2318yes—
290#381C2318yes—
291#381C2318yes—
292#380C2318yes—
293#380C2318yes—
294#380C2314yes—
295#380C2318yes—
296#380C2314yes—
297#380C2314yes—
298#380C23116yes—
299#380C23116yes—
300#380C2318yes—
301#380C2314yes—
302#380C2314yes—
303#379C23116yes—
304#379C2318yes—
305#379C2318yes—
306C4×C4⋊C4C2314yes—
307C4×C4⋊C4C2314yes—
308C4×C4⋊C4C2314yes—
309C4×C4⋊C4C2314yes—
310C4×C4⋊C4C2314yes—
311C4×C4⋊C4C2314yes—
312C4×C4⋊C4C2314yes—
313C4×C4⋊C4C2318yes—
314C4×C4⋊C4C2314yes—
315C4×C4⋊C4C2314yes—
316C4×C22⋊C4C2318yes—
317C4×C22⋊C4C2318yes—
318C4×C22⋊C4C2318yes—
319C4×C22⋊C4C2318yes—
320C4×C22⋊C4C2318yes—
321C4×C22⋊C4C23116yes—
322C4×C22⋊C4C2318yes—
323C4×C22⋊C4C2318yes—
324C4×C22⋊C4C2318yes—
325C4×C22⋊C4C2318yes—
326C43C2311yescharacteristic
327C43C2312yes—
328C43C2311yescharacteristic
329C43C2312yes—
330C43C2311yescharacteristic
331C43C2311yescharacteristic
332C25C2418yes—
333C2×#41—216no—
334C2×#41—216no—
335C2×#41—44no—
336C2×#41—44no—
337C2×#41—48no—
338C2×#41C2×D4116yescomplemented
339C22×Q8C2414yes—
340C22×Q8C2412yes—
341C22×D4—232no—
342C22×D4—232no—
343C22×D4—232no—
344C22×D4—48no—
345C22×D4—416no—
346C22×D4C2418yes—
347C22×D4C24116yes—
348C22×D4C2418yes—
349C22×D4C2414yes—
350C22×D4C2414yes—
351C22×D4C2414yes—
352C22×D4C2412yes—
353C22×D4C2414yes—
354C22×D4C2414yes—
355C23×C4—232no—
356C23×C4—416no—
357C23×C4—416no—
358C23×C4C2418yes—
359C23×C4C2414yes—
360C23×C4C2411yescharacteristic
361C23×C4C2418yes—
362C23×C4C2418yes—
363C23×C4C2412yes—
364C23×C4C2414yes—
365C23×C4C2411yescharacteristic
366C23×C4C2414yes—
367C23×C4C24116yes—
368C23×C4C2418yes—
369C23×C4C2411yescharacteristic
370C23×C4C2412yes—
371C4⋊Q8—28no—
372C4⋊Q8C2×D418yescomplemented
373#127C2×D418yes—
374#127#41116yescomplemented
375#126—264no—
376#125—232no—
377#124—232no—
378#124—216no—
379#124C2×D4116yescomplemented
380#123—232no—
381#123—232no—
382#123—264no—
383C22⋊Q8—264no—
384C22⋊Q8—232no—
385C22⋊Q8—416no—
386#121—264no—
387#121—232no—
388#121—216no—
389#121—216no—
390#121—232no—
391#121—232no—
392#121C2×D4132yescomplemented
393#120—232no—
394#120—232no—
395#120—264no—
396C4×Q8—216no—
397C4×Q8—216no—
398C4×Q8—44no—
399C4×Q8—44no—
400C4×D4—232no—
401C4×D4—216no—
402C4×D4—216no—
403C4×D4—264no—
404C4×D4—232no—
405C4×D4—232no—
406C4×D4—232no—
407C4×D4—264no—
408C4×D4—216no—
409C4×D4—216no—
410C4×D4—216no—
411C4×D4—216no—
412C4×D4—216no—
413C4×D4—416no—
414C4×D4—416no—
415C4×D4—48no—
416C4×D4—416no—
417C4×D4—48no—
418C4×D4—48no—
419C4×D4—48no—
420C4×D4—48no—
421C4×D4—44no—
422C4×D4—44no—
423C4×D4C2×D4132yescomplemented
424#117—216no—
425#117—232no—
426#117—232no—
427#117—48no—
428#117—44no—
429C2×C4⋊C4—232no—
430C2×C4⋊C4—48no—
431C2×C4⋊C4C2414yes—
432C2×C4⋊C4C2414yes—
433C2×C4⋊C4C24116yes—
434C2×C4⋊C4C2414yes—
435C2×C4⋊C4C2418yes—
436C2×C4⋊C4C2418yes—
437C2×C4⋊C4C24116yes—
438C2×C4⋊C4C2414yes—
439C2×C4⋊C4C2414yes—
440C2×C4⋊C4C2414yes—
441C2×C4⋊C4C2414yes—
442C2×C4⋊C4C2414yes—
443C2×C4⋊C4C2418yes—
444C2×C4⋊C4C2414yes—
445C2×C4⋊C4C2414yes—
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2414yes—
449C2×C4⋊C4C2414yes—
450C2×C4⋊C4C24116yes—
451C2×C4⋊C4C2414yes—
452C2×C22⋊C4—264no—
453C2×C22⋊C4—416no—
454C2×C22⋊C4C2418yes—
455C2×C22⋊C4C2418yes—
456C2×C22⋊C4C24116yes—
457C2×C22⋊C4C24116yes—
458C2×C22⋊C4C2418yes—
459C2×C22⋊C4C2418yes—
460C2×C22⋊C4C2418yes—
461C2×C22⋊C4C2418yes—
462C2×C22⋊C4C2418yes—
463C2×C22⋊C4C2418yes—
464C2×C22⋊C4C2418yes—
465C2×C22⋊C4C2418yes—
466C2×C22⋊C4C24116yes—
467C2×C22⋊C4C24116yes—
468C2×C22⋊C4C2414yes—
469C2×C22⋊C4C2414yes—
470C2×C22⋊C4C2414yes—
471C2×C22⋊C4C2418yes—
472C2×C22⋊C4C2418yes—
473C2×C22⋊C4C2418yes—
474C2×C22⋊C4C24116yes—
475C2×C22⋊C4C2418yes—
476C2×C42—232no—
477C2×C42—28no—
478C2×C42—216no—
479C2×C42—24no—
480C2×C42—44no—
481C2×C42—42no—
482C2×C42C2×D418yescomplemented
483C2×C42C2418yes—
484C2×C42C2418yes—
485C2×C42C2414yes—
486C2×C42C2414yes—
487C2×C42C2411yescharacteristic
488C2×C42C2411yescharacteristic
489C2×C42C2412yes—
490C2×C42C2412yes—
491C2×C42C2412yes—
492C2×C42C2412yes—
493C2×C42C2412yes—
494C2×C42C2411yescharacteristic
495C2×C42C2418yes—
496C2×C42C2414yes—
497C2×C42C2412yes—
498C2×C42C2412yes—
499C2×C42C2412yes—
500C2×C42C2411yescharacteristic
501C2×C42C2411yescharacteristic
502C2×C42C2411yescharacteristic
503C2×C42C2411yescharacteristic
504C2×C42C2412yes—
505C2×C42C2412yes—
506C2×C42C2411yescharacteristic
507#95C2418yes—
508#95C2418yes—
509#95C2418yes—
510#95C2418yes—
511#95C2418yes—
512#95C2418yes—
513#95C2418yes—
514#95C2418yes—
515#95C2418yes—
516#95C24116yes—
517#95C24116yes—
518#95C2418yes—
519#95C2418yes—
520C24—216no—
521C24—232no—
522C24—48no—
523C24—416no—
524C24—48no—
525C24C2514yes—
526C24C2511yescharacteristic
527C24C2518yes—
528#41—432no—
529#41—464no—
530C2×Q8—28no—
531C2×Q8—28no—
532C2×Q8—28no—
533C2×Q8—42no—
534C2×Q8—42no—
535C2×Q8C22×D418yes—
536C2×D4—216no—
537C2×D4—232no—
538C2×D4—232no—
539C2×D4—232no—
540C2×D4—216no—
541C2×D4—28no—
542C2×D4—28no—
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—48no—
548C2×D4—42no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—44no—
552C2×D4—416no—
553C2×D4—42no—
554C2×D4—44no—
555C2×D4—48no—
556C2×D4—4128no—
557C2×D4—464no—
558C2×D4C22×D4116yes—
559C2×D4C22×D418yes—
560C2×D4C22×D4116yes—
561C2×D4C2×#41116yes—
562C2×D4C2×#41116yes—
563C2×D4C2×#41116yes—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—28no—
570C22×C4—216no—
571C22×C4—216no—
572C22×C4—216no—
573C22×C4—216no—
574C22×C4—216no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—216no—
578C22×C4—216no—
579C22×C4—28no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—216no—
583C22×C4—216no—
584C22×C4—216no—
585C22×C4—232no—
586C22×C4—28no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—416no—
593C22×C4—48no—
594C22×C4—416no—
595C22×C4—48no—
596C22×C4—864no—
597C22×C4C22×D418yes—
598C22×C4C22×D414yes—
599C22×C4C22×D4116yes—
600C22×C4C2512yes—
601C22×C4C2514yes—
602C22×C4C2511yescharacteristic
603C22×C4C2511yescharacteristic
604C22×C4C2514yes—
605C22×C4C2518yes—
606C22×C4C2518yes—
607C22×C4C2518yes—
608C22×C4C2512yes—
609C22×C4C2514yes—
610C22×C4C2511yescharacteristic
611C22×C4C2512yes—
612C22×C4C2511yescharacteristic
613C22×C4C2512yes—
614C22×C4C2511yescharacteristic
615C22×C4C2511yescharacteristic
616C4⋊C4—28no—
617C4⋊C4—232no—
618C4⋊C4—28no—
619C4⋊C4—216no—
620C4⋊C4—216no—
621C4⋊C4—232no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—48no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—416no—
636C4⋊C4C22×D4116yes—
637C22⋊C4—232no—
638C22⋊C4—216no—
639C22⋊C4—216no—
640C22⋊C4—216no—
641C22⋊C4—216no—
642C22⋊C4—216no—
643C22⋊C4—232no—
644C22⋊C4—216no—
645C22⋊C4—232no—
646C22⋊C4—216no—
647C22⋊C4—216no—
648C22⋊C4—216no—
649C22⋊C4—216no—
650C22⋊C4—416no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—416no—
658C22⋊C4C22×D4132yes—
659C42—216no—
660C42—216no—
661C42—216no—
662C42—24no—
663C42—24no—
664C42—24no—
665C42—22no—
666C42—28no—
667C42—28no—
668C42—28no—
669C42—22no—
670C42—22no—
671C42—24no—
672C42—24no—
673C42—24no—
674C42—41no—
675C42—42no—
676C42—42no—
677C42—41no—
678C42C22×D418yes—
679C42C22×D414yes—
680C42C22×D414yes—
681C42C2×#4118yes—
682C42H(5,𝔽2)14yes—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—22no—
687C23—28no—
688C23—21no—
689C23—24no—
690C23—28no—
691C23—28no—
692C23—28no—
693C23—21no—
694C23—22no—
695C23—24no—
696C23—28no—
697C23—464no—
698C23—432no—
699C23—816no—
700C23—832no—
701C23—816no—
702C23C23×D418yes—
703C23C23×D412yes—
704C23C22×#41116yes—
705C23C2611yescharacteristic
706Q8—48no—
707Q8—416no—
708D4—232no—
709D4—232no—
710D4—232no—
711D4—416no—
712D4—48no—
713D4—416no—
714D4—464no—
715D4—432no—
716D4—432no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—24no—
726C2×C4—216no—
727C2×C4—232no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—28no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—24no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—432no—
750C2×C4—44no—
751C2×C4—48no—
752C2×C4—432no—
753C2×C4—44no—
754C2×C4—416no—
755C2×C4—432no—
756C2×C4—88no—
757C2×C4—832no—
758C2×C4—816no—
759C2×C4C23×D414yes—
760C2×C4C23×D412yes—
761C2×C4C23×D418yes—
762C2×C4C23×D414yes—
763C2×C4C23×D412yes—
764C2×C4C22×#4114yes—
765C2×C4C22×#4114yes—
766C2×C4C22×#4114yes—
767C2×C4C2×H(5,𝔽2)12yes—
768C2×C4C2×H(5,𝔽2)12yes—
769C2×C4C2×H(5,𝔽2)12yes—
770C2×C4#58514yes—
771C2×C4#58512yes—
772C22—28no—
773C22—22no—
774C22—216no—
775C22—24no—
776C22—216no—
777C22—216no—
778C22—216no—
779C22—41no—
780C22—44no—
781C22—48no—
782C22—48no—
783C22—42no—
784C22—48no—
785C22—48no—
786C22—48no—
787C22—41no—
788C22—44no—
789C22—864no—
790C22C24×D411yescharacteristic
791C22C23×#4112yes—
792C22C22×H(5,𝔽2)11yescharacteristic
793C22C2×#58512yes—
794C22C2×#58511yescharacteristic
795C4—22no—
796C4—28no—
797C4—22no—
798C4—24no—
799C4—24no—
800C4—41no—
801C4—44no—
802C4—48no—
803C4—42no—
804C4—48no—
805C4—48no—
806C4—41no—
807C4—44no—
808C4D4×#4118yes—
809C4#348114yescomplemented
810C4#349614yes—
811C2—42no—
812C2—48no—
813C2—416no—
814C2C2×D4×#4112yes—
815C2C2×#348111yescharacteristic
816C2#6275911yescharacteristic
817C2C2×#349611yescharacteristic
818C2#6278112yes—
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. C2×#3481C2semidirect
2. #59843C2semidirect
3. #59836C2semidirect
4. #59827C2semidirect
5. #59823C2semidirect
6. #59816C2semidirect
7. #59812C2semidirect
8. #59660C2semidirect
9. #59420C2semidirect
10. #59213C2semidirect
11. #59035C2semidirect
12. #52163C2semidirect
13. #34976C2semidirect
14. #34935C2semidirect
15. #34932C2semidirect
16. #34700C2semidirect
17. C4×D42C2semidirect
18. C4×#532C2semidirect
19. C4×#532C2semidirect
22. C2×#554C22semidirect
23. C2×#553C22semidirect
24. C2×#551C22semidirect
25. C2×#546C22semidirect
30. C2×#529C22semidirect
31. C2×#525C22semidirect
32. C2×C4×#41C22semidirect
33. C2×C4×#41C22semidirect
34. C22×C4×D4C22semidirect
35. C22×C4×D4C22semidirect
36. #2732C22semidirect
37. #2728C22semidirect
38. #2724C22semidirect
39. #2708C22semidirect
40. #2697C22semidirect
42. #2668C22semidirect
43. #2609C22semidirect
44. #2582C22semidirect
45. #2553C22semidirect
46. #2552C22semidirect
47. #2547C22semidirect
48. #2542C22semidirect
49. #2538C22semidirect
50. #2538C22semidirect
53. #2537C22semidirect
54. #2536C22semidirect
55. #2535C22semidirect
56. #2534C22semidirect
57. #2534C22semidirect
58. #2496C22semidirect
59. #2489C22semidirect
60. #2486C22semidirect
61. #2486C22semidirect
62. #2485C22semidirect
63. #2480C22semidirect
64. #2468C22semidirect
65. #2457C22semidirect
66. #2454C22semidirect
67. #2447C22semidirect
68. #2442C22semidirect
69. #2435C22semidirect
70. #2427C22semidirect
71. #2427C22semidirect
72. #2422C22semidirect
73. #2420C22semidirect
74. #2418C22semidirect
75. #2417C22semidirect
78. #2408C22semidirect
79. #2407C22semidirect
80. #2395C22semidirect
81. #2392C22semidirect
82. #2392C22semidirect
84. #2361C22semidirect
85. #2361C22semidirect
86. #2358C22semidirect
87. D4×C4⋊C4C22semidirect
88. D4×C4⋊C4C22semidirect
89. D4×C22⋊C4C22semidirect
90. D4×C22⋊C4C22semidirect
91. C4×C4⋊Q8C22semidirect
92. C4×C4⋊Q8C22semidirect
93. C4×C4⋊Q8C22semidirect
94. C4×C4⋊Q8C22semidirect
99. C4×#124C22semidirect
100. C4×#124C22semidirect
101. C4×#124C22semidirect
102. C4×#124C22semidirect
103. C4×C22⋊Q8C22semidirect
104. C4×#121C22semidirect
105. C4×#121C22semidirect
106. C4×#121C22semidirect
107. C4×#121C22semidirect
108. C4×#121C22semidirect
109. C4×#121C22semidirect
110. C4×#121C22semidirect
111. C4×#121C22semidirect
112. C4×#120C22semidirect
113. #2297C22semidirect
114. #2297C22semidirect
115. #2293C22semidirect
116. #2293C22semidirect
117. #2293C22semidirect
118. #2285C22semidirect
119. #2285C22semidirect
120. #2285C22semidirect
121. #2280C22semidirect
122. C42×D4C22semidirect
123. C42×D4C22semidirect
124. C42×D4C22semidirect
125. C2×C43C22semidirect
139. #532D4semidirect
338. C2×#41C2×D4semidirect
372. C4⋊Q8C2×D4semidirect
374. #127#41semidirect
379. #124C2×D4semidirect
392. #121C2×D4semidirect
423. C4×D4C2×D4semidirect
482. C2×C42C2×D4semidirect
809. C4#3481semidirect

Maximal subgroups

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

subgroupindex
C2×#34812
#598432
#598362
#598272
#598232
#598162
#598122
#596602
#594202
#592132
#590352
#521632
#349762
#349352
#349322
#347002
C4×D422
C4×#5322