Finite Group Databasebeta

← #7626621

Subgroups — #7626621

Order 512.

8206 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#548C211yesmaximal, characteristic
2#34496C218yesmaximal, complemented
3#34474C218yesmaximal, complemented
4#34472C218yesmaximal, complemented
5#34366C214yesmaximal, complemented
6#34359C214yesmaximal, complemented
7#34358C214yesmaximal, complemented
8#34327C218yesmaximal, complemented
9#34211C212yesmaximal, complemented
10#34204C212yesmaximal, complemented
11#34203C212yesmaximal, complemented
12#34190C214yesmaximal, complemented
13#34187C211yesmaximal, characteristic, complemented
14#34173C211yesmaximal, characteristic, complemented
15#34172C211yesmaximal, characteristic, complemented
16D4×#117C212yesmaximal, complemented
17#34059C211yesmaximal, characteristic, complemented
18#34044C211yesmaximal, characteristic, complemented
19C2×#2310C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C24×Q8C2211yescharacteristic
22C2×#548C4132yescomplemented
23C2×#548C2214yes—
24C2×#548C2214yes—
25C2×#548C2214yes—
26C2×#548C2214yes—
27C22×#124C2212yes—
28C22×#124C2211yescharacteristic
29C22×C22⋊Q8C2212yes—
30C22×C22⋊Q8C2211yescharacteristic
31C22×#121C2212yes—
32C22×#121C2211yescharacteristic
33C2×#519C2212yes—
34C2×#518C2212yes—
35C22×C4×Q8C2211yescharacteristic
36C22×C4×D4C2211yescharacteristic
37C22×C4×D4C2212yes—
38C22×#117C2212yes—
39C22×#117C2212yes—
40#2379C22116yescomplemented
41#2378C22116yescomplemented
42#2377C22116yescomplemented
43#2372C22116yescomplemented
44#2368C22116yescomplemented
45#2367C2218yescomplemented
46#2367C2218yescomplemented
47#2364C22116yescomplemented
48#2363C2218yescomplemented
49#2362C2218yescomplemented
50#2361C2218yescomplemented
51#2360C2218yescomplemented
52#2357C2218yescomplemented
53#2356C2218yescomplemented
54#2355C2218yescomplemented
55#2354C2214yescomplemented
56#2353C2218yescomplemented
57#2353C2218yescomplemented
58#2352C2214yescomplemented
59#2352C2214yescomplemented
60#2349C2218yescomplemented
61D4×C4⋊C4C2214yescomplemented
62#2344C2214yes—
63#2344C2218yes—
64#2342C2218yes—
65#2342C2218yes—
66#2342C2218yes—
67#2342C2214yes—
68#2342C2218yes—
69#2342C2214yes—
70Q8×C22⋊C4C2218yescomplemented
71Q8×C22⋊C4C2218yescomplemented
72#2339C2218yescomplemented
73#2339C2218yescomplemented
74D4×C22⋊C4C2214yes—
75D4×C22⋊C4C2218yes—
76#2337C22116yescomplemented
77#2337C22116yescomplemented
78#2333C22116yescomplemented
79#2332C22116yescomplemented
80#2329C22116yescomplemented
81#2326C2218yescomplemented
82#2325C22116yescomplemented
83#2324C2218yescomplemented
84#2323C2218yescomplemented
85#2320C2218yescomplemented
86#2319C2218yescomplemented
87#2318C2218yescomplemented
88#2318C2218yescomplemented
89#2316C2212yes—
90#2313C2214yes—
91#2313C2214yes—
92#2311C2218yescomplemented
93#2310C2211yescharacteristic
94#2310C2211yescharacteristic
95#2310C2214yes—
96#2310C2214yes—
97#2310C2211yescharacteristic
98#2310C2211yescharacteristic
99#2310C2212yes—
100#2310C2218yescomplemented
101#2309C2212yes—
102#2308C2214yes—
103#2308C2214yes—
104C4×#124C2218yescomplemented
105C4×C22⋊Q8C2218yescomplemented
106C4×#121C2218yescomplemented
107#2297C2218yescomplemented
108#2295C2218yescomplemented
109C2×#391C2218yescomplemented
110#2293C2214yescomplemented
111#2290C2214yescomplemented
112#2290C2214yescomplemented
113#2285C2212yes—
114#2283C2214yes—
115#2283C2214yes—
116#2280C2214yes—
117#2280C2214yes—
118#2280C2212yes—
119#2280C2212yes—
120C2×#381C2214yes—
121C2×#381C2214yes—
122#2275C2218yescomplemented
123#2274C2212yes—
124C42×D4C2214yescomplemented
125C4×#117C2212yes—
126C22×#41—48no—
127C22×#41C2×C4116yescomplemented
128C22×#41C2314yes—
129C22×#41C2314yes—
130C23×Q8—48no—
131C23×Q8C2×C4116yescomplemented
132C23×Q8C2311yescharacteristic
133C23×Q8C2311yescharacteristic
134C23×Q8C2312yes—
135C23×Q8C2314yes—
136C23×Q8C2314yes—
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2312yes—
144C24×C4C2312yes—
145#548C2×C4164yescomplemented
146#548C2×C4164yescomplemented
147#548C2×C4164yescomplemented
148#548C2×C4164yescomplemented
149C2×#124C2×C4116yescomplemented
150C2×#124C2×C4132yescomplemented
151C2×#124C2314yes—
152C2×#124C2318yes—
153C2×#124C2318yes—
154C2×#124C2314yes—
155C2×C22⋊Q8C2×C4116yescomplemented
156C2×C22⋊Q8C2×C4132yescomplemented
157C2×C22⋊Q8C2314yes—
158C2×C22⋊Q8C2318yes—
159C2×C22⋊Q8C2318yes—
160C2×C22⋊Q8C2314yes—
161C2×#121C2×C4116yescomplemented
162C2×#121C2×C4132yescomplemented
163C2×#121C2314yes—
164C2×#121C2318yes—
165C2×#121C2318yes—
166C2×#121C2314yes—
167#519—48no—
168#518—48no—
169C2×C4×Q8C2×C4116yescomplemented
170C2×C4×Q8C2318yes—
171C2×C4×Q8C2318yes—
172C2×C4×Q8C2314yes—
173C2×C4×Q8C2314yes—
174C2×C4×D4C2×C4116yescomplemented
175C2×C4×D4C2×C4132yescomplemented
176C2×C4×D4C2318yes—
177C2×C4×D4C2318yes—
178C2×C4×D4C23116yes—
179C2×C4×D4C2318yes—
180C2×C4×D4C2314yes—
181C2×C4×D4C2314yes—
182C2×C4×D4C2314yes—
183C2×C4×D4C2312yes—
184C2×C4×D4C2312yes—
185C2×C4×D4C2312yes—
186C2×C4×D4C2314yes—
187C2×C4×D4C2312yes—
188C2×#117—48no—
189C2×#117—48no—
190C2×#117C2312yes—
191C2×#117C2312yes—
192C2×#117C2312yes—
193C2×#117C2312yes—
194C2×#117C2314yes—
195C2×#117C2318yes—
196C2×#117C2314yes—
197C2×#117C2314yes—
198C2×#117C2314yes—
199C2×#117C2314yes—
200C2×#117C2314yes—
201C22×C4⋊C4C2314yes—
202C22×C4⋊C4C2314yes—
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2312yes—
207C22×C22⋊C4C2314yes—
208C22×C22⋊C4C2318yes—
209C22×C22⋊C4C2314yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C42C2314yes—
217C22×C42C2314yes—
218C22×C42C2311yescharacteristic
219C22×C42C2312yes—
220#391C2318yes—
221#391C2318yes—
222#391C23116yes—
223#391C2318yes—
224#391C2318yes—
225#391C23116yes—
226#391C2318yes—
227#391C2318yes—
228#391C23116yes—
229#391C23116yes—
230#390C2318yes—
231#390C2318yes—
232#390C23116yes—
233#390C2318yes—
234#389C2318yes—
235#389C2318yes—
236#389C23116yes—
237#389C2318yes—
238#388C2318yes—
239#388C23116yes—
240#388C2318yes—
241#388C23116yes—
242#388C23116yes—
243#388C23116yes—
244#388C23116yes—
245#388C23116yes—
246#388C23116yes—
247#388C23116yes—
248#388C2318yes—
249#388C2318yes—
250#387C23116yes—
251#387C23116yes—
252#387C23116yes—
253#387C23116yes—
254#387C23116yes—
255#387C23116yes—
256#387C2318yes—
257#387C2318yes—
258#386C23116yes—
259#386C23116yes—
260#386C23116yes—
261#386C23116yes—
262#386C23116yes—
263#386C23116yes—
264#386C2318yes—
265#386C2318yes—
266#385C2318yes—
267#385C23116yes—
268#385C23116yes—
269#385C23116yes—
270#385C23116yes—
271#385C2318yes—
272#384C2314yes—
273#383C2318yes—
274#383C2318yes—
275#382C2318yes—
276#382C2318yes—
277#382C2314yes—
278#381C2314yes—
279#381C2314yes—
280#381C2314yes—
281#381C2314yes—
282#381C2318yes—
283#381C2314yes—
284#381C2318yes—
285#381C2318yes—
286#381C2318yes—
287#381C2318yes—
288#381C2314yes—
289#380C2318yes—
290#380C2318yes—
291#380C2314yes—
292#380C2318yes—
293#380C2318yes—
294#380C2314yes—
295#380C2314yes—
296#380C2318yes—
297#380C2314yes—
298#380C2314yes—
299#380C2314yes—
300#379C2314yes—
301#379C2318yes—
302#379C2314yes—
303C4×C4⋊C4C2318yes—
304C4×C4⋊C4C2314yes—
305C4×C4⋊C4C2318yes—
306C4×C4⋊C4C2318yes—
307C4×C4⋊C4C2318yes—
308C4×C4⋊C4C23116yes—
309C4×C4⋊C4C2318yes—
310C4×C4⋊C4C2314yes—
311C4×C4⋊C4C2314yes—
312C4×C4⋊C4C2314yes—
313C4×C22⋊C4C2314yes—
314C4×C22⋊C4C2318yes—
315C4×C22⋊C4C2318yes—
316C4×C22⋊C4C2318yes—
317C4×C22⋊C4C23116yes—
318C4×C22⋊C4C23116yes—
319C4×C22⋊C4C2318yes—
320C4×C22⋊C4C23116yes—
321C4×C22⋊C4C2318yes—
322C4×C22⋊C4C23116yes—
323C4×C22⋊C4C2314yes—
324C4×C22⋊C4C2314yes—
325C4×C22⋊C4C2314yes—
326C4×C22⋊C4C2314yes—
327C4×C22⋊C4C2314yes—
328C4×C22⋊C4C2318yes—
329C4×C22⋊C4C2318yes—
330#376C2318yes—
331#376C2314yes—
332#376C2318yes—
333C2×#95C2318yes—
334C2×#95C2318yes—
335C2×#95C2318yes—
336C2×#95C2318yes—
337C43C2314yes—
338C25C2411yescharacteristic
339C25C2411yescharacteristic
340C25C2412yes—
341C2×#41—464no—
342C2×#41—48no—
343C2×#41—48no—
344C2×#41—48no—
345C2×#41—48no—
346C2×#41C22×C4132yes—
347C2×#41C22×C4132yes—
348C22×Q8—28no—
349C22×Q8—28no—
350C22×Q8—48no—
351C22×Q8—464no—
352C22×Q8—48no—
353C22×Q8—48no—
354C22×Q8—48no—
355C22×Q8—48no—
356C22×Q8C22×C418yes—
357C22×Q8C22×C418yes—
358C22×Q8C22×C4116yes—
359C22×Q8C22×C4132yes—
360C22×Q8C22×C4132yes—
361C22×Q8C2414yes—
362C22×Q8C2414yes—
363C22×Q8C2418yes—
364C22×D4—28no—
365C22×D4—48no—
366C22×D4—44no—
367C22×D4—48no—
368C22×D4C22×C418yes—
369C22×D4C22×C418yes—
370C22×D4C22×C4116yes—
371C22×D4C22×C4116yes—
372C22×D4C2412yes—
373C22×D4C2414yes—
374C22×D4C2414yes—
375C22×D4C2414yes—
376C22×D4C2412yes—
377C22×D4C2418yes—
378C23×C4—28no—
379C23×C4—28no—
380C23×C4—48no—
381C23×C4—48no—
382C23×C4C22×C418yes—
383C23×C4C22×C418yes—
384C23×C4C22×C4116yes—
385C23×C4C22×C4116yes—
386C23×C4C2411yescharacteristic
387C23×C4C2412yes—
388C23×C4C2411yescharacteristic
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2418yes—
395C23×C4C2418yes—
396C23×C4C24116yes—
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2412yes—
400C23×C4C2414yes—
401C23×C4C2414yes—
402C23×C4C2414yes—
403C23×C4C2414yes—
404C23×C4C2411yescharacteristic
405#124C22×C4132yes—
406#124C22×C4132yes—
407#124C22×C4164yes—
408#124C22×C4164yes—
409C22⋊Q8C22×C4132yes—
410C22⋊Q8C22×C4132yes—
411C22⋊Q8C22×C4164yes—
412C22⋊Q8C22×C4164yes—
413#121C22×C4132yes—
414#121C22×C4132yes—
415#121C22×C4164yes—
416#121C22×C4164yes—
417C4×Q8—416no—
418C4×Q8—416no—
419C4×Q8C22×C4132yes—
420C4×Q8C22×C4132yes—
421C4×D4—416no—
422C4×D4—416no—
423C4×D4—416no—
424C4×D4—432no—
425C4×D4C22×C4116yes—
426C4×D4C22×C4116yes—
427C4×D4C22×C4116yes—
428C4×D4C22×C4116yes—
429C4×D4C22×C4132yes—
430C4×D4C22×C4132yes—
431C4×D4C22×C4132yes—
432C4×D4C22×C4132yes—
433#117—28no—
434#117—28no—
435#117—28no—
436#117—28no—
437#117—48no—
438#117—48no—
439#117—48no—
440#117—48no—
441#117—416no—
442#117—48no—
443#117—48no—
444C2×C4⋊C4—48no—
445C2×C4⋊C4—48no—
446C2×C4⋊C4C22×C418yes—
447C2×C4⋊C4C22×C4116yes—
448C2×C4⋊C4C22×C4116yes—
449C2×C4⋊C4C22×C418yes—
450C2×C4⋊C4C2414yes—
451C2×C4⋊C4C2414yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C2418yes—
455C2×C4⋊C4C2418yes—
456C2×C4⋊C4C24116yes—
457C2×C4⋊C4C24116yes—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2412yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2418yes—
466C2×C22⋊C4—48no—
467C2×C22⋊C4—48no—
468C2×C22⋊C4—416no—
469C2×C22⋊C4C22×C418yes—
470C2×C22⋊C4C22×C418yes—
471C2×C22⋊C4C22×C4116yes—
472C2×C22⋊C4C22×C4116yes—
473C2×C22⋊C4C22×C4116yes—
474C2×C22⋊C4C22×C4116yes—
475C2×C22⋊C4C2414yes—
476C2×C22⋊C4C2414yes—
477C2×C22⋊C4C2414yes—
478C2×C22⋊C4C2414yes—
479C2×C22⋊C4C2418yes—
480C2×C22⋊C4C2418yes—
481C2×C22⋊C4C2418yes—
482C2×C22⋊C4C24116yes—
483C2×C22⋊C4C2418yes—
484C2×C22⋊C4C24116yes—
485C2×C22⋊C4C2418yes—
486C2×C22⋊C4C2418yes—
487C2×C22⋊C4C24116yes—
488C2×C22⋊C4C2411yescharacteristic
489C2×C22⋊C4C2411yescharacteristic
490C2×C22⋊C4C2411yescharacteristic
491C2×C22⋊C4C2411yescharacteristic
492C2×C22⋊C4C2414yes—
493C2×C22⋊C4C2412yes—
494C2×C22⋊C4C2414yes—
495C2×C22⋊C4C2412yes—
496C2×C22⋊C4C2418yes—
497C2×C22⋊C4C2418yes—
498C2×C22⋊C4C2418yes—
499C2×C42—48no—
500C2×C42—48no—
501C2×C42C22×C4116yes—
502C2×C42C22×C418yes—
503C2×C42C2414yes—
504C2×C42C2414yes—
505C2×C42C2414yes—
506C2×C42C2414yes—
507C2×C42C2418yes—
508C2×C42C2418yes—
509C2×C42C24116yes—
510C2×C42C2418yes—
511C2×C42C24116yes—
512C2×C42C2418yes—
513C2×C42C2412yes—
514C2×C42C2414yes—
515C2×C42C2412yes—
516C2×C42C2414yes—
517#95C2418yes—
518#95C2418yes—
519#95C2418yes—
520#95C2418yes—
521#95C2418yes—
522#95C2418yes—
523#95C24116yes—
524#95C2418yes—
525#95C2418yes—
526#95C24116yes—
527#95C2418yes—
528#95C2418yes—
529#95C24116yes—
530#95C2418yes—
531#95C2418yes—
532#95C2418yes—
533#95C2418yes—
534#95C2418yes—
535#95C2418yes—
536#95C24116yes—
537C24—24no—
538C24—24no—
539C24—24no—
540C24—28no—
541C24—42no—
542C24—42no—
543C24—44no—
544C24—42no—
545C24—44no—
546C24C23×C414yes—
547C24C23×C414yes—
548C24C23×C418yes—
549C24C2511yescharacteristic
550C24C2512yes—
551C24C2514yes—
552C24C2511yescharacteristic
553C24C2511yescharacteristic
554#41—464no—
555#41—464no—
556C2×Q8—232no—
557C2×Q8—232no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—28no—
562C2×Q8—432no—
563C2×Q8—48no—
564C2×Q8—48no—
565C2×Q8—464no—
566C2×Q8—464no—
567C2×Q8C23×C4116yes—
568C2×Q8C23×C4116yes—
569C2×Q8C23×C4132yes—
570C2×D4—28no—
571C2×D4—216no—
572C2×D4—232no—
573C2×D4—28no—
574C2×D4—28no—
575C2×D4—432no—
576C2×D4—44no—
577C2×D4—48no—
578C2×D4—48no—
579C2×D4—48no—
580C2×D4—416no—
581C2×D4—432no—
582C2×D4C23×C418yes—
583C2×D4C23×C4116yes—
584C2×D4C23×C4116yes—
585C2×D4C23×C418yes—
586C2×D4C23×C4116yes—
587C2×D4C23×C4132yes—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—232no—
593C22×C4—232no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—216no—
603C22×C4—432no—
604C22×C4—432no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—416no—
618C22×C4—416no—
619C22×C4—416no—
620C22×C4C23×C418yes—
621C22×C4C23×C414yes—
622C22×C4C23×C418yes—
623C22×C4C23×C414yes—
624C22×C4C23×C418yes—
625C22×C4C23×C418yes—
626C22×C4C23×C418yes—
627C22×C4C23×C418yes—
628C22×C4C23×C414yes—
629C22×C4C23×C418yes—
630C22×C4C23×C414yes—
631C22×C4C23×C4116yes—
632C22×C4C23×C4116yes—
633C22×C4C23×C4116yes—
634C22×C4C23×C4116yes—
635C22×C4C23×C414yes—
636C22×C4H(5,𝔽2)18yes—
637C22×C4C2518yes—
638C22×C4C2518yes—
639C22×C4C2518yes—
640C22×C4C2518yes—
641C22×C4C2514yes—
642C22×C4C2511yescharacteristic
643C22×C4C2511yescharacteristic
644C22×C4C2511yescharacteristic
645C22×C4C2514yes—
646C22×C4C2512yes—
647C22×C4C2512yes—
648C22×C4C2514yes—
649C22×C4C2511yescharacteristic
650C22×C4C2512yes—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—28no—
654C4⋊C4—28no—
655C4⋊C4—48no—
656C4⋊C4—48no—
657C4⋊C4—48no—
658C4⋊C4—416no—
659C4⋊C4—48no—
660C4⋊C4—416no—
661C4⋊C4C23×C418yes—
662C4⋊C4C23×C4116yes—
663C4⋊C4C23×C418yes—
664C4⋊C4C23×C4116yes—
665C4⋊C4C23×C4132yes—
666C4⋊C4C23×C4116yes—
667C22⋊C4—28no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—216no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—416no—
675C22⋊C4—48no—
676C22⋊C4—416no—
677C22⋊C4—48no—
678C22⋊C4—416no—
679C22⋊C4—48no—
680C22⋊C4C23×C414yes—
681C22⋊C4C23×C414yes—
682C22⋊C4C23×C414yes—
683C22⋊C4C23×C414yes—
684C22⋊C4C23×C418yes—
685C22⋊C4C23×C4116yes—
686C22⋊C4C23×C418yes—
687C22⋊C4C23×C4116yes—
688C22⋊C4C23×C4132yes—
689C22⋊C4C23×C4132yes—
690C22⋊C4C23×C4132yes—
691C42—28no—
692C42—28no—
693C42—28no—
694C42—28no—
695C42—48no—
696C42—48no—
697C42—48no—
698C42—416no—
699C42—416no—
700C42—48no—
701C42C23×C4116yes—
702C42C23×C4116yes—
703C42C23×C418yes—
704C42C23×C418yes—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—28no—
712C23—22no—
713C23—24no—
714C23—28no—
715C23—22no—
716C23—22no—
717C23—24no—
718C23—28no—
719C23—28no—
720C23—28no—
721C23—28no—
722C23—216no—
723C23—44no—
724C23—44no—
725C23—48no—
726C23—44no—
727C23—48no—
728C23—416no—
729C23—88no—
730C23—816no—
731C23C24×C414yes—
732C23C24×C418yes—
733C23C24×C412yes—
734C23C24×C412yes—
735C23C24×C412yes—
736C23C2×H(5,𝔽2)14yes—
737C23#58514yes—
738C23C2611yescharacteristic
739Q8—232no—
740Q8—232no—
741Q8—432no—
742D4—216no—
743D4—232no—
744D4—232no—
745D4—48no—
746D4—416no—
747D4—432no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—28no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—28no—
754C2×C4—28no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—28no—
759C2×C4—28no—
760C2×C4—216no—
761C2×C4—216no—
762C2×C4—216no—
763C2×C4—216no—
764C2×C4—216no—
765C2×C4—216no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—28no—
774C2×C4—28no—
775C2×C4—28no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—416no—
779C2×C4—416no—
780C2×C4—416no—
781C2×C4—416no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—48no—
785C2×C4—816no—
786C2×C4—816no—
787C2×C4—1616no—
788C2×C4#518116yes—
789C2×C4C24×C412yes—
790C2×C4C24×C412yes—
791C2×C4C24×C418yes—
792C2×C4C24×C414yes—
793C2×C4C24×C418yes—
794C2×C4C24×C414yes—
795C2×C4C24×C418yes—
796C2×C4C24×C412yes—
797C2×C4C24×C412yes—
798C2×C4C24×C414yes—
799C2×C4C2×H(5,𝔽2)14yes—
800C2×C4C2×H(5,𝔽2)14yes—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—28no—
806C22—28no—
807C22—22no—
808C22—24no—
809C22—28no—
810C22—24no—
811C22—28no—
812C22—22no—
813C22—22no—
814C22—24no—
815C22—28no—
816C22—416no—
817C22—44no—
818C22—416no—
819C22—44no—
820C22—44no—
821C22—88no—
822C22—816no—
823C22C2×#51814yes—
824C22#342814yes—
825C22C25×C411yescharacteristic
826C22C22×H(5,𝔽2)12yes—
827C22C2×#58512yes—
828C222−1+612yes—
829C4—22no—
830C4—22no—
831C4—24no—
832C4—28no—
833C4—28no—
834C4—28no—
835C4—24no—
836C4—22no—
837C4—22no—
838C4—48no—
839C4—48no—
840C4—48no—
841C4—48no—
842C4C2×#51818yes—
843C2—24no—
844C2—24no—
845C2—42no—
846C2—44no—
847C2—48no—
848C2C22×#51811yescharacteristic
849C2C2×#342811yescharacteristic
850C2#6265311yescharacteristic
851C2#6295414yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC22×#548C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34496C2semidirect
3. #34474C2semidirect
4. #34472C2semidirect
5. #34366C2semidirect
6. #34359C2semidirect
7. #34358C2semidirect
8. #34327C2semidirect
9. #34211C2semidirect
10. #34204C2semidirect
11. #34203C2semidirect
12. #34190C2semidirect
13. #34187C2semidirect
14. #34173C2semidirect
15. #34172C2semidirect
16. D4×#117C2semidirect
17. #34059C2semidirect
18. #34044C2semidirect
19. C2×#2310C2semidirect
22. C2×#548C4semidirect
40. #2379C22semidirect
41. #2378C22semidirect
42. #2377C22semidirect
43. #2372C22semidirect
44. #2368C22semidirect
45. #2367C22semidirect
46. #2367C22semidirect
47. #2364C22semidirect
48. #2363C22semidirect
49. #2362C22semidirect
50. #2361C22semidirect
51. #2360C22semidirect
52. #2357C22semidirect
53. #2356C22semidirect
54. #2355C22semidirect
55. #2354C22semidirect
56. #2353C22semidirect
57. #2353C22semidirect
58. #2352C22semidirect
59. #2352C22semidirect
60. #2349C22semidirect
61. D4×C4⋊C4C22semidirect
70. Q8×C22⋊C4C22semidirect
71. Q8×C22⋊C4C22semidirect
72. #2339C22semidirect
73. #2339C22semidirect
76. #2337C22semidirect
77. #2337C22semidirect
78. #2333C22semidirect
79. #2332C22semidirect
80. #2329C22semidirect
81. #2326C22semidirect
82. #2325C22semidirect
83. #2324C22semidirect
84. #2323C22semidirect
85. #2320C22semidirect
86. #2319C22semidirect
87. #2318C22semidirect
88. #2318C22semidirect
92. #2311C22semidirect
100. #2310C22semidirect
104. C4×#124C22semidirect
105. C4×C22⋊Q8C22semidirect
106. C4×#121C22semidirect
107. #2297C22semidirect
108. #2295C22semidirect
109. C2×#391C22semidirect
110. #2293C22semidirect
111. #2290C22semidirect
112. #2290C22semidirect
122. #2275C22semidirect
124. C42×D4C22semidirect
127. C22×#41C2×C4semidirect
131. C23×Q8C2×C4semidirect
145. #548C2×C4semidirect
146. #548C2×C4semidirect
147. #548C2×C4semidirect
148. #548C2×C4semidirect
149. C2×#124C2×C4semidirect
150. C2×#124C2×C4semidirect
155. C2×C22⋊Q8C2×C4semidirect
156. C2×C22⋊Q8C2×C4semidirect
161. C2×#121C2×C4semidirect
162. C2×#121C2×C4semidirect
169. C2×C4×Q8C2×C4semidirect
174. C2×C4×D4C2×C4semidirect
175. C2×C4×D4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C22×#5482
#344962
#344742
#344722
#343662
#343592
#343582
#343272
#342112
#342042
#342032
#341902
#341872
#341732
#341722
D4×#1172
#340592
#340442
C2×#23102