Finite Group Databasebeta

← #7626656

Subgroups — #7626656

Order 512.

7076 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3480C211yesmaximal, characteristic
2#34500C216yesmaximal, complemented
3#34483C216yesmaximal, complemented
4#34466C216yesmaximal, complemented
5#34463C216yesmaximal, complemented
6#34384C213yesmaximal, complemented
7#34383C213yesmaximal, complemented
8#34368C213yesmaximal, complemented
9#34367C213yesmaximal, complemented
10#34336C212yesmaximal, complemented
11#34312C212yesmaximal, complemented
12#34295C212yesmaximal, complemented
13#34293C212yesmaximal, complemented
14#34243C213yesmaximal, complemented
15#34242C213yesmaximal, complemented
16#34196C211yesmaximal, characteristic, complemented
17#34193C211yesmaximal, characteristic, complemented
18#34188C213yesmaximal, complemented
19#34183C211yesmaximal, characteristic, complemented
20#34182C211yesmaximal, characteristic, complemented
21#34129C211yesmaximal, characteristic, complemented
22C4⋊C4×#41C211yesmaximal, characteristic, complemented
23#34060C213yesmaximal, complemented
24#3480C4132yescomplemented
25C2×#559C2213yes—
26C2×#557C2211yescharacteristic
27C2×#556C2213yes—
28C2×#553C2213yes—
29C2×#553C2213yes—
30C2×#550C2211yescharacteristic
31C2×#548C2211yescharacteristic
32C2×#548C2211yescharacteristic
33C2×#532C2213yes—
34C2×#529C2213yes—
35C2×#529C2213yes—
36C2×#520C2212yes—
37C2×#519C2212yes—
38C2×C4×#41C2212yes—
39C2×C4×#41C2213yes—
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43#2383C22112yes—
44#2379C22112yes—
45#2377C22112yes—
46#2376C22112yes—
47#2373C22112yes—
48#2370C2216yes—
49#2370C2216yes—
50#2369C2216yes—
51#2367C2216yes—
52#2367C2216yes—
53#2366C2216yes—
54#2363C2216yes—
55#2363C2216yes—
56#2363C2216yes—
57#2362C2216yes—
58#2361C2216yes—
59#2360C2216yes—
60#2359C22112yes—
61#2355C2216yes—
62#2355C2213yes—
63#2355C2213yes—
64#2355C2216yes—
65#2354C2213yes—
66#2354C2213yes—
67#2354C2213yes—
68#2354C2216yes—
69#2354C2213yes—
70#2354C2216yes—
71#2354C2216yes—
72#2352C2216yes—
73#2352C2216yes—
74#2352C2216yes—
75#2352C2216yes—
76#2352C2216yes—
77#2352C2216yes—
78#2351C2212yes—
79#2351C2212yes—
80#2351C2216yes—
81Q8×C4⋊C4C2212yes—
82Q8×C4⋊C4C2211yescharacteristic
83Q8×C4⋊C4C2211yescharacteristic
84Q8×C4⋊C4C2213yes—
85Q8×C4⋊C4C2213yes—
86Q8×C4⋊C4C2211yescharacteristic
87Q8×C4⋊C4C2211yescharacteristic
88#2349C2216yes—
89D4×C4⋊C4C2213yes—
90D4×C4⋊C4C2213yes—
91D4×C4⋊C4C2213yes—
92D4×C4⋊C4C2216yes—
93D4×C4⋊C4C2213yes—
94D4×C4⋊C4C2216yes—
95#2347C2216yes—
96#2346C2216yes—
97#2344C2216yes—
98#2341C2212yes—
99#2341C2212yes—
100Q8×C22⋊C4C2212yes—
101#2337C22112yes—
102#2335C22112yes—
103#2334C22112yes—
104#2334C22112yes—
105#2331C2216yes—
106#2330C2216yes—
107#2328C2216yes—
108#2326C2216yes—
109#2324C2216yes—
110#2324C22112yes—
111#2324C2216yes—
112#2324C2216yes—
113#2323C2216yes—
114#2322C22112yes—
115#2320C2216yes—
116#2320C2216yes—
117#2319C2216yes—
118#2319C2216yes—
119#2318C2216yes—
120#2318C2216yes—
121#2317C2213yes—
122#2317C2213yes—
123#2317C2216yes—
124#2316C2216yes—
125#2314C2211yescharacteristic
126#2314C2213yes—
127#2314C2213yes—
128#2314C2213yes—
129#2314C2216yes—
130#2311C2213yes—
131#2311C2213yes—
132#2311C2216yes—
133C4×#125C2216yes—
134C4×#124C2216yes—
135C4×C22⋊Q8C2216yes—
136C4×#121C2216yes—
137#2296C2216yes—
138#2295C2216yes—
139#2293C2216yes—
140#2293C2216yes—
141#2290C2216yes—
142#2290C2216yes—
143#2285C2213yes—
144#2285C2213yes—
145#2285C2213yes—
146#2285C2213yes—
147#2285C2213yes—
148#2285C2213yes—
149#2285C2213yes—
150C2×#384C2213yes—
151#2283C2213yes—
152#2283C2213yes—
153#2276C2212yes—
154#2276C2212yes—
155#2274C2216yes—
156C42×Q8C2212yes—
157C4×#117C2213yes—
158C2×C4×C4⋊C4C2213yes—
159C22×#41C2311yescharacteristic
160C22×#41C2311yescharacteristic
161C22×#41C2313yes—
162C23×Q8C2311yescharacteristic
163#559C2×C4148yescomplemented
164#557C2×C4116yescomplemented
165#556C2×C4148yescomplemented
166#553C2×C4148yescomplemented
167#553C2×C4148yescomplemented
168#550C2×C4116yes—
169#548C2×C4116yescomplemented
170#548C2×C4116yescomplemented
171#532C2×C4148yescomplemented
172C2×C4⋊Q8C2313yes—
173C2×#127C2313yes—
174#529C2×C4148yescomplemented
175#529C2×C4148yescomplemented
176C2×#126C2316yes—
177C2×#126C2316yes—
178C2×#125C2313yes—
179C2×#125C2313yes—
180C2×#124C2313yes—
181C2×#124C2316yes—
182C2×#124C2313yes—
183C2×#123C2316yes—
184C2×#123C2316yes—
185C2×C22⋊Q8C2313yes—
186C2×C22⋊Q8C2313yes—
187C2×#121C2313yes—
188C2×#121C2313yes—
189C2×#121C2313yes—
190C2×#121C2316yes—
191C2×#121C2313yes—
192#520—48no—
193#519—48no—
194C4×#41—48no—
195C4×#41C2×C4148yescomplemented
196C4×#41C2×C4116yescomplemented
197C4×#41C2×C4116yescomplemented
198C2×C4×Q8C2×C4116yescomplemented
199C2×C4×Q8C2312yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2316yes—
204C2×C4×Q8C2316yes—
205C2×C4×Q8C2313yes—
206C2×C4×Q8C2313yes—
207C2×C4×Q8C2311yescharacteristic
208C2×C4×Q8C2313yes—
209C2×C4×Q8C2311yescharacteristic
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2311yescharacteristic
212C2×C4×Q8C2313yes—
213C2×C4×D4C2316yes—
214C2×C4×D4C2316yes—
215C2×C4×D4C2316yes—
216C2×C4×D4C2316yes—
217C2×C4×D4C23112yes—
218C2×C4×D4C2313yes—
219C2×C4×D4C2313yes—
220C2×C4×D4C2313yes—
221C2×C4×D4C2313yes—
222C2×C4×D4C2313yes—
223C2×C4×D4C2313yes—
224C2×C4×D4C2316yes—
225C2×C4×D4C2313yes—
226C2×C4×D4C2313yes—
227C2×C4×D4C2313yes—
228C2×C4×D4C2313yes—
229C2×#117C2313yes—
230C2×#117C2313yes—
231C2×#117C2316yes—
232C2×#117C2316yes—
233C2×#117C2316yes—
234C2×#117C2316yes—
235C2×#117C2316yes—
236C2×#117C2316yes—
237C2×#117C2316yes—
238C2×#117C2311yescharacteristic
239C2×#117C2313yes—
240C2×#117C2313yes—
241C2×#117C2313yes—
242C2×#117C2313yes—
243C22×C4⋊C4C2313yes—
244C22×C4⋊C4C2313yes—
245C22×C4⋊C4C2316yes—
246C22×C4⋊C4C2316yes—
247C22×C4⋊C4C2316yes—
248C22×C4⋊C4C2313yes—
249C22×C42C2316yes—
250C22×C42C2313yes—
251C22×C42C2313yes—
252C22×C42C2313yes—
253#391C2316yes—
254#391C2316yes—
255#391C23112yes—
256#391C2316yes—
257#391C2316yes—
258#390C2316yes—
259#390C2316yes—
260#390C23112yes—
261#390C2316yes—
262#390C2316yes—
263#390C23112yes—
264#390C2316yes—
265#390C2316yes—
266#389C2316yes—
267#389C2316yes—
268#389C2316yes—
269#389C2316yes—
270#389C23112yes—
271#389C2316yes—
272#389C23112yes—
273#389C2316yes—
274#389C2316yes—
275#389C2316yes—
276#389C2316yes—
277#389C2316yes—
278#389C2316yes—
279#389C2316yes—
280#389C2316yes—
281#389C23112yes—
282#389C2316yes—
283#388C2312yes—
284#388C2316yes—
285#388C2316yes—
286#388C2316yes—
287#388C2312yes—
288#388C2316yes—
289#388C2316yes—
290#388C2316yes—
291#388C23112yes—
292#388C23112yes—
293#388C23112yes—
294#388C23112yes—
295#388C23112yes—
296#388C23112yes—
297#388C23112yes—
298#388C23112yes—
299#388C23112yes—
300#388C23112yes—
301#387C2316yes—
302#387C23112yes—
303#387C2312yes—
304#387C2316yes—
305#387C2316yes—
306#387C2312yes—
307#387C2316yes—
308#387C2316yes—
309#387C2316yes—
310#387C23112yes—
311#387C23112yes—
312#387C23112yes—
313#387C23112yes—
314#387C23112yes—
315#386C2316yes—
316#386C2316yes—
317#386C2316yes—
318#386C2316yes—
319#386C23112yes—
320#386C23112yes—
321#386C23112yes—
322#386C23112yes—
323#385C2316yes—
324#385C2316yes—
325#385C2316yes—
326#385C2316yes—
327#385C23112yes—
328#385C23112yes—
329#385C23112yes—
330#385C23112yes—
331#385C23112yes—
332#385C23112yes—
333#384C2313yes—
334#384C2311yescharacteristic
335#384C2313yes—
336#384C2313yes—
337#384C2316yes—
338#384C2316yes—
339#384C2313yes—
340#384C2313yes—
341#384C2313yes—
342#384C2313yes—
343#383C2316yes—
344#383C2316yes—
345#382C2316yes—
346#382C2313yes—
347#382C2311yescharacteristic
348#382C2313yes—
349#382C2313yes—
350#382C2316yes—
351#382C2316yes—
352#382C2316yes—
353#382C2316yes—
354#382C2316yes—
355#381C2316yes—
356#381C2316yes—
357#380C2311yescharacteristic
358#380C2313yes—
359#380C2311yescharacteristic
360#380C2313yes—
361#380C2313yes—
362#380C2316yes—
363#380C2313yes—
364#380C2313yes—
365#380C2316yes—
366#380C2313yes—
367#380C2316yes—
368#380C2316yes—
369#380C2316yes—
370#380C2316yes—
371#380C2316yes—
372#380C2316yes—
373#380C2316yes—
374#380C2316yes—
375C4×C4⋊C4C23112yes—
376C4×C4⋊C4C2316yes—
377C4×C4⋊C4C2316yes—
378C4×C4⋊C4C23112yes—
379C4×C4⋊C4C2311yescharacteristic
380C4×C4⋊C4C2311yescharacteristic
381C4×C4⋊C4C2313yes—
382C4×C4⋊C4C2313yes—
383C4×C4⋊C4C2316yes—
384C4×C4⋊C4C2316yes—
385C4×C4⋊C4C2316yes—
386C4×C4⋊C4C2316yes—
387C4×C4⋊C4C2316yes—
388C4×C4⋊C4C2316yes—
389C4×C4⋊C4C2316yes—
390C4×C4⋊C4C2316yes—
391C4×C4⋊C4C2316yes—
392C4×C4⋊C4C2316yes—
393C4×C4⋊C4C23112yes—
394C4×C4⋊C4C2316yes—
395C4×C4⋊C4C2313yes—
396C4×C4⋊C4C2313yes—
397C4×C4⋊C4C2313yes—
398C4×C4⋊C4C2316yes—
399C4×C4⋊C4C2316yes—
400C4×C4⋊C4C2313yes—
401C4×C4⋊C4C2316yes—
402C4×C4⋊C4C2316yes—
403C4×C4⋊C4C2316yes—
404C4×C22⋊C4C2316yes—
405C4×C22⋊C4C23112yes—
406C4×C22⋊C4C23112yes—
407C4×C22⋊C4C23112yes—
408C4×C22⋊C4C23112yes—
409C4×C22⋊C4C2316yes—
410C4×C22⋊C4C2316yes—
411C4×C22⋊C4C2316yes—
412#376C2316yes—
413#376C2316yes—
414#376C2316yes—
415C2×#95C2316yes—
416C43C2316yes—
417C2×#41—24no—
418C2×#41—24no—
419C2×#41—24no—
420C2×#41—24no—
421C2×#41—46no—
422C2×#41—46no—
423C2×#41C22×C418yes—
424C2×#41C22×C418yes—
425C2×#41C22×C4124yes—
426C22×Q8—24no—
427C22×Q8—24no—
428C22×Q8C22×C418yes—
429C22×Q8C2413yes—
430C22×Q8C2413yes—
431C22×Q8C2411yescharacteristic
432C22×D4C2413yes—
433C22×D4C2413yes—
434C22×D4C2416yes—
435C22×D4C2413yes—
436C22×D4C2413yes—
437C22×D4C2413yes—
438C23×C4C2413yes—
439C23×C4C2413yes—
440C23×C4C2413yes—
441C23×C4C2413yes—
442C23×C4C2413yes—
443C23×C4C2411yescharacteristic
444C23×C4C24112yes—
445C23×C4C2416yes—
446C23×C4C2416yes—
447C23×C4C2413yes—
448C23×C4C2413yes—
449C23×C4C2413yes—
450C4⋊Q8C22×C4124yes—
451#127C22×C4124yes—
452#126C22×C4148yes—
453#126C22×C4148yes—
454#125C22×C4124yes—
455#125C22×C4124yes—
456#124C22×C4124yes—
457#124C22×C4124yes—
458#124C22×C4148yes—
459#123C22×C4148yes—
460#123C22×C4148yes—
461C22⋊Q8C22×C4124yes—
462C22⋊Q8C22×C4124yes—
463#121C22×C4124yes—
464#121C22×C4124yes—
465#121C22×C4124yes—
466#121C22×C4124yes—
467#121C22×C4148yes—
468C4×Q8—28no—
469C4×Q8—28no—
470C4×Q8—28no—
471C4×Q8—28no—
472C4×Q8—412no—
473C4×Q8—412no—
474C4×Q8C22×C418yes—
475C4×Q8C22×C4124yes—
476C4×Q8C22×C418yes—
477C4×Q8C22×C4124yes—
478C4×Q8C22×C418yes—
479C4×Q8C22×C418yes—
480C4×Q8C22×C4124yes—
481C4×Q8C22×C4124yes—
482C4×D4—412no—
483C4×D4—412no—
484C4×D4—412no—
485C4×D4—412no—
486C4×D4—812no—
487C4×D4C22×C4124yes—
488C4×D4C22×C4124yes—
489C4×D4C22×C4124yes—
490C4×D4C22×C4124yes—
491C4×D4C22×C4124yes—
492C4×D4C22×C4124yes—
493C4×D4C22×C4124yes—
494C4×D4C22×C4124yes—
495C4×D4C22×C4124yes—
496C4×D4C22×C4124yes—
497C4×D4C22×C4148yes—
498#117—412no—
499#117—412no—
500#117—46no—
501#117—412no—
502#117—46no—
503#117—412no—
504#117—412no—
505#117—86no—
506#117—86no—
507#117C22×C418yes—
508#117C22×C4124yes—
509#117C22×C4124yes—
510#117C22×C4124yes—
511#117C22×C4124yes—
512C2×C4⋊C4—46no—
513C2×C4⋊C4—412no—
514C2×C4⋊C4—46no—
515C2×C4⋊C4—412no—
516C2×C4⋊C4—86no—
517C2×C4⋊C4C22×C4124yes—
518C2×C4⋊C4C2411yescharacteristic
519C2×C4⋊C4C2411yescharacteristic
520C2×C4⋊C4C2413yes—
521C2×C4⋊C4C2413yes—
522C2×C4⋊C4C2413yes—
523C2×C4⋊C4C2416yes—
524C2×C4⋊C4C2416yes—
525C2×C4⋊C4C2411yescharacteristic
526C2×C4⋊C4C2413yes—
527C2×C4⋊C4C2411yescharacteristic
528C2×C4⋊C4C2416yes—
529C2×C4⋊C4C2416yes—
530C2×C4⋊C4C2416yes—
531C2×C4⋊C4C2416yes—
532C2×C4⋊C4C2416yes—
533C2×C4⋊C4C2416yes—
534C2×C4⋊C4C24112yes—
535C2×C4⋊C4C2416yes—
536C2×C4⋊C4C2416yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2416yes—
539C2×C4⋊C4C2416yes—
540C2×C4⋊C4C2416yes—
541C2×C4⋊C4C2416yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2416yes—
544C2×C4⋊C4C2416yes—
545C2×C4⋊C4C2413yes—
546C2×C4⋊C4C2413yes—
547C2×C4⋊C4C2416yes—
548C2×C4⋊C4C2411yescharacteristic
549C2×C4⋊C4C2411yescharacteristic
550C2×C4⋊C4C2413yes—
551C2×C4⋊C4C2413yes—
552C2×C4⋊C4C2413yes—
553C2×C4⋊C4C2413yes—
554C2×C4⋊C4C2413yes—
555C2×C4⋊C4C2413yes—
556C2×C4⋊C4C2416yes—
557C2×C22⋊C4C2416yes—
558C2×C22⋊C4C2412yes—
559C2×C22⋊C4C2416yes—
560C2×C22⋊C4C2416yes—
561C2×C22⋊C4C24112yes—
562C2×C22⋊C4C2416yes—
563C2×C22⋊C4C24112yes—
564C2×C22⋊C4C24112yes—
565C2×C22⋊C4C2416yes—
566C2×C22⋊C4C2416yes—
567C2×C22⋊C4C2416yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2416yes—
570C2×C22⋊C4C2411yescharacteristic
571C2×C22⋊C4C2411yescharacteristic
572C2×C22⋊C4C2413yes—
573C2×C22⋊C4C2413yes—
574C2×C22⋊C4C2416yes—
575C2×C22⋊C4C2416yes—
576C2×C22⋊C4C2413yes—
577C2×C22⋊C4C2413yes—
578C2×C22⋊C4C2416yes—
579C2×C22⋊C4C2416yes—
580C2×C42—412no—
581C2×C42C22×C4124yes—
582C2×C42C22×C4124yes—
583C2×C42C22×C4124yes—
584C2×C42C2416yes—
585C2×C42C2416yes—
586C2×C42C2416yes—
587C2×C42C2416yes—
588C2×C42C2416yes—
589C2×C42C2416yes—
590C2×C42C24112yes—
591C2×C42C24112yes—
592C2×C42C2416yes—
593C2×C42C2416yes—
594C2×C42C24112yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2411yescharacteristic
598C2×C42C2411yescharacteristic
599C2×C42C2413yes—
600C2×C42C2413yes—
601C2×C42C2413yes—
602C2×C42C2413yes—
603C2×C42C2413yes—
604C2×C42C2413yes—
605C2×C42C2413yes—
606C2×C42C2413yes—
607#95C2412yes—
608#95C2416yes—
609#95C2416yes—
610#95C2416yes—
611#95C2412yes—
612#95C2412yes—
613#95C2412yes—
614#95C2416yes—
615#95C2416yes—
616#95C2416yes—
617#95C2416yes—
618#95C2416yes—
619#95C2416yes—
620#95C2416yes—
621#95C2416yes—
622#95C2416yes—
623#95C2412yes—
624#95C2416yes—
625#95C2416yes—
626#95C2416yes—
627#95C2416yes—
628#95C24112yes—
629#95C24112yes—
630#95C24112yes—
631#95C2416yes—
632#95C2412yes—
633#95C2416yes—
634#95C24112yes—
635C24C2511yescharacteristic
636C24C2513yes—
637C24C2513yes—
638#41—232no—
639#41—232no—
640#41—448no—
641C2×Q8—232no—
642C2×Q8—26no—
643C2×Q8—26no—
644C2×Q8—43no—
645C2×Q8—43no—
646C2×Q8C23×C4112yes—
647C2×Q8C23×C4112yes—
648C2×Q8C23×C414yes—
649C2×Q8H(5,𝔽2)14yes—
650C2×Q82−1+414yes—
651C2×D4—26no—
652C2×D4—26no—
653C2×D4—26no—
654C2×D4—26no—
655C2×D4—46no—
656C2×D4—46no—
657C2×D4—43no—
658C2×D4—43no—
659C2×D4—43no—
660C2×D4—43no—
661C2×D4—43no—
662C2×D4—43no—
663C2×D4C23×C4112yes—
664C2×D4C23×C4112yes—
665C2×D4C23×C4112yes—
666C2×D4C23×C4112yes—
667C2×D4C23×C4112yes—
668C2×D4C23×C4124yes—
669C22×C4—26no—
670C22×C4—26no—
671C22×C4—26no—
672C22×C4—26no—
673C22×C4—26no—
674C22×C4—26no—
675C22×C4—26no—
676C22×C4—26no—
677C22×C4—26no—
678C22×C4—26no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—43no—
682C22×C4—43no—
683C22×C4—43no—
684C22×C4—43no—
685C22×C4—43no—
686C22×C4—43no—
687C22×C4—46no—
688C22×C4—46no—
689C22×C4—46no—
690C22×C4—46no—
691C22×C4—46no—
692C22×C4—46no—
693C22×C4—412no—
694C22×C4—412no—
695C22×C4—412no—
696C22×C4C23×C414yes—
697C22×C4C23×C4112yes—
698C22×C4C23×C4112yes—
699C22×C4C23×C4112yes—
700C22×C4C23×C4112yes—
701C22×C4C23×C4112yes—
702C22×C4C23×C4112yes—
703C22×C4C23×C4112yes—
704C22×C4C23×C4112yes—
705C22×C4C2512yes—
706C22×C4C2512yes—
707C22×C4C2516yes—
708C22×C4C2516yes—
709C22×C4C2512yes—
710C22×C4C2516yes—
711C22×C4C2512yes—
712C22×C4C2516yes—
713C22×C4C2511yescharacteristic
714C22×C4C2511yescharacteristic
715C22×C4C2511yescharacteristic
716C22×C4C2513yes—
717C22×C4C2513yes—
718C22×C4C2513yes—
719C22×C4C2513yes—
720C22×C4C2511yescharacteristic
721C22×C4C2513yes—
722C22×C4C2511yescharacteristic
723C22×C4C2513yes—
724C22×C4C2511yescharacteristic
725C4⋊C4—212no—
726C4⋊C4—212no—
727C4⋊C4—212no—
728C4⋊C4—212no—
729C4⋊C4—22no—
730C4⋊C4—22no—
731C4⋊C4—26no—
732C4⋊C4—26no—
733C4⋊C4—26no—
734C4⋊C4—22no—
735C4⋊C4—26no—
736C4⋊C4—22no—
737C4⋊C4—46no—
738C4⋊C4—46no—
739C4⋊C4—46no—
740C4⋊C4—412no—
741C4⋊C4—46no—
742C4⋊C4—46no—
743C4⋊C4—46no—
744C4⋊C4—42no—
745C4⋊C4—46no—
746C4⋊C4—46no—
747C4⋊C4—42no—
748C4⋊C4—46no—
749C4⋊C4—46no—
750C4⋊C4—46no—
751C4⋊C4—46no—
752C4⋊C4C23×C4112yes—
753C4⋊C4C23×C4112yes—
754C4⋊C4C23×C4124yes—
755C4⋊C4C23×C414yes—
756C4⋊C4C23×C414yes—
757C4⋊C4C23×C4112yes—
758C4⋊C4C23×C4112yes—
759C4⋊C4C23×C4112yes—
760C4⋊C4C23×C4112yes—
761C4⋊C4C23×C4112yes—
762C4⋊C4C23×C4112yes—
763C4⋊C4C23×C4124yes—
764C22⋊C4—46no—
765C22⋊C4—42no—
766C22⋊C4—46no—
767C22⋊C4—412no—
768C22⋊C4—46no—
769C22⋊C4—42no—
770C22⋊C4—46no—
771C22⋊C4—46no—
772C22⋊C4—46no—
773C22⋊C4—412no—
774C22⋊C4—46no—
775C22⋊C4—412no—
776C22⋊C4—46no—
777C22⋊C4C23×C414yes—
778C22⋊C4C23×C414yes—
779C22⋊C4C23×C4112yes—
780C22⋊C4C23×C4112yes—
781C22⋊C4C23×C4124yes—
782C22⋊C4C23×C4124yes—
783C22⋊C4C23×C4112yes—
784C22⋊C4C23×C4112yes—
785C22⋊C4C23×C4124yes—
786C22⋊C4C23×C4124yes—
787C42—212no—
788C42—212no—
789C42—212no—
790C42—212no—
791C42—42no—
792C42—46no—
793C42—42no—
794C42—412no—
795C42—46no—
796C42—46no—
797C42—412no—
798C42—46no—
799C42—412no—
800C42C23×C414yes—
801C42C23×C414yes—
802C42C23×C4112yes—
803C42C23×C4112yes—
804C42C23×C4112yes—
805C42C23×C4112yes—
806C42C23×C4112yes—
807C42C23×C4112yes—
808C42C23×C4112yes—
809C42C23×C4112yes—
810C23—21no—
811C23—23no—
812C23—23no—
813C23—21no—
814C23—23no—
815C23—23no—
816C23—23no—
817C23—23no—
818C23—23no—
819C23—23no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—23no—
824C23—23no—
825C23—21no—
826C23—23no—
827C23—23no—
828C23C24×C416yes—
829C23C24×C416yes—
830C23C24×C412yes—
831C23C2611yescharacteristic
832Q8—224no—
833Q8—412no—
834Q8#520116yes—
835D4—224no—
836D4—224no—
837D4—424no—
838D4—412no—
839D4—412no—
840D4—412no—
841C2×C4—21no—
842C2×C4—23no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—23no—
847C2×C4—23no—
848C2×C4—23no—
849C2×C4—23no—
850C2×C4—23no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—23no—
855C2×C4—21no—
856C2×C4—23no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—23no—
860C2×C4—23no—
861C2×C4—224no—
862C2×C4—224no—
863C2×C4—224no—
864C2×C4—224no—
865C2×C4—224no—
866C2×C4—28no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—26no—
871C2×C4—26no—
872C2×C4—26no—
873C2×C4—22no—
874C2×C4—26no—
875C2×C4—22no—
876C2×C4—26no—
877C2×C4—22no—
878C2×C4—26no—
879C2×C4—26no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—26no—
883C2×C4—26no—
884C2×C4—26no—
885C2×C4—26no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—26no—
890C2×C4—22no—
891C2×C4—412no—
892C2×C4—412no—
893C2×C4—412no—
894C2×C4—812no—
895C2×C4—812no—
896C2×C4—1612no—
897C2×C4C24×C412yes—
898C2×C4C24×C412yes—
899C2×C4C24×C412yes—
900C2×C4C24×C412yes—
901C2×C4C24×C412yes—
902C2×C4C24×C416yes—
903C2×C4C24×C416yes—
904C2×C4C24×C416yes—
905C2×C4C24×C416yes—
906C2×C4C24×C416yes—
907C2×C4C24×C416yes—
908C2×C4C24×C412yes—
909C2×C4C2×H(5,𝔽2)16yes—
910C2×C4C2×2−1+416yes—
911C2×C4#58512yes—
912C2×C4#58512yes—
913C22—22no—
914C22—26no—
915C22—26no—
916C22—22no—
917C22—26no—
918C22—26no—
919C22—22no—
920C22—26no—
921C22—26no—
922C22—43no—
923C22—41no—
924C22—43no—
925C22—43no—
926C22—43no—
927C22—41no—
928C22—41no—
929C22—43no—
930C22—43no—
931C22—41no—
932C22—43no—
933C22—43no—
934C22C25×C411yescharacteristic
935C22C22×H(5,𝔽2)11yescharacteristic
936C22C22×2−1+411yescharacteristic
937C22C2×#58511yescharacteristic
938C22C2×#58511yescharacteristic
939C22H(7,𝔽2)11yescharacteristic
940C222−1+611yescharacteristic
941C4—22no—
942C4—22no—
943C4—26no—
944C4—22no—
945C4—26no—
946C4—26no—
947C4—22no—
948C4—22no—
949C4—26no—
950C4—26no—
951C4—42no—
952C4—46no—
953C4—42no—
954C4—42no—
955C4—46no—
956C4—46no—
957C4—46no—
958C4—42no—
959C4C2×#520112yes—
960C4#342814yes—
961C2—42no—
962C2—46no—
963C2—46no—
964C2C22×#52011yescharacteristic
965C2C2×#342811yescharacteristic
966C2#6265411yescharacteristic
967C2#6292211yescharacteristic
968C2#6292311yescharacteristic
969C2#6295211yescharacteristic
970C2#6295311yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3480C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34500C2semidirect
3. #34483C2semidirect
4. #34466C2semidirect
5. #34463C2semidirect
6. #34384C2semidirect
7. #34383C2semidirect
8. #34368C2semidirect
9. #34367C2semidirect
10. #34336C2semidirect
11. #34312C2semidirect
12. #34295C2semidirect
13. #34293C2semidirect
14. #34243C2semidirect
15. #34242C2semidirect
16. #34196C2semidirect
17. #34193C2semidirect
18. #34188C2semidirect
19. #34183C2semidirect
20. #34182C2semidirect
21. #34129C2semidirect
22. C4⋊C4×#41C2semidirect
23. #34060C2semidirect
24. #3480C4semidirect
163. #559C2×C4semidirect
164. #557C2×C4semidirect
165. #556C2×C4semidirect
166. #553C2×C4semidirect
167. #553C2×C4semidirect
169. #548C2×C4semidirect
170. #548C2×C4semidirect
171. #532C2×C4semidirect
174. #529C2×C4semidirect
175. #529C2×C4semidirect
195. C4×#41C2×C4semidirect
196. C4×#41C2×C4semidirect
197. C4×#41C2×C4semidirect
198. C2×C4×Q8C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#34802
#345002
#344832
#344662
#344632
#343842
#343832
#343682
#343672
#343362
#343122
#342952
#342932
#342432
#342422
#341962
#341932
#341882
#341832
#341822
#341292
C4⋊C4×#412
#340602