Finite Group Databasebeta

← #7626919

Subgroups — #7626919

Order 512.

7142 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C211yesmaximal, characteristic
2#34498C213yesmaximal, complemented
3#34484C213yesmaximal, complemented
4#34480C216yesmaximal, complemented
5#34460C216yesmaximal, complemented
6#34428C216yesmaximal, complemented
7#34419C216yesmaximal, complemented
8#34383C213yesmaximal, complemented
9#34368C213yesmaximal, complemented
10#34335C211yesmaximal, characteristic, complemented
11#34332C213yesmaximal, complemented
12#34331C213yesmaximal, complemented
13#34313C211yesmaximal, characteristic, complemented
14#34312C212yesmaximal, complemented
15#34293C212yesmaximal, complemented
16#34263C212yesmaximal, complemented
17#34250C212yesmaximal, complemented
18#34226C213yesmaximal, complemented
19#34182C211yesmaximal, characteristic, complemented
20C4×Q82C211yesmaximal, characteristic, complemented
21C4×#550C211yesmaximal, characteristic, complemented
22Q8×#117C211yesmaximal, characteristic, complemented
23#34084C213yesmaximal, complemented
24#3522C4132yescomplemented
25C2×#559C2213yes—
26C2×Q82C2211yescharacteristic
27C2×#554C2213yes—
28C2×#550C2211yescharacteristic
29C2×#548C2212yes—
30C2×#547C2216yes—
31C2×#542C2216yes—
32C2×#532C2213yes—
33C2×#529C2213yes—
34C2×#520C2212yes—
35C2×#520C2212yes—
36C2×#519C2212yes—
37C2×C4×#41C2212yes—
38C22×C4×Q8C2211yescharacteristic
39#2379C22112yes—
40#2378C22112yes—
41#2376C22112yes—
42#2376C22112yes—
43#2370C2216yes—
44#2369C2213yes—
45#2369C2213yes—
46#2369C2216yes—
47#2367C2216yes—
48#2367C2216yes—
49#2367C2216yes—
50#2367C2216yes—
51#2367C2216yes—
52#2366C2213yes—
53#2366C2213yes—
54#2365C2216yes—
55#2363C2216yes—
56#2363C2216yes—
57#2363C2216yes—
58#2362C2216yes—
59#2361C2216yes—
60#2360C2216yes—
61#2360C22112yes—
62#2359C22112yes—
63#2357C2216yes—
64#2355C2213yes—
65#2355C2213yes—
66#2355C2213yes—
67#2354C2216yes—
68#2354C2216yes—
69#2354C2213yes—
70#2354C2216yes—
71#2352C2216yes—
72#2351C2212yes—
73#2351C2216yes—
74#2351C2212yes—
75Q8×C4⋊C4C2211yescharacteristic
76Q8×C4⋊C4C2213yes—
77Q8×C4⋊C4C2213yes—
78Q8×C4⋊C4C2211yescharacteristic
79Q8×C4⋊C4C2211yescharacteristic
80Q8×C4⋊C4C2211yescharacteristic
81Q8×C4⋊C4C2213yes—
82Q8×C4⋊C4C2212yes—
83#2349C2216yes—
84#2349C2216yes—
85D4×C4⋊C4C2213yes—
86D4×C4⋊C4C2216yes—
87D4×C4⋊C4C2216yes—
88D4×C4⋊C4C2216yes—
89#2345C2216yes—
90#2345C2213yes—
91#2345C2213yes—
92#2344C2216yes—
93#2341C2212yes—
94#2341C2212yes—
95#2341C2216yes—
96Q8×C22⋊C4C2211yescharacteristic
97Q8×C22⋊C4C2211yescharacteristic
98#2339C2216yes—
99#2335C22112yes—
100#2335C2216yes—
101#2335C2216yes—
102#2334C2216yes—
103#2334C2216yes—
104#2334C22112yes—
105#2331C2216yes—
106#2330C2213yes—
107#2330C2213yes—
108#2329C22112yes—
109#2326C2213yes—
110#2326C2213yes—
111#2326C2216yes—
112#2324C2216yes—
113#2324C2216yes—
114#2324C2213yes—
115#2324C2213yes—
116#2324C2216yes—
117#2324C2216yes—
118#2323C2216yes—
119#2323C2211yescharacteristic
120#2323C2213yes—
121#2323C22112yes—
122#2322C22112yes—
123#2319C2216yes—
124#2319C2216yes—
125#2317C2216yes—
126#2316C2216yes—
127#2316C2216yes—
128#2314C2216yes—
129#2311C22112yes—
130C4×C4⋊Q8C2213yes—
131C4×C4⋊Q8C2213yes—
132C4×C4⋊Q8C2216yes—
133C4×#127C2213yes—
134C4×#127C2213yes—
135C4×#124C2216yes—
136C4×C22⋊Q8C2216yes—
137C4×#121C2216yes—
138#2298C2216yes—
139#2296C2216yes—
140#2295C2213yes—
141#2295C2213yes—
142#2295C2213yes—
143#2293C2216yes—
144#2293C2213yes—
145#2293C2216yes—
146C2×#389C2216yes—
147#2290C2216yes—
148#2285C2213yes—
149#2285C2213yes—
150#2285C2213yes—
151#2276C2212yes—
152#2275C2216yes—
153C42×Q8C2212yes—
154C42×Q8C2211yescharacteristic
155C42×Q8C2213yes—
156C42×Q8C2211yescharacteristic
157C42×D4C2213yes—
158C4×#117C2213yes—
159C22×#41C2312yes—
160C22×#41C2316yes—
161C23×Q8C2311yescharacteristic
162#559C2×C4148yescomplemented
163Q82C2×C4116yescomplemented
164#554C2×C4148yescomplemented
165#550C2×C4116yes—
166#548C2×C4132yescomplemented
167#547C2×C4196yescomplemented
168#542C2×C4196yescomplemented
169#532C2×C4148yescomplemented
170C2×C4⋊Q8C2313yes—
171C2×C4⋊Q8C2316yes—
172C2×#127C2313yes—
173#529C2×C4148yescomplemented
174C2×#126C2316yes—
175C2×#125C2313yes—
176C2×#124C2313yes—
177C2×#124C2316yes—
178C2×#124C2316yes—
179C2×#123C23112yes—
180C2×#123C2316yes—
181C2×C22⋊Q8C2311yescharacteristic
182C2×C22⋊Q8C23112yes—
183C2×C22⋊Q8C2316yes—
184C2×#121C2313yes—
185C2×#121C2316yes—
186C2×#121C2316yes—
187#520—48no—
188#520C2×C4132yescomplemented
189#519—48no—
190C4×#41—48no—
191C2×C4×Q8C2×C4116yescomplemented
192C2×C4×Q8C2311yescharacteristic
193C2×C4×Q8C2311yescharacteristic
194C2×C4×Q8C2311yescharacteristic
195C2×C4×Q8C2311yescharacteristic
196C2×C4×Q8C2311yescharacteristic
197C2×C4×Q8C2312yes—
198C2×C4×Q8C2312yes—
199C2×C4×Q8C2313yes—
200C2×C4×Q8C2316yes—
201C2×C4×Q8C2316yes—
202C2×C4×Q8C2316yes—
203C2×C4×Q8C2316yes—
204C2×C4×Q8C2311yescharacteristic
205C2×C4×Q8C2311yescharacteristic
206C2×C4×Q8C2313yes—
207C2×C4×Q8C2312yes—
208C2×C4×Q8C2313yes—
209C2×C4×Q8C2313yes—
210C2×C4×D4C2313yes—
211C2×C4×D4C2316yes—
212C2×C4×D4C2316yes—
213C2×C4×D4C2316yes—
214C2×C4×D4C2316yes—
215C2×C4×D4C2313yes—
216C2×C4×D4C2316yes—
217C2×C4×D4C2316yes—
218C2×C4×D4C2316yes—
219C2×C4×D4C2316yes—
220C2×C4×D4C2316yes—
221C2×C4×D4C2316yes—
222C2×C4×D4C2313yes—
223C2×C4×D4C2316yes—
224C2×#117C2311yescharacteristic
225C2×#117C2316yes—
226C2×#117C2316yes—
227C2×#117C2316yes—
228C2×#117C2316yes—
229C2×#117C2313yes—
230C2×#117C23112yes—
231C2×#117C2316yes—
232C22×C4⋊C4C2316yes—
233C22×C4⋊C4C23112yes—
234C22×C4⋊C4C2313yes—
235C22×C4⋊C4C2316yes—
236C22×C42C2316yes—
237C22×C42C2313yes—
238#391C23112yes—
239#391C2316yes—
240#391C2316yes—
241#391C23112yes—
242#391C2313yes—
243#391C2311yescharacteristic
244#391C2313yes—
245#391C2313yes—
246#391C2313yes—
247#391C2313yes—
248#390C2313yes—
249#390C2316yes—
250#390C2316yes—
251#390C2316yes—
252#390C2316yes—
253#390C2316yes—
254#390C2316yes—
255#390C23112yes—
256#390C2316yes—
257#390C2316yes—
258#390C2313yes—
259#390C2316yes—
260#389C2313yes—
261#389C2316yes—
262#389C2316yes—
263#389C2316yes—
264#389C2316yes—
265#389C23112yes—
266#389C2316yes—
267#389C2316yes—
268#389C2316yes—
269#389C2313yes—
270#389C23112yes—
271#389C2316yes—
272#389C23112yes—
273#389C23112yes—
274#389C2316yes—
275#389C2316yes—
276#389C2313yes—
277#389C2316yes—
278#389C2311yescharacteristic
279#389C2313yes—
280#389C2312yes—
281#389C2313yes—
282#389C2316yes—
283#389C2316yes—
284#389C2316yes—
285#389C2313yes—
286#389C2313yes—
287#388C23112yes—
288#388C23112yes—
289#388C2316yes—
290#388C23112yes—
291#388C23112yes—
292#388C2316yes—
293#388C23112yes—
294#388C23112yes—
295#388C23112yes—
296#388C2312yes—
297#388C2312yes—
298#388C2316yes—
299#388C2316yes—
300#388C2316yes—
301#388C2316yes—
302#388C2316yes—
303#388C23112yes—
304#388C2316yes—
305#388C2316yes—
306#388C2316yes—
307#387C2316yes—
308#387C23112yes—
309#387C2316yes—
310#387C2316yes—
311#387C2316yes—
312#387C23112yes—
313#387C2312yes—
314#387C2316yes—
315#387C2316yes—
316#387C2316yes—
317#387C2316yes—
318#387C2316yes—
319#387C23112yes—
320#387C2316yes—
321#387C2316yes—
322#386C2316yes—
323#386C23112yes—
324#386C23112yes—
325#386C23112yes—
326#386C2316yes—
327#385C23112yes—
328#385C23112yes—
329#385C2316yes—
330#385C23112yes—
331#385C23112yes—
332#385C23112yes—
333#385C2316yes—
334#385C2316yes—
335#385C2316yes—
336#385C2316yes—
337#385C2316yes—
338#384C2313yes—
339#384C2313yes—
340#384C2316yes—
341#384C2313yes—
342#384C2313yes—
343#384C2313yes—
344#384C2313yes—
345#382C2316yes—
346#382C2316yes—
347#382C2316yes—
348#382C2316yes—
349#381C23112yes—
350#380C2316yes—
351#380C2316yes—
352#380C23112yes—
353#380C23112yes—
354#380C2316yes—
355#380C2316yes—
356#380C2316yes—
357#380C23112yes—
358#380C2311yescharacteristic
359#380C2313yes—
360#380C2313yes—
361#380C2313yes—
362C4×C4⋊C4C2313yes—
363C4×C4⋊C4C2316yes—
364C4×C4⋊C4C2313yes—
365C4×C4⋊C4C2316yes—
366C4×C4⋊C4C2316yes—
367C4×C4⋊C4C2316yes—
368C4×C4⋊C4C2316yes—
369C4×C4⋊C4C2316yes—
370C4×C4⋊C4C2316yes—
371C4×C4⋊C4C2316yes—
372C4×C4⋊C4C2311yescharacteristic
373C4×C4⋊C4C2313yes—
374C4×C4⋊C4C23112yes—
375C4×C4⋊C4C2313yes—
376C4×C4⋊C4C2313yes—
377C4×C4⋊C4C2316yes—
378C4×C4⋊C4C2313yes—
379C4×C4⋊C4C2316yes—
380C4×C4⋊C4C2313yes—
381C4×C4⋊C4C2313yes—
382C4×C4⋊C4C2316yes—
383C4×C4⋊C4C2313yes—
384C4×C4⋊C4C2316yes—
385C4×C4⋊C4C2316yes—
386C4×C4⋊C4C2316yes—
387C4×C4⋊C4C2313yes—
388C4×C4⋊C4C2313yes—
389C4×C4⋊C4C2316yes—
390C4×C4⋊C4C2313yes—
391C4×C4⋊C4C2313yes—
392C4×C4⋊C4C2313yes—
393C4×C4⋊C4C2313yes—
394C4×C22⋊C4C23112yes—
395C4×C22⋊C4C2316yes—
396C4×C22⋊C4C23112yes—
397C4×C22⋊C4C2316yes—
398C4×C22⋊C4C2313yes—
399C4×C22⋊C4C2313yes—
400C4×C22⋊C4C23112yes—
401C4×C22⋊C4C23112yes—
402C4×C22⋊C4C2313yes—
403C4×C22⋊C4C2313yes—
404C4×C22⋊C4C2316yes—
405C4×C22⋊C4C2316yes—
406#376C2313yes—
407#376C2316yes—
408#376C2313yes—
409C2×#95C23112yes—
410C43C2313yes—
411C43C2313yes—
412C43C2316yes—
413C2×#41—28no—
414C2×#41—28no—
415C2×#41—86no—
416C2×#41—86no—
417C2×#41C22×C4116yes—
418C2×#41C22×C4148yes—
419C22×Q8—24no—
420C22×Q8—24no—
421C22×Q8C22×C418yes—
422C22×Q8C2411yescharacteristic
423C22×Q8C2413yes—
424C22×Q8C2416yes—
425C22×Q8C2411yescharacteristic
426C22×D4C2413yes—
427C22×D4C2416yes—
428C22×D4C2416yes—
429C22×D4C2416yes—
430C23×C4C2416yes—
431C23×C4C2413yes—
432C23×C4C2411yescharacteristic
433C23×C4C2416yes—
434C23×C4C24112yes—
435C23×C4C2416yes—
436C23×C4C24112yes—
437C23×C4C2413yes—
438C4⋊Q8C22×C4124yes—
439C4⋊Q8C22×C4148yes—
440#127C22×C4124yes—
441#126C22×C4148yes—
442#125C22×C4124yes—
443#124C22×C4124yes—
444#124C22×C4148yes—
445#124C22×C4148yes—
446#123C22×C4148yes—
447#123C22×C4196yes—
448C22⋊Q8C22×C418yes—
449C22⋊Q8C22×C4196yes—
450C22⋊Q8C22×C4148yes—
451#121C22×C4124yes—
452#121C22×C4148yes—
453#121C22×C4148yes—
454C4×Q8—24no—
455C4×Q8—28no—
456C4×Q8—28no—
457C4×Q8—24no—
458C4×Q8—24no—
459C4×Q8—24no—
460C4×Q8—24no—
461C4×Q8—46no—
462C4×Q8—412no—
463C4×Q8—412no—
464C4×Q8—86no—
465C4×Q8—86no—
466C4×Q8C22×C418yes—
467C4×Q8C22×C4124yes—
468C4×Q8C22×C418yes—
469C4×Q8C22×C4124yes—
470C4×Q8C22×C4116yes—
471C4×Q8C22×C4124yes—
472C4×D4—212no—
473C4×D4—412no—
474C4×D4—46no—
475C4×D4—412no—
476C4×D4—412no—
477C4×D4—412no—
478C4×D4—412no—
479C4×D4—86no—
480C4×D4—86no—
481C4×D4C22×C4148yes—
482C4×D4C22×C4148yes—
483C4×D4C22×C4148yes—
484C4×D4C22×C4124yes—
485C4×D4C22×C4148yes—
486#117—24no—
487#117—46no—
488#117—412no—
489#117—412no—
490#117—412no—
491#117—412no—
492#117—812no—
493#117C22×C4148yes—
494C2×C4⋊C4—412no—
495C2×C4⋊C4—812no—
496C2×C4⋊C4C22×C4124yes—
497C2×C4⋊C4C22×C4148yes—
498C2×C4⋊C4C2413yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C2413yes—
501C2×C4⋊C4C2416yes—
502C2×C4⋊C4C2411yescharacteristic
503C2×C4⋊C4C2411yescharacteristic
504C2×C4⋊C4C2411yescharacteristic
505C2×C4⋊C4C2413yes—
506C2×C4⋊C4C2413yes—
507C2×C4⋊C4C2413yes—
508C2×C4⋊C4C2413yes—
509C2×C4⋊C4C2411yescharacteristic
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2416yes—
512C2×C4⋊C4C2416yes—
513C2×C4⋊C4C2416yes—
514C2×C4⋊C4C2416yes—
515C2×C4⋊C4C24112yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2416yes—
518C2×C4⋊C4C2416yes—
519C2×C4⋊C4C2416yes—
520C2×C4⋊C4C2416yes—
521C2×C4⋊C4C2413yes—
522C2×C4⋊C4C2413yes—
523C2×C4⋊C4C2416yes—
524C2×C4⋊C4C2416yes—
525C2×C4⋊C4C2416yes—
526C2×C4⋊C4C2416yes—
527C2×C4⋊C4C2413yes—
528C2×C4⋊C4C2416yes—
529C2×C4⋊C4C2416yes—
530C2×C4⋊C4C2413yes—
531C2×C4⋊C4C2416yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2411yescharacteristic
534C2×C4⋊C4C2413yes—
535C2×C4⋊C4C2416yes—
536C2×C4⋊C4C2416yes—
537C2×C22⋊C4C2411yescharacteristic
538C2×C22⋊C4C2411yescharacteristic
539C2×C22⋊C4C2416yes—
540C2×C22⋊C4C2416yes—
541C2×C22⋊C4C2412yes—
542C2×C22⋊C4C2416yes—
543C2×C22⋊C4C2416yes—
544C2×C22⋊C4C24112yes—
545C2×C22⋊C4C2416yes—
546C2×C22⋊C4C24112yes—
547C2×C22⋊C4C2413yes—
548C2×C22⋊C4C2413yes—
549C2×C22⋊C4C2416yes—
550C2×C22⋊C4C2416yes—
551C2×C22⋊C4C24112yes—
552C2×C22⋊C4C2416yes—
553C2×C22⋊C4C2416yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2416yes—
556C2×C22⋊C4C24112yes—
557C2×C22⋊C4C2416yes—
558C2×C42—412no—
559C2×C42C22×C4124yes—
560C2×C42C2413yes—
561C2×C42C2416yes—
562C2×C42C2413yes—
563C2×C42C2416yes—
564C2×C42C2413yes—
565C2×C42C2411yescharacteristic
566C2×C42C2413yes—
567C2×C42C2413yes—
568C2×C42C2412yes—
569C2×C42C2413yes—
570C2×C42C2416yes—
571C2×C42C2416yes—
572C2×C42C24112yes—
573C2×C42C24112yes—
574C2×C42C2413yes—
575C2×C42C2413yes—
576C2×C42C2416yes—
577C2×C42C2413yes—
578C2×C42C2413yes—
579C2×C42C2416yes—
580C2×C42C2412yes—
581C2×C42C2413yes—
582C2×C42C2416yes—
583C2×C42C2413yes—
584C2×C42C2413yes—
585C2×C42C2413yes—
586C2×C42C2411yescharacteristic
587#95C2413yes—
588#95C2416yes—
589#95C24112yes—
590#95C24112yes—
591#95C2412yes—
592#95C2413yes—
593#95C2413yes—
594#95C2413yes—
595#95C2413yes—
596#95C2413yes—
597#95C2413yes—
598#95C2413yes—
599#95C2416yes—
600#95C2416yes—
601#95C2416yes—
602#95C2412yes—
603#95C2412yes—
604#95C2416yes—
605#95C2416yes—
606#95C2416yes—
607#95C2416yes—
608#95C2416yes—
609#95C2416yes—
610#95C24112yes—
611#95C2416yes—
612#95C2412yes—
613#95C2416yes—
614#95C2416yes—
615#95C2416yes—
616#95C2416yes—
617#95C2412yes—
618C24C2511yescharacteristic
619C24C2516yes—
620#41—264no—
621#41—848no—
622C2×Q8—232no—
623C2×Q8—26no—
624C2×Q8—22no—
625C2×Q8—26no—
626C2×Q8—22no—
627C2×Q8—46no—
628C2×Q8—46no—
629C2×Q8C23×C414yes—
630C2×Q8C23×C4112yes—
631C2×Q8C23×C4124yes—
632C2×Q8C23×C414yes—
633C2×Q8H(5,𝔽2)14yes—
634C2×Q82−1+414yes—
635C2×D4—212no—
636C2×D4—26no—
637C2×D4—212no—
638C2×D4—26no—
639C2×D4—46no—
640C2×D4—46no—
641C2×D4—46no—
642C2×D4—46no—
643C2×D4C23×C4112yes—
644C2×D4C23×C4124yes—
645C2×D4C23×C4124yes—
646C2×D4C23×C4124yes—
647C22×C4—212no—
648C22×C4—26no—
649C22×C4—22no—
650C22×C4—26no—
651C22×C4—212no—
652C22×C4—22no—
653C22×C4—212no—
654C22×C4—412no—
655C22×C4—412no—
656C22×C4—43no—
657C22×C4—43no—
658C22×C4—46no—
659C22×C4—46no—
660C22×C4—46no—
661C22×C4—46no—
662C22×C4—46no—
663C22×C4—412no—
664C22×C4—412no—
665C22×C4—412no—
666C22×C4C23×C414yes—
667C22×C4C23×C4112yes—
668C22×C4C23×C4124yes—
669C22×C4C23×C4112yes—
670C22×C4C23×C4148yes—
671C22×C4C2511yescharacteristic
672C22×C4C2513yes—
673C22×C4C2513yes—
674C22×C4C2513yes—
675C22×C4C2516yes—
676C22×C4C2512yes—
677C22×C4C2511yescharacteristic
678C22×C4C2512yes—
679C22×C4C2513yes—
680C22×C4C2516yes—
681C22×C4C2512yes—
682C22×C4C2511yescharacteristic
683C22×C4C2513yes—
684C22×C4C2513yes—
685C22×C4C2516yes—
686C22×C4C2512yes—
687C22×C4C2513yes—
688C22×C4C2511yescharacteristic
689C22×C4C2511yescharacteristic
690C22×C4C2513yes—
691C22×C4C2511yescharacteristic
692C4⋊C4—26no—
693C4⋊C4—212no—
694C4⋊C4—26no—
695C4⋊C4—212no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—26no—
699C4⋊C4—24no—
700C4⋊C4—26no—
701C4⋊C4—26no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—26no—
705C4⋊C4—46no—
706C4⋊C4—46no—
707C4⋊C4—46no—
708C4⋊C4—46no—
709C4⋊C4—412no—
710C4⋊C4—43no—
711C4⋊C4—43no—
712C4⋊C4—42no—
713C4⋊C4—46no—
714C4⋊C4—46no—
715C4⋊C4—46no—
716C4⋊C4—46no—
717C4⋊C4—46no—
718C4⋊C4—46no—
719C4⋊C4—46no—
720C4⋊C4—46no—
721C4⋊C4C23×C4112yes—
722C4⋊C4C23×C4124yes—
723C4⋊C4C23×C4124yes—
724C4⋊C4C23×C4112yes—
725C4⋊C4C23×C4124yes—
726C4⋊C4C23×C418yes—
727C4⋊C4C23×C414yes—
728C4⋊C4C23×C4112yes—
729C4⋊C4C23×C4124yes—
730C4⋊C4C23×C4124yes—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—212no—
734C22⋊C4—43no—
735C22⋊C4—43no—
736C22⋊C4—42no—
737C22⋊C4—46no—
738C22⋊C4—46no—
739C22⋊C4—46no—
740C22⋊C4—412no—
741C22⋊C4—46no—
742C22⋊C4—412no—
743C22⋊C4—46no—
744C22⋊C4—412no—
745C22⋊C4—46no—
746C22⋊C4C23×C4124yes—
747C22⋊C4C23×C4124yes—
748C22⋊C4C23×C418yes—
749C22⋊C4C23×C4124yes—
750C22⋊C4C23×C4148yes—
751C22⋊C4C23×C4124yes—
752C42—26no—
753C42—212no—
754C42—26no—
755C42—212no—
756C42—22no—
757C42—26no—
758C42—24no—
759C42—26no—
760C42—26no—
761C42—26no—
762C42—42no—
763C42—46no—
764C42—412no—
765C42—46no—
766C42—412no—
767C42—43no—
768C42—43no—
769C42—46no—
770C42—43no—
771C42—46no—
772C42—43no—
773C42C23×C4112yes—
774C42C23×C4112yes—
775C42C23×C4112yes—
776C42C23×C4112yes—
777C42C23×C4124yes—
778C422−1+414yes—
779C23—21no—
780C23—26no—
781C23—21no—
782C23—26no—
783C23—21no—
784C23—26no—
785C23—21no—
786C23—26no—
787C23—26no—
788C23—26no—
789C23—21no—
790C23—21no—
791C23C24×C4112yes—
792C23C24×C412yes—
793C23C2611yescharacteristic
794Q8—224no—
795Q8—28no—
796Q8—424no—
797Q8#520116yes—
798D4—248no—
799D4—224no—
800D4—424no—
801D4—424no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—23no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—23no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—26no—
814C2×C4—21no—
815C2×C4—23no—
816C2×C4—23no—
817C2×C4—26no—
818C2×C4—23no—
819C2×C4—23no—
820C2×C4—224no—
821C2×C4—248no—
822C2×C4—28no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—26no—
827C2×C4—23no—
828C2×C4—26no—
829C2×C4—23no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—22no—
834C2×C4—23no—
835C2×C4—23no—
836C2×C4—26no—
837C2×C4—23no—
838C2×C4—23no—
839C2×C4—23no—
840C2×C4—23no—
841C2×C4—26no—
842C2×C4—22no—
843C2×C4—23no—
844C2×C4—21no—
845C2×C4—23no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—26no—
849C2×C4—26no—
850C2×C4—23no—
851C2×C4—23no—
852C2×C4—22no—
853C2×C4—448no—
854C2×C4—412no—
855C2×C4—812no—
856C2×C4—812no—
857C2×C4—1612no—
858C2×C4C24×C412yes—
859C2×C4C24×C414yes—
860C2×C4C24×C416yes—
861C2×C4C24×C416yes—
862C2×C4C24×C416yes—
863C2×C4C24×C4112yes—
864C2×C4C24×C414yes—
865C2×C4C24×C416yes—
866C2×C4C24×C412yes—
867C2×C4C2×H(5,𝔽2)16yes—
868C2×C4C2×2−1+412yes—
869C2×C4C2×2−1+412yes—
870C2×C4C2×2−1+416yes—
871C2×C4C2×2−1+412yes—
872C2×C4#58512yes—
873C22—22no—
874C22—212no—
875C22—22no—
876C22—212no—
877C22—22no—
878C22—212no—
879C22—46no—
880C22—41no—
881C22—46no—
882C22—41no—
883C22—41no—
884C22—46no—
885C22—41no—
886C22—46no—
887C22C25×C411yescharacteristic
888C22C22×H(5,𝔽2)11yescharacteristic
889C22C22×2−1+411yescharacteristic
890C22C22×2−1+411yescharacteristic
891C22C2×#58511yescharacteristic
892C22H(7,𝔽2)11yescharacteristic
893C22H(7,𝔽2)11yescharacteristic
894C4—24no—
895C4—26no—
896C4—22no—
897C4—24no—
898C4—26no—
899C4—212no—
900C4—26no—
901C4—22no—
902C4—22no—
903C4—41no—
904C4—42no—
905C4—46no—
906C4—43no—
907C4—42no—
908C4—46no—
909C4—43no—
910C4—41no—
911C4—43no—
912C4—43no—
913C4C2×#520112yes—
914C4C4×2−1+414yes—
915C2—42no—
916C2—412no—
917C2C22×#52011yescharacteristic
918C2C2×C4×2−1+411yescharacteristic
919C2#6265211yescharacteristic
920C2#6291711yescharacteristic
921C2#6292311yescharacteristic
922C2#6294311yescharacteristic
923C2#6295211yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3522C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34498C2semidirect
3. #34484C2semidirect
4. #34480C2semidirect
5. #34460C2semidirect
6. #34428C2semidirect
7. #34419C2semidirect
8. #34383C2semidirect
9. #34368C2semidirect
10. #34335C2semidirect
11. #34332C2semidirect
12. #34331C2semidirect
13. #34313C2semidirect
14. #34312C2semidirect
15. #34293C2semidirect
16. #34263C2semidirect
17. #34250C2semidirect
18. #34226C2semidirect
19. #34182C2semidirect
20. C4×Q82C2semidirect
21. C4×#550C2semidirect
22. Q8×#117C2semidirect
23. #34084C2semidirect
24. #3522C4semidirect
162. #559C2×C4semidirect
163. Q82C2×C4semidirect
164. #554C2×C4semidirect
166. #548C2×C4semidirect
167. #547C2×C4semidirect
168. #542C2×C4semidirect
169. #532C2×C4semidirect
173. #529C2×C4semidirect
188. #520C2×C4semidirect
191. 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×#35222
#344982
#344842
#344802
#344602
#344282
#344192
#343832
#343682
#343352
#343322
#343312
#343132
#343122
#342932
#342632
#342502
#342262
#341822
C4×Q822
C4×#5502
Q8×#1172
#340842