Finite Group Databasebeta

← C4×#3522 #7625659

Subgroups — C4×#3522 #7625659

Order 512.

7878 conjugacy classes of subgroups.

The subgroup lattice has 953 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C211yesmaximal, characteristic
2#34335C211yesmaximal, characteristic, complemented
3#34331C213yesmaximal, complemented
4#34317C213yesmaximal, complemented
5#34313C211yesmaximal, characteristic, complemented
6#34298C216yesmaximal, complemented
7#34294C212yesmaximal, complemented
8#34285C216yesmaximal, complemented
9#34263C212yesmaximal, complemented
10#34243C213yesmaximal, complemented
11#34236C213yesmaximal, complemented
12#34196C211yesmaximal, characteristic, complemented
13C4×Q82C211yesmaximal, characteristic, complemented
14C4×#559C213yesmaximal, complemented
15C4×#554C213yesmaximal, complemented
16C4×#550C211yesmaximal, characteristic, complemented
17C4×#547C216yesmaximal, complemented
18C4×#548C212yesmaximal, complemented
19C4×#542C216yesmaximal, complemented
20C4×#532C213yesmaximal, complemented
21C4×#529C213yesmaximal, complemented
22C4×#520C212yesmaximal, complemented
23C2×C42×Q8C211yesmaximal, characteristic, complemented
24#3522C4132yesdirect product factor
25C2×#559C2213yes—
26C2×Q82C2211yescharacteristic
27C2×#554C2213yes—
28C2×#550C2211yescharacteristic
29C2×#548C2212yes—
30C2×#547C2216yes—
31C2×#542C2216yes—
32C2×#532C2213yes—
33C2×#529C2213yes—
34C2×#520C2212yes—
35C2×#520C2212yes—
36C2×C4×#41C2212yes—
37C2×C4×#41C2216yes—
38C22×C4×Q8C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2374C22112yes—
42#2370C2216yes—
43#2369C2213yes—
44#2369C2213yes—
45#2369C2216yes—
46#2368C22112yes—
47#2367C2216yes—
48#2367C2216yes—
49#2367C2216yes—
50#2366C2213yes—
51#2366C2213yes—
52#2365C2216yes—
53#2363C2216yes—
54#2362C2216yes—
55#2362C22112yes—
56#2361C2216yes—
57#2361C2216yes—
58#2361C2216yes—
59#2360C2216yes—
60#2359C22112yes—
61#2359C22112yes—
62#2357C2216yes—
63#2357C2216yes—
64#2355C2213yes—
65#2355C2213yes—
66#2355C2213yes—
67#2354C2213yes—
68#2354C2216yes—
69#2352C2216yes—
70#2351C2212yes—
71Q8×C4⋊C4C2211yescharacteristic
72Q8×C4⋊C4C2213yes—
73Q8×C4⋊C4C2211yescharacteristic
74Q8×C4⋊C4C2212yes—
75#2349C2216yes—
76D4×C4⋊C4C2213yes—
77D4×C4⋊C4C2216yes—
78#2345C2216yes—
79#2344C2216yes—
80#2344C2216yes—
81#2341C2212yes—
82#2341C2212yes—
83Q8×C22⋊C4C2212yes—
84#2339C22112yes—
85#2337C22112yes—
86#2335C22112yes—
87#2334C22112yes—
88#2332C22112yes—
89#2331C2216yes—
90#2326C2216yes—
91#2324C2216yes—
92#2323C2216yes—
93#2320C2216yes—
94#2319C2216yes—
95#2314C2216yes—
96C4×C4⋊Q8C2213yes—
97C4×C4⋊Q8C2216yes—
98C4×C4⋊Q8C2213yes—
99C4×#127C2213yes—
100C4×#127C2213yes—
101C4×#125C2213yes—
102C4×#125C2213yes—
103C4×#126C2216yes—
104C4×#126C2216yes—
105C4×#124C2213yes—
106C4×#124C2216yes—
107C4×#124C2216yes—
108C4×#124C2213yes—
109C4×#124C2216yes—
110C4×C22⋊Q8C2216yes—
111C4×C22⋊Q8C22112yes—
112C4×C22⋊Q8C2213yes—
113C4×C22⋊Q8C2211yescharacteristic
114C4×#123C22112yes—
115C4×#123C2216yes—
116C4×#123C2216yes—
117C4×#121C2216yes—
118C4×#121C2216yes—
119C4×#121C2213yes—
120C4×#121C2216yes—
121C4×#121C2213yes—
122C4×#121C2216yes—
123#2298C2216yes—
124#2297C2216yes—
125#2295C2213yes—
126#2293C2213yes—
127#2293C2216yes—
128#2293C2216yes—
129#2290C2216yes—
130#2285C2213yes—
131#2283C2213yes—
132#2276C2212yes—
133#2276C2212yes—
134#2275C2216yes—
135#2275C2216yes—
136#2274C2216yes—
137#2274C2216yes—
138C42×Q8C2211yescharacteristic
139C42×Q8C2213yes—
140C42×Q8C2213yes—
141C42×Q8C2212yes—
142C42×Q8C2211yescharacteristic
143C42×Q8C2213yes—
144C42×Q8C2213yes—
145C42×Q8C2211yescharacteristic
146C42×Q8C2211yescharacteristic
147C42×Q8C2213yes—
148C42×D4C2216yes—
149C42×D4C2216yes—
150C42×D4C2216yes—
151C42×D4C2213yes—
152C42×D4C2216yes—
153C4×#117C2216yes—
154C2×C4×C4⋊C4C2213yes—
155C2×C4×C4⋊C4C2216yes—
156C2×C4×C4⋊C4C2213yes—
157C2×C4×C4⋊C4C2213yes—
158C2×C43C2213yes—
159C22×#41C2312yes—
160C22×#41C2316yes—
161C23×Q8C2311yescharacteristic
162#559C2×C4148yescomplemented
163Q82C2×C4116yescomplemented
164#554C2×C4148yescomplemented
165#550C2×C4116yescomplemented
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×#124C2316yes—
177C2×#124C2316yes—
178C2×#124C2313yes—
179C2×#123C23112yes—
180C2×#123C2316yes—
181C2×C22⋊Q8C2316yes—
182C2×C22⋊Q8C23112yes—
183C2×C22⋊Q8C2311yescharacteristic
184C2×#121C2316yes—
185C2×#121C2316yes—
186C2×#121C2313yes—
187#520—216no—
188#520C2×C4132yescomplemented
189C4×#41—216no—
190C4×#41—424no—
191C2×C4×Q8—28no—
192C2×C4×Q8—28no—
193C2×C4×Q8C2×C4116yescomplemented
194C2×C4×Q8C2313yes—
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2312yes—
197C2×C4×Q8C2311yescharacteristic
198C2×C4×Q8C2311yescharacteristic
199C2×C4×Q8C2313yes—
200C2×C4×Q8C2313yes—
201C2×C4×Q8C2313yes—
202C2×C4×Q8C2311yescharacteristic
203C2×C4×Q8C2316yes—
204C2×C4×Q8C2316yes—
205C2×C4×Q8C2313yes—
206C2×C4×Q8C2313yes—
207C2×C4×Q8C2311yescharacteristic
208C2×C4×Q8C2312yes—
209C2×C4×Q8C2313yes—
210C2×C4×Q8C2313yes—
211C2×C4×Q8C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×D4C2313yes—
215C2×C4×D4C2316yes—
216C2×C4×D4C2316yes—
217C2×C4×D4C2316yes—
218C2×C4×D4C2316yes—
219C2×C4×D4C2316yes—
220C2×C4×D4C2316yes—
221C2×C4×D4C2316yes—
222C2×C4×D4C2316yes—
223C2×C4×D4C2316yes—
224C2×C4×D4C23112yes—
225C2×C4×D4C2313yes—
226C2×C4×D4C2316yes—
227C2×C4×D4C2316yes—
228C2×C4×D4C2313yes—
229C2×C4×D4C2316yes—
230C2×C4×D4C2316yes—
231C2×#117C2316yes—
232C2×#117C2316yes—
233C2×#117C2316yes—
234C2×#117C23112yes—
235C2×#117C2316yes—
236C22×C4⋊C4C2316yes—
237C22×C4⋊C4C2313yes—
238C22×C4⋊C4C2313yes—
239C22×C4⋊C4C2313yes—
240C22×C4⋊C4C2316yes—
241C22×C42C2313yes—
242C22×C42C2313yes—
243C22×C42C2313yes—
244C22×C42C2316yes—
245C22×C42C2311yescharacteristic
246C22×C42C23112yes—
247C22×C42C2313yes—
248C22×C42C2313yes—
249C22×C42C2313yes—
250#391C2316yes—
251#391C23112yes—
252#391C2316yes—
253#391C2316yes—
254#391C2316yes—
255#391C23112yes—
256#391C2313yes—
257#391C2311yescharacteristic
258#390C2313yes—
259#390C2316yes—
260#390C2316yes—
261#390C2316yes—
262#390C2316yes—
263#390C2316yes—
264#390C2316yes—
265#390C2316yes—
266#390C2313yes—
267#389C2311yescharacteristic
268#389C2313yes—
269#389C2313yes—
270#389C2313yes—
271#389C2316yes—
272#389C2316yes—
273#389C23112yes—
274#389C2316yes—
275#389C2316yes—
276#389C2316yes—
277#389C2316yes—
278#389C2316yes—
279#389C23112yes—
280#388C2316yes—
281#388C2316yes—
282#388C2316yes—
283#388C2316yes—
284#388C2316yes—
285#388C2316yes—
286#388C23112yes—
287#388C23112yes—
288#388C23112yes—
289#388C23112yes—
290#388C23112yes—
291#388C23112yes—
292#388C23112yes—
293#388C2316yes—
294#388C2316yes—
295#388C23112yes—
296#387C2312yes—
297#387C2316yes—
298#387C2316yes—
299#387C2316yes—
300#387C2316yes—
301#387C2316yes—
302#387C2316yes—
303#387C2316yes—
304#387C23112yes—
305#387C23112yes—
306#387C23112yes—
307#387C23112yes—
308#387C23112yes—
309#386C23112yes—
310#386C23112yes—
311#386C2316yes—
312#386C23112yes—
313#386C2316yes—
314#385C23112yes—
315#385C23112yes—
316#385C23112yes—
317#385C23112yes—
318#385C2316yes—
319#385C2312yes—
320#384C2313yes—
321#384C2313yes—
322#384C2316yes—
323#383C2316yes—
324#382C2313yes—
325#382C2313yes—
326#382C2316yes—
327#382C2316yes—
328#381C23112yes—
329#381C2316yes—
330#380C2316yes—
331#380C2316yes—
332#380C23112yes—
333#380C2316yes—
334#380C2311yescharacteristic
335#380C2313yes—
336C4×C4⋊C4C2312yes—
337C4×C4⋊C4C2316yes—
338C4×C4⋊C4C2316yes—
339C4×C4⋊C4C2316yes—
340C4×C4⋊C4C2316yes—
341C4×C4⋊C4C2316yes—
342C4×C4⋊C4C2311yescharacteristic
343C4×C4⋊C4C2313yes—
344C4×C4⋊C4C2316yes—
345C4×C4⋊C4C2313yes—
346C4×C4⋊C4C2313yes—
347C4×C4⋊C4C2316yes—
348C4×C4⋊C4C2316yes—
349C4×C4⋊C4C2313yes—
350C4×C4⋊C4C2316yes—
351C4×C4⋊C4C2316yes—
352C4×C4⋊C4C2313yes—
353C4×C4⋊C4C2316yes—
354C4×C4⋊C4C2313yes—
355C4×C4⋊C4C2316yes—
356C4×C4⋊C4C2316yes—
357C4×C4⋊C4C2313yes—
358C4×C4⋊C4C2316yes—
359C4×C4⋊C4C2316yes—
360C4×C4⋊C4C2313yes—
361C4×C4⋊C4C2316yes—
362C4×C4⋊C4C2313yes—
363C4×C4⋊C4C2316yes—
364C4×C4⋊C4C2316yes—
365C4×C4⋊C4C2313yes—
366C4×C4⋊C4C2313yes—
367C4×C4⋊C4C2313yes—
368C4×C4⋊C4C2316yes—
369C4×C4⋊C4C2316yes—
370C4×C4⋊C4C2316yes—
371C4×C4⋊C4C2316yes—
372C4×C4⋊C4C23112yes—
373C4×C4⋊C4C2316yes—
374C4×C4⋊C4C2313yes—
375C4×C4⋊C4C2316yes—
376C4×C4⋊C4C2313yes—
377C4×C4⋊C4C2316yes—
378C4×C4⋊C4C2313yes—
379C4×C4⋊C4C2313yes—
380C4×C4⋊C4C2313yes—
381C4×C4⋊C4C2316yes—
382C4×C22⋊C4C2316yes—
383C4×C22⋊C4C2316yes—
384C4×C22⋊C4C2316yes—
385C4×C22⋊C4C2316yes—
386C4×C22⋊C4C2316yes—
387C4×C22⋊C4C2316yes—
388C4×C22⋊C4C23112yes—
389C4×C22⋊C4C23112yes—
390C4×C22⋊C4C2316yes—
391C4×C22⋊C4C23112yes—
392C4×C22⋊C4C2316yes—
393C4×C22⋊C4C2316yes—
394C4×C22⋊C4C2316yes—
395C4×C22⋊C4C23112yes—
396C4×C22⋊C4C2316yes—
397C4×C22⋊C4C23112yes—
398C4×C22⋊C4C23112yes—
399C4×C22⋊C4C2316yes—
400C4×C22⋊C4C2312yes—
401C4×C22⋊C4C23112yes—
402#376C2316yes—
403#376C2316yes—
404C2×#95C2316yes—
405C2×#95C23112yes—
406C43C2313yes—
407C43C2313yes—
408C43C2313yes—
409C43C2313yes—
410C43C2313yes—
411C43C2313yes—
412C43C2316yes—
413C43C2313yes—
414C43C2313yes—
415C2×#41—28no—
416C2×#41—28no—
417C2×#41—412no—
418C2×#41—412no—
419C2×#41C22×C4116yes—
420C2×#41C22×C4148yes—
421C22×Q8—24no—
422C22×Q8—24no—
423C22×Q8C22×C418yes—
424C22×Q8C2411yescharacteristic
425C22×Q8C2413yes—
426C22×Q8C2416yes—
427C22×Q8C2411yescharacteristic
428C22×D4C2413yes—
429C22×D4C2416yes—
430C22×D4C2416yes—
431C22×D4C2416yes—
432C23×C4C2411yescharacteristic
433C23×C4C2416yes—
434C23×C4C2413yes—
435C23×C4C2413yes—
436C23×C4C2413yes—
437C23×C4C2416yes—
438C23×C4C2413yes—
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C24112yes—
442C23×C4C2416yes—
443C23×C4C24112yes—
444C4⋊Q8C22×C4124yes—
445C4⋊Q8C22×C4148yes—
446#127C22×C4124yes—
447#126C22×C4148yes—
448#125C22×C4124yes—
449#124C22×C4124yes—
450#124C22×C4148yes—
451#124C22×C4148yes—
452#123C22×C4148yes—
453#123C22×C4196yes—
454C22⋊Q8C22×C418yes—
455C22⋊Q8C22×C4196yes—
456C22⋊Q8C22×C4148yes—
457#121C22×C4124yes—
458#121C22×C4148yes—
459#121C22×C4148yes—
460C4×Q8—24no—
461C4×Q8—24no—
462C4×Q8—28no—
463C4×Q8—28no—
464C4×Q8—212no—
465C4×Q8—212no—
466C4×Q8—212no—
467C4×Q8—212no—
468C4×Q8—24no—
469C4×Q8—412no—
470C4×Q8—412no—
471C4×Q8—46no—
472C4×Q8C22×C418yes—
473C4×Q8C22×C4124yes—
474C4×Q8C22×C418yes—
475C4×Q8C22×C4124yes—
476C4×Q8C22×C4116yes—
477C4×Q8C22×C4124yes—
478C4×Q8#4118yescomplemented
479C4×Q8#4118yescomplemented
480C4×D4—224no—
481C4×D4—224no—
482C4×D4—224no—
483C4×D4—224no—
484C4×D4—224no—
485C4×D4—212no—
486C4×D4—412no—
487C4×D4—412no—
488C4×D4—46no—
489C4×D4—412no—
490C4×D4—412no—
491C4×D4—424no—
492C4×D4C22×C4148yes—
493C4×D4C22×C4148yes—
494C4×D4C22×C4148yes—
495C4×D4C22×C4124yes—
496C4×D4C22×C4148yes—
497#117—224no—
498#117—224no—
499#117—424no—
500#117—412no—
501#117C22×C4148yes—
502C2×C4⋊C4—212no—
503C2×C4⋊C4—212no—
504C2×C4⋊C4—224no—
505C2×C4⋊C4C22×C4124yes—
506C2×C4⋊C4C22×C4148yes—
507C2×C4⋊C4C2416yes—
508C2×C4⋊C4C2416yes—
509C2×C4⋊C4C2413yes—
510C2×C4⋊C4C2413yes—
511C2×C4⋊C4C2416yes—
512C2×C4⋊C4C2416yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2416yes—
515C2×C4⋊C4C2416yes—
516C2×C4⋊C4C2411yescharacteristic
517C2×C4⋊C4C2413yes—
518C2×C4⋊C4C2413yes—
519C2×C4⋊C4C2411yescharacteristic
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C24112yes—
522C2×C4⋊C4C2416yes—
523C2×C4⋊C4C2416yes—
524C2×C4⋊C4C2416yes—
525C2×C4⋊C4C2416yes—
526C2×C4⋊C4C2413yes—
527C2×C4⋊C4C2416yes—
528C2×C4⋊C4C2416yes—
529C2×C4⋊C4C2413yes—
530C2×C4⋊C4C2416yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2411yescharacteristic
533C2×C4⋊C4C2413yes—
534C2×C4⋊C4C2416yes—
535C2×C4⋊C4C2416yes—
536C2×C4⋊C4C2413yes—
537C2×C4⋊C4C2413yes—
538C2×C22⋊C4C2416yes—
539C2×C22⋊C4C2416yes—
540C2×C22⋊C4C2416yes—
541C2×C22⋊C4C24112yes—
542C2×C22⋊C4C2416yes—
543C2×C22⋊C4C2412yes—
544C2×C22⋊C4C2416yes—
545C2×C22⋊C4C24112yes—
546C2×C22⋊C4C2416yes—
547C2×C22⋊C4C24112yes—
548C2×C22⋊C4C2416yes—
549C2×C22⋊C4C2416yes—
550C2×C22⋊C4C2416yes—
551C2×C22⋊C4C2412yes—
552C2×C22⋊C4C2416yes—
553C2×C22⋊C4C24112yes—
554C2×C22⋊C4C2416yes—
555C2×C42—212no—
556C2×C42—212no—
557C2×C42—212no—
558C2×C42—224no—
559C2×C42—24no—
560C2×C42—424no—
561C2×C42—46no—
562C2×C42—46no—
563C2×C42C22×C4124yes—
564C2×C42C2413yes—
565C2×C42C2416yes—
566C2×C42C2416yes—
567C2×C42C2413yes—
568C2×C42C2413yes—
569C2×C42C2413yes—
570C2×C42C2416yes—
571C2×C42C2413yes—
572C2×C42C2413yes—
573C2×C42C2413yes—
574C2×C42C2413yes—
575C2×C42C2413yes—
576C2×C42C2411yescharacteristic
577C2×C42C2411yescharacteristic
578C2×C42C2413yes—
579C2×C42C2416yes—
580C2×C42C2413yes—
581C2×C42C2412yes—
582C2×C42C2411yescharacteristic
583C2×C42C2413yes—
584C2×C42C2412yes—
585C2×C42C24112yes—
586C2×C42C24112yes—
587C2×C42C2416yes—
588C2×C42C2416yes—
589C2×C42C2413yes—
590C2×C42C2413yes—
591C2×C42C2413yes—
592C2×C42C2413yes—
593C2×C42C2413yes—
594C2×C42C2413yes—
595C2×C42C2413yes—
596C2×C42C2416yes—
597C2×C42C2413yes—
598C2×C42C2413yes—
599C2×C42C2413yes—
600C2×C42C2413yes—
601C2×C42C2413yes—
602C2×C42C2411yescharacteristic
603#95C2416yes—
604#95C2416yes—
605#95C2416yes—
606#95C24112yes—
607#95C2416yes—
608#95C2416yes—
609#95C2416yes—
610#95C2412yes—
611#95C2412yes—
612#95C2416yes—
613#95C2416yes—
614#95C2416yes—
615#95C2416yes—
616#95C2412yes—
617#95C2416yes—
618#95C2412yes—
619#95C2412yes—
620#95C2416yes—
621#95C2416yes—
622#95C24112yes—
623#95C24112yes—
624#95C2416yes—
625#95C2416yes—
626#95C2416yes—
627#95C2416yes—
628#95C2416yes—
629#95C2416yes—
630C24C2516yes—
631C24C2511yescharacteristic
632#41—264no—
633#41—496no—
634C2×Q8—232no—
635C2×Q8—26no—
636C2×Q8—26no—
637C2×Q8—22no—
638C2×Q8—22no—
639C2×Q8—46no—
640C2×Q8—46no—
641C2×Q8C23×C414yes—
642C2×Q8C23×C4112yes—
643C2×Q8C23×C4124yes—
644C2×Q8C23×C414yes—
645C2×Q8C2×#4114yes—
646C2×Q8C2×#4114yes—
647C2×D4—212no—
648C2×D4—212no—
649C2×D4—212no—
650C2×D4—212no—
651C2×D4—26no—
652C2×D4—26no—
653C2×D4—46no—
654C2×D4—46no—
655C2×D4C23×C4112yes—
656C2×D4C23×C4124yes—
657C2×D4C23×C4124yes—
658C2×D4C23×C4124yes—
659C22×C4—26no—
660C22×C4—22no—
661C22×C4—26no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—26no—
665C22×C4—26no—
666C22×C4—212no—
667C22×C4—212no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—26no—
673C22×C4—26no—
674C22×C4—26no—
675C22×C4—26no—
676C22×C4—212no—
677C22×C4—212no—
678C22×C4—212no—
679C22×C4—212no—
680C22×C4—224no—
681C22×C4—412no—
682C22×C4—43no—
683C22×C4—43no—
684C22×C4—412no—
685C22×C4—412no—
686C22×C4—46no—
687C22×C4—412no—
688C22×C4—46no—
689C22×C4C23×C414yes—
690C22×C4C23×C4112yes—
691C22×C4C23×C4112yes—
692C22×C4C23×C4124yes—
693C22×C4C23×C4148yes—
694C22×C4H(5,𝔽2)14yes—
695C22×C4C2512yes—
696C22×C4C2512yes—
697C22×C4C2516yes—
698C22×C4C2513yes—
699C22×C4C2516yes—
700C22×C4C2513yes—
701C22×C4C2511yescharacteristic
702C22×C4C2513yes—
703C22×C4C2512yes—
704C22×C4C2513yes—
705C22×C4C2513yes—
706C22×C4C2516yes—
707C22×C4C2512yes—
708C22×C4C2511yescharacteristic
709C22×C4C2513yes—
710C22×C4C2513yes—
711C22×C4C2511yescharacteristic
712C22×C4C2511yescharacteristic
713C22×C4C2513yes—
714C22×C4C2511yescharacteristic
715C22×C4C2511yescharacteristic
716C4⋊C4—212no—
717C4⋊C4—212no—
718C4⋊C4—212no—
719C4⋊C4—212no—
720C4⋊C4—26no—
721C4⋊C4—26no—
722C4⋊C4—24no—
723C4⋊C4—212no—
724C4⋊C4—212no—
725C4⋊C4—26no—
726C4⋊C4—24no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—26no—
730C4⋊C4—46no—
731C4⋊C4—46no—
732C4⋊C4—412no—
733C4⋊C4—46no—
734C4⋊C4—46no—
735C4⋊C4C23×C4112yes—
736C4⋊C4C23×C4124yes—
737C4⋊C4C23×C4124yes—
738C4⋊C4C23×C4112yes—
739C4⋊C4C23×C4124yes—
740C4⋊C4C23×C418yes—
741C4⋊C4C23×C414yes—
742C4⋊C4C23×C4112yes—
743C4⋊C4C23×C4124yes—
744C4⋊C4C23×C4124yes—
745C4⋊C4C2×#41112yes—
746C4⋊C4C2×#41112yes—
747C22⋊C4—212no—
748C22⋊C4—24no—
749C22⋊C4—212no—
750C22⋊C4—224no—
751C22⋊C4—212no—
752C22⋊C4—212no—
753C22⋊C4—212no—
754C22⋊C4—412no—
755C22⋊C4—412no—
756C22⋊C4—46no—
757C22⋊C4—46no—
758C22⋊C4C23×C4124yes—
759C22⋊C4C23×C4124yes—
760C22⋊C4C23×C418yes—
761C22⋊C4C23×C4124yes—
762C22⋊C4C23×C4148yes—
763C22⋊C4C23×C4124yes—
764C42—24no—
765C42—212no—
766C42—212no—
767C42—26no—
768C42—26no—
769C42—26no—
770C42—26no—
771C42—26no—
772C42—26no—
773C42—212no—
774C42—26no—
775C42—26no—
776C42—26no—
777C42—26no—
778C42—212no—
779C42—22no—
780C42—22no—
781C42—22no—
782C42—24no—
783C42—26no—
784C42—26no—
785C42—43no—
786C42—43no—
787C42—43no—
788C42—43no—
789C42—43no—
790C42—43no—
791C42—412no—
792C42—412no—
793C42—46no—
794C42—46no—
795C42C23×C4112yes—
796C42C23×C4112yes—
797C42C23×C4112yes—
798C42C23×C4112yes—
799C42C23×C4124yes—
800C42C2×#41112yes—
801C42C2×#41112yes—
802C422−1+414yes—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—26no—
808C23—26no—
809C23—26no—
810C23—26no—
811C23—26no—
812C23—26no—
813C23C24×C4112yes—
814C23C24×C412yes—
815C23C2×H(5,𝔽2)12yes—
816C23#58512yes—
817C23C2611yescharacteristic
818Q8—224no—
819Q8—28no—
820Q8—424no—
821Q8C4×#41116yescomplemented
822D4—248no—
823D4—248no—
824D4—224no—
825D4—424no—
826C2×C4—28no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—23no—
831C2×C4—23no—
832C2×C4—22no—
833C2×C4—23no—
834C2×C4—23no—
835C2×C4—23no—
836C2×C4—26no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—23no—
842C2×C4—23no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—23no—
847C2×C4—22no—
848C2×C4—23no—
849C2×C4—23no—
850C2×C4—26no—
851C2×C4—224no—
852C2×C4—224no—
853C2×C4—248no—
854C2×C4—28no—
855C2×C4—28no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—26no—
859C2×C4—23no—
860C2×C4—23no—
861C2×C4—26no—
862C2×C4—23no—
863C2×C4—26no—
864C2×C4—26no—
865C2×C4—22no—
866C2×C4—26no—
867C2×C4—23no—
868C2×C4—23no—
869C2×C4—22no—
870C2×C4—23no—
871C2×C4—26no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—448no—
875C2×C4—412no—
876C2×C4—412no—
877C2×C4—424no—
878C2×C4—824no—
879C2×C4—812no—
880C2×C4C24×C412yes—
881C2×C4C24×C414yes—
882C2×C4C24×C416yes—
883C2×C4C24×C416yes—
884C2×C4C24×C416yes—
885C2×C4C24×C4112yes—
886C2×C4C24×C414yes—
887C2×C4C24×C416yes—
888C2×C4C24×C412yes—
889C2×C4C22×#4112yes—
890C2×C4C22×#4116yes—
891C2×C4C22×#4116yes—
892C2×C4C22×#4116yes—
893C2×C4C22×#4116yes—
894C2×C4C22×#4112yes—
895C2×C4C2×H(5,𝔽2)12yes—
896C2×C4C2×H(5,𝔽2)12yes—
897C2×C4C2×2−1+412yes—
898C2×C4C2×2−1+412yes—
899C2×C4C2×2−1+412yes—
900C2×C4#58512yes—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—212no—
908C22—212no—
909C22—212no—
910C22—46no—
911C22—46no—
912C22—46no—
913C22—46no—
914C22C4×H(5,𝔽2)14yes—
915C22C25×C411yescharacteristic
916C22C23×#4111yescharacteristic
917C22C23×#4111yescharacteristic
918C22C22×H(5,𝔽2)11yescharacteristic
919C22C22×2−1+411yescharacteristic
920C22C2×#58511yescharacteristic
921C22C2×#58511yescharacteristic
922C4—22no—
923C4—22no—
924C4—22no—
925C4—26no—
926C4—26no—
927C4—24no—
928C4—26no—
929C4—26no—
930C4—26no—
931C4—212no—
932C4—22no—
933C4—24no—
934C4—46no—
935C4—42no—
936C4—43no—
937C4—46no—
938C4—43no—
939C4—42no—
940C4C2×C4×#41112yes—
941C4C4×2−1+414yes—
942C4#352214yesdirect product factor
943C2—24no—
944C2—412no—
945C2C22×C4×#4111yescharacteristic
946C2C2×C4×H(5,𝔽2)11yescharacteristic
947C2C2×C4×2−1+411yescharacteristic
948C2C2×#352211yescharacteristic
949C2#6278811yescharacteristic
950C2#6280011yescharacteristic
951C2#6281611yescharacteristic
subgroupG/H
centerC22×C4C25
commutatorC22C25×C4
Frattini, socle, cosocleC23C26
prime radicalC2×#3522C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34335C2semidirect
3. #34331C2semidirect
4. #34317C2semidirect
5. #34313C2semidirect
6. #34298C2semidirect
7. #34294C2semidirect
8. #34285C2semidirect
9. #34263C2semidirect
10. #34243C2semidirect
11. #34236C2semidirect
12. #34196C2semidirect
13. C4×Q82C2semidirect
14. C4×#559C2semidirect
15. C4×#554C2semidirect
16. C4×#550C2semidirect
17. C4×#547C2semidirect
18. C4×#548C2semidirect
19. C4×#542C2semidirect
20. C4×#532C2semidirect
21. C4×#529C2semidirect
22. C4×#520C2semidirect
23. C2×C42×Q8C2semidirect
24. #3522C4direct (N × H)
162. #559C2×C4semidirect
163. Q82C2×C4semidirect
164. #554C2×C4semidirect
165. #550C2×C4semidirect
166. #548C2×C4semidirect
167. #547C2×C4semidirect
168. #542C2×C4semidirect
169. #532C2×C4semidirect
173. #529C2×C4semidirect
188. #520C2×C4semidirect
193. C2×C4×Q8C2×C4semidirect
478. C4×Q8#41semidirect
479. C4×Q8#41semidirect
821. Q8C4×#41semidirect
942. C4#3522direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35222
#343352
#343312
#343172
#343132
#342982
#342942
#342852
#342632
#342432
#342362
#341962
C4×Q822
C4×#5592
C4×#5542
C4×#5502
C4×#5472
C4×#5482
C4×#5422
C4×#5322
C4×#5292
C4×#5202
C2×C42×Q82