Finite Group Databasebeta

← C4×#3500 #7625672

Subgroups — C4×#3500 #7625672

Order 512.

11234 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3500C211yesmaximal, characteristic
2C2×C4×2−1+4C211yesmaximal, characteristic, complemented
3C2×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
4#34312C214yesmaximal, complemented
5#34309C2112yesmaximal, complemented
6#34276C213yesmaximal, complemented
7#34275C213yesmaximal, complemented
8#34259C211yesmaximal, characteristic, complemented
9#34258C211yesmaximal, characteristic, complemented
10#34211C213yesmaximal, complemented
11#34208C213yesmaximal, complemented
12#34184C211yesmaximal, characteristic, complemented
13C4×#548C214yesmaximal, complemented
14C4×#546C2112yesmaximal, complemented
15C4×#536C213yesmaximal, complemented
16C4×#535C213yesmaximal, complemented
17C4×#532C213yesmaximal, complemented
18C2×C4×#124C213yesmaximal, complemented
19C42×#41C211yesmaximal, characteristic, complemented
20C22×2−1+4C2211yescharacteristic
21C22×H(5,𝔽2)C2211yescharacteristic
22#3500C4132yesdirect product factor
23C2×#548C2214yes—
24C2×#546C22112yes—
25C2×#536C2213yes—
26C2×#535C2213yes—
27C2×#532C2213yes—
28C22×#124C2213yes—
29C4×2−1+4—216no—
30C4×H(5,𝔽2)—216no—
31C2×#520C2212yes—
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#520C2213yes—
35C2×#520C2216yescomplemented
36C2×#520C2213yescomplemented
37C2×#519C2212yescomplemented
38C2×#519C2213yescomplemented
39C2×#518C2216yes—
40C2×#518C2213yes—
41C2×C4×#41C2213yes—
42C2×C4×#41C2212yes—
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46C2×C4×#41C2213yescomplemented
47C2×C4×#41C2216yescomplemented
48C22×C4×Q8C2213yescomplemented
49C22×C4×Q8C2212yescomplemented
50C22×C4×D4C2213yes—
51C22×C4×D4C2216yes—
52#2367C22112yescomplemented
53#2367C22112yescomplemented
54#2364C22124yescomplemented
55#2363C22112yescomplemented
56#2362C22112yescomplemented
57#2361C22112yescomplemented
58#2360C22112yescomplemented
59#2359C22124yescomplemented
60#2358C22124yescomplemented
61#2352C22112yescomplemented
62#2352C22112yescomplemented
63#2351C2214yescomplemented
64#2349C22112yescomplemented
65#2342C22124yescomplemented
66#2341C2214yes—
67Q8×C22⋊C4C2214yescomplemented
68#2339C22112yescomplemented
69D4×C22⋊C4C22112yes—
70#2328C2216yescomplemented
71#2327C2216yescomplemented
72#2326C2216yescomplemented
73#2326C2216yescomplemented
74#2324C22112yescomplemented
75#2323C22112yescomplemented
76#2322C22112yescomplemented
77#2321C22112yescomplemented
78#2317C2213yescomplemented
79#2317C2213yescomplemented
80#2311C2213yes—
81#2311C2213yescomplemented
82#2310C2213yescomplemented
83#2309C2213yes—
84C4×C4⋊Q8C2213yescomplemented
85C4×C4⋊Q8C2213yescomplemented
86C4×#127C2213yescomplemented
87C4×#127C2213yescomplemented
88C4×#124C22112yescomplemented
89C4×#124C2216yescomplemented
90C4×#124C22112yescomplemented
91C4×#124C2213yescomplemented
92C4×#124C2216yescomplemented
93C4×#124C2213yescomplemented
94C4×#124C2216yescomplemented
95C4×#124C2213yescomplemented
96C4×#124C2211yescharacteristic, complemented
97C4×C22⋊Q8C22112yescomplemented
98C4×#123C22112yescomplemented
99C4×#121C22112yescomplemented
100C4×#121C22112yescomplemented
101C4×#121C22112yescomplemented
102C4×#120C22112yescomplemented
103#2297C2213yes—
104#2297C2213yescomplemented
105C2×#391C2213yescomplemented
106#2293C22112yescomplemented
107C2×#390C2213yes—
108C2×#388C22112yescomplemented
109#2285C2213yescomplemented
110C2×#382C2213yescomplemented
111C42×Q8C2212yescomplemented
112C42×Q8C2212yescomplemented
113C42×D4C2216yescomplemented
114C42×D4C2216yescomplemented
115C42×D4C22112yescomplemented
116C4×#117C2213yescomplemented
117C4×#117C2213yescomplemented
118C4×#117C2213yescomplemented
119C2×C4×C22⋊C4C22112yescomplemented
120C2×C43C2213yescomplemented
121C2×2−1+4—28no—
122C2×2−1+4—28no—
123C2×2−1+4C2×C4116yescomplemented
124C2×H(5,𝔽2)—28no—
125C2×H(5,𝔽2)—28no—
126C2×H(5,𝔽2)C2×C4116yescomplemented
127C22×#41C2313yes—
128C22×#41C2312yes—
129C22×#41C2313yes—
130C22×#41C2316yes—
131C22×#41C2311yescharacteristic
132C23×Q8C2313yes—
133C23×Q8C2312yes—
134C23×D4C2313yes—
135C23×D4C2316yes—
136C24×C4C2316yes—
137#548C2×C4164yescomplemented
138#546C2×C41192yescomplemented
139#536C2×C4148yescomplemented
140#535C2×C4148yescomplemented
141#532C2×C4148yescomplemented
142C2×C4⋊Q8C2313yes—
143C2×#127C2313yes—
144C2×#124C2×C4148yescomplemented
145C2×#124C2316yes—
146C2×#124C23112yes—
147C2×#124C2313yes—
148C2×#124C2311yescharacteristic
149C2×#123C23112yes—
150C2×C22⋊Q8C23112yes—
151C2×#121C23112yes—
152C2×#121C23112yes—
153C2×#120C23112yes—
154#520—28no—
155#520—28no—
156#520—216no—
157#520—248no—
158#520—224no—
159#520—224no—
160#519—216no—
161#519—224no—
162#518—248no—
163#518—224no—
164C4×#41—28no—
165C4×#41—216no—
166C4×#41—248no—
167C4×#41—224no—
168C4×#41—224no—
169C4×#41C2×C4116yescomplemented
170C4×#41D4116yescomplemented
171C2×C4×Q8—216no—
172C2×C4×Q8—224no—
173C2×C4×Q8C2311yescharacteristic
174C2×C4×Q8C2313yes—
175C2×C4×Q8C2313yes—
176C2×C4×Q8C2313yes—
177C2×C4×Q8C2316yes—
178C2×C4×Q8C2316yes—
179C2×C4×Q8C2312yes—
180C2×C4×Q8C2312yes—
181C2×C4×Q8C2312yes—
182C2×C4×Q8C2316yes—
183C2×C4×Q8C2316yes—
184C2×C4×Q8C2316yes—
185C2×C4×Q8C2312yes—
186C2×C4×Q8C2311yescharacteristic
187C2×C4×Q8C2311yescharacteristic
188C2×C4×D4—248no—
189C2×C4×D4—224no—
190C2×C4×D4C2311yescharacteristic
191C2×C4×D4C2313yes—
192C2×C4×D4C2313yes—
193C2×C4×D4C2313yes—
194C2×C4×D4C2316yes—
195C2×C4×D4C2316yes—
196C2×C4×D4C2316yes—
197C2×C4×D4C2316yes—
198C2×C4×D4C2316yes—
199C2×C4×D4C2316yes—
200C2×C4×D4C2316yes—
201C2×C4×D4C23112yes—
202C2×C4×D4C23112yes—
203C2×C4×D4C2316yes—
204C2×C4×D4C2316yes—
205C2×C4×D4C2316yes—
206C2×C4×D4C2316yes—
207C2×C4×D4C2316yes—
208C2×C4×D4C23112yes—
209C2×C4×D4C23112yes—
210C2×C4×D4C2316yes—
211C2×C4×D4C23112yes—
212C2×C4×D4C2313yes—
213C2×C4×D4C2313yes—
214C2×#117C2313yes—
215C2×#117C2313yes—
216C2×#117C2313yes—
217C2×#117C2316yes—
218C2×#117C2316yes—
219C2×#117C23112yes—
220C2×#117C2316yes—
221C2×#117C2316yes—
222C2×#117C2313yes—
223C2×#117C2313yes—
224C22×C4⋊C4C2313yes—
225C22×C4⋊C4C2313yes—
226C22×C4⋊C4C2316yes—
227C22×C4⋊C4C2316yes—
228C22×C4⋊C4C2316yes—
229C22×C22⋊C4C2316yes—
230C22×C22⋊C4C23112yes—
231C22×C22⋊C4C23112yes—
232C22×C22⋊C4C23112yes—
233C22×C42C2316yes—
234C22×C42C2316yes—
235C22×C42C2316yes—
236C22×C42C2313yes—
237C22×C42C2316yes—
238C22×C42C2316yes—
239C22×C42C2313yes—
240C22×C42C2313yes—
241#391C2311yescharacteristic
242#391C2313yes—
243#391C2313yes—
244#391C2313yes—
245#391C2316yes—
246#391C23112yes—
247#391C23112yes—
248#390C2311yescharacteristic
249#390C2313yes—
250#390C2313yes—
251#390C23112yes—
252#390C23112yes—
253#390C2313yes—
254#390C2316yes—
255#390C23112yes—
256#390C23112yes—
257#389C23112yes—
258#389C23112yes—
259#389C23112yes—
260#389C23112yes—
261#388C23124yes—
262#388C23124yes—
263#388C23124yes—
264#388C23112yes—
265#388C23124yes—
266#388C23112yes—
267#388C23124yes—
268#388C23112yes—
269#388C2314yes—
270#387C23124yes—
271#387C23124yes—
272#386C23112yes—
273#386C23112yes—
274#386C23124yes—
275#386C23124yes—
276#386C23112yes—
277#386C23112yes—
278#385C23112yes—
279#385C23112yes—
280#385C23124yes—
281#385C23124yes—
282#384C2313yes—
283#384C2313yes—
284#382C2316yes—
285#382C23112yes—
286#382C2313yes—
287#382C2311yescharacteristic
288#381C23112yes—
289#380C23112yes—
290#380C23112yes—
291#380C23112yes—
292#379C23112yes—
293C4×C4⋊C4C23112yes—
294C4×C4⋊C4C23112yes—
295C4×C4⋊C4C2316yes—
296C4×C4⋊C4C23112yes—
297C4×C4⋊C4C2316yes—
298C4×C4⋊C4C2316yes—
299C4×C4⋊C4C2316yes—
300C4×C4⋊C4C2316yes—
301C4×C4⋊C4C2316yes—
302C4×C22⋊C4C2316yes—
303C4×C22⋊C4C23112yes—
304C4×C22⋊C4C23112yes—
305C4×C22⋊C4C23112yes—
306C4×C22⋊C4C23112yes—
307C4×C22⋊C4C23124yes—
308C4×C22⋊C4C23112yes—
309C4×C22⋊C4C23112yes—
310C4×C22⋊C4C23124yes—
311C4×C22⋊C4C23112yes—
312C4×C22⋊C4C23124yes—
313C4×C22⋊C4C2316yes—
314C4×C22⋊C4C2314yes—
315#376C2316yes—
316C2×#95C23112yes—
317C2×#95C23112yes—
318C43C2313yes—
319C43C2313yes—
320C43C2311yescharacteristic
321C43C2313yes—
322C43C2316yes—
323C43C2316yes—
324C25C2416yes—
3252−1+4—2128no—
326H(5,𝔽2)—2128no—
327C2×#41—28no—
328C2×#41—28no—
329C2×#41—224no—
330C2×#41—224no—
331C2×#41—212no—
332C2×#41—212no—
333C2×#41—212no—
334C2×#41—212no—
335C2×#41C22×C4124yes—
336C2×#41C22×C4116yes—
337C2×#41C22×C418yes—
338C2×#41C22×C4124yescomplemented
339C2×#41C22×C4148yescomplemented
340C2×#41C2×D418yes—
341C2×#41#4118yes—
342C22×Q8—28no—
343C22×Q8—28no—
344C22×Q8—212no—
345C22×Q8—212no—
346C22×Q8C22×C4124yescomplemented
347C22×Q8C22×C4116yescomplemented
348C22×Q8C2416yes—
349C22×Q8C2413yes—
350C22×Q8C2411yescharacteristic
351C22×Q8C2411yescharacteristic
352C22×D4—224no—
353C22×D4—224no—
354C22×D4—212no—
355C22×D4—212no—
356C22×D4C22×C4124yes—
357C22×D4C22×C4148yes—
358C22×D4C2416yes—
359C22×D4C2416yes—
360C22×D4C2416yes—
361C22×D4C2413yes—
362C22×D4C2411yescharacteristic
363C22×D4C24112yes—
364C22×D4C2413yes—
365C23×C4—224no—
366C23×C4—424no—
367C23×C4C2412yes—
368C23×C4C2416yes—
369C23×C4C2416yes—
370C23×C4C2416yes—
371C23×C4C2416yes—
372C23×C4C2416yes—
373C23×C4C2413yes—
374C23×C4C2416yes—
375C23×C4C2416yes—
376C23×C4C2416yes—
377C23×C4C24112yes—
378C23×C4C2416yes—
379C23×C4C2416yes—
380C23×C4C2413yes—
381C23×C4C2413yes—
382C4⋊Q8C22×C4124yescomplemented
383#127C22×C4124yescomplemented
384#124C22×C4124yescomplemented
385#124C22×C4148yescomplemented
386#124C22×C4196yescomplemented
387#124C22×C418yescomplemented
388#123C22×C4196yescomplemented
389C22⋊Q8C22×C4196yescomplemented
390#121C22×C4196yescomplemented
391#121C22×C4196yescomplemented
392#120C22×C4196yescomplemented
393C4×Q8—28no—
394C4×Q8—28no—
395C4×Q8—28no—
396C4×Q8—224no—
397C4×Q8—224no—
398C4×Q8—224no—
399C4×Q8—212no—
400C4×Q8—224no—
401C4×Q8—224no—
402C4×Q8—24no—
403C4×Q8—212no—
404C4×Q8—212no—
405C4×Q8C22×C4116yescomplemented
406C4×Q8C2×D418yes—
407C4×Q8C2×D418yes—
408C4×D4—224no—
409C4×D4—224no—
410C4×D4—224no—
411C4×D4—224no—
412C4×D4—224no—
413C4×D4—224no—
414C4×D4—224no—
415C4×D4—224no—
416C4×D4—224no—
417C4×D4—248no—
418C4×D4—248no—
419C4×D4—224no—
420C4×D4—212no—
421C4×D4—224no—
422C4×D4—224no—
423C4×D4—24no—
424C4×D4—212no—
425C4×D4—212no—
426C4×D4—424no—
427C4×D4—424no—
428C4×D4C22×C4148yescomplemented
429C4×D4C22×C4196yescomplemented
430C4×D4C2×D4124yes—
431C4×D4C2×D4124yes—
432#117—212no—
433#117—212no—
434#117—212no—
435#117—224no—
436#117—224no—
437#117—248no—
438#117—224no—
439#117—224no—
440#117C22×C4124yescomplemented
441#117C2×D4124yes—
442C2×C4⋊C4—212no—
443C2×C4⋊C4—224no—
444C2×C4⋊C4—212no—
445C2×C4⋊C4—224no—
446C2×C4⋊C4—224no—
447C2×C4⋊C4C2416yes—
448C2×C4⋊C4C2413yes—
449C2×C4⋊C4C2416yes—
450C2×C4⋊C4C2416yes—
451C2×C4⋊C4C2413yes—
452C2×C4⋊C4C24112yes—
453C2×C4⋊C4C2416yes—
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2412yes—
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2416yes—
458C2×C4⋊C4C2416yes—
459C2×C4⋊C4C24112yes—
460C2×C4⋊C4C24112yes—
461C2×C4⋊C4C2416yes—
462C2×C4⋊C4C24112yes—
463C2×C4⋊C4C2413yes—
464C2×C4⋊C4C2413yes—
465C2×C22⋊C4—224no—
466C2×C22⋊C4—248no—
467C2×C22⋊C4—424no—
468C2×C22⋊C4C22×C4196yescomplemented
469C2×C22⋊C4C2416yes—
470C2×C22⋊C4C24112yes—
471C2×C22⋊C4C2416yes—
472C2×C22⋊C4C2416yes—
473C2×C22⋊C4C24112yes—
474C2×C22⋊C4C2416yes—
475C2×C22⋊C4C2416yes—
476C2×C22⋊C4C2412yes—
477C2×C22⋊C4C2416yes—
478C2×C22⋊C4C2414yes—
479C2×C22⋊C4C24124yes—
480C2×C22⋊C4C24112yes—
481C2×C22⋊C4C24112yes—
482C2×C22⋊C4C24112yes—
483C2×C22⋊C4C24124yes—
484C2×C22⋊C4C2416yes—
485C2×C22⋊C4C2414yes—
486C2×C22⋊C4C2416yes—
487C2×C42—224no—
488C2×C42—212no—
489C2×C42—224no—
490C2×C42—224no—
491C2×C42—412no—
492C2×C42—412no—
493C2×C42C22×C4124yescomplemented
494C2×C42C2×D4124yes—
495C2×C42C2416yes—
496C2×C42C2416yes—
497C2×C42C24112yes—
498C2×C42C2416yes—
499C2×C42C2416yes—
500C2×C42C2413yes—
501C2×C42C2416yes—
502C2×C42C2416yes—
503C2×C42C2412yes—
504C2×C42C2411yescharacteristic
505C2×C42C2412yes—
506C2×C42C2416yes—
507C2×C42C2416yes—
508C2×C42C2412yes—
509C2×C42C2416yes—
510C2×C42C2416yes—
511C2×C42C2416yes—
512C2×C42C2416yes—
513C2×C42C2413yes—
514C2×C42C2416yes—
515C2×C42C2411yescharacteristic
516C2×C42C2413yes—
517C2×C42C2413yes—
518C2×C42C2411yescharacteristic
519C2×C42C2413yes—
520#95C24112yes—
521#95C24112yes—
522#95C24124yes—
523#95C24124yes—
524#95C24112yes—
525#95C24112yes—
526#95C2414yes—
527#95C2414yes—
528#95C24112yes—
529#95C24112yes—
530C24—212no—
531C24—212no—
532C24—412no—
533C24—412no—
534C24C23×C4124yes—
535C24C2516yes—
536C24C2512yes—
537C24C2513yes—
538#41—264no—
539#41—2192no—
540#41—296no—
541#41—296no—
542#41C4×D4164yescomplemented
543C2×Q8—264no—
544C2×Q8—296no—
545C2×Q8—212no—
546C2×Q8—26no—
547C2×Q8—22no—
548C2×Q8—26no—
549C2×Q8—212no—
550C2×Q8—22no—
551C2×Q8C23×C4124yes—
552C2×Q8C23×C4112yes—
553C2×Q8C23×C414yes—
554C2×Q8C23×C414yes—
555C2×Q8C22×D414yes—
556C2×Q8C2×#4114yes—
557C2×D4—212no—
558C2×D4—212no—
559C2×D4—212no—
560C2×D4—212no—
561C2×D4—2192no—
562C2×D4—296no—
563C2×D4—212no—
564C2×D4—26no—
565C2×D4—22no—
566C2×D4—26no—
567C2×D4—212no—
568C2×D4—22no—
569C2×D4—412no—
570C2×D4—412no—
571C2×D4C23×C4124yes—
572C2×D4C23×C4124yes—
573C2×D4C23×C4124yes—
574C2×D4C23×C4112yes—
575C2×D4C23×C414yes—
576C2×D4C23×C4148yes—
577C2×D4C23×C4112yes—
578C2×D4C22×D4112yes—
579C2×D4C2×#41112yes—
580C22×C4—212no—
581C22×C4—212no—
582C22×C4—212no—
583C22×C4—212no—
584C22×C4—212no—
585C22×C4—212no—
586C22×C4—212no—
587C22×C4—212no—
588C22×C4—212no—
589C22×C4—212no—
590C22×C4—24no—
591C22×C4—212no—
592C22×C4—212no—
593C22×C4—28no—
594C22×C4—224no—
595C22×C4—212no—
596C22×C4—212no—
597C22×C4—224no—
598C22×C4—46no—
599C22×C4—46no—
600C22×C4—46no—
601C22×C4—46no—
602C22×C4—412no—
603C22×C4—412no—
604C22×C4—412no—
605C22×C4—424no—
606C22×C4—412no—
607C22×C4—848no—
608C22×C4C23×C4124yes—
609C22×C4C23×C4124yes—
610C22×C4C23×C4124yes—
611C22×C4C23×C4124yes—
612C22×C4C23×C4112yes—
613C22×C4C22×D4112yes—
614C22×C4C22×D4112yes—
615C22×C4C22×D4112yes—
616C22×C4C2×#41112yes—
617C22×C4C2516yes—
618C22×C4C2516yes—
619C22×C4C2512yes—
620C22×C4C2516yes—
621C22×C4C2512yes—
622C22×C4C2512yes—
623C22×C4C2516yes—
624C22×C4C2516yes—
625C22×C4C2512yes—
626C22×C4C2513yes—
627C22×C4C2513yes—
628C22×C4C2511yescharacteristic
629C22×C4C2512yes—
630C22×C4C2511yescharacteristic
631C22×C4C2513yes—
632C22×C4C2511yescharacteristic
633C4⋊C4—212no—
634C4⋊C4—212no—
635C4⋊C4—26no—
636C4⋊C4—224no—
637C4⋊C4—212no—
638C4⋊C4—212no—
639C4⋊C4—26no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—212no—
643C4⋊C4—22no—
644C4⋊C4—212no—
645C4⋊C4—412no—
646C4⋊C4—412no—
647C4⋊C4C23×C4124yes—
648C4⋊C4C23×C4148yes—
649C4⋊C4C22×D4112yes—
650C4⋊C4C22×D4112yes—
651C22⋊C4—212no—
652C22⋊C4—212no—
653C22⋊C4—212no—
654C22⋊C4—212no—
655C22⋊C4—224no—
656C22⋊C4—212no—
657C22⋊C4—24no—
658C22⋊C4—212no—
659C22⋊C4—224no—
660C22⋊C4—28no—
661C22⋊C4—424no—
662C22⋊C4—412no—
663C22⋊C4—412no—
664C22⋊C4C23×C4148yes—
665C22⋊C4C23×C4196yes—
666C22⋊C4C23×C4124yes—
667C22⋊C4C23×C4116yes—
668C22⋊C4C22×D4124yes—
669C42—24no—
670C42—212no—
671C42—212no—
672C42—212no—
673C42—212no—
674C42—224no—
675C42—212no—
676C42—22no—
677C42—26no—
678C42—212no—
679C42—24no—
680C42—24no—
681C42—212no—
682C42—212no—
683C42—46no—
684C42—46no—
685C42—46no—
686C42—46no—
687C42C23×C414yes—
688C42C23×C4112yes—
689C42C23×C4124yes—
690C42C22×D4112yes—
691C42C22×D414yes—
692C42C22×D4112yes—
693C42C22×D4112yes—
694C23—26no—
695C23—26no—
696C23—22no—
697C23—26no—
698C23—22no—
699C23—26no—
700C23—212no—
701C23—24no—
702C23—24no—
703C23—212no—
704C23—248no—
705C23—448no—
706C23—812no—
707C23—824no—
708C23—812no—
709C23C24×C4112yes—
710C23C24×C414yes—
711C23C24×C416yes—
712C23C23×D416yes—
713C23C22×#4116yes—
714C23C2611yescharacteristic
715Q8—248no—
716Q8—224no—
717Q8—28no—
718Q8C2×C4×D4116yes—
719D4—248no—
720D4—248no—
721D4—248no—
722D4—224no—
723D4—28no—
724D4—448no—
725D4C2×C4×D4148yes—
726C2×C4—22no—
727C2×C4—26no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—26no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—26no—
736C2×C4—26no—
737C2×C4—26no—
738C2×C4—26no—
739C2×C4—248no—
740C2×C4—248no—
741C2×C4—248no—
742C2×C4—224no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—26no—
746C2×C4—26no—
747C2×C4—26no—
748C2×C4—26no—
749C2×C4—26no—
750C2×C4—212no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—212no—
754C2×C4—424no—
755C2×C4—412no—
756C2×C4—424no—
757C2×C4—48no—
758C2×C4—424no—
759C2×C4—812no—
760C2×C4—812no—
761C2×C4—824no—
762C2×C4—812no—
763C2×C4—812no—
764C2×C4C2×C4×D4148yes—
765C2×C4C24×C414yes—
766C2×C4C24×C4112yes—
767C2×C4C24×C4112yes—
768C2×C4C24×C414yes—
769C2×C4C24×C412yes—
770C2×C4C24×C416yes—
771C2×C4C23×D416yes—
772C2×C4C23×D416yes—
773C2×C4C23×D412yes—
774C2×C4C23×D416yes—
775C2×C4C23×D412yes—
776C2×C4C23×D412yes—
777C2×C4C22×#4112yes—
778C2×C4C22×#4116yes—
779C2×C4#58514yes—
780C2×C4#58514yes—
781C22—26no—
782C22—212no—
783C22—26no—
784C22—212no—
785C22—24no—
786C22—212no—
787C22—28no—
788C22—224no—
789C22—46no—
790C22—42no—
791C22—44no—
792C22—412no—
793C22—42no—
794C22—46no—
795C22—848no—
796C22C22×C4×D4112yes—
797C22C25×C411yescharacteristic
798C22C24×D411yescharacteristic
799C22C23×#4111yescharacteristic
800C22C2×#58512yes—
801C22C2×#58512yes—
802C4—26no—
803C4—24no—
804C4—22no—
805C4—26no—
806C4—24no—
807C4—212no—
808C4—24no—
809C4—212no—
810C4—42no—
811C4—46no—
812C4—46no—
813C4—42no—
814C4—46no—
815C4C22×C4×D4112yes—
816C4C22×C4×D414yes—
817C4#350014yesdirect product factor
818C2—212no—
819C2—44no—
820C2—412no—
821C2C23×C4×D411yescharacteristic
822C2C4×#58512yes—
823C2C2×#350011yescharacteristic
824C2#6281012yes—
825C2#6281211yescharacteristic
subgroupG/H
centerC22×C4C25
commutatorC22C25×C4
Frattini, socle, cosocleC23C26
prime radicalC2×#3500C2
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. C2×C4×2−1+4C2semidirect
3. C2×C4×H(5,𝔽2)C2semidirect
4. #34312C2semidirect
5. #34309C2semidirect
6. #34276C2semidirect
7. #34275C2semidirect
8. #34259C2semidirect
9. #34258C2semidirect
10. #34211C2semidirect
11. #34208C2semidirect
12. #34184C2semidirect
13. C4×#548C2semidirect
14. C4×#546C2semidirect
15. C4×#536C2semidirect
16. C4×#535C2semidirect
17. C4×#532C2semidirect
18. C2×C4×#124C2semidirect
19. C42×#41C2semidirect
22. #3500C4direct (N × H)
35. C2×#520C22semidirect
36. C2×#520C22semidirect
37. C2×#519C22semidirect
38. C2×#519C22semidirect
46. C2×C4×#41C22semidirect
47. C2×C4×#41C22semidirect
48. C22×C4×Q8C22semidirect
49. C22×C4×Q8C22semidirect
52. #2367C22semidirect
53. #2367C22semidirect
54. #2364C22semidirect
55. #2363C22semidirect
56. #2362C22semidirect
57. #2361C22semidirect
58. #2360C22semidirect
59. #2359C22semidirect
60. #2358C22semidirect
61. #2352C22semidirect
62. #2352C22semidirect
63. #2351C22semidirect
64. #2349C22semidirect
65. #2342C22semidirect
67. Q8×C22⋊C4C22semidirect
68. #2339C22semidirect
70. #2328C22semidirect
71. #2327C22semidirect
72. #2326C22semidirect
73. #2326C22semidirect
74. #2324C22semidirect
75. #2323C22semidirect
76. #2322C22semidirect
77. #2321C22semidirect
78. #2317C22semidirect
79. #2317C22semidirect
81. #2311C22semidirect
82. #2310C22semidirect
84. C4×C4⋊Q8C22semidirect
85. C4×C4⋊Q8C22semidirect
86. C4×#127C22semidirect
87. C4×#127C22semidirect
88. C4×#124C22semidirect
89. C4×#124C22semidirect
90. C4×#124C22semidirect
91. C4×#124C22semidirect
92. C4×#124C22semidirect
93. C4×#124C22semidirect
94. C4×#124C22semidirect
95. C4×#124C22semidirect
96. C4×#124C22semidirect
97. C4×C22⋊Q8C22semidirect
98. C4×#123C22semidirect
99. C4×#121C22semidirect
100. C4×#121C22semidirect
101. C4×#121C22semidirect
102. C4×#120C22semidirect
104. #2297C22semidirect
105. C2×#391C22semidirect
106. #2293C22semidirect
108. C2×#388C22semidirect
109. #2285C22semidirect
110. C2×#382C22semidirect
111. C42×Q8C22semidirect
112. C42×Q8C22semidirect
113. C42×D4C22semidirect
114. C42×D4C22semidirect
115. C42×D4C22semidirect
116. C4×#117C22semidirect
117. C4×#117C22semidirect
118. C4×#117C22semidirect
119. C2×C4×C22⋊C4C22semidirect
120. C2×C43C22semidirect
123. C2×2−1+4C2×C4semidirect
126. C2×H(5,𝔽2)C2×C4semidirect
137. #548C2×C4semidirect
138. #546C2×C4semidirect
139. #536C2×C4semidirect
140. #535C2×C4semidirect
141. #532C2×C4semidirect
144. C2×#124C2×C4semidirect
169. C4×#41C2×C4semidirect
170. C4×#41D4semidirect
338. C2×#41C22×C4semidirect
339. C2×#41C22×C4semidirect
346. C22×Q8C22×C4semidirect
347. C22×Q8C22×C4semidirect
382. C4⋊Q8C22×C4semidirect
383. #127C22×C4semidirect
384. #124C22×C4semidirect
385. #124C22×C4semidirect
386. #124C22×C4semidirect
387. #124C22×C4semidirect
388. #123C22×C4semidirect
389. C22⋊Q8C22×C4semidirect
390. #121C22×C4semidirect
391. #121C22×C4semidirect
392. #120C22×C4semidirect
405. C4×Q8C22×C4semidirect
428. C4×D4C22×C4semidirect
429. C4×D4C22×C4semidirect
440. #117C22×C4semidirect
468. C2×C22⋊C4C22×C4semidirect
493. C2×C42C22×C4semidirect
542. #41C4×D4semidirect
817. C4#3500direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35002
C2×C4×2−1+42
C2×C4×H(5,𝔽2)2
#343122
#343092
#342762
#342752
#342592
#342582
#342112
#342082
#341842
C4×#5482
C4×#5462
C4×#5362
C4×#5352
C4×#5322
C2×C4×#1242
C42×#412