Finite Group Databasebeta

← #35565447

Subgroups — #35565447

Order 21248.

5682 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581838C211yesmaximal, characteristic
2C2×#19128183C211yesmaximal, characteristic, complemented
3C2×C4×#13050591C211yesmaximal, characteristic, complemented
4#24910304C211yesmaximal, characteristic, complemented
5#24910301C211yesmaximal, characteristic, complemented
6#24910301C211yesmaximal, characteristic, complemented
7C22⋊C4×D332C213yesmaximal, complemented
8#24910284C213yesmaximal, complemented
9#24910284C213yesmaximal, complemented
10#24910283C213yesmaximal, complemented
11#24910052C213yesmaximal, complemented
12#24910042C213yesmaximal, complemented
13#24909949C213yesmaximal, complemented
14#390×D83C213yesmaximal, complemented
15C83×#2341C211yesmaximal, characteristic, complemented
16C2×#14581838—28no—
17C2×#14581838—28no—
18C2×#14581838C4116yescomplemented
19C22×#13050591C2211yescharacteristic
20C22×#13050591C2211yescharacteristic
21C22×#13050590C2213yes—
22C23×D332C2213yes—
23C22×D4×D83C2213yes—
24C22×D4×D83C2213yes—
25#19128183—28no—
26C4×#13050591—28no—
27C2×Q8×Dic83C2211yescharacteristic, complemented
28C2×Q8×Dic83C2211yescharacteristic, complemented
29C2×C4×D332C2213yescomplemented
30C2×C4×D332C2213yescomplemented
31C2×#14581754C2213yescomplemented
32C2×#14581754C2213yescomplemented
33C2×#14581750C2213yescomplemented
34C2×#14581749C2213yescomplemented
35C2×C4⋊C4×D83C2213yescomplemented
36C2×C22⋊C4×D83C2216yescomplemented
37C2×C22⋊C4×D83C2216yescomplemented
38C2×C42×D83C2213yescomplemented
39#19127605C2211yescharacteristic, complemented
40#19127605C2213yescomplemented
41#19127604C2213yescomplemented
42#19127604C2213yescomplemented
43#19127603C2213yescomplemented
44#19127603C2213yescomplemented
45#19127602C2213yescomplemented
46#19127602C2213yescomplemented
47#19127601C2213yescomplemented
48#19127601C2216yescomplemented
49#19127601C2213yescomplemented
50#19127579C2213yescomplemented
51#19127579C2213yescomplemented
52#19127579C2216yescomplemented
53#19127577C2213yescomplemented
54#19127577C2213yescomplemented
55#19127577C2216yescomplemented
56#19127561C2213yescomplemented
57#19127558C2213yescomplemented
58#19127558C2213yescomplemented
59#19127556C2216yescomplemented
60#19127556C2216yescomplemented
61C4×(C2×D83)⋊C4C2213yescomplemented
62C4×(C2×D83)⋊C4C2213yescomplemented
63C4×C22⋊Dic83C2213yescomplemented
64C22×#41×C83C2211yescharacteristic
65C2×C4×Q8×C83C2211yescharacteristic, complemented
66C2×C4×Q8×C83C2211yescharacteristic, complemented
67#390×C83C2213yescomplemented
68#390×C83C2213yescomplemented
69#380×C83C2213yescomplemented
70C4×C22⋊C4×C83C2213yescomplemented
71C24×D83C2316yes—
72#14581838—2128no—
73C2×#13050591—24no—
74C2×#13050591—24no—
75C2×#13050591C2×C418yes—
76C2×#13050591C2×C418yescomplemented
77C2×#13050591D418yes—
78C2×#13050591D418yes—
79C2×#13050590—212no—
80C2×#13050590—212no—
81C2×#13050590C2×C4124yescomplemented
82C22×Dic166C2311yescharacteristic
83C22×D332—212no—
84C22×D332—212no—
85C22×D332C2×C4124yescomplemented
86C22×D332C2313yes—
87C22×D332C2313yes—
88C22×D332C2313yes—
89C22×C22⋊D83C2313yes—
90C22×C22⋊D83C2313yes—
91C2×D4×D83—212no—
92C2×D4×D83—212no—
93C2×D4×D83—212no—
94C2×D4×D83—212no—
95C2×D4×D83C2×C4124yescomplemented
96C2×D4×D83C2×C4124yescomplemented
97C22×C4×D83C2313yes—
98C22×C4×D83C2313yes—
99C22×C4×D83C2313yes—
100C22×C4×D83C2316yes—
101C22×C4×D83C2313yes—
102Q8×Dic83—24no—
103Q8×Dic83—24no—
104C4×D332—212no—
105C4×D332—212no—
106#14581754—212no—
107#14581754—212no—
108#14581750—212no—
109#14581749—212no—
110C2×C4⋊Dic83C2313yes—
111C2×C4⋊Dic83C2313yes—
112C2×Dic83⋊C4C2313yes—
113C2×Dic83⋊C4C2311yescharacteristic
114C4⋊C4×D83—212no—
115C2×C22⋊Dic83C2313yes—
116C2×C22⋊Dic83C2313yes—
117C2×C22⋊Dic83C2316yes—
118C2×(C2×D83)⋊C4C2313yes—
119C2×(C2×D83)⋊C4C2313yes—
120C2×(C2×D83)⋊C4C2316yes—
121C2×(C2×D83)⋊C4C2313yes—
122C2×(C2×D83)⋊C4C2313yes—
123C2×(C2×D83)⋊C4C2313yes—
124C2×(C2×D83)⋊C4C2313yes—
125C2×(C2×D83)⋊C4C2316yes—
126C2×(C2×D83)⋊C4C2316yes—
127C22⋊C4×D83—412no—
128C22⋊C4×D83—412no—
129C2×C4×Dic83C2311yescharacteristic
130C2×C4×Dic83C2313yes—
131C2×C4×Dic83C2313yes—
132C2×C4×Dic83C2313yes—
133C42×D83—212no—
134C83⋊#95C2313yes—
135C83⋊#95C2313yes—
136C83⋊#95C2313yes—
137C83⋊#95C2311yescharacteristic
138C83⋊#95C2311yescharacteristic
139C83⋊#95C2311yescharacteristic
140C2×#41×C83—24no—
141C2×#41×C83—24no—
142C2×#41×C83C2×C418yescomplemented
143C22×Q8×C83C2311yescharacteristic
144C22×D4×C83C2313yes—
145C23×C4×C83C2313yes—
146C4×Q8×C83—24no—
147C4×Q8×C83—24no—
148C2×C4⋊C4×C83C2313yes—
149C2×C4⋊C4×C83C2313yes—
150C2×C22⋊C4×C83C2313yes—
151C2×C22⋊C4×C83C2313yes—
152C2×C22⋊C4×C83C2316yes—
153C2×C42×C83C2313yes—
154C2×C42×C83C2313yes—
155#95×C83C2311yescharacteristic
156#95×C83C2313yes—
157C23×D83—212no—
158C23×D83—212no—
159C23×D83—46no—
160C23×D83—46no—
161C23×D83—46no—
162C23×D83—46no—
163C23×D83C22×C4124yes—
164C23×D83C2413yes—
165C23×D83C2413yes—
166#13050591—232no—
167#13050591C22⋊C4164yescomplemented
168#13050590—296no—
169C2×Dic166—22no—
170C2×Dic166—22no—
171C2×Dic166C22×C414yes—
172C2×D332—26no—
173C2×D332—26no—
174C2×D332—26no—
175C2×D332—26no—
176C2×D332—296no—
177C2×D332C22×C4112yes—
178C2×D332C22×C4112yes—
179C2×D332C22×C4112yes—
180C2×D332C2×D4112yes—
181C2×D332C2×D4112yes—
182C2×C22⋊D83—26no—
183C2×C22⋊D83—26no—
184C2×C22⋊D83—26no—
185C2×C22⋊D83—26no—
186C2×C22⋊D83C22×C4112yes—
187C2×C22⋊D83C22×C4112yes—
188D4×D83—296no—
189D4×D83—296no—
190C22×Dic83C2413yes—
191C22×Dic83C2413yes—
192C22×Dic83C2411yescharacteristic
193C22×Dic83C2411yescharacteristic
194C22×Dic83C2411yescharacteristic
195C22×Dic83C2411yescharacteristic
196C2×C4×D83—26no—
197C2×C4×D83—26no—
198C2×C4×D83—26no—
199C2×C4×D83—26no—
200C2×C4×D83—26no—
201C2×C4×D83—26no—
202C2×C4×D83—212no—
203C2×C4×D83—43no—
204C2×C4×D83—43no—
205C2×C4×D83—46no—
206C2×C4×D83—46no—
207C2×C4×D83C22×C4112yes—
208C2×C4×D83C22×C4112yes—
209C2×C4×D83C2×D4112yes—
210C2×C4×D83C2×D4112yes—
211C4⋊Dic83—26no—
212C4⋊Dic83—26no—
213Dic83⋊C4—26no—
214Dic83⋊C4—22no—
215C22⋊Dic83—26no—
216C22⋊Dic83—46no—
217C22⋊Dic83—43no—
218(C2×D83)⋊C4—26no—
219(C2×D83)⋊C4—26no—
220(C2×D83)⋊C4—212no—
221(C2×D83)⋊C4—26no—
222(C2×D83)⋊C4—26no—
223(C2×D83)⋊C4—46no—
224(C2×D83)⋊C4—46no—
225(C2×D83)⋊C4—43no—
226(C2×D83)⋊C4—43no—
227C4×Dic83—26no—
228C4×Dic83—26no—
229C4×Dic83—22no—
230C4×Dic83—26no—
231C24×C83C2413yes—
232#41×C83—232no—
233C2×Q8×C83C22×C414yes—
234C2×Q8×C83C2×D414yes—
235C2×Q8×C83C2×D414yes—
236C2×D4×C83—26no—
237C2×D4×C83—26no—
238C2×D4×C83C22×C4112yes—
239C22×C4×C83—26no—
240C22×C4×C83—26no—
241C22×C4×C83C22×C4112yes—
242C22×C4×C83C2413yes—
243C22×C4×C83C2413yes—
244C22×C4×C83C2411yescharacteristic
245C22×C4×C83C2411yescharacteristic
246C22×C4×C83C2411yescharacteristic
247C22×C4×C83C2413yes—
248C4⋊C4×C83—26no—
249C4⋊C4×C83—26no—
250C22⋊C4×C83—26no—
251C22⋊C4×C83—43no—
252C22⋊C4×C83—46no—
253C42×C83—26no—
254C42×C83—26no—
255C23×C83—23no—
256C23×C83—23no—
257C23×C83—23no—
258C23×C83—23no—
259C23×C83—23no—
260C23×C83—23no—
261C23×C83C23×C416yes—
262C23×C83C2511yescharacteristic
263C22×D83—23no—
264C22×D83—23no—
265C22×D83—23no—
266C22×D83—23no—
267C22×D83—23no—
268C22×D83—23no—
269C22×D83—23no—
270C22×D83—23no—
271C22×D83—23no—
272C22×D83—23no—
273C22×D83—248no—
274C22×D83—424no—
275C22×D83—424no—
276C22×D83—812no—
277C22×D83—812no—
278C22×D83—812no—
279C22×D83—812no—
280C22×D83C23×C416yes—
281C22×D83C23×C416yes—
282C22×D83C22×D416yes—
283C22×D83C22×D416yes—
284Q8×C83C2×C22⋊C4116yescomplemented
285D4×C83—224no—
286C2×C4×C83—21no—
287C2×C4×C83—21no—
288C2×C4×C83—21no—
289C2×C4×C83—21no—
290C2×C4×C83—224no—
291C2×C4×C83—21no—
292C2×C4×C83—23no—
293C2×C4×C83—23no—
294C2×C4×C83—23no—
295C2×C4×C83—23no—
296C2×C4×C83—23no—
297C2×C4×C83—21no—
298C2×C4×C83—23no—
299C2×C4×C83—21no—
300C2×C4×C83C23×C412yes—
301C2×C4×C83C23×C416yes—
302C2×C4×C83C22×D416yes—
303C2×C4×C83C22×D416yes—
304C2×C4×C83H(5,𝔽2)12yescomplemented
305C22⋊D83—224no—
306C22⋊D83—224no—
307C2×Dic83—21no—
308C2×Dic83—21no—
309C2×Dic83—21no—
310C2×Dic83—21no—
311C2×Dic83—21no—
312C2×Dic83—23no—
313C2×Dic83—23no—
314C2×Dic83—23no—
315C2×Dic83—23no—
316C2×Dic83—23no—
317C2×Dic83—21no—
318C2×Dic83—23no—
319C2×Dic83—21no—
320C2×Dic83C23×C412yes—
321C2×Dic83C23×C412yes—
322C2×Dic83C22×D412yes—
323C2×Dic83C22×D412yes—
324C2×Dic83H(5,𝔽2)12yescomplemented
325D332—224no—
326D332—224no—
327D332C2×C22⋊C4148yescomplemented
328C4×D83—224no—
329C4×D83—412no—
330C4×D83—412no—
331C4×D83—812no—
332C4×D83C2×C22⋊C4148yescomplemented
333Dic166—28no—
334C22×C83—26no—
335C22×C83—26no—
336C22×C83—26no—
337C22×C83—43no—
338C22×C83—43no—
339C22×C83—43no—
340C22×C83—43no—
341C22×C83C24×C411yescharacteristic
342C22×C83C23×D411yescharacteristic
343C22×C83C23×D411yescharacteristic
344C22×C83C2×H(5,𝔽2)11yescharacteristic
345C22×C83C2×H(5,𝔽2)11yescharacteristic
346C22×C83#58511yescharacteristic
347C22×C83#58511yescharacteristic
348C2×D83—26no—
349C2×D83—26no—
350C2×D83—26no—
351C2×D83—26no—
352C2×D83—26no—
353C2×D83—26no—
354C2×D83—26no—
355C2×D83—26no—
356C2×D83—26no—
357C2×D83—43no—
358C2×D83—43no—
359C2×D83—43no—
360C2×D83—43no—
361C2×D83—848no—
362C2×D83C22×C22⋊C4112yes—
363C4×C83—22no—
364C4×C83—22no—
365C4×C83—43no—
366C4×C83—43no—
367C4×C83—41no—
368C4×C83C22×C22⋊C4112yes—
369Dic83—22no—
370Dic83—22no—
371Dic83—43no—
372Dic83—43no—
373Dic83—41no—
374Dic83C22×C22⋊C414yes—
375#34258—831nomaximal, Sylow
376C2×C83—46no—
377C2×C83C23×C22⋊C411yescharacteristic
378C2×C83C4×H(5,𝔽2)11yescharacteristic
379C2×C83C4×H(5,𝔽2)11yescharacteristic
380C2×C83#348811yescharacteristic
381C2×C83#348811yescharacteristic
382C2×C83#349811yescharacteristic
383C2×C83#350011yescharacteristic
384D83—212no—
385D83—46no—
386C22×H(5,𝔽2)—831no—
387C2×#520—831no—
388C2×C4×#41—831no—
389#2341—831no—
390#2341—831no—
391#2341—831no—
392#2341D8311yescharacteristic, complemented
393D4×C22⋊C4—833no—
394D4×C22⋊C4—833no—
395D4×C22⋊C4—833no—
396D4×C22⋊C4—833no—
397#2311—833no—
398#2309—833no—
399#2297—833no—
400C2×#390—833no—
401C83#3425811yescharacteristic, complemented, Sylow
402C2×H(5,𝔽2)—8316no—
403C2×H(5,𝔽2)—1668no—
404C2×H(5,𝔽2)—1668no—
405C22×#41—831no—
406C22×#41—831no—
407C22×#41—833no—
408C22×#41C2×D8311yescharacteristic
409C23×D4—833no—
410C23×D4—833no—
411C23×D4—833no—
412#520—1668no—
413C4×#41—1668no—
414C2×C4×Q8—831no—
415C2×C4×Q8—831no—
416C2×C4×Q8C2×D8311yescharacteristic, complemented
417C2×C4×Q8C2×D8311yescharacteristic, complemented
418C2×C4×D4—833no—
419C2×C4×D4—833no—
420C2×C4×D4—833no—
421C2×C4×D4—833no—
422C2×#117—833no—
423C2×#117—833no—
424C22×C4⋊C4—833no—
425C22×C22⋊C4—836no—
426C22×C22⋊C4—836no—
427C22×C42—833no—
428#391—833no—
429#391—831no—
430#390—833no—
431#390—833no—
432#390—833no—
433#390—833no—
434#390—833no—
435#390—836no—
436#390—833no—
437#390—833no—
438#390—833no—
439#390C2×D8313yescomplemented
440#390C2×D8313yescomplemented
441#386—836no—
442#386—833no—
443#386—833no—
444#386—836no—
445#386—833no—
446#386—833no—
447#380—833no—
448#380—833no—
449#380—833no—
450#380C2×D8313yescomplemented
451#379—836no—
452#379—836no—
453C4×C22⋊C4—833no—
454C4×C22⋊C4—833no—
455C4×C22⋊C4—833no—
456C4×C22⋊C4C2×D8313yescomplemented
457C25—836no—
458H(5,𝔽2)—166128no—
459C2×#41—24no—
460C2×#41—24no—
461C2×#41—838no—
462C2×#41—838no—
463C2×#41—838no—
464C2×#41—838no—
465C2×#41—8324no—
466C2×#41—16612no—
467C2×#41—16612no—
468C2×#41—1664no—
469C2×#41—1664no—
470C2×#41C4×D8318yescomplemented
471C22×Q8—831no—
472C22×Q8C22×D8311yescharacteristic
473C22×D4—833no—
474C22×D4—833no—
475C22×D4—8324no—
476C22×D4—8324no—
477C22×D4—8324no—
478C22×D4—833no—
479C22×D4—833no—
480C22×D4—833no—
481C22×D4—16612no—
482C22×D4—16612no—
483C22×D4—16612no—
484C22×D4—16612no—
485C22×D4—16612no—
486C22×D4—16612no—
487C22×D4C22×D8313yes—
488C23×C4—836no—
489C23×C4—833no—
490C23×C4—833no—
491C23×C4—833no—
492C23×C4—833no—
493C23×C4C22×D8313yes—
494C4×Q8—24no—
495C4×Q8—24no—
496C4×Q8—1664no—
497C4×Q8—1664no—
498C4×D4—16612no—
499C4×D4—16612no—
500C4×D4—16612no—
501C4×D4—16612no—
502#117—16612no—
503#117—16612no—
504C2×C4⋊C4—833no—
505C2×C4⋊C4—833no—
506C2×C4⋊C4—831no—
507C2×C4⋊C4—833no—
508C2×C4⋊C4—16612no—
509C2×C4⋊C4C22×D8313yes—
510C2×C4⋊C4C22×D8313yes—
511C2×C22⋊C4—33212no—
512C2×C22⋊C4—33212no—
513C2×C22⋊C4—836no—
514C2×C22⋊C4—833no—
515C2×C22⋊C4—836no—
516C2×C22⋊C4—836no—
517C2×C22⋊C4—833no—
518C2×C22⋊C4—833no—
519C2×C22⋊C4—833no—
520C2×C22⋊C4—833no—
521C2×C22⋊C4—833no—
522C2×C22⋊C4—833no—
523C2×C22⋊C4—836no—
524C2×C22⋊C4—833no—
525C2×C22⋊C4C22×D8313yes—
526C2×C22⋊C4C22×D8316yes—
527C2×C22⋊C4C22×D8313yes—
528C2×C42—833no—
529C2×C42—833no—
530C2×C42—833no—
531C2×C42—831no—
532C2×C42—16612no—
533C2×C42C22×D8313yes—
534C2×C42C22×D8313yes—
535#95—831no—
536#95—831no—
537#95—831no—
538#95—833no—
539#95—833no—
540#95—833no—
541#95C22×D8311yescharacteristic
542#95C22×D8313yes—
543C24—3326no—
544C24—3326no—
545C24—3326no—
546C24—3326no—
547C24—8324no—
548C24—833no—
549C24—833no—
550C24—16612no—
551C24—16612no—
552C24C23×D8313yes—
553#41—232no—
554#41—8364no—
555#41—16696no—
556#41—16632no—
557C2×Q8—834no—
558C2×Q8—1662no—
559C2×Q8—1662no—
560C2×Q8C2×C4×D8314yes—
561C2×Q8D4×D8314yes—
562C2×Q8D4×D8314yes—
563C2×D4—26no—
564C2×D4—26no—
565C2×D4—8312no—
566C2×D4—8312no—
567C2×D4—8312no—
568C2×D4—8312no—
569C2×D4—8312no—
570C2×D4—8312no—
571C2×D4—8312no—
572C2×D4—16696no—
573C2×D4—1666no—
574C2×D4—1666no—
575C2×D4—16696no—
576C2×D4—1666no—
577C2×D4—1666no—
578C2×D4—16696no—
579C2×D4—1666no—
580C2×D4—1666no—
581C2×D4—1666no—
582C2×D4—1666no—
583C2×D4C2×C4×D83112yes—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4—3323no—
587C22×C4—3323no—
588C22×C4—3326no—
589C22×C4—3326no—
590C22×C4—831no—
591C22×C4—8312no—
592C22×C4—8312no—
593C22×C4—8312no—
594C22×C4—831no—
595C22×C4—831no—
596C22×C4—8312no—
597C22×C4—831no—
598C22×C4—833no—
599C22×C4—833no—
600C22×C4—1666no—
601C22×C4—1666no—
602C22×C4—1666no—
603C22×C4—16612no—
604C22×C4—1666no—
605C22×C4—1666no—
606C22×C4—1666no—
607C22×C4C2×C4×D83112yes—
608C22×C4C23×D8313yes—
609C22×C4C23×D8311yescharacteristic
610C22×C4C23×D8313yes—
611C22×C4C23×D8311yescharacteristic
612C22×C4C23×D8311yescharacteristic
613C22×C4C23×D8313yes—
614C4⋊C4—26no—
615C4⋊C4—26no—
616C4⋊C4—1666no—
617C4⋊C4—1662no—
618C4⋊C4—1666no—
619C4⋊C4—1666no—
620C22⋊C4—26no—
621C22⋊C4—46no—
622C22⋊C4—43no—
623C22⋊C4—3326no—
624C22⋊C4—3326no—
625C22⋊C4—3323no—
626C22⋊C4—3323no—
627C22⋊C4—3326no—
628C22⋊C4—3323no—
629C22⋊C4—1666no—
630C22⋊C4—1666no—
631C22⋊C4—16612no—
632C22⋊C4—1666no—
633C22⋊C4—1666no—
634C22⋊C4—1666no—
635C42—26no—
636C42—26no—
637C42—1662no—
638C42—1666no—
639C42—1666no—
640C42—1666no—
641C23—23no—
642C23—23no—
643C23—23no—
644C23—23no—
645C23—23no—
646C23—23no—
647C23—33224no—
648C23—33224no—
649C23—836no—
650C23—836no—
651C23—836no—
652C23—836no—
653C23—66412no—
654C23—66412no—
655C23—66412no—
656C23—66412no—
657C23—16648no—
658C23—1663no—
659C23—1663no—
660C23—1663no—
661C23—1663no—
662C23—1663no—
663C23—1663no—
664C23—1663no—
665C23—1663no—
666C23—1663no—
667C23—1663no—
668C23C22×C4×D8316yes—
669C23C24×D8311yescharacteristic
670Q8—1668no—
671Q8C22⋊C4×D83116yescomplemented
672D4—224no—
673D4—8348no—
674D4—16624no—
675D4—16624no—
676D4—16624no—
677D4—16624no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—224no—
683C2×C4—21no—
684C2×C4—23no—
685C2×C4—23no—
686C2×C4—23no—
687C2×C4—23no—
688C2×C4—23no—
689C2×C4—21no—
690C2×C4—23no—
691C2×C4—21no—
692C2×C4—33212no—
693C2×C4—33212no—
694C2×C4—832no—
695C2×C4—832no—
696C2×C4—832no—
697C2×C4—8348no—
698C2×C4—832no—
699C2×C4—832no—
700C2×C4—66412no—
701C2×C4—1661no—
702C2×C4—1663no—
703C2×C4—1663no—
704C2×C4—1663no—
705C2×C4—1663no—
706C2×C4—1663no—
707C2×C4—1661no—
708C2×C4—1661no—
709C2×C4—1663no—
710C2×C4—1661no—
711C2×C4—1661no—
712C2×C4—1661no—
713C2×C4—1661no—
714C2×C4—16624no—
715C2×C4C22×C4×D8312yes—
716C2×C4C22×C4×D8316yes—
717C2×C4C2×D4×D8316yes—
718C2×C4C2×D4×D8316yes—
719C2×C4#1458183812yescomplemented
720C22—26no—
721C22—26no—
722C22—26no—
723C22—43no—
724C22—43no—
725C22—43no—
726C22—43no—
727C22—3323no—
728C22—3323no—
729C22—3323no—
730C22—3323no—
731C22—8312no—
732C22—66448no—
733C22—1666no—
734C22—1666no—
735C22—1666no—
736C22—1666no—
737C22—1666no—
738C22—1666no—
739C22—1666no—
740C22—1666no—
741C22—1666no—
742C22C23×C4×D8311yescharacteristic
743C22C22×D4×D8311yescharacteristic
744C22C22×D4×D8311yescharacteristic
745C22H(5,𝔽2)×D8311yescharacteristic
746C22C2×#1458183811yescharacteristic
747C22#1912853711yescharacteristic
748C22#1912853811yescharacteristic
749C4—22no—
750C4—22no—
751C4—43no—
752C4—43no—
753C4—41no—
754C4—3323no—
755C4—3323no—
756C4—3321no—
757C4—834no—
758C4—1662no—
759C4—1662no—
760C4C2×C22⋊C4×D83112yes—
761C2—46no—
762C2—3326no—
763C2—16612no—
764C2C22×C22⋊C4×D8311yescharacteristic
765C2#2492066911yescharacteristic
766C2C4×#1458183811yescharacteristic
767C2#2492112911yescharacteristic
768C2#2492113111yescharacteristic
769C2#2492124011yescharacteristic
770C2#2492125411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2341C2
socle, cosocleC23×C83C25
prime radicalC22×#14581838C2
hypercenter#2341D83
hypocenterC83#34258
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#19128183C2semidirect
3. C2×C4×#13050591C2semidirect
4. #24910304C2semidirect
5. #24910301C2semidirect
6. #24910301C2semidirect
7. C22⋊C4×D332C2semidirect
8. #24910284C2semidirect
9. #24910284C2semidirect
10. #24910283C2semidirect
11. #24910052C2semidirect
12. #24910042C2semidirect
13. #24909949C2semidirect
14. #390×D83C2semidirect
15. C83×#2341C2semidirect
18. C2×#14581838C4semidirect
27. C2×Q8×Dic83C22semidirect
28. C2×Q8×Dic83C22semidirect
29. C2×C4×D332C22semidirect
30. C2×C4×D332C22semidirect
31. C2×#14581754C22semidirect
32. C2×#14581754C22semidirect
33. C2×#14581750C22semidirect
34. C2×#14581749C22semidirect
35. C2×C4⋊C4×D83C22semidirect
36. C2×C22⋊C4×D83C22semidirect
37. C2×C22⋊C4×D83C22semidirect
38. C2×C42×D83C22semidirect
39. #19127605C22semidirect
40. #19127605C22semidirect
41. #19127604C22semidirect
42. #19127604C22semidirect
43. #19127603C22semidirect
44. #19127603C22semidirect
45. #19127602C22semidirect
46. #19127602C22semidirect
47. #19127601C22semidirect
48. #19127601C22semidirect
49. #19127601C22semidirect
50. #19127579C22semidirect
51. #19127579C22semidirect
52. #19127579C22semidirect
53. #19127577C22semidirect
54. #19127577C22semidirect
55. #19127577C22semidirect
56. #19127561C22semidirect
57. #19127558C22semidirect
58. #19127558C22semidirect
59. #19127556C22semidirect
60. #19127556C22semidirect
61. C4×(C2×D83)⋊C4C22semidirect
62. C4×(C2×D83)⋊C4C22semidirect
63. C4×C22⋊Dic83C22semidirect
65. C2×C4×Q8×C83C22semidirect
66. C2×C4×Q8×C83C22semidirect
67. #390×C83C22semidirect
68. #390×C83C22semidirect
69. #380×C83C22semidirect
70. C4×C22⋊C4×C83C22semidirect
76. C2×#13050591C2×C4semidirect
81. C2×#13050590C2×C4semidirect
85. C22×D332C2×C4semidirect
95. C2×D4×D83C2×C4semidirect
96. C2×D4×D83C2×C4semidirect
142. C2×#41×C83C2×C4semidirect
167. #13050591C22⋊C4semidirect
284. Q8×C83C2×C22⋊C4semidirect
304. C2×C4×C83H(5,𝔽2)semidirect
324. C2×Dic83H(5,𝔽2)semidirect
327. D332C2×C22⋊C4semidirect
332. C4×D83C2×C22⋊C4semidirect
392. #2341D83semidirect
401. C83#34258semidirect
416. C2×C4×Q8C2×D83semidirect
417. C2×C4×Q8C2×D83semidirect
439. #390C2×D83semidirect
440. #390C2×D83semidirect
450. #380C2×D83semidirect
456. C4×C22⋊C4C2×D83semidirect
470. C2×#41C4×D83semidirect
671. Q8C22⋊C4×D83semidirect
719. C2×C4#14581838semidirect

Maximal subgroups

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

subgroupindex
C22×#145818382
C2×#191281832
C2×C4×#130505912
#249103042
#249103012
C22⋊C4×D3322
#249102842
#249102832
#249100522
#249100422
#249099492
#390×D832
C83×#23412
#3425883