Finite Group Databasebeta

← C2×#24916177 #36268281

Subgroups — C2×#24916177 #36268281

Order 21248.

2806 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581800C211yesmaximal, characteristic, complemented
2C22×#14581798C211yesmaximal, characteristic, complemented
3C2×#19128248C211yesmaximal, characteristic
4#24916177C2116yesmaximal, direct product factor
5C2×#19127775C211yesmaximal, characteristic, complemented
6C2×#19127774C211yesmaximal, characteristic, complemented
7C2×#19127773C211yesmaximal, characteristic, complemented
8C2×#19127772C211yesmaximal, characteristic, complemented
9C2×#19127771C211yesmaximal, characteristic, complemented
10C2×#19127770C211yesmaximal, characteristic, complemented
11C2×#19127769C211yesmaximal, characteristic, complemented
12C2×#19127723C211yesmaximal, characteristic, complemented
13C2×#19127666C211yesmaximal, characteristic, complemented
14C2×#19127666C211yesmaximal, characteristic, complemented
15C2×#97×D83C211yesmaximal, characteristic, complemented
16C2×#435×C83C211yesmaximal, characteristic, complemented
17C22×#13050590C2211yescharacteristic
18C22×#13050590C2211yescharacteristic
19C2×#14581800—28no—
20C2×#14581800C2218yescomplemented
21C2×#14581798—28no—
22C2×#14581798C2218yescomplemented
23C22×#13050574C2211yescharacteristic
24C22×#13050573C2211yescharacteristic
25C22×#13050573C2211yescharacteristic
26C22×#13050573C2211yescharacteristic
27C22×#13050573C2211yescharacteristic
28C23×C83⋊C8C2211yescharacteristic
29C22×C8×D83C2211yescharacteristic
30C22×C8×D83C2211yescharacteristic
31C22×C8×D83C2211yescharacteristic
32C22×C8×D83C2211yescharacteristic
33#19128248C418yes—
34#19128248C2218yes—
35C2×#14581791C411yescharacteristic
36C2×#14581788C411yescharacteristic
37C2×#14581778C411yescharacteristic
38C2×#14581778C411yescharacteristic
39C2×#14581767C411yescharacteristic
40C2×#14581765C411yescharacteristic
41C2×#14581765C411yescharacteristic
42C2×#14581763C411yescharacteristic
43C2×C4×D332C2211yescharacteristic
44C2×C4×C22⋊D83C2211yescharacteristic
45C2×C4×C22⋊D83C2211yescharacteristic
46C2×C42×D83C2211yescharacteristic
47#19127775C2218yescomplemented
48#19127774C2218yescomplemented
49#19127773C2218yescomplemented
50#19127772C2218yescomplemented
51#19127771C2218yescomplemented
52#19127770C2218yescomplemented
53#19127769C2218yescomplemented
54#19127723C2218yescomplemented
55C2×C4⋊(C83⋊C8)C2211yescharacteristic
56C2×Dic83⋊C8C2211yescharacteristic
57C2×Dic83⋊C8C2211yescharacteristic
58#19127666C2218yescomplemented
59#19127666C2218yescomplemented
60C2×C22⋊(C83⋊C8)C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×(C2×D83)⋊C8C2211yescharacteristic
63C2×(C2×D83)⋊C8C2211yescharacteristic
64C2×(C2×D83)⋊C8C2211yescharacteristic
65C2×(C2×D83)⋊C8C2211yescharacteristic
66C2×#14581703C2211yescharacteristic
67C2×#14581702C2211yescharacteristic
68C2×#14581702C2211yescharacteristic
69#97×D83C2218yescomplemented
70C22×M16×C83C2211yescharacteristic
71C23×C8×C83C2211yescharacteristic
72C2×C4×D4×C83C2211yescharacteristic
73#435×C83C2218yescomplemented
74C2×C4⋊C8×C83C2211yescharacteristic
75C2×C22⋊C8×C83C2211yescharacteristic
76C2×C22⋊C8×C83C2211yescharacteristic
77C2×#97×C83C2211yescharacteristic
78C2×#13050590—24no—
79C2×#13050590—24no—
80C2×#13050590—24no—
81C2×#13050590—24no—
82C2×#13050590C2×C414yes—
83C2×#13050590C2×C414yes—
84C2×#13050590C2314yes—
85C2×#13050590C2314yes—
86C22×Dic166C2×C411yescharacteristic
87C22×Dic166C2×C411yescharacteristic
88C22×D332C2×C411yescharacteristic
89C22×D332C2×C411yescharacteristic
90C22×D332C2×C411yescharacteristic
91C22×C22⋊D83C2×C411yescharacteristic
92C22×C22⋊D83C2×C411yescharacteristic
93C22×C22⋊D83C2×C411yescharacteristic
94C22×C22⋊D83C2×C411yescharacteristic
95C22×C22⋊D83C2×C411yescharacteristic
96C22×C22⋊D83C2×C411yescharacteristic
97C22×C4×D83C2×C411yescharacteristic
98C22×C4×D83C2×C411yescharacteristic
99C22×C4×D83C2311yescharacteristic
100C22×C4×D83C2311yescharacteristic
101C22×C4×D83C2311yescharacteristic
102#14581800—232no—
103#14581798—232no—
104C2×#13050574—24no—
105C2×#13050574C2314yes—
106C2×#13050573—24no—
107C2×#13050573—24no—
108C2×#13050573—24no—
109C2×#13050573—24no—
110C2×#13050573C2314yes—
111C2×#13050573C2314yes—
112C2×#13050573C2314yes—
113C2×#13050573C2314yes—
114C22×C83⋊C8—24no—
115C22×C83⋊C8C2311yescharacteristic
116C22×C83⋊C8C2311yescharacteristic
117C22×C83⋊C8C2311yescharacteristic
118C22×C83⋊C8C2314yes—
119C22×C83⋊C8C2311yescharacteristic
120C2×C8×D83—24no—
121C2×C8×D83—24no—
122C2×C8×D83—24no—
123C2×C8×D83D418yescomplemented
124C2×C8×D83C2314yes—
125C2×C8×D83C2314yes—
126C2×C8×D83C2314yes—
127C2×C8×D83C2314yes—
128#14581791C2×C418yes—
129#14581788C2×C418yes—
130#14581778C2×C418yes—
131#14581778C2×C418yes—
132#14581767C2×C418yes—
133#14581765C2×C418yes—
134#14581765C2×C418yes—
135#14581763C2×C418yes—
136C4×D332C2×C414yes—
137C4×D332C2314yes—
138C4×C22⋊D83C2×C414yes—
139C4×C22⋊D83C2×C414yes—
140C4×C22⋊D83C2314yes—
141C4×C22⋊D83C2314yes—
142C2×C4⋊Dic83C2×C411yescharacteristic
143C2×Dic83⋊C4C2×C411yescharacteristic
144C2×Dic83⋊C4C2×C411yescharacteristic
145C2×C22⋊Dic83C2×C411yescharacteristic
146C2×C22⋊Dic83C2×C411yescharacteristic
147C2×(C2×D83)⋊C4C2×C411yescharacteristic
148C2×(C2×D83)⋊C4C2×C411yescharacteristic
149C2×(C2×D83)⋊C4C2×C411yescharacteristic
150C2×(C2×D83)⋊C4C2×C411yescharacteristic
151C2×C4×Dic83C2×C411yescharacteristic
152C2×C4×Dic83C2×C411yescharacteristic
153C2×C4×Dic83C2311yescharacteristic
154C42×D83C2×C414yes—
155C42×D83C2314yes—
156C4⋊(C83⋊C8)C2314yes—
157Dic83⋊C8C2314yes—
158Dic83⋊C8C2314yes—
159C22⋊(C83⋊C8)C2314yes—
160C22⋊(C83⋊C8)C2314yes—
161(C2×D83)⋊C8C2314yes—
162(C2×D83)⋊C8C2314yes—
163(C2×D83)⋊C8C2314yes—
164(C2×D83)⋊C8C2314yes—
165#14581703C2314yes—
166#14581702C2314yes—
167#14581702C2314yes—
168C22×D4×C83C2×C411yescharacteristic
169C23×C4×C83C2311yescharacteristic
170C23×C4×C83C2311yescharacteristic
171C2×M16×C83—24no—
172C2×M16×C83C2314yes—
173C22×C8×C83—24no—
174C22×C8×C83C2311yescharacteristic
175C22×C8×C83C2311yescharacteristic
176C22×C8×C83C2314yes—
177C22×C8×C83C2311yescharacteristic
178C22×C8×C83C2311yescharacteristic
179C4×D4×C83C2×C414yes—
180C4×D4×C83C2314yes—
181C2×C4⋊C4×C83C2×C411yescharacteristic
182C2×C22⋊C4×C83C2×C411yescharacteristic
183C2×C22⋊C4×C83C2×C411yescharacteristic
184C2×C42×C83C2311yescharacteristic
185C4⋊C8×C83C2314yes—
186C22⋊C8×C83C2314yes—
187C22⋊C8×C83C2314yes—
188#97×C83C2314yes—
189C23×D83C22×C411yescharacteristic
190C23×D83C22×C411yescharacteristic
191C23×D83C22×C411yescharacteristic
192#13050590—216no—
193#13050590—216no—
194#13050590—28no—
195#13050590—28no—
196#13050590—28no—
197#13050590—28no—
198C2×Dic166—24no—
199C2×Dic166—24no—
200C2×Dic166C22×C414yes—
201C2×Dic166C22×C414yes—
202C2×D332—24no—
203C2×D332—24no—
204C2×D332—42no—
205C2×D332C22×C414yes—
206C2×D332C22×C414yes—
207C2×D332C22×C414yes—
208C2×C22⋊D83—24no—
209C2×C22⋊D83—24no—
210C2×C22⋊D83—24no—
211C2×C22⋊D83—24no—
212C2×C22⋊D83—42no—
213C2×C22⋊D83—42no—
214C2×C22⋊D83C22×C414yes—
215C2×C22⋊D83C22×C414yes—
216C2×C22⋊D83C22×C414yes—
217C2×C22⋊D83C22×C414yes—
218C2×C22⋊D83C22×C414yes—
219C2×C22⋊D83C22×C414yes—
220C22×Dic83C22×C411yescharacteristic
221C22×Dic83C22×C411yescharacteristic
222C22×Dic83C22×C411yescharacteristic
223C22×Dic83C22×C411yescharacteristic
224C22×Dic83C22×C411yescharacteristic
225C2×C4×D83—22no—
226C2×C4×D83—22no—
227C2×C4×D83—22no—
228C2×C4×D83—22no—
229C2×C4×D83—42no—
230C2×C4×D83—42no—
231C2×C4×D83C22×C412yes—
232C2×C4×D83C22×C412yes—
233C2×C4×D83C22×C414yes—
234C2×C4×D83C22×C414yes—
235C2×C4×D83C22×C412yes—
236C2×C4×D83C2×D414yes—
237C2×C4×D83#4114yes—
238C2×C4×D83C2412yes—
239C2×C4×D83C2412yes—
240C2×C4×D83C2412yes—
241#13050574—28no—
242#13050573—28no—
243#13050573—28no—
244#13050573—28no—
245#13050573—28no—
246C2×C83⋊C8—22no—
247C2×C83⋊C8—22no—
248C2×C83⋊C8—22no—
249C2×C83⋊C8—28no—
250C2×C83⋊C8C2×D414yes—
251C2×C83⋊C8C2412yes—
252C2×C83⋊C8C2412yes—
253C2×C83⋊C8C2412yes—
254C2×C83⋊C8C2412yes—
255C8×D83—28no—
256C8×D83—28no—
257C8×D83—28no—
258C8×D83C2×D4116yescomplemented
259C4⋊Dic83C22×C414yes—
260Dic83⋊C4C22×C414yes—
261Dic83⋊C4C22×C414yes—
262C22⋊Dic83C22×C414yes—
263C22⋊Dic83C22×C414yes—
264(C2×D83)⋊C4C22×C414yes—
265(C2×D83)⋊C4C22×C414yes—
266(C2×D83)⋊C4C22×C414yes—
267(C2×D83)⋊C4C22×C414yes—
268C4×Dic83C22×C414yes—
269C4×Dic83C22×C414yes—
270C4×Dic83C22×C412yes—
271C4×Dic83C2412yes—
272C24×C83C22×C411yescharacteristic
273C24×C83C22×C411yescharacteristic
274C2×D4×C83—42no—
275C2×D4×C83C22×C414yes—
276C22×C4×C83—22no—
277C22×C4×C83—22no—
278C22×C4×C83—22no—
279C22×C4×C83—22no—
280C22×C4×C83C22×C411yescharacteristic
281C22×C4×C83C22×C411yescharacteristic
282C22×C4×C83C22×C411yescharacteristic
283C22×C4×C83C22×C411yescharacteristic
284C22×C4×C83C22×C412yes—
285C22×C4×C83C22×C412yes—
286C22×C4×C83C2412yes—
287C22×C4×C83C2412yes—
288C22×C4×C83C2411yescharacteristic
289M16×C83—28no—
290C2×C8×C83—22no—
291C2×C8×C83—22no—
292C2×C8×C83—22no—
293C2×C8×C83—28no—
294C2×C8×C83C2×D414yes—
295C2×C8×C83C2412yes—
296C2×C8×C83C2412yes—
297C2×C8×C83C2412yes—
298C2×C8×C83C2412yes—
299C4⋊C4×C83C22×C414yes—
300C22⋊C4×C83C22×C414yes—
301C22⋊C4×C83C22×C414yes—
302C42×C83C22×C412yes—
303C42×C83C2412yes—
304C23×C83—22no—
305C23×C83—22no—
306C23×C83—22no—
307C23×C83—22no—
308C23×C83—22no—
309C23×C83—22no—
310C23×C83C23×C412yes—
311C23×C83C23×C412yes—
312C23×C83C23×C411yescharacteristic
313C22×D83—22no—
314C22×D83—22no—
315C22×D83—22no—
316C22×D83—22no—
317C22×D83—22no—
318C22×D83—22no—
319C22×D83—22no—
320C22×D83—22no—
321C22×D83C4×D414yes—
322C22×D83C23×C412yes—
323C22×D83C23×C412yes—
324C22×D83C23×C412yes—
325D4×C83—44no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—24no—
331C2×C4×C83—24no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
334C2×C4×C83—22no—
335C2×C4×C83—22no—
336C2×C4×C83C23×C412yes—
337C2×C4×C83C23×C412yes—
338C2×C4×C83C23×C412yes—
339C2×C4×C83C23×C412yes—
340C2×C4×C83C23×C411yescharacteristic
341C2×C4×C83C22×D412yes—
342C2×C4×C83C2×#4112yes—
343C2×C4×C83C2511yescharacteristic
344C22⋊D83—28no—
345C22⋊D83—28no—
346C22⋊D83—28no—
347C22⋊D83—28no—
348C22⋊D83—44no—
349C22⋊D83—44no—
350C2×Dic83—22no—
351C2×Dic83—22no—
352C2×Dic83—22no—
353C2×Dic83—22no—
354C2×Dic83C4×D414yes—
355C2×Dic83C23×C412yes—
356C2×Dic83C23×C412yes—
357C2×Dic83C23×C412yes—
358C2×Dic83C23×C412yes—
359C2×Dic83C23×C412yes—
360D332—28no—
361D332—28no—
362D332—44no—
363C4×D83—24no—
364C4×D83—24no—
365C4×D83—22no—
366C4×D83—22no—
367C4×D83—22no—
368C4×D83—22no—
369C4×D83—44no—
370C4×D83—44no—
371C4×D83C4×D418yes—
372C4×D83C22×D414yes—
373C4×D83C2×#4114yes—
374Dic166—28no—
375Dic166—28no—
376C8×C83—22no—
377C8×C83—22no—
378C8×C83—22no—
379C8×C83C22×D414yes—
380C83⋊C8—22no—
381C83⋊C8—22no—
382C83⋊C8—22no—
383C83⋊C8C22×D414yes—
384C22×C83—22no—
385C22×C83—22no—
386C22×C83—22no—
387C22×C83—22no—
388C22×C83—22no—
389C22×C83—22no—
390C22×C83—44no—
391C22×C83—44no—
392C22×C83C2×C4×D412yes—
393C22×C83#56812yes—
394C22×C83#56812yes—
395C22×C83C24×C411yescharacteristic
396C2×D83—28no—
397C2×D83—22no—
398C2×D83—22no—
399C2×D83—22no—
400C2×D83—22no—
401C2×D83—22no—
402C2×D83—22no—
403C2×D83—22no—
404C2×D83—22no—
405C2×D83—44no—
406C2×D83—44no—
407C2×D83C2×C4×D414yes—
408C4×C83—22no—
409C4×C83—22no—
410C4×C83—22no—
411C4×C83—22no—
412C4×C83C2×C4×D412yes—
413C4×C83C23×D411yescharacteristic
414C4×C83C22×#4111yescharacteristic
415Dic83—22no—
416Dic83—22no—
417Dic83—22no—
418Dic83—22no—
419Dic83C2×C4×D414yes—
420C2×#2932—831nomaximal, Sylow
421C2×C83—42no—
422C2×C83—42no—
423C2×C83#293214yescomplemented
424C2×C83C22×C4×D411yescharacteristic
425C2×C83C2×#56811yescharacteristic
426C2×C83C2×#56811yescharacteristic
427D83—24no—
428D83—42no—
429D83—42no—
430C22×#131—831no—
431C22×#131—831no—
432C2×#532—831no—
433#2932—8316no—
434C2×#435—831no—
435C2×#435—831no—
436C2×#435—831no—
437C2×#435—831no—
438C2×#435—831no—
439C2×#435—831no—
440C2×#435—831no—
441C2×#435D8311yescharacteristic, complemented
442C2×#423—831no—
443C2×#408—831no—
444C2×#408—831no—
445C22×#97—831no—
446C83C2×#293211yescharacteristic, complemented, Sylow
447C22×#41—831no—
448C22×#41—831no—
449C2×#131—838no—
450C2×#131—838no—
451C2×#131—1668no—
452C2×#131—1668no—
453C22×M16—831no—
454C22×M16—831no—
455C22×M16—831no—
456C22×M16—831no—
457C22×M16—831no—
458C22×M16C2×D8311yescharacteristic
459C23×C8—831no—
460C23×C8—831no—
461C23×C8—831no—
462C23×C8—831no—
463C23×C8—831no—
464C23×C8C2×D8311yescharacteristic
465#532—838no—
466#532—838no—
467C2×C4⋊Q8—831no—
468C2×#127—831no—
469C2×#124—831no—
470C2×#124—831no—
471C2×#121—831no—
472C2×#121—831no—
473C2×#121—831no—
474C2×#121—831no—
475C2×C4×D4—831no—
476C2×C4×D4—831no—
477C2×C4×D4—831no—
478C2×C4×D4C2×D8311yescharacteristic
479C22×C42—831no—
480#435—838no—
481#435—838no—
482#435—838no—
483#435—838no—
484#435—838no—
485#435—838no—
486#435—838no—
487#435C2×D8318yescomplemented
488#423—838no—
489C2×C4⋊C8—831no—
490C2×C4⋊C8—831no—
491C2×C4⋊C8—831no—
492C2×C4⋊C8C2×D8311yescharacteristic
493#408—838no—
494#408—838no—
495C2×C22⋊C8—831no—
496C2×C22⋊C8—831no—
497C2×C22⋊C8—831no—
498C2×C22⋊C8—831no—
499C2×C22⋊C8—831no—
500C2×C22⋊C8—831no—
501C2×C22⋊C8C2×D8311yescharacteristic
502C2×C22⋊C8C2×D8311yescharacteristic
503C2×#97—831no—
504C2×#97—831no—
505C2×#97—831no—
506C2×#97—838no—
507C2×#97C2×D8311yescharacteristic
508C2×#41—834no—
509C2×#41—834no—
510C2×#41—834no—
511C2×#41—834no—
512C2×#41—1664no—
513C2×#41—1664no—
514C2×#41—1664no—
515C2×#41—1664no—
516C22×Q8—831no—
517C22×Q8—831no—
518C22×D4—831no—
519C22×D4—831no—
520C22×D4—831no—
521C22×D4—831no—
522C22×D4—831no—
523C22×D4—831no—
524C22×D4—831no—
525C22×D4—831no—
526C22×D4—831no—
527C22×D4C4×D8311yescharacteristic
528C23×C4—831no—
529C23×C4—831no—
530C23×C4—831no—
531C23×C4—831no—
532C23×C4—831no—
533C23×C4C22×D8311yescharacteristic
534C23×C4C22×D8311yescharacteristic
535#131—16632no—
536#131—16632no—
537C2×M16—24no—
538C2×M16—834no—
539C2×M16—834no—
540C2×M16—834no—
541C2×M16—834no—
542C2×M16—834no—
543C2×M16—1664no—
544C2×M16—1664no—
545C2×M16—1664no—
546C2×M16—1664no—
547C2×M16—1664no—
548C2×M16C22×D8314yes—
549C22×C8—24no—
550C22×C8—831no—
551C22×C8—838no—
552C22×C8—834no—
553C22×C8—834no—
554C22×C8—831no—
555C22×C8—831no—
556C22×C8—831no—
557C22×C8—834no—
558C22×C8—834no—
559C22×C8—834no—
560C22×C8—1664no—
561C22×C8—1664no—
562C22×C8—1664no—
563C22×C8—1664no—
564C22×C8C22×D8314yes—
565C22×C8C22×D8311yescharacteristic
566C22×C8C22×D8311yescharacteristic
567C22×C8C22×D8311yescharacteristic
568C22×C8C22×D8311yescharacteristic
569C4⋊Q8—838no—
570#127—838no—
571#124—838no—
572#124—838no—
573#121—838no—
574#121—838no—
575#121—838no—
576#121—838no—
577C4×D4—834no—
578C4×D4—834no—
579C4×D4—834no—
580C4×D4—834no—
581C4×D4—834no—
582C4×D4—834no—
583C4×D4C4×D8314yes—
584C4×D4C22×D8314yes—
585C2×C4⋊C4—831no—
586C2×C4⋊C4—831no—
587C2×C4⋊C4—831no—
588C2×C4⋊C4C4×D8311yescharacteristic
589C2×C22⋊C4—831no—
590C2×C22⋊C4—831no—
591C2×C22⋊C4—831no—
592C2×C22⋊C4—831no—
593C2×C22⋊C4—831no—
594C2×C22⋊C4—831no—
595C2×C22⋊C4C4×D8311yescharacteristic
596C2×C22⋊C4C4×D8311yescharacteristic
597C2×C42—831no—
598C2×C42—831no—
599C2×C42—831no—
600C2×C42—834no—
601C2×C42—834no—
602C2×C42C22×D8311yescharacteristic
603C4⋊C8—834no—
604C4⋊C8—834no—
605C4⋊C8—834no—
606C4⋊C8C22×D8314yes—
607C22⋊C8—834no—
608C22⋊C8—834no—
609C22⋊C8—834no—
610C22⋊C8—834no—
611C22⋊C8—834no—
612C22⋊C8—834no—
613C22⋊C8C22×D8314yes—
614C22⋊C8C22×D8314yes—
615#97—834no—
616#97—834no—
617#97—834no—
618#97C22×D8314yes—
619C24—831no—
620C24—831no—
621C24—831no—
622C24C2×C4×D8311yescharacteristic
623C24C2×C4×D8311yescharacteristic
624#41—1668no—
625#41—1668no—
626#41—16616no—
627#41—16616no—
628#41—1668no—
629#41—1668no—
630C2×Q8—834no—
631C2×Q8—834no—
632C2×Q8—1664no—
633C2×Q8—1664no—
634C2×D4—42no—
635C2×D4—3322no—
636C2×D4—3322no—
637C2×D4—3322no—
638C2×D4—834no—
639C2×D4—834no—
640C2×D4—834no—
641C2×D4—834no—
642C2×D4—834no—
643C2×D4—834no—
644C2×D4—834no—
645C2×D4—834no—
646C2×D4—834no—
647C2×D4—1664no—
648C2×D4—1664no—
649C2×D4—1664no—
650C2×D4—1664no—
651C2×D4—1664no—
652C2×D4—1664no—
653C2×D4C2×C4×D8314yes—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—3322no—
659C22×C4—3322no—
660C22×C4—834no—
661C22×C4—834no—
662C22×C4—831no—
663C22×C4—832no—
664C22×C4—834no—
665C22×C4—834no—
666C22×C4—832no—
667C22×C4—831no—
668C22×C4—831no—
669C22×C4—831no—
670C22×C4—831no—
671C22×C4—832no—
672C22×C4—832no—
673C22×C4—832no—
674C22×C4—832no—
675C22×C4—1662no—
676C22×C4—1662no—
677C22×C4—1662no—
678C22×C4—1662no—
679C22×C4C2×C4×D8311yescharacteristic
680C22×C4C2×C4×D8311yescharacteristic
681C22×C4C2×C4×D8311yescharacteristic
682C22×C4C2×C4×D8311yescharacteristic
683C22×C4C2×C4×D8312yes—
684C22×C4C2×C4×D8312yes—
685C22×C4C23×D8312yes—
686C22×C4C23×D8312yes—
687C22×C4C23×D8311yescharacteristic
688M16—28no—
689M16—1668no—
690M16—1668no—
691M16—1668no—
692M16—1668no—
693M16—1668no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—22no—
697C2×C8—28no—
698C2×C8—834no—
699C2×C8—832no—
700C2×C8—8316no—
701C2×C8—832no—
702C2×C8—832no—
703C2×C8—832no—
704C2×C8—1668no—
705C2×C8—1668no—
706C2×C8—1668no—
707C2×C8—1662no—
708C2×C8—1662no—
709C2×C8—1662no—
710C2×C8—1668no—
711C2×C8D4×D8314yes—
712C2×C8C23×D8312yes—
713C2×C8C23×D8312yes—
714C2×C8C23×D8312yes—
715C2×C8C23×D8312yes—
716C4⋊C4—834no—
717C4⋊C4—834no—
718C4⋊C4—834no—
719C4⋊C4C2×C4×D8314yes—
720C22⋊C4—834no—
721C22⋊C4—834no—
722C22⋊C4—834no—
723C22⋊C4—834no—
724C22⋊C4—834no—
725C22⋊C4—834no—
726C22⋊C4C2×C4×D8314yes—
727C22⋊C4C2×C4×D8314yes—
728C42—832no—
729C42—834no—
730C42—834no—
731C42—832no—
732C42C2×C4×D8312yes—
733C42C23×D8312yes—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—834no—
741C23—832no—
742C23—832no—
743C23—832no—
744C23—1662no—
745C23—1662no—
746C23—1662no—
747C23—1662no—
748C23—1662no—
749C23—1662no—
750C23—1662no—
751C23—1662no—
752C23C22×C4×D8312yes—
753C23C22×C4×D8312yes—
754C23C22×C4×D8311yescharacteristic
755Q8—1668no—
756Q8—1668no—
757D4—44no—
758D4—3324no—
759D4—3324no—
760D4—3324no—
761D4—1668no—
762D4—1668no—
763D4—1668no—
764D4—1668no—
765D4—1668no—
766D4—1668no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—3324no—
778C2×C4—3324no—
779C2×C4—834no—
780C2×C4—832no—
781C2×C4—838no—
782C2×C4—834no—
783C2×C4—834no—
784C2×C4—832no—
785C2×C4—832no—
786C2×C4—832no—
787C2×C4—832no—
788C2×C4—1662no—
789C2×C4—1662no—
790C2×C4—1662no—
791C2×C4—1662no—
792C2×C4—1664no—
793C2×C4—1664no—
794C2×C4—1662no—
795C2×C4—1662no—
796C2×C4—1662no—
797C2×C4—1662no—
798C2×C4C22×C4×D8312yes—
799C2×C4C22×C4×D8312yes—
800C2×C4C22×C4×D8312yes—
801C2×C4C22×C4×D8312yes—
802C2×C4C22×C4×D8311yescharacteristic
803C2×C4C2×D4×D8312yes—
804C2×C4#41×D8312yes—
805C2×C4C24×D8311yescharacteristic
806C8—22no—
807C8—22no—
808C8—22no—
809C8—834no—
810C8—1662no—
811C8—1662no—
812C8—1662no—
813C8C2×D4×D8314yes—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—44no—
821C22—44no—
822C22—3324no—
823C22—3324no—
824C22—834no—
825C22—1662no—
826C22—1662no—
827C22—1662no—
828C22—1662no—
829C22—1662no—
830C22—1662no—
831C22—1662no—
832C22—1662no—
833C22—1668no—
834C22C4×D4×D8312yes—
835C22#1912846612yes—
836C22#1912846712yes—
837C22C23×C4×D8311yescharacteristic
838C4—22no—
839C4—22no—
840C4—22no—
841C4—22no—
842C4—834no—
843C4—1662no—
844C4—1662no—
845C4—1662no—
846C4—1662no—
847C4C4×D4×D8312yes—
848C4C22×D4×D8311yescharacteristic
849C4C2×#41×D8311yescharacteristic
850C2—42no—
851C2—42no—
852C2—3322no—
853C2—3322no—
854C2—1664no—
855C2#2491617714yesdirect product factor
856C2C2×C4×D4×D8311yescharacteristic
857C2C2×#1912846611yescharacteristic
858C2C2×#1912846711yescharacteristic
subgroupG/H
centerC22×C4C23×D83
commutatorC22×C83C24×C4
FrattiniC2×C4C24×D83
FittingC2×#435×C83C2
socleC23×C83C23×C4
prime radicalC2×#19128248C2
cosocleC2×C4×C83C25
hypercenterC2×#435D83
hypocenterC83C2×#2932
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C22×#14581800C2semidirect
2. C22×#14581798C2semidirect
4. #24916177C2direct (N × H)
5. C2×#19127775C2semidirect
6. C2×#19127774C2semidirect
7. C2×#19127773C2semidirect
8. C2×#19127772C2semidirect
9. C2×#19127771C2semidirect
10. C2×#19127770C2semidirect
11. C2×#19127769C2semidirect
12. C2×#19127723C2semidirect
13. C2×#19127666C2semidirect
14. C2×#19127666C2semidirect
15. C2×#97×D83C2semidirect
16. C2×#435×C83C2semidirect
20. C2×#14581800C22semidirect
22. C2×#14581798C22semidirect
47. #19127775C22semidirect
48. #19127774C22semidirect
49. #19127773C22semidirect
50. #19127772C22semidirect
51. #19127771C22semidirect
52. #19127770C22semidirect
53. #19127769C22semidirect
54. #19127723C22semidirect
58. #19127666C22semidirect
59. #19127666C22semidirect
69. #97×D83C22semidirect
73. #435×C83C22semidirect
123. C2×C8×D83D4semidirect
258. C8×D83C2×D4semidirect
423. C2×C83#2932semidirect
441. C2×#435D83semidirect
446. C83C2×#2932semidirect
487. #435C2×D83semidirect
855. C2#24916177direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145818002
C22×#145817982
C2×#191282482
#249161772
C2×#191277752
C2×#191277742
C2×#191277732
C2×#191277722
C2×#191277712
C2×#191277702
C2×#191277692
C2×#191277232
C2×#191276662
C2×#97×D832
C2×#435×C832
C2×#293283