Finite Group Databasebeta

← C2×#24916603 #36269484

Subgroups — C2×#24916603 #36269484

Order 21248.

1938 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128231C211yesmaximal, characteristic
2#24916603C2116yesmaximal, direct product factor
3C2×#19127829C211yesmaximal, characteristic, complemented
4C2×#19127828C211yesmaximal, characteristic, complemented
5C2×#19127772C211yesmaximal, characteristic, complemented
6C2×#19127770C211yesmaximal, characteristic, complemented
7C2×#19127769C211yesmaximal, characteristic, complemented
8C2×D4×C83⋊C8C211yesmaximal, characteristic, complemented
9C2×(C22⋊D83)⋊C8C211yesmaximal, characteristic, complemented
10C2×#19127763C211yesmaximal, characteristic, complemented
11C2×#19127759C211yesmaximal, characteristic, complemented
12C2×#19127755C211yesmaximal, characteristic, complemented
13C2×#19127729C211yesmaximal, characteristic, complemented
14C2×#19127726C211yesmaximal, characteristic, complemented
15C22×Dic83⋊C8C211yesmaximal, characteristic, complemented
16C2×#435×C83C211yesmaximal, characteristic, complemented
17C22×#13050573C2211yescharacteristic
18C23×C83⋊C8C2211yescharacteristic
19C23×C83⋊C8C2211yescharacteristic
20C22×C8×D83C2211yescharacteristic
21#19128231C418yes—
22#19128231C2218yes—
23C2×#14581787C411yescharacteristic
24C2×#14581785C411yescharacteristic
25C2×#14581782C411yescharacteristic
26C2×#14581778C411yescharacteristic
27C2×#14581776C411yescharacteristic
28C2×#14581773C411yescharacteristic
29C2×#14581769C411yescharacteristic
30C2×#14581764C411yescharacteristic
31C2×C4×Dic166C2211yescharacteristic
32C2×C4×C22⋊D83C2211yescharacteristic
33C2×C4×C22⋊D83C2211yescharacteristic
34C2×#14581751C2211yescharacteristic
35C2×#14581749C2211yescharacteristic
36C22×C4×Dic83C2211yescharacteristic
37#19127829C2218yescomplemented
38#19127828C2218yescomplemented
39#19127772C2218yescomplemented
40#19127770C2218yescomplemented
41#19127769C2218yescomplemented
42D4×C83⋊C8C2218yescomplemented
43(C22⋊D83)⋊C8C2218yescomplemented
44#19127763C2218yescomplemented
45#19127759C2218yescomplemented
46#19127755C2218yescomplemented
47#19127729C2218yescomplemented
48#19127726C2218yescomplemented
49C2×C4⋊(C83⋊C8)C2211yescharacteristic
50C2×Dic83⋊C8C2211yescharacteristic
51C2×Dic83⋊C8C2211yescharacteristic
52C2×Dic83⋊C8C2211yescharacteristic
53C2×Dic83⋊C8C2211yescharacteristic
54C2×Dic83⋊C8C2211yescharacteristic
55C2×Dic83⋊C8C2211yescharacteristic
56C2×Dic83⋊C8C2211yescharacteristic
57C2×Dic83⋊C8C2211yescharacteristic
58C2×Dic83⋊C8C2218yescomplemented
59C2×C22⋊(C83⋊C8)C2211yescharacteristic
60C2×C22⋊(C83⋊C8)C2211yescharacteristic
61C2×(C2×D83)⋊C8C2211yescharacteristic
62C2×(C2×D83)⋊C8C2211yescharacteristic
63C2×#14581702C2211yescharacteristic
64C2×#14581702C2211yescharacteristic
65C2×#14581702C2211yescharacteristic
66C2×C4×C83⋊C8C2211yescharacteristic
67C2×C8×Dic83C2211yescharacteristic
68C22×M16×C83C2211yescharacteristic
69C23×C8×C83C2211yescharacteristic
70C2×C4×D4×C83C2211yescharacteristic
71#435×C83C2218yescomplemented
72C2×C4⋊C8×C83C2211yescharacteristic
73C2×C22⋊C8×C83C2211yescharacteristic
74C2×C22⋊C8×C83C2211yescharacteristic
75C2×#97×C83C2211yescharacteristic
76C22×Dic166C2×C411yescharacteristic
77C22×C22⋊D83C2×C411yescharacteristic
78C22×C22⋊D83C2×C411yescharacteristic
79C23×Dic83C2×C411yescharacteristic
80C23×Dic83C2×C411yescharacteristic
81C22×C4×D83C2311yescharacteristic
82C2×#13050573—42no—
83C2×#13050573C2314yes—
84C22×C83⋊C8—42no—
85C22×C83⋊C8—42no—
86C22×C83⋊C8C2311yescharacteristic
87C22×C83⋊C8C2311yescharacteristic
88C22×C83⋊C8C2311yescharacteristic
89C22×C83⋊C8C2311yescharacteristic
90C22×C83⋊C8C2314yes—
91C22×C83⋊C8C2314yes—
92C2×C8×D83—42no—
93C2×C8×D83C2314yes—
94#14581787C2×C418yes—
95#14581785C2×C418yes—
96#14581782C2×C418yes—
97#14581778C2×C418yes—
98#14581776C2×C418yes—
99#14581773C2×C418yes—
100#14581769C2×C418yes—
101#14581764C2×C418yes—
102C4×Dic166C2×C414yes—
103C4×Dic166C2314yes—
104C4×C22⋊D83C2×C414yes—
105C4×C22⋊D83C2×C414yes—
106C4×C22⋊D83C2314yes—
107C4×C22⋊D83C2314yes—
108#14581751C2×C414yes—
109#14581751C2314yes—
110#14581749C2×C414yes—
111#14581749C2314yes—
112C2×C4⋊Dic83C2×C411yescharacteristic
113C2×C4⋊Dic83C2×C411yescharacteristic
114C2×C4⋊Dic83C2×C411yescharacteristic
115C2×Dic83⋊C4C2×C411yescharacteristic
116C2×Dic83⋊C4C2×C411yescharacteristic
117C2×Dic83⋊C4C2×C411yescharacteristic
118C2×Dic83⋊C4C2×C411yescharacteristic
119C2×Dic83⋊C4C2×C411yescharacteristic
120C2×Dic83⋊C4C2×C411yescharacteristic
121C2×C22⋊Dic83C2×C411yescharacteristic
122C2×C22⋊Dic83C2×C411yescharacteristic
123C2×C22⋊Dic83C2×C411yescharacteristic
124C2×C22⋊Dic83C2×C411yescharacteristic
125C2×(C2×D83)⋊C4C2×C411yescharacteristic
126C2×(C2×D83)⋊C4C2×C411yescharacteristic
127C2×(C2×D83)⋊C4C2×C411yescharacteristic
128C2×(C2×D83)⋊C4C2×C411yescharacteristic
129C2×C4×Dic83C2×C411yescharacteristic
130C2×C4×Dic83C2×C411yescharacteristic
131C2×C4×Dic83C2×C414yes—
132C2×C4×Dic83C2311yescharacteristic
133C2×C4×Dic83C2311yescharacteristic
134C2×C4×Dic83C2314yes—
135C2×C4×Dic83C2311yescharacteristic
136C4⋊(C83⋊C8)C2314yes—
137Dic83⋊C8C2314yes—
138Dic83⋊C8C2314yes—
139Dic83⋊C8C2314yes—
140Dic83⋊C8C2314yes—
141Dic83⋊C8C2314yes—
142Dic83⋊C8C2314yes—
143Dic83⋊C8C2314yes—
144Dic83⋊C8C2314yes—
145C22⋊(C83⋊C8)C2314yes—
146C22⋊(C83⋊C8)C2314yes—
147(C2×D83)⋊C8C2314yes—
148(C2×D83)⋊C8C2314yes—
149#14581702C2314yes—
150#14581702C2314yes—
151#14581702C2314yes—
152C4×C83⋊C8C2314yes—
153C8×Dic83C2314yes—
154C22×D4×C83C2×C411yescharacteristic
155C23×C4×C83C2311yescharacteristic
156C23×C4×C83C2311yescharacteristic
157C2×M16×C83—42no—
158C2×M16×C83C2314yes—
159C22×C8×C83—42no—
160C22×C8×C83C2311yescharacteristic
161C22×C8×C83C2311yescharacteristic
162C22×C8×C83C2311yescharacteristic
163C22×C8×C83C2311yescharacteristic
164C22×C8×C83C2314yes—
165C4×D4×C83C2×C414yes—
166C4×D4×C83C2314yes—
167C2×C4⋊C4×C83C2×C411yescharacteristic
168C2×C22⋊C4×C83C2×C411yescharacteristic
169C2×C22⋊C4×C83C2×C411yescharacteristic
170C2×C42×C83C2311yescharacteristic
171C4⋊C8×C83C2314yes—
172C22⋊C8×C83C2314yes—
173C22⋊C8×C83C2314yes—
174#97×C83C2314yes—
175C23×D83C22×C411yescharacteristic
176C2×Dic166—42no—
177C2×Dic166C22×C414yes—
178C2×C22⋊D83—24no—
179C2×C22⋊D83—42no—
180C2×C22⋊D83C22×C414yes—
181C2×C22⋊D83C22×C414yes—
182C22×Dic83—24no—
183C22×Dic83—42no—
184C22×Dic83C22×C414yes—
185C22×Dic83C22×C411yescharacteristic
186C22×Dic83C22×C411yescharacteristic
187C22×Dic83C22×C411yescharacteristic
188C22×Dic83C22×C411yescharacteristic
189C22×Dic83C22×C411yescharacteristic
190C22×Dic83C22×C411yescharacteristic
191C22×Dic83C22×C411yescharacteristic
192C22×Dic83C22×C414yes—
193C2×C4×D83—22no—
194C2×C4×D83—22no—
195C2×C4×D83C22×C412yes—
196C2×C4×D83C2412yes—
197#13050573—44no—
198C2×C83⋊C8—22no—
199C2×C83⋊C8—22no—
200C2×C83⋊C8—22no—
201C2×C83⋊C8—22no—
202C2×C83⋊C8—44no—
203C2×C83⋊C8—44no—
204C2×C83⋊C8C2412yes—
205C2×C83⋊C8C2412yes—
206C2×C83⋊C8C2412yes—
207C2×C83⋊C8C2412yes—
208C8×D83—44no—
209C4⋊Dic83C22×C414yes—
210C4⋊Dic83C22×C414yes—
211C4⋊Dic83C22×C414yes—
212Dic83⋊C4C22×C414yes—
213Dic83⋊C4C22×C414yes—
214Dic83⋊C4C22×C414yes—
215Dic83⋊C4C22×C414yes—
216Dic83⋊C4C22×C414yes—
217Dic83⋊C4C22×C414yes—
218C22⋊Dic83C22×C414yes—
219C22⋊Dic83C22×C414yes—
220C22⋊Dic83C22×C414yes—
221C22⋊Dic83C22×C414yes—
222(C2×D83)⋊C4C22×C414yes—
223(C2×D83)⋊C4C22×C414yes—
224(C2×D83)⋊C4C22×C414yes—
225(C2×D83)⋊C4C22×C414yes—
226C4×Dic83C22×C414yes—
227C4×Dic83C22×C414yes—
228C4×Dic83C22×C412yes—
229C4×Dic83C22×C412yes—
230C4×Dic83C22×C412yes—
231C4×Dic83C2412yes—
232C4×Dic83C2412yes—
233C4×Dic83C2412yes—
234C24×C83C22×C411yescharacteristic
235C24×C83C22×C411yescharacteristic
236C2×D4×C83—24no—
237C2×D4×C83C22×C414yes—
238C22×C4×C83—22no—
239C22×C4×C83—22no—
240C22×C4×C83—22no—
241C22×C4×C83—22no—
242C22×C4×C83C22×C411yescharacteristic
243C22×C4×C83C22×C411yescharacteristic
244C22×C4×C83C22×C411yescharacteristic
245C22×C4×C83C22×C411yescharacteristic
246C22×C4×C83C22×C412yes—
247C22×C4×C83C22×C412yes—
248C22×C4×C83C2412yes—
249C22×C4×C83C2412yes—
250C22×C4×C83C2411yescharacteristic
251M16×C83—44no—
252C2×C8×C83—22no—
253C2×C8×C83—22no—
254C2×C8×C83—22no—
255C2×C8×C83—22no—
256C2×C8×C83—44no—
257C2×C8×C83C2412yes—
258C2×C8×C83C2412yes—
259C2×C8×C83C2412yes—
260C2×C8×C83C2412yes—
261C4⋊C4×C83C22×C414yes—
262C22⋊C4×C83C22×C414yes—
263C22⋊C4×C83C22×C414yes—
264C42×C83C22×C412yes—
265C42×C83C2412yes—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83#13114yes—
272C23×C83C23×C412yes—
273C23×C83C23×C412yes—
274C23×C83C23×C411yescharacteristic
275C22×D83—22no—
276C22×D83—22no—
277C22×D83—22no—
278C22×D83C23×C412yes—
279D4×C83—28no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—24no—
285C2×C4×C83—24no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83C23×C412yes—
291C2×C4×C83C23×C412yes—
292C2×C4×C83C23×C412yes—
293C2×C4×C83C23×C412yes—
294C2×C4×C83C23×C411yescharacteristic
295C2×C4×C83H(5,𝔽2)12yes—
296C2×C4×C832−1+412yes—
297C2×C4×C83C2511yescharacteristic
298C22⋊D83—28no—
299C22⋊D83—44no—
300C2×Dic83—22no—
301C2×Dic83—28no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—44no—
309C2×Dic83C23×C412yes—
310C2×Dic83C23×C412yes—
311C2×Dic83C23×C412yes—
312C2×Dic83C23×C412yes—
313C2×Dic83C23×C412yes—
314C2×Dic83C23×C412yes—
315C2×Dic83C23×C412yes—
316C4×D83—24no—
317C4×D83—22no—
318C4×D83—22no—
319Dic166—44no—
320C8×C83—22no—
321C8×C83—22no—
322C8×C83—22no—
323C8×C83—22no—
324C83⋊C8—22no—
325C83⋊C8—22no—
326C83⋊C8—22no—
327C83⋊C8—22no—
328C22×C83—22no—
329C22×C83—28no—
330C22×C83—22no—
331C22×C83—22no—
332C22×C83—22no—
333C22×C83—22no—
334C22×C83—44no—
335C22×C83#52012yes—
336C22×C83C2×#13114yes—
337C22×C83C2×#13112yes—
338C22×C83#56812yes—
339C22×C83C24×C411yescharacteristic
340C2×D83—22no—
341C2×D83—22no—
342C2×D83—22no—
343C2×D83—44no—
344C4×C83—22no—
345C4×C83—22no—
346C4×C83—22no—
347C4×C83—22no—
348C4×C83#52012yes—
349C4×C83C2×H(5,𝔽2)11yescharacteristic
350C4×C83C2×2−1+411yescharacteristic
351Dic83—22no—
352Dic83—22no—
353Dic83—22no—
354Dic83—22no—
355Dic83—22no—
356Dic83—22no—
357Dic83—22no—
358C2×#2992—831nomaximal, Sylow
359C2×C83—24no—
360C2×C83—42no—
361C2×C83#299214yescomplemented
362C2×C83C2×#52011yescharacteristic
363C2×C83C22×#13111yescharacteristic
364C2×C83C2×#56811yescharacteristic
365D83—42no—
366C2×#529—831no—
367#2992—8316no—
368C2×#446—831no—
369C2×#446—831no—
370C2×#435—831no—
371C2×#435—831no—
372C2×#435—831no—
373C2×#435D8311yescharacteristic, complemented
374C2×C8×D4—831no—
375C2×C8×D4—831no—
376C2×#433—831no—
377C2×#433—831no—
378C2×#432—831no—
379C2×#424—831no—
380C2×#424—831no—
381C22×C4⋊C8—831no—
382C83C2×#299211yescharacteristic, complemented, Sylow
383C22×M16—831no—
384C22×M16C2×D8311yescharacteristic
385C23×C8—831no—
386C23×C8—831no—
387C23×C8—831no—
388C23×C8C2×D8311yescharacteristic
389#529—838no—
390#529—838no—
391C2×#126—831no—
392C2×#126—831no—
393C2×#125—831no—
394C2×#124—831no—
395C2×#123—831no—
396C2×#123—831no—
397C2×C22⋊Q8—831no—
398C2×#121—831no—
399C2×C4×Q8—831no—
400C2×C4×D4—831no—
401C2×C4×D4—831no—
402C2×C4×D4C2×D8311yescharacteristic
403C2×#117—831no—
404C2×#117—831no—
405C22×C42—831no—
406#446—838no—
407#446—838no—
408#435—838no—
409#435—838no—
410#435—838no—
411#435C2×D8318yescomplemented
412C8×D4—838no—
413C8×D4—838no—
414#433—838no—
415#433—838no—
416#432—838no—
417#424—838no—
418#424—838no—
419C2×C4⋊C8—831no—
420C2×C4⋊C8—831no—
421C2×C4⋊C8—831no—
422C2×C4⋊C8—831no—
423C2×C4⋊C8—838no—
424C2×C4⋊C8—831no—
425C2×C4⋊C8—831no—
426C2×C4⋊C8—831no—
427C2×C4⋊C8—831no—
428C2×C4⋊C8—831no—
429C2×C4⋊C8C2×D8311yescharacteristic
430C2×C22⋊C8—831no—
431C2×C22⋊C8—831no—
432C2×C22⋊C8—831no—
433C2×C22⋊C8—831no—
434C2×C22⋊C8C2×D8311yescharacteristic
435C2×C22⋊C8C2×D8311yescharacteristic
436C2×#97—831no—
437C2×#97—831no—
438C2×#97—831no—
439C2×#97C2×D8311yescharacteristic
440C2×C4×C8—831no—
441C2×C4×C8—831no—
442C22×Q8—831no—
443C22×D4—831no—
444C22×D4—831no—
445C22×D4C4×D8311yescharacteristic
446C23×C4—831no—
447C23×C4—831no—
448C23×C4—831no—
449C23×C4C22×D8311yescharacteristic
450C23×C4C22×D8311yescharacteristic
451C2×M16—42no—
452C2×M16—3322no—
453C2×M16—834no—
454C2×M16C22×D8314yes—
455C22×C8—42no—
456C22×C8—3322no—
457C22×C8—3322no—
458C22×C8—3322no—
459C22×C8—834no—
460C22×C8—834no—
461C22×C8—834no—
462C22×C8—831no—
463C22×C8—831no—
464C22×C8—831no—
465C22×C8—831no—
466C22×C8C22×D8311yescharacteristic
467C22×C8C22×D8311yescharacteristic
468C22×C8C22×D8311yescharacteristic
469C22×C8C22×D8311yescharacteristic
470C22×C8C22×D8314yes—
471#126—838no—
472#126—838no—
473#125—838no—
474#124—838no—
475#123—838no—
476#123—838no—
477C22⋊Q8—838no—
478#121—838no—
479C4×Q8—834no—
480C4×Q8—834no—
481C4×D4—834no—
482C4×D4—834no—
483C4×D4—834no—
484C4×D4—834no—
485C4×D4C4×D8314yes—
486C4×D4C22×D8314yes—
487#117—834no—
488#117—834no—
489#117—834no—
490#117—834no—
491C2×C4⋊C4—831no—
492C2×C4⋊C4—831no—
493C2×C4⋊C4—831no—
494C2×C4⋊C4—831no—
495C2×C4⋊C4—831no—
496C2×C4⋊C4—831no—
497C2×C4⋊C4—831no—
498C2×C4⋊C4—831no—
499C2×C4⋊C4—831no—
500C2×C4⋊C4C4×D8311yescharacteristic
501C2×C22⋊C4—831no—
502C2×C22⋊C4—831no—
503C2×C22⋊C4—831no—
504C2×C22⋊C4—831no—
505C2×C22⋊C4—831no—
506C2×C22⋊C4—831no—
507C2×C22⋊C4—831no—
508C2×C22⋊C4—831no—
509C2×C22⋊C4C4×D8311yescharacteristic
510C2×C22⋊C4C4×D8311yescharacteristic
511C2×C42—831no—
512C2×C42—831no—
513C2×C42—834no—
514C2×C42—834no—
515C2×C42—831no—
516C2×C42—831no—
517C2×C42—831no—
518C2×C42C22×D8311yescharacteristic
519C4⋊C8—834no—
520C4⋊C8—834no—
521C4⋊C8—834no—
522C4⋊C8—834no—
523C4⋊C8—834no—
524C4⋊C8—834no—
525C4⋊C8—834no—
526C4⋊C8—834no—
527C4⋊C8—834no—
528C4⋊C8C22×D8314yes—
529C22⋊C8—834no—
530C22⋊C8—834no—
531C22⋊C8—834no—
532C22⋊C8—834no—
533C22⋊C8C22×D8314yes—
534C22⋊C8C22×D8314yes—
535#97—834no—
536#97—834no—
537#97—834no—
538#97C22×D8314yes—
539C4×C8—834no—
540C4×C8—834no—
541C24—831no—
542C24C2×C4×D8311yescharacteristic
543C24C2×C4×D8311yescharacteristic
544C2×Q8—3322no—
545C2×Q8—834no—
546C2×D4—24no—
547C2×D4—3322no—
548C2×D4—834no—
549C2×D4—834no—
550C2×D4—1664no—
551C2×D4C2×C4×D8314yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—3322no—
557C22×C4—834no—
558C22×C4—831no—
559C22×C4—831no—
560C22×C4—831no—
561C22×C4—831no—
562C22×C4—834no—
563C22×C4—831no—
564C22×C4—831no—
565C22×C4—831no—
566C22×C4—832no—
567C22×C4—832no—
568C22×C4—1664no—
569C22×C4—1662no—
570C22×C4—1662no—
571C22×C4C2×C4×D8311yescharacteristic
572C22×C4C2×C4×D8312yes—
573C22×C4C2×C4×D8311yescharacteristic
574C22×C4C2×C4×D8311yescharacteristic
575C22×C4C2×C4×D8311yescharacteristic
576C22×C4C2×C4×D8312yes—
577C22×C4C23×D8312yes—
578C22×C4C23×D8312yes—
579C22×C4C23×D8311yescharacteristic
580M16—44no—
581M16—3324no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—44no—
587C2×C8—3324no—
588C2×C8—3324no—
589C2×C8—3324no—
590C2×C8—832no—
591C2×C8—832no—
592C2×C8—832no—
593C2×C8—832no—
594C2×C8—1662no—
595C2×C8—1662no—
596C2×C8—1662no—
597C2×C8—1662no—
598C2×C8C23×D8312yes—
599C2×C8C23×D8312yes—
600C2×C8C23×D8312yes—
601C2×C8C23×D8312yes—
602C4⋊C4—834no—
603C4⋊C4—834no—
604C4⋊C4—834no—
605C4⋊C4—834no—
606C4⋊C4—834no—
607C4⋊C4—834no—
608C4⋊C4—834no—
609C4⋊C4—834no—
610C4⋊C4—834no—
611C4⋊C4C2×C4×D8314yes—
612C22⋊C4—834no—
613C22⋊C4—834no—
614C22⋊C4—834no—
615C22⋊C4—834no—
616C22⋊C4—834no—
617C22⋊C4—834no—
618C22⋊C4—834no—
619C22⋊C4—834no—
620C22⋊C4C2×C4×D8314yes—
621C22⋊C4C2×C4×D8314yes—
622C42—832no—
623C42—832no—
624C42—834no—
625C42—834no—
626C42—832no—
627C42—832no—
628C42—832no—
629C42—832no—
630C42C2×C4×D8312yes—
631C42C23×D8312yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—832no—
638C23—1662no—
639C23—1662no—
640C23—1662no—
641C23#1458180014yes—
642C23C22×C4×D8312yes—
643C23C22×C4×D8312yes—
644C23C22×C4×D8311yescharacteristic
645Q8—3324no—
646D4—28no—
647D4—3324no—
648D4—1668no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—3324no—
660C2×C4—832no—
661C2×C4—832no—
662C2×C4—832no—
663C2×C4—832no—
664C2×C4—832no—
665C2×C4—832no—
666C2×C4—832no—
667C2×C4—1662no—
668C2×C4—1668no—
669C2×C4—1662no—
670C2×C4—1662no—
671C2×C4—1662no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4—1664no—
676C2×C4—1662no—
677C2×C4—1662no—
678C2×C4C22×C4×D8312yes—
679C2×C4C22×C4×D8312yes—
680C2×C4C22×C4×D8312yes—
681C2×C4C22×C4×D8312yes—
682C2×C4C22×C4×D8311yescharacteristic
683C2×C4#1458183712yes—
684C2×C4#1458183912yes—
685C2×C4C24×D8311yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C8—1662no—
691C8—1662no—
692C8—1662no—
693C8—1662no—
694C22—22no—
695C22—22no—
696C22—28no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—3324no—
702C22—1662no—
703C22—1662no—
704C22—1662no—
705C22#1912818012yes—
706C22C2×#1458180014yes—
707C22C2×#1458180012yes—
708C22#1912846612yes—
709C22C23×C4×D8311yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—1662no—
715C4—1662no—
716C4—1662no—
717C4—1662no—
718C4—1662no—
719C4—1662no—
720C4—1662no—
721C4#1912818012yes—
722C4C2×#1458183711yescharacteristic
723C4C2×#1458183911yescharacteristic
724C2—24no—
725C2—42no—
726C2—3322no—
727C2#2491660314yesdirect product factor
728C2C2×#1912818011yescharacteristic
729C2C22×#1458180011yescharacteristic
730C2C2×#1912846611yescharacteristic
subgroupG/H
centerC22×C4C23×D83
commutatorC22×C83C24×C4
FrattiniC2×C4C24×D83
FittingC2×#435×C83C2
socleC23×C83C23×C4
prime radicalC2×#14581764C4
cosocleC2×C4×C83C25
hypercenterC2×#435D83
hypocenterC83C2×#2992
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #24916603C2direct (N × H)
3. C2×#19127829C2semidirect
4. C2×#19127828C2semidirect
5. C2×#19127772C2semidirect
6. C2×#19127770C2semidirect
7. C2×#19127769C2semidirect
8. C2×D4×C83⋊C8C2semidirect
9. C2×(C22⋊D83)⋊C8C2semidirect
10. C2×#19127763C2semidirect
11. C2×#19127759C2semidirect
12. C2×#19127755C2semidirect
13. C2×#19127729C2semidirect
14. C2×#19127726C2semidirect
15. C22×Dic83⋊C8C2semidirect
16. C2×#435×C83C2semidirect
37. #19127829C22semidirect
38. #19127828C22semidirect
39. #19127772C22semidirect
40. #19127770C22semidirect
41. #19127769C22semidirect
42. D4×C83⋊C8C22semidirect
43. (C22⋊D83)⋊C8C22semidirect
44. #19127763C22semidirect
45. #19127759C22semidirect
46. #19127755C22semidirect
47. #19127729C22semidirect
48. #19127726C22semidirect
58. C2×Dic83⋊C8C22semidirect
71. #435×C83C22semidirect
361. C2×C83#2992semidirect
373. C2×#435D83semidirect
382. C83C2×#2992semidirect
411. #435C2×D83semidirect
727. C2#24916603direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282312
#249166032
C2×#191278292
C2×#191278282
C2×#191277722
C2×#191277702
C2×#191277692
C2×D4×C83⋊C82
C2×(C22⋊D83)⋊C82
C2×#191277632
C2×#191277592
C2×#191277552
C2×#191277292
C2×#191277262
C22×Dic83⋊C82
C2×#435×C832
C2×#299283