Finite Group Databasebeta

← C2×#23772056 #35152021

Subgroups — C2×#23772056 #35152021

Order 20224.

2254 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D79C211yesmaximal, characteristic
2#23772056C2116yesmaximal, direct product factor
3C2×#19098624C211yesmaximal, characteristic, complemented
4C2×#19098621C211yesmaximal, characteristic, complemented
5C2×#19098621C211yesmaximal, characteristic, complemented
6C2×#19098619C211yesmaximal, characteristic, complemented
7C2×#19098618C211yesmaximal, characteristic, complemented
8C2×#19098615C211yesmaximal, characteristic, complemented
9C2×#19098614C211yesmaximal, characteristic, complemented
10C2×#19098588C211yesmaximal, characteristic, complemented
11C2×#19098588C211yesmaximal, characteristic, complemented
12C2×#19098525C211yesmaximal, characteristic
13C2×C22⋊C8×D79C211yesmaximal, characteristic
14C2×#19098520C211yesmaximal, characteristic, complemented
15C2×#19098517C211yesmaximal, characteristic, complemented
16C2×#433×C79C211yesmaximal, characteristic, complemented
17C23×C4×D79C2211yescharacteristic
18C22×#11929607C2211yescharacteristic
19C22×#11929607C2211yescharacteristic
20C22×C8×D79C2211yescharacteristic
21C22×C8×D79C2211yescharacteristic
22C2×#14579120C2211yescharacteristic
23C2×#14579119C411yescharacteristic
24C2×#14579119C411yescharacteristic
25C2×#14579118C2211yescharacteristic
26C2×#14579118C2211yescharacteristic
27C2×#14579117C411yescharacteristic
28C2×#14579117C411yescharacteristic
29#117×D79C418yes—
30#117×D79C2218yes—
31C2×C4⋊C4×D79C411yescharacteristic
32C2×C4⋊C4×D79C411yescharacteristic
33C2×C22⋊C4×D79C411yescharacteristic
34C2×C22⋊C4×D79C411yescharacteristic
35C2×C42×D79C2211yescharacteristic
36C2×C42×D79C2211yescharacteristic
37#19098624C2218yescomplemented
38#19098621C2218yescomplemented
39#19098621C2218yescomplemented
40#19098619C2218yescomplemented
41#19098618C2218yescomplemented
42#19098615C2218yescomplemented
43#19098614C2218yescomplemented
44#19098588C2218yescomplemented
45#19098588C2218yescomplemented
46C2×C4⋊(C79⋊C8)C2211yescharacteristic, complemented
47C2×C4⋊(C79⋊C8)C2211yescharacteristic, complemented
48C2×Dic79⋊C8C2211yescharacteristic, complemented
49C2×Dic79⋊C8C2211yescharacteristic, complemented
50C2×Dic79⋊C8C2211yescharacteristic, complemented
51C2×Dic79⋊C8C2211yescharacteristic, complemented
52#19098525C2218yes—
53C2×C22⋊(C79⋊C8)C2211yescharacteristic
54C2×C22⋊(C79⋊C8)C2211yescharacteristic
55C2×(C2×D79)⋊C8C2211yescharacteristic
56C2×(C2×D79)⋊C8C2211yescharacteristic
57C2×(C2×D79)⋊C8C2211yescharacteristic
58C2×(C2×D79)⋊C8C2211yescharacteristic
59C22⋊C8×D79C2218yes—
60#19098520C2218yescomplemented
61#19098517C2218yescomplemented
62C2×#14579072C2211yescharacteristic, complemented
63C2×#14579071C2211yescharacteristic, complemented
64C2×#14579071C2211yescharacteristic, complemented
65C2×C4×C79⋊C8C2211yescharacteristic, complemented
66C2×C8×Dic79C2211yescharacteristic, complemented
67C2×C8×Dic79C2211yescharacteristic, complemented
68C2×#117×C79C2211yescharacteristic
69#433×C79C2218yescomplemented
70C2×C4⋊C8×C79C2211yescharacteristic, complemented
71C2×C4⋊C8×C79C2211yescharacteristic, complemented
72C2×C22⋊C8×C79C2211yescharacteristic
73C2×C22⋊C8×C79C2211yescharacteristic
74C2×#97×C79C2211yescharacteristic, complemented
75C2×C4×C8×C79C2211yescharacteristic, complemented
76C24×D79C2×C411yescharacteristic
77C23×Dic79C2×C411yescharacteristic
78C22×C4×D79—24no—
79C22×C4×D79—24no—
80C22×C4×D79C2×C411yescharacteristic
81C22×C4×D79C2×C411yescharacteristic
82C22×C4×D79C2×C411yescharacteristic
83C22×C4×D79C2×C414yes—
84C22×C4×D79C2×C411yescharacteristic
85C22×C4×D79C2×C411yescharacteristic
86C22×C4×D79C2×C411yescharacteristic
87C22×C4×D79C2311yescharacteristic
88C22×C4×D79C2314yes—
89C22×C4×D79C2311yescharacteristic
90C2×#11929607—24no—
91C2×#11929607—24no—
92C2×#11929607C2314yes—
93C2×#11929607C2314yes—
94C22×C79⋊C8C2311yescharacteristic
95C22×C79⋊C8C2311yescharacteristic
96C22×C79⋊C8C2311yescharacteristic
97C22×C79⋊C8C2311yescharacteristic
98C2×C8×D79—24no—
99C2×C8×D79—24no—
100C2×C8×D79C2314yes—
101C2×C8×D79C2314yes—
102#14579120C2×C414yes—
103#14579120C2314yes—
104#14579119C2×C418yes—
105#14579119C2×C418yes—
106#14579118C2×C414yes—
107#14579118C2×C414yes—
108#14579118C2314yes—
109#14579118C2314yes—
110#14579117C2×C418yes—
111#14579117C2×C418yes—
112C2×C4⋊Dic79C2×C411yescharacteristic
113C2×C4⋊Dic79C2×C411yescharacteristic
114C2×Dic79⋊C4C2×C411yescharacteristic
115C2×Dic79⋊C4C2×C411yescharacteristic
116C2×Dic79⋊C4C2×C411yescharacteristic
117C2×Dic79⋊C4C2×C411yescharacteristic
118C4⋊C4×D79C2×C418yes—
119C4⋊C4×D79C2×C418yes—
120C2×C22⋊Dic79C2×C411yescharacteristic
121C2×C22⋊Dic79C2×C411yescharacteristic
122C2×(C2×D79)⋊C4C2×C411yescharacteristic
123C2×(C2×D79)⋊C4C2×C411yescharacteristic
124C2×(C2×D79)⋊C4C2×C411yescharacteristic
125C2×(C2×D79)⋊C4C2×C411yescharacteristic
126C22⋊C4×D79C2×C418yes—
127C22⋊C4×D79C2×C418yes—
128C2×C4×Dic79C2×C411yescharacteristic
129C2×C4×Dic79C2×C411yescharacteristic
130C2×C4×Dic79C2×C411yescharacteristic
131C2×C4×Dic79C2×C411yescharacteristic
132C2×C4×Dic79C2311yescharacteristic
133C2×C4×Dic79C2311yescharacteristic
134C42×D79C2×C414yes—
135C42×D79C2×C414yes—
136C42×D79C2314yes—
137C42×D79C2314yes—
138C4⋊(C79⋊C8)C2314yescomplemented
139C4⋊(C79⋊C8)C2314yescomplemented
140Dic79⋊C8C2314yescomplemented
141Dic79⋊C8C2314yescomplemented
142Dic79⋊C8C2314yescomplemented
143Dic79⋊C8C2314yescomplemented
144C22⋊(C79⋊C8)C2314yes—
145C22⋊(C79⋊C8)C2314yes—
146(C2×D79)⋊C8C2314yes—
147(C2×D79)⋊C8C2314yes—
148(C2×D79)⋊C8C2314yes—
149(C2×D79)⋊C8C2314yes—
150#14579072C2314yescomplemented
151#14579071C2314yescomplemented
152#14579071C2314yescomplemented
153C4×C79⋊C8C2314yescomplemented
154C8×Dic79C2314yescomplemented
155C8×Dic79C2314yescomplemented
156C23×C4×C79C2311yescharacteristic
157C22×C8×C79C2311yescharacteristic
158C22×C8×C79C2311yescharacteristic
159C22×C8×C79C2311yescharacteristic
160C22×C8×C79C2311yescharacteristic
161#117×C79C2×C414yes—
162#117×C79C2314yes—
163C2×C4⋊C4×C79C2×C411yescharacteristic
164C2×C4⋊C4×C79C2×C411yescharacteristic
165C2×C22⋊C4×C79C2×C411yescharacteristic
166C2×C22⋊C4×C79C2×C411yescharacteristic
167C2×C42×C79C2311yescharacteristic
168C2×C42×C79C2311yescharacteristic
169C4⋊C8×C79C2314yescomplemented
170C4⋊C8×C79C2314yescomplemented
171C22⋊C8×C79C2314yes—
172C22⋊C8×C79C2314yes—
173#97×C79C2314yescomplemented
174C4×C8×C79C2314yescomplemented
175C23×D79—24no—
176C23×D79—24no—
177C23×D79—42no—
178C23×D79C22×C414yes—
179C23×D79C22×C411yescharacteristic
180C23×D79C22×C411yescharacteristic
181C22×Dic79—24no—
182C22×Dic79C22×C411yescharacteristic
183C22×Dic79C22×C411yescharacteristic
184C22×Dic79C22×C411yescharacteristic
185C22×Dic79C22×C411yescharacteristic
186C22×Dic79C22×C411yescharacteristic
187C22×Dic79C22×C414yes—
188C22×Dic79C22×C411yescharacteristic
189C2×C4×D79—24no—
190C2×C4×D79—216no—
191C2×C4×D79—28no—
192C2×C4×D79—28no—
193C2×C4×D79—24no—
194C2×C4×D79—24no—
195C2×C4×D79—24no—
196C2×C4×D79—22no—
197C2×C4×D79—22no—
198C2×C4×D79—42no—
199C2×C4×D79—42no—
200C2×C4×D79C22×C412yes—
201C2×C4×D79C22×C414yes—
202C2×C4×D79C22×C414yes—
203C2×C4×D79C22×C414yes—
204C2×C4×D79C22×C414yes—
205C2×C4×D79C22×C414yes—
206C2×C4×D79C22×C414yes—
207C2×C4×D79C22×C412yes—
208C2×C4×D79#4114yes—
209C2×C4×D79#4114yes—
210C2×C4×D79C2412yes—
211C2×C4×D79C2412yes—
212#11929607—28no—
213#11929607—28no—
214C2×C79⋊C8—22no—
215C2×C79⋊C8—22no—
216C2×C79⋊C8—22no—
217C2×C79⋊C8—22no—
218C2×C79⋊C8C2412yes—
219C2×C79⋊C8C2412yes—
220C2×C79⋊C8C2412yes—
221C2×C79⋊C8C2412yes—
222C8×D79—28no—
223C8×D79—28no—
224C4⋊Dic79C22×C414yes—
225C4⋊Dic79C22×C414yes—
226Dic79⋊C4C22×C414yes—
227Dic79⋊C4C22×C414yes—
228Dic79⋊C4C22×C414yes—
229Dic79⋊C4C22×C414yes—
230C22⋊Dic79C22×C414yes—
231C22⋊Dic79C22×C414yes—
232(C2×D79)⋊C4C22×C414yes—
233(C2×D79)⋊C4C22×C414yes—
234(C2×D79)⋊C4C22×C414yes—
235(C2×D79)⋊C4C22×C414yes—
236C4×Dic79C22×C412yes—
237C4×Dic79C22×C412yes—
238C4×Dic79C22×C414yes—
239C4×Dic79C22×C414yes—
240C4×Dic79C22×C414yes—
241C4×Dic79C22×C414yes—
242C4×Dic79C2412yes—
243C4×Dic79C2412yes—
244C24×C79C22×C411yescharacteristic
245C22×C4×C79—22no—
246C22×C4×C79—22no—
247C22×C4×C79C22×C411yescharacteristic
248C22×C4×C79C22×C411yescharacteristic
249C22×C4×C79C22×C411yescharacteristic
250C22×C4×C79C22×C411yescharacteristic
251C22×C4×C79C22×C411yescharacteristic
252C22×C4×C79C22×C412yes—
253C22×C4×C79C2412yes—
254C22×C4×C79C2411yescharacteristic
255C2×C8×C79—22no—
256C2×C8×C79—22no—
257C2×C8×C79—22no—
258C2×C8×C79—22no—
259C2×C8×C79C2412yes—
260C2×C8×C79C2412yes—
261C2×C8×C79C2412yes—
262C2×C8×C79C2412yes—
263C4⋊C4×C79C22×C414yes—
264C4⋊C4×C79C22×C414yes—
265C22⋊C4×C79C22×C414yes—
266C22⋊C4×C79C22×C414yes—
267C42×C79C22×C412yes—
268C42×C79C22×C412yes—
269C42×C79C2412yes—
270C42×C79C2412yes—
271C23×C79—22no—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79C23×C412yes—
275C23×C79C23×C411yescharacteristic
276C22×D79—22no—
277C22×D79—22no—
278C22×D79—22no—
279C22×D79—22no—
280C22×D79—28no—
281C22×D79—28no—
282C22×D79—44no—
283C22×D79—416no—
284C22×D79#11714yes—
285C22×D79#13114yes—
286C22×D79C23×C412yes—
287C22×D79C23×C412yes—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—24no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79C23×C412yes—
297C2×C4×C79C23×C412yes—
298C2×C4×C79C23×C412yes—
299C2×C4×C79C23×C412yes—
300C2×C4×C79C23×C412yes—
301C2×C4×C79C23×C411yescharacteristic
302C2×C4×C79C2×#4112yes—
303C2×C4×C79C2×#4112yes—
304C2×C4×C79C2511yescharacteristic
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—28no—
311C2×Dic79#11714yes—
312C2×Dic79C23×C412yes—
313C2×Dic79C23×C412yes—
314C2×Dic79C23×C412yes—
315C2×Dic79C23×C412yes—
316C2×Dic79C23×C412yes—
317C2×Dic79C23×C412yes—
318C4×D79—28no—
319C4×D79—28no—
320C4×D79—28no—
321C4×D79—24no—
322C4×D79—22no—
323C4×D79—22no—
324C4×D79—28no—
325C4×D79—44no—
326C4×D79—44no—
327C4×D79#11718yes—
328C4×D79C2×#4114yes—
329C4×D79C2×#4114yes—
330C8×C79—22no—
331C8×C79—22no—
332C8×C79—22no—
333C8×C79—22no—
334C79⋊C8—22no—
335C79⋊C8—22no—
336C79⋊C8—22no—
337C79⋊C8—22no—
338C22×C79—22no—
339C22×C79—22no—
340C22×C79—22no—
341C22×C79—44no—
342C22×C79C2×#11712yes—
343C22×C79C2×#13112yes—
344C22×C79#56812yes—
345C22×C79C24×C411yescharacteristic
346C2×D79—22no—
347C2×D79—28no—
348C2×D79—28no—
349C2×D79—22no—
350C2×D79—22no—
351C2×D79—22no—
352C2×D79—416no—
353C2×D79C2×#11714yes—
354C2×D79C2×#13114yes—
355C4×C79—22no—
356C4×C79—22no—
357C4×C79—22no—
358C4×C79—22no—
359C4×C79—22no—
360C4×C79C2×#11712yes—
361C4×C79C22×#4111yescharacteristic
362C4×C79C22×#4111yescharacteristic
363Dic79—22no—
364Dic79—22no—
365Dic79—22no—
366Dic79—22no—
367Dic79—22no—
368Dic79C2×#11714yes—
369C2×#2924—791nomaximal, Sylow
370C2×C79—42no—
371C2×C79#292414yescomplemented
372C2×C79C22×#11711yescharacteristic
373C2×C79C22×#13111yescharacteristic
374C2×C79C2×#56811yescharacteristic
375D79—24no—
376D79—24no—
377C22×#117—791no—
378#2924—7916no—
379C2×#433—791no—
380C2×#433—791no—
381C2×#433—791no—
382C2×#433D7911yescharacteristic, complemented
383C2×#432—791no—
384C2×#432—791no—
385C2×#431—791no—
386C2×#431—791no—
387C2×#424—791no—
388C2×#424—791no—
389C2×#407—791no—
390C22×C22⋊C8—791no—
391C2×#405—791no—
392C2×#405—791no—
393C79C2×#292411yescharacteristic, complemented, Sylow
394C24×C4—791no—
395C22×M16—791no—
396C22×M16—791no—
397C23×C8—791no—
398C23×C8—791no—
399C2×#117—791no—
400C2×#117—798no—
401C2×#117—798no—
402C2×#117—791no—
403C2×#117—791no—
404C2×#117—791no—
405C2×#117—791no—
406C2×#117—791no—
407C2×#117—791no—
408C2×#117C2×D7911yescharacteristic
409C22×C4⋊C4—791no—
410C22×C4⋊C4—791no—
411C22×C22⋊C4—791no—
412C22×C22⋊C4—791no—
413C22×C42—791no—
414C22×C42—791no—
415#433—798no—
416#433—798no—
417#433—798no—
418#433C2×D7918yescomplemented
419#432—798no—
420#432—798no—
421#431—798no—
422#431—798no—
423#424—798no—
424#424—798no—
425C2×C4⋊C8—791no—
426C2×C4⋊C8—791no—
427C2×C4⋊C8—791no—
428C2×C4⋊C8—791no—
429C2×C4⋊C8—791no—
430C2×C4⋊C8—791no—
431C2×C4⋊C8C2×D7911yescharacteristic, complemented
432C2×C4⋊C8C2×D7911yescharacteristic, complemented
433#407—798no—
434C2×C22⋊C8—791no—
435C2×C22⋊C8—791no—
436C2×C22⋊C8—791no—
437C2×C22⋊C8—791no—
438C2×C22⋊C8—791no—
439C2×C22⋊C8—791no—
440C2×C22⋊C8—798no—
441C2×C22⋊C8C2×D7911yescharacteristic
442C2×C22⋊C8C2×D7911yescharacteristic
443#405—798no—
444#405—798no—
445C2×#97—791no—
446C2×#97—791no—
447C2×#97—791no—
448C2×#97C2×D7911yescharacteristic, complemented
449C2×C4×C8—791no—
450C2×C4×C8—791no—
451C2×C4×C8—791no—
452C2×C4×C8C2×D7911yescharacteristic, complemented
453C25—791no—
454C23×C4—791no—
455C23×C4—791no—
456C23×C4—791no—
457C23×C4—791no—
458C23×C4—791no—
459C23×C4—791no—
460C23×C4—791no—
461C23×C4—794no—
462C23×C4—791no—
463C23×C4—794no—
464C23×C4—791no—
465C23×C4—1584no—
466C23×C4—1584no—
467C23×C4C22×D7911yescharacteristic
468C2×M16—794no—
469C2×M16—794no—
470C2×M16—1584no—
471C2×M16—1584no—
472C22×C8—791no—
473C22×C8—791no—
474C22×C8—791no—
475C22×C8—791no—
476C22×C8—794no—
477C22×C8—794no—
478C22×C8—1584no—
479C22×C8—1584no—
480C22×C8C22×D7911yescharacteristic
481C22×C8C22×D7911yescharacteristic
482C22×C8C22×D7911yescharacteristic
483C22×C8C22×D7911yescharacteristic
484#117—794no—
485#117—794no—
486#117—798no—
487#117—798no—
488#117—798no—
489#117—798no—
490#117—794no—
491#117—794no—
492#117—794no—
493#117—794no—
494#117C4×D7914yes—
495#117C22×D7914yes—
496C2×C4⋊C4—791no—
497C2×C4⋊C4—791no—
498C2×C4⋊C4—791no—
499C2×C4⋊C4—791no—
500C2×C4⋊C4—791no—
501C2×C4⋊C4—791no—
502C2×C4⋊C4—798no—
503C2×C4⋊C4—798no—
504C2×C4⋊C4C4×D7911yescharacteristic
505C2×C4⋊C4C4×D7911yescharacteristic
506C2×C22⋊C4—791no—
507C2×C22⋊C4—791no—
508C2×C22⋊C4—791no—
509C2×C22⋊C4—791no—
510C2×C22⋊C4—791no—
511C2×C22⋊C4—791no—
512C2×C22⋊C4—798no—
513C2×C22⋊C4—798no—
514C2×C22⋊C4C4×D7911yescharacteristic
515C2×C22⋊C4C4×D7911yescharacteristic
516C2×C42—791no—
517C2×C42—791no—
518C2×C42—791no—
519C2×C42—791no—
520C2×C42—791no—
521C2×C42—791no—
522C2×C42—794no—
523C2×C42—794no—
524C2×C42—794no—
525C2×C42—794no—
526C2×C42C22×D7911yescharacteristic
527C2×C42C22×D7911yescharacteristic
528C4⋊C8—794no—
529C4⋊C8—794no—
530C4⋊C8—794no—
531C4⋊C8—794no—
532C4⋊C8—794no—
533C4⋊C8—794no—
534C4⋊C8C22×D7914yescomplemented
535C4⋊C8C22×D7914yescomplemented
536C22⋊C8—794no—
537C22⋊C8—794no—
538C22⋊C8—794no—
539C22⋊C8—794no—
540C22⋊C8—794no—
541C22⋊C8—794no—
542C22⋊C8C22×D7914yes—
543C22⋊C8C22×D7914yes—
544#97—794no—
545#97—794no—
546#97—794no—
547#97C22×D7914yescomplemented
548C4×C8—794no—
549C4×C8—794no—
550C4×C8—794no—
551C4×C8C22×D7914yescomplemented
552C24—3162no—
553C24—794no—
554C24—791no—
555C24—791no—
556C24—1584no—
557C24—1584no—
558C24C2×C4×D7911yescharacteristic
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—3162no—
562C22×C4—3162no—
563C22×C4—794no—
564C22×C4—794no—
565C22×C4—791no—
566C22×C4—794no—
567C22×C4—794no—
568C22×C4—792no—
569C22×C4—792no—
570C22×C4—791no—
571C22×C4—791no—
572C22×C4—791no—
573C22×C4—791no—
574C22×C4—791no—
575C22×C4—794no—
576C22×C4—792no—
577C22×C4—792no—
578C22×C4—794no—
579C22×C4—794no—
580C22×C4—794no—
581C22×C4—794no—
582C22×C4—1584no—
583C22×C4—15816no—
584C22×C4—1588no—
585C22×C4—1588no—
586C22×C4—1584no—
587C22×C4—1584no—
588C22×C4—1584no—
589C22×C4—1584no—
590C22×C4—1582no—
591C22×C4—1582no—
592C22×C4C2×C4×D7911yescharacteristic
593C22×C4C2×C4×D7911yescharacteristic
594C22×C4C2×C4×D7911yescharacteristic
595C22×C4C2×C4×D7911yescharacteristic
596C22×C4C2×C4×D7911yescharacteristic
597C22×C4C2×C4×D7912yes—
598C22×C4C23×D7912yes—
599C22×C4C23×D7911yescharacteristic
600M16—1588no—
601M16—1588no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—792no—
607C2×C8—792no—
608C2×C8—792no—
609C2×C8—792no—
610C2×C8—1588no—
611C2×C8—1588no—
612C2×C8—1582no—
613C2×C8—1582no—
614C2×C8—1582no—
615C2×C8—1582no—
616C2×C8C23×D7912yes—
617C2×C8C23×D7912yes—
618C2×C8C23×D7912yes—
619C2×C8C23×D7912yes—
620C4⋊C4—794no—
621C4⋊C4—794no—
622C4⋊C4—794no—
623C4⋊C4—794no—
624C4⋊C4—794no—
625C4⋊C4—794no—
626C4⋊C4C2×C4×D7914yes—
627C4⋊C4C2×C4×D7914yes—
628C22⋊C4—794no—
629C22⋊C4—794no—
630C22⋊C4—794no—
631C22⋊C4—794no—
632C22⋊C4—794no—
633C22⋊C4—794no—
634C22⋊C4C2×C4×D7914yes—
635C22⋊C4C2×C4×D7914yes—
636C42—792no—
637C42—792no—
638C42—794no—
639C42—794no—
640C42—794no—
641C42—794no—
642C42—792no—
643C42—792no—
644C42C2×C4×D7912yes—
645C42C2×C4×D7912yes—
646C42C23×D7912yes—
647C42C23×D7912yes—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—3164no—
652C23—31616no—
653C23—794no—
654C23—794no—
655C23—792no—
656C23—792no—
657C23—1588no—
658C23—1588no—
659C23—1582no—
660C23—1582no—
661C23—1582no—
662C23—1582no—
663C23C22×C4×D7912yes—
664C23C22×C4×D7911yescharacteristic
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—3164no—
674C2×C4—3164no—
675C2×C4—794no—
676C2×C4—792no—
677C2×C4—798no—
678C2×C4—794no—
679C2×C4—794no—
680C2×C4—792no—
681C2×C4—792no—
682C2×C4—792no—
683C2×C4—792no—
684C2×C4—792no—
685C2×C4—1588no—
686C2×C4—1588no—
687C2×C4—1588no—
688C2×C4—1588no—
689C2×C4—1588no—
690C2×C4—1582no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1584no—
696C2×C4—1582no—
697C2×C4—1582no—
698C2×C4C22×C4×D7912yes—
699C2×C4C22×C4×D7912yes—
700C2×C4C22×C4×D7912yes—
701C2×C4C22×C4×D7912yes—
702C2×C4C22×C4×D7912yes—
703C2×C4C22×C4×D7911yescharacteristic
704C2×C4#41×D7912yes—
705C2×C4#41×D7912yes—
706C2×C4C24×D7911yescharacteristic
707C8—22no—
708C8—22no—
709C8—22no—
710C8—22no—
711C8—1582no—
712C8—1582no—
713C8—1582no—
714C8—1582no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—44no—
719C22—31616no—
720C22—794no—
721C22—794no—
722C22—1582no—
723C22—1582no—
724C22—1582no—
725C22—1582no—
726C22—1588no—
727C22—1588no—
728C22#117×D7912yes—
729C22#131×D7912yes—
730C22#1909932812yes—
731C22C23×C4×D7911yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—22no—
736C4—22no—
737C4—794no—
738C4—1582no—
739C4—1582no—
740C4—1582no—
741C4—1582no—
742C4—1582no—
743C4#117×D7912yes—
744C4C2×#41×D7911yescharacteristic
745C4C2×#41×D7911yescharacteristic
746C2—42no—
747C2—1584no—
748C2—1584no—
749C2#2377205614yesdirect product factor
750C2C2×#117×D7911yescharacteristic
751C2C2×#131×D7911yescharacteristic
752C2C2×#1909932811yescharacteristic
subgroupG/H
centerC22×C4C23×D79
commutatorC22×C79C24×C4
FrattiniC2×C4C24×D79
FittingC2×#433×C79C2
socleC23×C79C23×C4
prime radicalC24×D79C2×C4
cosocleC2×C4×C79C25
hypercenterC2×#433D79
hypocenterC79C2×#2924
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #23772056C2direct (N × H)
3. C2×#19098624C2semidirect
4. C2×#19098621C2semidirect
5. C2×#19098621C2semidirect
6. C2×#19098619C2semidirect
7. C2×#19098618C2semidirect
8. C2×#19098615C2semidirect
9. C2×#19098614C2semidirect
10. C2×#19098588C2semidirect
11. C2×#19098588C2semidirect
14. C2×#19098520C2semidirect
15. C2×#19098517C2semidirect
16. C2×#433×C79C2semidirect
37. #19098624C22semidirect
38. #19098621C22semidirect
39. #19098621C22semidirect
40. #19098619C22semidirect
41. #19098618C22semidirect
42. #19098615C22semidirect
43. #19098614C22semidirect
44. #19098588C22semidirect
45. #19098588C22semidirect
46. C2×C4⋊(C79⋊C8)C22semidirect
47. C2×C4⋊(C79⋊C8)C22semidirect
48. C2×Dic79⋊C8C22semidirect
49. C2×Dic79⋊C8C22semidirect
50. C2×Dic79⋊C8C22semidirect
51. C2×Dic79⋊C8C22semidirect
60. #19098520C22semidirect
61. #19098517C22semidirect
62. C2×#14579072C22semidirect
63. C2×#14579071C22semidirect
64. C2×#14579071C22semidirect
65. C2×C4×C79⋊C8C22semidirect
66. C2×C8×Dic79C22semidirect
67. C2×C8×Dic79C22semidirect
69. #433×C79C22semidirect
70. C2×C4⋊C8×C79C22semidirect
71. C2×C4⋊C8×C79C22semidirect
74. C2×#97×C79C22semidirect
75. C2×C4×C8×C79C22semidirect
138. C4⋊(C79⋊C8)C23semidirect
139. C4⋊(C79⋊C8)C23semidirect
140. Dic79⋊C8C23semidirect
141. Dic79⋊C8C23semidirect
142. Dic79⋊C8C23semidirect
143. Dic79⋊C8C23semidirect
150. #14579072C23semidirect
151. #14579071C23semidirect
152. #14579071C23semidirect
153. C4×C79⋊C8C23semidirect
154. C8×Dic79C23semidirect
155. C8×Dic79C23semidirect
169. C4⋊C8×C79C23semidirect
170. C4⋊C8×C79C23semidirect
173. #97×C79C23semidirect
174. C4×C8×C79C23semidirect
371. C2×C79#2924semidirect
382. C2×#433D79semidirect
393. C79C2×#2924semidirect
418. #433C2×D79semidirect
431. C2×C4⋊C8C2×D79semidirect
432. C2×C4⋊C8C2×D79semidirect
448. C2×#97C2×D79semidirect
452. C2×C4×C8C2×D79semidirect
534. C4⋊C8C22×D79semidirect
535. C4⋊C8C22×D79semidirect
547. #97C22×D79semidirect
551. C4×C8C22×D79semidirect
749. C2#23772056direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117×D792
#237720562
C2×#190986242
C2×#190986212
C2×#190986192
C2×#190986182
C2×#190986152
C2×#190986142
C2×#190985882
C2×#190985252
C2×C22⋊C8×D792
C2×#190985202
C2×#190985172
C2×#433×C792
C2×#292479