Finite Group Databasebeta

← C2×#23772443 #35153014

Subgroups — C2×#23772443 #35153014

Order 20224.

2306 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099070C211yesmaximal, characteristic
2#23772443C2116yesmaximal, direct product factor
3C2×#19098639C211yesmaximal, characteristic, complemented
4C2×#19098638C211yesmaximal, characteristic, complemented
5C2×#19098637C211yesmaximal, characteristic, complemented
6C2×#19098634C211yesmaximal, characteristic, complemented
7C2×#19098632C211yesmaximal, characteristic, complemented
8C2×#19098631C211yesmaximal, characteristic, complemented
9C2×C8×C22⋊D79C211yesmaximal, characteristic, complemented
10C2×(C22⋊D79)⋊C8C211yesmaximal, characteristic, complemented
11C2×#19098621C211yesmaximal, characteristic, complemented
12C2×#19098621C211yesmaximal, characteristic, complemented
13C2×#19098530C211yesmaximal, characteristic, complemented
14C2×#19098525C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D79C211yesmaximal, characteristic, complemented
16C2×#408×C79C211yesmaximal, characteristic, complemented
17C23×C4×D79C2211yescharacteristic
18C22×#11929608C2211yescharacteristic, complemented
19C22×#11929607C2211yescharacteristic
20C22×#11929607C2211yescharacteristic
21C23×C79⋊C8C2211yescharacteristic, complemented
22C22×C8×D79C2211yescharacteristic
23C22×C8×D79C2211yescharacteristic
24#19099070C418yes—
25#19099070C2218yes—
26C2×#14579142C411yescharacteristic
27C2×#14579142C411yescharacteristic
28C2×#14579137C411yescharacteristic
29C2×#14579137C411yescharacteristic
30C2×#14579132C411yescharacteristic
31C2×#14579132C411yescharacteristic
32C2×#14579129C411yescharacteristic
33C2×#14579129C411yescharacteristic
34C2×C4×C22⋊D79C2211yescharacteristic
35C2×C4×C22⋊D79C2211yescharacteristic
36C2×C4×C22⋊D79C2211yescharacteristic
37C2×C4×C22⋊D79C2211yescharacteristic
38C2×#14579120C2211yescharacteristic
39#19098639C2218yescomplemented
40#19098638C2218yescomplemented
41#19098637C2218yescomplemented
42#19098634C2218yescomplemented
43#19098632C2218yescomplemented
44#19098631C2218yescomplemented
45C8×C22⋊D79C2218yescomplemented
46(C22⋊D79)⋊C8C2218yescomplemented
47#19098621C2218yescomplemented
48#19098621C2218yescomplemented
49C2×Dic79⋊C8C2211yescharacteristic, complemented
50C2×Dic79⋊C8C2211yescharacteristic, complemented
51C2×Dic79⋊C8C2211yescharacteristic, complemented
52C2×Dic79⋊C8C2211yescharacteristic, complemented
53#19098530C2218yescomplemented
54#19098525C2218yescomplemented
55C2×C22⋊(C79⋊C8)C2211yescharacteristic
56C2×C22⋊(C79⋊C8)C2211yescharacteristic
57C2×C22⋊(C79⋊C8)C2211yescharacteristic, complemented
58C2×C22⋊(C79⋊C8)C2211yescharacteristic, complemented
59C2×(C2×D79)⋊C8C2211yescharacteristic
60C2×(C2×D79)⋊C8C2211yescharacteristic
61C2×(C2×D79)⋊C8C2211yescharacteristic
62C2×(C2×D79)⋊C8C2211yescharacteristic
63C22⋊C8×D79C2218yescomplemented
64C2×#14579071C2211yescharacteristic, complemented
65C2×#14579071C2211yescharacteristic, complemented
66C2×C8×Dic79C2211yescharacteristic, complemented
67C2×C8×Dic79C2211yescharacteristic, complemented
68C22×#41×C79C2211yescharacteristic
69C22×M16×C79C2211yescharacteristic, complemented
70C23×C8×C79C2211yescharacteristic, complemented
71#408×C79C2218yescomplemented
72C2×C22⋊C8×C79C2211yescharacteristic
73C2×C22⋊C8×C79C2211yescharacteristic
74C2×C22⋊C8×C79C2211yescharacteristic, complemented
75C2×C22⋊C8×C79C2211yescharacteristic, complemented
76C24×D79C2×C411yescharacteristic
77C22×C22⋊D79C2×C411yescharacteristic
78C22×C22⋊D79C2×C411yescharacteristic
79C22×C22⋊D79C2×C411yescharacteristic
80C22×C22⋊D79C2×C411yescharacteristic
81C23×Dic79C2×C411yescharacteristic
82C22×C4×D79—42no—
83C22×C4×D79—42no—
84C22×C4×D79C2×C411yescharacteristic
85C22×C4×D79C2×C411yescharacteristic
86C22×C4×D79C2×C414yes—
87C22×C4×D79C2311yescharacteristic
88C22×C4×D79C2311yescharacteristic
89C22×C4×D79C2314yes—
90C2×#11929608—42no—
91C2×#11929608C2314yescomplemented
92C2×#11929607—42no—
93C2×#11929607—42no—
94C2×#11929607C2314yes—
95C2×#11929607C2314yes—
96C22×C79⋊C8—42no—
97C22×C79⋊C8C2311yescharacteristic
98C22×C79⋊C8C2311yescharacteristic
99C22×C79⋊C8C2311yescharacteristic
100C22×C79⋊C8C2311yescharacteristic
101C22×C79⋊C8C2314yescomplemented
102C2×C8×D79—42no—
103C2×C8×D79—42no—
104C2×C8×D79C2314yes—
105C2×C8×D79C2314yes—
106#14579142C2×C418yes—
107#14579142C2×C418yes—
108#14579137C2×C418yes—
109#14579137C2×C418yes—
110#14579132C2×C418yes—
111#14579132C2×C418yes—
112#14579129C2×C418yes—
113#14579129C2×C418yes—
114C4×C22⋊D79C2×C414yes—
115C4×C22⋊D79C2×C414yes—
116C4×C22⋊D79C2×C414yes—
117C4×C22⋊D79C2×C414yes—
118C4×C22⋊D79C2314yes—
119C4×C22⋊D79C2314yes—
120C4×C22⋊D79C2314yes—
121C4×C22⋊D79C2314yes—
122#14579120C2×C414yes—
123#14579120C2314yes—
124C2×C4⋊Dic79C2×C411yescharacteristic
125C2×C4⋊Dic79C2×C411yescharacteristic
126C2×Dic79⋊C4C2×C411yescharacteristic
127C2×Dic79⋊C4C2×C411yescharacteristic
128C2×Dic79⋊C4C2×C411yescharacteristic
129C2×Dic79⋊C4C2×C411yescharacteristic
130C2×C22⋊Dic79C2×C411yescharacteristic
131C2×C22⋊Dic79C2×C411yescharacteristic
132C2×C22⋊Dic79C2×C411yescharacteristic
133C2×C22⋊Dic79C2×C411yescharacteristic
134C2×C22⋊Dic79C2×C411yescharacteristic
135C2×C22⋊Dic79C2×C411yescharacteristic
136C2×(C2×D79)⋊C4C2×C411yescharacteristic
137C2×(C2×D79)⋊C4C2×C411yescharacteristic
138C2×(C2×D79)⋊C4C2×C411yescharacteristic
139C2×(C2×D79)⋊C4C2×C411yescharacteristic
140C2×C4×Dic79C2311yescharacteristic
141C2×C4×Dic79C2311yescharacteristic
142Dic79⋊C8C2314yescomplemented
143Dic79⋊C8C2314yescomplemented
144Dic79⋊C8C2314yescomplemented
145Dic79⋊C8C2314yescomplemented
146C22⋊(C79⋊C8)C2314yes—
147C22⋊(C79⋊C8)C2314yes—
148C22⋊(C79⋊C8)C2314yescomplemented
149C22⋊(C79⋊C8)C2314yescomplemented
150(C2×D79)⋊C8C2314yes—
151(C2×D79)⋊C8C2314yes—
152(C2×D79)⋊C8C2314yes—
153(C2×D79)⋊C8C2314yes—
154#14579071C2314yescomplemented
155#14579071C2314yescomplemented
156C8×Dic79C2314yescomplemented
157C8×Dic79C2314yescomplemented
158C2×#41×C79—42no—
159C2×#41×C79—42no—
160C2×#41×C79C2×C414yes—
161C2×#41×C79C2314yes—
162C22×Q8×C79C2×C411yescharacteristic
163C22×D4×C79C2×C411yescharacteristic
164C22×D4×C79C2×C411yescharacteristic
165C22×D4×C79C2×C411yescharacteristic
166C23×C4×C79C2311yescharacteristic
167C23×C4×C79C2311yescharacteristic
168C23×C4×C79C2311yescharacteristic
169C2×M16×C79—42no—
170C2×M16×C79C2314yescomplemented
171C22×C8×C79—42no—
172C22×C8×C79C2311yescharacteristic
173C22×C8×C79C2311yescharacteristic
174C22×C8×C79C2311yescharacteristic
175C22×C8×C79C2311yescharacteristic
176C22×C8×C79C2314yescomplemented
177C22⋊C8×C79C2314yes—
178C22⋊C8×C79C2314yes—
179C22⋊C8×C79C2314yescomplemented
180C22⋊C8×C79C2314yescomplemented
181C23×D79—24no—
182C23×D79—42no—
183C23×D79—42no—
184C23×D79C22×C411yescharacteristic
185C23×D79C22×C411yescharacteristic
186C23×D79C22×C414yes—
187C2×C22⋊D79—24no—
188C2×C22⋊D79—24no—
189C2×C22⋊D79—42no—
190C2×C22⋊D79—42no—
191C2×C22⋊D79C22×C414yes—
192C2×C22⋊D79C22×C414yes—
193C2×C22⋊D79C22×C414yes—
194C2×C22⋊D79C22×C414yes—
195C22×Dic79—42no—
196C22×Dic79C22×C411yescharacteristic
197C22×Dic79C22×C411yescharacteristic
198C22×Dic79C22×C411yescharacteristic
199C22×Dic79C22×C411yescharacteristic
200C22×Dic79C22×C411yescharacteristic
201C22×Dic79C22×C411yescharacteristic
202C22×Dic79C22×C414yes—
203C2×C4×D79—22no—
204C2×C4×D79—22no—
205C2×C4×D79—22no—
206C2×C4×D79—22no—
207C2×C4×D79—42no—
208C2×C4×D79—42no—
209C2×C4×D79—48no—
210C2×C4×D79—44no—
211C2×C4×D79—44no—
212C2×C4×D79C22×C412yes—
213C2×C4×D79C22×C412yes—
214C2×C4×D79C22×C414yes—
215C2×C4×D79C22×C414yes—
216C2×C4×D79C2412yes—
217C2×C4×D79C2412yes—
218#11929608—44no—
219#11929607—44no—
220#11929607—44no—
221C2×C79⋊C8—22no—
222C2×C79⋊C8—22no—
223C2×C79⋊C8—22no—
224C2×C79⋊C8—22no—
225C2×C79⋊C8—44no—
226C2×C79⋊C8C2412yes—
227C2×C79⋊C8C2412yes—
228C2×C79⋊C8C2412yes—
229C2×C79⋊C8C2412yes—
230C8×D79—44no—
231C8×D79—44no—
232C4⋊Dic79C22×C414yes—
233C4⋊Dic79C22×C414yes—
234Dic79⋊C4C22×C414yes—
235Dic79⋊C4C22×C414yes—
236Dic79⋊C4C22×C414yes—
237Dic79⋊C4C22×C414yes—
238C22⋊Dic79C22×C414yes—
239C22⋊Dic79C22×C414yes—
240C22⋊Dic79C22×C414yes—
241C22⋊Dic79C22×C414yes—
242C22⋊Dic79C22×C414yes—
243C22⋊Dic79C22×C414yes—
244(C2×D79)⋊C4C22×C414yes—
245(C2×D79)⋊C4C22×C414yes—
246(C2×D79)⋊C4C22×C414yes—
247(C2×D79)⋊C4C22×C414yes—
248C4×Dic79C22×C412yes—
249C4×Dic79C22×C412yes—
250C4×Dic79C2412yes—
251C4×Dic79C2412yes—
252C24×C79C22×C411yescharacteristic
253C24×C79C22×C411yescharacteristic
254C24×C79C22×C411yescharacteristic
255#41×C79—48no—
256#41×C79—44no—
257#41×C79—44no—
258C2×Q8×C79—42no—
259C2×Q8×C79C22×C414yes—
260C2×D4×C79—42no—
261C2×D4×C79—42no—
262C2×D4×C79—42no—
263C2×D4×C79C22×C414yes—
264C2×D4×C79C22×C414yes—
265C2×D4×C79C22×C414yes—
266C22×C4×C79—22no—
267C22×C4×C79—22no—
268C22×C4×C79—22no—
269C22×C4×C79—22no—
270C22×C4×C79—22no—
271C22×C4×C79—22no—
272C22×C4×C79C22×C411yescharacteristic
273C22×C4×C79C22×C411yescharacteristic
274C22×C4×C79C22×C411yescharacteristic
275C22×C4×C79C22×C412yes—
276C22×C4×C79C22×C412yes—
277C22×C4×C79C22×C412yes—
278C22×C4×C79C2412yes—
279C22×C4×C79C2412yes—
280C22×C4×C79C2412yes—
281C22×C4×C79C2411yescharacteristic
282M16×C79—44no—
283C2×C8×C79—22no—
284C2×C8×C79—22no—
285C2×C8×C79—22no—
286C2×C8×C79—22no—
287C2×C8×C79—44no—
288C2×C8×C79C2412yes—
289C2×C8×C79C2412yes—
290C2×C8×C79C2412yes—
291C2×C8×C79C2412yes—
292C23×C79—22no—
293C23×C79—22no—
294C23×C79—22no—
295C23×C79—22no—
296C23×C79—22no—
297C23×C79—22no—
298C23×C79—22no—
299C23×C79—22no—
300C23×C79—22no—
301C23×C79C23×C412yes—
302C23×C79C23×C412yes—
303C23×C79C23×C412yes—
304C23×C79C23×C411yescharacteristic
305C22×D79—22no—
306C22×D79—22no—
307C22×D79—22no—
308C22×D79—22no—
309C22×D79—22no—
310C22×D79—28no—
311C22×D79—44no—
312C22×D79—44no—
313C22×D79—416no—
314C22×D79#13114yes—
315C22×D79C23×C412yes—
316C22×D79C23×C412yes—
317Q8×C79—44no—
318D4×C79—44no—
319D4×C79—44no—
320D4×C79—44no—
321C2×C4×C79—22no—
322C2×C4×C79—22no—
323C2×C4×C79—22no—
324C2×C4×C79—24no—
325C2×C4×C79—24no—
326C2×C4×C79—24no—
327C2×C4×C79—22no—
328C2×C4×C79—22no—
329C2×C4×C79—22no—
330C2×C4×C79—22no—
331C2×C4×C79—22no—
332C2×C4×C79—22no—
333C2×C4×C79C23×C412yes—
334C2×C4×C79C23×C412yes—
335C2×C4×C79C23×C412yes—
336C2×C4×C79C23×C411yescharacteristic
337C2×C4×C79H(5,𝔽2)12yes—
338C2×C4×C79H(5,𝔽2)12yes—
339C2×C4×C79C2511yescharacteristic
340C22⋊D79—28no—
341C22⋊D79—28no—
342C22⋊D79—44no—
343C22⋊D79—44no—
344C2×Dic79—22no—
345C2×Dic79—22no—
346C2×Dic79—22no—
347C2×Dic79—22no—
348C2×Dic79—22no—
349C2×Dic79—22no—
350C2×Dic79—44no—
351C2×Dic79C23×C412yes—
352C2×Dic79C23×C412yes—
353C2×Dic79C23×C412yes—
354C2×Dic79C23×C412yes—
355C2×Dic79C23×C412yes—
356C2×Dic79C23×C412yes—
357C4×D79—24no—
358C4×D79—24no—
359C4×D79—22no—
360C4×D79—22no—
361C4×D79—22no—
362C4×D79—22no—
363C4×D79—44no—
364C4×D79—44no—
365C8×C79—22no—
366C8×C79—22no—
367C8×C79—22no—
368C8×C79—22no—
369C79⋊C8—22no—
370C79⋊C8—22no—
371C79⋊C8—22no—
372C79⋊C8—22no—
373C22×C79—22no—
374C22×C79—22no—
375C22×C79—22no—
376C22×C79—22no—
377C22×C79—22no—
378C22×C79—22no—
379C22×C79—22no—
380C22×C79—22no—
381C22×C79—22no—
382C22×C79—44no—
383C22×C79—44no—
384C22×C79—44no—
385C22×C79#51812yes—
386C22×C79C2×#13112yes—
387C22×C79#56812yes—
388C22×C79C24×C411yescharacteristic
389C2×D79—22no—
390C2×D79—28no—
391C2×D79—22no—
392C2×D79—22no—
393C2×D79—22no—
394C2×D79—22no—
395C2×D79—416no—
396C2×D79—44no—
397C2×D79C2×#13114yes—
398C4×C79—22no—
399C4×C79—22no—
400C4×C79—22no—
401C4×C79#51812yes—
402C4×C79C2×H(5,𝔽2)11yescharacteristic
403C4×C79C2×H(5,𝔽2)11yescharacteristic
404Dic79—22no—
405Dic79—22no—
406Dic79—22no—
407Dic79—22no—
408Dic79—22no—
409Dic79—22no—
410C2×#2976—791nomaximal, Sylow
411C2×C79—42no—
412C2×C79—42no—
413C2×C79—42no—
414C2×C79#297614yescomplemented
415C2×C79C2×#51811yescharacteristic
416C2×C79C22×#13111yescharacteristic
417C2×C79C2×#56811yescharacteristic
418D79—24no—
419D79—42no—
420C2×#525—791no—
421#2976—7916no—
422C2×#436—791no—
423C2×#436—791no—
424C2×#435—791no—
425C2×#435—791no—
426C2×#435—791no—
427C2×#435—791no—
428C2×C8×D4—791no—
429C2×C8×D4—791no—
430C2×#433—791no—
431C2×#433—791no—
432C2×#408—791no—
433C2×#408D7911yescharacteristic, complemented
434C2×#407—791no—
435C22×C22⋊C8—791no—
436C79C2×#297611yescharacteristic, complemented, Sylow
437C22×#41C2×D7911yescharacteristic
438C24×C4—791no—
439C22×M16—791no—
440C22×M16—791no—
441C22×M16—791no—
442C22×M16C2×D7911yescharacteristic, complemented
443C23×C8—791no—
444C23×C8—791no—
445C23×C8—791no—
446C23×C8C2×D7911yescharacteristic, complemented
447#525—798no—
448#525—798no—
449C2×#123—791no—
450C2×#123—791no—
451C2×C22⋊Q8—791no—
452C2×C22⋊Q8—791no—
453C2×#121—791no—
454C2×#121—791no—
455C2×#120—791no—
456C2×#120—791no—
457C2×C4×D4—791no—
458C2×C4×D4—791no—
459C2×C4×D4—791no—
460C2×C4×D4—791no—
461C2×#117—791no—
462#436—798no—
463#436—798no—
464#435—798no—
465#435—798no—
466#435—798no—
467#435—798no—
468C8×D4—798no—
469C8×D4—798no—
470#433—798no—
471#433—798no—
472C2×C4⋊C8—791no—
473C2×C4⋊C8—791no—
474C2×C4⋊C8—791no—
475C2×C4⋊C8—791no—
476#408—798no—
477#408C2×D7918yescomplemented
478#407—798no—
479C2×C22⋊C8—791no—
480C2×C22⋊C8—791no—
481C2×C22⋊C8—791no—
482C2×C22⋊C8—791no—
483C2×C22⋊C8—791no—
484C2×C22⋊C8—791no—
485C2×C22⋊C8—791no—
486C2×C22⋊C8—791no—
487C2×C22⋊C8—798no—
488C2×C22⋊C8C2×D7911yescharacteristic
489C2×C22⋊C8C2×D7911yescharacteristic
490C2×C22⋊C8C2×D7911yescharacteristic, complemented
491C2×C22⋊C8C2×D7911yescharacteristic, complemented
492C2×#97—791no—
493C2×#97—791no—
494C2×C4×C8—791no—
495C2×C4×C8—791no—
496C25—791no—
497C2×#41—42no—
498C2×#41—42no—
499C2×#41C4×D7914yes—
500C2×#41C22×D7914yes—
501C22×Q8C4×D7911yescharacteristic
502C22×D4—791no—
503C22×D4—791no—
504C22×D4—791no—
505C22×D4—791no—
506C22×D4C4×D7911yescharacteristic
507C22×D4C4×D7911yescharacteristic
508C22×D4C4×D7911yescharacteristic
509C23×C4—3162no—
510C23×C4—3162no—
511C23×C4—791no—
512C23×C4—791no—
513C23×C4—791no—
514C23×C4—794no—
515C23×C4—794no—
516C23×C4—791no—
517C23×C4—791no—
518C23×C4C22×D7911yescharacteristic
519C23×C4C22×D7911yescharacteristic
520C23×C4C22×D7911yescharacteristic
521C2×M16—42no—
522C2×M16—3162no—
523C2×M16—3162no—
524C2×M16—3162no—
525C2×M16—794no—
526C2×M16—794no—
527C2×M16—794no—
528C2×M16C22×D7914yescomplemented
529C22×C8—42no—
530C22×C8—3162no—
531C22×C8—3162no—
532C22×C8—3162no—
533C22×C8—794no—
534C22×C8—794no—
535C22×C8—794no—
536C22×C8—791no—
537C22×C8—791no—
538C22×C8—791no—
539C22×C8—791no—
540C22×C8C22×D7911yescharacteristic
541C22×C8C22×D7911yescharacteristic
542C22×C8C22×D7911yescharacteristic
543C22×C8C22×D7911yescharacteristic
544C22×C8C22×D7914yescomplemented
545#123—798no—
546#123—798no—
547C22⋊Q8—798no—
548C22⋊Q8—798no—
549#121—798no—
550#121—798no—
551#120—798no—
552#120—798no—
553C4×D4—794no—
554C4×D4—794no—
555C4×D4—794no—
556C4×D4—794no—
557C4×D4—794no—
558C4×D4—794no—
559C4×D4—794no—
560C4×D4—794no—
561#117—794no—
562#117—794no—
563C2×C4⋊C4—791no—
564C2×C4⋊C4—791no—
565C2×C4⋊C4—791no—
566C2×C4⋊C4—791no—
567C2×C4⋊C4—791no—
568C2×C4⋊C4—791no—
569C2×C22⋊C4—791no—
570C2×C22⋊C4—791no—
571C2×C22⋊C4—791no—
572C2×C22⋊C4—791no—
573C2×C22⋊C4—791no—
574C2×C22⋊C4—791no—
575C2×C22⋊C4—791no—
576C2×C22⋊C4—791no—
577C2×C22⋊C4—791no—
578C2×C22⋊C4—791no—
579C2×C42—791no—
580C2×C42—791no—
581C4⋊C8—794no—
582C4⋊C8—794no—
583C4⋊C8—794no—
584C4⋊C8—794no—
585C22⋊C8—794no—
586C22⋊C8—794no—
587C22⋊C8—794no—
588C22⋊C8—794no—
589C22⋊C8—794no—
590C22⋊C8—794no—
591C22⋊C8—794no—
592C22⋊C8—794no—
593C22⋊C8C22×D7914yes—
594C22⋊C8C22×D7914yes—
595C22⋊C8C22×D7914yescomplemented
596C22⋊C8C22×D7914yescomplemented
597#97—794no—
598#97—794no—
599C4×C8—794no—
600C4×C8—794no—
601C24—3162no—
602C24—3162no—
603C24—794no—
604C24—791no—
605C24—791no—
606C24—1584no—
607C24C2×C4×D7911yescharacteristic
608C24C2×C4×D7911yescharacteristic
609C24C2×C4×D7911yescharacteristic
610#41—44no—
611#41—44no—
612#41—48no—
613C2×Q8—42no—
614C2×Q8C2×C4×D7914yes—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—3162no—
619C2×D4—3162no—
620C2×D4—794no—
621C2×D4—794no—
622C2×D4—794no—
623C2×D4—794no—
624C2×D4—1584no—
625C2×D4—1584no—
626C2×D4C2×C4×D7914yes—
627C2×D4C2×C4×D7914yes—
628C2×D4C2×C4×D7914yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—3162no—
636C22×C4—3162no—
637C22×C4—3164no—
638C22×C4—3164no—
639C22×C4—3168no—
640C22×C4—3162no—
641C22×C4—794no—
642C22×C4—794no—
643C22×C4—794no—
644C22×C4—791no—
645C22×C4—791no—
646C22×C4—791no—
647C22×C4—791no—
648C22×C4—791no—
649C22×C4—791no—
650C22×C4—792no—
651C22×C4—792no—
652C22×C4—792no—
653C22×C4—792no—
654C22×C4—1582no—
655C22×C4—1582no—
656C22×C4—1582no—
657C22×C4—1582no—
658C22×C4C2×C4×D7911yescharacteristic
659C22×C4C2×C4×D7911yescharacteristic
660C22×C4C2×C4×D7911yescharacteristic
661C22×C4C2×C4×D7912yes—
662C22×C4C2×C4×D7912yes—
663C22×C4C2×C4×D7912yes—
664C22×C4C23×D7912yes—
665C22×C4C23×D7912yes—
666C22×C4C23×D7912yes—
667C22×C4C23×D7911yescharacteristic
668M16—44no—
669M16—3164no—
670M16—3164no—
671M16—3164no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8—3164no—
678C2×C8—3164no—
679C2×C8—3164no—
680C2×C8—792no—
681C2×C8—792no—
682C2×C8—792no—
683C2×C8—792no—
684C2×C8—1582no—
685C2×C8—1582no—
686C2×C8—1582no—
687C2×C8—1582no—
688C2×C8C23×D7912yes—
689C2×C8C23×D7912yes—
690C2×C8C23×D7912yes—
691C2×C8C23×D7912yes—
692C4⋊C4—794no—
693C4⋊C4—794no—
694C4⋊C4—794no—
695C4⋊C4—794no—
696C4⋊C4—794no—
697C4⋊C4—794no—
698C22⋊C4—794no—
699C22⋊C4—794no—
700C22⋊C4—794no—
701C22⋊C4—794no—
702C22⋊C4—794no—
703C22⋊C4—794no—
704C22⋊C4—794no—
705C22⋊C4—794no—
706C22⋊C4—794no—
707C22⋊C4—794no—
708C42—792no—
709C42—792no—
710C42—792no—
711C42—792no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—3164no—
722C23—3164no—
723C23—31616no—
724C23—794no—
725C23—792no—
726C23—792no—
727C23—1588no—
728C23—1582no—
729C23—1582no—
730C23—1582no—
731C23—1582no—
732C23—1582no—
733C23C22×C4×D7912yes—
734C23C22×C4×D7912yes—
735C23C22×C4×D7912yes—
736C23C22×C4×D7911yescharacteristic
737Q8—44no—
738D4—44no—
739D4—44no—
740D4—44no—
741D4—3164no—
742D4—3164no—
743D4—1588no—
744D4—1588no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—3164no—
758C2×C4—3164no—
759C2×C4—3164no—
760C2×C4—792no—
761C2×C4—792no—
762C2×C4—792no—
763C2×C4—792no—
764C2×C4—792no—
765C2×C4—792no—
766C2×C4—1582no—
767C2×C4—1582no—
768C2×C4—1582no—
769C2×C4—1582no—
770C2×C4—1582no—
771C2×C4—1582no—
772C2×C4—1582no—
773C2×C4—1582no—
774C2×C4—1582no—
775C2×C4—1582no—
776C2×C4—1584no—
777C2×C4—1584no—
778C2×C4C22×C4×D7912yes—
779C2×C4C22×C4×D7912yes—
780C2×C4C22×C4×D7912yes—
781C2×C4C22×C4×D7911yescharacteristic
782C2×C4#1457920612yes—
783C2×C4#1457920612yes—
784C2×C4C24×D7911yescharacteristic
785C8—22no—
786C8—22no—
787C8—22no—
788C8—22no—
789C8—1582no—
790C8—1582no—
791C8—1582no—
792C8—1582no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—44no—
803C22—44no—
804C22—44no—
805C22—31616no—
806C22—3164no—
807C22—794no—
808C22—1582no—
809C22—1582no—
810C22—1582no—
811C22—1588no—
812C22—1582no—
813C22—1582no—
814C22#1909903612yes—
815C22#131×D7912yes—
816C22#1909932812yes—
817C22C23×C4×D7911yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—1582no—
822C4—1582no—
823C4—1582no—
824C4—1582no—
825C4—1582no—
826C4—1582no—
827C4#1909903612yes—
828C4C2×#1457920611yescharacteristic
829C4C2×#1457920611yescharacteristic
830C2—42no—
831C2—42no—
832C2—42no—
833C2—3162no—
834C2—1584no—
835C2#2377244314yesdirect product factor
836C2C2×#1909903611yescharacteristic
837C2C2×#131×D7911yescharacteristic
838C2C2×#1909932811yescharacteristic
subgroupG/H
centerC22×C4C23×D79
commutatorC22×C79C24×C4
FrattiniC2×C4C24×D79
FittingC2×#408×C79C2
socleC23×C79C23×C4
prime radicalC2×#19099070C2
cosocleC2×C4×C79C25
hypercenterC2×#408D79
hypocenterC79C2×#2976
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. #23772443C2direct (N × H)
3. C2×#19098639C2semidirect
4. C2×#19098638C2semidirect
5. C2×#19098637C2semidirect
6. C2×#19098634C2semidirect
7. C2×#19098632C2semidirect
8. C2×#19098631C2semidirect
9. C2×C8×C22⋊D79C2semidirect
10. C2×(C22⋊D79)⋊C8C2semidirect
11. C2×#19098621C2semidirect
12. C2×#19098621C2semidirect
13. C2×#19098530C2semidirect
14. C2×#19098525C2semidirect
15. C2×C22⋊C8×D79C2semidirect
16. C2×#408×C79C2semidirect
18. C22×#11929608C22semidirect
21. C23×C79⋊C8C22semidirect
39. #19098639C22semidirect
40. #19098638C22semidirect
41. #19098637C22semidirect
42. #19098634C22semidirect
43. #19098632C22semidirect
44. #19098631C22semidirect
45. C8×C22⋊D79C22semidirect
46. (C22⋊D79)⋊C8C22semidirect
47. #19098621C22semidirect
48. #19098621C22semidirect
49. C2×Dic79⋊C8C22semidirect
50. C2×Dic79⋊C8C22semidirect
51. C2×Dic79⋊C8C22semidirect
52. C2×Dic79⋊C8C22semidirect
53. #19098530C22semidirect
54. #19098525C22semidirect
57. C2×C22⋊(C79⋊C8)C22semidirect
58. C2×C22⋊(C79⋊C8)C22semidirect
63. C22⋊C8×D79C22semidirect
64. C2×#14579071C22semidirect
65. C2×#14579071C22semidirect
66. C2×C8×Dic79C22semidirect
67. C2×C8×Dic79C22semidirect
69. C22×M16×C79C22semidirect
70. C23×C8×C79C22semidirect
71. #408×C79C22semidirect
74. C2×C22⋊C8×C79C22semidirect
75. C2×C22⋊C8×C79C22semidirect
91. C2×#11929608C23semidirect
101. C22×C79⋊C8C23semidirect
142. Dic79⋊C8C23semidirect
143. Dic79⋊C8C23semidirect
144. Dic79⋊C8C23semidirect
145. Dic79⋊C8C23semidirect
148. C22⋊(C79⋊C8)C23semidirect
149. C22⋊(C79⋊C8)C23semidirect
154. #14579071C23semidirect
155. #14579071C23semidirect
156. C8×Dic79C23semidirect
157. C8×Dic79C23semidirect
170. C2×M16×C79C23semidirect
176. C22×C8×C79C23semidirect
179. C22⋊C8×C79C23semidirect
180. C22⋊C8×C79C23semidirect
414. C2×C79#2976semidirect
433. C2×#408D79semidirect
436. C79C2×#2976semidirect
442. C22×M16C2×D79semidirect
446. C23×C8C2×D79semidirect
477. #408C2×D79semidirect
490. C2×C22⋊C8C2×D79semidirect
491. C2×C22⋊C8C2×D79semidirect
528. C2×M16C22×D79semidirect
544. C22×C8C22×D79semidirect
595. C22⋊C8C22×D79semidirect
596. C22⋊C8C22×D79semidirect
835. C2#23772443direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190990702
#237724432
C2×#190986392
C2×#190986382
C2×#190986372
C2×#190986342
C2×#190986322
C2×#190986312
C2×C8×C22⋊D792
C2×(C22⋊D79)⋊C82
C2×#190986212
C2×#190985302
C2×#190985252
C2×C22⋊C8×D792
C2×#408×C792
C2×#297679