Finite Group Databasebeta

← C2×#23777269 #35196622

Subgroups — C2×#23777269 #35196622

Order 20224.

8622 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777269C2132yesmaximal, direct product factor
2C2×#19099296C212yesmaximal, complemented
3C2×#19099295C212yesmaximal, complemented
4C2×#19099232C212yesmaximal, complemented
5C2×#19099231C212yesmaximal, complemented
6C2×#19099210C212yesmaximal, complemented
7C2×#19099208C212yesmaximal, complemented
8C2×#19099206C212yesmaximal, complemented
9C2×#19099201C212yesmaximal, complemented
10C2×#19099166C212yesmaximal, complemented
11C2×#19099164C212yesmaximal, complemented
12C2×#19099129C212yesmaximal, complemented
13C2×#19099118C211yesmaximal, characteristic, complemented
14C2×#19099114C211yesmaximal, characteristic, complemented
15C2×#19099113C211yesmaximal, characteristic, complemented
16C2×#19099111C211yesmaximal, characteristic, complemented
17C2×#127×D79C211yesmaximal, characteristic, complemented
18C2×#19099035C212yesmaximal, complemented
19C2×C4×#11929624C211yesmaximal, characteristic, complemented
20C2×#532×C79C211yesmaximal, characteristic, complemented
21C22×#11929625C2212yescomplemented
22C22×#11929624C2211yescharacteristic
23C22×#11929624C2212yescomplemented
24C22×#11929623C2212yescomplemented
25C22×D4×D79C2212yes—
26C22×D4×D79C2212yes—
27C22×D4×D79C2212yes—
28#19099296C22132yescomplemented
29#19099295C22132yescomplemented
30#19099232C22132yescomplemented
31#19099231C22132yescomplemented
32#19099210C22132yescomplemented
33#19099208C22132yescomplemented
34#19099206C22132yescomplemented
35#19099201C22132yescomplemented
36#19099166C22132yescomplemented
37#19099164C22132yescomplemented
38#19099129C22132yescomplemented
39#19099118C22116yescomplemented
40#19099114C22116yescomplemented
41#19099113C22116yescomplemented
42#19099111C22116yescomplemented
43C2×#14579161C2211yescharacteristic, complemented
44C2×#14579158C2211yescharacteristic
45C2×#14579157C2212yes—
46C2×#14579157C2212yes—
47C2×#14579157C2212yes—
48C2×#14579157C2214yescomplemented
49#127×D79C22116yescomplemented
50C2×#14579152C2212yescomplemented
51C2×#14579150C2212yescomplemented
52C2×#14579149C2212yescomplemented
53C2×#14579148C2212yescomplemented
54C2×#14579147C2214yescomplemented
55C2×#14579145C2214yescomplemented
56C2×#14579144C2214yescomplemented
57C2×#14579143C2214yescomplemented
58C2×#14579143C2214yescomplemented
59C2×#14579141C2212yes—
60C2×#14579137C2212yes—
61C2×#14579136C2212yescomplemented
62C2×#14579136C2212yescomplemented
63C2×#14579135C2212yescomplemented
64C2×#14579135C2214yescomplemented
65C2×#14579135C2212yescomplemented
66C2×#14579134C2214yescomplemented
67C2×#14579133C2214yescomplemented
68C2×#14579132C2212yescomplemented
69C2×#14579132C2214yescomplemented
70C2×#14579132C2212yescomplemented
71C2×#14579131C2214yes—
72C2×#14579129C2214yes—
73#19099035C22132yescomplemented
74C4×#11929624C22116yescomplemented
75C2×Q8×Dic79C2212yescomplemented
76C2×C4×Dic158C2211yescharacteristic, complemented
77C2×C4×Dic158C2211yescharacteristic, complemented
78C2×#14579126C2212yescomplemented
79C2×C4×D316C2211yescharacteristic
80C2×C4×D316C2211yescharacteristic
81C2×C4×D316C2212yescomplemented
82C2×C4×D316C2212yescomplemented
83C2×D4×Dic79C2212yescomplemented
84C2×D4×Dic79C2212yescomplemented
85C2×#14579123C2212yescomplemented
86C2×#14579123C2212yescomplemented
87C2×C4×C22⋊D79C2211yescharacteristic
88C2×C4×C22⋊D79C2211yescharacteristic
89C2×C4×C22⋊D79C2211yescharacteristic, complemented
90C2×C4×C22⋊D79C2211yescharacteristic, complemented
91C2×C4×C22⋊D79C2214yescomplemented
92C2×(C22⋊D79)⋊C4C2214yescomplemented
93C2×#14579120C2211yescharacteristic, complemented
94C2×#14579119C2212yes—
95C2×#14579118C2211yescharacteristic
96C2×#14579118C2211yescharacteristic, complemented
97C22×(C2×D79)⋊C4C2214yes—
98C2×C22⋊C4×D79C2214yes—
99C2×C42×D79C2211yescharacteristic
100C2×C42×D79C2211yescharacteristic, complemented
101C22×#41×C79C2212yescomplemented
102#532×C79C22116yescomplemented
103C2×C4⋊Q8×C79C2211yescharacteristic, complemented
104C2×#127×C79C2211yescharacteristic
105C2×#124×C79C2212yescomplemented
106C2×#121×C79C2212yescomplemented
107C2×#121×C79C2212yescomplemented
108C2×C4×D4×C79C2212yescomplemented
109C2×C4×D4×C79C2212yescomplemented
110C22×C42×C79C2211yescharacteristic, complemented
111C24×D79C2314yes—
112C2×#11929625—48no—
113C2×#11929625C23116yescomplemented
114C2×#11929624—28no—
115C2×#11929624—48no—
116C2×#11929624C2318yes—
117C2×#11929624C23116yescomplemented
118C2×#11929623—48no—
119C2×#11929623C23116yescomplemented
120C22×Dic158C2312yes—
121C22×Dic158C2311yescharacteristic
122C22×D316C2312yes—
123C22×D316C2312yes—
124C22×D316C2311yescharacteristic
125C22×D316C2312yes—
126C22×D316C2314yes—
127C22×C22⋊D79C2314yes—
128C22×C22⋊D79C2311yescharacteristic
129C22×C22⋊D79C2311yescharacteristic
130C22×C22⋊D79C2314yes—
131C22×C22⋊D79C2314yes—
132C22×C22⋊D79C2314yes—
133C22×C22⋊D79C2314yes—
134C2×D4×D79—216no—
135C2×D4×D79—48no—
136C2×D4×D79—48no—
137C2×D4×D79C23116yes—
138C2×D4×D79C23116yes—
139C2×D4×D79C23116yes—
140C23×Dic79C2314yes—
141C22×C4×D79C2311yescharacteristic
142C22×C4×D79C2311yescharacteristic
143C22×C4×D79C2311yescharacteristic
144C22×C4×D79C2311yescharacteristic
145C22×C4×D79C2311yescharacteristic
146C22×C4×D79C2314yes—
147C22×C4×D79C2314yes—
148C22×C4×D79C2311yescharacteristic
149#14579161C2318yescomplemented
150#14579158C2318yes—
151#14579157C23116yes—
152#14579157C23116yes—
153#14579157C23116yes—
154#14579157C23132yescomplemented
155#14579152C23116yescomplemented
156#14579150C23116yescomplemented
157#14579149C23116yescomplemented
158#14579148C23116yescomplemented
159#14579147C23132yescomplemented
160#14579145C23132yescomplemented
161#14579144C23132yescomplemented
162#14579143C23132yescomplemented
163#14579143C23132yescomplemented
164#14579141C23116yes—
165#14579137C23116yes—
166#14579136C23116yescomplemented
167#14579136C23116yescomplemented
168#14579135C23132yescomplemented
169#14579135C23116yescomplemented
170#14579135C23116yescomplemented
171#14579134C23132yescomplemented
172#14579133C23132yescomplemented
173#14579132C23116yescomplemented
174#14579132C23132yescomplemented
175#14579132C23116yescomplemented
176#14579131C23132yes—
177#14579129C23132yes—
178Q8×Dic79C23116yescomplemented
179C4×Dic158C2318yescomplemented
180C4×Dic158C2318yescomplemented
181#14579126C23116yescomplemented
182C4×D316C2318yes—
183C4×D316C2318yes—
184C4×D316C23116yescomplemented
185C4×D316C23116yescomplemented
186D4×Dic79C23116yescomplemented
187D4×Dic79C23116yescomplemented
188#14579123C23116yescomplemented
189#14579123C23116yescomplemented
190C4×C22⋊D79C2318yes—
191C4×C22⋊D79C2318yes—
192C4×C22⋊D79C2318yescomplemented
193C4×C22⋊D79C2318yescomplemented
194C4×C22⋊D79C23132yescomplemented
195(C22⋊D79)⋊C4C23132yescomplemented
196#14579120C2318yescomplemented
197#14579119C23116yes—
198#14579118C2318yes—
199#14579118C2318yescomplemented
200C2×C4⋊Dic79C2312yes—
201C2×C4⋊Dic79C2311yescharacteristic
202C2×C4⋊Dic79C2311yescharacteristic
203C2×C4⋊Dic79C2312yes—
204C2×C4⋊Dic79C2314yes—
205C2×Dic79⋊C4C2311yescharacteristic
206C2×Dic79⋊C4C2311yescharacteristic
207C2×Dic79⋊C4C2311yescharacteristic
208C2×Dic79⋊C4C2311yescharacteristic
209C2×Dic79⋊C4C2314yes—
210C2×C22⋊Dic79C2314yes—
211C2×C22⋊Dic79C2311yescharacteristic
212C2×C22⋊Dic79C2311yescharacteristic
213C2×C22⋊Dic79C2314yes—
214C2×(C2×D79)⋊C4C23132yes—
215C2×(C2×D79)⋊C4C2311yescharacteristic
216C2×(C2×D79)⋊C4C2314yes—
217C2×(C2×D79)⋊C4C2311yescharacteristic
218C2×(C2×D79)⋊C4C2314yes—
219C2×(C2×D79)⋊C4C2314yes—
220C2×(C2×D79)⋊C4C2311yescharacteristic
221C2×(C2×D79)⋊C4C2311yescharacteristic
222C2×(C2×D79)⋊C4C2314yes—
223C2×(C2×D79)⋊C4C2314yes—
224C22⋊C4×D79C23132yes—
225C2×C4×Dic79C2311yescharacteristic
226C2×C4×Dic79C2311yescharacteristic
227C2×C4×Dic79C2311yescharacteristic
228C2×C4×Dic79C2311yescharacteristic
229C2×C4×Dic79C2311yescharacteristic
230C2×C4×Dic79C2311yescharacteristic
231C2×C4×Dic79C2314yes—
232C42×D79C2318yes—
233C42×D79C2318yescomplemented
234C2×#41×C79—48no—
235C2×#41×C79C23116yescomplemented
236C22×Q8×C79C2312yes—
237C22×D4×C79C2312yes—
238C22×D4×C79C2312yes—
239C22×D4×C79C2312yes—
240C22×D4×C79C2314yes—
241C23×C4×C79C2311yescharacteristic
242C23×C4×C79C2311yescharacteristic
243C23×C4×C79C2311yescharacteristic
244C23×C4×C79C2314yes—
245C4⋊Q8×C79C2318yescomplemented
246#127×C79C2318yes—
247#124×C79C23116yescomplemented
248#121×C79C23116yescomplemented
249#121×C79C23116yescomplemented
250C4×D4×C79C23116yescomplemented
251C4×D4×C79C23116yescomplemented
252C2×C4⋊C4×C79C2312yes—
253C2×C4⋊C4×C79C2312yes—
254C2×C22⋊C4×C79C2314yes—
255C2×C22⋊C4×C79C2314yes—
256C2×C42×C79C2311yescharacteristic
257C2×C42×C79C2311yescharacteristic
258C2×C42×C79C2311yescharacteristic
259C2×C42×C79C2311yescharacteristic
260C2×C42×C79C2318yescomplemented
261C23×D79—216no—
262C23×D79—48no—
263C23×D79—48no—
264C23×D79C2414yes—
265C23×D79C2411yescharacteristic
266C23×D79C2411yescharacteristic
267C23×D79C24116yes—
268#11929625—432no—
269#11929624—232no—
270#11929624—432no—
271#11929623—432no—
272C2×Dic158—24no—
273C2×Dic158—28no—
274C2×Dic158C2418yes—
275C2×Dic158C2414yes—
276C2×D316—24no—
277C2×D316—28no—
278C2×D316—28no—
279C2×D316—28no—
280C2×D316—48no—
281C2×D316C2414yes—
282C2×D316C2418yes—
283C2×D316C2418yes—
284C2×D316C2418yes—
285C2×D316C24116yes—
286C2×C22⋊D79—24no—
287C2×C22⋊D79—216no—
288C2×C22⋊D79—24no—
289C2×C22⋊D79—48no—
290C2×C22⋊D79—48no—
291C2×C22⋊D79—48no—
292C2×C22⋊D79—48no—
293C2×C22⋊D79C2414yes—
294C2×C22⋊D79C2414yes—
295C2×C22⋊D79C24116yes—
296C2×C22⋊D79C24116yes—
297C2×C22⋊D79C24116yes—
298C2×C22⋊D79C24116yes—
299C2×C22⋊D79C24116yes—
300D4×D79—264no—
301D4×D79—432no—
302D4×D79—432no—
303C22×Dic79—48no—
304C22×Dic79C2411yescharacteristic
305C22×Dic79C2414yes—
306C22×Dic79C2411yescharacteristic
307C22×Dic79C2411yescharacteristic
308C22×Dic79C2411yescharacteristic
309C22×Dic79C2411yescharacteristic
310C22×Dic79C24116yes—
311C22×Dic79C2411yescharacteristic
312C2×C4×D79—24no—
313C2×C4×D79—24no—
314C2×C4×D79—24no—
315C2×C4×D79—24no—
316C2×C4×D79—24no—
317C2×C4×D79—48no—
318C2×C4×D79—48no—
319C2×C4×D79#4118yescomplemented
320C2×C4×D79C2414yes—
321C2×C4×D79C2414yes—
322C2×C4×D79C2414yes—
323C2×C4×D79C2414yes—
324C2×C4×D79C2414yes—
325C2×C4×D79C24116yes—
326C2×C4×D79C24116yes—
327C2×C4×D79C2414yes—
328C4⋊Dic79C2418yes—
329C4⋊Dic79C2414yes—
330C4⋊Dic79C2414yes—
331C4⋊Dic79C2418yes—
332C4⋊Dic79C24116yes—
333Dic79⋊C4C2414yes—
334Dic79⋊C4C2414yes—
335Dic79⋊C4C2414yes—
336Dic79⋊C4C2414yes—
337Dic79⋊C4C24116yes—
338C22⋊Dic79C24116yes—
339C22⋊Dic79C2414yes—
340C22⋊Dic79C2414yes—
341C22⋊Dic79C24116yes—
342(C2×D79)⋊C4C2414yes—
343(C2×D79)⋊C4C24116yes—
344(C2×D79)⋊C4C2414yes—
345(C2×D79)⋊C4C24116yes—
346(C2×D79)⋊C4C24116yes—
347(C2×D79)⋊C4C2414yes—
348(C2×D79)⋊C4C2414yes—
349(C2×D79)⋊C4C24116yes—
350(C2×D79)⋊C4C24116yes—
351C4×Dic79C2414yes—
352C4×Dic79C2414yes—
353C4×Dic79C2414yes—
354C4×Dic79C2414yes—
355C4×Dic79C2414yes—
356C4×Dic79C2414yes—
357C4×Dic79C24116yes—
358C24×C79C2414yes—
359C24×C79C2411yescharacteristic
360#41×C79—432no—
361C2×Q8×C79—28no—
362C2×Q8×C79C2418yes—
363C2×D4×C79—28no—
364C2×D4×C79—28no—
365C2×D4×C79—28no—
366C2×D4×C79—48no—
367C2×D4×C79C2418yes—
368C2×D4×C79C2418yes—
369C2×D4×C79C2418yes—
370C2×D4×C79C24116yes—
371C22×C4×C79—24no—
372C22×C4×C79—24no—
373C22×C4×C79—24no—
374C22×C4×C79—48no—
375C22×C4×C79C2411yescharacteristic
376C22×C4×C79C2414yes—
377C22×C4×C79C2414yes—
378C22×C4×C79C2411yescharacteristic
379C22×C4×C79C2411yescharacteristic
380C22×C4×C79C2414yes—
381C22×C4×C79C2414yes—
382C22×C4×C79C24116yes—
383C22×C4×C79C2411yescharacteristic
384C22×C4×C79C2411yescharacteristic
385C22×C4×C79C2411yescharacteristic
386C4⋊C4×C79C2418yes—
387C4⋊C4×C79C2418yes—
388C22⋊C4×C79C24116yes—
389C22⋊C4×C79C24116yes—
390C42×C79C2414yes—
391C42×C79C2414yes—
392C42×C79C2414yes—
393C42×C79C2414yes—
394C23×C79—22no—
395C23×C79—28no—
396C23×C79—28no—
397C23×C79—22no—
398C23×C79—28no—
399C23×C79—22no—
400C23×C79C2518yes—
401C23×C79C2512yes—
402C23×C79C2511yescharacteristic
403C22×D79—22no—
404C22×D79—22no—
405C22×D79—22no—
406C22×D79—28no—
407C22×D79—22no—
408C22×D79—22no—
409C22×D79—28no—
410C22×D79—28no—
411C22×D79—232no—
412C22×D79—416no—
413C22×D79—416no—
414C22×D79—832no—
415C22×D79C2×#4114yes—
416C22×D79C2518yes—
417C22×D79C2512yes—
418C22×D79C2512yes—
419Q8×C79—216no—
420D4×C79—216no—
421D4×C79—216no—
422D4×C79—216no—
423D4×C79—416no—
424C2×C4×C79—22no—
425C2×C4×C79—22no—
426C2×C4×C79—28no—
427C2×C4×C79—22no—
428C2×C4×C79—28no—
429C2×C4×C79—28no—
430C2×C4×C79—28no—
431C2×C4×C79—416no—
432C2×C4×C79C2×#4114yes—
433C2×C4×C79H(5,𝔽2)14yes—
434C2×C4×C79H(5,𝔽2)14yes—
435C2×C4×C79C2518yes—
436C2×C4×C79C2512yes—
437C2×C4×C79C2512yes—
438C2×C4×C79C2512yes—
439C2×C4×C79C2512yes—
440C2×C4×C79C2512yes—
441C2×C4×C79C2512yes—
442C22⋊D79—28no—
443C22⋊D79—232no—
444C22⋊D79—28no—
445C22⋊D79—416no—
446C22⋊D79—416no—
447C22⋊D79—416no—
448C22⋊D79—416no—
449C2×Dic79—22no—
450C2×Dic79—22no—
451C2×Dic79—22no—
452C2×Dic79—22no—
453C2×Dic79—22no—
454C2×Dic79—28no—
455C2×Dic79—416no—
456C2×Dic79C2×#4114yes—
457C2×Dic79C2512yes—
458C2×Dic79C2512yes—
459C2×Dic79C2512yes—
460C2×Dic79C2512yes—
461C2×Dic79C2512yes—
462C2×Dic79C2518yes—
463C2×Dic79C2512yes—
464D316—28no—
465D316—216no—
466D316—216no—
467D316—216no—
468D316—416no—
469C4×D79—28no—
470C4×D79—28no—
471C4×D79—28no—
472C4×D79—28no—
473C4×D79—28no—
474C4×D79—416no—
475C4×D79—416no—
476C4×D79C2×#41116yescomplemented
477Dic158—216no—
478Dic158—28no—
479C22×C79—22no—
480C22×C79—28no—
481C22×C79—22no—
482C22×C79—28no—
483C22×C79—28no—
484C22×C79—22no—
485C22×C79—416no—
486C22×C79—44no—
487C22×C79C22×#4112yes—
488C22×C79C2×H(5,𝔽2)12yes—
489C22×C79C2×H(5,𝔽2)12yes—
490C22×C79C2611yescharacteristic
491C2×D79—22no—
492C2×D79—22no—
493C2×D79—28no—
494C2×D79—28no—
495C2×D79—22no—
496C2×D79—22no—
497C2×D79—28no—
498C2×D79—28no—
499C2×D79—22no—
500C2×D79—44no—
501C2×D79—416no—
502C2×D79—832no—
503C2×D79C22×#4114yes—
504C4×C79—22no—
505C4×C79—22no—
506C4×C79—22no—
507C4×C79—28no—
508C4×C79C22×#4114yes—
509C4×C79C2×H(5,𝔽2)14yes—
510C4×C79C2×H(5,𝔽2)14yes—
511Dic79—22no—
512Dic79—22no—
513Dic79—22no—
514Dic79—28no—
515Dic79—22no—
516Dic79—22no—
517Dic79C22×#4114yes—
518C2×#3508—791nomaximal, Sylow
519C2×C79—48no—
520C2×C79—42no—
521C2×C79#350814yescomplemented
522C2×C79C23×#4111yescharacteristic
523C2×C79C22×H(5,𝔽2)11yescharacteristic
524C2×C79C22×H(5,𝔽2)11yescharacteristic
525D79—24no—
526D79—42no—
527D79—48no—
528#3508—7932no—
529C2×#559—792no—
530C2×#559—792no—
531C2×#550—792no—
532C2×#550—792no—
533C2×#546—792no—
534C2×#546—792no—
535C2×#546—792no—
536C2×#546—792no—
537C2×#540—792no—
538C2×#540—792no—
539C2×#535—792no—
540C2×#533—791no—
541C2×#532—791no—
542C2×#532—791no—
543C2×#532—791no—
544C2×#532D7911yescharacteristic, complemented
545C22×#127—791no—
546C2×#518—792no—
547C2×C4×#41—791no—
548C79C2×#350811yescharacteristic, complemented, Sylow
549C22×#41—792no—
550C22×#41—792no—
551C22×#41—792no—
552C22×#41—791no—
553C22×#41C2×D7912yescomplemented
554C23×D4—792no—
555C23×D4—792no—
556C23×D4—792no—
557#559—7932no—
558#559—7932no—
559#550—7932no—
560#550—7932no—
561#546—7932no—
562#546—7932no—
563#546—7932no—
564#546—7932no—
565#540—7932no—
566#540—7932no—
567#535—7932no—
568#533—7916no—
569#532—7916no—
570#532—7916no—
571#532—7916no—
572#532C2×D79116yescomplemented
573C2×C4⋊Q8—791no—
574C2×C4⋊Q8C2×D7911yescharacteristic, complemented
575C2×#127—792no—
576C2×#127—792no—
577C2×#127—792no—
578C2×#127—794no—
579C2×#127—7916no—
580C2×#127—791no—
581C2×#127C2×D7911yescharacteristic
582C2×#125—792no—
583C2×#124—792no—
584C2×#124—792no—
585C2×#124—794no—
586C2×#124—792no—
587C2×#124C2×D7912yescomplemented
588C2×#123—794no—
589C2×#123—794no—
590C2×#123—794no—
591C2×#123—794no—
592C2×C22⋊Q8—792no—
593C2×C22⋊Q8—792no—
594C2×#121—792no—
595C2×#121—792no—
596C2×#121—794no—
597C2×#121—794no—
598C2×#121—792no—
599C2×#121—792no—
600C2×#121—794no—
601C2×#121—792no—
602C2×#121—792no—
603C2×#121—794no—
604C2×#121C2×D7912yescomplemented
605C2×#121C2×D7912yescomplemented
606C2×#120—794no—
607C2×#120—794no—
608#518—7932no—
609C4×#41—7916no—
610C2×C4×Q8—792no—
611C2×C4×Q8—792no—
612C2×C4×Q8—791no—
613C2×C4×Q8—791no—
614C2×C4×D4—792no—
615C2×C4×D4—792no—
616C2×C4×D4—791no—
617C2×C4×D4—791no—
618C2×C4×D4—791no—
619C2×C4×D4—791no—
620C2×C4×D4—794no—
621C2×C4×D4—792no—
622C2×C4×D4—792no—
623C2×C4×D4—794no—
624C2×C4×D4—791no—
625C2×C4×D4—791no—
626C2×C4×D4—792no—
627C2×C4×D4—792no—
628C2×C4×D4C2×D7912yescomplemented
629C2×C4×D4C2×D7912yescomplemented
630C2×#117—791no—
631C2×#117—792no—
632C2×#117—791no—
633C2×#117—791no—
634C22×C22⋊C4—794no—
635C22×C22⋊C4—794no—
636C22×C42—791no—
637C22×C42—791no—
638C22×C42C2×D7911yescharacteristic, complemented
639C25—794no—
640C2×#41—48no—
641C2×#41—3168no—
642C2×#41—3168no—
643C2×#41—3168no—
644C2×#41—7916no—
645C2×#41—7916no—
646C2×#41—7916no—
647C2×#41—798no—
648C2×#41—1588no—
649C2×#41C22×D79116yescomplemented
650C22×Q8—791no—
651C22×Q8—792no—
652C22×Q8C22×D7912yes—
653C22×D4—3168no—
654C22×D4—3168no—
655C22×D4—794no—
656C22×D4—794no—
657C22×D4—794no—
658C22×D4—794no—
659C22×D4—7916no—
660C22×D4—7916no—
661C22×D4—791no—
662C22×D4—794no—
663C22×D4—791no—
664C22×D4—7916no—
665C22×D4—794no—
666C22×D4—791no—
667C22×D4—792no—
668C22×D4—792no—
669C22×D4—792no—
670C22×D4—15816no—
671C22×D4C22×D7912yes—
672C22×D4C22×D7912yes—
673C22×D4C22×D7912yes—
674C22×D4C22×D7914yes—
675C23×C4—794no—
676C23×C4—794no—
677C23×C4—794no—
678C23×C4—791no—
679C23×C4—791no—
680C23×C4—791no—
681C23×C4—791no—
682C23×C4—791no—
683C23×C4—791no—
684C23×C4C22×D7911yescharacteristic
685C23×C4C22×D7911yescharacteristic
686C23×C4C22×D7911yescharacteristic
687C23×C4C22×D7914yes—
688C4⋊Q8—798no—
689C4⋊Q8C22×D7918yescomplemented
690#127—7916no—
691#127—7916no—
692#127—7916no—
693#127—7932no—
694#127—798no—
695#127C22×D7918yes—
696#125—7916no—
697#124—7916no—
698#124—7916no—
699#124—7932no—
700#124—7916no—
701#124C22×D79116yescomplemented
702#123—7932no—
703#123—7932no—
704#123—7932no—
705#123—7932no—
706C22⋊Q8—7916no—
707C22⋊Q8—7916no—
708#121—7916no—
709#121—7916no—
710#121—7932no—
711#121—7932no—
712#121—7916no—
713#121—7916no—
714#121—7932no—
715#121—7916no—
716#121—7916no—
717#121—7932no—
718#121C22×D79116yescomplemented
719#121C22×D79116yescomplemented
720#120—7932no—
721#120—7932no—
722C4×Q8—7916no—
723C4×Q8—7916no—
724C4×Q8—798no—
725C4×Q8—798no—
726C4×D4—7916no—
727C4×D4—7916no—
728C4×D4—798no—
729C4×D4—798no—
730C4×D4—798no—
731C4×D4—798no—
732C4×D4—7932no—
733C4×D4—7916no—
734C4×D4—7916no—
735C4×D4—7932no—
736C4×D4—798no—
737C4×D4—798no—
738C4×D4—7916no—
739C4×D4—7916no—
740C4×D4C22×D79116yescomplemented
741C4×D4C22×D79116yescomplemented
742#117—798no—
743#117—7916no—
744#117—798no—
745#117—798no—
746C2×C4⋊C4—791no—
747C2×C4⋊C4—791no—
748C2×C4⋊C4—792no—
749C2×C4⋊C4—791no—
750C2×C4⋊C4—791no—
751C2×C4⋊C4—791no—
752C2×C4⋊C4—791no—
753C2×C4⋊C4—792no—
754C2×C4⋊C4—794no—
755C2×C4⋊C4—794no—
756C2×C4⋊C4C22×D7912yes—
757C2×C4⋊C4C22×D7912yes—
758C2×C22⋊C4—794no—
759C2×C22⋊C4—791no—
760C2×C22⋊C4—791no—
761C2×C22⋊C4—794no—
762C2×C22⋊C4—791no—
763C2×C22⋊C4—791no—
764C2×C22⋊C4—794no—
765C2×C22⋊C4—794no—
766C2×C22⋊C4—794no—
767C2×C22⋊C4—7932no—
768C2×C22⋊C4—791no—
769C2×C22⋊C4—791no—
770C2×C22⋊C4—794no—
771C2×C22⋊C4—794no—
772C2×C22⋊C4—7932no—
773C2×C22⋊C4C22×D7914yes—
774C2×C22⋊C4C22×D7914yes—
775C2×C42—791no—
776C2×C42—791no—
777C2×C42—794no—
778C2×C42—791no—
779C2×C42—791no—
780C2×C42—791no—
781C2×C42—791no—
782C2×C42—798no—
783C2×C42—798no—
784C2×C42C22×D7911yescharacteristic
785C2×C42C22×D7911yescharacteristic
786C2×C42C22×D7911yescharacteristic
787C2×C42C22×D7911yescharacteristic
788C2×C42C22×D7918yescomplemented
789C24—3168no—
790C24—3168no—
791C24—7916no—
792C24—791no—
793C24—794no—
794C24—791no—
795C24—15816no—
796C24C23×D7914yes—
797C24C23×D7911yescharacteristic
798#41—432no—
799#41—31632no—
800#41—31632no—
801#41—31632no—
802#41—15832no—
803C2×Q8—28no—
804C2×Q8—794no—
805C2×Q8—798no—
806C2×Q8—1584no—
807C2×Q8—1588no—
808C2×Q8C23×D7918yes—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—48no—
813C2×D4—3168no—
814C2×D4—31632no—
815C2×D4—31632no—
816C2×D4—3168no—
817C2×D4—3168no—
818C2×D4—3168no—
819C2×D4—3168no—
820C2×D4—7916no—
821C2×D4—7916no—
822C2×D4—7916no—
823C2×D4—7916no—
824C2×D4—794no—
825C2×D4—7916no—
826C2×D4—794no—
827C2×D4—7916no—
828C2×D4—794no—
829C2×D4—798no—
830C2×D4—798no—
831C2×D4—798no—
832C2×D4—1584no—
833C2×D4—15864no—
834C2×D4—15816no—
835C2×D4—1584no—
836C2×D4—1584no—
837C2×D4—1588no—
838C2×D4—1588no—
839C2×D4—1588no—
840C2×D4C23×D7918yes—
841C2×D4C23×D7918yes—
842C2×D4C23×D7918yes—
843C2×D4C23×D79116yes—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—48no—
848C22×C4—3168no—
849C22×C4—3168no—
850C22×C4—3168no—
851C22×C4—7916no—
852C22×C4—7916no—
853C22×C4—7916no—
854C22×C4—791no—
855C22×C4—798no—
856C22×C4—794no—
857C22×C4—791no—
858C22×C4—791no—
859C22×C4—791no—
860C22×C4—791no—
861C22×C4—791no—
862C22×C4—794no—
863C22×C4—794no—
864C22×C4—794no—
865C22×C4—794no—
866C22×C4—794no—
867C22×C4—794no—
868C22×C4—1584no—
869C22×C4—1584no—
870C22×C4—1584no—
871C22×C4—1584no—
872C22×C4—1584no—
873C22×C4C23×D7914yes—
874C22×C4C23×D7914yes—
875C22×C4C23×D7914yes—
876C22×C4C23×D7914yes—
877C22×C4C23×D7911yescharacteristic
878C22×C4C23×D7911yescharacteristic
879C22×C4C23×D7911yescharacteristic
880C22×C4C23×D79116yes—
881C22×C4C23×D7911yescharacteristic
882C22×C4C23×D7911yescharacteristic
883C22×C4C23×D7911yescharacteristic
884C4⋊C4—794no—
885C4⋊C4—794no—
886C4⋊C4—794no—
887C4⋊C4—794no—
888C4⋊C4—7916no—
889C4⋊C4—798no—
890C4⋊C4—794no—
891C4⋊C4—794no—
892C4⋊C4—798no—
893C4⋊C4—7916no—
894C4⋊C4C23×D7918yes—
895C4⋊C4C23×D7918yes—
896C22⋊C4—7916no—
897C22⋊C4—794no—
898C22⋊C4—794no—
899C22⋊C4—7916no—
900C22⋊C4—794no—
901C22⋊C4—794no—
902C22⋊C4—7916no—
903C22⋊C4—7916no—
904C22⋊C4—7916no—
905C22⋊C4—794no—
906C22⋊C4—794no—
907C22⋊C4—7916no—
908C22⋊C4—7916no—
909C22⋊C4C23×D79116yes—
910C22⋊C4C23×D79116yes—
911C42—794no—
912C42—794no—
913C42—794no—
914C42—794no—
915C42—794no—
916C42—794no—
917C42—7916no—
918C42C23×D7914yes—
919C42C23×D7914yes—
920C42C23×D7914yes—
921C42C23×D7914yes—
922C23—22no—
923C23—28no—
924C23—22no—
925C23—28no—
926C23—22no—
927C23—28no—
928C23—31616no—
929C23—31616no—
930C23—792no—
931C23—794no—
932C23—798no—
933C23—792no—
934C23—63232no—
935C23—15832no—
936C23—1588no—
937C23—1582no—
938C23—1588no—
939C23—1582no—
940C23—1582no—
941C23—1588no—
942C23—1582no—
943C23—1582no—
944C23C24×D7918yes—
945C23C24×D7912yes—
946C23C24×D7911yescharacteristic
947Q8—216no—
948Q8—1588no—
949Q8—15816no—
950D4—216no—
951D4—216no—
952D4—216no—
953D4—416no—
954D4—31616no—
955D4—31616no—
956D4—31616no—
957D4—31616no—
958D4—31616no—
959D4—1588no—
960D4—15832no—
961D4—1588no—
962D4—1588no—
963D4—15816no—
964D4—15816no—
965D4—15816no—
966C2×C4—22no—
967C2×C4—28no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—28no—
971C2×C4—28no—
972C2×C4—28no—
973C2×C4—416no—
974C2×C4—31616no—
975C2×C4—31616no—
976C2×C4—31616no—
977C2×C4—792no—
978C2×C4—794no—
979C2×C4—7916no—
980C2×C4—792no—
981C2×C4—792no—
982C2×C4—792no—
983C2×C4—792no—
984C2×C4—792no—
985C2×C4—798no—
986C2×C4—1582no—
987C2×C4—1582no—
988C2×C4—1582no—
989C2×C4—1588no—
990C2×C4—1582no—
991C2×C4—1582no—
992C2×C4—1588no—
993C2×C4—1588no—
994C2×C4—1588no—
995C2×C4—1588no—
996C2×C4—1588no—
997C2×C4#41×D7914yes—
998C2×C4#1457920614yes—
999C2×C4#1457920714yes—
1000C2×C4C24×D7918yes—
1001C2×C4C24×D7912yes—
1002C2×C4C24×D7912yes—
1003C2×C4C24×D7912yes—
1004C2×C4C24×D7912yes—
1005C2×C4C24×D7912yes—
1006C2×C4C24×D7912yes—
1007C22—22no—
1008C22—28no—
1009C22—22no—
1010C22—28no—
1011C22—22no—
1012C22—28no—
1013C22—416no—
1014C22—44no—
1015C22—31616no—
1016C22—3164no—
1017C22—794no—
1018C22—63232no—
1019C22—1582no—
1020C22—1588no—
1021C22—1588no—
1022C22—1582no—
1023C22—1588no—
1024C22—1582no—
1025C22—1582no—
1026C22—1582no—
1027C22—1588no—
1028C22C2×#41×D7912yes—
1029C22C2×#1457920612yes—
1030C22C2×#1457920712yes—
1031C22C25×D7911yescharacteristic
1032C4—22no—
1033C4—22no—
1034C4—28no—
1035C4—22no—
1036C4—794no—
1037C4—1582no—
1038C4—1582no—
1039C4—1582no—
1040C4—1582no—
1041C4—1588no—
1042C4—1582no—
1043C4C2×#41×D7914yes—
1044C4C2×#1457920614yes—
1045C4C2×#1457920714yes—
1046C2—48no—
1047C2—42no—
1048C2—3168no—
1049C2—3162no—
1050C2—1584no—
1051C2#2377726914yesdirect product factor
1052C2C22×#41×D7911yescharacteristic
1053C2C22×#1457920611yescharacteristic
1054C2C22×#1457920711yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#532×C79C2
socleC23×C79C25
hypercenterC2×#532D79
hypocenterC79C2×#3508
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #23777269C2direct (N × H)
2. C2×#19099296C2semidirect
3. C2×#19099295C2semidirect
4. C2×#19099232C2semidirect
5. C2×#19099231C2semidirect
6. C2×#19099210C2semidirect
7. C2×#19099208C2semidirect
8. C2×#19099206C2semidirect
9. C2×#19099201C2semidirect
10. C2×#19099166C2semidirect
11. C2×#19099164C2semidirect
12. C2×#19099129C2semidirect
13. C2×#19099118C2semidirect
14. C2×#19099114C2semidirect
15. C2×#19099113C2semidirect
16. C2×#19099111C2semidirect
17. C2×#127×D79C2semidirect
18. C2×#19099035C2semidirect
19. C2×C4×#11929624C2semidirect
20. C2×#532×C79C2semidirect
21. C22×#11929625C22semidirect
23. C22×#11929624C22semidirect
24. C22×#11929623C22semidirect
28. #19099296C22semidirect
29. #19099295C22semidirect
30. #19099232C22semidirect
31. #19099231C22semidirect
32. #19099210C22semidirect
33. #19099208C22semidirect
34. #19099206C22semidirect
35. #19099201C22semidirect
36. #19099166C22semidirect
37. #19099164C22semidirect
38. #19099129C22semidirect
39. #19099118C22semidirect
40. #19099114C22semidirect
41. #19099113C22semidirect
42. #19099111C22semidirect
43. C2×#14579161C22semidirect
48. C2×#14579157C22semidirect
49. #127×D79C22semidirect
50. C2×#14579152C22semidirect
51. C2×#14579150C22semidirect
52. C2×#14579149C22semidirect
53. C2×#14579148C22semidirect
54. C2×#14579147C22semidirect
55. C2×#14579145C22semidirect
56. C2×#14579144C22semidirect
57. C2×#14579143C22semidirect
58. C2×#14579143C22semidirect
61. C2×#14579136C22semidirect
62. C2×#14579136C22semidirect
63. C2×#14579135C22semidirect
64. C2×#14579135C22semidirect
65. C2×#14579135C22semidirect
66. C2×#14579134C22semidirect
67. C2×#14579133C22semidirect
68. C2×#14579132C22semidirect
69. C2×#14579132C22semidirect
70. C2×#14579132C22semidirect
73. #19099035C22semidirect
74. C4×#11929624C22semidirect
75. C2×Q8×Dic79C22semidirect
76. C2×C4×Dic158C22semidirect
77. C2×C4×Dic158C22semidirect
78. C2×#14579126C22semidirect
81. C2×C4×D316C22semidirect
82. C2×C4×D316C22semidirect
83. C2×D4×Dic79C22semidirect
84. C2×D4×Dic79C22semidirect
85. C2×#14579123C22semidirect
86. C2×#14579123C22semidirect
89. C2×C4×C22⋊D79C22semidirect
90. C2×C4×C22⋊D79C22semidirect
91. C2×C4×C22⋊D79C22semidirect
92. C2×(C22⋊D79)⋊C4C22semidirect
93. C2×#14579120C22semidirect
96. C2×#14579118C22semidirect
100. C2×C42×D79C22semidirect
101. C22×#41×C79C22semidirect
102. #532×C79C22semidirect
103. C2×C4⋊Q8×C79C22semidirect
105. C2×#124×C79C22semidirect
106. C2×#121×C79C22semidirect
107. C2×#121×C79C22semidirect
108. C2×C4×D4×C79C22semidirect
109. C2×C4×D4×C79C22semidirect
110. C22×C42×C79C22semidirect
113. C2×#11929625C23semidirect
117. C2×#11929624C23semidirect
119. C2×#11929623C23semidirect
149. #14579161C23semidirect
154. #14579157C23semidirect
155. #14579152C23semidirect
156. #14579150C23semidirect
157. #14579149C23semidirect
158. #14579148C23semidirect
159. #14579147C23semidirect
160. #14579145C23semidirect
161. #14579144C23semidirect
162. #14579143C23semidirect
163. #14579143C23semidirect
166. #14579136C23semidirect
167. #14579136C23semidirect
168. #14579135C23semidirect
169. #14579135C23semidirect
170. #14579135C23semidirect
171. #14579134C23semidirect
172. #14579133C23semidirect
173. #14579132C23semidirect
174. #14579132C23semidirect
175. #14579132C23semidirect
178. Q8×Dic79C23semidirect
179. C4×Dic158C23semidirect
180. C4×Dic158C23semidirect
181. #14579126C23semidirect
184. C4×D316C23semidirect
185. C4×D316C23semidirect
186. D4×Dic79C23semidirect
187. D4×Dic79C23semidirect
188. #14579123C23semidirect
189. #14579123C23semidirect
192. C4×C22⋊D79C23semidirect
193. C4×C22⋊D79C23semidirect
194. C4×C22⋊D79C23semidirect
195. (C22⋊D79)⋊C4C23semidirect
196. #14579120C23semidirect
199. #14579118C23semidirect
233. C42×D79C23semidirect
235. C2×#41×C79C23semidirect
245. C4⋊Q8×C79C23semidirect
247. #124×C79C23semidirect
248. #121×C79C23semidirect
249. #121×C79C23semidirect
250. C4×D4×C79C23semidirect
251. C4×D4×C79C23semidirect
260. C2×C42×C79C23semidirect
319. C2×C4×D79#41semidirect
476. C4×D79C2×#41semidirect
521. C2×C79#3508semidirect
544. C2×#532D79semidirect
548. C79C2×#3508semidirect
553. C22×#41C2×D79semidirect
572. #532C2×D79semidirect
574. C2×C4⋊Q8C2×D79semidirect
587. C2×#124C2×D79semidirect
604. C2×#121C2×D79semidirect
605. C2×#121C2×D79semidirect
628. C2×C4×D4C2×D79semidirect
629. C2×C4×D4C2×D79semidirect
638. C22×C42C2×D79semidirect
649. C2×#41C22×D79semidirect
689. C4⋊Q8C22×D79semidirect
701. #124C22×D79semidirect
718. #121C22×D79semidirect
719. #121C22×D79semidirect
740. C4×D4C22×D79semidirect
741. C4×D4C22×D79semidirect
788. C2×C42C22×D79semidirect
1051. C2#23777269direct (N × H)

Maximal subgroups

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

subgroupindex
#237772692
C2×#190992962
C2×#190992952
C2×#190992322
C2×#190992312
C2×#190992102
C2×#190992082
C2×#190992062
C2×#190992012
C2×#190991662
C2×#190991642
C2×#190991292
C2×#190991182
C2×#190991142
C2×#190991132
C2×#190991112
C2×#127×D792
C2×#190990352
C2×C4×#119296242
C2×#532×C792
C2×#350879