Finite Group Databasebeta

← C2×#23777838 #35195871

Subgroups — C2×#23777838 #35195871

Order 20224.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777838C2132yesmaximal, direct product factor
2C2×#19099316C214yesmaximal, complemented
3C2×#19099288C211yesmaximal, characteristic, complemented
4C2×#19099283C211yesmaximal, characteristic, complemented
5C2×#19099268C212yesmaximal, complemented
6C2×#19099260C212yesmaximal, complemented
7C2×D4×Dic158C211yesmaximal, characteristic, complemented
8C2×#19099226C212yesmaximal, complemented
9C2×#19099220C212yesmaximal, complemented
10C2×#19099194C212yesmaximal, complemented
11C2×#19099180C212yesmaximal, complemented
12C2×#19099173C212yesmaximal, complemented
13C2×#19099156C214yesmaximal, complemented
14C2×#19099134C212yesmaximal, complemented
15C2×C4⋊Q8×D79C211yesmaximal, characteristic, complemented
16C2×#19099095C211yesmaximal, characteristic, complemented
17C2×#19099095C211yesmaximal, characteristic, complemented
18C2×#547×C79C211yesmaximal, characteristic, complemented
19C23×Dic158C2212yes—
20C22×Q8×D79C2212yes—
21#19099316C22164yescomplemented
22#19099288C22116yescomplemented
23#19099283C22116yescomplemented
24#19099268C22132yescomplemented
25#19099260C22132yescomplemented
26D4×Dic158C22116yescomplemented
27#19099226C22132yescomplemented
28#19099220C22132yescomplemented
29#19099194C22132yescomplemented
30#19099180C22132yescomplemented
31#19099173C22132yescomplemented
32#19099156C22164yescomplemented
33#19099134C22132yescomplemented
34C2×#14579161C2211yescharacteristic
35C2×#14579160C2212yes—
36C2×#14579160C2214yes—
37C2×#14579160C2212yes—
38C2×#14579160C2212yes—
39C2×#14579159C2212yes—
40C2×#14579159C2212yes—
41C4⋊Q8×D79C22116yescomplemented
42#19099095C22116yescomplemented
43#19099095C22116yescomplemented
44C2×#14579154C2214yes—
45C2×#14579154C2212yes—
46C2×#14579154C2212yes—
47C2×#14579154C2214yes—
48C2×#14579154C2214yes—
49C2×#14579152C2211yescharacteristic
50C2×#14579152C2212yes—
51C2×#14579152C2214yes—
52C2×#14579152C2211yescharacteristic
53C2×#14579151C2214yes—
54C2×#14579151C2214yes—
55C2×#14579148C2211yescharacteristic
56C2×#14579148C2214yes—
57C2×#14579148C2212yes—
58C2×#14579148C2211yescharacteristic
59C2×#14579143C2212yes—
60C2×#14579143C2212yes—
61C2×#14579142C2214yes—
62C2×#14579142C2214yes—
63C2×#14579141C2211yescharacteristic
64C2×#14579141C2211yescharacteristic
65C2×#14579140C2212yes—
66C2×#14579140C2214yes—
67C2×#14579140C2214yes—
68C2×#14579140C2212yes—
69C2×#14579140C2214yes—
70C2×#14579139C2214yes—
71C2×#14579138C2214yes—
72C2×#14579138C2214yes—
73C2×#14579132C2211yescharacteristic
74C2×#14579132C2214yes—
75C2×#14579132C2211yescharacteristic
76C2×Q8×Dic79C2212yes—
77C2×C4×Dic158C2211yescharacteristic
78C2×C4×Dic158C2211yescharacteristic
79C2×#14579126C2212yes—
80C2×#14579126C2212yes—
81C2×D4×Dic79C2212yes—
82C2×C4×C22⋊D79C2212yes—
83C2×C4×C22⋊D79C2214yes—
84C2×C4×C22⋊D79C2212yes—
85C2×(C22⋊D79)⋊C4C2214yes—
86C2×#14579120C2212yes—
87C2×#14579120C2212yes—
88C2×#14579120C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C2×C4⋊C4×D79C2212yes—
91C2×C42×D79C2211yescharacteristic
92C22×#41×C79C2212yes—
93#547×C79C22116yescomplemented
94C2×C4⋊Q8×C79C2211yescharacteristic
95C2×#123×C79C2214yes—
96C2×C22⋊Q8×C79C2212yes—
97C2×#121×C79C2212yes—
98C2×C4×D4×C79C2211yescharacteristic
99C2×C4×D4×C79C2211yescharacteristic
100C22×C4⋊C4×C79C2212yes—
101C22×Dic158—48no—
102C22×Dic158C2311yescharacteristic
103C22×Dic158C2312yes—
104C22×Dic158C2311yescharacteristic
105C22×Dic158C23116yes—
106C22×Dic158C2314yes—
107C22×Dic158C2314yes—
108C2×Q8×D79—48no—
109C2×Q8×D79C23116yes—
110C22×C22⋊D79C2312yes—
111C22×C22⋊D79C2312yes—
112C23×Dic79C2314yes—
113C22×C4×D79C2311yescharacteristic
114C22×C4×D79C2311yescharacteristic
115C22×C4×D79C2311yescharacteristic
116C22×C4×D79C2314yes—
117#14579161C2318yes—
118#14579160C23116yes—
119#14579160C23132yes—
120#14579160C23116yes—
121#14579160C23116yes—
122#14579159C23116yes—
123#14579159C23116yes—
124#14579154C23132yes—
125#14579154C23132yes—
126#14579154C23132yes—
127#14579154C23116yes—
128#14579154C23116yes—
129#14579152C23132yes—
130#14579152C2318yes—
131#14579152C2318yes—
132#14579152C23116yes—
133#14579151C23132yes—
134#14579151C23132yes—
135#14579148C2318yes—
136#14579148C23132yes—
137#14579148C23116yes—
138#14579148C2318yes—
139#14579143C23116yes—
140#14579143C23116yes—
141#14579142C23132yes—
142#14579142C23132yes—
143#14579141C2318yes—
144#14579141C2318yes—
145#14579140C23132yes—
146#14579140C23116yes—
147#14579140C23116yes—
148#14579140C23132yes—
149#14579140C23132yes—
150#14579139C23132yes—
151#14579138C23132yes—
152#14579138C23132yes—
153#14579132C23132yes—
154#14579132C2318yes—
155#14579132C2318yes—
156Q8×Dic79C23116yes—
157C4×Dic158C2318yes—
158C4×Dic158C2318yes—
159#14579126C23116yes—
160#14579126C23116yes—
161D4×Dic79C23116yes—
162C4×C22⋊D79C23132yes—
163C4×C22⋊D79C23116yes—
164C4×C22⋊D79C23116yes—
165(C22⋊D79)⋊C4C23132yes—
166#14579120C23116yes—
167#14579120C23116yes—
168#14579120C23116yes—
169C2×C4⋊Dic79C2312yes—
170C2×C4⋊Dic79C2312yes—
171C2×C4⋊Dic79C2311yescharacteristic
172C2×C4⋊Dic79C2312yes—
173C2×C4⋊Dic79C2312yes—
174C2×C4⋊Dic79C2312yes—
175C2×C4⋊Dic79C2312yes—
176C2×C4⋊Dic79C2311yescharacteristic
177C2×C4⋊Dic79C2314yes—
178C2×Dic79⋊C4C2314yes—
179C2×Dic79⋊C4C2314yes—
180C2×Dic79⋊C4C2314yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2312yes—
183C2×Dic79⋊C4C2312yes—
184C2×Dic79⋊C4C2314yes—
185C2×Dic79⋊C4C2314yes—
186C2×Dic79⋊C4C2312yes—
187C2×Dic79⋊C4C2312yes—
188C4⋊C4×D79C23116yes—
189C4⋊C4×D79C23116yes—
190C2×C22⋊Dic79C2314yes—
191C2×C22⋊Dic79C2312yes—
192C2×C22⋊Dic79C2312yes—
193C2×C22⋊Dic79C2312yes—
194C2×C22⋊Dic79C2312yes—
195C2×C22⋊Dic79C2312yes—
196C2×C22⋊Dic79C2312yes—
197C2×C22⋊Dic79C2314yes—
198C2×C22⋊Dic79C2314yes—
199C2×(C2×D79)⋊C4C2312yes—
200C2×(C2×D79)⋊C4C2312yes—
201C2×C4×Dic79C2311yescharacteristic
202C2×C4×Dic79C2311yescharacteristic
203C2×C4×Dic79C2311yescharacteristic
204C2×C4×Dic79C2314yes—
205C2×C4×Dic79C2312yes—
206C2×C4×Dic79C2312yes—
207C2×C4×Dic79C2314yes—
208C42×D79C2318yes—
209C2×#41×C79—48no—
210C2×#41×C79C23116yes—
211C22×Q8×C79C2312yes—
212C22×D4×C79C2311yescharacteristic
213C22×D4×C79C2311yescharacteristic
214C22×D4×C79C2314yes—
215C23×C4×C79C2312yes—
216C23×C4×C79C2312yes—
217C23×C4×C79C2314yes—
218C4⋊Q8×C79C2318yes—
219#123×C79C23132yes—
220C22⋊Q8×C79C23116yes—
221#121×C79C23116yes—
222C4×D4×C79C2318yes—
223C4×D4×C79C2318yes—
224C2×C4⋊C4×C79C23116yes—
225C2×C4⋊C4×C79C2311yescharacteristic
226C2×C4⋊C4×C79C2312yes—
227C2×C4⋊C4×C79C2314yes—
228C2×C4⋊C4×C79C2311yescharacteristic
229C2×C4⋊C4×C79C2312yes—
230C2×C22⋊C4×C79C2312yes—
231C2×C22⋊C4×C79C2312yes—
232C2×C22⋊C4×C79C2314yes—
233C2×C42×C79C2311yescharacteristic
234C23×D79C2411yescharacteristic
235C2×Dic158—28no—
236C2×Dic158—24no—
237C2×Dic158—24no—
238C2×Dic158—432no—
239C2×Dic158—48no—
240C2×Dic158—48no—
241C2×Dic158C2418yes—
242C2×Dic158C2414yes—
243C2×Dic158C2414yes—
244C2×Dic158C24116yes—
245C2×Dic158C24116yes—
246Q8×D79—432no—
247C2×C22⋊D79—28no—
248C2×C22⋊D79—28no—
249C2×C22⋊D79C2418yes—
250C2×C22⋊D79C2418yes—
251C22×Dic79—48no—
252C22×Dic79C2411yescharacteristic
253C22×Dic79C2412yes—
254C22×Dic79C2414yes—
255C22×Dic79C2412yes—
256C22×Dic79C2412yes—
257C22×Dic79C2412yes—
258C22×Dic79C2411yescharacteristic
259C22×Dic79C2411yescharacteristic
260C22×Dic79C24116yes—
261C2×C4×D79—24no—
262C2×C4×D79—24no—
263C2×C4×D79—24no—
264C2×C4×D79—48no—
265C2×C4×D79C2414yes—
266C2×C4×D79C2414yes—
267C2×C4×D79C2414yes—
268C2×C4×D79C24116yes—
269C4⋊Dic79C2418yes—
270C4⋊Dic79C2418yes—
271C4⋊Dic79C2414yes—
272C4⋊Dic79C2418yes—
273C4⋊Dic79C2418yes—
274C4⋊Dic79C2418yes—
275C4⋊Dic79C2418yes—
276C4⋊Dic79C2414yes—
277C4⋊Dic79C24116yes—
278Dic79⋊C4C24116yes—
279Dic79⋊C4C24116yes—
280Dic79⋊C4C24116yes—
281Dic79⋊C4C24116yes—
282Dic79⋊C4C2418yes—
283Dic79⋊C4C2418yes—
284Dic79⋊C4C24116yes—
285Dic79⋊C4C24116yes—
286Dic79⋊C4C2418yes—
287Dic79⋊C4C2418yes—
288C22⋊Dic79C24116yes—
289C22⋊Dic79C2418yes—
290C22⋊Dic79C2418yes—
291C22⋊Dic79C2418yes—
292C22⋊Dic79C2418yes—
293C22⋊Dic79C2418yes—
294C22⋊Dic79C2418yes—
295C22⋊Dic79C24116yes—
296C22⋊Dic79C24116yes—
297(C2×D79)⋊C4C2418yes—
298(C2×D79)⋊C4C2418yes—
299C4×Dic79C2414yes—
300C4×Dic79C2414yes—
301C4×Dic79C2414yes—
302C4×Dic79C24116yes—
303C4×Dic79C2418yes—
304C4×Dic79C2418yes—
305C4×Dic79C24116yes—
306C24×C79C2412yes—
307C24×C79C2412yes—
308#41×C79—432no—
309C2×Q8×C79—28no—
310C2×Q8×C79C2418yes—
311C2×D4×C79—24no—
312C2×D4×C79—24no—
313C2×D4×C79—48no—
314C2×D4×C79C2414yes—
315C2×D4×C79C2414yes—
316C2×D4×C79C24116yes—
317C22×C4×C79—28no—
318C22×C4×C79—28no—
319C22×C4×C79—48no—
320C22×C4×C79C2412yes—
321C22×C4×C79C2418yes—
322C22×C4×C79C2414yes—
323C22×C4×C79C2411yescharacteristic
324C22×C4×C79C2412yes—
325C22×C4×C79C2418yes—
326C22×C4×C79C24116yes—
327C22×C4×C79C2411yescharacteristic
328C22×C4×C79C2411yescharacteristic
329C4⋊C4×C79C2414yes—
330C4⋊C4×C79C2418yes—
331C4⋊C4×C79C24116yes—
332C4⋊C4×C79C2414yes—
333C4⋊C4×C79C2418yes—
334C22⋊C4×C79C2418yes—
335C22⋊C4×C79C2418yes—
336C22⋊C4×C79C24116yes—
337C42×C79C2414yes—
338C23×C79—24no—
339C23×C79—24no—
340C23×C79—24no—
341C23×C79—24no—
342C23×C79—24no—
343C23×C79—24no—
344C23×C79C2514yes—
345C23×C79C2514yes—
346C23×C79C2511yescharacteristic
347C22×D79—22no—
348C22×D79—22no—
349C22×D792−1+414yes—
350C22×D79C2512yes—
351Q8×C79—216no—
352D4×C79—28no—
353D4×C79—28no—
354D4×C79—416no—
355C2×C4×C79—28no—
356C2×C4×C79—24no—
357C2×C4×C79—22no—
358C2×C4×C79—24no—
359C2×C4×C79—216no—
360C2×C4×C79—216no—
361C2×C4×C79—416no—
362C2×C4×C79H(5,𝔽2)14yes—
363C2×C4×C792−1+414yes—
364C2×C4×C79C2514yes—
365C2×C4×C79C2512yes—
366C2×C4×C79C2518yes—
367C2×C4×C79C2514yes—
368C2×C4×C79C2512yes—
369C2×C4×C79C2512yes—
370C22⋊D79—216no—
371C22⋊D79—216no—
372C2×Dic79—22no—
373C2×Dic79—28no—
374C2×Dic79—24no—
375C2×Dic79—22no—
376C2×Dic79—22no—
377C2×Dic79—24no—
378C2×Dic79—24no—
379C2×Dic79—24no—
380C2×Dic79—416no—
381C2×Dic79C2514yes—
382C2×Dic79C2514yes—
383C2×Dic79C2514yes—
384C2×Dic79C2512yes—
385C2×Dic79C2512yes—
386C2×Dic79C2512yes—
387C2×Dic79C2514yes—
388C2×Dic79C2518yes—
389C4×D79—28no—
390C4×D79—28no—
391C4×D79—28no—
392C4×D79—416no—
393Dic158—216no—
394Dic158—28no—
395Dic158—28no—
396Dic158—416no—
397Dic158—416no—
398C22×C79—24no—
399C22×C79—24no—
400C22×C79—24no—
401C22×C79—24no—
402C22×C79—24no—
403C22×C79—24no—
404C22×C79—48no—
405C22×C79—48no—
406C22×C79C2×H(5,𝔽2)12yes—
407C22×C79C2×2−1+412yes—
408C22×C79C2×2−1+412yes—
409C22×C79C2611yescharacteristic
410C2×D79—22no—
411C2×D79—22no—
412C2×D79—28no—
413C2×D79C2×2−1+414yes—
414C4×C79—24no—
415C4×C79—28no—
416C4×C79—24no—
417C4×C79—22no—
418C4×C79C2×H(5,𝔽2)14yes—
419C4×C79C2×2−1+414yes—
420Dic79—28no—
421Dic79—24no—
422Dic79—22no—
423Dic79—24no—
424Dic79—24no—
425Dic79—24no—
426Dic79—22no—
427Dic79—22no—
428C2×#3552—791nomaximal, Sylow
429C2×C79—44no—
430C2×C79—44no—
431C2×C79#355214yescomplemented
432C2×C79C22×H(5,𝔽2)11yescharacteristic
433C2×C79C22×2−1+411yescharacteristic
434C2×C79C22×2−1+411yescharacteristic
435D79—24no—
436#3552—7932no—
437C2×#563—794no—
438C2×#557—791no—
439C2×#556—791no—
440C2×#554—792no—
441C2×#553—792no—
442C2×D4×Q8—792no—
443C2×D4×Q8—791no—
444C2×#548—792no—
445C2×#547D7911yescharacteristic, complemented
446C2×#544—792no—
447C2×#542—792no—
448C2×#541—792no—
449C2×#539—794no—
450C2×#536—792no—
451C22×C4⋊Q8—791no—
452C2×#529—791no—
453C2×#529—791no—
454C79C2×#355211yescharacteristic, complemented, Sylow
455C22×#41C2×D7912yes—
456C23×Q8—792no—
457C23×Q8—792no—
458#563—7964no—
459#557—7916no—
460#556—7916no—
461#554—7932no—
462#553—7932no—
463D4×Q8—7932no—
464D4×Q8—7916no—
465#548—7932no—
466#547C2×D79116yescomplemented
467#544—7932no—
468#542—7932no—
469#541—7932no—
470#539—7964no—
471#536—7932no—
472C2×C4⋊Q8—792no—
473C2×C4⋊Q8—792no—
474C2×C4⋊Q8—7916no—
475C2×C4⋊Q8—792no—
476C2×C4⋊Q8—792no—
477C2×C4⋊Q8—792no—
478C2×C4⋊Q8—794no—
479C2×C4⋊Q8—791no—
480C2×C4⋊Q8C2×D7911yescharacteristic
481#529—7916no—
482#529—7916no—
483C2×#126—792no—
484C2×#126—792no—
485C2×#126—794no—
486C2×#126—794no—
487C2×#126—794no—
488C2×#125—791no—
489C2×#125—791no—
490C2×#125—794no—
491C2×#125—794no—
492C2×#125—794no—
493C2×#125—792no—
494C2×#124—791no—
495C2×#124—791no—
496C2×#124—792no—
497C2×#124—794no—
498C2×#123—794no—
499C2×#123—794no—
500C2×#123—792no—
501C2×#123—792no—
502C2×#123C2×D7914yes—
503C2×C22⋊Q8—794no—
504C2×C22⋊Q8—794no—
505C2×C22⋊Q8—792no—
506C2×C22⋊Q8—792no—
507C2×C22⋊Q8—794no—
508C2×C22⋊Q8—791no—
509C2×C22⋊Q8—791no—
510C2×C22⋊Q8—794no—
511C2×C22⋊Q8—794no—
512C2×C22⋊Q8—794no—
513C2×C22⋊Q8C2×D7912yes—
514C2×#121—791no—
515C2×#121—791no—
516C2×#121—794no—
517C2×#121C2×D7912yes—
518C2×C4×Q8—792no—
519C2×C4×Q8—792no—
520C2×C4×Q8—792no—
521C2×C4×Q8—791no—
522C2×C4×Q8—791no—
523C2×C4×D4—792no—
524C2×C4×D4—792no—
525C2×C4×D4—792no—
526C2×C4×D4—794no—
527C2×C4×D4—794no—
528C2×C4×D4C2×D7911yescharacteristic
529C2×C4×D4C2×D7911yescharacteristic
530C2×#117—792no—
531C2×#117—792no—
532C2×#117—792no—
533C22×C4⋊C4—792no—
534C22×C4⋊C4—792no—
535C22×C4⋊C4C2×D7912yes—
536C22×C42—791no—
537C2×#41—48no—
538C2×#41C22×D79116yes—
539C22×Q8—3168no—
540C22×Q8—3168no—
541C22×Q8—7916no—
542C22×Q8—794no—
543C22×Q8—794no—
544C22×Q8—7916no—
545C22×Q8—791no—
546C22×Q8—792no—
547C22×Q8—791no—
548C22×Q8C22×D7912yes—
549C22×D4—792no—
550C22×D4—792no—
551C22×D4C22×D7911yescharacteristic
552C22×D4C22×D7911yescharacteristic
553C22×D4C22×D7914yes—
554C23×C4—794no—
555C23×C4—794no—
556C23×C4—791no—
557C23×C4—791no—
558C23×C4—791no—
559C23×C4C22×D7912yes—
560C23×C4C22×D7912yes—
561C23×C4C22×D7914yes—
562C4⋊Q8—7916no—
563C4⋊Q8—7916no—
564C4⋊Q8—7916no—
565C4⋊Q8—7916no—
566C4⋊Q8—7916no—
567C4⋊Q8—7932no—
568C4⋊Q8—798no—
569C4⋊Q8C22×D7918yes—
570#126—7916no—
571#126—7916no—
572#126—7932no—
573#126—7932no—
574#126—7932no—
575#125—798no—
576#125—798no—
577#125—7932no—
578#125—7932no—
579#125—7932no—
580#125—7916no—
581#124—798no—
582#124—798no—
583#124—7916no—
584#124—7932no—
585#123—7932no—
586#123—7932no—
587#123—7916no—
588#123—7916no—
589#123C22×D79132yes—
590C22⋊Q8—7932no—
591C22⋊Q8—7932no—
592C22⋊Q8—7916no—
593C22⋊Q8—7916no—
594C22⋊Q8—7932no—
595C22⋊Q8—798no—
596C22⋊Q8—798no—
597C22⋊Q8—7932no—
598C22⋊Q8—7932no—
599C22⋊Q8—7932no—
600C22⋊Q8C22×D79116yes—
601#121—798no—
602#121—798no—
603#121—7932no—
604#121C22×D79116yes—
605C4×Q8—7916no—
606C4×Q8—7916no—
607C4×Q8—7916no—
608C4×Q8—798no—
609C4×Q8—798no—
610C4×D4—7916no—
611C4×D4—7916no—
612C4×D4—7916no—
613C4×D4—7932no—
614C4×D4—7932no—
615C4×D4C22×D7918yes—
616C4×D4C22×D7918yes—
617#117—7916no—
618#117—7916no—
619#117—7916no—
620C2×C4⋊C4—792no—
621C2×C4⋊C4—792no—
622C2×C4⋊C4—794no—
623C2×C4⋊C4—794no—
624C2×C4⋊C4—791no—
625C2×C4⋊C4—792no—
626C2×C4⋊C4—792no—
627C2×C4⋊C4—792no—
628C2×C4⋊C4—792no—
629C2×C4⋊C4—794no—
630C2×C4⋊C4—792no—
631C2×C4⋊C4—794no—
632C2×C4⋊C4—792no—
633C2×C4⋊C4—791no—
634C2×C4⋊C4—794no—
635C2×C4⋊C4—794no—
636C2×C4⋊C4—794no—
637C2×C4⋊C4—792no—
638C2×C4⋊C4—792no—
639C2×C4⋊C4—7916no—
640C2×C4⋊C4—7916no—
641C2×C4⋊C4C22×D7912yes—
642C2×C4⋊C4C22×D7912yes—
643C2×C4⋊C4C22×D7911yescharacteristic
644C2×C4⋊C4C22×D7914yes—
645C2×C4⋊C4C22×D79116yes—
646C2×C4⋊C4C22×D7911yescharacteristic
647C2×C22⋊C4—794no—
648C2×C22⋊C4—792no—
649C2×C22⋊C4—792no—
650C2×C22⋊C4—792no—
651C2×C22⋊C4—792no—
652C2×C22⋊C4—794no—
653C2×C22⋊C4—792no—
654C2×C22⋊C4—794no—
655C2×C22⋊C4—792no—
656C2×C22⋊C4—792no—
657C2×C22⋊C4—792no—
658C2×C22⋊C4C22×D7914yes—
659C2×C22⋊C4C22×D7912yes—
660C2×C22⋊C4C22×D7912yes—
661C2×C42—791no—
662C2×C42—791no—
663C2×C42—792no—
664C2×C42—792no—
665C2×C42—794no—
666C2×C42—794no—
667C2×C42—791no—
668C2×C42—798no—
669C2×C42C22×D7911yescharacteristic
670C24—791no—
671C24C23×D7912yes—
672C24C23×D7912yes—
673#41—432no—
674C2×Q8—28no—
675C2×Q8—31632no—
676C2×Q8—3168no—
677C2×Q8—3168no—
678C2×Q8—31632no—
679C2×Q8—7916no—
680C2×Q8—7916no—
681C2×Q8—794no—
682C2×Q8—798no—
683C2×Q8—794no—
684C2×Q8—1588no—
685C2×Q8—1584no—
686C2×Q8—1584no—
687C2×Q8C23×D7918yes—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—48no—
691C2×D4—798no—
692C2×D4—798no—
693C2×D4—1588no—
694C2×D4—1588no—
695C2×D4C23×D7914yes—
696C2×D4C23×D7914yes—
697C2×D4C23×D79116yes—
698C22×C4—28no—
699C22×C4—28no—
700C22×C4—48no—
701C22×C4—3168no—
702C22×C4—3168no—
703C22×C4—7916no—
704C22×C4—7916no—
705C22×C4—792no—
706C22×C4—792no—
707C22×C4—792no—
708C22×C4—791no—
709C22×C4—791no—
710C22×C4—791no—
711C22×C4—792no—
712C22×C4—794no—
713C22×C4—794no—
714C22×C4—794no—
715C22×C4—794no—
716C22×C4—1584no—
717C22×C4—1584no—
718C22×C4—1584no—
719C22×C4C23×D7918yes—
720C22×C4C23×D7918yes—
721C22×C4C23×D7912yes—
722C22×C4C23×D7911yescharacteristic
723C22×C4C23×D7914yes—
724C22×C4C23×D7912yes—
725C22×C4C23×D79116yes—
726C22×C4C23×D7911yescharacteristic
727C22×C4C23×D7911yescharacteristic
728C4⋊C4—7916no—
729C4⋊C4—7916no—
730C4⋊C4—7916no—
731C4⋊C4—798no—
732C4⋊C4—7916no—
733C4⋊C4—798no—
734C4⋊C4—7916no—
735C4⋊C4—7916no—
736C4⋊C4—798no—
737C4⋊C4—798no—
738C4⋊C4—798no—
739C4⋊C4—798no—
740C4⋊C4—794no—
741C4⋊C4—798no—
742C4⋊C4—798no—
743C4⋊C4—798no—
744C4⋊C4—798no—
745C4⋊C4—794no—
746C4⋊C4—7916no—
747C4⋊C4C23×D7918yes—
748C4⋊C4C23×D7918yes—
749C4⋊C4C23×D7914yes—
750C4⋊C4C23×D79116yes—
751C4⋊C4C23×D7914yes—
752C22⋊C4—7916no—
753C22⋊C4—798no—
754C22⋊C4—798no—
755C22⋊C4—798no—
756C22⋊C4—798no—
757C22⋊C4—7916no—
758C22⋊C4—798no—
759C22⋊C4—7916no—
760C22⋊C4—798no—
761C22⋊C4—798no—
762C22⋊C4—798no—
763C22⋊C4C23×D79116yes—
764C22⋊C4C23×D7918yes—
765C22⋊C4C23×D7918yes—
766C42—794no—
767C42—794no—
768C42—794no—
769C42—798no—
770C42—798no—
771C42—7916no—
772C42—7916no—
773C42C23×D7914yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—794no—
781C23—792no—
782C23—1582no—
783C23—1582no—
784C23C24×D7914yes—
785C23C24×D7914yes—
786C23C24×D7911yescharacteristic
787Q8—216no—
788Q8—31616no—
789Q8—31616no—
790Q8—1588no—
791Q8—15816no—
792Q8—1588no—
793D4—28no—
794D4—28no—
795D4—416no—
796D4—15816no—
797D4—15816no—
798C2×C4—24no—
799C2×C4—28no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—216no—
803C2×C4—216no—
804C2×C4—416no—
805C2×C4—31616no—
806C2×C4—31616no—
807C2×C4—794no—
808C2×C4—794no—
809C2×C4—794no—
810C2×C4—792no—
811C2×C4—792no—
812C2×C4—792no—
813C2×C4—794no—
814C2×C4—798no—
815C2×C4—1588no—
816C2×C4—1588no—
817C2×C4—1584no—
818C2×C4—1582no—
819C2×C4—1582no—
820C2×C4—1584no—
821C2×C4—1584no—
822C2×C4—1582no—
823C2×C4—1584no—
824C2×C4—1588no—
825C2×C4—1588no—
826C2×C4#1457920614yes—
827C2×C4#1457920814yes—
828C2×C4C24×D7914yes—
829C2×C4C24×D7912yes—
830C2×C4C24×D7918yes—
831C2×C4C24×D7914yes—
832C2×C4C24×D7912yes—
833C2×C4C24×D7912yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—48no—
841C22—48no—
842C22—794no—
843C22—1588no—
844C22—1582no—
845C22—1582no—
846C22C2×#1457920612yes—
847C222−1+4×D7912yes—
848C22C2×#1457920812yes—
849C22C25×D7911yescharacteristic
850C4—24no—
851C4—28no—
852C4—22no—
853C4—24no—
854C4—1588no—
855C4—1584no—
856C4—1582no—
857C4—1582no—
858C4—1584no—
859C4—1584no—
860C4—1582no—
861C4—1584no—
862C4C2×#1457920614yes—
863C4C2×#1457920814yes—
864C2—44no—
865C2—44no—
866C2—1584no—
867C2#2377783814yesdirect product factor
868C2C22×#1457920611yescharacteristic
869C2C2×2−1+4×D7911yescharacteristic
870C2C22×#1457920811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#547×C79C2
socleC23×C79C25
hypercenterC2×#547D79
hypocenterC79C2×#3552
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #23777838C2direct (N × H)
2. C2×#19099316C2semidirect
3. C2×#19099288C2semidirect
4. C2×#19099283C2semidirect
5. C2×#19099268C2semidirect
6. C2×#19099260C2semidirect
7. C2×D4×Dic158C2semidirect
8. C2×#19099226C2semidirect
9. C2×#19099220C2semidirect
10. C2×#19099194C2semidirect
11. C2×#19099180C2semidirect
12. C2×#19099173C2semidirect
13. C2×#19099156C2semidirect
14. C2×#19099134C2semidirect
15. C2×C4⋊Q8×D79C2semidirect
16. C2×#19099095C2semidirect
17. C2×#19099095C2semidirect
18. C2×#547×C79C2semidirect
21. #19099316C22semidirect
22. #19099288C22semidirect
23. #19099283C22semidirect
24. #19099268C22semidirect
25. #19099260C22semidirect
26. D4×Dic158C22semidirect
27. #19099226C22semidirect
28. #19099220C22semidirect
29. #19099194C22semidirect
30. #19099180C22semidirect
31. #19099173C22semidirect
32. #19099156C22semidirect
33. #19099134C22semidirect
41. C4⋊Q8×D79C22semidirect
42. #19099095C22semidirect
43. #19099095C22semidirect
93. #547×C79C22semidirect
431. C2×C79#3552semidirect
445. C2×#547D79semidirect
454. C79C2×#3552semidirect
466. #547C2×D79semidirect
867. C2#23777838direct (N × H)

Maximal subgroups

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

subgroupindex
#237778382
C2×#190993162
C2×#190992882
C2×#190992832
C2×#190992682
C2×#190992602
C2×D4×Dic1582
C2×#190992262
C2×#190992202
C2×#190991942
C2×#190991802
C2×#190991732
C2×#190991562
C2×#190991342
C2×C4⋊Q8×D792
C2×#190990952
C2×#547×C792
C2×#355279