Finite Group Databasebeta

← C2×#23777845 #35195872

Subgroups — C2×#23777845 #35195872

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#23777845C2132yesmaximal, direct product factor
2C2×#19099315C214yesmaximal, complemented
3C2×#19099292C211yesmaximal, characteristic, complemented
4C2×#19099286C211yesmaximal, characteristic, complemented
5C2×#19099271C212yesmaximal, complemented
6C2×#19099265C212yesmaximal, complemented
7C2×D4×Dic158C211yesmaximal, characteristic, complemented
8C2×D4×Dic158C212yesmaximal, complemented
9C2×#19099222C212yesmaximal, complemented
10C2×#19099218C211yesmaximal, characteristic, complemented
11C2×#19099193C212yesmaximal, complemented
12C2×#19099182C212yesmaximal, complemented
13C2×#19099175C212yesmaximal, complemented
14C2×#19099157C214yesmaximal, complemented
15C2×#19099139C212yesmaximal, complemented
16C22×#14579161C211yesmaximal, characteristic, complemented
17C2×#19099097C211yesmaximal, characteristic, complemented
18C2×#529×C79C211yesmaximal, characteristic, complemented
19C22×#11929624C2212yes—
20C23×Dic158C2212yes—
21C23×Dic158C2212yes—
22#19099315C22164yescomplemented
23#19099292C22116yescomplemented
24#19099286C22116yescomplemented
25#19099271C22132yescomplemented
26#19099265C22132yescomplemented
27D4×Dic158C22116yescomplemented
28D4×Dic158C22132yescomplemented
29#19099222C22132yescomplemented
30#19099218C22116yescomplemented
31#19099193C22132yescomplemented
32#19099182C22132yescomplemented
33#19099175C22132yescomplemented
34#19099157C22164yescomplemented
35#19099139C22132yescomplemented
36C2×#14579161C2212yes—
37C2×#14579161C2212yes—
38C2×#14579161C2211yescharacteristic
39C2×#14579161C2211yescharacteristic
40C2×#14579161C2212yes—
41C2×#14579161C2212yes—
42C2×#14579161C22116yescomplemented
43C2×#14579160C2212yes—
44C2×#14579160C2214yes—
45#19099097C22116yescomplemented
46C2×#14579156C2214yes—
47C2×#14579155C2212yes—
48C2×#14579154C2214yes—
49C2×#14579154C2214yes—
50C2×#14579153C2211yescharacteristic
51C2×#14579152C2212yes—
52C2×#14579152C2214yes—
53C2×#14579151C2214yes—
54C2×#14579151C2214yes—
55C2×#14579149C2212yes—
56C2×#14579149C2211yescharacteristic
57C2×#14579147C2214yes—
58C2×#14579145C2214yes—
59C2×#14579145C2214yes—
60C2×#14579144C2212yes—
61C2×#14579143C2214yes—
62C2×#14579141C2214yes—
63C2×#14579141C2214yes—
64C2×#14579140C2212yes—
65C2×#14579140C2212yes—
66C2×#14579140C2211yescharacteristic
67C2×#14579139C2214yes—
68C2×#14579138C2214yes—
69C2×#14579138C2214yes—
70C2×#14579138C2214yes—
71C2×#14579137C2212yes—
72C2×#14579135C2211yescharacteristic
73C2×#14579133C2214yes—
74C2×#14579132C2212yes—
75C2×Q8×Dic79C2212yes—
76C2×C4×Dic158C2212yes—
77C2×C4×Dic158C2212yes—
78C2×C4×Dic158C2211yescharacteristic
79C2×C4×D316C2211yescharacteristic
80C2×D4×Dic79C2212yes—
81C2×D4×Dic79C2214yes—
82C2×C4×C22⋊D79C2212yes—
83C2×(C22⋊D79)⋊C4C2214yes—
84C2×#14579119C2212yes—
85C2×#14579118C2212yes—
86C22×C4⋊Dic79C2212yes—
87C22×C4⋊Dic79C2212yes—
88C2×C4⋊C4×D79C2212yes—
89#529×C79C22116yescomplemented
90C2×#126×C79C2212yes—
91C2×#125×C79C2211yescharacteristic
92C2×#124×C79C2211yescharacteristic
93C2×#123×C79C2212yes—
94C2×C22⋊Q8×C79C2211yescharacteristic
95C2×#121×C79C2211yescharacteristic
96C2×C4×Q8×C79C2211yescharacteristic
97C2×C4×D4×C79C2211yescharacteristic
98C2×C4×D4×C79C2212yes—
99C2×#117×C79C2212yes—
100C22×C42×C79C2211yescharacteristic
101C2×#11929624—48no—
102C2×#11929624C23116yes—
103C22×Dic158—48no—
104C22×Dic158—48no—
105C22×Dic158C2312yes—
106C22×Dic158C2311yescharacteristic
107C22×Dic158C2312yes—
108C22×Dic158C23116yes—
109C22×Dic158C23116yes—
110C22×Dic158C2314yes—
111C22×Dic158C2314yes—
112C22×D316C2311yescharacteristic
113C22×C22⋊D79C2312yes—
114C22×C22⋊D79C2314yes—
115C23×Dic79C2314yes—
116C23×Dic79C2314yes—
117C22×C4×D79C2312yes—
118C22×C4×D79C2314yes—
119#14579161C23116yes—
120#14579161C23116yes—
121#14579161C23116yes—
122#14579161C2318yes—
123#14579161C2318yes—
124#14579161C23116yes—
125#14579160C23116yes—
126#14579160C23132yes—
127#14579156C23132yes—
128#14579155C23116yes—
129#14579154C23132yes—
130#14579154C23132yes—
131#14579153C2318yes—
132#14579152C23132yes—
133#14579152C23116yes—
134#14579151C23132yes—
135#14579151C23132yes—
136#14579149C2318yes—
137#14579149C23116yes—
138#14579147C23132yes—
139#14579145C23132yes—
140#14579145C23132yes—
141#14579144C23116yes—
142#14579143C23132yes—
143#14579141C23132yes—
144#14579141C23132yes—
145#14579140C23116yes—
146#14579140C23116yes—
147#14579140C2318yes—
148#14579139C23132yes—
149#14579138C23132yes—
150#14579138C23132yes—
151#14579138C23132yes—
152#14579137C23116yes—
153#14579135C2318yes—
154#14579133C23132yes—
155#14579132C23116yes—
156Q8×Dic79C23116yes—
157C4×Dic158C23116yes—
158C4×Dic158C23116yes—
159C4×Dic158C2318yes—
160C4×D316C2318yes—
161D4×Dic79C23132yes—
162D4×Dic79C23116yes—
163C4×C22⋊D79C23116yes—
164(C22⋊D79)⋊C4C23132yes—
165#14579119C23116yes—
166#14579118C23116yes—
167C2×C4⋊Dic79C23116yes—
168C2×C4⋊Dic79C23116yes—
169C2×C4⋊Dic79C2312yes—
170C2×C4⋊Dic79C2312yes—
171C2×C4⋊Dic79C2312yes—
172C2×C4⋊Dic79C2314yes—
173C2×C4⋊Dic79C2314yes—
174C2×C4⋊Dic79C2312yes—
175C2×C4⋊Dic79C2314yes—
176C2×C4⋊Dic79C2311yescharacteristic
177C2×C4⋊Dic79C2311yescharacteristic
178C2×C4⋊Dic79C2314yes—
179C2×Dic79⋊C4C2314yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2312yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2312yes—
184C2×Dic79⋊C4C2314yes—
185C2×Dic79⋊C4C2314yes—
186C2×Dic79⋊C4C2312yes—
187C4⋊C4×D79C23116yes—
188C2×C22⋊Dic79C2312yes—
189C2×C22⋊Dic79C2314yes—
190C2×C22⋊Dic79C2314yes—
191C2×(C2×D79)⋊C4C2312yes—
192C2×(C2×D79)⋊C4C2312yes—
193C2×(C2×D79)⋊C4C2314yes—
194C2×(C2×D79)⋊C4C2314yes—
195C2×(C2×D79)⋊C4C2312yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×C4×Dic79C2312yes—
198C2×C4×Dic79C2314yes—
199C2×C4×Dic79C2314yes—
200C22×Q8×C79C2311yescharacteristic
201C22×D4×C79C2312yes—
202C22×D4×C79C2311yescharacteristic
203C23×C4×C79C2311yescharacteristic
204C23×C4×C79C2311yescharacteristic
205C23×C4×C79C2311yescharacteristic
206C23×C4×C79C2312yes—
207#126×C79C23116yes—
208#125×C79C2318yes—
209#124×C79C2318yes—
210#123×C79C23116yes—
211C22⋊Q8×C79C2318yes—
212#121×C79C2318yes—
213C4×Q8×C79C2318yes—
214C4×D4×C79C2318yes—
215C4×D4×C79C23116yes—
216#117×C79C23116yes—
217C2×C4⋊C4×C79C2312yes—
218C2×C4⋊C4×C79C2312yes—
219C2×C4⋊C4×C79C2311yescharacteristic
220C2×C4⋊C4×C79C2312yes—
221C2×C4⋊C4×C79C2311yescharacteristic
222C2×C4⋊C4×C79C2312yes—
223C2×C22⋊C4×C79C2312yes—
224C2×C22⋊C4×C79C2312yes—
225C2×C22⋊C4×C79C2312yes—
226C2×C22⋊C4×C79C2312yes—
227C2×C22⋊C4×C79C2312yes—
228C2×C42×C79C2311yescharacteristic
229C2×C42×C79C2311yescharacteristic
230C2×C42×C79C2311yescharacteristic
231C2×C42×C79C2311yescharacteristic
232C2×C42×C79C2318yes—
233C2×C42×C79C2312yes—
234C23×D79C2412yes—
235#11929624—432no—
236C2×Dic158—24no—
237C2×Dic158—28no—
238C2×Dic158—28no—
239C2×Dic158—432no—
240C2×Dic158—432no—
241C2×Dic158—48no—
242C2×Dic158—48no—
243C2×Dic158C2414yes—
244C2×Dic158C2418yes—
245C2×Dic158C2418yes—
246C2×Dic158C24116yes—
247C2×Dic158C24116yes—
248C2×D316—24no—
249C2×D316C2414yes—
250C2×C22⋊D79—28no—
251C2×C22⋊D79—48no—
252C2×C22⋊D79C2418yes—
253C2×C22⋊D79C24116yes—
254C22×Dic79—48no—
255C22×Dic79—48no—
256C22×Dic79C2412yes—
257C22×Dic79C2414yes—
258C22×Dic79C2414yes—
259C22×Dic79C2412yes—
260C22×Dic79C2412yes—
261C22×Dic79C24116yes—
262C22×Dic79C24116yes—
263C2×C4×D79—28no—
264C2×C4×D79—48no—
265C2×C4×D79C2418yes—
266C2×C4×D79C24116yes—
267C4⋊Dic79C2418yes—
268C4⋊Dic79C2418yes—
269C4⋊Dic79C2418yes—
270C4⋊Dic79C24116yes—
271C4⋊Dic79C24116yes—
272C4⋊Dic79C2418yes—
273C4⋊Dic79C24116yes—
274C4⋊Dic79C2414yes—
275C4⋊Dic79C2414yes—
276C4⋊Dic79C24116yes—
277Dic79⋊C4C24116yes—
278Dic79⋊C4C2418yes—
279Dic79⋊C4C2418yes—
280Dic79⋊C4C24116yes—
281Dic79⋊C4C2418yes—
282Dic79⋊C4C24116yes—
283Dic79⋊C4C24116yes—
284Dic79⋊C4C2418yes—
285C22⋊Dic79C2418yes—
286C22⋊Dic79C24116yes—
287C22⋊Dic79C24116yes—
288(C2×D79)⋊C4C2418yes—
289(C2×D79)⋊C4C2418yes—
290(C2×D79)⋊C4C24116yes—
291(C2×D79)⋊C4C24116yes—
292(C2×D79)⋊C4C2418yes—
293(C2×D79)⋊C4C2418yes—
294C4×Dic79C2418yes—
295C4×Dic79C24116yes—
296C4×Dic79C24116yes—
297C24×C79C2412yes—
298C24×C79C2411yescharacteristic
299C2×Q8×C79—24no—
300C2×Q8×C79C2414yes—
301C2×D4×C79—28no—
302C2×D4×C79—24no—
303C2×D4×C79C2418yes—
304C2×D4×C79C2414yes—
305C22×C4×C79—24no—
306C22×C4×C79—24no—
307C22×C4×C79—28no—
308C22×C4×C79—24no—
309C22×C4×C79C2411yescharacteristic
310C22×C4×C79C2414yes—
311C22×C4×C79C2418yes—
312C22×C4×C79C2412yes—
313C22×C4×C79C2411yescharacteristic
314C22×C4×C79C2411yescharacteristic
315C22×C4×C79C2411yescharacteristic
316C22×C4×C79C2414yes—
317C22×C4×C79C2414yes—
318C22×C4×C79C2412yes—
319C22×C4×C79C2412yes—
320C22×C4×C79C2411yescharacteristic
321C22×C4×C79C2411yescharacteristic
322C4⋊C4×C79C2418yes—
323C4⋊C4×C79C2418yes—
324C4⋊C4×C79C2414yes—
325C4⋊C4×C79C2418yes—
326C4⋊C4×C79C2414yes—
327C4⋊C4×C79C2418yes—
328C22⋊C4×C79C2418yes—
329C22⋊C4×C79C2418yes—
330C22⋊C4×C79C2418yes—
331C22⋊C4×C79C2418yes—
332C22⋊C4×C79C2418yes—
333C42×C79C2414yes—
334C42×C79C2414yes—
335C42×C79C2414yes—
336C42×C79C2414yes—
337C42×C79C2418yes—
338C23×C79—22no—
339C23×C79—22no—
340C23×C79—24no—
341C23×C79—24no—
342C23×C79—24no—
343C23×C792−1+414yes—
344C23×C79C2514yes—
345C23×C79C2512yes—
346C23×C79C2511yescharacteristic
347C22×D79—24no—
348C22×D79—24no—
349C22×D79—24no—
350C22×D79C2514yes—
351Q8×C79—28no—
352D4×C79—216no—
353D4×C79—28no—
354C2×C4×C79—24no—
355C2×C4×C79—22no—
356C2×C4×C79—28no—
357C2×C4×C79—22no—
358C2×C4×C79—22no—
359C2×C4×C79—22no—
360C2×C4×C79—24no—
361C2×C4×C79—24no—
362C2×C4×C79—28no—
363C2×C4×C79—216no—
364C2×C4×C79—28no—
365C2×C4×C79H(5,𝔽2)14yes—
366C2×C4×C792−1+414yes—
367C2×C4×C79C2514yes—
368C2×C4×C79C2514yes—
369C2×C4×C79C2512yes—
370C2×C4×C79C2512yes—
371C2×C4×C79C2512yes—
372C2×C4×C79C2512yes—
373C2×C4×C79C2514yes—
374C2×C4×C79C2512yes—
375C2×C4×C79C2512yes—
376C22⋊D79—216no—
377C22⋊D79—416no—
378C2×Dic79—28no—
379C2×Dic79—28no—
380C2×Dic79—24no—
381C2×Dic79—24no—
382C2×Dic79—24no—
383C2×Dic79—416no—
384C2×Dic79—416no—
385C2×Dic79C2514yes—
386C2×Dic79C2514yes—
387C2×Dic79C2514yes—
388C2×Dic79C2518yes—
389C2×Dic79C2518yes—
390D316—28no—
391C4×D79—216no—
392C4×D79—416no—
393Dic158—216no—
394Dic158—28no—
395Dic158—216no—
396Dic158—416no—
397Dic158—416no—
398C22×C79—22no—
399C22×C79—22no—
400C22×C79—28no—
401C22×C79—24no—
402C22×C79—24no—
403C22×C79—24no—
404C22×C79—48no—
405C22×C79C2×H(5,𝔽2)12yes—
406C22×C79C2×2−1+414yes—
407C22×C79C2×2−1+412yes—
408C22×C79C2×2−1+412yes—
409C22×C79C2611yescharacteristic
410C2×D79—24no—
411C2×D79—24no—
412C2×D79—24no—
413C2×D79—48no—
414C4×C79—22no—
415C4×C79—24no—
416C4×C79—22no—
417C4×C79—22no—
418C4×C79—22no—
419C4×C79—24no—
420C4×C79—24no—
421C4×C79C2×H(5,𝔽2)14yes—
422C4×C79C2×2−1+414yes—
423Dic79—28no—
424Dic79—28no—
425Dic79—24no—
426Dic79—24no—
427Dic79—24no—
428C2×#3552—791nomaximal, Sylow
429C2×C79—24no—
430C2×C79—44no—
431C2×C79#355214yescomplemented
432C2×C79C22×H(5,𝔽2)11yescharacteristic
433C2×C79C22×2−1+411yescharacteristic
434C2×C79C22×2−1+411yescharacteristic
435D79—44no—
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×#547—791no—
446C2×#544—792no—
447C2×#542—792no—
448C2×#541—792no—
449C2×#539—794no—
450C2×#536—792no—
451C22×C4⋊Q8—791no—
452C2×#529—791no—
453C2×#529D7911yescharacteristic, complemented
454C79C2×#355211yescharacteristic, complemented, Sylow
455C22×#41—792no—
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#547—7916no—
467#544—7932no—
468#542—7932no—
469#541—7932no—
470#539—7964no—
471#536—7932no—
472C2×C4⋊Q8—792no—
473C2×C4⋊Q8—794no—
474C2×C4⋊Q8—792no—
475C2×C4⋊Q8—792no—
476C2×C4⋊Q8—791no—
477C2×C4⋊Q8—791no—
478C2×C4⋊Q8—792no—
479C2×C4⋊Q8—7916no—
480C2×C4⋊Q8—792no—
481#529—7916no—
482#529C2×D79116yescomplemented
483C2×#126—794no—
484C2×#126—794no—
485C2×#126—794no—
486C2×#126—792no—
487C2×#126C2×D7912yes—
488C2×#125—794no—
489C2×#125—794no—
490C2×#125—794no—
491C2×#125—792no—
492C2×#125—791no—
493C2×#125C2×D7911yescharacteristic
494C2×#124—794no—
495C2×#124—791no—
496C2×#124—792no—
497C2×#124C2×D7911yescharacteristic
498C2×#123—792no—
499C2×#123—794no—
500C2×#123—794no—
501C2×#123—794no—
502C2×#123C2×D7912yes—
503C2×C22⋊Q8—792no—
504C2×C22⋊Q8—791no—
505C2×C22⋊Q8—792no—
506C2×C22⋊Q8—792no—
507C2×C22⋊Q8—794no—
508C2×C22⋊Q8—794no—
509C2×C22⋊Q8—794no—
510C2×C22⋊Q8—794no—
511C2×C22⋊Q8—794no—
512C2×C22⋊Q8—794no—
513C2×C22⋊Q8C2×D7911yescharacteristic
514C2×#121—794no—
515C2×#121—792no—
516C2×#121—791no—
517C2×#121C2×D7911yescharacteristic
518C2×C4×Q8—792no—
519C2×C4×Q8—791no—
520C2×C4×Q8—792no—
521C2×C4×Q8—792no—
522C2×C4×Q8C2×D7911yescharacteristic
523C2×C4×D4—794no—
524C2×C4×D4—792no—
525C2×C4×D4—792no—
526C2×C4×D4—794no—
527C2×C4×D4—791no—
528C2×C4×D4C2×D7911yescharacteristic
529C2×C4×D4C2×D7912yes—
530C2×#117—792no—
531C2×#117—792no—
532C2×#117C2×D7912yes—
533C22×C4⋊C4—792no—
534C22×C4⋊C4—792no—
535C22×C4⋊C4—792no—
536C22×C42C2×D7911yescharacteristic
537C2×#41—3168no—
538C2×#41—7916no—
539C22×Q8—3168no—
540C22×Q8—3168no—
541C22×Q8—794no—
542C22×Q8—794no—
543C22×Q8—7916no—
544C22×Q8—7916no—
545C22×Q8—791no—
546C22×Q8—792no—
547C22×Q8—792no—
548C22×Q8C22×D7911yescharacteristic
549C22×D4—794no—
550C22×D4—792no—
551C22×D4—791no—
552C22×D4C22×D7912yes—
553C22×D4C22×D7911yescharacteristic
554C23×C4—794no—
555C23×C4—794no—
556C23×C4—794no—
557C23×C4—792no—
558C23×C4C22×D7911yescharacteristic
559C23×C4C22×D7911yescharacteristic
560C23×C4C22×D7912yes—
561C23×C4C22×D7911yescharacteristic
562C4⋊Q8—7916no—
563C4⋊Q8—7932no—
564C4⋊Q8—7916no—
565C4⋊Q8—7916no—
566C4⋊Q8—798no—
567C4⋊Q8—798no—
568C4⋊Q8—7916no—
569C4⋊Q8—7916no—
570#126—7932no—
571#126—7932no—
572#126—7932no—
573#126—7916no—
574#126C22×D79116yes—
575#125—7932no—
576#125—7932no—
577#125—7932no—
578#125—7916no—
579#125—798no—
580#125C22×D7918yes—
581#124—7932no—
582#124—798no—
583#124—7916no—
584#124C22×D7918yes—
585#123—7916no—
586#123—7932no—
587#123—7932no—
588#123—7932no—
589#123C22×D79116yes—
590C22⋊Q8—7916no—
591C22⋊Q8—798no—
592C22⋊Q8—7916no—
593C22⋊Q8—7916no—
594C22⋊Q8—7932no—
595C22⋊Q8—7932no—
596C22⋊Q8—7932no—
597C22⋊Q8—7932no—
598C22⋊Q8—7932no—
599C22⋊Q8—7932no—
600C22⋊Q8C22×D7918yes—
601#121—7932no—
602#121—7916no—
603#121—798no—
604#121C22×D7918yes—
605C4×Q8—7916no—
606C4×Q8—798no—
607C4×Q8—7916no—
608C4×Q8—7916no—
609C4×Q8C22×D7918yes—
610C4×D4—7932no—
611C4×D4—7916no—
612C4×D4—7916no—
613C4×D4—7932no—
614C4×D4—798no—
615C4×D4C22×D7918yes—
616C4×D4C22×D79116yes—
617#117—7916no—
618#117—7916no—
619#117C22×D79116yes—
620C2×C4⋊C4—792no—
621C2×C4⋊C4—792no—
622C2×C4⋊C4—794no—
623C2×C4⋊C4—792no—
624C2×C4⋊C4—794no—
625C2×C4⋊C4—794no—
626C2×C4⋊C4—792no—
627C2×C4⋊C4—7916no—
628C2×C4⋊C4—7916no—
629C2×C4⋊C4—792no—
630C2×C4⋊C4—792no—
631C2×C4⋊C4—791no—
632C2×C4⋊C4—794no—
633C2×C4⋊C4—794no—
634C2×C4⋊C4—792no—
635C2×C4⋊C4—791no—
636C2×C4⋊C4—794no—
637C2×C4⋊C4—794no—
638C2×C4⋊C4—794no—
639C2×C4⋊C4—792no—
640C2×C4⋊C4—7916no—
641C2×C4⋊C4C22×D7911yescharacteristic
642C2×C4⋊C4C22×D7911yescharacteristic
643C2×C4⋊C4C22×D7912yes—
644C2×C4⋊C4C22×D7912yes—
645C2×C4⋊C4C22×D7912yes—
646C2×C4⋊C4C22×D7912yes—
647C2×C22⋊C4—792no—
648C2×C22⋊C4—794no—
649C2×C22⋊C4—794no—
650C2×C22⋊C4—794no—
651C2×C22⋊C4—792no—
652C2×C22⋊C4—792no—
653C2×C22⋊C4—792no—
654C2×C22⋊C4—794no—
655C2×C22⋊C4—792no—
656C2×C22⋊C4C22×D7912yes—
657C2×C22⋊C4C22×D7912yes—
658C2×C22⋊C4C22×D7912yes—
659C2×C22⋊C4C22×D7912yes—
660C2×C22⋊C4C22×D7912yes—
661C2×C42—792no—
662C2×C42—794no—
663C2×C42—794no—
664C2×C42C22×D7911yescharacteristic
665C2×C42C22×D7911yescharacteristic
666C2×C42C22×D7912yes—
667C2×C42C22×D7911yescharacteristic
668C2×C42C22×D7911yescharacteristic
669C2×C42C22×D7918yes—
670C24—792no—
671C24C23×D7912yes—
672C24C23×D7911yescharacteristic
673#41—31632no—
674C2×Q8—24no—
675C2×Q8—31632no—
676C2×Q8—31632no—
677C2×Q8—3168no—
678C2×Q8—3168no—
679C2×Q8—7916no—
680C2×Q8—7916no—
681C2×Q8—794no—
682C2×Q8—798no—
683C2×Q8—798no—
684C2×Q8—1588no—
685C2×Q8—1584no—
686C2×Q8—1588no—
687C2×Q8C23×D7914yes—
688C2×D4—28no—
689C2×D4—24no—
690C2×D4—3168no—
691C2×D4—7916no—
692C2×D4—798no—
693C2×D4—794no—
694C2×D4—1588no—
695C2×D4—1584no—
696C2×D4C23×D7918yes—
697C2×D4C23×D7914yes—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—28no—
701C22×C4—24no—
702C22×C4—3168no—
703C22×C4—3168no—
704C22×C4—3168no—
705C22×C4—7916no—
706C22×C4—7916no—
707C22×C4—7916no—
708C22×C4—792no—
709C22×C4—792no—
710C22×C4—792no—
711C22×C4—794no—
712C22×C4—794no—
713C22×C4—798no—
714C22×C4—1588no—
715C22×C4C23×D7914yes—
716C22×C4C23×D7914yes—
717C22×C4C23×D7914yes—
718C22×C4C23×D7918yes—
719C22×C4C23×D7912yes—
720C22×C4C23×D7912yes—
721C22×C4C23×D7911yescharacteristic
722C22×C4C23×D7911yescharacteristic
723C22×C4C23×D7911yescharacteristic
724C22×C4C23×D7911yescharacteristic
725C22×C4C23×D7912yes—
726C22×C4C23×D7911yescharacteristic
727C22×C4C23×D7911yescharacteristic
728C4⋊C4—7916no—
729C4⋊C4—798no—
730C4⋊C4—798no—
731C4⋊C4—7916no—
732C4⋊C4—798no—
733C4⋊C4—7916no—
734C4⋊C4—7916no—
735C4⋊C4—798no—
736C4⋊C4—798no—
737C4⋊C4—798no—
738C4⋊C4—798no—
739C4⋊C4—7916no—
740C4⋊C4—7916no—
741C4⋊C4—798no—
742C4⋊C4—794no—
743C4⋊C4—7916no—
744C4⋊C4—794no—
745C4⋊C4—7916no—
746C4⋊C4C23×D7914yes—
747C4⋊C4C23×D7914yes—
748C4⋊C4C23×D7918yes—
749C4⋊C4C23×D7918yes—
750C4⋊C4C23×D7918yes—
751C4⋊C4C23×D7918yes—
752C22⋊C4—798no—
753C22⋊C4—7916no—
754C22⋊C4—7916no—
755C22⋊C4—7916no—
756C22⋊C4—798no—
757C22⋊C4—798no—
758C22⋊C4—798no—
759C22⋊C4—7916no—
760C22⋊C4—798no—
761C22⋊C4C23×D7918yes—
762C22⋊C4C23×D7918yes—
763C22⋊C4C23×D7918yes—
764C22⋊C4C23×D7918yes—
765C22⋊C4C23×D7918yes—
766C42—798no—
767C42—7916no—
768C42—7916no—
769C42C23×D7914yes—
770C42C23×D7914yes—
771C42C23×D7914yes—
772C42C23×D7914yes—
773C42C23×D7918yes—
774C23—22no—
775C23—22no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—794no—
780C23—1584no—
781C23—1584no—
782C23—1584no—
783C23#1457920814yes—
784C23C24×D7914yes—
785C23C24×D7912yes—
786C23C24×D7911yescharacteristic
787Q8—28no—
788Q8—31616no—
789Q8—31616no—
790Q8—15816no—
791Q8—1588no—
792Q8—15816no—
793D4—216no—
794D4—28no—
795D4—31616no—
796D4—15816no—
797D4—1588no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—28no—
807C2×C4—216no—
808C2×C4—28no—
809C2×C4—31616no—
810C2×C4—31616no—
811C2×C4—31616no—
812C2×C4—794no—
813C2×C4—794no—
814C2×C4—794no—
815C2×C4—798no—
816C2×C4—798no—
817C2×C4—1588no—
818C2×C4—1588no—
819C2×C4—1584no—
820C2×C4—1584no—
821C2×C4—1584no—
822C2×C4—15816no—
823C2×C4#1457920714yes—
824C2×C4#1457920814yes—
825C2×C4C24×D7914yes—
826C2×C4C24×D7914yes—
827C2×C4C24×D7912yes—
828C2×C4C24×D7912yes—
829C2×C4C24×D7912yes—
830C2×C4C24×D7912yes—
831C2×C4C24×D7914yes—
832C2×C4C24×D7912yes—
833C2×C4C24×D7912yes—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—48no—
841C22—3168no—
842C22—1584no—
843C22—1584no—
844C22—1584no—
845C22C2×#1457920712yes—
846C22C2×#1457920814yes—
847C22C2×#1457920812yes—
848C22C2×#1457920812yes—
849C22C25×D7911yescharacteristic
850C4—24no—
851C4—22no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—24no—
856C4—24no—
857C4—1588no—
858C4—1588no—
859C4—1584no—
860C4—1584no—
861C4—1584no—
862C4C2×#1457920714yes—
863C4C2×#1457920814yes—
864C2—24no—
865C2—44no—
866C2—3164no—
867C2#2377784514yesdirect product factor
868C2C22×#1457920711yescharacteristic
869C2C22×#1457920811yescharacteristic
870C2C22×#1457920811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#529×C79C2
socleC23×C79C25
hypercenterC2×#529D79
hypocenterC79C2×#3552
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #23777845C2direct (N × H)
2. C2×#19099315C2semidirect
3. C2×#19099292C2semidirect
4. C2×#19099286C2semidirect
5. C2×#19099271C2semidirect
6. C2×#19099265C2semidirect
7. C2×D4×Dic158C2semidirect
8. C2×D4×Dic158C2semidirect
9. C2×#19099222C2semidirect
10. C2×#19099218C2semidirect
11. C2×#19099193C2semidirect
12. C2×#19099182C2semidirect
13. C2×#19099175C2semidirect
14. C2×#19099157C2semidirect
15. C2×#19099139C2semidirect
16. C22×#14579161C2semidirect
17. C2×#19099097C2semidirect
18. C2×#529×C79C2semidirect
22. #19099315C22semidirect
23. #19099292C22semidirect
24. #19099286C22semidirect
25. #19099271C22semidirect
26. #19099265C22semidirect
27. D4×Dic158C22semidirect
28. D4×Dic158C22semidirect
29. #19099222C22semidirect
30. #19099218C22semidirect
31. #19099193C22semidirect
32. #19099182C22semidirect
33. #19099175C22semidirect
34. #19099157C22semidirect
35. #19099139C22semidirect
42. C2×#14579161C22semidirect
45. #19099097C22semidirect
89. #529×C79C22semidirect
431. C2×C79#3552semidirect
453. C2×#529D79semidirect
454. C79C2×#3552semidirect
482. #529C2×D79semidirect
867. C2#23777845direct (N × H)

Maximal subgroups

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

subgroupindex
#237778452
C2×#190993152
C2×#190992922
C2×#190992862
C2×#190992712
C2×#190992652
C2×D4×Dic1582
C2×#190992222
C2×#190992182
C2×#190991932
C2×#190991822
C2×#190991752
C2×#190991572
C2×#190991392
C22×#145791612
C2×#190990972
C2×#529×C792
C2×#355279