Finite Group Databasebeta

← C2×#23777865 #35195894

Subgroups — C2×#23777865 #35195894

Order 20224.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777865C2132yesmaximal, direct product factor
2C2×#19099308C214yesmaximal, complemented
3C2×#19099299C211yesmaximal, characteristic, complemented
4C2×#19099296C212yesmaximal, complemented
5C2×#19099288C211yesmaximal, characteristic, complemented
6C2×#19099272C212yesmaximal, complemented
7C2×#19099233C211yesmaximal, characteristic, complemented
8C2×#19099228C211yesmaximal, characteristic, complemented
9C2×#19099220C212yesmaximal, complemented
10C2×#19099212C212yesmaximal, complemented
11C2×#19099182C212yesmaximal, complemented
12C2×#19099180C212yesmaximal, complemented
13C2×#19099166C212yesmaximal, complemented
14C2×#19099155C214yesmaximal, complemented
15C2×#19099133C212yesmaximal, complemented
16C2×#19099120C211yesmaximal, characteristic, complemented
17C2×#19099097C211yesmaximal, characteristic, complemented
18C2×#532×C79C211yesmaximal, characteristic, complemented
19C22×#11929623C2212yes—
20C22×Q8×D79C2212yes—
21#19099308C22164yescomplemented
22#19099299C22116yescomplemented
23#19099296C22132yescomplemented
24#19099288C22116yescomplemented
25#19099272C22132yescomplemented
26#19099233C22116yescomplemented
27#19099228C22116yescomplemented
28#19099220C22132yescomplemented
29#19099212C22132yescomplemented
30#19099182C22132yescomplemented
31#19099180C22132yescomplemented
32#19099166C22132yescomplemented
33#19099155C22164yescomplemented
34#19099133C22132yescomplemented
35#19099120C22116yescomplemented
36C2×#14579161C2211yescharacteristic
37C2×#14579161C2211yescharacteristic
38C2×#14579160C2212yes—
39C2×#14579159C2212yes—
40C2×#14579157C2212yes—
41#19099097C22116yescomplemented
42C2×#14579155C2212yes—
43C2×#14579154C2214yes—
44C2×#14579153C2211yescharacteristic
45C2×#14579153C2212yes—
46C2×#14579152C2212yes—
47C2×#14579151C2214yes—
48C2×#14579149C2211yescharacteristic
49C2×#14579148C2214yes—
50C2×#14579148C2212yes—
51C2×#14579148C2212yes—
52C2×#14579147C2214yes—
53C2×#14579145C2214yes—
54C2×#14579144C2214yes—
55C2×#14579144C2212yes—
56C2×#14579143C2214yes—
57C2×#14579143C2214yes—
58C2×#14579142C2214yes—
59C2×#14579142C2214yes—
60C2×#14579140C2211yescharacteristic
61C2×#14579140C2211yescharacteristic
62C2×#14579140C2211yescharacteristic
63C2×#14579140C2214yes—
64C2×#14579140C2212yes—
65C2×#14579139C2214yes—
66C2×#14579138C2214yes—
67C2×#14579138C2214yes—
68C2×#14579138C2214yes—
69C2×#14579137C2212yes—
70C2×#14579135C2211yescharacteristic
71C2×#14579133C2214yes—
72C2×#14579133C2214yes—
73C2×#14579132C2212yes—
74C2×#14579132C2214yes—
75C2×Q8×Dic79C2212yes—
76C2×C4×Dic158C2211yescharacteristic
77C2×C4×Dic158C2211yescharacteristic
78C2×C4×Dic158C2211yescharacteristic
79C2×C4×Dic158C2212yes—
80C2×#14579126C2212yes—
81C2×C4×D316C2211yescharacteristic
82C2×D4×Dic79C2212yes—
83C2×D4×Dic79C2212yes—
84C2×D4×Dic79C2212yes—
85C2×#14579123C2212yes—
86C2×C4×C22⋊D79C2212yes—
87C2×C4×C22⋊D79C2214yes—
88C2×#14579120C2212yes—
89C2×#14579118C2212yes—
90C22×Dic79⋊C4C2214yes—
91C22×#41×C79C2212yes—
92#532×C79C22116yescomplemented
93C2×C4⋊Q8×C79C2211yescharacteristic
94C2×#127×C79C2211yescharacteristic
95C2×#124×C79C2212yes—
96C2×#121×C79C2212yes—
97C2×#121×C79C2212yes—
98C2×C4×D4×C79C2212yes—
99C2×C4×D4×C79C2212yes—
100C22×C42×C79C2211yescharacteristic
101C2×#11929623—48no—
102C2×#11929623C23116yes—
103C22×Dic158C2311yescharacteristic
104C22×Dic158C2311yescharacteristic
105C22×Dic158C2311yescharacteristic
106C22×Dic158C2312yes—
107C22×Dic158C2314yes—
108C2×Q8×D79—48no—
109C2×Q8×D79C23116yes—
110C22×D316C2311yescharacteristic
111C22×C22⋊D79C2312yes—
112C22×C22⋊D79C2314yes—
113C22×C22⋊D79C2314yes—
114C23×Dic79C2314yes—
115C23×Dic79C2314yes—
116C22×C4×D79C2312yes—
117C22×C4×D79C2314yes—
118#14579161C2318yes—
119#14579161C2318yes—
120#14579160C23116yes—
121#14579159C23116yes—
122#14579157C23116yes—
123#14579155C23116yes—
124#14579154C23132yes—
125#14579153C23116yes—
126#14579153C2318yes—
127#14579152C23116yes—
128#14579151C23132yes—
129#14579149C2318yes—
130#14579148C23132yes—
131#14579148C23116yes—
132#14579148C23116yes—
133#14579147C23132yes—
134#14579145C23132yes—
135#14579144C23132yes—
136#14579144C23116yes—
137#14579143C23132yes—
138#14579143C23132yes—
139#14579142C23132yes—
140#14579142C23132yes—
141#14579140C23132yes—
142#14579140C2318yes—
143#14579140C2318yes—
144#14579140C2318yes—
145#14579140C23116yes—
146#14579139C23132yes—
147#14579138C23132yes—
148#14579138C23132yes—
149#14579138C23132yes—
150#14579137C23116yes—
151#14579135C2318yes—
152#14579133C23132yes—
153#14579133C23132yes—
154#14579132C23132yes—
155#14579132C23116yes—
156Q8×Dic79C23116yes—
157C4×Dic158C2318yes—
158C4×Dic158C2318yes—
159C4×Dic158C23116yes—
160C4×Dic158C2318yes—
161#14579126C23116yes—
162C4×D316C2318yes—
163D4×Dic79C23116yes—
164D4×Dic79C23116yes—
165D4×Dic79C23116yes—
166#14579123C23116yes—
167C4×C22⋊D79C23132yes—
168C4×C22⋊D79C23116yes—
169#14579120C23116yes—
170#14579118C23116yes—
171C2×C4⋊Dic79C2312yes—
172C2×C4⋊Dic79C2312yes—
173C2×C4⋊Dic79C2311yescharacteristic
174C2×C4⋊Dic79C2311yescharacteristic
175C2×C4⋊Dic79C2311yescharacteristic
176C2×C4⋊Dic79C2311yescharacteristic
177C2×C4⋊Dic79C2312yes—
178C2×C4⋊Dic79C2314yes—
179C2×Dic79⋊C4C23132yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2312yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2312yes—
186C2×Dic79⋊C4C2312yes—
187C2×Dic79⋊C4C2314yes—
188C2×Dic79⋊C4C2312yes—
189C2×Dic79⋊C4C2312yes—
190C2×Dic79⋊C4C2312yes—
191C2×C22⋊Dic79C2312yes—
192C2×C22⋊Dic79C2312yes—
193C2×C22⋊Dic79C2314yes—
194C2×C22⋊Dic79C2312yes—
195C2×C22⋊Dic79C2314yes—
196C2×C22⋊Dic79C2314yes—
197C2×C22⋊Dic79C2314yes—
198C2×(C2×D79)⋊C4C2312yes—
199C2×(C2×D79)⋊C4C2312yes—
200C2×(C2×D79)⋊C4C2312yes—
201C2×(C2×D79)⋊C4C2314yes—
202C2×(C2×D79)⋊C4C2312yes—
203C2×C4×Dic79C2312yes—
204C2×C4×Dic79C2312yes—
205C2×C4×Dic79C2312yes—
206C2×C4×Dic79C2314yes—
207C2×#41×C79—48no—
208C2×#41×C79C23116yes—
209C22×Q8×C79C2312yes—
210C22×D4×C79C2312yes—
211C22×D4×C79C2312yes—
212C22×D4×C79C2312yes—
213C22×D4×C79C2314yes—
214C23×C4×C79C2311yescharacteristic
215C23×C4×C79C2311yescharacteristic
216C23×C4×C79C2311yescharacteristic
217C23×C4×C79C2314yes—
218C4⋊Q8×C79C2318yes—
219#127×C79C2318yes—
220#124×C79C23116yes—
221#121×C79C23116yes—
222#121×C79C23116yes—
223C4×D4×C79C23116yes—
224C4×D4×C79C23116yes—
225C2×C4⋊C4×C79C2312yes—
226C2×C4⋊C4×C79C2312yes—
227C2×C22⋊C4×C79C2314yes—
228C2×C22⋊C4×C79C2314yes—
229C2×C42×C79C2311yescharacteristic
230C2×C42×C79C2311yescharacteristic
231C2×C42×C79C2311yescharacteristic
232C2×C42×C79C2311yescharacteristic
233C2×C42×C79C2318yes—
234C23×D79C2412yes—
235#11929623—432no—
236C2×Dic158—24no—
237C2×Dic158—24no—
238C2×Dic158—24no—
239C2×Dic158—48no—
240C2×Dic158—44no—
241C2×Dic158C2414yes—
242C2×Dic158C2414yes—
243C2×Dic158C2414yes—
244C2×Dic158C24116yes—
245C2×Dic158C2418yes—
246Q8×D79—432no—
247C2×D316—24no—
248C2×D316C2414yes—
249C2×C22⋊D79—48no—
250C2×C22⋊D79—48no—
251C2×C22⋊D79—44no—
252C2×C22⋊D79C24116yes—
253C2×C22⋊D79C2418yes—
254C2×C22⋊D79C24116yes—
255C22×Dic79—48no—
256C22×Dic79—48no—
257C22×Dic79C2412yes—
258C22×Dic79C2412yes—
259C22×Dic79C2412yes—
260C22×Dic79C2412yes—
261C22×Dic79C2412yes—
262C22×Dic79C2412yes—
263C22×Dic79C2412yes—
264C22×Dic79C24116yes—
265C22×Dic79C24116yes—
266C2×C4×D79—28no—
267C2×C4×D79—48no—
268C2×C4×D79C2418yes—
269C2×C4×D79C24116yes—
270C4⋊Dic79C2418yes—
271C4⋊Dic79C2418yes—
272C4⋊Dic79C2414yes—
273C4⋊Dic79C2414yes—
274C4⋊Dic79C2414yes—
275C4⋊Dic79C2414yes—
276C4⋊Dic79C2418yes—
277C4⋊Dic79C24116yes—
278Dic79⋊C4C2418yes—
279Dic79⋊C4C2418yes—
280Dic79⋊C4C24116yes—
281Dic79⋊C4C24116yes—
282Dic79⋊C4C2418yes—
283Dic79⋊C4C2418yes—
284Dic79⋊C4C2418yes—
285Dic79⋊C4C24116yes—
286Dic79⋊C4C2418yes—
287Dic79⋊C4C2418yes—
288Dic79⋊C4C2418yes—
289C22⋊Dic79C2418yes—
290C22⋊Dic79C2418yes—
291C22⋊Dic79C24116yes—
292C22⋊Dic79C2418yes—
293C22⋊Dic79C24116yes—
294C22⋊Dic79C24116yes—
295C22⋊Dic79C24116yes—
296(C2×D79)⋊C4C2418yes—
297(C2×D79)⋊C4C2418yes—
298(C2×D79)⋊C4C2418yes—
299(C2×D79)⋊C4C24116yes—
300(C2×D79)⋊C4C2418yes—
301C4×Dic79C2418yes—
302C4×Dic79C2418yes—
303C4×Dic79C2418yes—
304C4×Dic79C24116yes—
305C24×C79C2414yes—
306C24×C79C2411yescharacteristic
307#41×C79—432no—
308C2×Q8×C79—28no—
309C2×Q8×C79C2418yes—
310C2×D4×C79—28no—
311C2×D4×C79—28no—
312C2×D4×C79—44no—
313C2×D4×C79—48no—
314C2×D4×C79C2418yes—
315C2×D4×C79C2418yes—
316C2×D4×C79C2418yes—
317C2×D4×C79C24116yes—
318C22×C4×C79—24no—
319C22×C4×C79—24no—
320C22×C4×C79—42no—
321C22×C4×C79—48no—
322C22×C4×C79C2411yescharacteristic
323C22×C4×C79C2414yes—
324C22×C4×C79C2411yescharacteristic
325C22×C4×C79C2411yescharacteristic
326C22×C4×C79C2414yes—
327C22×C4×C79C2411yescharacteristic
328C22×C4×C79C2414yes—
329C22×C4×C79C2414yes—
330C22×C4×C79C24116yes—
331C22×C4×C79C2411yescharacteristic
332C22×C4×C79C2411yescharacteristic
333C4⋊C4×C79C2418yes—
334C4⋊C4×C79C2418yes—
335C22⋊C4×C79C24116yes—
336C22⋊C4×C79C24116yes—
337C42×C79C2414yes—
338C42×C79C2414yes—
339C42×C79C2414yes—
340C42×C79C2414yes—
341C23×C79—28no—
342C23×C79—22no—
343C23×C79—22no—
344C23×C79—28no—
345C23×C79—28no—
346C23×C79—22no—
347C23×C79C2512yes—
348C23×C79C2518yes—
349C23×C79C2511yescharacteristic
350C22×D79—24no—
351C22×D79—24no—
352C22×D79—24no—
353C22×D79C2514yes—
354Q8×C79—216no—
355D4×C79—216no—
356D4×C79—216no—
357D4×C79—48no—
358D4×C79—416no—
359C2×C4×C79—28no—
360C2×C4×C79—22no—
361C2×C4×C79—22no—
362C2×C4×C79—22no—
363C2×C4×C79—22no—
364C2×C4×C79—28no—
365C2×C4×C79—28no—
366C2×C4×C79—44no—
367C2×C4×C79—416no—
368C2×C4×C79H(5,𝔽2)14yes—
369C2×C4×C792−1+414yes—
370C2×C4×C79C2518yes—
371C2×C4×C79C2512yes—
372C2×C4×C79C2512yes—
373C2×C4×C79C2512yes—
374C2×C4×C79C2512yes—
375C2×C4×C79C2512yes—
376C2×C4×C79C2512yes—
377C22⋊D79—416no—
378C22⋊D79—48no—
379C22⋊D79—416no—
380C2×Dic79—24no—
381C2×Dic79—24no—
382C2×Dic79—24no—
383C2×Dic79—24no—
384C2×Dic79—24no—
385C2×Dic79—24no—
386C2×Dic79—24no—
387C2×Dic79—416no—
388C2×Dic79—416no—
389C2×Dic79C2514yes—
390C2×Dic79C2514yes—
391C2×Dic79C2514yes—
392C2×Dic79C2514yes—
393C2×Dic79C2514yes—
394C2×Dic79C2514yes—
395C2×Dic79C2514yes—
396D316—28no—
397C4×D79—216no—
398C4×D79—416no—
399Dic158—28no—
400Dic158—28no—
401Dic158—28no—
402Dic158—416no—
403Dic158—48no—
404C22×C79—28no—
405C22×C79—22no—
406C22×C79—22no—
407C22×C79—28no—
408C22×C79—22no—
409C22×C79—28no—
410C22×C79—416no—
411C22×C79—44no—
412C22×C79C2×H(5,𝔽2)12yes—
413C22×C79C2×2−1+412yes—
414C22×C79#58512yes—
415C22×C79C2611yescharacteristic
416C2×D79—24no—
417C2×D79—24no—
418C2×D79—24no—
419C2×D79—48no—
420C4×C79—22no—
421C4×C79—28no—
422C4×C79—22no—
423C4×C79—22no—
424C4×C79—22no—
425C4×C79C2×H(5,𝔽2)14yes—
426C4×C79C2×2−1+414yes—
427Dic79—24no—
428Dic79—24no—
429Dic79—24no—
430Dic79—24no—
431Dic79—24no—
432Dic79—24no—
433Dic79—24no—
434C2×#3554—791nomaximal, Sylow
435C2×C79—48no—
436C2×C79—42no—
437C2×C79#355414yescomplemented
438C2×C79C22×H(5,𝔽2)11yescharacteristic
439C2×C79C22×2−1+411yescharacteristic
440C2×C79C2×#58511yescharacteristic
441D79—44no—
442#3554—7932no—
443C2×#562—794no—
444C2×#559—791no—
445C2×#559—792no—
446C2×#557—791no—
447C2×#554—792no—
448C2×#550—791no—
449C2×D4×Q8—791no—
450C2×#548—792no—
451C2×#547—792no—
452C2×#542—792no—
453C2×#542—792no—
454C2×#540—792no—
455C2×#539—794no—
456C2×#536—792no—
457C2×#533—791no—
458C2×#532D7911yescharacteristic, complemented
459C2×#529—791no—
460C79C2×#355411yescharacteristic, complemented, Sylow
461C22×#41—792no—
462C22×#41C2×D7912yes—
463C23×Q8—792no—
464#562—7964no—
465#559—7916no—
466#559—7932no—
467#557—7916no—
468#554—7932no—
469#550—7916no—
470D4×Q8—7916no—
471#548—7932no—
472#547—7932no—
473#542—7932no—
474#542—7932no—
475#540—7932no—
476#539—7964no—
477#536—7932no—
478#533—7916no—
479#532C2×D79116yescomplemented
480C2×C4⋊Q8—792no—
481C2×C4⋊Q8—792no—
482C2×C4⋊Q8—791no—
483C2×C4⋊Q8—791no—
484C2×C4⋊Q8C2×D7911yescharacteristic
485C2×#127—792no—
486C2×#127C2×D7911yescharacteristic
487#529—7916no—
488C2×#126—794no—
489C2×#126—792no—
490C2×#125—794no—
491C2×#125—792no—
492C2×#125—791no—
493C2×#125—792no—
494C2×#124—792no—
495C2×#124—794no—
496C2×#124—792no—
497C2×#124—794no—
498C2×#124—791no—
499C2×#124C2×D7912yes—
500C2×#123—794no—
501C2×#123—794no—
502C2×#123—792no—
503C2×#123—794no—
504C2×#123—794no—
505C2×#123—794no—
506C2×#123—794no—
507C2×C22⋊Q8—792no—
508C2×C22⋊Q8—791no—
509C2×C22⋊Q8—791no—
510C2×C22⋊Q8—791no—
511C2×C22⋊Q8—792no—
512C2×C22⋊Q8—794no—
513C2×C22⋊Q8—794no—
514C2×C22⋊Q8—794no—
515C2×C22⋊Q8—794no—
516C2×C22⋊Q8—794no—
517C2×#121—794no—
518C2×#121—794no—
519C2×#121—794no—
520C2×#121—792no—
521C2×#121—791no—
522C2×#121C2×D7912yes—
523C2×#121C2×D7912yes—
524C2×C4×Q8—792no—
525C2×C4×Q8—792no—
526C2×C4×Q8—791no—
527C2×C4×Q8—791no—
528C2×C4×Q8—791no—
529C2×C4×Q8—792no—
530C2×C4×D4—792no—
531C2×C4×D4—792no—
532C2×C4×D4—792no—
533C2×C4×D4—792no—
534C2×C4×D4—794no—
535C2×C4×D4—792no—
536C2×C4×D4—791no—
537C2×C4×D4C2×D7912yes—
538C2×C4×D4C2×D7912yes—
539C2×#117—792no—
540C2×#117—792no—
541C22×C4⋊C4—794no—
542C22×C42C2×D7911yescharacteristic
543C2×#41—48no—
544C2×#41—3168no—
545C2×#41—7916no—
546C2×#41C22×D79116yes—
547C22×Q8—3168no—
548C22×Q8—7916no—
549C22×Q8—792no—
550C22×Q8—794no—
551C22×Q8—791no—
552C22×Q8—791no—
553C22×Q8—791no—
554C22×Q8C22×D7912yes—
555C22×D4—792no—
556C22×D4—794no—
557C22×D4—794no—
558C22×D4—791no—
559C22×D4C22×D7912yes—
560C22×D4C22×D7912yes—
561C22×D4C22×D7912yes—
562C22×D4C22×D7914yes—
563C23×C4—794no—
564C23×C4—794no—
565C23×C4—794no—
566C23×C4—792no—
567C23×C4C22×D7911yescharacteristic
568C23×C4C22×D7911yescharacteristic
569C23×C4C22×D7914yes—
570C23×C4C22×D7911yescharacteristic
571C4⋊Q8—7916no—
572C4⋊Q8—7916no—
573C4⋊Q8—798no—
574C4⋊Q8—798no—
575C4⋊Q8C22×D7918yes—
576#127—7916no—
577#127C22×D7918yes—
578#126—7932no—
579#126—7916no—
580#125—7932no—
581#125—7916no—
582#125—798no—
583#125—7916no—
584#124—7916no—
585#124—7932no—
586#124—7916no—
587#124—7932no—
588#124—798no—
589#124C22×D79116yes—
590#123—7932no—
591#123—7932no—
592#123—7916no—
593#123—7932no—
594#123—7932no—
595#123—7932no—
596#123—7932no—
597C22⋊Q8—7916no—
598C22⋊Q8—798no—
599C22⋊Q8—798no—
600C22⋊Q8—798no—
601C22⋊Q8—7916no—
602C22⋊Q8—7932no—
603C22⋊Q8—7932no—
604C22⋊Q8—7932no—
605C22⋊Q8—7932no—
606C22⋊Q8—7932no—
607#121—7932no—
608#121—7932no—
609#121—7932no—
610#121—7916no—
611#121—798no—
612#121C22×D79116yes—
613#121C22×D79116yes—
614C4×Q8—7916no—
615C4×Q8—7916no—
616C4×Q8—798no—
617C4×Q8—798no—
618C4×Q8—798no—
619C4×Q8—7916no—
620C4×D4—7916no—
621C4×D4—7916no—
622C4×D4—7916no—
623C4×D4—7916no—
624C4×D4—7932no—
625C4×D4—7916no—
626C4×D4—798no—
627C4×D4C22×D79116yes—
628C4×D4C22×D79116yes—
629#117—7916no—
630#117—7916no—
631C2×C4⋊C4—792no—
632C2×C4⋊C4—792no—
633C2×C4⋊C4—794no—
634C2×C4⋊C4—794no—
635C2×C4⋊C4—7932no—
636C2×C4⋊C4—792no—
637C2×C4⋊C4—792no—
638C2×C4⋊C4—792no—
639C2×C4⋊C4—792no—
640C2×C4⋊C4—791no—
641C2×C4⋊C4—791no—
642C2×C4⋊C4—792no—
643C2×C4⋊C4—791no—
644C2×C4⋊C4—791no—
645C2×C4⋊C4—792no—
646C2×C4⋊C4—794no—
647C2×C4⋊C4—792no—
648C2×C4⋊C4—792no—
649C2×C4⋊C4—794no—
650C2×C4⋊C4—792no—
651C2×C4⋊C4C22×D7912yes—
652C2×C4⋊C4C22×D7912yes—
653C2×C22⋊C4—792no—
654C2×C22⋊C4—792no—
655C2×C22⋊C4—794no—
656C2×C22⋊C4—794no—
657C2×C22⋊C4—792no—
658C2×C22⋊C4—794no—
659C2×C22⋊C4—794no—
660C2×C22⋊C4—792no—
661C2×C22⋊C4—792no—
662C2×C22⋊C4—792no—
663C2×C22⋊C4—792no—
664C2×C22⋊C4—794no—
665C2×C22⋊C4C22×D7914yes—
666C2×C22⋊C4C22×D7914yes—
667C2×C42—792no—
668C2×C42—792no—
669C2×C42—792no—
670C2×C42—794no—
671C2×C42C22×D7911yescharacteristic
672C2×C42C22×D7911yescharacteristic
673C2×C42C22×D7911yescharacteristic
674C2×C42C22×D7911yescharacteristic
675C2×C42C22×D7918yes—
676C24—792no—
677C24C23×D7911yescharacteristic
678C24C23×D7914yes—
679#41—432no—
680#41—31632no—
681C2×Q8—28no—
682C2×Q8—3168no—
683C2×Q8—3164no—
684C2×Q8—31632no—
685C2×Q8—798no—
686C2×Q8—7916no—
687C2×Q8—794no—
688C2×Q8—794no—
689C2×Q8—794no—
690C2×Q8—1584no—
691C2×Q8—1584no—
692C2×Q8—1584no—
693C2×Q8C23×D7918yes—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—48no—
697C2×D4—44no—
698C2×D4—3164no—
699C2×D4—3168no—
700C2×D4—3168no—
701C2×D4—798no—
702C2×D4—7916no—
703C2×D4—7916no—
704C2×D4—794no—
705C2×D4—1584no—
706C2×D4C23×D7918yes—
707C2×D4C23×D7918yes—
708C2×D4C23×D7918yes—
709C2×D4C23×D79116yes—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—48no—
713C22×C4—42no—
714C22×C4—3168no—
715C22×C4—3168no—
716C22×C4—3168no—
717C22×C4—7916no—
718C22×C4—7916no—
719C22×C4—7916no—
720C22×C4—792no—
721C22×C4—792no—
722C22×C4—792no—
723C22×C4—792no—
724C22×C4—792no—
725C22×C4—792no—
726C22×C4—792no—
727C22×C4—798no—
728C22×C4—1588no—
729C22×C4C23×D7914yes—
730C22×C4C23×D7914yes—
731C22×C4C23×D7914yes—
732C22×C4C23×D7911yescharacteristic
733C22×C4C23×D7911yescharacteristic
734C22×C4C23×D7911yescharacteristic
735C22×C4C23×D7911yescharacteristic
736C22×C4C23×D7914yes—
737C22×C4C23×D79116yes—
738C22×C4C23×D7911yescharacteristic
739C22×C4C23×D7911yescharacteristic
740C4⋊C4—798no—
741C4⋊C4—798no—
742C4⋊C4—7916no—
743C4⋊C4—7916no—
744C4⋊C4—798no—
745C4⋊C4—798no—
746C4⋊C4—798no—
747C4⋊C4—798no—
748C4⋊C4—798no—
749C4⋊C4—7916no—
750C4⋊C4—798no—
751C4⋊C4—798no—
752C4⋊C4—798no—
753C4⋊C4—794no—
754C4⋊C4—794no—
755C4⋊C4—794no—
756C4⋊C4—794no—
757C4⋊C4—7916no—
758C4⋊C4—798no—
759C4⋊C4C23×D7918yes—
760C4⋊C4C23×D7918yes—
761C22⋊C4—798no—
762C22⋊C4—798no—
763C22⋊C4—7916no—
764C22⋊C4—7916no—
765C22⋊C4—798no—
766C22⋊C4—7916no—
767C22⋊C4—7916no—
768C22⋊C4—798no—
769C22⋊C4—798no—
770C22⋊C4—798no—
771C22⋊C4—798no—
772C22⋊C4—7916no—
773C22⋊C4C23×D79116yes—
774C22⋊C4C23×D79116yes—
775C42—798no—
776C42—798no—
777C42—798no—
778C42—7916no—
779C42C23×D7914yes—
780C42C23×D7914yes—
781C42C23×D7914yes—
782C42C23×D7914yes—
783C23—22no—
784C23—28no—
785C23—22no—
786C23—28no—
787C23—22no—
788C23—28no—
789C23—794no—
790C23—1584no—
791C23—1584no—
792C23—1584no—
793C23C24×D7912yes—
794C23C24×D7918yes—
795C23C24×D7911yescharacteristic
796Q8—216no—
797Q8—31616no—
798Q8—3168no—
799Q8—1588no—
800Q8—1588no—
801Q8—1588no—
802D4—216no—
803D4—216no—
804D4—48no—
805D4—416no—
806D4—3168no—
807D4—31616no—
808D4—31616no—
809D4—1588no—
810C2×C4—22no—
811C2×C4—28no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—28no—
816C2×C4—28no—
817C2×C4—44no—
818C2×C4—416no—
819C2×C4—31616no—
820C2×C4—31616no—
821C2×C4—31616no—
822C2×C4—794no—
823C2×C4—794no—
824C2×C4—794no—
825C2×C4—794no—
826C2×C4—794no—
827C2×C4—794no—
828C2×C4—794no—
829C2×C4—1584no—
830C2×C4—1584no—
831C2×C4—1584no—
832C2×C4—1584no—
833C2×C4—1584no—
834C2×C4—1584no—
835C2×C4—1584no—
836C2×C4—15816no—
837C2×C4#1457920614yes—
838C2×C4#1457920814yes—
839C2×C4C24×D7918yes—
840C2×C4C24×D7912yes—
841C2×C4C24×D7912yes—
842C2×C4C24×D7912yes—
843C2×C4C24×D7912yes—
844C2×C4C24×D7912yes—
845C2×C4C24×D7912yes—
846C22—22no—
847C22—28no—
848C22—22no—
849C22—28no—
850C22—22no—
851C22—28no—
852C22—44no—
853C22—416no—
854C22—3168no—
855C22—1584no—
856C22—1584no—
857C22—1584no—
858C22C2×#1457920612yes—
859C22C2×#1457920812yes—
860C22#1909939912yes—
861C22C25×D7911yescharacteristic
862C4—22no—
863C4—28no—
864C4—22no—
865C4—22no—
866C4—22no—
867C4—1584no—
868C4—1584no—
869C4—1584no—
870C4—1584no—
871C4—1584no—
872C4—1584no—
873C4—1584no—
874C4C2×#1457920614yes—
875C4C2×#1457920814yes—
876C2—42no—
877C2—48no—
878C2—3164no—
879C2#2377786514yesdirect product factor
880C2C22×#1457920611yescharacteristic
881C2C22×#1457920811yescharacteristic
882C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#532×C79C2
socleC23×C79C25
hypercenterC2×#532D79
hypocenterC79C2×#3554
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #23777865C2direct (N × H)
2. C2×#19099308C2semidirect
3. C2×#19099299C2semidirect
4. C2×#19099296C2semidirect
5. C2×#19099288C2semidirect
6. C2×#19099272C2semidirect
7. C2×#19099233C2semidirect
8. C2×#19099228C2semidirect
9. C2×#19099220C2semidirect
10. C2×#19099212C2semidirect
11. C2×#19099182C2semidirect
12. C2×#19099180C2semidirect
13. C2×#19099166C2semidirect
14. C2×#19099155C2semidirect
15. C2×#19099133C2semidirect
16. C2×#19099120C2semidirect
17. C2×#19099097C2semidirect
18. C2×#532×C79C2semidirect
21. #19099308C22semidirect
22. #19099299C22semidirect
23. #19099296C22semidirect
24. #19099288C22semidirect
25. #19099272C22semidirect
26. #19099233C22semidirect
27. #19099228C22semidirect
28. #19099220C22semidirect
29. #19099212C22semidirect
30. #19099182C22semidirect
31. #19099180C22semidirect
32. #19099166C22semidirect
33. #19099155C22semidirect
34. #19099133C22semidirect
35. #19099120C22semidirect
41. #19099097C22semidirect
92. #532×C79C22semidirect
437. C2×C79#3554semidirect
458. C2×#532D79semidirect
460. C79C2×#3554semidirect
479. #532C2×D79semidirect
879. C2#23777865direct (N × H)

Maximal subgroups

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

subgroupindex
#237778652
C2×#190993082
C2×#190992992
C2×#190992962
C2×#190992882
C2×#190992722
C2×#190992332
C2×#190992282
C2×#190992202
C2×#190992122
C2×#190991822
C2×#190991802
C2×#190991662
C2×#190991552
C2×#190991332
C2×#190991202
C2×#190990972
C2×#532×C792
C2×#355479