Finite Group Databasebeta

← C2×#23777477 #35196472

Subgroups — C2×#23777477 #35196472

Order 20224.

7758 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777477C2132yesmaximal, direct product factor
2C2×#19099299C211yesmaximal, characteristic, complemented
3C2×#19099296C212yesmaximal, complemented
4C2×#19099293C211yesmaximal, characteristic, complemented
5C2×#19099274C211yesmaximal, characteristic, complemented
6C2×#19099272C212yesmaximal, complemented
7C2×#19099233C211yesmaximal, characteristic, complemented
8C2×#19099219C212yesmaximal, complemented
9C2×#19099213C212yesmaximal, complemented
10C2×#19099212C214yesmaximal, complemented
11C2×#19099178C212yesmaximal, complemented
12C2×#19099177C214yesmaximal, complemented
13C2×#19099108C212yesmaximal, complemented
14C2×#19099097C211yesmaximal, characteristic, complemented
15C2×#19099094C212yesmaximal, complemented
16C2×#19099042C212yesmaximal, complemented
17C22×C4×Dic158C211yesmaximal, characteristic, complemented
18C2×#532×C79C211yesmaximal, characteristic, complemented
19C22×#11929623C2212yes—
20C22×#11929623C2214yes—
21C23×Dic158C2211yescharacteristic
22#19099299C22116yescomplemented
23#19099296C22132yescomplemented
24#19099293C22116yescomplemented
25#19099274C22116yescomplemented
26#19099272C22132yescomplemented
27#19099233C22116yescomplemented
28#19099219C22132yescomplemented
29#19099213C22132yescomplemented
30#19099212C22164yescomplemented
31#19099178C22132yescomplemented
32#19099177C22164yescomplemented
33#19099108C22132yescomplemented
34C2×#14579160C2212yes—
35C2×#14579160C2212yes—
36C2×#14579159C2214yes—
37C2×#14579157C2212yes—
38#19099097C22116yescomplemented
39#19099094C22132yescomplemented
40C2×#14579155C2212yes—
41C2×#14579154C2214yes—
42C2×#14579153C2211yescharacteristic
43C2×#14579152C2212yes—
44C2×#14579149C2211yescharacteristic
45C2×#14579148C2212yes—
46C2×#14579148C2212yes—
47C2×#14579147C2214yes—
48C2×#14579147C2214yes—
49C2×#14579144C2214yes—
50C2×#14579144C2212yes—
51C2×#14579143C2214yes—
52C2×#14579142C2214yes—
53C2×#14579142C2214yes—
54C2×#14579141C2212yes—
55C2×#14579140C2214yes—
56C2×#14579140C2211yescharacteristic
57C2×#14579138C2214yes—
58C2×#14579138C2214yes—
59C2×#14579137C2214yes—
60C2×#14579135C2211yescharacteristic
61C2×#14579133C2214yes—
62C2×#14579133C2214yes—
63C2×#14579132C2212yes—
64#19099042C22132yescomplemented
65C2×C4×Dic158C2212yes—
66C2×C4×Dic158C2211yescharacteristic
67C2×C4×Dic158C2211yescharacteristic
68C2×C4×Dic158C2211yescharacteristic
69C2×C4×Dic158C2212yes—
70C2×C4×Dic158C2211yescharacteristic
71C2×C4×Dic158C2211yescharacteristic
72C2×C4×Dic158C22116yescomplemented
73C2×#14579126C2212yes—
74C2×#14579126C2212yes—
75C2×C4×D316C2211yescharacteristic
76C2×D4×Dic79C2212yes—
77C2×D4×Dic79C2214yes—
78C2×D4×Dic79C2212yes—
79C2×D4×Dic79C2212yes—
80C2×#14579123C2212yes—
81C2×C4×C22⋊D79C2214yes—
82C2×C4×C22⋊D79C2212yes—
83C2×(C22⋊D79)⋊C4C2214yes—
84C2×#14579118C2212yes—
85C2×#14579117C2214yes—
86C22×C4⋊Dic79C2211yescharacteristic
87C22×Dic79⋊C4C2212yes—
88C22×Dic79⋊C4C2214yes—
89C2×C4⋊C4×D79C2212yes—
90C22×C4×Dic79C2212yes—
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—216no—
102C2×#11929623—416no—
103C2×#11929623C23116yes—
104C2×#11929623C23132yes—
105C22×Dic158—28no—
106C22×Dic158C2318yes—
107C22×Dic158C2311yescharacteristic
108C22×Dic158C2312yes—
109C22×Dic158C2311yescharacteristic
110C22×Dic158C2314yes—
111C22×Dic158C2311yescharacteristic
112C22×D316C2311yescharacteristic
113C22×C22⋊D79C2314yes—
114C22×C22⋊D79C2312yes—
115C22×C22⋊D79C2314yes—
116C23×Dic79C2312yes—
117C23×Dic79C2312yes—
118C23×Dic79C2314yes—
119C23×Dic79C2314yes—
120C22×C4×D79C2312yes—
121C22×C4×D79C2314yes—
122#14579160C23116yes—
123#14579160C23116yes—
124#14579159C23132yes—
125#14579157C23116yes—
126#14579155C23116yes—
127#14579154C23132yes—
128#14579153C2318yes—
129#14579152C23116yes—
130#14579149C2318yes—
131#14579148C23116yes—
132#14579148C23116yes—
133#14579147C23132yes—
134#14579147C23132yes—
135#14579144C23132yes—
136#14579144C23116yes—
137#14579143C23132yes—
138#14579142C23132yes—
139#14579142C23132yes—
140#14579141C23116yes—
141#14579140C23132yes—
142#14579140C2318yes—
143#14579138C23132yes—
144#14579138C23132yes—
145#14579137C23132yes—
146#14579135C2318yes—
147#14579133C23132yes—
148#14579133C23132yes—
149#14579132C23116yes—
150C4×Dic158C23116yes—
151C4×Dic158C2318yes—
152C4×Dic158C2318yes—
153C4×Dic158C23116yes—
154C4×Dic158C2318yes—
155C4×Dic158C2318yes—
156C4×Dic158C2318yes—
157#14579126C23116yes—
158#14579126C23116yes—
159C4×D316C2318yes—
160D4×Dic79C23132yes—
161D4×Dic79C23116yes—
162D4×Dic79C23116yes—
163D4×Dic79C23116yes—
164#14579123C23116yes—
165C4×C22⋊D79C23132yes—
166C4×C22⋊D79C23116yes—
167(C22⋊D79)⋊C4C23132yes—
168#14579118C23116yes—
169#14579117C23132yes—
170C2×C4⋊Dic79C2318yes—
171C2×C4⋊Dic79C2311yescharacteristic
172C2×C4⋊Dic79C2311yescharacteristic
173C2×C4⋊Dic79C2312yes—
174C2×C4⋊Dic79C2311yescharacteristic
175C2×C4⋊Dic79C2311yescharacteristic
176C2×C4⋊Dic79C2314yes—
177C2×Dic79⋊C4C23116yes—
178C2×Dic79⋊C4C23132yes—
179C2×Dic79⋊C4C2314yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2312yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2312yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2312yes—
186C2×Dic79⋊C4C2312yes—
187C2×Dic79⋊C4C2312yes—
188C2×Dic79⋊C4C2314yes—
189C2×Dic79⋊C4C2312yes—
190C4⋊C4×D79C23116yes—
191C2×C22⋊Dic79C2314yes—
192C2×C22⋊Dic79C2312yes—
193C2×C22⋊Dic79C2314yes—
194C2×C22⋊Dic79C2314yes—
195C2×C22⋊Dic79C2314yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×(C2×D79)⋊C4C2312yes—
199C2×(C2×D79)⋊C4C2314yes—
200C2×(C2×D79)⋊C4C2312yes—
201C2×C4×Dic79C2312yes—
202C2×C4×Dic79C2312yes—
203C2×C4×Dic79C2312yes—
204C2×C4×Dic79C2312yes—
205C2×C4×Dic79C23116yes—
206C2×C4×Dic79C2314yes—
207C2×C4×Dic79C2312yes—
208C2×#41×C79—48no—
209C2×#41×C79C23116yes—
210C22×Q8×C79C2312yes—
211C22×D4×C79C2312yes—
212C22×D4×C79C2312yes—
213C22×D4×C79C2314yes—
214C22×D4×C79C2312yes—
215C23×C4×C79C2311yescharacteristic
216C23×C4×C79C2311yescharacteristic
217C23×C4×C79C2311yescharacteristic
218C23×C4×C79C2314yes—
219C4⋊Q8×C79C2318yes—
220#127×C79C2318yes—
221#124×C79C23116yes—
222#121×C79C23116yes—
223#121×C79C23116yes—
224C4×D4×C79C23116yes—
225C4×D4×C79C23116yes—
226C2×C4⋊C4×C79C2312yes—
227C2×C4⋊C4×C79C2312yes—
228C2×C22⋊C4×C79C2314yes—
229C2×C22⋊C4×C79C2314yes—
230C2×C42×C79C2311yescharacteristic
231C2×C42×C79C2311yescharacteristic
232C2×C42×C79C2311yescharacteristic
233C2×C42×C79C2311yescharacteristic
234C2×C42×C79C2318yes—
235C23×D79C2412yes—
236#11929623—264no—
237#11929623—464no—
238C2×Dic158—28no—
239C2×Dic158—232no—
240C2×Dic158—24no—
241C2×Dic158—24no—
242C2×Dic158—48no—
243C2×Dic158#4118yescomplemented
244C2×Dic158C2418yes—
245C2×Dic158C2414yes—
246C2×Dic158C2414yes—
247C2×Dic158C24116yes—
248C2×Dic158C2414yes—
249C2×D316—24no—
250C2×D316C2414yes—
251C2×C22⋊D79—216no—
252C2×C22⋊D79—28no—
253C2×C22⋊D79—48no—
254C2×C22⋊D79C2418yes—
255C2×C22⋊D79C24116yes—
256C2×C22⋊D79C24116yes—
257C22×Dic79—28no—
258C22×Dic79—216no—
259C22×Dic79—28no—
260C22×Dic79—48no—
261C22×Dic79C2412yes—
262C22×Dic79C2412yes—
263C22×Dic79C2418yes—
264C22×Dic79C2412yes—
265C22×Dic79C2412yes—
266C22×Dic79C2418yes—
267C22×Dic79C24116yes—
268C22×Dic79C2412yes—
269C22×Dic79C2412yes—
270C22×Dic79C24116yes—
271C22×Dic79C2412yes—
272C2×C4×D79—28no—
273C2×C4×D79—48no—
274C2×C4×D79C2418yes—
275C2×C4×D79C24116yes—
276C4⋊Dic79C2414yes—
277C4⋊Dic79C2414yes—
278C4⋊Dic79C2418yes—
279C4⋊Dic79C2414yes—
280C4⋊Dic79C2414yes—
281C4⋊Dic79C24116yes—
282Dic79⋊C4C24116yes—
283Dic79⋊C4C2418yes—
284Dic79⋊C4C2418yes—
285Dic79⋊C4C24116yes—
286Dic79⋊C4C2418yes—
287Dic79⋊C4C2418yes—
288Dic79⋊C4C2418yes—
289Dic79⋊C4C2418yes—
290Dic79⋊C4C2418yes—
291Dic79⋊C4C24116yes—
292Dic79⋊C4C2418yes—
293C22⋊Dic79C24116yes—
294C22⋊Dic79C2418yes—
295C22⋊Dic79C24116yes—
296C22⋊Dic79C24116yes—
297C22⋊Dic79C24116yes—
298(C2×D79)⋊C4C2418yes—
299(C2×D79)⋊C4C2418yes—
300(C2×D79)⋊C4C2418yes—
301(C2×D79)⋊C4C24116yes—
302(C2×D79)⋊C4C2418yes—
303C4×Dic79C2418yes—
304C4×Dic79C2418yes—
305C4×Dic79C2418yes—
306C4×Dic79C2418yes—
307C4×Dic79C24116yes—
308C4×Dic79C2418yes—
309C24×C79C2414yes—
310C24×C79C2411yescharacteristic
311#41×C79—432no—
312C2×Q8×C79—44no—
313C2×Q8×C79C2418yes—
314C2×D4×C79—216no—
315C2×D4×C79—28no—
316C2×D4×C79—28no—
317C2×D4×C79—44no—
318C2×D4×C79C2418yes—
319C2×D4×C79C24116yes—
320C2×D4×C79C2418yes—
321C2×D4×C79C2418yes—
322C22×C4×C79—24no—
323C22×C4×C79—24no—
324C22×C4×C79—24no—
325C22×C4×C79—48no—
326C22×C4×C79C2411yescharacteristic
327C22×C4×C79C2414yes—
328C22×C4×C79C2414yes—
329C22×C4×C79C2411yescharacteristic
330C22×C4×C79C2414yes—
331C22×C4×C79C2411yescharacteristic
332C22×C4×C79C2411yescharacteristic
333C22×C4×C79C2414yes—
334C22×C4×C79C24116yes—
335C22×C4×C79C2411yescharacteristic
336C22×C4×C79C2411yescharacteristic
337C4⋊C4×C79C2418yes—
338C4⋊C4×C79C2418yes—
339C22⋊C4×C79C24116yes—
340C22⋊C4×C79C24116yes—
341C42×C79C2414yes—
342C42×C79C2414yes—
343C42×C79C2414yes—
344C42×C79C2414yes—
345C23×C79—22no—
346C23×C79—22no—
347C23×C79—28no—
348C23×C79—28no—
349C23×C79—28no—
350C23×C79H(5,𝔽2)14yes—
351C23×C79C2518yes—
352C23×C79C2512yes—
353C23×C79C2511yescharacteristic
354C22×D79—24no—
355C22×D79—24no—
356C22×D79—24no—
357C22×D79C2514yes—
358Q8×C79—48no—
359D4×C79—232no—
360D4×C79—216no—
361D4×C79—216no—
362D4×C79—48no—
363C2×C4×C79—22no—
364C2×C4×C79—28no—
365C2×C4×C79—22no—
366C2×C4×C79—22no—
367C2×C4×C79—28no—
368C2×C4×C79—22no—
369C2×C4×C79—28no—
370C2×C4×C79—28no—
371C2×C4×C79—416no—
372C2×C4×C79C2×#4114yes—
373C2×C4×C792−1+414yes—
374C2×C4×C79C2512yes—
375C2×C4×C79C2518yes—
376C2×C4×C79C2512yes—
377C2×C4×C79C2512yes—
378C2×C4×C79C2512yes—
379C2×C4×C79C2512yes—
380C2×C4×C79C2512yes—
381C22⋊D79—216no—
382C22⋊D79—232no—
383C22⋊D79—416no—
384C2×Dic79—24no—
385C2×Dic79—24no—
386C2×Dic79—24no—
387C2×Dic79—24no—
388C2×Dic79—216no—
389C2×Dic79—24no—
390C2×Dic79—24no—
391C2×Dic79—216no—
392C2×Dic79—232no—
393C2×Dic79—416no—
394C2×Dic79C2×#4118yes—
395C2×Dic79C2514yes—
396C2×Dic79C2514yes—
397C2×Dic79C2514yes—
398C2×Dic79C2514yes—
399C2×Dic79C2514yes—
400C2×Dic79C2514yes—
401C2×Dic79C2514yes—
402D316—28no—
403C4×D79—216no—
404C4×D79—416no—
405Dic158—28no—
406Dic158—28no—
407Dic158—216no—
408Dic158—416no—
409Dic158C2×#41116yescomplemented
410C22×C79—22no—
411C22×C79—22no—
412C22×C79—28no—
413C22×C79—28no—
414C22×C79—28no—
415C22×C79—28no—
416C22×C79—416no—
417C22×C79C22×#4112yes—
418C22×C79C2×H(5,𝔽2)14yes—
419C22×C79C2×H(5,𝔽2)12yes—
420C22×C79C2×2−1+412yes—
421C22×C79C2611yescharacteristic
422C2×D79—24no—
423C2×D79—24no—
424C2×D79—24no—
425C2×D79—48no—
426C4×C79—22no—
427C4×C79—22no—
428C4×C79—22no—
429C4×C79—28no—
430C4×C79—22no—
431C4×C79C22×#4114yes—
432C4×C79C2×2−1+414yes—
433Dic79—24no—
434Dic79—24no—
435Dic79—24no—
436Dic79—24no—
437Dic79—24no—
438Dic79—24no—
439Dic79C22×#4118yes—
440C2×#3522—791nomaximal, Sylow
441C2×C79—24no—
442C2×C79—48no—
443C2×C79#352214yescomplemented
444C2×C79C23×#4111yescharacteristic
445C2×C79C22×H(5,𝔽2)11yescharacteristic
446C2×C79C22×2−1+411yescharacteristic
447D79—44no—
448#3522—7932no—
449C2×#559—791no—
450C2×#559—792no—
451C2×Q82—791no—
452C2×#554—791no—
453C2×#554—792no—
454C2×#550—791no—
455C2×#548—792no—
456C2×#547—794no—
457C2×#547—792no—
458C2×#542—794no—
459C2×#542—792no—
460C2×#532—792no—
461C2×#532D7911yescharacteristic, complemented
462C2×#529—791no—
463C2×#529—792no—
464C2×#520—792no—
465C22×C4×Q8—791no—
466C79C2×#352211yescharacteristic, complemented, Sylow
467C22×#41—794no—
468C22×#41—792no—
469C22×#41C2×D7912yes—
470C23×Q8—791no—
471#559—7916no—
472#559—7932no—
473Q82—7916no—
474#554—7916no—
475#554—7932no—
476#550—7916no—
477#548—7932no—
478#547—7964no—
479#547—7932no—
480#542—7964no—
481#542—7932no—
482#532—7932no—
483#532C2×D79116yescomplemented
484C2×C4⋊Q8—794no—
485C2×C4⋊Q8—792no—
486C2×C4⋊Q8—792no—
487C2×C4⋊Q8C2×D7911yescharacteristic
488C2×#127—792no—
489C2×#127C2×D7911yescharacteristic
490#529—7932no—
491#529—7916no—
492C2×#126—794no—
493C2×#126—792no—
494C2×#125—792no—
495C2×#125—791no—
496C2×#124—792no—
497C2×#124—792no—
498C2×#124—794no—
499C2×#124—794no—
500C2×#124—791no—
501C2×#124C2×D7912yes—
502C2×#123—794no—
503C2×#123—794no—
504C2×#123—792no—
505C2×#123—794no—
506C2×#123—794no—
507C2×C22⋊Q8—794no—
508C2×C22⋊Q8—791no—
509C2×C22⋊Q8—794no—
510C2×C22⋊Q8—792no—
511C2×C22⋊Q8—794no—
512C2×C22⋊Q8—794no—
513C2×#121—794no—
514C2×#121—792no—
515C2×#121—794no—
516C2×#121—791no—
517C2×#121C2×D7912yes—
518C2×#121C2×D7912yes—
519#520—7932no—
520C2×C4×Q8—792no—
521C2×C4×Q8—792no—
522C2×C4×Q8—791no—
523C2×C4×Q8—792no—
524C2×C4×Q8—791no—
525C2×C4×Q8—791no—
526C2×C4×Q8—791no—
527C2×C4×Q8—792no—
528C2×C4×Q8—7916no—
529C2×C4×Q8—791no—
530C2×C4×D4—792no—
531C2×C4×D4—794no—
532C2×C4×D4—792no—
533C2×C4×D4—792no—
534C2×C4×D4—794no—
535C2×C4×D4—792no—
536C2×C4×D4—792no—
537C2×C4×D4—794no—
538C2×C4×D4—791no—
539C2×C4×D4C2×D7912yes—
540C2×C4×D4C2×D7912yes—
541C2×#117—794no—
542C2×#117—792no—
543C22×C4⋊C4—792no—
544C22×C4⋊C4—791no—
545C22×C4⋊C4—794no—
546C22×C4⋊C4—792no—
547C22×C42—792no—
548C22×C42C2×D7911yescharacteristic
549C2×#41—48no—
550C2×#41—31616no—
551C2×#41—7932no—
552C2×#41—7916no—
553C2×#41—15816no—
554C2×#41C22×D79116yes—
555C22×Q8—794no—
556C22×Q8—791no—
557C22×Q8—791no—
558C22×Q8—792no—
559C22×Q8—791no—
560C22×Q8—798no—
561C22×Q8—1588no—
562C22×Q8C22×D7912yes—
563C22×D4—794no—
564C22×D4—794no—
565C22×D4—792no—
566C22×D4—791no—
567C22×D4C22×D7912yes—
568C22×D4C22×D7912yes—
569C22×D4C22×D7914yes—
570C22×D4C22×D7912yes—
571C23×C4—794no—
572C23×C4—794no—
573C23×C4—792no—
574C23×C4—794no—
575C23×C4—792no—
576C23×C4—792no—
577C23×C4C22×D7911yescharacteristic
578C23×C4C22×D7911yescharacteristic
579C23×C4C22×D7911yescharacteristic
580C23×C4C22×D7914yes—
581C4⋊Q8—7932no—
582C4⋊Q8—7916no—
583C4⋊Q8—7916no—
584C4⋊Q8C22×D7918yes—
585#127—7916no—
586#127C22×D7918yes—
587#126—7932no—
588#126—7916no—
589#125—7916no—
590#125—798no—
591#124—7916no—
592#124—7916no—
593#124—7932no—
594#124—7932no—
595#124—798no—
596#124C22×D79116yes—
597#123—7932no—
598#123—7932no—
599#123—7916no—
600#123—7932no—
601#123—7932no—
602C22⋊Q8—7932no—
603C22⋊Q8—798no—
604C22⋊Q8—7932no—
605C22⋊Q8—7916no—
606C22⋊Q8—7932no—
607C22⋊Q8—7932no—
608#121—7932no—
609#121—7916no—
610#121—7932no—
611#121—798no—
612#121C22×D79116yes—
613#121C22×D79116yes—
614C4×Q8—7916no—
615C4×Q8—7916no—
616C4×Q8—798no—
617C4×Q8—7916no—
618C4×Q8—798no—
619C4×Q8—798no—
620C4×Q8—798no—
621C4×Q8—7916no—
622C4×Q8—798no—
623C4×D4—7916no—
624C4×D4—7932no—
625C4×D4—7916no—
626C4×D4—7916no—
627C4×D4—7932no—
628C4×D4—7916no—
629C4×D4—7916no—
630C4×D4—7932no—
631C4×D4—798no—
632C4×D4C22×D79116yes—
633C4×D4C22×D79116yes—
634#117—7932no—
635#117—7916no—
636C2×C4⋊C4—792no—
637C2×C4⋊C4—791no—
638C2×C4⋊C4—794no—
639C2×C4⋊C4—792no—
640C2×C4⋊C4—794no—
641C2×C4⋊C4—792no—
642C2×C4⋊C4—791no—
643C2×C4⋊C4—792no—
644C2×C4⋊C4—792no—
645C2×C4⋊C4—792no—
646C2×C4⋊C4—7916no—
647C2×C4⋊C4—798no—
648C2×C4⋊C4—7932no—
649C2×C4⋊C4—792no—
650C2×C4⋊C4—791no—
651C2×C4⋊C4—791no—
652C2×C4⋊C4—792no—
653C2×C4⋊C4—794no—
654C2×C4⋊C4—794no—
655C2×C4⋊C4—792no—
656C2×C4⋊C4—7916no—
657C2×C4⋊C4C22×D7912yes—
658C2×C4⋊C4C22×D7912yes—
659C2×C22⋊C4—794no—
660C2×C22⋊C4—792no—
661C2×C22⋊C4—794no—
662C2×C22⋊C4—794no—
663C2×C22⋊C4—794no—
664C2×C22⋊C4—792no—
665C2×C22⋊C4—792no—
666C2×C22⋊C4—792no—
667C2×C22⋊C4—794no—
668C2×C22⋊C4—792no—
669C2×C22⋊C4C22×D7914yes—
670C2×C22⋊C4C22×D7914yes—
671C2×C42—792no—
672C2×C42—794no—
673C2×C42—792no—
674C2×C42—792no—
675C2×C42—792no—
676C2×C42—792no—
677C2×C42—7916no—
678C2×C42C22×D7911yescharacteristic
679C2×C42C22×D7911yescharacteristic
680C2×C42C22×D7911yescharacteristic
681C2×C42C22×D7911yescharacteristic
682C2×C42C22×D7918yes—
683C24—792no—
684C24C23×D7914yes—
685C24C23×D7911yescharacteristic
686#41—432no—
687#41—31664no—
688#41—15864no—
689C2×Q8—44no—
690C2×Q8—3168no—
691C2×Q8—798no—
692C2×Q8—7916no—
693C2×Q8—794no—
694C2×Q8—794no—
695C2×Q8—798no—
696C2×Q8—794no—
697C2×Q8—1588no—
698C2×Q8—15832no—
699C2×Q8—1584no—
700C2×Q8—1584no—
701C2×Q8C23×D7918yes—
702C2×D4—216no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—44no—
706C2×D4—3168no—
707C2×D4—7916no—
708C2×D4—7916no—
709C2×D4—798no—
710C2×D4—794no—
711C2×D4—15816no—
712C2×D4—1588no—
713C2×D4—1584no—
714C2×D4C23×D7918yes—
715C2×D4C23×D7918yes—
716C2×D4C23×D79116yes—
717C2×D4C23×D7918yes—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—48no—
722C22×C4—3168no—
723C22×C4—3168no—
724C22×C4—7916no—
725C22×C4—7916no—
726C22×C4—792no—
727C22×C4—798no—
728C22×C4—798no—
729C22×C4—7916no—
730C22×C4—792no—
731C22×C4—792no—
732C22×C4—792no—
733C22×C4—792no—
734C22×C4—792no—
735C22×C4—792no—
736C22×C4—798no—
737C22×C4—1588no—
738C22×C4—15816no—
739C22×C4—1588no—
740C22×C4—1588no—
741C22×C4C23×D7914yes—
742C22×C4C23×D7914yes—
743C22×C4C23×D7914yes—
744C22×C4C23×D7911yescharacteristic
745C22×C4C23×D7914yes—
746C22×C4C23×D7911yescharacteristic
747C22×C4C23×D7911yescharacteristic
748C22×C4C23×D7911yescharacteristic
749C22×C4C23×D79116yes—
750C22×C4C23×D7911yescharacteristic
751C22×C4C23×D7911yescharacteristic
752C4⋊C4—798no—
753C4⋊C4—7916no—
754C4⋊C4—798no—
755C4⋊C4—7916no—
756C4⋊C4—798no—
757C4⋊C4—798no—
758C4⋊C4—798no—
759C4⋊C4—798no—
760C4⋊C4—798no—
761C4⋊C4—7916no—
762C4⋊C4—798no—
763C4⋊C4—794no—
764C4⋊C4—794no—
765C4⋊C4—798no—
766C4⋊C4—794no—
767C4⋊C4—794no—
768C4⋊C4—7916no—
769C4⋊C4C23×D7918yes—
770C4⋊C4C23×D7918yes—
771C22⋊C4—7916no—
772C22⋊C4—798no—
773C22⋊C4—7916no—
774C22⋊C4—7916no—
775C22⋊C4—7916no—
776C22⋊C4—798no—
777C22⋊C4—798no—
778C22⋊C4—798no—
779C22⋊C4—7916no—
780C22⋊C4—798no—
781C22⋊C4C23×D79116yes—
782C22⋊C4C23×D79116yes—
783C42—798no—
784C42—798no—
785C42—798no—
786C42—798no—
787C42—7916no—
788C42—798no—
789C42C23×D7914yes—
790C42C23×D7914yes—
791C42C23×D7914yes—
792C42C23×D7914yes—
793C23—22no—
794C23—22no—
795C23—28no—
796C23—28no—
797C23—28no—
798C23—794no—
799C23—1584no—
800C23—1584no—
801C23—1584no—
802C23#1457920614yes—
803C23C24×D7918yes—
804C23C24×D7912yes—
805C23C24×D7911yescharacteristic
806Q8—48no—
807Q8—31616no—
808Q8—7916no—
809Q8—15816no—
810Q8—1588no—
811Q8—1588no—
812D4—232no—
813D4—216no—
814D4—216no—
815D4—48no—
816D4—31616no—
817D4—15832no—
818D4—15816no—
819D4—1588no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—28no—
823C2×C4—28no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—28no—
827C2×C4—28no—
828C2×C4—416no—
829C2×C4—31616no—
830C2×C4—31616no—
831C2×C4—794no—
832C2×C4—798no—
833C2×C4—794no—
834C2×C4—794no—
835C2×C4—794no—
836C2×C4—794no—
837C2×C4—794no—
838C2×C4—794no—
839C2×C4—15816no—
840C2×C4—15832no—
841C2×C4—1584no—
842C2×C4—1584no—
843C2×C4—1584no—
844C2×C4—15816no—
845C2×C4—1584no—
846C2×C4—1584no—
847C2×C4—1584no—
848C2×C4—15816no—
849C2×C4#41×D7914yes—
850C2×C4#1457920814yes—
851C2×C4C24×D7912yes—
852C2×C4C24×D7918yes—
853C2×C4C24×D7912yes—
854C2×C4C24×D7912yes—
855C2×C4C24×D7912yes—
856C2×C4C24×D7912yes—
857C2×C4C24×D7912yes—
858C22—22no—
859C22—22no—
860C22—28no—
861C22—28no—
862C22—28no—
863C22—28no—
864C22—416no—
865C22—3168no—
866C22—1584no—
867C22—1584no—
868C22—1584no—
869C22C2×#41×D7912yes—
870C22C2×#1457920614yes—
871C22C2×#1457920612yes—
872C22C2×#1457920812yes—
873C22C25×D7911yescharacteristic
874C4—22no—
875C4—22no—
876C4—22no—
877C4—28no—
878C4—22no—
879C4—798no—
880C4—1584no—
881C4—1584no—
882C4—1584no—
883C4—1584no—
884C4—1584no—
885C4—1584no—
886C4C2×#41×D7914yes—
887C4C2×#1457920814yes—
888C2—24no—
889C2—48no—
890C2—3164no—
891C2#2377747714yesdirect product factor
892C2C22×#41×D7911yescharacteristic
893C2C22×#1457920611yescharacteristic
894C2C22×#1457920811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#532×C79C2
socleC23×C79C25
hypercenterC2×#532D79
hypocenterC79C2×#3522
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #23777477C2direct (N × H)
2. C2×#19099299C2semidirect
3. C2×#19099296C2semidirect
4. C2×#19099293C2semidirect
5. C2×#19099274C2semidirect
6. C2×#19099272C2semidirect
7. C2×#19099233C2semidirect
8. C2×#19099219C2semidirect
9. C2×#19099213C2semidirect
10. C2×#19099212C2semidirect
11. C2×#19099178C2semidirect
12. C2×#19099177C2semidirect
13. C2×#19099108C2semidirect
14. C2×#19099097C2semidirect
15. C2×#19099094C2semidirect
16. C2×#19099042C2semidirect
17. C22×C4×Dic158C2semidirect
18. C2×#532×C79C2semidirect
22. #19099299C22semidirect
23. #19099296C22semidirect
24. #19099293C22semidirect
25. #19099274C22semidirect
26. #19099272C22semidirect
27. #19099233C22semidirect
28. #19099219C22semidirect
29. #19099213C22semidirect
30. #19099212C22semidirect
31. #19099178C22semidirect
32. #19099177C22semidirect
33. #19099108C22semidirect
38. #19099097C22semidirect
39. #19099094C22semidirect
64. #19099042C22semidirect
72. C2×C4×Dic158C22semidirect
92. #532×C79C22semidirect
243. C2×Dic158#41semidirect
409. Dic158C2×#41semidirect
443. C2×C79#3522semidirect
461. C2×#532D79semidirect
466. C79C2×#3522semidirect
483. #532C2×D79semidirect
891. C2#23777477direct (N × H)

Maximal subgroups

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

subgroupindex
#237774772
C2×#190992992
C2×#190992962
C2×#190992932
C2×#190992742
C2×#190992722
C2×#190992332
C2×#190992192
C2×#190992132
C2×#190992122
C2×#190991782
C2×#190991772
C2×#190991082
C2×#190990972
C2×#190990942
C2×#190990422
C22×C4×Dic1582
C2×#532×C792
C2×#352279