Finite Group Databasebeta

← C2×#23777793 #35196063

Subgroups — C2×#23777793 #35196063

Order 20224.

7810 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777793C2132yesmaximal, direct product factor
2C2×#19099308C214yesmaximal, complemented
3C2×#19099273C211yesmaximal, characteristic, complemented
4C2×#19099272C212yesmaximal, complemented
5C2×#19099270C211yesmaximal, characteristic, complemented
6C2×#19099233C211yesmaximal, characteristic, complemented
7C2×#19099233C212yesmaximal, complemented
8C2×#19099213C212yesmaximal, complemented
9C2×#19099212C212yesmaximal, complemented
10C2×#19099167C212yesmaximal, complemented
11C2×#19099164C212yesmaximal, complemented
12C2×#19099142C212yesmaximal, complemented
13C2×#19099141C212yesmaximal, complemented
14C2×#19099140C214yesmaximal, complemented
15C2×#19099117C211yesmaximal, characteristic, complemented
16C2×#19099111C211yesmaximal, characteristic, complemented
17C2×#19099110C211yesmaximal, characteristic, complemented
18C2×#550×C79C211yesmaximal, characteristic, complemented
19C22×#11929624C2212yes—
20C22×#11929623C2212yes—
21C22×#11929623C2214yes—
22C22×#11929623C2212yes—
23#19099308C22164yescomplemented
24#19099273C22116yescomplemented
25#19099272C22132yescomplemented
26#19099270C22116yescomplemented
27#19099233C22132yescomplemented
28#19099233C22116yescomplemented
29#19099213C22132yescomplemented
30#19099212C22132yescomplemented
31#19099167C22132yescomplemented
32#19099164C22132yescomplemented
33#19099142C22132yescomplemented
34#19099141C22132yescomplemented
35#19099140C22164yescomplemented
36#19099117C22116yescomplemented
37#19099111C22116yescomplemented
38#19099110C22116yescomplemented
39C2×#14579161C2211yescharacteristic
40C2×#14579160C2211yescharacteristic
41C2×#14579160C2211yescharacteristic
42C2×#14579159C2211yescharacteristic
43C2×#14579157C2211yescharacteristic
44C2×#14579157C2212yes—
45C2×#14579153C2212yes—
46C2×#14579152C2212yes—
47C2×#14579151C2212yes—
48C2×#14579148C2212yes—
49C2×#14579147C2212yes—
50C2×#14579144C2214yes—
51C2×#14579143C2214yes—
52C2×#14579142C2214yes—
53C2×#14579142C2214yes—
54C2×#14579141C2211yescharacteristic
55C2×#14579140C2212yes—
56C2×#14579140C2214yes—
57C2×#14579139C2214yes—
58C2×#14579139C2212yes—
59C2×#14579138C2214yes—
60C2×#14579138C2214yes—
61C2×#14579138C2214yes—
62C2×#14579137C2212yes—
63C2×#14579137C2211yescharacteristic
64C2×#14579136C2211yescharacteristic
65C2×#14579135C2214yes—
66C2×#14579134C2212yes—
67C2×#14579134C2214yes—
68C2×#14579133C2214yes—
69C2×#14579133C2214yes—
70C2×#14579133C2214yes—
71C2×#14579133C2214yes—
72C2×#14579133C2214yes—
73C2×#14579132C2212yes—
74C2×#14579132C2214yes—
75C2×#14579132C2211yescharacteristic
76C2×#14579132C2212yes—
77C2×#14579132C2212yes—
78C2×C4×Dic158C2211yescharacteristic
79C2×C4×Dic158C2212yes—
80C2×C4×D316C2211yescharacteristic
81C2×C4×D316C2212yes—
82C2×D4×Dic79C2212yes—
83C2×D4×Dic79C2212yes—
84C2×D4×Dic79C2212yes—
85C2×D4×Dic79C2212yes—
86C2×C4×C22⋊D79C2212yes—
87C2×#14579118C2212yes—
88C22×C4⋊Dic79C2212yes—
89C22×Dic79⋊C4C2214yes—
90C2×C4⋊C4×D79C2212yes—
91C2×C42×D79C2211yescharacteristic
92C22×#41×C79C2212yes—
93#550×C79C22116yescomplemented
94C2×#127×C79C2211yescharacteristic
95C2×#127×C79C2212yes—
96C2×#121×C79C2212yes—
97C2×#121×C79C2214yes—
98C2×C4×Q8×C79C2211yescharacteristic
99C2×C4×D4×C79C2211yescharacteristic
100C2×C4×D4×C79C2212yes—
101C2×#11929624—48no—
102C2×#11929624C23116yes—
103C2×#11929623—48no—
104C2×#11929623—48no—
105C2×#11929623—416no—
106C2×#11929623C23116yes—
107C2×#11929623C23132yes—
108C2×#11929623C23116yes—
109C22×Dic158C2312yes—
110C22×Dic158C2311yescharacteristic
111C22×Dic158C2312yes—
112C22×Dic158C2312yes—
113C22×D316C2311yescharacteristic
114C22×D316C2312yes—
115C22×C22⋊D79C2312yes—
116C22×C22⋊D79C2314yes—
117C22×C22⋊D79C2312yes—
118C22×C22⋊D79C2312yes—
119C22×C22⋊D79C2314yes—
120C22×C22⋊D79C2314yes—
121C23×Dic79C2314yes—
122C23×Dic79C2314yes—
123C23×Dic79C2314yes—
124C22×C4×D79C2311yescharacteristic
125C22×C4×D79C2311yescharacteristic
126C22×C4×D79C2311yescharacteristic
127C22×C4×D79C2312yes—
128C22×C4×D79C2314yes—
129#14579161C2318yes—
130#14579160C2318yes—
131#14579160C2318yes—
132#14579159C2318yes—
133#14579157C23116yes—
134#14579157C2318yes—
135#14579153C23116yes—
136#14579152C23116yes—
137#14579151C23116yes—
138#14579148C23116yes—
139#14579147C23116yes—
140#14579144C23132yes—
141#14579143C23132yes—
142#14579142C23132yes—
143#14579142C23132yes—
144#14579141C2318yes—
145#14579140C23132yes—
146#14579140C23116yes—
147#14579139C23116yes—
148#14579139C23132yes—
149#14579138C23132yes—
150#14579138C23132yes—
151#14579138C23132yes—
152#14579137C2318yes—
153#14579137C23116yes—
154#14579136C2318yes—
155#14579135C23132yes—
156#14579134C23116yes—
157#14579134C23132yes—
158#14579133C23132yes—
159#14579133C23132yes—
160#14579133C23132yes—
161#14579133C23132yes—
162#14579133C23132yes—
163#14579132C23116yes—
164#14579132C23116yes—
165#14579132C23132yes—
166#14579132C23116yes—
167#14579132C2318yes—
168C4×Dic158C2318yes—
169C4×Dic158C23116yes—
170C4×D316C23116yes—
171C4×D316C2318yes—
172D4×Dic79C23116yes—
173D4×Dic79C23116yes—
174D4×Dic79C23116yes—
175D4×Dic79C23116yes—
176C4×C22⋊D79C23116yes—
177#14579118C23116yes—
178C2×C4⋊Dic79C23116yes—
179C2×C4⋊Dic79C2312yes—
180C2×C4⋊Dic79C2311yescharacteristic
181C2×C4⋊Dic79C2314yes—
182C2×C4⋊Dic79C2312yes—
183C2×C4⋊Dic79C2311yescharacteristic
184C2×C4⋊Dic79C2312yes—
185C2×Dic79⋊C4C23132yes—
186C2×Dic79⋊C4C2314yes—
187C2×Dic79⋊C4C2312yes—
188C2×Dic79⋊C4C2312yes—
189C2×Dic79⋊C4C2314yes—
190C2×Dic79⋊C4C2314yes—
191C2×Dic79⋊C4C2312yes—
192C2×Dic79⋊C4C2312yes—
193C2×Dic79⋊C4C2312yes—
194C2×Dic79⋊C4C2312yes—
195C4⋊C4×D79C23116yes—
196C2×C22⋊Dic79C2312yes—
197C2×C22⋊Dic79C2314yes—
198C2×C22⋊Dic79C2314yes—
199C2×C22⋊Dic79C2314yes—
200C2×C22⋊Dic79C2314yes—
201C2×(C2×D79)⋊C4C2312yes—
202C2×(C2×D79)⋊C4C2312yes—
203C2×(C2×D79)⋊C4C2312yes—
204C2×(C2×D79)⋊C4C2312yes—
205C2×(C2×D79)⋊C4C2314yes—
206C2×C4×Dic79C2311yescharacteristic
207C2×C4×Dic79C2311yescharacteristic
208C2×C4×Dic79C2311yescharacteristic
209C2×C4×Dic79C2312yes—
210C42×D79C2318yes—
211C2×#41×C79—48no—
212C2×#41×C79C23116yes—
213C22×Q8×C79C2311yescharacteristic
214C22×D4×C79C2311yescharacteristic
215C22×D4×C79C2312yes—
216C22×D4×C79C2312yes—
217C22×D4×C79C2314yes—
218C22×D4×C79C2312yes—
219C22×D4×C79C2314yes—
220C23×C4×C79C2312yes—
221C23×C4×C79C2314yes—
222#127×C79C23116yes—
223#127×C79C2318yes—
224#121×C79C23132yes—
225#121×C79C23116yes—
226C4×Q8×C79C2318yes—
227C4×D4×C79C23116yes—
228C4×D4×C79C2318yes—
229C2×C4⋊C4×C79C2311yescharacteristic
230C2×C4⋊C4×C79C2311yescharacteristic
231C2×C4⋊C4×C79C2312yes—
232C2×C22⋊C4×C79C2314yes—
233C2×C22⋊C4×C79C2312yes—
234C2×C42×C79C2311yescharacteristic
235C2×C42×C79C2312yes—
236C23×D79C2411yescharacteristic
237C23×D79C2412yes—
238#11929624—432no—
239#11929623—464no—
240#11929623—432no—
241#11929623—432no—
242C2×Dic158—28no—
243C2×Dic158—24no—
244C2×Dic158—44no—
245C2×Dic158—44no—
246C2×Dic158C2418yes—
247C2×Dic158C2414yes—
248C2×Dic158C2418yes—
249C2×Dic158C2418yes—
250C2×D316—24no—
251C2×D316—44no—
252C2×D316C2414yes—
253C2×D316C2418yes—
254C2×C22⋊D79—28no—
255C2×C22⋊D79—48no—
256C2×C22⋊D79—48no—
257C2×C22⋊D79—48no—
258C2×C22⋊D79—44no—
259C2×C22⋊D79—44no—
260C2×C22⋊D79C2418yes—
261C2×C22⋊D79C24116yes—
262C2×C22⋊D79C24116yes—
263C2×C22⋊D79C24116yes—
264C2×C22⋊D79C2418yes—
265C2×C22⋊D79C2418yes—
266C22×Dic79—216no—
267C22×Dic79—48no—
268C22×Dic79—48no—
269C22×Dic79C2411yescharacteristic
270C22×Dic79C2412yes—
271C22×Dic79C2412yes—
272C22×Dic79C2412yes—
273C22×Dic79C2414yes—
274C22×Dic79C24116yes—
275C22×Dic79C2411yescharacteristic
276C22×Dic79C24116yes—
277C22×Dic79C24116yes—
278C22×Dic79C2411yescharacteristic
279C2×C4×D79—24no—
280C2×C4×D79—28no—
281C2×C4×D79—24no—
282C2×C4×D79—24no—
283C2×C4×D79—48no—
284C2×C4×D79C2414yes—
285C2×C4×D79C2418yes—
286C2×C4×D79C2414yes—
287C2×C4×D79C2414yes—
288C2×C4×D79C24116yes—
289C4⋊Dic79C2418yes—
290C4⋊Dic79C2414yes—
291C4⋊Dic79C24116yes—
292C4⋊Dic79C2418yes—
293C4⋊Dic79C2414yes—
294C4⋊Dic79C2418yes—
295Dic79⋊C4C24116yes—
296Dic79⋊C4C2418yes—
297Dic79⋊C4C2418yes—
298Dic79⋊C4C24116yes—
299Dic79⋊C4C24116yes—
300Dic79⋊C4C2418yes—
301Dic79⋊C4C2418yes—
302Dic79⋊C4C2418yes—
303Dic79⋊C4C2418yes—
304C22⋊Dic79C2418yes—
305C22⋊Dic79C24116yes—
306C22⋊Dic79C24116yes—
307C22⋊Dic79C24116yes—
308C22⋊Dic79C24116yes—
309(C2×D79)⋊C4C2418yes—
310(C2×D79)⋊C4C2418yes—
311(C2×D79)⋊C4C2418yes—
312(C2×D79)⋊C4C2418yes—
313(C2×D79)⋊C4C24116yes—
314C4×Dic79C2414yes—
315C4×Dic79C2414yes—
316C4×Dic79C2414yes—
317C4×Dic79C2418yes—
318C24×C79C2414yes—
319C24×C79C2412yes—
320#41×C79—432no—
321C2×Q8×C79—24no—
322C2×Q8×C79C2414yes—
323C2×D4×C79—28no—
324C2×D4×C79—24no—
325C2×D4×C79—28no—
326C2×D4×C79—44no—
327C2×D4×C79—48no—
328C2×D4×C79—48no—
329C2×D4×C79C2418yes—
330C2×D4×C79C2418yes—
331C2×D4×C79C2414yes—
332C2×D4×C79C24116yes—
333C2×D4×C79C2418yes—
334C2×D4×C79C24116yes—
335C22×C4×C79—28no—
336C22×C4×C79—48no—
337C22×C4×C79C2411yescharacteristic
338C22×C4×C79C2412yes—
339C22×C4×C79C2412yes—
340C22×C4×C79C2418yes—
341C22×C4×C79C2412yes—
342C22×C4×C79C24116yes—
343C22×C4×C79C2411yescharacteristic
344C22×C4×C79C2411yescharacteristic
345C4⋊C4×C79C2414yes—
346C4⋊C4×C79C2414yes—
347C4⋊C4×C79C2418yes—
348C22⋊C4×C79C24116yes—
349C22⋊C4×C79C2418yes—
350C42×C79C2414yes—
351C42×C79C2418yes—
352C23×C79—28no—
353C23×C79—24no—
354C23×C79—28no—
355C23×C79—24no—
356C23×C79—28no—
357C23×C79—24no—
358C23×C79C2514yes—
359C23×C79C2518yes—
360C23×C79C2511yescharacteristic
361C22×D79—22no—
362C22×D79—24no—
363C22×D79—22no—
364C22×D79—24no—
365C22×D79—22no—
366C22×D79—24no—
367C22×D79C2514yes—
368C22×D79C2512yes—
369Q8×C79—28no—
370D4×C79—216no—
371D4×C79—216no—
372D4×C79—28no—
373D4×C79—416no—
374D4×C79—48no—
375D4×C79—416no—
376C2×C4×C79—22no—
377C2×C4×C79—24no—
378C2×C4×C79—24no—
379C2×C4×C79—24no—
380C2×C4×C79—216no—
381C2×C4×C79—416no—
382C2×C4×C79H(5,𝔽2)14yes—
383C2×C4×C792−1+414yes—
384C2×C4×C79C2512yes—
385C2×C4×C79C2514yes—
386C2×C4×C79C2514yes—
387C2×C4×C79C2514yes—
388C2×C4×C79C2512yes—
389C2×C4×C79C2512yes—
390C22⋊D79—216no—
391C22⋊D79—416no—
392C22⋊D79—416no—
393C22⋊D79—416no—
394C22⋊D79—48no—
395C22⋊D79—48no—
396C2×Dic79—24no—
397C2×Dic79—22no—
398C2×Dic79—28no—
399C2×Dic79—24no—
400C2×Dic79—24no—
401C2×Dic79—22no—
402C2×Dic79—232no—
403C2×Dic79—416no—
404C2×Dic79—416no—
405C2×Dic79H(5,𝔽2)14yes—
406C2×Dic79C2512yes—
407C2×Dic79C2512yes—
408C2×Dic79C2514yes—
409C2×Dic79C2514yes—
410C2×Dic79C2514yes—
411C2×Dic79C2518yes—
412C2×Dic79C2512yes—
413D316—28no—
414D316—48no—
415C4×D79—216no—
416C4×D79—28no—
417C4×D79—28no—
418C4×D79—28no—
419C4×D79—416no—
420Dic158—28no—
421Dic158—216no—
422Dic158—48no—
423Dic158—48no—
424C22×C79—24no—
425C22×C79—24no—
426C22×C79—28no—
427C22×C79—28no—
428C22×C79—24no—
429C22×C79—28no—
430C22×C79—416no—
431C22×C79—48no—
432C22×C79C2×H(5,𝔽2)12yes—
433C22×C79C2×H(5,𝔽2)12yes—
434C22×C79C2×2−1+412yes—
435C22×C79C2611yescharacteristic
436C2×D79—24no—
437C2×D79—22no—
438C2×D79—24no—
439C2×D79—22no—
440C2×D79—22no—
441C2×D79—24no—
442C2×D79—44no—
443C2×D79—48no—
444C4×C79—24no—
445C4×C79—24no—
446C4×C79—24no—
447C4×C79—22no—
448C4×C79C2×H(5,𝔽2)14yes—
449C4×C79C2×2−1+414yes—
450Dic79—24no—
451Dic79—24no—
452Dic79—22no—
453Dic79—24no—
454Dic79—28no—
455Dic79—22no—
456Dic79C2×H(5,𝔽2)14yes—
457C2×#3548—791nomaximal, Sylow
458C2×C79—44no—
459C2×C79—48no—
460C2×C79#354814yescomplemented
461C2×C79C22×H(5,𝔽2)11yescharacteristic
462C2×C79C22×H(5,𝔽2)11yescharacteristic
463C2×C79C22×2−1+411yescharacteristic
464D79—44no—
465D79—42no—
466#3548—7932no—
467C2×#562—794no—
468C2×#554—791no—
469C2×#554—791no—
470C2×#554—792no—
471C2×#550—792no—
472C2×#550—791no—
473C2×#550D7911yescharacteristic, complemented
474C2×#547—792no—
475C2×#547—792no—
476C2×#540—792no—
477C2×#540—792no—
478C2×#537—792no—
479C2×#537—794no—
480C2×#537—792no—
481C2×#533—791no—
482C2×#532—791no—
483C2×#532—791no—
484C79C2×#354811yescharacteristic, complemented, Sylow
485C22×#41—792no—
486C22×#41—792no—
487C22×#41—794no—
488C22×#41—792no—
489C22×#41C2×D7912yes—
490#562—7964no—
491#554—7916no—
492#554—7916no—
493#554—7932no—
494#550—7932no—
495#550—7916no—
496#550C2×D79116yescomplemented
497#547—7932no—
498#547—7932no—
499#540—7932no—
500#540—7932no—
501#537—7932no—
502#537—7964no—
503#537—7932no—
504#533—7916no—
505#532—7916no—
506#532—7916no—
507C2×C4⋊Q8—791no—
508C2×C4⋊Q8—791no—
509C2×C4⋊Q8—791no—
510C2×C4⋊Q8—791no—
511C2×#127—791no—
512C2×#127—792no—
513C2×#127C2×D7911yescharacteristic
514C2×#127C2×D7912yes—
515C2×#125—792no—
516C2×#125—792no—
517C2×#125—792no—
518C2×#124—792no—
519C2×#124—792no—
520C2×#123—794no—
521C2×#123—794no—
522C2×#123—794no—
523C2×#123—794no—
524C2×C22⋊Q8—791no—
525C2×C22⋊Q8—792no—
526C2×C22⋊Q8—792no—
527C2×C22⋊Q8—794no—
528C2×C22⋊Q8—792no—
529C2×C22⋊Q8—791no—
530C2×C22⋊Q8—794no—
531C2×C22⋊Q8—794no—
532C2×C22⋊Q8—794no—
533C2×C22⋊Q8—794no—
534C2×#121—792no—
535C2×#121—792no—
536C2×#121—791no—
537C2×#121—794no—
538C2×#121—794no—
539C2×#121—792no—
540C2×#121—794no—
541C2×#121—794no—
542C2×#121—794no—
543C2×#121—794no—
544C2×#121—794no—
545C2×#121—791no—
546C2×#121—792no—
547C2×#121—794no—
548C2×#121C2×D7912yes—
549C2×#121C2×D7914yes—
550C2×C4×Q8—791no—
551C2×C4×Q8—792no—
552C2×C4×Q8C2×D7911yescharacteristic
553C2×C4×D4—792no—
554C2×C4×D4—792no—
555C2×C4×D4—792no—
556C2×C4×D4—792no—
557C2×C4×D4—792no—
558C2×C4×D4—791no—
559C2×C4×D4—792no—
560C2×C4×D4C2×D7911yescharacteristic
561C2×C4×D4C2×D7912yes—
562C2×#117—792no—
563C22×C4⋊C4—794no—
564C22×C4⋊C4—792no—
565C22×C4⋊C4—792no—
566C22×C42—791no—
567C2×#41—48no—
568C2×#41—3168no—
569C2×#41—3168no—
570C2×#41—31616no—
571C2×#41—3168no—
572C2×#41—7916no—
573C2×#41—7916no—
574C2×#41—7932no—
575C2×#41—7916no—
576C2×#41C22×D79116yes—
577C22×Q8—792no—
578C22×Q8—792no—
579C22×Q8—792no—
580C22×Q8—791no—
581C22×Q8C22×D7911yescharacteristic
582C22×D4—794no—
583C22×D4—792no—
584C22×D4—794no—
585C22×D4—794no—
586C22×D4—792no—
587C22×D4—792no—
588C22×D4—792no—
589C22×D4—791no—
590C22×D4C22×D7912yes—
591C22×D4C22×D7911yescharacteristic
592C22×D4C22×D7912yes—
593C22×D4C22×D7914yes—
594C22×D4C22×D7914yes—
595C22×D4C22×D7912yes—
596C23×C4—794no—
597C23×C4—794no—
598C23×C4—794no—
599C23×C4—794no—
600C23×C4—792no—
601C23×C4—791no—
602C23×C4—791no—
603C23×C4—791no—
604C23×C4C22×D7912yes—
605C23×C4C22×D7914yes—
606C4⋊Q8—798no—
607C4⋊Q8—798no—
608C4⋊Q8—798no—
609C4⋊Q8—798no—
610#127—798no—
611#127—7916no—
612#127C22×D7918yes—
613#127C22×D79116yes—
614#125—7916no—
615#125—7916no—
616#125—7916no—
617#124—7916no—
618#124—7916no—
619#123—7932no—
620#123—7932no—
621#123—7932no—
622#123—7932no—
623C22⋊Q8—798no—
624C22⋊Q8—7916no—
625C22⋊Q8—7916no—
626C22⋊Q8—7932no—
627C22⋊Q8—7916no—
628C22⋊Q8—798no—
629C22⋊Q8—7932no—
630C22⋊Q8—7932no—
631C22⋊Q8—7932no—
632C22⋊Q8—7932no—
633#121—7916no—
634#121—7916no—
635#121—798no—
636#121—7932no—
637#121—7932no—
638#121—7916no—
639#121—7932no—
640#121—7932no—
641#121—7932no—
642#121—7932no—
643#121—7932no—
644#121—798no—
645#121—7916no—
646#121—7932no—
647#121C22×D79116yes—
648#121C22×D79132yes—
649C4×Q8—7916no—
650C4×Q8—798no—
651C4×Q8C22×D7918yes—
652C4×D4—7916no—
653C4×D4—7916no—
654C4×D4—7916no—
655C4×D4—7916no—
656C4×D4—7916no—
657C4×D4—798no—
658C4×D4—7916no—
659C4×D4C22×D7918yes—
660C4×D4C22×D79116yes—
661#117—7916no—
662C2×C4⋊C4—792no—
663C2×C4⋊C4—792no—
664C2×C4⋊C4—792no—
665C2×C4⋊C4—791no—
666C2×C4⋊C4—794no—
667C2×C4⋊C4—794no—
668C2×C4⋊C4—794no—
669C2×C4⋊C4—794no—
670C2×C4⋊C4—7932no—
671C2×C4⋊C4—7916no—
672C2×C4⋊C4—792no—
673C2×C4⋊C4—792no—
674C2×C4⋊C4—792no—
675C2×C4⋊C4—791no—
676C2×C4⋊C4—792no—
677C2×C4⋊C4—792no—
678C2×C4⋊C4—792no—
679C2×C4⋊C4—7916no—
680C2×C4⋊C4C22×D7911yescharacteristic
681C2×C4⋊C4C22×D7911yescharacteristic
682C2×C4⋊C4C22×D7912yes—
683C2×C22⋊C4—794no—
684C2×C22⋊C4—794no—
685C2×C22⋊C4—794no—
686C2×C22⋊C4—794no—
687C2×C22⋊C4—792no—
688C2×C22⋊C4—792no—
689C2×C22⋊C4—792no—
690C2×C22⋊C4—794no—
691C2×C22⋊C4—792no—
692C2×C22⋊C4—792no—
693C2×C22⋊C4C22×D7914yes—
694C2×C22⋊C4C22×D7912yes—
695C2×C42—792no—
696C2×C42—791no—
697C2×C42—791no—
698C2×C42—791no—
699C2×C42—798no—
700C2×C42C22×D7912yes—
701C2×C42C22×D7911yescharacteristic
702C24—792no—
703C24—791no—
704C24C23×D7912yes—
705C24C23×D7914yes—
706#41—432no—
707#41—31632no—
708#41—31632no—
709#41—31664no—
710#41—31632no—
711C2×Q8—24no—
712C2×Q8—3164no—
713C2×Q8—3164no—
714C2×Q8—798no—
715C2×Q8—798no—
716C2×Q8—798no—
717C2×Q8—794no—
718C2×Q8—1588no—
719C2×Q8—1584no—
720C2×Q8C23×D7914yes—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—24no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—44no—
727C2×D4—3164no—
728C2×D4—3168no—
729C2×D4—3168no—
730C2×D4—3164no—
731C2×D4—3168no—
732C2×D4—3164no—
733C2×D4—7916no—
734C2×D4—798no—
735C2×D4—7916no—
736C2×D4—7916no—
737C2×D4—798no—
738C2×D4—798no—
739C2×D4—798no—
740C2×D4—794no—
741C2×D4—1588no—
742C2×D4—1584no—
743C2×D4C23×D7918yes—
744C2×D4C23×D7914yes—
745C2×D4C23×D7918yes—
746C2×D4C23×D79116yes—
747C2×D4C23×D79116yes—
748C2×D4C23×D7918yes—
749C22×C4—28no—
750C22×C4—48no—
751C22×C4—3168no—
752C22×C4—3168no—
753C22×C4—3168no—
754C22×C4—7916no—
755C22×C4—7916no—
756C22×C4—7916no—
757C22×C4—791no—
758C22×C4—7916no—
759C22×C4—791no—
760C22×C4—791no—
761C22×C4—792no—
762C22×C4—792no—
763C22×C4—794no—
764C22×C4—792no—
765C22×C4—794no—
766C22×C4—794no—
767C22×C4—794no—
768C22×C4—798no—
769C22×C4—1584no—
770C22×C4—15816no—
771C22×C4—1588no—
772C22×C4—1584no—
773C22×C4—1584no—
774C22×C4C23×D7918yes—
775C22×C4C23×D7911yescharacteristic
776C22×C4C23×D7912yes—
777C22×C4C23×D7912yes—
778C22×C4C23×D7912yes—
779C22×C4C23×D79116yes—
780C22×C4C23×D7911yescharacteristic
781C22×C4C23×D7911yescharacteristic
782C4⋊C4—798no—
783C4⋊C4—798no—
784C4⋊C4—7916no—
785C4⋊C4—7916no—
786C4⋊C4—7916no—
787C4⋊C4—798no—
788C4⋊C4—798no—
789C4⋊C4—798no—
790C4⋊C4—798no—
791C4⋊C4—798no—
792C4⋊C4—794no—
793C4⋊C4—7916no—
794C4⋊C4—798no—
795C4⋊C4—794no—
796C4⋊C4—798no—
797C4⋊C4C23×D7914yes—
798C4⋊C4C23×D7914yes—
799C4⋊C4C23×D7918yes—
800C22⋊C4—7916no—
801C22⋊C4—7916no—
802C22⋊C4—7916no—
803C22⋊C4—798no—
804C22⋊C4—7916no—
805C22⋊C4—798no—
806C22⋊C4—798no—
807C22⋊C4—7916no—
808C22⋊C4—798no—
809C22⋊C4—798no—
810C22⋊C4C23×D79116yes—
811C22⋊C4C23×D7918yes—
812C42—794no—
813C42—794no—
814C42—794no—
815C42—798no—
816C42C23×D7914yes—
817C42C23×D7918yes—
818C23—24no—
819C23—28no—
820C23—24no—
821C23—28no—
822C23—24no—
823C23—28no—
824C23—794no—
825C23—792no—
826C23—1584no—
827C23—1582no—
828C23—1584no—
829C23—1582no—
830C23—1582no—
831C23—1584no—
832C23C24×D7914yes—
833C23C24×D7918yes—
834C23C24×D7911yescharacteristic
835Q8—28no—
836Q8—3168no—
837Q8—3168no—
838Q8—15816no—
839Q8—1588no—
840D4—216no—
841D4—216no—
842D4—28no—
843D4—416no—
844D4—416no—
845D4—48no—
846D4—3168no—
847D4—31616no—
848D4—31616no—
849D4—3168no—
850D4—31616no—
851D4—3168no—
852D4—15816no—
853D4—1588no—
854C2×C4—24no—
855C2×C4—22no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—216no—
859C2×C4—416no—
860C2×C4—31616no—
861C2×C4—31616no—
862C2×C4—31616no—
863C2×C4—794no—
864C2×C4—792no—
865C2×C4—792no—
866C2×C4—792no—
867C2×C4—794no—
868C2×C4—794no—
869C2×C4—798no—
870C2×C4—794no—
871C2×C4—1588no—
872C2×C4—15832no—
873C2×C4—1588no—
874C2×C4—1584no—
875C2×C4—1584no—
876C2×C4—1584no—
877C2×C4—1582no—
878C2×C4—1582no—
879C2×C4—15816no—
880C2×C4—1588no—
881C2×C4—1588no—
882C2×C4#1457920614yes—
883C2×C4#1457920814yes—
884C2×C4C24×D7912yes—
885C2×C4C24×D7914yes—
886C2×C4C24×D7914yes—
887C2×C4C24×D7914yes—
888C2×C4C24×D7912yes—
889C2×C4C24×D7912yes—
890C22—24no—
891C22—28no—
892C22—24no—
893C22—28no—
894C22—24no—
895C22—28no—
896C22—48no—
897C22—416no—
898C22—3168no—
899C22—3164no—
900C22—1584no—
901C22—1582no—
902C22—1582no—
903C22—1584no—
904C22—1582no—
905C22—1584no—
906C22H(5,𝔽2)×D7912yes—
907C22C2×#1457920612yes—
908C22C2×#1457920812yes—
909C22C25×D7911yescharacteristic
910C4—24no—
911C4—22no—
912C4—24no—
913C4—24no—
914C4—794no—
915C4—1588no—
916C4—1584no—
917C4—1584no—
918C4—1584no—
919C4—1582no—
920C4—1582no—
921C4C2×#1457920614yes—
922C4C2×#1457920814yes—
923C2—44no—
924C2—48no—
925C2—3164no—
926C2—3162no—
927C2#2377779314yesdirect product factor
928C2C2×H(5,𝔽2)×D7911yescharacteristic
929C2C22×#1457920611yescharacteristic
930C2C22×#1457920811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#550×C79C2
socleC23×C79C25
hypercenterC2×#550D79
hypocenterC79C2×#3548
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #23777793C2direct (N × H)
2. C2×#19099308C2semidirect
3. C2×#19099273C2semidirect
4. C2×#19099272C2semidirect
5. C2×#19099270C2semidirect
6. C2×#19099233C2semidirect
7. C2×#19099233C2semidirect
8. C2×#19099213C2semidirect
9. C2×#19099212C2semidirect
10. C2×#19099167C2semidirect
11. C2×#19099164C2semidirect
12. C2×#19099142C2semidirect
13. C2×#19099141C2semidirect
14. C2×#19099140C2semidirect
15. C2×#19099117C2semidirect
16. C2×#19099111C2semidirect
17. C2×#19099110C2semidirect
18. C2×#550×C79C2semidirect
23. #19099308C22semidirect
24. #19099273C22semidirect
25. #19099272C22semidirect
26. #19099270C22semidirect
27. #19099233C22semidirect
28. #19099233C22semidirect
29. #19099213C22semidirect
30. #19099212C22semidirect
31. #19099167C22semidirect
32. #19099164C22semidirect
33. #19099142C22semidirect
34. #19099141C22semidirect
35. #19099140C22semidirect
36. #19099117C22semidirect
37. #19099111C22semidirect
38. #19099110C22semidirect
93. #550×C79C22semidirect
460. C2×C79#3548semidirect
473. C2×#550D79semidirect
484. C79C2×#3548semidirect
496. #550C2×D79semidirect
927. C2#23777793direct (N × H)

Maximal subgroups

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

subgroupindex
#237777932
C2×#190993082
C2×#190992732
C2×#190992722
C2×#190992702
C2×#190992332
C2×#190992132
C2×#190992122
C2×#190991672
C2×#190991642
C2×#190991422
C2×#190991412
C2×#190991402
C2×#190991172
C2×#190991112
C2×#190991102
C2×#550×C792
C2×#354879