Finite Group Databasebeta

← C2×#23777309 #35196642

Subgroups — C2×#23777309 #35196642

Order 20224.

7758 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777309C2132yesmaximal, direct product factor
2C2×#19099284C212yesmaximal, complemented
3C2×#19099277C212yesmaximal, complemented
4C2×#19099271C212yesmaximal, complemented
5C2×#19099256C214yesmaximal, complemented
6C2×#19099219C214yesmaximal, complemented
7C2×#19099213C212yesmaximal, complemented
8C2×#19099186C212yesmaximal, complemented
9C2×#19099180C212yesmaximal, complemented
10C2×#19099141C211yesmaximal, characteristic, complemented
11C2×#19099115C212yesmaximal, complemented
12C2×#19099109C211yesmaximal, characteristic, complemented
13C2×#19099108C212yesmaximal, complemented
14C22×#14579160C211yesmaximal, characteristic, complemented
15C2×#19099046C211yesmaximal, characteristic, complemented
16C2×#19099044C211yesmaximal, characteristic, complemented
17C2×#41×Dic79C211yesmaximal, characteristic, complemented
18C2×#537×C79C211yesmaximal, characteristic, complemented
19C22×#11929624C2211yescharacteristic
20C22×#11929623C2214yes—
21C23×Dic158C2212yes—
22#19099284C22132yescomplemented
23#19099277C22132yescomplemented
24#19099271C22132yescomplemented
25#19099256C22164yescomplemented
26#19099219C22164yescomplemented
27#19099213C22132yescomplemented
28#19099186C22132yescomplemented
29#19099180C22132yescomplemented
30#19099141C22116yescomplemented
31#19099115C22132yescomplemented
32#19099109C22116yescomplemented
33#19099108C22132yescomplemented
34C2×#14579160C2212yes—
35C2×#14579160C2212yes—
36C2×#14579160C2212yes—
37C2×#14579160C2212yes—
38C2×#14579160C22116yescomplemented
39C2×#14579159C2211yescharacteristic
40C2×#14579157C2211yescharacteristic
41C2×#14579156C2214yes—
42C2×#14579154C2214yes—
43C2×#14579151C2214yes—
44C2×#14579150C2211yescharacteristic
45C2×#14579148C2211yescharacteristic
46C2×#14579148C2214yes—
47C2×#14579147C2214yes—
48C2×#14579147C2214yes—
49C2×#14579143C2214yes—
50C2×#14579142C2214yes—
51C2×#14579141C2214yes—
52C2×#14579140C2212yes—
53C2×#14579138C2214yes—
54C2×#14579138C2214yes—
55C2×#14579137C2212yes—
56C2×#14579135C2212yes—
57C2×#14579133C2212yes—
58C2×#14579133C2214yes—
59C2×#14579133C2212yes—
60C2×#14579133C2214yes—
61C2×#14579132C2212yes—
62#19099046C22116yescomplemented
63#19099044C22116yescomplemented
64#41×Dic79C22116yescomplemented
65C2×Q8×Dic79C2212yes—
66C2×Q8×Dic79C2211yescharacteristic
67C2×Q8×Dic79C2211yescharacteristic
68C2×#14579126C2212yes—
69C2×#14579126C2214yes—
70C2×D4×Dic79C2212yes—
71C2×D4×Dic79C2211yescharacteristic
72C2×D4×Dic79C2212yes—
73C2×D4×Dic79C2212yes—
74C2×D4×Dic79C2211yescharacteristic
75C2×D4×Dic79C2214yes—
76C2×#14579123C2212yes—
77C2×C4×C22⋊D79C2214yes—
78C2×C4×C22⋊D79C2212yes—
79C2×C4×C22⋊D79C2212yes—
80C2×(C22⋊D79)⋊C4C2214yes—
81C2×#14579120C2212yes—
82C2×#14579120C2211yescharacteristic
83C2×#14579120C2212yes—
84C2×#14579119C2212yes—
85C2×#14579117C2214yes—
86C22×C4⋊Dic79C2212yes—
87C22×C4⋊Dic79C2211yescharacteristic
88C22×Dic79⋊C4C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C22×C4×Dic79C2211yescharacteristic
91C22×C4×Dic79C2212yes—
92C22×#41×C79C2211yescharacteristic
93C22×#41×C79C2211yescharacteristic
94#537×C79C22116yescomplemented
95C2×C22⋊Q8×C79C2212yes—
96C2×C22⋊Q8×C79C2212yes—
97C2×#121×C79C2212yes—
98C2×#121×C79C2212yes—
99C2×#121×C79C2214yes—
100C22×C4⋊C4×C79C2211yescharacteristic
101C2×#11929624—28no—
102C2×#11929624C2318yes—
103C2×#11929623—416no—
104C2×#11929623C23132yes—
105C22×Dic158—48no—
106C22×Dic158C2311yescharacteristic
107C22×Dic158C2314yes—
108C22×Dic158C23116yes—
109C22×Dic158C2314yes—
110C22×D316C2311yescharacteristic
111C22×C22⋊D79C2312yes—
112C22×C22⋊D79C2312yes—
113C22×C22⋊D79C2312yes—
114C22×C22⋊D79C2314yes—
115C23×Dic79C2311yescharacteristic
116C23×Dic79C2312yes—
117C23×Dic79C2311yescharacteristic
118C23×Dic79C2312yes—
119C23×Dic79C2312yes—
120C23×Dic79C2314yes—
121C22×C4×D79C2312yes—
122C22×C4×D79C2314yes—
123#14579160C23116yes—
124#14579160C23116yes—
125#14579160C23116yes—
126#14579160C23116yes—
127#14579159C2318yes—
128#14579157C2318yes—
129#14579156C23132yes—
130#14579154C23132yes—
131#14579151C23132yes—
132#14579150C2318yes—
133#14579148C2318yes—
134#14579148C23132yes—
135#14579147C23132yes—
136#14579147C23132yes—
137#14579143C23132yes—
138#14579142C23132yes—
139#14579141C23132yes—
140#14579140C23116yes—
141#14579138C23132yes—
142#14579138C23132yes—
143#14579137C23116yes—
144#14579135C23116yes—
145#14579133C23132yes—
146#14579133C23116yes—
147#14579133C23116yes—
148#14579133C23132yes—
149#14579132C23116yes—
150Q8×Dic79C23116yes—
151Q8×Dic79C2318yes—
152Q8×Dic79C2318yes—
153#14579126C23116yes—
154#14579126C23132yes—
155D4×Dic79C23116yes—
156D4×Dic79C2318yes—
157D4×Dic79C23116yes—
158D4×Dic79C23132yes—
159D4×Dic79C23116yes—
160D4×Dic79C2318yes—
161#14579123C23116yes—
162C4×C22⋊D79C23116yes—
163C4×C22⋊D79C23132yes—
164C4×C22⋊D79C23116yes—
165(C22⋊D79)⋊C4C23132yes—
166#14579120C23116yes—
167#14579120C23116yes—
168#14579120C2318yes—
169#14579119C23116yes—
170#14579117C23132yes—
171C2×C4⋊Dic79C2318yes—
172C2×C4⋊Dic79C23116yes—
173C2×C4⋊Dic79C2311yescharacteristic
174C2×C4⋊Dic79C2312yes—
175C2×C4⋊Dic79C2312yes—
176C2×C4⋊Dic79C2314yes—
177C2×C4⋊Dic79C2311yescharacteristic
178C2×C4⋊Dic79C2312yes—
179C2×C4⋊Dic79C2312yes—
180C2×Dic79⋊C4C23116yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2312yes—
186C2×Dic79⋊C4C2314yes—
187C4⋊C4×D79C23116yes—
188C2×C22⋊Dic79C2314yes—
189C2×C22⋊Dic79C2312yes—
190C2×C22⋊Dic79C2314yes—
191C2×C22⋊Dic79C2312yes—
192C2×C22⋊Dic79C2312yes—
193C2×C22⋊Dic79C2312yes—
194C2×C22⋊Dic79C2312yes—
195C2×(C2×D79)⋊C4C2314yes—
196C2×(C2×D79)⋊C4C2314yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×(C2×D79)⋊C4C2312yes—
199C2×C4×Dic79C2311yescharacteristic
200C2×C4×Dic79C2312yes—
201C2×C4×Dic79C2311yescharacteristic
202C2×C4×Dic79C2312yes—
203C2×C4×Dic79C2311yescharacteristic
204C2×C4×Dic79C2311yescharacteristic
205C2×C4×Dic79C2312yes—
206C2×C4×Dic79C2318yes—
207C2×C4×Dic79C23116yes—
208C2×C4×Dic79C2314yes—
209C2×C4×Dic79C2314yes—
210C2×#41×C79—28no—
211C2×#41×C79—28no—
212C2×#41×C79C2318yes—
213C2×#41×C79C2318yes—
214C22×Q8×C79C2311yescharacteristic
215C22×Q8×C79C2311yescharacteristic
216C22×D4×C79C2311yescharacteristic
217C22×D4×C79C2312yes—
218C22×D4×C79C2312yes—
219C22×D4×C79C2311yescharacteristic
220C22×D4×C79C2314yes—
221C23×C4×C79C2312yes—
222C23×C4×C79C2312yes—
223C23×C4×C79C2312yes—
224C23×C4×C79C2311yescharacteristic
225C22⋊Q8×C79C23116yes—
226C22⋊Q8×C79C23116yes—
227#121×C79C23116yes—
228#121×C79C23116yes—
229#121×C79C23132yes—
230C2×C4⋊C4×C79C2312yes—
231C2×C4⋊C4×C79C2312yes—
232C2×C4⋊C4×C79C2318yes—
233C2×C4⋊C4×C79C2314yes—
234C2×C22⋊C4×C79C2314yes—
235C2×C22⋊C4×C79C2314yes—
236C23×D79C2412yes—
237#11929624—232no—
238#11929623—464no—
239C2×Dic158—216no—
240C2×Dic158—24no—
241C2×Dic158—48no—
242C2×Dic158—432no—
243C2×Dic158C24116yes—
244C2×Dic158C2414yes—
245C2×Dic158C24116yes—
246C2×D316—24no—
247C2×D316C2414yes—
248C2×C22⋊D79—28no—
249C2×C22⋊D79—28no—
250C2×C22⋊D79—28no—
251C2×C22⋊D79—48no—
252C2×C22⋊D79C2418yes—
253C2×C22⋊D79C2418yes—
254C2×C22⋊D79C2418yes—
255C2×C22⋊D79C24116yes—
256C22×Dic79—24no—
257C22×Dic79—28no—
258C22×Dic79—24no—
259C22×Dic79—28no—
260C22×Dic79—44no—
261C22×Dic79—48no—
262C22×Dic79C2411yescharacteristic
263C22×Dic79C2414yes—
264C22×Dic79C2414yes—
265C22×Dic79C2412yes—
266C22×Dic79C2418yes—
267C22×Dic79C2412yes—
268C22×Dic79C2411yescharacteristic
269C22×Dic79C2412yes—
270C22×Dic79C2414yes—
271C22×Dic79C2418yes—
272C22×Dic79C2418yes—
273C22×Dic79C24116yes—
274C22×Dic79C2411yescharacteristic
275C22×Dic79C2411yescharacteristic
276C2×C4×D79—28no—
277C2×C4×D79—48no—
278C2×C4×D79C2418yes—
279C2×C4×D79C24116yes—
280C4⋊Dic79C2414yes—
281C4⋊Dic79C2418yes—
282C4⋊Dic79C2418yes—
283C4⋊Dic79C24116yes—
284C4⋊Dic79C2414yes—
285C4⋊Dic79C2418yes—
286C4⋊Dic79C2418yes—
287Dic79⋊C4C24116yes—
288Dic79⋊C4C24116yes—
289Dic79⋊C4C24116yes—
290Dic79⋊C4C2418yes—
291Dic79⋊C4C2418yes—
292Dic79⋊C4C24116yes—
293C22⋊Dic79C24116yes—
294C22⋊Dic79C2418yes—
295C22⋊Dic79C24116yes—
296C22⋊Dic79C2418yes—
297C22⋊Dic79C2418yes—
298C22⋊Dic79C2418yes—
299C22⋊Dic79C2418yes—
300(C2×D79)⋊C4C24116yes—
301(C2×D79)⋊C4C24116yes—
302(C2×D79)⋊C4C2418yes—
303(C2×D79)⋊C4C2418yes—
304C4×Dic79C2414yes—
305C4×Dic79C2418yes—
306C4×Dic79C2414yes—
307C4×Dic79C2418yes—
308C4×Dic79C2414yes—
309C4×Dic79C2414yes—
310C4×Dic79C2418yes—
311C4×Dic79C24116yes—
312C4×Dic79C24116yes—
313C24×C79C2412yes—
314C24×C79C2412yes—
315C24×C79C2411yescharacteristic
316#41×C79—232no—
317#41×C79—232no—
318C2×Q8×C79—24no—
319C2×Q8×C79—24no—
320C2×Q8×C79C2414yes—
321C2×Q8×C79C2414yes—
322C2×D4×C79—28no—
323C2×D4×C79—28no—
324C2×D4×C79—24no—
325C2×D4×C79—24no—
326C2×D4×C79—48no—
327C2×D4×C79C2414yes—
328C2×D4×C79C2418yes—
329C2×D4×C79C2418yes—
330C2×D4×C79C2414yes—
331C2×D4×C79C24116yes—
332C22×C4×C79—28no—
333C22×C4×C79—28no—
334C22×C4×C79—44no—
335C22×C4×C79#4118yescomplemented
336C22×C4×C79C2414yes—
337C22×C4×C79C2412yes—
338C22×C4×C79C2412yes—
339C22×C4×C79C2418yes—
340C22×C4×C79C2418yes—
341C22×C4×C79C2418yes—
342C22×C4×C79C2411yescharacteristic
343C22×C4×C79C2411yescharacteristic
344C22×C4×C79C2414yes—
345C4⋊C4×C79C2418yes—
346C4⋊C4×C79C2418yes—
347C4⋊C4×C79C24116yes—
348C22⋊C4×C79C24116yes—
349C22⋊C4×C79C24116yes—
350C23×C79—22no—
351C23×C79—22no—
352C23×C79—24no—
353C23×C79—24no—
354C23×C79—24no—
355C23×C79—24no—
356C23×C79—24no—
357C23×C79—24no—
358C23×C79C2×#4114yes—
359C23×C79C2514yes—
360C23×C79C2514yes—
361C23×C79C2512yes—
362C23×C79C2511yescharacteristic
363C22×D79—24no—
364C22×D79—24no—
365C22×D79—24no—
366C22×D79C2514yes—
367Q8×C79—28no—
368Q8×C79—28no—
369D4×C79—216no—
370D4×C79—216no—
371D4×C79—28no—
372D4×C79—28no—
373D4×C79—416no—
374C2×C4×C79—24no—
375C2×C4×C79—24no—
376C2×C4×C79—28no—
377C2×C4×C79—216no—
378C2×C4×C79—216no—
379C2×C4×C79—48no—
380C2×C4×C79C2×#4114yes—
381C2×C4×C79C2×#4114yes—
382C2×C4×C79C2×#41116yescomplemented
383C2×C4×C79C2514yes—
384C2×C4×C79C2514yes—
385C2×C4×C79C2518yes—
386C2×C4×C79C2512yes—
387C2×C4×C79C2512yes—
388C22⋊D79—216no—
389C22⋊D79—216no—
390C22⋊D79—216no—
391C22⋊D79—416no—
392C2×Dic79—24no—
393C2×Dic79—24no—
394C2×Dic79—22no—
395C2×Dic79—28no—
396C2×Dic79—24no—
397C2×Dic79—22no—
398C2×Dic79—28no—
399C2×Dic79—216no—
400C2×Dic79—28no—
401C2×Dic79—216no—
402C2×Dic79—48no—
403C2×Dic79—416no—
404C2×Dic79H(5,𝔽2)14yes—
405C2×Dic792−1+414yes—
406C2×Dic79C2514yes—
407C2×Dic79C2512yes—
408C2×Dic79C2512yes—
409C2×Dic79C2514yes—
410C2×Dic79C2514yes—
411C2×Dic79C2518yes—
412C2×Dic79C2512yes—
413C2×Dic79C2512yes—
414D316—28no—
415C4×D79—216no—
416C4×D79—416no—
417Dic158—28no—
418Dic158—232no—
419Dic158—416no—
420C22×C79—22no—
421C22×C79—22no—
422C22×C79—28no—
423C22×C79—24no—
424C22×C79—24no—
425C22×C79—24no—
426C22×C79—24no—
427C22×C79—24no—
428C22×C79—24no—
429C22×C79—48no—
430C22×C79—48no—
431C22×C79C22×#4114yes—
432C22×C79C22×#4112yes—
433C22×C79C2×H(5,𝔽2)12yes—
434C22×C79C2×2−1+412yes—
435C22×C79C2611yescharacteristic
436C2×D79—24no—
437C2×D79—24no—
438C2×D79—24no—
439C2×D79—48no—
440C4×C79—24no—
441C4×C79—24no—
442C4×C79—28no—
443C4×C79C22×#4114yes—
444C4×C79C22×#4114yes—
445Dic79—24no—
446Dic79—28no—
447Dic79—22no—
448Dic79—24no—
449Dic79—24no—
450Dic79—22no—
451Dic79C2×H(5,𝔽2)14yes—
452Dic79C2×2−1+414yes—
453C2×#3511—791nomaximal, Sylow
454C2×C79—24no—
455C2×C79—44no—
456C2×C79—44no—
457C2×C79#351114yescomplemented
458C2×C79C23×#4111yescharacteristic
459C2×C79C22×H(5,𝔽2)11yescharacteristic
460C2×C79C22×2−1+411yescharacteristic
461D79—44no—
462#3511—7932no—
463C2×#556—792no—
464C2×#555—792no—
465C2×#554—792no—
466C2×#553—794no—
467C2×#548—794no—
468C2×#547—792no—
469C2×#542—792no—
470C2×#542—792no—
471C2×#537—791no—
472C2×#537D7911yescharacteristic, complemented
473C2×#533—792no—
474C2×#532—791no—
475C2×#532—792no—
476C22×C4⋊Q8—791no—
477C2×#520—791no—
478C2×#520—791no—
479C2×C4×#41—791no—
480C79C2×#351111yescharacteristic, complemented, Sylow
481C22×#41—794no—
482C22×#41—791no—
483C22×#41C2×D7911yescharacteristic
484C22×#41C2×D7911yescharacteristic
485C23×Q8—792no—
486#556—7932no—
487#555—7932no—
488#554—7932no—
489#553—7964no—
490#548—7964no—
491#547—7932no—
492#542—7932no—
493#542—7932no—
494#537—7916no—
495#537C2×D79116yescomplemented
496#533—7932no—
497#532—7916no—
498#532—7932no—
499C2×C4⋊Q8—791no—
500C2×C4⋊Q8—792no—
501C2×C4⋊Q8—792no—
502C2×C4⋊Q8—792no—
503C2×C4⋊Q8—792no—
504C2×C4⋊Q8—7916no—
505C2×#127—791no—
506C2×#126—794no—
507C2×#126—794no—
508C2×#125—794no—
509C2×#124—791no—
510C2×#124—791no—
511C2×#124—794no—
512C2×#124—794no—
513C2×#124—794no—
514C2×#123—794no—
515C2×#123—794no—
516C2×C22⋊Q8—792no—
517C2×C22⋊Q8—792no—
518C2×C22⋊Q8—794no—
519C2×C22⋊Q8—794no—
520C2×C22⋊Q8—794no—
521C2×C22⋊Q8C2×D7912yes—
522C2×C22⋊Q8C2×D7912yes—
523C2×#121—792no—
524C2×#121—792no—
525C2×#121—794no—
526C2×#121—792no—
527C2×#121—794no—
528C2×#121—792no—
529C2×#121C2×D7912yes—
530C2×#121C2×D7912yes—
531C2×#121C2×D7914yes—
532#520—7916no—
533#520—7916no—
534C4×#41—7916no—
535C2×C4×Q8—791no—
536C2×C4×Q8—791no—
537C2×C4×Q8—792no—
538C2×C4×Q8—792no—
539C2×C4×Q8—794no—
540C2×C4×D4—791no—
541C2×C4×D4—792no—
542C2×C4×D4—792no—
543C2×C4×D4—791no—
544C2×C4×D4—792no—
545C2×C4×D4—794no—
546C2×C4×D4—794no—
547C2×C4×D4—792no—
548C2×C4×D4—792no—
549C2×C4×D4—792no—
550C2×C4×D4—794no—
551C2×#117—791no—
552C2×#117—792no—
553C2×#117—792no—
554C2×#117—792no—
555C2×#117—794no—
556C22×C4⋊C4—791no—
557C22×C4⋊C4—792no—
558C22×C4⋊C4—792no—
559C22×C4⋊C4—792no—
560C22×C4⋊C4C2×D7911yescharacteristic
561C22×C42—791no—
562C22×C42—792no—
563C2×#41—28no—
564C2×#41—28no—
565C2×#41—31616no—
566C2×#41—7932no—
567C2×#41—798no—
568C2×#41—1588no—
569C2×#41C22×D7918yes—
570C2×#41C22×D7918yes—
571C22×Q8—3168no—
572C22×Q8—794no—
573C22×Q8—7916no—
574C22×Q8—791no—
575C22×Q8—794no—
576C22×Q8C22×D7911yescharacteristic
577C22×Q8C22×D7911yescharacteristic
578C22×D4—794no—
579C22×D4—792no—
580C22×D4—792no—
581C22×D4—792no—
582C22×D4—791no—
583C22×D4C22×D7912yes—
584C22×D4C22×D7912yes—
585C22×D4C22×D7911yescharacteristic
586C22×D4C22×D7911yescharacteristic
587C22×D4C22×D7914yes—
588C23×C4—792no—
589C23×C4—794no—
590C23×C4—794no—
591C23×C4—791no—
592C23×C4—792no—
593C23×C4—791no—
594C23×C4—792no—
595C23×C4—792no—
596C23×C4C22×D7912yes—
597C23×C4C22×D7912yes—
598C23×C4C22×D7912yes—
599C23×C4C22×D7911yescharacteristic
600C4⋊Q8—798no—
601C4⋊Q8—7916no—
602C4⋊Q8—7916no—
603C4⋊Q8—7916no—
604C4⋊Q8—7916no—
605#127—798no—
606#126—7932no—
607#126—7932no—
608#125—7932no—
609#124—798no—
610#124—798no—
611#124—7932no—
612#124—7932no—
613#124—7932no—
614#123—7932no—
615#123—7932no—
616C22⋊Q8—7916no—
617C22⋊Q8—7916no—
618C22⋊Q8—7932no—
619C22⋊Q8—7932no—
620C22⋊Q8—7932no—
621C22⋊Q8C22×D79116yes—
622C22⋊Q8C22×D79116yes—
623#121—7916no—
624#121—7916no—
625#121—7932no—
626#121—7916no—
627#121—7932no—
628#121—7916no—
629#121C22×D79116yes—
630#121C22×D79116yes—
631#121C22×D79132yes—
632C4×Q8—798no—
633C4×Q8—798no—
634C4×Q8—7916no—
635C4×Q8—7916no—
636C4×Q8—7932no—
637C4×D4—798no—
638C4×D4—7916no—
639C4×D4—7916no—
640C4×D4—798no—
641C4×D4—7916no—
642C4×D4—7932no—
643C4×D4—7932no—
644C4×D4—7916no—
645C4×D4—7916no—
646C4×D4—7916no—
647C4×D4—7932no—
648#117—798no—
649#117—7916no—
650#117—7916no—
651#117—7916no—
652#117—7932no—
653C2×C4⋊C4—791no—
654C2×C4⋊C4—792no—
655C2×C4⋊C4—794no—
656C2×C4⋊C4—792no—
657C2×C4⋊C4—794no—
658C2×C4⋊C4—794no—
659C2×C4⋊C4—798no—
660C2×C4⋊C4—7916no—
661C2×C4⋊C4—794no—
662C2×C4⋊C4—7916no—
663C2×C4⋊C4—791no—
664C2×C4⋊C4—792no—
665C2×C4⋊C4—792no—
666C2×C4⋊C4—792no—
667C2×C4⋊C4—792no—
668C2×C4⋊C4—794no—
669C2×C4⋊C4—7916no—
670C2×C4⋊C4C22×D7912yes—
671C2×C4⋊C4C22×D7912yes—
672C2×C4⋊C4C22×D7918yes—
673C2×C4⋊C4C22×D7914yes—
674C2×C22⋊C4—792no—
675C2×C22⋊C4—794no—
676C2×C22⋊C4—792no—
677C2×C22⋊C4—792no—
678C2×C22⋊C4—794no—
679C2×C22⋊C4—792no—
680C2×C22⋊C4—792no—
681C2×C22⋊C4—794no—
682C2×C22⋊C4—794no—
683C2×C22⋊C4—792no—
684C2×C22⋊C4—792no—
685C2×C22⋊C4C22×D7914yes—
686C2×C22⋊C4C22×D7914yes—
687C2×C42—792no—
688C2×C42—794no—
689C2×C42—794no—
690C2×C42—791no—
691C2×C42—792no—
692C2×C42—791no—
693C2×C42—791no—
694C2×C42—792no—
695C2×C42—798no—
696C2×C42—7916no—
697C2×C42—791no—
698C24—792no—
699C24C23×D7912yes—
700C24C23×D7912yes—
701C24C23×D7911yescharacteristic
702#41—232no—
703#41—232no—
704#41—31664no—
705#41—15832no—
706C2×Q8—24no—
707C2×Q8—24no—
708C2×Q8—3168no—
709C2×Q8—31632no—
710C2×Q8—7916no—
711C2×Q8—794no—
712C2×Q8—7916no—
713C2×Q8—15816no—
714C2×Q8—1584no—
715C2×Q8C23×D7914yes—
716C2×Q8C23×D7914yes—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—48no—
722C2×D4—3168no—
723C2×D4—7916no—
724C2×D4—798no—
725C2×D4—798no—
726C2×D4—798no—
727C2×D4—794no—
728C2×D4—1588no—
729C2×D4—1588no—
730C2×D4—1588no—
731C2×D4—1584no—
732C2×D4C23×D7918yes—
733C2×D4C23×D7918yes—
734C2×D4C23×D7914yes—
735C2×D4C23×D7914yes—
736C2×D4C23×D79116yes—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—44no—
740C22×C4—3168no—
741C22×C4—3164no—
742C22×C4—3168no—
743C22×C4—798no—
744C22×C4—7916no—
745C22×C4—7916no—
746C22×C4—791no—
747C22×C4—791no—
748C22×C4—794no—
749C22×C4—798no—
750C22×C4—794no—
751C22×C4—798no—
752C22×C4—792no—
753C22×C4—791no—
754C22×C4—791no—
755C22×C4—792no—
756C22×C4—792no—
757C22×C4—794no—
758C22×C4—798no—
759C22×C4—1584no—
760C22×C4—1588no—
761C22×C4—1584no—
762C22×C4—1588no—
763C22×C4—1588no—
764C22×C4#1192962318yescomplemented
765C22×C4C23×D7918yes—
766C22×C4C23×D7918yes—
767C22×C4C23×D7912yes—
768C22×C4C23×D7912yes—
769C22×C4C23×D7914yes—
770C22×C4C23×D7918yes—
771C22×C4C23×D7911yescharacteristic
772C22×C4C23×D7911yescharacteristic
773C22×C4C23×D7914yes—
774C4⋊C4—7916no—
775C4⋊C4—7916no—
776C4⋊C4—7916no—
777C4⋊C4—798no—
778C4⋊C4—798no—
779C4⋊C4—7916no—
780C4⋊C4—794no—
781C4⋊C4—798no—
782C4⋊C4—798no—
783C4⋊C4—7916no—
784C4⋊C4—794no—
785C4⋊C4—798no—
786C4⋊C4—798no—
787C4⋊C4C23×D7918yes—
788C4⋊C4C23×D7918yes—
789C4⋊C4C23×D79116yes—
790C22⋊C4—798no—
791C22⋊C4—7916no—
792C22⋊C4—798no—
793C22⋊C4—798no—
794C22⋊C4—7916no—
795C22⋊C4—798no—
796C22⋊C4—798no—
797C22⋊C4—7916no—
798C22⋊C4—7916no—
799C22⋊C4—798no—
800C22⋊C4—798no—
801C22⋊C4C23×D79116yes—
802C22⋊C4C23×D79116yes—
803C42—794no—
804C42—798no—
805C42—794no—
806C42—798no—
807C42—794no—
808C42—794no—
809C42—798no—
810C42—7916no—
811C42—7916no—
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—794no—
821C23—1584no—
822C23—1584no—
823C23—1584no—
824C23C2×#1192962314yes—
825C23C24×D7914yes—
826C23C24×D7914yes—
827C23C24×D7912yes—
828C23C24×D7911yescharacteristic
829Q8—28no—
830Q8—28no—
831Q8—31616no—
832Q8—15832no—
833Q8—1588no—
834D4—216no—
835D4—216no—
836D4—28no—
837D4—28no—
838D4—416no—
839D4—31616no—
840D4—15816no—
841D4—15816no—
842D4—15816no—
843D4—1588no—
844C2×C4—28no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—216no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—31616no—
851C2×C4—3168no—
852C2×C4—31616no—
853C2×C4—794no—
854C2×C4—794no—
855C2×C4—792no—
856C2×C4—792no—
857C2×C4—794no—
858C2×C4—792no—
859C2×C4—792no—
860C2×C4—794no—
861C2×C4—794no—
862C2×C4—798no—
863C2×C4—1588no—
864C2×C4—15816no—
865C2×C4—1588no—
866C2×C4—15816no—
867C2×C4—1584no—
868C2×C4—1588no—
869C2×C4—1582no—
870C2×C4—1584no—
871C2×C4—1582no—
872C2×C4—1584no—
873C2×C4—15816no—
874C2×C4C2×#1192962314yes—
875C2×C4C2×#1192962314yes—
876C2×C4C2×#11929623116yescomplemented
877C2×C4C24×D7914yes—
878C2×C4C24×D7914yes—
879C2×C4C24×D7918yes—
880C2×C4C24×D7912yes—
881C2×C4C24×D7912yes—
882C22—28no—
883C22—22no—
884C22—22no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—48no—
892C22—48no—
893C22—3168no—
894C22—1584no—
895C22—1584no—
896C22—1584no—
897C22C22×#1192962314yes—
898C22C22×#1192962312yes—
899C22H(5,𝔽2)×D7912yes—
900C222−1+4×D7912yes—
901C22C25×D7911yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—794no—
906C4—794no—
907C4—1584no—
908C4—1584no—
909C4—1588no—
910C4—1582no—
911C4—1584no—
912C4—1582no—
913C4C22×#1192962314yes—
914C4C22×#1192962314yes—
915C2—24no—
916C2—44no—
917C2—44no—
918C2—3164no—
919C2#2377730914yesdirect product factor
920C2C23×#1192962311yescharacteristic
921C2C2×H(5,𝔽2)×D7911yescharacteristic
922C2C2×2−1+4×D7911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#537×C79C2
socleC23×C79C25
hypercenterC2×#537D79
hypocenterC79C2×#3511
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #23777309C2direct (N × H)
2. C2×#19099284C2semidirect
3. C2×#19099277C2semidirect
4. C2×#19099271C2semidirect
5. C2×#19099256C2semidirect
6. C2×#19099219C2semidirect
7. C2×#19099213C2semidirect
8. C2×#19099186C2semidirect
9. C2×#19099180C2semidirect
10. C2×#19099141C2semidirect
11. C2×#19099115C2semidirect
12. C2×#19099109C2semidirect
13. C2×#19099108C2semidirect
14. C22×#14579160C2semidirect
15. C2×#19099046C2semidirect
16. C2×#19099044C2semidirect
17. C2×#41×Dic79C2semidirect
18. C2×#537×C79C2semidirect
22. #19099284C22semidirect
23. #19099277C22semidirect
24. #19099271C22semidirect
25. #19099256C22semidirect
26. #19099219C22semidirect
27. #19099213C22semidirect
28. #19099186C22semidirect
29. #19099180C22semidirect
30. #19099141C22semidirect
31. #19099115C22semidirect
32. #19099109C22semidirect
33. #19099108C22semidirect
38. C2×#14579160C22semidirect
62. #19099046C22semidirect
63. #19099044C22semidirect
64. #41×Dic79C22semidirect
94. #537×C79C22semidirect
335. C22×C4×C79#41semidirect
382. C2×C4×C79C2×#41semidirect
457. C2×C79#3511semidirect
472. C2×#537D79semidirect
480. C79C2×#3511semidirect
495. #537C2×D79semidirect
764. C22×C4#11929623semidirect
876. C2×C4C2×#11929623semidirect
919. C2#23777309direct (N × H)

Maximal subgroups

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

subgroupindex
#237773092
C2×#190992842
C2×#190992772
C2×#190992712
C2×#190992562
C2×#190992192
C2×#190992132
C2×#190991862
C2×#190991802
C2×#190991412
C2×#190991152
C2×#190991092
C2×#190991082
C22×#145791602
C2×#190990462
C2×#190990442
C2×#41×Dic792
C2×#537×C792
C2×#351179