Finite Group Databasebeta

← C2×#23777317 #35196770

Subgroups — C2×#23777317 #35196770

Order 20224.

7238 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777317C2132yesmaximal, direct product factor
2C2×#19099262C214yesmaximal, complemented
3C2×#19099261C212yesmaximal, complemented
4C2×#19099259C214yesmaximal, complemented
5C2×#19099257C212yesmaximal, complemented
6C2×#19099252C212yesmaximal, complemented
7C2×#19099248C212yesmaximal, complemented
8C2×#19099171C212yesmaximal, complemented
9C2×#19099164C212yesmaximal, complemented
10C2×#19099144C211yesmaximal, characteristic, complemented
11C2×#19099141C211yesmaximal, characteristic, complemented
12C2×#19099109C211yesmaximal, characteristic, complemented
13C2×#19099100C212yesmaximal, complemented
14C2×#19099095C212yesmaximal, complemented
15C22×#14579152C211yesmaximal, characteristic, complemented
16C2×#19099043C211yesmaximal, characteristic, complemented
17C2×#19099031C211yesmaximal, characteristic, complemented
18C2×#520×C79C211yesmaximal, characteristic, complemented
19C22×#11929624C2211yescharacteristic
20C22×#11929624C2211yescharacteristic
21#19099262C22164yescomplemented
22#19099261C22132yescomplemented
23#19099259C22164yescomplemented
24#19099257C22132yescomplemented
25#19099252C22132yescomplemented
26#19099248C22132yescomplemented
27#19099171C22132yescomplemented
28#19099164C22132yescomplemented
29#19099144C22116yescomplemented
30#19099141C22116yescomplemented
31#19099109C22116yescomplemented
32C2×#14579159C2211yescharacteristic
33C2×#14579157C2211yescharacteristic
34#19099100C22132yescomplemented
35#19099095C22132yescomplemented
36C2×#14579156C2214yes—
37C2×#14579156C2214yes—
38C2×#14579155C2214yes—
39C2×#14579154C2214yes—
40C2×#14579153C2214yes—
41C2×#14579152C2212yes—
42C2×#14579152C2212yes—
43C2×#14579152C2212yes—
44C2×#14579152C2212yes—
45C2×#14579152C22116yescomplemented
46C2×#14579151C2214yes—
47C2×#14579150C2211yescharacteristic
48C2×#14579148C2211yescharacteristic
49C2×#14579146C2214yes—
50C2×#14579144C2214yes—
51C2×#14579143C2214yes—
52C2×#14579143C2214yes—
53C2×#14579141C2212yes—
54C2×#14579141C2212yes—
55C2×#14579140C2212yes—
56C2×#14579137C2212yes—
57C2×#14579136C2212yes—
58C2×#14579136C2212yes—
59C2×#14579135C2212yes—
60C2×#14579135C2214yes—
61C2×#14579135C2214yes—
62C2×#14579134C2214yes—
63C2×#14579133C2212yes—
64C2×#14579133C2214yes—
65C2×#14579133C2212yes—
66C2×#14579132C2212yes—
67#19099043C22116yescomplemented
68#19099031C22116yescomplemented
69C2×C4×Dic158C2212yes—
70C2×#14579126C2211yescharacteristic
71C2×#14579126C2211yescharacteristic
72C2×C4×D316C2212yes—
73C2×C4×D316C2214yes—
74C2×#14579123C2211yescharacteristic
75C2×#14579123C2211yescharacteristic
76C2×C4×C22⋊D79C2212yes—
77C2×C4×C22⋊D79C2212yes—
78C2×C4×C22⋊D79C2214yes—
79C2×(C22⋊D79)⋊C4C2212yes—
80C2×(C22⋊D79)⋊C4C2212yes—
81C2×(C22⋊D79)⋊C4C2214yes—
82C2×#14579120C2214yes—
83C2×#14579119C2212yes—
84C2×#14579118C2212yes—
85C2×#14579118C2214yes—
86C22×C4⋊Dic79C2211yescharacteristic
87C22×C4⋊Dic79C2212yes—
88C22×Dic79⋊C4C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C22×C4×Dic79C2211yescharacteristic
91C2×C42×D79C2212yes—
92C22×#41×C79C2211yescharacteristic
93#520×C79C22116yescomplemented
94C2×C4×Q8×C79C2212yes—
95C2×C4×D4×C79C2214yes—
96C2×C4×D4×C79C2212yes—
97C2×#117×C79C2211yescharacteristic
98C2×#117×C79C2212yes—
99C22×C4⋊C4×C79C2212yes—
100C22×C4⋊C4×C79C2211yescharacteristic
101C2×#11929624—28no—
102C2×#11929624—28no—
103C2×#11929624C2318yes—
104C2×#11929624C2318yes—
105C22×Dic158C2311yescharacteristic
106C22×Dic158C2311yescharacteristic
107C22×D316C2311yescharacteristic
108C22×D316C2311yescharacteristic
109C22×D316C2314yes—
110C22×C22⋊D79C2312yes—
111C22×C22⋊D79C2312yes—
112C22×C22⋊D79C2314yes—
113C22×C22⋊D79C2312yes—
114C22×C22⋊D79C2312yes—
115C23×Dic79C2311yescharacteristic
116C23×Dic79C2311yescharacteristic
117C23×Dic79C2312yes—
118C22×C4×D79C2312yes—
119C22×C4×D79C2312yes—
120C22×C4×D79C2312yes—
121C22×C4×D79C2312yes—
122C22×C4×D79C2314yes—
123#14579159C2318yes—
124#14579157C2318yes—
125#14579156C23132yes—
126#14579156C23132yes—
127#14579155C23132yes—
128#14579154C23132yes—
129#14579153C23132yes—
130#14579152C23116yes—
131#14579152C23116yes—
132#14579152C23116yes—
133#14579152C23116yes—
134#14579151C23132yes—
135#14579150C2318yes—
136#14579148C2318yes—
137#14579146C23132yes—
138#14579144C23132yes—
139#14579143C23132yes—
140#14579143C23132yes—
141#14579141C23116yes—
142#14579141C23116yes—
143#14579140C23116yes—
144#14579137C23116yes—
145#14579136C23116yes—
146#14579136C23116yes—
147#14579135C23116yes—
148#14579135C23132yes—
149#14579135C23132yes—
150#14579134C23132yes—
151#14579133C23132yes—
152#14579133C23116yes—
153#14579133C23116yes—
154#14579132C23116yes—
155C4×Dic158C23116yes—
156#14579126C2318yes—
157#14579126C2318yes—
158C4×D316C23116yes—
159C4×D316C23132yes—
160#14579123C2318yes—
161#14579123C2318yes—
162C4×C22⋊D79C23116yes—
163C4×C22⋊D79C23116yes—
164C4×C22⋊D79C23132yes—
165(C22⋊D79)⋊C4C23116yes—
166(C22⋊D79)⋊C4C23132yes—
167(C22⋊D79)⋊C4C23116yes—
168#14579120C23132yes—
169#14579119C23116yes—
170#14579118C23116yes—
171#14579118C23132yes—
172C2×C4⋊Dic79C2318yes—
173C2×C4⋊Dic79C23116yes—
174C2×C4⋊Dic79C2312yes—
175C2×C4⋊Dic79C2314yes—
176C2×C4⋊Dic79C2312yes—
177C2×C4⋊Dic79C2314yes—
178C2×C4⋊Dic79C2314yes—
179C2×Dic79⋊C4C23116yes—
180C2×Dic79⋊C4C2314yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2312yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2314yes—
186C2×Dic79⋊C4C2312yes—
187C2×Dic79⋊C4C2312yes—
188C4⋊C4×D79C23116yes—
189C2×C22⋊Dic79C2312yes—
190C2×C22⋊Dic79C2314yes—
191C2×C22⋊Dic79C2312yes—
192C2×(C2×D79)⋊C4C2312yes—
193C2×(C2×D79)⋊C4C2312yes—
194C2×(C2×D79)⋊C4C2312yes—
195C2×(C2×D79)⋊C4C2314yes—
196C2×(C2×D79)⋊C4C2314yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×(C2×D79)⋊C4C2314yes—
199C2×(C2×D79)⋊C4C2314yes—
200C2×C4×Dic79C2311yescharacteristic
201C2×C4×Dic79C2312yes—
202C2×C4×Dic79C2312yes—
203C2×C4×Dic79C2311yescharacteristic
204C2×C4×Dic79C2311yescharacteristic
205C2×C4×Dic79C2311yescharacteristic
206C2×C4×Dic79C2318yes—
207C2×C4×Dic79C2314yes—
208C42×D79C23116yes—
209C2×#41×C79—28no—
210C2×#41×C79C2318yes—
211C22×Q8×C79C2311yescharacteristic
212C22×D4×C79C2311yescharacteristic
213C22×D4×C79C2312yes—
214C23×C4×C79C2312yes—
215C23×C4×C79C2312yes—
216C23×C4×C79C2314yes—
217C23×C4×C79C2311yescharacteristic
218C4×Q8×C79C23116yes—
219C4×D4×C79C23116yes—
220C4×D4×C79C23132yes—
221#117×C79C23116yes—
222#117×C79C2318yes—
223C2×C4⋊C4×C79C2318yes—
224C2×C4⋊C4×C79C2311yescharacteristic
225C2×C4⋊C4×C79C2312yes—
226C2×C4⋊C4×C79C2312yes—
227C2×C4⋊C4×C79C2314yes—
228C2×C4⋊C4×C79C23116yes—
229C2×C4⋊C4×C79C2311yescharacteristic
230C2×C22⋊C4×C79C2312yes—
231C2×C22⋊C4×C79C2314yes—
232C2×C42×C79C2312yes—
233C2×C42×C79C2314yes—
234C23×D79C2412yes—
235C23×D79C2412yes—
236#11929624—232no—
237#11929624—232no—
238C2×Dic158—24no—
239C2×Dic158—24no—
240C2×Dic158C2414yes—
241C2×Dic158C2414yes—
242C2×D316—24no—
243C2×D316—24no—
244C2×D316—48no—
245C2×D316C2414yes—
246C2×D316C2414yes—
247C2×D316C24116yes—
248C2×C22⋊D79—28no—
249C2×C22⋊D79—28no—
250C2×C22⋊D79—44no—
251C2×C22⋊D79—48no—
252C2×C22⋊D79—44no—
253C2×C22⋊D79C2418yes—
254C2×C22⋊D79C2418yes—
255C2×C22⋊D79C24116yes—
256C2×C22⋊D79C2418yes—
257C2×C22⋊D79C2418yes—
258C22×Dic79—42no—
259C22×Dic79—44no—
260C22×Dic79—42no—
261C22×Dic79C2412yes—
262C22×Dic79C2412yes—
263C22×Dic79C2411yescharacteristic
264C22×Dic79C2411yescharacteristic
265C22×Dic79C2411yescharacteristic
266C22×Dic79C2411yescharacteristic
267C22×Dic79C2414yes—
268C22×Dic79C2414yes—
269C22×Dic79C2414yes—
270C22×Dic79C2418yes—
271C2×C4×D79—28no—
272C2×C4×D79—28no—
273C2×C4×D79—48no—
274C2×C4×D79—44no—
275C2×C4×D79—44no—
276C2×C4×D79C2418yes—
277C2×C4×D79C2418yes—
278C2×C4×D79C2418yes—
279C2×C4×D79C2418yes—
280C2×C4×D79C24116yes—
281C4⋊Dic79C2418yes—
282C4⋊Dic79C24116yes—
283C4⋊Dic79C2418yes—
284C4⋊Dic79C24116yes—
285C4⋊Dic79C24116yes—
286Dic79⋊C4C24116yes—
287Dic79⋊C4C24116yes—
288Dic79⋊C4C24116yes—
289Dic79⋊C4C2418yes—
290Dic79⋊C4C2418yes—
291Dic79⋊C4C24116yes—
292Dic79⋊C4C2418yes—
293Dic79⋊C4C2418yes—
294C22⋊Dic79C2418yes—
295C22⋊Dic79C24116yes—
296C22⋊Dic79C2418yes—
297(C2×D79)⋊C4C2418yes—
298(C2×D79)⋊C4C2418yes—
299(C2×D79)⋊C4C2418yes—
300(C2×D79)⋊C4C24116yes—
301(C2×D79)⋊C4C24116yes—
302(C2×D79)⋊C4C2418yes—
303(C2×D79)⋊C4C24116yes—
304(C2×D79)⋊C4C24116yes—
305C4×Dic79C2414yes—
306C4×Dic79C2418yes—
307C4×Dic79C2418yes—
308C4×Dic79C2414yes—
309C4×Dic79C2414yes—
310C4×Dic79C2414yes—
311C4×Dic79C24116yes—
312C24×C79C2412yes—
313C24×C79C2411yescharacteristic
314#41×C79—232no—
315C2×Q8×C79—24no—
316C2×Q8×C79C2414yes—
317C2×D4×C79—28no—
318C2×D4×C79—24no—
319C2×D4×C79C2414yes—
320C2×D4×C79C2418yes—
321C22×C4×C79—28no—
322C22×C4×C79—48no—
323C22×C4×C79—44no—
324C22×C4×C79#4118yes—
325C22×C4×C79C2412yes—
326C22×C4×C79C2412yes—
327C22×C4×C79C2412yes—
328C22×C4×C79C2414yes—
329C22×C4×C79C2418yes—
330C22×C4×C79C2418yes—
331C22×C4×C79C24116yes—
332C22×C4×C79C2411yescharacteristic
333C22×C4×C79C2411yescharacteristic
334C22×C4×C79C2414yes—
335C4⋊C4×C79C2414yes—
336C4⋊C4×C79C2418yes—
337C4⋊C4×C79C2418yes—
338C4⋊C4×C79C24116yes—
339C4⋊C4×C79C2414yes—
340C22⋊C4×C79C2418yes—
341C22⋊C4×C79C24116yes—
342C42×C79C2418yes—
343C42×C79C24116yes—
344C23×C79—22no—
345C23×C79—22no—
346C23×C79—24no—
347C23×C79—24no—
348C23×C79—24no—
349C23×C79C2×#4114yes—
350C23×C79C2514yes—
351C23×C79C2512yes—
352C23×C79C2511yescharacteristic
353C22×D79—24no—
354C22×D79—24no—
355C22×D79—24no—
356C22×D79—24no—
357C22×D79—24no—
358C22×D79—24no—
359C22×D79C2514yes—
360C22×D79C2514yes—
361Q8×C79—28no—
362D4×C79—216no—
363D4×C79—28no—
364C2×C4×C79—24no—
365C2×C4×C79—24no—
366C2×C4×C79—24no—
367C2×C4×C79—28no—
368C2×C4×C79—216no—
369C2×C4×C79—416no—
370C2×C4×C79—48no—
371C2×C4×C79C2×#4114yes—
372C2×C4×C79C2×#4114yes—
373C2×C4×C79C2×#41116yes—
374C2×C4×C79C2514yes—
375C2×C4×C79C2514yes—
376C2×C4×C79C2514yes—
377C2×C4×C79C2518yes—
378C2×C4×C79C2512yes—
379C2×C4×C79C2512yes—
380C22⋊D79—216no—
381C22⋊D79—216no—
382C22⋊D79—48no—
383C22⋊D79—48no—
384C22⋊D79—416no—
385C2×Dic79—24no—
386C2×Dic79—24no—
387C2×Dic79—22no—
388C2×Dic79—22no—
389C2×Dic79—28no—
390C2×Dic79—22no—
391C2×Dic79—22no—
392C2×Dic79—44no—
393C2×Dic79—44no—
394C2×Dic79—48no—
395C2×Dic79C2512yes—
396C2×Dic79C2512yes—
397C2×Dic79C2514yes—
398C2×Dic79C2514yes—
399C2×Dic79C2512yes—
400C2×Dic79C2512yes—
401C2×Dic79C2518yes—
402D316—28no—
403D316—28no—
404D316—416no—
405C4×D79—216no—
406C4×D79—216no—
407C4×D79—416no—
408C4×D79—48no—
409C4×D79—48no—
410Dic158—28no—
411Dic158—28no—
412C22×C79—22no—
413C22×C79—22no—
414C22×C79—28no—
415C22×C79—24no—
416C22×C79—24no—
417C22×C79—24no—
418C22×C79—48no—
419C22×C79C22×#4114yes—
420C22×C79C22×#4112yes—
421C22×C79#58512yes—
422C22×C79#58512yes—
423C22×C79C2611yescharacteristic
424C2×D79—24no—
425C2×D79—24no—
426C2×D79—24no—
427C2×D79—24no—
428C2×D79—24no—
429C2×D79—24no—
430C2×D79—48no—
431C2×D79—48no—
432C4×C79—24no—
433C4×C79—24no—
434C4×C79—28no—
435C4×C79—24no—
436C4×C79C22×#4114yes—
437C4×C79C22×#4114yes—
438Dic79—24no—
439Dic79—24no—
440Dic79—22no—
441Dic79—22no—
442Dic79—28no—
443Dic79—22no—
444Dic79—22no—
445C2×#3512—791nomaximal, Sylow
446C2×C79—24no—
447C2×C79—44no—
448C2×C79#351214yescomplemented
449C2×C79C23×#4111yescharacteristic
450C2×C79C2×#58511yescharacteristic
451C2×C79C2×#58511yescharacteristic
452D79—44no—
453D79—44no—
454#3512—7932no—
455C2×#553—794no—
456C2×#553—794no—
457C2×#553—792no—
458C2×#553—792no—
459C2×#552—792no—
460C2×#552—792no—
461C2×#541—792no—
462C2×#540—792no—
463C2×#537—791no—
464C2×#537—791no—
465C2×#532—791no—
466C2×#529—792no—
467C2×#529—792no—
468C22×#125—791no—
469C2×#520—791no—
470C2×#520D7911yescharacteristic, complemented
471C2×C4×#41—791no—
472C79C2×#351211yescharacteristic, complemented, Sylow
473C22×#41—791no—
474C22×#41—791no—
475C22×#41C2×D7911yescharacteristic
476#553—7964no—
477#553—7964no—
478#553—7932no—
479#553—7932no—
480#552—7932no—
481#552—7932no—
482#541—7932no—
483#540—7932no—
484#537—7916no—
485#537—7916no—
486#532—7916no—
487C2×C4⋊Q8—791no—
488C2×#127—791no—
489#529—7932no—
490#529—7932no—
491C2×#126—794no—
492C2×#126—794no—
493C2×#126—794no—
494C2×#126—794no—
495C2×#125—792no—
496C2×#125—792no—
497C2×#125—792no—
498C2×#125—792no—
499C2×#125—7916no—
500C2×#125—794no—
501C2×#125—794no—
502C2×#124—791no—
503C2×#124—791no—
504C2×#123—794no—
505C2×#123—794no—
506C2×#123—794no—
507C2×#123—794no—
508C2×C22⋊Q8—792no—
509C2×C22⋊Q8—792no—
510C2×C22⋊Q8—792no—
511C2×C22⋊Q8—792no—
512C2×#121—792no—
513C2×#121—792no—
514C2×#121—792no—
515C2×#121—794no—
516C2×#121—794no—
517C2×#121—792no—
518C2×#121—794no—
519C2×#121—792no—
520C2×#121—792no—
521C2×#121—794no—
522#520—7916no—
523#520C2×D79116yescomplemented
524C4×#41—7916no—
525C2×C4×Q8—791no—
526C2×C4×Q8—791no—
527C2×C4×Q8—792no—
528C2×C4×Q8C2×D7912yes—
529C2×C4×D4—794no—
530C2×C4×D4—792no—
531C2×C4×D4—792no—
532C2×C4×D4—791no—
533C2×C4×D4—791no—
534C2×C4×D4—792no—
535C2×C4×D4—792no—
536C2×C4×D4—794no—
537C2×C4×D4—792no—
538C2×C4×D4—794no—
539C2×C4×D4C2×D7912yes—
540C2×C4×D4C2×D7914yes—
541C2×#117—794no—
542C2×#117—792no—
543C2×#117—792no—
544C2×#117—794no—
545C2×#117C2×D7911yescharacteristic
546C2×#117C2×D7912yes—
547C22×C4⋊C4—791no—
548C22×C4⋊C4—792no—
549C22×C4⋊C4—792no—
550C22×C4⋊C4—792no—
551C22×C4⋊C4C2×D7911yescharacteristic
552C22×C4⋊C4C2×D7912yes—
553C22×C42—791no—
554C22×C42—792no—
555C2×#41—28no—
556C2×#41—798no—
557C2×#41—798no—
558C2×#41—1588no—
559C2×#41—1588no—
560C2×#41C22×D7918yes—
561C22×Q8—791no—
562C22×Q8—791no—
563C22×Q8C22×D7911yescharacteristic
564C22×D4—794no—
565C22×D4—792no—
566C22×D4—792no—
567C22×D4—792no—
568C22×D4—792no—
569C22×D4—794no—
570C22×D4—791no—
571C22×D4—791no—
572C22×D4C22×D7912yes—
573C22×D4C22×D7911yescharacteristic
574C23×C4—792no—
575C23×C4—791no—
576C23×C4—791no—
577C23×C4—794no—
578C23×C4—792no—
579C23×C4—792no—
580C23×C4—792no—
581C23×C4—792no—
582C23×C4C22×D7912yes—
583C23×C4C22×D7912yes—
584C23×C4C22×D7914yes—
585C23×C4C22×D7911yescharacteristic
586C4⋊Q8—798no—
587#127—798no—
588#126—7932no—
589#126—7932no—
590#126—7932no—
591#126—7932no—
592#125—7916no—
593#125—7916no—
594#125—7916no—
595#125—7916no—
596#125—7932no—
597#125—7932no—
598#124—798no—
599#124—798no—
600#123—7932no—
601#123—7932no—
602#123—7932no—
603#123—7932no—
604C22⋊Q8—7916no—
605C22⋊Q8—7916no—
606C22⋊Q8—7916no—
607C22⋊Q8—7916no—
608#121—7916no—
609#121—7916no—
610#121—7916no—
611#121—7932no—
612#121—7932no—
613#121—7916no—
614#121—7932no—
615#121—7916no—
616#121—7916no—
617#121—7932no—
618C4×Q8—798no—
619C4×Q8—798no—
620C4×Q8—7916no—
621C4×Q8C22×D79116yes—
622C4×D4—7932no—
623C4×D4—7916no—
624C4×D4—7916no—
625C4×D4—798no—
626C4×D4—798no—
627C4×D4—7916no—
628C4×D4—7916no—
629C4×D4—7932no—
630C4×D4—7916no—
631C4×D4—7932no—
632C4×D4C22×D79116yes—
633C4×D4C22×D79132yes—
634#117—7932no—
635#117—7916no—
636#117—7916no—
637#117—7932no—
638#117C22×D7918yes—
639#117C22×D79116yes—
640C2×C4⋊C4—792no—
641C2×C4⋊C4—794no—
642C2×C4⋊C4—794no—
643C2×C4⋊C4—792no—
644C2×C4⋊C4—794no—
645C2×C4⋊C4—798no—
646C2×C4⋊C4—794no—
647C2×C4⋊C4—794no—
648C2×C4⋊C4—7916no—
649C2×C4⋊C4—7916no—
650C2×C4⋊C4—792no—
651C2×C4⋊C4—792no—
652C2×C4⋊C4—794no—
653C2×C4⋊C4—794no—
654C2×C4⋊C4—792no—
655C2×C4⋊C4—792no—
656C2×C4⋊C4—7916no—
657C2×C4⋊C4C22×D7911yescharacteristic
658C2×C4⋊C4C22×D7911yescharacteristic
659C2×C4⋊C4C22×D7912yes—
660C2×C4⋊C4C22×D7912yes—
661C2×C4⋊C4C22×D7914yes—
662C2×C4⋊C4C22×D7918yes—
663C2×C4⋊C4C22×D79116yes—
664C2×C22⋊C4—792no—
665C2×C22⋊C4—794no—
666C2×C22⋊C4—792no—
667C2×C22⋊C4—792no—
668C2×C22⋊C4—792no—
669C2×C22⋊C4—792no—
670C2×C22⋊C4—794no—
671C2×C22⋊C4—794no—
672C2×C22⋊C4—792no—
673C2×C22⋊C4—794no—
674C2×C22⋊C4—794no—
675C2×C22⋊C4C22×D7912yes—
676C2×C22⋊C4C22×D7914yes—
677C2×C42—794no—
678C2×C42—792no—
679C2×C42—792no—
680C2×C42—791no—
681C2×C42—791no—
682C2×C42—791no—
683C2×C42—798no—
684C2×C42—791no—
685C2×C42—7916no—
686C2×C42C22×D7912yes—
687C2×C42C22×D7914yes—
688C24—792no—
689C24—792no—
690C24C23×D7912yes—
691C24C23×D7911yescharacteristic
692#41—232no—
693#41—15832no—
694#41—15832no—
695C2×Q8—24no—
696C2×Q8—794no—
697C2×Q8—794no—
698C2×Q8—1584no—
699C2×Q8—1584no—
700C2×Q8C23×D7914yes—
701C2×D4—28no—
702C2×D4—24no—
703C2×D4—3168no—
704C2×D4—3164no—
705C2×D4—3168no—
706C2×D4—3164no—
707C2×D4—7916no—
708C2×D4—798no—
709C2×D4—798no—
710C2×D4—798no—
711C2×D4—798no—
712C2×D4—7916no—
713C2×D4—794no—
714C2×D4—794no—
715C2×D4—1588no—
716C2×D4—1588no—
717C2×D4—1584no—
718C2×D4—1584no—
719C2×D4C23×D7918yes—
720C2×D4C23×D7914yes—
721C22×C4—28no—
722C22×C4—48no—
723C22×C4—44no—
724C22×C4—3164no—
725C22×C4—3164no—
726C22×C4—3168no—
727C22×C4—3162no—
728C22×C4—3162no—
729C22×C4—3164no—
730C22×C4—794no—
731C22×C4—794no—
732C22×C4—798no—
733C22×C4—798no—
734C22×C4—798no—
735C22×C4—7916no—
736C22×C4—791no—
737C22×C4—791no—
738C22×C4—792no—
739C22×C4—792no—
740C22×C4—791no—
741C22×C4—791no—
742C22×C4—794no—
743C22×C4—798no—
744C22×C4—798no—
745C22×C4—1588no—
746C22×C4—1588no—
747C22×C4#1192962418yes—
748C22×C4C23×D7918yes—
749C22×C4C23×D7912yes—
750C22×C4C23×D7912yes—
751C22×C4C23×D7912yes—
752C22×C4C23×D7914yes—
753C22×C4C23×D7918yes—
754C22×C4C23×D79116yes—
755C22×C4C23×D7914yes—
756C22×C4C23×D7911yescharacteristic
757C22×C4C23×D7911yescharacteristic
758C4⋊C4—7916no—
759C4⋊C4—7916no—
760C4⋊C4—7916no—
761C4⋊C4—798no—
762C4⋊C4—798no—
763C4⋊C4—7916no—
764C4⋊C4—798no—
765C4⋊C4—798no—
766C4⋊C4—798no—
767C4⋊C4—7916no—
768C4⋊C4—798no—
769C4⋊C4—7916no—
770C4⋊C4—7916no—
771C4⋊C4C23×D7914yes—
772C4⋊C4C23×D7914yes—
773C4⋊C4C23×D7918yes—
774C4⋊C4C23×D7918yes—
775C4⋊C4C23×D79116yes—
776C22⋊C4—798no—
777C22⋊C4—7916no—
778C22⋊C4—798no—
779C22⋊C4—798no—
780C22⋊C4—798no—
781C22⋊C4—798no—
782C22⋊C4—7916no—
783C22⋊C4—7916no—
784C22⋊C4—798no—
785C22⋊C4—7916no—
786C22⋊C4—7916no—
787C22⋊C4C23×D7918yes—
788C22⋊C4C23×D79116yes—
789C42—794no—
790C42—798no—
791C42—798no—
792C42—794no—
793C42—794no—
794C42—794no—
795C42—7916no—
796C42C23×D7918yes—
797C42C23×D79116yes—
798C23—22no—
799C23—22no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—794no—
804C23—794no—
805C23—1584no—
806C23—1584no—
807C23—1584no—
808C23—1584no—
809C23—1584no—
810C23—1584no—
811C23C2×#1192962414yes—
812C23C24×D7914yes—
813C23C24×D7912yes—
814C23C24×D7911yescharacteristic
815Q8—28no—
816Q8—1588no—
817Q8—1588no—
818D4—216no—
819D4—28no—
820D4—31616no—
821D4—3168no—
822D4—31616no—
823D4—3168no—
824D4—15816no—
825D4—15816no—
826D4—1588no—
827D4—1588no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—216no—
833C2×C4—416no—
834C2×C4—48no—
835C2×C4—3168no—
836C2×C4—3168no—
837C2×C4—31616no—
838C2×C4—3164no—
839C2×C4—3164no—
840C2×C4—3168no—
841C2×C4—792no—
842C2×C4—792no—
843C2×C4—794no—
844C2×C4—794no—
845C2×C4—792no—
846C2×C4—792no—
847C2×C4—798no—
848C2×C4—1582no—
849C2×C4—1582no—
850C2×C4—1582no—
851C2×C4—1588no—
852C2×C4—1582no—
853C2×C4—1584no—
854C2×C4—1584no—
855C2×C4—15816no—
856C2×C4—15816no—
857C2×C4C2×#1192962414yes—
858C2×C4C2×#1192962414yes—
859C2×C4C2×#11929624116yes—
860C2×C4C24×D7914yes—
861C2×C4C24×D7914yes—
862C2×C4C24×D7914yes—
863C2×C4C24×D7918yes—
864C2×C4C24×D7912yes—
865C2×C4C24×D7912yes—
866C22—28no—
867C22—22no—
868C22—22no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—48no—
873C22—3168no—
874C22—3168no—
875C22—1584no—
876C22—1584no—
877C22—1584no—
878C22—1584no—
879C22—1584no—
880C22—1584no—
881C22C22×#1192962414yes—
882C22C22×#1192962412yes—
883C22#1909939812yes—
884C22#1909940012yes—
885C22C25×D7911yescharacteristic
886C4—24no—
887C4—24no—
888C4—28no—
889C4—24no—
890C4—1584no—
891C4—1584no—
892C4—1582no—
893C4—1582no—
894C4—1582no—
895C4—1588no—
896C4—1582no—
897C4C22×#1192962414yes—
898C4C22×#1192962414yes—
899C2—24no—
900C2—44no—
901C2—3164no—
902C2—3164no—
903C2#2377731714yesdirect product factor
904C2C23×#1192962411yescharacteristic
905C2C2×#1909939811yescharacteristic
906C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#520×C79C2
socleC23×C79C25
hypercenterC2×#520D79
hypocenterC79C2×#3512
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #23777317C2direct (N × H)
2. C2×#19099262C2semidirect
3. C2×#19099261C2semidirect
4. C2×#19099259C2semidirect
5. C2×#19099257C2semidirect
6. C2×#19099252C2semidirect
7. C2×#19099248C2semidirect
8. C2×#19099171C2semidirect
9. C2×#19099164C2semidirect
10. C2×#19099144C2semidirect
11. C2×#19099141C2semidirect
12. C2×#19099109C2semidirect
13. C2×#19099100C2semidirect
14. C2×#19099095C2semidirect
15. C22×#14579152C2semidirect
16. C2×#19099043C2semidirect
17. C2×#19099031C2semidirect
18. C2×#520×C79C2semidirect
21. #19099262C22semidirect
22. #19099261C22semidirect
23. #19099259C22semidirect
24. #19099257C22semidirect
25. #19099252C22semidirect
26. #19099248C22semidirect
27. #19099171C22semidirect
28. #19099164C22semidirect
29. #19099144C22semidirect
30. #19099141C22semidirect
31. #19099109C22semidirect
34. #19099100C22semidirect
35. #19099095C22semidirect
45. C2×#14579152C22semidirect
67. #19099043C22semidirect
68. #19099031C22semidirect
93. #520×C79C22semidirect
448. C2×C79#3512semidirect
470. C2×#520D79semidirect
472. C79C2×#3512semidirect
523. #520C2×D79semidirect
903. C2#23777317direct (N × H)

Maximal subgroups

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

subgroupindex
#237773172
C2×#190992622
C2×#190992612
C2×#190992592
C2×#190992572
C2×#190992522
C2×#190992482
C2×#190991712
C2×#190991642
C2×#190991442
C2×#190991412
C2×#190991092
C2×#190991002
C2×#190990952
C22×#145791522
C2×#190990432
C2×#190990312
C2×#520×C792
C2×#351279