Finite Group Databasebeta

← C2×#23774563 #35160294

Subgroups — C2×#23774563 #35160294

Order 20224.

1822 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099092C211yesmaximal, characteristic
2C2×#125×D79C211yesmaximal, characteristic, complemented
3#23774563C2116yesmaximal, direct product factor
4C2×#19098965C211yesmaximal, characteristic, complemented
5C2×#19098962C211yesmaximal, characteristic, complemented
6C2×#19098917C211yesmaximal, characteristic, complemented
7C2×#19098897C211yesmaximal, characteristic, complemented
8C2×#19098880C211yesmaximal, characteristic
9C2×#19098892C211yesmaximal, characteristic, complemented
10C2×#19098875C211yesmaximal, characteristic
11C2×#19098872C211yesmaximal, characteristic, complemented
12C2×#19098868C211yesmaximal, characteristic, complemented
13C2×#19098865C211yesmaximal, characteristic, complemented
14C2×#19098861C211yesmaximal, characteristic, complemented
15C2×#19098614C211yesmaximal, characteristic, complemented
16C2×#488×C79C211yesmaximal, characteristic, complemented
17#19099092—24no—
18#19099092C2218yes—
19C2×#14579154—21no—
20C2×#14579153C2211yescharacteristic
21C2×#14579153C2211yescharacteristic
22C2×#14579152C2211yescharacteristic
23C2×#14579152C2211yescharacteristic
24C2×#14579151—21no—
25C2×#14579151—21no—
26#125×D79—24no—
27#125×D79C2218yescomplemented
28C2×#14579143—21no—
29C2×#14579137C2211yescharacteristic
30C2×#14579132C2211yescharacteristic
31C2×Q8×Dic79C2211yescharacteristic
32C2×D4×Dic79C2211yescharacteristic
33C2×(C22⋊D79)⋊C4—21no—
34C2×#14579117—21no—
35C2×C4⋊C4×D79—21no—
36C2×C4⋊C4×D79—21no—
37C2×C4⋊C4×D79C2211yescharacteristic
38C2×C4⋊C4×D79C2211yescharacteristic
39C2×C42×D79C2211yescharacteristic
40#19098965C2218yescomplemented
41#19098962C2218yescomplemented
42#19098917C2218yescomplemented
43#19098897C2218yescomplemented
44#19098892C2218yescomplemented
45#19098880C2218yes—
46#19098875C2218yes—
47#19098872C2218yescomplemented
48#19098868C2218yescomplemented
49#19098865C2218yescomplemented
50#19098861C2218yescomplemented
51#19098614C2218yescomplemented
52C2×#14579095C2211yescharacteristic
53C2×#14579095C2211yescharacteristic
54C2×#14579094C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579093C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59C2×#14579092C2211yescharacteristic
60C2×Dic79⋊C8C2211yescharacteristic
61C2×Dic79⋊C8C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×(C2×D79)⋊C8C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C4×C79⋊C8C2211yescharacteristic
69C2×#125×C79C2211yescharacteristic
70C2×#124×C79C2211yescharacteristic
71#488×C79C2218yescomplemented
72C2×#103×C79C2211yescharacteristic
73C2×#103×C79C2211yescharacteristic
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×C4×C8×C79C2211yescharacteristic
77C22×C22⋊D79—21no—
78C23×Dic79—21no—
79C22×C4×D79—21no—
80C22×C4×D79—21no—
81C22×C4×D79D411yescharacteristic
82C22×C4×D79D411yescharacteristic
83C22×C4×D79C2311yescharacteristic
84C22×C79⋊C8C2311yescharacteristic
85C22×C79⋊C8C2311yescharacteristic
86#14579154—28no—
87#14579153—22no—
88#14579153—22no—
89#14579153C2314yes—
90#14579153C2314yes—
91#14579152—22no—
92#14579152—22no—
93#14579152C2314yes—
94#14579152C2314yes—
95#14579151—28no—
96#14579151—28no—
97#14579143—28no—
98#14579137—22no—
99#14579137C2314yes—
100#14579132—22no—
101#14579132C2314yes—
102Q8×Dic79—22no—
103Q8×Dic79C2314yes—
104D4×Dic79—22no—
105D4×Dic79C2314yes—
106(C22⋊D79)⋊C4—28no—
107#14579117—28no—
108C2×C4⋊Dic79—21no—
109C2×C4⋊Dic79—21no—
110C2×C4⋊Dic79—21no—
111C2×C4⋊Dic79C2311yescharacteristic
112C2×C4⋊Dic79C2311yescharacteristic
113C2×C4⋊Dic79C2311yescharacteristic
114C2×C4⋊Dic79C2311yescharacteristic
115C2×Dic79⋊C4—21no—
116C2×Dic79⋊C4—21no—
117C2×Dic79⋊C4—21no—
118C2×Dic79⋊C4—21no—
119C2×Dic79⋊C4—21no—
120C2×Dic79⋊C4—21no—
121C2×Dic79⋊C4—21no—
122C2×Dic79⋊C4—21no—
123C2×Dic79⋊C4—21no—
124C4⋊C4×D79—28no—
125C4⋊C4×D79—28no—
126C4⋊C4×D79—22no—
127C4⋊C4×D79—22no—
128C4⋊C4×D79C2314yes—
129C4⋊C4×D79C2314yes—
130C2×C22⋊Dic79—21no—
131C2×C22⋊Dic79—21no—
132C2×(C2×D79)⋊C4—21no—
133C2×C4×Dic79—21no—
134C2×C4×Dic79D411yescharacteristic
135C2×C4×Dic79D411yescharacteristic
136C2×C4×Dic79C2311yescharacteristic
137C42×D79D414yes—
138C42×D79C2314yes—
139#14579095C2314yes—
140#14579095C2314yes—
141#14579094C2314yes—
142#14579094C2314yes—
143#14579093C2314yes—
144#14579093C2314yes—
145#14579092C2314yes—
146#14579092C2314yes—
147Dic79⋊C8C2314yes—
148Dic79⋊C8C2314yes—
149#14579085C2314yes—
150#14579085C2314yes—
151#14579082C2314yes—
152#14579082C2314yes—
153(C2×D79)⋊C8C2314yes—
154(C2×D79)⋊C8C2314yes—
155C4×C79⋊C8C2314yes—
156C22×Q8×C79C2311yescharacteristic
157C22×D4×C79C2311yescharacteristic
158C22×C8×C79C2311yescharacteristic
159C22×C8×C79C2311yescharacteristic
160#125×C79—22no—
161#125×C79C2314yes—
162#124×C79—22no—
163#124×C79C2314yes—
164C2×C4⋊C4×C79—21no—
165C2×C4⋊C4×C79—21no—
166C2×C4⋊C4×C79C2311yescharacteristic
167C2×C4⋊C4×C79C2311yescharacteristic
168C2×C22⋊C4×C79—21no—
169C2×C22⋊C4×C79—21no—
170C2×C42×C79C2311yescharacteristic
171#103×C79C2314yes—
172#103×C79C2314yes—
173#102×C79C2314yes—
174#102×C79C2314yes—
175C4×C8×C79C2314yes—
176C23×D79C2×D411yescharacteristic
177C2×C22⋊D79—24no—
178C2×C22⋊D79—44no—
179C22×Dic79—24no—
180C22×Dic79—21no—
181C22×Dic79—21no—
182C22×Dic79—21no—
183C22×Dic79—21no—
184C22×Dic79—44no—
185C22×Dic79C2×D411yescharacteristic
186C22×Dic79C2×D411yescharacteristic
187C22×Dic79C2×D411yescharacteristic
188C2×C4×D79—24no—
189C2×C4×D79—24no—
190C2×C4×D79—24no—
191C2×C4×D79—22no—
192C2×C4×D79—22no—
193C2×C4×D79—42no—
194C2×C4×D79—44no—
195C2×C4×D79—44no—
196C2×C4×D79C2×D412yes—
197C2×C4×D79C2×D414yes—
198C2×C4×D79C2×D414yes—
199C2×C4×D79C2412yes—
200C2×C79⋊C8—22no—
201C2×C79⋊C8—22no—
202C2×C79⋊C8C2412yes—
203C2×C79⋊C8C2412yes—
204C4⋊Dic79—24no—
205C4⋊Dic79—24no—
206C4⋊Dic79—24no—
207C4⋊Dic79—21no—
208C4⋊Dic79—21no—
209C4⋊Dic79—21no—
210C4⋊Dic79—21no—
211C4⋊Dic79C2412yes—
212C4⋊Dic79C2412yes—
213C4⋊Dic79C2412yes—
214C4⋊Dic79C2412yes—
215Dic79⋊C4—24no—
216Dic79⋊C4—24no—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224C22⋊Dic79—24no—
225C22⋊Dic79—24no—
226(C2×D79)⋊C4—24no—
227C4×Dic79—24no—
228C4×Dic79C2×D412yes—
229C4×Dic79C2×D414yes—
230C4×Dic79C2×D414yes—
231C4×Dic79C2412yes—
232C24×C79—21no—
233C2×Q8×C79—21no—
234C2×Q8×C79—22no—
235C2×Q8×C79—22no—
236C2×Q8×C79C2412yes—
237C2×D4×C79—21no—
238C2×D4×C79—22no—
239C2×D4×C79—22no—
240C2×D4×C79C2412yes—
241C22×C4×C79—21no—
242C22×C4×C79—21no—
243C22×C4×C79—21no—
244C22×C4×C79C2×D411yescharacteristic
245C22×C4×C79C2×D411yescharacteristic
246C22×C4×C79C2411yescharacteristic
247C2×C8×C79—22no—
248C2×C8×C79—22no—
249C2×C8×C79C2412yes—
250C2×C8×C79C2412yes—
251C4⋊C4×C79—24no—
252C4⋊C4×C79—24no—
253C4⋊C4×C79—21no—
254C4⋊C4×C79—21no—
255C4⋊C4×C79C2412yes—
256C4⋊C4×C79C2412yes—
257C22⋊C4×C79—24no—
258C22⋊C4×C79—24no—
259C42×C79C2×D412yes—
260C42×C79C2412yes—
261C23×C79—22no—
262C23×C79—42no—
263C23×C79—42no—
264C23×C79—42no—
265C23×C79C22×D411yescharacteristic
266C22×D79—22no—
267C22×D79—22no—
268C22×D79#13514yes—
269C22×D79C22×D412yes—
270Q8×C79—22no—
271Q8×C79—22no—
272Q8×C79—42no—
273D4×C79—22no—
274D4×C79—22no—
275D4×C79—42no—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—42no—
282C2×C4×C79—42no—
283C2×C4×C79—42no—
284C2×C4×C79C22×D412yes—
285C2×C4×C79C22×D412yes—
286C2×C4×C79C22×D411yescharacteristic
287C2×C4×C792−1+412yes—
288C2×C4×C792−1+412yes—
289C2×C4×C79C2511yescharacteristic
290C22⋊D79—48no—
291C2×Dic79—22no—
292C2×Dic79—22no—
293C2×Dic79—22no—
294C2×Dic79—22no—
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—48no—
299C2×Dic79—42no—
300C2×Dic79—42no—
301C2×Dic79—42no—
302C2×Dic79—42no—
303C2×Dic79C22×D412yes—
304C2×Dic79C22×D412yes—
305C2×Dic79C22×D412yes—
306C4×D79—28no—
307C4×D79—24no—
308C4×D79—22no—
309C4×D79—22no—
310C4×D79—44no—
311C4×D79—48no—
312C4×D79—48no—
313C8×C79—22no—
314C8×C79—22no—
315C79⋊C8—22no—
316C79⋊C8—22no—
317C22×C79—42no—
318C22×C79—42no—
319C22×C79—42no—
320C22×C79—84no—
321C22×C79#53612yes—
322C22×C79C2×#13512yes—
323C22×C79#57512yes—
324C22×C79C23×D411yescharacteristic
325C2×D79—22no—
326C2×D79—28no—
327C2×D79—22no—
328C2×D79C2×#13514yes—
329C4×C79—22no—
330C4×C79—22no—
331C4×C79—42no—
332C4×C79—42no—
333C4×C79—42no—
334C4×C79#53612yes—
335C4×C79C2×2−1+411yescharacteristic
336C4×C79C2×2−1+411yescharacteristic
337Dic79—22no—
338Dic79—22no—
339Dic79—22no—
340Dic79—42no—
341Dic79—42no—
342Dic79—42no—
343Dic79—42no—
344C2×#3232—791nomaximal, Sylow
345C2×C79—82no—
346C2×C79#323214yescomplemented
347C2×C79C2×#53611yescharacteristic
348C2×C79C22×#13511yescharacteristic
349C2×C79C2×#57511yescharacteristic
350D79—24no—
351C2×#529—791no—
352C22×#125—791no—
353#3232—7916no—
354C2×#499—791no—
355C2×#499—791no—
356C2×#488—791no—
357C2×#488D7911yescharacteristic, complemented
358C2×#484—791no—
359C2×#481—791no—
360C2×#483—791no—
361C2×#480—791no—
362C2×#479—791no—
363C2×#479—791no—
364C2×#478—791no—
365C2×#478—791no—
366C2×#431—791no—
367C79C2×#323211yescharacteristic, complemented, Sylow
368#529—798no—
369#529—1584no—
370C2×#126—1581no—
371C2×#125—798no—
372C2×#125—791no—
373C2×#125—791no—
374C2×#125—791no—
375C2×#125—791no—
376C2×#125—1581no—
377C2×#125—1581no—
378C2×#125—1584no—
379C2×#125C2×D7911yescharacteristic
380C2×#124C2×D7911yescharacteristic
381C2×#123—1581no—
382C2×C22⋊Q8—791no—
383C2×#121—791no—
384C2×C4×Q8—791no—
385C2×C4×D4—791no—
386C2×C4×D4—1581no—
387C2×#117—1581no—
388C22×C4⋊C4—791no—
389C22×C4⋊C4—791no—
390C22×C4⋊C4—1581no—
391C22×C4⋊C4—1581no—
392C22×C42—791no—
393#499—798no—
394#499—798no—
395#488—798no—
396#488C2×D7918yescomplemented
397#484—798no—
398#483—798no—
399#481—798no—
400#480—798no—
401#479—798no—
402#479—798no—
403#478—798no—
404#478—798no—
405#431—798no—
406C2×#107—791no—
407C2×#107—791no—
408C2×#107—791no—
409C2×#107—791no—
410C2×#106—791no—
411C2×#106—791no—
412C2×#106—791no—
413C2×#106—791no—
414C2×C4⋊C8—791no—
415C2×C4⋊C8—791no—
416C2×#103—791no—
417C2×#103—791no—
418C2×#103C2×D7911yescharacteristic
419C2×#103C2×D7911yescharacteristic
420C2×#102—791no—
421C2×#102—791no—
422C2×#102C2×D7911yescharacteristic
423C2×#102C2×D7911yescharacteristic
424C2×C22⋊C8—791no—
425C2×C22⋊C8—791no—
426C2×C4×C8—791no—
427C2×C4×C8C2×D7911yescharacteristic
428C22×Q8C22×D7911yescharacteristic
429C22×D4—1581no—
430C22×D4C22×D7911yescharacteristic
431C23×C4—791no—
432C23×C4—791no—
433C23×C4—791no—
434C23×C4—1581no—
435C23×C4—1581no—
436C23×C4—1581no—
437C22×C8—791no—
438C22×C8—791no—
439C22×C8C22×D7911yescharacteristic
440C22×C8C22×D7911yescharacteristic
441#126—1588no—
442#125—22no—
443#125—794no—
444#125—794no—
445#125—794no—
446#125—794no—
447#125—1588no—
448#125—1588no—
449#125—1582no—
450#125—1582no—
451#125—1582no—
452#125—1582no—
453#125C22×D7914yes—
454#124—22no—
455#124C22×D7914yes—
456#123—1588no—
457C22⋊Q8—794no—
458C22⋊Q8—1582no—
459#121—794no—
460#121—1582no—
461C4×Q8—794no—
462C4×Q8—1582no—
463C4×D4—794no—
464C4×D4—1582no—
465C4×D4—1588no—
466#117—1588no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—791no—
470C2×C4⋊C4—791no—
471C2×C4⋊C4—791no—
472C2×C4⋊C4—791no—
473C2×C4⋊C4—794no—
474C2×C4⋊C4—794no—
475C2×C4⋊C4—1582no—
476C2×C4⋊C4—1582no—
477C2×C4⋊C4—1588no—
478C2×C4⋊C4—1588no—
479C2×C4⋊C4—1581no—
480C2×C4⋊C4—1581no—
481C2×C4⋊C4—1581no—
482C2×C4⋊C4—1581no—
483C2×C4⋊C4—1581no—
484C2×C4⋊C4—1581no—
485C2×C4⋊C4—1581no—
486C2×C4⋊C4—1581no—
487C2×C4⋊C4—1581no—
488C2×C4⋊C4—1581no—
489C2×C4⋊C4—1581no—
490C2×C4⋊C4—1581no—
491C2×C4⋊C4C22×D7911yescharacteristic
492C2×C4⋊C4C22×D7911yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—1581no—
496C2×C22⋊C4—1581no—
497C2×C22⋊C4—1581no—
498C2×C42—791no—
499C2×C42—791no—
500C2×C42—791no—
501C2×C42—794no—
502C2×C42—794no—
503C2×C42—1581no—
504C2×C42C22×D7911yescharacteristic
505#107—794no—
506#107—794no—
507#107—794no—
508#107—794no—
509#106—794no—
510#106—794no—
511#106—794no—
512#106—794no—
513C4⋊C8—794no—
514C4⋊C8—794no—
515#103—794no—
516#103—794no—
517#103C22×D7914yes—
518#103C22×D7914yes—
519#102—794no—
520#102—794no—
521#102C22×D7914yes—
522#102C22×D7914yes—
523C22⋊C8—794no—
524C22⋊C8—794no—
525C4×C8—794no—
526C4×C8C22×D7914yes—
527C24—21no—
528C24—791no—
529C2×Q8—21no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8C23×D7912yes—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—21no—
536C2×D4—3164no—
537C2×D4—1584no—
538C2×D4C23×D7912yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—3162no—
543C22×C4—3164no—
544C22×C4—3164no—
545C22×C4—3164no—
546C22×C4—794no—
547C22×C4—791no—
548C22×C4—791no—
549C22×C4—791no—
550C22×C4—792no—
551C22×C4—792no—
552C22×C4—794no—
553C22×C4—1584no—
554C22×C4—1584no—
555C22×C4—1584no—
556C22×C4—1584no—
557C22×C4—1581no—
558C22×C4—1581no—
559C22×C4—1581no—
560C22×C4—1581no—
561C22×C4—1582no—
562C22×C4—1582no—
563C22×C4D4×D7911yescharacteristic
564C22×C4D4×D7911yescharacteristic
565C22×C4C23×D7911yescharacteristic
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—792no—
569C2×C8—792no—
570C2×C8—1582no—
571C2×C8—1582no—
572C2×C8C23×D7912yes—
573C2×C8C23×D7912yes—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—792no—
579C4⋊C4—792no—
580C4⋊C4—792no—
581C4⋊C4—792no—
582C4⋊C4—1584no—
583C4⋊C4—1584no—
584C4⋊C4—1584no—
585C4⋊C4—1584no—
586C4⋊C4—1584no—
587C4⋊C4—1584no—
588C4⋊C4—1584no—
589C4⋊C4—1584no—
590C4⋊C4—1584no—
591C4⋊C4—1584no—
592C4⋊C4—1584no—
593C4⋊C4—1584no—
594C4⋊C4—1581no—
595C4⋊C4—1581no—
596C4⋊C4—1581no—
597C4⋊C4—1581no—
598C4⋊C4C23×D7912yes—
599C4⋊C4C23×D7912yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—1584no—
603C22⋊C4—1584no—
604C22⋊C4—1584no—
605C42—792no—
606C42—794no—
607C42—792no—
608C42—794no—
609C42—1584no—
610C42D4×D7912yes—
611C42C23×D7912yes—
612C23—22no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—794no—
617C23—792no—
618C23—1582no—
619C23—1582no—
620C23C2×D4×D7911yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—42no—
624D4—22no—
625D4—22no—
626D4—42no—
627D4—3168no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—3164no—
637C2×C4—3168no—
638C2×C4—3168no—
639C2×C4—3162no—
640C2×C4—3162no—
641C2×C4—3162no—
642C2×C4—3162no—
643C2×C4—3168no—
644C2×C4—792no—
645C2×C4—792no—
646C2×C4—792no—
647C2×C4—1588no—
648C2×C4—1582no—
649C2×C4—1582no—
650C2×C4—1582no—
651C2×C4—1582no—
652C2×C4—1582no—
653C2×C4—1582no—
654C2×C4—1582no—
655C2×C4—1582no—
656C2×C4—1582no—
657C2×C4—1584no—
658C2×C4C2×D4×D7912yes—
659C2×C4C2×D4×D7912yes—
660C2×C4C2×D4×D7911yescharacteristic
661C2×C4#1457920812yes—
662C2×C4#1457920812yes—
663C2×C4C24×D7911yescharacteristic
664C8—22no—
665C8—22no—
666C8—1582no—
667C8—1582no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—84no—
672C22—794no—
673C22—1582no—
674C22—1588no—
675C22—1582no—
676C22#1909913312yes—
677C22#135×D7912yes—
678C22#1909936012yes—
679C22C22×D4×D7911yescharacteristic
680C4—22no—
681C4—22no—
682C4—42no—
683C4—42no—
684C4—42no—
685C4—3162no—
686C4—3162no—
687C4—3162no—
688C4—3162no—
689C4—1582no—
690C4—1582no—
691C4—1582no—
692C4#1909913312yes—
693C4C2×#1457920811yescharacteristic
694C4C2×#1457920811yescharacteristic
695C2—82no—
696C2—1584no—
697C2#2377456314yesdirect product factor
698C2C2×#1909913311yescharacteristic
699C2C2×#135×D7911yescharacteristic
700C2C2×#1909936011yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#488×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579132C22
hypercenterC2×#488D79
hypocenterC79C2×#3232
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
2. C2×#125×D79C2semidirect
3. #23774563C2direct (N × H)
4. C2×#19098965C2semidirect
5. C2×#19098962C2semidirect
6. C2×#19098917C2semidirect
7. C2×#19098897C2semidirect
9. C2×#19098892C2semidirect
11. C2×#19098872C2semidirect
12. C2×#19098868C2semidirect
13. C2×#19098865C2semidirect
14. C2×#19098861C2semidirect
15. C2×#19098614C2semidirect
16. C2×#488×C79C2semidirect
27. #125×D79C22semidirect
40. #19098965C22semidirect
41. #19098962C22semidirect
42. #19098917C22semidirect
43. #19098897C22semidirect
44. #19098892C22semidirect
47. #19098872C22semidirect
48. #19098868C22semidirect
49. #19098865C22semidirect
50. #19098861C22semidirect
51. #19098614C22semidirect
71. #488×C79C22semidirect
346. C2×C79#3232semidirect
357. C2×#488D79semidirect
367. C79C2×#3232semidirect
396. #488C2×D79semidirect
697. C2#23774563direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190990922
C2×#125×D792
#237745632
C2×#190989652
C2×#190989622
C2×#190989172
C2×#190988972
C2×#190988802
C2×#190988922
C2×#190988752
C2×#190988722
C2×#190988682
C2×#190988652
C2×#190988612
C2×#190986142
C2×#488×C792
C2×#323279