Finite Group Databasebeta

← #34299498

Subgroups — #34299498

Order 20224.

1000 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098725C211yesmaximal, characteristic
2C4×#14579140C211yesmaximal, characteristic, complemented
3#23764280C211yesmaximal, characteristic, complemented
4#23764270C211yesmaximal, characteristic, complemented
5#23764100C211yesmaximal, characteristic, complemented
6#23764093C211yesmaximal, characteristic, complemented
7#23764038C211yesmaximal, characteristic, complemented
8#23764024C211yesmaximal, characteristic, complemented
9#23763758C211yesmaximal, characteristic, complemented
10#23763744C211yesmaximal, characteristic, complemented
11#23763712C211yesmaximal, characteristic, complemented
12#23763599C211yesmaximal, characteristic, complemented
13#23763340C211yesmaximal, characteristic
14#23763162C211yesmaximal, characteristic, complemented
15C79×#2297C211yesmaximal, characteristic
16C22×#11929614C2211yescharacteristic
17C22×#11929612C2211yescharacteristic
18C2×#14579140C2211yescharacteristic
19C2×C4×Dic158C2211yescharacteristic
20#19098725C418yescomplemented
21C2×#14579094C2211yescharacteristic
22C2×#14579092C2211yescharacteristic
23C2×#14579085C2211yescharacteristic
24C2×#14579085C2211yescharacteristic
25C2×#14579085C2211yescharacteristic
26C2×#14579084C2211yescharacteristic
27C2×#14579084C2211yescharacteristic
28C2×#14579082C2211yescharacteristic
29C2×#14579082C2211yescharacteristic
30C2×#14579082C2211yescharacteristic
31C2×C22⋊(C79⋊C8)C2211yescharacteristic
32C2×C22⋊(C79⋊C8)C2211yescharacteristic
33C2×#14579072C2211yescharacteristic
34C2×#14579072C2211yescharacteristic
35#19098469C2211yescharacteristic
36#19098461C2211yescharacteristic
37#19098447—21no—
38#19098436—21no—
39#19098423C2211yescharacteristic
40C4×Dic79⋊C4—21no—
41C4×C4⋊Dic79C2211yescharacteristic
42C4×C22⋊Dic79—21no—
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098318C2211yescharacteristic
48#19098318C2211yescharacteristic
49C22×#41×C79C2211yescharacteristic
50C2×#117×C79C2211yescharacteristic
51C22×C42×C79C2211yescharacteristic
52#391×C79C2211yescharacteristic
53#391×C79C2211yescharacteristic
54#390×C79C2211yescharacteristic
55#390×C79C2211yescharacteristic
56#386×C79—21no—
57#386×C79—21no—
58C4×C22⋊C4×C79—21no—
59C4×C22⋊C4×C79—21no—
60C22×Dic158C2311yescharacteristic
61C2×#11929614—41no—
62C2×#11929614—41no—
63C2×#11929614C2×C414yescomplemented
64C2×#11929612—41no—
65C2×#11929612—41no—
66C2×#11929612C2×C414yescomplemented
67C22×C79⋊C8C2311yescharacteristic
68C22×C79⋊C8C2311yescharacteristic
69C22×C79⋊C8C2311yescharacteristic
70C22×C79⋊C8C2311yescharacteristic
71#14579140—22no—
72#14579140C2×C414yes—
73C4×Dic158—41no—
74C4×Dic158—41no—
75C2×C4⋊Dic79C2311yescharacteristic
76C2×C4⋊Dic79C2311yescharacteristic
77C2×C4⋊Dic79C2311yescharacteristic
78C2×Dic79⋊C4—21no—
79C2×Dic79⋊C4—21no—
80C2×Dic79⋊C4—21no—
81C2×C22⋊Dic79—21no—
82C2×C22⋊Dic79—21no—
83C2×C4×Dic79—21no—
84C2×C4×Dic79—21no—
85#14579094—41no—
86#14579092—41no—
87#14579085—41no—
88#14579085—41no—
89#14579085C2×C414yescomplemented
90#14579084—41no—
91#14579084—41no—
92#14579082—41no—
93#14579082—41no—
94#14579082C2×C414yescomplemented
95C22⋊(C79⋊C8)—22no—
96C22⋊(C79⋊C8)C2×C414yes—
97#14579072—41no—
98#14579072—41no—
99C79⋊#95—21no—
100C79⋊#95—21no—
101C79⋊#95—21no—
102C79⋊#95—21no—
103C79⋊#95—21no—
104C2×#41×C79—22no—
105C2×#41×C79—41no—
106C2×#41×C79—41no—
107C2×#41×C79—41no—
108C2×#41×C79—41no—
109C2×#41×C79C2×C414yes—
110C22×Q8×C79C2311yescharacteristic
111C22×D4×C79—21no—
112C22×D4×C79C2311yescharacteristic
113C23×C4×C79—21no—
114C23×C4×C79D411yescharacteristic
115C23×C4×C79D411yescharacteristic
116C23×C4×C79C2311yescharacteristic
117#117×C79—41no—
118#117×C79—41no—
119C2×C4⋊C4×C79C2311yescharacteristic
120C2×C4⋊C4×C79C2311yescharacteristic
121C2×C22⋊C4×C79—21no—
122C2×C22⋊C4×C79—21no—
123C2×C22⋊C4×C79—21no—
124C2×C22⋊C4×C79—21no—
125C2×C22⋊C4×C79—21no—
126C2×C42×C79—21no—
127C2×C42×C79—41no—
128C2×C42×C79—41no—
129C2×C42×C79D411yescharacteristic
130C2×C42×C79D411yescharacteristic
131C2×C42×C79C2311yescharacteristic
132C2×C42×C79C2311yescharacteristic
133#95×C79—21no—
134#95×C79—21no—
135#95×C79—21no—
136#95×C79—21no—
137C2×Dic158—21no—
138C2×Dic158—21no—
139C2×Dic158—21no—
140C2×Dic158—21no—
141C2×Dic158—21no—
142C2×Dic158C22×C412yes—
143C22×Dic79—21no—
144C22×Dic79—21no—
145C22×Dic79—21no—
146C22×Dic79—21no—
147#11929614—44no—
148#11929612—44no—
149C2×C79⋊C8—21no—
150C2×C79⋊C8—21no—
151C2×C79⋊C8—21no—
152C2×C79⋊C8—21no—
153C2×C79⋊C8—21no—
154C2×C79⋊C8—21no—
155C2×C79⋊C8—21no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8—21no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8C22×C412yes—
160C2×C79⋊C8C22×C412yes—
161C4⋊Dic79—21no—
162C4⋊Dic79—21no—
163C4⋊Dic79—21no—
164C4⋊Dic79—21no—
165C4⋊Dic79—21no—
166C4⋊Dic79C22×C412yes—
167Dic79⋊C4—24no—
168Dic79⋊C4—42no—
169Dic79⋊C4—42no—
170C22⋊Dic79—24no—
171C22⋊Dic79—42no—
172C4×Dic79—42no—
173C4×Dic79—42no—
174C24×C79—21no—
175C24×C79C2×D411yescharacteristic
176#41×C79—44no—
177#41×C79—44no—
178#41×C79—44no—
179#41×C79—44no—
180C2×Q8×C79—21no—
181C2×Q8×C79—21no—
182C2×Q8×C79—21no—
183C2×Q8×C79—21no—
184C2×Q8×C79—21no—
185C2×Q8×C79C22×C412yes—
186C2×D4×C79—24no—
187C2×D4×C79—21no—
188C2×D4×C79—21no—
189C2×D4×C79—21no—
190C2×D4×C79—21no—
191C2×D4×C79—21no—
192C2×D4×C79—42no—
193C2×D4×C79—42no—
194C2×D4×C79C22×C412yes—
195C22×C4×C79—21no—
196C22×C4×C79—21no—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—21no—
200C22×C4×C79—24no—
201C22×C4×C79—22no—
202C22×C4×C79—21no—
203C22×C4×C79—21no—
204C22×C4×C79—41no—
205C22×C4×C79—41no—
206C22×C4×C79—41no—
207C22×C4×C79—41no—
208C22×C4×C79—41no—
209C22×C4×C79—42no—
210C22×C4×C79—42no—
211C22×C4×C79C22×C412yes—
212C22×C4×C79C2×D411yescharacteristic
213C22×C4×C79C2×D411yescharacteristic
214C22×C4×C79C2×D411yescharacteristic
215C22×C4×C79C2×D411yescharacteristic
216C22×C4×C79C2×D411yescharacteristic
217C22×C4×C79#4112yes—
218C22×C4×C79C2411yescharacteristic
219C4⋊C4×C79—21no—
220C4⋊C4×C79—21no—
221C4⋊C4×C79—21no—
222C4⋊C4×C79—21no—
223C22⋊C4×C79—42no—
224C22⋊C4×C79—42no—
225C22⋊C4×C79—42no—
226C22⋊C4×C79—42no—
227C22⋊C4×C79—42no—
228C42×C79—21no—
229C42×C79—21no—
230C42×C79—21no—
231C42×C79—21no—
232C42×C79—41no—
233C42×C79—41no—
234C42×C79—42no—
235C23×C79—21no—
236C23×C79—21no—
237C23×C79—21no—
238C23×C79—21no—
239C23×C79—21no—
240C23×C79—21no—
241C23×C79—22no—
242C23×C79—41no—
243C23×C79—41no—
244C23×C79—41no—
245C23×C79—41no—
246C23×C79—41no—
247C23×C79—41no—
248C23×C79C4×D412yes—
249C23×C79C22×D411yescharacteristic
250Q8×C79—22no—
251Q8×C79—22no—
252Q8×C79—41no—
253Q8×C79—41no—
254D4×C79—22no—
255D4×C79—22no—
256D4×C79—48no—
257D4×C79—41no—
258D4×C79—41no—
259C2×C4×C79—21no—
260C2×C4×C79—21no—
261C2×C4×C79—21no—
262C2×C4×C79—21no—
263C2×C4×C79—22no—
264C2×C4×C79—22no—
265C2×C4×C79—22no—
266C2×C4×C79—22no—
267C2×C4×C79—22no—
268C2×C4×C79—21no—
269C2×C4×C79—21no—
270C2×C4×C79—21no—
271C2×C4×C79—21no—
272C2×C4×C79—21no—
273C2×C4×C79—21no—
274C2×C4×C79—21no—
275C2×C4×C79—21no—
276C2×C4×C79—21no—
277C2×C4×C79—44no—
278C2×C4×C79—48no—
279C2×C4×C79—44no—
280C2×C4×C79—41no—
281C2×C4×C79—41no—
282C2×C4×C79—41no—
283C2×C4×C79—41no—
284C2×C4×C79—41no—
285C2×C4×C79—41no—
286C2×C4×C79—41no—
287C2×C4×C79—41no—
288C2×C4×C79C4×D412yes—
289C2×C4×C79#13712yes—
290C2×C4×C79C23×C411yescharacteristic
291C2×C4×C79C2×#4111yescharacteristic
292C2×C4×C79H(5,𝔽2)11yescharacteristic
293C2×C4×C79H(5,𝔽2)11yescharacteristic
294C2×C4×C79H(5,𝔽2)11yescharacteristic
295C2×C4×C79H(5,𝔽2)11yescharacteristic
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—41no—
299C2×Dic79—41no—
300C2×Dic79—41no—
301C2×Dic79—41no—
302C2×Dic79—41no—
303C2×Dic79—41no—
304C2×Dic79—41no—
305C2×Dic79—41no—
306C2×Dic79—41no—
307C2×Dic79—41no—
308Dic158—22no—
309Dic158—22no—
310Dic158—41no—
311Dic158—41no—
312C79⋊C8—22no—
313C79⋊C8—22no—
314C79⋊C8—41no—
315C79⋊C8—41no—
316C22×C79—22no—
317C22×C79—22no—
318C22×C79—22no—
319C22×C79—41no—
320C22×C79—41no—
321C22×C79—41no—
322C22×C79—41no—
323C22×C79—42no—
324C22×C79—42no—
325C22×C79—42no—
326C22×C79—81no—
327C22×C79—81no—
328C22×C79—81no—
329C22×C79—81no—
330C22×C79C2×C4×D411yescharacteristic
331C22×C79#53411yescharacteristic
332C22×C79#53511yescharacteristic
333C22×C79C2×#13711yescharacteristic
334C22×C79#57511yescharacteristic
335C22×C79#57511yescharacteristic
336C22×C79#57511yescharacteristic
337C4×C79—22no—
338C4×C79—22no—
339C4×C79—42no—
340C4×C79—41no—
341C4×C79—41no—
342C4×C79—41no—
343C4×C79—81no—
344C4×C79—81no—
345C4×C79#51811yescharacteristic
346C4×C79#51811yescharacteristic
347C4×C79#53811yescharacteristic
348C4×C79#53811yescharacteristic
349Dic79—42no—
350Dic79—42no—
351Dic79—81no—
352Dic79—81no—
353#22048—791nomaximal, Sylow
354C2×C79—42no—
355C2×C79—82no—
356C2×C79#232111yescharacteristic
357C2×C79#294311yescharacteristic
358C2×C79C4×#13711yescharacteristic
359C2×C79#319611yescharacteristic
360C2×C79#319711yescharacteristic
361C2×C79#321611yescharacteristic
362C2×C79#321911yescharacteristic
363C2×#452—791no—
364C4×C22⋊Q8—791no—
365#2297D7911yescharacteristic
366#1973—791no—
367#1971—791no—
368#1936—791no—
369#1935—791no—
370#1928—791no—
371#1926—791no—
372#1880—791no—
373#1878—791no—
374#1873—791no—
375#1854—791no—
376#1788—791no—
377#1749—791no—
378C79#2204811yescharacteristic, complemented, Sylow
379C22×#41C2×D7911yescharacteristic
380C22×Q16—791no—
381C22×SD16—791no—
382C2×C22⋊Q8—791no—
383C2×C4×Q8—791no—
384C2×#117C2×D7911yescharacteristic
385C22×C42C2×D7911yescharacteristic
386#452—798no—
387C2×#107—791no—
388C2×#106—791no—
389C2×#103—791no—
390C2×#103—791no—
391C2×#103—791no—
392C2×#103—791no—
393C2×#103—791no—
394C2×#102—791no—
395C2×#102—791no—
396C2×#102—791no—
397C2×C22⋊C8—791no—
398C2×C22⋊C8—791no—
399C2×#97—791no—
400C2×#97—791no—
401#391—791no—
402#391C2×D7911yescharacteristic
403#391C2×D7911yescharacteristic
404#390C2×D7911yescharacteristic
405#390C2×D7911yescharacteristic
406#389—791no—
407#387—1581no—
408#386—21no—
409#386—21no—
410#385—1581no—
411#380—791no—
412C4×C4⋊C4—791no—
413C4×C4⋊C4—1581no—
414C4×C22⋊C4—21no—
415C4×C22⋊C4—21no—
416C4×C22⋊C4—1581no—
417#340—791no—
418#340—791no—
419#340—791no—
420#340—791no—
421#336—791no—
422#336—791no—
423C2×#41—22no—
424C2×#41—41no—
425C2×#41—41no—
426C2×#41—41no—
427C2×#41—41no—
428C2×#41C4×D7914yes—
429C22×Q8—791no—
430C22×Q8C22×D7911yescharacteristic
431C22×D4—21no—
432C22×D4C22×D7911yescharacteristic
433C23×C4—21no—
434C23×C4C22⋊D7911yescharacteristic
435C23×C4C22⋊D7911yescharacteristic
436C23×C4C22×D7911yescharacteristic
437C2×Q16—3161no—
438C2×Q16—3161no—
439C2×Q16—794no—
440C2×SD16—3161no—
441C2×SD16—3161no—
442C2×SD16—794no—
443C22×C8—791no—
444C22×C8—791no—
445C22×C8—791no—
446C22×C8—791no—
447C22⋊Q8—794no—
448C22⋊Q8—1582no—
449C4×Q8—3161no—
450C4×Q8—3161no—
451#117—41no—
452#117—41no—
453C2×C4⋊C4—791no—
454C2×C4⋊C4—791no—
455C2×C4⋊C4—791no—
456C2×C4⋊C4—1581no—
457C2×C4⋊C4—1581no—
458C2×C4⋊C4—1581no—
459C2×C4⋊C4C22×D7911yescharacteristic
460C2×C4⋊C4C22×D7911yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—1581no—
467C2×C22⋊C4—1581no—
468C2×C42—21no—
469C2×C42—41no—
470C2×C42—41no—
471C2×C42—1581no—
472C2×C42—1581no—
473C2×C42C22⋊D7911yescharacteristic
474C2×C42C22⋊D7911yescharacteristic
475C2×C42C22×D7911yescharacteristic
476C2×C42C22×D7911yescharacteristic
477#107—3161no—
478#106—3161no—
479#103—3161no—
480#103—3161no—
481#103—3161no—
482#103—3161no—
483#103—794no—
484#102—3161no—
485#102—3161no—
486#102—794no—
487C22⋊C8—794no—
488C22⋊C8—1582no—
489#97—3161no—
490#97—3161no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—1581no—
496#95—1581no—
497#95—1581no—
498#95—1581no—
499#95—1581no—
500C24—21no—
501C24C2×C22⋊D7911yescharacteristic
502#41—44no—
503#41—44no—
504#41—44no—
505#41—44no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—792no—
512C2×Q8—1581no—
513C2×Q8—1581no—
514C2×Q8—1581no—
515C2×Q8—1581no—
516C2×Q8—1581no—
517C2×Q8C2×C4×D7912yes—
518C2×D4—24no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4C2×C4×D7912yes—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—1581no—
544C22×C4—1581no—
545C22×C4—1581no—
546C22×C4—1581no—
547C22×C4C2×C4×D7912yes—
548C22×C4C2×C22⋊D7911yescharacteristic
549C22×C4C2×C22⋊D7911yescharacteristic
550C22×C4C2×C22⋊D7911yescharacteristic
551C22×C4C2×C22⋊D7911yescharacteristic
552C22×C4C2×C22⋊D7911yescharacteristic
553C22×C4#1192962412yes—
554C22×C4C23×D7911yescharacteristic
555Q16—3164no—
556SD16—3164no—
557C2×C8—792no—
558C2×C8—792no—
559C2×C8—1581no—
560C2×C8—1581no—
561C2×C8—1581no—
562C2×C8—1581no—
563C2×C8—1581no—
564C2×C8—1581no—
565C2×C8—1581no—
566C2×C8—1581no—
567C2×C8—1581no—
568C2×C8—1581no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—3162no—
574C4⋊C4—3162no—
575C4⋊C4—792no—
576C4⋊C4—1581no—
577C4⋊C4—1581no—
578C4⋊C4—1581no—
579C4⋊C4—1581no—
580C4⋊C4—1581no—
581C4⋊C4—1584no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—3162no—
588C22⋊C4—1584no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—41no—
594C42—41no—
595C42—42no—
596C42—3162no—
597C42—3162no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23C4×C22⋊D7912yes—
612C23C22×C22⋊D7911yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—41no—
616Q8—41no—
617Q8—3161no—
618Q8—3161no—
619Q8—1582no—
620Q8—1582no—
621D4—22no—
622D4—22no—
623D4—48no—
624D4—41no—
625D4—41no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—44no—
645C2×C4—48no—
646C2×C4—44no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—3161no—
656C2×C4—3161no—
657C2×C4—3161no—
658C2×C4—3161no—
659C2×C4—3161no—
660C2×C4—3161no—
661C2×C4—3161no—
662C2×C4—3161no—
663C2×C4—3161no—
664C2×C4—3161no—
665C2×C4—1582no—
666C2×C4—1582no—
667C2×C4C4×C22⋊D7912yes—
668C2×C4#1457919112yes—
669C2×C4C22×C4×D7911yescharacteristic
670C2×C4C2×#1192962411yescharacteristic
671C2×C4#1457920611yescharacteristic
672C2×C4#1457920611yescharacteristic
673C2×C4#1457920611yescharacteristic
674C2×C4#1457920611yescharacteristic
675C8—3161no—
676C8—3161no—
677C8—1582no—
678C8—1582no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22C2×C4×C22⋊D7911yescharacteristic
694C22#1909912211yescharacteristic
695C22#1909913011yescharacteristic
696C22C2×#1457919111yescharacteristic
697C22#1909936111yescharacteristic
698C22#1909936111yescharacteristic
699C22#1909936111yescharacteristic
700C4—22no—
701C4—22no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—42no—
706C4—81no—
707C4—81no—
708C4—3162no—
709C4—3162no—
710C4—6321no—
711C4—6321no—
712C4#1909903611yescharacteristic
713C4#1909903611yescharacteristic
714C4#1909915111yescharacteristic
715C4#1909915111yescharacteristic
716C2—42no—
717C2—82no—
718C2#2376605811yescharacteristic
719C2#2377219811yescharacteristic
720C2C4×#1457919111yescharacteristic
721C2#2377422611yescharacteristic
722C2#2377423711yescharacteristic
723C2#2377441111yescharacteristic
724C2#2377443711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2297C2
socleC23×C79C22×D4
prime radicalC22×#41×C79C22
cosocleC22×C4×C79C24
hypercenter#2297D79
hypocenterC79#22048
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C4×#14579140C2semidirect
3. #23764280C2semidirect
4. #23764270C2semidirect
5. #23764100C2semidirect
6. #23764093C2semidirect
7. #23764038C2semidirect
8. #23764024C2semidirect
9. #23763758C2semidirect
10. #23763744C2semidirect
11. #23763712C2semidirect
12. #23763599C2semidirect
14. #23763162C2semidirect
20. #19098725C4semidirect
63. C2×#11929614C2×C4semidirect
66. C2×#11929612C2×C4semidirect
89. #14579085C2×C4semidirect
94. #14579082C2×C4semidirect
378. C79#22048semidirect

Maximal subgroups

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

subgroupindex
C2×#190987252
C4×#145791402
#237642802
#237642702
#237641002
#237640932
#237640382
#237640242
#237637582
#237637442
#237637122
#237635992
#237633402
#237631622
C79×#22972
#2204879