Finite Group Databasebeta

← #34308552

Subgroups — #34308552

Order 20224.

1118 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098725C211yesmaximal, characteristic
2C2×#19098663C211yesmaximal, characteristic, complemented
3C2×#19098559C211yesmaximal, characteristic
4#23766425C211yesmaximal, characteristic, complemented
5#23764270C211yesmaximal, characteristic, complemented
6#23764093C211yesmaximal, characteristic, complemented
7#23764038C211yesmaximal, characteristic, complemented
8#23763821C211yesmaximal, characteristic, complemented
9#23763744C211yesmaximal, characteristic, complemented
10#23763734C211yesmaximal, characteristic, complemented
11#23763661C211yesmaximal, characteristic, complemented
12#23763597C211yesmaximal, characteristic, complemented
13#23763225C211yesmaximal, characteristic, complemented
14#23763178C211yesmaximal, characteristic, complemented
15C79×#2339C211yesmaximal, characteristic
16C22×#11929614C2211yescharacteristic
17C22×#11929612C2211yescharacteristic
18C23×C79⋊C8C2211yescharacteristic
19C2×#14579140C2211yescharacteristic
20C2×C4×Dic158C2211yescharacteristic
21C2×#14579120C2211yescharacteristic
22#19098725C418yescomplemented
23#19098663—24no—
24C2×#14579094C2211yescharacteristic
25C2×#14579092C2211yescharacteristic
26#19098559—24no—
27C2×#14579085C2211yescharacteristic
28C2×#14579085C2211yescharacteristic
29C2×#14579085C2211yescharacteristic
30C2×#14579084C2211yescharacteristic
31C2×#14579084C2211yescharacteristic
32C2×#14579082C2211yescharacteristic
33C2×#14579082C2211yescharacteristic
34C2×#14579082C2211yescharacteristic
35C2×C22⋊(C79⋊C8)C2211yescharacteristic
36C2×#14579072C2211yescharacteristic
37C2×#14579072C2211yescharacteristic
38#19098469C2211yescharacteristic
39#19098461C2211yescharacteristic
40#19098457—21no—
41#19098451—21no—
42#19098445—21no—
43C4×C4⋊Dic79C2211yescharacteristic
44#19098414—21no—
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098318C2211yescharacteristic
50#19098318C2211yescharacteristic
51C22×#41×C79C2211yescharacteristic
52C2×C4×D4×C79C2211yescharacteristic
53C2×C4×D4×C79C2211yescharacteristic
54#391×C79C2211yescharacteristic
55#391×C79C2211yescharacteristic
56#386×C79—21no—
57#386×C79—21no—
58#381×C79—21no—
59#380×C79C2211yescharacteristic
60C4×C22⋊C4×C79C2211yescharacteristic
61C2×#95×C79—21no—
62C22×Dic158C2311yescharacteristic
63C2×#11929614—41no—
64C2×#11929614—41no—
65C2×#11929614C2×C414yescomplemented
66C2×#11929612—22no—
67C2×#11929612—22no—
68C2×#11929612C2×C414yes—
69C22×C79⋊C8—22no—
70C22×C79⋊C8—22no—
71C22×C79⋊C8—41no—
72C22×C79⋊C8C2311yescharacteristic
73C22×C79⋊C8C2311yescharacteristic
74C22×C79⋊C8C2311yescharacteristic
75C22×C79⋊C8C2311yescharacteristic
76#14579140—22no—
77#14579140C2×C414yescomplemented
78C4×Dic158—22no—
79C4×Dic158—41no—
80#14579120—22no—
81#14579120—41no—
82C2×C4⋊Dic79C2311yescharacteristic
83C2×C4⋊Dic79C2311yescharacteristic
84C2×C4⋊Dic79C2311yescharacteristic
85C2×Dic79⋊C4—21no—
86C2×Dic79⋊C4—21no—
87C2×Dic79⋊C4—21no—
88C2×C22⋊Dic79—21no—
89C2×C22⋊Dic79—21no—
90C2×C4×Dic79—21no—
91C2×C4×Dic79—21no—
92C2×C4×Dic79—21no—
93#14579094—22no—
94#14579092—41no—
95#14579085—22no—
96#14579085—22no—
97#14579085C2×C414yescomplemented
98#14579084—22no—
99#14579084—41no—
100#14579082—22no—
101#14579082C2×C414yes—
102#14579082D414yes—
103C22⋊(C79⋊C8)C2×C414yescomplemented
104#14579072—22no—
105#14579072—41no—
106C79⋊#95—21no—
107C79⋊#95—21no—
108C79⋊#95—21no—
109C79⋊#95—21no—
110C2×#41×C79—22no—
111C2×#41×C79—22no—
112C2×#41×C79—22no—
113C2×#41×C79—41no—
114C2×#41×C79—41no—
115C2×#41×C79C2×C414yes—
116C22×Q8×C79C2311yescharacteristic
117C22×D4×C79—21no—
118C22×D4×C79C2311yescharacteristic
119C23×C4×C79—21no—
120C23×C4×C79—21no—
121C23×C4×C79—21no—
122C23×C4×C79C2311yescharacteristic
123C4×D4×C79—22no—
124C4×D4×C79—22no—
125C4×D4×C79—41no—
126C4×D4×C79—41no—
127C2×C4⋊C4×C79C2311yescharacteristic
128C2×C4⋊C4×C79C2311yescharacteristic
129C2×C22⋊C4×C79—21no—
130C2×C22⋊C4×C79—21no—
131C2×C22⋊C4×C79—21no—
132C2×C22⋊C4×C79D411yescharacteristic
133C2×C22⋊C4×C79D411yescharacteristic
134C2×C42×C79C2311yescharacteristic
135C2×C42×C79C2311yescharacteristic
136#95×C79—21no—
137#95×C79—21no—
138#95×C79—21no—
139#95×C79—21no—
140#95×C79—21no—
141#95×C79D411yescharacteristic
142#95×C79D411yescharacteristic
143C2×Dic158—21no—
144C2×Dic158—21no—
145C2×Dic158—21no—
146C2×Dic158—21no—
147C2×Dic158—21no—
148C2×Dic158C22×C412yes—
149C22×Dic79—21no—
150C22×Dic79—21no—
151C22×Dic79—21no—
152C22×Dic79—21no—
153#11929614—44no—
154#11929612—28no—
155C2×C79⋊C8—21no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8—21no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8—21no—
160C2×C79⋊C8—21no—
161C2×C79⋊C8—21no—
162C2×C79⋊C8—21no—
163C2×C79⋊C8—21no—
164C2×C79⋊C8—44no—
165C2×C79⋊C8C22×C412yes—
166C2×C79⋊C8C22×C412yes—
167C2×C79⋊C8C2×D412yes—
168C4⋊Dic79—21no—
169C4⋊Dic79—21no—
170C4⋊Dic79—21no—
171C4⋊Dic79—21no—
172C4⋊Dic79C22×C412yes—
173C4⋊Dic79C2×D412yes—
174Dic79⋊C4—24no—
175Dic79⋊C4—42no—
176Dic79⋊C4—42no—
177C22⋊Dic79—24no—
178C22⋊Dic79—42no—
179C4×Dic79—42no—
180C4×Dic79—42no—
181C4×Dic79—42no—
182C24×C79—21no—
183C24×C79C2×D411yescharacteristic
184#41×C79—28no—
185#41×C79—44no—
186#41×C79—44no—
187#41×C79—44no—
188C2×Q8×C79—21no—
189C2×Q8×C79—21no—
190C2×Q8×C79—21no—
191C2×Q8×C79—21no—
192C2×Q8×C79—21no—
193C2×Q8×C79C22×C412yes—
194C2×D4×C79—24no—
195C2×D4×C79—21no—
196C2×D4×C79—21no—
197C2×D4×C79—21no—
198C2×D4×C79—42no—
199C2×D4×C79—42no—
200C2×D4×C79C22×C412yes—
201C2×D4×C79C2×D412yes—
202C2×D4×C79#4112yes—
203C22×C4×C79—21no—
204C22×C4×C79—21no—
205C22×C4×C79—21no—
206C22×C4×C79—21no—
207C22×C4×C79—21no—
208C22×C4×C79—24no—
209C22×C4×C79—21no—
210C22×C4×C79—21no—
211C22×C4×C79—42no—
212C22×C4×C79—42no—
213C22×C4×C79—42no—
214C22×C4×C79—42no—
215C22×C4×C79—42no—
216C22×C4×C79—42no—
217C22×C4×C79—81no—
218C22×C4×C79—81no—
219C22×C4×C79C22×C412yes—
220C22×C4×C79C2×D411yescharacteristic
221C22×C4×C79C2×D411yescharacteristic
222C22×C4×C79C2×D411yescharacteristic
223C22×C4×C79C2×D411yescharacteristic
224C22×C4×C79C2×D411yescharacteristic
225C22×C4×C79#4112yes—
226C22×C4×C79C2411yescharacteristic
227C4⋊C4×C79—21no—
228C4⋊C4×C79—21no—
229C4⋊C4×C79—21no—
230C4⋊C4×C79—21no—
231C22⋊C4×C79—41no—
232C22⋊C4×C79—41no—
233C22⋊C4×C79—42no—
234C22⋊C4×C79—42no—
235C22⋊C4×C79—81no—
236C42×C79—21no—
237C42×C79—21no—
238C42×C79—21no—
239C42×C79—21no—
240C23×C79—22no—
241C23×C79—21no—
242C23×C79—22no—
243C23×C79—22no—
244C23×C79—21no—
245C23×C79—21no—
246C23×C79—21no—
247C23×C79—21no—
248C23×C79—21no—
249C23×C79—41no—
250C23×C79—41no—
251C23×C79—41no—
252C23×C79—41no—
253C23×C79C4×D412yes—
254C23×C79C22×D411yescharacteristic
255Q8×C79—22no—
256Q8×C79—22no—
257Q8×C79—41no—
258Q8×C79—41no—
259D4×C79—22no—
260D4×C79—22no—
261D4×C79—22no—
262D4×C79—48no—
263D4×C79C4×D414yes—
264C2×C4×C79—21no—
265C2×C4×C79—21no—
266C2×C4×C79—22no—
267C2×C4×C79—22no—
268C2×C4×C79—22no—
269C2×C4×C79—22no—
270C2×C4×C79—22no—
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—21no—
278C2×C4×C79—21no—
279C2×C4×C79—21no—
280C2×C4×C79—21no—
281C2×C4×C79—21no—
282C2×C4×C79—21no—
283C2×C4×C79—48no—
284C2×C4×C79—41no—
285C2×C4×C79—41no—
286C2×C4×C79—41no—
287C2×C4×C79—41no—
288C2×C4×C79—41no—
289C2×C4×C79—41no—
290C2×C4×C79—41no—
291C2×C4×C79—41no—
292C2×C4×C79—84no—
293C2×C4×C79—84no—
294C2×C4×C79C4×D412yes—
295C2×C4×C79C23×C411yescharacteristic
296C2×C4×C79C22×D411yescharacteristic
297C2×C4×C79C2×#4111yescharacteristic
298C2×C4×C79C2×#4111yescharacteristic
299C2×C4×C79H(5,𝔽2)11yescharacteristic
300C2×C4×C79H(5,𝔽2)11yescharacteristic
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—41no—
305C2×Dic79—41no—
306C2×Dic79—41no—
307C2×Dic79—41no—
308C2×Dic79—41no—
309C2×Dic79—41no—
310C2×Dic79—41no—
311C2×Dic79—41no—
312C2×Dic79—41no—
313Dic158—22no—
314Dic158—22no—
315Dic158—41no—
316Dic158—41no—
317C79⋊C8—22no—
318C79⋊C8—22no—
319C79⋊C8—22no—
320C79⋊C8—41no—
321C22×C79—22no—
322C22×C79—24no—
323C22×C79—22no—
324C22×C79—22no—
325C22×C79—42no—
326C22×C79—42no—
327C22×C79—42no—
328C22×C79—41no—
329C22×C79—41no—
330C22×C79—42no—
331C22×C79—42no—
332C22×C79—41no—
333C22×C79—41no—
334C22×C79—42no—
335C22×C79C2×C4×D411yescharacteristic
336C22×C79D4211yescharacteristic
337C22×C79#54611yescharacteristic
338C22×C79#57511yescharacteristic
339C22×C79#57511yescharacteristic
340C22×C79#57711yescharacteristic
341C22×C79#57811yescharacteristic
342C4×C79—22no—
343C4×C79—42no—
344C4×C79—41no—
345C4×C79—41no—
346C4×C79—41no—
347C4×C79—41no—
348C4×C79—81no—
349C4×C79—81no—
350C4×C79C2×C4×D411yescharacteristic
351C4×C79#51811yescharacteristic
352C4×C79#54611yescharacteristic
353C4×C79#55111yescharacteristic
354Dic79—42no—
355Dic79—42no—
356Dic79—42no—
357Dic79—81no—
358#22856—791nomaximal, Sylow
359C2×C79—42no—
360C2×C79—44no—
361C2×C79#235811yescharacteristic
362C2×C79#294311yescharacteristic
363C2×C79#294711yescharacteristic
364C2×C79#326711yescharacteristic
365C2×C79#326911yescharacteristic
366C2×C79#331111yescharacteristic
367C2×C79#331511yescharacteristic
368C2×#452—791no—
369C2×#440—791no—
370C2×#416—791no—
371#2362—791no—
372#2339D7911yescharacteristic
373#1971—791no—
374#1935—791no—
375#1928—791no—
376#1892—791no—
377#1878—791no—
378#1877—791no—
379#1864—791no—
380#1854—791no—
381#1762—791no—
382#1752—791no—
383C79#2285611yescharacteristic, complemented, Sylow
384C22×#41C2×D7911yescharacteristic
385C22×Q16—791no—
386C22×SD16—791no—
387C23×C8—791no—
388C2×C22⋊Q8—791no—
389C2×C4×Q8—791no—
390C2×C4×D4C2×D7911yescharacteristic
391C2×C4×D4C2×D7911yescharacteristic
392C2×#117—791no—
393#452—798no—
394#440—1584no—
395C2×#107—791no—
396C2×#106—791no—
397#416—1584no—
398C2×#103—791no—
399C2×#103—791no—
400C2×#103—791no—
401C2×#103—791no—
402C2×#103—791no—
403C2×#102—791no—
404C2×#102—791no—
405C2×#102—791no—
406C2×C22⋊C8—791no—
407C2×#97—791no—
408C2×#97—791no—
409#391—791no—
410#391C2×D7911yescharacteristic
411#391C2×D7911yescharacteristic
412#389—791no—
413#388—1581no—
414#388—1581no—
415#387—1581no—
416#386—21no—
417#386—21no—
418#381—21no—
419#380C2×D7911yescharacteristic
420C4×C4⋊C4—791no—
421C4×C4⋊C4—1581no—
422C4×C22⋊C4C2×D7911yescharacteristic
423C2×#95—21no—
424#340—791no—
425#340—791no—
426#340—791no—
427#340—791no—
428#336—791no—
429#336—791no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41C4×D7914yes—
436C22×Q8—791no—
437C22×Q8C22×D7911yescharacteristic
438C22×D4—21no—
439C22×D4C22×D7911yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—21no—
443C23×C4C22×D7911yescharacteristic
444C2×Q16—3161no—
445C2×Q16—3161no—
446C2×Q16—794no—
447C2×SD16—794no—
448C2×SD16—1582no—
449C2×SD16—1582no—
450C22×C8—3161no—
451C22×C8—791no—
452C22×C8—791no—
453C22×C8—791no—
454C22×C8—791no—
455C22×C8—1582no—
456C22×C8—1582no—
457C22⋊Q8—794no—
458C22⋊Q8—1582no—
459C4×Q8—3161no—
460C4×Q8—1582no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—41no—
464C4×D4—41no—
465#117—3161no—
466#117—1582no—
467C2×C4⋊C4—791no—
468C2×C4⋊C4—791no—
469C2×C4⋊C4—791no—
470C2×C4⋊C4—1581no—
471C2×C4⋊C4—1581no—
472C2×C4⋊C4—1581no—
473C2×C4⋊C4C22×D7911yescharacteristic
474C2×C4⋊C4C22×D7911yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—1581no—
479C2×C22⋊C4—1581no—
480C2×C22⋊C4C22⋊D7911yescharacteristic
481C2×C22⋊C4C22⋊D7911yescharacteristic
482C2×C42—1581no—
483C2×C42—1581no—
484C2×C42—1581no—
485C2×C42C22×D7911yescharacteristic
486C2×C42C22×D7911yescharacteristic
487#107—1582no—
488#106—3161no—
489#103—3161no—
490#103—794no—
491#103—1582no—
492#103—1582no—
493#103—1582no—
494#102—794no—
495#102—794no—
496#102—1582no—
497C22⋊C8—794no—
498#97—3161no—
499#97—1582no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—1581no—
506#95—1581no—
507#95—1581no—
508#95—1581no—
509#95C22⋊D7911yescharacteristic
510#95C22⋊D7911yescharacteristic
511C24—21no—
512C24C2×C22⋊D7911yescharacteristic
513#41—28no—
514#41—44no—
515#41—44no—
516#41—44no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—792no—
523C2×Q8—1581no—
524C2×Q8—1581no—
525C2×Q8—1581no—
526C2×Q8—1581no—
527C2×Q8—1581no—
528C2×Q8C2×C4×D7912yes—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4C2×C4×D7912yes—
536C2×D4D4×D7912yes—
537C2×D4#1192962312yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—24no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—1581no—
555C22×C4—1581no—
556C22×C4—1581no—
557C22×C4—1581no—
558C22×C4C2×C4×D7912yes—
559C22×C4C2×C22⋊D7911yescharacteristic
560C22×C4C2×C22⋊D7911yescharacteristic
561C22×C4C2×C22⋊D7911yescharacteristic
562C22×C4C2×C22⋊D7911yescharacteristic
563C22×C4C2×C22⋊D7911yescharacteristic
564C22×C4#1192962412yes—
565C22×C4C23×D7911yescharacteristic
566Q16—3164no—
567SD16—1588no—
568C2×C8—3164no—
569C2×C8—792no—
570C2×C8—792no—
571C2×C8—792no—
572C2×C8—1581no—
573C2×C8—1581no—
574C2×C8—1581no—
575C2×C8—1581no—
576C2×C8—1581no—
577C2×C8—1581no—
578C2×C8—1581no—
579C2×C8—1581no—
580C2×C8—1581no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—3162no—
586C4⋊C4—3162no—
587C4⋊C4—792no—
588C4⋊C4—792no—
589C4⋊C4—1581no—
590C4⋊C4—1581no—
591C4⋊C4—1581no—
592C4⋊C4—1581no—
593C4⋊C4—1584no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—81no—
599C22⋊C4—3162no—
600C22⋊C4—1584no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—3162no—
606C42—3162no—
607C42—3162no—
608C23—22no—
609C23—21no—
610C23—22no—
611C23—21no—
612C23—22no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23C4×C22⋊D7912yes—
622C23C22×C22⋊D7911yescharacteristic
623Q8—22no—
624Q8—22no—
625Q8—41no—
626Q8—41no—
627Q8—3161no—
628Q8—3161no—
629Q8—1582no—
630Q8—1582no—
631D4—22no—
632D4—22no—
633D4—22no—
634D4—48no—
635D4(C22⋊D79)⋊C414yes—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—48no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4—3161no—
667C2×C4—3161no—
668C2×C4—3161no—
669C2×C4—3161no—
670C2×C4—3161no—
671C2×C4—3161no—
672C2×C4—3161no—
673C2×C4—3161no—
674C2×C4—3161no—
675C2×C4—1582no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4C4×C22⋊D7912yes—
679C2×C4C22×C4×D7911yescharacteristic
680C2×C4C2×D4×D7911yescharacteristic
681C2×C4C2×#1192962311yescharacteristic
682C2×C4C2×#1192962411yescharacteristic
683C2×C4#1457920611yescharacteristic
684C2×C4#1457920611yescharacteristic
685C8—3161no—
686C8—1582no—
687C8—1582no—
688C8—1582no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—24no—
693C22—41no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—41no—
699C22—42no—
700C22—41no—
701C22—41no—
702C22—42no—
703C22C2×C4×C22⋊D7911yescharacteristic
704C22D4×C22⋊D7911yescharacteristic
705C22#1909920711yescharacteristic
706C22#1909936111yescharacteristic
707C22#1909936111yescharacteristic
708C22#1909937411yescharacteristic
709C22#1909937811yescharacteristic
710C4—22no—
711C4—41no—
712C4—42no—
713C4—41no—
714C4—41no—
715C4—41no—
716C4—81no—
717C4—81no—
718C4—3162no—
719C4—3162no—
720C4—3162no—
721C4—6321no—
722C4C2×(C22⋊D79)⋊C411yescharacteristic
723C4#1909903611yescharacteristic
724C4#1909920311yescharacteristic
725C4#1909923911yescharacteristic
726C2—42no—
727C2—44no—
728C2#2376637911yescharacteristic
729C2#2377219811yescharacteristic
730C2#2377223911yescharacteristic
731C2#2377492111yescharacteristic
732C2#2377495111yescharacteristic
733C2#2377543611yescharacteristic
734C2#2377549611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2339C2
socleC23×C79C22×D4
prime radicalC22×#41×C79C22
cosocleC22×C4×C79C24
hypercenter#2339D79
hypocenterC79#22856
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. C2×#19098663C2semidirect
4. #23766425C2semidirect
5. #23764270C2semidirect
6. #23764093C2semidirect
7. #23764038C2semidirect
8. #23763821C2semidirect
9. #23763744C2semidirect
10. #23763734C2semidirect
11. #23763661C2semidirect
12. #23763597C2semidirect
13. #23763225C2semidirect
14. #23763178C2semidirect
22. #19098725C4semidirect
65. C2×#11929614C2×C4semidirect
77. #14579140C2×C4semidirect
97. #14579085C2×C4semidirect
103. C22⋊(C79⋊C8)C2×C4semidirect
383. C79#22856semidirect

Maximal subgroups

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

subgroupindex
C2×#190987252
C2×#190986632
C2×#190985592
#237664252
#237642702
#237640932
#237640382
#237638212
#237637442
#237637342
#237636612
#237635972
#237632252
#237631782
C79×#23392
#2285679