Finite Group Databasebeta

← C2×#23773265 #35155865

Subgroups — C2×#23773265 #35155865

Order 20224.

2094 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099193C211yesmaximal, characteristic, complemented
2C2×#19099045C211yesmaximal, characteristic
3#23773265C2116yesmaximal, direct product factor
4C2×#19098868C211yesmaximal, characteristic, complemented
5C2×#19098848C211yesmaximal, characteristic, complemented
6C2×#19098846C211yesmaximal, characteristic, complemented
7C2×#19098866C211yesmaximal, characteristic, complemented
8C2×#19098860C211yesmaximal, characteristic, complemented
9C2×#19098854C211yesmaximal, characteristic, complemented
10C2×#19098852C211yesmaximal, characteristic, complemented
11C2×#19098604C211yesmaximal, characteristic, complemented
12C2×#106×D79C211yesmaximal, characteristic, complemented
13C2×#19098588C211yesmaximal, characteristic, complemented
14C2×#19098563C211yesmaximal, characteristic
15C2×#19098558C211yesmaximal, characteristic
16C2×#479×C79C211yesmaximal, characteristic, complemented
17C22×#11929625C2211yescharacteristic
18C22×#11929607C2211yescharacteristic
19C22×C8×D79C2211yescharacteristic
20#19099193—24no—
21#19099193C2218yescomplemented
22C2×#14579161C2211yescharacteristic
23C2×#14579160—21no—
24C2×#14579160C2211yescharacteristic
25C2×#14579152C2211yescharacteristic
26C2×#14579151—21no—
27C2×#14579141—21no—
28C2×#14579139—21no—
29#19099045—24no—
30#19099045C2218yes—
31C2×Q8×Dic79C2211yescharacteristic
32C2×C4×D316—21no—
33C2×C4×D316C2211yescharacteristic
34C2×#14579123—21no—
35C2×#14579123C2211yescharacteristic
36C2×#14579119C2211yescharacteristic
37C2×#14579118—21no—
38C2×#14579118C2211yescharacteristic
39C2×C4⋊C4×D79—21no—
40C2×C4⋊C4×D79C2211yescharacteristic
41C2×C4⋊C4×D79C2211yescharacteristic
42#19098868C2218yescomplemented
43#19098866C2218yescomplemented
44#19098860C2218yescomplemented
45#19098854C2218yescomplemented
46#19098852C2218yescomplemented
47#19098848C2218yescomplemented
48#19098846C2218yescomplemented
49#19098604C2218yescomplemented
50C2×#14579094C2211yescharacteristic
51C2×#14579093C2211yescharacteristic
52C2×#14579093C2211yescharacteristic
53C2×#14579092C2211yescharacteristic
54C2×#14579092C2211yescharacteristic
55C2×#14579092C2211yescharacteristic
56#106×D79C2218yescomplemented
57#19098588C2218yescomplemented
58C2×C4⋊(C79⋊C8)C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×Dic79⋊C8C2211yescharacteristic
61#19098563C2218yes—
62#19098558C2218yes—
63C2×#14579085C2211yescharacteristic
64C2×#14579085C2211yescharacteristic
65C2×#14579083C2211yescharacteristic
66C2×#14579083C2211yescharacteristic
67C2×#14579081C2211yescharacteristic
68C2×#14579081C2211yescharacteristic
69C2×#125×C79C2211yescharacteristic
70C2×C4×Q8×C79C2211yescharacteristic
71#479×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×C4⋊C8×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C2×#11929625—22no—
78C2×#11929625—24no—
79C2×#11929625Q818yescomplemented
80C2×#11929625C2314yes—
81C22×Dic158—21no—
82C22×Dic158—21no—
83C22×D316—21no—
84C22×D316C2311yescharacteristic
85C22×C4×D79—21no—
86C22×C4×D79—21no—
87C22×C4×D79—21no—
88C22×C4×D79—21no—
89C22×C4×D79—21no—
90C22×C4×D79C2311yescharacteristic
91C2×#11929607—24no—
92C2×#11929607C2314yes—
93C22×C79⋊C8C2311yescharacteristic
94C22×C79⋊C8C2311yescharacteristic
95C2×C8×D79—24no—
96C2×C8×D79C2314yes—
97#14579161—22no—
98#14579161C2314yes—
99#14579160—28no—
100#14579160—22no—
101#14579160C2314yes—
102#14579152—22no—
103#14579152C2314yes—
104#14579151—28no—
105#14579141—28no—
106#14579139—28no—
107Q8×Dic79—22no—
108Q8×Dic79C2314yes—
109C4×D316—22no—
110C4×D316—28no—
111C4×D316C2314yes—
112#14579123—28no—
113#14579123—22no—
114#14579123C2314yes—
115#14579119—22no—
116#14579119C2314yes—
117#14579118—28no—
118#14579118D414yes—
119#14579118C2314yes—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79—21no—
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×C4⋊Dic79C2311yescharacteristic
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4D411yescharacteristic
131C2×Dic79⋊C4D411yescharacteristic
132C4⋊C4×D79—22no—
133C4⋊C4×D79—22no—
134C4⋊C4×D79—28no—
135C4⋊C4×D79C2314yes—
136C4⋊C4×D79C2314yes—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4D411yescharacteristic
141C2×(C2×D79)⋊C4D411yescharacteristic
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79C2311yescharacteristic
145#14579094C2314yes—
146#14579093C2314yes—
147#14579093C2314yes—
148#14579092C2314yes—
149#14579092C2314yes—
150#14579092C2314yes—
151C4⋊(C79⋊C8)C2314yes—
152Dic79⋊C8C2314yes—
153Dic79⋊C8C2314yes—
154#14579085C2314yes—
155#14579085C2314yes—
156#14579083C2314yes—
157#14579083C2314yes—
158#14579081C2314yes—
159#14579081C2314yes—
160C22×Q8×C79C2311yescharacteristic
161C22×C8×C79C2311yescharacteristic
162C22×C8×C79C2311yescharacteristic
163#125×C79—22no—
164#125×C79C2314yes—
165C4×Q8×C79—22no—
166C4×Q8×C79C2314yes—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C42×C79—21no—
174C2×C42×C79C2311yescharacteristic
175#107×C79C2314yes—
176#106×C79C2314yes—
177C4⋊C8×C79C2314yes—
178#103×C79C2314yes—
179#103×C79C2314yes—
180C23×D79—21no—
181C23×D79C2×D411yescharacteristic
182#11929625—216no—
183#11929625—28no—
184#11929625C2×Q8116yescomplemented
185C2×Dic158—24no—
186C2×Dic158—24no—
187C2×Dic158—82no—
188C2×Dic158—82no—
189C2×D316—28no—
190C2×D316—24no—
191C2×D316—21no—
192C2×D316—22no—
193C2×D316C2×Q814yes—
194C2×D316C2412yes—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79C2×D411yescharacteristic
199C22×Dic79C2×D411yescharacteristic
200C22×Dic79C2×D411yescharacteristic
201C2×C4×D79—28no—
202C2×C4×D79—24no—
203C2×C4×D79—24no—
204C2×C4×D79—24no—
205C2×C4×D79—24no—
206C2×C4×D79—24no—
207C2×C4×D79—82no—
208C2×C4×D79—82no—
209C2×C4×D79—82no—
210C2×C4×D79—82no—
211C2×C4×D79C2×D412yes—
212C2×C4×D79C2×Q814yes—
213C2×C4×D79#4114yes—
214C2×C4×D79C2412yes—
215#11929607—28no—
216C2×C79⋊C8—22no—
217C2×C79⋊C8—22no—
218C2×C79⋊C8C2412yes—
219C2×C79⋊C8C2412yes—
220C8×D79—28no—
221C4⋊Dic79—24no—
222C4⋊Dic79—24no—
223C4⋊Dic79—21no—
224C4⋊Dic79—21no—
225C4⋊Dic79—24no—
226C4⋊Dic79—21no—
227C4⋊Dic79C2412yes—
228C4⋊Dic79C2412yes—
229C4⋊Dic79C2412yes—
230Dic79⋊C4—24no—
231Dic79⋊C4—24no—
232Dic79⋊C4—24no—
233Dic79⋊C4—24no—
234Dic79⋊C4C2×D414yes—
235Dic79⋊C4C2×D414yes—
236(C2×D79)⋊C4—24no—
237(C2×D79)⋊C4—24no—
238(C2×D79)⋊C4—24no—
239(C2×D79)⋊C4C2×D414yes—
240(C2×D79)⋊C4C2×D414yes—
241C4×Dic79—24no—
242C4×Dic79—24no—
243C4×Dic79C2×D412yes—
244C4×Dic79C2412yes—
245C2×Q8×C79—21no—
246C2×Q8×C79—22no—
247C2×Q8×C79C2×Q814yes—
248C2×Q8×C79C2412yes—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79—21no—
252C22×C4×C79—21no—
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2411yescharacteristic
256C2×C8×C79—22no—
257C2×C8×C79—22no—
258C2×C8×C79C2412yes—
259C2×C8×C79C2412yes—
260C4⋊C4×C79—24no—
261C4⋊C4×C79—24no—
262C4⋊C4×C79—24no—
263C4⋊C4×C79—21no—
264C4⋊C4×C79—21no—
265C4⋊C4×C79—21no—
266C4⋊C4×C79C2412yes—
267C4⋊C4×C79C2412yes—
268C4⋊C4×C79C2412yes—
269C42×C79—24no—
270C42×C79C2×D412yes—
271C42×C79C2412yes—
272C23×C79C22×D411yescharacteristic
273C22×D79—22no—
274C22×D79—22no—
275C22×D79—24no—
276C22×D79—22no—
277C22×D79—42no—
278C22×D79—42no—
279C22×D79C22⋊Q814yes—
280C22×D79C22×D412yes—
281Q8×C79—24no—
282Q8×C79—22no—
283Q8×C79C22×Q814yes—
284C2×C4×C79—24no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—42no—
292C2×C4×C79—42no—
293C2×C4×C79—42no—
294C2×C4×C79C22×D412yes—
295C2×C4×C79C22×D412yes—
296C2×C4×C79C22×D411yescharacteristic
297C2×C4×C79C22×Q812yes—
298C2×C4×C79C2×#4112yes—
299C2×C4×C79C2511yescharacteristic
300C2×Dic79—22no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—42no—
306C2×Dic79—42no—
307C2×Dic79—42no—
308C2×Dic79C22⋊Q814yes—
309C2×Dic79C22×D412yes—
310C2×Dic79C22×D412yes—
311C2×Dic79C22×D412yes—
312D316—216no—
313D316—24no—
314D316—22no—
315D316C22×Q814yes—
316C4×D79—216no—
317C4×D79—84no—
318C4×D79—84no—
319C4×D79—84no—
320C4×D79—84no—
321C4×D79C22⋊Q818yes—
322C4×D79C22×Q814yes—
323C4×D79C2×#4114yes—
324Dic158—84no—
325Dic158—84no—
326C8×C79—22no—
327C8×C79—22no—
328C79⋊C8—22no—
329C79⋊C8—22no—
330C22×C79C2×C22⋊Q812yes—
331C22×C79#57712yes—
332C22×C79#57712yes—
333C22×C79C23×D411yescharacteristic
334C2×D79—28no—
335C2×D79—22no—
336C2×D79—22no—
337C2×D79—24no—
338C2×D79—48no—
339C2×D79—42no—
340C2×D79—42no—
341C2×D79C2×C22⋊Q814yes—
342C4×C79—24no—
343C4×C79—22no—
344C4×C79—22no—
345C4×C79—42no—
346C4×C79—42no—
347C4×C79—42no—
348C4×C79C2×C22⋊Q812yes—
349C4×C79C23×Q811yescharacteristic
350C4×C79C22×#4111yescharacteristic
351Dic79—22no—
352Dic79—22no—
353Dic79—42no—
354Dic79—42no—
355Dic79—42no—
356Dic79C2×C22⋊Q814yes—
357C2×#3084—791nomaximal, Sylow
358C2×C79#308414yescomplemented
359C2×C79C22×C22⋊Q811yescharacteristic
360C2×C79C2×#57711yescharacteristic
361C2×C79C2×#57711yescharacteristic
362D79—24no—
363D79—44no—
364C2×#544—791no—
365C2×#520—791no—
366#3084—7916no—
367C2×#479—791no—
368C2×#479D7911yescharacteristic, complemented
369C2×#475—791no—
370C2×#475—791no—
371C2×#478—791no—
372C2×#478—791no—
373C2×#476—791no—
374C2×#476—791no—
375C2×#428—791no—
376C22×#106—791no—
377C2×#424—791no—
378C2×#417—791no—
379C2×#416—791no—
380C79C2×#308411yescharacteristic, complemented, Sylow
381C22×#41—791no—
382C22×M16—791no—
383C23×C8—791no—
384#544—798no—
385#544—1584no—
386C2×C4⋊Q8—791no—
387C2×C4⋊Q8—791no—
388C2×C4⋊Q8—1581no—
389C2×#125—791no—
390C2×#125—1581no—
391C2×#125C2×D7911yescharacteristic
392C2×C22⋊Q8—1581no—
393C2×C22⋊Q8—1581no—
394#520—798no—
395#520—1584no—
396C2×C4×Q8—791no—
397C2×C4×Q8C2×D7911yescharacteristic
398C2×C4×D4—791no—
399C2×C4×D4—791no—
400C2×C4×D4—1581no—
401C2×C4×D4—1581no—
402C2×#117—791no—
403C2×#117—791no—
404C2×#117—1581no—
405C22×C4⋊C4—791no—
406C22×C4⋊C4—791no—
407C22×C4⋊C4—1581no—
408#479—798no—
409#479C2×D7918yescomplemented
410#478—798no—
411#478—798no—
412#476—798no—
413#476—798no—
414#475—798no—
415#475—798no—
416#428—798no—
417C2×#107—791no—
418C2×#107C2×D7911yescharacteristic
419C2×#106—791no—
420C2×#106—791no—
421C2×#106—791no—
422C2×#106—791no—
423C2×#106—791no—
424C2×#106—798no—
425C2×#106C2×D7911yescharacteristic
426#424—798no—
427C2×C4⋊C8—791no—
428C2×C4⋊C8—791no—
429C2×C4⋊C8—791no—
430C2×C4⋊C8C2×D7911yescharacteristic
431#417—798no—
432#416—798no—
433C2×#103—791no—
434C2×#103—791no—
435C2×#103C2×D7911yescharacteristic
436C2×#103C2×D7911yescharacteristic
437C2×#102—791no—
438C2×#102—791no—
439C2×#102—791no—
440C2×#102—791no—
441C2×#41—798no—
442C2×#41—794no—
443C2×#41—1582no—
444C2×#41—1584no—
445C22×Q8—1581no—
446C22×Q8—1581no—
447C22×Q8C22×D7911yescharacteristic
448C22×D4—791no—
449C22×D4—1581no—
450C23×C4—791no—
451C23×C4—1581no—
452C23×C4—1581no—
453C23×C4—1581no—
454C23×C4—1581no—
455C23×C4—1581no—
456C2×M16—794no—
457C2×M16—1584no—
458C22×C8—791no—
459C22×C8—791no—
460C22×C8—794no—
461C22×C8—1584no—
462C22×C8C22×D7911yescharacteristic
463C22×C8C22×D7911yescharacteristic
464C4⋊Q8—794no—
465C4⋊Q8—794no—
466C4⋊Q8—1582no—
467C4⋊Q8—1588no—
468C4⋊Q8—1582no—
469#125—22no—
470#125—794no—
471#125—1582no—
472#125—1588no—
473#125C22×D7914yes—
474C22⋊Q8—1588no—
475C22⋊Q8—1588no—
476C4×Q8—22no—
477C4×Q8—794no—
478C4×Q8—1582no—
479C4×Q8C22×D7914yes—
480C4×D4—794no—
481C4×D4—794no—
482C4×D4—1588no—
483C4×D4—1582no—
484C4×D4—1588no—
485C4×D4—1582no—
486#117—794no—
487#117—794no—
488#117—794no—
489#117—1588no—
490#117—1582no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—791no—
495C2×C4⋊C4—791no—
496C2×C4⋊C4—791no—
497C2×C4⋊C4—791no—
498C2×C4⋊C4—791no—
499C2×C4⋊C4—794no—
500C2×C4⋊C4—794no—
501C2×C4⋊C4—1588no—
502C2×C4⋊C4—1582no—
503C2×C4⋊C4—1582no—
504C2×C4⋊C4—1581no—
505C2×C4⋊C4—1581no—
506C2×C4⋊C4—1581no—
507C2×C4⋊C4—1581no—
508C2×C4⋊C4—1581no—
509C2×C4⋊C4—1581no—
510C2×C4⋊C4—1581no—
511C2×C4⋊C4C22×D7911yescharacteristic
512C2×C4⋊C4C22×D7911yescharacteristic
513C2×C4⋊C4C22×D7911yescharacteristic
514C2×C22⋊C4—791no—
515C2×C22⋊C4—791no—
516C2×C22⋊C4—1581no—
517C2×C22⋊C4—1581no—
518C2×C22⋊C4—1581no—
519C2×C42—21no—
520C2×C42—791no—
521C2×C42—1581no—
522C2×C42—1581no—
523C2×C42C22×D7911yescharacteristic
524#107—794no—
525#107C22×D7914yes—
526#106—794no—
527#106—794no—
528#106—794no—
529#106—794no—
530#106—794no—
531#106C22×D7914yes—
532C4⋊C8—794no—
533C4⋊C8—794no—
534C4⋊C8—794no—
535C4⋊C8C22×D7914yes—
536#103—794no—
537#103—794no—
538#103C22×D7914yes—
539#103C22×D7914yes—
540#102—794no—
541#102—794no—
542#102—794no—
543#102—794no—
544C24—791no—
545C24—1581no—
546#41—7916no—
547#41—15816no—
548#41—1588no—
549C2×Q8—22no—
550C2×Q8—21no—
551C2×Q8—6322no—
552C2×Q8—6322no—
553C2×Q8—1584no—
554C2×Q8—1584no—
555C2×Q8Q8×D7914yes—
556C2×Q8C23×D7912yes—
557C2×D4—794no—
558C2×D4—792no—
559C2×D4—1584no—
560C2×D4—1588no—
561C2×D4—1582no—
562C2×D4—1581no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—791no—
568C22×C4—794no—
569C22×C4—794no—
570C22×C4—792no—
571C22×C4—792no—
572C22×C4—791no—
573C22×C4—791no—
574C22×C4—6322no—
575C22×C4—6322no—
576C22×C4—6322no—
577C22×C4—6322no—
578C22×C4—1584no—
579C22×C4—1584no—
580C22×C4—1588no—
581C22×C4—1584no—
582C22×C4—1584no—
583C22×C4—1581no—
584C22×C4—1581no—
585C22×C4—1581no—
586C22×C4—1584no—
587C22×C4D4×D7911yescharacteristic
588C22×C4D4×D7911yescharacteristic
589C22×C4C23×D7911yescharacteristic
590M16—1588no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—792no—
594C2×C8—792no—
595C2×C8—1588no—
596C2×C8—1582no—
597C2×C8—1582no—
598C2×C8C23×D7912yes—
599C2×C8C23×D7912yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—794no—
607C4⋊C4—794no—
608C4⋊C4—792no—
609C4⋊C4—792no—
610C4⋊C4—792no—
611C4⋊C4—1584no—
612C4⋊C4—1584no—
613C4⋊C4—1584no—
614C4⋊C4—1584no—
615C4⋊C4—1584no—
616C4⋊C4—1584no—
617C4⋊C4—1581no—
618C4⋊C4—1581no—
619C4⋊C4—1581no—
620C4⋊C4—1584no—
621C4⋊C4C23×D7912yes—
622C4⋊C4C23×D7912yes—
623C4⋊C4C23×D7912yes—
624C22⋊C4—794no—
625C22⋊C4—794no—
626C22⋊C4—1584no—
627C22⋊C4—1584no—
628C22⋊C4—1584no—
629C42—24no—
630C42—792no—
631C42—792no—
632C42—1584no—
633C42—1584no—
634C42D4×D7912yes—
635C42C23×D7912yes—
636C23—3162no—
637C23—3162no—
638C23—794no—
639C23—792no—
640C23—1584no—
641C23—1582no—
642C23—1582no—
643C23—1582no—
644C23C2×D4×D7911yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8—6324no—
648Q8—6324no—
649Q8C2×Q8×D7914yes—
650D4—794no—
651D4—15816no—
652D4—1584no—
653D4—1582no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—3162no—
665C2×C4—3162no—
666C2×C4—3162no—
667C2×C4—794no—
668C2×C4—792no—
669C2×C4—798no—
670C2×C4—794no—
671C2×C4—794no—
672C2×C4—792no—
673C2×C4—792no—
674C2×C4—6324no—
675C2×C4—6324no—
676C2×C4—6324no—
677C2×C4—6324no—
678C2×C4—15816no—
679C2×C4—1582no—
680C2×C4—1582no—
681C2×C4—1582no—
682C2×C4—1582no—
683C2×C4—1582no—
684C2×C4C2×D4×D7912yes—
685C2×C4C2×D4×D7912yes—
686C2×C4C2×D4×D7911yescharacteristic
687C2×C4C2×Q8×D7912yes—
688C2×C4#41×D7912yes—
689C2×C4C24×D7911yescharacteristic
690C8—22no—
691C8—22no—
692C8—1582no—
693C8—1582no—
694C22—3168no—
695C22—3162no—
696C22—3162no—
697C22—794no—
698C22—1584no—
699C22—1588no—
700C22—1582no—
701C22—1582no—
702C22C22⋊Q8×D7912yes—
703C22#1909937012yes—
704C22#1909937212yes—
705C22C22×D4×D7911yescharacteristic
706C4—22no—
707C4—22no—
708C4—24no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—3162no—
713C4—3162no—
714C4—3162no—
715C4—794no—
716C4—1582no—
717C4—1582no—
718C4C22⋊Q8×D7912yes—
719C4C22×Q8×D7911yescharacteristic
720C4C2×#41×D7911yescharacteristic
721C2—3164no—
722C2—1584no—
723C2#2377326514yesdirect product factor
724C2C2×C22⋊Q8×D7911yescharacteristic
725C2C2×#1909937011yescharacteristic
726C2C2×#1909937211yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#479×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929625C22
hypercenterC2×#479D79
hypocenterC79C2×#3084
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#19099193C2semidirect
3. #23773265C2direct (N × H)
4. C2×#19098868C2semidirect
5. C2×#19098848C2semidirect
6. C2×#19098846C2semidirect
7. C2×#19098866C2semidirect
8. C2×#19098860C2semidirect
9. C2×#19098854C2semidirect
10. C2×#19098852C2semidirect
11. C2×#19098604C2semidirect
12. C2×#106×D79C2semidirect
13. C2×#19098588C2semidirect
16. C2×#479×C79C2semidirect
21. #19099193C22semidirect
42. #19098868C22semidirect
43. #19098866C22semidirect
44. #19098860C22semidirect
45. #19098854C22semidirect
46. #19098852C22semidirect
47. #19098848C22semidirect
48. #19098846C22semidirect
49. #19098604C22semidirect
56. #106×D79C22semidirect
57. #19098588C22semidirect
71. #479×C79C22semidirect
79. C2×#11929625Q8semidirect
184. #11929625C2×Q8semidirect
358. C2×C79#3084semidirect
368. C2×#479D79semidirect
380. C79C2×#3084semidirect
409. #479C2×D79semidirect
723. C2#23773265direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991932
C2×#190990452
#237732652
C2×#190988682
C2×#190988482
C2×#190988462
C2×#190988662
C2×#190988602
C2×#190988542
C2×#190988522
C2×#190986042
C2×#106×D792
C2×#190985882
C2×#190985632
C2×#190985582
C2×#479×C792
C2×#308479