Finite Group Databasebeta

← C2×#23776302 #35168749

Subgroups — C2×#23776302 #35168749

Order 20224.

2082 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099269C211yesmaximal, characteristic, complemented
2C2×D4×Dic158C211yesmaximal, characteristic, complemented
3#23776302C2116yesmaximal, direct product factor
4C2×#19098973C211yesmaximal, characteristic, complemented
5C2×#19098971C211yesmaximal, characteristic, complemented
6C2×#19098960C211yesmaximal, characteristic, complemented
7C2×#19098865C211yesmaximal, characteristic, complemented
8C2×#19098854C211yesmaximal, characteristic, complemented
9C2×#19098852C211yesmaximal, characteristic, complemented
10C2×#19098851C211yesmaximal, characteristic, complemented
11C2×#19098842C211yesmaximal, characteristic, complemented
12C2×#19098692C211yesmaximal, characteristic, complemented
13C2×#19098673C211yesmaximal, characteristic
14C2×#19098672C211yesmaximal, characteristic
15C2×#19098643C211yesmaximal, characteristic
16C2×#478×C79C211yesmaximal, characteristic, complemented
17C23×Dic158—21no—
18C22×#11929609C2211yescharacteristic
19#19099269—24no—
20#19099269C2218yescomplemented
21D4×Dic158—24no—
22D4×Dic158C2218yescomplemented
23C2×#14579161C2211yescharacteristic
24C2×#14579160C2211yescharacteristic
25C2×#14579160C2211yescharacteristic
26C2×#14579160C2211yescharacteristic
27C2×#14579152C2211yescharacteristic
28C2×#14579141—21no—
29C2×#14579140—21no—
30C2×#14579139—21no—
31C2×#14579139—21no—
32C2×#14579138—21no—
33C2×#14579138—21no—
34C2×C4×Dic158C2211yescharacteristic
35C2×C4×D316C2211yescharacteristic
36C2×D4×Dic79C2211yescharacteristic
37C2×D4×Dic79C2211yescharacteristic
38C2×#14579123C2211yescharacteristic
39C2×#14579123C2211yescharacteristic
40C2×C4⋊C4×D79—21no—
41#19098973C2218yescomplemented
42#19098971C2218yescomplemented
43#19098960C2218yescomplemented
44#19098865C2218yescomplemented
45#19098854C2218yescomplemented
46#19098852C2218yescomplemented
47#19098851C2218yescomplemented
48#19098842C2218yescomplemented
49#19098692C2218yescomplemented
50#19098673C2218yes—
51#19098672C2218yes—
52#19098643C2218yes—
53C2×#14579094C2211yescharacteristic
54C2×#14579094C2211yescharacteristic
55C2×#14579093C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59C2×#14579092C2211yescharacteristic
60C2×Dic79⋊C8C2211yescharacteristic
61C2×Dic79⋊C8C2211yescharacteristic
62C2×#14579083C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579081C2211yescharacteristic
66C2×#14579072C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C2×#125×C79C2211yescharacteristic
70C2×C4×D4×C79C2211yescharacteristic
71#478×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×C4⋊C8×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—28no—
79C22×Dic158—21no—
80C22×Dic158—21no—
81C22×Dic158—21no—
82C22×Dic158—48no—
83C22×Dic158D411yescharacteristic
84C22×D316C2311yescharacteristic
85C23×Dic79—21no—
86C23×Dic79—21no—
87C22×C4×D79—21no—
88C22×C4×D79—21no—
89C22×C4×D79—21no—
90C2×#11929609Q818yescomplemented
91C2×#11929609C2314yes—
92C22×C79⋊C8C2311yescharacteristic
93C22×C79⋊C8C2311yescharacteristic
94#14579161—22no—
95#14579161C2314yes—
96#14579160—22no—
97#14579160—22no—
98#14579160—22no—
99#14579160C2314yes—
100#14579160C2314yes—
101#14579160C2314yes—
102#14579152—22no—
103#14579152C2314yes—
104#14579141—28no—
105#14579140—28no—
106#14579139—28no—
107#14579139—28no—
108#14579138—28no—
109#14579138—28no—
110C4×Dic158D414yes—
111C4×Dic158C2314yes—
112C4×D316—22no—
113C4×D316C2314yes—
114D4×Dic79—22no—
115D4×Dic79—22no—
116D4×Dic79C2314yes—
117D4×Dic79C2314yes—
118#14579123—22no—
119#14579123—22no—
120#14579123C2314yes—
121#14579123C2314yes—
122C2×C4⋊Dic79—21no—
123C2×C4⋊Dic79—21no—
124C2×C4⋊Dic79D411yescharacteristic
125C2×C4⋊Dic79C2311yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×C4⋊Dic79C2311yescharacteristic
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4D411yescharacteristic
133C2×Dic79⋊C4D411yescharacteristic
134C4⋊C4×D79—28no—
135C2×C22⋊Dic79—21no—
136C2×C22⋊Dic79—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×C4×Dic79C2311yescharacteristic
141C2×C4×Dic79C2311yescharacteristic
142#14579094C2314yes—
143#14579094C2314yes—
144#14579093C2314yes—
145#14579093C2314yes—
146#14579092C2314yes—
147#14579092C2314yes—
148#14579092C2314yes—
149Dic79⋊C8C2314yes—
150Dic79⋊C8C2314yes—
151#14579083C2314yes—
152#14579083C2314yes—
153#14579082C2314yes—
154#14579081C2314yes—
155#14579072C2314yes—
156#14579071C2314yes—
157C8×Dic79C2314yes—
158C22×D4×C79C2311yescharacteristic
159C23×C4×C79—21no—
160C22×C8×C79C2311yescharacteristic
161C22×C8×C79C2311yescharacteristic
162#125×C79—22no—
163#125×C79C2314yes—
164C4×D4×C79—22no—
165C4×D4×C79C2314yes—
166C2×C4⋊C4×C79—21no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79C2311yescharacteristic
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C22⋊C4×C79—21no—
172C2×C42×C79C2311yescharacteristic
173#107×C79C2314yes—
174#106×C79C2314yes—
175C4⋊C8×C79C2314yes—
176#102×C79C2314yes—
177#102×C79C2314yes—
178C23×D79—21no—
179C2×Dic158—24no—
180C2×Dic158—24no—
181C2×Dic158—24no—
182C2×Dic158—24no—
183C2×Dic158—24no—
184C2×Dic158—44no—
185C2×Dic158—432no—
186C2×Dic158—44no—
187C2×Dic158—44no—
188C2×Dic158—82no—
189C2×Dic158C2×D414yes—
190C2×D316—21no—
191C2×D316—22no—
192C2×D316C2×Q814yescomplemented
193C2×D316C2412yes—
194C22×Dic79—24no—
195C22×Dic79—24no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79—44no—
200C22×Dic79—44no—
201C22×Dic79C2×D411yescharacteristic
202C22×Dic79C2×D411yescharacteristic
203C22×Dic79C2×D411yescharacteristic
204C22×Dic79C2×D411yescharacteristic
205C2×C4×D79—24no—
206C2×C4×D79—24no—
207C2×C4×D79—24no—
208C2×C4×D79—44no—
209C2×C4×D79—82no—
210C2×C4×D79—82no—
211#11929609C2×Q8116yescomplemented
212C2×C79⋊C8—22no—
213C2×C79⋊C8C2×Q814yescomplemented
214C2×C79⋊C8C2412yes—
215C2×C79⋊C8C2412yes—
216C4⋊Dic79—24no—
217C4⋊Dic79—24no—
218C4⋊Dic79—21no—
219C4⋊Dic79—21no—
220C4⋊Dic79—21no—
221C4⋊Dic79C2×D414yes—
222C4⋊Dic79C2412yes—
223C4⋊Dic79C2412yes—
224C4⋊Dic79C2412yes—
225Dic79⋊C4—24no—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228Dic79⋊C4—24no—
229Dic79⋊C4C2×D414yes—
230Dic79⋊C4C2×D414yes—
231C22⋊Dic79—24no—
232C22⋊Dic79—24no—
233(C2×D79)⋊C4—24no—
234(C2×D79)⋊C4—24no—
235(C2×D79)⋊C4—24no—
236C4×Dic79C2×D412yes—
237C4×Dic79C2×D412yes—
238C4×Dic79C2412yes—
239C4×Dic79C2412yes—
240C24×C79—21no—
241C2×D4×C79—21no—
242C2×D4×C79—22no—
243C2×D4×C79C2×Q814yes—
244C2×D4×C79C2412yes—
245C22×C4×C79—21no—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79—24no—
249C22×C4×C79—44no—
250C22×C4×C79C2×D411yescharacteristic
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2411yescharacteristic
253C2×C8×C79—22no—
254C2×C8×C79—22no—
255C2×C8×C79C2412yes—
256C2×C8×C79C2412yes—
257C4⋊C4×C79—24no—
258C4⋊C4×C79—24no—
259C4⋊C4×C79—21no—
260C4⋊C4×C79—21no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79C2412yes—
263C4⋊C4×C79C2412yes—
264C4⋊C4×C79C2412yes—
265C22⋊C4×C79—24no—
266C42×C79C2×D412yes—
267C42×C79C2412yes—
268C23×C79—24no—
269C23×C79—22no—
270C23×C79—42no—
271C23×C79—42no—
272C23×C79C22×D411yescharacteristic
273C22×D79—24no—
274C22×D79—22no—
275C22×D79—42no—
276C22×D79—42no—
277D4×C79—24no—
278D4×C79—22no—
279D4×C79C22×Q814yes—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—48no—
286C2×C4×C79—42no—
287C2×C4×C79—42no—
288C2×C4×C79—42no—
289C2×C4×C79C22×D412yes—
290C2×C4×C79C22×D412yes—
291C2×C4×C79C22×D411yescharacteristic
292C2×C4×C79C22×Q812yes—
293C2×C4×C792−1+412yes—
294C2×C4×C79C2511yescharacteristic
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—48no—
302C2×Dic79—42no—
303C2×Dic79—42no—
304C2×Dic79—42no—
305C2×Dic79—48no—
306C2×Dic79AGL(1,ℤ/8)14yes—
307C2×Dic79C22×D412yes—
308C2×Dic79C22×D412yes—
309C2×Dic79C22×D412yes—
310C2×Dic79C22×D412yes—
311D316—24no—
312D316—22no—
313D316C22×Q814yescomplemented
314C4×D79—48no—
315C4×D79—84no—
316C4×D79—84no—
317Dic158—28no—
318Dic158—48no—
319Dic158—48no—
320Dic158—48no—
321Dic158—84no—
322C8×C79—22no—
323C8×C79—22no—
324C79⋊C8—22no—
325C79⋊C8C22×Q814yescomplemented
326C22×C79—24no—
327C22×C79—48no—
328C22×C79—42no—
329C22×C79—42no—
330C22×C79D4×Q812yes—
331C22×C79C2×AGL(1,ℤ/8)12yes—
332C22×C79#57712yes—
333C22×C79C23×D411yescharacteristic
334C2×D79—24no—
335C2×D79—48no—
336C2×D79—42no—
337C2×D79—42no—
338C4×C79—22no—
339C4×C79—22no—
340C4×C79—42no—
341C4×C79—42no—
342C4×C79—42no—
343C4×C79D4×Q812yes—
344C4×C79C23×Q811yescharacteristic
345C4×C79C2×2−1+411yescharacteristic
346Dic79—22no—
347Dic79—22no—
348Dic79—22no—
349Dic79—42no—
350Dic79—42no—
351Dic79—42no—
352Dic79C2×AGL(1,ℤ/8)14yes—
353C2×#3384—791nomaximal, Sylow
354C2×C79—44no—
355C2×C79#338414yescomplemented
356C2×C79C2×D4×Q811yescharacteristic
357C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
358C2×C79C2×#57711yescharacteristic
359D79—44no—
360C2×#554—791no—
361C2×D4×Q8—791no—
362#3384—7916no—
363C2×#501—791no—
364C2×#501—791no—
365C2×#498—791no—
366C2×#478—791no—
367C2×#478D7911yescharacteristic, complemented
368C2×#476—791no—
369C2×#476—791no—
370C2×#476—791no—
371C2×#474—791no—
372C2×#446—791no—
373C2×#442—791no—
374C2×#442—791no—
375C2×C4×D8—791no—
376C79C2×#338411yescharacteristic, complemented, Sylow
377C23×Q8—1581no—
378C22×D8—791no—
379#554—798no—
380#554—1584no—
381D4×Q8—798no—
382D4×Q8—1584no—
383C2×C4⋊Q8—791no—
384C2×C4⋊Q8—791no—
385C2×C4⋊Q8—791no—
386C2×C4⋊Q8—791no—
387C2×#125—791no—
388C2×#125C2×D7911yescharacteristic
389C2×C22⋊Q8—1581no—
390C2×C22⋊Q8—1581no—
391C2×C22⋊Q8—1581no—
392C2×C22⋊Q8—1581no—
393C2×C22⋊Q8—1581no—
394C2×C22⋊Q8—1581no—
395C2×C4×Q8—791no—
396C2×C4×D4—791no—
397C2×C4×D4—791no—
398C2×C4×D4—791no—
399C2×C4×D4—791no—
400C2×C4×D4—791no—
401C2×C4×D4C2×D7911yescharacteristic
402C22×C4⋊C4—1581no—
403#501—798no—
404#501—798no—
405#498—798no—
406#478—798no—
407#478C2×D7918yescomplemented
408#476—798no—
409#476—798no—
410#476—798no—
411#474—798no—
412#446—798no—
413#442—798no—
414#442—798no—
415C4×D8—798no—
416C2×#107—791no—
417C2×#107—791no—
418C2×#107C2×D7911yescharacteristic
419C2×#106—791no—
420C2×#106—791no—
421C2×#106—791no—
422C2×#106—791no—
423C2×#106—791no—
424C2×#106C2×D7911yescharacteristic
425C2×C4⋊C8—791no—
426C2×C4⋊C8—791no—
427C2×C4⋊C8C2×D7911yescharacteristic
428C2×#102—791no—
429C2×#102—791no—
430C2×#102—791no—
431C2×#102—791no—
432C2×#102C2×D7911yescharacteristic
433C2×#102C2×D7911yescharacteristic
434C2×#97—791no—
435C2×#97—791no—
436C2×C4×C8—791no—
437C22×Q8—3168no—
438C22×Q8—791no—
439C22×Q8—1581no—
440C22×Q8—1581no—
441C22×Q8—1581no—
442C22×Q8—1588no—
443C22×Q8—1581no—
444C22×D4—791no—
445C22×D4C22×D7911yescharacteristic
446C23×C4—21no—
447C23×C4—1581no—
448C23×C4—1581no—
449C23×C4—1581no—
450C23×C4—1581no—
451C23×C4—1581no—
452C2×D8—798no—
453C2×D8—794no—
454C22×C8—791no—
455C22×C8—791no—
456C22×C8C22×D7911yescharacteristic
457C22×C8C22×D7911yescharacteristic
458C4⋊Q8—794no—
459C4⋊Q8—794no—
460C4⋊Q8—794no—
461C4⋊Q8—794no—
462C4⋊Q8—1582no—
463C4⋊Q8—1582no—
464C4⋊Q8—1582no—
465C4⋊Q8—1582no—
466#125—22no—
467#125—794no—
468#125—1582no—
469#125C22×D7914yes—
470C22⋊Q8—1588no—
471C22⋊Q8—1588no—
472C22⋊Q8—1588no—
473C22⋊Q8—1588no—
474C22⋊Q8—1588no—
475C22⋊Q8—1588no—
476C4×Q8—794no—
477C4×Q8—794no—
478C4×D4—22no—
479C4×D4—794no—
480C4×D4—794no—
481C4×D4—794no—
482C4×D4—794no—
483C4×D4—794no—
484C4×D4—1582no—
485C4×D4—1582no—
486C4×D4—1582no—
487C4×D4—1582no—
488C4×D4—1582no—
489C4×D4C22×D7914yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—791no—
493C2×C4⋊C4—791no—
494C2×C4⋊C4—791no—
495C2×C4⋊C4—791no—
496C2×C4⋊C4—791no—
497C2×C4⋊C4—791no—
498C2×C4⋊C4—1588no—
499C2×C4⋊C4—1581no—
500C2×C4⋊C4—1581no—
501C2×C4⋊C4—1581no—
502C2×C4⋊C4—1581no—
503C2×C4⋊C4—1581no—
504C2×C4⋊C4—1581no—
505C2×C4⋊C4C22×D7911yescharacteristic
506C2×C4⋊C4C22×D7911yescharacteristic
507C2×C4⋊C4C22×D7911yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—1581no—
510C2×C22⋊C4—1581no—
511C2×C22⋊C4—1581no—
512C2×C22⋊C4—1581no—
513C2×C22⋊C4—1581no—
514C2×C42—791no—
515C2×C42—791no—
516C2×C42C22×D7911yescharacteristic
517#107—794no—
518#107—794no—
519#107C22×D7914yes—
520#106—794no—
521#106—794no—
522#106—794no—
523#106—794no—
524#106—794no—
525#106C22×D7914yes—
526C4⋊C8—794no—
527C4⋊C8—794no—
528C4⋊C8C22×D7914yes—
529#102—794no—
530#102—794no—
531#102—794no—
532#102—794no—
533#102C22×D7914yes—
534#102C22×D7914yes—
535#97—794no—
536#97—794no—
537C4×C8—794no—
538C24—21no—
539C24—1581no—
540C2×Q8—3164no—
541C2×Q8—31632no—
542C2×Q8—3164no—
543C2×Q8—3164no—
544C2×Q8—794no—
545C2×Q8—6322no—
546C2×Q8—1584no—
547C2×Q8—1584no—
548C2×Q8—1584no—
549C2×Q8—1584no—
550C2×Q8—1584no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—794no—
554C2×D4—792no—
555C2×D4—1582no—
556C2×D4—1581no—
557C2×D4Q8×D7914yes—
558C2×D4C23×D7912yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—44no—
564C22×C4—3164no—
565C22×C4—3164no—
566C22×C4—3164no—
567C22×C4—791no—
568C22×C4—791no—
569C22×C4—791no—
570C22×C4—791no—
571C22×C4—6322no—
572C22×C4—6322no—
573C22×C4—1584no—
574C22×C4—1584no—
575C22×C4—1584no—
576C22×C4—1584no—
577C22×C4—1581no—
578C22×C4—1581no—
579C22×C4—1581no—
580C22×C4—1584no—
581C22×C4D4×D7911yescharacteristic
582C22×C4D4×D7911yescharacteristic
583C22×C4C23×D7911yescharacteristic
584D8—7916no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—794no—
588C2×C8—792no—
589C2×C8—792no—
590C2×C8—1582no—
591C2×C8C23×D7912yes—
592C2×C8C23×D7912yes—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—794no—
599C4⋊C4—794no—
600C4⋊C4—794no—
601C4⋊C4—792no—
602C4⋊C4—792no—
603C4⋊C4—792no—
604C4⋊C4—1584no—
605C4⋊C4—1584no—
606C4⋊C4—1584no—
607C4⋊C4—1584no—
608C4⋊C4—1584no—
609C4⋊C4—1581no—
610C4⋊C4—1581no—
611C4⋊C4—1581no—
612C4⋊C4—1584no—
613C4⋊C4C23×D7912yes—
614C4⋊C4C23×D7912yes—
615C4⋊C4C23×D7912yes—
616C22⋊C4—24no—
617C22⋊C4—1584no—
618C22⋊C4—1584no—
619C22⋊C4—1584no—
620C22⋊C4—1584no—
621C22⋊C4—1584no—
622C42—792no—
623C42—792no—
624C42—792no—
625C42—792no—
626C42D4×D7912yes—
627C42C23×D7912yes—
628C23—24no—
629C23—22no—
630C23—42no—
631C23—42no—
632C23—3162no—
633C23—3162no—
634C23—1584no—
635C23—1582no—
636C23C2×D4×D7911yescharacteristic
637Q8—3168no—
638Q8—3168no—
639Q8—3168no—
640Q8—6324no—
641Q8—1588no—
642D4—22no—
643D4—24no—
644D4—794no—
645D4—1582no—
646D4—1584no—
647D4C2×Q8×D7914yes—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—48no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—3168no—
658C2×C4—3162no—
659C2×C4—3162no—
660C2×C4—3162no—
661C2×C4—3168no—
662C2×C4—3168no—
663C2×C4—794no—
664C2×C4—792no—
665C2×C4—792no—
666C2×C4—792no—
667C2×C4—792no—
668C2×C4—6324no—
669C2×C4—6324no—
670C2×C4—1582no—
671C2×C4—1582no—
672C2×C4—1582no—
673C2×C4—1582no—
674C2×C4—1582no—
675C2×C4—1582no—
676C2×C4C2×D4×D7912yes—
677C2×C4C2×D4×D7912yes—
678C2×C4C2×D4×D7911yescharacteristic
679C2×C4C2×Q8×D7912yes—
680C2×C4#1457920812yes—
681C2×C4C24×D7911yescharacteristic
682C8—22no—
683C8—22no—
684C8—794no—
685C8—1582no—
686C22—24no—
687C22—48no—
688C22—42no—
689C22—42no—
690C22—3168no—
691C22—3162no—
692C22—3162no—
693C22—1584no—
694C22#1909922612yes—
695C22AGL(1,ℤ/8)×D7912yes—
696C22#1909937012yes—
697C22C22×D4×D7911yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—3162no—
704C4—3162no—
705C4—3162no—
706C4—794no—
707C4—1582no—
708C4—1582no—
709C4—1582no—
710C4#1909922612yes—
711C4C22×Q8×D7911yescharacteristic
712C4C2×#1457920811yescharacteristic
713C2—44no—
714C2—3164no—
715C2#2377630214yesdirect product factor
716C2C2×#1909922611yescharacteristic
717C2C2×AGL(1,ℤ/8)×D7911yescharacteristic
718C2C2×#1909937011yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#478×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929609C22
hypercenterC2×#478D79
hypocenterC79C2×#3384
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#19099269C2semidirect
2. C2×D4×Dic158C2semidirect
3. #23776302C2direct (N × H)
4. C2×#19098973C2semidirect
5. C2×#19098971C2semidirect
6. C2×#19098960C2semidirect
7. C2×#19098865C2semidirect
8. C2×#19098854C2semidirect
9. C2×#19098852C2semidirect
10. C2×#19098851C2semidirect
11. C2×#19098842C2semidirect
12. C2×#19098692C2semidirect
16. C2×#478×C79C2semidirect
20. #19099269C22semidirect
22. D4×Dic158C22semidirect
41. #19098973C22semidirect
42. #19098971C22semidirect
43. #19098960C22semidirect
44. #19098865C22semidirect
45. #19098854C22semidirect
46. #19098852C22semidirect
47. #19098851C22semidirect
48. #19098842C22semidirect
49. #19098692C22semidirect
71. #478×C79C22semidirect
90. C2×#11929609Q8semidirect
192. C2×D316C2×Q8semidirect
211. #11929609C2×Q8semidirect
213. C2×C79⋊C8C2×Q8semidirect
313. D316C22×Q8semidirect
325. C79⋊C8C22×Q8semidirect
355. C2×C79#3384semidirect
367. C2×#478D79semidirect
376. C79C2×#3384semidirect
407. #478C2×D79semidirect
715. C2#23776302direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992692
C2×D4×Dic1582
#237763022
C2×#190989732
C2×#190989712
C2×#190989602
C2×#190988652
C2×#190988542
C2×#190988522
C2×#190988512
C2×#190988422
C2×#190986922
C2×#190986732
C2×#190986722
C2×#190986432
C2×#478×C792
C2×#338479