Finite Group Databasebeta

← C2×#23776345 #35168796

Subgroups — C2×#23776345 #35168796

Order 20224.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099291C211yesmaximal, characteristic, complemented
2#23776345C2116yesmaximal, direct product factor
3C2×#19098973C211yesmaximal, characteristic, complemented
4C2×#19098969C211yesmaximal, characteristic, complemented
5C2×#19098962C211yesmaximal, characteristic, complemented
6C2×#19098867C211yesmaximal, characteristic, complemented
7C2×#19098867C211yesmaximal, characteristic, complemented
8C2×#19098845C211yesmaximal, characteristic, complemented
9C2×#19098863C211yesmaximal, characteristic
10C2×#19098863C211yesmaximal, characteristic
11C2×#19098853C211yesmaximal, characteristic
12C2×#19098694C211yesmaximal, characteristic, complemented
13C2×#19098663C211yesmaximal, characteristic
14C2×#19098663C211yesmaximal, characteristic
15C2×C4×#11929612C211yesmaximal, characteristic
16C2×#554×C79C211yesmaximal, characteristic
17C22×#11929612C2211yescharacteristic
18#19099291—24no—
19#19099291C2218yescomplemented
20C2×#14579161C2211yescharacteristic
21C2×#14579159—21no—
22C2×#14579153C2211yescharacteristic
23C2×#14579153C2211yescharacteristic
24C2×#14579151—21no—
25C2×#14579151—21no—
26C2×C4×Dic158C2211yescharacteristic
27C2×C4×Dic158C2211yescharacteristic
28C2×C4×Dic158C2211yescharacteristic
29C2×#14579126—21no—
30#19098973C2218yescomplemented
31#19098969C2218yescomplemented
32#19098962C2218yescomplemented
33#19098867C2218yescomplemented
34#19098867C2218yescomplemented
35#19098863C2218yes—
36#19098863C2218yes—
37#19098853C2218yes—
38#19098845C2218yescomplemented
39#19098694C2218yescomplemented
40#19098663C2218yes—
41#19098663C2218yes—
42C4×#11929612C2218yes—
43C2×#14579094C2211yescharacteristic
44C2×#14579094C2211yescharacteristic
45C2×#14579094C2211yescharacteristic
46C2×#14579094C2211yescharacteristic
47C2×#14579092C2211yescharacteristic
48C2×#14579092C2211yescharacteristic
49C2×#14579092C2211yescharacteristic
50C2×#14579092C2211yescharacteristic
51C2×#14579092C2211yescharacteristic
52C2×C4⋊(C79⋊C8)C2211yescharacteristic
53C2×C4⋊(C79⋊C8)C2211yescharacteristic
54C2×C4⋊(C79⋊C8)C2211yescharacteristic
55C2×#14579084C2211yescharacteristic
56C2×#14579084C2211yescharacteristic
57C2×#14579084C2211yescharacteristic
58C2×#14579082C2211yescharacteristic
59C2×#14579082C2211yescharacteristic
60C2×#14579082C2211yescharacteristic
61C2×#14579072C2211yescharacteristic
62C2×#14579072C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64#554×C79—24no—
65#554×C79C2218yes—
66C2×C4⋊Q8×C79C2211yescharacteristic
67C2×#125×C79C2211yescharacteristic
68C2×#125×C79C2211yescharacteristic
69C2×C22⋊Q8×C79—21no—
70C2×C22⋊Q8×C79—21no—
71C2×C22⋊Q8×C79—21no—
72C2×C4×Q8×C79C2211yescharacteristic
73C2×C4×D4×C79C2211yescharacteristic
74C2×C4×D4×C79C2211yescharacteristic
75C2×C4×D4×C79C2211yescharacteristic
76C22×C4⋊C4×C79—21no—
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C2×#11929612Q818yescomplemented
80C2×#11929612C2314yes—
81C22×C79⋊C8C2311yescharacteristic
82C22×C79⋊C8C2311yescharacteristic
83C22×C79⋊C8C2311yescharacteristic
84C22×C79⋊C8C2311yescharacteristic
85#14579161—22no—
86#14579161C2314yes—
87#14579159—28no—
88#14579153—22no—
89#14579153—22no—
90#14579153C2314yes—
91#14579153C2314yes—
92#14579151—28no—
93#14579151—28no—
94C4×Dic158—22no—
95C4×Dic158—22no—
96C4×Dic158—22no—
97C4×Dic158C2314yes—
98C4×Dic158C2314yes—
99C4×Dic158C2314yes—
100#14579126—28no—
101C2×C4⋊Dic79—21no—
102C2×C4⋊Dic79C2311yescharacteristic
103C2×C4⋊Dic79C2311yescharacteristic
104C2×C4⋊Dic79C2311yescharacteristic
105C2×Dic79⋊C4—21no—
106C2×Dic79⋊C4—21no—
107C2×Dic79⋊C4—21no—
108C2×Dic79⋊C4—21no—
109C2×Dic79⋊C4—21no—
110C2×Dic79⋊C4—21no—
111C2×Dic79⋊C4—21no—
112C2×C4×Dic79—21no—
113C2×C4×Dic79—21no—
114C2×C4×Dic79—21no—
115#14579094C2314yes—
116#14579094C2314yes—
117#14579094C2314yes—
118#14579094C2314yes—
119#14579092C2314yes—
120#14579092C2314yes—
121#14579092C2314yes—
122#14579092C2314yes—
123#14579092C2314yes—
124C4⋊(C79⋊C8)C2314yes—
125C4⋊(C79⋊C8)C2314yes—
126C4⋊(C79⋊C8)C2314yes—
127#14579084C2314yes—
128#14579084C2314yes—
129#14579084C2314yes—
130#14579082C2314yes—
131#14579082C2314yes—
132#14579082C2314yes—
133#14579072C2314yes—
134#14579072C2314yes—
135C4×C79⋊C8C2314yes—
136C22×Q8×C79—21no—
137C22×Q8×C79D411yescharacteristic
138C22×D4×C79C2311yescharacteristic
139C23×C4×C79—21no—
140C23×C4×C79—21no—
141C23×C4×C79—21no—
142C4⋊Q8×C79—22no—
143C4⋊Q8×C79C2314yes—
144#125×C79—22no—
145#125×C79—22no—
146#125×C79C2314yes—
147#125×C79C2314yes—
148C22⋊Q8×C79—28no—
149C22⋊Q8×C79—28no—
150C22⋊Q8×C79—28no—
151C4×Q8×C79D414yes—
152C4×Q8×C79C2314yes—
153C4×D4×C79—22no—
154C4×D4×C79—22no—
155C4×D4×C79—22no—
156C4×D4×C79C2314yes—
157C4×D4×C79C2314yes—
158C4×D4×C79C2314yes—
159C2×C4⋊C4×C79—21no—
160C2×C4⋊C4×C79—21no—
161C2×C4⋊C4×C79—21no—
162C2×C4⋊C4×C79—21no—
163C2×C4⋊C4×C79—21no—
164C2×C4⋊C4×C79—28no—
165C2×C4⋊C4×C79D411yescharacteristic
166C2×C4⋊C4×C79D411yescharacteristic
167C2×C4⋊C4×C79D411yescharacteristic
168C2×C4⋊C4×C79C2311yescharacteristic
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C22⋊C4×C79—21no—
172C2×C22⋊C4×C79—21no—
173C2×C22⋊C4×C79—21no—
174C2×C42×C79C2311yescharacteristic
175C2×C42×C79C2311yescharacteristic
176C2×C42×C79C2311yescharacteristic
177C2×Dic158—21no—
178C2×Dic158—24no—
179C2×Dic158—22no—
180C2×Dic158—44no—
181C2×Dic158C2×Q814yes—
182C2×Dic158C2412yes—
183C22×Dic79—21no—
184C22×Dic79—21no—
185C22×Dic79—21no—
186C22×Dic79—21no—
187#11929612C2×Q8116yescomplemented
188C2×C79⋊C8—22no—
189C2×C79⋊C8—22no—
190C2×C79⋊C8—22no—
191C2×C79⋊C8C2×Q814yes—
192C2×C79⋊C8C2412yes—
193C2×C79⋊C8C2412yes—
194C2×C79⋊C8C2412yes—
195C2×C79⋊C8C2412yes—
196C4⋊Dic79—24no—
197C4⋊Dic79—21no—
198C4⋊Dic79—21no—
199C4⋊Dic79—21no—
200C4⋊Dic79C2412yes—
201C4⋊Dic79C2412yes—
202C4⋊Dic79C2412yes—
203Dic79⋊C4—24no—
204Dic79⋊C4—24no—
205Dic79⋊C4—24no—
206Dic79⋊C4—24no—
207Dic79⋊C4—24no—
208Dic79⋊C4—24no—
209Dic79⋊C4—24no—
210C4×Dic79—24no—
211C4×Dic79—24no—
212C4×Dic79—24no—
213C24×C79—21no—
214C2×Q8×C79—24no—
215C2×Q8×C79—42no—
216C2×Q8×C79—82no—
217C2×Q8×C79C2×D414yes—
218C2×D4×C79—21no—
219C2×D4×C79—22no—
220C2×D4×C79C2×Q814yes—
221C2×D4×C79C2412yes—
222C22×C4×C79—21no—
223C22×C4×C79—21no—
224C22×C4×C79—21no—
225C22×C4×C79—24no—
226C22×C4×C79—24no—
227C22×C4×C79—24no—
228C22×C4×C79—44no—
229C22×C4×C79—82no—
230C22×C4×C79—82no—
231C22×C4×C79C2×D411yescharacteristic
232C22×C4×C79C2×D411yescharacteristic
233C22×C4×C79C2×D411yescharacteristic
234C22×C4×C79C2×D411yescharacteristic
235C22×C4×C79C2×D411yescharacteristic
236C22×C4×C79C2×D411yescharacteristic
237C22×C4×C79C2411yescharacteristic
238C4⋊C4×C79—24no—
239C4⋊C4×C79—24no—
240C4⋊C4×C79—24no—
241C4⋊C4×C79—24no—
242C4⋊C4×C79—24no—
243C4⋊C4×C79—21no—
244C4⋊C4×C79—21no—
245C4⋊C4×C79—21no—
246C4⋊C4×C79C2×D414yes—
247C4⋊C4×C79C2×D414yes—
248C4⋊C4×C79C2×D414yes—
249C4⋊C4×C79C2412yes—
250C4⋊C4×C79C2412yes—
251C4⋊C4×C79C2412yes—
252C22⋊C4×C79—24no—
253C22⋊C4×C79—24no—
254C22⋊C4×C79—24no—
255C42×C79C2×D412yes—
256C42×C79C2×D412yes—
257C42×C79C2×D412yes—
258C42×C79C2412yes—
259C42×C79C2412yes—
260C42×C79C2412yes—
261C23×C79—24no—
262C23×C79—22no—
263C23×C79—42no—
264C23×C79—42no—
265C23×C79C22×D411yescharacteristic
266Q8×C79—44no—
267Q8×C79—84no—
268D4×C79—24no—
269D4×C79—22no—
270D4×C79C22×Q814yes—
271C2×C4×C79—22no—
272C2×C4×C79—22no—
273C2×C4×C79—22no—
274C2×C4×C79—22no—
275C2×C4×C79—22no—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—48no—
281C2×C4×C79—42no—
282C2×C4×C79—42no—
283C2×C4×C79—42no—
284C2×C4×C79—84no—
285C2×C4×C79—84no—
286C2×C4×C79C22×D412yes—
287C2×C4×C79C22×D412yes—
288C2×C4×C79C22×D412yes—
289C2×C4×C79C22×D412yes—
290C2×C4×C79C22×D412yes—
291C2×C4×C79C22×D412yes—
292C2×C4×C79C22×D411yescharacteristic
293C2×C4×C79C22×Q812yes—
294C2×C4×C792−1+412yes—
295C2×C4×C79C2511yescharacteristic
296C2×Dic79—24no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—42no—
302C2×Dic79—42no—
303C2×Dic79—42no—
304Dic158—24no—
305Dic158—22no—
306Dic158—48no—
307Dic158C22×Q814yes—
308C79⋊C8—22no—
309C79⋊C8—22no—
310C79⋊C8—22no—
311C79⋊C8C22×Q814yes—
312C22×C79—24no—
313C22×C79—48no—
314C22×C79—42no—
315C22×C79—42no—
316C22×C79D4×Q812yes—
317C22×C79#57512yes—
318C22×C79#57712yes—
319C22×C79C23×D411yescharacteristic
320C4×C79—22no—
321C4×C79—22no—
322C4×C79—22no—
323C4×C79—22no—
324C4×C79—22no—
325C4×C79—22no—
326C4×C79—42no—
327C4×C79—42no—
328C4×C79—42no—
329C4×C79D4×Q812yes—
330C4×C79C23×Q811yescharacteristic
331C4×C79C2×2−1+411yescharacteristic
332Dic79—24no—
333Dic79—42no—
334Dic79—42no—
335Dic79—42no—
336C2×#3388—791nomaximal, Sylow
337C2×C79—44no—
338C2×C79#338814yescomplemented
339C2×C79C2×D4×Q811yescharacteristic
340C2×C79C2×#57511yescharacteristic
341C2×C79C2×#57711yescharacteristic
342C2×#557—791no—
343C2×#554D7911yescharacteristic
344#3388—7916no—
345C2×#501—791no—
346C2×#501—791no—
347C2×#499—791no—
348C2×#479—791no—
349C2×#479—791no—
350C2×#475—791no—
351C2×#478—791no—
352C2×#478—791no—
353C2×#476—791no—
354C2×#446—791no—
355C2×#440—791no—
356C2×#440—791no—
357C2×C4×SD16—791no—
358C79C2×#338811yescharacteristic, complemented, Sylow
359C22×SD16—791no—
360#557—798no—
361#557—1584no—
362#554—24no—
363#554C2×D7918yes—
364C2×C4⋊Q8—791no—
365C2×C4⋊Q8—1581no—
366C2×C4⋊Q8C2×D7911yescharacteristic
367C2×#125—791no—
368C2×#125—791no—
369C2×#125—1581no—
370C2×#125—1581no—
371C2×#125C2×D7911yescharacteristic
372C2×#125C2×D7911yescharacteristic
373C2×C22⋊Q8—21no—
374C2×C22⋊Q8—21no—
375C2×C22⋊Q8—21no—
376C2×C4×Q8—791no—
377C2×C4×Q8—791no—
378C2×C4×Q8—791no—
379C2×C4×Q8—1581no—
380C2×C4×Q8C2×D7911yescharacteristic
381C2×C4×D4C2×D7911yescharacteristic
382C2×C4×D4C2×D7911yescharacteristic
383C2×C4×D4C2×D7911yescharacteristic
384C22×C4⋊C4—21no—
385#501—798no—
386#501—798no—
387#499—798no—
388#479—798no—
389#479—798no—
390#478—798no—
391#478—798no—
392#476—798no—
393#475—798no—
394#446—798no—
395#440—798no—
396#440—798no—
397C4×SD16—798no—
398C2×#107—791no—
399C2×#107—791no—
400C2×#107—791no—
401C2×#107—791no—
402C2×#106—791no—
403C2×#106—791no—
404C2×#106—791no—
405C2×#106—791no—
406C2×#106—791no—
407C2×C4⋊C8—791no—
408C2×C4⋊C8—791no—
409C2×C4⋊C8—791no—
410C2×#103—791no—
411C2×#103—791no—
412C2×#103—791no—
413C2×#102—791no—
414C2×#102—791no—
415C2×#102—791no—
416C2×#97—791no—
417C2×#97—791no—
418C2×C4×C8—791no—
419C22×Q8—21no—
420C22×Q8—791no—
421C22×Q8—1581no—
422C22×Q8C22⋊D7911yescharacteristic
423C22×D4C22×D7911yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C2×SD16—798no—
428C2×SD16—794no—
429C22×C8—791no—
430C22×C8—791no—
431C22×C8—791no—
432C22×C8—791no—
433C4⋊Q8—22no—
434C4⋊Q8—794no—
435C4⋊Q8—1588no—
436C4⋊Q8—1582no—
437C4⋊Q8C22×D7914yes—
438#125—22no—
439#125—22no—
440#125—794no—
441#125—794no—
442#125—1588no—
443#125—1588no—
444#125—1582no—
445#125—1582no—
446#125C22×D7914yes—
447#125C22×D7914yes—
448C22⋊Q8—28no—
449C22⋊Q8—28no—
450C22⋊Q8—28no—
451C4×Q8—794no—
452C4×Q8—794no—
453C4×Q8—794no—
454C4×Q8—1588no—
455C4×Q8—1582no—
456C4×Q8—1582no—
457C4×Q8—1582no—
458C4×Q8C22⋊D7914yes—
459C4×Q8C22×D7914yes—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4C22×D7914yes—
464C4×D4C22×D7914yes—
465C4×D4C22×D7914yes—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—28no—
472C2×C4⋊C4—791no—
473C2×C4⋊C4—791no—
474C2×C4⋊C4—791no—
475C2×C4⋊C4—1581no—
476C2×C4⋊C4—1581no—
477C2×C4⋊C4—1581no—
478C2×C4⋊C4—1581no—
479C2×C4⋊C4—1581no—
480C2×C4⋊C4—1581no—
481C2×C4⋊C4—1581no—
482C2×C4⋊C4—1581no—
483C2×C4⋊C4C22⋊D7911yescharacteristic
484C2×C4⋊C4C22⋊D7911yescharacteristic
485C2×C4⋊C4C22⋊D7911yescharacteristic
486C2×C4⋊C4C22×D7911yescharacteristic
487C2×C4⋊C4C22×D7911yescharacteristic
488C2×C4⋊C4C22×D7911yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C42—1581no—
493C2×C42—1581no—
494C2×C42—1581no—
495C2×C42C22×D7911yescharacteristic
496C2×C42C22×D7911yescharacteristic
497C2×C42C22×D7911yescharacteristic
498#107—794no—
499#107—794no—
500#107—794no—
501#107—794no—
502#106—794no—
503#106—794no—
504#106—794no—
505#106—794no—
506#106—794no—
507C4⋊C8—794no—
508C4⋊C8—794no—
509C4⋊C8—794no—
510#103—794no—
511#103—794no—
512#103—794no—
513#102—794no—
514#102—794no—
515#102—794no—
516#97—794no—
517#97—794no—
518C4×C8—794no—
519C24—21no—
520C2×Q8—24no—
521C2×Q8—42no—
522C2×Q8—82no—
523C2×Q8—3164no—
524C2×Q8—794no—
525C2×Q8—792no—
526C2×Q8—1582no—
527C2×Q8—1584no—
528C2×Q8—1581no—
529C2×Q8C2×C22⋊D7914yes—
530C2×D4—22no—
531C2×D4—21no—
532C2×D4Q8×D7914yes—
533C2×D4C23×D7912yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—44no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4—1581no—
544C22×C4—1581no—
545C22×C4—1581no—
546C22×C4—1581no—
547C22×C4C2×C22⋊D7911yescharacteristic
548C22×C4C2×C22⋊D7911yescharacteristic
549C22×C4C2×C22⋊D7911yescharacteristic
550C22×C4C2×C22⋊D7911yescharacteristic
551C22×C4C2×C22⋊D7911yescharacteristic
552C22×C4C2×C22⋊D7911yescharacteristic
553C22×C4C23×D7911yescharacteristic
554SD16—7916no—
555C2×C8—794no—
556C2×C8—792no—
557C2×C8—792no—
558C2×C8—792no—
559C2×C8—792no—
560C2×C8—1582no—
561C2×C8—1582no—
562C2×C8—1582no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—792no—
572C4⋊C4—792no—
573C4⋊C4—792no—
574C4⋊C4—1584no—
575C4⋊C4—1584no—
576C4⋊C4—1584no—
577C4⋊C4—1584no—
578C4⋊C4—1584no—
579C4⋊C4—1584no—
580C4⋊C4—1584no—
581C4⋊C4—1581no—
582C4⋊C4—1581no—
583C4⋊C4—1581no—
584C4⋊C4—1584no—
585C4⋊C4C2×C22⋊D7914yes—
586C4⋊C4C2×C22⋊D7914yes—
587C4⋊C4C2×C22⋊D7914yes—
588C4⋊C4C23×D7912yes—
589C4⋊C4C23×D7912yes—
590C4⋊C4C23×D7912yes—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C42—1584no—
595C42—1584no—
596C42—1584no—
597C42C2×C22⋊D7912yes—
598C42C2×C22⋊D7912yes—
599C42C2×C22⋊D7912yes—
600C42C23×D7912yes—
601C42C23×D7912yes—
602C42C23×D7912yes—
603C23—24no—
604C23—22no—
605C23—42no—
606C23—42no—
607C23C22×C22⋊D7911yescharacteristic
608Q8—44no—
609Q8—84no—
610Q8—3168no—
611Q8—794no—
612Q8—1582no—
613Q8—1584no—
614D4—22no—
615D4—24no—
616D4C2×Q8×D7914yes—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—48no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—84no—
631C2×C4—84no—
632C2×C4—3162no—
633C2×C4—3162no—
634C2×C4—3162no—
635C2×C4—1582no—
636C2×C4—1582no—
637C2×C4—1582no—
638C2×C4—1584no—
639C2×C4—1582no—
640C2×C4C22×C22⋊D7912yes—
641C2×C4C22×C22⋊D7912yes—
642C2×C4C22×C22⋊D7912yes—
643C2×C4C22×C22⋊D7912yes—
644C2×C4C22×C22⋊D7912yes—
645C2×C4C22×C22⋊D7912yes—
646C2×C4C22×C22⋊D7911yescharacteristic
647C2×C4C2×Q8×D7912yes—
648C2×C4#1457920912yes—
649C2×C4C24×D7911yescharacteristic
650C8—794no—
651C8—1582no—
652C8—1582no—
653C8—1582no—
654C22—24no—
655C22—48no—
656C22—42no—
657C22—42no—
658C22Q8×C22⋊D7912yes—
659C22#1909936112yes—
660C22#1909937412yes—
661C22C23×C22⋊D7911yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—22no—
667C4—22no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—3162no—
672C4—3162no—
673C4—3162no—
674C4—1584no—
675C4Q8×C22⋊D7912yes—
676C4C22×Q8×D7911yescharacteristic
677C4C2×#1457920911yescharacteristic
678C2—44no—
679C2#2377634514yesdirect product factor
680C2C2×Q8×C22⋊D7911yescharacteristic
681C2C2×#1909936111yescharacteristic
682C2C2×#1909937411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#554×C79C2
socleC23×C79C22×D4
prime radicalC22×D4×C79C23
hypercenterC2×#554D79
hypocenterC79C2×#3388
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#19099291C2semidirect
2. #23776345C2direct (N × H)
3. C2×#19098973C2semidirect
4. C2×#19098969C2semidirect
5. C2×#19098962C2semidirect
6. C2×#19098867C2semidirect
7. C2×#19098867C2semidirect
8. C2×#19098845C2semidirect
12. C2×#19098694C2semidirect
19. #19099291C22semidirect
30. #19098973C22semidirect
31. #19098969C22semidirect
32. #19098962C22semidirect
33. #19098867C22semidirect
34. #19098867C22semidirect
38. #19098845C22semidirect
39. #19098694C22semidirect
79. C2×#11929612Q8semidirect
187. #11929612C2×Q8semidirect
338. C2×C79#3388semidirect
358. C79C2×#3388semidirect
679. C2#23776345direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992912
#237763452
C2×#190989732
C2×#190989692
C2×#190989622
C2×#190988672
C2×#190988452
C2×#190988632
C2×#190988532
C2×#190986942
C2×#190986632
C2×C4×#119296122
C2×#554×C792
C2×#338879