Finite Group Databasebeta

← C2×#23776220 #35168027

Subgroups — C2×#23776220 #35168027

Order 20224.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099287C211yesmaximal, characteristic, complemented
2C2×#19099272C211yesmaximal, characteristic, complemented
3#23776220C2116yesmaximal, direct product factor
4C2×#19098931C211yesmaximal, characteristic, complemented
5C2×#19098924C211yesmaximal, characteristic, complemented
6C2×#19098919C211yesmaximal, characteristic, complemented
7C2×#19098872C211yesmaximal, characteristic, complemented
8C2×#19098846C211yesmaximal, characteristic, complemented
9C2×#19098864C211yesmaximal, characteristic, complemented
10C2×#19098780C211yesmaximal, characteristic
11C2×#19098780C211yesmaximal, characteristic
12C2×#19098692C211yesmaximal, characteristic, complemented
13C2×#19098673C211yesmaximal, characteristic
14C2×#19098664C211yesmaximal, characteristic, complemented
15C2×SD16×Dic79C211yesmaximal, characteristic, complemented
16C2×#461×C79C211yesmaximal, characteristic, complemented
17C22×#11929609C2211yescharacteristic
18#19099287—24no—
19#19099287C2218yescomplemented
20#19099272—24no—
21#19099272C2218yescomplemented
22C2×#14579160C2211yescharacteristic
23C2×#14579156—21no—
24C2×#14579156—21no—
25C2×#14579153C2211yescharacteristic
26C2×#14579152C2211yescharacteristic
27C2×#14579150C2211yescharacteristic
28C2×#14579150C2211yescharacteristic
29C2×#14579141—21no—
30C2×#14579140—21no—
31C2×#14579138—21no—
32C2×#14579138—21no—
33C2×Q8×Dic79C2211yescharacteristic
34C2×Q8×Dic79C2211yescharacteristic
35C2×C4×Dic158C2211yescharacteristic
36C2×C4×D316C2211yescharacteristic
37C2×D4×Dic79C2211yescharacteristic
38C2×D4×Dic79C2211yescharacteristic
39C2×#14579119—21no—
40C22×Dic79⋊C4—21no—
41#19098931C2218yescomplemented
42#19098924C2218yescomplemented
43#19098919C2218yescomplemented
44#19098872C2218yescomplemented
45#19098864C2218yescomplemented
46#19098846C2218yescomplemented
47#19098780C2218yes—
48#19098780C2218yes—
49#19098692C2218yescomplemented
50#19098673C2218yes—
51#19098664C2218yescomplemented
52SD16×Dic79C2218yescomplemented
53C2×#14579095C2211yescharacteristic
54C2×#14579093C2211yescharacteristic
55C2×#14579092C2211yescharacteristic
56C2×Dic79⋊C8C2211yescharacteristic
57C2×Dic79⋊C8C2211yescharacteristic
58C2×#14579085C2211yescharacteristic
59C2×#14579085C2211yescharacteristic
60C2×#14579085C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579083C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579081C2211yescharacteristic
66C2×#14579072C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C22×SD16×C79C2211yescharacteristic
71C2×C4⋊Q8×C79C2211yescharacteristic
72C2×C4×D4×C79C2211yescharacteristic
73#461×C79C2218yescomplemented
74C2×C4⋊C8×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158D411yescharacteristic
79C22×D316C2311yescharacteristic
80C23×Dic79—21no—
81C23×Dic79—21no—
82C22×C4×D79—21no—
83C2×#11929609—24no—
84C2×#11929609C2314yes—
85C22×C79⋊C8C2311yescharacteristic
86C22×C79⋊C8C2311yescharacteristic
87#14579160—22no—
88#14579160C2314yes—
89#14579156—28no—
90#14579156—28no—
91#14579153—22no—
92#14579153C2314yes—
93#14579152—22no—
94#14579152C2314yes—
95#14579150—22no—
96#14579150—22no—
97#14579150C2314yes—
98#14579150C2314yes—
99#14579141—28no—
100#14579140—28no—
101#14579138—28no—
102#14579138—28no—
103Q8×Dic79—22no—
104Q8×Dic79—22no—
105Q8×Dic79C2314yes—
106Q8×Dic79C2314yes—
107C4×Dic158D414yes—
108C4×Dic158C2314yes—
109C4×D316—22no—
110C4×D316C2314yes—
111D4×Dic79—22no—
112D4×Dic79—22no—
113D4×Dic79C2314yes—
114D4×Dic79C2314yes—
115#14579119—28no—
116C2×C4⋊Dic79—21no—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79D411yescharacteristic
120C2×C4⋊Dic79C2311yescharacteristic
121C2×C4⋊Dic79C2311yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×Dic79⋊C4—21no—
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—28no—
128C2×Dic79⋊C4D411yescharacteristic
129C2×Dic79⋊C4D411yescharacteristic
130C2×C22⋊Dic79—21no—
131C2×C22⋊Dic79—21no—
132C2×(C2×D79)⋊C4—21no—
133C2×(C2×D79)⋊C4—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79C2311yescharacteristic
140C2×C4×Dic79C2311yescharacteristic
141#14579095C2314yes—
142#14579093C2314yes—
143#14579092C2314yes—
144Dic79⋊C8C2314yes—
145Dic79⋊C8C2314yes—
146#14579085C2314yes—
147#14579085C2314yes—
148#14579085C2314yes—
149#14579085C2314yes—
150#14579083C2314yes—
151#14579083C2314yes—
152#14579082C2314yes—
153#14579081C2314yes—
154#14579072C2314yes—
155#14579071C2314yes—
156C8×Dic79C2314yes—
157C22×Q8×C79C2311yescharacteristic
158C22×Q8×C79C2311yescharacteristic
159C22×D4×C79C2311yescharacteristic
160C23×C4×C79—21no—
161C2×SD16×C79—24no—
162C2×SD16×C79—24no—
163C2×SD16×C79C2314yes—
164C2×SD16×C79C2314yes—
165C22×C8×C79C2311yescharacteristic
166C22×C8×C79C2311yescharacteristic
167C4⋊Q8×C79—22no—
168C4⋊Q8×C79C2314yes—
169C4×D4×C79—22no—
170C4×D4×C79C2314yes—
171C2×C4⋊C4×C79—21no—
172C2×C4⋊C4×C79—21no—
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C22⋊C4×C79—21no—
175C2×C42×C79C2311yescharacteristic
176C4⋊C8×C79C2314yes—
177#103×C79C2314yes—
178#103×C79C2314yes—
179C23×D79—21no—
180C2×Dic158—24no—
181C2×Dic158—42no—
182C2×Dic158—82no—
183C2×Dic158C2×D414yes—
184C2×D316—21no—
185C2×D316—22no—
186C2×D316—22no—
187C2×D316C2412yes—
188C22×Dic79—24no—
189C22×Dic79—24no—
190C22×Dic79—21no—
191C22×Dic79—21no—
192C22×Dic79—21no—
193C22×Dic79—44no—
194C22×Dic79—82no—
195C22×Dic79C2×D411yescharacteristic
196C22×Dic79C2×D411yescharacteristic
197C22×Dic79C2×D411yescharacteristic
198C22×Dic79C2×D411yescharacteristic
199C2×C4×D79—24no—
200C2×C4×D79—44no—
201#11929609—28no—
202C2×C79⋊C8—22no—
203C2×C79⋊C8—22no—
204C2×C79⋊C8C2412yes—
205C2×C79⋊C8C2412yes—
206C4⋊Dic79—24no—
207C4⋊Dic79—24no—
208C4⋊Dic79—24no—
209C4⋊Dic79—21no—
210C4⋊Dic79—21no—
211C4⋊Dic79—21no—
212C4⋊Dic79C2×D414yes—
213C4⋊Dic79C2412yes—
214C4⋊Dic79C2412yes—
215C4⋊Dic79C2412yes—
216Dic79⋊C4—24no—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4C2×D414yes—
221Dic79⋊C4C2×D414yes—
222C22⋊Dic79—24no—
223C22⋊Dic79—24no—
224(C2×D79)⋊C4—24no—
225(C2×D79)⋊C4—24no—
226(C2×D79)⋊C4—24no—
227(C2×D79)⋊C4—24no—
228(C2×D79)⋊C4—24no—
229C4×Dic79—24no—
230C4×Dic79—24no—
231C4×Dic79C2×D412yes—
232C4×Dic79C2×D412yes—
233C4×Dic79C2412yes—
234C4×Dic79C2412yes—
235C24×C79—21no—
236C2×Q8×C79—21no—
237C2×Q8×C79—21no—
238C2×Q8×C79—22no—
239C2×Q8×C79—22no—
240C2×Q8×C79—22no—
241C2×Q8×C79—22no—
242C2×Q8×C79C2412yes—
243C2×Q8×C79C2412yes—
244C2×D4×C79—21no—
245C2×D4×C79—22no—
246C2×D4×C79#4114yes—
247C2×D4×C79C2412yes—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79—24no—
252C22×C4×C79—82no—
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2411yescharacteristic
256SD16×C79—28no—
257SD16×C79—28no—
258C2×C8×C79—22no—
259C2×C8×C79—22no—
260C2×C8×C79C2412yes—
261C2×C8×C79C2412yes—
262C4⋊C4×C79—24no—
263C4⋊C4×C79—24no—
264C4⋊C4×C79—21no—
265C4⋊C4×C79C2412yes—
266C22⋊C4×C79—24no—
267C42×C79C2×D412yes—
268C42×C79C2412yes—
269C23×C79—24no—
270C23×C79—22no—
271C23×C79—42no—
272C23×C79—42no—
273C23×C79C22×D411yescharacteristic
274C22×D79—22no—
275C22×D79—42no—
276C22×D79—42no—
277C22×D79—42no—
278Q8×C79—22no—
279Q8×C79—22no—
280Q8×C79—22no—
281Q8×C79—22no—
282Q8×C79—42no—
283Q8×C79—42no—
284D4×C79—24no—
285D4×C79—22no—
286D4×C79C2×#4114yes—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—42no—
293C2×C4×C79—42no—
294C2×C4×C79—42no—
295C2×C4×C79—84no—
296C2×C4×C79C22×D412yes—
297C2×C4×C79C22×D412yes—
298C2×C4×C79C22×D411yescharacteristic
299C2×C4×C79C2×#4112yes—
300C2×C4×C792−1+412yes—
301C2×C4×C79C2511yescharacteristic
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—48no—
310C2×Dic79—42no—
311C2×Dic79—42no—
312C2×Dic79—42no—
313C2×Dic79—84no—
314C2×Dic79C22×D412yes—
315C2×Dic79C22×D412yes—
316C2×Dic79C22×D412yes—
317C2×Dic79C22×D412yes—
318D316—22no—
319D316—22no—
320D316—42no—
321C4×D79—48no—
322Dic158—44no—
323Dic158—84no—
324C8×C79—22no—
325C8×C79—22no—
326C79⋊C8—22no—
327C79⋊C8—22no—
328C22×C79—24no—
329C22×C79—48no—
330C22×C79—42no—
331C22×C79—42no—
332C22×C79#54812yes—
333C22×C79#57512yes—
334C22×C79#57712yes—
335C22×C79C23×D411yescharacteristic
336C2×D79—42no—
337C2×D79—42no—
338C2×D79—42no—
339C2×D79—84no—
340C4×C79—22no—
341C4×C79—22no—
342C4×C79—42no—
343C4×C79—42no—
344C4×C79—42no—
345C4×C79#54812yes—
346C4×C79C22×#4111yescharacteristic
347C4×C79C2×2−1+411yescharacteristic
348Dic79—22no—
349Dic79—22no—
350Dic79—22no—
351Dic79—22no—
352Dic79—42no—
353Dic79—42no—
354Dic79—42no—
355C2×#3376—791nomaximal, Sylow
356C2×C79—44no—
357C2×C79#337614yescomplemented
358C2×C79C2×#54811yescharacteristic
359C2×C79C2×#57511yescharacteristic
360C2×C79C2×#57711yescharacteristic
361D79—82no—
362C2×#556—791no—
363C2×#554—791no—
364#3376—7916no—
365C2×#491—791no—
366C2×#489—791no—
367C2×#488—791no—
368C2×#479—791no—
369C2×#475—791no—
370C2×#478—791no—
371C2×#463—791no—
372C2×#463—791no—
373C2×#461D7911yescharacteristic, complemented
374C2×#446—791no—
375C2×#442—791no—
376C2×#440—791no—
377C2×C4×SD16—791no—
378C79C2×#337611yescharacteristic, complemented, Sylow
379C22×SD16C2×D7911yescharacteristic
380C22×SD16C2×D7911yescharacteristic
381C22×D8—791no—
382#556—798no—
383#556—1584no—
384#554—798no—
385#554—1584no—
386C2×C4⋊Q8—791no—
387C2×C4⋊Q8C2×D7911yescharacteristic
388C2×#126—1581no—
389C2×#126—1581no—
390C2×#125—791no—
391C2×#125—791no—
392C2×#124—791no—
393C2×#124—791no—
394C2×C22⋊Q8—1581no—
395C2×C22⋊Q8—1581no—
396C2×C22⋊Q8—1581no—
397C2×C22⋊Q8—1581no—
398C2×C4×Q8—791no—
399C2×C4×Q8—791no—
400C2×C4×Q8—791no—
401C2×C4×D4—791no—
402C2×C4×D4—791no—
403C2×C4×D4—791no—
404C2×C4×D4C2×D7911yescharacteristic
405C2×#117—1581no—
406C22×C4⋊C4—1581no—
407#491—798no—
408#489—798no—
409#488—798no—
410#479—798no—
411#478—798no—
412#475—798no—
413#463—798no—
414#463—798no—
415#461C2×D7918yescomplemented
416#446—798no—
417#442—798no—
418#440—798no—
419C4×SD16—798no—
420C2×#107—791no—
421C2×#106—791no—
422C2×#106—791no—
423C2×C4⋊C8—791no—
424C2×C4⋊C8—791no—
425C2×C4⋊C8C2×D7911yescharacteristic
426C2×#103—791no—
427C2×#103—791no—
428C2×#103—791no—
429C2×#103—791no—
430C2×#103C2×D7911yescharacteristic
431C2×#103C2×D7911yescharacteristic
432C2×#102—791no—
433C2×#102—791no—
434C2×#102—791no—
435C2×#102—791no—
436C2×#97—791no—
437C2×#97—791no—
438C2×C4×C8—791no—
439C22×Q8—791no—
440C22×Q8—1581no—
441C22×Q8C22×D7911yescharacteristic
442C22×Q8C22×D7911yescharacteristic
443C22×D4—791no—
444C22×D4C22×D7911yescharacteristic
445C23×C4—21no—
446C23×C4—1581no—
447C23×C4—1581no—
448C23×C4—1581no—
449C2×SD16—24no—
450C2×SD16—24no—
451C2×SD16C22×D7914yes—
452C2×SD16C22×D7914yes—
453C2×D8—794no—
454C2×D8—1584no—
455C22×C8—791no—
456C22×C8—791no—
457C22×C8C22×D7911yescharacteristic
458C22×C8C22×D7911yescharacteristic
459C4⋊Q8—22no—
460C4⋊Q8—794no—
461C4⋊Q8—1582no—
462C4⋊Q8C22×D7914yes—
463#126—1588no—
464#126—1588no—
465#125—794no—
466#125—794no—
467#125—1582no—
468#125—1582no—
469#124—794no—
470#124—794no—
471#124—1582no—
472#124—1582no—
473C22⋊Q8—1588no—
474C22⋊Q8—1588no—
475C22⋊Q8—1588no—
476C22⋊Q8—1588no—
477C4×Q8—794no—
478C4×Q8—794no—
479C4×Q8—794no—
480C4×Q8—794no—
481C4×Q8—1582no—
482C4×Q8—1582no—
483C4×D4—22no—
484C4×D4—794no—
485C4×D4—794no—
486C4×D4—794no—
487C4×D4—1582no—
488C4×D4—1582no—
489C4×D4—1582no—
490C4×D4C22×D7914yes—
491#117—1588no—
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—791no—
500C2×C4⋊C4—1588no—
501C2×C4⋊C4—1581no—
502C2×C4⋊C4—1581no—
503C2×C4⋊C4—1581no—
504C2×C4⋊C4—1581no—
505C2×C4⋊C4—1581no—
506C2×C4⋊C4—1581no—
507C2×C4⋊C4—1581no—
508C2×C4⋊C4C22×D7911yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—1581no—
511C2×C22⋊C4—1581no—
512C2×C22⋊C4—1581no—
513C2×C22⋊C4—1581no—
514C2×C22⋊C4—1581no—
515C2×C22⋊C4—1581no—
516C2×C22⋊C4—1581no—
517C2×C42—791no—
518C2×C42—791no—
519C2×C42—1581no—
520C2×C42—1581no—
521C2×C42C22×D7911yescharacteristic
522#107—794no—
523#106—794no—
524#106—794no—
525C4⋊C8—794no—
526C4⋊C8—794no—
527C4⋊C8C22×D7914yes—
528#103—794no—
529#103—794no—
530#103—794no—
531#103—794no—
532#103C22×D7914yes—
533#103C22×D7914yes—
534#102—794no—
535#102—794no—
536#102—794no—
537#102—794no—
538#97—794no—
539#97—794no—
540C4×C8—794no—
541C24—21no—
542C24—1581no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—3162no—
550C2×Q8—794no—
551C2×Q8—6322no—
552C2×Q8—1584no—
553C2×Q8C23×D7912yes—
554C2×Q8C23×D7912yes—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—792no—
558C2×D4—1582no—
559C2×D4—1582no—
560C2×D4—1581no—
561C2×D4#1192962314yes—
562C2×D4C23×D7912yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—82no—
568C22×C4—3164no—
569C22×C4—3164no—
570C22×C4—791no—
571C22×C4—791no—
572C22×C4—791no—
573C22×C4—791no—
574C22×C4—6322no—
575C22×C4—1584no—
576C22×C4—1581no—
577C22×C4—1581no—
578C22×C4—1581no—
579C22×C4—1584no—
580C22×C4—1584no—
581C22×C4D4×D7911yescharacteristic
582C22×C4D4×D7911yescharacteristic
583C22×C4C23×D7911yescharacteristic
584SD16—28no—
585SD16—28no—
586D8—1588no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—792no—
590C2×C8—792no—
591C2×C8—1582no—
592C2×C8—1582no—
593C2×C8C23×D7912yes—
594C2×C8C23×D7912yes—
595C4⋊C4—24no—
596C4⋊C4—24no—
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—1584no—
610C4⋊C4—1584no—
611C4⋊C4—1581no—
612C4⋊C4—1581no—
613C4⋊C4—1581no—
614C4⋊C4C23×D7912yes—
615C22⋊C4—24no—
616C22⋊C4—1584no—
617C22⋊C4—1584no—
618C22⋊C4—1584no—
619C22⋊C4—1584no—
620C22⋊C4—1584no—
621C22⋊C4—1584no—
622C22⋊C4—1584no—
623C42—792no—
624C42—792no—
625C42—792no—
626C42—792no—
627C42—1584no—
628C42—1584no—
629C42D4×D7912yes—
630C42C23×D7912yes—
631C23—24no—
632C23—22no—
633C23—42no—
634C23—42no—
635C23—3162no—
636C23—3162no—
637C23—3162no—
638C23—1582no—
639C23C2×D4×D7911yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—42no—
645Q8—42no—
646Q8—3164no—
647Q8—6324no—
648D4—22no—
649D4—24no—
650D4—3162no—
651D4—1582no—
652D4—1582no—
653D4C2×#1192962314yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—84no—
663C2×C4—3168no—
664C2×C4—3162no—
665C2×C4—3162no—
666C2×C4—3162no—
667C2×C4—3168no—
668C2×C4—792no—
669C2×C4—792no—
670C2×C4—792no—
671C2×C4—792no—
672C2×C4—6324no—
673C2×C4—1582no—
674C2×C4—1582no—
675C2×C4—1582no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4—1582no—
679C2×C4—1582no—
680C2×C4C2×D4×D7912yes—
681C2×C4C2×D4×D7912yes—
682C2×C4C2×D4×D7911yescharacteristic
683C2×C4C2×#1192962312yes—
684C2×C4#1457920812yes—
685C2×C4C24×D7911yescharacteristic
686C8—22no—
687C8—22no—
688C8—1582no—
689C8—1582no—
690C22—24no—
691C22—42no—
692C22—42no—
693C22—48no—
694C22—3162no—
695C22—3162no—
696C22—3162no—
697C22—6324no—
698C22#1909921912yes—
699C22#1909936212yes—
700C22#1909936912yes—
701C22C22×D4×D7911yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—3162no—
708C4—3162no—
709C4—3162no—
710C4—1582no—
711C4—1582no—
712C4—1582no—
713C4—1582no—
714C4#1909921912yes—
715C4C22×#1192962311yescharacteristic
716C4C2×#1457920811yescharacteristic
717C2—44no—
718C2—6322no—
719C2#2377622014yesdirect product factor
720C2C2×#1909921911yescharacteristic
721C2C2×#1909936211yescharacteristic
722C2C2×#1909936911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#461×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929609C22
hypercenterC2×#461D79
hypocenterC79C2×#3376
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#19099287C2semidirect
2. C2×#19099272C2semidirect
3. #23776220C2direct (N × H)
4. C2×#19098931C2semidirect
5. C2×#19098924C2semidirect
6. C2×#19098919C2semidirect
7. C2×#19098872C2semidirect
8. C2×#19098846C2semidirect
9. C2×#19098864C2semidirect
12. C2×#19098692C2semidirect
14. C2×#19098664C2semidirect
15. C2×SD16×Dic79C2semidirect
16. C2×#461×C79C2semidirect
19. #19099287C22semidirect
21. #19099272C22semidirect
41. #19098931C22semidirect
42. #19098924C22semidirect
43. #19098919C22semidirect
44. #19098872C22semidirect
45. #19098864C22semidirect
46. #19098846C22semidirect
49. #19098692C22semidirect
51. #19098664C22semidirect
52. SD16×Dic79C22semidirect
73. #461×C79C22semidirect
357. C2×C79#3376semidirect
373. C2×#461D79semidirect
378. C79C2×#3376semidirect
415. #461C2×D79semidirect
719. C2#23776220direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992872
C2×#190992722
#237762202
C2×#190989312
C2×#190989242
C2×#190989192
C2×#190988722
C2×#190988462
C2×#190988642
C2×#190987802
C2×#190986922
C2×#190986732
C2×#190986642
C2×SD16×Dic792
C2×#461×C792
C2×#337679