Finite Group Databasebeta

← C2×#23776135 #35167987

Subgroups — C2×#23776135 #35167987

Order 20224.

1842 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic158C211yesmaximal, characteristic, complemented
2C2×#19099282C211yesmaximal, characteristic
3#23776135C2116yesmaximal, direct product factor
4C2×#19098922C211yesmaximal, characteristic
5C2×#19098921C211yesmaximal, characteristic
6C2×#19098912C211yesmaximal, characteristic, complemented
7C2×#19098849C211yesmaximal, characteristic, complemented
8C2×#19098846C211yesmaximal, characteristic, complemented
9C2×#19098851C211yesmaximal, characteristic
10C2×#19098783C211yesmaximal, characteristic
11C2×#19098771C211yesmaximal, characteristic, complemented
12C2×#19098692C211yesmaximal, characteristic, complemented
13C2×#19098670C211yesmaximal, characteristic, complemented
14C2×#19098668C211yesmaximal, characteristic, complemented
15C2×SD16×Dic79C211yesmaximal, characteristic
16C2×#464×C79C211yesmaximal, characteristic
17C22×#11929614C2211yescharacteristic
18Q8×Dic158—24no—
19Q8×Dic158C2218yescomplemented
20#19099282—24no—
21#19099282C2218yes—
22C2×#14579161—21no—
23C2×#14579161C2211yescharacteristic
24C2×#14579160—21no—
25C2×#14579160—21no—
26C2×#14579160C2211yescharacteristic
27C2×#14579160C2211yescharacteristic
28C2×#14579159C2211yescharacteristic
29C2×#14579154—21no—
30C2×#14579154—21no—
31C2×#14579148C2211yescharacteristic
32C2×#14579138—21no—
33C2×Q8×Dic79C2211yescharacteristic
34C2×Q8×Dic79C2211yescharacteristic
35C2×Q8×Dic79C2211yescharacteristic
36C2×C4×Dic158—21no—
37C2×C4×Dic158C2211yescharacteristic
38C2×C4×Dic158C2211yescharacteristic
39C2×D4×Dic79C2211yescharacteristic
40C2×#14579117—21no—
41#19098922C2218yes—
42#19098921C2218yes—
43#19098912C2218yescomplemented
44#19098851C2218yes—
45#19098849C2218yescomplemented
46#19098846C2218yescomplemented
47#19098783C2218yes—
48#19098771C2218yescomplemented
49#19098692C2218yescomplemented
50#19098670C2218yescomplemented
51#19098668C2218yescomplemented
52SD16×Dic79C2218yes—
53C2×#14579093C2211yescharacteristic
54C2×#14579093C2211yescharacteristic
55C2×#14579092C2211yescharacteristic
56C2×Dic79⋊C8C2211yescharacteristic
57C2×Dic79⋊C8C2211yescharacteristic
58C2×#14579086C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579085C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579084C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×#14579072C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×Q16×C79C2211yescharacteristic
70C22×SD16×C79C2211yescharacteristic
71C2×#124×C79C2211yescharacteristic
72C2×C4×Q8×C79C2211yescharacteristic
73#464×C79C2218yes—
74C2×C4⋊C8×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×Dic158—21no—
80C22×Dic158D411yescharacteristic
81C22×Dic158C2311yescharacteristic
82C23×Dic79—21no—
83C2×#11929614—24no—
84C2×#11929614C2314yes—
85C22×C79⋊C8C2311yescharacteristic
86C22×C79⋊C8C2311yescharacteristic
87#14579161—22no—
88#14579161—28no—
89#14579161C2314yes—
90#14579160—28no—
91#14579160—28no—
92#14579160—22no—
93#14579160—22no—
94#14579160C2314yes—
95#14579160C2314yes—
96#14579159—22no—
97#14579159C2314yes—
98#14579154—28no—
99#14579154—28no—
100#14579148—22no—
101#14579148C2314yes—
102#14579138—28no—
103Q8×Dic79—22no—
104Q8×Dic79—22no—
105Q8×Dic79—22no—
106Q8×Dic79C2314yes—
107Q8×Dic79C2314yes—
108Q8×Dic79C2314yes—
109C4×Dic158—22no—
110C4×Dic158—28no—
111C4×Dic158D414yes—
112C4×Dic158C2314yes—
113C4×Dic158C2314yes—
114D4×Dic79—22no—
115D4×Dic79C2314yes—
116#14579117—28no—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79D411yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4D411yescharacteristic
131C2×Dic79⋊C4D411yescharacteristic
132C2×C22⋊Dic79—21no—
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79—21no—
135C2×C4×Dic79—21no—
136C2×C4×Dic79—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79C2311yescharacteristic
140C2×C4×Dic79C2311yescharacteristic
141#14579093C2314yes—
142#14579093C2314yes—
143#14579092C2314yes—
144Dic79⋊C8C2314yes—
145Dic79⋊C8C2314yes—
146#14579086C2314yes—
147#14579086C2314yes—
148#14579085C2314yes—
149#14579085C2314yes—
150#14579085C2314yes—
151#14579084C2314yes—
152#14579082C2314yes—
153#14579082C2314yes—
154#14579072C2314yes—
155#14579071C2314yes—
156C8×Dic79C2314yes—
157C22×Q8×C79C2311yescharacteristic
158C22×Q8×C79C2311yescharacteristic
159C22×D4×C79C2311yescharacteristic
160C2×Q16×C79—24no—
161C2×Q16×C79C2314yes—
162C2×SD16×C79—24no—
163C2×SD16×C79C2314yes—
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166#124×C79—22no—
167#124×C79C2314yes—
168C4×Q8×C79—22no—
169C4×Q8×C79C2314yes—
170C2×C4⋊C4×C79—21no—
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C22⋊C4×C79—21no—
173C2×C22⋊C4×C79—21no—
174C2×C42×C79—21no—
175C2×C42×C79C2311yescharacteristic
176C4⋊C8×C79C2314yes—
177#103×C79C2314yes—
178#102×C79C2314yes—
179C2×Dic158—24no—
180C2×Dic158—24no—
181C2×Dic158—24no—
182C2×Dic158—21no—
183C2×Dic158—24no—
184C2×Dic158—22no—
185C2×Dic158—22no—
186C2×Dic158—82no—
187C2×Dic158—82no—
188C2×Dic158—82no—
189C2×Dic158C2×D414yes—
190C2×Dic158C2412yes—
191C22×Dic79—24no—
192C22×Dic79—21no—
193C22×Dic79—21no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—44no—
197C22×Dic79C2×D411yescharacteristic
198C22×Dic79C2×D411yescharacteristic
199C22×Dic79C2×D411yescharacteristic
200C22×Dic79C2×D411yescharacteristic
201#11929614—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—24no—
210C4⋊Dic79—21no—
211C4⋊Dic79—21no—
212C4⋊Dic79—21no—
213C4⋊Dic79C2×D414yes—
214C4⋊Dic79C2412yes—
215C4⋊Dic79C2412yes—
216C4⋊Dic79C2412yes—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4C2×D414yes—
223Dic79⋊C4C2×D414yes—
224C22⋊Dic79—24no—
225C22⋊Dic79—24no—
226C22⋊Dic79—24no—
227C4×Dic79—24no—
228C4×Dic79—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#4114yes—
242C2×Q8×C79C2412yes—
243C2×Q8×C79C2412yes—
244C2×D4×C79—21no—
245C2×D4×C79—22no—
246C2×D4×C79—22no—
247C2×D4×C79C2412yes—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2411yescharacteristic
254Q16×C79—28no—
255SD16×C79—28no—
256C2×C8×C79—22no—
257C2×C8×C79—22no—
258C2×C8×C79C2412yes—
259C2×C8×C79C2412yes—
260C4⋊C4×C79—24no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79C2412yes—
263C22⋊C4×C79—24no—
264C22⋊C4×C79—24no—
265C42×C79—24no—
266C42×C79C2×D412yes—
267C42×C79C2412yes—
268C23×C79—22no—
269C23×C79—42no—
270C23×C79—42no—
271C23×C79—42no—
272C23×C79C22×D411yescharacteristic
273Q8×C79—24no—
274Q8×C79—22no—
275Q8×C79—22no—
276Q8×C79—22no—
277Q8×C79—42no—
278Q8×C79C2×#4114yes—
279D4×C79—22no—
280D4×C79—22no—
281D4×C79—42no—
282C2×C4×C79—24no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—42no—
289C2×C4×C79—42no—
290C2×C4×C79C22×D412yes—
291C2×C4×C79C22×D412yes—
292C2×C4×C79C22×D411yescharacteristic
293C2×C4×C79C2×#4112yes—
294C2×C4×C792−1+412yes—
295C2×C4×C79C2511yescharacteristic
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—42no—
304C2×Dic79—42no—
305C2×Dic79—42no—
306C2×Dic79—42no—
307C2×Dic79—48no—
308C2×Dic79#13714yes—
309C2×Dic79C22×D412yes—
310C2×Dic79C22×D412yes—
311C2×Dic79C22×D412yes—
312C2×Dic79C22×D412yes—
313Dic158—28no—
314Dic158—22no—
315Dic158—22no—
316Dic158—42no—
317Dic158—84no—
318Dic158—84no—
319Dic158—84no—
320C8×C79—22no—
321C8×C79—22no—
322C79⋊C8—22no—
323C79⋊C8—22no—
324C22×C79—42no—
325C22×C79—42no—
326C22×C79—42no—
327C22×C79—84no—
328C22×C79#54812yes—
329C22×C79C2×#13712yes—
330C22×C79#57712yes—
331C22×C79C23×D411yescharacteristic
332C4×C79—24no—
333C4×C79—22no—
334C4×C79—22no—
335C4×C79—42no—
336C4×C79—42no—
337C4×C79#54812yes—
338C4×C79C22×#4111yescharacteristic
339C4×C79C2×2−1+411yescharacteristic
340Dic79—22no—
341Dic79—22no—
342Dic79—22no—
343Dic79—42no—
344Dic79—42no—
345Dic79—42no—
346Dic79—42no—
347Dic79C2×#13714yes—
348C2×#3369—791nomaximal, Sylow
349C2×C79—82no—
350C2×C79#336914yescomplemented
351C2×C79C2×#54811yescharacteristic
352C2×C79C22×#13711yescharacteristic
353C2×C79C2×#57711yescharacteristic
354C2×Q82—791no—
355C2×#556—791no—
356#3369—7916no—
357C2×#489—791no—
358C2×#489—791no—
359C2×#487—791no—
360C2×#475—791no—
361C2×#475—791no—
362C2×#476—791no—
363C2×#464—791no—
364C2×#464D7911yescharacteristic
365C2×#462—791no—
366C2×#446—791no—
367C2×#441—791no—
368C2×#441—791no—
369C2×C4×SD16—791no—
370C79C2×#336911yescharacteristic, complemented, Sylow
371C22×Q16—791no—
372C22×Q16C2×D7911yescharacteristic
373C22×SD16C2×D7911yescharacteristic
374Q82—798no—
375Q82—1584no—
376#556—798no—
377#556—1584no—
378C2×C4⋊Q8—791no—
379C2×C4⋊Q8—791no—
380C2×C4⋊Q8—791no—
381C2×C4⋊Q8—791no—
382C2×C4⋊Q8—1581no—
383C2×C4⋊Q8—1581no—
384C2×C4⋊Q8—1581no—
385C2×#126—1581no—
386C2×#126—1581no—
387C2×#124—791no—
388C2×#124C2×D7911yescharacteristic
389C2×C22⋊Q8—1581no—
390C2×C4×Q8—791no—
391C2×C4×Q8—791no—
392C2×C4×Q8—791no—
393C2×C4×Q8—791no—
394C2×C4×Q8—791no—
395C2×C4×Q8—1581no—
396C2×C4×Q8C2×D7911yescharacteristic
397C2×C4×D4—791no—
398C2×#117—1581no—
399#489—798no—
400#489—798no—
401#487—798no—
402#476—798no—
403#475—798no—
404#475—798no—
405#464—798no—
406#464C2×D7918yes—
407#462—798no—
408#446—798no—
409#441—798no—
410#441—798no—
411C4×SD16—798no—
412C2×#106—791no—
413C2×#106—791no—
414C2×#106—791no—
415C2×C4⋊C8—791no—
416C2×C4⋊C8—791no—
417C2×C4⋊C8C2×D7911yescharacteristic
418C2×#103—791no—
419C2×#103—791no—
420C2×#103—791no—
421C2×#103—791no—
422C2×#103—791no—
423C2×#103—791no—
424C2×#103C2×D7911yescharacteristic
425C2×#102—791no—
426C2×#102—791no—
427C2×#102C2×D7911yescharacteristic
428C2×#97—791no—
429C2×#97—791no—
430C2×C4×C8—791no—
431C22×Q8—791no—
432C22×Q8—791no—
433C22×Q8—1581no—
434C22×Q8—1581no—
435C22×Q8—1581no—
436C22×Q8C22×D7911yescharacteristic
437C22×Q8C22×D7911yescharacteristic
438C22×D4C22×D7911yescharacteristic
439C23×C4—1581no—
440C2×Q16—24no—
441C2×Q16—794no—
442C2×Q16—1584no—
443C2×Q16C22×D7914yes—
444C2×SD16—24no—
445C2×SD16C22×D7914yes—
446C22×C8—791no—
447C22×C8—791no—
448C22×C8C22×D7911yescharacteristic
449C22×C8C22×D7911yescharacteristic
450C4⋊Q8—794no—
451C4⋊Q8—794no—
452C4⋊Q8—794no—
453C4⋊Q8—794no—
454C4⋊Q8—1588no—
455C4⋊Q8—1582no—
456C4⋊Q8—1582no—
457C4⋊Q8—1582no—
458C4⋊Q8—1588no—
459C4⋊Q8—1588no—
460C4⋊Q8—1582no—
461#126—1588no—
462#126—1588no—
463#124—22no—
464#124—794no—
465#124—1582no—
466#124C22×D7914yes—
467C22⋊Q8—1588no—
468C4×Q8—22no—
469C4×Q8—794no—
470C4×Q8—794no—
471C4×Q8—794no—
472C4×Q8—794no—
473C4×Q8—794no—
474C4×Q8—794no—
475C4×Q8—1588no—
476C4×Q8—1582no—
477C4×Q8—1582no—
478C4×Q8—1582no—
479C4×Q8—1582no—
480C4×Q8C22×D7914yes—
481C4×D4—794no—
482C4×D4—1582no—
483#117—1588no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—791no—
486C2×C4⋊C4—791no—
487C2×C4⋊C4—791no—
488C2×C4⋊C4—791no—
489C2×C4⋊C4—791no—
490C2×C4⋊C4—791no—
491C2×C4⋊C4—1581no—
492C2×C4⋊C4—1581no—
493C2×C4⋊C4—1581no—
494C2×C4⋊C4—1581no—
495C2×C4⋊C4—1581no—
496C2×C4⋊C4—1581no—
497C2×C4⋊C4—1581no—
498C2×C4⋊C4—1581no—
499C2×C4⋊C4—1581no—
500C2×C4⋊C4C22×D7911yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—1581no—
504C2×C22⋊C4—1581no—
505C2×C22⋊C4—1581no—
506C2×C42—21no—
507C2×C42—791no—
508C2×C42—791no—
509C2×C42—1581no—
510C2×C42—1581no—
511C2×C42—1581no—
512C2×C42—1581no—
513C2×C42C22×D7911yescharacteristic
514#106—794no—
515#106—794no—
516#106—794no—
517C4⋊C8—794no—
518C4⋊C8—794no—
519C4⋊C8C22×D7914yes—
520#103—794no—
521#103—794no—
522#103—794no—
523#103—794no—
524#103—794no—
525#103—794no—
526#103C22×D7914yes—
527#102—794no—
528#102—794no—
529#102C22×D7914yes—
530#97—794no—
531#97—794no—
532C4×C8—794no—
533C24—21no—
534C2×Q8—22no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—794no—
540C2×Q8—792no—
541C2×Q8—6322no—
542C2×Q8—6322no—
543C2×Q8—6322no—
544C2×Q8—1584no—
545C2×Q8—1584no—
546C2×Q8—1584no—
547C2×Q8—1582no—
548C2×Q8—1582no—
549C2×Q8—1581no—
550C2×Q8—1584no—
551C2×Q8#1192962314yes—
552C2×Q8C23×D7912yes—
553C2×Q8C23×D7912yes—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4C23×D7912yes—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—3164no—
562C22×C4—791no—
563C22×C4—791no—
564C22×C4—791no—
565C22×C4—791no—
566C22×C4—1584no—
567C22×C4—1581no—
568C22×C4—1581no—
569C22×C4—1581no—
570C22×C4—1581no—
571C22×C4D4×D7911yescharacteristic
572C22×C4D4×D7911yescharacteristic
573C22×C4C23×D7911yescharacteristic
574Q16—28no—
575Q16—1588no—
576SD16—28no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—792no—
580C2×C8—792no—
581C2×C8—1582no—
582C2×C8—1582no—
583C2×C8C23×D7912yes—
584C2×C8C23×D7912yes—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—794no—
588C4⋊C4—794no—
589C4⋊C4—794no—
590C4⋊C4—792no—
591C4⋊C4—792no—
592C4⋊C4—792no—
593C4⋊C4—1584no—
594C4⋊C4—1584no—
595C4⋊C4—1584no—
596C4⋊C4—1584no—
597C4⋊C4—1584no—
598C4⋊C4—1584no—
599C4⋊C4—1584no—
600C4⋊C4—1584no—
601C4⋊C4—1581no—
602C4⋊C4—1581no—
603C4⋊C4—1581no—
604C4⋊C4—1584no—
605C4⋊C4C23×D7912yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—1584no—
609C22⋊C4—1584no—
610C22⋊C4—1584no—
611C42—24no—
612C42—792no—
613C42—792no—
614C42—792no—
615C42—792no—
616C42—1584no—
617C42—1584no—
618C42—1584no—
619C42—1584no—
620C42D4×D7912yes—
621C42C23×D7912yes—
622C23—22no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23C2×D4×D7911yescharacteristic
627Q8—22no—
628Q8—24no—
629Q8—22no—
630Q8—22no—
631Q8—42no—
632Q8—3162no—
633Q8—6324no—
634Q8—6324no—
635Q8—6324no—
636Q8—1588no—
637Q8—1582no—
638Q8—1582no—
639Q8C2×#1192962314yes—
640D4—22no—
641D4—22no—
642D4—42no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—3162no—
652C2×C4—3162no—
653C2×C4—3162no—
654C2×C4—3162no—
655C2×C4—3168no—
656C2×C4—794no—
657C2×C4—792no—
658C2×C4—792no—
659C2×C4—792no—
660C2×C4—792no—
661C2×C4—1582no—
662C2×C4—1582no—
663C2×C4—1582no—
664C2×C4—1582no—
665C2×C4—1582no—
666C2×C4—1582no—
667C2×C4—1582no—
668C2×C4C2×D4×D7912yes—
669C2×C4C2×D4×D7912yes—
670C2×C4C2×D4×D7911yescharacteristic
671C2×C4C2×#1192962312yes—
672C2×C4#1457920812yes—
673C2×C4C24×D7911yescharacteristic
674C8—22no—
675C8—22no—
676C8—1582no—
677C8—1582no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—84no—
682C22#1909921912yes—
683C22#137×D7912yes—
684C22#1909937012yes—
685C22C22×D4×D7911yescharacteristic
686C4—22no—
687C4—24no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—3162no—
692C4—3162no—
693C4—3162no—
694C4—3162no—
695C4—794no—
696C4—1582no—
697C4—1582no—
698C4—1582no—
699C4#1909921912yes—
700C4C22×#1192962311yescharacteristic
701C4C2×#1457920811yescharacteristic
702C2—82no—
703C2#2377613514yesdirect product factor
704C2C2×#1909921911yescharacteristic
705C2C2×#137×D7911yescharacteristic
706C2C2×#1909937011yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#464×C79C2
socleC23×C79C22×D4
prime radicalC22×D4×C79C23
hypercenterC2×#464D79
hypocenterC79C2×#3369
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic158C2semidirect
3. #23776135C2direct (N × H)
6. C2×#19098912C2semidirect
7. C2×#19098849C2semidirect
8. C2×#19098846C2semidirect
11. C2×#19098771C2semidirect
12. C2×#19098692C2semidirect
13. C2×#19098670C2semidirect
14. C2×#19098668C2semidirect
19. Q8×Dic158C22semidirect
43. #19098912C22semidirect
45. #19098849C22semidirect
46. #19098846C22semidirect
48. #19098771C22semidirect
49. #19098692C22semidirect
50. #19098670C22semidirect
51. #19098668C22semidirect
350. C2×C79#3369semidirect
370. C79C2×#3369semidirect
703. C2#23776135direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1582
C2×#190992822
#237761352
C2×#190989222
C2×#190989212
C2×#190989122
C2×#190988492
C2×#190988462
C2×#190988512
C2×#190987832
C2×#190987712
C2×#190986922
C2×#190986702
C2×#190986682
C2×SD16×Dic792
C2×#464×C792
C2×#336979