Finite Group Databasebeta

← C2×#23776176 #35167927

Subgroups — C2×#23776176 #35167927

Order 20224.

1854 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×#19099288C211yesmaximal, characteristic, complemented
2C2×#19099272C211yesmaximal, characteristic
3#23776176C2116yesmaximal, direct product factor
4C2×#19098931C211yesmaximal, characteristic, complemented
5C2×#19098930C211yesmaximal, characteristic, complemented
6C2×#19098912C211yesmaximal, characteristic, complemented
7C2×#19098871C211yesmaximal, characteristic, complemented
8C2×#19098868C211yesmaximal, characteristic, complemented
9C2×#19098856C211yesmaximal, characteristic, complemented
10C2×#19098766C211yesmaximal, characteristic
11C2×#19098766C211yesmaximal, characteristic
12C2×#19098692C211yesmaximal, characteristic, complemented
13C2×#19098664C211yesmaximal, characteristic
14C2×#19098663C211yesmaximal, characteristic
15C2×SD16×Dic79C211yesmaximal, characteristic
16C2×#461×C79C211yesmaximal, characteristic
17C22×#11929612C2211yescharacteristic
18#19099288—24no—
19#19099288C2218yescomplemented
20#19099272—24no—
21#19099272C2218yes—
22C2×#14579160C2211yescharacteristic
23C2×#14579159C2211yescharacteristic
24C2×#14579159C2211yescharacteristic
25C2×#14579153C2211yescharacteristic
26C2×#14579152—21no—
27C2×#14579152C2211yescharacteristic
28C2×#14579151—21no—
29C2×#14579151—21no—
30C2×#14579140—21no—
31C2×#14579138—21no—
32C2×#14579138—21no—
33C2×Q8×Dic79C2211yescharacteristic
34C2×Q8×Dic79C2211yescharacteristic
35C2×C4×Dic158C2211yescharacteristic
36C2×C4×Dic158C2211yescharacteristic
37C2×#14579126—21no—
38C2×D4×Dic79C2211yescharacteristic
39C2×D4×Dic79C2211yescharacteristic
40C22×Dic79⋊C4—21no—
41#19098931C2218yescomplemented
42#19098930C2218yescomplemented
43#19098912C2218yescomplemented
44#19098871C2218yescomplemented
45#19098868C2218yescomplemented
46#19098856C2218yescomplemented
47#19098766C2218yes—
48#19098766C2218yes—
49#19098692C2218yescomplemented
50#19098664C2218yes—
51#19098663C2218yes—
52SD16×Dic79C2218yes—
53C2×#14579095C2211yescharacteristic
54C2×#14579094C2211yescharacteristic
55C2×#14579093C2211yescharacteristic
56C2×Dic79⋊C8C2211yescharacteristic
57C2×Dic79⋊C8C2211yescharacteristic
58C2×#14579086C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579085C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579084C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×#14579072C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C22×SD16×C79C2211yescharacteristic
71C2×C4⋊Q8×C79C2211yescharacteristic
72C2×C4×D4×C79C2211yescharacteristic
73#461×C79C2218yes—
74C2×C4⋊C8×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158D411yescharacteristic
79C22×Dic158C2311yescharacteristic
80C23×Dic79—21no—
81C23×Dic79—21no—
82C2×#11929612—24no—
83C2×#11929612C2314yes—
84C22×C79⋊C8C2311yescharacteristic
85C22×C79⋊C8C2311yescharacteristic
86#14579160—22no—
87#14579160C2314yes—
88#14579159—22no—
89#14579159—22no—
90#14579159C2314yes—
91#14579159C2314yes—
92#14579153—22no—
93#14579153C2314yes—
94#14579152—28no—
95#14579152—22no—
96#14579152C2314yes—
97#14579151—28no—
98#14579151—28no—
99#14579140—28no—
100#14579138—28no—
101#14579138—28no—
102Q8×Dic79—22no—
103Q8×Dic79—22no—
104Q8×Dic79C2314yes—
105Q8×Dic79C2314yes—
106C4×Dic158—22no—
107C4×Dic158D414yes—
108C4×Dic158C2314yes—
109C4×Dic158C2314yes—
110#14579126—28no—
111D4×Dic79—22no—
112D4×Dic79—22no—
113D4×Dic79C2314yes—
114D4×Dic79C2314yes—
115C2×C4⋊Dic79—21no—
116C2×C4⋊Dic79—21no—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79D411yescharacteristic
119C2×C4⋊Dic79C2311yescharacteristic
120C2×C4⋊Dic79C2311yescharacteristic
121C2×C4⋊Dic79C2311yescharacteristic
122C2×Dic79⋊C4—21no—
123C2×Dic79⋊C4—21no—
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—28no—
132C2×Dic79⋊C4D411yescharacteristic
133C2×Dic79⋊C4D411yescharacteristic
134C2×C22⋊Dic79—21no—
135C2×C22⋊Dic79—21no—
136C2×C4×Dic79—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79C2311yescharacteristic
140C2×C4×Dic79C2311yescharacteristic
141#14579095C2314yes—
142#14579094C2314yes—
143#14579093C2314yes—
144Dic79⋊C8C2314yes—
145Dic79⋊C8C2314yes—
146#14579086C2314yes—
147#14579086C2314yes—
148#14579085C2314yes—
149#14579085C2314yes—
150#14579085C2314yes—
151#14579085C2314yes—
152#14579084C2314yes—
153#14579082C2314yes—
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—
179C2×Dic158—24no—
180C2×Dic158—24no—
181C2×Dic158—21no—
182C2×Dic158—22no—
183C2×Dic158—22no—
184C2×Dic158—82no—
185C2×Dic158C2×D414yes—
186C2×Dic158C2412yes—
187C22×Dic79—24no—
188C22×Dic79—24no—
189C22×Dic79—21no—
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
199#11929612—28no—
200C2×C79⋊C8—22no—
201C2×C79⋊C8—22no—
202C2×C79⋊C8C2412yes—
203C2×C79⋊C8C2412yes—
204C4⋊Dic79—24no—
205C4⋊Dic79—24no—
206C4⋊Dic79—24no—
207C4⋊Dic79—21no—
208C4⋊Dic79—21no—
209C4⋊Dic79—21no—
210C4⋊Dic79C2×D414yes—
211C4⋊Dic79C2412yes—
212C4⋊Dic79C2412yes—
213C4⋊Dic79C2412yes—
214Dic79⋊C4—24no—
215Dic79⋊C4—24no—
216Dic79⋊C4—24no—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4C2×D414yes—
224Dic79⋊C4C2×D414yes—
225C22⋊Dic79—24no—
226C22⋊Dic79—24no—
227C4×Dic79—24no—
228C4×Dic79—24no—
229C4×Dic79—24no—
230C4×Dic79C2×D412yes—
231C4×Dic79C2×D412yes—
232C4×Dic79C2412yes—
233C4×Dic79C2412yes—
234C24×C79—21no—
235C2×Q8×C79—21no—
236C2×Q8×C79—21no—
237C2×Q8×C79—22no—
238C2×Q8×C79—22no—
239C2×Q8×C79—22no—
240C2×Q8×C79—22no—
241C2×Q8×C79C2412yes—
242C2×Q8×C79C2412yes—
243C2×D4×C79—21no—
244C2×D4×C79—22no—
245C2×D4×C79#4114yes—
246C2×D4×C79C2412yes—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79—24no—
251C22×C4×C79—82no—
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2411yescharacteristic
255SD16×C79—28no—
256SD16×C79—28no—
257C2×C8×C79—22no—
258C2×C8×C79—22no—
259C2×C8×C79C2412yes—
260C2×C8×C79C2412yes—
261C4⋊C4×C79—24no—
262C4⋊C4×C79—24no—
263C4⋊C4×C79—21no—
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
273Q8×C79—22no—
274Q8×C79—22no—
275Q8×C79—22no—
276Q8×C79—22no—
277Q8×C79—42no—
278Q8×C79—42no—
279D4×C79—24no—
280D4×C79—22no—
281D4×C79C2×#4114yes—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—42no—
288C2×C4×C79—42no—
289C2×C4×C79—42no—
290C2×C4×C79—84no—
291C2×C4×C79C22×D412yes—
292C2×C4×C79C22×D412yes—
293C2×C4×C79C22×D411yescharacteristic
294C2×C4×C79C2×#4112yes—
295C2×C4×C792−1+412yes—
296C2×C4×C79C2511yescharacteristic
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—22no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—42no—
305C2×Dic79—42no—
306C2×Dic79—42no—
307C2×Dic79—42no—
308C2×Dic79—48no—
309C2×Dic79—84no—
310C2×Dic79#13714yes—
311C2×Dic79C22×D412yes—
312C2×Dic79C22×D412yes—
313C2×Dic79C22×D412yes—
314C2×Dic79C22×D412yes—
315Dic158—28no—
316Dic158—22no—
317Dic158—22no—
318Dic158—42no—
319Dic158—84no—
320C8×C79—22no—
321C8×C79—22no—
322C79⋊C8—22no—
323C79⋊C8—22no—
324C22×C79—24no—
325C22×C79—48no—
326C22×C79—42no—
327C22×C79—42no—
328C22×C79#54812yes—
329C22×C79C2×#13712yes—
330C22×C79#57712yes—
331C22×C79C23×D411yescharacteristic
332C4×C79—22no—
333C4×C79—22no—
334C4×C79—42no—
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×#3372—791nomaximal, Sylow
349C2×C79—44no—
350C2×C79#337214yescomplemented
351C2×C79C2×#54811yescharacteristic
352C2×C79C22×#13711yescharacteristic
353C2×C79C2×#57711yescharacteristic
354C2×#557—791no—
355C2×#554—791no—
356#3372—7916no—
357C2×#491—791no—
358C2×#491—791no—
359C2×#487—791no—
360C2×#479—791no—
361C2×#479—791no—
362C2×#477—791no—
363C2×#461—791no—
364C2×#461—791no—
365C2×#461D7911yescharacteristic
366C2×#446—791no—
367C2×#440—791no—
368C2×#440—791no—
369C2×C4×SD16—791no—
370C79C2×#337211yescharacteristic, complemented, Sylow
371C22×SD16—791no—
372C22×SD16C2×D7911yescharacteristic
373C22×SD16C2×D7911yescharacteristic
374#557—798no—
375#557—1584no—
376#554—798no—
377#554—1584no—
378C2×C4⋊Q8—791no—
379C2×C4⋊Q8—791no—
380C2×C4⋊Q8—791no—
381C2×C4⋊Q8C2×D7911yescharacteristic
382C2×#125—791no—
383C2×#125—791no—
384C2×#125—1581no—
385C2×#125—1581no—
386C2×#125—1581no—
387C2×C22⋊Q8—1581no—
388C2×C22⋊Q8—1581no—
389C2×C22⋊Q8—1581no—
390C2×C4×Q8—791no—
391C2×C4×Q8—791no—
392C2×C4×Q8—791no—
393C2×C4×Q8—791no—
394C2×C4×Q8—1581no—
395C2×C4×D4—791no—
396C2×C4×D4—791no—
397C2×C4×D4C2×D7911yescharacteristic
398C22×C4⋊C4—1581no—
399#491—798no—
400#491—798no—
401#487—798no—
402#479—798no—
403#479—798no—
404#477—798no—
405#461—798no—
406#461—798no—
407#461C2×D7918yes—
408#446—798no—
409#440—798no—
410#440—798no—
411C4×SD16—798no—
412C2×#107—791no—
413C2×#107—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×#103—791no—
425C2×#103C2×D7911yescharacteristic
426C2×#103C2×D7911yescharacteristic
427C2×#102—791no—
428C2×#97—791no—
429C2×#97—791no—
430C2×C4×C8—791no—
431C22×Q8—791no—
432C22×Q8—791no—
433C22×Q8—1581no—
434C22×Q8C22×D7911yescharacteristic
435C22×Q8C22×D7911yescharacteristic
436C22×D4C22×D7911yescharacteristic
437C23×C4—21no—
438C23×C4—1581no—
439C23×C4—1581no—
440C2×SD16—24no—
441C2×SD16—24no—
442C2×SD16—794no—
443C2×SD16—1584no—
444C2×SD16C22×D7914yes—
445C2×SD16C22×D7914yes—
446C22×C8—791no—
447C22×C8—791no—
448C22×C8C22×D7911yescharacteristic
449C22×C8C22×D7911yescharacteristic
450C4⋊Q8—22no—
451C4⋊Q8—794no—
452C4⋊Q8—794no—
453C4⋊Q8—794no—
454C4⋊Q8—1582no—
455C4⋊Q8—1582no—
456C4⋊Q8—1582no—
457C4⋊Q8C22×D7914yes—
458#125—794no—
459#125—794no—
460#125—1582no—
461#125—1588no—
462#125—1588no—
463#125—1588no—
464#125—1582no—
465C22⋊Q8—1588no—
466C22⋊Q8—1588no—
467C22⋊Q8—1588no—
468C4×Q8—794no—
469C4×Q8—794no—
470C4×Q8—794no—
471C4×Q8—794no—
472C4×Q8—794no—
473C4×Q8—1582no—
474C4×Q8—1582no—
475C4×Q8—1588no—
476C4×Q8—1582no—
477C4×D4—22no—
478C4×D4—794no—
479C4×D4—794no—
480C4×D4—1582no—
481C4×D4—1582no—
482C4×D4C22×D7914yes—
483C2×C4⋊C4—21no—
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—1588no—
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⋊C4—1581no—
501C2×C4⋊C4—1581no—
502C2×C4⋊C4—1581no—
503C2×C4⋊C4—1581no—
504C2×C4⋊C4C22×D7911yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—1581no—
507C2×C22⋊C4—1581no—
508C2×C42—791no—
509C2×C42—791no—
510C2×C42—1581no—
511C2×C42—1581no—
512C2×C42—1581no—
513C2×C42C22×D7911yescharacteristic
514#107—794no—
515#107—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#103—794no—
527#103C22×D7914yes—
528#103C22×D7914yes—
529#102—794no—
530#97—794no—
531#97—794no—
532C4×C8—794no—
533C24—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—794no—
541C2×Q8—792no—
542C2×Q8—6322no—
543C2×Q8—1584no—
544C2×Q8—1584no—
545C2×Q8—1582no—
546C2×Q8—1582no—
547C2×Q8—1581no—
548C2×Q8C23×D7912yes—
549C2×Q8C23×D7912yes—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4#1192962314yes—
553C2×D4C23×D7912yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—82no—
559C22×C4—3164no—
560C22×C4—791no—
561C22×C4—791no—
562C22×C4—791no—
563C22×C4—791no—
564C22×C4—6322no—
565C22×C4—1584no—
566C22×C4—1581no—
567C22×C4—1581no—
568C22×C4—1581no—
569C22×C4—1581no—
570C22×C4—1584no—
571C22×C4D4×D7911yescharacteristic
572C22×C4D4×D7911yescharacteristic
573C22×C4C23×D7911yescharacteristic
574SD16—28no—
575SD16—28no—
576SD16—1588no—
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—24no—
587C4⋊C4—21no—
588C4⋊C4—794no—
589C4⋊C4—794no—
590C4⋊C4—794no—
591C4⋊C4—792no—
592C4⋊C4—792no—
593C4⋊C4—792no—
594C4⋊C4—1584no—
595C4⋊C4—1584no—
596C4⋊C4—1584no—
597C4⋊C4—1584no—
598C4⋊C4—1584no—
599C4⋊C4—1584no—
600C4⋊C4—1584no—
601C4⋊C4—1584no—
602C4⋊C4—1584no—
603C4⋊C4—1584no—
604C4⋊C4—1584no—
605C4⋊C4—1584no—
606C4⋊C4—1581no—
607C4⋊C4—1581no—
608C4⋊C4—1581no—
609C4⋊C4C23×D7912yes—
610C22⋊C4—24no—
611C22⋊C4—1584no—
612C22⋊C4—1584no—
613C42—792no—
614C42—792no—
615C42—792no—
616C42—792no—
617C42—1584no—
618C42—1584no—
619C42—1584no—
620C42D4×D7912yes—
621C42C23×D7912yes—
622C23—24no—
623C23—22no—
624C23—42no—
625C23—42no—
626C23C2×D4×D7911yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—42no—
632Q8—42no—
633Q8—3162no—
634Q8—6324no—
635Q8—1588no—
636Q8—1582no—
637Q8—1582no—
638D4—22no—
639D4—24no—
640D4C2×#1192962314yes—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—84no—
650C2×C4—3162no—
651C2×C4—3162no—
652C2×C4—3162no—
653C2×C4—3162no—
654C2×C4—3168no—
655C2×C4—794no—
656C2×C4—792no—
657C2×C4—792no—
658C2×C4—792no—
659C2×C4—792no—
660C2×C4—6324no—
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—24no—
679C22—42no—
680C22—42no—
681C22—48no—
682C22#1909921912yes—
683C22#137×D7912yes—
684C22#1909936912yes—
685C22C22×D4×D7911yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
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—44no—
703C2#2377617614yesdirect product factor
704C2C2×#1909921911yescharacteristic
705C2C2×#137×D7911yescharacteristic
706C2C2×#1909936911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#461×C79C2
socleC23×C79C22×D4
prime radicalC22×D4×C79C23
hypercenterC2×#461D79
hypocenterC79C2×#3372
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×#19099288C2semidirect
3. #23776176C2direct (N × H)
4. C2×#19098931C2semidirect
5. C2×#19098930C2semidirect
6. C2×#19098912C2semidirect
7. C2×#19098871C2semidirect
8. C2×#19098868C2semidirect
9. C2×#19098856C2semidirect
12. C2×#19098692C2semidirect
19. #19099288C22semidirect
41. #19098931C22semidirect
42. #19098930C22semidirect
43. #19098912C22semidirect
44. #19098871C22semidirect
45. #19098868C22semidirect
46. #19098856C22semidirect
49. #19098692C22semidirect
350. C2×C79#3372semidirect
370. C79C2×#3372semidirect
703. C2#23776176direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992882
C2×#190992722
#237761762
C2×#190989312
C2×#190989302
C2×#190989122
C2×#190988712
C2×#190988682
C2×#190988562
C2×#190987662
C2×#190986922
C2×#190986642
C2×#190986632
C2×SD16×Dic792
C2×#461×C792
C2×#337279