Finite Group Databasebeta

← C2×#23776262 #35168694

Subgroups — C2×#23776262 #35168694

Order 20224.

1918 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×#19099272C211yesmaximal, characteristic, complemented
2C2×#19099269C211yesmaximal, characteristic, complemented
3#23776262C2116yesmaximal, direct product factor
4C2×#19098967C211yesmaximal, characteristic, complemented
5C2×#19098963C211yesmaximal, characteristic, complemented
6C2×#19098962C211yesmaximal, characteristic, complemented
7C2×#19098866C211yesmaximal, characteristic, complemented
8C2×#19098864C211yesmaximal, characteristic, complemented
9C2×#19098861C211yesmaximal, characteristic, complemented
10C2×#19098852C211yesmaximal, characteristic, complemented
11C2×#19098851C211yesmaximal, characteristic, complemented
12C2×#19098687C211yesmaximal, characteristic, complemented
13C2×C4×#11929609C211yesmaximal, characteristic
14C2×#19098643C211yesmaximal, characteristic
15C2×#19098643C211yesmaximal, characteristic
16C2×#478×C79C211yesmaximal, characteristic, complemented
17C22×#11929609C2211yescharacteristic
18#19099272—24no—
19#19099272C2218yescomplemented
20#19099269—24no—
21#19099269C2218yescomplemented
22C2×#14579160C2211yescharacteristic
23C2×#14579160C2211yescharacteristic
24C2×#14579153C2211yescharacteristic
25C2×#14579152C2211yescharacteristic
26C2×#14579152C2211yescharacteristic
27C2×#14579141—21no—
28C2×#14579140—21no—
29C2×#14579139—21no—
30C2×#14579139—21no—
31C2×#14579138—21no—
32C2×#14579138—21no—
33C2×C4×Dic158C2211yescharacteristic
34C2×C4×D316C2211yescharacteristic
35C2×D4×Dic79C2211yescharacteristic
36C2×D4×Dic79C2211yescharacteristic
37C2×#14579123C2211yescharacteristic
38C2×#14579123C2211yescharacteristic
39C22×Dic79⋊C4—21no—
40C2×C4⋊C4×D79—21no—
41#19098967C2218yescomplemented
42#19098963C2218yescomplemented
43#19098962C2218yescomplemented
44#19098866C2218yescomplemented
45#19098864C2218yescomplemented
46#19098861C2218yescomplemented
47#19098852C2218yescomplemented
48#19098851C2218yescomplemented
49#19098687C2218yescomplemented
50C4×#11929609C2218yes—
51#19098643C2218yes—
52#19098643C2218yes—
53C2×#14579095C2211yescharacteristic
54C2×#14579094C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579093C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59C2×#14579092C2211yescharacteristic
60C2×Dic79⋊C8C2211yescharacteristic
61C2×Dic79⋊C8C2211yescharacteristic
62C2×#14579083C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579081C2211yescharacteristic
66C2×C4×C79⋊C8C2211yescharacteristic
67C2×C8×Dic79C2211yescharacteristic
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—21no—
79C22×Dic158D411yescharacteristic
80C22×D316C2311yescharacteristic
81C23×Dic79—21no—
82C23×Dic79—21no—
83C22×C4×D79—21no—
84C22×C4×D79—21no—
85C22×C4×D79—21no—
86C2×#11929609Q818yescomplemented
87C2×#11929609C2314yes—
88C22×C79⋊C8C2311yescharacteristic
89C22×C79⋊C8C2311yescharacteristic
90#14579160—22no—
91#14579160—22no—
92#14579160C2314yes—
93#14579160C2314yes—
94#14579153—22no—
95#14579153C2314yes—
96#14579152—22no—
97#14579152—22no—
98#14579152C2314yes—
99#14579152C2314yes—
100#14579141—28no—
101#14579140—28no—
102#14579139—28no—
103#14579139—28no—
104#14579138—28no—
105#14579138—28no—
106C4×Dic158D414yes—
107C4×Dic158C2314yes—
108C4×D316—22no—
109C4×D316C2314yes—
110D4×Dic79—22no—
111D4×Dic79—22no—
112D4×Dic79C2314yes—
113D4×Dic79C2314yes—
114#14579123—22no—
115#14579123—22no—
116#14579123C2314yes—
117#14579123C2314yes—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79D411yescharacteristic
121C2×C4⋊Dic79C2311yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
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—28no—
131C2×Dic79⋊C4D411yescharacteristic
132C2×Dic79⋊C4D411yescharacteristic
133C4⋊C4×D79—28no—
134C2×C22⋊Dic79—21no—
135C2×C22⋊Dic79—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×C4×Dic79C2311yescharacteristic
140C2×C4×Dic79C2311yescharacteristic
141#14579095C2314yes—
142#14579094C2314yes—
143#14579094C2314yes—
144#14579094C2314yes—
145#14579093C2314yes—
146#14579092C2314yes—
147#14579092C2314yes—
148Dic79⋊C8C2314yes—
149Dic79⋊C8C2314yes—
150#14579083C2314yes—
151#14579083C2314yes—
152#14579082C2314yes—
153#14579081C2314yes—
154C4×C79⋊C8C2314yes—
155C8×Dic79C2314yes—
156C8×Dic79C2314yes—
157C22×D4×C79C2311yescharacteristic
158C23×C4×C79—21no—
159C22×C8×C79C2311yescharacteristic
160C22×C8×C79C2311yescharacteristic
161#125×C79—22no—
162#125×C79C2314yes—
163C4×D4×C79—22no—
164C4×D4×C79C2314yes—
165C2×C4⋊C4×C79—21no—
166C2×C4⋊C4×C79—21no—
167C2×C4⋊C4×C79C2311yescharacteristic
168C2×C4⋊C4×C79C2311yescharacteristic
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C22⋊C4×C79—21no—
171C2×C42×C79C2311yescharacteristic
172#107×C79C2314yes—
173#106×C79C2314yes—
174C4⋊C8×C79C2314yes—
175#102×C79C2314yes—
176#102×C79C2314yes—
177C23×D79—21no—
178C2×Dic158—24no—
179C2×Dic158—24no—
180C2×Dic158—24no—
181C2×Dic158—82no—
182C2×Dic158—82no—
183C2×Dic158C2×D414yes—
184C2×D316—21no—
185C2×D316—22no—
186C2×D316C2×Q814yes—
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—24no—
201C2×C4×D79—24no—
202C2×C4×D79—44no—
203C2×C4×D79—82no—
204C2×C4×D79—82no—
205#11929609C2×Q8116yescomplemented
206C2×C79⋊C8—22no—
207C2×C79⋊C8C2×Q814yes—
208C2×C79⋊C8C2412yes—
209C2×C79⋊C8C2412yes—
210C4⋊Dic79—24no—
211C4⋊Dic79—24no—
212C4⋊Dic79—21no—
213C4⋊Dic79—21no—
214C4⋊Dic79—21no—
215C4⋊Dic79C2×D414yes—
216C4⋊Dic79C2412yes—
217C4⋊Dic79C2412yes—
218C4⋊Dic79C2412yes—
219Dic79⋊C4—24no—
220Dic79⋊C4—24no—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4C2×D414yes—
226Dic79⋊C4C2×D414yes—
227C22⋊Dic79—24no—
228C22⋊Dic79—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4—24no—
232C4×Dic79C2×D412yes—
233C4×Dic79C2×D412yes—
234C4×Dic79C2412yes—
235C4×Dic79C2412yes—
236C24×C79—21no—
237C2×D4×C79—21no—
238C2×D4×C79—22no—
239C2×D4×C79C2×Q814yes—
240C2×D4×C79C2412yes—
241C22×C4×C79—21no—
242C22×C4×C79—21no—
243C22×C4×C79—21no—
244C22×C4×C79—24no—
245C22×C4×C79—82no—
246C22×C4×C79C2×D411yescharacteristic
247C22×C4×C79C2×D411yescharacteristic
248C22×C4×C79C2411yescharacteristic
249C2×C8×C79—22no—
250C2×C8×C79—22no—
251C2×C8×C79C2412yes—
252C2×C8×C79C2412yes—
253C4⋊C4×C79—24no—
254C4⋊C4×C79—24no—
255C4⋊C4×C79—21no—
256C4⋊C4×C79—21no—
257C4⋊C4×C79—21no—
258C4⋊C4×C79C2412yes—
259C4⋊C4×C79C2412yes—
260C4⋊C4×C79C2412yes—
261C22⋊C4×C79—24no—
262C42×C79C2×D412yes—
263C42×C79C2412yes—
264C23×C79—24no—
265C23×C79—22no—
266C23×C79—42no—
267C23×C79—42no—
268C23×C79C22×D411yescharacteristic
269C22×D79—24no—
270C22×D79—22no—
271C22×D79—42no—
272C22×D79—42no—
273D4×C79—24no—
274D4×C79—22no—
275D4×C79C22×Q814yes—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—42no—
282C2×C4×C79—42no—
283C2×C4×C79—42no—
284C2×C4×C79—84no—
285C2×C4×C79C22×D412yes—
286C2×C4×C79C22×D412yes—
287C2×C4×C79C22×D411yescharacteristic
288C2×C4×C79C22×Q812yes—
289C2×C4×C792−1+412yes—
290C2×C4×C79C2511yescharacteristic
291C2×Dic79—22no—
292C2×Dic79—22no—
293C2×Dic79—22no—
294C2×Dic79—22no—
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—42no—
298C2×Dic79—42no—
299C2×Dic79—42no—
300C2×Dic79—48no—
301C2×Dic79—84no—
302C2×Dic79#13514yes—
303C2×Dic79C22×D412yes—
304C2×Dic79C22×D412yes—
305C2×Dic79C22×D412yes—
306C2×Dic79C22×D412yes—
307D316—24no—
308D316—22no—
309D316C22×Q814yes—
310C4×D79—48no—
311C4×D79—84no—
312C4×D79—84no—
313Dic158—28no—
314Dic158—84no—
315Dic158—84no—
316C8×C79—22no—
317C8×C79—22no—
318C79⋊C8—22no—
319C79⋊C8C22×Q814yes—
320C22×C79—24no—
321C22×C79—48no—
322C22×C79—42no—
323C22×C79—42no—
324C22×C79D4×Q812yes—
325C22×C79C2×#13512yes—
326C22×C79#57612yes—
327C22×C79C23×D411yescharacteristic
328C2×D79—24no—
329C2×D79—48no—
330C2×D79—42no—
331C2×D79—42no—
332C4×C79—22no—
333C4×C79—22no—
334C4×C79—42no—
335C4×C79—42no—
336C4×C79—42no—
337C4×C79D4×Q812yes—
338C4×C79C23×Q811yescharacteristic
339C4×C79C2×2−1+411yescharacteristic
340Dic79—22no—
341Dic79—22no—
342Dic79—22no—
343Dic79—42no—
344Dic79—42no—
345Dic79—42no—
346Dic79C2×#13514yes—
347C2×#3380—791nomaximal, Sylow
348C2×C79—44no—
349C2×C79#338014yescomplemented
350C2×C79C2×D4×Q811yescharacteristic
351C2×C79C22×#13511yescharacteristic
352C2×C79C2×#57611yescharacteristic
353D79—44no—
354C2×#554—791no—
355C2×#554—791no—
356#3380—7916no—
357C2×#500—791no—
358C2×#499—791no—
359C2×#499—791no—
360C2×#478—791no—
361C2×#478—791no—
362C2×#478—791no—
363C2×#478D7911yescharacteristic, complemented
364C2×#476—791no—
365C2×#476—791no—
366C2×C8×Q8—791no—
367C2×C4×D8—791no—
368C2×C4×D8—791no—
369C2×C4×D8—791no—
370C79C2×#338011yescharacteristic, complemented, Sylow
371C22×D8—791no—
372#554—798no—
373#554—798no—
374#554—1584no—
375#554—1584no—
376C2×C4⋊Q8—791no—
377C2×C4⋊Q8—791no—
378C2×#125—791no—
379C2×#125—791no—
380C2×#125—791no—
381C2×#125C2×D7911yescharacteristic
382C2×C22⋊Q8—1581no—
383C2×C22⋊Q8—1581no—
384C2×C22⋊Q8—1581no—
385C2×C22⋊Q8—1581no—
386C2×C22⋊Q8—1581no—
387C2×C22⋊Q8—1581no—
388C2×C4×Q8—791no—
389C2×C4×D4—791no—
390C2×C4×D4—791no—
391C2×C4×D4—791no—
392C2×C4×D4—791no—
393C2×C4×D4—791no—
394C2×C4×D4C2×D7911yescharacteristic
395C22×C4⋊C4—1581no—
396C22×C4⋊C4—1581no—
397#500—798no—
398#499—798no—
399#499—798no—
400#478—798no—
401#478—798no—
402#478—798no—
403#478C2×D7918yescomplemented
404#476—798no—
405#476—798no—
406C8×Q8—798no—
407C4×D8—798no—
408C4×D8—798no—
409C4×D8—798no—
410C2×#107—791no—
411C2×#107—791no—
412C2×#107—791no—
413C2×#107—791no—
414C2×#107C2×D7911yescharacteristic
415C2×#106—791no—
416C2×#106—791no—
417C2×#106—791no—
418C2×#106C2×D7911yescharacteristic
419C2×C4⋊C8—791no—
420C2×C4⋊C8—791no—
421C2×C4⋊C8C2×D7911yescharacteristic
422C2×#102—791no—
423C2×#102—791no—
424C2×#102—791no—
425C2×#102—791no—
426C2×#102C2×D7911yescharacteristic
427C2×#102C2×D7911yescharacteristic
428C2×C4×C8—791no—
429C2×C4×C8—791no—
430C2×C4×C8—791no—
431C22×Q8—791no—
432C22×Q8—1581no—
433C22×Q8—1581no—
434C22×D4—791no—
435C22×D4C22×D7911yescharacteristic
436C23×C4—21no—
437C23×C4—1581no—
438C23×C4—1581no—
439C23×C4—1581no—
440C23×C4—1581no—
441C23×C4—1581no—
442C2×D8—798no—
443C2×D8—794no—
444C22×C8—791no—
445C22×C8—791no—
446C22×C8C22×D7911yescharacteristic
447C22×C8C22×D7911yescharacteristic
448C4⋊Q8—794no—
449C4⋊Q8—794no—
450C4⋊Q8—1582no—
451C4⋊Q8—1582no—
452#125—22no—
453#125—794no—
454#125—794no—
455#125—794no—
456#125—1582no—
457#125—1582no—
458#125—1582no—
459#125C22×D7914yes—
460C22⋊Q8—1588no—
461C22⋊Q8—1588no—
462C22⋊Q8—1588no—
463C22⋊Q8—1588no—
464C22⋊Q8—1588no—
465C22⋊Q8—1588no—
466C4×Q8—794no—
467C4×Q8—794no—
468C4×D4—22no—
469C4×D4—794no—
470C4×D4—794no—
471C4×D4—794no—
472C4×D4—794no—
473C4×D4—794no—
474C4×D4—1582no—
475C4×D4—1582no—
476C4×D4—1582no—
477C4×D4—1582no—
478C4×D4—1582no—
479C4×D4C22×D7914yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—791no—
483C2×C4⋊C4—791no—
484C2×C4⋊C4—791no—
485C2×C4⋊C4—791no—
486C2×C4⋊C4—791no—
487C2×C4⋊C4—791no—
488C2×C4⋊C4—1588no—
489C2×C4⋊C4—1588no—
490C2×C4⋊C4—1581no—
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⋊C4C22×D7911yescharacteristic
499C2×C4⋊C4C22×D7911yescharacteristic
500C2×C4⋊C4C22×D7911yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—1581no—
503C2×C22⋊C4—1581no—
504C2×C22⋊C4—1581no—
505C2×C22⋊C4—1581no—
506C2×C22⋊C4—1581no—
507C2×C42—791no—
508C2×C42—791no—
509C2×C42C22×D7911yescharacteristic
510#107—794no—
511#107—794no—
512#107—794no—
513#107—794no—
514#107C22×D7914yes—
515#106—794no—
516#106—794no—
517#106—794no—
518#106C22×D7914yes—
519C4⋊C8—794no—
520C4⋊C8—794no—
521C4⋊C8C22×D7914yes—
522#102—794no—
523#102—794no—
524#102—794no—
525#102—794no—
526#102C22×D7914yes—
527#102C22×D7914yes—
528C4×C8—794no—
529C4×C8—794no—
530C4×C8—794no—
531C24—21no—
532C24—1581no—
533C2×Q8—794no—
534C2×Q8—6322no—
535C2×Q8—6322no—
536C2×Q8—1584no—
537C2×Q8—1584no—
538C2×Q8—1584no—
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—794no—
542C2×D4—792no—
543C2×D4—1582no—
544C2×D4—1581no—
545C2×D4Q8×D7914yes—
546C2×D4C23×D7912yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—82no—
552C22×C4—3164no—
553C22×C4—3164no—
554C22×C4—791no—
555C22×C4—791no—
556C22×C4—791no—
557C22×C4—791no—
558C22×C4—6322no—
559C22×C4—6322no—
560C22×C4—6322no—
561C22×C4—1584no—
562C22×C4—1584no—
563C22×C4—1584no—
564C22×C4—1581no—
565C22×C4—1581no—
566C22×C4—1581no—
567C22×C4—1584no—
568C22×C4—1584no—
569C22×C4D4×D7911yescharacteristic
570C22×C4D4×D7911yescharacteristic
571C22×C4C23×D7911yescharacteristic
572D8—7916no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—794no—
576C2×C8—792no—
577C2×C8—792no—
578C2×C8—1582no—
579C2×C8C23×D7912yes—
580C2×C8C23×D7912yes—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—794no—
587C4⋊C4—794no—
588C4⋊C4—794no—
589C4⋊C4—792no—
590C4⋊C4—792no—
591C4⋊C4—792no—
592C4⋊C4—1584no—
593C4⋊C4—1584no—
594C4⋊C4—1584no—
595C4⋊C4—1584no—
596C4⋊C4—1584no—
597C4⋊C4—1584no—
598C4⋊C4—1584no—
599C4⋊C4—1584no—
600C4⋊C4—1581no—
601C4⋊C4—1581no—
602C4⋊C4—1581no—
603C4⋊C4C23×D7912yes—
604C4⋊C4C23×D7912yes—
605C4⋊C4C23×D7912yes—
606C22⋊C4—24no—
607C22⋊C4—1584no—
608C22⋊C4—1584no—
609C22⋊C4—1584no—
610C22⋊C4—1584no—
611C22⋊C4—1584no—
612C42—792no—
613C42—792no—
614C42—792no—
615C42—792no—
616C42D4×D7912yes—
617C42C23×D7912yes—
618C23—24no—
619C23—22no—
620C23—42no—
621C23—42no—
622C23—3162no—
623C23—3162no—
624C23—1584no—
625C23—1582no—
626C23C2×D4×D7911yescharacteristic
627Q8—6324no—
628Q8—6324no—
629Q8—1588no—
630D4—22no—
631D4—24no—
632D4—794no—
633D4—1582no—
634D4—1584no—
635D4C2×Q8×D7914yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—84no—
645C2×C4—3168no—
646C2×C4—3162no—
647C2×C4—3162no—
648C2×C4—3162no—
649C2×C4—3168no—
650C2×C4—794no—
651C2×C4—792no—
652C2×C4—792no—
653C2×C4—792no—
654C2×C4—792no—
655C2×C4—6324no—
656C2×C4—6324no—
657C2×C4—6324no—
658C2×C4—1582no—
659C2×C4—1582no—
660C2×C4—1582no—
661C2×C4—1582no—
662C2×C4—1582no—
663C2×C4—1582no—
664C2×C4C2×D4×D7912yes—
665C2×C4C2×D4×D7912yes—
666C2×C4C2×D4×D7911yescharacteristic
667C2×C4C2×Q8×D7912yes—
668C2×C4#1457920812yes—
669C2×C4C24×D7911yescharacteristic
670C8—22no—
671C8—22no—
672C8—794no—
673C8—1582no—
674C22—24no—
675C22—48no—
676C22—42no—
677C22—42no—
678C22—3168no—
679C22—3162no—
680C22—3162no—
681C22—1584no—
682C22#1909922612yes—
683C22#135×D7912yes—
684C22#1909936712yes—
685C22C22×D4×D7911yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—3162no—
692C4—3162no—
693C4—3162no—
694C4—794no—
695C4—1582no—
696C4—1582no—
697C4—1582no—
698C4#1909922612yes—
699C4C22×Q8×D7911yescharacteristic
700C4C2×#1457920811yescharacteristic
701C2—44no—
702C2—3164no—
703C2#2377626214yesdirect product factor
704C2C2×#1909922611yescharacteristic
705C2C2×#135×D7911yescharacteristic
706C2C2×#1909936711yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#478×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929609C22
hypercenterC2×#478D79
hypocenterC79C2×#3380
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×#19099272C2semidirect
2. C2×#19099269C2semidirect
3. #23776262C2direct (N × H)
4. C2×#19098967C2semidirect
5. C2×#19098963C2semidirect
6. C2×#19098962C2semidirect
7. C2×#19098866C2semidirect
8. C2×#19098864C2semidirect
9. C2×#19098861C2semidirect
10. C2×#19098852C2semidirect
11. C2×#19098851C2semidirect
12. C2×#19098687C2semidirect
16. C2×#478×C79C2semidirect
19. #19099272C22semidirect
21. #19099269C22semidirect
41. #19098967C22semidirect
42. #19098963C22semidirect
43. #19098962C22semidirect
44. #19098866C22semidirect
45. #19098864C22semidirect
46. #19098861C22semidirect
47. #19098852C22semidirect
48. #19098851C22semidirect
49. #19098687C22semidirect
71. #478×C79C22semidirect
86. C2×#11929609Q8semidirect
205. #11929609C2×Q8semidirect
349. C2×C79#3380semidirect
363. C2×#478D79semidirect
370. C79C2×#3380semidirect
403. #478C2×D79semidirect
703. C2#23776262direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992722
C2×#190992692
#237762622
C2×#190989672
C2×#190989632
C2×#190989622
C2×#190988662
C2×#190988642
C2×#190988612
C2×#190988522
C2×#190988512
C2×#190986872
C2×C4×#119296092
C2×#190986432
C2×#478×C792
C2×#338079