Finite Group Databasebeta

← C2×#23776080 #35167876

Subgroups — C2×#23776080 #35167876

Order 20224.

1830 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099289C211yesmaximal, characteristic, complemented
2C2×#19099282C211yesmaximal, characteristic
3#23776080C2116yesmaximal, direct product factor
4C2×#19098917C211yesmaximal, characteristic
5C2×#19098916C211yesmaximal, characteristic
6C2×#19098912C211yesmaximal, characteristic, complemented
7C2×#19098871C211yesmaximal, characteristic, complemented
8C2×#19098868C211yesmaximal, characteristic, complemented
9C2×#19098841C211yesmaximal, characteristic
10C2×#19098783C211yesmaximal, characteristic
11C2×#19098771C211yesmaximal, characteristic, complemented
12C2×#19098687C211yesmaximal, characteristic, complemented
13C2×Q16×Dic79C211yesmaximal, characteristic, complemented
14C2×C4×#11929614C211yesmaximal, characteristic, complemented
15C2×SD16×Dic79C211yesmaximal, characteristic
16C2×#464×C79C211yesmaximal, characteristic
17C22×#11929614C2211yescharacteristic
18#19099289—24no—
19#19099289C2218yescomplemented
20#19099282—24no—
21#19099282C2218yes—
22C2×#14579160—21no—
23C2×#14579160C2211yescharacteristic
24C2×#14579159C2211yescharacteristic
25C2×#14579154—21no—
26C2×#14579154—21no—
27C2×#14579153—21no—
28C2×#14579153C2211yescharacteristic
29C2×#14579152—21no—
30C2×#14579152C2211yescharacteristic
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#19098917C2218yes—
42#19098916C2218yes—
43#19098912C2218yescomplemented
44#19098871C2218yescomplemented
45#19098868C2218yescomplemented
46#19098841C2218yes—
47#19098783C2218yes—
48#19098771C2218yescomplemented
49#19098687C2218yescomplemented
50Q16×Dic79C2218yescomplemented
51C4×#11929614C2218yescomplemented
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×#14579084C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×C4×C79⋊C8C2211yescharacteristic
67C2×C8×Dic79C2211yescharacteristic
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×Dic158D411yescharacteristic
79C22×Dic158C2311yescharacteristic
80C23×Dic79—21no—
81C2×#11929614—24no—
82C2×#11929614C2314yes—
83C22×C79⋊C8C2311yescharacteristic
84C22×C79⋊C8C2311yescharacteristic
85#14579160—28no—
86#14579160—22no—
87#14579160C2314yes—
88#14579159—22no—
89#14579159C2314yes—
90#14579154—28no—
91#14579154—28no—
92#14579153—22no—
93#14579153—28no—
94#14579153C2314yes—
95#14579152—28no—
96#14579152—22no—
97#14579152C2314yes—
98#14579148—22no—
99#14579148C2314yes—
100#14579138—28no—
101Q8×Dic79—22no—
102Q8×Dic79—22no—
103Q8×Dic79—22no—
104Q8×Dic79C2314yes—
105Q8×Dic79C2314yes—
106Q8×Dic79C2314yes—
107C4×Dic158—22no—
108C4×Dic158—28no—
109C4×Dic158D414yes—
110C4×Dic158C2314yes—
111C4×Dic158C2314yes—
112D4×Dic79—22no—
113D4×Dic79C2314yes—
114#14579117—28no—
115C2×C4⋊Dic79—21no—
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—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#14579095C2314yes—
142#14579094C2314yes—
143#14579093C2314yes—
144Dic79⋊C8C2314yes—
145Dic79⋊C8C2314yes—
146#14579086C2314yes—
147#14579086C2314yes—
148#14579085C2314yes—
149#14579085C2314yes—
150#14579085C2314yes—
151#14579084C2314yes—
152#14579082C2314yes—
153#14579082C2314yes—
154C4×C79⋊C8C2314yes—
155C8×Dic79C2314yes—
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—21no—
182C2×Dic158—22no—
183C2×Dic158—22no—
184C2×Dic158—44no—
185C2×Dic158C2×D414yes—
186C2×Dic158C2412yes—
187C22×Dic79—24no—
188C22×Dic79—21no—
189C22×Dic79—21no—
190C22×Dic79—21no—
191C22×Dic79—21no—
192C22×Dic79—44no—
193C22×Dic79C2×D411yescharacteristic
194C22×Dic79C2×D411yescharacteristic
195C22×Dic79C2×D411yescharacteristic
196C22×Dic79C2×D411yescharacteristic
197#11929614—28no—
198C2×C79⋊C8—22no—
199C2×C79⋊C8—22no—
200C2×C79⋊C8C2412yes—
201C2×C79⋊C8C2412yes—
202C4⋊Dic79—24no—
203C4⋊Dic79—24no—
204C4⋊Dic79—24no—
205C4⋊Dic79—24no—
206C4⋊Dic79—21no—
207C4⋊Dic79—21no—
208C4⋊Dic79—21no—
209C4⋊Dic79C2×D414yes—
210C4⋊Dic79C2412yes—
211C4⋊Dic79C2412yes—
212C4⋊Dic79C2412yes—
213Dic79⋊C4—24no—
214Dic79⋊C4—24no—
215Dic79⋊C4—24no—
216Dic79⋊C4—24no—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219Dic79⋊C4—24no—
220Dic79⋊C4C2×D414yes—
221Dic79⋊C4C2×D414yes—
222C22⋊Dic79—24no—
223C22⋊Dic79—24no—
224C22⋊Dic79—24no—
225C4×Dic79—24no—
226C4×Dic79—24no—
227C4×Dic79—24no—
228C4×Dic79—24no—
229C4×Dic79C2×D412yes—
230C4×Dic79C2×D412yes—
231C4×Dic79C2412yes—
232C4×Dic79C2412yes—
233C24×C79—21no—
234C2×Q8×C79—21no—
235C2×Q8×C79—21no—
236C2×Q8×C79—22no—
237C2×Q8×C79—22no—
238C2×Q8×C79—22no—
239C2×Q8×C79#4114yes—
240C2×Q8×C79C2412yes—
241C2×Q8×C79C2412yes—
242C2×D4×C79—21no—
243C2×D4×C79—22no—
244C2×D4×C79—22no—
245C2×D4×C79C2412yes—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2×D411yescharacteristic
251C22×C4×C79C2411yescharacteristic
252Q16×C79—28no—
253SD16×C79—28no—
254C2×C8×C79—22no—
255C2×C8×C79—22no—
256C2×C8×C79C2412yes—
257C2×C8×C79C2412yes—
258C4⋊C4×C79—24no—
259C4⋊C4×C79—21no—
260C4⋊C4×C79C2412yes—
261C22⋊C4×C79—24no—
262C22⋊C4×C79—24no—
263C42×C79—24no—
264C42×C79C2×D412yes—
265C42×C79C2412yes—
266C23×C79—22no—
267C23×C79—42no—
268C23×C79—42no—
269C23×C79—42no—
270C23×C79C22×D411yescharacteristic
271Q8×C79—24no—
272Q8×C79—22no—
273Q8×C79—22no—
274Q8×C79—22no—
275Q8×C79—42no—
276Q8×C79C2×#4114yes—
277D4×C79—22no—
278D4×C79—22no—
279D4×C79—42no—
280C2×C4×C79—24no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—42no—
287C2×C4×C79—42no—
288C2×C4×C79C22×D412yes—
289C2×C4×C79C22×D412yes—
290C2×C4×C79C22×D411yescharacteristic
291C2×C4×C79C2×#4112yes—
292C2×C4×C792−1+412yes—
293C2×C4×C79C2511yescharacteristic
294C2×Dic79—22no—
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—42no—
302C2×Dic79—42no—
303C2×Dic79—42no—
304C2×Dic79—42no—
305C2×Dic79—48no—
306C2×Dic79#13514yes—
307C2×Dic79C22×D412yes—
308C2×Dic79C22×D412yes—
309C2×Dic79C22×D412yes—
310C2×Dic79C22×D412yes—
311Dic158—28no—
312Dic158—22no—
313Dic158—22no—
314Dic158—42no—
315Dic158—48no—
316C8×C79—22no—
317C8×C79—22no—
318C79⋊C8—22no—
319C79⋊C8—22no—
320C22×C79—42no—
321C22×C79—42no—
322C22×C79—42no—
323C22×C79—84no—
324C22×C79#54812yes—
325C22×C79C2×#13512yes—
326C22×C79#57812yes—
327C22×C79C23×D411yescharacteristic
328C4×C79—24no—
329C4×C79—22no—
330C4×C79—22no—
331C4×C79—42no—
332C4×C79—42no—
333C4×C79#54812yes—
334C4×C79C22×#4111yescharacteristic
335C4×C79C2×2−1+411yescharacteristic
336Dic79—22no—
337Dic79—22no—
338Dic79—22no—
339Dic79—42no—
340Dic79—42no—
341Dic79—42no—
342Dic79—42no—
343Dic79C2×#13514yes—
344C2×#3364—791nomaximal, Sylow
345C2×C79—82no—
346C2×C79#336414yescomplemented
347C2×C79C2×#54811yescharacteristic
348C2×C79C22×#13511yescharacteristic
349C2×C79C2×#57811yescharacteristic
350C2×#557—791no—
351C2×#556—791no—
352#3364—7916no—
353C2×#488—791no—
354C2×#488—791no—
355C2×#487—791no—
356C2×#479—791no—
357C2×#479—791no—
358C2×#474—791no—
359C2×#464—791no—
360C2×#464D7911yescharacteristic
361C2×#462—791no—
362C2×C8×Q8—791no—
363C2×C4×Q16—791no—
364C2×C4×Q16—791no—
365C2×C4×SD16—791no—
366C79C2×#336411yescharacteristic, complemented, Sylow
367C22×Q16—791no—
368C22×Q16C2×D7911yescharacteristic
369C22×SD16C2×D7911yescharacteristic
370#557—798no—
371#557—1584no—
372#556—798no—
373#556—1584no—
374C2×C4⋊Q8—791no—
375C2×C4⋊Q8—791no—
376C2×C4⋊Q8—1581no—
377C2×#126—1581no—
378C2×#126—1581no—
379C2×#125—791no—
380C2×#125—791no—
381C2×#125—1581no—
382C2×#125—1581no—
383C2×#124—791no—
384C2×#124C2×D7911yescharacteristic
385C2×C22⋊Q8—1581no—
386C2×C4×Q8—791no—
387C2×C4×Q8—791no—
388C2×C4×Q8—791no—
389C2×C4×Q8—791no—
390C2×C4×Q8—791no—
391C2×C4×Q8—1581no—
392C2×C4×Q8C2×D7911yescharacteristic
393C2×C4×D4—791no—
394C2×#117—1581no—
395#488—798no—
396#488—798no—
397#487—798no—
398#479—798no—
399#479—798no—
400#474—798no—
401#464—798no—
402#464C2×D7918yes—
403#462—798no—
404C8×Q8—798no—
405C4×Q16—798no—
406C4×Q16—798no—
407C4×SD16—798no—
408C2×#107—791no—
409C2×#107—791no—
410C2×#106—791no—
411C2×C4⋊C8—791no—
412C2×C4⋊C8—791no—
413C2×C4⋊C8C2×D7911yescharacteristic
414C2×#103—791no—
415C2×#103—791no—
416C2×#103—791no—
417C2×#103—791no—
418C2×#103—791no—
419C2×#103—791no—
420C2×#103C2×D7911yescharacteristic
421C2×#102—791no—
422C2×#102—791no—
423C2×#102C2×D7911yescharacteristic
424C2×C4×C8—791no—
425C2×C4×C8—791no—
426C2×C4×C8—791no—
427C22×Q8—791no—
428C22×Q8—791no—
429C22×Q8—1581no—
430C22×Q8C22×D7911yescharacteristic
431C22×Q8C22×D7911yescharacteristic
432C22×D4C22×D7911yescharacteristic
433C23×C4—1581no—
434C2×Q16—24no—
435C2×Q16—794no—
436C2×Q16—1584no—
437C2×Q16C22×D7914yes—
438C2×SD16—24no—
439C2×SD16C22×D7914yes—
440C22×C8—791no—
441C22×C8—791no—
442C22×C8C22×D7911yescharacteristic
443C22×C8C22×D7911yescharacteristic
444C4⋊Q8—794no—
445C4⋊Q8—794no—
446C4⋊Q8—1582no—
447C4⋊Q8—1582no—
448C4⋊Q8—1588no—
449#126—1588no—
450#126—1588no—
451#125—794no—
452#125—794no—
453#125—1588no—
454#125—1582no—
455#125—1588no—
456#125—1582no—
457#124—22no—
458#124—794no—
459#124—1582no—
460#124C22×D7914yes—
461C22⋊Q8—1588no—
462C4×Q8—22no—
463C4×Q8—794no—
464C4×Q8—794no—
465C4×Q8—794no—
466C4×Q8—794no—
467C4×Q8—794no—
468C4×Q8—794no—
469C4×Q8—1588no—
470C4×Q8—1582no—
471C4×Q8—1582no—
472C4×Q8—1582no—
473C4×Q8—1582no—
474C4×Q8C22×D7914yes—
475C4×D4—794no—
476C4×D4—1582no—
477#117—1588no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—791no—
480C2×C4⋊C4—791no—
481C2×C4⋊C4—791no—
482C2×C4⋊C4—791no—
483C2×C4⋊C4—791no—
484C2×C4⋊C4—791no—
485C2×C4⋊C4—1581no—
486C2×C4⋊C4—1581no—
487C2×C4⋊C4—1581no—
488C2×C4⋊C4—1581no—
489C2×C4⋊C4—1581no—
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⋊C4C22×D7911yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—1581no—
500C2×C22⋊C4—1581no—
501C2×C22⋊C4—1581no—
502C2×C42—21no—
503C2×C42—791no—
504C2×C42—791no—
505C2×C42—1581no—
506C2×C42—1581no—
507C2×C42—1581no—
508C2×C42—1581no—
509C2×C42C22×D7911yescharacteristic
510#107—794no—
511#107—794no—
512#106—794no—
513C4⋊C8—794no—
514C4⋊C8—794no—
515C4⋊C8C22×D7914yes—
516#103—794no—
517#103—794no—
518#103—794no—
519#103—794no—
520#103—794no—
521#103—794no—
522#103C22×D7914yes—
523#102—794no—
524#102—794no—
525#102C22×D7914yes—
526C4×C8—794no—
527C4×C8—794no—
528C4×C8—794no—
529C24—21no—
530C2×Q8—22no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—3164no—
536C2×Q8—794no—
537C2×Q8—792no—
538C2×Q8—1584no—
539C2×Q8—1584no—
540C2×Q8—1582no—
541C2×Q8—1582no—
542C2×Q8—1581no—
543C2×Q8#1192962314yes—
544C2×Q8C23×D7912yes—
545C2×Q8C23×D7912yes—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4C23×D7912yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—3164no—
554C22×C4—791no—
555C22×C4—791no—
556C22×C4—791no—
557C22×C4—791no—
558C22×C4—1584no—
559C22×C4—1581no—
560C22×C4—1581no—
561C22×C4—1581no—
562C22×C4—1581no—
563C22×C4D4×D7911yescharacteristic
564C22×C4D4×D7911yescharacteristic
565C22×C4C23×D7911yescharacteristic
566Q16—28no—
567Q16—1588no—
568SD16—28no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—792no—
572C2×C8—792no—
573C2×C8—1582no—
574C2×C8—1582no—
575C2×C8C23×D7912yes—
576C2×C8C23×D7912yes—
577C4⋊C4—24no—
578C4⋊C4—21no—
579C4⋊C4—794no—
580C4⋊C4—794no—
581C4⋊C4—794no—
582C4⋊C4—792no—
583C4⋊C4—792no—
584C4⋊C4—792no—
585C4⋊C4—1584no—
586C4⋊C4—1584no—
587C4⋊C4—1584no—
588C4⋊C4—1584no—
589C4⋊C4—1584no—
590C4⋊C4—1584no—
591C4⋊C4—1584no—
592C4⋊C4—1584no—
593C4⋊C4—1584no—
594C4⋊C4—1584no—
595C4⋊C4—1584no—
596C4⋊C4—1581no—
597C4⋊C4—1581no—
598C4⋊C4—1581no—
599C4⋊C4C23×D7912yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—1584no—
603C22⋊C4—1584no—
604C22⋊C4—1584no—
605C42—24no—
606C42—792no—
607C42—792no—
608C42—792no—
609C42—792no—
610C42—1584no—
611C42—1584no—
612C42—1584no—
613C42—1584no—
614C42D4×D7912yes—
615C42C23×D7912yes—
616C23—22no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23C2×D4×D7911yescharacteristic
621Q8—22no—
622Q8—24no—
623Q8—22no—
624Q8—22no—
625Q8—42no—
626Q8—3168no—
627Q8—3162no—
628Q8—1588no—
629Q8—1582no—
630Q8—1582no—
631Q8C2×#1192962314yes—
632D4—22no—
633D4—22no—
634D4—42no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—3162no—
644C2×C4—3162no—
645C2×C4—3162no—
646C2×C4—3162no—
647C2×C4—3168no—
648C2×C4—794no—
649C2×C4—792no—
650C2×C4—792no—
651C2×C4—792no—
652C2×C4—792no—
653C2×C4—1582no—
654C2×C4—1582no—
655C2×C4—1582no—
656C2×C4—1582no—
657C2×C4—1582no—
658C2×C4—1582no—
659C2×C4—1582no—
660C2×C4C2×D4×D7912yes—
661C2×C4C2×D4×D7912yes—
662C2×C4C2×D4×D7911yescharacteristic
663C2×C4C2×#1192962312yes—
664C2×C4#1457920812yes—
665C2×C4C24×D7911yescharacteristic
666C8—22no—
667C8—22no—
668C8—1582no—
669C8—1582no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—84no—
674C22#1909921912yes—
675C22#135×D7912yes—
676C22#1909937912yes—
677C22C22×D4×D7911yescharacteristic
678C4—22no—
679C4—24no—
680C4—22no—
681C4—42no—
682C4—42no—
683C4—3162no—
684C4—3162no—
685C4—3162no—
686C4—3162no—
687C4—794no—
688C4—1582no—
689C4—1582no—
690C4—1582no—
691C4#1909921912yes—
692C4C22×#1192962311yescharacteristic
693C4C2×#1457920811yescharacteristic
694C2—82no—
695C2#2377608014yesdirect product factor
696C2C2×#1909921911yescharacteristic
697C2C2×#135×D7911yescharacteristic
698C2C2×#1909937911yescharacteristic
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×#3364
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×#19099289C2semidirect
3. #23776080C2direct (N × H)
6. C2×#19098912C2semidirect
7. C2×#19098871C2semidirect
8. C2×#19098868C2semidirect
11. C2×#19098771C2semidirect
12. C2×#19098687C2semidirect
13. C2×Q16×Dic79C2semidirect
14. C2×C4×#11929614C2semidirect
19. #19099289C22semidirect
43. #19098912C22semidirect
44. #19098871C22semidirect
45. #19098868C22semidirect
48. #19098771C22semidirect
49. #19098687C22semidirect
50. Q16×Dic79C22semidirect
51. C4×#11929614C22semidirect
346. C2×C79#3364semidirect
366. C79C2×#3364semidirect
695. C2#23776080direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992892
C2×#190992822
#237760802
C2×#190989172
C2×#190989162
C2×#190989122
C2×#190988712
C2×#190988682
C2×#190988412
C2×#190987832
C2×#190987712
C2×#190986872
C2×Q16×Dic792
C2×C4×#119296142
C2×SD16×Dic792
C2×#464×C792
C2×#336479