Finite Group Databasebeta

← C2×#23774662 #35160468

Subgroups — C2×#23774662 #35160468

Order 20224.

1678 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099191C211yesmaximal, characteristic
2#23774662C2116yesmaximal, direct product factor
3C2×#19098973C211yesmaximal, characteristic, complemented
4C2×#19098962C211yesmaximal, characteristic, complemented
5C2×#19098931C211yesmaximal, characteristic, complemented
6C2×#19098913C211yesmaximal, characteristic, complemented
7C2×#19098896C211yesmaximal, characteristic
8C2×#19098901C211yesmaximal, characteristic
9C2×#19098901C211yesmaximal, characteristic
10C2×#19098891C211yesmaximal, characteristic
11C2×#19098870C211yesmaximal, characteristic, complemented
12C2×#19098870C211yesmaximal, characteristic, complemented
13C2×#19098858C211yesmaximal, characteristic, complemented
14C2×#19098848C211yesmaximal, characteristic, complemented
15C2×#19098624C211yesmaximal, characteristic
16C2×#541×C79C211yesmaximal, characteristic
17#19099191—24no—
18#19099191C2218yes—
19C2×#14579161C2211yescharacteristic
20C2×#14579161C2211yescharacteristic
21C2×#14579160—21no—
22C2×#14579153C2211yescharacteristic
23C2×#14579153C2211yescharacteristic
24C2×#14579152—21no—
25C2×#14579138—21no—
26C2×#14579138—21no—
27C2×#14579120C2211yescharacteristic
28C22×C4⋊Dic79C2211yescharacteristic
29#19098973C2218yescomplemented
30#19098962C2218yescomplemented
31#19098931C2218yescomplemented
32#19098913C2218yescomplemented
33#19098901C2218yes—
34#19098901C2218yes—
35#19098896C2218yes—
36#19098891C2218yes—
37#19098870C2218yescomplemented
38#19098870C2218yescomplemented
39#19098858C2218yescomplemented
40#19098848C2218yescomplemented
41#19098624C2218yes—
42C2×#14579094C2211yescharacteristic
43C2×#14579094C2211yescharacteristic
44C2×#14579094C2211yescharacteristic
45C2×#14579094C2211yescharacteristic
46C2×#14579092C2211yescharacteristic
47C2×#14579092C2211yescharacteristic
48C2×#14579092C2211yescharacteristic
49C2×#14579092C2211yescharacteristic
50C2×C4⋊(C79⋊C8)C2211yescharacteristic
51C2×C4⋊(C79⋊C8)C2211yescharacteristic
52C2×#14579085C2211yescharacteristic
53C2×#14579085C2211yescharacteristic
54C2×#14579085C2211yescharacteristic
55C2×#14579085C2211yescharacteristic
56C2×#14579085C2211yescharacteristic
57C2×#14579085C2211yescharacteristic
58C2×#14579085C2211yescharacteristic
59C2×#14579085C2211yescharacteristic
60C2×C22⋊(C79⋊C8)C2211yescharacteristic
61C2×C22⋊(C79⋊C8)C2211yescharacteristic
62C2×#14579072C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64#541×C79—24no—
65#541×C79C2218yes—
66C2×C4⋊Q8×C79C2211yescharacteristic
67C2×#126×C79—21no—
68C2×#126×C79—21no—
69C2×#125×C79—21no—
70C2×#125×C79—21no—
71C2×#125×C79C2211yescharacteristic
72C2×C22⋊Q8×C79C2211yescharacteristic
73C2×C22⋊Q8×C79C2211yescharacteristic
74C2×C4×Q8×C79C2211yescharacteristic
75C2×C4×Q8×C79C2211yescharacteristic
76C2×#117×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C23×Dic79—21no—
80C22×C79⋊C8C2311yescharacteristic
81C22×C79⋊C8C2311yescharacteristic
82C22×C79⋊C8C2311yescharacteristic
83C22×C79⋊C8C2311yescharacteristic
84#14579161—22no—
85#14579161—22no—
86#14579161C2314yes—
87#14579161C2314yes—
88#14579160—28no—
89#14579153—22no—
90#14579153—22no—
91#14579153C2314yes—
92#14579153C2314yes—
93#14579152—28no—
94#14579138—28no—
95#14579138—28no—
96#14579120—22no—
97#14579120C2314yes—
98C2×C4⋊Dic79—22no—
99C2×C4⋊Dic79—21no—
100C2×C4⋊Dic79—21no—
101C2×C4⋊Dic79—21no—
102C2×C4⋊Dic79C2314yes—
103C2×C4⋊Dic79C2311yescharacteristic
104C2×C4⋊Dic79C2311yescharacteristic
105C2×C4⋊Dic79C2311yescharacteristic
106C2×C4⋊Dic79C2311yescharacteristic
107C2×Dic79⋊C4—21no—
108C2×Dic79⋊C4—21no—
109C2×Dic79⋊C4—21no—
110C2×Dic79⋊C4—21no—
111C2×C22⋊Dic79—21no—
112C2×C4×Dic79—21no—
113#14579094C2314yes—
114#14579094C2314yes—
115#14579094C2314yes—
116#14579094C2314yes—
117#14579092C2314yes—
118#14579092C2314yes—
119#14579092C2314yes—
120#14579092C2314yes—
121C4⋊(C79⋊C8)C2314yes—
122C4⋊(C79⋊C8)C2314yes—
123#14579085C2314yes—
124#14579085C2314yes—
125#14579085C2314yes—
126#14579085C2314yes—
127#14579085C2314yes—
128#14579085C2314yes—
129#14579085C2314yes—
130#14579085C2314yes—
131C22⋊(C79⋊C8)C2314yes—
132C22⋊(C79⋊C8)C2314yes—
133#14579072C2314yes—
134C4×C79⋊C8C2314yes—
135C22×Q8×C79C2311yescharacteristic
136C22×Q8×C79C2311yescharacteristic
137C23×C4×C79C2311yescharacteristic
138C4⋊Q8×C79—22no—
139C4⋊Q8×C79C2314yes—
140#126×C79—28no—
141#126×C79—28no—
142#125×C79—28no—
143#125×C79—28no—
144#125×C79—22no—
145#125×C79C2314yes—
146C22⋊Q8×C79—22no—
147C22⋊Q8×C79—22no—
148C22⋊Q8×C79C2314yes—
149C22⋊Q8×C79C2314yes—
150C4×Q8×C79—22no—
151C4×Q8×C79—22no—
152C4×Q8×C79C2314yes—
153C4×Q8×C79C2314yes—
154#117×C79D414yes—
155#117×C79C2314yes—
156C2×C4⋊C4×C79—21no—
157C2×C4⋊C4×C79—21no—
158C2×C4⋊C4×C79—21no—
159C2×C4⋊C4×C79—21no—
160C2×C4⋊C4×C79—21no—
161C2×C4⋊C4×C79—21no—
162C2×C4⋊C4×C79—21no—
163C2×C4⋊C4×C79—21no—
164C2×C4⋊C4×C79D411yescharacteristic
165C2×C4⋊C4×C79D411yescharacteristic
166C2×C4⋊C4×C79C2311yescharacteristic
167C2×C4⋊C4×C79C2311yescharacteristic
168C2×C22⋊C4×C79—21no—
169C2×C22⋊C4×C79—21no—
170C2×C22⋊C4×C79D411yescharacteristic
171C2×C22⋊C4×C79D411yescharacteristic
172C2×C42×C79—21no—
173C2×C42×C79—21no—
174C2×C42×C79C2311yescharacteristic
175C2×C42×C79C2311yescharacteristic
176C2×Dic158—24no—
177C2×Dic158—24no—
178C2×Dic158—82no—
179C2×Dic158—82no—
180C22×Dic79—21no—
181C22×Dic79—21no—
182C22×Dic79—21no—
183C22×Dic79—21no—
184C22×Dic79—24no—
185C22×Dic79—82no—
186C2×C79⋊C8—22no—
187C2×C79⋊C8—22no—
188C2×C79⋊C8—22no—
189C2×C79⋊C8—22no—
190C2×C79⋊C8C2412yes—
191C2×C79⋊C8C2412yes—
192C2×C79⋊C8C2412yes—
193C2×C79⋊C8C2412yes—
194C4⋊Dic79—24no—
195C4⋊Dic79—21no—
196C4⋊Dic79—21no—
197C4⋊Dic79—24no—
198C4⋊Dic79—24no—
199C4⋊Dic79—21no—
200C4⋊Dic79—21no—
201C4⋊Dic79C2412yes—
202C4⋊Dic79C2412yes—
203C4⋊Dic79C2412yes—
204C4⋊Dic79C2412yes—
205Dic79⋊C4—24no—
206Dic79⋊C4—24no—
207Dic79⋊C4—24no—
208Dic79⋊C4—24no—
209C22⋊Dic79—24no—
210C4×Dic79—24no—
211C24×C79C2×D411yescharacteristic
212C2×Q8×C79—21no—
213C2×Q8×C79—21no—
214C2×Q8×C79—22no—
215C2×Q8×C79—22no—
216C2×Q8×C79—22no—
217C2×Q8×C79—22no—
218C2×Q8×C79C2412yes—
219C2×Q8×C79C2412yes—
220C22×C4×C79—22no—
221C22×C4×C79—22no—
222C22×C4×C79—21no—
223C22×C4×C79—21no—
224C22×C4×C79—21no—
225C22×C4×C79—21no—
226C22×C4×C79C2×D411yescharacteristic
227C22×C4×C79C2×D411yescharacteristic
228C22×C4×C79C2×D411yescharacteristic
229C22×C4×C79C2×D411yescharacteristic
230C22×C4×C79C2×D411yescharacteristic
231C22×C4×C79C2×D412yes—
232C22×C4×C79C2412yes—
233C22×C4×C79C2411yescharacteristic
234C4⋊C4×C79—24no—
235C4⋊C4×C79—24no—
236C4⋊C4×C79—24no—
237C4⋊C4×C79—24no—
238C4⋊C4×C79—24no—
239C4⋊C4×C79—24no—
240C4⋊C4×C79—24no—
241C4⋊C4×C79—24no—
242C4⋊C4×C79—21no—
243C4⋊C4×C79—21no—
244C4⋊C4×C79C2×D414yes—
245C4⋊C4×C79C2×D414yes—
246C4⋊C4×C79C2412yes—
247C4⋊C4×C79C2412yes—
248C22⋊C4×C79—24no—
249C22⋊C4×C79—24no—
250C22⋊C4×C79C2×D414yes—
251C22⋊C4×C79C2×D414yes—
252C42×C79—24no—
253C42×C79—24no—
254C42×C79C2×D412yes—
255C42×C79C2×D412yes—
256C42×C79C2412yes—
257C42×C79C2412yes—
258C23×C79—22no—
259C23×C79—22no—
260C23×C79—22no—
261C23×C79C22×D412yes—
262C23×C79C22×D411yescharacteristic
263Q8×C79—22no—
264Q8×C79—22no—
265Q8×C79—22no—
266Q8×C79—22no—
267Q8×C79—42no—
268Q8×C79—42no—
269C2×C4×C79—22no—
270C2×C4×C79—22no—
271C2×C4×C79—22no—
272C2×C4×C79—22no—
273C2×C4×C79—22no—
274C2×C4×C79—24no—
275C2×C4×C79—22no—
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—42no—
285C2×C4×C79C22×D412yes—
286C2×C4×C79C22×D412yes—
287C2×C4×C79C22×D412yes—
288C2×C4×C79C22×D412yes—
289C2×C4×C79C22×D412yes—
290C2×C4×C79C22×D411yescharacteristic
291C2×C4×C792−1+412yes—
292C2×C4×C792−1+412yes—
293C2×C4×C79C2511yescharacteristic
294C2×Dic79—22no—
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—42no—
299C2×Dic79—42no—
300C2×Dic79—42no—
301C2×Dic79—42no—
302C2×Dic79—84no—
303Dic158—84no—
304Dic158—84no—
305C79⋊C8—22no—
306C79⋊C8—22no—
307C79⋊C8—22no—
308C79⋊C8—22no—
309C22×C79—22no—
310C22×C79—22no—
311C22×C79—22no—
312C22×C79—44no—
313C22×C79#53612yes—
314C22×C79#57712yes—
315C22×C79#57812yes—
316C22×C79C23×D411yescharacteristic
317C4×C79—22no—
318C4×C79—22no—
319C4×C79—22no—
320C4×C79—22no—
321C4×C79—22no—
322C4×C79—42no—
323C4×C79—42no—
324C4×C79—42no—
325C4×C79—42no—
326C4×C79#53612yes—
327C4×C79C2×2−1+411yescharacteristic
328C4×C79C2×2−1+411yescharacteristic
329Dic79—42no—
330Dic79—42no—
331Dic79—42no—
332Dic79—42no—
333C2×#3242—791nomaximal, Sylow
334C2×C79—42no—
335C2×C79#324214yescomplemented
336C2×C79C2×#53611yescharacteristic
337C2×C79C2×#57711yescharacteristic
338C2×C79C2×#57811yescharacteristic
339C2×#544—791no—
340C2×#541D7911yescharacteristic
341#3242—7916no—
342C2×#501—791no—
343C2×#499—791no—
344C2×#491—791no—
345C2×#487—791no—
346C2×#484—791no—
347C2×#485—791no—
348C2×#485—791no—
349C2×#483—791no—
350C2×#479—791no—
351C2×#479—791no—
352C2×#477—791no—
353C2×#475—791no—
354C2×#433—791no—
355C79C2×#324211yescharacteristic, complemented, Sylow
356#544—798no—
357#544—1584no—
358#541—24no—
359#541C2×D7918yes—
360C2×C4⋊Q8—791no—
361C2×C4⋊Q8—791no—
362C2×C4⋊Q8—1581no—
363C2×C4⋊Q8C2×D7911yescharacteristic
364C2×#126—21no—
365C2×#126—21no—
366C2×#125—21no—
367C2×#125—21no—
368C2×#125—791no—
369C2×#125—791no—
370C2×#125—1581no—
371C2×#125C2×D7911yescharacteristic
372C2×C22⋊Q8—1581no—
373C2×C22⋊Q8—1581no—
374C2×C22⋊Q8C2×D7911yescharacteristic
375C2×C22⋊Q8C2×D7911yescharacteristic
376C2×C4×Q8C2×D7911yescharacteristic
377C2×C4×Q8C2×D7911yescharacteristic
378C2×#117—791no—
379C2×#117C2×D7911yescharacteristic
380C22×C4⋊C4—791no—
381#501—798no—
382#499—798no—
383#491—798no—
384#487—798no—
385#485—798no—
386#485—798no—
387#484—798no—
388#483—798no—
389#479—798no—
390#479—798no—
391#477—798no—
392#475—798no—
393#433—798no—
394C2×#107—791no—
395C2×#107—791no—
396C2×#107—791no—
397C2×#107—791no—
398C2×#106—791no—
399C2×#106—791no—
400C2×#106—791no—
401C2×#106—791no—
402C2×C4⋊C8—791no—
403C2×C4⋊C8—791no—
404C2×#103—791no—
405C2×#103—791no—
406C2×#103—791no—
407C2×#103—791no—
408C2×#103—791no—
409C2×#103—791no—
410C2×#103—791no—
411C2×#103—791no—
412C2×C22⋊C8—791no—
413C2×C22⋊C8—791no—
414C2×#97—791no—
415C2×C4×C8—791no—
416C22×Q8—1581no—
417C22×Q8—1581no—
418C22×Q8C22×D7911yescharacteristic
419C22×Q8C22×D7911yescharacteristic
420C23×C4—1581no—
421C23×C4C22×D7911yescharacteristic
422C22×C8—791no—
423C22×C8—791no—
424C22×C8—791no—
425C22×C8—791no—
426C4⋊Q8—22no—
427C4⋊Q8—794no—
428C4⋊Q8—794no—
429C4⋊Q8—1588no—
430C4⋊Q8—1582no—
431C4⋊Q8—1582no—
432C4⋊Q8C22×D7914yes—
433#126—28no—
434#126—28no—
435#125—28no—
436#125—28no—
437#125—22no—
438#125—794no—
439#125—794no—
440#125—1588no—
441#125—1582no—
442#125—1582no—
443#125C22×D7914yes—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—1588no—
447C22⋊Q8—1588no—
448C22⋊Q8C22×D7914yes—
449C22⋊Q8C22×D7914yes—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8C22×D7914yes—
453C4×Q8C22×D7914yes—
454#117—794no—
455#117—1582no—
456#117C22⋊D7914yes—
457#117C22×D7914yes—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—791no—
467C2×C4⋊C4—791no—
468C2×C4⋊C4—794no—
469C2×C4⋊C4—791no—
470C2×C4⋊C4—791no—
471C2×C4⋊C4—1581no—
472C2×C4⋊C4—1582no—
473C2×C4⋊C4—1581no—
474C2×C4⋊C4—1581no—
475C2×C4⋊C4—1581no—
476C2×C4⋊C4—1581no—
477C2×C4⋊C4—1581no—
478C2×C4⋊C4—1581no—
479C2×C4⋊C4C22⋊D7911yescharacteristic
480C2×C4⋊C4C22⋊D7911yescharacteristic
481C2×C4⋊C4C22×D7911yescharacteristic
482C2×C4⋊C4C22×D7911yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1581no—
486C2×C22⋊C4C22⋊D7911yescharacteristic
487C2×C22⋊C4C22⋊D7911yescharacteristic
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—1581no—
491C2×C42C22×D7911yescharacteristic
492C2×C42C22×D7911yescharacteristic
493#107—794no—
494#107—794no—
495#107—794no—
496#107—794no—
497#106—794no—
498#106—794no—
499#106—794no—
500#106—794no—
501C4⋊C8—794no—
502C4⋊C8—794no—
503#103—794no—
504#103—794no—
505#103—794no—
506#103—794no—
507#103—794no—
508#103—794no—
509#103—794no—
510#103—794no—
511C22⋊C8—794no—
512C22⋊C8—794no—
513#97—794no—
514C4×C8—794no—
515C24C2×C22⋊D7911yescharacteristic
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—6322no—
523C2×Q8—6322no—
524C2×Q8—1584no—
525C2×Q8—1584no—
526C2×Q8C23×D7912yes—
527C2×Q8C23×D7912yes—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—6322no—
535C22×C4—1581no—
536C22×C4—1581no—
537C22×C4—1581no—
538C22×C4—1581no—
539C22×C4—1584no—
540C22×C4C2×C22⋊D7912yes—
541C22×C4C2×C22⋊D7911yescharacteristic
542C22×C4C2×C22⋊D7911yescharacteristic
543C22×C4C2×C22⋊D7911yescharacteristic
544C22×C4C2×C22⋊D7911yescharacteristic
545C22×C4C2×C22⋊D7911yescharacteristic
546C22×C4C23×D7912yes—
547C22×C4C23×D7911yescharacteristic
548C2×C8—792no—
549C2×C8—792no—
550C2×C8—792no—
551C2×C8—792no—
552C2×C8—1582no—
553C2×C8—1582no—
554C2×C8—1582no—
555C2×C8—1582no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—792no—
567C4⋊C4—792no—
568C4⋊C4—792no—
569C4⋊C4—792no—
570C4⋊C4—1584no—
571C4⋊C4—1584no—
572C4⋊C4—1584no—
573C4⋊C4—1584no—
574C4⋊C4—1584no—
575C4⋊C4—1581no—
576C4⋊C4—1581no—
577C4⋊C4—1581no—
578C4⋊C4—1581no—
579C4⋊C4—1584no—
580C4⋊C4—1584no—
581C4⋊C4C2×C22⋊D7914yes—
582C4⋊C4C2×C22⋊D7914yes—
583C4⋊C4C23×D7912yes—
584C4⋊C4C23×D7912yes—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—1584no—
588C22⋊C4C2×C22⋊D7914yes—
589C22⋊C4C2×C22⋊D7914yes—
590C42—24no—
591C42—24no—
592C42—1584no—
593C42C2×C22⋊D7912yes—
594C42C2×C22⋊D7912yes—
595C42C23×D7912yes—
596C42C23×D7912yes—
597C23—22no—
598C23—22no—
599C23—22no—
600C23C22×C22⋊D7912yes—
601C23C22×C22⋊D7911yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—22no—
605Q8—22no—
606Q8—42no—
607Q8—42no—
608Q8—6324no—
609Q8—6324no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—3162no—
627C2×C4—3162no—
628C2×C4—3162no—
629C2×C4—3162no—
630C2×C4—6324no—
631C2×C4—1582no—
632C2×C4—1582no—
633C2×C4—1582no—
634C2×C4—1582no—
635C2×C4C22×C22⋊D7912yes—
636C2×C4C22×C22⋊D7912yes—
637C2×C4C22×C22⋊D7912yes—
638C2×C4C22×C22⋊D7912yes—
639C2×C4C22×C22⋊D7912yes—
640C2×C4C22×C22⋊D7911yescharacteristic
641C2×C4#1457920812yes—
642C2×C4#1457920812yes—
643C2×C4C24×D7911yescharacteristic
644C8—1582no—
645C8—1582no—
646C8—1582no—
647C8—1582no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—44no—
652C22#1909913412yes—
653C22#1909937112yes—
654C22#1909937812yes—
655C22C23×C22⋊D7911yescharacteristic
656C4—22no—
657C4—22no—
658C4—22no—
659C4—22no—
660C4—22no—
661C4—42no—
662C4—42no—
663C4—42no—
664C4—42no—
665C4—3162no—
666C4—3162no—
667C4—3162no—
668C4—3162no—
669C4#1909913412yes—
670C4C2×#1457920811yescharacteristic
671C4C2×#1457920811yescharacteristic
672C2—42no—
673C2#2377466214yesdirect product factor
674C2C2×#1909913411yescharacteristic
675C2C2×#1909937111yescharacteristic
676C2C2×#1909937811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#541×C79C2
socleC23×C79C22×D4
prime radicalC24×C79C2×D4
hypercenterC2×#541D79
hypocenterC79C2×#3242
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #23774662C2direct (N × H)
3. C2×#19098973C2semidirect
4. C2×#19098962C2semidirect
5. C2×#19098931C2semidirect
6. C2×#19098913C2semidirect
11. C2×#19098870C2semidirect
12. C2×#19098870C2semidirect
13. C2×#19098858C2semidirect
14. C2×#19098848C2semidirect
29. #19098973C22semidirect
30. #19098962C22semidirect
31. #19098931C22semidirect
32. #19098913C22semidirect
37. #19098870C22semidirect
38. #19098870C22semidirect
39. #19098858C22semidirect
40. #19098848C22semidirect
335. C2×C79#3242semidirect
355. C79C2×#3242semidirect
673. C2#23774662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991912
#237746622
C2×#190989732
C2×#190989622
C2×#190989312
C2×#190989132
C2×#190988962
C2×#190989012
C2×#190988912
C2×#190988702
C2×#190988582
C2×#190988482
C2×#190986242
C2×#541×C792
C2×#324279