Finite Group Databasebeta

← C2×#24918725 #36276603

Subgroups — C2×#24918725 #36276603

Order 21248.

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×#19128329C211yesmaximal, characteristic
2#24918725C2116yesmaximal, direct product factor
3C2×#19128111C211yesmaximal, characteristic, complemented
4C2×#19128100C211yesmaximal, characteristic, complemented
5C2×#19128069C211yesmaximal, characteristic, complemented
6C2×#19128051C211yesmaximal, characteristic, complemented
7C2×#19128034C211yesmaximal, characteristic
8C2×#19128039C211yesmaximal, characteristic
9C2×#19128039C211yesmaximal, characteristic
10C2×#19128029C211yesmaximal, characteristic
11C2×#19128008C211yesmaximal, characteristic, complemented
12C2×#19128008C211yesmaximal, characteristic, complemented
13C2×#19127996C211yesmaximal, characteristic, complemented
14C2×#19127986C211yesmaximal, characteristic, complemented
15C2×#19127762C211yesmaximal, characteristic
16C2×#541×C83C211yesmaximal, characteristic
17#19128329—24no—
18#19128329C2218yes—
19C2×#14581792C2211yescharacteristic
20C2×#14581792C2211yescharacteristic
21C2×#14581791—21no—
22C2×#14581784C2211yescharacteristic
23C2×#14581784C2211yescharacteristic
24C2×#14581783—21no—
25C2×#14581769—21no—
26C2×#14581769—21no—
27C2×#14581751C2211yescharacteristic
28C22×C4⋊Dic83C2211yescharacteristic
29#19128111C2218yescomplemented
30#19128100C2218yescomplemented
31#19128069C2218yescomplemented
32#19128051C2218yescomplemented
33#19128039C2218yes—
34#19128039C2218yes—
35#19128034C2218yes—
36#19128029C2218yes—
37#19128008C2218yescomplemented
38#19128008C2218yescomplemented
39#19127996C2218yescomplemented
40#19127986C2218yescomplemented
41#19127762C2218yes—
42C2×#14581725C2211yescharacteristic
43C2×#14581725C2211yescharacteristic
44C2×#14581725C2211yescharacteristic
45C2×#14581725C2211yescharacteristic
46C2×#14581723C2211yescharacteristic
47C2×#14581723C2211yescharacteristic
48C2×#14581723C2211yescharacteristic
49C2×#14581723C2211yescharacteristic
50C2×C4⋊(C83⋊C8)C2211yescharacteristic
51C2×C4⋊(C83⋊C8)C2211yescharacteristic
52C2×#14581716C2211yescharacteristic
53C2×#14581716C2211yescharacteristic
54C2×#14581716C2211yescharacteristic
55C2×#14581716C2211yescharacteristic
56C2×#14581716C2211yescharacteristic
57C2×#14581716C2211yescharacteristic
58C2×#14581716C2211yescharacteristic
59C2×#14581716C2211yescharacteristic
60C2×C22⋊(C83⋊C8)C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×#14581703C2211yescharacteristic
63C2×C4×C83⋊C8C2211yescharacteristic
64#541×C83—24no—
65#541×C83C2218yes—
66C2×C4⋊Q8×C83C2211yescharacteristic
67C2×#126×C83—21no—
68C2×#126×C83—21no—
69C2×#125×C83—21no—
70C2×#125×C83—21no—
71C2×#125×C83C2211yescharacteristic
72C2×C22⋊Q8×C83C2211yescharacteristic
73C2×C22⋊Q8×C83C2211yescharacteristic
74C2×C4×Q8×C83C2211yescharacteristic
75C2×C4×Q8×C83C2211yescharacteristic
76C2×#117×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—21no—
79C23×Dic83—21no—
80C22×C83⋊C8C2311yescharacteristic
81C22×C83⋊C8C2311yescharacteristic
82C22×C83⋊C8C2311yescharacteristic
83C22×C83⋊C8C2311yescharacteristic
84#14581792—22no—
85#14581792—22no—
86#14581792C2314yes—
87#14581792C2314yes—
88#14581791—28no—
89#14581784—22no—
90#14581784—22no—
91#14581784C2314yes—
92#14581784C2314yes—
93#14581783—28no—
94#14581769—28no—
95#14581769—28no—
96#14581751—22no—
97#14581751C2314yes—
98C2×C4⋊Dic83—22no—
99C2×C4⋊Dic83—21no—
100C2×C4⋊Dic83—21no—
101C2×C4⋊Dic83—21no—
102C2×C4⋊Dic83C2314yes—
103C2×C4⋊Dic83C2311yescharacteristic
104C2×C4⋊Dic83C2311yescharacteristic
105C2×C4⋊Dic83C2311yescharacteristic
106C2×C4⋊Dic83C2311yescharacteristic
107C2×Dic83⋊C4—21no—
108C2×Dic83⋊C4—21no—
109C2×Dic83⋊C4—21no—
110C2×Dic83⋊C4—21no—
111C2×C22⋊Dic83—21no—
112C2×C4×Dic83—21no—
113#14581725C2314yes—
114#14581725C2314yes—
115#14581725C2314yes—
116#14581725C2314yes—
117#14581723C2314yes—
118#14581723C2314yes—
119#14581723C2314yes—
120#14581723C2314yes—
121C4⋊(C83⋊C8)C2314yes—
122C4⋊(C83⋊C8)C2314yes—
123#14581716C2314yes—
124#14581716C2314yes—
125#14581716C2314yes—
126#14581716C2314yes—
127#14581716C2314yes—
128#14581716C2314yes—
129#14581716C2314yes—
130#14581716C2314yes—
131C22⋊(C83⋊C8)C2314yes—
132C22⋊(C83⋊C8)C2314yes—
133#14581703C2314yes—
134C4×C83⋊C8C2314yes—
135C22×Q8×C83C2311yescharacteristic
136C22×Q8×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C4⋊Q8×C83—22no—
139C4⋊Q8×C83C2314yes—
140#126×C83—28no—
141#126×C83—28no—
142#125×C83—28no—
143#125×C83—28no—
144#125×C83—22no—
145#125×C83C2314yes—
146C22⋊Q8×C83—22no—
147C22⋊Q8×C83—22no—
148C22⋊Q8×C83C2314yes—
149C22⋊Q8×C83C2314yes—
150C4×Q8×C83—22no—
151C4×Q8×C83—22no—
152C4×Q8×C83C2314yes—
153C4×Q8×C83C2314yes—
154#117×C83D414yes—
155#117×C83C2314yes—
156C2×C4⋊C4×C83—21no—
157C2×C4⋊C4×C83—21no—
158C2×C4⋊C4×C83—21no—
159C2×C4⋊C4×C83—21no—
160C2×C4⋊C4×C83—21no—
161C2×C4⋊C4×C83—21no—
162C2×C4⋊C4×C83—21no—
163C2×C4⋊C4×C83—21no—
164C2×C4⋊C4×C83D411yescharacteristic
165C2×C4⋊C4×C83D411yescharacteristic
166C2×C4⋊C4×C83C2311yescharacteristic
167C2×C4⋊C4×C83C2311yescharacteristic
168C2×C22⋊C4×C83—21no—
169C2×C22⋊C4×C83—21no—
170C2×C22⋊C4×C83D411yescharacteristic
171C2×C22⋊C4×C83D411yescharacteristic
172C2×C42×C83—21no—
173C2×C42×C83—21no—
174C2×C42×C83C2311yescharacteristic
175C2×C42×C83C2311yescharacteristic
176C2×Dic166—24no—
177C2×Dic166—24no—
178C2×Dic166—82no—
179C2×Dic166—82no—
180C22×Dic83—21no—
181C22×Dic83—21no—
182C22×Dic83—21no—
183C22×Dic83—21no—
184C22×Dic83—24no—
185C22×Dic83—82no—
186C2×C83⋊C8—22no—
187C2×C83⋊C8—22no—
188C2×C83⋊C8—22no—
189C2×C83⋊C8—22no—
190C2×C83⋊C8C2412yes—
191C2×C83⋊C8C2412yes—
192C2×C83⋊C8C2412yes—
193C2×C83⋊C8C2412yes—
194C4⋊Dic83—24no—
195C4⋊Dic83—24no—
196C4⋊Dic83—24no—
197C4⋊Dic83—21no—
198C4⋊Dic83—21no—
199C4⋊Dic83—21no—
200C4⋊Dic83—21no—
201C4⋊Dic83C2412yes—
202C4⋊Dic83C2412yes—
203C4⋊Dic83C2412yes—
204C4⋊Dic83C2412yes—
205Dic83⋊C4—24no—
206Dic83⋊C4—24no—
207Dic83⋊C4—24no—
208Dic83⋊C4—24no—
209C22⋊Dic83—24no—
210C4×Dic83—24no—
211C24×C83C2×D411yescharacteristic
212C2×Q8×C83—21no—
213C2×Q8×C83—21no—
214C2×Q8×C83—22no—
215C2×Q8×C83—22no—
216C2×Q8×C83—22no—
217C2×Q8×C83—22no—
218C2×Q8×C83C2412yes—
219C2×Q8×C83C2412yes—
220C22×C4×C83—22no—
221C22×C4×C83—22no—
222C22×C4×C83—21no—
223C22×C4×C83—21no—
224C22×C4×C83—21no—
225C22×C4×C83—21no—
226C22×C4×C83C2×D411yescharacteristic
227C22×C4×C83C2×D411yescharacteristic
228C22×C4×C83C2×D411yescharacteristic
229C22×C4×C83C2×D411yescharacteristic
230C22×C4×C83C2×D411yescharacteristic
231C22×C4×C83C2×D412yes—
232C22×C4×C83C2412yes—
233C22×C4×C83C2411yescharacteristic
234C4⋊C4×C83—24no—
235C4⋊C4×C83—24no—
236C4⋊C4×C83—24no—
237C4⋊C4×C83—24no—
238C4⋊C4×C83—24no—
239C4⋊C4×C83—24no—
240C4⋊C4×C83—24no—
241C4⋊C4×C83—24no—
242C4⋊C4×C83—21no—
243C4⋊C4×C83—21no—
244C4⋊C4×C83C2×D414yes—
245C4⋊C4×C83C2×D414yes—
246C4⋊C4×C83C2412yes—
247C4⋊C4×C83C2412yes—
248C22⋊C4×C83—24no—
249C22⋊C4×C83—24no—
250C22⋊C4×C83C2×D414yes—
251C22⋊C4×C83C2×D414yes—
252C42×C83—24no—
253C42×C83—24no—
254C42×C83C2×D412yes—
255C42×C83C2×D412yes—
256C42×C83C2412yes—
257C42×C83C2412yes—
258C23×C83—22no—
259C23×C83—22no—
260C23×C83—22no—
261C23×C83C22×D412yes—
262C23×C83C22×D411yescharacteristic
263Q8×C83—22no—
264Q8×C83—22no—
265Q8×C83—22no—
266Q8×C83—22no—
267Q8×C83—42no—
268Q8×C83—42no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—24no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—42no—
282C2×C4×C83—42no—
283C2×C4×C83—42no—
284C2×C4×C83—42no—
285C2×C4×C83C22×D412yes—
286C2×C4×C83C22×D412yes—
287C2×C4×C83C22×D412yes—
288C2×C4×C83C22×D412yes—
289C2×C4×C83C22×D412yes—
290C2×C4×C83C22×D411yescharacteristic
291C2×C4×C832−1+412yes—
292C2×C4×C832−1+412yes—
293C2×C4×C83C2511yescharacteristic
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—42no—
299C2×Dic83—42no—
300C2×Dic83—42no—
301C2×Dic83—42no—
302C2×Dic83—84no—
303Dic166—84no—
304Dic166—84no—
305C83⋊C8—22no—
306C83⋊C8—22no—
307C83⋊C8—22no—
308C83⋊C8—22no—
309C22×C83—22no—
310C22×C83—22no—
311C22×C83—22no—
312C22×C83—44no—
313C22×C83#53612yes—
314C22×C83#57712yes—
315C22×C83#57812yes—
316C22×C83C23×D411yescharacteristic
317C4×C83—22no—
318C4×C83—22no—
319C4×C83—22no—
320C4×C83—22no—
321C4×C83—22no—
322C4×C83—42no—
323C4×C83—42no—
324C4×C83—42no—
325C4×C83—42no—
326C4×C83#53612yes—
327C4×C83C2×2−1+411yescharacteristic
328C4×C83C2×2−1+411yescharacteristic
329Dic83—42no—
330Dic83—42no—
331Dic83—42no—
332Dic83—42no—
333C2×#3242—831nomaximal, Sylow
334C2×C83—42no—
335C2×C83#324214yescomplemented
336C2×C83C2×#53611yescharacteristic
337C2×C83C2×#57711yescharacteristic
338C2×C83C2×#57811yescharacteristic
339C2×#544—831no—
340C2×#541D8311yescharacteristic
341#3242—8316no—
342C2×#501—831no—
343C2×#499—831no—
344C2×#491—831no—
345C2×#487—831no—
346C2×#484—831no—
347C2×#485—831no—
348C2×#485—831no—
349C2×#483—831no—
350C2×#479—831no—
351C2×#479—831no—
352C2×#477—831no—
353C2×#475—831no—
354C2×#433—831no—
355C83C2×#324211yescharacteristic, complemented, Sylow
356#544—838no—
357#544—1664no—
358#541—24no—
359#541C2×D8318yes—
360C2×C4⋊Q8—831no—
361C2×C4⋊Q8—831no—
362C2×C4⋊Q8—1661no—
363C2×C4⋊Q8C2×D8311yescharacteristic
364C2×#126—21no—
365C2×#126—21no—
366C2×#125—21no—
367C2×#125—21no—
368C2×#125—831no—
369C2×#125—831no—
370C2×#125—1661no—
371C2×#125C2×D8311yescharacteristic
372C2×C22⋊Q8—1661no—
373C2×C22⋊Q8—1661no—
374C2×C22⋊Q8C2×D8311yescharacteristic
375C2×C22⋊Q8C2×D8311yescharacteristic
376C2×C4×Q8C2×D8311yescharacteristic
377C2×C4×Q8C2×D8311yescharacteristic
378C2×#117—831no—
379C2×#117C2×D8311yescharacteristic
380C22×C4⋊C4—831no—
381#501—838no—
382#499—838no—
383#491—838no—
384#487—838no—
385#485—838no—
386#485—838no—
387#484—838no—
388#483—838no—
389#479—838no—
390#479—838no—
391#477—838no—
392#475—838no—
393#433—838no—
394C2×#107—831no—
395C2×#107—831no—
396C2×#107—831no—
397C2×#107—831no—
398C2×#106—831no—
399C2×#106—831no—
400C2×#106—831no—
401C2×#106—831no—
402C2×C4⋊C8—831no—
403C2×C4⋊C8—831no—
404C2×#103—831no—
405C2×#103—831no—
406C2×#103—831no—
407C2×#103—831no—
408C2×#103—831no—
409C2×#103—831no—
410C2×#103—831no—
411C2×#103—831no—
412C2×C22⋊C8—831no—
413C2×C22⋊C8—831no—
414C2×#97—831no—
415C2×C4×C8—831no—
416C22×Q8—1661no—
417C22×Q8—1661no—
418C22×Q8C22×D8311yescharacteristic
419C22×Q8C22×D8311yescharacteristic
420C23×C4—1661no—
421C23×C4C22×D8311yescharacteristic
422C22×C8—831no—
423C22×C8—831no—
424C22×C8—831no—
425C22×C8—831no—
426C4⋊Q8—22no—
427C4⋊Q8—834no—
428C4⋊Q8—834no—
429C4⋊Q8—1668no—
430C4⋊Q8—1662no—
431C4⋊Q8—1662no—
432C4⋊Q8C22×D8314yes—
433#126—28no—
434#126—28no—
435#125—28no—
436#125—28no—
437#125—22no—
438#125—834no—
439#125—834no—
440#125—1668no—
441#125—1662no—
442#125—1662no—
443#125C22×D8314yes—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—1668no—
447C22⋊Q8—1668no—
448C22⋊Q8C22×D8314yes—
449C22⋊Q8C22×D8314yes—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8C22×D8314yes—
453C4×Q8C22×D8314yes—
454#117—834no—
455#117—1662no—
456#117C22⋊D8314yes—
457#117C22×D8314yes—
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—831no—
467C2×C4⋊C4—831no—
468C2×C4⋊C4—834no—
469C2×C4⋊C4—831no—
470C2×C4⋊C4—831no—
471C2×C4⋊C4—1661no—
472C2×C4⋊C4—1662no—
473C2×C4⋊C4—1661no—
474C2×C4⋊C4—1661no—
475C2×C4⋊C4—1661no—
476C2×C4⋊C4—1661no—
477C2×C4⋊C4—1661no—
478C2×C4⋊C4—1661no—
479C2×C4⋊C4C22⋊D8311yescharacteristic
480C2×C4⋊C4C22⋊D8311yescharacteristic
481C2×C4⋊C4C22×D8311yescharacteristic
482C2×C4⋊C4C22×D8311yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1661no—
486C2×C22⋊C4C22⋊D8311yescharacteristic
487C2×C22⋊C4C22⋊D8311yescharacteristic
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—1661no—
491C2×C42C22×D8311yescharacteristic
492C2×C42C22×D8311yescharacteristic
493#107—834no—
494#107—834no—
495#107—834no—
496#107—834no—
497#106—834no—
498#106—834no—
499#106—834no—
500#106—834no—
501C4⋊C8—834no—
502C4⋊C8—834no—
503#103—834no—
504#103—834no—
505#103—834no—
506#103—834no—
507#103—834no—
508#103—834no—
509#103—834no—
510#103—834no—
511C22⋊C8—834no—
512C22⋊C8—834no—
513#97—834no—
514C4×C8—834no—
515C24C2×C22⋊D8311yescharacteristic
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—6642no—
523C2×Q8—6642no—
524C2×Q8—1664no—
525C2×Q8—1664no—
526C2×Q8C23×D8312yes—
527C2×Q8C23×D8312yes—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—6642no—
535C22×C4—1661no—
536C22×C4—1661no—
537C22×C4—1661no—
538C22×C4—1661no—
539C22×C4—1664no—
540C22×C4C2×C22⋊D8312yes—
541C22×C4C2×C22⋊D8311yescharacteristic
542C22×C4C2×C22⋊D8311yescharacteristic
543C22×C4C2×C22⋊D8311yescharacteristic
544C22×C4C2×C22⋊D8311yescharacteristic
545C22×C4C2×C22⋊D8311yescharacteristic
546C22×C4C23×D8312yes—
547C22×C4C23×D8311yescharacteristic
548C2×C8—832no—
549C2×C8—832no—
550C2×C8—832no—
551C2×C8—832no—
552C2×C8—1662no—
553C2×C8—1662no—
554C2×C8—1662no—
555C2×C8—1662no—
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—832no—
567C4⋊C4—832no—
568C4⋊C4—832no—
569C4⋊C4—832no—
570C4⋊C4—1664no—
571C4⋊C4—1661no—
572C4⋊C4—1661no—
573C4⋊C4—1661no—
574C4⋊C4—1661no—
575C4⋊C4—1664no—
576C4⋊C4—1664no—
577C4⋊C4—1664no—
578C4⋊C4—1664no—
579C4⋊C4—1664no—
580C4⋊C4—1664no—
581C4⋊C4C2×C22⋊D8314yes—
582C4⋊C4C2×C22⋊D8314yes—
583C4⋊C4C23×D8312yes—
584C4⋊C4C23×D8312yes—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—1664no—
588C22⋊C4C2×C22⋊D8314yes—
589C22⋊C4C2×C22⋊D8314yes—
590C42—24no—
591C42—24no—
592C42—1664no—
593C42C2×C22⋊D8312yes—
594C42C2×C22⋊D8312yes—
595C42C23×D8312yes—
596C42C23×D8312yes—
597C23—22no—
598C23—22no—
599C23—22no—
600C23C22×C22⋊D8312yes—
601C23C22×C22⋊D8311yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—22no—
605Q8—22no—
606Q8—42no—
607Q8—42no—
608Q8—6644no—
609Q8—6644no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
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—3322no—
627C2×C4—3322no—
628C2×C4—3322no—
629C2×C4—3322no—
630C2×C4—6644no—
631C2×C4—1662no—
632C2×C4—1662no—
633C2×C4—1662no—
634C2×C4—1662no—
635C2×C4C22×C22⋊D8312yes—
636C2×C4C22×C22⋊D8312yes—
637C2×C4C22×C22⋊D8312yes—
638C2×C4C22×C22⋊D8312yes—
639C2×C4C22×C22⋊D8312yes—
640C2×C4C22×C22⋊D8311yescharacteristic
641C2×C4#1458183912yes—
642C2×C4#1458183912yes—
643C2×C4C24×D8311yescharacteristic
644C8—1662no—
645C8—1662no—
646C8—1662no—
647C8—1662no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—44no—
652C22#1912827212yes—
653C22#1912850912yes—
654C22#1912851612yes—
655C22C23×C22⋊D8311yescharacteristic
656C4—22no—
657C4—22no—
658C4—22no—
659C4—22no—
660C4—22no—
661C4—42no—
662C4—42no—
663C4—42no—
664C4—42no—
665C4—3322no—
666C4—3322no—
667C4—3322no—
668C4—3322no—
669C4#1912827212yes—
670C4C2×#1458183911yescharacteristic
671C4C2×#1458183911yescharacteristic
672C2—42no—
673C2#2491872514yesdirect product factor
674C2C2×#1912827211yescharacteristic
675C2C2×#1912850911yescharacteristic
676C2C2×#1912851611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#541×C83C2
socleC23×C83C22×D4
prime radicalC24×C83C2×D4
hypercenterC2×#541D83
hypocenterC83C2×#3242
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #24918725C2direct (N × H)
3. C2×#19128111C2semidirect
4. C2×#19128100C2semidirect
5. C2×#19128069C2semidirect
6. C2×#19128051C2semidirect
11. C2×#19128008C2semidirect
12. C2×#19128008C2semidirect
13. C2×#19127996C2semidirect
14. C2×#19127986C2semidirect
29. #19128111C22semidirect
30. #19128100C22semidirect
31. #19128069C22semidirect
32. #19128051C22semidirect
37. #19128008C22semidirect
38. #19128008C22semidirect
39. #19127996C22semidirect
40. #19127986C22semidirect
335. C2×C83#3242semidirect
355. C83C2×#3242semidirect
673. C2#24918725direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283292
#249187252
C2×#191281112
C2×#191281002
C2×#191280692
C2×#191280512
C2×#191280342
C2×#191280392
C2×#191280292
C2×#191280082
C2×#191279962
C2×#191279862
C2×#191277622
C2×#541×C832
C2×#324283