Finite Group Databasebeta

← C2×#11738763 #14225825

Subgroups — C2×#11738763 #14225825

Order 1792.

1822 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90291C211yesmaximal, characteristic
2C22×#6453C211yesmaximal, characteristic, complemented
3C2×C7×#481C211yesmaximal, characteristic
4C2×#89805C211yesmaximal, characteristic
5C2×#89742C211yesmaximal, characteristic, complemented
6#11738763C2116yesmaximal, direct product factor
7C2×#89629C212yesmaximal, complemented
8C2×#89630C212yesmaximal, complemented
9C2×#89540C212yesmaximal, complemented
10C2×#89535C212yesmaximal, complemented
11C2×#89493C211yesmaximal, characteristic, complemented
12C2×#89490C211yesmaximal, characteristic, complemented
13C2×C7×#121C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C2×#6499C2211yescharacteristic
16C2×#6498—21no—
17C2×D4×Dic7—21no—
18C2×D4×Dic7C2211yescharacteristic
19C22×C4⋊Dic7—21no—
20C22×C4⋊Dic7C2211yescharacteristic
21C2×#6487C2211yescharacteristic
22C22×Dic7⋊C4—21no—
23C22×C4×Dic7C2211yescharacteristic
24#90291—24no—
25#90291C2218yes—
26C2×#6453—24no—
27C2×#6453—21no—
28C2×#6453—21no—
29C2×#6453C2212yes—
30C2×#6453C2211yescharacteristic
31C2×#6453C2212yes—
32C2×#6453C2218yescomplemented
33C2×#6450C2211yescharacteristic
34C2×#6442—21no—
35C2×#6440—21no—
36C7×#481C2218yes—
37C2×C7×#106C2212yes—
38C2×C7×#102C2212yes—
39C2×C7×C22⋊C8C2211yescharacteristic
40C2×#6406C2212yes—
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42C2×#6391C2212yes—
43C2×#6390C2212yes—
44C2×Dic7⋊C8C2212yes—
45C2×C8×Dic7C2212yes—
46#89805C2218yes—
47#89742C2218yescomplemented
48C2×#6384C2212yes—
49C2×#6381C2212yes—
50C2×#6381C2212yes—
51#89630C22116yescomplemented
52#89629C22116yescomplemented
53#89540C22116yescomplemented
54#89535C22116yescomplemented
55#89493C2218yescomplemented
56#89490C2218yescomplemented
57C2×#3232—71nomaximal, Sylow
58C22×C7×D4—21no—
59C22×C7×D4C2311yescharacteristic
60C23×C4×C7—21no—
61C23×C4×C7C2311yescharacteristic
62C23×Dic7—21no—
63C23×Dic7—21no—
64C23×Dic7D411yescharacteristic
65C23×Dic7D411yescharacteristic
66C22×Dic14C2311yescharacteristic
67C22×C7×C8C2312yes—
68C7×#121—22no—
69C7×#121C2314yes—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4C2314yes—
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C4⋊C4C2312yes—
75C2×C7×C22⋊C4—21no—
76C2×C22⋊Dic7—21no—
77C2×C22⋊Dic7—21no—
78C2×C22⋊Dic7—21no—
79C2×C22⋊Dic7—21no—
80#6499—22no—
81#6499C2314yes—
82#6498—28no—
83D4×Dic7—28no—
84D4×Dic7—22no—
85D4×Dic7C2314yes—
86C2×C4⋊Dic7—21no—
87C2×C4⋊Dic7—22no—
88C2×C4⋊Dic7—21no—
89C2×C4⋊Dic7—22no—
90C2×C4⋊Dic7—22no—
91C2×C4⋊Dic7—28no—
92C2×C4⋊Dic7C2312yes—
93C2×C4⋊Dic7C2311yescharacteristic
94C2×C4⋊Dic7C2314yes—
95#6487—22no—
96#6487C2314yes—
97C2×Dic7⋊C4—21no—
98C2×Dic7⋊C4—21no—
99C2×Dic7⋊C4—21no—
100C2×Dic7⋊C4—22no—
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—28no—
103C2×C4×Dic7—21no—
104C2×C4×Dic7D411yescharacteristic
105C2×C4×Dic7D411yescharacteristic
106C2×C4×Dic7D414yes—
107C2×C4×Dic7C2311yescharacteristic
108C2×C4×Dic7C2311yescharacteristic
109C2×C4×Dic7C2314yes—
110C22×C7⋊C8C2312yes—
111#6453—24no—
112#6453—24no—
113#6453—28no—
114#6453—28no—
115#6453—22no—
116#6453C2318yes—
117#6453C2314yes—
118#6453C2318yes—
119#6450—22no—
120#6450C2314yes—
121#6442—28no—
122#6440—28no—
123C7×#106C2318yes—
124C7×#102C2318yes—
125C7×C22⋊C8C2314yes—
126#6406C2318yes—
127C22⋊(C7⋊C8)C2314yes—
128#6391C2318yes—
129#6390C2318yes—
130Dic7⋊C8C2318yes—
131C8×Dic7C2318yes—
132#6384C2318yes—
133#6381C2318yes—
134#6381C2318yes—
135C2×#529—71no—
136C22×#125—71no—
137#3232—716no—
138C2×#499—72no—
139C2×#488—72no—
140C2×#484—71no—
141C2×#481D711yescharacteristic
142C2×#483—71no—
143C2×#480—71no—
144C2×#479—72no—
145C2×#478—72no—
146C2×#431—71no—
147C24×C7—21no—
148C24×C7C2×D411yescharacteristic
149C2×C7×D4—24no—
150C2×C7×D4—21no—
151C2×C7×D4—24no—
152C2×C7×D4—44no—
153C2×C7×D4C2412yes—
154C22×C4×C7—24no—
155C22×C4×C7—21no—
156C22×C4×C7—24no—
157C22×C4×C7—22no—
158C22×C4×C7—44no—
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D412yes—
161C22×C4×C7C2412yes—
162C22×C4×C7C2411yescharacteristic
163C22×Dic7—24no—
164C22×Dic7—21no—
165C22×Dic7—24no—
166C22×Dic7—22no—
167C22×Dic7—21no—
168C22×Dic7—24no—
169C22×Dic7—42no—
170C22×Dic7—44no—
171C22×Dic7—44no—
172C22×Dic7C2×D411yescharacteristic
173C22×Dic7C2×D411yescharacteristic
174C22×Dic7C2×D411yescharacteristic
175C22×Dic7C2×D411yescharacteristic
176C22×Dic7C2×D414yes—
177C22×Dic7C2×D414yes—
178C2×Dic14—24no—
179C2×Dic14—21no—
180C2×Dic14C2412yes—
181C2×C7×C8—24no—
182C2×C7×C8C2414yes—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—24no—
185C7×C4⋊C4—22no—
186C7×C4⋊C4C2414yes—
187C7×C4⋊C4C2412yes—
188C7×C22⋊C4—24no—
189C22⋊Dic7—24no—
190C22⋊Dic7—24no—
191C22⋊Dic7—24no—
192C22⋊Dic7—24no—
193C4⋊Dic7—24no—
194C4⋊Dic7—22no—
195C4⋊Dic7—21no—
196C4⋊Dic7—24no—
197C4⋊Dic7—28no—
198C4⋊Dic7—28no—
199C4⋊Dic7C2414yes—
200C4⋊Dic7C2412yes—
201Dic7⋊C4—24no—
202Dic7⋊C4—24no—
203Dic7⋊C4—24no—
204Dic7⋊C4—28no—
205Dic7⋊C4—28no—
206C4×Dic7—24no—
207C4×Dic7C2×D414yes—
208C4×Dic7C2×D414yes—
209C4×Dic7C2×D412yes—
210C4×Dic7C2×D412yes—
211C4×Dic7C2412yes—
212C4×Dic7C2412yes—
213C2×C7⋊C8—24no—
214C2×C7⋊C8C2414yes—
215#529—78no—
216#529—144no—
217C2×#126—141no—
218C2×#125—72no—
219C2×#125—72no—
220C2×#125—71no—
221C2×#125—78no—
222C2×#125—141no—
223C2×#125—141no—
224C2×#125—144no—
225C2×#124—71no—
226C2×#123—141no—
227C2×C22⋊Q8—71no—
228C2×#121C2×D711yescharacteristic
229C2×C4×Q8—71no—
230C2×C4×D4—71no—
231C2×C4×D4—141no—
232C2×#117—141no—
233C22×C4⋊C4—71no—
234C22×C4⋊C4—141no—
235C22×C4⋊C4—141no—
236C22×C4⋊C4C2×D711yescharacteristic
237C22×C42—71no—
238#499—716no—
239#488—716no—
240#484—78no—
241#483—78no—
242#481C2×D718yes—
243#480—78no—
244#479—716no—
245#478—716no—
246#431—78no—
247C2×#107—72no—
248C2×#107—72no—
249C2×#106—72no—
250C2×#106C2×D712yes—
251C2×C4⋊C8—72no—
252C2×#103—72no—
253C2×#103—72no—
254C2×#102—72no—
255C2×#102C2×D712yes—
256C2×C22⋊C8—71no—
257C2×C22⋊C8C2×D711yescharacteristic
258C2×C4×C8—72no—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—42no—
263C23×C7—42no—
264C23×C7—42no—
265C23×C7#13514yes—
266C23×C7C22×D412yes—
267C23×C7C22×D411yescharacteristic
268C7×D4—24no—
269C7×D4—48no—
270C7×D4—42no—
271C2×C4×C7—22no—
272C2×C4×C7—24no—
273C2×C4×C7—24no—
274C2×C4×C7—22no—
275C2×C4×C7—24no—
276C2×C4×C7—48no—
277C2×C4×C7—42no—
278C2×C4×C7—44no—
279C2×C4×C7C22×D412yes—
280C2×C4×C7C22×D411yescharacteristic
281C2×C4×C72−1+414yes—
282C2×C4×C7C2511yescharacteristic
283C2×Dic7—28no—
284C2×Dic7—22no—
285C2×Dic7—22no—
286C2×Dic7—22no—
287C2×Dic7—22no—
288C2×Dic7—22no—
289C2×Dic7—24no—
290C2×Dic7—22no—
291C2×Dic7—44no—
292C2×Dic7—48no—
293C2×Dic7—42no—
294C2×Dic7—48no—
295C2×Dic7—44no—
296C2×Dic7—42no—
297C2×Dic7C22×D412yes—
298C2×Dic7C22×D412yes—
299C2×Dic7C22×D412yes—
300C2×Dic7C22×D412yes—
301Dic14—24no—
302Dic14—42no—
303C7×C8—24no—
304C7⋊C8—24no—
305C22×Q8—71no—
306C22×D4—21no—
307C22×D4C22×D711yescharacteristic
308C23×C4—21no—
309C23×C4—71no—
310C23×C4—71no—
311C23×C4—141no—
312C23×C4—141no—
313C23×C4C22×D711yescharacteristic
314C22×C8—72no—
315C22×C8C22×D712yes—
316#126—148no—
317#125—78no—
318#125—78no—
319#125—74no—
320#125—148no—
321#125—144no—
322#125—144no—
323#125—148no—
324#125—142no—
325#124—74no—
326#124—142no—
327#123—148no—
328C22⋊Q8—74no—
329C22⋊Q8—142no—
330#121—22no—
331#121C22×D714yes—
332C4×Q8—74no—
333C4×Q8—142no—
334C4×D4—74no—
335C4×D4—142no—
336C4×D4—148no—
337#117—148no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—72no—
341C2×C4⋊C4—74no—
342C2×C4⋊C4—71no—
343C2×C4⋊C4—148no—
344C2×C4⋊C4—142no—
345C2×C4⋊C4—142no—
346C2×C4⋊C4—148no—
347C2×C4⋊C4—142no—
348C2×C4⋊C4—142no—
349C2×C4⋊C4—141no—
350C2×C4⋊C4—141no—
351C2×C4⋊C4—141no—
352C2×C4⋊C4—142no—
353C2×C4⋊C4—141no—
354C2×C4⋊C4—141no—
355C2×C4⋊C4C22×D712yes—
356C2×C4⋊C4C22×D714yes—
357C2×C4⋊C4C22×D711yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—141no—
360C2×C22⋊C4—141no—
361C2×C22⋊C4—141no—
362C2×C22⋊C4—141no—
363C2×C42—71no—
364C2×C42—71no—
365C2×C42—74no—
366C2×C42—71no—
367C2×C42—71no—
368C2×C42—74no—
369C2×C42—141no—
370#107—78no—
371#107—78no—
372#106—78no—
373#106C22×D718yes—
374C4⋊C8—78no—
375#103—78no—
376#103—78no—
377#102—78no—
378#102C22×D718yes—
379C22⋊C8—74no—
380C22⋊C8C22×D714yes—
381C4×C8—78no—
382C22×C7—22no—
383C22×C7—28no—
384C22×C7—22no—
385C22×C7—42no—
386C22×C7—42no—
387C22×C7—42no—
388C22×C7—84no—
389C22×C7#53612yes—
390C22×C7C2×#13514yes—
391C22×C7C2×#13512yes—
392C22×C7#57512yes—
393C22×C7C23×D411yescharacteristic
394C4×C7—22no—
395C4×C7—42no—
396C4×C7—44no—
397C4×C7#53612yes—
398C4×C7C2×2−1+412yes—
399Dic7—22no—
400Dic7—22no—
401Dic7—22no—
402Dic7—22no—
403Dic7—42no—
404Dic7—44no—
405Dic7—42no—
406C24—21no—
407C24D4×D711yescharacteristic
408C2×Q8—72no—
409C2×Q8—141no—
410C2×Q8—144no—
411C2×D4—24no—
412C2×D4—21no—
413C2×D4—24no—
414C2×D4—44no—
415C2×D4C23×D712yes—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—44no—
421C22×C4—74no—
422C22×C4—71no—
423C22×C4—71no—
424C22×C4—71no—
425C22×C4—71no—
426C22×C4—74no—
427C22×C4—144no—
428C22×C4—144no—
429C22×C4—144no—
430C22×C4—141no—
431C22×C4—141no—
432C22×C4—142no—
433C22×C4—282no—
434C22×C4—284no—
435C22×C4—284no—
436C22×C4D4×D712yes—
437C22×C4D4×D711yescharacteristic
438C22×C4C23×D712yes—
439C22×C4C23×D711yescharacteristic
440C2×C8—24no—
441C2×C8—74no—
442C2×C8—144no—
443C2×C8C23×D714yes—
444C4⋊C4—24no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—74no—
448C4⋊C4—72no—
449C4⋊C4—148no—
450C4⋊C4—148no—
451C4⋊C4—144no—
452C4⋊C4—144no—
453C4⋊C4—148no—
454C4⋊C4—148no—
455C4⋊C4—144no—
456C4⋊C4—144no—
457C4⋊C4—144no—
458C4⋊C4—142no—
459C4⋊C4—141no—
460C4⋊C4C23×D714yes—
461C4⋊C4C23×D712yes—
462C22⋊C4—24no—
463C22⋊C4—144no—
464C22⋊C4—144no—
465C22⋊C4—144no—
466C22⋊C4—144no—
467C42—74no—
468C42—72no—
469C42—72no—
470C42—74no—
471C42—72no—
472C42—72no—
473C42—144no—
474C2×C7—24no—
475C2×C7—82no—
476C2×C7#323214yescomplemented
477C2×C7C2×#53611yescharacteristic
478C2×C7C22×#13511yescharacteristic
479C2×C7C2×#57511yescharacteristic
480C23—22no—
481C23—22no—
482C23—22no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23#647914yes—
487C23C2×D4×D712yes—
488C23C2×D4×D711yescharacteristic
489Q8—144no—
490Q8—282no—
491D4—24no—
492D4—48no—
493D4—42no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—48no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—72no—
503C2×C4—72no—
504C2×C4—72no—
505C2×C4—72no—
506C2×C4—148no—
507C2×C4—142no—
508C2×C4—142no—
509C2×C4—142no—
510C2×C4—142no—
511C2×C4—142no—
512C2×C4—142no—
513C2×C4—144no—
514C2×C4—284no—
515C2×C4—288no—
516C2×C4—288no—
517C2×C4—284no—
518C2×C4—282no—
519C2×C4—282no—
520C2×C4C2×D4×D712yes—
521C2×C4C2×D4×D711yescharacteristic
522C2×C4#655414yes—
523C2×C4C24×D711yescharacteristic
524C8—24no—
525C8—144no—
526C7C2×#323211yescharacteristic, complemented, Sylow
527C22—22no—
528C22—22no—
529C22—28no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—84no—
534C22#9033912yes—
535C22C2×#647914yes—
536C22C2×#647912yes—
537C22#9046412yes—
538C22C22×D4×D711yescharacteristic
539C4—22no—
540C4—44no—
541C4—42no—
542C4—142no—
543C4—142no—
544C4—142no—
545C4—142no—
546C4—282no—
547C4—282no—
548C4—284no—
549C4#9033912yes—
550C4C2×#655412yes—
551C2—24no—
552C2—82no—
553C2#1173876314yesdirect product factor
554C2C2×#9033911yescharacteristic
555C2C22×#647911yescharacteristic
556C2C2×#9046411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#481C2
socleC23×C7C22×D4
prime radicalC2×C7×#121C22
hypercenterC2×#481D7
hypocenterC7C2×#3232
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C22×#6453C2semidirect
5. C2×#89742C2semidirect
6. #11738763C2direct (N × H)
7. C2×#89629C2semidirect
8. C2×#89630C2semidirect
9. C2×#89540C2semidirect
10. C2×#89535C2semidirect
11. C2×#89493C2semidirect
12. C2×#89490C2semidirect
32. C2×#6453C22semidirect
47. #89742C22semidirect
51. #89630C22semidirect
52. #89629C22semidirect
53. #89540C22semidirect
54. #89535C22semidirect
55. #89493C22semidirect
56. #89490C22semidirect
476. C2×C7#3232semidirect
526. C7C2×#3232semidirect
553. C2#11738763direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902912
C22×#64532
C2×C7×#4812
C2×#898052
C2×#897422
#117387632
C2×#896292
C2×#896302
C2×#895402
C2×#895352
C2×#894932
C2×#894902
C2×#32327