Finite Group Databasebeta

← C2×#11739138 #14225954

Subgroups — C2×#11739138 #14225954

Order 1792.

1790 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×#90419C211yesmaximal, characteristic, complemented
2C2×#90371C211yesmaximal, characteristic
3C2×C7×#489C211yesmaximal, characteristic, complemented
4C2×#89852C211yesmaximal, characteristic, complemented
5C2×#89827C211yesmaximal, characteristic, complemented
6#11739138C2116yesmaximal, direct product factor
7C2×#89586C212yesmaximal, complemented
8C2×#89571C212yesmaximal, complemented
9C2×#89551C212yesmaximal
10C2×#89538C212yesmaximal, complemented
11C2×#89477C211yesmaximal, characteristic, complemented
12C2×#89474C211yesmaximal, characteristic, complemented
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C7×#124C2211yescharacteristic
15C2×#6509—21no—
16C2×#6509C2211yescharacteristic
17C2×Q8×Dic7—21no—
18C2×Q8×Dic7C2211yescharacteristic
19C2×#6501C2211yescharacteristic
20C2×D4×Dic7C2211yescharacteristic
21#90419—24no—
22#90419C2218yescomplemented
23#90371—24no—
24#90371C2218yes—
25C2×#6460—21no—
26C2×#6455C2212yes—
27C2×#6453C2212yes—
28C2×#6450—21no—
29C2×#6446—21no—
30C2×(C22⋊D7)⋊C4—21no—
31C2×#6442—21no—
32C2×#6440—21no—
33C2×C42×D7C2211yescharacteristic
34C2×#6433C2211yescharacteristic
35C2×#6432C2211yescharacteristic
36C7×#489C2218yescomplemented
37C2×C7×#103C2212yes—
38C2×C7×#102C2212yes—
39C2×C7×#97C2211yescharacteristic
40C2×#6409C2212yes—
41C2×#6406C2212yes—
42C2×(C2×D7)⋊C8C2212yes—
43C2×#6392C2212yes—
44C2×#6391C2212yes—
45C2×Dic7⋊C8C2212yes—
46#89852C2218yescomplemented
47#89827C2218yescomplemented
48C2×#6382C2212yes—
49C2×#6381C2212yes—
50C2×#6377C2211yescharacteristic
51#89586C22116yescomplemented
52#89571C22116yescomplemented
53#89551C22116yes—
54#89538C22116yescomplemented
55#89477C2218yescomplemented
56#89474C2218yescomplemented
57C2×#3240—71nomaximal, Sylow
58C22×C7×Q8—21no—
59C22×C7×Q8C2311yescharacteristic
60C22×C7×D4C2311yescharacteristic
61C22×C22⋊D7—21no—
62C23×Dic7—21no—
63C22×C4×D7D411yescharacteristic
64C22×C4×D7D411yescharacteristic
65C22×C4×D7C2311yescharacteristic
66C22×Dic14—21no—
67C22×C7×C8C2312yes—
68C7×C4⋊Q8—22no—
69C7×C4⋊Q8C2314yes—
70C7×#124—22no—
71C7×#124C2314yes—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4C2312yes—
74C2×C7×C22⋊C4—21no—
75C2×C7×C22⋊C4—21no—
76C2×C42×C7C2311yescharacteristic
77C2×C22⋊Dic7—21no—
78C2×C22⋊Dic7—21no—
79#6509—22no—
80#6509—28no—
81#6509C2314yes—
82Q8×Dic7—22no—
83Q8×Dic7—28no—
84Q8×Dic7C2314yes—
85#6501—22no—
86#6501C2314yes—
87D4×Dic7—22no—
88D4×Dic7C2314yes—
89C2×(C2×D7)⋊C4—21no—
90C2×(C2×D7)⋊C4—22no—
91C2×C4⋊Dic7—21no—
92C2×C4⋊Dic7—21no—
93C2×C4⋊Dic7—22no—
94C2×C4⋊Dic7C2311yescharacteristic
95C2×C4⋊Dic7C2312yes—
96C2×C4⋊Dic7C2311yescharacteristic
97C2×Dic7⋊C4—21no—
98C2×Dic7⋊C4—21no—
99C2×Dic7⋊C4—21no—
100C2×Dic7⋊C4—22no—
101C2×C4×Dic7—21no—
102C2×C4×Dic7—22no—
103C2×C4×Dic7D411yescharacteristic
104C2×C4×Dic7D411yescharacteristic
105C2×C4×Dic7C2311yescharacteristic
106C22×C7⋊C8C2312yes—
107#6460—28no—
108#6455—24no—
109#6455C2318yes—
110#6453—24no—
111#6453C2318yes—
112#6450—28no—
113#6446—28no—
114(C22⋊D7)⋊C4—28no—
115#6442—28no—
116#6440—28no—
117C42×D7D414yes—
118C42×D7C2314yes—
119#6433—22no—
120#6433C2314yes—
121#6432—22no—
122#6432C2314yes—
123C7×#103C2318yes—
124C7×#102C2318yes—
125C7×#97C2314yes—
126#6409C2318yes—
127#6406C2318yes—
128(C2×D7)⋊C8C2318yes—
129#6392C2318yes—
130#6391C2318yes—
131Dic7⋊C8C2318yes—
132#6382C2318yes—
133#6381C2318yes—
134#6377C2314yes—
135C2×#533—71no—
136C2×#529—71no—
137#3240—716no—
138C2×#501—71no—
139C2×#501—71no—
140C2×#489—71no—
141C2×#489D711yescharacteristic, complemented
142C2×#485—72no—
143C2×#482—72no—
144C2×#479—72no—
145C2×#478—72no—
146C2×#432—71no—
147C24×C7—21no—
148C23×D7C2×D411yescharacteristic
149C2×C7×Q8—21no—
150C2×C7×Q8—24no—
151C2×C7×Q8—24no—
152C2×C7×Q8—44no—
153C2×C7×Q8C2412yes—
154C2×C7×D4—21no—
155C2×C7×D4—24no—
156C2×C7×D4C2412yes—
157C22×C4×C7—21no—
158C22×C4×C7—22no—
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2411yescharacteristic
162C2×C22⋊D7—24no—
163C2×C22⋊D7—44no—
164C22×Dic7—21no—
165C22×Dic7—22no—
166C22×Dic7—21no—
167C22×Dic7—24no—
168C22×Dic7—44no—
169C22×Dic7C2×D411yescharacteristic
170C22×Dic7C2×D411yescharacteristic
171C22×Dic7C2×D411yescharacteristic
172C2×C4×D7—24no—
173C2×C4×D7—42no—
174C2×C4×D7—42no—
175C2×C4×D7C2×D412yes—
176C2×C4×D7C2×D414yes—
177C2×C4×D7C2×D414yes—
178C2×C4×D7C2412yes—
179C2×Dic14—24no—
180C2×Dic14—44no—
181C2×C7×C8—24no—
182C2×C7×C8C2414yes—
183C7×C4⋊C4—24no—
184C7×C4⋊C4—22no—
185C7×C4⋊C4C2414yes—
186C7×C22⋊C4—24no—
187C7×C22⋊C4—24no—
188C42×C7C2×D412yes—
189C42×C7C2412yes—
190C22⋊Dic7—24no—
191C22⋊Dic7—24no—
192(C2×D7)⋊C4—24no—
193(C2×D7)⋊C4—28no—
194C4⋊Dic7—22no—
195C4⋊Dic7—24no—
196C4⋊Dic7—21no—
197C4⋊Dic7—21no—
198C4⋊Dic7—24no—
199C4⋊Dic7—28no—
200C4⋊Dic7C2414yes—
201C4⋊Dic7C2412yes—
202C4⋊Dic7C2412yes—
203Dic7⋊C4—24no—
204Dic7⋊C4—24no—
205Dic7⋊C4—24no—
206Dic7⋊C4—28no—
207C4×Dic7—24no—
208C4×Dic7—28no—
209C4×Dic7C2×D412yes—
210C4×Dic7C2×D414yes—
211C4×Dic7C2×D414yes—
212C4×Dic7C2412yes—
213C2×C7⋊C8—24no—
214C2×C7⋊C8C2414yes—
215#533—78no—
216#533—144no—
217C2×C4⋊Q8—71no—
218C2×C4⋊Q8C2×D711yescharacteristic
219#529—78no—
220#529—144no—
221C2×#126—141no—
222C2×#125—72no—
223C2×#125—71no—
224C2×#124C2×D711yescharacteristic
225C2×#123—141no—
226C2×C22⋊Q8—71no—
227C2×C22⋊Q8—141no—
228C2×C22⋊Q8—141no—
229C2×#121—71no—
230C2×C4×Q8—71no—
231C2×C4×Q8—141no—
232C2×C4×Q8—141no—
233C2×C4×D4—71no—
234C2×C4×D4—141no—
235C2×#117—72no—
236C2×#117—141no—
237C22×C42—71no—
238#501—78no—
239#501—78no—
240#489—78no—
241#489C2×D718yescomplemented
242#485—716no—
243#482—716no—
244#479—716no—
245#478—716no—
246#432—78no—
247C2×#107—72no—
248C2×#107—72no—
249C2×#106—72no—
250C2×#106—72no—
251C2×C4⋊C8—72no—
252C2×#103—72no—
253C2×#103C2×D712yes—
254C2×#102—72no—
255C2×#102C2×D712yes—
256C2×C22⋊C8—72no—
257C2×#97—71no—
258C2×#97C2×D711yescharacteristic
259C23×C7—22no—
260C23×C7—42no—
261C23×C7—42no—
262C23×C7—42no—
263C23×C7C22×D411yescharacteristic
264C22×D7—22no—
265C22×D7—22no—
266C22×D7—22no—
267C22×D7C22×D412yes—
268C7×Q8—24no—
269C7×Q8—48no—
270C7×Q8—42no—
271C7×D4—24no—
272C7×D4—42no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—24no—
277C2×C4×C7—42no—
278C2×C4×C7—44no—
279C2×C4×C7C22×D412yes—
280C2×C4×C7C22×D412yes—
281C2×C4×C7C22×D411yescharacteristic
282C2×C4×C72−1+414yes—
283C2×C4×C7C2511yescharacteristic
284C22⋊D7—48no—
285C2×Dic7—22no—
286C2×Dic7—22no—
287C2×Dic7—22no—
288C2×Dic7—22no—
289C2×Dic7—24no—
290C2×Dic7—22no—
291C2×Dic7—48no—
292C2×Dic7—44no—
293C2×Dic7—42no—
294C2×Dic7—42no—
295C2×Dic7C22×D412yes—
296C2×Dic7C22×D412yes—
297C2×Dic7C22×D412yes—
298C4×D7—24no—
299C4×D7—24no—
300C4×D7—44no—
301C4×D7—44no—
302Dic14—48no—
303C7×C8—24no—
304C7⋊C8—24no—
305C22×Q8—21no—
306C22×Q8—141no—
307C22×Q8C22×D711yescharacteristic
308C22×D4—141no—
309C22×D4C22×D711yescharacteristic
310C23×C4—71no—
311C23×C4—71no—
312C23×C4—71no—
313C23×C4—141no—
314C22×C8—72no—
315C22×C8C22×D712yes—
316C4⋊Q8—22no—
317C4⋊Q8—74no—
318C4⋊Q8—142no—
319C4⋊Q8C22×D714yes—
320#126—148no—
321#125—78no—
322#125—74no—
323#125—144no—
324#125—142no—
325#124—22no—
326#124C22×D714yes—
327#123—148no—
328C22⋊Q8—74no—
329C22⋊Q8—148no—
330C22⋊Q8—142no—
331C22⋊Q8—148no—
332#121—74no—
333#121—142no—
334C4×Q8—74no—
335C4×Q8—148no—
336C4×Q8—142no—
337C4×Q8—148no—
338C4×D4—74no—
339C4×D4—142no—
340C4×D4—148no—
341#117—78no—
342#117—148no—
343#117—144no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—72no—
346C2×C4⋊C4—71no—
347C2×C4⋊C4—71no—
348C2×C4⋊C4—141no—
349C2×C4⋊C4—141no—
350C2×C4⋊C4—142no—
351C2×C4⋊C4—142no—
352C2×C4⋊C4—141no—
353C2×C4⋊C4—141no—
354C2×C4⋊C4—141no—
355C2×C4⋊C4C22×D712yes—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—142no—
359C2×C22⋊C4—141no—
360C2×C22⋊C4—141no—
361C2×C22⋊C4—141no—
362C2×C42—71no—
363C2×C42—71no—
364C2×C42—71no—
365C2×C42—74no—
366C2×C42—74no—
367C2×C42—142no—
368C2×C42—141no—
369C2×C42C22×D711yescharacteristic
370#107—78no—
371#107—78no—
372#106—78no—
373#106—78no—
374C4⋊C8—78no—
375#103—78no—
376#103C22×D718yes—
377#102—78no—
378#102C22×D718yes—
379C22⋊C8—78no—
380#97—74no—
381#97C22×D714yes—
382C22×C7—42no—
383C22×C7—42no—
384C22×C7—42no—
385C22×C7—84no—
386C22×C7#53612yes—
387C22×C7#57512yes—
388C22×C7#57512yes—
389C22×C7C23×D411yescharacteristic
390C2×D7—22no—
391C2×D7—22no—
392C2×D7—22no—
393C2×D7—44no—
394C4×C7—22no—
395C4×C7—22no—
396C4×C7—42no—
397C4×C7—44no—
398C4×C7#53612yes—
399C4×C7C2×2−1+412yes—
400Dic7—22no—
401Dic7—22no—
402Dic7—22no—
403Dic7—44no—
404Dic7—42no—
405Dic7—42no—
406C24—21no—
407C24—71no—
408C2×Q8—21no—
409C2×Q8—24no—
410C2×Q8—24no—
411C2×Q8—44no—
412C2×Q8—144no—
413C2×Q8—284no—
414C2×Q8C23×D712yes—
415C2×D4—21no—
416C2×D4—24no—
417C2×D4—144no—
418C2×D4—284no—
419C2×D4C23×D712yes—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—71no—
423C22×C4—71no—
424C22×C4—71no—
425C22×C4—72no—
426C22×C4—72no—
427C22×C4—74no—
428C22×C4—74no—
429C22×C4—144no—
430C22×C4—144no—
431C22×C4—141no—
432C22×C4—142no—
433C22×C4—141no—
434C22×C4—282no—
435C22×C4—282no—
436C22×C4—284no—
437C22×C4D4×D711yescharacteristic
438C22×C4D4×D711yescharacteristic
439C22×C4C23×D711yescharacteristic
440C2×C8—24no—
441C2×C8—74no—
442C2×C8—144no—
443C2×C8C23×D714yes—
444C4⋊C4—24no—
445C4⋊C4—22no—
446C4⋊C4—74no—
447C4⋊C4—72no—
448C4⋊C4—72no—
449C4⋊C4—144no—
450C4⋊C4—148no—
451C4⋊C4—144no—
452C4⋊C4—148no—
453C4⋊C4—144no—
454C4⋊C4—144no—
455C4⋊C4—142no—
456C4⋊C4—141no—
457C4⋊C4—141no—
458C4⋊C4—144no—
459C4⋊C4C23×D714yes—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—148no—
463C22⋊C4—144no—
464C22⋊C4—144no—
465C22⋊C4—144no—
466C42—74no—
467C42—72no—
468C42—74no—
469C42—72no—
470C42—148no—
471C42—144no—
472C42D4×D712yes—
473C42C23×D712yes—
474C2×C7—82no—
475C2×C7#324014yescomplemented
476C2×C7C2×#53611yescharacteristic
477C2×C7C2×#57511yescharacteristic
478C2×C7C2×#57511yescharacteristic
479D7—42no—
480C23—22no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—72no—
485C23—142no—
486C23—142no—
487C23—142no—
488C23C2×D4×D711yescharacteristic
489Q8—24no—
490Q8—48no—
491Q8—42no—
492Q8—288no—
493D4—24no—
494D4—42no—
495D4—288no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—44no—
501C2×C4—42no—
502C2×C4—72no—
503C2×C4—72no—
504C2×C4—72no—
505C2×C4—142no—
506C2×C4—142no—
507C2×C4—142no—
508C2×C4—144no—
509C2×C4—144no—
510C2×C4—142no—
511C2×C4—144no—
512C2×C4—142no—
513C2×C4—284no—
514C2×C4—284no—
515C2×C4—288no—
516C2×C4—282no—
517C2×C4—282no—
518C2×C4—284no—
519C2×C4C2×D4×D712yes—
520C2×C4C2×D4×D712yes—
521C2×C4C2×D4×D711yescharacteristic
522C2×C4#655414yes—
523C2×C4C24×D711yescharacteristic
524C8—24no—
525C8—144no—
526C7C2×#324011yescharacteristic, complemented, Sylow
527C22—42no—
528C22—42no—
529C22—42no—
530C22—84no—
531C22—142no—
532C22—142no—
533C22—142no—
534C22—284no—
535C22#9036612yes—
536C22#9046412yes—
537C22#9046812yes—
538C22C22×D4×D711yescharacteristic
539C4—22no—
540C4—22no—
541C4—44no—
542C4—42no—
543C4—142no—
544C4—142no—
545C4—142no—
546C4—282no—
547C4—282no—
548C4—284no—
549C4#9036612yes—
550C4C2×#655412yes—
551C2—82no—
552C2—282no—
553C2#1173913814yesdirect product factor
554C2C2×#9036611yescharacteristic
555C2C2×#9046411yescharacteristic
556C2C2×#9046811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#489C2
socleC23×C7C22×D4
prime radicalC2×#6501C22
hypercenterC2×#489D7
hypocenterC7C2×#3240
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#90419C2semidirect
3. C2×C7×#489C2semidirect
4. C2×#89852C2semidirect
5. C2×#89827C2semidirect
6. #11739138C2direct (N × H)
7. C2×#89586C2semidirect
8. C2×#89571C2semidirect
10. C2×#89538C2semidirect
11. C2×#89477C2semidirect
12. C2×#89474C2semidirect
22. #90419C22semidirect
36. C7×#489C22semidirect
46. #89852C22semidirect
47. #89827C22semidirect
51. #89586C22semidirect
52. #89571C22semidirect
54. #89538C22semidirect
55. #89477C22semidirect
56. #89474C22semidirect
141. C2×#489D7semidirect
241. #489C2×D7semidirect
475. C2×C7#3240semidirect
526. C7C2×#3240semidirect
553. C2#11739138direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904192
C2×#903712
C2×C7×#4892
C2×#898522
C2×#898272
#117391382
C2×#895862
C2×#895712
C2×#895512
C2×#895382
C2×#894772
C2×#894742
C2×#32407