Finite Group Databasebeta

← C2×#11739190 #14225905

Subgroups — C2×#11739190 #14225905

Order 1792.

1770 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90419C211yesmaximal, characteristic
2C2×D7×#125C211yesmaximal, characteristic
3C2×C7×#491C211yesmaximal, characteristic, complemented
4C2×#89854C211yesmaximal, characteristic, complemented
5C2×#89837C211yesmaximal, characteristic, complemented
6#11739190C2116yesmaximal, direct product factor
7C2×#89581C212yesmaximal
8C2×#89577C212yesmaximal
9C2×#89568C212yesmaximal, complemented
10C2×#89571C212yesmaximal, complemented
11C2×#89477C211yesmaximal, characteristic
12C2×#89474C211yesmaximal, characteristic, complemented
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C7×#125C2211yescharacteristic
15C2×#6509C2212yes—
16C2×Q8×Dic7C2212yes—
17#90419—24no—
18#90419C2218yes—
19D7×#125—24no—
20D7×#125C2218yes—
21C2×#6460—21no—
22C2×#6455—21no—
23C2×D7×C4⋊C4—21no—
24C2×D7×C4⋊C4—21no—
25C2×D7×C4⋊C4C2211yescharacteristic
26C2×D7×C4⋊C4C2211yescharacteristic
27C2×#6453—21no—
28C2×#6453C2211yescharacteristic
29C2×#6453C2211yescharacteristic
30C2×#6452—21no—
31C2×#6452—21no—
32C2×#6450—21no—
33C2×C42×D7C2211yescharacteristic
34C2×#6433C2211yescharacteristic
35C2×#6432C2211yescharacteristic
36C7×#491C2218yescomplemented
37C2×C7×#103C2212yes—
38C2×C7×#103C2212yes—
39C2×C7×#97C2211yescharacteristic
40C2×#6409C2212yes—
41C2×#6409C2212yes—
42C2×(C2×D7)⋊C8C2212yes—
43C2×#6392C2212yes—
44C2×#6391C2212yes—
45C2×Dic7⋊C8C2212yes—
46#89854C2218yescomplemented
47#89837C2218yescomplemented
48C2×#6382C2212yes—
49C2×#6381C2212yes—
50C2×#6377C2211yescharacteristic
51#89581C22116yes—
52#89577C22116yes—
53#89571C22116yescomplemented
54#89568C22116yescomplemented
55#89477C2218yes—
56#89474C2218yescomplemented
57C2×#3236—71nomaximal, Sylow
58C22×C7×Q8C2312yes—
59C22×C4×D7—21no—
60C22×C4×D7—21no—
61C22×C4×D7D411yescharacteristic
62C22×C4×D7D411yescharacteristic
63C22×C4×D7C2311yescharacteristic
64C22×Dic14—21no—
65C22×C7×C8C2312yes—
66C7×C4⋊Q8—22no—
67C7×C4⋊Q8C2314yes—
68C7×#125—22no—
69C7×#125C2314yes—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C42×C7C2311yescharacteristic
77#6509—24no—
78#6509C2318yes—
79Q8×Dic7—24no—
80Q8×Dic7C2318yes—
81C2×(C2×D7)⋊C4—22no—
82C2×C4⋊Dic7—21no—
83C2×C4⋊Dic7—21no—
84C2×C4⋊Dic7—21no—
85C2×C4⋊Dic7—22no—
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2312yes—
88C2×C4⋊Dic7C2311yescharacteristic
89C2×Dic7⋊C4—21no—
90C2×Dic7⋊C4—21no—
91C2×Dic7⋊C4—22no—
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×Dic7⋊C4—21no—
95C2×Dic7⋊C4—21no—
96C2×C4×Dic7—22no—
97C2×C4×Dic7D411yescharacteristic
98C2×C4×Dic7D411yescharacteristic
99C2×C4×Dic7C2311yescharacteristic
100C22×C7⋊C8C2312yes—
101#6460—28no—
102#6455—28no—
103D7×C4⋊C4—22no—
104D7×C4⋊C4—22no—
105D7×C4⋊C4—28no—
106D7×C4⋊C4—28no—
107D7×C4⋊C4C2314yes—
108D7×C4⋊C4C2314yes—
109#6453—22no—
110#6453—22no—
111#6453—28no—
112#6453C2314yes—
113#6453C2314yes—
114#6452—28no—
115#6452—28no—
116#6450—28no—
117C42×D7D414yes—
118C42×D7C2314yes—
119#6433—22no—
120#6433C2314yes—
121#6432—22no—
122#6432C2314yes—
123C7×#103C2318yes—
124C7×#103C2318yes—
125C7×#97C2314yes—
126#6409C2318yes—
127#6409C2318yes—
128(C2×D7)⋊C8C2318yes—
129#6392C2318yes—
130#6391C2318yes—
131Dic7⋊C8C2318yes—
132#6382C2318yes—
133#6381C2318yes—
134#6377C2314yes—
135C2×#533—71no—
136C22×#125—71no—
137#3236—716no—
138C2×#501—71no—
139C2×#501—71no—
140C2×#491—71no—
141C2×#491D711yescharacteristic, complemented
142C2×#484—72no—
143C2×#483—72no—
144C2×#479—72no—
145C2×#479—72no—
146C2×#432—71no—
147C23×D7C2×D411yescharacteristic
148C2×C7×Q8—22no—
149C2×C7×Q8—28no—
150C2×C7×Q8C2414yes—
151C22×C4×C7—22no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2411yescharacteristic
157C22×Dic7—22no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7C2×D411yescharacteristic
161C22×Dic7C2×D411yescharacteristic
162C22×Dic7C2×D411yescharacteristic
163C2×C4×D7—24no—
164C2×C4×D7—24no—
165C2×C4×D7—24no—
166C2×C4×D7—24no—
167C2×C4×D7—42no—
168C2×C4×D7—44no—
169C2×C4×D7—44no—
170C2×C4×D7C2×D412yes—
171C2×C4×D7C2×D414yes—
172C2×C4×D7C2×D414yes—
173C2×C4×D7C2412yes—
174C2×Dic14—24no—
175C2×Dic14—44no—
176C2×C7×C8—24no—
177C2×C7×C8C2414yes—
178C7×C4⋊C4—24no—
179C7×C4⋊C4—24no—
180C7×C4⋊C4—24no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—24no—
184C7×C4⋊C4C2412yes—
185C7×C4⋊C4C2412yes—
186C42×C7C2×D412yes—
187C42×C7C2412yes—
188(C2×D7)⋊C4—28no—
189C4⋊Dic7—22no—
190C4⋊Dic7—24no—
191C4⋊Dic7—21no—
192C4⋊Dic7—21no—
193C4⋊Dic7—24no—
194C4⋊Dic7—24no—
195C4⋊Dic7—28no—
196C4⋊Dic7C2412yes—
197C4⋊Dic7C2412yes—
198C4⋊Dic7C2414yes—
199Dic7⋊C4—24no—
200Dic7⋊C4—24no—
201Dic7⋊C4—28no—
202Dic7⋊C4—24no—
203Dic7⋊C4—24no—
204Dic7⋊C4—24no—
205Dic7⋊C4—24no—
206C4×Dic7—28no—
207C4×Dic7C2×D412yes—
208C4×Dic7C2×D414yes—
209C4×Dic7C2×D414yes—
210C4×Dic7C2412yes—
211C2×C7⋊C8—24no—
212C2×C7⋊C8C2414yes—
213#533—78no—
214#533—144no—
215C2×C4⋊Q8—71no—
216C2×C4⋊Q8C2×D711yescharacteristic
217C2×#125—78no—
218C2×#125—71no—
219C2×#125—71no—
220C2×#125—71no—
221C2×#125—141no—
222C2×#125—141no—
223C2×#125—141no—
224C2×#125—144no—
225C2×#125C2×D711yescharacteristic
226C2×C22⋊Q8—72no—
227C2×C22⋊Q8—141no—
228C2×C4×Q8—72no—
229C2×C4×Q8—141no—
230C2×#117—141no—
231C22×C4⋊C4—71no—
232C22×C4⋊C4—71no—
233C22×C4⋊C4—141no—
234C22×C4⋊C4—141no—
235C22×C42—71no—
236#501—78no—
237#501—78no—
238#491—78no—
239#491C2×D718yescomplemented
240#484—716no—
241#483—716no—
242#479—716no—
243#479—716no—
244#432—78no—
245C2×#107—72no—
246C2×#107—72no—
247C2×#106—72no—
248C2×#106—72no—
249C2×C4⋊C8—72no—
250C2×#103—72no—
251C2×#103—72no—
252C2×#103C2×D712yes—
253C2×#103C2×D712yes—
254C2×C22⋊C8—72no—
255C2×#97—71no—
256C2×#97C2×D711yescharacteristic
257C23×C7C22×D411yescharacteristic
258C22×D7—22no—
259C22×D7—22no—
260C22×D7#13714yes—
261C22×D7C22×D412yes—
262C7×Q8—28no—
263C7×Q8—44no—
264C2×C4×C7—22no—
265C2×C4×C7—22no—
266C2×C4×C7—24no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—44no—
270C2×C4×C7—42no—
271C2×C4×C7—42no—
272C2×C4×C7C22×D412yes—
273C2×C4×C7C22×D412yes—
274C2×C4×C7C22×D411yescharacteristic
275C2×C4×C72−1+414yes—
276C2×C4×C7C2511yescharacteristic
277C2×Dic7—22no—
278C2×Dic7—22no—
279C2×Dic7—22no—
280C2×Dic7—24no—
281C2×Dic7—22no—
282C2×Dic7—22no—
283C2×Dic7—42no—
284C2×Dic7—44no—
285C2×Dic7—42no—
286C2×Dic7C22×D412yes—
287C2×Dic7C22×D412yes—
288C2×Dic7C22×D412yes—
289C4×D7—28no—
290C4×D7—24no—
291C4×D7—24no—
292C4×D7—44no—
293C4×D7—48no—
294C4×D7—48no—
295Dic14—48no—
296C7×C8—24no—
297C7⋊C8—24no—
298C22×Q8—141no—
299C22×Q8C22×D712yes—
300C23×C4—71no—
301C23×C4—71no—
302C23×C4—71no—
303C23×C4—141no—
304C23×C4—141no—
305C22×C8—72no—
306C22×C8C22×D712yes—
307C4⋊Q8—22no—
308C4⋊Q8—74no—
309C4⋊Q8—142no—
310C4⋊Q8C22×D714yes—
311#125—22no—
312#125—74no—
313#125—74no—
314#125—74no—
315#125—148no—
316#125—148no—
317#125—142no—
318#125—142no—
319#125—148no—
320#125—142no—
321#125C22×D714yes—
322C22⋊Q8—78no—
323C22⋊Q8—148no—
324C22⋊Q8—144no—
325C4×Q8—78no—
326C4×Q8—148no—
327C4×Q8—144no—
328#117—148no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—71no—
334C2×C4⋊C4—71no—
335C2×C4⋊C4—72no—
336C2×C4⋊C4—74no—
337C2×C4⋊C4—74no—
338C2×C4⋊C4—142no—
339C2×C4⋊C4—142no—
340C2×C4⋊C4—148no—
341C2×C4⋊C4—148no—
342C2×C4⋊C4—141no—
343C2×C4⋊C4—141no—
344C2×C4⋊C4—141no—
345C2×C4⋊C4—141no—
346C2×C4⋊C4—141no—
347C2×C4⋊C4—141no—
348C2×C4⋊C4—142no—
349C2×C4⋊C4—142no—
350C2×C4⋊C4—141no—
351C2×C4⋊C4—141no—
352C2×C4⋊C4—141no—
353C2×C4⋊C4C22×D711yescharacteristic
354C2×C4⋊C4C22×D711yescharacteristic
355C2×C22⋊C4—142no—
356C2×C42—71no—
357C2×C42—71no—
358C2×C42—71no—
359C2×C42—74no—
360C2×C42—74no—
361C2×C42—142no—
362C2×C42C22×D711yescharacteristic
363#107—78no—
364#107—78no—
365#106—78no—
366#106—78no—
367C4⋊C8—78no—
368#103—78no—
369#103—78no—
370#103C22×D718yes—
371#103C22×D718yes—
372C22⋊C8—78no—
373#97—74no—
374#97C22×D714yes—
375C22×C7#53612yes—
376C22×C7C2×#13712yes—
377C22×C7#57512yes—
378C22×C7C23×D411yescharacteristic
379C2×D7—22no—
380C2×D7—28no—
381C2×D7—22no—
382C2×D7C2×#13714yes—
383C4×C7—22no—
384C4×C7—22no—
385C4×C7—44no—
386C4×C7—42no—
387C4×C7—42no—
388C4×C7#53612yes—
389C4×C7C2×2−1+412yes—
390Dic7—22no—
391Dic7—22no—
392Dic7—22no—
393Dic7—42no—
394Dic7—44no—
395Dic7—42no—
396C24—71no—
397C2×Q8—22no—
398C2×Q8—28no—
399C2×Q8—144no—
400C2×Q8—284no—
401C2×Q8C23×D714yes—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—71no—
406C22×C4—71no—
407C22×C4—71no—
408C22×C4—74no—
409C22×C4—72no—
410C22×C4—72no—
411C22×C4—74no—
412C22×C4—144no—
413C22×C4—144no—
414C22×C4—144no—
415C22×C4—144no—
416C22×C4—142no—
417C22×C4—141no—
418C22×C4—141no—
419C22×C4—282no—
420C22×C4—284no—
421C22×C4—284no—
422C22×C4D4×D711yescharacteristic
423C22×C4D4×D711yescharacteristic
424C22×C4C23×D711yescharacteristic
425C2×C8—24no—
426C2×C8—74no—
427C2×C8—144no—
428C2×C8C23×D714yes—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—72no—
436C4⋊C4—72no—
437C4⋊C4—74no—
438C4⋊C4—144no—
439C4⋊C4—144no—
440C4⋊C4—144no—
441C4⋊C4—144no—
442C4⋊C4—148no—
443C4⋊C4—144no—
444C4⋊C4—144no—
445C4⋊C4—148no—
446C4⋊C4—144no—
447C4⋊C4—144no—
448C4⋊C4—141no—
449C4⋊C4—141no—
450C4⋊C4—142no—
451C4⋊C4—144no—
452C4⋊C4C23×D712yes—
453C4⋊C4C23×D712yes—
454C22⋊C4—148no—
455C42—74no—
456C42—72no—
457C42—74no—
458C42—72no—
459C42—148no—
460C42D4×D712yes—
461C42C23×D712yes—
462C2×C7#323614yescomplemented
463C2×C7C2×#53611yescharacteristic
464C2×C7C22×#13711yescharacteristic
465C2×C7C2×#57511yescharacteristic
466D7—24no—
467C23—74no—
468C23—72no—
469C23—142no—
470C23—142no—
471C23C2×D4×D711yescharacteristic
472Q8—28no—
473Q8—44no—
474Q8—288no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—44no—
483C2×C4—72no—
484C2×C4—72no—
485C2×C4—72no—
486C2×C4—148no—
487C2×C4—142no—
488C2×C4—142no—
489C2×C4—142no—
490C2×C4—144no—
491C2×C4—144no—
492C2×C4—144no—
493C2×C4—142no—
494C2×C4—142no—
495C2×C4—284no—
496C2×C4—288no—
497C2×C4—288no—
498C2×C4—282no—
499C2×C4—282no—
500C2×C4—284no—
501C2×C4C2×D4×D712yes—
502C2×C4C2×D4×D712yes—
503C2×C4C2×D4×D711yescharacteristic
504C2×C4#655414yes—
505C2×C4C24×D711yescharacteristic
506C8—24no—
507C8—144no—
508C7C2×#323611yescharacteristic, complemented, Sylow
509C22—74no—
510C22—142no—
511C22—148no—
512C22—142no—
513C22#9036612yes—
514C22D7×#13712yes—
515C22#9046812yes—
516C22C22×D4×D711yescharacteristic
517C4—22no—
518C4—22no—
519C4—42no—
520C4—42no—
521C4—44no—
522C4—142no—
523C4—142no—
524C4—142no—
525C4—282no—
526C4—282no—
527C4—284no—
528C4#9036612yes—
529C4C2×#655412yes—
530C2—144no—
531C2#1173919014yesdirect product factor
532C2C2×#9036611yescharacteristic
533C2C2×D7×#13711yescharacteristic
534C2C2×#9046811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#491C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
hypercenterC2×#491D7
hypocenterC7C2×#3236
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
3. C2×C7×#491C2semidirect
4. C2×#89854C2semidirect
5. C2×#89837C2semidirect
6. #11739190C2direct (N × H)
9. C2×#89568C2semidirect
10. C2×#89571C2semidirect
12. C2×#89474C2semidirect
36. C7×#491C22semidirect
46. #89854C22semidirect
47. #89837C22semidirect
53. #89571C22semidirect
54. #89568C22semidirect
56. #89474C22semidirect
141. C2×#491D7semidirect
239. #491C2×D7semidirect
462. C2×C7#3236semidirect
508. C7C2×#3236semidirect
531. C2#11739190direct (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×D7×#1252
C2×C7×#4912
C2×#898542
C2×#898372
#117391902
C2×#895812
C2×#895772
C2×#895682
C2×#895712
C2×#894772
C2×#894742
C2×#32367