Finite Group Databasebeta

← C2×#11726064 #13320944

Subgroups — C2×#11726064 #13320944

Order 1792.

1130 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90313C211yesmaximal, characteristic
2C2×#89491C211yesmaximal, characteristic
3C2×#89420C211yesmaximal, characteristic
4C2×C7×#328C211yesmaximal, characteristic
5C2×#89333C211yesmaximal, characteristic
6C2×#89262C211yesmaximal, characteristic
7C2×#89247C211yesmaximal, characteristic
8#11726064C218yesmaximal, direct product factor
9C2×C7×C22⋊Q8C2211yescharacteristic
10C2×Q8×Dic7C411yescharacteristic, complemented
11C2×#6507C411yescharacteristic, complemented
12C2×#6487C2211yescharacteristic
13C22×C4×Dic7—21no—
14C22×C4×Dic7C2211yescharacteristic
15#90313—22no—
16#90313—22no—
17#90313C414yescomplemented
18#90313C2214yes—
19C2×#6452—21no—
20C2×#6451C411yescharacteristic, complemented
21C2×#6450—21no—
22C2×#6450C411yescharacteristic, complemented
23C2×#6441—21no—
24C2×#6440—21no—
25C2×C7×C22⋊C8C2211yescharacteristic
26C2×C7×#95C2211yescharacteristic
27C2×C7⋊#95—21no—
28C2×C7⋊#95C2211yescharacteristic
29C2×C22⋊(C7⋊C8)C2211yescharacteristic
30C2×#6389—21no—
31C2×Dic7⋊C8—21no—
32#89491—22no—
33#89491C2214yes—
34#89420—22no—
35#89420C2214yes—
36C7×#328C2214yes—
37#89333C2214yes—
38#89262C2214yes—
39#89247C2214yes—
40C2×#1506—71nomaximal, Sylow
41C22×C7×Q8C2×C411yescharacteristic
42C23×C4×C7—21no—
43C23×C4×C7C2311yescharacteristic
44C23×Dic7—21no—
45C23×Dic7D411yescharacteristic
46C23×Dic7D411yescharacteristic
47C22×Dic14—21no—
48C22×Dic14C2×C411yescharacteristic
49C22×C7×C8—21no—
50C7×C22⋊Q8—21no—
51C7×C22⋊Q8—21no—
52C7×C22⋊Q8C2×C412yes—
53C7×C22⋊Q8C2312yes—
54C2×C7×C4⋊C4—21no—
55C2×C7×C4⋊C4C2×C411yescharacteristic
56C2×C7×C22⋊C4—21no—
57C2×C22⋊Dic7—21no—
58Q8×Dic7—22no—
59Q8×Dic7C2×C414yescomplemented
60#6507—22no—
61#6507C2×C414yescomplemented
62C2×C4⋊Dic7—21no—
63C2×C4⋊Dic7C2×C411yescharacteristic
64#6487—21no—
65#6487—21no—
66#6487C2×C412yes—
67#6487C2312yes—
68C2×Dic7⋊C4—21no—
69C2×Dic7⋊C4—21no—
70C2×Dic7⋊C4—21no—
71C2×Dic7⋊C4—21no—
72C2×Dic7⋊C4—21no—
73C2×C4×Dic7—28no—
74C2×C4×Dic7—21no—
75C2×C4×Dic7—21no—
76C2×C4×Dic7—24no—
77C2×C4×Dic7C2×C411yescharacteristic
78C2×C4×Dic7C2×C411yescharacteristic
79C2×C4×Dic7C2×C412yes—
80C2×C4×Dic7D412yes—
81C2×C4×Dic7D411yescharacteristic
82C2×C4×Dic7D411yescharacteristic
83C2×C4×Dic7D412yes—
84C2×C4×Dic7C2312yes—
85C22×C7⋊C8—21no—
86#6452—24no—
87#6452—24no—
88#6451—22no—
89#6451C2×C414yescomplemented
90#6450—24no—
91#6450—22no—
92#6450—24no—
93#6450C2×C414yescomplemented
94#6441—24no—
95#6441—24no—
96#6440—24no—
97#6440—24no—
98C7×C22⋊C8—21no—
99C7×C22⋊C8C2312yes—
100C7×#95—21no—
101C7×#95C2312yes—
102C7⋊#95—21no—
103C7⋊#95—24no—
104C7⋊#95C2312yes—
105C22⋊(C7⋊C8)—21no—
106C22⋊(C7⋊C8)C2312yes—
107#6389—24no—
108Dic7⋊C8—24no—
109C2×#533—71no—
110C2×#432—71no—
111C2×#376—71no—
112#1506—78no—
113C2×#328—71no—
114C2×#328—71no—
115C2×#328—71no—
116C2×#328D711yescharacteristic
117C24×C7C2×D411yescharacteristic
118C2×C7×Q8—21no—
119C2×C7×Q8—42no—
120C2×C7×Q8C22×C412yes—
121C22×C4×C7—24no—
122C22×C4×C7—21no—
123C22×C4×C7—21no—
124C22×C4×C7—22no—
125C22×C4×C7—42no—
126C22×C4×C7—42no—
127C22×C4×C7—42no—
128C22×C4×C7C22×C411yescharacteristic
129C22×C4×C7C22×C411yescharacteristic
130C22×C4×C7C2×D411yescharacteristic
131C22×C4×C7C2×D411yescharacteristic
132C22×C4×C7C2×D411yescharacteristic
133C22×C4×C7C2411yescharacteristic
134C22×Dic7—22no—
135C22×Dic7—22no—
136C22×Dic7—24no—
137C22×Dic7—24no—
138C22×Dic7—21no—
139C22×Dic7—21no—
140C22×Dic7—22no—
141C22×Dic7—42no—
142C22×Dic7—42no—
143C22×Dic7C22⋊C412yes—
144C22×Dic7C22⋊C412yes—
145C22×Dic7C22⋊C411yescharacteristic
146C22×Dic7C22⋊C411yescharacteristic
147C22×Dic7C22⋊C411yescharacteristic
148C22×Dic7C22⋊C411yescharacteristic
149C22×Dic7C2×D412yes—
150C22×Dic7C2×D412yes—
151C2×Dic14—21no—
152C2×Dic14—24no—
153C2×Dic14—44no—
154C2×Dic14—42no—
155C2×Dic14C22×C412yes—
156C2×C7×C8—22no—
157C2×C7×C8—42no—
158C7×C4⋊C4—21no—
159C7×C4⋊C4—22no—
160C7×C4⋊C4—22no—
161C7×C4⋊C4C22×C412yes—
162C7×C22⋊C4—22no—
163C7×C22⋊C4—22no—
164C22⋊Dic7—22no—
165C22⋊Dic7—22no—
166C4⋊Dic7—21no—
167C4⋊Dic7—24no—
168C4⋊Dic7C22×C412yes—
169Dic7⋊C4—22no—
170Dic7⋊C4—22no—
171Dic7⋊C4—24no—
172Dic7⋊C4—24no—
173Dic7⋊C4—24no—
174Dic7⋊C4—24no—
175C4×Dic7—216no—
176C4×Dic7—24no—
177C4×Dic7—24no—
178C4×Dic7C22⋊C412yes—
179C4×Dic7C22⋊C412yes—
180C4×Dic7C22⋊C412yes—
181C4×Dic7C22⋊C412yes—
182C4×Dic7C22×C412yes—
183C4×Dic7C22×C412yes—
184C4×Dic7C2×D412yes—
185C4×Dic7C2×D412yes—
186C2×C7⋊C8—22no—
187C2×C7⋊C8—42no—
188#533—74no—
189#533—74no—
190#533—142no—
191#533—142no—
192C2×C4⋊Q8—71no—
193C2×C4⋊Q8—71no—
194C2×#125—141no—
195C2×C22⋊Q8—71no—
196C2×C22⋊Q8—141no—
197C2×C22⋊Q8C2×D711yescharacteristic
198C2×C4×Q8—71no—
199C2×C4×Q8—71no—
200C2×C4×Q8—141no—
201C2×#117—141no—
202C22×C42—71no—
203C22×C42—141no—
204#432—74no—
205#432—142no—
206C2×C4⋊C8—141no—
207C2×C22⋊C8—71no—
208C2×C22⋊C8C2×D711yescharacteristic
209C2×#97—141no—
210#376—74no—
211#376—142no—
212C2×#95—71no—
213C2×#95—141no—
214C2×#95C2×D711yescharacteristic
215#328—74no—
216#328—74no—
217#328—74no—
218#328C2×D714yes—
219C23×C7—22no—
220C23×C7—22no—
221C23×C7C2×C22⋊C411yescharacteristic
222C23×C7C2×C22⋊C411yescharacteristic
223C23×C7#13712yes—
224C23×C7#13712yes—
225C23×C7C22×D411yescharacteristic
226C7×Q8—42no—
227C7×Q8—42no—
228C2×C4×C7—22no—
229C2×C4×C7—22no—
230C2×C4×C7—24no—
231C2×C4×C7—22no—
232C2×C4×C7—22no—
233C2×C4×C7—41no—
234C2×C4×C7—41no—
235C2×C4×C7—41no—
236C2×C4×C7—41no—
237C2×C4×C7—42no—
238C2×C4×C7—48no—
239C2×C4×C7—42no—
240C2×C4×C7—42no—
241C2×C4×C7—42no—
242C2×C4×C7C2×C22⋊C411yescharacteristic
243C2×C4×C7C2×C22⋊C411yescharacteristic
244C2×C4×C7C23×C411yescharacteristic
245C2×C4×C7C22×D411yescharacteristic
246C2×Dic7—22no—
247C2×Dic7—22no—
248C2×Dic7—24no—
249C2×Dic7—22no—
250C2×Dic7—22no—
251C2×Dic7—22no—
252C2×Dic7—24no—
253C2×Dic7—24no—
254C2×Dic7—24no—
255C2×Dic7—22no—
256C2×Dic7—22no—
257C2×Dic7—42no—
258C2×Dic7—48no—
259C2×Dic7—42no—
260C2×Dic7—42no—
261C2×Dic7—42no—
262C2×Dic7#10414yes—
263C2×Dic7C2×C22⋊C412yes—
264C2×Dic7C2×C22⋊C412yes—
265C2×Dic7C2×C22⋊C412yes—
266C2×Dic7C2×C22⋊C412yes—
267Dic14—42no—
268Dic14—48no—
269Dic14—42no—
270C7×C8—42no—
271C7⋊C8—42no—
272C22×Q8—71no—
273C22×Q8—141no—
274C22×Q8C4×D711yescharacteristic
275C23×C4—21no—
276C23×C4—71no—
277C23×C4—71no—
278C23×C4—141no—
279C23×C4C22×D711yescharacteristic
280C22×C8—21no—
281C22×C8—141no—
282C4⋊Q8—74no—
283C4⋊Q8—74no—
284C4⋊Q8—142no—
285C4⋊Q8—142no—
286#125—144no—
287#125—144no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—72no—
291C22⋊Q8—72no—
292C22⋊Q8—144no—
293C22⋊Q8—144no—
294C22⋊Q8—141no—
295C22⋊Q8—141no—
296C22⋊Q8C4×D712yes—
297C22⋊Q8C22×D712yes—
298C4×Q8—74no—
299C4×Q8—74no—
300C4×Q8—142no—
301C4×Q8—144no—
302C4×Q8—144no—
303C4×Q8—142no—
304#117—144no—
305#117—144no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—71no—
308C2×C4⋊C4—141no—
309C2×C4⋊C4—141no—
310C2×C4⋊C4—141no—
311C2×C4⋊C4—141no—
312C2×C4⋊C4—141no—
313C2×C4⋊C4—141no—
314C2×C4⋊C4C4×D711yescharacteristic
315C2×C22⋊C4—21no—
316C2×C22⋊C4—141no—
317C2×C42—71no—
318C2×C42—71no—
319C2×C42—72no—
320C2×C42—71no—
321C2×C42—71no—
322C2×C42—72no—
323C2×C42—72no—
324C2×C42—72no—
325C2×C42—141no—
326C2×C42—141no—
327C2×C42—144no—
328C2×C42—148no—
329C4⋊C8—144no—
330C22⋊C8—21no—
331C22⋊C8—72no—
332C22⋊C8—141no—
333C22⋊C8C22×D712yes—
334#97—144no—
335#95—21no—
336#95—72no—
337#95—144no—
338#95—141no—
339#95C22×D712yes—
340C22×C7—21no—
341C22×C7—21no—
342C22×C7—21no—
343C22×C7—21no—
344C22×C7—24no—
345C22×C7—24no—
346C22×C7#41012yes—
347C22×C7#41912yes—
348C22×C7#41912yes—
349C22×C7C2×#10412yes—
350C22×C7C22×C22⋊C411yescharacteristic
351C22×C7C2×#13711yescharacteristic
352C22×C7C2×#13711yescharacteristic
353C4×C7—21no—
354C4×C7—21no—
355C4×C7—21no—
356C4×C7—21no—
357C4×C7—44no—
358C4×C7—42no—
359C4×C7—42no—
360Dic7—22no—
361Dic7—22no—
362Dic7—22no—
363Dic7—44no—
364Dic7—42no—
365Dic7—42no—
366Dic7C2×#10414yes—
367C24D4×D711yescharacteristic
368C2×Q8—21no—
369C2×Q8—42no—
370C2×Q8—72no—
371C2×Q8—144no—
372C2×Q8—141no—
373C2×Q8—282no—
374C2×Q8—284no—
375C2×Q8C2×C4×D712yes—
376C22×C4—24no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—71no—
384C22×C4—72no—
385C22×C4—72no—
386C22×C4—71no—
387C22×C4—71no—
388C22×C4—71no—
389C22×C4—72no—
390C22×C4—72no—
391C22×C4—144no—
392C22×C4—142no—
393C22×C4—142no—
394C22×C4—144no—
395C22×C4—141no—
396C22×C4—141no—
397C22×C4—142no—
398C22×C4—282no—
399C22×C4—282no—
400C22×C4C2×C4×D711yescharacteristic
401C22×C4C2×C4×D711yescharacteristic
402C22×C4D4×D711yescharacteristic
403C22×C4D4×D711yescharacteristic
404C22×C4D4×D711yescharacteristic
405C22×C4C23×D711yescharacteristic
406C2×C8—22no—
407C2×C8—42no—
408C2×C8—142no—
409C2×C8—282no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—72no—
414C4⋊C4—144no—
415C4⋊C4—144no—
416C4⋊C4—144no—
417C4⋊C4—144no—
418C4⋊C4—144no—
419C4⋊C4—142no—
420C4⋊C4—141no—
421C4⋊C4—142no—
422C4⋊C4C2×C4×D712yes—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—142no—
426C22⋊C4—142no—
427C42—72no—
428C42—72no—
429C42—72no—
430C42—72no—
431C42—72no—
432C42—72no—
433C42—72no—
434C42—72no—
435C42—144no—
436C42—144no—
437C42—1416no—
438C2×C7—21no—
439C2×C7—21no—
440C2×C7—22no—
441C2×C7#150614yescomplemented
442C2×C7C2×#41011yescharacteristic
443C2×C7C2×#41911yescharacteristic
444C2×C7C22×#10411yescharacteristic
445C23—22no—
446C23—22no—
447C23D7×C22⋊C411yescharacteristic
448C23D7×C22⋊C411yescharacteristic
449C23#647812yes—
450C23#648112yes—
451C23C2×D4×D711yescharacteristic
452Q8—42no—
453Q8—42no—
454Q8—282no—
455Q8—282no—
456Q8—288no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—48no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—72no—
472C2×C4—74no—
473C2×C4—72no—
474C2×C4—72no—
475C2×C4—72no—
476C2×C4—144no—
477C2×C4—144no—
478C2×C4—142no—
479C2×C4—142no—
480C2×C4—144no—
481C2×C4—142no—
482C2×C4—142no—
483C2×C4—142no—
484C2×C4—144no—
485C2×C4—142no—
486C2×C4—142no—
487C2×C4—282no—
488C2×C4—288no—
489C2×C4—282no—
490C2×C4—282no—
491C2×C4—282no—
492C2×C4D7×C22⋊C411yescharacteristic
493C2×C4D7×C22⋊C411yescharacteristic
494C2×C4C22×C4×D711yescharacteristic
495C2×C4C2×D4×D711yescharacteristic
496C8—42no—
497C8—282no—
498C7C2×#150611yescharacteristic, complemented, Sylow
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—24no—
504C22—24no—
505C22#8951212yes—
506C22#8957412yes—
507C22#8957412yes—
508C22D7×#10412yes—
509C22C2×D7×C22⋊C411yescharacteristic
510C22C2×#647811yescharacteristic
511C22C2×#648111yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—44no—
517C4—42no—
518C4—42no—
519C4—74no—
520C4—142no—
521C4—142no—
522C4—142no—
523C4—284no—
524C4—282no—
525C4—282no—
526C2—21no—
527C2—21no—
528C2—22no—
529C2#1172606414yesdirect product factor
530C2C2×#8951211yescharacteristic
531C2C2×#8957411yescharacteristic
532C2C2×D7×#10411yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#328C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C2×D4
cosocleC22×C4×C7C24
hypercenterC2×#328D7
hypocenterC7C2×#1506
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
8. #11726064C2direct (N × H)
10. C2×Q8×Dic7C4semidirect
11. C2×#6507C4semidirect
17. #90313C4semidirect
20. C2×#6451C4semidirect
22. C2×#6450C4semidirect
59. Q8×Dic7C2×C4semidirect
61. #6507C2×C4semidirect
89. #6451C2×C4semidirect
93. #6450C2×C4semidirect
441. C2×C7#1506semidirect
498. C7C2×#1506semidirect
529. C2#11726064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903132
C2×#894912
C2×#894202
C2×C7×#3282
C2×#893332
C2×#892622
C2×#892472
#117260642
C2×#15067