Finite Group Databasebeta

← C2×#11744110 #14262062

Subgroups — C2×#11744110 #14262062

Order 1792.

7118 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×Q82C211yesmaximal, characteristic, complemented
2#11744110C2132yesmaximal, direct product factor
3C2×#90424C216yesmaximal, complemented
4C2×#90423C216yesmaximal, complemented
5C2×#90425C213yesmaximal, complemented
6C2×#90419C213yesmaximal, complemented
7C2×Q8×D28C211yesmaximal, characteristic, complemented
8C2×#90267C212yesmaximal, complemented
9C2×#90271C213yesmaximal, complemented
10C2×#90263C212yesmaximal, complemented
11C2×#90275C213yesmaximal, complemented
12C2×C4×#1161C211yesmaximal, characteristic, complemented
13C22×#1161C2211yescharacteristic
14C22×Q8×D7C2212yes—
15C7×Q82C22116yescomplemented
16C2×C7×C4⋊Q8C2213yes—
17C2×C7×C4⋊Q8C2216yes—
18C2×C4×C7×Q8C2211yescharacteristic
19C2×C4×C7×Q8C2213yes—
20C2×C4×C7×Q8C2212yes—
21C2×#6510C22112yes—
22C2×#6510C2211yescharacteristic
23C2×#6509C2216yes—
24C2×#6509C2213yes—
25C2×Q8×Dic7C2216yes—
26C2×Q8×Dic7C2211yescharacteristic
27#90425C22148yescomplemented
28#90424C22196yescomplemented
29#90423C22196yescomplemented
30#90419C22148yescomplemented
31#90275C22148yescomplemented
32#90271C22148yescomplemented
33#90267C22132yescomplemented
34Q8×D28C22116yescomplemented
35C4×#1161C22116yescomplemented
36#90263C22132yescomplemented
37C2×#6461C2216yes—
38C2×#6461C22112yes—
39C2×#6460C2216yes—
40C2×#6460C2216yes—
41C2×#6458C2213yes—
42C2×#6458C2216yes—
43C2×#6457C2216yes—
44C2×#6456C2213yes—
45C2×#6455C2216yes—
46C2×#6455C2216yes—
47C2×#6455C2213yes—
48C2×#6453C2213yes—
49C2×#6450C2216yes—
50C2×#6438C2216yes—
51C2×C4×D28C2213yes—
52C2×C4×D28C2213yes—
53C2×C4×D28C2216yes—
54C2×#6435C2216yes—
55C2×C42×D7C2213yes—
56C2×#6432C2213yes—
57C2×C4×Dic14C2216yes—
58C2×#3518—71nomaximal, Sylow
59C22×C7×Q8C2311yescharacteristic
60C22×C7×Q8C2316yes—
61C22×C7×Q8C2311yescharacteristic
62C2×#1161—28no—
63C2×#1161C2318yes—
64C2×Q8×D7—216no—
65C2×Q8×D7C23116yes—
66C22×D28C2311yescharacteristic
67C22×D28C2313yes—
68C22×D28C2316yes—
69C22×C4×D7C2313yes—
70C22×C4×D7C2313yes—
71C22×C4×D7C2316yes—
72C22×C4×D7C2313yes—
73C22×Dic14C2316yes—
74C7×C4⋊Q8C23124yes—
75C7×C4⋊Q8C23148yes—
76C4×C7×Q8C23116yes—
77C4×C7×Q8C2318yes—
78C4×C7×Q8C23124yes—
79C2×C7×C4⋊C4C2316yes—
80C2×C7×C4⋊C4C2313yes—
81C2×C7×C4⋊C4C2313yes—
82C2×C7×C4⋊C4C2316yes—
83C2×C42×C7C2316yes—
84C2×C42×C7C2313yes—
85#6510C23196yes—
86#6510C2318yes—
87#6509C23148yes—
88#6509C23124yes—
89Q8×Dic7C23148yes—
90Q8×Dic7C2318yes—
91C2×(C2×D7)⋊C4C2312yes—
92C2×(C2×D7)⋊C4C2316yes—
93C2×(C2×D7)⋊C4C2312yes—
94C2×(C2×D7)⋊C4C2316yes—
95C2×(C2×D7)⋊C4C2316yes—
96C2×(C2×D7)⋊C4C2316yes—
97C2×(C2×D7)⋊C4C23112yes—
98C2×C4⋊Dic7C2313yes—
99C2×C4⋊Dic7C2313yes—
100C2×C4⋊Dic7C2316yes—
101C2×C4⋊Dic7C2316yes—
102C2×Dic7⋊C4C2316yes—
103C2×Dic7⋊C4C2316yes—
104C2×C4×Dic7C23112yes—
105C2×C4×Dic7C2311yescharacteristic
106C2×C4×Dic7C2313yes—
107C2×C4×Dic7C2313yes—
108#6461C23148yes—
109#6461C23196yes—
110#6460C23148yes—
111#6460C23148yes—
112#6458C23148yes—
113#6458C23124yes—
114#6457C23148yes—
115#6456C23124yes—
116#6455C23148yes—
117#6455C23124yes—
118#6455C23148yes—
119#6453C23124yes—
120#6450C23148yes—
121#6438C23148yes—
122C4×D28C23148yes—
123C4×D28C23124yes—
124C4×D28C23124yes—
125#6435C23148yes—
126C42×D7C23124yes—
127#6432C23124yes—
128C4×Dic14C23148yes—
129#3518—732no—
130C2×Q82D711yescharacteristic, complemented
131C2×#556—76no—
132C2×#556—73no—
133C2×#555—73no—
134C2×D4×Q8—71no—
135C2×#548—72no—
136C2×#542—76no—
137C2×#533—73no—
138C2×#529—73no—
139C2×#519—72no—
140C2×C4×#41—71no—
141C23×D7C2412yes—
142C23×D7C2413yes—
143C2×C7×Q8—24no—
144C2×C7×Q8—412no—
145C2×C7×Q8#4118yes—
146C2×C7×Q8C2414yes—
147C2×C7×Q8C24124yes—
148C2×C7×Q8C2414yes—
149C22×C4×C7C2416yes—
150C22×C4×C7C2413yes—
151C22×C4×C7C2412yes—
152C22×C4×C7C2413yes—
153C22×C4×C7C2411yescharacteristic
154C22×Dic7C2413yes—
155C22×Dic7C2411yescharacteristic
156C22×Dic7C2411yescharacteristic
157C22×Dic7C2416yes—
158#1161—232no—
159Q8×D7—264no—
160C2×D28—212no—
161C2×D28—24no—
162C2×D28—412no—
163C2×D28C2414yes—
164C2×D28C24112yes—
165C2×D28C24124yes—
166C2×C4×D7—224no—
167C2×C4×D7—212no—
168C2×C4×D7—212no—
169C2×C4×D7—46no—
170C2×C4×D7C24112yes—
171C2×C4×D7C24112yes—
172C2×C4×D7C24124yes—
173C2×C4×D7C24112yes—
174C2×Dic14—224no—
175C2×Dic14C24124yes—
176C7×C4⋊C4C24124yes—
177C7×C4⋊C4C24112yes—
178C7×C4⋊C4C24112yes—
179C7×C4⋊C4C24124yes—
180C42×C7C24124yes—
181C42×C7C24112yes—
182(C2×D7)⋊C4C2418yes—
183(C2×D7)⋊C4C24124yes—
184(C2×D7)⋊C4C2418yes—
185(C2×D7)⋊C4C24124yes—
186(C2×D7)⋊C4C24124yes—
187(C2×D7)⋊C4C24124yes—
188(C2×D7)⋊C4C24148yes—
189C4⋊Dic7C24112yes—
190C4⋊Dic7C24112yes—
191C4⋊Dic7C24124yes—
192C4⋊Dic7C24124yes—
193Dic7⋊C4C24124yes—
194Dic7⋊C4C24124yes—
195C4×Dic7C24148yes—
196C4×Dic7C2414yes—
197C4×Dic7C24112yes—
198C4×Dic7C24112yes—
199C22×#41—71no—
200C23×Q8—72no—
201Q82C2×D7116yescomplemented
202#556—796no—
203#556—748no—
204#555—748no—
205D4×Q8—716no—
206#548—732no—
207#542—796no—
208#533—748no—
209C2×C4⋊Q8—73no—
210C2×C4⋊Q8C2×D713yes—
211C2×C4⋊Q8C2×D716yes—
212#529—748no—
213C2×#126—76no—
214C2×#126—712no—
215C2×#125—73no—
216C2×#124—71no—
217C2×#124—712no—
218C2×#124—76no—
219C2×#123—76no—
220C2×C22⋊Q8—73no—
221C2×C22⋊Q8—76no—
222C2×C22⋊Q8—76no—
223C2×C22⋊Q8—76no—
224C2×#121—73no—
225C2×#121—76no—
226#519—732no—
227C4×#41—716no—
228C2×C4×Q8—71no—
229C2×C4×Q8—76no—
230C2×C4×Q8—76no—
231C2×C4×Q8—76no—
232C2×C4×Q8C2×D711yescharacteristic
233C2×C4×Q8C2×D712yes—
234C2×C4×Q8C2×D713yes—
235C2×C4×D4—73no—
236C2×C4×D4—73no—
237C2×C4×D4—76no—
238C2×C4×D4—73no—
239C2×#117—73no—
240C2×#117—76no—
241C2×#117—76no—
242C2×#117—76no—
243C22×C42—73no—
244C23×C7C2511yescharacteristic
245C22×D7—24no—
246C22×D7—26no—
247C22×D7—26no—
248C22×D7—24no—
249C22×D7—26no—
250C22×D7—24no—
251C22×D7C2514yes—
252C22×D7C2516yes—
253C7×Q8—28no—
254C7×Q8—424no—
255C7×Q8C2×#41116yes—
256C2×C4×C7—24no—
257C2×C4×C7—26no—
258C2×C4×C7—212no—
259C2×C4×C7C2×#41112yes—
260C2×C4×C72−1+414yes—
261C2×C4×C7C25112yes—
262C2×C4×C7C2516yes—
263C2×C4×C7C2514yes—
264C2×C4×C7C2516yes—
265C2×C4×C7C2512yes—
266C2×Dic7—212no—
267C2×Dic7—22no—
268C2×Dic7—26no—
269C2×Dic7—22no—
270C2×Dic7C2516yes—
271C2×Dic7C2512yes—
272C2×Dic7C2512yes—
273C2×Dic7C25112yes—
274D28—224no—
275D28—28no—
276D28—424no—
277C4×D7—248no—
278C4×D7—224no—
279C4×D7—224no—
280C4×D7—412no—
281Dic14—248no—
282C2×#41—78no—
283C2×#41—148no—
284C22×Q8—716no—
285C22×Q8—76no—
286C22×Q8—1416no—
287C22×Q8C22×D711yescharacteristic
288C22×Q8C22×D716yes—
289C22×Q8C22×D711yescharacteristic
290C22×D4—71no—
291C22×D4—73no—
292C22×D4—76no—
293C23×C4—76no—
294C23×C4—73no—
295C23×C4—73no—
296C23×C4—73no—
297C4⋊Q8—724no—
298C4⋊Q8C22×D7124yes—
299C4⋊Q8C22×D7148yes—
300#126—748no—
301#126—796no—
302#125—724no—
303#124—78no—
304#124—796no—
305#124—748no—
306#123—748no—
307C22⋊Q8—724no—
308C22⋊Q8—748no—
309C22⋊Q8—748no—
310C22⋊Q8—748no—
311#121—724no—
312#121—748no—
313C4×Q8—78no—
314C4×Q8—748no—
315C4×Q8—748no—
316C4×Q8—748no—
317C4×Q8C22×D718yes—
318C4×Q8C22×D7116yes—
319C4×Q8C22×D7124yes—
320C4×D4—724no—
321C4×D4—724no—
322C4×D4—748no—
323C4×D4—724no—
324#117—724no—
325#117—748no—
326#117—748no—
327#117—748no—
328C2×C4⋊C4—73no—
329C2×C4⋊C4—73no—
330C2×C4⋊C4—76no—
331C2×C4⋊C4—76no—
332C2×C4⋊C4—76no—
333C2×C4⋊C4—76no—
334C2×C4⋊C4C22×D713yes—
335C2×C4⋊C4C22×D713yes—
336C2×C4⋊C4C22×D716yes—
337C2×C4⋊C4C22×D716yes—
338C2×C22⋊C4—76no—
339C2×C22⋊C4—72no—
340C2×C22⋊C4—76no—
341C2×C22⋊C4—712no—
342C2×C22⋊C4—72no—
343C2×C22⋊C4—76no—
344C2×C22⋊C4—76no—
345C2×C42—73no—
346C2×C42—712no—
347C2×C42—73no—
348C2×C42—71no—
349C2×C42—724no—
350C2×C42C22×D716yes—
351C2×C42C22×D713yes—
352C22×C7C22×#4112yes—
353C22×C7C2×2−1+412yes—
354C22×C7#58512yes—
355C22×C7C2611yescharacteristic
356C2×D7—24no—
357C2×D7—26no—
358C2×D7—26no—
359C2×D7—24no—
360C2×D7—26no—
361C2×D7—24no—
362C2×D7—48no—
363C2×D7—412no—
364C4×C7—24no—
365C4×C7—26no—
366C4×C7—212no—
367C4×C7C22×#41112yes—
368C4×C7C2×2−1+414yes—
369Dic7—212no—
370Dic7—22no—
371Dic7—26no—
372Dic7—22no—
373C24—72no—
374C24—73no—
375#41—1432no—
376C2×Q8—24no—
377C2×Q8—412no—
378C2×Q8—724no—
379C2×Q8—1464no—
380C2×Q8—1424no—
381C2×Q8#116118yes—
382C2×Q8C23×D714yes—
383C2×Q8C23×D7124yes—
384C2×Q8C23×D714yes—
385C2×D4—74no—
386C2×D4—712no—
387C2×D4—724no—
388C2×D4—1412no—
389C2×D4—144no—
390C2×D4—2812no—
391C22×C4—73no—
392C22×C4—71no—
393C22×C4—71no—
394C22×C4—76no—
395C22×C4—712no—
396C22×C4—712no—
397C22×C4—724no—
398C22×C4—712no—
399C22×C4—1424no—
400C22×C4—1412no—
401C22×C4—1412no—
402C22×C4—286no—
403C22×C4C23×D716yes—
404C22×C4C23×D713yes—
405C22×C4C23×D712yes—
406C22×C4C23×D713yes—
407C22×C4C23×D711yescharacteristic
408C4⋊C4—724no—
409C4⋊C4—724no—
410C4⋊C4—712no—
411C4⋊C4—712no—
412C4⋊C4—724no—
413C4⋊C4—724no—
414C4⋊C4C23×D7112yes—
415C4⋊C4C23×D7112yes—
416C4⋊C4C23×D7124yes—
417C4⋊C4C23×D7124yes—
418C22⋊C4—724no—
419C22⋊C4—78no—
420C22⋊C4—724no—
421C22⋊C4—748no—
422C22⋊C4—78no—
423C22⋊C4—724no—
424C22⋊C4—724no—
425C42—74no—
426C42—712no—
427C42—712no—
428C42—748no—
429C42C23×D7112yes—
430C42C23×D7124yes—
431C2×C7#351814yescomplemented
432C2×C7C23×#4111yescharacteristic
433C2×C7C22×2−1+411yescharacteristic
434C2×C7C2×#58511yescharacteristic
435D7—44no—
436D7—46no—
437C23—74no—
438C23—76no—
439C23—144no—
440C23—146no—
441C23—146no—
442C23—144no—
443C23—146no—
444C23—144no—
445C23C24×D711yescharacteristic
446Q8—28no—
447Q8—424no—
448Q8—1448no—
449Q8C2×#1161116yes—
450D4—1424no—
451D4—148no—
452D4—2824no—
453C2×C4—24no—
454C2×C4—26no—
455C2×C4—212no—
456C2×C4—76no—
457C2×C4—72no—
458C2×C4—72no—
459C2×C4—712no—
460C2×C4—142no—
461C2×C4—1412no—
462C2×C4—146no—
463C2×C4—142no—
464C2×C4—1448no—
465C2×C4—1424no—
466C2×C4—1424no—
467C2×C4—2812no—
468C2×C4C2×#1161112yes—
469C2×C4#655114yes—
470C2×C4C24×D7112yes—
471C2×C4C24×D716yes—
472C2×C4C24×D714yes—
473C2×C4C24×D716yes—
474C2×C4C24×D712yes—
475C7C2×#351811yescharacteristic, complemented, Sylow
476C22—144no—
477C22—146no—
478C22—146no—
479C22—144no—
480C22—146no—
481C22—144no—
482C22—288no—
483C22—2812no—
484C22C22×#116112yes—
485C22C2×#655112yes—
486C22#9061812yes—
487C22C25×D711yescharacteristic
488C4—24no—
489C4—26no—
490C4—212no—
491C4—142no—
492C4—1412no—
493C4—146no—
494C4—142no—
495C4C22×#1161112yes—
496C4C2×#655114yes—
497C2—284no—
498C2—286no—
499C2#1174411014yesdirect product factor
500C2C23×#116111yescharacteristic
501C2C22×#655111yescharacteristic
502C2C2×#9061811yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×Q82C2
socleC23×C7C25
hypercenterC2×Q82D7
hypocenterC7C2×#3518
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
1. C2×C7×Q82C2semidirect
2. #11744110C2direct (N × H)
3. C2×#90424C2semidirect
4. C2×#90423C2semidirect
5. C2×#90425C2semidirect
6. C2×#90419C2semidirect
7. C2×Q8×D28C2semidirect
8. C2×#90267C2semidirect
9. C2×#90271C2semidirect
10. C2×#90263C2semidirect
11. C2×#90275C2semidirect
12. C2×C4×#1161C2semidirect
15. C7×Q82C22semidirect
27. #90425C22semidirect
28. #90424C22semidirect
29. #90423C22semidirect
30. #90419C22semidirect
31. #90275C22semidirect
32. #90271C22semidirect
33. #90267C22semidirect
34. Q8×D28C22semidirect
35. C4×#1161C22semidirect
36. #90263C22semidirect
130. C2×Q82D7semidirect
201. Q82C2×D7semidirect
431. C2×C7#3518semidirect
475. C7C2×#3518semidirect
499. C2#11744110direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×Q822
#117441102
C2×#904242
C2×#904232
C2×#904252
C2×#904192
C2×Q8×D282
C2×#902672
C2×#902712
C2×#902632
C2×#902752
C2×C4×#11612
C2×#35187