Finite Group Databasebeta

← #14218340

Subgroups — #14218340

Order 1792.

1962 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11743325C211yesmaximal, characteristic
2C7×#2961C211yesmaximal, characteristic, complemented
3#11740774C211yesmaximal, characteristic, complemented
4#11737388C218yesmaximal, complemented
5#11737386C218yesmaximal, complemented
6#11736518C212yesmaximal, complemented
7#11736516C212yesmaximal, complemented
8#11736487C211yesmaximal, characteristic, complemented
9#11736483C211yesmaximal, characteristic, complemented
10#11735998C212yesmaximal, complemented
11#11735995C212yesmaximal, complemented
12#11735936C211yesmaximal, characteristic, complemented
13C2×D7×#97C211yesmaximal, characteristic, complemented
14C7×#533C2211yescharacteristic
15C2×#6470C2212yes—
16C2×#6464C2212yes—
17C22×C8×D7C2211yescharacteristic
18C22×C8×D7C2211yescharacteristic
19#90419C412yes—
20#90416C412yes—
21#90382C414yes—
22#90318C414yes—
23#90315C414yes—
24#90271C2214yes—
25C4×#1161C2214yes—
26#90215C2212yes—
27#90213C2212yes—
28#90168C2211yescharacteristic
29C2×C42×D7C2211yescharacteristic
30C7×#446C2218yescomplemented
31C7×#424C2212yes—
32C7×#423C2211yescharacteristic
33C7×#405C2212yes—
34C2×C7×#97C2211yescharacteristic
35#89901C2212yes—
36#89898C2212yes—
37M16×Dic7C2212yes—
38#89882C2212yes—
39C2×#6389C2211yescharacteristic
40C2×#6389C2211yescharacteristic
41#89796C2218yescomplemented
42#89771C2212yes—
43#89769C2212yes—
44#89696C2211yescharacteristic
45C2×#6377C2211yescharacteristic
46#89612C2218yescomplemented
47#89608C2218yes—
48#89608C2218yescomplemented
49#89607C2214yes—
50#89607C2218yescomplemented
51#89606C2218yes—
52#89605C2214yes—
53#89480C2214yescomplemented
54#89478C2218yes—
55#89478C2218yescomplemented
56D7×#97C2214yes—
57D7×#97C2214yes—
58D7×#97C2214yescomplemented
59#89461C2214yescomplemented
60C4×#1131C2214yescomplemented
61C8×D28C2218yes—
62#60207—71nomaximal, Sylow
63C2×#1161C2×C414yes—
64C2×#1157C2312yes—
65C22×C4×D7C2×C412yes—
66C22×C4×D7C2311yescharacteristic
67C2×C7×M16C2312yes—
68C22×C7×C8C2311yescharacteristic
69C22×C7×C8C2311yescharacteristic
70C7×C4⋊Q8C2×C412yes—
71C7×#125C2×C412yes—
72C7×C22⋊Q8C2×C414yes—
73C4×C7×Q8C2314yes—
74C7×#117C2312yes—
75C2×C42×C7C2311yescharacteristic
76#6510C2×C414yes—
77#6509C2×C414yes—
78Q8×Dic7C2×C414yes—
79#6493C2×C414yes—
80C2×C4×Dic7C2×C412yes—
81C2×C4×Dic7C2311yescharacteristic
82C2×#1136C2312yes—
83C22×C7⋊C8C2311yescharacteristic
84C22×C7⋊C8C2311yescharacteristic
85#6470—28no—
86#6464—28no—
87C2×#1131C2314yes—
88C2×#1131C2314yes—
89C2×C8×D7—24no—
90C2×C8×D7—24no—
91C2×C8×D7C2314yes—
92C2×C8×D7C2314yes—
93C2×C8×D7C2314yes—
94C2×C8×D7C2314yes—
95#6461C2×C418yes—
96#6460C2×C414yes—
97#6458C2×C414yes—
98#6458C2×C414yes—
99#6457C2×C418yes—
100#6456C2×C414yes—
101#6456C2×C418yes—
102#6456C2×C414yes—
103#6455C2×C418yes—
104#6455C2×C414yes—
105#6453C2×C414yes—
106#6450C2×C414yes—
107#6449C2×C414yes—
108#6445C2×C414yes—
109(C22⋊D7)⋊C4C2×C418yes—
110#6438C2×C412yes—
111#6437C2×C411yescharacteristic
112C4×D28C2318yes—
113C4×D28C2314yes—
114#6435C2314yes—
115C42×D7C2×C412yes—
116C42×D7C2×C412yes—
117C42×D7C2312yes—
118C42×D7C2312yes—
119C42×D7C2314yes—
120#6432C2×C411yescharacteristic
121C7×C4⋊C8C2314yes—
122C7×C4⋊C8C2318yes—
123C7×#97C2314yes—
124C7×#97C2314yes—
125C4×C7×C8C2314yes—
126(C2×D7)⋊C8C2318yes—
127(C2×D7)⋊C8C2318yes—
128(C2×D7)⋊C8C2318yes—
129#6389C2314yes—
130#6389C2312yes—
131#6389C2312yes—
132#6389C2312yes—
133#6389C2312yes—
134C8×Dic7C2314yes—
135C4⋊(C7⋊C8)C2314yes—
136C4⋊(C7⋊C8)C2318yes—
137#6377C2314yes—
138#6377C2314yes—
139C4×C7⋊C8C2314yes—
140#3444—71no—
141#2970—78no—
142#2968—78no—
143#2961—71no—
144#2961D711yescharacteristic, complemented
145#2932—71no—
146#2932—71no—
147#2929—72no—
148#2929—72no—
149#2923—72no—
150#2920—71no—
151#2875—72no—
152C22×#97—71no—
153C23×D7C22×C411yescharacteristic
154C2×C7×Q8C22×C414yes—
155C22×C4×C7C22×C412yes—
156C22×C4×C7C2411yescharacteristic
157C2×C22⋊D7C22×C414yes—
158C22×Dic7C22×C411yescharacteristic
159C22×Dic7C22×C412yes—
160#1161—48no—
161#1157—24no—
162#1157—24no—
163C2×D28C22×C418yes—
164C2×D28C22×C412yes—
165C2×D28C22×C414yes—
166C2×C4×D7—22no—
167C2×C4×D7—22no—
168C2×C4×D7—44no—
169C2×C4×D7C22×C412yes—
170C2×C4×D7C22×C412yes—
171C2×C4×D7C22×C412yes—
172C2×C4×D7C22×C412yes—
173C2×C4×D7C22×C412yes—
174C2×C4×D7C22×C418yes—
175C2×C4×D7C2412yes—
176C2×C4×D7C2414yes—
177C2×Dic14C22×C412yes—
178C7×M16—24no—
179C2×C7×C8—22no—
180C2×C7×C8#4114yescomplemented
181C2×C7×C8C2414yes—
182C2×C7×C8C2412yes—
183C2×C7×C8C2412yes—
184C7×C4⋊C4C22×C414yes—
185C7×C4⋊C4C22×C414yes—
186C7×C4⋊C4C22×C418yes—
187C7×C22⋊C4C22×C414yes—
188C42×C7C22×C411yescharacteristic
189C42×C7C22×C411yescharacteristic
190C42×C7C2414yes—
191C42×C7C2412yes—
192(C2×D7)⋊C4C22×C418yes—
193(C2×D7)⋊C4C22×C418yes—
194(C2×D7)⋊C4C22×C418yes—
195(C2×D7)⋊C4C22×C418yes—
196C4⋊Dic7C22×C414yes—
197C4⋊Dic7C22×C418yes—
198Dic7⋊C4C22×C418yes—
199C4×Dic7C22×C412yes—
200C4×Dic7C22×C412yes—
201C4×Dic7C22×C412yes—
202C4×Dic7C22×C412yes—
203C4×Dic7C22×C412yes—
204C4×Dic7C22×C418yes—
205C4×Dic7C2411yescharacteristic
206C4×Dic7C2411yescharacteristic
207#1136—24no—
208C2×C7⋊C8—22no—
209C2×C7⋊C8#4114yescomplemented
210C2×C7⋊C8C2412yes—
211C2×C7⋊C8C2414yes—
212C2×C7⋊C8C2412yes—
213#1131—28no—
214#1131—28no—
215C8×D7—28no—
216C8×D7—28no—
217C8×D7—28no—
218C8×D7—28no—
219C2×#131—72no—
220C2×#131—72no—
221C23×C8—71no—
222C23×C8—71no—
223#533—72no—
224#533C2×D711yescharacteristic
225#532—72no—
226#532—71no—
227#529—74no—
228#529—74no—
229#529—74no—
230#525—74no—
231#525—72no—
232C4×#41—74no—
233C4×#41—72no—
234C22×C42—71no—
235#446—78no—
236#446C2×D718yescomplemented
237#435—78no—
238#435—78no—
239#435—78no—
240#435—78no—
241C8×D4—78no—
242C8×D4—78no—
243#433—78no—
244#432—74no—
245#432—78no—
246#431—74no—
247#424—72no—
248#424C2×D712yes—
249#423—71no—
250#423C2×D711yescharacteristic
251#408—72no—
252#408—72no—
253#407—72no—
254#405—72no—
255#405—74no—
256#405—74no—
257#405C2×D712yes—
258C4×M16—72no—
259C4×M16—74no—
260C2×#97—71no—
261C2×#97—71no—
262C2×#97—71no—
263C2×#97—74no—
264C2×#97—74no—
265C2×#97—74no—
266C2×#97C2×D711yescharacteristic
267C23×C7C23×C411yescharacteristic
268C22×D7—22no—
269C22×D7—24no—
270C22×D7C23×C414yes—
271C22×D7C23×C412yes—
272C7×Q8—44no—
273C2×C4×C7—42no—
274C2×C4×C7C23×C412yes—
275C2×C4×C7C23×C412yes—
276C2×C4×C7C23×C418yes—
277C2×C4×C7C23×C411yescharacteristic
278C2×C4×C7C2×#4112yes—
279C2×C4×C7C2×#4112yes—
280C2×C4×C7C2511yescharacteristic
281C22⋊D7—28no—
282C2×Dic7—22no—
283C2×Dic7—42no—
284C2×Dic7C23×C412yes—
285C2×Dic7C23×C412yes—
286C2×Dic7C23×C412yes—
287C2×Dic7C23×C414yes—
288D28—216no—
289D28—24no—
290D28—44no—
291C4×D7—24no—
292C4×D7—24no—
293C4×D7—24no—
294C4×D7—22no—
295C4×D7—22no—
296C4×D7—24no—
297C4×D7—24no—
298C4×D7—42no—
299C4×D7—42no—
300C4×D7—48no—
301Dic14—24no—
302C7×C8—22no—
303C7×C8—24no—
304C7×C8C2×#4114yes—
305C7⋊C8—22no—
306C7⋊C8—24no—
307C7⋊C8C2×#4114yes—
308C2×#41—74no—
309C2×#41—72no—
310C23×C4—71no—
311C23×C4—72no—
312#131—148no—
313#131—148no—
314C2×M16—72no—
315C2×M16—74no—
316C2×M16—74no—
317C2×M16C22×D712yes—
318C22×C8—71no—
319C22×C8—71no—
320C22×C8—74no—
321C22×C8—74no—
322C22×C8—74no—
323C22×C8—74no—
324C22×C8—144no—
325C22×C8—144no—
326C22×C8C22×D711yescharacteristic
327C22×C8C22×D711yescharacteristic
328C4⋊Q8—71no—
329C4⋊Q8C4×D712yes—
330#127—71no—
331#126—78no—
332#125—74no—
333#125C4×D712yes—
334#124—74no—
335#124—72no—
336#123—78no—
337#123—74no—
338C22⋊Q8—74no—
339C22⋊Q8—74no—
340C22⋊Q8C4×D714yes—
341#121—74no—
342#121—74no—
343#121—74no—
344#120—74no—
345C4×Q8—74no—
346C4×Q8—74no—
347C4×Q8C22×D714yes—
348C4×D4—78no—
349C4×D4—74no—
350C4×D4—74no—
351C4×D4—78no—
352C4×D4—78no—
353C4×D4—74no—
354#117—74no—
355#117—78no—
356#117—74no—
357#117C22×D712yes—
358C2×C42—72no—
359C2×C42—71no—
360C2×C42—72no—
361C2×C42—72no—
362C2×C42—74no—
363C2×C42—72no—
364C2×C42—72no—
365C2×C42C22×D711yescharacteristic
366C4⋊C8—74no—
367C4⋊C8—78no—
368C4⋊C8C22×D714yes—
369C4⋊C8C22×D718yes—
370C22⋊C8—78no—
371C22⋊C8—78no—
372C22⋊C8—78no—
373#97—72no—
374#97—72no—
375#97—72no—
376#97—72no—
377#97—74no—
378#97—74no—
379#97—74no—
380#97C22×D714yes—
381#97C22×D714yes—
382C4×C8—74no—
383C4×C8—74no—
384C4×C8C22×D714yes—
385C22×C7—22no—
386C22×C7C4×#4112yes—
387C22×C7C24×C411yescharacteristic
388C2×D7—28no—
389C2×D7—22no—
390C2×D7—22no—
391C2×D7—24no—
392C2×D7—28no—
393C2×D7#56814yes—
394C4×C7—22no—
395C4×C7—22no—
396C4×C7—28no—
397C4×C7C4×#4112yes—
398C4×C7C22×#4111yescharacteristic
399C4×C7C22×#4111yescharacteristic
400Dic7—24no—
401Dic7—22no—
402Dic7—22no—
403Dic7—22no—
404C24—71no—
405#41—144no—
406#41—144no—
407#41—288no—
408C2×Q8—72no—
409C2×Q8C2×C4×D714yes—
410C2×D4—74no—
411C2×D4—78no—
412C2×D4—72no—
413C2×D4—74no—
414C22×C4—71no—
415C22×C4—72no—
416C22×C4—72no—
417C22×C4—72no—
418C22×C4—72no—
419C22×C4—72no—
420C22×C4—74no—
421C22×C4—72no—
422C22×C4—72no—
423C22×C4—78no—
424C22×C4—142no—
425C22×C4—142no—
426C22×C4—284no—
427C22×C4C2×C4×D712yes—
428C22×C4C23×D711yescharacteristic
429M16—24no—
430M16—148no—
431M16—144no—
432M16—148no—
433C2×C8—22no—
434C2×C8—74no—
435C2×C8—72no—
436C2×C8—74no—
437C2×C8—72no—
438C2×C8—148no—
439C2×C8—148no—
440C2×C8—142no—
441C2×C8—148no—
442C2×C8—148no—
443C2×C8#116114yescomplemented
444C2×C8C23×D714yes—
445C2×C8C23×D712yes—
446C2×C8C23×D712yes—
447C4⋊C4—78no—
448C4⋊C4—74no—
449C4⋊C4—78no—
450C4⋊C4C2×C4×D714yes—
451C4⋊C4C2×C4×D718yes—
452C4⋊C4C2×C4×D714yes—
453C22⋊C4—78no—
454C22⋊C4—78no—
455C22⋊C4—78no—
456C22⋊C4—78no—
457C22⋊C4C2×C4×D714yes—
458C42—72no—
459C42—72no—
460C42—72no—
461C42—72no—
462C42—72no—
463C42—78no—
464C42—71no—
465C42—71no—
466C42C2×C4×D711yescharacteristic
467C42C2×C4×D711yescharacteristic
468C42C23×D714yes—
469C42C23×D712yes—
470C2×C7—22no—
471C2×C7C2×C4×#4111yescharacteristic
472C2×C7C2×#56812yes—
473D7—24no—
474D7—44no—
475C23—72no—
476C23—74no—
477C23—144no—
478C23—142no—
479C23C22×C4×D711yescharacteristic
480Q8—44no—
481Q8—144no—
482D4—1416no—
483D4—148no—
484D4—144no—
485D4—284no—
486C2×C4—42no—
487C2×C4—72no—
488C2×C4—72no—
489C2×C4—72no—
490C2×C4—74no—
491C2×C4—144no—
492C2×C4—144no—
493C2×C4—142no—
494C2×C4—144no—
495C2×C4—142no—
496C2×C4—144no—
497C2×C4—142no—
498C2×C4—144no—
499C2×C4—282no—
500C2×C4—282no—
501C2×C4—288no—
502C2×C4—282no—
503C2×C4C22×C4×D712yes—
504C2×C4C22×C4×D712yes—
505C2×C4C22×C4×D718yes—
506C2×C4C22×C4×D711yescharacteristic
507C2×C4C2×#116112yes—
508C2×C4D7×#4112yes—
509C2×C4C24×D711yescharacteristic
510C8—22no—
511C8—24no—
512C8—74no—
513C8—142no—
514C8—144no—
515C8C2×#116114yes—
516C7#6020711yescharacteristic, complemented, Sylow
517C22—22no—
518C22—74no—
519C22—148no—
520C22—142no—
521C22—142no—
522C22—144no—
523C22—148no—
524C22C4×#116112yes—
525C22C23×C4×D711yescharacteristic
526C4—22no—
527C4—22no—
528C4—28no—
529C4—142no—
530C4—144no—
531C4—142no—
532C4—142no—
533C4C4×#116112yes—
534C4C22×#116111yescharacteristic
535C4C2×D7×#4111yescharacteristic
536C2—22no—
537C2—144no—
538C2—284no—
539C2C2×C4×#116111yescharacteristic
540C2D7×#56812yes—
subgroupG/H
center, FrattiniC2×C4C24×D7
commutator, socleC22×C7C24×C4
FittingC7×#2961C2
prime radical#11743325C2
cosocleC2×C4×C7C25
hypercenter#2961D7
hypocenterC7#60207
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. C7×#2961C2semidirect
3. #11740774C2semidirect
4. #11737388C2semidirect
5. #11737386C2semidirect
6. #11736518C2semidirect
7. #11736516C2semidirect
8. #11736487C2semidirect
9. #11736483C2semidirect
10. #11735998C2semidirect
11. #11735995C2semidirect
12. #11735936C2semidirect
13. C2×D7×#97C2semidirect
30. C7×#446C22semidirect
41. #89796C22semidirect
46. #89612C22semidirect
48. #89608C22semidirect
50. #89607C22semidirect
53. #89480C22semidirect
55. #89478C22semidirect
58. D7×#97C22semidirect
59. #89461C22semidirect
60. C4×#1131C22semidirect
144. #2961D7semidirect
180. C2×C7×C8#41semidirect
209. C2×C7⋊C8#41semidirect
236. #446C2×D7semidirect
443. C2×C8#1161semidirect
516. C7#60207semidirect

Maximal subgroups

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

subgroupindex
#117433252
C7×#29612
#117407742
#117373882
#117373862
#117365182
#117365162
#117364872
#117364832
#117359982
#117359952
#117359362
C2×D7×#972
#602077