Finite Group Databasebeta

← #11732985

Subgroups — #11732985

Order 896.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C22⋊C4C211yesmaximal, characteristic
2C2×#6442C211yesmaximal, characteristic, complemented
3C7×#388C211yesmaximal, characteristic, complemented
4#89766C211yesmaximal, characteristic, complemented
5#89759C211yesmaximal, characteristic, complemented
6#89727C211yesmaximal, characteristic
7#89727C211yesmaximal, characteristic
8#89725C211yesmaximal, characteristic, complemented
9#89725C211yesmaximal, characteristic, complemented
10#89712C211yesmaximal, characteristic, complemented
11C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
12#89446C211yesmaximal, characteristic, complemented
13#89442C211yesmaximal, characteristic, complemented
14#89440C211yesmaximal, characteristic, complemented
15#89440C211yesmaximal, characteristic, complemented
16C24×D7C2211yescharacteristic
17C22×C4×D7C2211yescharacteristic
18C22×C4×D7C2211yescharacteristic
19C2×C7×C4⋊C4C2211yescharacteristic, complemented
20C2×C7×C22⋊C4C2211yescharacteristic
21C2×C7×C22⋊C4C2211yescharacteristic
22C2×C7×C22⋊C4C2211yescharacteristic
23C2×C42×C7C2211yescharacteristic, complemented
24C2×C22⋊Dic7C2211yescharacteristic
25C2×C22⋊Dic7C2211yescharacteristic
26C2×C22⋊Dic7C2211yescharacteristic
27C2×(C2×D7)⋊C4C2211yescharacteristic
28C2×(C2×D7)⋊C4C2211yescharacteristic
29C2×(C2×D7)⋊C4C2211yescharacteristic
30C2×(C2×D7)⋊C4C2211yescharacteristic
31C2×(C2×D7)⋊C4C2211yescharacteristic
32C2×(C2×D7)⋊C4C2211yescharacteristic
33C2×(C2×D7)⋊C4C2211yescharacteristic
34C2×(C2×D7)⋊C4C2211yescharacteristic
35C2×(C2×D7)⋊C4C2211yescharacteristic
36C2×(C2×D7)⋊C4C2211yescharacteristic
37C2×C4⋊Dic7C2211yescharacteristic, complemented
38C2×C4⋊Dic7C2211yescharacteristic, complemented
39C2×C4⋊Dic7C2211yescharacteristic, complemented
40C2×Dic7⋊C4C2211yescharacteristic, complemented
41C2×Dic7⋊C4C2211yescharacteristic, complemented
42C2×C4×Dic7C2211yescharacteristic, complemented
43D7×C22⋊C4—24no—
44#6442—24no—
45C7×#95C2211yescharacteristic, complemented
46C7×#95C2211yescharacteristic, complemented
47C7⋊#95C2211yescharacteristic, complemented
48C7⋊#95C2211yescharacteristic, complemented
49C7⋊#95C2211yescharacteristic, complemented
50C7⋊#95C2211yescharacteristic, complemented
51C7⋊#95C2211yescharacteristic, complemented
52C7⋊#95C2211yescharacteristic, complemented
53#2480—71nomaximal, Sylow
54C24×C7C2311yescharacteristic
55C23×D7—22no—
56C23×D7—22no—
57C23×D7—22no—
58C23×D7—22no—
59C23×D7—22no—
60C23×D7—41no—
61C23×D7—41no—
62C23×D7C2311yescharacteristic
63C23×D7C2311yescharacteristic
64C22×C4×C7C2311yescharacteristic
65C22×C4×C7C2311yescharacteristic
66C22×C4×C7C2311yescharacteristic
67C22×C4×C7C2311yescharacteristic
68C22×C4×C7C2311yescharacteristic
69C22×C4×C7C2311yescharacteristic
70C22×Dic7C2311yescharacteristic
71C22×Dic7C2311yescharacteristic
72C22×Dic7C2311yescharacteristic
73C22×Dic7C2311yescharacteristic
74C22×Dic7C2311yescharacteristic
75C22×Dic7C2311yescharacteristic
76C2×C4×D7—22no—
77C2×C4×D7—22no—
78C2×C4×D7—22no—
79C2×C4×D7—22no—
80C2×C4×D7—41no—
81C2×C4×D7—41no—
82C7×C4⋊C4—41no—
83C7×C22⋊C4—41no—
84C7×C22⋊C4—41no—
85C7×C22⋊C4D414yes—
86C42×C7—41no—
87C22⋊Dic7—22no—
88C22⋊Dic7—22no—
89C22⋊Dic7—22no—
90(C2×D7)⋊C4—22no—
91(C2×D7)⋊C4—22no—
92(C2×D7)⋊C4—22no—
93(C2×D7)⋊C4—22no—
94(C2×D7)⋊C4—22no—
95(C2×D7)⋊C4—22no—
96(C2×D7)⋊C4—22no—
97(C2×D7)⋊C4—22no—
98(C2×D7)⋊C4—41no—
99(C2×D7)⋊C4—41no—
100C4⋊Dic7—22no—
101C4⋊Dic7—41no—
102C4⋊Dic7—41no—
103Dic7⋊C4—22no—
104Dic7⋊C4—22no—
105C4×Dic7—22no—
106C2×#126—71no—
107C22×C22⋊C4—71no—
108#397—71no—
109#397—71no—
110#397—71no—
111#396—71no—
112#388—71no—
113#388—71no—
114#388D711yescharacteristic, complemented
115#385—71no—
116#385—71no—
117#380—71no—
118#379—71no—
119#379—71no—
120C4×C22⋊C4—71no—
121C23×C7—21no—
122C23×C7—21no—
123C23×C7—21no—
124C23×C7—21no—
125C23×C7—21no—
126C23×C7—21no—
127C23×C7C2×D412yes—
128C23×C7C2411yescharacteristic
129C22×D7—21no—
130C22×D7—21no—
131C22×D7—21no—
132C22×D7—21no—
133C22×D7—28no—
134C22×D7—21no—
135C22×D7—21no—
136C22×D7—21no—
137C22×D7—21no—
138C22×D7—21no—
139C22×D7—21no—
140C22×D7—44no—
141C22×D7—44no—
142C22×D7—44no—
143C22×D7—44no—
144C22×D7—44no—
145C22×D7—44no—
146C22×D7#4112yes—
147C22×D7#4112yes—
148C22×D7#4112yes—
149C22×D7#4112yes—
150C2×C4×C7—21no—
151C2×C4×C7—21no—
152C2×C4×C7—21no—
153C2×C4×C7—21no—
154C2×C4×C7—21no—
155C2×C4×C7—21no—
156C2×C4×C7—21no—
157C2×C4×C7—21no—
158C2×C4×C7—21no—
159C2×C4×C7—21no—
160C2×C4×C7—21no—
161C2×C4×C7—21no—
162C2×C4×C7—21no—
163C2×C4×C7—21no—
164C2×C4×C7—21no—
165C2×C4×C7—21no—
166C2×C4×C7C2×D412yes—
167C2×C4×C7C2×D412yes—
168C2×Dic7—21no—
169C2×Dic7—21no—
170C2×Dic7—21no—
171C2×Dic7—21no—
172C2×Dic7—21no—
173C2×Dic7—21no—
174C2×Dic7—21no—
175C2×Dic7—21no—
176C2×Dic7—21no—
177C2×Dic7—21no—
178C2×Dic7—21no—
179C2×Dic7—21no—
180C2×Dic7—21no—
181C2×Dic7—21no—
182C2×Dic7—21no—
183C2×Dic7—21no—
184C2×Dic7—21no—
185C2×Dic7—21no—
186C4×D7—44no—
187C4×D7—44no—
188C25—71no—
189C23×C4—71no—
190C23×C4—71no—
191#126—144no—
192C2×C4⋊C4—71no—
193C2×C4⋊C4—71no—
194C2×C4⋊C4—71no—
195C2×C4⋊C4—71no—
196C2×C4⋊C4—71no—
197C2×C4⋊C4C2×D711yescharacteristic, complemented
198C2×C22⋊C4—71no—
199C2×C22⋊C4—71no—
200C2×C22⋊C4—71no—
201C2×C22⋊C4—71no—
202C2×C22⋊C4—71no—
203C2×C22⋊C4—71no—
204C2×C22⋊C4—71no—
205C2×C22⋊C4—71no—
206C2×C22⋊C4—71no—
207C2×C22⋊C4—71no—
208C2×C22⋊C4—71no—
209C2×C22⋊C4—71no—
210C2×C22⋊C4—71no—
211C2×C22⋊C4—144no—
212C2×C22⋊C4C2×D711yescharacteristic
213C2×C22⋊C4C2×D711yescharacteristic
214C2×C22⋊C4C2×D711yescharacteristic
215C2×C42—71no—
216C2×C42C2×D711yescharacteristic, complemented
217#95—71no—
218#95—71no—
219#95—71no—
220#95—71no—
221#95—71no—
222#95—71no—
223#95C2×D711yescharacteristic, complemented
224#95C2×D711yescharacteristic, complemented
225C22×C7—22no—
226C22×C7—22no—
227C22×C7—22no—
228C22×C7—41no—
229C22×C7—41no—
230C22×C7—41no—
231C22×C7—41no—
232C22×C7C22×D411yescharacteristic
233C22×C7C2×#4111yescharacteristic
234C22×C7C2×#4111yescharacteristic
235C22×C7C2×#4111yescharacteristic
236C22×C7C2×#4111yescharacteristic
237C22×C7H(5,𝔽2)11yescharacteristic
238C22×C7H(5,𝔽2)11yescharacteristic
239C2×D7—22no—
240C2×D7—22no—
241C2×D7—22no—
242C2×D7—22no—
243C2×D7—22no—
244C2×D7—22no—
245C2×D7—22no—
246C2×D7—22no—
247C2×D7—22no—
248C2×D7—416no—
249C2×D7—41no—
250C2×D7—41no—
251C2×D7—41no—
252C2×D7—41no—
253C2×D7#12614yescomplemented
254C4×C7—22no—
255C4×C7—22no—
256C4×C7—41no—
257C4×C7—41no—
258C4×C7—41no—
259C4×C7—41no—
260Dic7—41no—
261Dic7—41no—
262Dic7—41no—
263Dic7—41no—
264Dic7—41no—
265Dic7—41no—
266C24—71no—
267C24—71no—
268C24—142no—
269C24—142no—
270C24—142no—
271C24—142no—
272C24—142no—
273C24—281no—
274C24—281no—
275C24C22×D711yescharacteristic
276C22×C4—71no—
277C22×C4—71no—
278C22×C4—71no—
279C22×C4—71no—
280C22×C4—71no—
281C22×C4—71no—
282C22×C4—142no—
283C22×C4—142no—
284C22×C4—142no—
285C22×C4—142no—
286C22×C4—281no—
287C22×C4—281no—
288C22×C4C22×D711yescharacteristic
289C22×C4C22×D711yescharacteristic
290C22×C4C22×D711yescharacteristic
291C22×C4C22×D711yescharacteristic
292C22×C4C22×D711yescharacteristic
293C22×C4C22×D711yescharacteristic
294C4⋊C4—41no—
295C4⋊C4—142no—
296C4⋊C4—142no—
297C4⋊C4—142no—
298C4⋊C4—281no—
299C4⋊C4—281no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—142no—
303C22⋊C4—142no—
304C22⋊C4—142no—
305C22⋊C4—142no—
306C22⋊C4—142no—
307C22⋊C4—142no—
308C22⋊C4—142no—
309C22⋊C4—142no—
310C22⋊C4—142no—
311C22⋊C4—142no—
312C22⋊C4—142no—
313C22⋊C4—281no—
314C22⋊C4—281no—
315C22⋊C4D2814yes—
316C42—41no—
317C42—142no—
318C2×C7—42no—
319C2×C7#52511yescharacteristic
320C2×C7C2×#12611yescharacteristic
321C2×C7#53811yescharacteristic
322C2×C7#54611yescharacteristic
323C2×C7#54611yescharacteristic
324C2×C7#55111yescharacteristic
325C2×C7#55111yescharacteristic
326D7—24no—
327D7—42no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—72no—
335C23—72no—
336C23—72no—
337C23—72no—
338C23—148no—
339C23—141no—
340C23—141no—
341C23—141no—
342C23—141no—
343C23—141no—
344C23—141no—
345C23—141no—
346C23—141no—
347C23—141no—
348C23—141no—
349C23—284no—
350C23—284no—
351C23—284no—
352C23—284no—
353C23—284no—
354C23—284no—
355C23C2×D2812yes—
356C23C23×D711yescharacteristic
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—141no—
374C2×C4—141no—
375C2×C4—141no—
376C2×C4—141no—
377C2×C4—141no—
378C2×C4—141no—
379C2×C4—141no—
380C2×C4—141no—
381C2×C4—141no—
382C2×C4—141no—
383C2×C4—141no—
384C2×C4—141no—
385C2×C4—141no—
386C2×C4—141no—
387C2×C4—141no—
388C2×C4—141no—
389C2×C4—141no—
390C2×C4—141no—
391C2×C4—284no—
392C2×C4—284no—
393C2×C4C2×D2812yes—
394C2×C4C2×D2812yes—
395C7#248011yescharacteristic, complemented, Sylow
396C22—22no—
397C22—22no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—74no—
404C22—142no—
405C22—142no—
406C22—142no—
407C22—142no—
408C22—142no—
409C22—142no—
410C22—142no—
411C22—142no—
412C22—142no—
413C22—2816no—
414C22—281no—
415C22—281no—
416C22—281no—
417C22—281no—
418C22C22×D2811yescharacteristic
419C22#654811yescharacteristic
420C22#654811yescharacteristic
421C22D7×#4111yescharacteristic
422C22D7×#4111yescharacteristic
423C22D7×#4111yescharacteristic
424C22D7×#4111yescharacteristic
425C4—22no—
426C4—22no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—281no—
432C4—281no—
433C4—281no—
434C4—281no—
435C4—281no—
436C4—281no—
437C2—42no—
438C2—144no—
439C2—282no—
440C2#9021511yescharacteristic
441C2#9024511yescharacteristic
442C2#9024511yescharacteristic
443C2#9030411yescharacteristic
444C2#9035011yescharacteristic
445C2#9037011yescharacteristic
446C2D7×#12611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D7
commutator, socle, cosocleC23×C7C24
FittingC7×#388C2
prime radicalC24×D7C22
hypercenter#388D7
hypocenterC7#2480
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#6442C2semidirect
3. C7×#388C2semidirect
4. #89766C2semidirect
5. #89759C2semidirect
8. #89725C2semidirect
9. #89725C2semidirect
10. #89712C2semidirect
11. C4×(C2×D7)⋊C4C2semidirect
12. #89446C2semidirect
13. #89442C2semidirect
14. #89440C2semidirect
15. #89440C2semidirect
19. C2×C7×C4⋊C4C22semidirect
23. C2×C42×C7C22semidirect
37. C2×C4⋊Dic7C22semidirect
38. C2×C4⋊Dic7C22semidirect
39. C2×C4⋊Dic7C22semidirect
40. C2×Dic7⋊C4C22semidirect
41. C2×Dic7⋊C4C22semidirect
42. C2×C4×Dic7C22semidirect
45. C7×#95C22semidirect
46. C7×#95C22semidirect
47. C7⋊#95C22semidirect
48. C7⋊#95C22semidirect
49. C7⋊#95C22semidirect
50. C7⋊#95C22semidirect
51. C7⋊#95C22semidirect
52. C7⋊#95C22semidirect
114. #388D7semidirect
197. C2×C4⋊C4C2×D7semidirect
216. C2×C42C2×D7semidirect
223. #95C2×D7semidirect
224. #95C2×D7semidirect
253. C2×D7#126semidirect
395. C7#2480semidirect

Maximal subgroups

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

subgroupindex
C2×D7×C22⋊C42
C2×#64422
C7×#3882
#897662
#897592
#897272
#897252
#897122
C4×(C2×D7)⋊C42
#894462
#894422
#894402
#24807