Finite Group Databasebeta

← #11731024

Subgroups — #11731024

Order 896.

716 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D7C211yesmaximal, characteristic, complemented
2C2×#6447C211yesmaximal, characteristic
3C2×C4×D28C211yesmaximal, characteristic, complemented
4C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
5#89985C211yesmaximal, characteristic, complemented
6#89728C211yesmaximal, characteristic, complemented
7#89728C211yesmaximal, characteristic, complemented
8#89723C211yesmaximal, characteristic, complemented
9#89712C211yesmaximal, characteristic, complemented
10C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
11#89705C211yesmaximal, characteristic, complemented
12#89438C211yesmaximal, characteristic, complemented
13#89437C211yesmaximal, characteristic, complemented
14D7×#95C211yesmaximal, characteristic, complemented
15#89427C211yesmaximal, characteristic, complemented
16C23×C4×C7C2211yescharacteristic
17C22×C22⋊D7C2211yescharacteristic
18C22×C22⋊D7C2211yescharacteristic
19C22×D28C2211yescharacteristic
20C22×C4×D7C2211yescharacteristic
21C22×C4×D7C2211yescharacteristic
22C22×C4×D7C2211yescharacteristic
23C22×C4×D7C2211yescharacteristic
24C2×C7×C22⋊C4C2211yescharacteristic
25C2×C7×C22⋊C4C2211yescharacteristic
26C2×C42×C7C2211yescharacteristic
27C2×C42×C7C2211yescharacteristic
28C2×C22⋊Dic7C2211yescharacteristic
29C2×C22⋊Dic7C2211yescharacteristic
30C4×C22⋊D7—24no—
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
38C2×Dic7⋊C4C2211yescharacteristic
39C2×Dic7⋊C4C2211yescharacteristic
40C2×C4×Dic7C2211yescharacteristic
41C2×C4×Dic7C2211yescharacteristic
42#6447C418yescomplemented
43C4×D28—24no—
44C7×#95C2211yescharacteristic
45C7×#95C2211yescharacteristic
46C7⋊#95C2211yescharacteristic
47C7⋊#95C2211yescharacteristic
48C7⋊#95C2211yescharacteristic
49C7⋊#95C2211yescharacteristic
50C7⋊#95C2211yescharacteristic
51C7⋊#95C2211yescharacteristic
52C7⋊#95C2211yescharacteristic
53C7⋊#95C2211yescharacteristic
54#2364—71nomaximal, Sylow
55C24×C7C2311yescharacteristic
56C23×D7C2311yescharacteristic
57C23×D7C2311yescharacteristic
58C22×C4×C7—22no—
59C22×C4×C7—22no—
60C22×C4×C7—41no—
61C22×C4×C7C2311yescharacteristic
62C22×C4×C7C2311yescharacteristic
63C22×C4×C7C2311yescharacteristic
64C22×C4×C7C2311yescharacteristic
65C22×C4×C7C2311yescharacteristic
66C22×C4×C7C2311yescharacteristic
67C2×C22⋊D7—22no—
68C2×C22⋊D7—22no—
69C2×C22⋊D7—41no—
70C2×C22⋊D7—41no—
71C2×C22⋊D7C2×C414yescomplemented
72C2×C22⋊D7C2×C414yescomplemented
73C22×Dic7C2311yescharacteristic
74C22×Dic7C2311yescharacteristic
75C22×Dic7C2311yescharacteristic
76C22×Dic7C2311yescharacteristic
77C22×Dic7C2311yescharacteristic
78C22×Dic7C2311yescharacteristic
79C2×D28—22no—
80C2×D28—22no—
81C2×D28C2×C414yescomplemented
82C2×C4×D7—22no—
83C2×C4×D7—22no—
84C2×C4×D7—22no—
85C2×C4×D7—22no—
86C2×C4×D7—22no—
87C2×C4×D7—22no—
88C2×C4×D7—41no—
89C2×C4×D7—41no—
90C2×C4×D7—41no—
91C2×C4×D7—41no—
92C2×C4×D7—41no—
93C2×C4×D7C2×C414yescomplemented
94C7×C22⋊C4—22no—
95C7×C22⋊C4C2×C414yescomplemented
96C42×C7—22no—
97C42×C7—41no—
98C22⋊Dic7—22no—
99C22⋊Dic7—41no—
100(C2×D7)⋊C4—22no—
101(C2×D7)⋊C4—22no—
102(C2×D7)⋊C4—22no—
103(C2×D7)⋊C4—41no—
104(C2×D7)⋊C4C2×C414yescomplemented
105(C2×D7)⋊C4D414yescomplemented
106C4⋊Dic7—22no—
107Dic7⋊C4—22no—
108Dic7⋊C4C2×C414yescomplemented
109C4×Dic7—22no—
110C4×Dic7—41no—
111C2×#121—71no—
112C2×C4×D4—71no—
113C2×C4×D4—71no—
114#388—71no—
115#388—71no—
116#387—71no—
117#387—71no—
118#386—71no—
119#386—71no—
120#386—71no—
121#386—71no—
122C4×C22⋊C4—71no—
123C4×C22⋊C4—71no—
124C4×C22⋊C4D711yescharacteristic, complemented
125C2×#95—71no—
126C23×C7—21no—
127C23×C7—21no—
128C23×C7—21no—
129C23×C7—21no—
130C23×C7—21no—
131C23×C7—21no—
132C23×C7C22×C412yes—
133C23×C7C2411yescharacteristic
134C22×D7—21no—
135C22×D7—21no—
136C22×D7—21no—
137C22×D7—21no—
138C22×D7—21no—
139C22×D7—21no—
140C22×D7—21no—
141C22×D7—21no—
142C22×D7—21no—
143C22×D7—21no—
144C22×D7C22×C412yes—
145C22×D7C22×C412yes—
146C22×D7C2×D412yes—
147C22×D7#4112yes—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
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—44no—
162C2×C4×C7C22×C412yes—
163C2×C4×C7C22×C412yes—
164C2×C4×C7C2×D412yes—
165C2×C4×C7#4112yes—
166C2×C4×C7#4112yes—
167C22⋊D7—28no—
168C22⋊D7—44no—
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×Dic7C22×C412yes—
185C2×Dic7C22×C412yes—
186C2×Dic7C2×D412yes—
187D28—28no—
188C4×D7—44no—
189C4×D7—44no—
190C4×D7—44no—
191C4×D7—44no—
192C22×D4—71no—
193C22×D4—71no—
194C22×D4—71no—
195C23×C4—71no—
196C23×C4—71no—
197C23×C4—71no—
198C23×C4—71no—
199C23×C4C2×D711yescharacteristic
200#121—78no—
201C4×D4—144no—
202C4×D4—144no—
203C2×C4⋊C4—71no—
204C2×C4⋊C4—71no—
205C2×C4⋊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—71no—
212C2×C22⋊C4—71no—
213C2×C22⋊C4—71no—
214C2×C22⋊C4C2×D711yescharacteristic
215C2×C22⋊C4C2×D711yescharacteristic
216C2×C42—71no—
217C2×C42—71no—
218C2×C42C2×D711yescharacteristic
219C2×C42C2×D711yescharacteristic
220#95—71no—
221#95—71no—
222#95—71no—
223#95—71no—
224#95—71no—
225#95—71no—
226#95—71no—
227#95—71no—
228#95C2×D711yescharacteristic
229#95C2×D711yescharacteristic
230C22×C7—22no—
231C22×C7—22no—
232C22×C7—22no—
233C22×C7—41no—
234C22×C7—41no—
235C22×C7—41no—
236C22×C7—41no—
237C22×C7C23×C411yescharacteristic
238C22×C7C22×D411yescharacteristic
239C22×C7C2×#4111yescharacteristic
240C22×C7C2×#4111yescharacteristic
241C22×C7C2×#4111yescharacteristic
242C22×C7H(5,𝔽2)11yescharacteristic
243C22×C7H(5,𝔽2)11yescharacteristic
244C2×D7—22no—
245C2×D7—22no—
246C2×D7—22no—
247C2×D7—22no—
248C2×D7—22no—
249C2×D7—22no—
250C2×D7—22no—
251C2×D7—22no—
252C2×D7—22no—
253C2×D7—41no—
254C2×D7—41no—
255C2×D7—41no—
256C2×D7—41no—
257C2×D7C4×D414yes—
258C4×C7—22no—
259C4×C7—22no—
260C4×C7—22no—
261C4×C7—22no—
262C4×C7—22no—
263C4×C7—41no—
264Dic7—22no—
265Dic7—22no—
266Dic7—22no—
267Dic7—41no—
268Dic7—41no—
269Dic7—41no—
270C24—71no—
271C24—71no—
272C24C22×D711yescharacteristic
273C2×D4—74no—
274C2×D4—74no—
275C2×D4—74no—
276C2×D4—142no—
277C2×D4—142no—
278C2×D4—142no—
279C2×D4—142no—
280C2×D4—281no—
281C2×D4—281no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—71no—
286C22×C4—71no—
287C22×C4—71no—
288C22×C4—74no—
289C22×C4—71no—
290C22×C4—71no—
291C22×C4—71no—
292C22×C4—142no—
293C22×C4—142no—
294C22×C4—142no—
295C22×C4—142no—
296C22×C4—142no—
297C22×C4—142no—
298C22×C4—281no—
299C22×C4—281no—
300C22×C4—281no—
301C22×C4—281no—
302C22×C4—281no—
303C22×C4C22×D711yescharacteristic
304C22×C4C22×D711yescharacteristic
305C22×C4C22×D711yescharacteristic
306C22×C4C22×D711yescharacteristic
307C22×C4C22×D711yescharacteristic
308C22×C4C22×D711yescharacteristic
309C4⋊C4—74no—
310C4⋊C4—142no—
311C4⋊C4—142no—
312C22⋊C4—22no—
313C22⋊C4—74no—
314C22⋊C4—74no—
315C22⋊C4—142no—
316C22⋊C4—142no—
317C22⋊C4—142no—
318C22⋊C4—142no—
319C22⋊C4—281no—
320C22⋊C4—281no—
321C22⋊C4C4×D714yescomplemented
322C42—22no—
323C42—41no—
324C42—142no—
325C42—281no—
326C2×C7—42no—
327C2×C7C2×C4×D411yescharacteristic
328C2×C7C4×#4111yescharacteristic
329C2×C7#51811yescharacteristic
330C2×C7#54611yescharacteristic
331C2×C7#54611yescharacteristic
332C2×C7#55311yescharacteristic
333C2×C7#55311yescharacteristic
334D7—24no—
335D7—42no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—72no—
343C23—72no—
344C23—72no—
345C23—72no—
346C23—141no—
347C23—141no—
348C23—141no—
349C23—141no—
350C23—141no—
351C23—141no—
352C23—141no—
353C23—141no—
354C23—141no—
355C23—141no—
356C23C2×C4×D712yes—
357C23C23×D711yescharacteristic
358D4—148no—
359D4—148no—
360D4—284no—
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—21no—
374C2×C4—44no—
375C2×C4—72no—
376C2×C4—72no—
377C2×C4—72no—
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—141no—
392C2×C4—141no—
393C2×C4—284no—
394C2×C4—284no—
395C2×C4—284no—
396C2×C4—284no—
397C2×C4C2×C4×D712yes—
398C2×C4C2×C4×D712yes—
399C2×C4#115712yes—
400C2×C4#115712yes—
401C2×C4D4×D712yes—
402C7#236411yescharacteristic, complemented, Sylow
403C22—22no—
404C22—22no—
405C22—22no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—74no—
411C22—142no—
412C22—142no—
413C22—142no—
414C22—142no—
415C22—142no—
416C22—142no—
417C22—142no—
418C22—142no—
419C22—142no—
420C22—281no—
421C22—281no—
422C22—281no—
423C22—281no—
424C22C22×C4×D711yescharacteristic
425C22C2×#115711yescharacteristic
426C22C2×#115711yescharacteristic
427C22C2×D4×D711yescharacteristic
428C22#654811yescharacteristic
429C22D7×#4111yescharacteristic
430C22#655311yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—22no—
435C4—22no—
436C4—41no—
437C4—142no—
438C4—142no—
439C4—142no—
440C4—281no—
441C4—281no—
442C4—281no—
443C2—42no—
444C2—144no—
445C2—282no—
446C2C4×#115711yescharacteristic
447C2#9018111yescharacteristic
448C2#9022111yescharacteristic
449C2C4×D4×D711yescharacteristic
450C2#9023611yescharacteristic
451C2#9024111yescharacteristic
452C2#9024911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D7
commutatorC22×C7C23×C4
FittingC4×C7×C22⋊C4C2
socle, cosocleC23×C7C24
prime radicalC2×#6447C2
hypercenterC4×C22⋊C4D7
hypocenterC7#2364
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D7C2semidirect
3. C2×C4×D28C2semidirect
4. C4×C7×C22⋊C4C2semidirect
5. #89985C2semidirect
6. #89728C2semidirect
7. #89728C2semidirect
8. #89723C2semidirect
9. #89712C2semidirect
10. C4×(C2×D7)⋊C4C2semidirect
11. #89705C2semidirect
12. #89438C2semidirect
13. #89437C2semidirect
14. D7×#95C2semidirect
15. #89427C2semidirect
42. #6447C4semidirect
71. C2×C22⋊D7C2×C4semidirect
72. C2×C22⋊D7C2×C4semidirect
81. C2×D28C2×C4semidirect
93. C2×C4×D7C2×C4semidirect
95. C7×C22⋊C4C2×C4semidirect
104. (C2×D7)⋊C4C2×C4semidirect
105. (C2×D7)⋊C4D4semidirect
108. Dic7⋊C4C2×C4semidirect
124. C4×C22⋊C4D7semidirect
321. C22⋊C4C4×D7semidirect
402. C7#2364semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D72
C2×#64472
C2×C4×D282
C4×C7×C22⋊C42
#899852
#897282
#897232
#897122
C4×(C2×D7)⋊C42
#897052
#894382
#894372
D7×#952
#894272
#23647