Finite Group Databasebeta

← #11730997

Subgroups — #11730997

Order 896.

454 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
2#89985C211yesmaximal, characteristic
3#89982C211yesmaximal, characteristic, complemented
4#89731C211yesmaximal, characteristic
5#89729C211yesmaximal, characteristic
6#89724C211yesmaximal, characteristic, complemented
7#89717C211yesmaximal, characteristic, complemented
8#89712C211yesmaximal, characteristic, complemented
9#89712C211yesmaximal, characteristic, complemented
10#89705C211yesmaximal, characteristic, complemented
11C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
12#89447C211yesmaximal, characteristic, complemented
13#89441C211yesmaximal, characteristic, complemented
14#89430C211yesmaximal, characteristic, complemented
15#89424C211yesmaximal, characteristic, complemented
16C23×C4×C7C2211yescharacteristic
17C22×C22⋊D7C2211yescharacteristic
18C2×C7×C22⋊C4C2211yescharacteristic
19C2×C7×C22⋊C4C2211yescharacteristic
20C2×C42×C7C2211yescharacteristic
21C2×C42×C7C2211yescharacteristic
22C2×C22⋊Dic7C2211yescharacteristic
23C2×C22⋊Dic7C2211yescharacteristic
24C2×C22⋊Dic7C2211yescharacteristic
25C2×(C2×D7)⋊C4C2211yescharacteristic
26C2×(C2×D7)⋊C4C2211yescharacteristic
27C2×(C2×D7)⋊C4C2211yescharacteristic
28C2×(C2×D7)⋊C4C2211yescharacteristic
29C2×(C2×D7)⋊C4C2211yescharacteristic
30C2×(C2×D7)⋊C4C2211yescharacteristic
31C2×Dic7⋊C4C2211yescharacteristic
32C2×Dic7⋊C4C2211yescharacteristic
33C2×Dic7⋊C4C2211yescharacteristic
34C2×Dic7⋊C4C2211yescharacteristic
35C2×Dic7⋊C4C2211yescharacteristic
36C2×Dic7⋊C4C2211yescharacteristic
37C2×C4×Dic7C2211yescharacteristic
38C2×C4×Dic7C2211yescharacteristic
39C7×#95C2211yescharacteristic
40C7×#95C2211yescharacteristic
41C7⋊#95C2211yescharacteristic
42C7⋊#95C2211yescharacteristic
43C7⋊#95C2211yescharacteristic
44C7⋊#95C2211yescharacteristic
45C7⋊#95C2211yescharacteristic
46C7⋊#95C2211yescharacteristic
47C7⋊#95C2211yescharacteristic
48C7⋊#95C2211yescharacteristic
49C7⋊#95C2211yescharacteristic
50C7⋊#95C2211yescharacteristic
51#2597—71nomaximal, Sylow
52C24×C7C2311yescharacteristic
53C23×D7C2311yescharacteristic
54C22×C4×C7—22no—
55C22×C4×C7—41no—
56C22×C4×C7—41no—
57C22×C4×C7C2311yescharacteristic
58C22×C4×C7C2311yescharacteristic
59C22×C4×C7C2311yescharacteristic
60C22×C4×C7C2311yescharacteristic
61C22×C4×C7C2311yescharacteristic
62C22×C4×C7C2311yescharacteristic
63C2×C22⋊D7—22no—
64C2×C22⋊D7—22no—
65C2×C22⋊D7—41no—
66C22×Dic7C2311yescharacteristic
67C22×Dic7C2311yescharacteristic
68C22×Dic7C2311yescharacteristic
69C22×Dic7C2311yescharacteristic
70C22×Dic7C2311yescharacteristic
71C22×Dic7C2311yescharacteristic
72C22×Dic7C2311yescharacteristic
73C7×C22⋊C4—22no—
74C7×C22⋊C4—22no—
75C42×C7—41no—
76C42×C7—41no—
77C22⋊Dic7—22no—
78C22⋊Dic7—22no—
79C22⋊Dic7—41no—
80(C2×D7)⋊C4—22no—
81(C2×D7)⋊C4—22no—
82(C2×D7)⋊C4—22no—
83(C2×D7)⋊C4—41no—
84(C2×D7)⋊C4—41no—
85(C2×D7)⋊C4—41no—
86Dic7⋊C4—22no—
87Dic7⋊C4—22no—
88Dic7⋊C4—22no—
89Dic7⋊C4—22no—
90Dic7⋊C4—41no—
91Dic7⋊C4—41no—
92C4×Dic7—22no—
93C4×Dic7—41no—
94#400—71no—
95#397—71no—
96#397—71no—
97#394—71no—
98#390—71no—
99#388—71no—
100#388—71no—
101#388—71no—
102#388—71no—
103#387—71no—
104#387—71no—
105#386—71no—
106#385—71no—
107C4×C4⋊C4—71no—
108C4×C22⋊C4D711yescharacteristic, complemented
109C23×C7—21no—
110C23×C7—21no—
111C23×C7—21no—
112C23×C7—21no—
113C23×C7—21no—
114C23×C7—21no—
115C23×C7#4112yes—
116C23×C7C2411yescharacteristic
117C22×D7—21no—
118C22×D7—21no—
119C22×D7—21no—
120C22×D7—21no—
121C22×D7—21no—
122C22×D7—21no—
123C22×D7—21no—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—21no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—21no—
136C2×C4×C7—21no—
137C2×C4×C7—21no—
138C2×C4×C7—21no—
139C2×C4×C7—21no—
140C2×C4×C7—44no—
141C2×C4×C7#4112yes—
142C2×C4×C7#4112yes—
143C22⋊D7—44no—
144C2×Dic7—21no—
145C2×Dic7—21no—
146C2×Dic7—21no—
147C2×Dic7—21no—
148C2×Dic7—21no—
149C2×Dic7—21no—
150C2×Dic7—21no—
151C2×Dic7—21no—
152C2×Dic7—21no—
153C2×Dic7—21no—
154C2×Dic7—21no—
155C2×Dic7—21no—
156C2×Dic7—21no—
157C2×Dic7—21no—
158C2×Dic7—21no—
159C2×Dic7—21no—
160C2×Dic7—21no—
161C2×Dic7—21no—
162C2×Dic7—21no—
163C2×Dic7#4112yes—
164C2×Dic7#4112yes—
165C22×D4—71no—
166C23×C4C2×D711yescharacteristic
167C2×C4⋊C4—71no—
168C2×C4⋊C4—71no—
169C2×C4⋊C4—71no—
170C2×C4⋊C4—71no—
171C2×C4⋊C4—71no—
172C2×C4⋊C4—71no—
173C2×C22⋊C4—71no—
174C2×C22⋊C4—71no—
175C2×C22⋊C4—71no—
176C2×C22⋊C4—71no—
177C2×C22⋊C4—71no—
178C2×C22⋊C4—71no—
179C2×C22⋊C4—71no—
180C2×C22⋊C4—71no—
181C2×C22⋊C4—71no—
182C2×C22⋊C4C2×D711yescharacteristic
183C2×C22⋊C4C2×D711yescharacteristic
184C2×C42—71no—
185C2×C42—71no—
186C2×C42C2×D711yescharacteristic
187C2×C42C2×D711yescharacteristic
188#95—71no—
189#95—71no—
190#95—71no—
191#95—71no—
192#95—71no—
193#95—71no—
194#95—71no—
195#95—71no—
196#95—71no—
197#95—71no—
198#95C2×D711yescharacteristic
199#95C2×D711yescharacteristic
200C22×C7—22no—
201C22×C7—22no—
202C22×C7—22no—
203C22×C7—41no—
204C22×C7—41no—
205C22×C7—41no—
206C22×C7—41no—
207C22×C7C2×#4111yescharacteristic
208C22×C7C2×#4111yescharacteristic
209C22×C7C2×#4111yescharacteristic
210C22×C7C2×#4111yescharacteristic
211C22×C7C2×#4111yescharacteristic
212C22×C7H(5,𝔽2)11yescharacteristic
213C22×C7H(5,𝔽2)11yescharacteristic
214C2×D7—41no—
215C2×D7—41no—
216C2×D7—41no—
217C2×D7—41no—
218C2×D7—41no—
219C2×D7—41no—
220C2×D7—41no—
221C4×C7—22no—
222C4×C7—22no—
223C4×C7—41no—
224C4×C7—41no—
225C4×C7—41no—
226C4×C7—41no—
227Dic7—22no—
228Dic7—22no—
229Dic7—41no—
230Dic7—41no—
231Dic7—41no—
232Dic7—41no—
233Dic7—41no—
234C24—71no—
235C24C22×D711yescharacteristic
236C2×D4—142no—
237C2×D4—142no—
238C2×D4—281no—
239C22×C4—22no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—71no—
243C22×C4—71no—
244C22×C4—71no—
245C22×C4—71no—
246C22×C4—71no—
247C22×C4—71no—
248C22×C4—71no—
249C22×C4C22×D711yescharacteristic
250C22×C4C22×D711yescharacteristic
251C22×C4C22×D711yescharacteristic
252C22×C4C22×D711yescharacteristic
253C22×C4C22×D711yescharacteristic
254C22×C4C22×D711yescharacteristic
255C4⋊C4—142no—
256C4⋊C4—142no—
257C4⋊C4—142no—
258C4⋊C4—142no—
259C4⋊C4—281no—
260C4⋊C4—281no—
261C22⋊C4—22no—
262C22⋊C4—22no—
263C22⋊C4—142no—
264C22⋊C4—142no—
265C22⋊C4—142no—
266C22⋊C4—142no—
267C22⋊C4—142no—
268C22⋊C4—281no—
269C22⋊C4—281no—
270C22⋊C4—281no—
271C22⋊C4—281no—
272C42—41no—
273C42—41no—
274C42—142no—
275C42—281no—
276C2×C7—42no—
277C2×C7#52911yescharacteristic
278C2×C7#52911yescharacteristic
279C2×C7#53811yescharacteristic
280C2×C7#55111yescharacteristic
281C2×C7#55311yescharacteristic
282C2×C7#55311yescharacteristic
283C2×C7#55911yescharacteristic
284D7—81no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—141no—
292C23—141no—
293C23—141no—
294C23—141no—
295C23—141no—
296C23—141no—
297C23—141no—
298C23#115712yes—
299C23C23×D711yescharacteristic
300D4—284no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—44no—
318C2×C4—72no—
319C2×C4—72no—
320C2×C4—141no—
321C2×C4—141no—
322C2×C4—141no—
323C2×C4—141no—
324C2×C4—141no—
325C2×C4—141no—
326C2×C4—141no—
327C2×C4—141no—
328C2×C4—141no—
329C2×C4—141no—
330C2×C4—141no—
331C2×C4—141no—
332C2×C4—141no—
333C2×C4—141no—
334C2×C4—141no—
335C2×C4—141no—
336C2×C4—141no—
337C2×C4—141no—
338C2×C4—141no—
339C2×C4#115712yes—
340C2×C4#115712yes—
341C7#259711yescharacteristic, complemented, Sylow
342C22—22no—
343C22—22no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—281no—
350C22—281no—
351C22—281no—
352C22—281no—
353C22—281no—
354C22—281no—
355C22—281no—
356C22C2×#115711yescharacteristic
357C22C2×#115711yescharacteristic
358C22C2×#115711yescharacteristic
359C22#654811yescharacteristic
360C22#654811yescharacteristic
361C22D7×#4111yescharacteristic
362C22D7×#4111yescharacteristic
363C4—22no—
364C4—22no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—142no—
370C4—142no—
371C4—281no—
372C4—281no—
373C4—281no—
374C4—281no—
375C4—281no—
376C2—42no—
377C2—561no—
378C2#9017011yescharacteristic
379C2#9018511yescharacteristic
380C2#9021911yescharacteristic
381C2#9023111yescharacteristic
382C2#9023111yescharacteristic
383C2#9024711yescharacteristic
384C2#9025011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D7
commutator, socle, cosocleC23×C7C24
FittingC4×C7×C22⋊C4C2
prime radicalC22×C22⋊D7C22
hypercenterC4×C22⋊C4D7
hypocenterC7#2597
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C4×C7×C22⋊C4C2semidirect
3. #89982C2semidirect
6. #89724C2semidirect
7. #89717C2semidirect
8. #89712C2semidirect
9. #89712C2semidirect
10. #89705C2semidirect
11. C4×Dic7⋊C4C2semidirect
12. #89447C2semidirect
13. #89441C2semidirect
14. #89430C2semidirect
15. #89424C2semidirect
108. C4×C22⋊C4D7semidirect
341. C7#2597semidirect

Maximal subgroups

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

subgroupindex
C4×C7×C22⋊C42
#899852
#899822
#897312
#897292
#897242
#897172
#897122
#897052
C4×Dic7⋊C42
#894472
#894412
#894302
#894242
#25977