Finite Group Databasebeta

← #11732928

Subgroups — #11732928

Order 896.

560 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6448C211yesmaximal, characteristic
2C7×#388C211yesmaximal, characteristic, complemented
3#89762C211yesmaximal, characteristic, complemented
4#89746C211yesmaximal, characteristic, complemented
5#89730C211yesmaximal, characteristic
6#89728C211yesmaximal, characteristic
7#89717C211yesmaximal, characteristic, complemented
8C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
10C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
11#89704C211yesmaximal, characteristic, complemented
12#89441C211yesmaximal, characteristic, complemented
13#89438C211yesmaximal, characteristic, complemented
14#89420C211yesmaximal, characteristic, complemented
15#89418C211yesmaximal, characteristic, complemented
16C22×C22⋊D7C2211yescharacteristic
17C23×Dic7C2211yescharacteristic
18C22×C4×D7C2211yescharacteristic
19C22×Dic14C2211yescharacteristic
20C2×C7×C4⋊C4C2211yescharacteristic
21C2×C7×C22⋊C4C2211yescharacteristic
22C2×C7×C22⋊C4C2211yescharacteristic
23C2×C7×C22⋊C4C2211yescharacteristic
24C2×C42×C7C2211yescharacteristic
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×Dic7⋊C4C2211yescharacteristic
33C2×C4×Dic7C2211yescharacteristic
34C2×C4×Dic7C2211yescharacteristic
35C2×C4×Dic7C2211yescharacteristic
36C2×C4×Dic7C2211yescharacteristic
37C2×C4×Dic7C2211yescharacteristic
38C2×C4×Dic7C2211yescharacteristic
39#6448C418yescomplemented
40C7×#95C2211yescharacteristic
41C7×#95C2211yescharacteristic
42C7⋊#95C2211yescharacteristic
43C7⋊#95C2211yescharacteristic
44C7⋊#95C2211yescharacteristic
45C7⋊#95C2211yescharacteristic
46C7⋊#95C2211yescharacteristic
47C7⋊#95C2211yescharacteristic
48C7⋊#95C2211yescharacteristic
49C7⋊#95C2211yescharacteristic
50C7⋊#95C2211yescharacteristic
51C7⋊#95C2211yescharacteristic
52#2372—71nomaximal, Sylow
53C24×C7C2311yescharacteristic
54C23×D7C2311yescharacteristic
55C22×C4×C7C2311yescharacteristic
56C22×C4×C7C2311yescharacteristic
57C22×C4×C7C2311yescharacteristic
58C22×C4×C7C2311yescharacteristic
59C22×C4×C7C2311yescharacteristic
60C22×C4×C7C2311yescharacteristic
61C2×C22⋊D7—41no—
62C2×C22⋊D7—41no—
63C2×C22⋊D7C2×C414yes—
64C22×Dic7—22no—
65C22×Dic7—22no—
66C22×Dic7—41no—
67C22×Dic7C2311yescharacteristic
68C22×Dic7C2311yescharacteristic
69C22×Dic7C2311yescharacteristic
70C22×Dic7C2311yescharacteristic
71C22×Dic7C2311yescharacteristic
72C22×Dic7C2311yescharacteristic
73C22×Dic7C2311yescharacteristic
74C2×C4×D7—22no—
75C2×C4×D7—22no—
76C2×C4×D7—41no—
77C2×Dic14—41no—
78C2×Dic14—41no—
79C2×Dic14C2×C414yescomplemented
80C7×C4⋊C4—41no—
81C7×C22⋊C4—22no—
82C7×C22⋊C4—41no—
83C7×C22⋊C4C2×C414yescomplemented
84C42×C7—22no—
85C22⋊Dic7—22no—
86C22⋊Dic7C2×C414yescomplemented
87(C2×D7)⋊C4—22no—
88(C2×D7)⋊C4—22no—
89(C2×D7)⋊C4—41no—
90(C2×D7)⋊C4C2×C414yescomplemented
91(C2×D7)⋊C4C2×C414yescomplemented
92Dic7⋊C4—41no—
93C4×Dic7—22no—
94C4×Dic7—22no—
95C4×Dic7—22no—
96C4×Dic7—41no—
97C4×Dic7—41no—
98C4×Dic7C2×C414yescomplemented
99C2×#124—71no—
100#391—71no—
101#391—71no—
102#388—71no—
103#388—71no—
104#388—71no—
105#388D711yescharacteristic, complemented
106#386—71no—
107#386—71no—
108C4×C22⋊C4—71no—
109C4×C22⋊C4—71no—
110C4×C22⋊C4—71no—
111C4×C22⋊C4—71no—
112#376—71no—
113#376—71no—
114C23×C7—21no—
115C23×C7—21no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7C22×C412yes—
121C23×C7C2411yescharacteristic
122C22×D7—21no—
123C22×D7—21no—
124C22×D7—21no—
125C22×D7—21no—
126C22×D7—21no—
127C22×D7—21no—
128C22×D7C22×C412yes—
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—21no—
141C2×C4×C7—21no—
142C2×C4×C7—21no—
143C2×C4×C7—21no—
144C2×C4×C7C22×C412yes—
145C2×C4×C7C22×C412yes—
146C2×C4×C7#4112yes—
147C22⋊D7—44no—
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—44no—
164C2×Dic7C22×C412yes—
165C2×Dic7C22×C412yes—
166C2×Dic7C22×C412yes—
167C2×Dic7#4112yes—
168C2×Dic7#4112yes—
169C2×Dic7#4112yes—
170C4×D7—44no—
171Dic14—44no—
172C22×Q8—71no—
173C22×D4—71no—
174C23×C4—71no—
175C23×C4—71no—
176#124—78no—
177C2×C4⋊C4—71no—
178C2×C4⋊C4C2×D711yescharacteristic
179C2×C22⋊C4—71no—
180C2×C22⋊C4—71no—
181C2×C22⋊C4—71no—
182C2×C22⋊C4—71no—
183C2×C22⋊C4—71no—
184C2×C22⋊C4—71no—
185C2×C22⋊C4—71no—
186C2×C22⋊C4C2×D711yescharacteristic
187C2×C22⋊C4C2×D711yescharacteristic
188C2×C22⋊C4C2×D711yescharacteristic
189C2×C42—71no—
190C2×C42—71no—
191C2×C42—71no—
192C2×C42—71no—
193C2×C42—71no—
194C2×C42—71no—
195C2×C42C2×D711yescharacteristic
196#95—71no—
197#95—71no—
198#95—71no—
199#95—71no—
200#95—71no—
201#95—71no—
202#95—71no—
203#95—71no—
204#95—71no—
205#95—71no—
206#95C2×D711yescharacteristic
207#95C2×D711yescharacteristic
208C22×C7—22no—
209C22×C7—22no—
210C22×C7—22no—
211C22×C7—41no—
212C22×C7—41no—
213C22×C7—41no—
214C22×C7—41no—
215C22×C7C23×C411yescharacteristic
216C22×C7C2×#4111yescharacteristic
217C22×C7C2×#4111yescharacteristic
218C22×C7C2×#4111yescharacteristic
219C22×C7C2×#4111yescharacteristic
220C22×C7H(5,𝔽2)11yescharacteristic
221C22×C7H(5,𝔽2)11yescharacteristic
222C2×D7—22no—
223C2×D7—22no—
224C2×D7—22no—
225C2×D7—41no—
226C2×D7—41no—
227C2×D7—41no—
228C2×D7—41no—
229C4×C7—22no—
230C4×C7—22no—
231C4×C7—22no—
232C4×C7—41no—
233C4×C7—41no—
234C4×C7—41no—
235Dic7—22no—
236Dic7—22no—
237Dic7—22no—
238Dic7—22no—
239Dic7—22no—
240Dic7—22no—
241Dic7—41no—
242C24—71no—
243C24C22×D711yescharacteristic
244C2×Q8—74no—
245C2×Q8—281no—
246C2×Q8—281no—
247C2×D4—74no—
248C2×D4—281no—
249C2×D4—281no—
250C22×C4—71no—
251C22×C4—71no—
252C22×C4—71no—
253C22×C4—71no—
254C22×C4—71no—
255C22×C4—71no—
256C22×C4—71no—
257C22×C4—142no—
258C22×C4—142no—
259C22×C4—142no—
260C22×C4—142no—
261C22×C4—281no—
262C22×C4—281no—
263C22×C4C22×D711yescharacteristic
264C22×C4C22×D711yescharacteristic
265C22×C4C22×D711yescharacteristic
266C22×C4C22×D711yescharacteristic
267C22×C4C22×D711yescharacteristic
268C22×C4C22×D711yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—281no—
271C22⋊C4—22no—
272C22⋊C4—41no—
273C22⋊C4—74no—
274C22⋊C4—74no—
275C22⋊C4—74no—
276C22⋊C4—142no—
277C22⋊C4—142no—
278C22⋊C4—142no—
279C22⋊C4—281no—
280C22⋊C4C4×D714yescomplemented
281C42—22no—
282C42—74no—
283C42—142no—
284C42—142no—
285C42—142no—
286C42—281no—
287C42—281no—
288C2×C7—42no—
289C2×C7C4×#4111yescharacteristic
290C2×C7C4×#4111yescharacteristic
291C2×C7#51811yescharacteristic
292C2×C7#55111yescharacteristic
293C2×C7#55111yescharacteristic
294C2×C7#55511yescharacteristic
295C2×C7#55511yescharacteristic
296D7—42no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—72no—
304C23—141no—
305C23—141no—
306C23—141no—
307C23—141no—
308C23—141no—
309C23—141no—
310C23C2×C4×D712yes—
311C23C23×D711yescharacteristic
312Q8—284no—
313D4—284no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—72no—
330C2×C4—72no—
331C2×C4—72no—
332C2×C4—72no—
333C2×C4—72no—
334C2×C4—72no—
335C2×C4—141no—
336C2×C4—141no—
337C2×C4—141no—
338C2×C4—141no—
339C2×C4—141no—
340C2×C4—141no—
341C2×C4—141no—
342C2×C4—141no—
343C2×C4—141no—
344C2×C4—141no—
345C2×C4—141no—
346C2×C4—141no—
347C2×C4—141no—
348C2×C4—141no—
349C2×C4—141no—
350C2×C4—284no—
351C2×C4—284no—
352C2×C4C2×C4×D712yes—
353C2×C4C2×C4×D712yes—
354C2×C4#115912yes—
355C7#237211yescharacteristic, complemented, Sylow
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—142no—
364C22—142no—
365C22—142no—
366C22—281no—
367C22—281no—
368C22—281no—
369C22—281no—
370C22C22×C4×D711yescharacteristic
371C22C2×#115911yescharacteristic
372C22#654811yescharacteristic
373C22D7×#4111yescharacteristic
374C22D7×#4111yescharacteristic
375C22D7×#4111yescharacteristic
376C22#655311yescharacteristic
377C4—22no—
378C4—22no—
379C4—22no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—142no—
384C4—142no—
385C4—142no—
386C4—142no—
387C4—142no—
388C4—142no—
389C4—281no—
390C2—42no—
391C2—282no—
392C2#9021311yescharacteristic
393C2C4×#115911yescharacteristic
394C2#9023611yescharacteristic
395C2#9030711yescharacteristic
396C2#9034911yescharacteristic
397C2#9036111yescharacteristic
398C2#9039611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D7
commutatorC22×C7C23×C4
FittingC7×#388C2
socle, cosocleC23×C7C24
prime radicalC22×C22⋊D7C22
hypercenter#388D7
hypocenterC7#2372
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C7×#388C2semidirect
3. #89762C2semidirect
4. #89746C2semidirect
7. #89717C2semidirect
8. C22⋊C4×Dic7C2semidirect
9. C22⋊C4×Dic7C2semidirect
10. C4×(C2×D7)⋊C4C2semidirect
11. #89704C2semidirect
12. #89441C2semidirect
13. #89438C2semidirect
14. #89420C2semidirect
15. #89418C2semidirect
39. #6448C4semidirect
79. C2×Dic14C2×C4semidirect
83. C7×C22⋊C4C2×C4semidirect
86. C22⋊Dic7C2×C4semidirect
90. (C2×D7)⋊C4C2×C4semidirect
91. (C2×D7)⋊C4C2×C4semidirect
98. C4×Dic7C2×C4semidirect
105. #388D7semidirect
280. C22⋊C4C4×D7semidirect
355. C7#2372semidirect

Maximal subgroups

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

subgroupindex
C2×#64482
C7×#3882
#897622
#897462
#897302
#897282
#897172
C22⋊C4×Dic72
C4×(C2×D7)⋊C42
#897042
#894412
#894382
#894202
#894182
#23727