Finite Group Databasebeta

← #11736829

Subgroups — #11736829

Order 896.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#90226C211yesmaximal, characteristic, complemented
2#90214C211yesmaximal, characteristic, complemented
3C7×#433C211yesmaximal, characteristic, complemented
4#89620C211yesmaximal, characteristic, complemented
5#89619C211yesmaximal, characteristic, complemented
6#89615C211yesmaximal, characteristic, complemented
7#89601C211yesmaximal, characteristic, complemented
8#89508C211yesmaximal, characteristic, complemented
9#89507C211yesmaximal, characteristic, complemented
10#89506C211yesmaximal, characteristic, complemented
11#89506C211yesmaximal, characteristic, complemented
12#89483C211yesmaximal, characteristic, complemented
13#89482C211yesmaximal, characteristic, complemented
14C4×D56C211yesmaximal, characteristic, complemented
15C4×#1132C211yesmaximal, characteristic, complemented
16C2×#1157C2211yescharacteristic
17C7×#117C2211yescharacteristic
18#6493C2211yescharacteristic
19#6493C2211yescharacteristic
20C2×C4⋊Dic7C2211yescharacteristic
21C2×D56C2211yescharacteristic
22C2×D56C2211yescharacteristic
23C2×#1132C2211yescharacteristic
24C2×#1132C2211yescharacteristic
25#6457—21no—
26#6457—21no—
27#6455—21no—
28D7×C4⋊C4—21no—
29#6447—21no—
30#6447—21no—
31(C22⋊D7)⋊C4—21no—
32(C22⋊D7)⋊C4—21no—
33#6437C2211yescharacteristic
34C4×D28C2211yescharacteristic
35C4×D28C2211yescharacteristic
36C4×D28C2211yescharacteristic
37C4×D28C2211yescharacteristic
38#6433C2211yescharacteristic
39C4×Dic14C2211yescharacteristic
40C4×Dic14C2211yescharacteristic
41C7×C4⋊C8C2211yescharacteristic
42C7×C4⋊C8C2211yescharacteristic
43C7×C22⋊C8C2211yescharacteristic
44C7×C22⋊C8C2211yescharacteristic
45C7×#97C2211yescharacteristic
46C4×C7×C8C2211yescharacteristic
47#6395C2211yescharacteristic
48#6395C2211yescharacteristic
49#6395C2211yescharacteristic
50#6395C2211yescharacteristic
51#6395C2211yescharacteristic
52#6395C2211yescharacteristic
53#6392C2211yescharacteristic
54#6392C2211yescharacteristic
55#6391C2211yescharacteristic
56#6391C2211yescharacteristic
57#6390C2211yescharacteristic
58#6390C2211yescharacteristic
59#3119—71nomaximal, Sylow
60C22×C4×C7C2311yescharacteristic
61C2×C22⋊D7—21no—
62C2×C22⋊D7—21no—
63C2×C22⋊D7—21no—
64C22×Dic7—21no—
65#1157—22no—
66#1157—22no—
67C2×D28—21no—
68C2×D28—21no—
69C2×D28C2311yescharacteristic
70C2×D28C2311yescharacteristic
71C2×D28C2311yescharacteristic
72C2×C4×D7—21no—
73C2×C4×D7—21no—
74C2×C4×D7—21no—
75C2×C4×D7—21no—
76C2×C4×D7—21no—
77C2×Dic14C2311yescharacteristic
78C2×C7×C8C2311yescharacteristic
79C2×C7×C8C2311yescharacteristic
80C2×C7×C8C2311yescharacteristic
81C2×C7×C8C2311yescharacteristic
82C7×C4⋊C4D411yescharacteristic
83C7×C4⋊C4D411yescharacteristic
84C7×C22⋊C4D411yescharacteristic
85C7×C22⋊C4D411yescharacteristic
86C42×C7C2311yescharacteristic
87C42×C7C2311yescharacteristic
88(C2×D7)⋊C4—21no—
89(C2×D7)⋊C4—21no—
90(C2×D7)⋊C4—21no—
91(C2×D7)⋊C4—21no—
92(C2×D7)⋊C4—21no—
93(C2×D7)⋊C4—21no—
94C4⋊Dic7—21no—
95C4⋊Dic7C2311yescharacteristic
96C4⋊Dic7C2311yescharacteristic
97C4⋊Dic7C2311yescharacteristic
98C4⋊Dic7C2311yescharacteristic
99Dic7⋊C4—21no—
100Dic7⋊C4—21no—
101Dic7⋊C4—21no—
102Dic7⋊C4—21no—
103C4×Dic7—21no—
104C4×Dic7—21no—
105D56—22no—
106D56—22no—
107#1132—22no—
108#1132—22no—
109#540—71no—
110#520—71no—
111#481—71no—
112#480—71no—
113#479—71no—
114#478—71no—
115#460—71no—
116#459—71no—
117#449—71no—
118#449—71no—
119#442—71no—
120#440—71no—
121C4×SD16—71no—
122C4×D8—71no—
123#433D711yescharacteristic, complemented
124C23×C7C2×D411yescharacteristic
125C22×D7—21no—
126C22×D7—21no—
127C22×D7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7C2×D411yescharacteristic
131C2×C4×C7C2×D411yescharacteristic
132C2×C4×C7C2×D411yescharacteristic
133C2×C4×C7C2×D411yescharacteristic
134C2×C4×C7C2×D411yescharacteristic
135C2×C4×C7C2411yescharacteristic
136C22⋊D7—24no—
137C22⋊D7—81no—
138C22⋊D7—81no—
139C2×Dic7—21no—
140C2×Dic7—21no—
141C2×Dic7—21no—
142C2×Dic7—21no—
143C2×Dic7—21no—
144C2×Dic7—81no—
145D28—21no—
146D28—21no—
147D28—21no—
148D28—21no—
149D28—21no—
150D28—81no—
151D28—81no—
152D28#4112yes—
153C4×D7—24no—
154C4×D7—81no—
155C4×D7—81no—
156C4×D7—81no—
157C4×D7—81no—
158Dic14—21no—
159Dic14#4112yes—
160C7×C8—21no—
161C7×C8—21no—
162C7×C8—21no—
163C7×C8—21no—
164C2×#41—71no—
165C2×SD16—71no—
166C2×SD16—71no—
167C2×D8—71no—
168C2×D8—71no—
169#127—71no—
170#125—71no—
171#123—141no—
172#123—141no—
173#121—71no—
174#121—71no—
175#121—141no—
176#121—141no—
177C4×Q8—71no—
178C4×Q8—71no—
179C4×D4—71no—
180C4×D4—71no—
181C4×D4—71no—
182C4×D4—71no—
183C4×D4—141no—
184C4×D4—141no—
185#117—141no—
186#117C2×D711yescharacteristic
187C2×C4⋊C4—71no—
188C2×C4⋊C4—141no—
189#107—71no—
190#107—71no—
191#106—71no—
192#106—71no—
193C4⋊C8C2×D711yescharacteristic
194C4⋊C8C2×D711yescharacteristic
195#103—71no—
196#103—71no—
197#102—71no—
198#102—71no—
199#102—71no—
200#102—71no—
201#102—71no—
202#102—71no—
203C22⋊C8C2×D711yescharacteristic
204C22⋊C8C2×D711yescharacteristic
205#97C2×D711yescharacteristic
206C4×C8C2×D711yescharacteristic
207C22×C7—21no—
208C22×C7—21no—
209C22×C7—21no—
210C22×C7C22×D411yescharacteristic
211C2×D7—22no—
212C2×D7—41no—
213C2×D7—41no—
214C2×D7—41no—
215C2×D7—41no—
216C2×D7—41no—
217C2×D7—41no—
218C2×D7—41no—
219C2×D7—41no—
220C4×C7—21no—
221C4×C7—21no—
222C4×C7—21no—
223C4×C7—21no—
224C4×C7—21no—
225C4×C7C2×#4111yescharacteristic
226C4×C7C2×#4111yescharacteristic
227Dic7—22no—
228Dic7—41no—
229Dic7—41no—
230Dic7—41no—
231Dic7—41no—
232#41—142no—
233#41—142no—
234C2×Q8—71no—
235C2×D4—71no—
236C2×D4—71no—
237C2×D4—71no—
238C2×D4—141no—
239C2×D4—141no—
240C2×D4—141no—
241C2×D4—141no—
242C2×D4—141no—
243C22×C4—141no—
244C22×C4—141no—
245C22×C4—141no—
246C22×C4—141no—
247C22×C4—141no—
248C22×C4—141no—
249C22×C4C22×D711yescharacteristic
250SD16—142no—
251SD16—142no—
252D8—142no—
253D8—142no—
254C2×C8C22×D711yescharacteristic
255C2×C8C22×D711yescharacteristic
256C2×C8C22×D711yescharacteristic
257C2×C8C22×D711yescharacteristic
258C4⋊C4—71no—
259C4⋊C4—71no—
260C4⋊C4—71no—
261C4⋊C4—71no—
262C4⋊C4—141no—
263C4⋊C4—141no—
264C4⋊C4—141no—
265C4⋊C4—141no—
266C4⋊C4—141no—
267C4⋊C4D2811yescharacteristic
268C4⋊C4D2811yescharacteristic
269C22⋊C4—141no—
270C22⋊C4—141no—
271C22⋊C4—141no—
272C22⋊C4—141no—
273C22⋊C4—141no—
274C22⋊C4—141no—
275C22⋊C4D2811yescharacteristic
276C22⋊C4D2811yescharacteristic
277C42—141no—
278C42—141no—
279C42C22×D711yescharacteristic
280C42C22×D711yescharacteristic
281C2×C7—41no—
282C2×C7#52511yescharacteristic
283C2×C7#57611yescharacteristic
284C2×C7#57711yescharacteristic
285D7—42no—
286D7—81no—
287D7—81no—
288C23—141no—
289C23—141no—
290C23—141no—
291C23C2×D2811yescharacteristic
292Q8—72no—
293Q8—141no—
294D4—72no—
295D4—144no—
296D4—141no—
297D4—141no—
298D4—141no—
299D4—141no—
300D4—141no—
301D4—561no—
302D4—561no—
303D4—561no—
304D4—561no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—144no—
308C2×C4—141no—
309C2×C4—141no—
310C2×C4—141no—
311C2×C4—141no—
312C2×C4—141no—
313C2×C4—561no—
314C2×C4—561no—
315C2×C4—561no—
316C2×C4—561no—
317C2×C4—561no—
318C2×C4C2×D2811yescharacteristic
319C2×C4C2×D2811yescharacteristic
320C2×C4C2×D2811yescharacteristic
321C2×C4C2×D2811yescharacteristic
322C2×C4C2×D2811yescharacteristic
323C2×C4C23×D711yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C7#311911yescharacteristic, complemented, Sylow
329C22—21no—
330C22—21no—
331C22—21no—
332C22—142no—
333C22—281no—
334C22—281no—
335C22—281no—
336C22—281no—
337C22—281no—
338C22—281no—
339C22—281no—
340C22—281no—
341C22C22×D2811yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—142no—
348C4—281no—
349C4—281no—
350C4—281no—
351C4—281no—
352C4D7×#4111yescharacteristic
353C4D7×#4111yescharacteristic
354C2—41no—
355C2—282no—
356C2—561no—
357C2—561no—
358C2#9021511yescharacteristic
359C2#9044211yescharacteristic
360C2#9044311yescharacteristic
subgroupG/H
centerC22C22×D28
commutator, cosocleC2×C4×C7C24
FrattiniC2×C4C23×D7
FittingC7×#433C2
socleC22×C7C22×D4
hypercenter#433D7
hypocenterC7#3119
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #90226C2semidirect
2. #90214C2semidirect
3. C7×#433C2semidirect
4. #89620C2semidirect
5. #89619C2semidirect
6. #89615C2semidirect
7. #89601C2semidirect
8. #89508C2semidirect
9. #89507C2semidirect
10. #89506C2semidirect
11. #89506C2semidirect
12. #89483C2semidirect
13. #89482C2semidirect
14. C4×D56C2semidirect
15. C4×#1132C2semidirect
123. #433D7semidirect
328. C7#3119semidirect

Maximal subgroups

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

subgroupindex
#902262
#902142
C7×#4332
#896202
#896192
#896152
#896012
#895082
#895072
#895062
#894832
#894822
C4×D562
C4×#11322
#31197