Finite Group Databasebeta

← D97⋊#435 #27158444

Subgroups — D97⋊#435 #27158444

Order 12416.

564 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D97⋊M16C211yesmaximal, characteristic, complemented
2C22×#13095519C211yesmaximal, characteristic, complemented
3#20261767C212yesmaximal, complemented
4#20261766C212yesmaximal, complemented
5#20261765C212yesmaximal, complemented
6#20261764C212yesmaximal, complemented
7#20261736C211yesmaximal, characteristic, complemented
8#20261703C211yesmaximal, characteristic, complemented
9#20261703C211yesmaximal, characteristic, complemented
10#20261694C211yesmaximal, characteristic, complemented
11C4×D4×D97C211yesmaximal, characteristic
12C2×#13095521C2212yescomplemented
13D97⋊M16—24no—
14C2×#13095520C2212yescomplemented
15C2×#13095519—24no—
16C2×#13095519C2211yescharacteristic
17C2×#13095519C2211yescharacteristic
18C2×#13095519C2211yescharacteristic
19C2×#13095519C2211yescharacteristic
20C2×#13095519C2212yescomplemented
21C22×#11715897C2212yescomplemented
22#15690877C2212yescomplemented
23C4⋊#11715897C2212yescomplemented
24#15690867C2212yescomplemented
25#15690867C2212yescomplemented
26C22⋊#11715897C2212yescomplemented
27C22⋊#11715897C2212yescomplemented
28#15690865C2212yescomplemented
29#15690865C2212yescomplemented
30C2×D4×D97C411yescharacteristic
31C22×C4×D97C2211yescharacteristic
32C22×C4×D97C2211yescharacteristic
33C4×D388C411yescharacteristic
34D4×Dic97C2211yescharacteristic
35#15690772C2211yescharacteristic
36C4×C22⋊D97C411yescharacteristic
37C4×C22⋊D97C411yescharacteristic
38#15690770C2211yescharacteristic
39#15690770C2211yescharacteristic
40C4⋊C4×D97C411yescharacteristic
41C22⋊C4×D97C411yescharacteristic
42C22⋊C4×D97C411yescharacteristic
43C42×D97C2211yescharacteristic
44C4×D4×C97C411yescharacteristic
45#13095521—24no—
46#13095520—24no—
47#13095519—22no—
48#13095519—22no—
49#13095519—22no—
50#13095519—24no—
51#13095519D414yescomplemented
52C2×#11715897—24no—
53C2×#11715897C2312yes—
54C2×#11715897C2312yes—
55C2×#11715897C2312yes—
56C2×#11715897C2312yes—
57C23×D97C2×C411yescharacteristic
58C23×D97C2×C411yescharacteristic
59C2×D388C2×C411yescharacteristic
60C2×C22⋊D97C2×C411yescharacteristic
61C2×C22⋊D97C2×C411yescharacteristic
62D4×D97—24no—
63C22×Dic97C2311yescharacteristic
64C22×Dic97C2311yescharacteristic
65C2×C4×D97—22no—
66C2×C4×D97—22no—
67C2×C4×D97—22no—
68C2×C4×D97—22no—
69C2×C4×D97C2×C411yescharacteristic
70C2×C4×D97C2×C411yescharacteristic
71C2×C4×D97C2×C411yescharacteristic
72C2×C4×D97C2×C411yescharacteristic
73C2×C4×D97C2×C411yescharacteristic
74C2×C4×D97C2×C411yescharacteristic
75C2×C4×D97C2311yescharacteristic
76C2×C4×D97C2311yescharacteristic
77C2×C4×D97C2311yescharacteristic
78C4⋊Dic97C2×C411yescharacteristic
79#13095490C2×C411yescharacteristic
80#13095490C2×C411yescharacteristic
81C22⋊Dic97C2×C411yescharacteristic
82C22⋊Dic97C2×C411yescharacteristic
83#13095488C2×C411yescharacteristic
84#13095488C2×C411yescharacteristic
85#13095488C2×C411yescharacteristic
86#13095488C2×C411yescharacteristic
87C4×Dic97C2×C411yescharacteristic
88C4×Dic97C2311yescharacteristic
89C4×Dic97C2311yescharacteristic
90C2×D4×C97C2×C411yescharacteristic
91C22×C4×C97C2×C411yescharacteristic
92C22×C4×C97C2×C411yescharacteristic
93C4⋊C4×C97C2×C411yescharacteristic
94C22⋊C4×C97C2×C411yescharacteristic
95C22⋊C4×C97C2×C411yescharacteristic
96C42×C97C2×C411yescharacteristic
97C23×C97C22×C411yescharacteristic
98C23×C97C22×C411yescharacteristic
99C22×D97—22no—
100C22×D97—22no—
101C22×D97—22no—
102C22×D97—22no—
103C22×D97—22no—
104C22×D97M1614yescomplemented
105C22×D97C22×C411yescharacteristic
106C22×D97C22×C411yescharacteristic
107C22×D97C22×C411yescharacteristic
108D4×C97—22no—
109C2×C4×C97—22no—
110C2×C4×C97—22no—
111C2×C4×C97C22×C411yescharacteristic
112C2×C4×C97C22×C411yescharacteristic
113C2×C4×C97C22×C411yescharacteristic
114C2×C4×C97C22×C411yescharacteristic
115C2×C4×C97C22×C411yescharacteristic
116C22⋊D97—22no—
117C22⋊D97—22no—
118C2×Dic97—21no—
119C2×Dic97—21no—
120C2×Dic97—21no—
121C2×Dic97—21no—
122C2×Dic97C22×C411yescharacteristic
123C2×Dic97C22×C411yescharacteristic
124C2×Dic97C22×C411yescharacteristic
125C2×Dic97C22×C411yescharacteristic
126C2×Dic97C2411yescharacteristic
127D388—22no—
128C4×D97—22no—
129C4×D97—22no—
130C4×D97—22no—
131C4×D97—22no—
132C4×D97—22no—
133C4×D97—22no—
134C4×D97—21no—
135C4×D97—21no—
136C4×D97—21no—
137C4×D97—21no—
138C4×D97C2×D412yes—
139C4×D97#4112yes—
140#11715897—22no—
141#11715897—22no—
142#11715897—22no—
143#11715897C2×D414yescomplemented
144C22×C97—21no—
145C22×C97—21no—
146C22×C97—21no—
147C22×C97—21no—
148C22×C97—21no—
149C22×C97C2×M1612yescomplemented
150C22×C97C23×C411yescharacteristic
151C2×D97—21no—
152C2×D97—21no—
153C2×D97—28no—
154C2×D97—21no—
155C2×D97—21no—
156C2×D97—21no—
157C2×D97—44no—
158C2×D97C4×D412yes—
159C2×D97C2×M1612yes—
160C2×D97C2×M1612yescomplemented
161C2×D97#13112yes—
162C4×C97—21no—
163C4×C97—21no—
164C4×C97—21no—
165C4×C97—21no—
166C4×C97C4×D412yes—
167Dic97—21no—
168Dic97—21no—
169Dic97—21no—
170Dic97—21no—
171Dic97C22×D411yescharacteristic
172Dic97C2×#4111yescharacteristic
173C2×C97—22no—
174C2×C97—41no—
175C2×C97C2×C4×D411yescharacteristic
176C2×C97C22×M1611yescharacteristic
177C2×C97C2×#13111yescharacteristic
178D97—22no—
179D97—41no—
180D97#43514yescomplemented
181C2×#435—971nomaximal, Sylow
182C97C2×#43511yescharacteristic, complemented, Sylow
183C22×M16—971no—
184C23×C8—971no—
185C2×C4×D4—971no—
186#435—972no—
187#435—972no—
188#435—972no—
189#435—972no—
190C2×C4⋊C8—971no—
191C2×C22⋊C8—971no—
192C2×C22⋊C8—971no—
193C2×#97—971no—
194C22×D4—971no—
195C23×C4—971no—
196C23×C4—971no—
197C2×M16—972no—
198C2×M16—972no—
199C2×M16—1944no—
200C22×C8—971no—
201C22×C8—972no—
202C22×C8—971no—
203C22×C8—972no—
204C22×C8—971no—
205C22×C8—971no—
206C22×C8—1944no—
207C4×D4—971no—
208C4×D4—971no—
209C4×D4—971no—
210C4×D4—971no—
211C4×D4—971no—
212C4×D4—971no—
213C4×D4—971no—
214C4×D4#8760411yescharacteristic
215C2×C4⋊C4—971no—
216C2×C22⋊C4—971no—
217C2×C22⋊C4—971no—
218C2×C42—971no—
219C4⋊C8—972no—
220C4⋊C8—972no—
221C22⋊C8—972no—
222C22⋊C8—972no—
223C22⋊C8—972no—
224C22⋊C8—972no—
225#97—972no—
226#97—972no—
227C24—971no—
228C24—971no—
229C2×D4—971no—
230C2×D4—971no—
231C2×D4—971no—
232C2×D4—1944no—
233C2×D4C2×#8760411yescharacteristic
234C22×C4—971no—
235C22×C4—971no—
236C22×C4—971no—
237C22×C4—971no—
238C22×C4—971no—
239C22×C4—971no—
240C22×C4—971no—
241C22×C4—971no—
242C22×C4—971no—
243C22×C4—971no—
244C22×C4—971no—
245C22×C4—1942no—
246C22×C4—1942no—
247C22×C4—1942no—
248C22×C4—1942no—
249C22×C4C2×#8760411yescharacteristic
250C22×C4C2×#8760411yescharacteristic
251M16—1944no—
252M16—1944no—
253C2×C8—972no—
254C2×C8—974no—
255C2×C8—972no—
256C2×C8—972no—
257C2×C8—972no—
258C2×C8—1944no—
259C2×C8—1944no—
260C2×C8—1942no—
261C2×C8—1942no—
262C2×C8—1942no—
263C4⋊C4—971no—
264C4⋊C4—971no—
265C4⋊C4—971no—
266C4⋊C4C2×#8760411yescharacteristic
267C22⋊C4—971no—
268C22⋊C4—971no—
269C22⋊C4—971no—
270C22⋊C4—971no—
271C22⋊C4—971no—
272C22⋊C4—971no—
273C22⋊C4C2×#8760411yescharacteristic
274C22⋊C4C2×#8760411yescharacteristic
275C42—971no—
276C42—971no—
277C42—971no—
278C42C2×#8760411yescharacteristic
279C23—971no—
280C23—974no—
281C23—971no—
282C23—971no—
283C23—1942no—
284C23—1942no—
285C23—1942no—
286C23—1942no—
287C23—1942no—
288C23C22×#8760411yescharacteristic
289C23C22×#8760411yescharacteristic
290D4—22no—
291D4—1942no—
292D4—1942no—
293D4—1942no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—971no—
297C2×C4—972no—
298C2×C4—972no—
299C2×C4—971no—
300C2×C4—971no—
301C2×C4—971no—
302C2×C4—971no—
303C2×C4—1941no—
304C2×C4—1941no—
305C2×C4—1941no—
306C2×C4—1941no—
307C2×C4—1942no—
308C2×C4—1942no—
309C2×C4—1942no—
310C2×C4—1942no—
311C2×C4—1941no—
312C2×C4—1941no—
313C2×C4—1941no—
314C2×C4—1941no—
315C2×C4—1942no—
316C2×C4—1942no—
317C2×C4C22×#8760411yescharacteristic
318C2×C4C22×#8760411yescharacteristic
319C2×C4C22×#8760411yescharacteristic
320C2×C4C22×#8760411yescharacteristic
321C2×C4C22×#8760411yescharacteristic
322C8—974no—
323C8—1942no—
324C8—1942no—
325C8—1942no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—972no—
332C22—972no—
333C22—972no—
334C22—972no—
335C22—3884no—
336C22—1948no—
337C22—1941no—
338C22—1941no—
339C22—1941no—
340C22—1941no—
341C22—1941no—
342C22D97⋊M1612yescomplemented
343C22C23×#8760411yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—971no—
349C4—971no—
350C4—1941no—
351C4—1941no—
352C4—1941no—
353C4—1941no—
354C4D4×#8760412yes—
355C2—22no—
356C2—41no—
357C2—974no—
358C2—3881no—
359C2—1942no—
360C2C2×D4×#8760411yescharacteristic
361C2C2×D97⋊M1611yescharacteristic
362C2D97⋊#13111yescharacteristic
subgroupG/H
centerC2×C4C22×#87604
commutator, socleC22×C97C23×C4
FrattiniC22C23×#87604
FittingC4×D4×C97C4
prime radicalC2×D4×D97C4
cosocleC2×Dic97C24
hypercenterC4×D4#87604
hypocenterC97C2×#435
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×D97⋊M16C2semidirect
2. C22×#13095519C2semidirect
3. #20261767C2semidirect
4. #20261766C2semidirect
5. #20261765C2semidirect
6. #20261764C2semidirect
7. #20261736C2semidirect
8. #20261703C2semidirect
9. #20261703C2semidirect
10. #20261694C2semidirect
12. C2×#13095521C22semidirect
14. C2×#13095520C22semidirect
20. C2×#13095519C22semidirect
21. C22×#11715897C22semidirect
22. #15690877C22semidirect
23. C4⋊#11715897C22semidirect
24. #15690867C22semidirect
25. #15690867C22semidirect
26. C22⋊#11715897C22semidirect
27. C22⋊#11715897C22semidirect
28. #15690865C22semidirect
29. #15690865C22semidirect
51. #13095519D4semidirect
104. C22×D97M16semidirect
143. #11715897C2×D4semidirect
149. C22×C97C2×M16semidirect
160. C2×D97C2×M16semidirect
180. D97#435semidirect
182. C97C2×#435semidirect
342. C22D97⋊M16semidirect

Maximal subgroups

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

subgroupindex
C2×D97⋊M162
C22×#130955192
#202617672
#202617662
#202617652
#202617642
#202617362
#202617032
#202616942
C4×D4×D972
C2×#43597