Finite Group Databasebeta

← C31×#9270 #21466029

Subgroups — C31×#9270 #21466029

Order 7936.

412 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3230C211yesmaximal, characteristic
2C31×#2962C211yesmaximal, characteristic
3C31×#1997C211yesmaximal, characteristic
4C31×#1550C211yesmaximal, characteristic
5C2×C31×#332C211yesmaximal, characteristic
6C31×#1301C211yesmaximal, characteristic
7C31×#1283C211yesmaximal, characteristic
8C31×#533C2211yescharacteristic
9C2×C31×C4⋊Q8C2211yescharacteristic
10C31×#500—21no—
11C31×#487—21no—
12C31×#484C414yes—
13C31×#477—22no—
14C31×#446—22no—
15C31×#446—21no—
16C8×Q8×C31—21no—
17C31×#431C2211yescharacteristic
18C31×#424—21no—
19C31×#423C2211yescharacteristic
20C2×C31×C4⋊C8C2211yescharacteristic
21C2×C31×C4⋊C8C2211yescharacteristic
22C31×#405—21no—
23C4×M16×C31C2211yescharacteristic
24C31×#343—21no—
25C31×#343—21no—
26C31×#333—21no—
27C31×#332—21no—
28C31×#332—21no—
29C31×#332—21no—
30C22×Q8×C31—21no—
31C2×M16×C31—21no—
32C2×M16×C31D411yescharacteristic
33C2×M16×C31D411yescharacteristic
34C22×C8×C31—21no—
35C22×C8×C31—21no—
36C31×C4⋊Q8—21no—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8D411yescharacteristic
41C31×C4⋊Q8D411yescharacteristic
42C31×#125—21no—
43C31×C22⋊Q8—21no—
44C31×C22⋊Q8C2×C412yes—
45C4×Q8×C31—21no—
46C4×Q8×C31D412yes—
47C31×#117—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31C2×C412yes—
50C2×C42×C31C2311yescharacteristic
51C31×#107—24no—
52C31×C4⋊C8—22no—
53C31×C4⋊C8—22no—
54C31×C4⋊C8—21no—
55C31×C4⋊C8—21no—
56C31×C4⋊C8—21no—
57C31×C4⋊C8—21no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8—21no—
60C31×C4⋊C8D411yescharacteristic
61C31×C4⋊C8D411yescharacteristic
62C31×#103—24no—
63C31×C22⋊C8C2×C412yes—
64C31×#97—22no—
65C31×#97—21no—
66C4×C8×C31—22no—
67C4×C8×C31—21no—
68C4×C8×C31—21no—
69C2×Q8×C31—21no—
70C2×Q8×C31—41no—
71C2×Q8×C31—41no—
72C2×Q8×C31—81no—
73C2×Q8×C31—81no—
74C2×Q8×C31C22⋊C412yes—
75C22×C4×C31—22no—
76C22×C4×C31C22×C411yescharacteristic
77C22×C4×C31C2×D411yescharacteristic
78C22×C4×C31#4111yescharacteristic
79M16×C31—21no—
80M16×C31—21no—
81M16×C31—21no—
82M16×C31—41no—
83M16×C31—41no—
84M16×C31Q1612yes—
85C2×C8×C31—21no—
86C2×C8×C31—22no—
87C2×C8×C31—21no—
88C2×C8×C31—21no—
89C2×C8×C31—21no—
90C2×C8×C31—41no—
91C2×C8×C31—41no—
92C2×C8×C31—41no—
93C2×C8×C31—41no—
94C2×C8×C31—81no—
95C4⋊C4×C31—22no—
96C4⋊C4×C31—21no—
97C4⋊C4×C31—21no—
98C4⋊C4×C31—21no—
99C4⋊C4×C31—22no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—22no—
102C4⋊C4×C31—41no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31C22⋊C412yes—
105C22⋊C4×C31—22no—
106C42×C31—22no—
107C42×C31C2×D411yescharacteristic
108C42×C31C2×D411yescharacteristic
109C42×C31C2×D411yescharacteristic
110C42×C31#4111yescharacteristic
111#9270C3111yesmaximal, characteristic, direct product factor, Sylow
112C23×C31C4×D411yescharacteristic
113Q8×C31—42no—
114Q8×C31—41no—
115Q8×C31—41no—
116Q8×C31—82no—
117Q8×C31—81no—
118Q8×C31—81no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—22no—
122C2×C4×C31—22no—
123C2×C4×C31—41no—
124C2×C4×C31—42no—
125C2×C4×C31—82no—
126C2×C4×C31C2×C22⋊C411yescharacteristic
127C2×C4×C31C4×D411yescharacteristic
128C2×C4×C31#12011yescharacteristic
129C2×C4×C31#12111yescharacteristic
130C2×C4×C31#12111yescharacteristic
131C2×C4×C31#12311yescharacteristic
132C2×C4×C31C2×Q1611yescharacteristic
133C2×C4×C31#13511yescharacteristic
134C2×C4×C31#13711yescharacteristic
135C2×C4×C31#13711yescharacteristic
136C8×C31—22no—
137C8×C31—42no—
138C8×C31—41no—
139C8×C31—41no—
140C8×C31—41no—
141C8×C31—81no—
142C8×C31—81no—
143#3230C2×C3111yescharacteristic
144#2962C2×C3111yescharacteristic
145#1997C2×C3111yescharacteristic
146#1550C2×C3111yescharacteristic
147C2×#332C2×C3111yescharacteristic
148#1301C2×C3111yescharacteristic
149#1283C2×C3111yescharacteristic
150C22×C31—21no—
151C22×C31—21no—
152C22×C31#38611yescharacteristic
153C22×C31C4×Q1611yescharacteristic
154C22×C31#44111yescharacteristic
155C4×C31—21no—
156C4×C31—21no—
157C4×C31—21no—
158C4×C31—42no—
159C4×C31—42no—
160C4×C31—82no—
161C4×C31#45111yescharacteristic
162C4×C31#45211yescharacteristic
163C4×C31#46211yescharacteristic
164C4×C31#46411yescharacteristic
165C4×C31#47111yescharacteristic
166C4×C31#47211yescharacteristic
167#533C22×C3111yescharacteristic
168C2×C4⋊Q8C22×C3111yescharacteristic
169#500—21no—
170#487—21no—
171#484C4×C3114yes—
172#477—22no—
173#446—22no—
174#446—21no—
175C8×Q8—21no—
176#431C22×C3111yescharacteristic
177#424—21no—
178#423C22×C3111yescharacteristic
179C2×C4⋊C8C22×C3111yescharacteristic
180C2×C4⋊C8C22×C3111yescharacteristic
181#405—21no—
182C4×M16C22×C3111yescharacteristic
183#343—21no—
184#343—21no—
185#333—21no—
186#332—21no—
187#332—21no—
188#332—21no—
189C2×C31—21no—
190C2×C31—21no—
191C2×C31#187811yescharacteristic
192C2×C31#190711yescharacteristic
193C2×C31#191511yescharacteristic
194C22×Q8—21no—
195C2×M16—21no—
196C2×M16D4×C3111yescharacteristic
197C2×M16D4×C3111yescharacteristic
198C22×C8—21no—
199C22×C8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8D4×C3111yescharacteristic
205C4⋊Q8D4×C3111yescharacteristic
206#125—21no—
207C22⋊Q8—21no—
208C22⋊Q8C2×C4×C3112yes—
209C4×Q8—21no—
210C4×Q8D4×C3112yes—
211#117—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×C4×C3112yes—
214C2×C42C23×C3111yescharacteristic
215#107—24no—
216C4⋊C8—22no—
217C4⋊C8—22no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8D4×C3111yescharacteristic
225C4⋊C8D4×C3111yescharacteristic
226#103—24no—
227C22⋊C8C2×C4×C3112yes—
228#97—22no—
229#97—21no—
230C4×C8—22no—
231C4×C8—21no—
232C4×C8—21no—
233C31#927011yescharacteristic, direct product factor, Sylow
234C2×Q8—21no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—81no—
238C2×Q8—81no—
239C2×Q8C22⋊C4×C3112yes—
240C22×C4—22no—
241C22×C4C22×C4×C3111yescharacteristic
242C22×C4C2×D4×C3111yescharacteristic
243C22×C4#41×C3111yescharacteristic
244M16—21no—
245M16—21no—
246M16—21no—
247M16—41no—
248M16—41no—
249M16Q16×C3112yes—
250C2×C8—21no—
251C2×C8—22no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—81no—
260C4⋊C4—22no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4C22⋊C4×C3112yes—
270C22⋊C4—22no—
271C42—22no—
272C42C2×D4×C3111yescharacteristic
273C42C2×D4×C3111yescharacteristic
274C42C2×D4×C3111yescharacteristic
275C42#41×C3111yescharacteristic
276C23C4×D4×C3111yescharacteristic
277Q8—42no—
278Q8—41no—
279Q8—41no—
280Q8—82no—
281Q8—81no—
282Q8—81no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—82no—
290C2×C4C2×C22⋊C4×C3111yescharacteristic
291C2×C4C4×D4×C3111yescharacteristic
292C2×C4C31×#12011yescharacteristic
293C2×C4C31×#12111yescharacteristic
294C2×C4C31×#12111yescharacteristic
295C2×C4C31×#12311yescharacteristic
296C2×C4C2×Q16×C3111yescharacteristic
297C2×C4C31×#13511yescharacteristic
298C2×C4C31×#13711yescharacteristic
299C2×C4C31×#13711yescharacteristic
300C8—22no—
301C8—42no—
302C8—41no—
303C8—41no—
304C8—41no—
305C8—81no—
306C8—81no—
307C22—21no—
308C22—21no—
309C22C31×#38611yescharacteristic
310C22C4×Q16×C3111yescharacteristic
311C22C31×#44111yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—42no—
317C4—82no—
318C4C31×#45111yescharacteristic
319C4C31×#45211yescharacteristic
320C4C31×#46211yescharacteristic
321C4C31×#46411yescharacteristic
322C4C31×#47111yescharacteristic
323C4C31×#47211yescharacteristic
324C2—21no—
325C2—21no—
326C2C31×#187811yescharacteristic
327C2C31×#190711yescharacteristic
328C2C31×#191511yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
111. #9270C31direct (N × H)
233. C31#9270direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32302
C31×#29622
C31×#19972
C31×#15502
C2×C31×#3322
C31×#13012
C31×#12832
#927031