Finite Group Databasebeta

← C31×#10083 #21466842

Subgroups — C31×#10083 #21466842

Order 7936.

526 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#491C211yesmaximal, characteristic, complemented
2C2×C31×#489C211yesmaximal, characteristic
3C31×#2820C211yesmaximal, characteristic
4C31×#1993C211yesmaximal, characteristic, complemented
5C2×C31×#330C211yesmaximal, characteristic, complemented
6C2×C31×#329C211yesmaximal, characteristic
7C31×#1295C211yesmaximal, characteristic, complemented
8C2×C31×C4⋊Q8C2211yescharacteristic
9C2×C31×#125C2211yescharacteristic
10C2×C31×#124C2211yescharacteristic
11C31×#491—22no—
12C31×#491—22no—
13C31×#489—22no—
14C31×#489—22no—
15C2×C31×#103—21no—
16C2×C31×#103—21no—
17C2×C31×#103—21no—
18C2×C31×#102—21no—
19C2×C31×#97C2211yescharacteristic
20C2×C31×#97C2211yescharacteristic
21C2×C31×#97C2211yescharacteristic
22C31×#399—21no—
23C31×#397—21no—
24C31×#396—22no—
25C31×#395—21no—
26C31×#394—21no—
27C31×#382C2211yescharacteristic
28C31×#340—22no—
29C31×#330—22no—
30C31×#329—22no—
31C22×Q8×C31—21no—
32C22×Q8×C31D411yescharacteristic
33C22×D4×C31D411yescharacteristic
34C22×C8×C31—21no—
35C22×C8×C31—21no—
36C22×C8×C31—21no—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8D412yes—
41C31×#125—21no—
42C31×#125—21no—
43C31×#125—21no—
44C31×#125—21no—
45C31×#124—21no—
46C31×#124—21no—
47C31×#124—21no—
48C31×#124—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31D411yescharacteristic
55C2×C4⋊C4×C31D411yescharacteristic
56C2×C4⋊C4×C31D412yes—
57C2×C22⋊C4×C31—21no—
58C2×C22⋊C4×C31—21no—
59C2×C22⋊C4×C31—22no—
60C2×C22⋊C4×C31—22no—
61C2×C42×C31C2311yescharacteristic
62C31×#103—24no—
63C31×#103—24no—
64C31×#103—24no—
65C31×#102—24no—
66C31×#97—21no—
67C31×#97—21no—
68C31×#97—21no—
69C31×#97—21no—
70C31×#97D412yes—
71C31×#97D412yes—
72C31×#95—22no—
73C31×#95—21no—
74C31×#95—21no—
75C24×C31—21no—
76C2×Q8×C31—21no—
77C2×Q8×C31—22no—
78C2×Q8×C31—21no—
79C2×Q8×C31—42no—
80C2×Q8×C31—44no—
81C2×Q8×C31—41no—
82C2×D4×C31—21no—
83C2×D4×C31—21no—
84C2×D4×C31—42no—
85C22×C4×C31—22no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—41no—
90C22×C4×C31C2×D411yescharacteristic
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2×D411yescharacteristic
93C2×C8×C31—22no—
94C2×C8×C31—22no—
95C2×C8×C31—22no—
96C2×C8×C31—42no—
97C2×C8×C31—41no—
98C2×C8×C31—42no—
99C2×C8×C31—41no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—21no—
103C4⋊C4×C31—22no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—42no—
107C4⋊C4×C31—41no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—82no—
114C22⋊C4×C31—41no—
115C22⋊C4×C31—41no—
116C22⋊C4×C31—41no—
117C22⋊C4×C31—41no—
118C22⋊C4×C31—82no—
119C22⋊C4×C31—82no—
120C42×C31C2×D411yescharacteristic
121C42×C31C2×D411yescharacteristic
122C42×C31C2×D411yescharacteristic
123C42×C31#4111yescharacteristic
124#10083C3111yesmaximal, characteristic, direct product factor, Sylow
125C23×C31—41no—
126C23×C31—42no—
127C23×C31—41no—
128C23×C31—42no—
129C23×C31—41no—
130C23×C31#12011yescharacteristic
131Q8×C31—44no—
132Q8×C31—42no—
133Q8×C31—81no—
134Q8×C31—82no—
135D4×C31—42no—
136D4×C31—81no—
137C2×C4×C31—22no—
138C2×C4×C31—21no—
139C2×C4×C31—22no—
140C2×C4×C31—21no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—42no—
145C2×C4×C31—42no—
146C2×C4×C31—41no—
147C2×C4×C31—42no—
148C2×C4×C31—42no—
149C2×C4×C31—42no—
150C2×C4×C31—42no—
151C2×C4×C31—41no—
152C2×C4×C31—82no—
153C2×C4×C31#12011yescharacteristic
154C2×C4×C31#12011yescharacteristic
155C2×C4×C31#12111yescharacteristic
156C2×C4×C31#12111yescharacteristic
157C2×C4×C31#12111yescharacteristic
158C2×C4×C31#12711yescharacteristic
159C8×C31—42no—
160C8×C31—42no—
161C8×C31—42no—
162C2×#491C2×C3111yescharacteristic, complemented
163C2×#489C2×C3111yescharacteristic
164#2820C2×C3111yescharacteristic
165#1993C2×C3111yescharacteristic, complemented
166C2×#330C2×C3111yescharacteristic, complemented
167C2×#329C2×C3111yescharacteristic
168#1295C2×C3111yescharacteristic, complemented
169C22×C31—82no—
170C22×C31—82no—
171C22×C31—81no—
172C22×C31—81no—
173C22×C31—81no—
174C22×C31#39211yescharacteristic
175C22×C31#45412yes—
176C22×C31#45511yescharacteristic
177C22×C31#45512yes—
178C22×C31#45611yescharacteristic
179C4×C31—21no—
180C4×C31—21no—
181C4×C31—21no—
182C4×C31—21no—
183C4×C31—21no—
184C4×C31—21no—
185C4×C31—82no—
186C4×C31—82no—
187C4×C31—81no—
188C4×C31—81no—
189C4×C31—81no—
190C2×C4⋊Q8C22×C3111yescharacteristic
191C2×#125C22×C3111yescharacteristic
192C2×#124C22×C3111yescharacteristic
193#491—22no—
194#491—22no—
195#489—22no—
196#489—22no—
197C2×#103—21no—
198C2×#103—21no—
199C2×#103—21no—
200C2×#102—21no—
201C2×#97C22×C3111yescharacteristic
202C2×#97C22×C3111yescharacteristic
203C2×#97C22×C3111yescharacteristic
204#399—21no—
205#397—21no—
206#396—22no—
207#395—21no—
208#394—21no—
209#382C22×C3111yescharacteristic
210#340—22no—
211#330—22no—
212#329—22no—
213C2×C31—161no—
214C2×C31#166212yes—
215C2×C31#166412yes—
216C2×C31#200311yescharacteristic
217C2×C31#200411yescharacteristic
218C2×C31#200711yescharacteristic
219C22×Q8—21no—
220C22×Q8D4×C3111yescharacteristic
221C22×D4D4×C3111yescharacteristic
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8D4×C3112yes—
229#125—21no—
230#125—21no—
231#125—21no—
232#125—21no—
233#124—21no—
234#124—21no—
235#124—21no—
236#124—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4D4×C3111yescharacteristic
243C2×C4⋊C4D4×C3111yescharacteristic
244C2×C4⋊C4D4×C3112yes—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—22no—
249C2×C42C23×C3111yescharacteristic
250#103—24no—
251#103—24no—
252#103—24no—
253#102—24no—
254#97—21no—
255#97—21no—
256#97—21no—
257#97—21no—
258#97D4×C3112yes—
259#97D4×C3112yes—
260#95—22no—
261#95—21no—
262#95—21no—
263C31#1008311yescharacteristic, direct product factor, Sylow
264C24—21no—
265C2×Q8—21no—
266C2×Q8—22no—
267C2×Q8—21no—
268C2×Q8—42no—
269C2×Q8—44no—
270C2×Q8—41no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—42no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4C2×D4×C3111yescharacteristic
280C22×C4C2×D4×C3111yescharacteristic
281C22×C4C2×D4×C3111yescharacteristic
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—42no—
286C2×C8—41no—
287C2×C8—42no—
288C2×C8—41no—
289C4⋊C4—22no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—82no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—82no—
308C22⋊C4—82no—
309C42C2×D4×C3111yescharacteristic
310C42C2×D4×C3111yescharacteristic
311C42C2×D4×C3111yescharacteristic
312C42#41×C3111yescharacteristic
313C23—42no—
314C23—41no—
315C23—42no—
316C23—41no—
317C23—41no—
318C23C31×#12011yescharacteristic
319Q8—44no—
320Q8—42no—
321Q8—81no—
322Q8—82no—
323D4—42no—
324D4—81no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—82no—
341C2×C4C31×#12011yescharacteristic
342C2×C4C31×#12011yescharacteristic
343C2×C4C31×#12111yescharacteristic
344C2×C4C31×#12111yescharacteristic
345C2×C4C31×#12111yescharacteristic
346C2×C4C31×#12711yescharacteristic
347C8—42no—
348C8—42no—
349C8—42no—
350C22—82no—
351C22—82no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22C31×#39211yescharacteristic
356C22C31×#45412yes—
357C22C31×#45511yescharacteristic
358C22C31×#45512yes—
359C22C31×#45611yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—81no—
369C4—81no—
370C4—81no—
371C2—161no—
372C2C31×#166212yes—
373C2C31×#166412yes—
374C2C31×#200311yescharacteristic
375C2C31×#200411yescharacteristic
376C2C31×#200711yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#491C2semidirect
4. C31×#1993C2semidirect
5. C2×C31×#330C2semidirect
7. C31×#1295C2semidirect
124. #10083C31direct (N × H)
162. C2×#491C2×C31semidirect
165. #1993C2×C31semidirect
166. C2×#330C2×C31semidirect
168. #1295C2×C31semidirect
263. C31#10083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4912
C2×C31×#4892
C31×#28202
C31×#19932
C2×C31×#3302
C2×C31×#3292
C31×#12952
#1008331