Finite Group Databasebeta

← C31×#9937 #21466696

Subgroups — C31×#9937 #21466696

Order 7936.

526 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C31×#3195C211yesmaximal, characteristic
2C31×#3095C211yesmaximal, characteristic
3C31×#2625C211yesmaximal, characteristic
4C31×#1996C211yesmaximal, characteristic
5C31×#1826C211yesmaximal, characteristic
6C31×#1508C211yesmaximal, characteristic
7C31×#1305C211yesmaximal, characteristic
8C2×C31×C22⋊Q8C2211yescharacteristic
9C2×C31×C22⋊Q8C2211yescharacteristic
10C2×C31×#117C2211yescharacteristic
11C31×#485—22no—
12C31×#484—21no—
13C31×#483—21no—
14C31×#483—21no—
15C31×#483—21no—
16C31×#470—22no—
17C31×#451—21no—
18C31×#451—21no—
19C31×#428—21no—
20C31×#419—21no—
21C31×#407C2211yescharacteristic
22C31×#407C2211yescharacteristic
23C31×#400—21no—
24C31×#398—21no—
25C31×#397—22no—
26C31×#391—21no—
27C31×#389—21no—
28C31×#380C2211yescharacteristic
29C4×C22⋊C4×C31C2211yescharacteristic
30C31×#342—22no—
31C31×#339—22no—
32C31×#328—22no—
33C22×Q8×C31D411yescharacteristic
34C22×Q8×C31D411yescharacteristic
35C23×C4×C31C2311yescharacteristic
36C2×Q16×C31—22no—
37C2×M16×C31—21no—
38C2×M16×C31D412yes—
39C31×C22⋊Q8—21no—
40C31×C22⋊Q8—21no—
41C31×C22⋊Q8—21no—
42C31×C22⋊Q8—21no—
43C31×C22⋊Q8—21no—
44C31×C22⋊Q8—21no—
45C31×C22⋊Q8—21no—
46C31×C22⋊Q8—21no—
47C31×#117—21no—
48C31×#117—21no—
49C31×#117—21no—
50C31×#117—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31D411yescharacteristic
56C2×C4⋊C4×C31D411yescharacteristic
57C2×C4⋊C4×C31D411yescharacteristic
58C2×C4⋊C4×C31D411yescharacteristic
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—21no—
62C2×C22⋊C4×C31—21no—
63C2×C22⋊C4×C31D412yes—
64C2×C42×C31—21no—
65C2×C42×C31—21no—
66C31×#107—22no—
67C31×#106—22no—
68C31×#106—22no—
69C31×#103—22no—
70C31×#103—22no—
71C31×#103—22no—
72C31×#103—22no—
73C31×C22⋊C8—21no—
74C31×C22⋊C8—21no—
75C31×C22⋊C8—21no—
76C31×C22⋊C8D412yes—
77C31×#95—22no—
78C31×#95—22no—
79C31×#95—22no—
80C31×#95—21no—
81C31×#95—21no—
82C24×C31C2×D411yescharacteristic
83C2×Q8×C31—21no—
84C2×Q8×C31—21no—
85C2×Q8×C31—21no—
86C2×Q8×C31—21no—
87C2×Q8×C31—42no—
88C2×Q8×C31—42no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—22no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—42no—
97C22×C4×C31—41no—
98C22×C4×C31C2×D411yescharacteristic
99C22×C4×C31C2×D411yescharacteristic
100C22×C4×C31C2×D411yescharacteristic
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31C2×D411yescharacteristic
103C22×C4×C31#4111yescharacteristic
104Q16×C31—82no—
105M16×C31—42no—
106M16×C31—42no—
107C2×C8×C31—22no—
108C2×C8×C31—22no—
109C4⋊C4×C31—21no—
110C4⋊C4×C31—21no—
111C4⋊C4×C31—21no—
112C4⋊C4×C31—21no—
113C4⋊C4×C31—21no—
114C4⋊C4×C31—21no—
115C4⋊C4×C31—21no—
116C4⋊C4×C31—21no—
117C4⋊C4×C31—42no—
118C4⋊C4×C31—41no—
119C4⋊C4×C31—41no—
120C4⋊C4×C31—41no—
121C4⋊C4×C31—41no—
122C4⋊C4×C31—82no—
123C22⋊C4×C31—22no—
124C22⋊C4×C31—41no—
125C22⋊C4×C31—41no—
126C22⋊C4×C31—41no—
127C22⋊C4×C31—41no—
128C22⋊C4×C31—41no—
129C22⋊C4×C31—41no—
130C22⋊C4×C31—41no—
131C22⋊C4×C31—42no—
132C42×C31—42no—
133C42×C31—41no—
134C42×C31—41no—
135#9937C3111yesmaximal, characteristic, direct product factor, Sylow
136C23×C31—21no—
137C23×C31—21no—
138C23×C31—41no—
139C23×C31—41no—
140C23×C31#12011yescharacteristic
141C23×C31#12111yescharacteristic
142C23×C31#12711yescharacteristic
143Q8×C31—42no—
144Q8×C31—42no—
145Q8×C31—42no—
146Q8×C31—81no—
147C2×C4×C31—22no—
148C2×C4×C31—22no—
149C2×C4×C31—22no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—42no—
154C2×C4×C31—42no—
155C2×C4×C31—42no—
156C2×C4×C31—42no—
157C2×C4×C31—42no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31—41no—
162C2×C4×C31—41no—
163C2×C4×C31—41no—
164C2×C4×C31—42no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—41no—
168C2×C4×C31—41no—
169C2×C4×C31—81no—
170C2×C4×C31—81no—
171C2×C4×C31—81no—
172C2×C4×C31—81no—
173C2×C4×C31#12011yescharacteristic
174C2×C4×C31#12011yescharacteristic
175C2×C4×C31#12111yescharacteristic
176C2×C4×C31#12111yescharacteristic
177C8×C31—42no—
178C8×C31—42no—
179#3195C2×C3111yescharacteristic
180#3095C2×C3111yescharacteristic
181#2625C2×C3111yescharacteristic
182#1996C2×C3111yescharacteristic
183#1826C2×C3111yescharacteristic
184#1508C2×C3111yescharacteristic
185#1305C2×C3111yescharacteristic
186C22×C31—21no—
187C22×C31—21no—
188C22×C31—21no—
189C22×C31—21no—
190C22×C31—21no—
191C22×C31—21no—
192C22×C31—21no—
193C22×C31—21no—
194C22×C31—81no—
195C22×C31—81no—
196C22×C31#39211yescharacteristic
197C22×C31#45511yescharacteristic
198C22×C31#45611yescharacteristic
199C4×C31—21no—
200C4×C31—21no—
201C4×C31—21no—
202C4×C31—82no—
203C4×C31—82no—
204C4×C31—81no—
205C4×C31—81no—
206C4×C31—81no—
207C4×C31—81no—
208C4×C31—81no—
209C4×C31—81no—
210C4×C31#45812yes—
211C2×C22⋊Q8C22×C3111yescharacteristic
212C2×C22⋊Q8C22×C3111yescharacteristic
213C2×#117C22×C3111yescharacteristic
214#485—22no—
215#484—21no—
216#483—21no—
217#483—21no—
218#483—21no—
219#470—22no—
220#451—21no—
221#451—21no—
222#428—21no—
223#419—21no—
224#407C22×C3111yescharacteristic
225#407C22×C3111yescharacteristic
226#400—21no—
227#398—21no—
228#397—22no—
229#391—21no—
230#389—21no—
231#380C22×C3111yescharacteristic
232C4×C22⋊C4C22×C3111yescharacteristic
233#342—22no—
234#339—22no—
235#328—22no—
236C2×C31—21no—
237C2×C31—21no—
238C2×C31—41no—
239C2×C31—41no—
240C2×C31#200711yescharacteristic
241C2×C31#200911yescharacteristic
242C2×C31#202211yescharacteristic
243C22×Q8D4×C3111yescharacteristic
244C22×Q8D4×C3111yescharacteristic
245C23×C4C23×C3111yescharacteristic
246C2×Q16—22no—
247C2×M16—21no—
248C2×M16D4×C3112yes—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257#117—21no—
258#117—21no—
259#117—21no—
260#117—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4D4×C3111yescharacteristic
266C2×C4⋊C4D4×C3111yescharacteristic
267C2×C4⋊C4D4×C3111yescharacteristic
268C2×C4⋊C4D4×C3111yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4D4×C3112yes—
274C2×C42—21no—
275C2×C42—21no—
276#107—22no—
277#106—22no—
278#106—22no—
279#103—22no—
280#103—22no—
281#103—22no—
282#103—22no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8D4×C3112yes—
287#95—22no—
288#95—22no—
289#95—22no—
290#95—21no—
291#95—21no—
292C31#993711yescharacteristic, direct product factor, Sylow
293C24C2×D4×C3111yescharacteristic
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—42no—
299C2×Q8—42no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—41no—
309C22×C4C2×D4×C3111yescharacteristic
310C22×C4C2×D4×C3111yescharacteristic
311C22×C4C2×D4×C3111yescharacteristic
312C22×C4C2×D4×C3111yescharacteristic
313C22×C4C2×D4×C3111yescharacteristic
314C22×C4#41×C3111yescharacteristic
315Q16—82no—
316M16—42no—
317M16—42no—
318C2×C8—22no—
319C2×C8—22no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—82no—
334C22⋊C4—22no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—42no—
343C42—42no—
344C42—41no—
345C42—41no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23C31×#12011yescharacteristic
351C23C31×#12111yescharacteristic
352C23C31×#12711yescharacteristic
353Q8—42no—
354Q8—42no—
355Q8—42no—
356Q8—81no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4C31×#12011yescharacteristic
384C2×C4C31×#12011yescharacteristic
385C2×C4C31×#12111yescharacteristic
386C2×C4C31×#12111yescharacteristic
387C8—42no—
388C8—42no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—81no—
398C22—81no—
399C22C31×#39211yescharacteristic
400C22C31×#45511yescharacteristic
401C22C31×#45611yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—82no—
406C4—82no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4C31×#45812yes—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2C31×#200711yescharacteristic
419C2C31×#200911yescharacteristic
420C2C31×#202211yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
135. #9937C31direct (N × H)
292. C31#9937direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31952
C31×#30952
C31×#26252
C31×#19962
C31×#18262
C31×#15082
C31×#13052
#993731