Finite Group Databasebeta

← C31×#13462 #21470221

Subgroups — C31×#13462 #21470221

Order 7936.

476 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2748C211yesmaximal, characteristic
2C31×#1867C211yesmaximal, characteristic
3C31×#1867C211yesmaximal, characteristic
4C31×#1856C211yesmaximal, characteristic
5C31×#1393C211yesmaximal, characteristic
6C31×#1390C211yesmaximal, characteristic
7C31×#1390C211yesmaximal, characteristic
8C31×#518C2211yescharacteristic
9C31×#428—21no—
10C2×C31×#100C2211yescharacteristic
11C2×C31×#99C2211yescharacteristic
12C2×C31×#99C2211yescharacteristic
13C31×#399—21no—
14C31×#398—21no—
15C31×#396—21no—
16C31×#390C2211yescharacteristic
17C31×#387—21no—
18C31×#386C2211yescharacteristic
19C31×#386C2211yescharacteristic
20C31×#385—21no—
21C31×#385—21no—
22C31×#385—21no—
23C31×#380—21no—
24C31×#342—21no—
25C31×#342—21no—
26C31×#339—21no—
27C22×D4×C31C2311yescharacteristic
28C23×C4×C31D411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C2×M16×C31—21no—
31C4×D4×C31—41no—
32C4×D4×C31—41no—
33C31×#117—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31—41no—
40C2×C4⋊C4×C31—41no—
41C2×C4⋊C4×C31D411yescharacteristic
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—21no—
48C2×C22⋊C4×C31—21no—
49C2×C22⋊C4×C31—21no—
50C2×C22⋊C4×C31D411yescharacteristic
51C2×C22⋊C4×C31D411yescharacteristic
52C2×C42×C31D411yescharacteristic
53C31×#107—41no—
54C31×#106—41no—
55C31×#100—21no—
56C31×#100Q812yes—
57C31×#99—21no—
58C31×#99—21no—
59C31×#99Q812yes—
60C31×#99Q812yes—
61C31×#95—21no—
62C31×#95—21no—
63C31×#95—21no—
64C31×#95—21no—
65C31×#95—21no—
66C31×#95—41no—
67C31×#95—41no—
68C24×C31C2×D411yescharacteristic
69C24×C31C2×D411yescharacteristic
70C2×D4×C31—41no—
71C2×D4×C31—41no—
72C2×D4×C31C2×Q811yescharacteristic
73C2×D4×C31C2×Q811yescharacteristic
74C2×D4×C31C2×Q811yescharacteristic
75C2×D4×C31#4111yescharacteristic
76C22×C4×C31—21no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—42no—
87C22×C4×C31—41no—
88C22×C4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31—81no—
92C22×C4×C31C2×D411yescharacteristic
93M16×C31—22no—
94M16×C31—41no—
95C2×C8×C31—41no—
96C4⋊C4×C31—21no—
97C4⋊C4×C31—21no—
98C4⋊C4×C31—42no—
99C4⋊C4×C31—41no—
100C4⋊C4×C31—81no—
101C4⋊C4×C31—81no—
102C4⋊C4×C31—81no—
103C4⋊C4×C31—81no—
104C4⋊C4×C31—82no—
105C4⋊C4×C31—82no—
106C22⋊C4×C31—22no—
107C22⋊C4×C31—22no—
108C22⋊C4×C31—42no—
109C22⋊C4×C31—41no—
110C22⋊C4×C31—41no—
111C22⋊C4×C31—41no—
112C22⋊C4×C31—41no—
113C22⋊C4×C31—41no—
114C22⋊C4×C31—41no—
115C22⋊C4×C31—41no—
116C22⋊C4×C31—81no—
117C22⋊C4×C31—81no—
118C22⋊C4×C31—81no—
119C42×C31—41no—
120C42×C31—41no—
121#13462C3111yesmaximal, characteristic, direct product factor, Sylow
122C23×C31—21no—
123C23×C31—21no—
124C23×C31—21no—
125C23×C31—21no—
126C23×C31—41no—
127C23×C31—41no—
128C23×C31—41no—
129C23×C31—41no—
130C23×C31#12011yescharacteristic
131C23×C31C22⋊Q811yescharacteristic
132C23×C31C22⋊Q811yescharacteristic
133C23×C31C4⋊Q811yescharacteristic
134C23×C31C4⋊Q811yescharacteristic
135D4×C31—41no—
136D4×C31—41no—
137D4×C31—41no—
138D4×C31—41no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—22no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—42no—
145C2×C4×C31—42no—
146C2×C4×C31—42no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
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—41no—
165C2×C4×C31—81no—
166C2×C4×C31—81no—
167C2×C4×C31—81no—
168C2×C4×C31—81no—
169C2×C4×C31—81no—
170C2×C4×C31—81no—
171C2×C4×C31—81no—
172C2×C4×C31—81no—
173C2×C4×C31—81no—
174C2×C4×C31—81no—
175C2×C4×C31C22⋊Q811yescharacteristic
176C2×C4×C31C4⋊Q811yescharacteristic
177C8×C31—42no—
178#2748C2×C3111yescharacteristic
179#1867C2×C3111yescharacteristic
180#1867C2×C3111yescharacteristic
181#1856C2×C3111yescharacteristic
182#1393C2×C3111yescharacteristic
183#1390C2×C3111yescharacteristic
184#1390C2×C3111yescharacteristic
185C22×C31—21no—
186C22×C31—21no—
187C22×C31—21no—
188C22×C31—21no—
189C22×C31—21no—
190C22×C31—21no—
191C22×C31—41no—
192C22×C31—41no—
193C22×C31—41no—
194C22×C31—41no—
195C22×C31—41no—
196C22×C31—41no—
197C22×C31—41no—
198C22×C31—41no—
199C22×C31—81no—
200C22×C31—81no—
201C22×C31#39511yescharacteristic
202C22×C31B(4,𝔽2)11yescharacteristic
203C22×C31#45811yescharacteristic
204C4×C31—21no—
205C4×C31—21no—
206C4×C31—42no—
207C4×C31—81no—
208C4×C31—81no—
209C4×C31—81no—
210C4×C31—82no—
211C4×C31—82no—
212C4×C31—81no—
213C4×C31—81no—
214C4×C31—81no—
215C4×C31—81no—
216#518C22×C3111yescharacteristic
217#428—21no—
218C2×#100C22×C3111yescharacteristic
219C2×#99C22×C3111yescharacteristic
220C2×#99C22×C3111yescharacteristic
221#399—21no—
222#398—21no—
223#396—21no—
224#390C22×C3111yescharacteristic
225#387—21no—
226#386C22×C3111yescharacteristic
227#386C22×C3111yescharacteristic
228#385—21no—
229#385—21no—
230#385—21no—
231#380—21no—
232#342—21no—
233#342—21no—
234#339—21no—
235C2×C31—21no—
236C2×C31—21no—
237C2×C31—41no—
238C2×C31—41no—
239C2×C31—41no—
240C2×C31—41no—
241C2×C31#206211yescharacteristic
242C2×C31#219711yescharacteristic
243C2×C31#220011yescharacteristic
244C22×D4C23×C3111yescharacteristic
245C23×C4D4×C3111yescharacteristic
246C23×C4D4×C3111yescharacteristic
247C2×M16—21no—
248C4×D4—41no—
249C4×D4—41no—
250#117—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—41no—
257C2×C4⋊C4—41no—
258C2×C4⋊C4D4×C3111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4D4×C3111yescharacteristic
268C2×C22⋊C4D4×C3111yescharacteristic
269C2×C42D4×C3111yescharacteristic
270#107—41no—
271#106—41no—
272#100—21no—
273#100Q8×C3112yes—
274#99—21no—
275#99—21no—
276#99Q8×C3112yes—
277#99Q8×C3112yes—
278#95—21no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—41no—
284#95—41no—
285C31#1346211yescharacteristic, direct product factor, Sylow
286C24C2×D4×C3111yescharacteristic
287C24C2×D4×C3111yescharacteristic
288C2×D4—41no—
289C2×D4—41no—
290C2×D4C2×Q8×C3111yescharacteristic
291C2×D4C2×Q8×C3111yescharacteristic
292C2×D4C2×Q8×C3111yescharacteristic
293C2×D4#41×C3111yescharacteristic
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—81no—
310C22×C4C2×D4×C3111yescharacteristic
311M16—22no—
312M16—41no—
313C2×C8—41no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—42no—
318C4⋊C4—81no—
319C4⋊C4—81no—
320C4⋊C4—81no—
321C4⋊C4—81no—
322C4⋊C4—82no—
323C4⋊C4—82no—
324C22⋊C4—22no—
325C22⋊C4—22no—
326C22⋊C4—42no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—81no—
335C22⋊C4—81no—
336C22⋊C4—81no—
337C42—41no—
338C42—41no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23C31×#12011yescharacteristic
348C23C31×C22⋊Q811yescharacteristic
349C23C31×C22⋊Q811yescharacteristic
350C23C31×C4⋊Q811yescharacteristic
351C23C31×C4⋊Q811yescharacteristic
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4C31×C22⋊Q811yescharacteristic
393C2×C4C31×C4⋊Q811yescharacteristic
394C8—42no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22C31×#39511yescharacteristic
412C22C31×B(4,𝔽2)11yescharacteristic
413C22C31×#45811yescharacteristic
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—81no—
419C4—81no—
420C4—82no—
421C4—82no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4—81no—
426C2—21no—
427C2—21no—
428C2—41no—
429C2—41no—
430C2—41no—
431C2—41no—
432C2C31×#206211yescharacteristic
433C2C31×#219711yescharacteristic
434C2C31×#220011yescharacteristic
subgroupG/H
center, socleC22×C31B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C31
prime radicalC22×D4×C31C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
121. #13462C31direct (N × H)
285. C31#13462direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#27482
C31×#18672
C31×#18562
C31×#13932
C31×#13902
#1346231