Finite Group Databasebeta

← C31×#10019 #21466778

Subgroups — C31×#10019 #21466778

Order 7936.

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

normal subgroups only

This group has 540 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×#3142C211yesmaximal, characteristic, complemented
2C31×#3109C211yesmaximal, characteristic
3C31×#2633C211yesmaximal, characteristic, complemented
4C31×#1534C211yesmaximal, characteristic, complemented
5C31×#1514C211yesmaximal, characteristic, complemented
6C31×#1490C211yesmaximal, characteristic, complemented
7C31×#1288C211yesmaximal, characteristic, complemented
8C31×#532C2211yescharacteristic
9C2×C31×#125C2211yescharacteristic
10C2×C4×D4×C31C2211yescharacteristic
11C31×#491—21no—
12C31×#490—21no—
13C31×#488—22no—
14C31×#481—21no—
15C31×#476—21no—
16C31×#459—21no—
17C31×#447—21no—
18C31×#442—22no—
19C31×#432C2211yescharacteristic
20C31×#432C2211yescharacteristic
21C31×#417—21no—
22C31×#417—21no—
23C4×M16×C31C2211yescharacteristic
24C31×#399—21no—
25C31×#398—21no—
26C31×#397—21no—
27C31×#394—21no—
28C31×#385—22no—
29C31×#383C2211yescharacteristic
30C31×#330—22no—
31C31×#327—22no—
32C31×D4⋊C8—22no—
33C2×#41×C31—21no—
34C22×D4×C31D411yescharacteristic
35C23×C4×C31—21no—
36C2×D8×C31—22no—
37C2×M16×C31—21no—
38C31×C4⋊Q8D411yescharacteristic
39C31×#127D411yescharacteristic
40C31×#125—21no—
41C31×#125—21no—
42C31×#125—21no—
43C31×#125—21no—
44C31×#124—21no—
45C31×#121—21no—
46C31×#121—21no—
47C4×D4×C31—21no—
48C4×D4×C31—21no—
49C4×D4×C31—21no—
50C4×D4×C31—21no—
51C4×D4×C31—21no—
52C4×D4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31D411yescharacteristic
57C2×C4⋊C4×C31D411yescharacteristic
58C2×C4⋊C4×C31D411yescharacteristic
59C2×C22⋊C4×C31—22no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—22no—
62C2×C42×C31C2311yescharacteristic
63C31×#106—22no—
64C31×C4⋊C8—21no—
65C31×C4⋊C8—21no—
66C31×#103—22no—
67C31×#103—22no—
68C31×#102—22no—
69C31×#102—22no—
70C31×#102—22no—
71C31×#102—22no—
72C31×C22⋊C8—21no—
73C31×C22⋊C8—21no—
74C31×#97—21no—
75C31×#97—21no—
76C31×#97D412yes—
77C4×C8×C31D412yes—
78C31×#95—22no—
79C31×#95—21no—
80C31×#95—21no—
81C31×#95D412yes—
82C24×C31—21no—
83#41×C31—44no—
84C2×Q8×C31—21no—
85C2×D4×C31—21no—
86C2×D4×C31—21no—
87C2×D4×C31—21no—
88C2×D4×C31—21no—
89C2×D4×C31—21no—
90C2×D4×C31—42no—
91C2×D4×C31—41no—
92C22×C4×C31—22no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—41no—
97C22×C4×C31—41no—
98C22×C4×C31—41no—
99C22×C4×C31—82no—
100C22×C4×C31C2×D411yescharacteristic
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31C2×D411yescharacteristic
103D8×C31—44no—
104M16×C31—42no—
105C2×C8×C31—22no—
106C2×C8×C31—22no—
107C2×C8×C31—41no—
108C4⋊C4×C31—21no—
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—41no—
117C4⋊C4×C31—41no—
118C4⋊C4×C31—41no—
119C4⋊C4×C31—41no—
120C4⋊C4×C31—82no—
121C22⋊C4×C31—44no—
122C22⋊C4×C31—41no—
123C22⋊C4×C31—41no—
124C22⋊C4×C31—41no—
125C22⋊C4×C31—41no—
126C22⋊C4×C31—82no—
127C42×C31C2×D411yescharacteristic
128C42×C31C2×D411yescharacteristic
129C42×C31C2×D411yescharacteristic
130C42×C31#4111yescharacteristic
131#10019C3111yesmaximal, characteristic, direct product factor, Sylow
132C23×C31—22no—
133C23×C31—42no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31—42no—
137C23×C31—41no—
138C23×C31#12011yescharacteristic
139Q8×C31—42no—
140D4×C31—22no—
141D4×C31—22no—
142D4×C31—41no—
143D4×C31—41no—
144D4×C31—42no—
145D4×C31—42no—
146D4×C31—81no—
147D4×C31—82no—
148C2×C4×C31—22no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—42no—
152C2×C4×C31—42no—
153C2×C4×C31—41no—
154C2×C4×C31—42no—
155C2×C4×C31—41no—
156C2×C4×C31—42no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31—42no—
162C2×C4×C31—82no—
163C2×C4×C31—82no—
164C2×C4×C31—82no—
165C2×C4×C31#12011yescharacteristic
166C2×C4×C31#12011yescharacteristic
167C2×C4×C31#12111yescharacteristic
168C2×C4×C31#12111yescharacteristic
169C2×C4×C31#12111yescharacteristic
170C2×C4×C31#12711yescharacteristic
171C8×C31—42no—
172C8×C31—42no—
173C8×C31—81no—
174#3142C2×C3111yescharacteristic, complemented
175#3109C2×C3111yescharacteristic
176#2633C2×C3111yescharacteristic, complemented
177#1534C2×C3111yescharacteristic, complemented
178#1514C2×C3111yescharacteristic, complemented
179#1490C2×C3111yescharacteristic, complemented
180#1288C2×C3111yescharacteristic, complemented
181C22×C31—21no—
182C22×C31—21no—
183C22×C31—44no—
184C22×C31—42no—
185C22×C31—82no—
186C22×C31—81no—
187C22×C31—81no—
188C22×C31—81no—
189C22×C31—81no—
190C22×C31—81no—
191C22×C31#39211yescharacteristic
192C22×C31#45412yes—
193C4×C31—21no—
194C4×C31—21no—
195C4×C31—21no—
196C4×C31—21no—
197C4×C31—21no—
198C4×C31—21no—
199C4×C31—82no—
200C4×C31—81no—
201C4×C31—81no—
202C4×C31—81no—
203C4×C31—81no—
204#532C22×C3111yescharacteristic
205C2×#125C22×C3111yescharacteristic
206C2×C4×D4C22×C3111yescharacteristic
207#491—21no—
208#490—21no—
209#488—22no—
210#481—21no—
211#476—21no—
212#459—21no—
213#447—21no—
214#442—22no—
215#432C22×C3111yescharacteristic
216#432C22×C3111yescharacteristic
217#417—21no—
218#417—21no—
219C4×M16C22×C3111yescharacteristic
220#399—21no—
221#398—21no—
222#397—21no—
223#394—21no—
224#385—22no—
225#383C22×C3111yescharacteristic
226#330—22no—
227#327—22no—
228D4⋊C8—22no—
229C2×C31—22no—
230C2×C31—82no—
231C2×C31—161no—
232C2×C31#200311yescharacteristic
233C2×C31#200811yescharacteristic
234C2×C31#201011yescharacteristic
235C2×#41—21no—
236C22×D4D4×C3111yescharacteristic
237C23×C4—21no—
238C2×D8—22no—
239C2×M16—21no—
240C4⋊Q8D4×C3111yescharacteristic
241#127D4×C3111yescharacteristic
242#125—21no—
243#125—21no—
244#125—21no—
245#125—21no—
246#124—21no—
247#121—21no—
248#121—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4D4×C3111yescharacteristic
259C2×C4⋊C4D4×C3111yescharacteristic
260C2×C4⋊C4D4×C3111yescharacteristic
261C2×C22⋊C4—22no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—22no—
264C2×C42C23×C3111yescharacteristic
265#106—22no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268#103—22no—
269#103—22no—
270#102—22no—
271#102—22no—
272#102—22no—
273#102—22no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276#97—21no—
277#97—21no—
278#97D4×C3112yes—
279C4×C8D4×C3112yes—
280#95—22no—
281#95—21no—
282#95—21no—
283#95D4×C3112yes—
284C31#1001911yescharacteristic, direct product factor, Sylow
285C24—21no—
286#41—44no—
287C2×Q8—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—42no—
294C2×D4—41no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—82no—
303C22×C4C2×D4×C3111yescharacteristic
304C22×C4C2×D4×C3111yescharacteristic
305C22×C4C2×D4×C3111yescharacteristic
306D8—44no—
307M16—42no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—41no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—82no—
324C22⋊C4—44no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—82no—
330C42C2×D4×C3111yescharacteristic
331C42C2×D4×C3111yescharacteristic
332C42C2×D4×C3111yescharacteristic
333C42#41×C3111yescharacteristic
334C23—22no—
335C23—42no—
336C23—41no—
337C23—42no—
338C23—41no—
339C23—41no—
340C23C31×#12011yescharacteristic
341Q8—42no—
342D4—22no—
343D4—22no—
344D4—41no—
345D4—41no—
346D4—42no—
347D4—42no—
348D4—81no—
349D4—82no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4C31×#12011yescharacteristic
368C2×C4C31×#12011yescharacteristic
369C2×C4C31×#12111yescharacteristic
370C2×C4C31×#12111yescharacteristic
371C2×C4C31×#12111yescharacteristic
372C2×C4C31×#12711yescharacteristic
373C8—42no—
374C8—42no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22—44no—
379C22—42no—
380C22—82no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C31×#39211yescharacteristic
387C22C31×#45412yes—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—82no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—81no—
399C2—22no—
400C2—82no—
401C2—161no—
402C2C31×#200311yescharacteristic
403C2C31×#200811yescharacteristic
404C2C31×#201011yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3109C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3142C2semidirect
3. C31×#2633C2semidirect
4. C31×#1534C2semidirect
5. C31×#1514C2semidirect
6. C31×#1490C2semidirect
7. C31×#1288C2semidirect
131. #10019C31direct (N × H)
174. #3142C2×C31semidirect
176. #2633C2×C31semidirect
177. #1534C2×C31semidirect
178. #1514C2×C31semidirect
179. #1490C2×C31semidirect
180. #1288C2×C31semidirect
284. C31#10019direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31422
C31×#31092
C31×#26332
C31×#15342
C31×#15142
C31×#14902
C31×#12882
#1001931