Finite Group Databasebeta

← C31×#9119 #21465878

Subgroups — C31×#9119 #21465878

Order 7936.

696 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#97C211yesmaximal, characteristic, complemented
2C31×#2850C211yesmaximal, characteristic
3C31×#1749C211yesmaximal, characteristic, complemented
4C2×C31×#329C212yesmaximal, complemented
5C31×#1295C212yesmaximal, complemented
6C23×C8×C31—21no—
7C2×C31×#124C2211yescharacteristic
8C2×C31×C22⋊Q8C411yescharacteristic
9C2×C31×#121C411yescharacteristic
10C22×C42×C31C2211yescharacteristic
11C2×C31×C22⋊C8—21no—
12C2×C31×#97—21no—
13C2×C31×#97—24no—
14C2×C31×#97C2212yes—
15C2×C31×#97C2212yes—
16C31×#391C411yescharacteristic
17C31×#390C411yescharacteristic
18C31×#388—21no—
19C31×#388—21no—
20C31×#386—21no—
21C31×#386—21no—
22C31×#382C2211yescharacteristic
23C31×#336—21no—
24C31×#329—24no—
25C22×Q8×C31C2×C411yescharacteristic
26C22×D4×C31—21no—
27C22×D4×C31C2×C411yescharacteristic
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C23×C4×C31D411yescharacteristic
31C22×C8×C31—24no—
32C22×C8×C31—24no—
33C22×C8×C31—24no—
34C22×C8×C31—22no—
35C22×C8×C31—22no—
36C31×#124—22no—
37C31×#124—22no—
38C31×C22⋊Q8—42no—
39C31×#121—42no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31C2×C411yescharacteristic
42C2×C4⋊C4×C31C2×C411yescharacteristic
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×C42×C31—22no—
50C2×C42×C31—22no—
51C2×C42×C31C2×C411yescharacteristic
52C2×C42×C31D411yescharacteristic
53C2×C42×C31D411yescharacteristic
54C2×C42×C31C2311yescharacteristic
55C31×C22⋊C8—24no—
56C31×#97—24no—
57C31×#97—22no—
58C31×#97—22no—
59C31×#97—22no—
60C31×#97D414yescomplemented
61C31×#95—21no—
62C31×#95—21no—
63C31×#95—21no—
64C31×#95—21no—
65C24×C31—21no—
66C24×C31C22⋊C411yescharacteristic
67C2×Q8×C31—22no—
68C2×Q8×C31—41no—
69C2×Q8×C31—41no—
70C2×D4×C31—22no—
71C2×D4×C31—41no—
72C2×D4×C31—41no—
73C2×D4×C31—42no—
74C2×D4×C31—42no—
75C2×D4×C31—42no—
76C22×C4×C31—22no—
77C22×C4×C31—22no—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31—22no—
81C22×C4×C31—22no—
82C22×C4×C31—22no—
83C22×C4×C31—22no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—21no—
87C22×C4×C31—41no—
88C22×C4×C31—41no—
89C22×C4×C31C22⋊C411yescharacteristic
90C22×C4×C31C22⋊C411yescharacteristic
91C22×C4×C31C22⋊C411yescharacteristic
92C22×C4×C31C22×C411yescharacteristic
93C22×C4×C31C2×D411yescharacteristic
94C22×C4×C31C2×D411yescharacteristic
95C2×C8×C31—216no—
96C2×C8×C31—24no—
97C2×C8×C31—24no—
98C2×C8×C31—24no—
99C2×C8×C31—24no—
100C2×C8×C31—42no—
101C2×C8×C31—42no—
102C4⋊C4×C31—42no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31—41no—
105C22⋊C4×C31—42no—
106C22⋊C4×C31—42no—
107C22⋊C4×C31—42no—
108C22⋊C4×C31—42no—
109C22⋊C4×C31—41no—
110C22⋊C4×C31—42no—
111C22⋊C4×C31—41no—
112C42×C31—22no—
113C42×C31—21no—
114C42×C31—22no—
115C42×C31—21no—
116C42×C31C2×D412yes—
117C42×C31#4112yes—
118#9119C3111yesmaximal, characteristic, direct product factor, Sylow
119C23×C31—21no—
120C23×C31—21no—
121C23×C31—21no—
122C23×C31—21no—
123C23×C31—41no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—41no—
127C23×C31—41no—
128C23×C31—41no—
129C23×C31—41no—
130C23×C31#10012yes—
131C23×C31#10412yes—
132C23×C31#10412yes—
133C23×C31C2×C22⋊C411yescharacteristic
134Q8×C31—82no—
135D4×C31—82no—
136D4×C31—84no—
137C2×C4×C31—24no—
138C2×C4×C31—24no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—21no—
143C2×C4×C31—21no—
144C2×C4×C31—21no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—21no—
148C2×C4×C31—21no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—21no—
153C2×C4×C31—44no—
154C2×C4×C31—44no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
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#10412yes—
165C2×C4×C31C4×D412yes—
166C2×C4×C31#12011yescharacteristic
167C2×C4×C31#12112yes—
168C2×C4×C31#12311yescharacteristic
169C8×C31—28no—
170C8×C31—44no—
171C22×#97C2×C3111yescharacteristic, complemented
172#2850C2×C3111yescharacteristic
173#1749C2×C3111yescharacteristic, complemented
174C2×#329C2×C3112yescomplemented
175#1295C2×C3112yescomplemented
176C22×C31—22no—
177C22×C31—22no—
178C22×C31—22no—
179C22×C31—22no—
180C22×C31—22no—
181C22×C31—22no—
182C22×C31—81no—
183C22×C31—81no—
184C22×C31—81no—
185C22×C31—81no—
186C22×C31—81no—
187C22×C31—81no—
188C22×C31—81no—
189C22×C31#32914yescomplemented
190C22×C31#38611yescharacteristic
191C22×C31C2×#10011yescharacteristic
192C22×C31#41311yescharacteristic
193C22×C31C2×#10411yescharacteristic
194C22×C31C2×#10411yescharacteristic
195C22×C31C2×#10411yescharacteristic
196C22×C31#42111yescharacteristic
197C4×C31—22no—
198C4×C31—21no—
199C4×C31—22no—
200C4×C31—21no—
201C4×C31—22no—
202C4×C31—41no—
203C4×C31—41no—
204C4×C31—81no—
205C4×C31—81no—
206C4×C31—81no—
207C23×C8—21no—
208C2×#124C22×C3111yescharacteristic
209C2×C22⋊Q8C4×C3111yescharacteristic
210C2×#121C4×C3111yescharacteristic
211C22×C42C22×C3111yescharacteristic
212C2×C22⋊C8—21no—
213C2×#97—21no—
214C2×#97—24no—
215C2×#97C22×C3112yes—
216C2×#97C22×C3112yes—
217#391C4×C3111yescharacteristic
218#390C4×C3111yescharacteristic
219#388—21no—
220#388—21no—
221#386—21no—
222#386—21no—
223#382C22×C3111yescharacteristic
224#336—21no—
225#329—24no—
226C2×C31—24no—
227C2×C31—161no—
228C2×C31C2×#32911yescharacteristic
229C2×C31#152411yescharacteristic
230C2×C31#153011yescharacteristic
231C2×C31#153211yescharacteristic
232C2×C31#187111yescharacteristic
233C2×C31#189611yescharacteristic
234C2×C31#190011yescharacteristic
235C22×Q8C2×C4×C3111yescharacteristic
236C22×D4—21no—
237C22×D4C2×C4×C3111yescharacteristic
238C23×C4C2×C4×C3111yescharacteristic
239C23×C4D4×C3111yescharacteristic
240C23×C4D4×C3111yescharacteristic
241C22×C8—24no—
242C22×C8—24no—
243C22×C8—24no—
244C22×C8—22no—
245C22×C8—22no—
246#124—22no—
247#124—22no—
248C22⋊Q8—42no—
249#121—42no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C2×C4×C3111yescharacteristic
252C2×C4⋊C4C2×C4×C3111yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C42—22no—
260C2×C42—22no—
261C2×C42C2×C4×C3111yescharacteristic
262C2×C42D4×C3111yescharacteristic
263C2×C42D4×C3111yescharacteristic
264C2×C42C23×C3111yescharacteristic
265C22⋊C8—24no—
266#97—24no—
267#97—22no—
268#97—22no—
269#97—22no—
270#97D4×C3114yescomplemented
271#95—21no—
272#95—21no—
273#95—21no—
274#95—21no—
275C31#911911yescharacteristic, direct product factor, Sylow
276C24—21no—
277C24C22⋊C4×C3111yescharacteristic
278C2×Q8—22no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×D4—22no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4C22⋊C4×C3111yescharacteristic
301C22×C4C22⋊C4×C3111yescharacteristic
302C22×C4C22⋊C4×C3111yescharacteristic
303C22×C4C22×C4×C3111yescharacteristic
304C22×C4C2×D4×C3111yescharacteristic
305C22×C4C2×D4×C3111yescharacteristic
306C2×C8—216no—
307C2×C8—24no—
308C2×C8—24no—
309C2×C8—24no—
310C2×C8—24no—
311C2×C8—42no—
312C2×C8—42no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—41no—
321C22⋊C4—42no—
322C22⋊C4—41no—
323C42—22no—
324C42—21no—
325C42—22no—
326C42—21no—
327C42C2×D4×C3112yes—
328C42#41×C3112yes—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23C31×#10012yes—
341C23C31×#10412yes—
342C23C31×#10412yes—
343C23C2×C22⋊C4×C3111yescharacteristic
344Q8—82no—
345D4—82no—
346D4—84no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—44no—
364C2×C4—44no—
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×C4C31×#10412yes—
375C2×C4C4×D4×C3112yes—
376C2×C4C31×#12011yescharacteristic
377C2×C4C31×#12112yes—
378C2×C4C31×#12311yescharacteristic
379C8—28no—
380C8—44no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22C31×#32914yescomplemented
395C22C31×#38611yescharacteristic
396C22C2×C31×#10011yescharacteristic
397C22C31×#41311yescharacteristic
398C22C2×C31×#10411yescharacteristic
399C22C2×C31×#10411yescharacteristic
400C22C2×C31×#10411yescharacteristic
401C22C31×#42111yescharacteristic
402C4—22no—
403C4—21no—
404C4—22no—
405C4—21no—
406C4—22no—
407C4—41no—
408C4—41no—
409C4—81no—
410C4—81no—
411C4—81no—
412C2—24no—
413C2—161no—
414C2C2×C31×#32911yescharacteristic
415C2C31×#152411yescharacteristic
416C2C31×#153011yescharacteristic
417C2C31×#153211yescharacteristic
418C2C31×#187111yescharacteristic
419C2C31×#189611yescharacteristic
420C2C31×#190011yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#97C2semidirect
3. C31×#1749C2semidirect
4. C2×C31×#329C2semidirect
5. C31×#1295C2semidirect
60. C31×#97D4semidirect
118. #9119C31direct (N × H)
171. C22×#97C2×C31semidirect
173. #1749C2×C31semidirect
174. C2×#329C2×C31semidirect
175. #1295C2×C31semidirect
189. C22×C31#329semidirect
270. #97D4×C31semidirect
275. C31#9119direct (N × H)
394. C22C31×#329semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#972
C31×#28502
C31×#17492
C2×C31×#3292
C31×#12952
#911931