Finite Group Databasebeta

← C31×#11205 #21467964

Subgroups — C31×#11205 #21467964

Order 7936.

918 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2315C211yesmaximal, characteristic
2C31×#2315C211yesmaximal, characteristic
3C2×C31×#342C212yesmaximal
4C2×C31×#342C212yesmaximal
5C2×C31×#342C211yesmaximal, characteristic
6C22×C22⋊C4×C31C2211yescharacteristic
7C22×C22⋊C4×C31C2212yes—
8C22×C22⋊C4×C31C2212yes—
9C22×C22⋊C4×C31C2211yescharacteristic
10C22×C22⋊C4×C31C2211yescharacteristic
11C31×#385—22no—
12C31×#385—24no—
13C31×#385C414yescomplemented
14C31×#380—22no—
15C31×#380—22no—
16C31×#342—22no—
17C31×#342—24no—
18C31×#342—24no—
19C25×C31C2311yescharacteristic
20C23×C4×C31—21no—
21C23×C4×C31—22no—
22C23×C4×C31—22no—
23C23×C4×C31C2×C412yes—
24C23×C4×C31D412yes—
25C2×C4⋊C4×C31—24no—
26C2×C4⋊C4×C31—24no—
27C2×C22⋊C4×C31—22no—
28C2×C22⋊C4×C31—21no—
29C2×C22⋊C4×C31—21no—
30C2×C22⋊C4×C31—21no—
31C2×C22⋊C4×C31—22no—
32C2×C22⋊C4×C31—22no—
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—22no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—22no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—22no—
46C2×C22⋊C4×C31C2×C412yes—
47C2×C22⋊C4×C31C2×C412yes—
48C2×C22⋊C4×C31D414yes—
49C2×C22⋊C4×C31D412yes—
50C2×C22⋊C4×C31D412yes—
51C2×C22⋊C4×C31Q814yes—
52C2×C22⋊C4×C31Q812yes—
53C31×#95—24no—
54C31×#95—24no—
55C24×C31—82no—
56C24×C31C22×C411yescharacteristic
57C24×C31C2×D411yescharacteristic
58C24×C31C2×D411yescharacteristic
59C24×C31C2×D412yes—
60C24×C31C2×D411yescharacteristic
61C24×C31C2×Q811yescharacteristic
62C24×C31C2×Q812yes—
63C24×C31#4112yes—
64C24×C31#4111yescharacteristic
65C24×C31#4111yescharacteristic
66C24×C31#4112yes—
67C22×C4×C31—22no—
68C22×C4×C31—22no—
69C22×C4×C31—22no—
70C22×C4×C31—22no—
71C22×C4×C31—22no—
72C22×C4×C31—22no—
73C22×C4×C31—24no—
74C22×C4×C31—24no—
75C22×C4×C31—24no—
76C22×C4×C31—42no—
77C22×C4×C31—42no—
78C22×C4×C31—42no—
79C22×C4×C31—42no—
80C22×C4×C31—82no—
81C22×C4×C31—82no—
82C22×C4×C31—84no—
83C22×C4×C31—82no—
84C22×C4×C31—84no—
85C22×C4×C31C22⋊C414yes—
86C4⋊C4×C31—84no—
87C4⋊C4×C31—84no—
88C22⋊C4×C31—22no—
89C22⋊C4×C31—24no—
90C22⋊C4×C31—22no—
91C22⋊C4×C31—24no—
92C22⋊C4×C31—22no—
93C22⋊C4×C31—24no—
94C22⋊C4×C31—24no—
95C22⋊C4×C31—24no—
96C22⋊C4×C31—24no—
97C22⋊C4×C31—41no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—42no—
100C22⋊C4×C31—42no—
101C22⋊C4×C31—42no—
102C22⋊C4×C31—41no—
103C22⋊C4×C31—42no—
104C22⋊C4×C31C4⋊C414yescomplemented
105#11205C3111yesmaximal, characteristic, direct product factor, Sylow
106C23×C31—42no—
107C23×C31—42no—
108C23×C31—42no—
109C23×C31—44no—
110C23×C31—44no—
111C23×C31—81no—
112C23×C31—81no—
113C23×C31—82no—
114C23×C31—82no—
115C23×C31—81no—
116C23×C31—81no—
117C23×C31C2×C22⋊C411yescharacteristic
118C23×C31C2×C4⋊C411yescharacteristic
119C23×C31#11711yescharacteristic
120C23×C31C4×D412yes—
121C23×C31C4×Q812yes—
122C23×C31#12011yescharacteristic
123C23×C31#12112yes—
124C23×C31#12111yescharacteristic
125C23×C31#12111yescharacteristic
126C23×C31#12112yes—
127C23×C31C22⋊Q811yescharacteristic
128C23×C31C22⋊Q811yescharacteristic
129C23×C31C22⋊Q812yes—
130C23×C31C22⋊Q812yes—
131C23×C31C22⋊Q812yes—
132C23×C31#12311yescharacteristic
133C23×C31#12312yes—
134C23×C31#12411yescharacteristic
135C23×C31#12512yes—
136C23×C31#12512yes—
137C23×C31#12612yes—
138C23×C31C4⋊Q812yes—
139C23×C31C4⋊Q811yescharacteristic
140C2×C4×C31—24no—
141C2×C4×C31—24no—
142C2×C4×C31—44no—
143C2×C4×C31—44no—
144C2×C4×C31—44no—
145C2×C4×C31—48no—
146C2×C4×C31—44no—
147C2×C4×C31—42no—
148C2×C4×C31—44no—
149C2×C4×C31—44no—
150C2×C4×C31—82no—
151C2×C4×C31—82no—
152C2×C4×C31—82no—
153C2×C4×C31—84no—
154C2×C4×C31—84no—
155C2×C4×C31—84no—
156C2×C4×C31—84no—
157C2×C4×C31—84no—
158C2×C4×C31—84no—
159#2315C2×C3111yescharacteristic
160#2315C2×C3111yescharacteristic
161C2×#342C2×C3112yes—
162C2×#342C2×C3112yes—
163C2×#342C2×C3111yescharacteristic
164C22×C31—22no—
165C22×C31—22no—
166C22×C31—24no—
167C22×C31—24no—
168C22×C31—22no—
169C22×C31—41no—
170C22×C31—42no—
171C22×C31—41no—
172C22×C31—42no—
173C22×C31—42no—
174C22×C31—42no—
175C22×C31—41no—
176C22×C31—41no—
177C22×C31—42no—
178C22×C31—41no—
179C22×C31—41no—
180C22×C31—42no—
181C22×C31—42no—
182C22×C31—41no—
183C22×C31—42no—
184C22×C31—42no—
185C22×C31—42no—
186C22×C31—41no—
187C22×C31#38011yescharacteristic
188C22×C31#38611yescharacteristic
189C22×C31#38712yes—
190C22×C31#38912yes—
191C22×C31#39111yescharacteristic
192C22×C31#39411yescharacteristic
193C22×C31#39511yescharacteristic
194C22×C31#39612yes—
195C22×C31#39812yes—
196C22×C31#39811yescharacteristic
197C22×C31#40011yescharacteristic
198C4×C31—44no—
199C4×C31—44no—
200C4×C31—84no—
201C4×C31—84no—
202C4×C31—82no—
203C22×C22⋊C4C22×C3111yescharacteristic
204C22×C22⋊C4C22×C3112yes—
205C22×C22⋊C4C22×C3112yes—
206C22×C22⋊C4C22×C3111yescharacteristic
207C22×C22⋊C4C22×C3111yescharacteristic
208#385—22no—
209#385—24no—
210#385C4×C3114yescomplemented
211#380—22no—
212#380—22no—
213#342—22no—
214#342—24no—
215#342—24no—
216C2×C31—21no—
217C2×C31—21no—
218C2×C31—22no—
219C2×C31—22no—
220C2×C31—22no—
221C2×C31—21no—
222C2×C31—21no—
223C2×C31—22no—
224C2×C31—21no—
225C2×C31—21no—
226C2×C31#144111yescharacteristic
227C2×C31#191312yes—
228C25C23×C3111yescharacteristic
229C23×C4—21no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4C2×C4×C3112yes—
233C23×C4D4×C3112yes—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—24no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4C2×C4×C3112yes—
256C2×C22⋊C4C2×C4×C3112yes—
257C2×C22⋊C4D4×C3114yes—
258C2×C22⋊C4D4×C3112yes—
259C2×C22⋊C4D4×C3112yes—
260C2×C22⋊C4Q8×C3114yes—
261C2×C22⋊C4Q8×C3112yes—
262#95—24no—
263#95—24no—
264C31#1120511yescharacteristic, direct product factor, Sylow
265C24—82no—
266C24C22×C4×C3111yescharacteristic
267C24C2×D4×C3111yescharacteristic
268C24C2×D4×C3111yescharacteristic
269C24C2×D4×C3112yes—
270C24C2×D4×C3111yescharacteristic
271C24C2×Q8×C3111yescharacteristic
272C24C2×Q8×C3112yes—
273C24#41×C3112yes—
274C24#41×C3111yescharacteristic
275C24#41×C3111yescharacteristic
276C24#41×C3112yes—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—82no—
291C22×C4—82no—
292C22×C4—84no—
293C22×C4—82no—
294C22×C4—84no—
295C22×C4C22⋊C4×C3114yes—
296C4⋊C4—84no—
297C4⋊C4—84no—
298C22⋊C4—22no—
299C22⋊C4—24no—
300C22⋊C4—22no—
301C22⋊C4—24no—
302C22⋊C4—22no—
303C22⋊C4—24no—
304C22⋊C4—24no—
305C22⋊C4—24no—
306C22⋊C4—24no—
307C22⋊C4—41no—
308C22⋊C4—42no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—41no—
313C22⋊C4—42no—
314C22⋊C4C4⋊C4×C3114yescomplemented
315C23—42no—
316C23—42no—
317C23—42no—
318C23—44no—
319C23—44no—
320C23—81no—
321C23—81no—
322C23—82no—
323C23—82no—
324C23—81no—
325C23—81no—
326C23C2×C22⋊C4×C3111yescharacteristic
327C23C2×C4⋊C4×C3111yescharacteristic
328C23C31×#11711yescharacteristic
329C23C4×D4×C3112yes—
330C23C4×Q8×C3112yes—
331C23C31×#12011yescharacteristic
332C23C31×#12112yes—
333C23C31×#12111yescharacteristic
334C23C31×#12112yes—
335C23C31×#12111yescharacteristic
336C23C31×C22⋊Q812yes—
337C23C31×C22⋊Q811yescharacteristic
338C23C31×C22⋊Q812yes—
339C23C31×C22⋊Q812yes—
340C23C31×C22⋊Q811yescharacteristic
341C23C31×#12311yescharacteristic
342C23C31×#12312yes—
343C23C31×#12411yescharacteristic
344C23C31×#12512yes—
345C23C31×#12512yes—
346C23C31×#12612yes—
347C23C31×C4⋊Q812yes—
348C23C31×C4⋊Q811yescharacteristic
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—48no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—44no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—84no—
363C2×C4—84no—
364C2×C4—84no—
365C2×C4—84no—
366C2×C4—84no—
367C2×C4—84no—
368C22—22no—
369C22—22no—
370C22—24no—
371C22—24no—
372C22—22no—
373C22—41no—
374C22—42no—
375C22—41no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—41no—
380C22—41no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—42no—
385C22—42no—
386C22—41no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—41no—
391C22C31×#38011yescharacteristic
392C22C31×#38611yescharacteristic
393C22C31×#38712yes—
394C22C31×#38912yes—
395C22C31×#39111yescharacteristic
396C22C31×#39411yescharacteristic
397C22C31×#39511yescharacteristic
398C22C31×#39612yes—
399C22C31×#39812yes—
400C22C31×#39811yescharacteristic
401C22C31×#40011yescharacteristic
402C4—44no—
403C4—44no—
404C4—84no—
405C4—84no—
406C4—82no—
407C2—21no—
408C2—21no—
409C2—22no—
410C2—21no—
411C2—22no—
412C2—21no—
413C2—21no—
414C2—22no—
415C2—22no—
416C2—21no—
417C2C31×#144111yescharacteristic
418C2C31×#191312yes—
subgroupG/H
center, socleC22×C31#386
commutatorC24C22×C4×C31
Frattini, cosocleC25C23×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
13. C31×#385C4semidirect
104. C22⋊C4×C31C4⋊C4semidirect
105. #11205C31direct (N × H)
210. #385C4×C31semidirect
264. C31#11205direct (N × H)
314. C22⋊C4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#23152
C2×C31×#3422
#1120531