Finite Group Databasebeta

← C31×#9950 #21466709

Subgroups — C31×#9950 #21466709

Order 7936.

636 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3186C211yesmaximal, characteristic
2C2×C31×#481C211yesmaximal, characteristic, complemented
3C31×#2504C211yesmaximal, characteristic, complemented
4C31×#1964C211yesmaximal, characteristic, complemented
5C31×#1824C211yesmaximal, characteristic, complemented
6C31×#1519C211yesmaximal, characteristic, complemented
7C31×#1282C211yesmaximal, characteristic, complemented
8C2×C31×#121C2211yescharacteristic
9C2×C31×#121C2211yescharacteristic
10C22×C4⋊C4×C31C2211yescharacteristic
11C31×#481—22no—
12C31×#481—22no—
13C31×#480—21no—
14C31×#480—21no—
15C31×#466—22no—
16C31×#447—21no—
17C31×#447—21no—
18C2×C31×#106—21no—
19C2×C31×#102—21no—
20C2×C31×#99—22no—
21C2×C31×C22⋊C8C2211yescharacteristic
22C2×C31×C22⋊C8C2211yescharacteristic
23C31×#397—22no—
24C31×#390—21no—
25C31×#386—22no—
26C31×#382—21no—
27C31×#380C2211yescharacteristic
28C4×C22⋊C4×C31C2211yescharacteristic
29C31×#340—22no—
30C31×#327—22no—
31C22×D4×C31—21no—
32C22×D4×C31—21no—
33C22×D4×C31D411yescharacteristic
34C22×D4×C31D411yescharacteristic
35C23×C4×C31—21no—
36C23×C4×C31C2311yescharacteristic
37C2×D8×C31—22no—
38C22×C8×C31—21no—
39C22×C8×C31D412yes—
40C31×#121—21no—
41C31×#121—21no—
42C31×#121—21no—
43C31×#121—21no—
44C31×#121—21no—
45C31×#121—21no—
46C31×#121—21no—
47C31×#121—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31D412yes—
55C2×C4⋊C4×C31D411yescharacteristic
56C2×C4⋊C4×C31D411yescharacteristic
57C2×C22⋊C4×C31—21no—
58C2×C22⋊C4×C31—21no—
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—24no—
61C2×C22⋊C4×C31D412yes—
62C2×C42×C31—21no—
63C31×#107—22no—
64C31×#106—24no—
65C31×#102—24no—
66C31×#102—22no—
67C31×#102—22no—
68C31×#99—44no—
69C31×C22⋊C8—21no—
70C31×C22⋊C8—21no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8D412yes—
73C31×#95—24no—
74C31×#95—21no—
75C31×#95—21no—
76C24×C31—21no—
77C24×C31—21no—
78C24×C31C2×D411yescharacteristic
79C2×D4×C31—21no—
80C2×D4×C31—21no—
81C2×D4×C31—21no—
82C2×D4×C31—21no—
83C2×D4×C31—42no—
84C2×D4×C31—42no—
85C2×D4×C31—41no—
86C2×D4×C31—41no—
87C2×D4×C31—41no—
88C2×D4×C31—41no—
89C2×D4×C31—42no—
90C2×D4×C31—42no—
91C2×D4×C31—42no—
92C2×D4×C31—42no—
93C22×C4×C31—21no—
94C22×C4×C31—22no—
95C22×C4×C31—22no—
96C22×C4×C31—21no—
97C22×C4×C31—42no—
98C22×C4×C31—41no—
99C22×C4×C31—41no—
100C22×C4×C31—41no—
101C22×C4×C31—82no—
102C22×C4×C31C2×D411yescharacteristic
103C22×C4×C31C2×D411yescharacteristic
104C22×C4×C31C2×D411yescharacteristic
105C22×C4×C31C2×D411yescharacteristic
106C22×C4×C31C2×D411yescharacteristic
107C22×C4×C31#4111yescharacteristic
108D8×C31—82no—
109C2×C8×C31—22no—
110C2×C8×C31—22no—
111C2×C8×C31—42no—
112C2×C8×C31—42no—
113C4⋊C4×C31—22no—
114C4⋊C4×C31—21no—
115C4⋊C4×C31—21no—
116C4⋊C4×C31—21no—
117C4⋊C4×C31—22no—
118C4⋊C4×C31—21no—
119C4⋊C4×C31—42no—
120C4⋊C4×C31—41no—
121C4⋊C4×C31—41no—
122C22⋊C4×C31—22no—
123C22⋊C4×C31—22no—
124C22⋊C4×C31—41no—
125C22⋊C4×C31—41no—
126C22⋊C4×C31—41no—
127C22⋊C4×C31—41no—
128C22⋊C4×C31—42no—
129C22⋊C4×C31—84no—
130C42×C31—42no—
131#9950C3111yesmaximal, characteristic, direct product factor, Sylow
132C23×C31—41no—
133C23×C31—41no—
134C23×C31—42no—
135C23×C31—42no—
136C23×C31—41no—
137C23×C31—41no—
138C23×C31—42no—
139C23×C31—42no—
140C23×C31—81no—
141C23×C31—81no—
142C23×C31#12011yescharacteristic
143C23×C31#12111yescharacteristic
144C23×C31#12711yescharacteristic
145C23×C31#13512yes—
146C23×C31AGL(1,ℤ/8)12yes—
147D4×C31—42no—
148D4×C31—42no—
149D4×C31—42no—
150D4×C31—81no—
151D4×C31—82no—
152D4×C31—82no—
153D4×C31—81no—
154D4×C31—81no—
155D4×C31—81no—
156D4×C31—81no—
157C2×C4×C31—22no—
158C2×C4×C31—22no—
159C2×C4×C31—22no—
160C2×C4×C31—41no—
161C2×C4×C31—41no—
162C2×C4×C31—41no—
163C2×C4×C31—42no—
164C2×C4×C31—42no—
165C2×C4×C31—44no—
166C2×C4×C31—41no—
167C2×C4×C31—41no—
168C2×C4×C31—42no—
169C2×C4×C31—42no—
170C2×C4×C31—42no—
171C2×C4×C31—42no—
172C2×C4×C31—82no—
173C2×C4×C31—82no—
174C2×C4×C31—81no—
175C2×C4×C31—81no—
176C2×C4×C31—81no—
177C2×C4×C31#12011yescharacteristic
178C2×C4×C31#12011yescharacteristic
179C2×C4×C31#12111yescharacteristic
180C2×C4×C31#12111yescharacteristic
181C8×C31—42no—
182C8×C31—42no—
183#3186C2×C3111yescharacteristic
184C2×#481C2×C3111yescharacteristic, complemented
185#2504C2×C3111yescharacteristic, complemented
186#1964C2×C3111yescharacteristic, complemented
187#1824C2×C3111yescharacteristic, complemented
188#1519C2×C3111yescharacteristic, complemented
189#1282C2×C3111yescharacteristic, complemented
190C22×C31—21no—
191C22×C31—21no—
192C22×C31—21no—
193C22×C31—21no—
194C22×C31—21no—
195C22×C31—21no—
196C22×C31—42no—
197C22×C31—42no—
198C22×C31—84no—
199C22×C31—81no—
200C22×C31—81no—
201C22×C31—81no—
202C22×C31—81no—
203C22×C31—81no—
204C22×C31—81no—
205C22×C31—162no—
206C22×C31#39211yescharacteristic
207C22×C31#44912yes—
208C22×C31#46312yes—
209C22×C31#49511yescharacteristic
210C22×C31#49611yescharacteristic
211C4×C31—21no—
212C4×C31—21no—
213C4×C31—21no—
214C4×C31—82no—
215C4×C31—82no—
216C4×C31—81no—
217C4×C31—81no—
218C4×C31—161no—
219C4×C31#45812yes—
220C2×#121C22×C3111yescharacteristic
221C2×#121C22×C3111yescharacteristic
222C22×C4⋊C4C22×C3111yescharacteristic
223#481—22no—
224#481—22no—
225#480—21no—
226#480—21no—
227#466—22no—
228#447—21no—
229#447—21no—
230C2×#106—21no—
231C2×#102—21no—
232C2×#99—22no—
233C2×C22⋊C8C22×C3111yescharacteristic
234C2×C22⋊C8C22×C3111yescharacteristic
235#397—22no—
236#390—21no—
237#386—22no—
238#382—21no—
239#380C22×C3111yescharacteristic
240C4×C22⋊C4C22×C3111yescharacteristic
241#340—22no—
242#327—22no—
243C2×C31—22no—
244C2×C31—21no—
245C2×C31—22no—
246C2×C31—21no—
247C2×C31—161no—
248C2×C31—161no—
249C2×C31#200811yescharacteristic
250C2×C31#201211yescharacteristic
251C2×C31#202211yescharacteristic
252C22×D4—21no—
253C22×D4—21no—
254C22×D4D4×C3111yescharacteristic
255C22×D4D4×C3111yescharacteristic
256C23×C4—21no—
257C23×C4C23×C3111yescharacteristic
258C2×D8—22no—
259C22×C8—21no—
260C22×C8D4×C3112yes—
261#121—21no—
262#121—21no—
263#121—21no—
264#121—21no—
265#121—21no—
266#121—21no—
267#121—21no—
268#121—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4D4×C3112yes—
276C2×C4⋊C4D4×C3111yescharacteristic
277C2×C4⋊C4D4×C3111yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—24no—
282C2×C22⋊C4D4×C3112yes—
283C2×C42—21no—
284#107—22no—
285#106—24no—
286#102—24no—
287#102—22no—
288#102—22no—
289#99—44no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8D4×C3112yes—
294#95—24no—
295#95—21no—
296#95—21no—
297C31#995011yescharacteristic, direct product factor, Sylow
298C24—21no—
299C24—21no—
300C24C2×D4×C3111yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—42no—
306C2×D4—42no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—42no—
312C2×D4—42no—
313C2×D4—42no—
314C2×D4—42no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—82no—
324C22×C4C2×D4×C3111yescharacteristic
325C22×C4C2×D4×C3111yescharacteristic
326C22×C4C2×D4×C3111yescharacteristic
327C22×C4C2×D4×C3111yescharacteristic
328C22×C4C2×D4×C3111yescharacteristic
329C22×C4#41×C3111yescharacteristic
330D8—82no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—42no—
334C2×C8—42no—
335C4⋊C4—22no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—22no—
340C4⋊C4—21no—
341C4⋊C4—42no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—42no—
351C22⋊C4—84no—
352C42—42no—
353C23—41no—
354C23—41no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23—42no—
361C23—81no—
362C23—81no—
363C23C31×#12011yescharacteristic
364C23C31×#12111yescharacteristic
365C23C31×#12711yescharacteristic
366C23C31×#13512yes—
367C23C31×AGL(1,ℤ/8)12yes—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—82no—
373D4—82no—
374D4—81no—
375D4—81no—
376D4—81no—
377D4—81no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4C31×#12011yescharacteristic
399C2×C4C31×#12011yescharacteristic
400C2×C4C31×#12111yescharacteristic
401C2×C4C31×#12111yescharacteristic
402C8—42no—
403C8—42no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—42no—
411C22—42no—
412C22—84no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—162no—
420C22C31×#39211yescharacteristic
421C22C31×#44912yes—
422C22C31×#46312yes—
423C22C31×#49511yescharacteristic
424C22C31×#49611yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—82no—
429C4—82no—
430C4—81no—
431C4—81no—
432C4—161no—
433C4C31×#45812yes—
434C2—22no—
435C2—21no—
436C2—22no—
437C2—21no—
438C2—161no—
439C2—161no—
440C2C31×#200811yescharacteristic
441C2C31×#201211yescharacteristic
442C2C31×#202211yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC31×#3186C2
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
2. C2×C31×#481C2semidirect
3. C31×#2504C2semidirect
4. C31×#1964C2semidirect
5. C31×#1824C2semidirect
6. C31×#1519C2semidirect
7. C31×#1282C2semidirect
131. #9950C31direct (N × H)
184. C2×#481C2×C31semidirect
185. #2504C2×C31semidirect
186. #1964C2×C31semidirect
187. #1824C2×C31semidirect
188. #1519C2×C31semidirect
189. #1282C2×C31semidirect
297. C31#9950direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31862
C2×C31×#4812
C31×#25042
C31×#19642
C31×#18242
C31×#15192
C31×#12822
#995031