Finite Group Databasebeta

← C31×#11342 #21468101

Subgroups — C31×#11342 #21468101

Order 7936.

822 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#428C212yesmaximal
2C31×#2316C211yesmaximal, characteristic
3C2×C31×#343C211yesmaximal, characteristic
4C2×C31×#339C212yesmaximal
5C31×C4⋊#95C211yesmaximal, characteristic
6C22×M16×C31C2212yes—
7C2×C31×#117C2212yes—
8C22×C4⋊C4×C31C2211yescharacteristic
9C22×C4⋊C4×C31C2211yescharacteristic
10C22×C42×C31C2211yescharacteristic
11C31×#428—24no—
12C31×#428—24no—
13C2×C31×#107—22no—
14C2×C31×#106—22no—
15C31×#389—22no—
16C31×#389—22no—
17C31×#380—22no—
18C2×C31×#95—22no—
19C31×#343C414yescomplemented
20C31×#339—24no—
21C23×C4×C31—21no—
22C23×C4×C31—21no—
23C23×C4×C31D412yes—
24C23×C4×C31C2311yescharacteristic
25C2×M16×C31—22no—
26C2×M16×C31—22no—
27C2×M16×C31—22no—
28C2×M16×C31C2×C414yes—
29C2×M16×C31D414yes—
30C2×M16×C31Q814yes—
31C22×C8×C31—22no—
32C31×#117—22no—
33C31×#117—22no—
34C31×#117—22no—
35C31×#117—22no—
36C2×C4⋊C4×C31—22no—
37C2×C4⋊C4×C31—22no—
38C2×C4⋊C4×C31—22no—
39C2×C4⋊C4×C31—22no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31—22no—
42C2×C4⋊C4×C31—22no—
43C2×C4⋊C4×C31C2×C412yes—
44C2×C4⋊C4×C31D412yes—
45C2×C4⋊C4×C31D412yes—
46C2×C4⋊C4×C31D412yes—
47C2×C4⋊C4×C31Q812yes—
48C2×C22⋊C4×C31—22no—
49C2×C42×C31—22no—
50C2×C42×C31—22no—
51C2×C42×C31—22no—
52C2×C42×C31—21no—
53C2×C42×C31Q812yes—
54C31×#107—28no—
55C31×#106—28no—
56C31×#95—24no—
57C31×#95—44no—
58C24×C31C2×D411yescharacteristic
59C22×C4×C31—22no—
60C22×C4×C31—22no—
61C22×C4×C31—22no—
62C22×C4×C31—22no—
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31—22no—
66C22×C4×C31—22no—
67C22×C4×C31—41no—
68C22×C4×C31—41no—
69C22×C4×C31—41no—
70C22×C4×C31—41no—
71C22×C4×C31—42no—
72C22×C4×C31—42no—
73C22×C4×C31—42no—
74C22×C4×C31—42no—
75C22×C4×C31—41no—
76C22×C4×C31—41no—
77C22×C4×C31C4⋊C414yes—
78C22×C4×C31C22×C411yescharacteristic
79C22×C4×C31C2×D412yes—
80C22×C4×C31C2×D411yescharacteristic
81C22×C4×C31C2×D412yes—
82C22×C4×C31C2×Q812yes—
83C22×C4×C31C2×Q811yescharacteristic
84C22×C4×C31C2×Q811yescharacteristic
85C22×C4×C31#4112yes—
86C22×C4×C31#4111yescharacteristic
87C22×C4×C31#4111yescharacteristic
88M16×C31—24no—
89M16×C31—24no—
90M16×C31—24no—
91M16×C31C4⋊C418yescomplemented
92C2×C8×C31—24no—
93C2×C8×C31—24no—
94C2×C8×C31—24no—
95C4⋊C4×C31—24no—
96C4⋊C4×C31—24no—
97C4⋊C4×C31—22no—
98C4⋊C4×C31—24no—
99C4⋊C4×C31—22no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—22no—
102C4⋊C4×C31—42no—
103C4⋊C4×C31—82no—
104C4⋊C4×C31—82no—
105C22⋊C4×C31—42no—
106C22⋊C4×C31—42no—
107C42×C31—24no—
108C42×C31—42no—
109C42×C31—42no—
110C42×C31—42no—
111#11342C3111yesmaximal, characteristic, direct product factor, Sylow
112C23×C31—21no—
113C23×C31—21no—
114C23×C31—21no—
115C23×C31—21no—
116C23×C31C2×C4⋊C411yescharacteristic
117C23×C31#12011yescharacteristic
118C23×C31#12111yescharacteristic
119C23×C31C22⋊Q811yescharacteristic
120C23×C31#12311yescharacteristic
121C23×C31#12711yescharacteristic
122C23×C31C4⋊Q811yescharacteristic
123C2×C4×C31—24no—
124C2×C4×C31—24no—
125C2×C4×C31—42no—
126C2×C4×C31—42no—
127C2×C4×C31—42no—
128C2×C4×C31—42no—
129C2×C4×C31—42no—
130C2×C4×C31—42no—
131C2×C4×C31—42no—
132C2×C4×C31—42no—
133C2×C4×C31—44no—
134C2×C4×C31—44no—
135C2×C4×C31—42no—
136C2×C4×C31—42no—
137C2×C4×C31—42no—
138C2×C4×C31—42no—
139C2×C4×C31—42no—
140C2×C4×C31—42no—
141C2×C4×C31—42no—
142C2×C4×C31—82no—
143C2×C4×C31—82no—
144C2×C4×C31—81no—
145C2×C4×C31—81no—
146C2×C4×C31C2×C4⋊C412yes—
147C2×C4×C31C4×D411yescharacteristic
148C2×C4×C31C4×D412yes—
149C2×C4×C31C4×Q811yescharacteristic
150C2×C4×C31#12012yes—
151C2×C4×C31#12112yes—
152C2×C4×C31C22⋊Q812yes—
153C2×C4×C31C22⋊Q812yes—
154C2×C4×C31C22⋊Q812yes—
155C2×C4×C31C22⋊Q812yes—
156C2×C4×C31#12312yes—
157C2×C4×C31#12512yes—
158C2×C4×C31#12511yescharacteristic
159C2×C4×C31C4⋊Q812yes—
160C2×C4×C31C4⋊Q811yescharacteristic
161C2×C4×C31C4⋊Q812yes—
162C8×C31—28no—
163C2×#428C2×C3112yes—
164#2316C2×C3111yescharacteristic
165C2×#343C2×C3111yescharacteristic
166C2×#339C2×C3112yes—
167C4⋊#95C2×C3111yescharacteristic
168C22×C31—21no—
169C22×C31—21no—
170C22×C31—21no—
171C22×C31—21no—
172C22×C31—21no—
173C22×C31—21no—
174C22×C31—21no—
175C22×C31—21no—
176C22×C31—21no—
177C22×C31—21no—
178C22×C31—21no—
179C22×C31—21no—
180C22×C31#38411yescharacteristic
181C22×C31#38511yescharacteristic
182C22×C31#38911yescharacteristic
183C22×C31#39211yescharacteristic
184C22×C31#39511yescharacteristic
185C22×C31#39811yescharacteristic
186C22×C31#39911yescharacteristic
187C22×C31#45311yescharacteristic
188C22×C31#45411yescharacteristic
189C22×C31#45511yescharacteristic
190C22×C31#45611yescharacteristic
191C4×C31—44no—
192C4×C31—44no—
193C4×C31—82no—
194C4×C31—82no—
195C4×C31—82no—
196C4×C31#38512yes—
197C4×C31#38912yes—
198C4×C31#39512yes—
199C4×C31#39812yes—
200C22×M16C22×C3112yes—
201C2×#117C22×C3112yes—
202C22×C4⋊C4C22×C3111yescharacteristic
203C22×C4⋊C4C22×C3111yescharacteristic
204C22×C42C22×C3111yescharacteristic
205#428—24no—
206#428—24no—
207C2×#107—22no—
208C2×#106—22no—
209#389—22no—
210#389—22no—
211#380—22no—
212C2×#95—22no—
213#343C4×C3114yescomplemented
214#339—24no—
215C2×C31—21no—
216C2×C31—21no—
217C2×C31—21no—
218C2×C31—21no—
219C2×C31#144411yescharacteristic
220C2×C31#185611yescharacteristic
221C2×C31#185711yescharacteristic
222C2×C31#200611yescharacteristic
223C2×C31#200711yescharacteristic
224C2×C31#206011yescharacteristic
225C2×C31#206111yescharacteristic
226C23×C4—21no—
227C23×C4—21no—
228C23×C4D4×C3112yes—
229C23×C4C23×C3111yescharacteristic
230C2×M16—22no—
231C2×M16—22no—
232C2×M16—22no—
233C2×M16C2×C4×C3114yes—
234C2×M16D4×C3114yes—
235C2×M16Q8×C3114yes—
236C22×C8—22no—
237#117—22no—
238#117—22no—
239#117—22no—
240#117—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4C2×C4×C3112yes—
249C2×C4⋊C4D4×C3112yes—
250C2×C4⋊C4D4×C3112yes—
251C2×C4⋊C4D4×C3112yes—
252C2×C4⋊C4Q8×C3112yes—
253C2×C22⋊C4—22no—
254C2×C42—22no—
255C2×C42—22no—
256C2×C42—22no—
257C2×C42—21no—
258C2×C42Q8×C3112yes—
259#107—28no—
260#106—28no—
261#95—24no—
262#95—44no—
263C31#1134211yescharacteristic, direct product factor, Sylow
264C24C2×D4×C3111yescharacteristic
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4C4⋊C4×C3114yes—
284C22×C4C22×C4×C3111yescharacteristic
285C22×C4C2×D4×C3112yes—
286C22×C4C2×D4×C3111yescharacteristic
287C22×C4C2×D4×C3112yes—
288C22×C4C2×Q8×C3112yes—
289C22×C4C2×Q8×C3111yescharacteristic
290C22×C4C2×Q8×C3111yescharacteristic
291C22×C4#41×C3112yes—
292C22×C4#41×C3111yescharacteristic
293C22×C4#41×C3111yescharacteristic
294M16—24no—
295M16—24no—
296M16—24no—
297M16C4⋊C4×C3118yescomplemented
298C2×C8—24no—
299C2×C8—24no—
300C2×C8—24no—
301C4⋊C4—24no—
302C4⋊C4—24no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—42no—
309C4⋊C4—82no—
310C4⋊C4—82no—
311C22⋊C4—42no—
312C22⋊C4—42no—
313C42—24no—
314C42—42no—
315C42—42no—
316C42—42no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C4⋊C4×C3111yescharacteristic
322C23C31×#12011yescharacteristic
323C23C31×#12111yescharacteristic
324C23C31×C22⋊Q811yescharacteristic
325C23C31×#12311yescharacteristic
326C23C31×#12711yescharacteristic
327C23C31×C4⋊Q811yescharacteristic
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4C2×C4⋊C4×C3112yes—
352C2×C4C4×D4×C3111yescharacteristic
353C2×C4C4×D4×C3112yes—
354C2×C4C4×Q8×C3111yescharacteristic
355C2×C4C31×#12012yes—
356C2×C4C31×#12112yes—
357C2×C4C31×C22⋊Q812yes—
358C2×C4C31×C22⋊Q812yes—
359C2×C4C31×C22⋊Q812yes—
360C2×C4C31×C22⋊Q812yes—
361C2×C4C31×#12312yes—
362C2×C4C31×#12511yescharacteristic
363C2×C4C31×#12512yes—
364C2×C4C31×C4⋊Q811yescharacteristic
365C2×C4C31×C4⋊Q812yes—
366C2×C4C31×C4⋊Q812yes—
367C8—28no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22C31×#38411yescharacteristic
381C22C31×#38511yescharacteristic
382C22C31×#38911yescharacteristic
383C22C31×#39211yescharacteristic
384C22C31×#39511yescharacteristic
385C22C31×#39811yescharacteristic
386C22C31×#39911yescharacteristic
387C22C31×#45311yescharacteristic
388C22C31×#45411yescharacteristic
389C22C31×#45511yescharacteristic
390C22C31×#45611yescharacteristic
391C4—44no—
392C4—44no—
393C4—82no—
394C4—82no—
395C4—82no—
396C4C31×#38512yes—
397C4C31×#38912yes—
398C4C31×#39512yes—
399C4C31×#39812yes—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2C31×#144411yescharacteristic
405C2C31×#185611yescharacteristic
406C2C31×#185711yescharacteristic
407C2C31×#200611yescharacteristic
408C2C31×#200711yescharacteristic
409C2C31×#206011yescharacteristic
410C2C31×#206111yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
19. C31×#343C4semidirect
91. M16×C31C4⋊C4semidirect
111. #11342C31direct (N × H)
213. #343C4×C31semidirect
263. C31#11342direct (N × H)
297. M16C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4282
C31×#23162
C2×C31×#3432
C2×C31×#3392
C31×C4⋊#952
#1134231