Finite Group Databasebeta

← C31×#13425 #21470184

Subgroups — C31×#13425 #21470184

Order 7936.

508 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2717C211yesmaximal, characteristic
2C2×C31×#354C211yesmaximal, characteristic
3C2×C31×#352C211yesmaximal, characteristic
4C31×#1890C211yesmaximal, characteristic
5C31×#1885C211yesmaximal, characteristic
6C31×#1867C211yesmaximal, characteristic
7C31×#1390C211yesmaximal, characteristic
8C2×C31×#124C2211yescharacteristic
9C2×C31×#123C2211yescharacteristic
10C31×#518C2211yescharacteristic
11C31×#419—21no—
12C2×C31×#100C2211yescharacteristic
13C2×C31×#99C2211yescharacteristic
14C2×C31×#99C2211yescharacteristic
15C31×#397—21no—
16C31×#397—21no—
17C31×#395—21no—
18C31×#387—21no—
19C31×#386C2211yescharacteristic
20C31×#385—21no—
21C31×#385—21no—
22C31×#381—21no—
23C31×#380—21no—
24C31×#354—22no—
25C31×#352—22no—
26C31×#342—21no—
27C31×#342—21no—
28C31×#339—21no—
29C22×Q8×C31D411yescharacteristic
30C22×D4×C31C2311yescharacteristic
31C23×C4×C31D411yescharacteristic
32C23×C4×C31D411yescharacteristic
33C2×M16×C31—21no—
34C31×#124—21no—
35C31×#124—21no—
36C31×#124—21no—
37C31×#124—21no—
38C31×#123—21no—
39C31×#123—21no—
40C31×#123—21no—
41C31×#123—21no—
42C4×D4×C31—41no—
43C4×D4×C31—41no—
44C31×#117—21no—
45C2×C4⋊C4×C31—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—41no—
50C2×C22⋊C4×C31—21no—
51C2×C22⋊C4×C31—21no—
52C2×C22⋊C4×C31—21no—
53C2×C22⋊C4×C31—21no—
54C2×C22⋊C4×C31—21no—
55C2×C22⋊C4×C31—21no—
56C2×C22⋊C4×C31—21no—
57C2×C22⋊C4×C31—21no—
58C2×C22⋊C4×C31D411yescharacteristic
59C2×C22⋊C4×C31D411yescharacteristic
60C2×C42×C31D411yescharacteristic
61C31×#103—41no—
62C31×#103—41no—
63C31×#100—21no—
64C31×#100—21no—
65C31×#99—21no—
66C31×#99—21no—
67C31×#99—21no—
68C31×#99D412yes—
69C31×#95—21no—
70C31×#95—21no—
71C31×#95—21no—
72C31×#95—21no—
73C31×#95—21no—
74C31×#95—21no—
75C31×#95—41no—
76C31×#95—41no—
77C31×#95—41no—
78C24×C31C2×D411yescharacteristic
79C24×C31C2×D411yescharacteristic
80C2×Q8×C31—21no—
81C2×Q8×C31—21no—
82C2×Q8×C31—41no—
83C2×Q8×C31—41no—
84C2×D4×C31—41no—
85C2×D4×C31—41no—
86C2×D4×C31C2×D411yescharacteristic
87C2×D4×C31#4111yescharacteristic
88C2×D4×C31#4111yescharacteristic
89C2×D4×C31#4111yescharacteristic
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—21no—
98C22×C4×C31—21no—
99C22×C4×C31—21no—
100C22×C4×C31—21no—
101C22×C4×C31—21no—
102C22×C4×C31—42no—
103C22×C4×C31—41no—
104C22×C4×C31—41no—
105C22×C4×C31—41no—
106C22×C4×C31—41no—
107C22×C4×C31—41no—
108C22×C4×C31C2×D411yescharacteristic
109M16×C31—41no—
110M16×C31—41no—
111C2×C8×C31—41no—
112C4⋊C4×C31—21no—
113C4⋊C4×C31—21no—
114C4⋊C4×C31—42no—
115C4⋊C4×C31—41no—
116C4⋊C4×C31—41no—
117C4⋊C4×C31—81no—
118C4⋊C4×C31—81no—
119C4⋊C4×C31—82no—
120C22⋊C4×C31—22no—
121C22⋊C4×C31—21no—
122C22⋊C4×C31—21no—
123C22⋊C4×C31—42no—
124C22⋊C4×C31—41no—
125C22⋊C4×C31—41no—
126C22⋊C4×C31—41no—
127C22⋊C4×C31—41no—
128C22⋊C4×C31—41no—
129C22⋊C4×C31—41no—
130C22⋊C4×C31—41no—
131C22⋊C4×C31—41no—
132C22⋊C4×C31—41no—
133C22⋊C4×C31—41no—
134C22⋊C4×C31—41no—
135C22⋊C4×C31—41no—
136C22⋊C4×C31—41no—
137C42×C31—21no—
138C42×C31—21no—
139C42×C31—41no—
140#13425C3111yesmaximal, characteristic, direct product factor, Sylow
141C23×C31—21no—
142C23×C31—21no—
143C23×C31—21no—
144C23×C31—21no—
145C23×C31—41no—
146C23×C31—41no—
147C23×C31—41no—
148C23×C31—41no—
149C23×C31#12011yescharacteristic
150C23×C31#12111yescharacteristic
151C23×C31#12111yescharacteristic
152C23×C31#12311yescharacteristic
153C23×C31#12411yescharacteristic
154Q8×C31—42no—
155Q8×C31—81no—
156D4×C31—41no—
157D4×C31—41no—
158D4×C31—41no—
159D4×C31—41no—
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31—22no—
163C2×C4×C31—41no—
164C2×C4×C31—41no—
165C2×C4×C31—42no—
166C2×C4×C31—42no—
167C2×C4×C31—41no—
168C2×C4×C31—41no—
169C2×C4×C31—41no—
170C2×C4×C31—41no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—42no—
174C2×C4×C31—41no—
175C2×C4×C31—41no—
176C2×C4×C31—41no—
177C2×C4×C31—41no—
178C2×C4×C31—41no—
179C2×C4×C31—41no—
180C2×C4×C31—41no—
181C2×C4×C31—41no—
182C2×C4×C31—41no—
183C2×C4×C31—41no—
184C2×C4×C31—41no—
185C2×C4×C31—81no—
186C2×C4×C31—81no—
187C2×C4×C31—81no—
188C2×C4×C31—81no—
189C2×C4×C31—81no—
190C2×C4×C31—81no—
191C2×C4×C31—81no—
192C2×C4×C31—81no—
193C2×C4×C31—81no—
194C2×C4×C31—81no—
195C2×C4×C31—81no—
196C2×C4×C31#12111yescharacteristic
197C2×C4×C31#12311yescharacteristic
198C8×C31—81no—
199#2717C2×C3111yescharacteristic
200C2×#354C2×C3111yescharacteristic
201C2×#352C2×C3111yescharacteristic
202#1890C2×C3111yescharacteristic
203#1885C2×C3111yescharacteristic
204#1867C2×C3111yescharacteristic
205#1390C2×C3111yescharacteristic
206C22×C31—21no—
207C22×C31—21no—
208C22×C31—21no—
209C22×C31—21no—
210C22×C31—21no—
211C22×C31—21no—
212C22×C31—41no—
213C22×C31—41no—
214C22×C31—41no—
215C22×C31—41no—
216C22×C31—41no—
217C22×C31—41no—
218C22×C31—41no—
219C22×C31—41no—
220C22×C31—81no—
221C22×C31—81no—
222C22×C31#39411yescharacteristic
223C22×C31B(4,𝔽2)11yescharacteristic
224C22×C31#45811yescharacteristic
225C4×C31—21no—
226C4×C31—21no—
227C4×C31—42no—
228C4×C31—81no—
229C4×C31—81no—
230C4×C31—81no—
231C4×C31—82no—
232C4×C31—81no—
233C4×C31—81no—
234C4×C31—81no—
235C4×C31—81no—
236C4×C31—161no—
237C2×#124C22×C3111yescharacteristic
238C2×#123C22×C3111yescharacteristic
239#518C22×C3111yescharacteristic
240#419—21no—
241C2×#100C22×C3111yescharacteristic
242C2×#99C22×C3111yescharacteristic
243C2×#99C22×C3111yescharacteristic
244#397—21no—
245#397—21no—
246#395—21no—
247#387—21no—
248#386C22×C3111yescharacteristic
249#385—21no—
250#385—21no—
251#381—21no—
252#380—21no—
253#354—22no—
254#352—22no—
255#342—21no—
256#342—21no—
257#339—21no—
258C2×C31—21no—
259C2×C31—21no—
260C2×C31—41no—
261C2×C31—41no—
262C2×C31—41no—
263C2×C31—41no—
264C2×C31#204411yescharacteristic
265C2×C31#219711yescharacteristic
266C2×C31#220111yescharacteristic
267C22×Q8D4×C3111yescharacteristic
268C22×D4C23×C3111yescharacteristic
269C23×C4D4×C3111yescharacteristic
270C23×C4D4×C3111yescharacteristic
271C2×M16—21no—
272#124—21no—
273#124—21no—
274#124—21no—
275#124—21no—
276#123—21no—
277#123—21no—
278#123—21no—
279#123—21no—
280C4×D4—41no—
281C4×D4—41no—
282#117—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—41no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4D4×C3111yescharacteristic
297C2×C22⋊C4D4×C3111yescharacteristic
298C2×C42D4×C3111yescharacteristic
299#103—41no—
300#103—41no—
301#100—21no—
302#100—21no—
303#99—21no—
304#99—21no—
305#99—21no—
306#99D4×C3112yes—
307#95—21no—
308#95—21no—
309#95—21no—
310#95—21no—
311#95—21no—
312#95—21no—
313#95—41no—
314#95—41no—
315#95—41no—
316C31#1342511yescharacteristic, direct product factor, Sylow
317C24C2×D4×C3111yescharacteristic
318C24C2×D4×C3111yescharacteristic
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—41no—
322C2×Q8—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4C2×D4×C3111yescharacteristic
326C2×D4#41×C3111yescharacteristic
327C2×D4#41×C3111yescharacteristic
328C2×D4#41×C3111yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4C2×D4×C3111yescharacteristic
348M16—41no—
349M16—41no—
350C2×C8—41no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—42no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—81no—
357C4⋊C4—81no—
358C4⋊C4—82no—
359C22⋊C4—22no—
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—42no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C42—21no—
377C42—21no—
378C42—41no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23C31×#12011yescharacteristic
388C23C31×#12111yescharacteristic
389C23C31×#12111yescharacteristic
390C23C31×#12311yescharacteristic
391C23C31×#12411yescharacteristic
392Q8—42no—
393Q8—81no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4—41no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4C31×#12111yescharacteristic
435C2×C4C31×#12311yescharacteristic
436C8—81no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—81no—
452C22—81no—
453C22C31×#39411yescharacteristic
454C22C31×B(4,𝔽2)11yescharacteristic
455C22C31×#45811yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—82no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4—161no—
468C2—21no—
469C2—21no—
470C2—41no—
471C2—41no—
472C2—41no—
473C2—41no—
474C2C31×#204411yescharacteristic
475C2C31×#219711yescharacteristic
476C2C31×#220111yescharacteristic
subgroupG/H
center, socleC22×C31B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C31
prime radicalC22×D4×C31C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
140. #13425C31direct (N × H)
316. C31#13425direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#27172
C2×C31×#3542
C2×C31×#3522
C31×#18902
C31×#18852
C31×#18672
C31×#13902
#1342531