Finite Group Databasebeta

← C131×#29706 #45715590

Subgroups — C131×#29706 #45715590

Order 33536.

954 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3461×C131C211yesmaximal, characteristic
2#3079×C131C212yesmaximal, complemented
3#2567×C131C211yesmaximal, characteristic, complemented
4#2060×C131C212yesmaximal, complemented
5#2039×C131C212yesmaximal
6#2038×C131C214yesmaximal, complemented
7#1806×C131C212yesmaximal, complemented
8#1801×C131C211yesmaximal, characteristic, complemented
9#544×C131C2211yescharacteristic
10#542×C131—22no—
11#541×C131—22no—
12#539×C131—22no—
13#537×C131C2211yescharacteristic
14#536×C131C2212yes—
15#533×C131—22no—
16C2×C4⋊Q8×C131C2211yescharacteristic
17#529×C131—22no—
18#529×C131—22no—
19C4×#41×C131C2212yes—
20C2×C4×Q8×C131C2211yescharacteristic
21#477×C131—22no—
22#476×C131—22no—
23#475×C131—22no—
24#474×C131—22no—
25#428×C131C2214yes—
26#423×C131C2212yes—
27C2×#104×C131C2214yes—
28#417×C131C2214yes—
29C2×#101×C131C2212yes—
30#395×C131—22no—
31#391×C131C2212yes—
32#389×C131—22no—
33#384×C131C2212yes—
34C4×C4⋊C4×C131C2211yescharacteristic
35#343×C131C2212yes—
36#339×C131C2214yes—
37C2×#41×C131C2312yes—
38C22×Q8×C131—21no—
39C22×Q8×C131C2311yescharacteristic
40C2×M16×C131C2314yes—
41C4⋊Q8×C131—22no—
42C4⋊Q8×C131—22no—
43C4⋊Q8×C131—22no—
44C4⋊Q8×C131—22no—
45#126×C131—24no—
46#126×C131—24no—
47#125×C131—22no—
48#125×C131—24no—
49#125×C131—22no—
50#124×C131—22no—
51#124×C131—22no—
52#123×C131—24no—
53#123×C131—24no—
54C22⋊Q8×C131—24no—
55C22⋊Q8×C131—22no—
56C22⋊Q8×C131—22no—
57C22⋊Q8×C131—22no—
58C22⋊Q8×C131—22no—
59#121×C131—22no—
60#121×C131—22no—
61C4×Q8×C131—22no—
62C4×Q8×C131—22no—
63C4×Q8×C131—22no—
64C4×Q8×C131D412yes—
65C4×Q8×C131D412yes—
66C4×D4×C131—22no—
67C4×D4×C131—22no—
68C4×D4×C131—22no—
69C4×D4×C131D412yes—
70C4×D4×C131D412yes—
71#117×C131—24no—
72#117×C131—22no—
73#117×C131C2312yes—
74C2×C4⋊C4×C131—21no—
75C2×C4⋊C4×C131—21no—
76C2×C4⋊C4×C131—24no—
77C2×C4⋊C4×C131D412yes—
78C2×C4⋊C4×C131C2312yes—
79C2×C4⋊C4×C131C2311yescharacteristic
80C2×C42×C131—22no—
81C2×C42×C131D412yes—
82C2×C42×C131C2312yes—
83C2×C42×C131C2311yescharacteristic
84#107×C131—24no—
85#106×C131—24no—
86C4⋊C8×C131—22no—
87C4⋊C8×C131—22no—
88#104×C131—44no—
89#103×C131—24no—
90#102×C131—24no—
91#101×C131—42no—
92#95×C131—24no—
93#95×C131—21no—
94#41×C131—22no—
95#41×C131—22no—
96#41×C131—22no—
97#41×C131—22no—
98C2×Q8×C131—22no—
99C2×Q8×C131—22no—
100C2×Q8×C131—21no—
101C2×Q8×C131—22no—
102C2×Q8×C131—21no—
103C2×Q8×C131—42no—
104C2×Q8×C131—82no—
105C2×Q8×C131C2×D412yes—
106C2×D4×C131—22no—
107C2×D4×C131—22no—
108C2×D4×C131C2×D412yes—
109C22×C4×C131—22no—
110C22×C4×C131—22no—
111C22×C4×C131—22no—
112C22×C4×C131—22no—
113C22×C4×C131—22no—
114C22×C4×C131C2×D412yes—
115C22×C4×C131C2×D411yescharacteristic
116C22×C4×C131C2×D412yes—
117C22×C4×C131C2×D411yescharacteristic
118C22×C4×C131C2411yescharacteristic
119M16×C131—24no—
120M16×C131—24no—
121C2×C8×C131—24no—
122C4⋊C4×C131—24no—
123C4⋊C4×C131—24no—
124C4⋊C4×C131—24no—
125C4⋊C4×C131—22no—
126C4⋊C4×C131—22no—
127C4⋊C4×C131—24no—
128C4⋊C4×C131—24no—
129C4⋊C4×C131—22no—
130C4⋊C4×C131—22no—
131C4⋊C4×C131—22no—
132C4⋊C4×C131—24no—
133C4⋊C4×C131—41no—
134C4⋊C4×C131—41no—
135C4⋊C4×C131—84no—
136C4⋊C4×C131C2×D412yes—
137C4⋊C4×C131C2×D412yes—
138C22⋊C4×C131—24no—
139C22⋊C4×C131—24no—
140C22⋊C4×C131—24no—
141C22⋊C4×C131—22no—
142C22⋊C4×C131—22no—
143C22⋊C4×C131—22no—
144C42×C131—22no—
145C42×C131—22no—
146C42×C131—22no—
147C42×C131—22no—
148C42×C131—22no—
149C42×C131—22no—
150C42×C131—22no—
151C42×C131C2×D412yes—
152C42×C131C2×D412yes—
153C23×C131—22no—
154C23×C131C22×D411yescharacteristic
155Q8×C131—22no—
156Q8×C131—22no—
157Q8×C131—42no—
158Q8×C131—42no—
159Q8×C131—84no—
160Q8×C131—82no—
161D4×C131—22no—
162D4×C131—22no—
163D4×C131—42no—
164D4×C131—42no—
165D4×C131—82no—
166C2×C4×C131—22no—
167C2×C4×C131—24no—
168C2×C4×C131—22no—
169C2×C4×C131—22no—
170C2×C4×C131—22no—
171C2×C4×C131—22no—
172C2×C4×C131—22no—
173C2×C4×C131—22no—
174C2×C4×C131—22no—
175C2×C4×C131—41no—
176C2×C4×C131—42no—
177C2×C4×C131—42no—
178C2×C4×C131—42no—
179C2×C4×C131—42no—
180C2×C4×C131—44no—
181C2×C4×C131—42no—
182C2×C4×C131—44no—
183C2×C4×C131—42no—
184C2×C4×C131—82no—
185C2×C4×C131#12011yescharacteristic
186C2×C4×C131#12012yes—
187C2×C4×C131#12011yescharacteristic
188C2×C4×C131C22×D412yes—
189C2×C4×C131H(5,𝔽2)11yescharacteristic
190C2×C4×C1312−1+411yescharacteristic
191C2×C4×C1312−1+412yes—
192C8×C131—44no—
193C22×C131—21no—
194C22×C131—21no—
195C22×C131—42no—
196C22×C131—42no—
197C22×C131—42no—
198C22×C131C2×#12011yescharacteristic
199C22×C131#53611yescharacteristic
200C22×C131#53711yescharacteristic
201C4×C131—21no—
202C4×C131—22no—
203C4×C131—44no—
204C4×C131—42no—
205C4×C131—42no—
206C4×C131—42no—
207C4×C131—42no—
208C4×C131—42no—
209C4×C131—82no—
210C4×C131#45612yes—
211C4×C131#53612yes—
212C4×C131#53712yes—
213C2×C131—21no—
214C2×C131—21no—
215C2×C131—82no—
216C2×C131#261611yescharacteristic
217C2×C131C2×#45611yescharacteristic
218C2×C131#302111yescharacteristic
219#29706C13111yesmaximal, characteristic, direct product factor, Sylow
220C131#2970611yescharacteristic, direct product factor, Sylow
221#3461C2×C13111yescharacteristic
222#3079C2×C13112yescomplemented
223#2567C2×C13111yescharacteristic, complemented
224#2060C2×C13112yescomplemented
225#2039C2×C13112yes—
226#2038C2×C13114yescomplemented
227#1806C2×C13112yescomplemented
228#1801C2×C13111yescharacteristic, complemented
229#544C22×C13111yescharacteristic
230#542—22no—
231#541—22no—
232#539—22no—
233#537C22×C13111yescharacteristic
234#536C22×C13112yes—
235#533—22no—
236C2×C4⋊Q8C22×C13111yescharacteristic
237#529—22no—
238#529—22no—
239C4×#41C22×C13112yes—
240C2×C4×Q8C22×C13111yescharacteristic
241#477—22no—
242#476—22no—
243#475—22no—
244#474—22no—
245#428C22×C13114yes—
246#423C22×C13112yes—
247C2×#104C22×C13114yes—
248#417C22×C13114yes—
249C2×#101C22×C13112yes—
250#395—22no—
251#391C22×C13112yes—
252#389—22no—
253#384C22×C13112yes—
254C4×C4⋊C4C22×C13111yescharacteristic
255#343C22×C13112yes—
256#339C22×C13114yes—
257C2×#41C23×C13112yes—
258C22×Q8—21no—
259C22×Q8C23×C13111yescharacteristic
260C2×M16C23×C13114yes—
261C4⋊Q8—22no—
262C4⋊Q8—22no—
263C4⋊Q8—22no—
264C4⋊Q8—22no—
265#126—24no—
266#126—24no—
267#125—22no—
268#125—24no—
269#125—22no—
270#124—22no—
271#124—22no—
272#123—24no—
273#123—24no—
274C22⋊Q8—24no—
275C22⋊Q8—22no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279#121—22no—
280#121—22no—
281C4×Q8—22no—
282C4×Q8—22no—
283C4×Q8—22no—
284C4×Q8D4×C13112yes—
285C4×Q8D4×C13112yes—
286C4×D4—22no—
287C4×D4—22no—
288C4×D4—22no—
289C4×D4D4×C13112yes—
290C4×D4D4×C13112yes—
291#117—24no—
292#117—22no—
293#117C23×C13112yes—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4D4×C13112yes—
298C2×C4⋊C4C23×C13112yes—
299C2×C4⋊C4C23×C13111yescharacteristic
300C2×C42—22no—
301C2×C42D4×C13112yes—
302C2×C42C23×C13112yes—
303C2×C42C23×C13111yescharacteristic
304#107—24no—
305#106—24no—
306C4⋊C8—22no—
307C4⋊C8—22no—
308#104—44no—
309#103—24no—
310#102—24no—
311#101—42no—
312#95—21no—
313#95—24no—
314#41—22no—
315#41—22no—
316#41—22no—
317#41—22no—
318C2×Q8—22no—
319C2×Q8—22no—
320C2×Q8—21no—
321C2×Q8—22no—
322C2×Q8—21no—
323C2×Q8—42no—
324C2×Q8—82no—
325C2×Q8C2×D4×C13112yes—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4C2×D4×C13112yes—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4C2×D4×C13112yes—
335C22×C4C2×D4×C13111yescharacteristic
336C22×C4C2×D4×C13112yes—
337C22×C4C2×D4×C13111yescharacteristic
338C22×C4C24×C13111yescharacteristic
339M16—24no—
340M16—24no—
341C2×C8—24no—
342C4⋊C4—24no—
343C4⋊C4—24no—
344C4⋊C4—24no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—24no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—84no—
356C4⋊C4C2×D4×C13112yes—
357C4⋊C4C2×D4×C13112yes—
358C22⋊C4—24no—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C42—22no—
365C42—22no—
366C42—22no—
367C42—22no—
368C42—22no—
369C42—22no—
370C42—22no—
371C42C2×D4×C13112yes—
372C42C2×D4×C13112yes—
373C23—22no—
374C23C22×D4×C13111yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—42no—
378Q8—42no—
379Q8—84no—
380Q8—82no—
381D4—22no—
382D4—22no—
383D4—42no—
384D4—42no—
385D4—82no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—44no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—82no—
405C2×C4#120×C13111yescharacteristic
406C2×C4#120×C13112yes—
407C2×C4#120×C13111yescharacteristic
408C2×C4C22×D4×C13112yes—
409C2×C4H(5,𝔽2)×C13111yescharacteristic
410C2×C42−1+4×C13111yescharacteristic
411C2×C42−1+4×C13112yes—
412C8—44no—
413C22—21no—
414C22—21no—
415C22—42no—
416C22—42no—
417C22—42no—
418C22C2×#120×C13111yescharacteristic
419C22#536×C13111yescharacteristic
420C22#537×C13111yescharacteristic
421C4—21no—
422C4—22no—
423C4—44no—
424C4—42no—
425C4—42no—
426C4—42no—
427C4—42no—
428C4—42no—
429C4—82no—
430C4#456×C13112yes—
431C4#536×C13112yes—
432C4#537×C13112yes—
433C2—21no—
434C2—21no—
435C2—82no—
436C2#2616×C13111yescharacteristic
437C2C2×#456×C13111yescharacteristic
438C2#3021×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#537×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3079×C131C2semidirect
3. #2567×C131C2semidirect
4. #2060×C131C2semidirect
6. #2038×C131C2semidirect
7. #1806×C131C2semidirect
8. #1801×C131C2semidirect
219. #29706C131direct (N × H)
220. C131#29706direct (N × H)
222. #3079C2×C131semidirect
223. #2567C2×C131semidirect
224. #2060C2×C131semidirect
226. #2038C2×C131semidirect
227. #1806C2×C131semidirect
228. #1801C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3461×C1312
#3079×C1312
#2567×C1312
#2060×C1312
#2039×C1312
#2038×C1312
#1806×C1312
#1801×C1312
#29706131