Finite Group Databasebeta

← C131×#9999 #45695883

Subgroups — C131×#9999 #45695883

Order 33536.

554 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#3103×C131C211yesmaximal, characteristic
2#3037×C131C211yesmaximal, characteristic
3#2581×C131C211yesmaximal, characteristic, complemented
4#1517×C131C211yesmaximal, characteristic
5#1487×C131C211yesmaximal, characteristic, complemented
6#1479×C131C211yesmaximal, characteristic, complemented
7#1286×C131C211yesmaximal, characteristic, complemented
8C2×#137×C131—21no—
9#532×C131C2211yescharacteristic
10C2×C4×Q8×C131C2211yescharacteristic
11C2×C4×Q8×C131C2211yescharacteristic
12#481×C131—21no—
13#475×C131—21no—
14#464×C131—22no—
15#462×C131—21no—
16#460×C131—21no—
17#460×C131—21no—
18#448×C131—21no—
19C4×SD16×C131—22no—
20#431×C131C2211yescharacteristic
21#431×C131C2211yescharacteristic
22#423×C131C2211yescharacteristic
23#417×C131—21no—
24#400×C131—21no—
25#395×C131—21no—
26#391×C131—21no—
27#389×C131—21no—
28#387×C131—22no—
29#382×C131C2211yescharacteristic
30#327×C131—22no—
31Q8⋊C8×C131—22no—
32Q8⋊C8×C131—22no—
33C2×#41×C131—21no—
34C22×Q8×C131D411yescharacteristic
35C22×Q8×C131D411yescharacteristic
36#137×C131—42no—
37#137×C131—42no—
38C2×Q16×C131—22no—
39C2×SD16×C131—22no—
40C2×SD16×C131—22no—
41C2×M16×C131—21no—
42C4⋊Q8×C131D411yescharacteristic
43#127×C131D411yescharacteristic
44#124×C131—21no—
45#121×C131—21no—
46#121×C131—21no—
47C4×Q8×C131—21no—
48C4×Q8×C131—21no—
49C4×Q8×C131—21no—
50C4×Q8×C131—21no—
51C4×Q8×C131—21no—
52C4×Q8×C131—21no—
53C4×Q8×C131—21no—
54C4×Q8×C131—21no—
55C4×D4×C131—21no—
56C4×D4×C131—21no—
57C2×C4⋊C4×C131—22no—
58C2×C4⋊C4×C131—21no—
59C2×C4⋊C4×C131—21no—
60C2×C4⋊C4×C131—21no—
61C2×C4⋊C4×C131D411yescharacteristic
62C2×C4⋊C4×C131D411yescharacteristic
63C2×C42×C131—21no—
64C2×C42×C131—21no—
65C2×C42×C131C2311yescharacteristic
66#106×C131—22no—
67C4⋊C8×C131—21no—
68C4⋊C8×C131—21no—
69C4⋊C8×C131—21no—
70C4⋊C8×C131D412yes—
71#103×C131—22no—
72#103×C131—22no—
73#102×C131—22no—
74#102×C131—22no—
75C22⋊C8×C131—21no—
76C22⋊C8×C131—21no—
77C4×C8×C131—21no—
78C4×C8×C131D412yes—
79#95×C131—22no—
80#95×C131—22no—
81#95×C131—22no—
82#95×C131—21no—
83#95×C131D412yes—
84#41×C131—41no—
85#41×C131—41no—
86#41×C131—41no—
87#41×C131—41no—
88C2×Q8×C131—21no—
89C2×Q8×C131—21no—
90C2×Q8×C131—21no—
91C2×Q8×C131—21no—
92C2×Q8×C131—21no—
93C2×Q8×C131—21no—
94C2×Q8×C131—21no—
95C2×Q8×C131—21no—
96C2×Q8×C131—42no—
97C2×Q8×C131SD1612yescomplemented
98C2×D4×C131—21no—
99C2×D4×C131—21no—
100C2×D4×C131—21no—
101C2×D4×C131—41no—
102C22×C4×C131—21no—
103C22×C4×C131—21no—
104C22×C4×C131—22no—
105C22×C4×C131—21no—
106C22×C4×C131—21no—
107C22×C4×C131—41no—
108C22×C4×C131C2×D411yescharacteristic
109C22×C4×C131C2×D411yescharacteristic
110C22×C4×C131C2×D411yescharacteristic
111Q16×C131—44no—
112SD16×C131—44no—
113SD16×C131—44no—
114M16×C131—41no—
115M16×C131—41no—
116C2×C8×C131—22no—
117C2×C8×C131—22no—
118C2×C8×C131—41no—
119C4⋊C4×C131—21no—
120C4⋊C4×C131—21no—
121C4⋊C4×C131—21no—
122C4⋊C4×C131—21no—
123C4⋊C4×C131—21no—
124C4⋊C4×C131—21no—
125C4⋊C4×C131—44no—
126C4⋊C4×C131—41no—
127C4⋊C4×C131—41no—
128C4⋊C4×C131—41no—
129C4⋊C4×C131—41no—
130C4⋊C4×C131—41no—
131C4⋊C4×C131—41no—
132C22⋊C4×C131—41no—
133C22⋊C4×C131—41no—
134C42×C131—41no—
135C42×C131—41no—
136C42×C131—41no—
137C42×C131—41no—
138C42×C131C2×D411yescharacteristic
139C42×C131C2×D411yescharacteristic
140C42×C131C2×D411yescharacteristic
141C42×C131#4111yescharacteristic
142C23×C131—41no—
143C23×C131#12011yescharacteristic
144Q8×C131—22no—
145Q8×C131—22no—
146Q8×C131—22no—
147Q8×C131—22no—
148Q8×C131—41no—
149Q8×C131—41no—
150Q8×C131—41no—
151Q8×C131—41no—
152Q8×C131—41no—
153Q8×C131—41no—
154D4×C131—42no—
155D4×C131—41no—
156D4×C131—41no—
157D4×C131—81no—
158D4×C131—81no—
159D4×C131—81no—
160C2×C4×C131—22no—
161C2×C4×C131—22no—
162C2×C4×C131—41no—
163C2×C4×C131—41no—
164C2×C4×C131—41no—
165C2×C4×C131—41no—
166C2×C4×C131—41no—
167C2×C4×C131—41no—
168C2×C4×C131—42no—
169C2×C4×C131—42no—
170C2×C4×C131—42no—
171C2×C4×C131—42no—
172C2×C4×C131—41no—
173C2×C4×C131—41no—
174C2×C4×C131—41no—
175C2×C4×C131—42no—
176C2×C4×C131—81no—
177C2×C4×C131—81no—
178C2×C4×C131#12011yescharacteristic
179C2×C4×C131#12011yescharacteristic
180C2×C4×C131#12111yescharacteristic
181C2×C4×C131#12111yescharacteristic
182C2×C4×C131#12111yescharacteristic
183C2×C4×C131#12711yescharacteristic
184C2×C4×C131C2×SD1611yescharacteristic
185C2×C4×C131#13511yescharacteristic
186C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C131#13711yescharacteristic
188C8×C131—42no—
189C8×C131—42no—
190C8×C131—81no—
191C22×C131—21no—
192C22×C131—21no—
193C22×C131—81no—
194C22×C131—81no—
195C22×C131—81no—
196C22×C131#39211yescharacteristic
197C22×C131#44811yescharacteristic
198C22×C131#44911yescharacteristic
199C4×C131—21no—
200C4×C131—21no—
201C4×C131—21no—
202C4×C131—21no—
203C4×C131—42no—
204C4×C131—42no—
205C4×C131—82no—
206C4×C131—81no—
207C4×C131—81no—
208C4×C131—81no—
209C4×C131#45011yescharacteristic
210C4×C131#45211yescharacteristic
211C4×C131#46511yescharacteristic
212C4×C131#46811yescharacteristic
213C2×C131—21no—
214C2×C131—21no—
215C2×C131—161no—
216C2×C131#200011yescharacteristic
217C2×C131#200911yescharacteristic
218C2×C131#201011yescharacteristic
219#9999C13111yesmaximal, characteristic, direct product factor, Sylow
220C131#999911yescharacteristic, direct product factor, Sylow
221#3103C2×C13111yescharacteristic
222#3037C2×C13111yescharacteristic
223#2581C2×C13111yescharacteristic, complemented
224#1517C2×C13111yescharacteristic
225#1487C2×C13111yescharacteristic, complemented
226#1479C2×C13111yescharacteristic, complemented
227#1286C2×C13111yescharacteristic, complemented
228C2×#137—21no—
229#532C22×C13111yescharacteristic
230C2×C4×Q8C22×C13111yescharacteristic
231C2×C4×Q8C22×C13111yescharacteristic
232#481—21no—
233#475—21no—
234#464—22no—
235#462—21no—
236#460—21no—
237#460—21no—
238#448—21no—
239C4×SD16—22no—
240#431C22×C13111yescharacteristic
241#431C22×C13111yescharacteristic
242#423C22×C13111yescharacteristic
243#417—21no—
244#400—21no—
245#395—21no—
246#391—21no—
247#389—21no—
248#387—22no—
249#382C22×C13111yescharacteristic
250#327—22no—
251Q8⋊C8—22no—
252Q8⋊C8—22no—
253C2×#41—21no—
254C22×Q8D4×C13111yescharacteristic
255C22×Q8D4×C13111yescharacteristic
256#137—42no—
257#137—42no—
258C2×Q16—22no—
259C2×SD16—22no—
260C2×SD16—22no—
261C2×M16—21no—
262C4⋊Q8D4×C13111yescharacteristic
263#127D4×C13111yescharacteristic
264#124—21no—
265#121—21no—
266#121—21no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×Q8—21no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×D4—21no—
276C4×D4—21no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4D4×C13111yescharacteristic
282C2×C4⋊C4D4×C13111yescharacteristic
283C2×C42—21no—
284C2×C42—21no—
285C2×C42C23×C13111yescharacteristic
286#106—22no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8D4×C13112yes—
291#103—22no—
292#103—22no—
293#102—22no—
294#102—22no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C4×C8—21no—
298C4×C8D4×C13112yes—
299#95—22no—
300#95—22no—
301#95—22no—
302#95—21no—
303#95D4×C13112yes—
304#41—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—42no—
317C2×Q8SD16×C13112yescomplemented
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—41no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—41no—
328C22×C4C2×D4×C13111yescharacteristic
329C22×C4C2×D4×C13111yescharacteristic
330C22×C4C2×D4×C13111yescharacteristic
331Q16—44no—
332SD16—44no—
333SD16—44no—
334M16—41no—
335M16—41no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—41no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—44no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C42—41no—
355C42—41no—
356C42—41no—
357C42—41no—
358C42C2×D4×C13111yescharacteristic
359C42C2×D4×C13111yescharacteristic
360C42C2×D4×C13111yescharacteristic
361C42#41×C13111yescharacteristic
362C23—41no—
363C23#120×C13111yescharacteristic
364Q8—22no—
365Q8—22no—
366Q8—22no—
367Q8—22no—
368Q8—41no—
369Q8—41no—
370Q8—41no—
371Q8—41no—
372Q8—41no—
373Q8—41no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—81no—
378D4—81no—
379D4—81no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4#120×C13111yescharacteristic
399C2×C4#120×C13111yescharacteristic
400C2×C4#121×C13111yescharacteristic
401C2×C4#121×C13111yescharacteristic
402C2×C4#121×C13111yescharacteristic
403C2×C4#127×C13111yescharacteristic
404C2×C4C2×SD16×C13111yescharacteristic
405C2×C4#135×C13111yescharacteristic
406C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
407C2×C4#137×C13111yescharacteristic
408C8—42no—
409C8—42no—
410C8—81no—
411C22—21no—
412C22—21no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22#392×C13111yescharacteristic
417C22#448×C13111yescharacteristic
418C22#449×C13111yescharacteristic
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—42no—
425C4—82no—
426C4—81no—
427C4—81no—
428C4—81no—
429C4#450×C13111yescharacteristic
430C4#452×C13111yescharacteristic
431C4#465×C13111yescharacteristic
432C4#468×C13111yescharacteristic
433C2—21no—
434C2—21no—
435C2—161no—
436C2#2000×C13111yescharacteristic
437C2#2009×C13111yescharacteristic
438C2#2010×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#392
commutator, Frattini, cosocleC2×C42C23×C131
prime radical#532×C131C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2581×C131C2semidirect
5. #1487×C131C2semidirect
6. #1479×C131C2semidirect
7. #1286×C131C2semidirect
97. C2×Q8×C131SD16semidirect
219. #9999C131direct (N × H)
220. C131#9999direct (N × H)
223. #2581C2×C131semidirect
225. #1487C2×C131semidirect
226. #1479C2×C131semidirect
227. #1286C2×C131semidirect
317. C2×Q8SD16×C131semidirect

Maximal subgroups

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

subgroupindex
#3103×C1312
#3037×C1312
#2581×C1312
#1517×C1312
#1487×C1312
#1479×C1312
#1286×C1312
#9999131