Finite Group Databasebeta

← C131×#7801 #45693685

Subgroups — C131×#7801 #45693685

Order 33536.

446 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 102 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
1#2732×C131C211yesmaximal, characteristic
2#2096×C131C211yesmaximal, characteristic, complemented
3#2084×C131C211yesmaximal, characteristic, complemented
4#2071×C131C211yesmaximal, characteristic
5#1272×C131C211yesmaximal, characteristic, complemented
6#1271×C131C211yesmaximal, characteristic, complemented
7#1270×C131C211yesmaximal, characteristic
8C2×C22⋊Q8×C131—21no—
9C2×#106×C131—21no—
10C2×#106×C131—21no—
11C2×#103×C131—21no—
12C2×#102×C131—21no—
13#399×C131—21no—
14#398×C131—21no—
15#396×C131—21no—
16#391×C131C2211yescharacteristic
17#390×C131C2211yescharacteristic
18#389×C131C2211yescharacteristic
19#386×C131—21no—
20#385×C131—21no—
21#384×C131C2211yescharacteristic
22#340×C131—21no—
23#340×C131—21no—
24#336×C131C2211yescharacteristic
25#336×C131C2211yescharacteristic
26#336×C131C2211yescharacteristic
27C22×Q8×C131D411yescharacteristic
28C22×D4×C131D411yescharacteristic
29C23×C4×C131—21no—
30C22×C8×C131—21no—
31C22×C8×C131—21no—
32C22×C8×C131—21no—
33C22⋊Q8×C131—42no—
34C22⋊Q8×C131—42no—
35C2×C4⋊C4×C131—21no—
36C2×C4⋊C4×C131—21no—
37C2×C4⋊C4×C131—21no—
38C2×C4⋊C4×C131—21no—
39C2×C4⋊C4×C131—21no—
40C2×C4⋊C4×C131—21no—
41C2×C4⋊C4×C131—21no—
42C2×C4⋊C4×C131D411yescharacteristic
43C2×C4⋊C4×C131D411yescharacteristic
44C2×C4⋊C4×C131D411yescharacteristic
45C2×C4⋊C4×C131D411yescharacteristic
46C2×C22⋊C4×C131—21no—
47C2×C22⋊C4×C131—21no—
48C2×C22⋊C4×C131—21no—
49C2×C22⋊C4×C131—21no—
50C2×C22⋊C4×C131—21no—
51C2×C42×C131C2311yescharacteristic
52#106×C131—42no—
53#106×C131—42no—
54#103×C131—42no—
55#102×C131—42no—
56#95×C131—21no—
57#95×C131—21no—
58#95×C131—21no—
59#95×C131—21no—
60C24×C131—21no—
61C2×Q8×C131—21no—
62C2×Q8×C131—41no—
63C2×Q8×C131—41no—
64C2×Q8×C131SD1612yes—
65C2×D4×C131—21no—
66C2×D4×C131—41no—
67C2×D4×C131—41no—
68C2×D4×C131SD1612yes—
69C22×C4×C131—21no—
70C22×C4×C131—21no—
71C22×C4×C131—21no—
72C22×C4×C131—21no—
73C22×C4×C131—21no—
74C22×C4×C131—42no—
75C22×C4×C131—41no—
76C22×C4×C131—81no—
77C22×C4×C131—81no—
78C22×C4×C131C2×D411yescharacteristic
79C22×C4×C131C2×D411yescharacteristic
80C22×C4×C131C2×D411yescharacteristic
81C2×C8×C131—22no—
82C2×C8×C131—22no—
83C2×C8×C131—41no—
84C2×C8×C131—41no—
85C2×C8×C131—41no—
86C2×C8×C131—41no—
87C2×C8×C131—41no—
88C2×C8×C131—41no—
89C2×C8×C131—41no—
90C4⋊C4×C131—21no—
91C4⋊C4×C131—21no—
92C4⋊C4×C131—41no—
93C4⋊C4×C131—41no—
94C4⋊C4×C131—41no—
95C4⋊C4×C131—42no—
96C4⋊C4×C131—42no—
97C4⋊C4×C131—41no—
98C4⋊C4×C131—41no—
99C4⋊C4×C131—41no—
100C4⋊C4×C131—41no—
101C4⋊C4×C131—41no—
102C4⋊C4×C131—41no—
103C4⋊C4×C131—41no—
104C4⋊C4×C131—41no—
105C4⋊C4×C131—81no—
106C22⋊C4×C131—42no—
107C22⋊C4×C131—41no—
108C22⋊C4×C131—41no—
109C22⋊C4×C131—41no—
110C22⋊C4×C131—41no—
111C22⋊C4×C131—81no—
112C22⋊C4×C131—81no—
113C42×C131—41no—
114C23×C131—22no—
115C23×C131—41no—
116C23×C131—41no—
117C23×C131—41no—
118C23×C131—41no—
119C23×C131—41no—
120C23×C131—41no—
121C23×C131#12011yescharacteristic
122Q8×C131—42no—
123Q8×C131—81no—
124D4×C131—42no—
125D4×C131—81no—
126C2×C4×C131—21no—
127C2×C4×C131—21no—
128C2×C4×C131—21no—
129C2×C4×C131—21no—
130C2×C4×C131—21no—
131C2×C4×C131—21no—
132C2×C4×C131—22no—
133C2×C4×C131—41no—
134C2×C4×C131—41no—
135C2×C4×C131—41no—
136C2×C4×C131—41no—
137C2×C4×C131—41no—
138C2×C4×C131—41no—
139C2×C4×C131—41no—
140C2×C4×C131—41no—
141C2×C4×C131—41no—
142C2×C4×C131—41no—
143C2×C4×C131—41no—
144C2×C4×C131—41no—
145C2×C4×C131—41no—
146C2×C4×C131—41no—
147C2×C4×C131—84no—
148C2×C4×C131—81no—
149C2×C4×C131—81no—
150C2×C4×C131—81no—
151C2×C4×C131C2×SD1611yescharacteristic
152C2×C4×C131C2×SD1611yescharacteristic
153C2×C4×C131#13511yescharacteristic
154C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C131#13711yescharacteristic
157C8×C131—42no—
158C8×C131—42no—
159C8×C131—81no—
160C22×C131—42no—
161C22×C131—42no—
162C22×C131—42no—
163C22×C131—81no—
164C22×C131—81no—
165C22×C131—81no—
166C22×C131—81no—
167C22×C131#44811yescharacteristic
168C22×C131#44911yescharacteristic
169C22×C131#45011yescharacteristic
170C22×C131#45311yescharacteristic
171C22×C131#45511yescharacteristic
172C22×C131#45611yescharacteristic
173C22×C131#45811yescharacteristic
174C4×C131—21no—
175C4×C131—21no—
176C4×C131—21no—
177C4×C131—21no—
178C4×C131—21no—
179C4×C131—21no—
180C4×C131—42no—
181C4×C131—81no—
182C4×C131—81no—
183C4×C131—81no—
184C4×C131—81no—
185C4×C131—161no—
186C2×C131—82no—
187C2×C131#160811yescharacteristic
188C2×C131#160911yescharacteristic
189C2×C131#161311yescharacteristic
190C2×C131#162211yescharacteristic
191C2×C131#164211yescharacteristic
192C2×C131#165111yescharacteristic
193C2×C131#166111yescharacteristic
194#7801C13111yesmaximal, characteristic, direct product factor, Sylow
195C131#780111yescharacteristic, direct product factor, Sylow
196#2732C2×C13111yescharacteristic
197#2096C2×C13111yescharacteristic, complemented
198#2084C2×C13111yescharacteristic, complemented
199#2071C2×C13111yescharacteristic
200#1272C2×C13111yescharacteristic, complemented
201#1271C2×C13111yescharacteristic, complemented
202#1270C2×C13111yescharacteristic
203C2×C22⋊Q8—21no—
204C2×#106—21no—
205C2×#106—21no—
206C2×#103—21no—
207C2×#102—21no—
208#399—21no—
209#398—21no—
210#396—21no—
211#391C22×C13111yescharacteristic
212#390C22×C13111yescharacteristic
213#389C22×C13111yescharacteristic
214#386—21no—
215#385—21no—
216#384C22×C13111yescharacteristic
217#340—21no—
218#340—21no—
219#336C22×C13111yescharacteristic
220#336C22×C13111yescharacteristic
221#336C22×C13111yescharacteristic
222C22×Q8D4×C13111yescharacteristic
223C22×D4D4×C13111yescharacteristic
224C23×C4—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22⋊Q8—42no—
229C22⋊Q8—42no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4D4×C13111yescharacteristic
238C2×C4⋊C4D4×C13111yescharacteristic
239C2×C4⋊C4D4×C13111yescharacteristic
240C2×C4⋊C4D4×C13111yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C42C23×C13111yescharacteristic
247#106—42no—
248#106—42no—
249#103—42no—
250#102—42no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255C24—21no—
256C2×Q8—21no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8SD16×C13112yes—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4SD16×C13112yes—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—81no—
272C22×C4—81no—
273C22×C4C2×D4×C13111yescharacteristic
274C22×C4C2×D4×C13111yescharacteristic
275C22×C4C2×D4×C13111yescharacteristic
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—81no—
301C22⋊C4—42no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—81no—
307C22⋊C4—81no—
308C42—41no—
309C23—22no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23#120×C13111yescharacteristic
317Q8—42no—
318Q8—81no—
319D4—42no—
320D4—81no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—84no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4C2×SD16×C13111yescharacteristic
347C2×C4C2×SD16×C13111yescharacteristic
348C2×C4#135×C13111yescharacteristic
349C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
350C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
351C2×C4#137×C13111yescharacteristic
352C8—42no—
353C8—42no—
354C8—81no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22#448×C13111yescharacteristic
363C22#449×C13111yescharacteristic
364C22#450×C13111yescharacteristic
365C22#453×C13111yescharacteristic
366C22#455×C13111yescharacteristic
367C22#456×C13111yescharacteristic
368C22#458×C13111yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—161no—
381C2—82no—
382C2#1608×C13111yescharacteristic
383C2#1609×C13111yescharacteristic
384C2#1613×C13111yescharacteristic
385C2#1622×C13111yescharacteristic
386C2#1642×C13111yescharacteristic
387C2#1651×C13111yescharacteristic
388C2#1661×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#120
commutator, Frattini, cosocleC2×C42C23×C131
prime radicalC22×D4×C131D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2096×C131C2semidirect
3. #2084×C131C2semidirect
5. #1272×C131C2semidirect
6. #1271×C131C2semidirect
194. #7801C131direct (N × H)
195. C131#7801direct (N × H)
197. #2096C2×C131semidirect
198. #2084C2×C131semidirect
200. #1272C2×C131semidirect
201. #1271C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2732×C1312
#2096×C1312
#2084×C1312
#2071×C1312
#1272×C1312
#1271×C1312
#1270×C1312
#7801131