Finite Group Databasebeta

← C131×#13377 #45699261

Subgroups — C131×#13377 #45699261

Order 33536.

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

normal subgroups only

This group has 648 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
1#2804×C131C211yesmaximal, characteristic, complemented
2#1792×C131C211yesmaximal, characteristic
3#1790×C131C212yesmaximal
4#1393×C131C211yesmaximal, characteristic, complemented
5#1390×C131C212yesmaximal, complemented
6C2×H(5,𝔽2)×C131C2211yescharacteristic
7C2×#104×C131—21no—
8#417×C131—21no—
9C2×#100×C131C2211yescharacteristic
10C2×#99×C131—22no—
11C2×#99×C131C2212yes—
12#400×C131—21no—
13#393×C131—22no—
14#391×C131—21no—
15#390×C131C2211yescharacteristic
16#386×C131—22no—
17#386×C131C2212yes—
18#385×C131—22no—
19H(5,𝔽2)×C131—22no—
20H(5,𝔽2)×C131—21no—
21H(5,𝔽2)×C131—42no—
22H(5,𝔽2)×C131Q812yescomplemented
23C2×#41×C131—21no—
24C2×#41×C131—41no—
25C22×Q8×C131—21no—
26C22×D4×C131—22no—
27C22×D4×C131—41no—
28C22×D4×C131C2311yescharacteristic
29C23×C4×C131D412yes—
30C2×M16×C131—21no—
31C2×C4⋊C4×C131—21no—
32C2×C4⋊C4×C131—21no—
33C2×C4⋊C4×C131D411yescharacteristic
34C2×C22⋊C4×C131—22no—
35C2×C22⋊C4×C131—22no—
36C2×C22⋊C4×C131—22no—
37C2×C22⋊C4×C131—42no—
38C2×C22⋊C4×C131D412yes—
39C2×C42×C131D411yescharacteristic
40#104×C131—42no—
41#103×C131—41no—
42#102×C131—41no—
43#100×C131—22no—
44#99×C131—22no—
45#99×C131—22no—
46#99×C131—44no—
47#95×C131—22no—
48#95×C131—21no—
49#95×C131—22no—
50#95×C131—22no—
51#95×C131—42no—
52C24×C131—22no—
53C24×C131C2×D412yes—
54#41×C131—22no—
55#41×C131—22no—
56#41×C131—42no—
57#41×C131—41no—
58#41×C131—44no—
59#41×C131—42no—
60#41×C131—41no—
61C2×Q8×C131—21no—
62C2×Q8×C131—42no—
63C2×Q8×C131—81no—
64C2×Q8×C131—81no—
65C2×D4×C131—21no—
66C2×D4×C131—24no—
67C2×D4×C131—24no—
68C2×D4×C131—41no—
69C2×D4×C131—41no—
70C2×D4×C131—42no—
71C2×D4×C131—42no—
72C2×D4×C131—42no—
73C2×D4×C131—42no—
74C2×D4×C131—44no—
75C2×D4×C131—41no—
76C2×D4×C131—42no—
77C2×D4×C131C2×Q811yescharacteristic
78C2×D4×C131#4111yescharacteristic
79C2×D4×C131#4112yes—
80C22×C4×C131—22no—
81C22×C4×C131—21no—
82C22×C4×C131—22no—
83C22×C4×C131—21no—
84C22×C4×C131—22no—
85C22×C4×C131—41no—
86C22×C4×C131—42no—
87C22×C4×C131—42no—
88C22×C4×C131—82no—
89C22×C4×C131C2×D411yescharacteristic
90M16×C131—41no—
91M16×C131—41no—
92C2×C8×C131—41no—
93C4⋊C4×C131—41no—
94C4⋊C4×C131—81no—
95C4⋊C4×C131—81no—
96C22⋊C4×C131—44no—
97C22⋊C4×C131—42no—
98C22⋊C4×C131—42no—
99C22⋊C4×C131—42no—
100C22⋊C4×C131—82no—
101C22⋊C4×C131—84no—
102C42×C131—41no—
103C23×C131—22no—
104C23×C131—22no—
105C23×C131—24no—
106C23×C131—42no—
107C23×C131—42no—
108C23×C131—42no—
109C23×C131—41no—
110C23×C131—82no—
111C23×C131—82no—
112C23×C131#12011yescharacteristic
113C23×C131C22⋊Q812yes—
114C23×C131#12412yes—
115Q8×C131—22no—
116Q8×C131—41no—
117Q8×C131—84no—
118D4×C131—22no—
119D4×C131—41no—
120D4×C131—42no—
121D4×C131—41no—
122D4×C131—41no—
123D4×C131—44no—
124D4×C131—44no—
125D4×C131—42no—
126D4×C131—42no—
127C2×C4×C131—21no—
128C2×C4×C131—21no—
129C2×C4×C131—22no—
130C2×C4×C131—24no—
131C2×C4×C131—42no—
132C2×C4×C131—42no—
133C2×C4×C131—41no—
134C2×C4×C131—42no—
135C2×C4×C131—41no—
136C2×C4×C131—41no—
137C2×C4×C131—42no—
138C2×C4×C131—42no—
139C2×C4×C131—42no—
140C2×C4×C131—42no—
141C2×C4×C131—42no—
142C2×C4×C131—44no—
143C2×C4×C131—42no—
144C2×C4×C131—41no—
145C2×C4×C131—42no—
146C2×C4×C131—82no—
147C2×C4×C131—82no—
148C2×C4×C131—82no—
149C2×C4×C131—82no—
150C2×C4×C131C22⋊Q811yescharacteristic
151C2×C4×C131#12411yescharacteristic
152C8×C131—81no—
153C22×C131—21no—
154C22×C131—21no—
155C22×C131—22no—
156C22×C131—22no—
157C22×C131—42no—
158C22×C131—42no—
159C22×C131—42no—
160C22×C131—42no—
161C22×C131—42no—
162C22×C131—82no—
163C22×C131—84no—
164C22×C131—81no—
165C22×C131—81no—
166C22×C131—162no—
167C22×C131#39311yescharacteristic
168C22×C131B(4,𝔽2)11yescharacteristic
169C22×C131B(4,𝔽2)11yescharacteristic
170C4×C131—21no—
171C4×C131—21no—
172C4×C131—42no—
173C4×C131—42no—
174C4×C131—82no—
175C4×C131—81no—
176C4×C131—82no—
177C4×C131—162no—
178C2×C131—21no—
179C2×C131—21no—
180C2×C131—42no—
181C2×C131—42no—
182C2×C131—82no—
183C2×C131#202911yescharacteristic
184C2×C131#219811yescharacteristic
185C2×C131#219911yescharacteristic
186#13377C13111yesmaximal, characteristic, direct product factor, Sylow
187C131#1337711yescharacteristic, direct product factor, Sylow
188#2804C2×C13111yescharacteristic, complemented
189#1792C2×C13111yescharacteristic
190#1790C2×C13112yes—
191#1393C2×C13111yescharacteristic, complemented
192#1390C2×C13112yescomplemented
193C2×H(5,𝔽2)C22×C13111yescharacteristic
194C2×#104—21no—
195#417—21no—
196C2×#100C22×C13111yescharacteristic
197C2×#99—22no—
198C2×#99C22×C13112yes—
199#400—21no—
200#393—22no—
201#391—21no—
202#390C22×C13111yescharacteristic
203#386—22no—
204#386C22×C13112yes—
205#385—22no—
206H(5,𝔽2)—22no—
207H(5,𝔽2)—21no—
208H(5,𝔽2)—42no—
209H(5,𝔽2)Q8×C13112yescomplemented
210C2×#41—21no—
211C2×#41—41no—
212C22×Q8—21no—
213C22×D4—22no—
214C22×D4—41no—
215C22×D4C23×C13111yescharacteristic
216C23×C4D4×C13112yes—
217C2×M16—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4D4×C13111yescharacteristic
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—42no—
225C2×C22⋊C4D4×C13112yes—
226C2×C42D4×C13111yescharacteristic
227#104—42no—
228#103—41no—
229#102—41no—
230#100—22no—
231#99—22no—
232#99—22no—
233#99—44no—
234#95—22no—
235#95—22no—
236#95—21no—
237#95—22no—
238#95—42no—
239C24—22no—
240C24C2×D4×C13112yes—
241#41—22no—
242#41—22no—
243#41—42no—
244#41—41no—
245#41—44no—
246#41—42no—
247#41—41no—
248C2×Q8—21no—
249C2×Q8—42no—
250C2×Q8—81no—
251C2×Q8—81no—
252C2×D4—21no—
253C2×D4—24no—
254C2×D4—24no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—44no—
262C2×D4—41no—
263C2×D4—42no—
264C2×D4C2×Q8×C13111yescharacteristic
265C2×D4#41×C13111yescharacteristic
266C2×D4#41×C13112yes—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—41no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—82no—
276C22×C4C2×D4×C13111yescharacteristic
277M16—41no—
278M16—41no—
279C2×C8—41no—
280C4⋊C4—41no—
281C4⋊C4—81no—
282C4⋊C4—81no—
283C22⋊C4—44no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—82no—
288C22⋊C4—84no—
289C42—41no—
290C23—22no—
291C23—22no—
292C23—24no—
293C23—42no—
294C23—42no—
295C23—42no—
296C23—41no—
297C23—82no—
298C23—82no—
299C23#120×C13111yescharacteristic
300C23C22⋊Q8×C13112yes—
301C23#124×C13112yes—
302Q8—22no—
303Q8—41no—
304Q8—84no—
305D4—22no—
306D4—41no—
307D4—42no—
308D4—41no—
309D4—41no—
310D4—44no—
311D4—44no—
312D4—42no—
313D4—42no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—44no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4C22⋊Q8×C13111yescharacteristic
338C2×C4#124×C13111yescharacteristic
339C8—81no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—22no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—42no—
348C22—42no—
349C22—82no—
350C22—84no—
351C22—81no—
352C22—81no—
353C22—162no—
354C22#393×C13111yescharacteristic
355C22B(4,𝔽2)×C13111yescharacteristic
356C22B(4,𝔽2)×C13111yescharacteristic
357C4—21no—
358C4—21no—
359C4—42no—
360C4—42no—
361C4—82no—
362C4—81no—
363C4—82no—
364C4—162no—
365C2—21no—
366C2—21no—
367C2—42no—
368C2—42no—
369C2—82no—
370C2#2029×C13111yescharacteristic
371C2#2198×C13111yescharacteristic
372C2#2199×C13111yescharacteristic
subgroupG/H
center, socleC22×C131B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C131
prime radicalC2×H(5,𝔽2)×C131C22
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C131 ◁ C22×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2804×C131C2semidirect
4. #1393×C131C2semidirect
5. #1390×C131C2semidirect
22. H(5,𝔽2)×C131Q8semidirect
186. #13377C131direct (N × H)
187. C131#13377direct (N × H)
188. #2804C2×C131semidirect
191. #1393C2×C131semidirect
192. #1390C2×C131semidirect
209. H(5,𝔽2)Q8×C131semidirect

Maximal subgroups

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

subgroupindex
#2804×C1312
#1792×C1312
#1790×C1312
#1393×C1312
#1390×C1312
#13377131