Finite Group Databasebeta

← C127×#2737 #30635689

Subgroups — C127×#2737 #30635689

Order 16256.

442 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#397×C127C211yesmaximal, characteristic, complemented
2#397×C127C211yesmaximal, characteristic, complemented
3#395×C127C211yesmaximal, characteristic, complemented
4#394×C127C211yesmaximal, characteristic
5#393×C127C211yesmaximal, characteristic, complemented
6#393×C127C211yesmaximal, characteristic, complemented
7#390×C127C211yesmaximal, characteristic
8#388×C127C211yesmaximal, characteristic, complemented
9#388×C127C211yesmaximal, characteristic, complemented
10#387×C127C211yesmaximal, characteristic, complemented
11#387×C127C211yesmaximal, characteristic, complemented
12#386×C127C211yesmaximal, characteristic
13#383×C127C211yesmaximal, characteristic, complemented
14#381×C127C211yesmaximal, characteristic, complemented
15#380×C127C211yesmaximal, characteristic, complemented
16C22×Q8×C127C2211yescharacteristic
17C22×D4×C127C2211yescharacteristic
18C23×C4×C127C2211yescharacteristic
19C2×C4⋊C4×C127C2211yescharacteristic
20C2×C4⋊C4×C127C2211yescharacteristic
21C2×C4⋊C4×C127C2211yescharacteristic
22C2×C4⋊C4×C127C2211yescharacteristic
23C2×C4⋊C4×C127C2211yescharacteristic
24C2×C22⋊C4×C127C2211yescharacteristic
25C2×C22⋊C4×C127C2211yescharacteristic
26C2×C22⋊C4×C127C2211yescharacteristic
27C2×C22⋊C4×C127C2211yescharacteristic
28C2×C22⋊C4×C127C2211yescharacteristic
29C2×C22⋊C4×C127C2211yescharacteristic
30C2×C22⋊C4×C127C2211yescharacteristic
31C2×C22⋊C4×C127C2211yescharacteristic
32C2×C22⋊C4×C127C2211yescharacteristic
33C2×C22⋊C4×C127C2211yescharacteristic
34C2×C22⋊C4×C127C2211yescharacteristic
35C2×C42×C127C2211yescharacteristic
36C2×C42×C127C2211yescharacteristic
37#95×C127C2211yescharacteristic
38#95×C127C2211yescharacteristic
39#95×C127C2211yescharacteristic
40#95×C127C2211yescharacteristic
41#95×C127C2211yescharacteristic
42#95×C127C2211yescharacteristic
43#95×C127C2211yescharacteristic
44#95×C127C2211yescharacteristic
45#95×C127C2211yescharacteristic
46#95×C127C2211yescharacteristic
47#95×C127C2211yescharacteristic
48#95×C127C2211yescharacteristic
49#95×C127C2211yescharacteristic
50#95×C127C2211yescharacteristic
51C24×C127C2311yescharacteristic
52C24×C127C2311yescharacteristic
53C2×Q8×C127—41no—
54C2×Q8×C127—41no—
55C2×Q8×C127—41no—
56C2×D4×C127—22no—
57C2×D4×C127—22no—
58C2×D4×C127—41no—
59C22×C4×C127—22no—
60C22×C4×C127—22no—
61C22×C4×C127—41no—
62C22×C4×C127C2311yescharacteristic
63C22×C4×C127C2311yescharacteristic
64C22×C4×C127C2311yescharacteristic
65C22×C4×C127C2311yescharacteristic
66C22×C4×C127C2311yescharacteristic
67C22×C4×C127C2311yescharacteristic
68C22×C4×C127C2311yescharacteristic
69C22×C4×C127C2311yescharacteristic
70C22×C4×C127C2311yescharacteristic
71C22×C4×C127C2311yescharacteristic
72C22×C4×C127C2311yescharacteristic
73C22×C4×C127C2311yescharacteristic
74C22×C4×C127C2311yescharacteristic
75C4⋊C4×C127—22no—
76C4⋊C4×C127—22no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C22⋊C4×C127—22no—
81C22⋊C4×C127—22no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—41no—
84C22⋊C4×C127—41no—
85C22⋊C4×C127—41no—
86C22⋊C4×C127—41no—
87C22⋊C4×C127—41no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—41no—
91C42×C127—22no—
92C42×C127—41no—
93C23×C127—21no—
94C23×C127—21no—
95C23×C127—21no—
96C23×C127—21no—
97C23×C127—21no—
98C23×C127—21no—
99C23×C127—21no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—21no—
103C23×C127—21no—
104C23×C127—21no—
105C23×C127—21no—
106C23×C127#4112yes—
107C23×C127C2411yescharacteristic
108Q8×C127—44no—
109D4×C127—44no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—21no—
125C2×C4×C127—21no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—21no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—21no—
136C2×C4×C127—21no—
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127—21no—
147C2×C4×C127—44no—
148C2×C4×C127#4112yes—
149C2×C4×C127#4112yes—
150C22×C127—22no—
151C22×C127—22no—
152C22×C127—22no—
153C22×C127—41no—
154C22×C127—41no—
155C22×C127—41no—
156C22×C127—41no—
157C22×C127—41no—
158C22×C127—41no—
159C22×C127—41no—
160C22×C127—41no—
161C22×C127—41no—
162C22×C127—41no—
163C22×C127—41no—
164C22×C127C2×#4111yescharacteristic
165C22×C127C2×#4111yescharacteristic
166C22×C127C2×#4111yescharacteristic
167C22×C127H(5,𝔽2)11yescharacteristic
168C22×C127H(5,𝔽2)11yescharacteristic
169C22×C127H(5,𝔽2)11yescharacteristic
170C22×C1272−1+411yescharacteristic
171C4×C127—22no—
172C4×C127—22no—
173C4×C127—41no—
174C4×C127—41no—
175C4×C127—41no—
176C4×C127—41no—
177C4×C127—41no—
178C4×C127—41no—
179C4×C127—41no—
180C4×C127—41no—
181C4×C127—41no—
182C4×C127—41no—
183C4×C127—41no—
184C2×C127—42no—
185C2×C127—81no—
186C2×C127#53911yescharacteristic
187C2×C127#54211yescharacteristic
188C2×C127#54211yescharacteristic
189C2×C127#55111yescharacteristic
190C2×C127#55111yescharacteristic
191C2×C127#55511yescharacteristic
192C2×C127#56011yescharacteristic
193#2737C12711yesmaximal, characteristic, direct product factor, Sylow
194C127#273711yescharacteristic, direct product factor, Sylow
195#397C2×C12711yescharacteristic, complemented
196#397C2×C12711yescharacteristic, complemented
197#395C2×C12711yescharacteristic, complemented
198#394C2×C12711yescharacteristic
199#393C2×C12711yescharacteristic, complemented
200#393C2×C12711yescharacteristic, complemented
201#390C2×C12711yescharacteristic
202#388C2×C12711yescharacteristic, complemented
203#388C2×C12711yescharacteristic, complemented
204#387C2×C12711yescharacteristic, complemented
205#387C2×C12711yescharacteristic, complemented
206#386C2×C12711yescharacteristic
207#383C2×C12711yescharacteristic, complemented
208#381C2×C12711yescharacteristic, complemented
209#380C2×C12711yescharacteristic, complemented
210C22×Q8C22×C12711yescharacteristic
211C22×D4C22×C12711yescharacteristic
212C23×C4C22×C12711yescharacteristic
213C2×C4⋊C4C22×C12711yescharacteristic
214C2×C4⋊C4C22×C12711yescharacteristic
215C2×C4⋊C4C22×C12711yescharacteristic
216C2×C4⋊C4C22×C12711yescharacteristic
217C2×C4⋊C4C22×C12711yescharacteristic
218C2×C22⋊C4C22×C12711yescharacteristic
219C2×C22⋊C4C22×C12711yescharacteristic
220C2×C22⋊C4C22×C12711yescharacteristic
221C2×C22⋊C4C22×C12711yescharacteristic
222C2×C22⋊C4C22×C12711yescharacteristic
223C2×C22⋊C4C22×C12711yescharacteristic
224C2×C22⋊C4C22×C12711yescharacteristic
225C2×C22⋊C4C22×C12711yescharacteristic
226C2×C22⋊C4C22×C12711yescharacteristic
227C2×C22⋊C4C22×C12711yescharacteristic
228C2×C22⋊C4C22×C12711yescharacteristic
229C2×C42C22×C12711yescharacteristic
230C2×C42C22×C12711yescharacteristic
231#95C22×C12711yescharacteristic
232#95C22×C12711yescharacteristic
233#95C22×C12711yescharacteristic
234#95C22×C12711yescharacteristic
235#95C22×C12711yescharacteristic
236#95C22×C12711yescharacteristic
237#95C22×C12711yescharacteristic
238#95C22×C12711yescharacteristic
239#95C22×C12711yescharacteristic
240#95C22×C12711yescharacteristic
241#95C22×C12711yescharacteristic
242#95C22×C12711yescharacteristic
243#95C22×C12711yescharacteristic
244#95C22×C12711yescharacteristic
245C24C23×C12711yescharacteristic
246C24C23×C12711yescharacteristic
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—41no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—41no—
256C22×C4C23×C12711yescharacteristic
257C22×C4C23×C12711yescharacteristic
258C22×C4C23×C12711yescharacteristic
259C22×C4C23×C12711yescharacteristic
260C22×C4C23×C12711yescharacteristic
261C22×C4C23×C12711yescharacteristic
262C22×C4C23×C12711yescharacteristic
263C22×C4C23×C12711yescharacteristic
264C22×C4C23×C12711yescharacteristic
265C22×C4C23×C12711yescharacteristic
266C22×C4C23×C12711yescharacteristic
267C22×C4C23×C12711yescharacteristic
268C22×C4C23×C12711yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C42—22no—
286C42—41no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23#41×C12712yes—
301C23C24×C12711yescharacteristic
302Q8—44no—
303D4—44no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—44no—
342C2×C4#41×C12712yes—
343C2×C4#41×C12712yes—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22C2×#41×C12711yescharacteristic
359C22C2×#41×C12711yescharacteristic
360C22C2×#41×C12711yescharacteristic
361C22H(5,𝔽2)×C12711yescharacteristic
362C22H(5,𝔽2)×C12711yescharacteristic
363C22H(5,𝔽2)×C12711yescharacteristic
364C222−1+4×C12711yescharacteristic
365C4—22no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—41no—
378C2—42no—
379C2—81no—
380C2#539×C12711yescharacteristic
381C2#542×C12711yescharacteristic
382C2#542×C12711yescharacteristic
383C2#551×C12711yescharacteristic
384C2#551×C12711yescharacteristic
385C2#555×C12711yescharacteristic
386C2#560×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC22×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #397×C127C2semidirect
2. #397×C127C2semidirect
3. #395×C127C2semidirect
5. #393×C127C2semidirect
6. #393×C127C2semidirect
8. #388×C127C2semidirect
9. #388×C127C2semidirect
10. #387×C127C2semidirect
11. #387×C127C2semidirect
13. #383×C127C2semidirect
14. #381×C127C2semidirect
15. #380×C127C2semidirect
193. #2737C127direct (N × H)
194. C127#2737direct (N × H)
195. #397C2×C127semidirect
196. #397C2×C127semidirect
197. #395C2×C127semidirect
199. #393C2×C127semidirect
200. #393C2×C127semidirect
202. #388C2×C127semidirect
203. #388C2×C127semidirect
204. #387C2×C127semidirect
205. #387C2×C127semidirect
207. #383C2×C127semidirect
208. #381C2×C127semidirect
209. #380C2×C127semidirect

Maximal subgroups

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

subgroupindex
#397×C1272
#395×C1272
#394×C1272
#393×C1272
#390×C1272
#388×C1272
#387×C1272
#386×C1272
#383×C1272
#381×C1272
#380×C1272
#2737127