Finite Group Databasebeta

← C127×#9337 #44573010

Subgroups — C127×#9337 #44573010

Order 32512.

412 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3218C211yesmaximal, characteristic
2C127×#2995C211yesmaximal, characteristic
3C127×#1997C211yesmaximal, characteristic, complemented
4C127×#1558C211yesmaximal, characteristic, complemented
5C127×#1529C211yesmaximal, characteristic
6C127×#1307C211yesmaximal, characteristic, complemented
7C127×#1291C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C127C2211yescharacteristic
9#529×C127C2211yescharacteristic
10#497×C127—21no—
11#491×C127—21no—
12#462×C127—21no—
13#461×C127—21no—
14#451×C127C412yes—
15#448×C127C412yes—
16#446×C127—21no—
17#436×C127—21no—
18#435×C127—21no—
19#435×C127—21no—
20#433×C127—21no—
21#432×C127C2211yescharacteristic
22#432×C127C2211yescharacteristic
23#432×C127C2211yescharacteristic
24#424×C127—21no—
25#423×C127C2211yescharacteristic
26C4×M16×C127C2211yescharacteristic
27#343×C127—21no—
28#343×C127—21no—
29#333×C127—21no—
30#333×C127—21no—
31#330×C127—21no—
32#329×C127—21no—
33C22×Q8×C127C2×C412yes—
34C2×Q16×C127—22no—
35C2×SD16×C127—22no—
36C2×M16×C127—21no—
37C2×M16×C127—21no—
38C2×M16×C127D411yescharacteristic
39C2×M16×C127D411yescharacteristic
40C22×C8×C127—21no—
41C4⋊Q8×C127—21no—
42C4⋊Q8×C127—21no—
43C4⋊Q8×C127—21no—
44C4⋊Q8×C127—21no—
45#126×C127—21no—
46#125×C127D411yescharacteristic
47#124×C127D411yescharacteristic
48#123×C127—21no—
49C22⋊Q8×C127C2×C411yescharacteristic
50#121×C127C2×C411yescharacteristic
51C4×Q8×C127D411yescharacteristic
52C4×D4×C127—21no—
53C4×D4×C127D411yescharacteristic
54#117×C127—21no—
55C2×C4⋊C4×C127—21no—
56C2×C4⋊C4×C127—21no—
57C2×C42×C127C2311yescharacteristic
58C4⋊C8×C127—21no—
59C4⋊C8×C127—21no—
60C4⋊C8×C127—21no—
61C4⋊C8×C127—21no—
62C4⋊C8×C127—21no—
63C4⋊C8×C127—21no—
64C4⋊C8×C127D411yescharacteristic
65C4⋊C8×C127D411yescharacteristic
66#103×C127—22no—
67#103×C127—22no—
68C22⋊C8×C127—21no—
69C22⋊C8×C127—21no—
70C22⋊C8×C127—21no—
71C22⋊C8×C127—21no—
72C22⋊C8×C127C2×C412yes—
73#97×C127—21no—
74#97×C127—21no—
75#97×C127—21no—
76#97×C127—21no—
77#97×C127—21no—
78C4×C8×C127—21no—
79C4×C8×C127—21no—
80C2×Q8×C127—22no—
81C2×Q8×C127—22no—
82C2×Q8×C127—82no—
83C2×Q8×C127C22⋊C411yescharacteristic
84C2×D4×C127—21no—
85C2×D4×C127C22⋊C411yescharacteristic
86C22×C4×C127—21no—
87C22×C4×C127—22no—
88C22×C4×C127C22×C411yescharacteristic
89C22×C4×C127C2×D411yescharacteristic
90C22×C4×C127#4111yescharacteristic
91Q16×C127—82no—
92SD16×C127—82no—
93M16×C127—22no—
94M16×C127—41no—
95M16×C127—41no—
96M16×C127—41no—
97M16×C127—81no—
98C2×C8×C127—22no—
99C2×C8×C127—21no—
100C2×C8×C127—21no—
101C2×C8×C127—21no—
102C2×C8×C127—21no—
103C2×C8×C127—41no—
104C2×C8×C127—41no—
105C2×C8×C127—81no—
106C4⋊C4×C127—21no—
107C4⋊C4×C127—21no—
108C4⋊C4×C127—21no—
109C4⋊C4×C127—21no—
110C4⋊C4×C127—41no—
111C4⋊C4×C127—41no—
112C4⋊C4×C127—41no—
113C4⋊C4×C127—41no—
114C4⋊C4×C127C22⋊C411yescharacteristic
115C4⋊C4×C127C22⋊C411yescharacteristic
116C22⋊C4×C127—21no—
117C22⋊C4×C127—21no—
118C22⋊C4×C127—21no—
119C22⋊C4×C127—21no—
120C22⋊C4×C127—21no—
121C42×C127—21no—
122C42×C127C2×D411yescharacteristic
123C42×C127C2×D411yescharacteristic
124C42×C127C2×D411yescharacteristic
125C42×C127#4111yescharacteristic
126C23×C127—21no—
127C23×C127C4×D411yescharacteristic
128Q8×C127—41no—
129Q8×C127—42no—
130Q8×C127—42no—
131Q8×C127—82no—
132D4×C127—41no—
133D4×C127—81no—
134C2×C4×C127—21no—
135C2×C4×C127—21no—
136C2×C4×C127—21no—
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—42no—
144C2×C4×C127—82no—
145C2×C4×C127C2×C22⋊C411yescharacteristic
146C2×C4×C127C4×D411yescharacteristic
147C2×C4×C127#12011yescharacteristic
148C2×C4×C127#12111yescharacteristic
149C2×C4×C127#12111yescharacteristic
150C2×C4×C127#12311yescharacteristic
151C8×C127—42no—
152C8×C127—42no—
153C8×C127—41no—
154C8×C127—41no—
155C8×C127—41no—
156C8×C127—41no—
157C8×C127—81no—
158C22×C127—21no—
159C22×C127—21no—
160C22×C127—21no—
161C22×C127—41no—
162C22×C127—41no—
163C22×C127—41no—
164C22×C127#38611yescharacteristic
165C4×C127—21no—
166C4×C127—21no—
167C4×C127—21no—
168C4×C127—21no—
169C4×C127—21no—
170C4×C127—41no—
171C4×C127—41no—
172C4×C127—41no—
173C4×C127—82no—
174C4×C127#45511yescharacteristic
175C4×C127#45611yescharacteristic
176#9337C12711yesmaximal, characteristic, direct product factor, Sylow
177C2×C127—41no—
178C2×C127—81no—
179C2×C127#188211yescharacteristic
180C2×C127#190211yescharacteristic
181C2×C127#191411yescharacteristic
182#3218C2×C12711yescharacteristic
183#2995C2×C12711yescharacteristic
184#1997C2×C12711yescharacteristic, complemented
185#1558C2×C12711yescharacteristic, complemented
186#1529C2×C12711yescharacteristic
187#1307C2×C12711yescharacteristic, complemented
188#1291C2×C12711yescharacteristic, complemented
189C127#933711yescharacteristic, direct product factor, Sylow
190C2×C4⋊Q8C22×C12711yescharacteristic
191#529C22×C12711yescharacteristic
192#497—21no—
193#491—21no—
194#462—21no—
195#461—21no—
196#451C4×C12712yes—
197#448C4×C12712yes—
198#446—21no—
199#436—21no—
200#435—21no—
201#435—21no—
202#433—21no—
203#432C22×C12711yescharacteristic
204#432C22×C12711yescharacteristic
205#432C22×C12711yescharacteristic
206#424—21no—
207#423C22×C12711yescharacteristic
208C4×M16C22×C12711yescharacteristic
209#343—21no—
210#343—21no—
211#333—21no—
212#333—21no—
213#330—21no—
214#329—21no—
215C22×Q8C2×C4×C12712yes—
216C2×Q16—22no—
217C2×SD16—22no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16D4×C12711yescharacteristic
221C2×M16D4×C12711yescharacteristic
222C22×C8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227#126—21no—
228#125D4×C12711yescharacteristic
229#124D4×C12711yescharacteristic
230#123—21no—
231C22⋊Q8C2×C4×C12711yescharacteristic
232#121C2×C4×C12711yescharacteristic
233C4×Q8D4×C12711yescharacteristic
234C4×D4—21no—
235C4×D4D4×C12711yescharacteristic
236#117—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C42C23×C12711yescharacteristic
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8D4×C12711yescharacteristic
247C4⋊C8D4×C12711yescharacteristic
248#103—22no—
249#103—22no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8C2×C4×C12712yes—
255#97—21no—
256#97—21no—
257#97—21no—
258#97—21no—
259#97—21no—
260C4×C8—21no—
261C4×C8—21no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—82no—
265C2×Q8C22⋊C4×C12711yescharacteristic
266C2×D4—21no—
267C2×D4C22⋊C4×C12711yescharacteristic
268C22×C4—21no—
269C22×C4—22no—
270C22×C4C22×C4×C12711yescharacteristic
271C22×C4C2×D4×C12711yescharacteristic
272C22×C4#41×C12711yescharacteristic
273Q16—82no—
274SD16—82no—
275M16—22no—
276M16—41no—
277M16—41no—
278M16—41no—
279M16—81no—
280C2×C8—22no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—81no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4C22⋊C4×C12711yescharacteristic
297C4⋊C4C22⋊C4×C12711yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C42—21no—
304C42C2×D4×C12711yescharacteristic
305C42C2×D4×C12711yescharacteristic
306C42C2×D4×C12711yescharacteristic
307C42#41×C12711yescharacteristic
308C23—21no—
309C23C4×D4×C12711yescharacteristic
310Q8—41no—
311Q8—42no—
312Q8—42no—
313Q8—82no—
314D4—41no—
315D4—81no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—82no—
327C2×C4C2×C22⋊C4×C12711yescharacteristic
328C2×C4C4×D4×C12711yescharacteristic
329C2×C4#120×C12711yescharacteristic
330C2×C4#121×C12711yescharacteristic
331C2×C4#121×C12711yescharacteristic
332C2×C4#123×C12711yescharacteristic
333C8—42no—
334C8—42no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—41no—
339C8—81no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22#386×C12711yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—82no—
356C4#455×C12711yescharacteristic
357C4#456×C12711yescharacteristic
358C2—41no—
359C2—81no—
360C2C127×#188211yescharacteristic
361C2C127×#190211yescharacteristic
362C2C127×#191411yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#121×C127C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1997C2semidirect
4. C127×#1558C2semidirect
6. C127×#1307C2semidirect
7. C127×#1291C2semidirect
176. #9337C127direct (N × H)
184. #1997C2×C127semidirect
185. #1558C2×C127semidirect
187. #1307C2×C127semidirect
188. #1291C2×C127semidirect
189. C127#9337direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32182
C127×#29952
C127×#19972
C127×#15582
C127×#15292
C127×#13072
C127×#12912
#9337127