Finite Group Databasebeta

← C127×#10468 #44574141

Subgroups — C127×#10468 #44574141

Order 32512.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3077C211yesmaximal, characteristic
2C127×#1804C211yesmaximal, characteristic
3C127×#1570C211yesmaximal, characteristic, complemented
4C127×#1542C211yesmaximal, characteristic, complemented
5C127×#1518C211yesmaximal, characteristic, complemented
6C127×#1460C211yesmaximal, characteristic
7C127×#1286C211yesmaximal, characteristic, complemented
8#533×C127C2211yescharacteristic
9C2×C4×D4×C127C2211yescharacteristic
10#478×C127—22no—
11#476×C127—21no—
12#474×C127—21no—
13#431×C127C2211yescharacteristic
14#431×C127C2211yescharacteristic
15#428×C127—21no—
16#423×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18#418×C127—21no—
19C2×#102×C127—21no—
20#382×C127C2211yescharacteristic
21#340×C127—21no—
22#334×C127—22no—
23#333×C127—21no—
24#332×C127—21no—
25#328×C127—22no—
26#323×C127—22no—
27C22×D4×C127D411yescharacteristic
28C23×C4×C127—21no—
29C2×M16×C127—21no—
30C22×C8×C127—21no—
31C4⋊Q8×C127D411yescharacteristic
32C4⋊Q8×C127D411yescharacteristic
33#125×C127—21no—
34C22⋊Q8×C127—21no—
35C22⋊Q8×C127—21no—
36C4×Q8×C127—21no—
37C4×Q8×C127—21no—
38C4×D4×C127—21no—
39C4×D4×C127—21no—
40C4×D4×C127—21no—
41C4×D4×C127—21no—
42#117×C127—21no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127D411yescharacteristic
45C2×C22⋊C4×C127—21no—
46C2×C42×C127C2311yescharacteristic
47#107×C127—22no—
48#106×C127—22no—
49C4⋊C8×C127—21no—
50C4⋊C8×C127—21no—
51C4⋊C8×C127—21no—
52C4⋊C8×C127—21no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127D412yes—
55#102×C127—22no—
56#102×C127—22no—
57#102×C127—42no—
58C22⋊C8×C127—21no—
59C22⋊C8×C127D412yes—
60C4×C8×C127—21no—
61C4×C8×C127—21no—
62#95×C127—21no—
63#95×C127—21no—
64C24×C127—21no—
65C2×Q8×C127—21no—
66C2×Q8×C127—21no—
67C2×D4×C127—21no—
68C2×D4×C127—21no—
69C2×D4×C127—21no—
70C2×D4×C127—21no—
71C2×D4×C127—21no—
72C2×D4×C127SD1612yes—
73C22×C4×C127—21no—
74C22×C4×C127—41no—
75C22×C4×C127—41no—
76C22×C4×C127—41no—
77C22×C4×C127—82no—
78C22×C4×C127C2×D411yescharacteristic
79C22×C4×C127C2×D411yescharacteristic
80C22×C4×C127#4111yescharacteristic
81M16×C127—41no—
82M16×C127—41no—
83C2×C8×C127—22no—
84C2×C8×C127—22no—
85C2×C8×C127—41no—
86C2×C8×C127—41no—
87C2×C8×C127—41no—
88C2×C8×C127—41no—
89C4⋊C4×C127—21no—
90C4⋊C4×C127—21no—
91C4⋊C4×C127—21no—
92C4⋊C4×C127—21no—
93C4⋊C4×C127—21no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—41no—
97C4⋊C4×C127—41no—
98C4⋊C4×C127—41no—
99C22⋊C4×C127—41no—
100C22⋊C4×C127—41no—
101C22⋊C4×C127—41no—
102C42×C127—41no—
103C42×C127C2×D411yescharacteristic
104C42×C127C2×D411yescharacteristic
105C42×C127#4111yescharacteristic
106C42×C127#4111yescharacteristic
107C23×C127—22no—
108C23×C127—41no—
109C23×C127—41no—
110C23×C127—81no—
111C23×C127—81no—
112C23×C127#12111yescharacteristic
113Q8×C127—81no—
114Q8×C127—81no—
115D4×C127—22no—
116D4×C127—22no—
117D4×C127—41no—
118D4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—41no—
121C2×C4×C127—41no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—82no—
125C2×C4×C127—82no—
126C2×C4×C127—81no—
127C2×C4×C127—81no—
128C2×C4×C127—81no—
129C2×C4×C127—81no—
130C2×C4×C127#12011yescharacteristic
131C2×C4×C127#12111yescharacteristic
132C2×C4×C127#12111yescharacteristic
133C2×C4×C127#12311yescharacteristic
134C2×C4×C127#12311yescharacteristic
135C2×C4×C127#12411yescharacteristic
136C2×C4×C127C2×SD1611yescharacteristic
137C2×C4×C127#13511yescharacteristic
138C2×C4×C127#13711yescharacteristic
139C2×C4×C127#13711yescharacteristic
140C8×C127—42no—
141C8×C127—42no—
142C8×C127—81no—
143C8×C127—81no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—42no—
147C22×C127—82no—
148C22×C127—82no—
149C22×C127—81no—
150C22×C127—81no—
151C22×C127#39411yescharacteristic
152C22×C127#46511yescharacteristic
153C22×C127#47011yescharacteristic
154C4×C127—21no—
155C4×C127—21no—
156C4×C127—21no—
157C4×C127—21no—
158C4×C127—81no—
159C4×C127—81no—
160C4×C127—81no—
161C4×C127—161no—
162C4×C127#44811yescharacteristic
163C4×C127#45211yescharacteristic
164C4×C127#48311yescharacteristic
165C4×C127#48511yescharacteristic
166#10468C12711yesmaximal, characteristic, direct product factor, Sylow
167C2×C127—21no—
168C2×C127—21no—
169C2×C127—82no—
170C2×C127#203511yescharacteristic
171C2×C127#204811yescharacteristic
172C2×C127#205311yescharacteristic
173#3077C2×C12711yescharacteristic
174#1804C2×C12711yescharacteristic
175#1570C2×C12711yescharacteristic, complemented
176#1542C2×C12711yescharacteristic, complemented
177#1518C2×C12711yescharacteristic, complemented
178#1460C2×C12711yescharacteristic
179#1286C2×C12711yescharacteristic, complemented
180C127#1046811yescharacteristic, direct product factor, Sylow
181#533C22×C12711yescharacteristic
182C2×C4×D4C22×C12711yescharacteristic
183#478—22no—
184#476—21no—
185#474—21no—
186#431C22×C12711yescharacteristic
187#431C22×C12711yescharacteristic
188#428—21no—
189#423C22×C12711yescharacteristic
190C2×C4⋊C8C22×C12711yescharacteristic
191#418—21no—
192C2×#102—21no—
193#382C22×C12711yescharacteristic
194#340—21no—
195#334—22no—
196#333—21no—
197#332—21no—
198#328—22no—
199#323—22no—
200C22×D4D4×C12711yescharacteristic
201C23×C4—21no—
202C2×M16—21no—
203C22×C8—21no—
204C4⋊Q8D4×C12711yescharacteristic
205C4⋊Q8D4×C12711yescharacteristic
206#125—21no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×D4—21no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—21no—
215#117—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4D4×C12711yescharacteristic
218C2×C22⋊C4—21no—
219C2×C42C23×C12711yescharacteristic
220#107—22no—
221#106—22no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8D4×C12712yes—
228#102—22no—
229#102—22no—
230#102—42no—
231C22⋊C8—21no—
232C22⋊C8D4×C12712yes—
233C4×C8—21no—
234C4×C8—21no—
235#95—21no—
236#95—21no—
237C24—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4SD16×C12712yes—
246C22×C4—21no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—82no—
251C22×C4C2×D4×C12711yescharacteristic
252C22×C4C2×D4×C12711yescharacteristic
253C22×C4#41×C12711yescharacteristic
254M16—41no—
255M16—41no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C42—41no—
276C42C2×D4×C12711yescharacteristic
277C42C2×D4×C12711yescharacteristic
278C42#41×C12711yescharacteristic
279C42#41×C12711yescharacteristic
280C23—22no—
281C23—41no—
282C23—41no—
283C23—81no—
284C23—81no—
285C23#121×C12711yescharacteristic
286Q8—81no—
287Q8—81no—
288D4—22no—
289D4—22no—
290D4—41no—
291D4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4#120×C12711yescharacteristic
304C2×C4#121×C12711yescharacteristic
305C2×C4#121×C12711yescharacteristic
306C2×C4#123×C12711yescharacteristic
307C2×C4#123×C12711yescharacteristic
308C2×C4#124×C12711yescharacteristic
309C2×C4C2×SD16×C12711yescharacteristic
310C2×C4#135×C12711yescharacteristic
311C2×C4#137×C12711yescharacteristic
312C2×C4#137×C12711yescharacteristic
313C8—42no—
314C8—42no—
315C8—81no—
316C8—81no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—82no—
321C22—82no—
322C22—81no—
323C22—81no—
324C22#394×C12711yescharacteristic
325C22#465×C12711yescharacteristic
326C22#470×C12711yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—161no—
335C4#448×C12711yescharacteristic
336C4#452×C12711yescharacteristic
337C4#483×C12711yescharacteristic
338C4#485×C12711yescharacteristic
339C2—21no—
340C2—21no—
341C2—82no—
342C2C127×#203511yescharacteristic
343C2C127×#204811yescharacteristic
344C2C127×#205311yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C2×C42 ▷ 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×#1570C2semidirect
4. C127×#1542C2semidirect
5. C127×#1518C2semidirect
7. C127×#1286C2semidirect
166. #10468C127direct (N × H)
175. #1570C2×C127semidirect
176. #1542C2×C127semidirect
177. #1518C2×C127semidirect
179. #1286C2×C127semidirect
180. C127#10468direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#30772
C127×#18042
C127×#15702
C127×#15422
C127×#15182
C127×#14602
C127×#12862
#10468127