Finite Group Databasebeta

← C127×#10509 #44574182

Subgroups — C127×#10509 #44574182

Order 32512.

360 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C127×#3234C211yesmaximal, characteristic
2C127×#1989C211yesmaximal, characteristic, complemented
3C127×#1573C211yesmaximal, characteristic, complemented
4C127×#1551C211yesmaximal, characteristic
5C127×#1502C211yesmaximal, characteristic
6C127×#1470C211yesmaximal, characteristic, complemented
7C127×#1285C211yesmaximal, characteristic, complemented
8#532×C127C2211yescharacteristic
9C2×#125×C127C2211yescharacteristic
10#501×C127—21no—
11#490×C127—21no—
12#481×C127—21no—
13#480×C127—21no—
14#478×C127—21no—
15#478×C127—21no—
16#432×C127C2211yescharacteristic
17#432×C127C2211yescharacteristic
18#431×C127C2211yescharacteristic
19C2×C4⋊C8×C127C2211yescharacteristic
20C4×C4⋊C4×C127C2211yescharacteristic
21#340×C127—21no—
22#340×C127—21no—
23#335×C127—21no—
24#334×C127—21no—
25#333×C127—21no—
26#331×C127—21no—
27#327×C127—22no—
28#324×C127—22no—
29C2×#41×C127—21no—
30C22×C8×C127—21no—
31C4⋊Q8×C127D411yescharacteristic
32#127×C127D411yescharacteristic
33#125×C127—21no—
34#125×C127—21no—
35#125×C127—21no—
36#125×C127—21no—
37#124×C127—21no—
38#121×C127—21no—
39#121×C127—21no—
40C4×D4×C127—21no—
41C4×D4×C127—21no—
42C2×C4⋊C4×C127—21no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127—21no—
45C2×C4⋊C4×C127D411yescharacteristic
46C2×C4⋊C4×C127D411yescharacteristic
47C2×C42×C127—21no—
48C2×C42×C127C2311yescharacteristic
49#107×C127—21no—
50#107×C127—21no—
51#106×C127—21no—
52#106×C127—21no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127D411yescharacteristic
58C4⋊C8×C127D411yescharacteristic
59#102×C127—21no—
60#102×C127—21no—
61#102×C127—21no—
62#102×C127—21no—
63C22⋊C8×C127—21no—
64C22⋊C8×C127—21no—
65C22⋊C8×C127D412yes—
66#97×C127—21no—
67#97×C127—21no—
68C4×C8×C127—21no—
69#95×C127—21no—
70#41×C127—81no—
71#41×C127—81no—
72C2×Q8×C127—21no—
73C2×D4×C127—21no—
74C2×D4×C127—21no—
75C2×D4×C127—21no—
76C2×D4×C127—41no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—41no—
80C22×C4×C127—41no—
81C22×C4×C127C2×D411yescharacteristic
82C22×C4×C127C2×D411yescharacteristic
83C22×C4×C127#4111yescharacteristic
84C2×C8×C127—21no—
85C2×C8×C127—21no—
86C2×C8×C127—22no—
87C2×C8×C127—42no—
88C2×C8×C127—41no—
89C2×C8×C127—41no—
90C4⋊C4×C127—22no—
91C4⋊C4×C127—21no—
92C4⋊C4×C127—21no—
93C4⋊C4×C127—21no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—21no—
96C4⋊C4×C127—21no—
97C4⋊C4×C127—41no—
98C4⋊C4×C127—41no—
99C4⋊C4×C127—41no—
100C4⋊C4×C127—41no—
101C4⋊C4×C127—41no—
102C22⋊C4×C127—41no—
103C22⋊C4×C127—41no—
104C42×C127—81no—
105C42×C127C2×D411yescharacteristic
106C42×C127C2×D411yescharacteristic
107C42×C127#4111yescharacteristic
108C42×C127#4111yescharacteristic
109C23×C127—41no—
110C23×C127#12111yescharacteristic
111Q8×C127—81no—
112D4×C127—41no—
113D4×C127—41no—
114D4×C127—81no—
115D4×C127—81no—
116D4×C127—81no—
117D4×C127—81no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—41no—
123C2×C4×C127—42no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—82no—
130C2×C4×C127—81no—
131C2×C4×C127—81no—
132C2×C4×C127—81no—
133C2×C4×C127#12011yescharacteristic
134C2×C4×C127#12111yescharacteristic
135C2×C4×C127#12111yescharacteristic
136C2×C4×C127#12311yescharacteristic
137C2×C4×C127#12311yescharacteristic
138C2×C4×C127#12411yescharacteristic
139C8×C127—42no—
140C8×C127—41no—
141C8×C127—41no—
142C8×C127—81no—
143C8×C127—81no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—81no—
147C22×C127—81no—
148C22×C127—81no—
149C22×C127#39411yescharacteristic
150C22×C127#47111yescharacteristic
151C22×C127#47211yescharacteristic
152C4×C127—21no—
153C4×C127—21no—
154C4×C127—21no—
155C4×C127—21no—
156C4×C127—21no—
157C4×C127—82no—
158C4×C127—81no—
159C4×C127—81no—
160C4×C127—81no—
161C4×C127#45411yescharacteristic
162C4×C127#45611yescharacteristic
163#10509C12711yesmaximal, characteristic, direct product factor, Sylow
164C2×C127—21no—
165C2×C127—21no—
166C2×C127—161no—
167C2×C127#203811yescharacteristic
168C2×C127#205111yescharacteristic
169C2×C127#205311yescharacteristic
170#3234C2×C12711yescharacteristic
171#1989C2×C12711yescharacteristic, complemented
172#1573C2×C12711yescharacteristic, complemented
173#1551C2×C12711yescharacteristic
174#1502C2×C12711yescharacteristic
175#1470C2×C12711yescharacteristic, complemented
176#1285C2×C12711yescharacteristic, complemented
177C127#1050911yescharacteristic, direct product factor, Sylow
178#532C22×C12711yescharacteristic
179C2×#125C22×C12711yescharacteristic
180#501—21no—
181#490—21no—
182#481—21no—
183#480—21no—
184#478—21no—
185#478—21no—
186#432C22×C12711yescharacteristic
187#432C22×C12711yescharacteristic
188#431C22×C12711yescharacteristic
189C2×C4⋊C8C22×C12711yescharacteristic
190C4×C4⋊C4C22×C12711yescharacteristic
191#340—21no—
192#340—21no—
193#335—21no—
194#334—21no—
195#333—21no—
196#331—21no—
197#327—22no—
198#324—22no—
199C2×#41—21no—
200C22×C8—21no—
201C4⋊Q8D4×C12711yescharacteristic
202#127D4×C12711yescharacteristic
203#125—21no—
204#125—21no—
205#125—21no—
206#125—21no—
207#124—21no—
208#121—21no—
209#121—21no—
210C4×D4—21no—
211C4×D4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4D4×C12711yescharacteristic
216C2×C4⋊C4D4×C12711yescharacteristic
217C2×C42—21no—
218C2×C42C23×C12711yescharacteristic
219#107—21no—
220#107—21no—
221#106—21no—
222#106—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8D4×C12711yescharacteristic
228C4⋊C8D4×C12711yescharacteristic
229#102—21no—
230#102—21no—
231#102—21no—
232#102—21no—
233C22⋊C8—21no—
234C22⋊C8—21no—
235C22⋊C8D4×C12712yes—
236#97—21no—
237#97—21no—
238C4×C8—21no—
239#95—21no—
240#41—81no—
241#41—81no—
242C2×Q8—21no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C2×D4×C12711yescharacteristic
252C22×C4C2×D4×C12711yescharacteristic
253C22×C4#41×C12711yescharacteristic
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—22no—
257C2×C8—42no—
258C2×C8—41no—
259C2×C8—41no—
260C4⋊C4—22no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C42—81no—
275C42C2×D4×C12711yescharacteristic
276C42C2×D4×C12711yescharacteristic
277C42#41×C12711yescharacteristic
278C42#41×C12711yescharacteristic
279C23—41no—
280C23#121×C12711yescharacteristic
281Q8—81no—
282D4—41no—
283D4—41no—
284D4—81no—
285D4—81no—
286D4—81no—
287D4—81no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—82no—
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
309C8—42no—
310C8—41no—
311C8—41no—
312C8—81no—
313C8—81no—
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22#394×C12711yescharacteristic
320C22#471×C12711yescharacteristic
321C22#472×C12711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—82no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4#454×C12711yescharacteristic
332C4#456×C12711yescharacteristic
333C2—21no—
334C2—21no—
335C2—161no—
336C2C127×#203811yescharacteristic
337C2C127×#205111yescharacteristic
338C2C127×#205311yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radical#532×C127C22
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
2. C127×#1989C2semidirect
3. C127×#1573C2semidirect
6. C127×#1470C2semidirect
7. C127×#1285C2semidirect
163. #10509C127direct (N × H)
171. #1989C2×C127semidirect
172. #1573C2×C127semidirect
175. #1470C2×C127semidirect
176. #1285C2×C127semidirect
177. C127#10509direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32342
C127×#19892
C127×#15732
C127×#15512
C127×#15022
C127×#14702
C127×#12852
#10509127