Finite Group Databasebeta

← C127×#10460 #44574133

Subgroups — C127×#10460 #44574133

Order 32512.

406 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×#3077C211yesmaximal, characteristic
2C127×#1800C211yesmaximal, characteristic
3C127×#1566C211yesmaximal, characteristic, complemented
4C127×#1550C211yesmaximal, characteristic, complemented
5C127×#1493C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C127C211yesmaximal, characteristic
7C127×#1292C211yesmaximal, characteristic, complemented
8#533×C127C2211yescharacteristic
9C2×C4×D4×C127C2211yescharacteristic
10#478×C127—22no—
11#476×C127—21no—
12#474×C127—21no—
13#428×C127—21no—
14#423×C127C2211yescharacteristic
15#423×C127C2211yescharacteristic
16#423×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18#418×C127—21no—
19C2×#100×C127—21no—
20C2×C4×C8×C127C2211yescharacteristic
21#343×C127—21no—
22#334×C127—22no—
23#333×C127—21no—
24#332×C127—21no—
25Q8⋊C8×C127—21no—
26Q8⋊C8×C127—21no—
27D4⋊C8×C127—21no—
28D4⋊C8×C127—21no—
29C22×D4×C127D411yescharacteristic
30C23×C4×C127—21no—
31C2×M16×C127—21no—
32C2×M16×C127—21no—
33C2×M16×C127—21no—
34C22×C8×C127—21no—
35C22×C8×C127—21no—
36C4⋊Q8×C127D411yescharacteristic
37C4⋊Q8×C127D411yescharacteristic
38#125×C127—21no—
39C22⋊Q8×C127—21no—
40C22⋊Q8×C127—21no—
41C4×Q8×C127—21no—
42C4×Q8×C127—21no—
43C4×D4×C127—21no—
44C4×D4×C127—21no—
45C4×D4×C127—21no—
46C4×D4×C127—21no—
47#117×C127—21no—
48C2×C4⋊C4×C127D411yescharacteristic
49C2×C22⋊C4×C127—21no—
50C2×C42×C127C2311yescharacteristic
51#107×C127—22no—
52#106×C127—22no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127—21no—
58C4⋊C8×C127—21no—
59C4⋊C8×C127—21no—
60C4⋊C8×C127D412yes—
61#102×C127—22no—
62#102×C127—22no—
63#100×C127—42no—
64C4×C8×C127—21no—
65C4×C8×C127D411yescharacteristic
66C4×C8×C127D411yescharacteristic
67C24×C127—21no—
68C2×Q8×C127—21no—
69C2×Q8×C127—21no—
70C2×D4×C127—21no—
71C2×D4×C127—21no—
72C2×D4×C127—21no—
73C2×D4×C127—21no—
74C2×D4×C127—21no—
75C2×D4×C127SD1612yes—
76C22×C4×C127—21no—
77C22×C4×C127—41no—
78C22×C4×C127—41no—
79C22×C4×C127—81no—
80C22×C4×C127—81no—
81C22×C4×C127C2×D411yescharacteristic
82C22×C4×C127#4111yescharacteristic
83C22×C4×C127#4111yescharacteristic
84M16×C127—41no—
85M16×C127—41no—
86M16×C127—41no—
87M16×C127—41no—
88M16×C127—41no—
89M16×C127—41no—
90C2×C8×C127—21no—
91C2×C8×C127—22no—
92C2×C8×C127—21no—
93C2×C8×C127—42no—
94C2×C8×C127—41no—
95C2×C8×C127—41no—
96C2×C8×C127—41no—
97C2×C8×C127—81no—
98C4⋊C4×C127—21no—
99C4⋊C4×C127—21no—
100C4⋊C4×C127—21no—
101C4⋊C4×C127—21no—
102C4⋊C4×C127—21no—
103C4⋊C4×C127—21no—
104C4⋊C4×C127—41no—
105C4⋊C4×C127—41no—
106C22⋊C4×C127—41no—
107C22⋊C4×C127—41no—
108C22⋊C4×C127—41no—
109C42×C127—41no—
110C42×C127C2×D411yescharacteristic
111C42×C127C2×D411yescharacteristic
112C42×C127C2×D411yescharacteristic
113C42×C127#4111yescharacteristic
114C23×C127—22no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127—81no—
118C23×C127—81no—
119C23×C127#12311yescharacteristic
120Q8×C127—41no—
121Q8×C127—41no—
122Q8×C127—81no—
123D4×C127—22no—
124D4×C127—22no—
125D4×C127—41no—
126D4×C127—41no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—41no—
130C2×C4×C127—41no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—82no—
134C2×C4×C127—81no—
135C2×C4×C127—81no—
136C2×C4×C127—81no—
137C2×C4×C127#12011yescharacteristic
138C2×C4×C127#12111yescharacteristic
139C2×C4×C127#12111yescharacteristic
140C2×C4×C127#12111yescharacteristic
141C2×C4×C127#12311yescharacteristic
142C2×C4×C127#12411yescharacteristic
143C2×C4×C127C2×SD1611yescharacteristic
144C2×C4×C127#13511yescharacteristic
145C2×C4×C127#13711yescharacteristic
146C2×C4×C127#13711yescharacteristic
147C8×C127—22no—
148C8×C127—41no—
149C8×C127—42no—
150C8×C127—81no—
151C8×C127—81no—
152C8×C127—81no—
153C22×C127—21no—
154C22×C127—21no—
155C22×C127—42no—
156C22×C127—82no—
157C22×C127—82no—
158C22×C127—81no—
159C22×C127—81no—
160C22×C127#39411yescharacteristic
161C22×C127#48311yescharacteristic
162C22×C127#48511yescharacteristic
163C4×C127—21no—
164C4×C127—21no—
165C4×C127—21no—
166C4×C127—81no—
167C4×C127—81no—
168C4×C127—81no—
169C4×C127#44811yescharacteristic
170C4×C127#45211yescharacteristic
171C4×C127#46511yescharacteristic
172C4×C127#47011yescharacteristic
173C4×C127#47111yescharacteristic
174C4×C127#47211yescharacteristic
175#10460C12711yesmaximal, characteristic, direct product factor, Sylow
176C2×C127—21no—
177C2×C127—21no—
178C2×C127—82no—
179C2×C127#203511yescharacteristic
180C2×C127#205011yescharacteristic
181C2×C127#205111yescharacteristic
182#3077C2×C12711yescharacteristic
183#1800C2×C12711yescharacteristic
184#1566C2×C12711yescharacteristic, complemented
185#1550C2×C12711yescharacteristic, complemented
186#1493C2×C12711yescharacteristic, complemented
187C2×D4⋊C8C2×C12711yescharacteristic
188#1292C2×C12711yescharacteristic, complemented
189C127#1046011yescharacteristic, direct product factor, Sylow
190#533C22×C12711yescharacteristic
191C2×C4×D4C22×C12711yescharacteristic
192#478—22no—
193#476—21no—
194#474—21no—
195#428—21no—
196#423C22×C12711yescharacteristic
197#423C22×C12711yescharacteristic
198#423C22×C12711yescharacteristic
199C2×C4⋊C8C22×C12711yescharacteristic
200#418—21no—
201C2×#100—21no—
202C2×C4×C8C22×C12711yescharacteristic
203#343—21no—
204#334—22no—
205#333—21no—
206#332—21no—
207Q8⋊C8—21no—
208Q8⋊C8—21no—
209D4⋊C8—21no—
210D4⋊C8—21no—
211C22×D4D4×C12711yescharacteristic
212C23×C4—21no—
213C2×M16—21no—
214C2×M16—21no—
215C2×M16—21no—
216C22×C8—21no—
217C22×C8—21no—
218C4⋊Q8D4×C12711yescharacteristic
219C4⋊Q8D4×C12711yescharacteristic
220#125—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×D4—21no—
226C4×D4—21no—
227C4×D4—21no—
228C4×D4—21no—
229#117—21no—
230C2×C4⋊C4D4×C12711yescharacteristic
231C2×C22⋊C4—21no—
232C2×C42C23×C12711yescharacteristic
233#107—22no—
234#106—22no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8D4×C12712yes—
243#102—22no—
244#102—22no—
245#100—42no—
246C4×C8—21no—
247C4×C8D4×C12711yescharacteristic
248C4×C8D4×C12711yescharacteristic
249C24—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4SD16×C12712yes—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4C2×D4×C12711yescharacteristic
264C22×C4#41×C12711yescharacteristic
265C22×C4#41×C12711yescharacteristic
266M16—41no—
267M16—41no—
268M16—41no—
269M16—41no—
270M16—41no—
271M16—41no—
272C2×C8—21no—
273C2×C8—22no—
274C2×C8—21no—
275C2×C8—42no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—81no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C42—41no—
292C42C2×D4×C12711yescharacteristic
293C42C2×D4×C12711yescharacteristic
294C42C2×D4×C12711yescharacteristic
295C42#41×C12711yescharacteristic
296C23—22no—
297C23—41no—
298C23—41no—
299C23—81no—
300C23—81no—
301C23#123×C12711yescharacteristic
302Q8—41no—
303Q8—41no—
304Q8—81no—
305D4—22no—
306D4—22no—
307D4—41no—
308D4—41no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—82no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4#120×C12711yescharacteristic
320C2×C4#121×C12711yescharacteristic
321C2×C4#121×C12711yescharacteristic
322C2×C4#121×C12711yescharacteristic
323C2×C4#123×C12711yescharacteristic
324C2×C4#124×C12711yescharacteristic
325C2×C4C2×SD16×C12711yescharacteristic
326C2×C4#135×C12711yescharacteristic
327C2×C4#137×C12711yescharacteristic
328C2×C4#137×C12711yescharacteristic
329C8—22no—
330C8—41no—
331C8—42no—
332C8—81no—
333C8—81no—
334C8—81no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—82no—
339C22—82no—
340C22—81no—
341C22—81no—
342C22#394×C12711yescharacteristic
343C22#483×C12711yescharacteristic
344C22#485×C12711yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4#448×C12711yescharacteristic
352C4#452×C12711yescharacteristic
353C4#465×C12711yescharacteristic
354C4#470×C12711yescharacteristic
355C4#471×C12711yescharacteristic
356C4#472×C12711yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2C127×#203511yescharacteristic
361C2C127×#205011yescharacteristic
362C2C127×#205111yescharacteristic
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×#1566C2semidirect
4. C127×#1550C2semidirect
5. C127×#1493C2semidirect
7. C127×#1292C2semidirect
175. #10460C127direct (N × H)
184. #1566C2×C127semidirect
185. #1550C2×C127semidirect
186. #1493C2×C127semidirect
188. #1292C2×C127semidirect
189. C127#10460direct (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×#18002
C127×#15662
C127×#15502
C127×#14932
C2×D4⋊C8×C1272
C127×#12922
#10460127