Finite Group Databasebeta

← C127×#13332 #44577005

Subgroups — C127×#13332 #44577005

Order 32512.

566 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C127C211yesmaximal, characteristic, complemented
2C2×#509×C127C211yesmaximal, characteristic
3C2×#495×C127C211yesmaximal, characteristic, complemented
4C2×#362×C127C211yesmaximal, characteristic, complemented
5C2×#361×C127C211yesmaximal, characteristic, complemented
6C127×#1974C211yesmaximal, characteristic, complemented
7C127×#1376C211yesmaximal, characteristic, complemented
8C2×#135×C127C2211yescharacteristic
9C22×Q16×C127C2211yescharacteristic
10C22×SD16×C127—21no—
11C22×D8×C127C2211yescharacteristic
12C2×#124×C127—21no—
13#510×C127—22no—
14#510×C127—22no—
15#509×C127—22no—
16#509×C127—22no—
17C2×Q32×C127—21no—
18C2×SD32×C127—21no—
19C2×SD32×C127—21no—
20C2×D16×C127—21no—
21C2×M32×C127C2211yescharacteristic
22C2×M32×C127C2211yescharacteristic
23#495×C127—22no—
24#495×C127—22no—
25C2×#108×C127C2211yescharacteristic
26C2×#104×C127—21no—
27#408×C127—21no—
28C2×C4×C8×C127C2211yescharacteristic
29#362×C127—22no—
30#361×C127—22no—
31C2×#41×C127—21no—
32C22×Q8×C127—21no—
33C22×D4×C127—21no—
34#135×C127—21no—
35#135×C127—21no—
36#135×C127—21no—
37#135×C127—21no—
38C2×Q16×C127—21no—
39C2×Q16×C127—21no—
40C2×Q16×C127—21no—
41C2×Q16×C127—21no—
42C2×Q16×C127—21no—
43C2×Q16×C127D411yescharacteristic
44C2×Q16×C127D412yes—
45C2×SD16×C127—24no—
46C2×SD16×C127—21no—
47C2×SD16×C127—42no—
48C2×SD16×C127—42no—
49C2×D8×C127—21no—
50C2×D8×C127—21no—
51C2×D8×C127—21no—
52C2×D8×C127—21no—
53C2×D8×C127—21no—
54C2×D8×C127D411yescharacteristic
55C2×D8×C127D412yes—
56C2×M16×C127—21no—
57C22×C8×C127D411yescharacteristic
58C22×C8×C127C2311yescharacteristic
59#124×C127—24no—
60#124×C127—42no—
61C2×C22⋊C4×C127—42no—
62C2×C42×C127D411yescharacteristic
63Q32×C127—24no—
64SD32×C127—24no—
65SD32×C127—24no—
66D16×C127—24no—
67M32×C127—21no—
68M32×C127—21no—
69M32×C127D412yes—
70M32×C127D412yes—
71C2×C16×C127—21no—
72C2×C16×C127—21no—
73#108×C127—21no—
74#108×C127—21no—
75#104×C127—42no—
76C22⋊C8×C127—42no—
77C4×C8×C127—21no—
78C4×C8×C127—21no—
79C24×C127—41no—
80#41×C127—41no—
81#41×C127—41no—
82#41×C127—41no—
83#41×C127—41no—
84C2×Q8×C127—22no—
85C2×Q8×C127—21no—
86C2×Q8×C127—41no—
87C2×Q8×C127—41no—
88C2×Q8×C127—41no—
89C2×Q8×C127—41no—
90C2×Q8×C127—41no—
91C2×D4×C127—22no—
92C2×D4×C127—21no—
93C2×D4×C127—41no—
94C2×D4×C127—41no—
95C2×D4×C127—41no—
96C2×D4×C127—41no—
97C2×D4×C127—41no—
98C2×D4×C127—41no—
99C22×C4×C127—21no—
100C22×C4×C127—41no—
101C22×C4×C127—41no—
102C22×C4×C127C2×D411yescharacteristic
103Q16×C127—21no—
104Q16×C127—22no—
105Q16×C127—21no—
106Q16×C127—22no—
107Q16×C127—41no—
108Q16×C127—41no—
109SD16×C127—48no—
110SD16×C127—41no—
111SD16×C127—41no—
112D8×C127—21no—
113D8×C127—22no—
114D8×C127—21no—
115D8×C127—22no—
116D8×C127—41no—
117D8×C127—41no—
118M16×C127—41no—
119M16×C127—41no—
120C2×C8×C127—21no—
121C2×C8×C127—21no—
122C2×C8×C127—41no—
123C2×C8×C127D812yes—
124C2×C8×C127C2×D411yescharacteristic
125C2×C8×C127C2×D411yescharacteristic
126C2×C8×C127C2×D411yescharacteristic
127C2×C8×C127C2×D411yescharacteristic
128C2×C8×C127C2×D411yescharacteristic
129C2×C8×C127#4111yescharacteristic
130C22⋊C4×C127—48no—
131C42×C127—21no—
132C42×C127D812yes—
133C16×C127—22no—
134C16×C127—22no—
135C23×C127—42no—
136C23×C127—41no—
137C23×C127—84no—
138C23×C127—81no—
139C23×C127—81no—
140C23×C127AGL(1,ℤ/8)11yescharacteristic
141Q8×C127—41no—
142Q8×C127—42no—
143Q8×C127—42no—
144Q8×C127—41no—
145Q8×C127—81no—
146Q8×C127—81no—
147D4×C127—42no—
148D4×C127—41no—
149D4×C127—42no—
150D4×C127—41no—
151D4×C127—81no—
152D4×C127—81no—
153D4×C127—81no—
154D4×C127—81no—
155C2×C4×C127—22no—
156C2×C4×C127—42no—
157C2×C4×C127—42no—
158C2×C4×C127—41no—
159C2×C4×C127—81no—
160C2×C4×C127—81no—
161C2×C4×C127—81no—
162C2×C4×C127—81no—
163C2×C4×C127#12011yescharacteristic
164C2×C4×C127#12111yescharacteristic
165C2×C4×C127#12711yescharacteristic
166C2×C4×C127C2×D811yescharacteristic
167C2×C4×C127C2×D811yescharacteristic
168C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
169C8×C127—22no—
170C8×C127—81no—
171C8×C127#12011yescharacteristic
172C8×C127#12011yescharacteristic
173C8×C127#12111yescharacteristic
174C8×C127#12111yescharacteristic
175C22×C127—22no—
176C22×C127—84no—
177C22×C127—82no—
178C22×C127—81no—
179C22×C127—82no—
180C22×C127—162no—
181C22×C127—162no—
182C22×C127#44711yescharacteristic
183C22×C127#45911yescharacteristic
184C22×C127#49611yescharacteristic
185C4×C127—42no—
186C4×C127—81no—
187C4×C127—82no—
188C4×C127#39211yescharacteristic
189C4×C127#44711yescharacteristic
190C4×C127#45911yescharacteristic
191C4×C127#49311yescharacteristic
192#13332C12711yesmaximal, characteristic, direct product factor, Sylow
193C2×C127—21no—
194C2×C127—21no—
195C2×C127—161no—
196C2×C127—162no—
197C2×C127#201111yescharacteristic
198C2×C127#221212yes—
199C2×#510C2×C12711yescharacteristic, complemented
200C2×#509C2×C12711yescharacteristic
201C2×#495C2×C12711yescharacteristic, complemented
202C2×#362C2×C12711yescharacteristic, complemented
203C2×#361C2×C12711yescharacteristic, complemented
204#1974C2×C12711yescharacteristic, complemented
205#1376C2×C12711yescharacteristic, complemented
206C127#1333211yescharacteristic, direct product factor, Sylow
207C2×#135C22×C12711yescharacteristic
208C22×Q16C22×C12711yescharacteristic
209C22×SD16—21no—
210C22×D8C22×C12711yescharacteristic
211C2×#124—21no—
212#510—22no—
213#510—22no—
214#509—22no—
215#509—22no—
216C2×Q32—21no—
217C2×SD32—21no—
218C2×SD32—21no—
219C2×D16—21no—
220C2×M32C22×C12711yescharacteristic
221C2×M32C22×C12711yescharacteristic
222#495—22no—
223#495—22no—
224C2×#108C22×C12711yescharacteristic
225C2×#104—21no—
226#408—21no—
227C2×C4×C8C22×C12711yescharacteristic
228#362—22no—
229#361—22no—
230C2×#41—21no—
231C22×Q8—21no—
232C22×D4—21no—
233#135—21no—
234#135—21no—
235#135—21no—
236#135—21no—
237C2×Q16—21no—
238C2×Q16—21no—
239C2×Q16—21no—
240C2×Q16—21no—
241C2×Q16—21no—
242C2×Q16D4×C12712yes—
243C2×Q16D4×C12711yescharacteristic
244C2×SD16—24no—
245C2×SD16—21no—
246C2×SD16—42no—
247C2×SD16—42no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—21no—
251C2×D8—21no—
252C2×D8—21no—
253C2×D8D4×C12712yes—
254C2×D8D4×C12711yescharacteristic
255C2×M16—21no—
256C22×C8D4×C12711yescharacteristic
257C22×C8C23×C12711yescharacteristic
258#124—24no—
259#124—42no—
260C2×C22⋊C4—42no—
261C2×C42D4×C12711yescharacteristic
262Q32—24no—
263SD32—24no—
264SD32—24no—
265D16—24no—
266M32—21no—
267M32—21no—
268M32D4×C12712yes—
269M32D4×C12712yes—
270C2×C16—21no—
271C2×C16—21no—
272#108—21no—
273#108—21no—
274#104—42no—
275C22⋊C8—42no—
276C4×C8—21no—
277C4×C8—21no—
278C24—41no—
279#41—41no—
280#41—41no—
281#41—41no—
282#41—41no—
283C2×Q8—22no—
284C2×Q8—21no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4C2×D4×C12711yescharacteristic
302Q16—21no—
303Q16—22no—
304Q16—21no—
305Q16—22no—
306Q16—41no—
307Q16—41no—
308SD16—48no—
309SD16—41no—
310SD16—41no—
311D8—21no—
312D8—22no—
313D8—21no—
314D8—22no—
315D8—41no—
316D8—41no—
317M16—41no—
318M16—41no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—41no—
322C2×C8D8×C12712yes—
323C2×C8C2×D4×C12711yescharacteristic
324C2×C8C2×D4×C12711yescharacteristic
325C2×C8C2×D4×C12711yescharacteristic
326C2×C8C2×D4×C12711yescharacteristic
327C2×C8C2×D4×C12711yescharacteristic
328C2×C8#41×C12711yescharacteristic
329C22⋊C4—48no—
330C42—21no—
331C42D8×C12712yes—
332C16—22no—
333C16—22no—
334C23—42no—
335C23—41no—
336C23—84no—
337C23—81no—
338C23—81no—
339C23AGL(1,ℤ/8)×C12711yescharacteristic
340Q8—41no—
341Q8—42no—
342Q8—42no—
343Q8—41no—
344Q8—81no—
345Q8—81no—
346D4—42no—
347D4—41no—
348D4—42no—
349D4—41no—
350D4—81no—
351D4—81no—
352D4—81no—
353D4—81no—
354C2×C4—22no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4#120×C12711yescharacteristic
363C2×C4#121×C12711yescharacteristic
364C2×C4#127×C12711yescharacteristic
365C2×C4C2×D8×C12711yescharacteristic
366C2×C4C2×D8×C12711yescharacteristic
367C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
368C8—22no—
369C8—81no—
370C8#120×C12711yescharacteristic
371C8#120×C12711yescharacteristic
372C8#121×C12711yescharacteristic
373C8#121×C12711yescharacteristic
374C22—22no—
375C22—84no—
376C22—82no—
377C22—81no—
378C22—82no—
379C22—162no—
380C22—162no—
381C22#447×C12711yescharacteristic
382C22#459×C12711yescharacteristic
383C22#496×C12711yescharacteristic
384C4—42no—
385C4—81no—
386C4—82no—
387C4#392×C12711yescharacteristic
388C4#447×C12711yescharacteristic
389C4#459×C12711yescharacteristic
390C4#493×C12711yescharacteristic
391C2—21no—
392C2—21no—
393C2—162no—
394C2—161no—
395C2C127×#201111yescharacteristic
396C2C127×#221212yes—
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC2×#509×C127C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#510×C127C2semidirect
3. C2×#495×C127C2semidirect
4. C2×#362×C127C2semidirect
5. C2×#361×C127C2semidirect
6. C127×#1974C2semidirect
7. C127×#1376C2semidirect
192. #13332C127direct (N × H)
199. C2×#510C2×C127semidirect
201. C2×#495C2×C127semidirect
202. C2×#362C2×C127semidirect
203. C2×#361C2×C127semidirect
204. #1974C2×C127semidirect
205. #1376C2×C127semidirect
206. C127#13332direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#510×C1272
C2×#509×C1272
C2×#495×C1272
C2×#362×C1272
C2×#361×C1272
C127×#19742
C127×#13762
#13332127