Finite Group Databasebeta

← C127×#11342 #44575015

Subgroups — C127×#11342 #44575015

Order 32512.

822 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#428×C127C212yesmaximal
2C127×#2316C211yesmaximal, characteristic
3C2×#343×C127C211yesmaximal, characteristic
4C2×#339×C127C212yesmaximal
5C127×C4⋊#95C211yesmaximal, characteristic
6C22×M16×C127C2212yes—
7C2×#117×C127C2212yes—
8C22×C4⋊C4×C127C2211yescharacteristic
9C22×C4⋊C4×C127C2211yescharacteristic
10C22×C42×C127C2211yescharacteristic
11#428×C127—24no—
12#428×C127—24no—
13C2×#107×C127—22no—
14C2×#106×C127—22no—
15#389×C127—22no—
16#389×C127—22no—
17#380×C127—22no—
18C2×#95×C127—22no—
19#343×C127C414yescomplemented
20#339×C127—24no—
21C23×C4×C127—21no—
22C23×C4×C127—21no—
23C23×C4×C127D412yes—
24C23×C4×C127C2311yescharacteristic
25C2×M16×C127—22no—
26C2×M16×C127—22no—
27C2×M16×C127—22no—
28C2×M16×C127C2×C414yes—
29C2×M16×C127D414yes—
30C2×M16×C127Q814yes—
31C22×C8×C127—22no—
32#117×C127—22no—
33#117×C127—22no—
34#117×C127—22no—
35#117×C127—22no—
36C2×C4⋊C4×C127—22no—
37C2×C4⋊C4×C127—22no—
38C2×C4⋊C4×C127—22no—
39C2×C4⋊C4×C127—22no—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127C2×C412yes—
44C2×C4⋊C4×C127D412yes—
45C2×C4⋊C4×C127D412yes—
46C2×C4⋊C4×C127D412yes—
47C2×C4⋊C4×C127Q812yes—
48C2×C22⋊C4×C127—22no—
49C2×C42×C127—22no—
50C2×C42×C127—22no—
51C2×C42×C127—22no—
52C2×C42×C127—21no—
53C2×C42×C127Q812yes—
54#107×C127—28no—
55#106×C127—28no—
56#95×C127—24no—
57#95×C127—44no—
58C24×C127C2×D411yescharacteristic
59C22×C4×C127—22no—
60C22×C4×C127—22no—
61C22×C4×C127—22no—
62C22×C4×C127—22no—
63C22×C4×C127—22no—
64C22×C4×C127—22no—
65C22×C4×C127—22no—
66C22×C4×C127—22no—
67C22×C4×C127—41no—
68C22×C4×C127—41no—
69C22×C4×C127—41no—
70C22×C4×C127—41no—
71C22×C4×C127—42no—
72C22×C4×C127—42no—
73C22×C4×C127—42no—
74C22×C4×C127—42no—
75C22×C4×C127—41no—
76C22×C4×C127—41no—
77C22×C4×C127C4⋊C414yes—
78C22×C4×C127C22×C411yescharacteristic
79C22×C4×C127C2×D412yes—
80C22×C4×C127C2×D411yescharacteristic
81C22×C4×C127C2×D412yes—
82C22×C4×C127C2×Q812yes—
83C22×C4×C127C2×Q811yescharacteristic
84C22×C4×C127C2×Q811yescharacteristic
85C22×C4×C127#4112yes—
86C22×C4×C127#4111yescharacteristic
87C22×C4×C127#4111yescharacteristic
88M16×C127—24no—
89M16×C127—24no—
90M16×C127—24no—
91M16×C127C4⋊C418yescomplemented
92C2×C8×C127—24no—
93C2×C8×C127—24no—
94C2×C8×C127—24no—
95C4⋊C4×C127—24no—
96C4⋊C4×C127—24no—
97C4⋊C4×C127—22no—
98C4⋊C4×C127—24no—
99C4⋊C4×C127—22no—
100C4⋊C4×C127—22no—
101C4⋊C4×C127—22no—
102C4⋊C4×C127—42no—
103C4⋊C4×C127—82no—
104C4⋊C4×C127—82no—
105C22⋊C4×C127—42no—
106C22⋊C4×C127—42no—
107C42×C127—24no—
108C42×C127—42no—
109C42×C127—42no—
110C42×C127—42no—
111C23×C127—21no—
112C23×C127—21no—
113C23×C127—21no—
114C23×C127—21no—
115C23×C127C2×C4⋊C411yescharacteristic
116C23×C127#12011yescharacteristic
117C23×C127#12111yescharacteristic
118C23×C127C22⋊Q811yescharacteristic
119C23×C127#12311yescharacteristic
120C23×C127#12711yescharacteristic
121C23×C127C4⋊Q811yescharacteristic
122C2×C4×C127—24no—
123C2×C4×C127—24no—
124C2×C4×C127—42no—
125C2×C4×C127—42no—
126C2×C4×C127—42no—
127C2×C4×C127—42no—
128C2×C4×C127—42no—
129C2×C4×C127—42no—
130C2×C4×C127—42no—
131C2×C4×C127—42no—
132C2×C4×C127—44no—
133C2×C4×C127—44no—
134C2×C4×C127—42no—
135C2×C4×C127—42no—
136C2×C4×C127—42no—
137C2×C4×C127—42no—
138C2×C4×C127—42no—
139C2×C4×C127—42no—
140C2×C4×C127—42no—
141C2×C4×C127—82no—
142C2×C4×C127—82no—
143C2×C4×C127—81no—
144C2×C4×C127—81no—
145C2×C4×C127C2×C4⋊C412yes—
146C2×C4×C127C4×D411yescharacteristic
147C2×C4×C127C4×D412yes—
148C2×C4×C127C4×Q811yescharacteristic
149C2×C4×C127#12012yes—
150C2×C4×C127#12112yes—
151C2×C4×C127C22⋊Q812yes—
152C2×C4×C127C22⋊Q812yes—
153C2×C4×C127C22⋊Q812yes—
154C2×C4×C127C22⋊Q812yes—
155C2×C4×C127#12312yes—
156C2×C4×C127#12512yes—
157C2×C4×C127#12511yescharacteristic
158C2×C4×C127C4⋊Q812yes—
159C2×C4×C127C4⋊Q811yescharacteristic
160C2×C4×C127C4⋊Q812yes—
161C8×C127—28no—
162C22×C127—21no—
163C22×C127—21no—
164C22×C127—21no—
165C22×C127—21no—
166C22×C127—21no—
167C22×C127—21no—
168C22×C127—21no—
169C22×C127—21no—
170C22×C127—21no—
171C22×C127—21no—
172C22×C127—21no—
173C22×C127—21no—
174C22×C127#38411yescharacteristic
175C22×C127#38511yescharacteristic
176C22×C127#38911yescharacteristic
177C22×C127#39211yescharacteristic
178C22×C127#39511yescharacteristic
179C22×C127#39811yescharacteristic
180C22×C127#39911yescharacteristic
181C22×C127#45311yescharacteristic
182C22×C127#45411yescharacteristic
183C22×C127#45511yescharacteristic
184C22×C127#45611yescharacteristic
185C4×C127—44no—
186C4×C127—44no—
187C4×C127—82no—
188C4×C127—82no—
189C4×C127—82no—
190C4×C127#38512yes—
191C4×C127#38912yes—
192C4×C127#39512yes—
193C4×C127#39812yes—
194#11342C12711yesmaximal, characteristic, direct product factor, Sylow
195C2×C127—21no—
196C2×C127—21no—
197C2×C127—21no—
198C2×C127—21no—
199C2×C127#144411yescharacteristic
200C2×C127#185611yescharacteristic
201C2×C127#185711yescharacteristic
202C2×C127#200611yescharacteristic
203C2×C127#200711yescharacteristic
204C2×C127#206011yescharacteristic
205C2×C127#206111yescharacteristic
206C2×#428C2×C12712yes—
207#2316C2×C12711yescharacteristic
208C2×#343C2×C12711yescharacteristic
209C2×#339C2×C12712yes—
210C4⋊#95C2×C12711yescharacteristic
211C127#1134211yescharacteristic, direct product factor, Sylow
212C22×M16C22×C12712yes—
213C2×#117C22×C12712yes—
214C22×C4⋊C4C22×C12711yescharacteristic
215C22×C4⋊C4C22×C12711yescharacteristic
216C22×C42C22×C12711yescharacteristic
217#428—24no—
218#428—24no—
219C2×#107—22no—
220C2×#106—22no—
221#389—22no—
222#389—22no—
223#380—22no—
224C2×#95—22no—
225#343C4×C12714yescomplemented
226#339—24no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4D4×C12712yes—
230C23×C4C23×C12711yescharacteristic
231C2×M16—22no—
232C2×M16—22no—
233C2×M16—22no—
234C2×M16C2×C4×C12714yes—
235C2×M16D4×C12714yes—
236C2×M16Q8×C12714yes—
237C22×C8—22no—
238#117—22no—
239#117—22no—
240#117—22no—
241#117—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4C2×C4×C12712yes—
250C2×C4⋊C4D4×C12712yes—
251C2×C4⋊C4D4×C12712yes—
252C2×C4⋊C4D4×C12712yes—
253C2×C4⋊C4Q8×C12712yes—
254C2×C22⋊C4—22no—
255C2×C42—22no—
256C2×C42—22no—
257C2×C42—22no—
258C2×C42—21no—
259C2×C42Q8×C12712yes—
260#107—28no—
261#106—28no—
262#95—24no—
263#95—44no—
264C24C2×D4×C12711yescharacteristic
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4C4⋊C4×C12714yes—
284C22×C4C22×C4×C12711yescharacteristic
285C22×C4C2×D4×C12712yes—
286C22×C4C2×D4×C12711yescharacteristic
287C22×C4C2×D4×C12712yes—
288C22×C4C2×Q8×C12712yes—
289C22×C4C2×Q8×C12711yescharacteristic
290C22×C4C2×Q8×C12711yescharacteristic
291C22×C4#41×C12712yes—
292C22×C4#41×C12711yescharacteristic
293C22×C4#41×C12711yescharacteristic
294M16—24no—
295M16—24no—
296M16—24no—
297M16C4⋊C4×C12718yescomplemented
298C2×C8—24no—
299C2×C8—24no—
300C2×C8—24no—
301C4⋊C4—24no—
302C4⋊C4—24no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—42no—
309C4⋊C4—82no—
310C4⋊C4—82no—
311C22⋊C4—42no—
312C22⋊C4—42no—
313C42—24no—
314C42—42no—
315C42—42no—
316C42—42no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C4⋊C4×C12711yescharacteristic
322C23#120×C12711yescharacteristic
323C23#121×C12711yescharacteristic
324C23C22⋊Q8×C12711yescharacteristic
325C23#123×C12711yescharacteristic
326C23#127×C12711yescharacteristic
327C23C4⋊Q8×C12711yescharacteristic
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4C2×C4⋊C4×C12712yes—
352C2×C4C4×D4×C12711yescharacteristic
353C2×C4C4×D4×C12712yes—
354C2×C4C4×Q8×C12711yescharacteristic
355C2×C4#120×C12712yes—
356C2×C4#121×C12712yes—
357C2×C4C22⋊Q8×C12712yes—
358C2×C4C22⋊Q8×C12712yes—
359C2×C4C22⋊Q8×C12712yes—
360C2×C4C22⋊Q8×C12712yes—
361C2×C4#123×C12712yes—
362C2×C4#125×C12712yes—
363C2×C4#125×C12711yescharacteristic
364C2×C4C4⋊Q8×C12712yes—
365C2×C4C4⋊Q8×C12711yescharacteristic
366C2×C4C4⋊Q8×C12712yes—
367C8—28no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22#384×C12711yescharacteristic
381C22#385×C12711yescharacteristic
382C22#389×C12711yescharacteristic
383C22#392×C12711yescharacteristic
384C22#395×C12711yescharacteristic
385C22#398×C12711yescharacteristic
386C22#399×C12711yescharacteristic
387C22#453×C12711yescharacteristic
388C22#454×C12711yescharacteristic
389C22#455×C12711yescharacteristic
390C22#456×C12711yescharacteristic
391C4—44no—
392C4—44no—
393C4—82no—
394C4—82no—
395C4—82no—
396C4#385×C12712yes—
397C4#389×C12712yes—
398C4#395×C12712yes—
399C4#398×C12712yes—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2C127×#144411yescharacteristic
405C2C127×#185611yescharacteristic
406C2C127×#185711yescharacteristic
407C2C127×#200611yescharacteristic
408C2C127×#200711yescharacteristic
409C2C127×#206011yescharacteristic
410C2C127×#206111yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
19. #343×C127C4semidirect
91. M16×C127C4⋊C4semidirect
194. #11342C127direct (N × H)
211. C127#11342direct (N × H)
225. #343C4×C127semidirect
297. M16C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#428×C1272
C127×#23162
C2×#343×C1272
C2×#339×C1272
C127×C4⋊#952
#11342127