Finite Group Databasebeta

← C127×#13094 #44576767

Subgroups — C127×#13094 #44576767

Order 32512.

676 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#101×C127C211yesmaximal, characteristic
2C127×#2434C211yesmaximal, characteristic
3C2×#356×C127C212yesmaximal, complemented
4C127×#1784C211yesmaximal, characteristic
5C127×#1394C212yesmaximal, complemented
6C23×Q8×C127C2211yescharacteristic
7C22×M16×C127—21no—
8C2×C4⋊Q8×C127C411yescharacteristic
9C2×C4⋊Q8×C127C2211yescharacteristic
10C2×C22⋊Q8×C127C411yescharacteristic
11C2×#101×C127—21no—
12C2×#101×C127—24no—
13C2×#101×C127—21no—
14C2×#101×C127C2212yes—
15C2×#101×C127C2212yes—
16#407×C127—21no—
17#395×C127—21no—
18#395×C127—21no—
19#391×C127C411yescharacteristic
20#391×C127C2211yescharacteristic
21#385×C127—21no—
22#385×C127—21no—
23C4×C22⋊C4×C127C411yescharacteristic
24#356×C127—24no—
25C22×Q8×C127—22no—
26C22×Q8×C127—22no—
27C22×Q8×C127—41no—
28C22×Q8×C127—41no—
29C22×Q8×C127—42no—
30C22×Q8×C127C2×C411yescharacteristic
31C22×Q8×C127C2×C411yescharacteristic
32C22×Q8×C127D411yescharacteristic
33C22×Q8×C127D411yescharacteristic
34C22×Q8×C127C2311yescharacteristic
35C23×C4×C127C2×C411yescharacteristic
36C23×C4×C127D411yescharacteristic
37C23×C4×C127D411yescharacteristic
38C2×M16×C127—24no—
39C2×M16×C127—22no—
40C2×M16×C127—22no—
41C2×M16×C127—41no—
42C2×M16×C127—42no—
43C22×C8×C127—41no—
44C4⋊Q8×C127—22no—
45C4⋊Q8×C127—22no—
46C4⋊Q8×C127—42no—
47C22⋊Q8×C127—41no—
48C22⋊Q8×C127—41no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127—21no—
51C2×C4⋊C4×C127—21no—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127—21no—
54C2×C4⋊C4×C127C2×C411yescharacteristic
55C2×C22⋊C4×C127—21no—
56C2×C22⋊C4×C127—21no—
57C2×C42×C127C2×C411yescharacteristic
58C2×C42×C127C2×C411yescharacteristic
59#101×C127—24no—
60#101×C127—22no—
61#101×C127—22no—
62#101×C127—22no—
63#101×C127—42no—
64#101×C127D414yes—
65C22⋊C8×C127—41no—
66C22⋊C8×C127—41no—
67#95×C127—21no—
68#95×C127—21no—
69#95×C127—21no—
70#95×C127—21no—
71#95×C127—21no—
72C24×C127C22⋊C411yescharacteristic
73C2×Q8×C127—22no—
74C2×Q8×C127—22no—
75C2×Q8×C127—22no—
76C2×Q8×C127—21no—
77C2×Q8×C127—22no—
78C2×Q8×C127—21no—
79C2×Q8×C127—22no—
80C2×Q8×C127—41no—
81C2×Q8×C127—41no—
82C2×Q8×C127—41no—
83C2×Q8×C127—41no—
84C2×Q8×C127—41no—
85C2×Q8×C127—41no—
86C2×Q8×C127—44no—
87C2×Q8×C127—44no—
88C2×Q8×C127—44no—
89C2×Q8×C127—44no—
90C2×Q8×C127—41no—
91C2×Q8×C127—41no—
92C2×Q8×C127C2×D412yes—
93C2×Q8×C127#4112yes—
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—22no—
97C22×C4×C127—21no—
98C22×C4×C127—21no—
99C22×C4×C127—21no—
100C22×C4×C127—21no—
101C22×C4×C127—21no—
102C22×C4×C127—21no—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—41no—
110C22×C4×C127—41no—
111C22×C4×C127C22⋊C411yescharacteristic
112C22×C4×C127C22⋊C411yescharacteristic
113C22×C4×C127C22⋊C411yescharacteristic
114C22×C4×C127C22×C411yescharacteristic
115C22×C4×C127C2×D411yescharacteristic
116C22×C4×C127C2×D411yescharacteristic
117M16×C127—24no—
118M16×C127—44no—
119M16×C127—42no—
120M16×C127—42no—
121M16×C127—42no—
122C2×C8×C127—44no—
123C2×C8×C127—42no—
124C2×C8×C127—42no—
125C4⋊C4×C127—41no—
126C4⋊C4×C127—42no—
127C4⋊C4×C127—42no—
128C4⋊C4×C127—42no—
129C4⋊C4×C127—41no—
130C4⋊C4×C127—42no—
131C4⋊C4×C127—41no—
132C22⋊C4×C127—24no—
133C22⋊C4×C127—41no—
134C22⋊C4×C127—41no—
135C42×C127—22no—
136C42×C127—41no—
137C23×C127—22no—
138C23×C127—21no—
139C23×C127—21no—
140C23×C127—41no—
141C23×C127#9911yescharacteristic
142C23×C127#9911yescharacteristic
143C23×C127C2×C22⋊C411yescharacteristic
144Q8×C127—42no—
145Q8×C127—42no—
146Q8×C127—44no—
147Q8×C127—44no—
148Q8×C127—42no—
149Q8×C127—42no—
150Q8×C127—82no—
151C2×C4×C127—22no—
152C2×C4×C127—22no—
153C2×C4×C127—22no—
154C2×C4×C127—22no—
155C2×C4×C127—21no—
156C2×C4×C127—21no—
157C2×C4×C127—21no—
158C2×C4×C127—21no—
159C2×C4×C127—21no—
160C2×C4×C127—21no—
161C2×C4×C127—21no—
162C2×C4×C127—21no—
163C2×C4×C127—22no—
164C2×C4×C127—22no—
165C2×C4×C127—21no—
166C2×C4×C127—21no—
167C2×C4×C127—21no—
168C2×C4×C127—21no—
169C2×C4×C127—21no—
170C2×C4×C127—21no—
171C2×C4×C127—42no—
172C2×C4×C127—42no—
173C2×C4×C127—42no—
174C2×C4×C127—42no—
175C2×C4×C127—41no—
176C2×C4×C127—41no—
177C2×C4×C127—41no—
178C2×C4×C127—41no—
179C2×C4×C127—42no—
180C2×C4×C127—41no—
181C2×C4×C127—41no—
182C2×C4×C127—41no—
183C2×C4×C127—41no—
184C2×C4×C127#9912yes—
185C2×C4×C127C4×D412yes—
186C2×C4×C127#12011yescharacteristic
187C2×C4×C127#12112yes—
188C2×C4×C127#12311yescharacteristic
189C8×C127—44no—
190C8×C127—82no—
191C22×C127—21no—
192C22×C127—21no—
193C22×C127—21no—
194C22×C127—21no—
195C22×C127—21no—
196C22×C127—21no—
197C22×C127—21no—
198C22×C127—42no—
199C22×C127—42no—
200C22×C127#35612yescomplemented
201C22×C127#38611yescharacteristic
202C22×C127C2×#9911yescharacteristic
203C22×C127C2×#9911yescharacteristic
204C4×C127—21no—
205C4×C127—22no—
206C4×C127—22no—
207C4×C127—21no—
208C4×C127—22no—
209C4×C127—42no—
210C4×C127—42no—
211C4×C127—41no—
212C4×C127—41no—
213C4×C127—81no—
214C4×C127—81no—
215#13094C12711yesmaximal, characteristic, direct product factor, Sylow
216C2×C127—21no—
217C2×C127—21no—
218C2×C127—22no—
219C2×C127—41no—
220C2×C127#189811yescharacteristic
221C2×C127C2×#35611yescharacteristic
222C2×C127#213311yescharacteristic
223C22×#101C2×C12711yescharacteristic
224#2434C2×C12711yescharacteristic
225C2×#356C2×C12712yescomplemented
226#1784C2×C12711yescharacteristic
227#1394C2×C12712yescomplemented
228C127#1309411yescharacteristic, direct product factor, Sylow
229C23×Q8C22×C12711yescharacteristic
230C22×M16—21no—
231C2×C4⋊Q8C4×C12711yescharacteristic
232C2×C4⋊Q8C22×C12711yescharacteristic
233C2×C22⋊Q8C4×C12711yescharacteristic
234C2×#101—21no—
235C2×#101—24no—
236C2×#101—21no—
237C2×#101C22×C12712yes—
238C2×#101C22×C12712yes—
239#407—21no—
240#395—21no—
241#395—21no—
242#391C4×C12711yescharacteristic
243#391C22×C12711yescharacteristic
244#385—21no—
245#385—21no—
246C4×C22⋊C4C4×C12711yescharacteristic
247#356—24no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—41no—
251C22×Q8—41no—
252C22×Q8—42no—
253C22×Q8C2×C4×C12711yescharacteristic
254C22×Q8C2×C4×C12711yescharacteristic
255C22×Q8D4×C12711yescharacteristic
256C22×Q8D4×C12711yescharacteristic
257C22×Q8C23×C12711yescharacteristic
258C23×C4C2×C4×C12711yescharacteristic
259C23×C4D4×C12711yescharacteristic
260C23×C4D4×C12711yescharacteristic
261C2×M16—24no—
262C2×M16—22no—
263C2×M16—22no—
264C2×M16—41no—
265C2×M16—42no—
266C22×C8—41no—
267C4⋊Q8—22no—
268C4⋊Q8—22no—
269C4⋊Q8—42no—
270C22⋊Q8—41no—
271C22⋊Q8—41no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4C2×C4×C12711yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C42C2×C4×C12711yescharacteristic
281C2×C42C2×C4×C12711yescharacteristic
282#101—24no—
283#101—22no—
284#101—22no—
285#101—22no—
286#101—42no—
287#101D4×C12714yes—
288C22⋊C8—41no—
289C22⋊C8—41no—
290#95—21no—
291#95—21no—
292#95—21no—
293#95—21no—
294#95—21no—
295C24C22⋊C4×C12711yescharacteristic
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—22no—
299C2×Q8—21no—
300C2×Q8—22no—
301C2×Q8—21no—
302C2×Q8—22no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—44no—
310C2×Q8—44no—
311C2×Q8—44no—
312C2×Q8—44no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8C2×D4×C12712yes—
316C2×Q8#41×C12712yes—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4C22⋊C4×C12711yescharacteristic
335C22×C4C22⋊C4×C12711yescharacteristic
336C22×C4C22⋊C4×C12711yescharacteristic
337C22×C4C22×C4×C12711yescharacteristic
338C22×C4C2×D4×C12711yescharacteristic
339C22×C4C2×D4×C12711yescharacteristic
340M16—24no—
341M16—44no—
342M16—42no—
343M16—42no—
344M16—42no—
345C2×C8—44no—
346C2×C8—42no—
347C2×C8—42no—
348C4⋊C4—41no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—41no—
353C4⋊C4—42no—
354C4⋊C4—41no—
355C22⋊C4—24no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C42—22no—
359C42—41no—
360C23—22no—
361C23—21no—
362C23—21no—
363C23—41no—
364C23#99×C12711yescharacteristic
365C23#99×C12711yescharacteristic
366C23C2×C22⋊C4×C12711yescharacteristic
367Q8—42no—
368Q8—42no—
369Q8—44no—
370Q8—44no—
371Q8—42no—
372Q8—42no—
373Q8—82no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4#99×C12712yes—
408C2×C4C4×D4×C12712yes—
409C2×C4#120×C12711yescharacteristic
410C2×C4#121×C12712yes—
411C2×C4#123×C12711yescharacteristic
412C8—44no—
413C8—82no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—42no—
422C22—42no—
423C22#356×C12712yescomplemented
424C22#386×C12711yescharacteristic
425C22C2×#99×C12711yescharacteristic
426C22C2×#99×C12711yescharacteristic
427C4—21no—
428C4—22no—
429C4—22no—
430C4—21no—
431C4—22no—
432C4—42no—
433C4—42no—
434C4—41no—
435C4—41no—
436C4—81no—
437C4—81no—
438C2—21no—
439C2—21no—
440C2—22no—
441C2—41no—
442C2C127×#189811yescharacteristic
443C2C2×#356×C12711yescharacteristic
444C2C127×#213311yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC22×Q8C23×C127
prime radicalC24×C127C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C23×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#356×C127C2semidirect
5. C127×#1394C2semidirect
200. C22×C127#356semidirect
215. #13094C127direct (N × H)
225. C2×#356C2×C127semidirect
227. #1394C2×C127semidirect
228. C127#13094direct (N × H)
423. C22#356×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#101×C1272
C127×#24342
C2×#356×C1272
C127×#17842
C127×#13942
#13094127