Finite Group Databasebeta

← C127×#12099 #44575772

Subgroups — C127×#12099 #44575772

Order 32512.

526 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2699C211yesmaximal, characteristic, complemented
2C127×#2006C211yesmaximal, characteristic, complemented
3C127×#1610C211yesmaximal, characteristic, complemented
4C127×#1598C211yesmaximal, characteristic, complemented
5C127×#1346C211yesmaximal, characteristic, complemented
6C127×#1345C211yesmaximal, characteristic, complemented
7C127×#1318C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C127—21no—
9#537×C127C2211yescharacteristic
10C2×#121×C127—21no—
11#480×C127—21no—
12#447×C127—21no—
13C2×#104×C127—21no—
14#398×C127C2211yescharacteristic
15#394×C127—21no—
16#394×C127C2211yescharacteristic
17#392×C127—21no—
18#390×C127C2211yescharacteristic
19#388×C127—21no—
20#386×C127—21no—
21#381×C127—21no—
22#343×C127C2211yescharacteristic
23#327×C127—21no—
24#327×C127—21no—
25#324×C127C2211yescharacteristic
26#324×C127C2211yescharacteristic
27C2×#41×C127—21no—
28C22×D4×C127—21no—
29C22×D4×C127—21no—
30C22×D4×C127D411yescharacteristic
31C22×D4×C127D411yescharacteristic
32C23×C4×C127—21no—
33AGL(1,ℤ/8)×C127—42no—
34AGL(1,ℤ/8)×C127—42no—
35C2×SD16×C127—41no—
36C2×D8×C127—41no—
37C2×D8×C127—41no—
38C2×M16×C127—21no—
39C22⋊Q8×C127—41no—
40#121×C127—21no—
41#121×C127—21no—
42#121×C127—41no—
43#121×C127—42no—
44#121×C127—42no—
45C2×C4⋊C4×C127—21no—
46C2×C4⋊C4×C127D411yescharacteristic
47C2×C4⋊C4×C127C2311yescharacteristic
48C2×C22⋊C4×C127—21no—
49C2×C22⋊C4×C127—21no—
50C2×C22⋊C4×C127—21no—
51C2×C22⋊C4×C127—21no—
52C2×C22⋊C4×C127—21no—
53C2×C22⋊C4×C127—21no—
54C2×C22⋊C4×C127—21no—
55C2×C42×C127D411yescharacteristic
56#107×C127—41no—
57#104×C127—42no—
58#102×C127—41no—
59#102×C127—41no—
60C22⋊C8×C127—21no—
61C22⋊C8×C127—21no—
62#95×C127—21no—
63#95×C127—21no—
64#95×C127—21no—
65#95×C127D411yescharacteristic
66#95×C127D411yescharacteristic
67C24×C127—21no—
68C24×C127—21no—
69#41×C127—41no—
70#41×C127—41no—
71#41×C127—41no—
72#41×C127—41no—
73C2×Q8×C127—21no—
74C2×D4×C127—21no—
75C2×D4×C127—21no—
76C2×D4×C127—21no—
77C2×D4×C127—21no—
78C2×D4×C127—41no—
79C2×D4×C127—41no—
80C2×D4×C127—41no—
81C2×D4×C127—42no—
82C2×D4×C127—42no—
83C2×D4×C127—42no—
84C2×D4×C127—41no—
85C2×D4×C127—81no—
86C2×D4×C127—81no—
87C2×D4×C127—81no—
88C2×D4×C127—81no—
89C2×D4×C127D812yescomplemented
90C22×C4×C127—21no—
91C22×C4×C127—21no—
92C22×C4×C127—21no—
93C22×C4×C127—21no—
94C22×C4×C127—41no—
95C22×C4×C127—42no—
96C22×C4×C127—42no—
97C22×C4×C127—81no—
98C22×C4×C127C2×D411yescharacteristic
99C22×C4×C127C2×D411yescharacteristic
100C22×C4×C127C2×D411yescharacteristic
101SD16×C127—44no—
102D8×C127—44no—
103D8×C127—82no—
104M16×C127—22no—
105M16×C127—41no—
106C2×C8×C127—41no—
107C2×C8×C127—41no—
108C2×C8×C127—41no—
109C4⋊C4×C127—21no—
110C4⋊C4×C127—21no—
111C4⋊C4×C127—41no—
112C4⋊C4×C127—41no—
113C4⋊C4×C127—41no—
114C4⋊C4×C127—41no—
115C22⋊C4×C127—42no—
116C22⋊C4×C127—41no—
117C22⋊C4×C127—41no—
118C22⋊C4×C127—42no—
119C22⋊C4×C127—41no—
120C22⋊C4×C127—41no—
121C22⋊C4×C127—81no—
122C22⋊C4×C127—81no—
123C22⋊C4×C127—81no—
124C22⋊C4×C127—81no—
125C42×C127—41no—
126C23×C127—22no—
127C23×C127—41no—
128C23×C127—41no—
129C23×C127—41no—
130C23×C127—41no—
131C23×C127—41no—
132C23×C127—41no—
133C23×C127—41no—
134C23×C127—41no—
135C23×C127—41no—
136C23×C127—41no—
137C23×C127—41no—
138C23×C127—41no—
139C23×C127—41no—
140C23×C127—41no—
141C23×C127#12011yescharacteristic
142Q8×C127—41no—
143Q8×C127—41no—
144D4×C127—42no—
145D4×C127—41no—
146D4×C127—41no—
147D4×C127—42no—
148D4×C127—81no—
149D4×C127—84no—
150D4×C127—81no—
151D4×C127—81no—
152D4×C127—81no—
153D4×C127—84no—
154D4×C127—81no—
155D4×C127—81no—
156C2×C4×C127—21no—
157C2×C4×C127—21no—
158C2×C4×C127—22no—
159C2×C4×C127—21no—
160C2×C4×C127—21no—
161C2×C4×C127—41no—
162C2×C4×C127—41no—
163C2×C4×C127—41no—
164C2×C4×C127—41no—
165C2×C4×C127—41no—
166C2×C4×C127—41no—
167C2×C4×C127—41no—
168C2×C4×C127—41no—
169C2×C4×C127—41no—
170C2×C4×C127—41no—
171C2×C4×C127—41no—
172C2×C4×C127—41no—
173C2×C4×C127—41no—
174C2×C4×C127—41no—
175C2×C4×C127—81no—
176C2×C4×C127—81no—
177C2×C4×C127—84no—
178C2×C4×C127C2×D811yescharacteristic
179C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
180C8×C127—42no—
181C8×C127—81no—
182C8×C127—81no—
183C22×C127—21no—
184C22×C127—21no—
185C22×C127—42no—
186C22×C127—42no—
187C22×C127—42no—
188C22×C127—81no—
189C22×C127—81no—
190C22×C127—81no—
191C22×C127—81no—
192C22×C127—81no—
193C22×C127—81no—
194C22×C127—81no—
195C22×C127—81no—
196C22×C127—81no—
197C22×C127—81no—
198C22×C127—81no—
199C22×C127—81no—
200C22×C127—81no—
201C22×C127—81no—
202C22×C127#44711yescharacteristic
203C22×C127#45311yescharacteristic
204C22×C127B(4,𝔽2)11yescharacteristic
205C4×C127—21no—
206C4×C127—21no—
207C4×C127—42no—
208C4×C127—41no—
209C4×C127—41no—
210C4×C127—81no—
211C4×C127—81no—
212C4×C127—81no—
213C4×C127—81no—
214#12099C12711yesmaximal, characteristic, direct product factor, Sylow
215C2×C127—21no—
216C2×C127—21no—
217C2×C127—82no—
218C2×C127—161no—
219C2×C127—161no—
220C2×C127#159511yescharacteristic
221C2×C127#220011yescharacteristic
222C2×C127#220411yescharacteristic
223#2699C2×C12711yescharacteristic, complemented
224#2006C2×C12711yescharacteristic, complemented
225#1610C2×C12711yescharacteristic, complemented
226#1598C2×C12711yescharacteristic, complemented
227#1346C2×C12711yescharacteristic, complemented
228#1345C2×C12711yescharacteristic, complemented
229#1318C2×C12711yescharacteristic, complemented
230C127#1209911yescharacteristic, direct product factor, Sylow
231C2×AGL(1,ℤ/8)—21no—
232#537C22×C12711yescharacteristic
233C2×#121—21no—
234#480—21no—
235#447—21no—
236C2×#104—21no—
237#398C22×C12711yescharacteristic
238#394—21no—
239#394C22×C12711yescharacteristic
240#392—21no—
241#390C22×C12711yescharacteristic
242#388—21no—
243#386—21no—
244#381—21no—
245#343C22×C12711yescharacteristic
246#327—21no—
247#327—21no—
248#324C22×C12711yescharacteristic
249#324C22×C12711yescharacteristic
250C2×#41—21no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4D4×C12711yescharacteristic
254C22×D4D4×C12711yescharacteristic
255C23×C4—21no—
256AGL(1,ℤ/8)—42no—
257AGL(1,ℤ/8)—42no—
258C2×SD16—41no—
259C2×D8—41no—
260C2×D8—41no—
261C2×M16—21no—
262C22⋊Q8—41no—
263#121—21no—
264#121—21no—
265#121—41no—
266#121—42no—
267#121—42no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4D4×C12711yescharacteristic
270C2×C4⋊C4C23×C12711yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C42D4×C12711yescharacteristic
279#107—41no—
280#104—42no—
281#102—41no—
282#102—41no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285#95—21no—
286#95—21no—
287#95—21no—
288#95D4×C12711yescharacteristic
289#95D4×C12711yescharacteristic
290C24—21no—
291C24—21no—
292#41—41no—
293#41—41no—
294#41—41no—
295#41—41no—
296C2×Q8—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—42no—
305C2×D4—42no—
306C2×D4—42no—
307C2×D4—41no—
308C2×D4—81no—
309C2×D4—81no—
310C2×D4—81no—
311C2×D4—81no—
312C2×D4D8×C12712yescomplemented
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—81no—
321C22×C4C2×D4×C12711yescharacteristic
322C22×C4C2×D4×C12711yescharacteristic
323C22×C4C2×D4×C12711yescharacteristic
324SD16—44no—
325D8—44no—
326D8—82no—
327M16—22no—
328M16—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C22⋊C4—42no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—42no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—81no—
345C22⋊C4—81no—
346C22⋊C4—81no—
347C22⋊C4—81no—
348C42—41no—
349C23—22no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23#120×C12711yescharacteristic
365Q8—41no—
366Q8—41no—
367D4—42no—
368D4—41no—
369D4—41no—
370D4—42no—
371D4—81no—
372D4—84no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—84no—
377D4—81no—
378D4—81no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—84no—
401C2×C4C2×D8×C12711yescharacteristic
402C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
403C8—42no—
404C8—81no—
405C8—81no—
406C22—21no—
407C22—21no—
408C22—42no—
409C22—42no—
410C22—42no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22#447×C12711yescharacteristic
426C22#453×C12711yescharacteristic
427C22B(4,𝔽2)×C12711yescharacteristic
428C4—21no—
429C4—21no—
430C4—42no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—81no—
437C2—21no—
438C2—21no—
439C2—82no—
440C2—161no—
441C2—161no—
442C2C127×#159511yescharacteristic
443C2C127×#220011yescharacteristic
444C2C127×#220411yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C127
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C2×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2699C2semidirect
2. C127×#2006C2semidirect
3. C127×#1610C2semidirect
4. C127×#1598C2semidirect
5. C127×#1346C2semidirect
6. C127×#1345C2semidirect
7. C127×#1318C2semidirect
89. C2×D4×C127D8semidirect
214. #12099C127direct (N × H)
223. #2699C2×C127semidirect
224. #2006C2×C127semidirect
225. #1610C2×C127semidirect
226. #1598C2×C127semidirect
227. #1346C2×C127semidirect
228. #1345C2×C127semidirect
229. #1318C2×C127semidirect
230. C127#12099direct (N × H)
312. C2×D4D8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#26992
C127×#20062
C127×#16102
C127×#15982
C127×#13462
C127×#13452
C127×#13182
#12099127