Finite Group Databasebeta

← C127×#2700 #30635652

Subgroups — C127×#2700 #30635652

Order 16256.

506 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#124×C127C211yesmaximal, characteristic
2C2×C22⋊Q8×C127C211yesmaximal, characteristic, complemented
3#397×C127C211yesmaximal, characteristic, complemented
4#397×C127C211yesmaximal, characteristic, complemented
5#396×C127C211yesmaximal, characteristic, complemented
6#395×C127C211yesmaximal, characteristic, complemented
7#394×C127C211yesmaximal, characteristic
8#393×C127C211yesmaximal, characteristic, complemented
9#391×C127C211yesmaximal, characteristic, complemented
10#391×C127C211yesmaximal, characteristic, complemented
11#388×C127C211yesmaximal, characteristic, complemented
12#388×C127C211yesmaximal, characteristic, complemented
13#387×C127C211yesmaximal, characteristic, complemented
14#386×C127C211yesmaximal, characteristic
15#381×C127C211yesmaximal, characteristic, complemented
16C22×Q8×C127C2211yescharacteristic
17C22×Q8×C127C2211yescharacteristic
18C22×D4×C127C2211yescharacteristic
19C23×C4×C127C2211yescharacteristic
20#124×C127—24no—
21C22⋊Q8×C127—24no—
22C2×C4⋊C4×C127C2211yescharacteristic
23C2×C4⋊C4×C127C2211yescharacteristic
24C2×C4⋊C4×C127C2211yescharacteristic
25C2×C4⋊C4×C127C2211yescharacteristic
26C2×C4⋊C4×C127C2211yescharacteristic
27C2×C4⋊C4×C127C2211yescharacteristic
28C2×C22⋊C4×C127C2211yescharacteristic
29C2×C22⋊C4×C127C2211yescharacteristic
30C2×C22⋊C4×C127C2211yescharacteristic
31C2×C22⋊C4×C127C2211yescharacteristic
32C2×C22⋊C4×C127C2211yescharacteristic
33C2×C22⋊C4×C127C2211yescharacteristic
34C2×C22⋊C4×C127C2211yescharacteristic
35C2×C22⋊C4×C127C2211yescharacteristic
36C2×C22⋊C4×C127C2211yescharacteristic
37C2×C22⋊C4×C127C2211yescharacteristic
38C2×C22⋊C4×C127C2211yescharacteristic
39C2×C42×C127C2211yescharacteristic
40C2×C42×C127C2211yescharacteristic
41#95×C127C2211yescharacteristic
42#95×C127C2211yescharacteristic
43#95×C127C2211yescharacteristic
44#95×C127C2211yescharacteristic
45#95×C127C2211yescharacteristic
46#95×C127C2211yescharacteristic
47#95×C127C2211yescharacteristic
48#95×C127C2211yescharacteristic
49#95×C127C2211yescharacteristic
50#95×C127C2211yescharacteristic
51#95×C127C2211yescharacteristic
52#95×C127C2211yescharacteristic
53C24×C127C2311yescharacteristic
54C24×C127C2311yescharacteristic
55C2×Q8×C127—22no—
56C2×Q8×C127—22no—
57C2×Q8×C127—22no—
58C2×Q8×C127—22no—
59C2×Q8×C127—41no—
60C2×Q8×C127—41no—
61C2×D4×C127—22no—
62C2×D4×C127—22no—
63C2×D4×C127—41no—
64C22×C4×C127—22no—
65C22×C4×C127—22no—
66C22×C4×C127—41no—
67C22×C4×C127C2311yescharacteristic
68C22×C4×C127C2311yescharacteristic
69C22×C4×C127C2311yescharacteristic
70C22×C4×C127C2311yescharacteristic
71C22×C4×C127C2311yescharacteristic
72C22×C4×C127C2311yescharacteristic
73C22×C4×C127C2311yescharacteristic
74C22×C4×C127C2311yescharacteristic
75C22×C4×C127C2311yescharacteristic
76C22×C4×C127C2311yescharacteristic
77C22×C4×C127C2311yescharacteristic
78C22×C4×C127C2311yescharacteristic
79C22×C4×C127C2311yescharacteristic
80C4⋊C4×C127—22no—
81C4⋊C4×C127—22no—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—22no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C22⋊C4×C127—22no—
87C22⋊C4×C127—22no—
88C22⋊C4×C127—22no—
89C22⋊C4×C127—22no—
90C22⋊C4×C127—22no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127—41no—
93C22⋊C4×C127—41no—
94C22⋊C4×C127—41no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127D414yes—
97C42×C127—22no—
98C42×C127—41no—
99C23×C127—21no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—21no—
103C23×C127—21no—
104C23×C127—21no—
105C23×C127—21no—
106C23×C127—21no—
107C23×C127—21no—
108C23×C127—21no—
109C23×C127—21no—
110C23×C127—21no—
111C23×C127—21no—
112C23×C127C2×D412yes—
113C23×C127C2411yescharacteristic
114Q8×C127—44no—
115Q8×C127—44no—
116D4×C127—44no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—21no—
125C2×C4×C127—21no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—21no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—21no—
136C2×C4×C127—21no—
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127—21no—
147C2×C4×C127—21no—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
150C2×C4×C127—21no—
151C2×C4×C127—21no—
152C2×C4×C127—44no—
153C2×C4×C127C2×D412yes—
154C2×C4×C127C2×D412yes—
155C2×C4×C127#4112yes—
156C2×C4×C127#4112yes—
157C22×C127—22no—
158C22×C127—22no—
159C22×C127—22no—
160C22×C127—41no—
161C22×C127—41no—
162C22×C127—41no—
163C22×C127—41no—
164C22×C127—41no—
165C22×C127—41no—
166C22×C127—41no—
167C22×C127—41no—
168C22×C127—41no—
169C22×C127—41no—
170C22×C127—41no—
171C22×C127C22×D411yescharacteristic
172C22×C127C2×#4111yescharacteristic
173C22×C127C2×#4111yescharacteristic
174C22×C127H(5,𝔽2)11yescharacteristic
175C22×C127H(5,𝔽2)11yescharacteristic
176C22×C1272−1+411yescharacteristic
177C22×C1272−1+411yescharacteristic
178C4×C127—22no—
179C4×C127—22no—
180C4×C127—22no—
181C4×C127—22no—
182C4×C127—41no—
183C4×C127—41no—
184C4×C127—41no—
185C4×C127—41no—
186C4×C127—41no—
187C4×C127—41no—
188C4×C127—41no—
189C4×C127—41no—
190C4×C127—41no—
191C2×C127—42no—
192C2×C127—81no—
193C2×C127#53611yescharacteristic
194C2×C127#54211yescharacteristic
195C2×C127#54211yescharacteristic
196C2×C127#54611yescharacteristic
197C2×C127#54611yescharacteristic
198C2×C127#55611yescharacteristic
199C2×C127#56211yescharacteristic
200#2700C12711yesmaximal, characteristic, direct product factor, Sylow
201C127#270011yescharacteristic, direct product factor, Sylow
202C2×#124C2×C12711yescharacteristic
203C2×C22⋊Q8C2×C12711yescharacteristic, complemented
204#397C2×C12711yescharacteristic, complemented
205#397C2×C12711yescharacteristic, complemented
206#396C2×C12711yescharacteristic, complemented
207#395C2×C12711yescharacteristic, complemented
208#394C2×C12711yescharacteristic
209#393C2×C12711yescharacteristic, complemented
210#391C2×C12711yescharacteristic, complemented
211#391C2×C12711yescharacteristic, complemented
212#388C2×C12711yescharacteristic, complemented
213#388C2×C12711yescharacteristic, complemented
214#387C2×C12711yescharacteristic, complemented
215#386C2×C12711yescharacteristic
216#381C2×C12711yescharacteristic, complemented
217C22×Q8C22×C12711yescharacteristic
218C22×Q8C22×C12711yescharacteristic
219C22×D4C22×C12711yescharacteristic
220C23×C4C22×C12711yescharacteristic
221#124—24no—
222C22⋊Q8—24no—
223C2×C4⋊C4C22×C12711yescharacteristic
224C2×C4⋊C4C22×C12711yescharacteristic
225C2×C4⋊C4C22×C12711yescharacteristic
226C2×C4⋊C4C22×C12711yescharacteristic
227C2×C4⋊C4C22×C12711yescharacteristic
228C2×C4⋊C4C22×C12711yescharacteristic
229C2×C22⋊C4C22×C12711yescharacteristic
230C2×C22⋊C4C22×C12711yescharacteristic
231C2×C22⋊C4C22×C12711yescharacteristic
232C2×C22⋊C4C22×C12711yescharacteristic
233C2×C22⋊C4C22×C12711yescharacteristic
234C2×C22⋊C4C22×C12711yescharacteristic
235C2×C22⋊C4C22×C12711yescharacteristic
236C2×C22⋊C4C22×C12711yescharacteristic
237C2×C22⋊C4C22×C12711yescharacteristic
238C2×C22⋊C4C22×C12711yescharacteristic
239C2×C22⋊C4C22×C12711yescharacteristic
240C2×C42C22×C12711yescharacteristic
241C2×C42C22×C12711yescharacteristic
242#95C22×C12711yescharacteristic
243#95C22×C12711yescharacteristic
244#95C22×C12711yescharacteristic
245#95C22×C12711yescharacteristic
246#95C22×C12711yescharacteristic
247#95C22×C12711yescharacteristic
248#95C22×C12711yescharacteristic
249#95C22×C12711yescharacteristic
250#95C22×C12711yescharacteristic
251#95C22×C12711yescharacteristic
252#95C22×C12711yescharacteristic
253#95C22×C12711yescharacteristic
254C24C23×C12711yescharacteristic
255C24C23×C12711yescharacteristic
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—41no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—41no—
268C22×C4C23×C12711yescharacteristic
269C22×C4C23×C12711yescharacteristic
270C22×C4C23×C12711yescharacteristic
271C22×C4C23×C12711yescharacteristic
272C22×C4C23×C12711yescharacteristic
273C22×C4C23×C12711yescharacteristic
274C22×C4C23×C12711yescharacteristic
275C22×C4C23×C12711yescharacteristic
276C22×C4C23×C12711yescharacteristic
277C22×C4C23×C12711yescharacteristic
278C22×C4C23×C12711yescharacteristic
279C22×C4C23×C12711yescharacteristic
280C22×C4C23×C12711yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4D4×C12714yes—
298C42—22no—
299C42—41no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23C2×D4×C12712yes—
314C23C24×C12711yescharacteristic
315Q8—44no—
316Q8—44no—
317D4—44no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—44no—
354C2×C4C2×D4×C12712yes—
355C2×C4C2×D4×C12712yes—
356C2×C4#41×C12712yes—
357C2×C4#41×C12712yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22C22×D4×C12711yescharacteristic
373C22C2×#41×C12711yescharacteristic
374C22C2×#41×C12711yescharacteristic
375C22H(5,𝔽2)×C12711yescharacteristic
376C22H(5,𝔽2)×C12711yescharacteristic
377C222−1+4×C12711yescharacteristic
378C222−1+4×C12711yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—41no—
392C2—42no—
393C2—81no—
394C2#536×C12711yescharacteristic
395C2#542×C12711yescharacteristic
396C2#542×C12711yescharacteristic
397C2#546×C12711yescharacteristic
398C2#546×C12711yescharacteristic
399C2#556×C12711yescharacteristic
400C2#562×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC22×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊Q8×C127C2semidirect
3. #397×C127C2semidirect
4. #397×C127C2semidirect
5. #396×C127C2semidirect
6. #395×C127C2semidirect
8. #393×C127C2semidirect
9. #391×C127C2semidirect
10. #391×C127C2semidirect
11. #388×C127C2semidirect
12. #388×C127C2semidirect
13. #387×C127C2semidirect
15. #381×C127C2semidirect
200. #2700C127direct (N × H)
201. C127#2700direct (N × H)
203. C2×C22⋊Q8C2×C127semidirect
204. #397C2×C127semidirect
205. #397C2×C127semidirect
206. #396C2×C127semidirect
207. #395C2×C127semidirect
209. #393C2×C127semidirect
210. #391C2×C127semidirect
211. #391C2×C127semidirect
212. #388C2×C127semidirect
213. #388C2×C127semidirect
214. #387C2×C127semidirect
216. #381C2×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#124×C1272
C2×C22⋊Q8×C1272
#397×C1272
#396×C1272
#395×C1272
#394×C1272
#393×C1272
#391×C1272
#388×C1272
#387×C1272
#386×C1272
#381×C1272
#2700127