Finite Group Databasebeta

← C127×#2694 #30635646

Subgroups — C127×#2694 #30635646

Order 16256.

490 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×#125×C127C211yesmaximal, characteristic, complemented
2C2×#123×C127C211yesmaximal, characteristic
3#399×C127C211yesmaximal, characteristic, complemented
4#399×C127C211yesmaximal, characteristic, complemented
5#398×C127C211yesmaximal, characteristic, complemented
6#397×C127C211yesmaximal, characteristic, complemented
7#396×C127C211yesmaximal, characteristic, complemented
8#394×C127C211yesmaximal, characteristic
9#390×C127C211yesmaximal, characteristic
10#389×C127C211yesmaximal, characteristic, complemented
11#388×C127C211yesmaximal, characteristic, complemented
12#388×C127C211yesmaximal, characteristic, complemented
13#387×C127C211yesmaximal, characteristic, complemented
14#385×C127C211yesmaximal, characteristic, complemented
15#380×C127C211yesmaximal, characteristic, complemented
16C22×D4×C127C2211yescharacteristic
17C23×C4×C127C2211yescharacteristic
18#125×C127—24no—
19#123×C127—24no—
20C2×C4⋊C4×C127C2211yescharacteristic
21C2×C4⋊C4×C127C2211yescharacteristic
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×C4⋊C4×C127C2211yescharacteristic
29C2×C4⋊C4×C127C2211yescharacteristic
30C2×C4⋊C4×C127C2211yescharacteristic
31C2×C4⋊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×C22⋊C4×C127C2211yescharacteristic
40C2×C22⋊C4×C127C2211yescharacteristic
41C2×C22⋊C4×C127C2211yescharacteristic
42C2×C22⋊C4×C127C2211yescharacteristic
43C2×C42×C127C2211yescharacteristic
44C2×C42×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×D4×C127—22no—
56C2×D4×C127—22no—
57C2×D4×C127—41no—
58C22×C4×C127—22no—
59C22×C4×C127—22no—
60C22×C4×C127—41no—
61C22×C4×C127C2311yescharacteristic
62C22×C4×C127C2311yescharacteristic
63C22×C4×C127C2311yescharacteristic
64C22×C4×C127C2311yescharacteristic
65C22×C4×C127C2311yescharacteristic
66C22×C4×C127C2311yescharacteristic
67C22×C4×C127C2311yescharacteristic
68C22×C4×C127C2311yescharacteristic
69C22×C4×C127C2311yescharacteristic
70C22×C4×C127C2311yescharacteristic
71C22×C4×C127C2311yescharacteristic
72C22×C4×C127C2311yescharacteristic
73C22×C4×C127C2311yescharacteristic
74C4⋊C4×C127—22no—
75C4⋊C4×C127—22no—
76C4⋊C4×C127—22no—
77C4⋊C4×C127—22no—
78C4⋊C4×C127—22no—
79C4⋊C4×C127—22no—
80C4⋊C4×C127—22no—
81C4⋊C4×C127—41no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127D414yes—
86C22⋊C4×C127—22no—
87C22⋊C4×C127—22no—
88C22⋊C4×C127—22no—
89C22⋊C4×C127—22no—
90C22⋊C4×C127—22no—
91C22⋊C4×C127—22no—
92C22⋊C4×C127—41no—
93C22⋊C4×C127—41no—
94C22⋊C4×C127—41no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—41no—
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×C127#4112yes—
113C23×C127C2411yescharacteristic
114D4×C127—44no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
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—44no—
151C2×C4×C127C2×D412yes—
152C2×C4×C127C2×D412yes—
153C2×C4×C127C2×D412yes—
154C2×C4×C127#4112yes—
155C22×C127—22no—
156C22×C127—22no—
157C22×C127—22no—
158C22×C127—41no—
159C22×C127—41no—
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×C127C22×D411yescharacteristic
170C22×C127C2×#4111yescharacteristic
171C22×C127C2×#4111yescharacteristic
172C22×C127H(5,𝔽2)11yescharacteristic
173C22×C127H(5,𝔽2)11yescharacteristic
174C22×C1272−1+411yescharacteristic
175C22×C1272−1+411yescharacteristic
176C4×C127—22no—
177C4×C127—22no—
178C4×C127—22no—
179C4×C127—22no—
180C4×C127—41no—
181C4×C127—41no—
182C4×C127—41no—
183C4×C127—41no—
184C4×C127—41no—
185C4×C127—41no—
186C4×C127—41no—
187C4×C127—41no—
188C4×C127—41no—
189C2×C127—42no—
190C2×C127—81no—
191C2×C127#53611yescharacteristic
192C2×C127#53911yescharacteristic
193C2×C127#53911yescharacteristic
194C2×C127#54611yescharacteristic
195C2×C127#55011yescharacteristic
196C2×C127#55211yescharacteristic
197C2×C127#56211yescharacteristic
198#2694C12711yesmaximal, characteristic, direct product factor, Sylow
199C127#269411yescharacteristic, direct product factor, Sylow
200C2×#125C2×C12711yescharacteristic, complemented
201C2×#123C2×C12711yescharacteristic
202#399C2×C12711yescharacteristic, complemented
203#399C2×C12711yescharacteristic, complemented
204#398C2×C12711yescharacteristic, complemented
205#397C2×C12711yescharacteristic, complemented
206#396C2×C12711yescharacteristic, complemented
207#394C2×C12711yescharacteristic
208#390C2×C12711yescharacteristic
209#389C2×C12711yescharacteristic, complemented
210#388C2×C12711yescharacteristic, complemented
211#388C2×C12711yescharacteristic, complemented
212#387C2×C12711yescharacteristic, complemented
213#385C2×C12711yescharacteristic, complemented
214#380C2×C12711yescharacteristic, complemented
215C22×D4C22×C12711yescharacteristic
216C23×C4C22×C12711yescharacteristic
217#125—24no—
218#123—24no—
219C2×C4⋊C4C22×C12711yescharacteristic
220C2×C4⋊C4C22×C12711yescharacteristic
221C2×C4⋊C4C22×C12711yescharacteristic
222C2×C4⋊C4C22×C12711yescharacteristic
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×C4⋊C4C22×C12711yescharacteristic
230C2×C4⋊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×C22⋊C4C22×C12711yescharacteristic
241C2×C22⋊C4C22×C12711yescharacteristic
242C2×C42C22×C12711yescharacteristic
243C2×C42C22×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
252C24C23×C12711yescharacteristic
253C24C23×C12711yescharacteristic
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—41no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4C23×C12711yescharacteristic
261C22×C4C23×C12711yescharacteristic
262C22×C4C23×C12711yescharacteristic
263C22×C4C23×C12711yescharacteristic
264C22×C4C23×C12711yescharacteristic
265C22×C4C23×C12711yescharacteristic
266C22×C4C23×C12711yescharacteristic
267C22×C4C23×C12711yescharacteristic
268C22×C4C23×C12711yescharacteristic
269C22×C4C23×C12711yescharacteristic
270C22×C4C23×C12711yescharacteristic
271C22×C4C23×C12711yescharacteristic
272C22×C4C23×C12711yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4D4×C12714yes—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C42—22no—
297C42—41no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23#41×C12712yes—
312C23C24×C12711yescharacteristic
313D4—44no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
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—44no—
350C2×C4C2×D4×C12712yes—
351C2×C4C2×D4×C12712yes—
352C2×C4C2×D4×C12712yes—
353C2×C4#41×C12712yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22C22×D4×C12711yescharacteristic
369C22C2×#41×C12711yescharacteristic
370C22C2×#41×C12711yescharacteristic
371C22H(5,𝔽2)×C12711yescharacteristic
372C22H(5,𝔽2)×C12711yescharacteristic
373C222−1+4×C12711yescharacteristic
374C222−1+4×C12711yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C2—42no—
389C2—81no—
390C2#536×C12711yescharacteristic
391C2#539×C12711yescharacteristic
392C2#539×C12711yescharacteristic
393C2#546×C12711yescharacteristic
394C2#550×C12711yescharacteristic
395C2#552×C12711yescharacteristic
396C2#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
1. C2×#125×C127C2semidirect
3. #399×C127C2semidirect
4. #399×C127C2semidirect
5. #398×C127C2semidirect
6. #397×C127C2semidirect
7. #396×C127C2semidirect
10. #389×C127C2semidirect
11. #388×C127C2semidirect
12. #388×C127C2semidirect
13. #387×C127C2semidirect
14. #385×C127C2semidirect
15. #380×C127C2semidirect
198. #2694C127direct (N × H)
199. C127#2694direct (N × H)
200. C2×#125C2×C127semidirect
202. #399C2×C127semidirect
203. #399C2×C127semidirect
204. #398C2×C127semidirect
205. #397C2×C127semidirect
206. #396C2×C127semidirect
209. #389C2×C127semidirect
210. #388C2×C127semidirect
211. #388C2×C127semidirect
212. #387C2×C127semidirect
213. #385C2×C127semidirect
214. #380C2×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#125×C1272
C2×#123×C1272
#399×C1272
#398×C1272
#397×C1272
#396×C1272
#394×C1272
#390×C1272
#389×C1272
#388×C1272
#387×C1272
#385×C1272
#380×C1272
#2694127