Finite Group Databasebeta

← C4×C67⋊#564 #31018552

Subgroups — C4×C67⋊#564 #31018552

Order 17152.

1800 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C67⋊#564C211yesmaximal, characteristic
2#22563395C211yesmaximal, characteristic
3#22563394C212yesmaximal
4#22563393C214yesmaximal
5#22563392C214yesmaximal
6#22563391C214yesmaximal
7C4×#14524035C212yesmaximal
8C4×#14524034C214yesmaximal
9C4×#14524033C214yesmaximal
10C4×#14524033C214yesmaximal
11C4×#125×C67C211yesmaximal, characteristic
12C67⋊#564C4116yesdirect product factor
13C2×#14524035C2212yes—
14C2×#14524034C2214yes—
15C2×#14524033C2214yes—
16C2×#14524033C2214yes—
17#16863295C2214yes—
18#16863294C2212yes—
19#16863294C2212yes—
20#16863293C2214yes—
21#16863293C2214yes—
22#16863292C2214yes—
23#16863291C2214yes—
24#16863291C2214yes—
25#16863283C2214yes—
26#16863283C2214yes—
27#16863282C2214yes—
28#16863282C2214yes—
29#16863281C2214yes—
30#16863281C2214yes—
31#16863280C2214yes—
32#16863280C2214yes—
33#16863279C2214yes—
34#16863279C2214yes—
35#16863278C2214yes—
36#16863278C2214yes—
37#16863277C2214yes—
38#16863277C2214yes—
39#16863262C2212yes—
40#16863261C2214yes—
41#16863260C2214yes—
42#16863260C2214yes—
43C4×Dic67⋊C4C2214yes—
44C4×Dic67⋊C4C2214yes—
45C4×Dic67⋊C4C2214yes—
46C4×Dic67⋊C4C2214yes—
47C4×C4⋊Dic67C2212yes—
48C4×C4⋊Dic67C2214yes—
49C4×C4⋊Dic67C2212yes—
50C42×Dic67C2214yes—
51C2×#125×C67C2211yescharacteristic
52#389×C67C2212yes—
53#387×C67C2214yes—
54#382×C67C2211yescharacteristic
55C4×C4⋊C4×C67C2212yes—
56C4×C4⋊C4×C67C2214yes—
57C43×C67C2211yescharacteristic
58#14524035C2×C4116yes—
59#14524034C2×C4132yes—
60#14524033C2×C4132yes—
61#14524033C2×C4132yes—
62C2×C4⋊Dic67C2314yes—
63C2×C4⋊Dic67C2312yes—
64C2×C4⋊Dic67C2312yes—
65C2×C4⋊Dic67C2312yes—
66C2×C4⋊Dic67C2314yes—
67C2×C4⋊Dic67C2312yes—
68C2×Dic67⋊C4C2314yes—
69C2×Dic67⋊C4C2314yes—
70C2×Dic67⋊C4C2314yes—
71C2×Dic67⋊C4C2314yes—
72C2×Dic67⋊C4C2314yes—
73C2×Dic67⋊C4C2314yes—
74C2×Dic67⋊C4C2314yes—
75C2×Dic67⋊C4C2314yes—
76C2×C4×Dic67C2314yes—
77C2×C4×Dic67C2314yes—
78C2×C4×Dic67C2314yes—
79C2×C4×Dic67C2314yes—
80C2×C4×Dic67C2314yes—
81C2×C4×Dic67C2314yes—
82C67⋊#95C2314yes—
83C67⋊#95C2314yes—
84C67⋊#95C2314yes—
85C67⋊#95C2314yes—
86C67⋊#95C2314yes—
87C67⋊#95C2314yes—
88C67⋊#95C2314yes—
89C67⋊#95C2314yes—
90C67⋊#95C2314yes—
91C67⋊#95C2314yes—
92C67⋊#95C2314yes—
93C67⋊#95C2314yes—
94#125×C67C2×C418yes—
95C2×C4⋊C4×C67C2314yes—
96C2×C4⋊C4×C67C2312yes—
97C2×C4⋊C4×C67C2312yes—
98C2×C4⋊C4×C67C2314yes—
99C2×C42×C67C2314yes—
100C2×C42×C67C2312yes—
101C2×C42×C67C2311yescharacteristic
102C2×C42×C67C2311yescharacteristic
103C2×C42×C67C2312yes—
104C2×C42×C67C2311yescharacteristic
105#95×C67C2314yes—
106#95×C67C2314yes—
107#95×C67C2314yes—
108C22×Dic67C2414yes—
109C22×Dic67C2414yes—
110C22×Dic67C2414yes—
111C22×Dic67C2414yes—
112C4⋊Dic67—42no—
113C4⋊Dic67—44no—
114C4⋊Dic67—42no—
115C4⋊Dic67C22×C418yes—
116C4⋊Dic67C22×C4116yes—
117C4⋊Dic67C22×C418yes—
118Dic67⋊C4—44no—
119Dic67⋊C4—44no—
120Dic67⋊C4—44no—
121Dic67⋊C4—44no—
122Dic67⋊C4C22×C4116yes—
123Dic67⋊C4C22×C4116yes—
124Dic67⋊C4C22×C4116yes—
125Dic67⋊C4C22×C4116yes—
126C4×Dic67—28no—
127C4×Dic67—28no—
128C4×Dic67—44no—
129C4×Dic67—44no—
130C4×Dic67—44no—
131C4×Dic67C22×C4116yes—
132C22×C4×C67C2412yes—
133C22×C4×C67C2411yescharacteristic
134C22×C4×C67C2414yes—
135C22×C4×C67C2411yescharacteristic
136C22×C4×C67C2412yes—
137C22×C4×C67C2414yes—
138C22×C4×C67C2411yescharacteristic
139C4⋊C4×C67—42no—
140C4⋊C4×C67—44no—
141C4⋊C4×C67C22×C418yes—
142C4⋊C4×C67C22×C4116yes—
143C42×C67—28no—
144C42×C67—24no—
145C42×C67—22no—
146C42×C67—41no—
147C42×C67—42no—
148C42×C67C22×C414yes—
149C23×C67C2511yescharacteristic
150C2×C4×C67—22no—
151C2×C4×C67—24no—
152C2×C4×C67—21no—
153C2×C4×C67—21no—
154C2×C4×C67—22no—
155C2×C4×C67—24no—
156C2×C4×C67—22no—
157C2×C4×C67—24no—
158C2×C4×C67—21no—
159C2×C4×C67—22no—
160C2×C4×C67—22no—
161C2×C4×C67—22no—
162C2×C4×C67—24no—
163C2×C4×C67—24no—
164C2×C4×C67C23×C412yes—
165C2×C4×C67C23×C414yes—
166C2×C4×C67C23×C418yes—
167C2×C4×C672−1+414yes—
168C2×C4×C672−1+412yes—
169C2×Dic67—24no—
170C2×Dic67—24no—
171C2×Dic67—24no—
172C2×Dic67—24no—
173C2×Dic67—24no—
174C2×Dic67—24no—
175C2×Dic67—24no—
176C2×Dic67—24no—
177C2×Dic67—24no—
178C2×Dic67—24no—
179C2×Dic67C23×C418yes—
180C2×Dic67C23×C418yes—
181C22×C67C24×C411yescharacteristic
182C22×C67C2×2−1+412yes—
183C22×C67C2×2−1+411yescharacteristic
184C22×C67#58511yescharacteristic
185C22×C67#58512yes—
186C4×C67—24no—
187C4×C67—28no—
188C4×C67—22no—
189C4×C67—42no—
190C4×C67—44no—
191C4×C67—41no—
192C4×C67#56414yescomplemented
193Dic67—28no—
194Dic67—28no—
195Dic67—44no—
196Dic67—44no—
197C4×#564—671nomaximal, Sylow
198C2×C67C4×2−1+412yes—
199C2×C67C4×2−1+411yescharacteristic
200C2×C67C2×#56411yescharacteristic
201C2×C67#353112yes—
202C2×C67#353111yescharacteristic
203C2×#564—671no—
204#2382—674no—
205#2382—674no—
206#2382—674no—
207#2382—672no—
208#2382—671no—
209C4×#125—674no—
210C4×#125—674no—
211C4×#125—674no—
212C4×#125—672no—
213C4×#125D6711yescharacteristic
214C67C4×#56411yescharacteristic, complemented, Sylow
215#564—6716no—
216C2×#125—674no—
217C2×#125—674no—
218C2×#125—674no—
219C2×#125—672no—
220C2×#125C2×D6711yescharacteristic
221#389—674no—
222#389—674no—
223#389—674no—
224#389—674no—
225#389—672no—
226#389—672no—
227#389—674no—
228#389—674no—
229#389C2×D6712yes—
230#387—674no—
231#387—674no—
232#387—674no—
233#387—674no—
234#387—674no—
235#387—674no—
236#387—674no—
237#387—674no—
238#387—674no—
239#387—674no—
240#387—674no—
241#387—674no—
242#387—674no—
243#387—674no—
244#387C2×D6714yes—
245#382—674no—
246#382—672no—
247#382—674no—
248#382—674no—
249#382C2×D6711yescharacteristic
250C4×C4⋊C4—674no—
251C4×C4⋊C4—672no—
252C4×C4⋊C4—672no—
253C4×C4⋊C4—674no—
254C4×C4⋊C4—674no—
255C4×C4⋊C4—674no—
256C4×C4⋊C4—674no—
257C4×C4⋊C4C2×D6714yes—
258C4×C4⋊C4C2×D6712yes—
259C43—674no—
260C43C2×D6711yescharacteristic
261#125—6732no—
262#125—6732no—
263#125—6732no—
264#125—6716no—
265#125C4×D6718yes—
266C2×C4⋊C4—674no—
267C2×C4⋊C4—674no—
268C2×C4⋊C4—674no—
269C2×C4⋊C4—674no—
270C2×C4⋊C4—674no—
271C2×C4⋊C4—672no—
272C2×C4⋊C4—672no—
273C2×C4⋊C4—674no—
274C2×C4⋊C4—674no—
275C2×C4⋊C4—674no—
276C2×C4⋊C4—674no—
277C2×C4⋊C4—674no—
278C2×C4⋊C4—672no—
279C2×C4⋊C4—672no—
280C2×C4⋊C4C22×D6714yes—
281C2×C4⋊C4C22×D6712yes—
282C2×C4⋊C4C22×D6712yes—
283C2×C4⋊C4C22×D6714yes—
284C2×C42—674no—
285C2×C42—674no—
286C2×C42—674no—
287C2×C42—674no—
288C2×C42—674no—
289C2×C42—674no—
290C2×C42C22×D6714yes—
291C2×C42C22×D6712yes—
292C2×C42C22×D6711yescharacteristic
293C2×C42C22×D6711yescharacteristic
294C2×C42C22×D6712yes—
295C2×C42C22×D6711yescharacteristic
296#95—674no—
297#95—674no—
298#95—674no—
299#95—674no—
300#95—674no—
301#95—674no—
302#95—674no—
303#95—674no—
304#95—674no—
305#95—674no—
306#95—674no—
307#95—674no—
308#95C22×D6714yes—
309#95C22×D6714yes—
310#95C22×D6714yes—
311C22×C4—674no—
312C22×C4—674no—
313C22×C4—674no—
314C22×C4—674no—
315C22×C4C23×D6712yes—
316C22×C4C23×D6714yes—
317C22×C4C23×D6711yescharacteristic
318C22×C4C23×D6711yescharacteristic
319C22×C4C23×D6714yes—
320C22×C4C23×D6712yes—
321C22×C4C23×D6711yescharacteristic
322C4⋊C4—42no—
323C4⋊C4—44no—
324C4⋊C4—2684no—
325C4⋊C4—2684no—
326C4⋊C4—2684no—
327C4⋊C4—2684no—
328C4⋊C4—2682no—
329C4⋊C4—2682no—
330C4⋊C4—2684no—
331C4⋊C4—6716no—
332C4⋊C4—6716no—
333C4⋊C4—6716no—
334C4⋊C4—6716no—
335C4⋊C4—6716no—
336C4⋊C4—678no—
337C4⋊C4—678no—
338C4⋊C4C2×C4×D6718yes—
339C4⋊C4C2×C4×D67116yes—
340C42—28no—
341C42—24no—
342C42—22no—
343C42—41no—
344C42—42no—
345C42—2684no—
346C42—2684no—
347C42—2684no—
348C42—6716no—
349C42—1348no—
350C42—1348no—
351C42C2×C4×D6714yes—
352C23C24×D6711yescharacteristic
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—22no—
360C2×C4—24no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—678no—
368C2×C4—678no—
369C2×C4—1344no—
370C2×C4—1344no—
371C2×C4—1344no—
372C2×C4—1344no—
373C2×C4—1344no—
374C2×C4—1344no—
375C2×C4—1344no—
376C2×C4—1344no—
377C2×C4—1344no—
378C2×C4—1344no—
379C2×C4C22×C4×D6718yes—
380C2×C4C22×C4×D6714yes—
381C2×C4C22×C4×D6712yes—
382C2×C4#1452409014yes—
383C2×C4#1452409112yes—
384C22C23×C4×D6711yescharacteristic
385C22C2×#1452409012yes—
386C22C2×#1452409111yescharacteristic
387C22#1686423211yescharacteristic
388C22#1686423212yes—
389C4—24no—
390C4—28no—
391C4—22no—
392C4—42no—
393C4—44no—
394C4—41no—
395C4—2684no—
396C4—2684no—
397C4—1348no—
398C4—1348no—
399C4C67⋊#56414yesdirect product factor
400C2C4×#1452409012yes—
401C2C4×#1452409111yescharacteristic
402C2C2×C67⋊#56411yescharacteristic
403C2#2257435412yes—
404C2#2257435611yescharacteristic
subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC4×#125×C67C2
socle, prime radical, cosocleC23×C67C25
hypercenterC4×#125D67
hypocenterC67C4×#564
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
12. C67⋊#564C4direct (N × H)
192. C4×C67#564semidirect
214. C67C4×#564semidirect
399. C4C67⋊#564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C67⋊#5642
#225633952
#225633942
#225633932
#225633922
#225633912
C4×#145240352
C4×#145240342
C4×#145240332
C4×#125×C672
C4×#56467