Finite Group Databasebeta

← #20249886

Subgroups — #20249886

Order 6016.

536 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094002C211yesmaximal, characteristic, complemented
2C2×#13094002C211yesmaximal, characteristic, complemented
3#15689058C211yesmaximal, characteristic, complemented
4#15689045C211yesmaximal, characteristic, complemented
5#15689043C211yesmaximal, characteristic, complemented
6#15689036C211yesmaximal, characteristic, complemented
7#15689036C211yesmaximal, characteristic, complemented
8#15689027C211yesmaximal, characteristic, complemented
9#15689024C211yesmaximal, characteristic
10#15689010C211yesmaximal, characteristic, complemented
11#15689001C211yesmaximal, characteristic
12#15689001C211yesmaximal, characteristic
13#15688994C211yesmaximal, characteristic, complemented
14#15688980C211yesmaximal, characteristic, complemented
15C47×#398C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C22×D188C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21#13094002—24no—
22#13094002—24no—
23C2×C4⋊Dic47C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×C4×Dic47C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C23×D47C2311yescharacteristic
54C23×D47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C2×D188—41no—
69C2×D188—41no—
70C2×D188Q814yescomplemented
71C2×C4×D47—22no—
72C2×C4×D47—22no—
73C2×C4×D47—22no—
74C2×C4×D47—41no—
75C2×C4×D47—41no—
76C2×C4×D47—41no—
77C2×Dic94—22no—
78C2×Dic94—22no—
79C2×Dic94—22no—
80C2×Dic94—41no—
81C2×Dic94—41no—
82C2×Dic94—41no—
83C4⋊C4×C47—22no—
84C4⋊C4×C47—22no—
85C4⋊C4×C47—41no—
86C4⋊C4×C47—41no—
87(C2×D47)⋊C4—22no—
88(C2×D47)⋊C4—22no—
89(C2×D47)⋊C4—22no—
90(C2×D47)⋊C4—22no—
91(C2×D47)⋊C4—22no—
92(C2×D47)⋊C4—41no—
93(C2×D47)⋊C4—41no—
94(C2×D47)⋊C4—41no—
95(C2×D47)⋊C4—41no—
96(C2×D47)⋊C4—41no—
97C4⋊Dic47—41no—
98Dic47⋊C4—22no—
99Dic47⋊C4—22no—
100Dic47⋊C4—41no—
101Dic47⋊C4D414yescomplemented
102C4×Dic47—41no—
103C23×C47C2411yescharacteristic
104C22×D47—21no—
105C22×D47—21no—
106C22×D47—21no—
107C22×D47—21no—
108C22×D47—21no—
109C22×D47—21no—
110C22×D47—21no—
111C22×D47—21no—
112C22×D47—21no—
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—21no—
116C22×D47C2×Q812yes—
117C22×D47C2×Q812yes—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47C2×D412yes—
138C2×C4×C47C2×Q812yes—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47C2×D412yes—
155C2×Dic47C2×D412yes—
156C2×Dic47#4112yes—
157D188—44no—
158C4×D47—44no—
159C4×D47—44no—
160Dic94—44no—
161Dic94—44no—
162C22×C47C22×D411yescharacteristic
163C22×C47C22×Q811yescharacteristic
164C22×C47C2×#4111yescharacteristic
165C22×C47H(5,𝔽2)11yescharacteristic
166C22×C47H(5,𝔽2)11yescharacteristic
167C22×C47H(5,𝔽2)11yescharacteristic
168C22×C472−1+411yescharacteristic
169C2×D47—22no—
170C2×D47—22no—
171C2×D47—22no—
172C2×D47—22no—
173C2×D47—22no—
174C2×D47—22no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C4×C47—22no—
184C4×C47—22no—
185C4×C47—41no—
186C4×C47—41no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47—41no—
190Dic47—22no—
191Dic47—22no—
192Dic47—22no—
193Dic47—41no—
194Dic47—41no—
195Dic47—41no—
196#2692—471nomaximal, Sylow
197C2×C47#53511yescharacteristic
198C2×C47#54211yescharacteristic
199C2×C47#54311yescharacteristic
200C2×C47#54611yescharacteristic
201C2×C47D4×Q811yescharacteristic
202C2×C47#55411yescharacteristic
203C2×C47#56211yescharacteristic
204D47—42no—
205D47—42no—
206C2×C22⋊Q8—471no—
207C2×C22⋊Q8—471no—
208#399—471no—
209#398D4711yescharacteristic, complemented
210#396—471no—
211#395—471no—
212#393—471no—
213#393—471no—
214#391—471no—
215#390—471no—
216#387—471no—
217#386—471no—
218#386—471no—
219#385—471no—
220#380—471no—
221C47#269211yescharacteristic, complemented, Sylow
222C22×Q8—471no—
223C22×Q8—471no—
224C22×D4—471no—
225C23×C4—471no—
226C23×C4—471no—
227C22⋊Q8—944no—
228C22⋊Q8—944no—
229C2×C4⋊C4—471no—
230C2×C4⋊C4—471no—
231C2×C4⋊C4—471no—
232C2×C4⋊C4—471no—
233C2×C4⋊C4—471no—
234C2×C4⋊C4C2×D4711yescharacteristic
235C2×C4⋊C4C2×D4711yescharacteristic
236C2×C4⋊C4C2×D4711yescharacteristic
237C2×C4⋊C4C2×D4711yescharacteristic
238C2×C22⋊C4—471no—
239C2×C22⋊C4—471no—
240C2×C22⋊C4—471no—
241C2×C22⋊C4—471no—
242C2×C22⋊C4—471no—
243C2×C22⋊C4—471no—
244C2×C22⋊C4—471no—
245C2×C22⋊C4—471no—
246C2×C22⋊C4—471no—
247C2×C22⋊C4—471no—
248C2×C42—471no—
249#95—471no—
250#95—471no—
251#95—471no—
252#95—471no—
253#95—471no—
254#95—471no—
255#95—471no—
256#95C2×D4711yescharacteristic
257#95C2×D4711yescharacteristic
258#95C2×D4711yescharacteristic
259C24—471no—
260C24—471no—
261C2×Q8—942no—
262C2×Q8—942no—
263C2×Q8—942no—
264C2×Q8—1881no—
265C2×Q8—1881no—
266C2×Q8—1881no—
267C2×D4—474no—
268C2×D4—1881no—
269C2×D4—1881no—
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—471no—
273C22×C4—471no—
274C22×C4—471no—
275C22×C4—471no—
276C22×C4—942no—
277C22×C4—942no—
278C22×C4—942no—
279C22×C4—1881no—
280C22×C4—1881no—
281C22×C4—1881no—
282C22×C4C22×D4711yescharacteristic
283C22×C4C22×D4711yescharacteristic
284C22×C4C22×D4711yescharacteristic
285C22×C4C22×D4711yescharacteristic
286C22×C4C22×D4711yescharacteristic
287C22×C4C22×D4711yescharacteristic
288C22×C4C22×D4711yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—474no—
294C4⋊C4—942no—
295C4⋊C4—942no—
296C4⋊C4—1881no—
297C4⋊C4—1881no—
298C22⋊C4—942no—
299C22⋊C4—942no—
300C22⋊C4—942no—
301C22⋊C4—942no—
302C22⋊C4—942no—
303C22⋊C4—1881no—
304C22⋊C4—1881no—
305C22⋊C4—1881no—
306C22⋊C4—1881no—
307C22⋊C4—1881no—
308C42—1881no—
309C23—472no—
310C23—472no—
311C23—941no—
312C23—941no—
313C23—941no—
314C23—941no—
315C23—941no—
316C23—941no—
317C23—941no—
318C23—941no—
319C23—941no—
320C23—941no—
321C23—941no—
322C23—941no—
323C23C23×D4711yescharacteristic
324Q8—1884no—
325Q8—1884no—
326D4—1884no—
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—472no—
347C2×C4—472no—
348C2×C4—472no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—941no—
364C2×C4—1884no—
365C2×C4—1884no—
366C2×C4D4×D4712yes—
367C2×C4Q8×D4712yes—
368C22—942no—
369C22—942no—
370C22—942no—
371C22—942no—
372C22—942no—
373C22—942no—
374C22—1881no—
375C22—1881no—
376C22—1881no—
377C22—1881no—
378C22—1881no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22C2×D4×D4711yescharacteristic
383C22C2×Q8×D4711yescharacteristic
384C22#41×D4711yescharacteristic
385C22#1309406911yescharacteristic
386C22#1309407011yescharacteristic
387C22#1309407011yescharacteristic
388C22#1309407211yescharacteristic
389C4—22no—
390C4—22no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—942no—
397C4—942no—
398C4—942no—
399C4—1881no—
400C4—1881no—
401C4—1881no—
402C2—1882no—
403C2—1882no—
404C2#1568968911yescharacteristic
405C2#1568974311yescharacteristic
406C2#1568974811yescharacteristic
407C2#1568976511yescharacteristic
408C2#1568978811yescharacteristic
409C2#1568982911yescharacteristic
410C2#1568987111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2692
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#13094002C2semidirect
2. C2×#13094002C2semidirect
3. #15689058C2semidirect
4. #15689045C2semidirect
5. #15689043C2semidirect
6. #15689036C2semidirect
7. #15689036C2semidirect
8. #15689027C2semidirect
10. #15689010C2semidirect
13. #15688994C2semidirect
14. #15688980C2semidirect
15. C47×#398C2semidirect
70. C2×D188Q8semidirect
101. Dic47⋊C4D4semidirect
209. #398D47semidirect
221. C47#2692semidirect