Finite Group Databasebeta

← #20246152

Subgroups — #20246152

Order 6016.

596 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093999C211yesmaximal, characteristic
2#15689025C211yesmaximal, characteristic, complemented
3#15689024C211yesmaximal, characteristic, complemented
4#15689015C211yesmaximal, characteristic, complemented
5#15689013C211yesmaximal, characteristic, complemented
6#15689009C211yesmaximal, characteristic, complemented
7#15689001C211yesmaximal, characteristic, complemented
8#15689001C211yesmaximal, characteristic, complemented
9#15689001C211yesmaximal, characteristic, complemented
10#15689001C211yesmaximal, characteristic, complemented
11#15688985C211yesmaximal, characteristic, complemented
12C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
13#15688970C211yesmaximal, characteristic, complemented
14#15688970C211yesmaximal, characteristic, complemented
15C47×#387C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×D188C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21C22×C4×D47C2211yescharacteristic
22#13093999C418yescomplemented
23C2×C4⋊Dic47C2211yescharacteristic
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊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×C4×Dic47C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C2×C4×Dic47C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C2×C4⋊C4×C47C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C42×C47C2211yescharacteristic
48#95×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52C23×D47C2311yescharacteristic
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
67C2×D188—41no—
68C2×D188—41no—
69C2×D188—41no—
70C2×D188—41no—
71C2×D188—41no—
72C2×D188—41no—
73C2×D188C2×C414yes—
74C2×D188C2×C414yescomplemented
75C2×D188C2×C414yescomplemented
76C2×C4×D47—22no—
77C2×C4×D47—22no—
78C2×C4×D47—41no—
79C2×C4×D47—41no—
80C2×C4×D47—41no—
81C2×C4×D47—41no—
82C2×C4×D47—41no—
83C2×C4×D47—41no—
84C2×C4×D47C2×C414yescomplemented
85C4⋊C4×C47—41no—
86C4⋊C4×C47C2×C414yescomplemented
87C42×C47—41no—
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—
97(C2×D47)⋊C4—41no—
98(C2×D47)⋊C4C2×C414yescomplemented
99(C2×D47)⋊C4C2×C414yescomplemented
100C4⋊Dic47—41no—
101C4×Dic47—41no—
102C4×Dic47—41no—
103C4×Dic47—41no—
104C23×C47C2411yescharacteristic
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×D47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—21no—
121C22×D47—21no—
122C22×D47—21no—
123C22×D47C22×C412yes—
124C22×D47C22×C412yes—
125C22×D47C22×C412yes—
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×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47C22×C412yes—
144C2×C4×C47C22×C412yes—
145C2×C4×C47C22×C412yes—
146C2×C4×C47#4112yes—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—21no—
160C2×Dic47C22×C412yes—
161C2×Dic47#4112yes—
162D188—44no—
163D188—44no—
164D188—44no—
165C4×D47—44no—
166C4×D47—44no—
167C4×D47—44no—
168C22×C47C23×C411yescharacteristic
169C22×C47C2×#4111yescharacteristic
170C22×C47C2×#4111yescharacteristic
171C22×C47H(5,𝔽2)11yescharacteristic
172C22×C47H(5,𝔽2)11yescharacteristic
173C22×C47H(5,𝔽2)11yescharacteristic
174C22×C47H(5,𝔽2)11yescharacteristic
175C2×D47—22no—
176C2×D47—22no—
177C2×D47—22no—
178C2×D47—22no—
179C2×D47—22no—
180C2×D47—22no—
181C2×D47—22no—
182C2×D47—22no—
183C2×D47—22no—
184C2×D47—41no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—41no—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—41no—
195C2×D47—41no—
196C4×C47—22no—
197C4×C47—22no—
198C4×C47—22no—
199C4×C47—22no—
200C4×C47—41no—
201C4×C47—41no—
202C4×C47—41no—
203Dic47—22no—
204Dic47—22no—
205Dic47—41no—
206Dic47—41no—
207Dic47—41no—
208#2333—471nomaximal, Sylow
209C2×C47C4×#4111yescharacteristic
210C2×C47#51811yescharacteristic
211C2×C47#51811yescharacteristic
212C2×C47#53811yescharacteristic
213C2×C47#53811yescharacteristic
214C2×C47#54011yescharacteristic
215C2×C47#54011yescharacteristic
216D47—42no—
217D47—42no—
218D47—42no—
219C2×#121—471no—
220#390—471no—
221#390—471no—
222#388—471no—
223#388—471no—
224#387—471no—
225#387D4711yescharacteristic, complemented
226#386—471no—
227#386—471no—
228#386—471no—
229#386—471no—
230#381—471no—
231C4×C22⋊C4—471no—
232C4×C22⋊C4—471no—
233C4×C22⋊C4—471no—
234C47#233311yescharacteristic, complemented, Sylow
235C22×D4—471no—
236C22×D4—471no—
237C22×D4—471no—
238C23×C4—471no—
239C23×C4—471no—
240C23×C4—471no—
241#121—478no—
242C2×C4⋊C4—471no—
243C2×C4⋊C4C2×D4711yescharacteristic
244C2×C4⋊C4C2×D4711yescharacteristic
245C2×C22⋊C4—471no—
246C2×C22⋊C4—471no—
247C2×C22⋊C4—471no—
248C2×C22⋊C4—471no—
249C2×C22⋊C4—471no—
250C2×C22⋊C4—471no—
251C2×C22⋊C4—471no—
252C2×C22⋊C4—471no—
253C2×C22⋊C4—471no—
254C2×C22⋊C4—471no—
255C2×C22⋊C4—471no—
256C2×C22⋊C4—471no—
257C2×C42—471no—
258C2×C42—471no—
259C2×C42—471no—
260C2×C42C2×D4711yescharacteristic
261#95—471no—
262#95—471no—
263#95—471no—
264#95—471no—
265#95—471no—
266#95—471no—
267#95C2×D4711yescharacteristic
268#95C2×D4711yescharacteristic
269#95C2×D4711yescharacteristic
270#95C2×D4711yescharacteristic
271C24—471no—
272C24—471no—
273C24—471no—
274C2×D4—474no—
275C2×D4—474no—
276C2×D4—474no—
277C2×D4—1881no—
278C2×D4—1881no—
279C2×D4—1881no—
280C2×D4—1881no—
281C2×D4—1881no—
282C2×D4—1881no—
283C22×C4—471no—
284C22×C4—471no—
285C22×C4—474no—
286C22×C4—471no—
287C22×C4—471no—
288C22×C4—471no—
289C22×C4—942no—
290C22×C4—942no—
291C22×C4—1881no—
292C22×C4—1881no—
293C22×C4—1881no—
294C22×C4—1881no—
295C22×C4—1881no—
296C22×C4—1881no—
297C22×C4C22×D4711yescharacteristic
298C22×C4C22×D4711yescharacteristic
299C22×C4C22×D4711yescharacteristic
300C22×C4C22×D4711yescharacteristic
301C22×C4C22×D4711yescharacteristic
302C22×C4C22×D4711yescharacteristic
303C22×C4C22×D4711yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—1881no—
306C4⋊C4C4×D4714yescomplemented
307C22⋊C4—474no—
308C22⋊C4—474no—
309C22⋊C4—942no—
310C22⋊C4—942no—
311C22⋊C4—942no—
312C22⋊C4—942no—
313C22⋊C4—1881no—
314C22⋊C4—1881no—
315C22⋊C4—1881no—
316C22⋊C4—1881no—
317C22⋊C4—1881no—
318C22⋊C4—1881no—
319C42—41no—
320C42—1881no—
321C42—1881no—
322C42—1881no—
323C23—472no—
324C23—472no—
325C23—472no—
326C23—941no—
327C23—941no—
328C23—941no—
329C23—941no—
330C23—941no—
331C23—941no—
332C23—941no—
333C23—941no—
334C23—941no—
335C23—941no—
336C23—941no—
337C23—941no—
338C23—941no—
339C23—941no—
340C23—941no—
341C23—941no—
342C23—941no—
343C23—941no—
344C23C23×D4711yescharacteristic
345D4—1884no—
346D4—1884no—
347D4—1884no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—472no—
366C2×C4—472no—
367C2×C4—941no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—941no—
371C2×C4—941no—
372C2×C4—941no—
373C2×C4—941no—
374C2×C4—941no—
375C2×C4—941no—
376C2×C4—941no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—941no—
380C2×C4—1884no—
381C2×C4—1884no—
382C2×C4—1884no—
383C2×C4C2×C4×D4712yes—
384C2×C4C2×C4×D4712yes—
385C2×C4C2×C4×D4712yes—
386C2×C4#1062535412yes—
387C22—942no—
388C22—942no—
389C22—942no—
390C22—942no—
391C22—942no—
392C22—942no—
393C22—942no—
394C22—942no—
395C22—942no—
396C22—1881no—
397C22—1881no—
398C22—1881no—
399C22—1881no—
400C22—1881no—
401C22—1881no—
402C22—1881no—
403C22—1881no—
404C22—1881no—
405C22—1881no—
406C22—1881no—
407C22—1881no—
408C22C22×C4×D4711yescharacteristic
409C22#41×D4711yescharacteristic
410C22C2×#1062535411yescharacteristic
411C22#1309406911yescharacteristic
412C22#1309407011yescharacteristic
413C22#1309407011yescharacteristic
414C22#1309407011yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—22no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—942no—
423C4—942no—
424C4—1881no—
425C4—1881no—
426C4—1881no—
427C2—1882no—
428C2—1882no—
429C2—1882no—
430C2C4×#1062535411yescharacteristic
431C2#1568959511yescharacteristic
432C2#1568959711yescharacteristic
433C2#1568971211yescharacteristic
434C2#1568971311yescharacteristic
435C2#1568972511yescharacteristic
436C2#1568972911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#387C2
socleC23×C47C24
hypercenter#387D47
hypocenterC47#2333
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #15689025C2semidirect
3. #15689024C2semidirect
4. #15689015C2semidirect
5. #15689013C2semidirect
6. #15689009C2semidirect
7. #15689001C2semidirect
8. #15689001C2semidirect
9. #15689001C2semidirect
10. #15689001C2semidirect
11. #15688985C2semidirect
12. C4×(C2×D47)⋊C4C2semidirect
13. #15688970C2semidirect
14. #15688970C2semidirect
15. C47×#387C2semidirect
22. #13093999C4semidirect
74. C2×D188C2×C4semidirect
75. C2×D188C2×C4semidirect
84. C2×C4×D47C2×C4semidirect
86. C4⋊C4×C47C2×C4semidirect
98. (C2×D47)⋊C4C2×C4semidirect
99. (C2×D47)⋊C4C2×C4semidirect
225. #387D47semidirect
234. C47#2333semidirect
306. C4⋊C4C4×D47semidirect