Finite Group Databasebeta

← #20247709

Subgroups — #20247709

Order 6016.

546 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094009C211yesmaximal, characteristic
2C2×#13094002C211yesmaximal, characteristic, complemented
3#15689064C211yesmaximal, characteristic, complemented
4#15689052C211yesmaximal, characteristic, complemented
5#15689036C211yesmaximal, characteristic, complemented
6#15689028C211yesmaximal, characteristic, complemented
7#15689013C211yesmaximal, characteristic, complemented
8#15689012C211yesmaximal, characteristic, complemented
9#15689001C211yesmaximal, characteristic
10#15689001C211yesmaximal, characteristic
11#15688987C211yesmaximal, characteristic, complemented
12#15688985C211yesmaximal, characteristic, complemented
13#15688970C211yesmaximal, characteristic, complemented
14#95×D47C211yesmaximal, characteristic, complemented
15C47×#400C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21#13094009—24no—
22#13094002—24no—
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊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×C4×Dic47C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48#95×C47C2211yescharacteristic
49#95×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—22no—
69C2×D188—22no—
70C2×D188—22no—
71C2×C4×D47—22no—
72C2×C4×D47—22no—
73C2×C4×D47—22no—
74C2×C4×D47—22no—
75C2×C4×D47—22no—
76C2×C4×D47—22no—
77C2×C4×D47—22no—
78C2×C4×D47—41no—
79C2×C4×D47—41no—
80C2×Dic94—22no—
81C2×Dic94—22no—
82C2×Dic94—41no—
83C4⋊C4×C47—22no—
84C4⋊C4×C47—22no—
85(C2×D47)⋊C4—22no—
86(C2×D47)⋊C4—22no—
87(C2×D47)⋊C4—22no—
88(C2×D47)⋊C4—22no—
89(C2×D47)⋊C4—22no—
90(C2×D47)⋊C4—22no—
91(C2×D47)⋊C4—41no—
92(C2×D47)⋊C4—41no—
93(C2×D47)⋊C4D414yes—
94Dic47⋊C4—22no—
95Dic47⋊C4—22no—
96Dic47⋊C4—22no—
97C4×Dic47—22no—
98C4×Dic47—41no—
99C23×C47C2411yescharacteristic
100C22×D47—21no—
101C22×D47—21no—
102C22×D47—21no—
103C22×D47—21no—
104C22×D47—21no—
105C22×D47—21no—
106C22×D47—21no—
107C22×D47—21no—
108C22×D47—21no—
109C22×D47—21no—
110C22×D47—21no—
111C22×D47C2×D412yes—
112C22×D47#4112yes—
113C22×D47#4112yes—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
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×C47C2×D412yes—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
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×Dic47C2×D412yes—
151C2×Dic47#4112yes—
152C2×Dic47#4112yes—
153D188—44no—
154C4×D47—44no—
155C4×D47—44no—
156C4×D47—44no—
157Dic94—44no—
158C22×C47C22×D411yescharacteristic
159C22×C47C2×#4111yescharacteristic
160C22×C47C2×#4111yescharacteristic
161C22×C47C2×#4111yescharacteristic
162C22×C47C2×#4111yescharacteristic
163C22×C47H(5,𝔽2)11yescharacteristic
164C22×C472−1+411yescharacteristic
165C2×D47—22no—
166C2×D47—22no—
167C2×D47—22no—
168C2×D47—22no—
169C2×D47—22no—
170C2×D47—22no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C2×D47#12414yes—
179C4×C47—22no—
180C4×C47—41no—
181C4×C47—41no—
182C4×C47—41no—
183C4×C47—41no—
184C4×C47—41no—
185C4×C47—41no—
186Dic47—22no—
187Dic47—22no—
188Dic47—22no—
189Dic47—41no—
190Dic47—41no—
191Dic47—41no—
192#2488—471nomaximal, Sylow
193C2×C47C2×#12411yescharacteristic
194C2×C47#52911yescharacteristic
195C2×C47#53911yescharacteristic
196C2×C47#54611yescharacteristic
197C2×C47#54711yescharacteristic
198C2×C47#55111yescharacteristic
199C2×C47#55211yescharacteristic
200D47—24no—
201D47—81no—
202C2×#123—471no—
203C2×C22⋊Q8—471no—
204#400—471no—
205#400D4711yescharacteristic, complemented
206#397—471no—
207#393—471no—
208#391—471no—
209#388—471no—
210#388—471no—
211#386—471no—
212#386—471no—
213#382—471no—
214#381—471no—
215C4×C22⋊C4—471no—
216C2×#95—471no—
217C47#248811yescharacteristic, complemented, Sylow
218C22×Q8—471no—
219C22×D4—471no—
220C23×C4—471no—
221C23×C4—471no—
222C23×C4—471no—
223#123—944no—
224C22⋊Q8—944no—
225C2×C4⋊C4—471no—
226C2×C4⋊C4—471no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4C2×D4711yescharacteristic
229C2×C4⋊C4C2×D4711yescharacteristic
230C2×C22⋊C4—471no—
231C2×C22⋊C4—471no—
232C2×C22⋊C4—471no—
233C2×C22⋊C4—471no—
234C2×C22⋊C4—471no—
235C2×C22⋊C4—471no—
236C2×C22⋊C4—471no—
237C2×C22⋊C4—471no—
238C2×C22⋊C4—471no—
239C2×C42—471no—
240C2×C42—471no—
241#95—471no—
242#95—471no—
243#95—471no—
244#95—471no—
245#95—471no—
246#95—471no—
247#95—471no—
248#95—471no—
249#95—471no—
250#95C2×D4711yescharacteristic
251#95C2×D4711yescharacteristic
252#95C2×D4711yescharacteristic
253#95C2×D4711yescharacteristic
254#95C2×D4711yescharacteristic
255C24—471no—
256C24—471no—
257C2×Q8—942no—
258C2×Q8—942no—
259C2×Q8—1881no—
260C2×D4—942no—
261C2×D4—942no—
262C2×D4—942no—
263C22×C4—471no—
264C22×C4—471no—
265C22×C4—471no—
266C22×C4—471no—
267C22×C4—471no—
268C22×C4—471no—
269C22×C4—942no—
270C22×C4—942no—
271C22×C4—942no—
272C22×C4—942no—
273C22×C4—942no—
274C22×C4—942no—
275C22×C4—942no—
276C22×C4—1881no—
277C22×C4—1881no—
278C22×C4C22×D4711yescharacteristic
279C22×C4C22×D4711yescharacteristic
280C22×C4C22×D4711yescharacteristic
281C22×C4C22×D4711yescharacteristic
282C22×C4C22×D4711yescharacteristic
283C22×C4C22×D4711yescharacteristic
284C22×C4C22×D4711yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—942no—
288C4⋊C4—942no—
289C4⋊C4—942no—
290C22⋊C4—474no—
291C22⋊C4—942no—
292C22⋊C4—942no—
293C22⋊C4—942no—
294C22⋊C4—942no—
295C22⋊C4—942no—
296C22⋊C4—942no—
297C22⋊C4—1881no—
298C22⋊C4—1881no—
299C42—942no—
300C42—1881no—
301C23—472no—
302C23—472no—
303C23—472no—
304C23—941no—
305C23—941no—
306C23—941no—
307C23—941no—
308C23—941no—
309C23—941no—
310C23—941no—
311C23—941no—
312C23—941no—
313C23—941no—
314C23—941no—
315C23C23×D4711yescharacteristic
316Q8—1884no—
317D4—1884no—
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—472no—
339C2×C4—472no—
340C2×C4—472no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—1884no—
357C2×C4—1884no—
358C2×C4—1884no—
359C2×C4D4×D4712yes—
360C22—474no—
361C22—942no—
362C22—942no—
363C22—942no—
364C22—942no—
365C22—942no—
366C22—942no—
367C22—1881no—
368C22—1881no—
369C22—1881no—
370C22—1881no—
371C22—1881no—
372C22—1881no—
373C22—1881no—
374C22C2×D4×D4711yescharacteristic
375C22#41×D4711yescharacteristic
376C22#41×D4711yescharacteristic
377C22#41×D4711yescharacteristic
378C22#41×D4711yescharacteristic
379C22#1309407011yescharacteristic
380C22#1309407211yescharacteristic
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—942no—
389C4—942no—
390C4—942no—
391C4—1881no—
392C4—1881no—
393C4—1881no—
394C2—944no—
395C2—3761no—
396C2#124×D4711yescharacteristic
397C2#1568965611yescharacteristic
398C2#1568972111yescharacteristic
399C2#1568976511yescharacteristic
400C2#1568977511yescharacteristic
401C2#1568979811yescharacteristic
402C2#1568980511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2488
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×#13094002C2semidirect
3. #15689064C2semidirect
4. #15689052C2semidirect
5. #15689036C2semidirect
6. #15689028C2semidirect
7. #15689013C2semidirect
8. #15689012C2semidirect
11. #15688987C2semidirect
12. #15688985C2semidirect
13. #15688970C2semidirect
14. #95×D47C2semidirect
15. C47×#400C2semidirect
205. #400D47semidirect
217. C47#2488semidirect