Finite Group Databasebeta

← #21428428

Subgroups — #21428428

Order 7552.

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×#14273711C211yesmaximal, characteristic
2#16837341C211yesmaximal, characteristic, complemented
3#16837341C211yesmaximal, characteristic, complemented
4#16837328C211yesmaximal, characteristic, complemented
5#16837313C211yesmaximal, characteristic, complemented
6#16837309C211yesmaximal, characteristic, complemented
7#16837292C211yesmaximal, characteristic, complemented
8#16837292C211yesmaximal, characteristic, complemented
9#16837281C211yesmaximal, characteristic
10#16837279C211yesmaximal, characteristic
11#16837267C211yesmaximal, characteristic, complemented
12#16837263C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic59C211yesmaximal, characteristic, complemented
14C2×C59⋊#95C211yesmaximal, characteristic, complemented
15C2×C22⋊Q8×C59C211yesmaximal, characteristic, complemented
16C22×C22⋊D59C2211yescharacteristic
17C23×Dic59C2211yescharacteristic
18C23×Dic59C2211yescharacteristic
19#14273711—24no—
20C2×C4⋊Dic59C2211yescharacteristic
21C2×C4⋊Dic59C2211yescharacteristic
22C2×C22⋊Dic59C2211yescharacteristic
23C2×(C2×D59)⋊C4C2211yescharacteristic
24C2×(C2×D59)⋊C4C2211yescharacteristic
25C2×(C2×D59)⋊C4C2211yescharacteristic
26C2×(C2×D59)⋊C4C2211yescharacteristic
27C2×(C2×D59)⋊C4C2211yescharacteristic
28C2×(C2×D59)⋊C4C2211yescharacteristic
29C2×C4×Dic59C2211yescharacteristic
30C2×C4×Dic59C2211yescharacteristic
31C59⋊#95C2211yescharacteristic
32C59⋊#95C2211yescharacteristic
33C59⋊#95C2211yescharacteristic
34C59⋊#95C2211yescharacteristic
35C59⋊#95C2211yescharacteristic
36C59⋊#95C2211yescharacteristic
37C59⋊#95C2211yescharacteristic
38C59⋊#95C2211yescharacteristic
39C59⋊#95C2211yescharacteristic
40C59⋊#95C2211yescharacteristic
41C59⋊#95C2211yescharacteristic
42C59⋊#95C2211yescharacteristic
43C59⋊#95C2211yescharacteristic
44C59⋊#95C2211yescharacteristic
45C22×Q8×C59C2211yescharacteristic
46C23×C4×C59C2211yescharacteristic
47C22⋊Q8×C59—24no—
48C2×C4⋊C4×C59C2211yescharacteristic
49C2×C4⋊C4×C59C2211yescharacteristic
50C2×C4⋊C4×C59C2211yescharacteristic
51C2×C22⋊C4×C59C2211yescharacteristic
52C2×C22⋊C4×C59C2211yescharacteristic
53C24×C59C2311yescharacteristic
54C23×D59C2311yescharacteristic
55C2×Q8×C59—22no—
56C2×Q8×C59—22no—
57C2×Q8×C59—41no—
58C22×C4×C59—22no—
59C22×C4×C59—22no—
60C22×C4×C59—41no—
61C22×C4×C59C2311yescharacteristic
62C22×C4×C59C2311yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C22×C4×C59C2311yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C2×C22⋊D59—22no—
68C2×C22⋊D59—22no—
69C2×C22⋊D59—22no—
70C22×Dic59—22no—
71C22×Dic59—22no—
72C22×Dic59—22no—
73C22×Dic59—22no—
74C22×Dic59—22no—
75C22×Dic59—41no—
76C22×Dic59C2311yescharacteristic
77C22×Dic59C2311yescharacteristic
78C22×Dic59C2311yescharacteristic
79C22×Dic59C2311yescharacteristic
80C22×Dic59C2311yescharacteristic
81C22×Dic59C2311yescharacteristic
82C22×Dic59C2311yescharacteristic
83C4⋊C4×C59—22no—
84C4⋊C4×C59—22no—
85C4⋊C4×C59—22no—
86C22⋊C4×C59—22no—
87C22⋊C4×C59D414yes—
88C22⋊Dic59—22no—
89(C2×D59)⋊C4—22no—
90(C2×D59)⋊C4—22no—
91(C2×D59)⋊C4—22no—
92(C2×D59)⋊C4—22no—
93(C2×D59)⋊C4—41no—
94(C2×D59)⋊C4—41no—
95C4⋊Dic59—22no—
96C4⋊Dic59—22no—
97C4×Dic59—22no—
98C4×Dic59—41no—
99C23×C59—21no—
100C23×C59—21no—
101C23×C59—21no—
102C23×C59—21no—
103C23×C59C2×D412yes—
104C23×C59#4112yes—
105C23×C59#4112yes—
106C23×C59C2411yescharacteristic
107C22×D59—21no—
108C22×D59—21no—
109C22×D59—21no—
110C22×D59—21no—
111C22×D59—21no—
112C22×D59—21no—
113C22×D59—21no—
114Q8×C59—44no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—44no—
131C2×C4×C59C2×D412yes—
132C2×C4×C59C2×D412yes—
133C2×C4×C59#4112yes—
134C22⋊D59—44no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—21no—
151C2×Dic59—21no—
152C2×Dic59—21no—
153C2×Dic59—21no—
154C2×Dic59—21no—
155C2×Dic59—44no—
156C2×Dic59—44no—
157C2×Dic59#4112yes—
158C22×C59—22no—
159C22×C59—22no—
160C22×C59—22no—
161C22×C59—22no—
162C22×C59—22no—
163C22×C59—22no—
164C22×C59#12414yes—
165C22×C59C22×D411yescharacteristic
166C22×C59C2×#4111yescharacteristic
167C22×C59C2×#4111yescharacteristic
168C22×C59C2×#4111yescharacteristic
169C22×C59C2×#4111yescharacteristic
170C22×C59H(5,𝔽2)11yescharacteristic
171C22×C592−1+411yescharacteristic
172C2×D59—41no—
173C2×D59—41no—
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—41no—
177C2×D59—41no—
178C2×D59—41no—
179C4×C59—22no—
180C4×C59—22no—
181C4×C59—22no—
182C4×C59—41no—
183C4×C59—41no—
184C4×C59—41no—
185Dic59—22no—
186Dic59—41no—
187Dic59—41no—
188Dic59—41no—
189Dic59—41no—
190Dic59—41no—
191Dic59—41no—
192#2488—591nomaximal, Sylow
193C2×C59—24no—
194C2×C59C2×#12411yescharacteristic
195C2×C59#52911yescharacteristic
196C2×C59#53911yescharacteristic
197C2×C59#54611yescharacteristic
198C2×C59#54711yescharacteristic
199C2×C59#55111yescharacteristic
200C2×C59#55211yescharacteristic
201D59—81no—
202C2×#123—591no—
203C2×C22⋊Q8D5911yescharacteristic, complemented
204#400—591no—
205#400—591no—
206#397—591no—
207#393—591no—
208#391—591no—
209#388—591no—
210#388—591no—
211#386—591no—
212#386—591no—
213#382—591no—
214#381—591no—
215C4×C22⋊C4—591no—
216C2×#95—591no—
217C59#248811yescharacteristic, complemented, Sylow
218C22×Q8C2×D5911yescharacteristic
219C22×D4—591no—
220C23×C4—591no—
221C23×C4—591no—
222C23×C4C2×D5911yescharacteristic
223#123—1184no—
224C22⋊Q8—24no—
225C2×C4⋊C4—591no—
226C2×C4⋊C4—591no—
227C2×C4⋊C4C2×D5911yescharacteristic
228C2×C4⋊C4C2×D5911yescharacteristic
229C2×C4⋊C4C2×D5911yescharacteristic
230C2×C22⋊C4—591no—
231C2×C22⋊C4—591no—
232C2×C22⋊C4—591no—
233C2×C22⋊C4—591no—
234C2×C22⋊C4—591no—
235C2×C22⋊C4—591no—
236C2×C22⋊C4—591no—
237C2×C22⋊C4C2×D5911yescharacteristic
238C2×C22⋊C4C2×D5911yescharacteristic
239C2×C42—591no—
240C2×C42—591no—
241#95—591no—
242#95—591no—
243#95—591no—
244#95—591no—
245#95—591no—
246#95—591no—
247#95—591no—
248#95—591no—
249#95—591no—
250#95—591no—
251#95—591no—
252#95—591no—
253#95—591no—
254#95—591no—
255C24—591no—
256C24C22×D5911yescharacteristic
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—41no—
260C2×D4—1182no—
261C2×D4—1182no—
262C2×D4—1182no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—41no—
266C22×C4—591no—
267C22×C4—591no—
268C22×C4—591no—
269C22×C4—591no—
270C22×C4—591no—
271C22×C4—591no—
272C22×C4—591no—
273C22×C4—1182no—
274C22×C4—1182no—
275C22×C4—1182no—
276C22×C4—1182no—
277C22×C4—1182no—
278C22×C4—2361no—
279C22×C4C22×D5911yescharacteristic
280C22×C4C22×D5911yescharacteristic
281C22×C4C22×D5911yescharacteristic
282C22×C4C22×D5911yescharacteristic
283C22×C4C22×D5911yescharacteristic
284C22×C4C22×D5911yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—1182no—
289C4⋊C4—1182no—
290C22⋊C4—22no—
291C22⋊C4—1182no—
292C22⋊C4—1182no—
293C22⋊C4—1182no—
294C22⋊C4—1182no—
295C22⋊C4—1182no—
296C22⋊C4—2361no—
297C22⋊C4—2361no—
298C22⋊C4C22⋊D5914yes—
299C42—1182no—
300C42—2361no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—1181no—
306C23—1181no—
307C23—1181no—
308C23—1181no—
309C23—1181no—
310C23—1181no—
311C23—1181no—
312C23#1174568912yes—
313C23#1174568912yes—
314C23C2×C22⋊D5912yes—
315C23C23×D5911yescharacteristic
316Q8—44no—
317D4—2364no—
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—44no—
334C2×C4—592no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—1181no—
341C2×C4—1181no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—1181no—
348C2×C4—1181no—
349C2×C4—1181no—
350C2×C4—1181no—
351C2×C4—1181no—
352C2×C4—1181no—
353C2×C4—1181no—
354C2×C4—1181no—
355C2×C4—2364no—
356C2×C4—2364no—
357C2×C4#1174568712yes—
358C2×C4C2×C22⋊D5912yes—
359C2×C4C2×C22⋊D5912yes—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—2361no—
367C22—2361no—
368C22—2361no—
369C22—2361no—
370C22—2361no—
371C22—2361no—
372C22—2361no—
373C22#1427371614yes—
374C22C22×C22⋊D5911yescharacteristic
375C22#41×D5911yescharacteristic
376C22C2×#1174568711yescharacteristic
377C22C2×#1174568911yescharacteristic
378C22C2×#1174568911yescharacteristic
379C22#1427377211yescharacteristic
380C22#1427377411yescharacteristic
381C4—22no—
382C4—22no—
383C4—22no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—1182no—
388C4—2361no—
389C4—2361no—
390C4—2361no—
391C4—2361no—
392C4—2361no—
393C4—2361no—
394C2—24no—
395C2—4721no—
396C2C2×#1427371611yescharacteristic
397C2#1683793811yescharacteristic
398C2#1683800111yescharacteristic
399C2#1683804611yescharacteristic
400C2#1683805111yescharacteristic
401C2#1683807911yescharacteristic
402C2#1683809411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC2×C22⋊Q8×C59C2
hypercenterC2×C22⋊Q8D59
hypocenterC59#2488
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16837341C2semidirect
3. #16837341C2semidirect
4. #16837328C2semidirect
5. #16837313C2semidirect
6. #16837309C2semidirect
7. #16837292C2semidirect
8. #16837292C2semidirect
11. #16837267C2semidirect
12. #16837263C2semidirect
13. C22⋊C4×Dic59C2semidirect
14. C2×C59⋊#95C2semidirect
15. C2×C22⋊Q8×C59C2semidirect
203. C2×C22⋊Q8D59semidirect
217. C59#2488semidirect