Finite Group Databasebeta

← #21430713

Subgroups — #21430713

Order 7552.

554 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×#14273709C211yesmaximal, characteristic, complemented
2C2×#14273701C211yesmaximal, characteristic
3#16837336C211yesmaximal, characteristic, complemented
4#16837328C211yesmaximal, characteristic, complemented
5#16837324C211yesmaximal, characteristic, complemented
6#16837319C211yesmaximal, characteristic, complemented
7#16837318C211yesmaximal, characteristic, complemented
8#16837317C211yesmaximal, characteristic, complemented
9#16837302C211yesmaximal, characteristic, complemented
10#16837301C211yesmaximal, characteristic, complemented
11#16837291C211yesmaximal, characteristic, complemented
12#16837280C211yesmaximal, characteristic, complemented
13#16837276C211yesmaximal, characteristic, complemented
14#16837265C211yesmaximal, characteristic, complemented
15C59×#385C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C22×C22⋊D59C2211yescharacteristic
18C22×C22⋊D59C2211yescharacteristic
19C22×C4×D59C2211yescharacteristic
20#14273709—24no—
21#14273701—24no—
22C2×C4⋊Dic59C2211yescharacteristic
23C2×C4⋊Dic59C2211yescharacteristic
24C2×C4⋊Dic59C2211yescharacteristic
25C2×Dic59⋊C4C2211yescharacteristic
26C2×Dic59⋊C4C2211yescharacteristic
27C2×Dic59⋊C4C2211yescharacteristic
28C2×C22⋊Dic59C2211yescharacteristic
29C2×C22⋊Dic59C2211yescharacteristic
30C2×(C2×D59)⋊C4C2211yescharacteristic
31C2×(C2×D59)⋊C4C2211yescharacteristic
32C2×(C2×D59)⋊C4C2211yescharacteristic
33C2×(C2×D59)⋊C4C2211yescharacteristic
34C2×(C2×D59)⋊C4C2211yescharacteristic
35C2×(C2×D59)⋊C4C2211yescharacteristic
36C2×(C2×D59)⋊C4C2211yescharacteristic
37C2×(C2×D59)⋊C4C2211yescharacteristic
38C2×(C2×D59)⋊C4C2211yescharacteristic
39C2×C4×Dic59C2211yescharacteristic
40C59⋊#95C2211yescharacteristic
41C59⋊#95C2211yescharacteristic
42C59⋊#95C2211yescharacteristic
43C59⋊#95C2211yescharacteristic
44C59⋊#95C2211yescharacteristic
45C59⋊#95C2211yescharacteristic
46C23×C4×C59C2211yescharacteristic
47C2×C4⋊C4×C59C2211yescharacteristic
48C2×C4⋊C4×C59C2211yescharacteristic
49C2×C22⋊C4×C59C2211yescharacteristic
50C2×C22⋊C4×C59C2211yescharacteristic
51#95×C59C2211yescharacteristic
52#95×C59C2211yescharacteristic
53C24×C59C2311yescharacteristic
54C23×D59C2311yescharacteristic
55C23×D59C2311yescharacteristic
56C22×C4×C59—22no—
57C22×C4×C59—22no—
58C22×C4×C59—41no—
59C22×C4×C59C2311yescharacteristic
60C22×C4×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C22×C4×C59C2311yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C22×C4×C59C2311yescharacteristic
65C2×C22⋊D59—22no—
66C2×C22⋊D59—41no—
67C2×C22⋊D59—41no—
68C2×C22⋊D59—41no—
69C2×C22⋊D59—41no—
70C2×C22⋊D59D414yes—
71C22×Dic59C2311yescharacteristic
72C22×Dic59C2311yescharacteristic
73C22×Dic59C2311yescharacteristic
74C22×Dic59C2311yescharacteristic
75C22×Dic59C2311yescharacteristic
76C22×Dic59C2311yescharacteristic
77C2×D236—22no—
78C2×D236—22no—
79C2×D236—41no—
80C2×C4×D59—22no—
81C2×C4×D59—41no—
82C2×C4×D59—41no—
83C4⋊C4×C59—22no—
84C4⋊C4×C59—41no—
85C22⋊C4×C59—22no—
86C22⋊C4×C59—22no—
87C22⋊Dic59—22no—
88C22⋊Dic59—41no—
89(C2×D59)⋊C4—22no—
90(C2×D59)⋊C4—22no—
91(C2×D59)⋊C4—22no—
92(C2×D59)⋊C4—22no—
93(C2×D59)⋊C4—22no—
94(C2×D59)⋊C4—41no—
95(C2×D59)⋊C4—41no—
96(C2×D59)⋊C4—41no—
97(C2×D59)⋊C4—41no—
98C4⋊Dic59—22no—
99C4⋊Dic59—22no—
100C4⋊Dic59—41no—
101Dic59⋊C4—22no—
102Dic59⋊C4—41no—
103Dic59⋊C4—41no—
104C4×Dic59—41no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—21no—
111C23×C59C2×D412yes—
112C23×C59C2411yescharacteristic
113C22×D59—21no—
114C22×D59—21no—
115C22×D59—21no—
116C22×D59—21no—
117C22×D59—21no—
118C22×D59—21no—
119C22×D59—21no—
120C22×D59—21no—
121C22×D59—21no—
122C22×D59—21no—
123C22×D59—21no—
124C22×D59—21no—
125C22×D59—21no—
126C22×D59C2×D412yes—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—44no—
144C2×C4×C59#4112yes—
145C2×C4×C59#4112yes—
146C22⋊D59—44no—
147C22⋊D59—44no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—21no—
151C2×Dic59—21no—
152C2×Dic59—21no—
153C2×Dic59—21no—
154C2×Dic59—21no—
155C2×Dic59—21no—
156C2×Dic59—21no—
157C2×Dic59—21no—
158C2×Dic59—21no—
159C2×Dic59—21no—
160C2×Dic59—21no—
161C2×Dic59—21no—
162C2×Dic59—21no—
163C2×Dic59—21no—
164C2×Dic59—21no—
165C2×Dic59C2×D412yes—
166D236—44no—
167C4×D59—44no—
168C22×C59—22no—
169C22×C59—22no—
170C22×C59—22no—
171C22×C59—41no—
172C22×C59—41no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59C22×D411yescharacteristic
176C22×C59C2×#4111yescharacteristic
177C22×C59C2×#4111yescharacteristic
178C22×C59H(5,𝔽2)11yescharacteristic
179C22×C59H(5,𝔽2)11yescharacteristic
180C22×C59H(5,𝔽2)11yescharacteristic
181C22×C592−1+411yescharacteristic
182C2×D59—22no—
183C2×D59—22no—
184C2×D59—22no—
185C2×D59—41no—
186C2×D59—41no—
187C2×D59—41no—
188C2×D59—41no—
189C2×D59—41no—
190C2×D59—41no—
191C2×D59—41no—
192C2×D59—41no—
193C2×D59—41no—
194C2×D59—41no—
195C2×D59—41no—
196C4×C59—22no—
197C4×C59—22no—
198C4×C59—41no—
199C4×C59—41no—
200C4×C59—41no—
201C4×C59—41no—
202Dic59—22no—
203Dic59—41no—
204Dic59—41no—
205Dic59—41no—
206Dic59—41no—
207Dic59—41no—
208#2701—591nomaximal, Sylow
209C2×C59—42no—
210C2×C59#53411yescharacteristic
211C2×C59#54011yescharacteristic
212C2×C59#54211yescharacteristic
213C2×C59#54611yescharacteristic
214C2×C59#54711yescharacteristic
215C2×C59#55311yescharacteristic
216C2×C59#56211yescharacteristic
217D59—42no—
218D59—81no—
219C2×#123—591no—
220C2×#121—591no—
221#398—591no—
222#397—591no—
223#396—591no—
224#394—591no—
225#394—591no—
226#394—591no—
227#390—591no—
228#389—591no—
229#388—591no—
230#386—591no—
231#385—591no—
232#385D5911yescharacteristic, complemented
233#381—591no—
234C59#270111yescharacteristic, complemented, Sylow
235C22×D4—591no—
236C22×D4—591no—
237C22×D4—591no—
238C23×C4—591no—
239C23×C4C2×D5911yescharacteristic
240#123—1184no—
241#121—1184no—
242C2×C4⋊C4—591no—
243C2×C4⋊C4—591no—
244C2×C4⋊C4—591no—
245C2×C4⋊C4—591no—
246C2×C4⋊C4—591no—
247C2×C4⋊C4—591no—
248C2×C4⋊C4C2×D5911yescharacteristic
249C2×C4⋊C4C2×D5911yescharacteristic
250C2×C22⋊C4—591no—
251C2×C22⋊C4—591no—
252C2×C22⋊C4—591no—
253C2×C22⋊C4—591no—
254C2×C22⋊C4—591no—
255C2×C22⋊C4—591no—
256C2×C22⋊C4—591no—
257C2×C22⋊C4—591no—
258C2×C22⋊C4—591no—
259C2×C22⋊C4—591no—
260C2×C22⋊C4—591no—
261C2×C22⋊C4C2×D5911yescharacteristic
262C2×C22⋊C4C2×D5911yescharacteristic
263C2×C42—591no—
264#95—591no—
265#95—591no—
266#95—591no—
267#95—591no—
268#95—591no—
269#95—591no—
270#95C2×D5911yescharacteristic
271#95C2×D5911yescharacteristic
272C24—591no—
273C24—591no—
274C24C22×D5911yescharacteristic
275C2×D4—594no—
276C2×D4—1182no—
277C2×D4—1182no—
278C2×D4—1182no—
279C2×D4—2361no—
280C2×D4—2361no—
281C2×D4—2361no—
282C2×D4—2361no—
283C2×D4—2361no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—591no—
288C22×C4—591no—
289C22×C4—591no—
290C22×C4—591no—
291C22×C4—591no—
292C22×C4—591no—
293C22×C4—1182no—
294C22×C4—2361no—
295C22×C4—2361no—
296C22×C4C22×D5911yescharacteristic
297C22×C4C22×D5911yescharacteristic
298C22×C4C22×D5911yescharacteristic
299C22×C4C22×D5911yescharacteristic
300C22×C4C22×D5911yescharacteristic
301C22×C4C22×D5911yescharacteristic
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—1182no—
305C4⋊C4—1182no—
306C4⋊C4—1182no—
307C4⋊C4—2361no—
308C4⋊C4—2361no—
309C4⋊C4—2361no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—1182no—
313C22⋊C4—1182no—
314C22⋊C4—1182no—
315C22⋊C4—1182no—
316C22⋊C4—1182no—
317C22⋊C4—1182no—
318C22⋊C4—2361no—
319C22⋊C4—2361no—
320C22⋊C4—2361no—
321C22⋊C4—2361no—
322C22⋊C4—2361no—
323C42—2361no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—592no—
331C23—1181no—
332C23—1181no—
333C23—1181no—
334C23—1181no—
335C23—1181no—
336C23—1181no—
337C23—1181no—
338C23—1181no—
339C23—1181no—
340C23—1181no—
341C23—1181no—
342C23—1181no—
343C23—1181no—
344C23D4×D5912yes—
345C23C23×D5911yescharacteristic
346D4—2364no—
347D4—2364no—
348D4—2364no—
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—44no—
366C2×C4—592no—
367C2×C4—1181no—
368C2×C4—1181no—
369C2×C4—1181no—
370C2×C4—1181no—
371C2×C4—1181no—
372C2×C4—1181no—
373C2×C4—1181no—
374C2×C4—1181no—
375C2×C4—1181no—
376C2×C4—1181no—
377C2×C4—1181no—
378C2×C4—1181no—
379C2×C4—1181no—
380C2×C4—1181no—
381C2×C4—1181no—
382C2×C4—1181no—
383C2×C4—1181no—
384C2×C4—2364no—
385C2×C4#1174568512yes—
386C2×C4#1174568712yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—1182no—
395C22—1182no—
396C22—1182no—
397C22—2361no—
398C22—2361no—
399C22—2361no—
400C22—2361no—
401C22—2361no—
402C22—2361no—
403C22—2361no—
404C22—2361no—
405C22—2361no—
406C22—2361no—
407C22—2361no—
408C22C2×D4×D5911yescharacteristic
409C22C2×#1174568711yescharacteristic
410C22C2×#1174568511yescharacteristic
411C22#1427377211yescharacteristic
412C22#1427377311yescharacteristic
413C22#1427377311yescharacteristic
414C22#1427377511yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—1182no—
422C4—2361no—
423C4—2361no—
424C4—2361no—
425C4—2361no—
426C4—2361no—
427C2—42no—
428C2—4721no—
429C2—2362no—
430C2#1683796311yescharacteristic
431C2#1683800311yescharacteristic
432C2#1683802511yescharacteristic
433C2#1683803911yescharacteristic
434C2#1683805311yescharacteristic
435C2#1683809811yescharacteristic
436C2#1683814811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#385C2
hypercenter#385D59
hypocenterC59#2701
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14273709C2semidirect
3. #16837336C2semidirect
4. #16837328C2semidirect
5. #16837324C2semidirect
6. #16837319C2semidirect
7. #16837318C2semidirect
8. #16837317C2semidirect
9. #16837302C2semidirect
10. #16837301C2semidirect
11. #16837291C2semidirect
12. #16837280C2semidirect
13. #16837276C2semidirect
14. #16837265C2semidirect
15. C59×#385C2semidirect
232. #385D59semidirect
234. C59#2701semidirect