Finite Group Databasebeta

← #21427840

Subgroups — #21427840

Order 7552.

610 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273699C211yesmaximal, characteristic
2#16837340C211yesmaximal, characteristic, complemented
3#16837330C211yesmaximal, characteristic, complemented
4#16837328C211yesmaximal, characteristic, complemented
5#16837317C211yesmaximal, characteristic, complemented
6#16837293C211yesmaximal, characteristic, complemented
7#16837286C211yesmaximal, characteristic, complemented
8#16837282C211yesmaximal, characteristic, complemented
9#16837281C211yesmaximal, characteristic, complemented
10#16837281C211yesmaximal, characteristic, complemented
11#16837279C211yesmaximal, characteristic, complemented
12#16837274C211yesmaximal, characteristic, complemented
13#16837265C211yesmaximal, characteristic, complemented
14C2×C59⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×D4×C59C211yesmaximal, characteristic, complemented
16C22×C22⋊D59C2211yescharacteristic
17C22×C22⋊D59C2211yescharacteristic
18C23×Dic59C2211yescharacteristic
19C23×Dic59C2211yescharacteristic
20#14273699—24no—
21C2×Dic59⋊C4C2211yescharacteristic
22C2×Dic59⋊C4C2211yescharacteristic
23C2×Dic59⋊C4C2211yescharacteristic
24C2×C22⋊Dic59C2211yescharacteristic
25C2×C22⋊Dic59C2211yescharacteristic
26C2×C22⋊Dic59C2211yescharacteristic
27C2×C22⋊Dic59C2211yescharacteristic
28C2×(C2×D59)⋊C4C2211yescharacteristic
29C2×(C2×D59)⋊C4C2211yescharacteristic
30C2×(C2×D59)⋊C4C2211yescharacteristic
31C2×(C2×D59)⋊C4C2211yescharacteristic
32C2×(C2×D59)⋊C4C2211yescharacteristic
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×D4×C59C2211yescharacteristic
46C23×C4×C59C2211yescharacteristic
47C23×C4×C59C2211yescharacteristic
48C4×D4×C59—24no—
49C2×C4⋊C4×C59C2211yescharacteristic
50C2×C22⋊C4×C59C2211yescharacteristic
51C2×C22⋊C4×C59C2211yescharacteristic
52C2×C42×C59C2211yescharacteristic
53C24×C59C2311yescharacteristic
54C24×C59C2311yescharacteristic
55C23×D59C2311yescharacteristic
56C2×D4×C59—22no—
57C2×D4×C59—22no—
58C2×D4×C59D414yes—
59C22×C4×C59—22no—
60C22×C4×C59—22no—
61C22×C4×C59—22no—
62C22×C4×C59—22no—
63C22×C4×C59—41no—
64C22×C4×C59—41no—
65C22×C4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C22×C4×C59C2311yescharacteristic
68C22×C4×C59C2311yescharacteristic
69C22×C4×C59C2311yescharacteristic
70C2×C22⋊D59—22no—
71C2×C22⋊D59—22no—
72C2×C22⋊D59—22no—
73C2×C22⋊D59—22no—
74C2×C22⋊D59—22no—
75C2×C22⋊D59—41no—
76C22×Dic59—22no—
77C22×Dic59—22no—
78C22×Dic59—22no—
79C22×Dic59—41no—
80C22×Dic59—41no—
81C22×Dic59—41no—
82C22×Dic59C2311yescharacteristic
83C22×Dic59C2311yescharacteristic
84C22×Dic59C2311yescharacteristic
85C22×Dic59C2311yescharacteristic
86C22×Dic59C2311yescharacteristic
87C22×Dic59C2311yescharacteristic
88C22×Dic59C2311yescharacteristic
89C4⋊C4×C59—22no—
90C22⋊C4×C59—22no—
91C22⋊C4×C59—22no—
92C42×C59—22no—
93C22⋊Dic59—22no—
94C22⋊Dic59—22no—
95C22⋊Dic59—41no—
96C22⋊Dic59—41no—
97(C2×D59)⋊C4—22no—
98(C2×D59)⋊C4—22no—
99(C2×D59)⋊C4—41no—
100(C2×D59)⋊C4—41no—
101(C2×D59)⋊C4—41no—
102Dic59⋊C4—22no—
103Dic59⋊C4—22no—
104Dic59⋊C4—41no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—21no—
111C23×C59—21no—
112C23×C59—21no—
113C23×C59—21no—
114C23×C59—21no—
115C23×C59C2×D412yes—
116C23×C59C2×D412yes—
117C23×C59#4112yes—
118C23×C59#4112yes—
119C23×C59C2411yescharacteristic
120C22×D59—21no—
121C22×D59—21no—
122C22×D59—21no—
123C22×D59—21no—
124C22×D59—21no—
125C22×D59—21no—
126C22×D59—21no—
127D4×C59—28no—
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—44no—
142C2×C4×C59—44no—
143C2×C4×C59C2×D412yes—
144C2×C4×C59#4112yes—
145C22⋊D59—44no—
146C22⋊D59—44no—
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—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×Dic59—21no—
166C2×Dic59—21no—
167C2×Dic59—44no—
168C2×Dic59—44no—
169C2×Dic59#4112yes—
170C22×C59—22no—
171C22×C59—22no—
172C22×C59—22no—
173C22×C59—22no—
174C22×C59—22no—
175C22×C59—22no—
176C22×C59—22no—
177C22×C59—22no—
178C22×C59—22no—
179C22×C59—41no—
180C22×C59—41no—
181C22×C59—41no—
182C22×C59—41no—
183C22×C59#12314yes—
184C22×C59C22×D411yescharacteristic
185C22×C59C2×#4111yescharacteristic
186C22×C59C2×#4111yescharacteristic
187C22×C59C2×#4111yescharacteristic
188C22×C59C2×#4111yescharacteristic
189C22×C59H(5,𝔽2)11yescharacteristic
190C22×C59H(5,𝔽2)11yescharacteristic
191C2×D59—41no—
192C2×D59—41no—
193C2×D59—41no—
194C2×D59—41no—
195C2×D59—41no—
196C2×D59—41no—
197C2×D59—41no—
198C4×C59—22no—
199C4×C59—22no—
200C4×C59—41no—
201C4×C59—41no—
202C4×C59—41no—
203Dic59—22no—
204Dic59—41no—
205Dic59—41no—
206Dic59—41no—
207Dic59—41no—
208Dic59—41no—
209Dic59—41no—
210#2444—591nomaximal, Sylow
211C2×C59—24no—
212C2×C59—42no—
213C2×C59C2×#12311yescharacteristic
214C2×C59#52911yescharacteristic
215C2×C59#53811yescharacteristic
216C2×C59#54611yescharacteristic
217C2×C59#54611yescharacteristic
218C2×C59#55311yescharacteristic
219C2×C59#55311yescharacteristic
220D59—81no—
221C2×#121—591no—
222C2×C4×D4D5911yescharacteristic, complemented
223#400—591no—
224#397—591no—
225#397—591no—
226#394—591no—
227#388—591no—
228#387—591no—
229#386—591no—
230#386—591no—
231#386—591no—
232#386—591no—
233#385—591no—
234#381—591no—
235C2×#95—591no—
236C59#244411yescharacteristic, complemented, Sylow
237C22×D4—591no—
238C22×D4—591no—
239C22×D4C2×D5911yescharacteristic
240C23×C4—591no—
241C23×C4—591no—
242C23×C4C2×D5911yescharacteristic
243C23×C4C2×D5911yescharacteristic
244#121—1184no—
245C4×D4—24no—
246C2×C4⋊C4—591no—
247C2×C4⋊C4—591no—
248C2×C4⋊C4—591no—
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⋊C4C2×D5911yescharacteristic
260C2×C22⋊C4C2×D5911yescharacteristic
261C2×C42C2×D5911yescharacteristic
262#95—591no—
263#95—591no—
264#95—591no—
265#95—591no—
266#95—591no—
267#95—591no—
268#95—591no—
269#95—591no—
270#95—591no—
271#95—591no—
272#95—591no—
273#95—591no—
274C24—591no—
275C24C22×D5911yescharacteristic
276C24C22×D5911yescharacteristic
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—1182no—
280C2×D4—1182no—
281C2×D4—1182no—
282C2×D4—1182no—
283C2×D4—1182no—
284C2×D4—2361no—
285C2×D4C22⋊D5914yes—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—591no—
293C22×C4—591no—
294C22×C4—591no—
295C22×C4—591no—
296C22×C4—591no—
297C22×C4—591no—
298C22×C4—591no—
299C22×C4—1182no—
300C22×C4—1182no—
301C22×C4—1182no—
302C22×C4—2361no—
303C22×C4—2361no—
304C22×C4—2361no—
305C22×C4C22×D5911yescharacteristic
306C22×C4C22×D5911yescharacteristic
307C22×C4C22×D5911yescharacteristic
308C22×C4C22×D5911yescharacteristic
309C22×C4C22×D5911yescharacteristic
310C4⋊C4—22no—
311C4⋊C4—1182no—
312C4⋊C4—1182no—
313C4⋊C4—2361no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—1182no—
317C22⋊C4—1182no—
318C22⋊C4—1182no—
319C22⋊C4—1182no—
320C22⋊C4—2361no—
321C22⋊C4—2361no—
322C22⋊C4—2361no—
323C22⋊C4—2361no—
324C22⋊C4—2361no—
325C42—22no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—1181no—
337C23—1181no—
338C23—1181no—
339C23—1181no—
340C23—1181no—
341C23—1181no—
342C23—1181no—
343C23#1174568512yes—
344C23#1174568512yes—
345C23C2×C22⋊D5912yes—
346C23C2×C22⋊D5912yes—
347C23C23×D5911yescharacteristic
348D4—28no—
349D4—2364no—
350D4—2364no—
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—44no—
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—1181no—
385C2×C4—1181no—
386C2×C4—1181no—
387C2×C4—2364no—
388C2×C4—2364no—
389C2×C4#1174568712yes—
390C2×C4C2×C22⋊D5912yes—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—2361no—
405C22—2361no—
406C22—2361no—
407C22—2361no—
408C22—2361no—
409C22—2361no—
410C22—2361no—
411C22#1427371014yes—
412C22C22×C22⋊D5911yescharacteristic
413C22#41×D5911yescharacteristic
414C22C2×#1174568711yescharacteristic
415C22C2×#1174568511yescharacteristic
416C22C2×#1174568511yescharacteristic
417C22#1427377211yescharacteristic
418C22#1427377311yescharacteristic
419C4—22no—
420C4—22no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—1182no—
425C4—2361no—
426C4—2361no—
427C4—2361no—
428C4—2361no—
429C4—2361no—
430C4—2361no—
431C2—24no—
432C2—42no—
433C2—4721no—
434C2C2×#1427371011yescharacteristic
435C2#1683793211yescharacteristic
436C2#1683798511yescharacteristic
437C2#1683804011yescharacteristic
438C2#1683804611yescharacteristic
439C2#1683809811yescharacteristic
440C2#1683810111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC2×C4×D4×C59C2
hypercenterC2×C4×D4D59
hypocenterC59#2444
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #16837340C2semidirect
3. #16837330C2semidirect
4. #16837328C2semidirect
5. #16837317C2semidirect
6. #16837293C2semidirect
7. #16837286C2semidirect
8. #16837282C2semidirect
9. #16837281C2semidirect
10. #16837281C2semidirect
11. #16837279C2semidirect
12. #16837274C2semidirect
13. #16837265C2semidirect
14. C2×C59⋊#95C2semidirect
15. C2×C4×D4×C59C2semidirect
222. C2×C4×D4D59semidirect
236. C59#2444semidirect