Finite Group Databasebeta

← #28507388

Subgroups — #28507388

Order 15104.

618 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837640C211yesmaximal, characteristic, complemented
2C2×#16837635C211yesmaximal, characteristic
3C2×#16837206C211yesmaximal, characteristic, complemented
4C2×#16837203C211yesmaximal, characteristic, complemented
5C2×(C2×D59)⋊C16C211yesmaximal, characteristic, complemented
6#21422188C211yesmaximal, characteristic, complemented
7C22×SD32×C59C211yesmaximal, characteristic, complemented
8C22×C8×D59C2211yescharacteristic
9C2×#14273703—21no—
10C2×#14273698—21no—
11C22×C59⋊C16C2211yescharacteristic
12#16837640—22no—
13#16837640—22no—
14#16837635—22no—
15#16837635—22no—
16C2×#14273661C2211yescharacteristic
17C2×#14273661C2211yescharacteristic
18C2×#14273651—21no—
19C2×#14273648—21no—
20#16837206—22no—
21#16837203—22no—
22(C2×D59)⋊C16—22no—
23C22×Q16×C59C2211yescharacteristic
24C22×D8×C59C2211yescharacteristic
25C2×SD32×C59—22no—
26C2×SD32×C59—22no—
27C2×SD32×C59—22no—
28C22×C16×C59C2211yescharacteristic
29C22×C22⋊D59—41no—
30C22×C4×D59D411yescharacteristic
31C22×C59⋊C8D411yescharacteristic
32C2×C8×D59—21no—
33C2×C8×D59—21no—
34C2×C8×D59—21no—
35C2×C8×D59—21no—
36C2×C8×D59—21no—
37C2×C8×D59—21no—
38#14273703—24no—
39#14273703—42no—
40#14273698—24no—
41#14273698—42no—
42C2×C4⋊Dic59—21no—
43C2×C4⋊Dic59—21no—
44C2×Dic59⋊C4—41no—
45C2×C22⋊Dic59—41no—
46C2×(C2×D59)⋊C4—41no—
47C2×C59⋊C16—21no—
48C2×C59⋊C16—21no—
49C2×C59⋊C16—21no—
50#14273661—21no—
51#14273661—21no—
52#14273661D412yes—
53#14273661D412yescomplemented
54#14273651—24no—
55#14273648—24no—
56C22×Q8×C59—21no—
57C22×D4×C59—21no—
58C2×Q16×C59—21no—
59C2×Q16×C59—21no—
60C2×Q16×C59—21no—
61C2×Q16×C59—21no—
62C2×Q16×C59—21no—
63C2×Q16×C59D412yescomplemented
64C2×D8×C59—21no—
65C2×D8×C59—21no—
66C2×D8×C59—21no—
67C2×D8×C59—21no—
68C2×D8×C59—21no—
69C2×D8×C59D412yes—
70C22×C8×C59C2311yescharacteristic
71SD32×C59—28no—
72C2×C16×C59—21no—
73C2×C16×C59—21no—
74C2×C16×C59D412yescomplemented
75C24×C59—41no—
76C23×D59D811yescharacteristic
77C2×Q8×C59—22no—
78C2×Q8×C59—41no—
79C2×Q8×C59—41no—
80C2×Q8×C59—41no—
81C2×Q8×C59—41no—
82C2×Q8×C59—41no—
83C2×D4×C59—22no—
84C2×D4×C59—41no—
85C2×D4×C59—41no—
86C2×D4×C59—41no—
87C2×D4×C59—41no—
88C2×D4×C59—41no—
89C22×C4×C59—41no—
90C22×C4×C59C2×D411yescharacteristic
91C2×C22⋊D59—44no—
92C2×C22⋊D59—82no—
93C2×C22⋊D59—82no—
94C22×Dic59—41no—
95C22×Dic59—41no—
96C22×Dic59D811yescharacteristic
97C2×C4×D59—21no—
98C2×C4×D59—21no—
99C2×C4×D59—21no—
100C2×C4×D59—21no—
101C2×C4×D59—21no—
102C2×C4×D59—21no—
103Q16×C59—22no—
104Q16×C59—22no—
105Q16×C59—41no—
106Q16×C59—41no—
107D8×C59—22no—
108D8×C59—22no—
109D8×C59—41no—
110D8×C59—41no—
111C2×C8×C59C2×D411yescharacteristic
112C2×C8×C59C2×D411yescharacteristic
113C2×C8×C59C2×D411yescharacteristic
114C2×C8×C59C2×D411yescharacteristic
115C2×C8×C59C2×D411yescharacteristic
116C2×C8×C59#4111yescharacteristic
117C22⋊Dic59—44no—
118(C2×D59)⋊C4—44no—
119C4⋊Dic59—22no—
120C4⋊Dic59—22no—
121C4⋊Dic59—41no—
122C4⋊Dic59—41no—
123Dic59⋊C4—44no—
124C2×C59⋊C8—21no—
125C2×C59⋊C8—21no—
126C2×C59⋊C8—21no—
127C8×D59—41no—
128C8×D59—41no—
129C8×D59—41no—
130C8×D59—41no—
131C16×C59—22no—
132C59⋊C16—41no—
133C23×C59—42no—
134C23×C59—81no—
135C23×C59—81no—
136C23×C59—81no—
137C23×C59—81no—
138C23×C59—81no—
139C23×C59—81no—
140C23×C59C2×D811yescharacteristic
141C22×D59—21no—
142C22×D59—21no—
143C22×D59—21no—
144C22×D59—21no—
145C22×D59—21no—
146C22×D59—21no—
147C22×D59SD3212yescomplemented
148Q8×C59—42no—
149Q8×C59—42no—
150Q8×C59—81no—
151Q8×C59—81no—
152D4×C59—42no—
153D4×C59—42no—
154D4×C59—81no—
155D4×C59—81no—
156C2×C4×C59—42no—
157C2×C4×C59—81no—
158C2×C4×C59—81no—
159C2×C4×C59#12011yescharacteristic
160C2×C4×C59#12011yescharacteristic
161C2×C4×C59#12111yescharacteristic
162C2×C4×C59#13511yescharacteristic
163C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
165C22⋊D59—88no—
166C2×Dic59—21no—
167C2×Dic59—21no—
168C2×Dic59—21no—
169C2×Dic59—42no—
170C2×Dic59—42no—
171C2×Dic59—81no—
172C2×Dic59—81no—
173C2×Dic59—81no—
174C2×Dic59—81no—
175C4×D59—41no—
176C4×D59—41no—
177C4×D59—41no—
178C4×D59—41no—
179C8×C59#12011yescharacteristic
180C8×C59#12111yescharacteristic
181C8×C59#12111yescharacteristic
182C8×C59#12711yescharacteristic
183C59⋊C8—41no—
184#13305—591nomaximal, Sylow
185C22×C59—82no—
186C22×C59—82no—
187C22×C59—82no—
188C22×C59—161no—
189C22×C59—161no—
190C22×C59—161no—
191C22×C59—161no—
192C22×C59#44711yescharacteristic
193C22×C59#44711yescharacteristic
194C22×C59#46611yescharacteristic
195C22×C59C2×SD3211yescharacteristic
196C22×C59#50811yescharacteristic
197C22×C59#50911yescharacteristic
198C22×C59#51011yescharacteristic
199C2×D59—22no—
200C2×D59—22no—
201C2×D59—22no—
202C2×D59—41no—
203C2×D59—41no—
204C2×D59—41no—
205C2×D59—41no—
206C4×C59—82no—
207C4×C59#39211yescharacteristic
208C4×C59#44911yescharacteristic
209C4×C59#44911yescharacteristic
210C4×C59#46911yescharacteristic
211Dic59—41no—
212Dic59—82no—
213Dic59—82no—
214C22×SD32D5911yescharacteristic, complemented
215C2×#467—591no—
216C2×#466—591no—
217C2×#358—591no—
218C2×#357—591no—
219C2×C22⋊C16—591no—
220#1380—591no—
221C2×C59—162no—
222C2×C59#199911yescharacteristic
223C2×C59#218511yescharacteristic
224C2×C59#218611yescharacteristic
225C2×C59#218711yescharacteristic
226C2×C59#218911yescharacteristic
227C2×C59#221711yescharacteristic
228C2×C59#222011yescharacteristic
229D59—42no—
230C22×Q16C2×D5911yescharacteristic
231C22×D8C2×D5911yescharacteristic
232C23×C8—591no—
233C2×C22⋊Q8—1181no—
234C2×#121—1181no—
235C2×SD32—22no—
236C2×SD32—22no—
237C2×SD32—22no—
238C22×C16—591no—
239C22×C16C2×D5911yescharacteristic
240#467—1182no—
241#467—1182no—
242#466—1182no—
243#466—1182no—
244C2×#107—591no—
245C2×#107—591no—
246C2×#103—1181no—
247C2×#102—1181no—
248#358—1182no—
249#357—1182no—
250C22⋊C16—1182no—
251C59#1330511yescharacteristic, complemented, Sylow
252C22×Q8—21no—
253C22×D4—21no—
254C22×D4—2361no—
255C23×C4—591no—
256C2×Q16—21no—
257C2×Q16—21no—
258C2×Q16—21no—
259C2×Q16—21no—
260C2×Q16—21no—
261C2×Q16C22⋊D5912yescomplemented
262C2×D8—21no—
263C2×D8—21no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8C22⋊D5912yes—
268C22×C8—591no—
269C22×C8—1181no—
270C22×C8—1181no—
271C22×C8—1181no—
272C22×C8—1181no—
273C22×C8—1181no—
274C22×C8—1181no—
275C22×C8C22×D5911yescharacteristic
276C22⋊Q8—1184no—
277C22⋊Q8—2362no—
278#121—1184no—
279#121—2362no—
280C2×C4⋊C4—1181no—
281C2×C4⋊C4—1181no—
282C2×C4⋊C4—2361no—
283C2×C22⋊C4—2361no—
284C2×C22⋊C4—2361no—
285SD32—28no—
286C2×C16—21no—
287C2×C16—21no—
288C2×C16—1181no—
289C2×C16—1181no—
290C2×C16—1181no—
291C2×C16C22⋊D5912yescomplemented
292#107—592no—
293#107—592no—
294#107—1181no—
295#107—1181no—
296#103—1184no—
297#102—1184no—
298C24—41no—
299C24—591no—
300C2×Q8—22no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×D4—22no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—4722no—
313C2×D4—4722no—
314C2×D4—2364no—
315C22×C4—41no—
316C22×C4—591no—
317C22×C4—1181no—
318C22×C4—1181no—
319C22×C4—1181no—
320C22×C4—1181no—
321C22×C4—1181no—
322C22×C4—1181no—
323C22×C4—2361no—
324C22×C4—2361no—
325C22×C4D4×D5911yescharacteristic
326Q16—22no—
327Q16—22no—
328Q16—41no—
329Q16—41no—
330D8—22no—
331D8—22no—
332D8—41no—
333D8—41no—
334C2×C8—1181no—
335C2×C8—1181no—
336C2×C8—1181no—
337C2×C8—2361no—
338C2×C8—2361no—
339C2×C8—2361no—
340C2×C8—2361no—
341C2×C8D4×D5911yescharacteristic
342C2×C8D4×D5911yescharacteristic
343C2×C8#1174568711yescharacteristic
344C2×C8C2×C22⋊D5911yescharacteristic
345C2×C8C2×C22⋊D5911yescharacteristic
346C2×C8C2×C22⋊D5911yescharacteristic
347C4⋊C4—1182no—
348C4⋊C4—1182no—
349C4⋊C4—2364no—
350C4⋊C4—2361no—
351C4⋊C4—2361no—
352C22⋊C4—2364no—
353C22⋊C4—2364no—
354C16—22no—
355C16—2361no—
356C23—42no—
357C23—81no—
358C23—81no—
359C23—81no—
360C23—81no—
361C23—81no—
362C23—81no—
363C23—592no—
364C23—1181no—
365C23—1181no—
366C23—1181no—
367C23—1181no—
368C23—1181no—
369C23—1181no—
370C23D8×D5911yescharacteristic
371Q8—42no—
372Q8—42no—
373Q8—81no—
374Q8—81no—
375D4—42no—
376D4—42no—
377D4—81no—
378D4—81no—
379D4—4728no—
380C2×C4—42no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—1181no—
384C2×C4—1181no—
385C2×C4—1181no—
386C2×C4—4721no—
387C2×C4—4721no—
388C2×C4—4721no—
389C2×C4—4721no—
390C2×C4—2362no—
391C2×C4—2362no—
392C2×C4—2361no—
393C2×C4—2361no—
394C2×C4—2361no—
395C2×C4—2361no—
396C2×C4#1427369511yescharacteristic
397C2×C4#1427369511yescharacteristic
398C2×C4#1427369811yescharacteristic
399C2×C4#1427374611yescharacteristic
400C2×C4#1427375111yescharacteristic
401C2×C4#1427375111yescharacteristic
402C8—2361no—
403C8#1427369611yescharacteristic
404C8#1427369911yescharacteristic
405C8#1427369911yescharacteristic
406C8#1427372311yescharacteristic
407C22—82no—
408C22—82no—
409C22—82no—
410C22—161no—
411C22—161no—
412C22—161no—
413C22—161no—
414C22—1182no—
415C22—1182no—
416C22—1182no—
417C22—2361no—
418C22—2361no—
419C22—2361no—
420C22—2361no—
421C22#1683753411yescharacteristic
422C22#1683753411yescharacteristic
423C22#1683763511yescharacteristic
424C22SD32×D5911yescharacteristic
425C22#1683783311yescharacteristic
426C22#1683783911yescharacteristic
427C22#1683784111yescharacteristic
428C4—82no—
429C4—4722no—
430C4—4722no—
431C4—2361no—
432C4#1683731011yescharacteristic
433C4#1683754411yescharacteristic
434C4#1683754411yescharacteristic
435C4#1683765211yescharacteristic
436C2—162no—
437C2—2362no—
438C2#2142509111yescharacteristic
439C2#2142601111yescharacteristic
440C2#2142601811yescharacteristic
441C2#2142602311yescharacteristic
442C2#2142603311yescharacteristic
443C2#2142618911yescharacteristic
444C2#2142620611yescharacteristic
subgroupG/H
centerC23D8×D59
commutator, cosocleC22×C8×C59C23
FrattiniC22×C8C22×D59
FittingC22×SD32×C59C2
socleC23×C59C2×D8
prime radicalC2×#16837635C2
hypercenterC22×SD32D59
hypocenterC59#13305
LCSG ▷ C22×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#16837640C2semidirect
3. C2×#16837206C2semidirect
4. C2×#16837203C2semidirect
5. C2×(C2×D59)⋊C16C2semidirect
6. #21422188C2semidirect
7. C22×SD32×C59C2semidirect
53. #14273661D4semidirect
63. C2×Q16×C59D4semidirect
74. C2×C16×C59D4semidirect
147. C22×D59SD32semidirect
214. C22×SD32D59semidirect
251. C59#13305semidirect
261. C2×Q16C22⋊D59semidirect
291. C2×C16C22⋊D59semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168376402
C2×#168376352
C2×#168372062
C2×#168372032
C2×(C2×D59)⋊C162
#214221882
C22×SD32×C592
#1330559