Finite Group Databasebeta

← #28491860

Subgroups — #28491860

Order 15104.

422 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21429320C211yesmaximal, characteristic
2#21425082C211yesmaximal, characteristic
3#21422668C211yesmaximal, characteristic
4#21421975C211yesmaximal, characteristic
5#21421964C211yesmaximal, characteristic
6#21421942C211yesmaximal, characteristic
7C2×C59×#328C211yesmaximal, characteristic
8C2×C22⋊(C59⋊C8)C2211yescharacteristic
9#16837344—21no—
10#16837334—21no—
11#16837289—21no—
12#16837285—21no—
13#16837275—21no—
14#16837262—21no—
15#16837262C2211yescharacteristic
16#16837262C2211yescharacteristic
17C4×C22⋊Dic59C2211yescharacteristic
18#16837169—21no—
19#16837169—21no—
20#16837139—21no—
21#16837139—21no—
22C2×C22⋊Q8×C59C2211yescharacteristic
23C2×C22⋊C8×C59C2211yescharacteristic
24C2×#95×C59C2211yescharacteristic
25C59×#328—21no—
26C59×#328—21no—
27C22×C59⋊C8—21no—
28C2×C4⋊Dic59—21no—
29C2×C4⋊Dic59—21no—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59—21no—
32C2×Dic59⋊C4—21no—
33C2×Dic59⋊C4—21no—
34C2×C22⋊Dic59—21no—
35C2×C22⋊Dic59—21no—
36C2×C22⋊Dic59D411yescharacteristic
37C2×C22⋊Dic59D411yescharacteristic
38C2×C4×Dic59—21no—
39C22⋊(C59⋊C8)—21no—
40C22⋊(C59⋊C8)—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95D411yescharacteristic
48C59⋊#95D411yescharacteristic
49C22×Q8×C59Q811yescharacteristic
50C23×C4×C59—21no—
51C23×C4×C59C2311yescharacteristic
52C22×C8×C59—21no—
53C22⋊Q8×C59—21no—
54C22⋊Q8×C59—21no—
55C22⋊Q8×C59—21no—
56C22⋊Q8×C59—21no—
57C2×C4⋊C4×C59—21no—
58C2×C4⋊C4×C59Q811yescharacteristic
59C2×C22⋊C4×C59—21no—
60C22⋊C8×C59—21no—
61C22⋊C8×C59—21no—
62#95×C59—21no—
63#95×C59D411yescharacteristic
64#95×C59D411yescharacteristic
65C24×C59C2×D411yescharacteristic
66C2×Q8×C59—21no—
67C2×Q8×C59—21no—
68C2×Q8×C59—81no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59—42no—
74C22×C4×C59—41no—
75C22×C4×C59—41no—
76C22×C4×C59—81no—
77C22×C4×C59—81no—
78C22×C4×C59C2×D411yescharacteristic
79C22×C4×C59C2×D411yescharacteristic
80C22×C4×C59C2×Q811yescharacteristic
81C22×C4×C59#4111yescharacteristic
82C22×C4×C59#4111yescharacteristic
83C22×C4×C59#4111yescharacteristic
84C22×Dic59—21no—
85C22×Dic59—21no—
86C22×Dic59—21no—
87C22×Dic59—21no—
88C22×Dic59—41no—
89C2×C8×C59—41no—
90C2×C8×C59—81no—
91C4⋊C4×C59—21no—
92C4⋊C4×C59—21no—
93C4⋊C4×C59—41no—
94C4⋊C4×C59—41no—
95C22⋊C4×C59—41no—
96C22⋊C4×C59—41no—
97C22⋊Dic59—21no—
98C22⋊Dic59—21no—
99C22⋊Dic59—21no—
100C22⋊Dic59—21no—
101C22⋊Dic59—41no—
102C22⋊Dic59—41no—
103C22⋊Dic59—41no—
104C22⋊Dic59—41no—
105C4⋊Dic59—42no—
106C4⋊Dic59—81no—
107C4⋊Dic59—81no—
108C4⋊Dic59—81no—
109Dic59⋊C4—42no—
110Dic59⋊C4—81no—
111C4×Dic59—81no—
112C2×C59⋊C8—41no—
113C2×C59⋊C8—81no—
114C23×C59—41no—
115C23×C59—41no—
116C23×C59#12011yescharacteristic
117C23×C59C22⋊Q811yescharacteristic
118C23×C59#12411yescharacteristic
119C23×C59#13511yescharacteristic
120C23×C59#13511yescharacteristic
121C23×C59#13711yescharacteristic
122C23×C59#13711yescharacteristic
123Q8×C59—81no—
124Q8×C59—81no—
125C2×C4×C59—22no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59—41no—
131C2×C4×C59—41no—
132C2×C4×C59—41no—
133C2×C4×C59—41no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59—41no—
137C2×C4×C59—41no—
138C2×C4×C59—41no—
139C2×C4×C59—82no—
140C2×C4×C59—82no—
141C2×C4×C59—81no—
142C2×C4×C59—81no—
143C2×C4×C59C22⋊Q811yescharacteristic
144C2×C4×C59C22⋊Q811yescharacteristic
145C2×C4×C59#12411yescharacteristic
146C2×C4×C59#12411yescharacteristic
147C2×Dic59—41no—
148C2×Dic59—41no—
149C2×Dic59—41no—
150C2×Dic59—41no—
151C2×Dic59—41no—
152C2×Dic59—41no—
153C2×Dic59—41no—
154C2×Dic59—41no—
155C2×Dic59—41no—
156C2×Dic59—41no—
157C2×Dic59—41no—
158C2×Dic59—41no—
159C2×Dic59—81no—
160C2×Dic59—81no—
161C2×Dic59—81no—
162C8×C59—81no—
163C59⋊C8—81no—
164#10377—591nomaximal, Sylow
165C22×C59—21no—
166C22×C59—21no—
167C22×C59—21no—
168C22×C59—21no—
169C22×C59—21no—
170C22×C59—21no—
171C22×C59—41no—
172C22×C59—41no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59#39311yescharacteristic
176C22×C59#45211yescharacteristic
177C22×C59#45211yescharacteristic
178C22×C59#47911yescharacteristic
179C22×C59#47911yescharacteristic
180C22×C59#48811yescharacteristic
181C22×C59#49111yescharacteristic
182C4×C59—21no—
183C4×C59—21no—
184C4×C59—21no—
185C4×C59—21no—
186C4×C59—42no—
187C4×C59—81no—
188C4×C59—81no—
189C4×C59—81no—
190Dic59—81no—
191Dic59—81no—
192Dic59—81no—
193Dic59—81no—
194Dic59—161no—
195#2569—591no—
196#1996—591no—
197#1520—591no—
198C2×#328D5911yescharacteristic
199#1294—591no—
200#1289—591no—
201#1282—591no—
202C2×C59—21no—
203C2×C59—21no—
204C2×C59—21no—
205C2×C59—21no—
206C2×C59—21no—
207C2×C59—21no—
208C2×C59#202611yescharacteristic
209C2×C59#203111yescharacteristic
210C2×C59#203211yescharacteristic
211C2×C22⋊Q8C2×D5911yescharacteristic
212C2×C22⋊C8—591no—
213C2×C22⋊C8C2×D5911yescharacteristic
214#400—1181no—
215#398—1181no—
216#387—1181no—
217#387—1181no—
218#385—1181no—
219#380—591no—
220#380—591no—
221#380—1181no—
222C4×C22⋊C4—591no—
223C2×#95C2×D5911yescharacteristic
224#342—1181no—
225#342—1181no—
226#328—21no—
227#328—21no—
228#328—1181no—
229#328—1181no—
230C59#1037711yescharacteristic, complemented, Sylow
231C22×Q8Dic11811yescharacteristic
232C23×C4—21no—
233C23×C4C22×D5911yescharacteristic
234C22×C8—21no—
235C22×C8—1181no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—1181no—
242C2×C4⋊C4—1181no—
243C2×C4⋊C4—1181no—
244C2×C4⋊C4—1181no—
245C2×C4⋊C4—1181no—
246C2×C4⋊C4—1181no—
247C2×C4⋊C4Dic11811yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—591no—
250C2×C22⋊C4—591no—
251C2×C22⋊C4—1181no—
252C2×C22⋊C4—1181no—
253C2×C42—1181no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—1181no—
257C22⋊C8—1181no—
258#95—21no—
259#95—591no—
260#95—591no—
261#95—1181no—
262#95—1181no—
263#95—1181no—
264#95—1181no—
265#95—1181no—
266#95—1181no—
267#95C22⋊D5911yescharacteristic
268#95C22⋊D5911yescharacteristic
269C24D4×D5911yescharacteristic
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—81no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—42no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—81no—
281C22×C4—81no—
282C22×C4—1181no—
283C22×C4—1181no—
284C22×C4—1181no—
285C22×C4—1181no—
286C22×C4—2361no—
287C22×C4C2×Dic11811yescharacteristic
288C22×C4#1174568511yescharacteristic
289C22×C4D4×D5911yescharacteristic
290C22×C4#1174568711yescharacteristic
291C22×C4#1174568711yescharacteristic
292C22×C4C2×C22⋊D5911yescharacteristic
293C2×C8—41no—
294C2×C8—81no—
295C2×C8—4721no—
296C2×C8—2361no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—4721no—
302C4⋊C4—4721no—
303C4⋊C4—4721no—
304C4⋊C4—4721no—
305C4⋊C4—2362no—
306C4⋊C4—2362no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—1181no—
310C22⋊C4—1181no—
311C22⋊C4—1181no—
312C22⋊C4—1181no—
313C22⋊C4—2361no—
314C22⋊C4—2361no—
315C22⋊C4—2361no—
316C22⋊C4—2361no—
317C42—4721no—
318C23—41no—
319C23—41no—
320C23#1427369511yescharacteristic
321C23#1427370411yescharacteristic
322C23#1427371311yescharacteristic
323C23#1427374811yescharacteristic
324C23#1427375011yescharacteristic
325C23#1427375611yescharacteristic
326C23#1427375911yescharacteristic
327Q8—81no—
328Q8—81no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—4721no—
348C2×C4—4721no—
349C2×C4—4721no—
350C2×C4—2361no—
351C2×C4—2361no—
352C2×C4—2361no—
353C2×C4—2361no—
354C2×C4—2361no—
355C2×C4—2361no—
356C2×C4—2361no—
357C2×C4—2361no—
358C2×C4—2361no—
359C2×C4—2361no—
360C2×C4—2361no—
361C2×C4—2361no—
362C2×C4#1427370411yescharacteristic
363C2×C4#1427370611yescharacteristic
364C2×C4#1427371311yescharacteristic
365C2×C4#1427371411yescharacteristic
366C8—81no—
367C8—4721no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1683731411yescharacteristic
379C22#1683756111yescharacteristic
380C22#1683756311yescharacteristic
381C22#1683770711yescharacteristic
382C22#1683771111yescharacteristic
383C22#1683775811yescharacteristic
384C22#1683776911yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—9441no—
394C4—4721no—
395C4—4721no—
396C4—4721no—
397C4—4721no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#2142524511yescharacteristic
405C2#2142526811yescharacteristic
406C2#2142527311yescharacteristic
subgroupG/H
centerC22#16837314
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC2×C59×#328C2
socleC22×C59#393
prime radicalC24×C59C2×D4
hypercenterC2×#328D59
hypocenterC59#10377
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
230. C59#10377semidirect

Maximal subgroups

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

subgroupindex
#214293202
#214250822
#214226682
#214219752
#214219642
#214219422
C2×C59×#3282
#1037759