Finite Group Databasebeta

← #28488989

Subgroups — #28488989

Order 15104.

610 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C2×#16837735C211yesmaximal, characteristic
2#21429911C211yesmaximal, characteristic
3C2×#16837342C211yesmaximal, characteristic
4#21424187C211yesmaximal, characteristic
5C2×#16837127C211yesmaximal, characteristic
6#21421975C211yesmaximal, characteristic
7C2×C59×#328C211yesmaximal, characteristic
8C22×C4⋊Dic59C2211yescharacteristic
9C22×Dic59⋊C4C2211yescharacteristic
10#16837735—22no—
11#16837735—22no—
12C2×#14273660—21no—
13C2×#14273651—21no—
14C2×C22⋊(C59⋊C8)C2211yescharacteristic
15#16837342—22no—
16#16837342—22no—
17#16837340—21no—
18#16837335—22no—
19#16837321—21no—
20#16837274—21no—
21#16837263—21no—
22#16837262C2211yescharacteristic
23C2×C59⋊#95—21no—
24C2×C59⋊#95—21no—
25#16837165—22no—
26#16837127—22no—
27C2×C22⋊Q8×C59C2211yescharacteristic
28C2×C22⋊C8×C59C2211yescharacteristic
29C2×#95×C59C2211yescharacteristic
30C59×#328—22no—
31C23×Dic59—21no—
32C23×Dic59D411yescharacteristic
33C23×Dic59D411yescharacteristic
34C22×C59⋊C8—21no—
35C2×C4⋊Dic59—21no—
36C2×C4⋊Dic59—21no—
37C2×C4⋊Dic59—21no—
38C2×C4⋊Dic59—21no—
39C2×C4⋊Dic59—21no—
40C2×C4⋊Dic59D412yes—
41C2×C4⋊Dic59D412yes—
42C2×Dic59⋊C4—21no—
43C2×Dic59⋊C4—21no—
44C2×Dic59⋊C4—21no—
45C2×Dic59⋊C4—21no—
46C2×Dic59⋊C4—21no—
47C2×Dic59⋊C4—21no—
48C2×Dic59⋊C4—22no—
49C2×C22⋊Dic59—21no—
50#14273660—24no—
51#14273651—24no—
52C22⋊(C59⋊C8)—21no—
53C22⋊(C59⋊C8)D412yes—
54C59⋊#95—24no—
55C59⋊#95—24no—
56C59⋊#95—22no—
57C59⋊#95—22no—
58C59⋊#95—22no—
59C59⋊#95—21no—
60C22×Q8×C59D411yescharacteristic
61C23×C4×C59—21no—
62C23×C4×C59C2311yescharacteristic
63C22×C8×C59—21no—
64C22⋊Q8×C59—21no—
65C22⋊Q8×C59—21no—
66C22⋊Q8×C59—21no—
67C22⋊Q8×C59—21no—
68C2×C4⋊C4×C59—21no—
69C2×C4⋊C4×C59D411yescharacteristic
70C2×C22⋊C4×C59—21no—
71C22⋊C8×C59—21no—
72C22⋊C8×C59—21no—
73#95×C59—21no—
74#95×C59D412yes—
75C24×C59C2×D411yescharacteristic
76C2×Q8×C59—21no—
77C2×Q8×C59—21no—
78C2×Q8×C59—42no—
79C22×C4×C59—22no—
80C22×C4×C59—21no—
81C22×C4×C59—21no—
82C22×C4×C59—42no—
83C22×C4×C59—42no—
84C22×C4×C59—42no—
85C22×C4×C59—41no—
86C22×C4×C59—41no—
87C22×C4×C59C2×D411yescharacteristic
88C22×C4×C59C2×D411yescharacteristic
89C22×C4×C59C2×D411yescharacteristic
90C22×C4×C59C2×D411yescharacteristic
91C22×C4×C59C2×D411yescharacteristic
92C22×C4×C59#4111yescharacteristic
93C22×Dic59—21no—
94C22×Dic59—21no—
95C22×Dic59—21no—
96C22×Dic59—21no—
97C22×Dic59—21no—
98C22×Dic59—21no—
99C22×Dic59—22no—
100C22×Dic59—21no—
101C22×Dic59—22no—
102C22×Dic59—21no—
103C22×Dic59—21no—
104C22×Dic59—42no—
105C22×Dic59—44no—
106C22×Dic59—41no—
107C22×Dic59—41no—
108C22×Dic59Q1612yes—
109C2×C8×C59—42no—
110C2×C8×C59—41no—
111C4⋊C4×C59—21no—
112C4⋊C4×C59—21no—
113C4⋊C4×C59—41no—
114C4⋊C4×C59—41no—
115C22⋊C4×C59—41no—
116C22⋊C4×C59—41no—
117C22⋊Dic59—41no—
118C22⋊Dic59—41no—
119C4⋊Dic59—22no—
120C4⋊Dic59—22no—
121C4⋊Dic59—41no—
122C4⋊Dic59—41no—
123C4⋊Dic59—42no—
124Dic59⋊C4—41no—
125Dic59⋊C4—41no—
126Dic59⋊C4—41no—
127Dic59⋊C4—41no—
128Dic59⋊C4—82no—
129C2×C59⋊C8—22no—
130C2×C59⋊C8—42no—
131C23×C59—22no—
132C23×C59—22no—
133C23×C59#12011yescharacteristic
134C23×C59#12011yescharacteristic
135C23×C59#12111yescharacteristic
136C23×C59C2×Q1611yescharacteristic
137C23×C59#13511yescharacteristic
138C23×C59#13711yescharacteristic
139C23×C59#13711yescharacteristic
140Q8×C59—42no—
141Q8×C59—81no—
142C2×C4×C59—22no—
143C2×C4×C59—22no—
144C2×C4×C59—41no—
145C2×C4×C59—41no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—42no—
149C2×C4×C59—42no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59—42no—
153C2×C4×C59—42no—
154C2×C4×C59—42no—
155C2×C4×C59—82no—
156C2×C4×C59—82no—
157C2×C4×C59#12011yescharacteristic
158C2×C4×C59#12111yescharacteristic
159C2×C4×C59#12111yescharacteristic
160C2×C4×C59#12711yescharacteristic
161C2×Dic59—22no—
162C2×Dic59—22no—
163C2×Dic59—22no—
164C2×Dic59—41no—
165C2×Dic59—41no—
166C2×Dic59—41no—
167C2×Dic59—41no—
168C2×Dic59—44no—
169C2×Dic59—42no—
170C2×Dic59—41no—
171C2×Dic59—42no—
172C2×Dic59—42no—
173C2×Dic59—42no—
174C2×Dic59—42no—
175C2×Dic59—42no—
176C2×Dic59—82no—
177C2×Dic59—82no—
178C2×Dic59—81no—
179C8×C59—81no—
180C59⋊C8—42no—
181#9929—591nomaximal, Sylow
182C22×C59—22no—
183C22×C59—22no—
184C22×C59—22no—
185C22×C59—22no—
186C22×C59—21no—
187C22×C59—21no—
188C22×C59—21no—
189C22×C59—21no—
190C22×C59#39211yescharacteristic
191C22×C59#45111yescharacteristic
192C22×C59#45111yescharacteristic
193C22×C59#45211yescharacteristic
194C22×C59#45211yescharacteristic
195C22×C59#45412yes—
196C22×C59#45812yes—
197C22×C59#46711yescharacteristic
198C22×C59#47011yescharacteristic
199C4×C59—21no—
200C4×C59—21no—
201C4×C59—21no—
202C4×C59—21no—
203C4×C59—82no—
204C4×C59—81no—
205C4×C59—81no—
206Dic59—42no—
207Dic59—82no—
208Dic59—82no—
209Dic59—81no—
210C2×#484—591no—
211#2627—591no—
212C2×#400—591no—
213#1824—591no—
214C2×#328D5911yescharacteristic
215C2×#324—591no—
216#1294—591no—
217C2×C59—21no—
218C2×C59—21no—
219C2×C59—21no—
220C2×C59—21no—
221C2×C59#161512yes—
222C2×C59#161712yes—
223C2×C59#200111yescharacteristic
224C2×C59#200311yescharacteristic
225C2×C59#202211yescharacteristic
226C2×C22⋊Q8C2×D5911yescharacteristic
227C22×C4⋊C4—591no—
228C22×C4⋊C4—591no—
229#484—1182no—
230#484—1182no—
231C2×#107—1181no—
232C2×#103—1181no—
233C2×C22⋊C8—591no—
234C2×C22⋊C8C2×D5911yescharacteristic
235#400—1182no—
236#400—1181no—
237#400—1182no—
238#398—1182no—
239#395—1181no—
240#385—1181no—
241#381—1181no—
242#380—591no—
243C2×#95—1181no—
244C2×#95—1181no—
245C2×#95C2×D5911yescharacteristic
246#340—1182no—
247#328—22no—
248#324—1182no—
249C59#992911yescharacteristic, complemented, Sylow
250C22×Q8D23611yescharacteristic
251C23×C4—21no—
252C23×C4—591no—
253C23×C4—591no—
254C23×C4—1181no—
255C23×C4C22×D5911yescharacteristic
256C22×C8—21no—
257C22×C8—1181no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—592no—
264C2×C4⋊C4—592no—
265C2×C4⋊C4—1181no—
266C2×C4⋊C4—1181no—
267C2×C4⋊C4—1181no—
268C2×C4⋊C4—1181no—
269C2×C4⋊C4—1182no—
270C2×C4⋊C4—1181no—
271C2×C4⋊C4—1181no—
272C2×C4⋊C4—1181no—
273C2×C4⋊C4—1181no—
274C2×C4⋊C4—1181no—
275C2×C4⋊C4—1181no—
276C2×C4⋊C4—1181no—
277C2×C4⋊C4D23611yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—1181no—
280#107—1184no—
281#103—1184no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—592no—
285C22⋊C8—1181no—
286#95—21no—
287#95—1184no—
288#95—1184no—
289#95—1182no—
290#95—1182no—
291#95—1182no—
292#95—1181no—
293#95C22⋊D5912yes—
294C24D4×D5911yescharacteristic
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—42no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—592no—
307C22×C4—1181no—
308C22×C4—1181no—
309C22×C4—1181no—
310C22×C4—1181no—
311C22×C4—1181no—
312C22×C4—1181no—
313C22×C4—1181no—
314C22×C4—1182no—
315C22×C4—1181no—
316C22×C4—1182no—
317C22×C4—1181no—
318C22×C4—2364no—
319C22×C4—2361no—
320C22×C4—2361no—
321C22×C4—2362no—
322C22×C4C2×D23611yescharacteristic
323C22×C4#1174568511yescharacteristic
324C22×C4D4×D5911yescharacteristic
325C22×C4D4×D5911yescharacteristic
326C22×C4D4×D5911yescharacteristic
327C22×C4C2×C22⋊D5911yescharacteristic
328C2×C8—42no—
329C2×C8—41no—
330C2×C8—1182no—
331C2×C8—2362no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—1182no—
337C4⋊C4—1182no—
338C4⋊C4—4722no—
339C4⋊C4—2362no—
340C4⋊C4—2361no—
341C4⋊C4—2361no—
342C4⋊C4—2361no—
343C4⋊C4—2361no—
344C4⋊C4—2361no—
345C4⋊C4—2361no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—2361no—
349C22⋊C4—2361no—
350C23—22no—
351C23—22no—
352C23#1427369511yescharacteristic
353C23#1427369711yescharacteristic
354C23#1427370011yescharacteristic
355C23Q16×D5911yescharacteristic
356C23#1427374811yescharacteristic
357C23#1427375611yescharacteristic
358C23#1427375911yescharacteristic
359Q8—42no—
360Q8—81no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—1182no—
377C2×C4—1182no—
378C2×C4—1182no—
379C2×C4—4722no—
380C2×C4—4722no—
381C2×C4—4721no—
382C2×C4—2362no—
383C2×C4—2364no—
384C2×C4—2362no—
385C2×C4—2361no—
386C2×C4—2362no—
387C2×C4—2362no—
388C2×C4—2362no—
389C2×C4—2362no—
390C2×C4—2361no—
391C2×C4—2361no—
392C2×C4—2361no—
393C2×C4—2361no—
394C2×C4#1427369711yescharacteristic
395C2×C4#1427370011yescharacteristic
396C2×C4#1427370111yescharacteristic
397C2×C4#1427372311yescharacteristic
398C8—81no—
399C8—2362no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22#1683731111yescharacteristic
409C22#1683755611yescharacteristic
410C22#1683755911yescharacteristic
411C22#1683756111yescharacteristic
412C22#1683756711yescharacteristic
413C22#1683757612yes—
414C22#1683759312yes—
415C22#1683764211yescharacteristic
416C22#1683765911yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—82no—
422C4—81no—
423C4—81no—
424C4—4722no—
425C4—4721no—
426C4—4722no—
427C4—2362no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2—21no—
432C2#2142313012yes—
433C2#2142313912yes—
434C2#2142510511yescharacteristic
435C2#2142511711yescharacteristic
436C2#2142522611yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC2×C59×#328C2
socleC23×C59#120
prime radicalC24×C59C2×D4
hypercenterC2×#328D59
hypocenterC59#9929
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
249. C59#9929semidirect

Maximal subgroups

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

subgroupindex
C2×#168377352
#214299112
C2×#168373422
#214241872
C2×#168371272
#214219752
C2×C59×#3282
#992959