Finite Group Databasebeta

← #29576068

Subgroups — #29576068

Order 15616.

516 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 105 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#21451634C211yesmaximal, characteristic
2#21448421C211yesmaximal, characteristic
3#21444391C211yesmaximal, characteristic
4C2×#16839487C211yesmaximal, characteristic
5#21443687C211yesmaximal, characteristic
6#21443686C211yesmaximal, characteristic
7C61×#1520C211yesmaximal, characteristic
8C22×#11758196C2211yescharacteristic
9C2×C22⋊#92418C2211yescharacteristic
10#16839700C412yescomplemented
11#16839695—22no—
12#16839681C412yescomplemented
13#16839649—22no—
14#16839643—22no—
15#16839634—21no—
16#16839623—21no—
17#16839623—21no—
18#16839622C2211yescharacteristic
19#16839622C2211yescharacteristic
20C22⋊C4×Dic61—21no—
21#16839499—22no—
22#16839487—22no—
23C2×C22⋊Q8×C61C2211yescharacteristic
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C61×#328—22no—
27C23×Dic61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C22×#92418—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—22no—
37C2×#11758196C2×C412yes—
38C2×#11758196D412yes—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C4×Dic61—22no—
42C22⋊#92418—21no—
43C22⋊#92418—21no—
44#14519684—22no—
45#14519684—24no—
46#14519684—22no—
47#14519684—22no—
48#14519684—22no—
49#14519684C2×C412yes—
50#14519684D412yes—
51C22×Q8×C61C2×C411yescharacteristic
52C23×C4×C61C2311yescharacteristic
53C22×C8×C61—21no—
54C22⋊Q8×C61—21no—
55C22⋊Q8×C61—21no—
56C22⋊Q8×C61—21no—
57C22⋊Q8×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C22⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65#95×C61D412yes—
66C24×C61C2×D411yescharacteristic
67C2×Q8×C61—21no—
68C2×Q8×C61—21no—
69C2×Q8×C61—81no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—22no—
73C22×C4×C61—81no—
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—22no—
89C22×Dic61—22no—
90C22×Dic61—81no—
91C22×Dic61C22⋊C412yes—
92C22×Dic61C22⋊C412yes—
93C2×C8×C61—41no—
94C2×C8×C61—81no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—81no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C22⋊Dic61—41no—
105C22⋊Dic61—41no—
106C22⋊Dic61—41no—
107C22⋊Dic61—41no—
108C4⋊Dic61—81no—
109C4⋊Dic61—81no—
110#11758196—22no—
111#11758196—22no—
112#11758196—22no—
113#11758196—22no—
114#11758196—82no—
115C4×Dic61—82no—
116C2×#92418—41no—
117C2×#92418—81no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61C2×C22⋊C411yescharacteristic
121C23×C61#12011yescharacteristic
122C23×C61#12311yescharacteristic
123C23×C61#13511yescharacteristic
124C23×C61#13511yescharacteristic
125C23×C61#13711yescharacteristic
126C23×C61#13711yescharacteristic
127Q8×C61—81no—
128Q8×C61—81no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—42no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160C2×Dic61—42no—
161C2×Dic61—42no—
162C2×Dic61—81no—
163C8×C61—81no—
164#92418—81no—
165#9202—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61#38611yescharacteristic
177C22×C61#41611yescharacteristic
178C22×C61#41911yescharacteristic
179C22×C61#45211yescharacteristic
180C22×C61#45211yescharacteristic
181C22×C61#48511yescharacteristic
182C22×C61#48511yescharacteristic
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—82no—
188C4×C61—81no—
189C4×C61—81no—
190Dic61—42no—
191Dic61—42no—
192Dic61—82no—
193Dic61—82no—
194#2627—611no—
195#2313—611no—
196#1520—611no—
197#1520D6111yescharacteristic
198C2×#324—611no—
199#1289—611no—
200#1289—611no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—21no—
204C2×C61—21no—
205C2×C61—21no—
206C2×C61—21no—
207C2×C61#187311yescharacteristic
208C2×C61#191211yescharacteristic
209C2×C61#191311yescharacteristic
210C2×C22⋊Q8C2×D6111yescharacteristic
211C22×C4⋊C4—611no—
212C2×C22⋊C8—611no—
213C2×C22⋊C8C2×D6111yescharacteristic
214#400—612no—
215#398—1222no—
216#395—612no—
217#387—1222no—
218#387—1222no—
219#385—1221no—
220#381—1221no—
221#381—1221no—
222#380—611no—
223#380—611no—
224#380C2×D6111yescharacteristic
225C4×C22⋊C4—1221no—
226#328—22no—
227#328—1222no—
228#324—1222no—
229C61#920211yescharacteristic, complemented, Sylow
230C22×Q8C4×D6111yescharacteristic
231C23×C4—611no—
232C23×C4—611no—
233C23×C4C22×D6111yescharacteristic
234C22×C8—21no—
235C22×C8—1221no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—612no—
243C2×C4⋊C4—612no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1222no—
249C2×C4⋊C4—1221no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4C4×D6111yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C42—1222no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—1221no—
260C22⋊C8—1221no—
261#95—612no—
262#95—612no—
263#95—1222no—
264#95—1222no—
265#95—1222no—
266#95—1222no—
267#95—1224no—
268#95C22⋊D6112yes—
269C24D4×D6111yescharacteristic
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—81no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—81no—
277C22×C4—612no—
278C22×C4—612no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—4881no—
290C22×C4C2×C4×D6111yescharacteristic
291C22×C4#1175822211yescharacteristic
292C22×C4D4×D6111yescharacteristic
293C22×C4D4×D6111yescharacteristic
294C22×C4#1175822411yescharacteristic
295C22×C4C2×C22⋊D6111yescharacteristic
296C2×C8—41no—
297C2×C8—81no—
298C2×C8—4881no—
299C2×C8—2441no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—81no—
305C4⋊C4—1222no—
306C4⋊C4—1222no—
307C4⋊C4—1222no—
308C4⋊C4—1222no—
309C4⋊C4—4882no—
310C4⋊C4—4881no—
311C4⋊C4—4881no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—2441no—
317C22⋊C4—2441no—
318C22⋊C4—2441no—
319C22⋊C4—2441no—
320C42—4882no—
321C23—41no—
322C23—41no—
323C23C22⋊C4×D6111yescharacteristic
324C23#1451974511yescharacteristic
325C23#1451975911yescharacteristic
326C23#1451979811yescharacteristic
327C23#1451980011yescharacteristic
328C23#1451980611yescharacteristic
329C23#1451980911yescharacteristic
330Q8—81no—
331Q8—81no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—4881no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2442no—
362C2×C4#1451973711yescharacteristic
363C2×C4C4×C22⋊D6111yescharacteristic
364C2×C4#1451974811yescharacteristic
365C2×C4#1451975011yescharacteristic
366C8—81no—
367C8—4881no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1683963811yescharacteristic
379C22#1683975711yescharacteristic
380C22#1683976911yescharacteristic
381C22#1683992111yescharacteristic
382C22#1683992311yescharacteristic
383C22#1684010111yescharacteristic
384C22#1684010211yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—81no—
391C4—81no—
392C4—4882no—
393C4—4882no—
394C4—2442no—
395C4—2442no—
396C2—21no—
397C2—21no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2#2144612811yescharacteristic
403C2#2144635311yescharacteristic
404C2#2144635811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1520C2
socleC22×C61#386
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1520D61
hypocenterC61#9202
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
10. #16839700C4semidirect
12. #16839681C4semidirect
229. C61#9202semidirect

Maximal subgroups

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

subgroupindex
#214516342
#214484212
#214443912
C2×#168394872
#214436872
#214436862
C61×#15202
#920261