Finite Group Databasebeta

← #29575882

Subgroups — #29575882

Order 15616.

432 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455628C211yesmaximal, characteristic
2#21454487C211yesmaximal, characteristic
3C2×#16839511C211yesmaximal, characteristic, complemented
4#21444207C211yesmaximal, characteristic
5#21443715C211yesmaximal, characteristic, complemented
6#21443693C211yesmaximal, characteristic, complemented
7C61×#1549C211yesmaximal, characteristic, complemented
8C4×#11758222C2211yescharacteristic
9#16840054—21no—
10#16840049—21no—
11#16840044C412yes—
12#16840039C412yes—
13#16839822—22no—
14#16839818—21no—
15#16839814—21no—
16#16839802—21no—
17#16839786C2211yescharacteristic
18C2×C4⋊#92418C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20#16839761—21no—
21#16839730—21no—
22#16839720—21no—
23#16839511—21no—
24#16839511—21no—
25#16839494—21no—
26#16839491—21no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C61×#332—22no—
31C2×#11758222D411yescharacteristic
32C2×#11758194—21no—
33C22×#92418—21no—
34C22×#92418—21no—
35C4×Dic122C2×C411yescharacteristic
36C4×Dic122D411yescharacteristic
37C4×D244C2×C411yescharacteristic
38C4×D244D411yescharacteristic
39C4×C22⋊D61—21no—
40C4×C22⋊D61—21no—
41#14519736D411yescharacteristic
42#14519734—21no—
43C42×D61—21no—
44#14519710—22no—
45#14519708—22no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50C4⋊#92418C2×C412yes—
51C4⋊#92418D411yescharacteristic
52C4⋊#92418D411yescharacteristic
53#14519700—22no—
54#14519697—22no—
55#14519689—22no—
56#14519689—22no—
57#14519687—22no—
58C8×Dic61—22no—
59C22×Q8×C61—21no—
60C2×M16×C61—21no—
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61C2×C412yes—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61D412yes—
71C22⋊C8×C61—21no—
72C4×C8×C61—21no—
73C2×Q8×C61—22no—
74C2×Q8×C61—41no—
75C2×Q8×C61—82no—
76C22×C4×C61—41no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C2×C22⋊D61—21no—
81#11758222—21no—
82#11758222—21no—
83#11758222—21no—
84#11758222—21no—
85C2×D244C22⋊C411yescharacteristic
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×Dic122C22⋊C411yescharacteristic
90M16×C61—41no—
91M16×C61—41no—
92C2×C8×C61—22no—
93C2×C8×C61—41no—
94C4⋊C4×C61—22no—
95C4⋊C4×C61—22no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C42×C61C22×C411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C22⋊Dic61—21no—
103#11758198—21no—
104#11758198—21no—
105C4⋊Dic61C22⋊C411yescharacteristic
106C4⋊Dic61C22⋊C411yescharacteristic
107#11758196—21no—
108#11758196—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112#11758194—41no—
113#11758194—41no—
114C2×#92418—22no—
115C2×#92418—21no—
116C2×#92418—21no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—81no—
121C23×C61#12311yescharacteristic
122C22×D61—21no—
123Q8×C61—82no—
124Q8×C61—82no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61—42no—
129C2×C4×C61—82no—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61#13511yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C2×C4×C61#13711yescharacteristic
140C22⋊D61—41no—
141C22⋊D61—41no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145D244—21no—
146D244—21no—
147C4×D61—41no—
148C4×D61—41no—
149C4×D61—41no—
150C4×D61—41no—
151C4×D61—81no—
152Dic122—21no—
153Dic122—21no—
154C8×C61—42no—
155C8×C61—81no—
156#92418—42no—
157#92418—41no—
158#92418—41no—
159#92418—81no—
160#9170—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61#38611yescharacteristic
164C22×C61#48511yescharacteristic
165C22×C61#48511yescharacteristic
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—82no—
173C4×C61#41611yescharacteristic
174C4×C61#41911yescharacteristic
175C4×C61#45211yescharacteristic
176C4×C61#45211yescharacteristic
177C4×C61#47111yescharacteristic
178C4×C61#47311yescharacteristic
179Dic61—41no—
180Dic61—41no—
181Dic61—41no—
182#3079—611no—
183#2925—611no—
184#1549D6111yescharacteristic, complemented
185C2×#333—611no—
186#1477—611no—
187#1301—611no—
188#1292—611no—
189C2×C61—21no—
190C2×C61—21no—
191C2×C61#187311yescharacteristic
192C2×C61#190311yescharacteristic
193C2×C61#190811yescharacteristic
194D61—81no—
195C2×C4⋊Q8C2×D6111yescharacteristic
196C4×#41—611no—
197#477—1221no—
198#476—1221no—
199#475—612no—
200#474—612no—
201#433—1222no—
202#432—1221no—
203#431—1221no—
204#431C2×D6111yescharacteristic
205#428—1221no—
206#423—611no—
207#423C2×D6111yescharacteristic
208C2×C4⋊C8—611no—
209C2×C4⋊C8—611no—
210#417—1221no—
211#408—1221no—
212#405—1221no—
213#333—1221no—
214#333—1221no—
215#332—22no—
216Q8⋊C8—1221no—
217D4⋊C8—1221no—
218C61#917011yescharacteristic, complemented, Sylow
219C2×#41—611no—
220C22×Q8—21no—
221C2×M16—21no—
222C2×M16—1221no—
223C22×C8—1221no—
224C22×C8—1221no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8C4×D6112yes—
229C4×Q8—611no—
230C4×Q8—611no—
231C4×D4—611no—
232C4×D4—611no—
233C4×D4—1221no—
234C4×D4—1221no—
235#117—611no—
236#117—1221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C42—1221no—
240C2×C42C22×D6111yescharacteristic
241#107—1222no—
242#106—1222no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—612no—
246C4⋊C8—611no—
247C4⋊C8—611no—
248C4⋊C8—1221no—
249C4⋊C8—1221no—
250C4⋊C8—1221no—
251C4⋊C8—1221no—
252C4⋊C8C22⋊D6112yes—
253#103—1222no—
254#102—1222no—
255C22⋊C8—21no—
256C22⋊C8—1222no—
257C22⋊C8—1222no—
258#97—1222no—
259C4×C8—21no—
260C4×C8—1222no—
261#41—1221no—
262#41—1221no—
263#41—1221no—
264#41—1221no—
265C2×Q8—22no—
266C2×Q8—41no—
267C2×Q8—82no—
268C2×Q8—611no—
269C2×D4—611no—
270C2×D4—1221no—
271C22×C4—41no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4#1175822211yescharacteristic
276C22×C4D4×D6111yescharacteristic
277C22×C4#1175822411yescharacteristic
278M16—41no—
279M16—41no—
280M16—2441no—
281M16—2441no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—1222no—
285C2×C8—1221no—
286C2×C8—1221no—
287C2×C8—4881no—
288C2×C8—2441no—
289C2×C8—2441no—
290C2×C8—2441no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—611no—
296C4⋊C4—611no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C42—1221no—
303C42—1221no—
304C42—1221no—
305C42C2×C4×D6111yescharacteristic
306C42D4×D6111yescharacteristic
307C42D4×D6111yescharacteristic
308C42C2×C22⋊D6111yescharacteristic
309C23—1221no—
310C23#1451975911yescharacteristic
311Q8—82no—
312Q8—82no—
313Q8—1221no—
314Q8—1221no—
315D4—1221no—
316D4—1221no—
317D4—2441no—
318D4—2441no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—82no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—4881no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4C22⋊C4×D6111yescharacteristic
333C2×C4#1451973711yescharacteristic
334C2×C4C4×C22⋊D6111yescharacteristic
335C2×C4#1451974511yescharacteristic
336C2×C4#1451974811yescharacteristic
337C2×C4#1451975011yescharacteristic
338C2×C4#1451979811yescharacteristic
339C2×C4#1451980011yescharacteristic
340C2×C4#1451980611yescharacteristic
341C2×C4#1451980911yescharacteristic
342C8—42no—
343C8—81no—
344C8—4881no—
345C8—2442no—
346C8—2441no—
347C8—2441no—
348C22—21no—
349C22—21no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22#1683963811yescharacteristic
354C22#1684010111yescharacteristic
355C22#1684010211yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—82no—
360C4—2441no—
361C4—2441no—
362C4—2441no—
363C4#1683975711yescharacteristic
364C4#1683976911yescharacteristic
365C4#1683992111yescharacteristic
366C4#1683992311yescharacteristic
367C4#1684002811yescharacteristic
368C4#1684003611yescharacteristic
369C2—21no—
370C2—21no—
371C2—4881no—
372C2#2144612811yescharacteristic
373C2#2144629611yescharacteristic
374C2#2144633111yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1549C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1549D61
hypocenterC61#9170
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
3. C2×#16839511C2semidirect
5. #21443715C2semidirect
6. #21443693C2semidirect
7. C61×#1549C2semidirect
184. #1549D61semidirect
218. C61#9170semidirect

Maximal subgroups

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

subgroupindex
#214556282
#214544872
C2×#168395112
#214442072
#214437152
#214436932
C61×#15492
#917061