Finite Group Databasebeta

← #29575888

Subgroups — #29575888

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#21454484C211yesmaximal, characteristic
3#21444504C211yesmaximal, characteristic, complemented
4#21444204C211yesmaximal, characteristic
5#21443716C211yesmaximal, characteristic, complemented
6#21443694C211yesmaximal, characteristic, complemented
7C2×C61×#333C211yesmaximal, characteristic, complemented
8C4×#11758222C2211yescharacteristic
9#16840054—21no—
10#16840049—21no—
11#16840044C412yes—
12#16840039C412yes—
13#16839822—22no—
14#16839818—21no—
15#16839815C2211yescharacteristic
16#16839814—21no—
17#16839802—21no—
18#16839786C2211yescharacteristic
19#16839786C2211yescharacteristic
20#16839761—21no—
21#16839728—21no—
22#16839717—21no—
23#16839508—22no—
24#16839492—21no—
25#16839489—21no—
26C2×C4⋊Q8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C61×#333—21no—
30C61×#333—21no—
31C2×#11758222D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758194—21no—
34C4×Dic122C2×C411yescharacteristic
35C4×Dic122D411yescharacteristic
36C4×D244C2×C411yescharacteristic
37C4×D244D411yescharacteristic
38C4×C22⋊D61—21no—
39C4×C22⋊D61—21no—
40#14519736D411yescharacteristic
41#14519734—21no—
42C42×D61—21no—
43#14519710—22no—
44#14519708—22no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418C2×C412yes—
49C4⋊#92418D412yes—
50#14519700—22no—
51#14519697—22no—
52C22⋊#92418—21no—
53#14519689—22no—
54#14519689—22no—
55#14519687—22no—
56C4×#92418—21no—
57C8×Dic61—22no—
58C22×Q8×C61—21no—
59C22×C8×C61—21no—
60C22×C8×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×C61—21no—
71C4⋊C8×C61D411yescharacteristic
72C4⋊C8×C61D411yescharacteristic
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
90C2×C8×C61—21no—
91C2×C8×C61—21no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—81no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C42×C61C22×C411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C22⋊Dic61—21no—
105#11758198—21no—
106#11758198—21no—
107C4⋊Dic61C22⋊C411yescharacteristic
108C4⋊Dic61C22⋊C411yescharacteristic
109#11758196—21no—
110#11758196—21no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114#11758194—41no—
115#11758194—41no—
116#11758194—41no—
117#11758194—41no—
118C2×#92418—22no—
119C2×#92418—22no—
120C2×#92418—41no—
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—41no—
155C8×C61—41no—
156C8×C61—81no—
157#92418—42no—
158#92418—42no—
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#1549—611no—
185C2×#333D6111yescharacteristic, complemented
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—611no—
204#431—1221no—
205#428—1221no—
206#423—611no—
207#423—611no—
208C2×C4⋊C8C2×D6111yescharacteristic
209C2×C4⋊C8C2×D6111yescharacteristic
210#417—1221no—
211#408—1221no—
212#405—1221no—
213#333—21no—
214#333—21no—
215#332—1222no—
216Q8⋊C8—1221no—
217D4⋊C8—1221no—
218C61#917011yescharacteristic, complemented, Sylow
219C2×#41—611no—
220C22×Q8—21no—
221C2×M16—1221no—
222C2×M16—1221no—
223C22×C8—21no—
224C22×C8—21no—
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—21no—
246C4⋊C8—612no—
247C4⋊C8—612no—
248C4⋊C8—1221no—
249C4⋊C8—1221no—
250C4⋊C8—1221no—
251C4⋊C8C22⋊D6111yescharacteristic
252C4⋊C8C22⋊D6111yescharacteristic
253#103—1222no—
254#102—1222no—
255C22⋊C8—1222no—
256C22⋊C8—1222no—
257C22⋊C8—1221no—
258#97—1222no—
259C4×C8—1222no—
260C4×C8—1221no—
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—2441no—
279M16—2441no—
280M16—2441no—
281M16—2441no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—81no—
288C2×C8—1222no—
289C2×C8—1222no—
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—41no—
343C8—41no—
344C8—81no—
345C8—4881no—
346C8—2442no—
347C8—2442no—
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#1684002211yescharacteristic
368C4#1684003411yescharacteristic
369C2—21no—
370C2—21no—
371C2—4881no—
372C2#2144612811yescharacteristic
373C2#2144630211yescharacteristic
374C2#2144633711yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#333C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenterC2×#333D61
hypocenterC61#9170
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
3. #21444504C2semidirect
5. #21443716C2semidirect
6. #21443694C2semidirect
7. C2×C61×#333C2semidirect
185. C2×#333D61semidirect
218. C61#9170semidirect

Maximal subgroups

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

subgroupindex
#214556282
#214544842
#214445042
#214442042
#214437162
#214436942
C2×C61×#3332
#917061