Finite Group Databasebeta

← #29575902

Subgroups — #29575902

Order 15616.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455302C211yesmaximal, characteristic
2#21454484C211yesmaximal, characteristic
3#21444491C211yesmaximal, characteristic, complemented
4#21444204C211yesmaximal, characteristic
5#21443716C211yesmaximal, characteristic, complemented
6#21443694C211yesmaximal, characteristic, complemented
7C2×C61×#332C211yesmaximal, characteristic, complemented
8C2×#14519808—21no—
9C4×#11758222C2211yescharacteristic
10#16839969—21no—
11#16839969C412yes—
12#16839964—21no—
13#16839964C412yes—
14#16839822—22no—
15#16839818—21no—
16#16839815C2211yescharacteristic
17#16839814—21no—
18#16839786C2211yescharacteristic
19#16839786C2211yescharacteristic
20#16839771—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×#332—21no—
30C61×#332—21no—
31C2×#11758222D411yescharacteristic
32#14519808—42no—
33#14519808—42no—
34C2×#11758202—22no—
35C2×#11758201—22no—
36C2×#11758194—21no—
37C2×#11758194—21no—
38C4×Dic122C2×C411yescharacteristic
39C4×Dic122D411yescharacteristic
40C4×D244C2×C411yescharacteristic
41C4×D244D411yescharacteristic
42C4×C22⋊D61—21no—
43C4×C22⋊D61—21no—
44#14519736D411yescharacteristic
45#14519734—21no—
46C42×D61—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50C4⋊#92418C2×C412yes—
51C4⋊#92418D412yes—
52#14519701—22no—
53#14519701—22no—
54C22⋊#92418—21no—
55#14519689—22no—
56#14519689—22no—
57#14519687—22no—
58C4×#92418—21no—
59C8×Dic61—22no—
60C22×Q8×C61—21no—
61C22×C8×C61—21no—
62C22×C8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61C2×C412yes—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C4⋊C8×C61D411yescharacteristic
74C4⋊C8×C61D411yescharacteristic
75C2×Q8×C61—22no—
76C2×Q8×C61—41no—
77C2×Q8×C61—41no—
78C2×Q8×C61—41no—
79C2×Q8×C61—41no—
80C2×Q8×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61#4111yescharacteristic
84C22×C4×C61#4111yescharacteristic
85C2×C22⋊D61—21no—
86#11758222—21no—
87#11758222—21no—
88#11758222—21no—
89#11758222—21no—
90C2×D244C22⋊C411yescharacteristic
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×Dic122C22⋊C411yescharacteristic
95C2×C8×C61—21no—
96C2×C8×C61—21no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—81no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61—22no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C42×C61C22×C411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C22⋊Dic61—21no—
110#11758202—44no—
111#11758201—44no—
112#11758198—21no—
113#11758198—21no—
114C4⋊Dic61C22⋊C411yescharacteristic
115C4⋊Dic61C22⋊C411yescharacteristic
116#11758196—21no—
117#11758196—21no—
118C4×Dic61—21no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121#11758194—41no—
122#11758194—41no—
123#11758194—41no—
124#11758194—41no—
125C2×#92418—22no—
126C2×#92418—22no—
127C2×#92418—41no—
128C23×C61#12311yescharacteristic
129C22×D61—21no—
130Q8×C61—42no—
131Q8×C61—42no—
132Q8×C61—81no—
133Q8×C61—81no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#13511yescharacteristic
147C2×C4×C61#13511yescharacteristic
148C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
150C22⋊D61—41no—
151C22⋊D61—41no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155D244—21no—
156D244—21no—
157C4×D61—41no—
158C4×D61—41no—
159C4×D61—41no—
160C4×D61—41no—
161C4×D61—81no—
162Dic122—21no—
163Dic122—21no—
164C8×C61—41no—
165C8×C61—41no—
166C8×C61—81no—
167#92418—42no—
168#92418—42no—
169#92418—81no—
170#9172—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61#38611yescharacteristic
174C22×C61#48211yescharacteristic
175C22×C61#48211yescharacteristic
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—82no—
183C4×C61#41611yescharacteristic
184C4×C61#41811yescharacteristic
185C4×C61#44911yescharacteristic
186C4×C61#44911yescharacteristic
187C4×C61#47111yescharacteristic
188C4×C61#47311yescharacteristic
189Dic61—41no—
190Dic61—41no—
191Dic61—41no—
192#3039—611no—
193#2925—611no—
194#1546—611no—
195C2×#332D6111yescharacteristic, complemented
196#1477—611no—
197#1301—611no—
198#1292—611no—
199C2×C61—21no—
200C2×C61—21no—
201C2×C61#187511yescharacteristic
202C2×C61#190211yescharacteristic
203C2×C61#190811yescharacteristic
204D61—81no—
205C2×#137—1221no—
206C2×C4⋊Q8C2×D6111yescharacteristic
207C4×#41—611no—
208#462—612no—
209#462—1221no—
210#461—612no—
211#461—1221no—
212#433—1222no—
213#432—1221no—
214#431—611no—
215#431—1221no—
216#423—611no—
217#423—611no—
218C2×C4⋊C8C2×D6111yescharacteristic
219C2×C4⋊C8C2×D6111yescharacteristic
220#419—1221no—
221#408—1221no—
222#405—1221no—
223#332—21no—
224#332—21no—
225#332—1222no—
226Q8⋊C8—1221no—
227D4⋊C8—1221no—
228C61#917211yescharacteristic, complemented, Sylow
229C2×#41—611no—
230C22×Q8—21no—
231#137—2442no—
232#137—2442no—
233C2×Q16—1222no—
234C2×SD16—1222no—
235C2×M16—1221no—
236C2×M16—1221no—
237C22×C8—21no—
238C22×C8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8C4×D6112yes—
243C4×Q8—611no—
244C4×Q8—611no—
245C4×D4—611no—
246C4×D4—611no—
247C4×D4—1221no—
248C4×D4—1221no—
249#117—611no—
250#117—1221no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C42—1221no—
254C2×C42C22×D6111yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—612no—
259C4⋊C8—612no—
260C4⋊C8—1221no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263C4⋊C8C22⋊D6111yescharacteristic
264C4⋊C8C22⋊D6111yescharacteristic
265#103—1222no—
266#103—1222no—
267C22⋊C8—1222no—
268C22⋊C8—1222no—
269C22⋊C8—1221no—
270#97—1222no—
271C4×C8—1222no—
272C4×C8—1221no—
273#41—1221no—
274#41—1221no—
275#41—1221no—
276#41—1221no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—611no—
284C2×D4—611no—
285C2×D4—1221no—
286C22×C4—41no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4#1175822211yescharacteristic
291C22×C4D4×D6111yescharacteristic
292C22×C4#1175822411yescharacteristic
293Q16—2444no—
294SD16—2444no—
295M16—2441no—
296M16—2441no—
297M16—2441no—
298M16—2441no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—81no—
305C2×C8—1222no—
306C2×C8—1222no—
307C2×C8—2441no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—611no—
313C4⋊C4—611no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C42—1221no—
320C42—1221no—
321C42—1221no—
322C42C2×C4×D6111yescharacteristic
323C42D4×D6111yescharacteristic
324C42D4×D6111yescharacteristic
325C42C2×C22⋊D6111yescharacteristic
326C23—1221no—
327C23#1451975911yescharacteristic
328Q8—42no—
329Q8—42no—
330Q8—81no—
331Q8—81no—
332Q8—1221no—
333Q8—1221no—
334D4—1221no—
335D4—1221no—
336D4—2441no—
337D4—2441no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—4881no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4C22⋊C4×D6111yescharacteristic
353C2×C4#1451973711yescharacteristic
354C2×C4C4×C22⋊D6111yescharacteristic
355C2×C4#1451974511yescharacteristic
356C2×C4#1451974811yescharacteristic
357C2×C4#1451975011yescharacteristic
358C2×C4#1451979611yescharacteristic
359C2×C4#1451979811yescharacteristic
360C2×C4#1451980111yescharacteristic
361C2×C4#1451980411yescharacteristic
362C8—41no—
363C8—41no—
364C8—81no—
365C8—4881no—
366C8—2442no—
367C8—2442no—
368C22—21no—
369C22—21no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22#1683963811yescharacteristic
374C22#1684008411yescharacteristic
375C22#1684008511yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—82no—
380C4—2441no—
381C4—2441no—
382C4—2441no—
383C4#1683975511yescharacteristic
384C4#1683976511yescharacteristic
385C4#1683990411yescharacteristic
386C4#1683990611yescharacteristic
387C4#1684002211yescharacteristic
388C4#1684003411yescharacteristic
389C2—21no—
390C2—21no—
391C2—4881no—
392C2#2144613811yescharacteristic
393C2#2144629511yescharacteristic
394C2#2144633711yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#332C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenterC2×#332D61
hypocenterC61#9172
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #21444491C2semidirect
5. #21443716C2semidirect
6. #21443694C2semidirect
7. C2×C61×#332C2semidirect
195. C2×#332D61semidirect
228. C61#9172semidirect

Maximal subgroups

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

subgroupindex
#214553022
#214544842
#214444912
#214442042
#214437162
#214436942
C2×C61×#3322
#917261