Finite Group Databasebeta

← #29575900

Subgroups — #29575900

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#21455307C211yesmaximal, characteristic
2#21454487C211yesmaximal, characteristic
3#21444492C211yesmaximal, characteristic, complemented
4C2×#16839507C211yesmaximal, characteristic, complemented
5#21444204C211yesmaximal, characteristic
6#21443714C211yesmaximal, characteristic, complemented
7C61×#1292C211yesmaximal, characteristic, complemented
8C2×#14519810—21no—
9C2×#14519777C2211yescharacteristic
10C4×#11758222C2211yescharacteristic
11#16839973—21no—
12#16839973C412yes—
13#16839968—21no—
14#16839968C412yes—
15#16839822—22no—
16#16839818—21no—
17#16839815C2211yescharacteristic
18#16839814—21no—
19C2×C4⋊#92418C2211yescharacteristic
20#16839772—21no—
21#16839730—21no—
22#16839720—21no—
23#16839509—22no—
24#16839507—21no—
25#16839507—21no—
26#16839492—21no—
27#16839489—21no—
28C61×#423C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×#11758222D411yescharacteristic
32C22×Dic122—21no—
33#14519810—42no—
34#14519810—42no—
35C2×Dic244—22no—
36C2×#11758190—22no—
37C22×#92418—21no—
38#14519777—21no—
39#14519777—21no—
40#14519777—21no—
41#14519777C2×C412yes—
42C4×Dic122C2×C411yescharacteristic
43C4×Dic122D411yescharacteristic
44C4×D244C2×C411yescharacteristic
45C4×D244D411yescharacteristic
46C4×C22⋊D61—21no—
47C4×C22⋊D61—21no—
48#14519736D411yescharacteristic
49#14519734—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—21no—
52C42×D61—21no—
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55C4⋊#92418D411yescharacteristic
56C4⋊#92418D411yescharacteristic
57#14519702—22no—
58#14519702—22no—
59C22⋊#92418—21no—
60#14519689—22no—
61#14519689—22no—
62#14519687—22no—
63C4×#92418—21no—
64C8×Dic61—22no—
65C2×M16×C61—21no—
66C2×M16×C61—21no—
67C22×C8×C61—21no—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C4⋊C8×C61C2×C412yes—
74C4⋊C8×C61D412yes—
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C2×C22⋊D61—21no—
79C22×Dic61—41no—
80#11758222—21no—
81#11758222—21no—
82#11758222—21no—
83#11758222—21no—
84C2×D244C22⋊C411yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×Dic122—22no—
89C2×Dic122—41no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×Dic122C22⋊C411yescharacteristic
95M16×C61—41no—
96M16×C61—41no—
97M16×C61—41no—
98M16×C61—41no—
99C2×C8×C61—22no—
100C2×C8×C61—22no—
101C2×C8×C61—41no—
102C2×C8×C61—81no—
103C42×C61C22×C411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C22⋊Dic61—21no—
108#11758198—21no—
109#11758198—21no—
110C4⋊Dic61—22no—
111C4⋊Dic61—22no—
112C4⋊Dic61—41no—
113C4⋊Dic61—41no—
114C4⋊Dic61C22⋊C411yescharacteristic
115C4⋊Dic61C22⋊C411yescharacteristic
116#11758196—21no—
117#11758196—21no—
118C4×Dic61—21no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C2×#92418—21no—
122C2×#92418—21no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126Dic244—44no—
127#11758190—44no—
128C23×C61#12311yescharacteristic
129C22×D61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61#12011yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#13511yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C22⋊D61—41no—
144C22⋊D61—41no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—42no—
149C2×Dic61—81no—
150C2×Dic61—81no—
151D244—21no—
152D244—21no—
153C4×D61—41no—
154C4×D61—41no—
155C4×D61—41no—
156C4×D61—41no—
157C4×D61—81no—
158Dic122—21no—
159Dic122—21no—
160Dic122—42no—
161Dic122—42no—
162Dic122—81no—
163Dic122—81no—
164C8×C61—42no—
165C8×C61—42no—
166C8×C61—81no—
167#92418—41no—
168#92418—41no—
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#41611yescharacteristic
183C4×C61#41811yescharacteristic
184C4×C61#44911yescharacteristic
185C4×C61#44911yescharacteristic
186C4×C61#47111yescharacteristic
187C4×C61#47311yescharacteristic
188Dic61—41no—
189Dic61—41no—
190Dic61—41no—
191Dic61—82no—
192#3039—611no—
193#2925—611no—
194#1546—611no—
195C2×#332—611no—
196#1477—611no—
197#1301—611no—
198#1292D6111yescharacteristic, complemented
199C2×C61—21no—
200C2×C61—21no—
201C2×C61#187511yescharacteristic
202C2×C61#190211yescharacteristic
203C2×C61#190811yescharacteristic
204D61—81no—
205C2×#137—1221no—
206C2×C4⋊Q8—611no—
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#423C2×D6111yescharacteristic
217#423C2×D6111yescharacteristic
218C2×C4⋊C8—611no—
219C2×C4⋊C8C2×D6111yescharacteristic
220#419—1221no—
221#408—1221no—
222#405—1221no—
223#332—1221no—
224#332—1221no—
225#332—1222no—
226Q8⋊C8—1221no—
227D4⋊C8—1221no—
228C61#917211yescharacteristic, complemented, Sylow
229C2×#41—611no—
230C22×Q8—1221no—
231#137—2442no—
232#137—2442no—
233C2×Q16—1222no—
234C2×SD16—1222no—
235C2×M16—21no—
236C2×M16—21no—
237C22×C8—21no—
238C22×C8—1221no—
239C4⋊Q8—612no—
240C4⋊Q8—1221no—
241C4⋊Q8—1221no—
242C4⋊Q8—1221no—
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—1221no—
252C2×C4⋊C4—1221no—
253C2×C42—1221no—
254C2×C42C22×D6111yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—611no—
260C4⋊C8—611no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263C4⋊C8C4×D6112yes—
264C4⋊C8D24412yes—
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—611no—
278C2×Q8—1222no—
279C2×Q8—2441no—
280C2×Q8—2441no—
281C2×Q8—2441no—
282C2×Q8—2441no—
283C2×Q8—2441no—
284C2×D4—611no—
285C2×D4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—2441no—
290C22×C4#1175822211yescharacteristic
291C22×C4D4×D6111yescharacteristic
292C22×C4#1175822611yescharacteristic
293Q16—2444no—
294SD16—2444no—
295M16—41no—
296M16—41no—
297M16—41no—
298M16—41no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—81no—
303C2×C8—1221no—
304C2×C8—1221no—
305C2×C8—2441no—
306C2×C8—2441no—
307C2×C8—2441no—
308C4⋊C4—611no—
309C4⋊C4—611no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1222no—
313C4⋊C4—1222no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C42—1221no—
320C42—1221no—
321C42—1221no—
322C42C2×C4×D6111yescharacteristic
323C42C2×D24411yescharacteristic
324C42D4×D6111yescharacteristic
325C42D4×D6111yescharacteristic
326C23—1221no—
327C23#1451976211yescharacteristic
328Q8—1221no—
329Q8—1221no—
330Q8—4881no—
331Q8—4881no—
332Q8—2442no—
333Q8—2442no—
334D4—1221no—
335D4—1221no—
336D4—2441no—
337D4—2441no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—4881no—
345C2×C4—4881no—
346C2×C4—4881no—
347C2×C4—2442no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4C22⋊C4×D6111yescharacteristic
353C2×C4#1451973911yescharacteristic
354C2×C4C4×D24411yescharacteristic
355C2×C4#1451974711yescharacteristic
356C2×C4#1451975011yescharacteristic
357C2×C4#1451975211yescharacteristic
358C2×C4#1451979811yescharacteristic
359C2×C4#1451980011yescharacteristic
360C2×C4#1451980111yescharacteristic
361C2×C4#1451980411yescharacteristic
362C8—42no—
363C8—42no—
364C8—81no—
365C8—4881no—
366C8—2441no—
367C8—2441no—
368C22—21no—
369C22—21no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22#1683964011yescharacteristic
374C22#1684008811yescharacteristic
375C22#1684008911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—4882no—
380C4—2441no—
381C4—2441no—
382C4—2441no—
383C4#1683975711yescharacteristic
384C4#1683976511yescharacteristic
385C4#1683990811yescharacteristic
386C4#1683991011yescharacteristic
387C4#1684002411yescharacteristic
388C4#1684003611yescharacteristic
389C2—21no—
390C2—21no—
391C2—4881no—
392C2#2144614011yescharacteristic
393C2#2144629311yescharacteristic
394C2#2144633511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1292C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1292D61
hypocenterC61#9172
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
3. #21444492C2semidirect
4. C2×#16839507C2semidirect
6. #21443714C2semidirect
7. C61×#1292C2semidirect
198. #1292D61semidirect
228. C61#9172semidirect

Maximal subgroups

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

subgroupindex
#214553072
#214544872
#214444922
C2×#168395072
#214442042
#214437142
C61×#12922
#917261