Finite Group Databasebeta

← #30600176

Subgroups — #30600176

Order 15616.

670 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758213C211yesmaximal, characteristic
2#21461674C211yesmaximal, characteristic
3C2×#16840612C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5#21448349C211yesmaximal, characteristic
6C22×#11758213—21no—
7C2×C4⋊#92420C2212yes—
8C2×#14519834—21no—
9C4×#11758213—24no—
10C2×#14519832—21no—
11C2×C4×#92420C2212yes—
12#16840628—21no—
13#16840612—24no—
14C2×#14519757C411yescharacteristic
15C2×#14519742C2211yescharacteristic
16C2×C42×D61C2211yescharacteristic
17#16839668C411yescharacteristic
18#16839645—21no—
19#16839633—21no—
20#16839619C411yescharacteristic
21C4⋊C4×Dic61—21no—
22C4⋊C4×Dic61C2211yescharacteristic
23#16839609—21no—
24C61×#389C411yescharacteristic
25C2×#11758213—24no—
26C2×#11758213—24no—
27C2×#11758213—24no—
28C22×#92420—22no—
29C22×#92420—22no—
30C4⋊#92420—22no—
31C4⋊#92420—22no—
32#14519834—42no—
33#14519832—24no—
34C4×#92420—22no—
35C4×#92420D414yes—
36C22×Dic122C2×C411yescharacteristic
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40#14519757—22no—
41#14519757—22no—
42#14519742—22no—
43#14519742—22no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758196—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—21no—
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61C2311yescharacteristic
54C42×D61—22no—
55C42×D61—22no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C42×C61C2×C411yescharacteristic
64#95×C61—21no—
65C23×D61C22⋊C411yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—22no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—21no—
86C2×C4×D61—22no—
87C2×C4×D61—21no—
88C2×Dic122—22no—
89C2×Dic122—22no—
90C2×Dic122—21no—
91C2×Dic122M1612yescomplemented
92C2×#92420—24no—
93C2×#92420—24no—
94C2×#92420—24no—
95C2×#92420—42no—
96C2×#92420—42no—
97C2×#92420—42no—
98#11758213—216no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—42no—
102C4⋊C4×C61M1612yescomplemented
103C42×C61—22no—
104#11758198—24no—
105#11758198—42no—
106C4⋊Dic61—24no—
107C4⋊Dic61—22no—
108#11758196—41no—
109#11758196—41no—
110C4×Dic61—21no—
111C4×Dic61—22no—
112C4×Dic61—21no—
113C4×Dic61—42no—
114C4×Dic61—41no—
115C4×Dic61—41no—
116C4×Dic61C2×D412yes—
117C4×Dic61#4112yes—
118C23×C61C2×C22⋊C411yescharacteristic
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61#10412yes—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—22no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61#10412yes—
138C2×C4×C61C4×D412yes—
139C2×C4×C61C2×M1611yescharacteristic
140C2×C4×C61C2×M1611yescharacteristic
141C2×C4×C61#13112yes—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—22no—
147C2×Dic61—21no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61#12011yescharacteristic
154C2×Dic61#12112yes—
155C2×Dic61#12311yescharacteristic
156C2×Dic61AGL(1,ℤ/8)11yescharacteristic
157C2×Dic61#13712yes—
158C2×Dic61#13711yescharacteristic
159C4×D61—24no—
160C4×D61—24no—
161C4×D61—42no—
162C4×D61—42no—
163C4×D61—42no—
164C4×D61—42no—
165Dic122—24no—
166Dic122—42no—
167#92420—28no—
168#92420—82no—
169#9077—611nomaximal, Sylow
170C22×C61#38611yescharacteristic
171C22×C61#40711yescharacteristic
172C22×C61#40811yescharacteristic
173C22×C61#41711yescharacteristic
174C22×C61#41911yescharacteristic
175C22×C61C2×#10411yescharacteristic
176C22×C61C2×#10411yescharacteristic
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—22no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C4×C61—22no—
185C4×C61—41no—
186C4×C61—42no—
187C4×C61—81no—
188C4×C61#43512yes—
189C4×C61#43612yes—
190Dic61—21no—
191Dic61—21no—
192Dic61—42no—
193Dic61—41no—
194Dic61—81no—
195Dic61#46812yes—
196Dic61#47012yes—
197C2×C4×M16—611no—
198C4×C22⋊Q8—611no—
199#1797—611no—
200C2×Q8⋊C8—612no—
201#1279—612no—
202C2×C61#148311yescharacteristic
203C2×C61#148511yescharacteristic
204C2×C61#148911yescharacteristic
205C2×C61#149111yescharacteristic
206C2×C61#187011yescharacteristic
207C2×C61#189411yescharacteristic
208C2×C61#189611yescharacteristic
209D61—42no—
210C22×M16—1221no—
211C2×C22⋊Q8—611no—
212C2×C4×Q8—611no—
213C22×C42—611no—
214C2×C4⋊C8—612no—
215C2×C22⋊C8—1221no—
216C4×M16—1224no—
217C2×#97—1221no—
218C2×C4×C8—612no—
219#391—611no—
220#389#692311yescharacteristic
221#387—1221no—
222#385—1221no—
223#380—611no—
224C4×C4⋊C4—611no—
225C4×C4⋊C4—1221no—
226C4×C22⋊C4—1221no—
227#336—1221no—
228Q8⋊C8—1224no—
229C61#907711yescharacteristic, complemented, Sylow
230C22×Q8—611no—
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—611no—
234C2×M16—1224no—
235C2×M16—1224no—
236C2×M16—1224no—
237C22×C8—1222no—
238C22×C8—1222no—
239C22⋊Q8—1222no—
240C22⋊Q8—1222no—
241C4×Q8—1222no—
242C4×Q8—1222no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4C2×#692311yescharacteristic
248C2×C4⋊C4C2×#692311yescharacteristic
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—1222no—
255C2×C42—1222no—
256C2×C42—1221no—
257C2×C42—1221no—
258C2×C42C2×#692311yescharacteristic
259C4⋊C8—1222no—
260C4⋊C8—1222no—
261C22⋊C8—2442no—
262#97—1224no—
263C4×C8—614no—
264C4×C8—1222no—
265#95—21no—
266#95—1221no—
267#95—1221no—
268#95—1221no—
269#95—1221no—
270C24—611no—
271C2×Q8—612no—
272C2×Q8—1221no—
273C2×Q8—1222no—
274C2×Q8—1222no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1222no—
284C22×C4—1221no—
285C22×C4—1222no—
286C22×C4—1222no—
287C22×C4—1222no—
288C22×C4—1221no—
289C22×C4—1222no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1222no—
293C22×C4—1221no—
294C22×C4C22⋊#692311yescharacteristic
295C22×C4C22⋊#692311yescharacteristic
296C22×C4C22×#692311yescharacteristic
297M16—12216no—
298C2×C8—1224no—
299C2×C8—1224no—
300C2×C8—1224no—
301C2×C8—2442no—
302C2×C8—2442no—
303C2×C8—2442no—
304C4⋊C4—21no—
305C4⋊C4—22no—
306C4⋊C4—42no—
307C4⋊C4—1224no—
308C4⋊C4—1222no—
309C4⋊C4—2441no—
310C4⋊C4—2441no—
311C4⋊C4#1175821312yescomplemented
312C22⋊C4—1224no—
313C22⋊C4—2442no—
314C42—22no—
315C42—612no—
316C42—612no—
317C42—1221no—
318C42—1222no—
319C42—1221no—
320C42—2441no—
321C42—2441no—
322C42—2442no—
323C23—612no—
324C23—1221no—
325C23—1221no—
326C23—1221no—
327C23—1221no—
328C23—1221no—
329C23—1221no—
330C23C2×C22⋊#692311yescharacteristic
331Q8—1224no—
332Q8—2442no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—612no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—612no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—1224no—
351C2×C4—1224no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1222no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2442no—
366C2×C4—2442no—
367C2×C4#1451984112yes—
368C2×C4D4×#692312yes—
369C2×C4D61⋊M1611yescharacteristic
370C2×C4C2×#1175821311yescharacteristic
371C2×C4#1451986512yes—
372C8—1228no—
373C8—4882no—
374C22—1222no—
375C22—1222no—
376C22—1222no—
377C22—2441no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22#1684071011yescharacteristic
382C22#1684073311yescharacteristic
383C22#1684073711yescharacteristic
384C22#1684075311yescharacteristic
385C22#1684075511yescharacteristic
386C22C2×#1451984111yescharacteristic
387C22D61⋊#10411yescharacteristic
388C4—22no—
389C4—41no—
390C4—42no—
391C4—81no—
392C4—612no—
393C4—612no—
394C4—1221no—
395C4—1221no—
396C4—4881no—
397C4—2441no—
398C4—2442no—
399C4#1684079212yes—
400C4#1684079612yes—
401C2—2442no—
402C2#2146113711yescharacteristic
403C2#2146114311yescharacteristic
404C2#2146115511yescharacteristic
405C2#2146116211yescharacteristic
406C2#2146179911yescharacteristic
407C2#2146183411yescharacteristic
408C2#2146183711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#9077
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. C2×#16840612C2semidirect
4. #21460655C2semidirect
91. C2×Dic122M16semidirect
102. C4⋊C4×C61M16semidirect
229. C61#9077semidirect
311. C4⋊C4#11758213semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582132
#214616742
C2×#168406122
#214606552
#214483492
#907761