Finite Group Databasebeta

← #30600210

Subgroups — #30600210

Order 15616.

604 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840783C211yesmaximal, characteristic
2#21461710C211yesmaximal, characteristic
3C2×#16840607C212yesmaximal
4#21460657C212yesmaximal
5C2×#16839649C211yesmaximal, characteristic
6#16840783—24no—
7C2×C4⋊#92420—21no—
8C2×C22⋊#92420C2212yes—
9C2×C22⋊#92420C2212yes—
10C2×#14519832—21no—
11#16840628—21no—
12#16840628—21no—
13#16840607—24no—
14C22×C4⋊Dic61C2211yescharacteristic
15C22×#11758196C411yescharacteristic
16C22×C4×Dic61C2211yescharacteristic
17#16839649—21no—
18#16839649—21no—
19#16839649—21no—
20#16839649—21no—
21C2×#14519684C411yescharacteristic
22C2×#14519684C411yescharacteristic
23C2×#14519684C2211yescharacteristic
24C2×#95×C61C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27C4⋊#92420—24no—
28C22⋊#92420—22no—
29C22⋊#92420—22no—
30C22⋊#92420—22no—
31C22⋊#92420D414yes—
32#14519832—24no—
33C23×Dic61C2×C411yescharacteristic
34C23×Dic61C2×C411yescharacteristic
35C23×Dic61C2×C411yescharacteristic
36C23×Dic61C2311yescharacteristic
37C2×C4⋊Dic61—22no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—22no—
41C2×#11758196—22no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—22no—
45C2×C4×Dic61—22no—
46C2×C4×Dic61—22no—
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C23×C4×C61C2×C411yescharacteristic
58C23×C4×C61C2×C411yescharacteristic
59C23×C4×C61C2×C411yescharacteristic
60#95×C61—21no—
61#95×C61—21no—
62C24×C61C22×C411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—22no—
65C22×C4×C61—22no—
66C22×C4×C61—21no—
67C22×C4×C61—22no—
68C22×C4×C61—22no—
69C22×C4×C61—21no—
70C22×C4×C61—22no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61M1612yes—
77C22×Dic61—21no—
78C22×Dic61—22no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—22no—
83C22×Dic61—21no—
84C22×Dic61—22no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C22×Dic61—41no—
89C22×Dic61—41no—
90C22×Dic61—41no—
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61M1612yes—
94C22×Dic61C2×D411yescharacteristic
95C22×Dic61C2×D411yescharacteristic
96C22×Dic61C2×D412yes—
97C22×Dic61#4112yes—
98C2×#92420—24no—
99C2×#92420—42no—
100C2×#92420—42no—
101C2×#92420—42no—
102C2×#92420—42no—
103C2×#92420—42no—
104C4⋊Dic61—41no—
105C4⋊Dic61—42no—
106C4⋊Dic61—41no—
107#11758196—24no—
108#11758196—24no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—22no—
112C4×Dic61—22no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61C2×C22⋊C411yescharacteristic
120C23×C61C4×D412yes—
121C23×C61C2×M1611yescharacteristic
122C23×C61C2×M1611yescharacteristic
123C23×C61#13112yes—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—22no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—24no—
131C2×C4×C61—44no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—42no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—82no—
139C2×C4×C61#10112yes—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—22no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—42no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—82no—
163C2×Dic61#12011yescharacteristic
164C2×Dic61#12112yes—
165C2×Dic61#12311yescharacteristic
166#92420—44no—
167#92420—82no—
168#9086—611nomaximal, Sylow
169C22×C61—22no—
170C22×C61—22no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—22no—
176C22×C61—22no—
177C22×C61#38611yescharacteristic
178C22×C61#40711yescharacteristic
179C22×C61#40811yescharacteristic
180C22×C61#41011yescharacteristic
181C22×C61#41011yescharacteristic
182C22×C61C2×#10111yescharacteristic
183C22×C61#41311yescharacteristic
184C22×C61#43512yes—
185C22×C61#43612yes—
186C4×C61—22no—
187C4×C61—42no—
188C4×C61—41no—
189C4×C61—81no—
190Dic61—21no—
191Dic61—22no—
192Dic61—21no—
193Dic61—41no—
194Dic61—41no—
195Dic61—42no—
196Dic61—81no—
197C2×#432—611no—
198C2×#387—611no—
199#1817—611no—
200C2×#324—612no—
201#1280—612no—
202C2×C61—22no—
203C2×C61—22no—
204C2×C61#146411yescharacteristic
205C2×C61#146711yescharacteristic
206C2×C61#147011yescharacteristic
207C2×C61#147311yescharacteristic
208C2×C61#187011yescharacteristic
209C2×C61#189911yescharacteristic
210C2×C61#190111yescharacteristic
211C22×C4⋊C4—611no—
212C22×C4⋊C4—611no—
213C22×C42—611no—
214#432—1224no—
215C2×C4⋊C8—1221no—
216C2×C22⋊C8—612no—
217C2×C22⋊C8—612no—
218C2×#97—1221no—
219#387—1221no—
220#387—1221no—
221#387—1221no—
222#387—1221no—
223C2×#95—611no—
224C2×#95—611no—
225C2×#95—611no—
226C2×#95#692311yescharacteristic
227#336—1221no—
228#336—1221no—
229#324—1224no—
230C61#908611yescharacteristic, complemented, Sylow
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—611no—
234C23×C4—611no—
235C23×C4C2×#692311yescharacteristic
236C23×C4C2×#692311yescharacteristic
237C23×C4C2×#692311yescharacteristic
238C22×C8—1222no—
239C22×C8—1222no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1222no—
243C2×C4⋊C4—1222no—
244C2×C4⋊C4—1222no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1222no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—1222no—
253C2×C42—1222no—
254C4⋊C8—1224no—
255C22⋊C8—614no—
256C22⋊C8—1222no—
257C22⋊C8—1222no—
258C22⋊C8—1222no—
259#97—1224no—
260#95—21no—
261#95—21no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95—1221no—
266#95—1221no—
267#95—1221no—
268C24C22×#692311yescharacteristic
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—612no—
283C22×C4—612no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—612no—
287C22×C4—1221no—
288C22×C4—1222no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1222no—
293C22×C4—1222no—
294C22×C4—1221no—
295C22×C4—2441no—
296C22×C4—2441no—
297C22×C4—2441no—
298C22×C4—2441no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4#1175821312yes—
302C22×C4C22⋊#692311yescharacteristic
303C22×C4C22⋊#692311yescharacteristic
304C2×C8—1224no—
305C2×C8—2442no—
306C2×C8—2442no—
307C2×C8—2442no—
308C2×C8—2442no—
309C2×C8—2442no—
310C4⋊C4—1224no—
311C4⋊C4—1224no—
312C4⋊C4—2441no—
313C4⋊C4—2442no—
314C4⋊C4—2441no—
315C42—1221no—
316C42—1221no—
317C42—1222no—
318C42—1221no—
319C42—1222no—
320C42—1221no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23C2×C22⋊#692311yescharacteristic
326C23D4×#692312yes—
327C23D61⋊M1611yescharacteristic
328C23C2×#1175821311yescharacteristic
329C23#1451986412yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—24no—
337C2×C4—44no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—82no—
345C2×C4—611no—
346C2×C4—612no—
347C2×C4—611no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1222no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—4882no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2442no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4#1451983812yes—
372C8—4882no—
373C8—2444no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—22no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—22no—
382C22#1684071011yescharacteristic
383C22#1684073311yescharacteristic
384C22#1684073611yescharacteristic
385C22#1684074111yescharacteristic
386C22#1684074311yescharacteristic
387C22C2×#1451983811yescharacteristic
388C22#1684074911yescharacteristic
389C22#1684079112yes—
390C22#1684079512yes—
391C4—22no—
392C4—42no—
393C4—41no—
394C4—81no—
395C4—1222no—
396C4—1221no—
397C4—1221no—
398C4—4881no—
399C4—2441no—
400C4—2441no—
401C4—2442no—
402C2—22no—
403C2—22no—
404C2#2146107311yescharacteristic
405C2#2146108111yescharacteristic
406C2#2146109211yescharacteristic
407C2#2146110011yescharacteristic
408C2#2146179711yescharacteristic
409C2#2146184311yescharacteristic
410C2#2146184611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC2×#95×C61C4
socleC23×C61C2×C22⋊C4
cosocleC23×Dic61C23
hypercenterC2×#95#6923
hypocenterC61#9086
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
230. C61#9086semidirect

Maximal subgroups

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

subgroupindex
C2×#168407832
#214617102
C2×#168406072
#214606572
C2×#168396492
#908661