Finite Group Databasebeta

← #30602180

Subgroups — #30602180

Order 15616.

664 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 122 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
1#21461673C211yesmaximal, characteristic
2#21461545C211yesmaximal, characteristic
3#21460657C212yesmaximal
4#21460657C212yesmaximal
5C2×#16839666C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C22⋊#92420C2212yes—
8C2×C22⋊#92420C2212yes—
9C2×#14519832—21no—
10#16840628—21no—
11#16840628—21no—
12C23×Dic122C411yescharacteristic
13C22×#11758196C411yescharacteristic
14C22×C4×Dic61C2211yescharacteristic
15#16839666—21no—
16#16839666—21no—
17#16839666—21no—
18#16839666—21no—
19C2×#14519684C411yescharacteristic
20C2×#14519684C2211yescharacteristic
21C2×#14519684C2211yescharacteristic
22C2×#95×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26C22⋊#92420—22no—
27C22⋊#92420—24no—
28C22⋊#92420Q814yescomplemented
29#14519832—42no—
30C22×Dic122—22no—
31C22×Dic122—21no—
32C22×Dic122—21no—
33C22×Dic122—22no—
34C22×Dic122—42no—
35C22×Dic122—42no—
36C23×Dic61C2×C411yescharacteristic
37C23×Dic61C2×C411yescharacteristic
38C23×Dic61C2×C411yescharacteristic
39C23×Dic61C2311yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—42no—
43C2×C4×Dic61—42no—
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54C23×C4×C61C2×C411yescharacteristic
55C23×C4×C61C2×C411yescharacteristic
56C23×C4×C61C2×C411yescharacteristic
57#95×C61—21no—
58#95×C61—21no—
59C24×C61C22×C411yescharacteristic
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—22no—
63C22×C4×C61—22no—
64C22×C4×C61—21no—
65C22×C4×C61—22no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61M1612yes—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—22no—
77C22×Dic61—22no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—22no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61—41no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61M1612yes—
91C22×Dic61C2×D411yescharacteristic
92C22×Dic61C2×D411yescharacteristic
93C22×Dic61C2×Q812yes—
94C22×Dic61#4112yes—
95C2×Dic122—24no—
96C2×Dic122—24no—
97C2×Dic122—48no—
98C2×Dic122—48no—
99C2×Dic122—42no—
100C2×Dic122—42no—
101C2×Dic122—42no—
102C2×Dic122—42no—
103C2×#92420—24no—
104C2×#92420—42no—
105C2×#92420—42no—
106C2×#92420—42no—
107C2×#92420—42no—
108C2×#92420—42no—
109#11758196—42no—
110#11758196—42no—
111C4×Dic61—22no—
112C4×Dic61—22no—
113C4×Dic61—41no—
114C4×Dic61—41no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61C2×C22⋊C411yescharacteristic
120C23×C61C4×Q812yes—
121C23×C61C2×M1611yescharacteristic
122C23×C61C2×M1611yescharacteristic
123C23×C61#13112yes—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—22no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—44no—
131C2×C4×C61—42no—
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—24no—
141C2×Dic61—24no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—22no—
151C2×Dic61—42no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—82no—
161C2×Dic61#9912yes—
162C2×Dic61#10012yes—
163C2×Dic61C22⋊Q812yes—
164C2×Dic61#12411yescharacteristic
165C2×Dic61C4⋊Q811yescharacteristic
166Dic122—48no—
167Dic122—48no—
168#92420—44no—
169#92420—82no—
170#9882—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—22no—
176C22×C61—22no—
177C22×C61—22no—
178C22×C61—22no—
179C22×C61#39111yescharacteristic
180C22×C61#40711yescharacteristic
181C22×C61#40811yescharacteristic
182C22×C61C2×#9911yescharacteristic
183C22×C61#41011yescharacteristic
184C22×C61C2×#10011yescharacteristic
185C22×C61C2×#10111yescharacteristic
186C22×C61#44612yes—
187C22×C61#44612yes—
188C4×C61—22no—
189C4×C61—42no—
190C4×C61—41no—
191C4×C61—81no—
192Dic61—22no—
193Dic61—22no—
194Dic61—22no—
195Dic61—21no—
196Dic61—21no—
197Dic61—42no—
198Dic61—81no—
199C2×#391—611no—
200#1797—611no—
201#1749—611no—
202#1280—612no—
203#1280—612no—
204C2×C61—22no—
205C2×C61—22no—
206C2×C61#146211yescharacteristic
207C2×C61#146711yescharacteristic
208C2×C61#146911yescharacteristic
209C2×C61#147211yescharacteristic
210C2×C61#198511yescharacteristic
211C2×C61#199611yescharacteristic
212C2×C61#199711yescharacteristic
213C23×Q8—611no—
214C22×C4⋊C4—611no—
215C22×C42—611no—
216C2×C4⋊C8—1221no—
217C2×C22⋊C8—612no—
218C2×C22⋊C8—612no—
219C2×#97—1221no—
220#391—1221no—
221#391—1221no—
222#391—1221no—
223#391—1221no—
224C2×#95—611no—
225C2×#95—611no—
226C2×#95—611no—
227C2×#95#692311yescharacteristic
228#336—1221no—
229#336—1221no—
230C61#988211yescharacteristic, complemented, Sylow
231C22×Q8—1222no—
232C22×Q8—1221no—
233C22×Q8—1221no—
234C22×Q8—1222no—
235C22×Q8—2442no—
236C22×Q8—2442no—
237C23×C4—611no—
238C23×C4—611no—
239C23×C4—611no—
240C23×C4—611no—
241C23×C4C2×#692311yescharacteristic
242C23×C4C2×#692311yescharacteristic
243C23×C4C2×#692311yescharacteristic
244C22×C8—1222no—
245C22×C8—1222no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—2442no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—2442no—
254C4⋊C8—2442no—
255C22⋊C8—614no—
256C22⋊C8—1222no—
257C22⋊C8—1224no—
258#97—2442no—
259#95—21no—
260#95—21no—
261#95—1221no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95—1221no—
266#95—1221no—
267C24C22×#692311yescharacteristic
268C2×Q8—1224no—
269C2×Q8—1224no—
270C2×Q8—2442no—
271C2×Q8—2442no—
272C2×Q8—2448no—
273C2×Q8—2442no—
274C2×Q8—2442no—
275C2×Q8—2448no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—612no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—1222no—
295C22×C4—1222no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1222no—
301C22×C4—1221no—
302C22×C4—2441no—
303C22×C4—2441no—
304C22×C4—2441no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4—2441no—
308C22×C4#1175821312yes—
309C22×C4C22⋊#692311yescharacteristic
310C22×C4C22⋊#692311yescharacteristic
311C2×C8—1224no—
312C2×C8—2442no—
313C2×C8—2442no—
314C2×C8—2442no—
315C2×C8—2442no—
316C2×C8—2442no—
317C4⋊C4—2442no—
318C4⋊C4—2442no—
319C42—1222no—
320C42—1222no—
321C42—2441no—
322C42—2441no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23C2×C22⋊#692311yescharacteristic
328C23Q8×#692312yes—
329C23D61⋊M1611yescharacteristic
330C23C2×#1175821311yescharacteristic
331C23#1451986412yes—
332Q8—2448no—
333Q8—2448no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—82no—
349C2×C4—612no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—612no—
353C2×C4—612no—
354C2×C4—1224no—
355C2×C4—1224no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1222no—
365C2×C4—4882no—
366C2×C4—2442no—
367C2×C4—2442no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2442no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2442no—
375C2×C4#1451983812yes—
376C8—4882no—
377C8—2444no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22(C2×#6923)⋊Q811yescharacteristic
387C22#1684073311yescharacteristic
388C22#1684073511yescharacteristic
389C22D61⋊#9911yescharacteristic
390C22#1684074111yescharacteristic
391C22D61⋊#10011yescharacteristic
392C22C2×#1451983811yescharacteristic
393C22#1684081212yes—
394C22#1684081412yes—
395C4—22no—
396C4—42no—
397C4—41no—
398C4—81no—
399C4—1222no—
400C4—1222no—
401C4—1221no—
402C4—1222no—
403C4—1221no—
404C4—4881no—
405C4—2442no—
406C2—22no—
407C2—22no—
408C2#2146106511yescharacteristic
409C2#2146108111yescharacteristic
410C2#2146108811yescharacteristic
411C2#2146109811yescharacteristic
412C2#2146199211yescharacteristic
413C2#2146201011yescharacteristic
414C2#2146201211yescharacteristic
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#9882
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
28. C22⋊#92420Q8semidirect
230. C61#9882semidirect

Maximal subgroups

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

subgroupindex
#214616732
#214615452
#214606572
C2×#168396662
#988261