Finite Group Databasebeta

← #30603602

Subgroups — #30603602

Order 15616.

666 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 136 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#21461524C211yesmaximal, characteristic
2#21461518C211yesmaximal, characteristic
3C2×#16840633C212yesmaximal
4C2×#16840629C212yesmaximal
5#21448299C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C2×#14519856C2212yes—
8#16840642—21no—
9#16840642—21no—
10#16840640—21no—
11#16840640—21no—
12#16840633—24no—
13#16840629—24no—
14C2×#14519734C2211yescharacteristic
15C2×#14519734C2211yescharacteristic
16C2×C42×D61C2211yescharacteristic
17#16839659—21no—
18#16839657—21no—
19#16839636—21no—
20#16839633—21no—
21C4×#11758196C411yescharacteristic, complemented
22C4×#11758196C411yescharacteristic, complemented
23C4×C4⋊Dic61C411yescharacteristic, complemented
24C4×C4⋊C4×C61C411yescharacteristic, complemented
25C2×#11758213—22no—
26D61⋊M16—22no—
27D61⋊M16—22no—
28D61⋊M16—22no—
29D61⋊M16Q814yes—
30C2×#11758217—22no—
31C2×D61⋊C8—22no—
32#14519856—22no—
33#14519856—22no—
34#14519856—22no—
35#14519856D414yes—
36C2×C4⋊#6923—22no—
37C2×C22⋊#6923—22no—
38C2×C4×#6923—22no—
39C22×C4×D61—21no—
40C22×C4×D61C2311yescharacteristic
41#14519734—22no—
42#14519734—22no—
43#14519734—22no—
44#14519734—22no—
45C2×C4⋊Dic61—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758196D411yescharacteristic
50C2×#11758196D411yescharacteristic
51C2×#11758198—21no—
52C2×#11758198D411yescharacteristic
53C2×#11758198D411yescharacteristic
54C2×C4×Dic61—21no—
55C2×C4×Dic61C2×C411yescharacteristic
56C2×C4×Dic61C2×C411yescharacteristic
57C2×C4×Dic61C2×C411yescharacteristic
58C42×D61—22no—
59C42×D61—22no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63C2×C4⋊C4×C61—21no—
64C2×C42×C61C2×C411yescharacteristic
65C2×C42×C61C2×C411yescharacteristic
66C2×C42×C61C2×C411yescharacteristic
67#95×C61—21no—
68C23×D61C2×D411yescharacteristic
69C22×#6923—42no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80C2×C4×D61—42no—
81C2×C4×D61—42no—
82C2×C4×D61—42no—
83C2×C4×D61C2×D412yes—
84C2×C4×D61C2×Q812yes—
85C2×C4×D61#4112yes—
86C2×C4×D61#4112yes—
87C2×C4×D61#4112yes—
88C2×C4×D61#4112yes—
89C22⋊#6923—24no—
90C22⋊#6923—42no—
91#11758217—24no—
92#11758217—42no—
93C2×#92420—42no—
94C4⋊#6923—24no—
95C4⋊#6923—42no—
96C4×#6923—24no—
97C4×#6923—42no—
98#11758213—24no—
99#11758213—42no—
100D61⋊C8—24no—
101D61⋊C8—42no—
102C4⋊C4×C61—42no—
103C42×C61—21no—
104C42×C61—21no—
105C42×C61—22no—
106C42×C61—22no—
107#11758198—22no—
108#11758198—22no—
109#11758198—42no—
110C4⋊Dic61—42no—
111#11758196—22no—
112#11758196—22no—
113#11758196—42no—
114#11758196—42no—
115#11758196—41no—
116#11758196—41no—
117C4×Dic61—21no—
118C4×Dic61—21no—
119C4×Dic61—22no—
120C4×Dic61—22no—
121C4×Dic61—41no—
122C4×Dic61—41no—
123C23×C61C2×C22⋊C411yescharacteristic
124C22×D61—41no—
125C22×D61—41no—
126C22×D61#12112yes—
127C22×D61#12312yes—
128C22×D61#12411yescharacteristic
129C22×D61C4⋊Q811yescharacteristic
130C2×#6923—44no—
131C2×#6923—82no—
132C2×#6923—82no—
133C2×C4×C61—22no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61#11711yescharacteristic
144C2×C4×C61#11711yescharacteristic
145C2×C4×C61C4×D412yes—
146C2×C4×C61C4×Q812yes—
147C2×Dic61—22no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61C22⋊Q812yes—
158C2×Dic61#12312yes—
159C2×Dic61#12411yescharacteristic
160C2×Dic61#12711yescharacteristic
161C4×D61—48no—
162C4×D61C22⋊Q812yes—
163C4×D61C22⋊Q812yes—
164C4×D61#12312yes—
165C4×D61#12312yes—
166C4×D61#12512yes—
167C4×D61#12512yes—
168C4×D61#12612yes—
169C4×D61#12612yes—
170#92420—44no—
171#11347—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61#38111yescharacteristic
175C22×C61#39011yescharacteristic
176C22×C61#39111yescharacteristic
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—42no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61#39712yes—
183C2×D61#39812yes—
184#6923—84no—
185C4×C61—42no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61—81no—
189C4×C61#38712yes—
190C4×C61#38712yes—
191Dic61—42no—
192Dic61—41no—
193Dic61—41no—
194Dic61—81no—
195Dic61#39912yes—
196Dic61#40012yes—
197#2296—611no—
198#1742—611no—
199#1740—611no—
200C2×#339—612no—
201C2×H(3,ℤ/4)—612no—
202C2×C61—21no—
203C2×C61—21no—
204C2×C61#144511yescharacteristic
205C2×C61#182711yescharacteristic
206C2×C61#182711yescharacteristic
207D61—22no—
208D61—22no—
209C22×M16—612no—
210C2×#117—611no—
211C2×#117—611no—
212C2×#117—612no—
213C22×C42—611no—
214#389—1221no—
215#389—1221no—
216#385—1221no—
217#385—1221no—
218C4×C4⋊C4—611no—
219C4×C4⋊C4—611no—
220C4×C4⋊C4—611no—
221C4×C4⋊C4#692311yescharacteristic, complemented
222#343—1221no—
223#343—1221no—
224#342—1221no—
225#342—1221no—
226#339—1224no—
227H(3,ℤ/4)—1224no—
228C61#1134711yescharacteristic, complemented, Sylow
229C23×C4—611no—
230C23×C4—1221no—
231C2×M16—614no—
232C2×M16—1222no—
233C2×M16—1222no—
234C2×M16—1222no—
235C2×M16—1222no—
236C2×M16—1222no—
237C22×C8—1222no—
238#117—614no—
239#117—1222no—
240#117—1222no—
241#117—1222no—
242#117—1222no—
243#117—1222no—
244#117—1222no—
245#117—1222no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—611no—
249C2×C4⋊C4—1222no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C22⋊C4—611no—
255C2×C22⋊C4—611no—
256C2×C22⋊C4—1222no—
257C2×C22⋊C4—1221no—
258C2×C42—611no—
259C2×C42—611no—
260C2×C42—611no—
261C2×C42—1222no—
262C2×C42—1222no—
263C2×C42—1222no—
264C2×C42—1221no—
265C2×C42C2×#692311yescharacteristic
266C2×C42C2×#692311yescharacteristic
267C2×C42C2×#692311yescharacteristic
268#95—21no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272C24—611no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—611no—
276C22×C4—612no—
277C22×C4—612no—
278C22×C4—612no—
279C22×C4—612no—
280C22×C4—612no—
281C22×C4—612no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—2442no—
287C22×C4—2442no—
288C22×C4—2442no—
289C22×C4—2442no—
290C22×C4C22⋊#692311yescharacteristic
291C22×C4C22⋊#692311yescharacteristic
292C22×C4C22×#692311yescharacteristic
293M16—1224no—
294M16—1224no—
295M16—2442no—
296M16—2442no—
297C2×C8—1224no—
298C2×C8—2442no—
299C2×C8—2442no—
300C4⋊C4—42no—
301C4⋊C4—1222no—
302C4⋊C4—1222no—
303C4⋊C4—1224no—
304C4⋊C4—2442no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C4⋊C4—2442no—
308C4⋊C4—2442no—
309C4⋊C4—2442no—
310C22⋊C4—1222no—
311C22⋊C4—1222no—
312C22⋊C4—1224no—
313C22⋊C4—2442no—
314C22⋊C4—2442no—
315C42—21no—
316C42—21no—
317C42—22no—
318C42—22no—
319C42—1224no—
320C42—1221no—
321C42—1221no—
322C42—1222no—
323C42—1222no—
324C42—2441no—
325C42—2441no—
326C42—2442no—
327C23—612no—
328C23—612no—
329C23—611no—
330C23—611no—
331C23—2441no—
332C23—2441no—
333C23C2×C22⋊#692311yescharacteristic
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
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—612no—
349C2×C4—612no—
350C2×C4—612no—
351C2×C4—612no—
352C2×C4—612no—
353C2×C4—612no—
354C2×C4—612no—
355C2×C4—612no—
356C2×C4—1222no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—4882no—
360C2×C4—4882no—
361C2×C4—2448no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2444no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4#1451985611yescharacteristic
371C2×C4#1451985611yescharacteristic
372C2×C4D4×#692312yes—
373C2×C4Q8×#692312yes—
374C8—2444no—
375C22—21no—
376C22—21no—
377C22—612no—
378C22—612no—
379C22—1222no—
380C22—1222no—
381C22—2442no—
382C22—2441no—
383C22—2441no—
384C22#1684070511yescharacteristic
385C22#1684071411yescharacteristic
386C22(C2×#6923)⋊Q811yescharacteristic
387C4—42no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4—612no—
392C4—612no—
393C4—4881no—
394C4—4884no—
395C4—2442no—
396C4—2441no—
397C4—2441no—
398C4#1684071112yes—
399C4#1684071112yes—
400C2—21no—
401C2—21no—
402C2—1222no—
403C2—1222no—
404C2#2146100811yescharacteristic
405C2#2146172811yescharacteristic
406C2#2146172911yescharacteristic
subgroupG/H
centerC2×C4#14519856
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC22×C61#381
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#11347
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
21. C4×#11758196C4semidirect
22. C4×#11758196C4semidirect
23. C4×C4⋊Dic61C4semidirect
24. C4×C4⋊C4×C61C4semidirect
221. C4×C4⋊C4#6923semidirect
228. C61#11347semidirect

Maximal subgroups

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

subgroupindex
#214615242
#214615182
C2×#168406332
C2×#168406292
#214482992
#1134761