Finite Group Databasebeta

← #30604848

Subgroups — #30604848

Order 15616.

648 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#14519835C211yesmaximal, characteristic, complemented
2#21461058C211yesmaximal, characteristic, complemented
3#21460813C212yesmaximal, complemented
4#21460798C212yesmaximal, complemented
5#21449035C211yesmaximal, characteristic
6#16840779—21no—
7C2×#14519835—21no—
8C4×C22⋊#6923—21no—
9#16840640C2212yes—
10#16840606C2212yes—
11#16840605—21no—
12C22×#11758222C411yescharacteristic, complemented
13C2×C4×D244—21no—
14C2×C4×C22⋊D61C2211yescharacteristic
15#16839683C411yescharacteristic, complemented
16#16839680C411yescharacteristic, complemented
17#16839678—21no—
18#16839675C2211yescharacteristic
19#16839672C2211yescharacteristic
20#16839671—21no—
21C4×#11758198—21no—
22C4×C22⋊C4×C61C411yescharacteristic, complemented
23C2×C22⋊#6923—22no—
24C2×C4×#6923—41no—
25#14519844—41no—
26#14519835—24no—
27C22⋊#92420—22no—
28C4×#92420—41no—
29(C2×#6923)⋊C4—41no—
30C2×#11758222—44no—
31C2×#11758222—41no—
32C2×#11758222—41no—
33C22×Dic122C2×C411yescharacteristic
34C22×D244—21no—
35C22×D244C2×C411yescharacteristic
36C22×C22⋊D61—21no—
37C22×C22⋊D61D411yescharacteristic
38C22×C4×D61—21no—
39C22×C4×D61D411yescharacteristic
40C4×D244—44no—
41C4×C22⋊D61—41no—
42C4×C22⋊D61—41no—
43C2×C4⋊Dic61—21no—
44C2×#11758196C2×C411yescharacteristic
45C2×C22⋊Dic61D411yescharacteristic
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198C2311yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52#14519684—21no—
53#14519684—21no—
54C23×C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C42×C61—21no—
57#95×C61C2×C411yescharacteristic
58#95×C61C2×C411yescharacteristic
59C24×C61C22⋊C411yescharacteristic
60C23×D61—21no—
61C23×D61C2×D411yescharacteristic
62C22×#6923—42no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—42no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C2×C22⋊D61—22no—
71C2×C22⋊D61—22no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C22×Dic61—21no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80#11758222—44no—
81#11758222—44no—
82#11758222—44no—
83#11758222—44no—
84C2×D244—42no—
85C2×D244—41no—
86C2×D244—42no—
87C2×D244—42no—
88C2×D244—42no—
89C2×C4×D61—24no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—42no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—42no—
96C2×Dic122—41no—
97C2×Dic122—42no—
98C22⋊#6923—24no—
99C22⋊#6923—42no—
100C2×#92420—42no—
101C4×#6923—82no—
102C22⋊C4×C61—42no—
103C42×C61—42no—
104C22⋊Dic61—41no—
105#11758198—41no—
106#11758198—42no—
107#11758198—42no—
108#11758198—42no—
109#11758198—42no—
110C4⋊Dic61—42no—
111#11758196—41no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61C2×C22⋊C411yescharacteristic
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—22no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61#13512yes—
132C2×#6923—44no—
133C2×#6923—82no—
134C2×#6923—82no—
135C2×C4×C61—22no—
136C2×C4×C61—22no—
137C2×C4×C61—21no—
138C2×C4×C61—42no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61#9911yescharacteristic
147C2×C4×C61#9911yescharacteristic
148C22⋊D61—44no—
149C22⋊D61—48no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—22no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61#10412yes—
160D244—42no—
161D244—48no—
162D244—42no—
163C4×D61—44no—
164C4×D61—42no—
165C4×D61—44no—
166C4×D61—81no—
167Dic122—42no—
168Dic122—42no—
169#92420—82no—
170#11725—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61C2×#9911yescharacteristic
179C22×C61#41611yescharacteristic
180C22×C61C2×#10411yescharacteristic
181C2×D61—22no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—42no—
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—81no—
193#6923—84no—
194C4×C61—21no—
195C4×C61—42no—
196C4×C61—41no—
197C4×C61—81no—
198C4×C61AΣL(1,𝔽16)12yes—
199Dic61—22no—
200Dic61—42no—
201Dic61—41no—
202Dic61—41no—
203#2388—611no—
204C4×#99—611no—
205#1460—611no—
206#1351—612no—
207#1343—612no—
208C2×C61—21no—
209C2×C61—21no—
210C2×C61—81no—
211C2×C61#150111yescharacteristic
212C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
213C2×C61#212611yescharacteristic
214D61—42no—
215D61—82no—
216C22×#41—611no—
217C2×C4×D4—611no—
218C2×C4×D4—1221no—
219#431—1221no—
220C2×#99—1221no—
221#395—611no—
222#394—611no—
223#394—1221no—
224#393—611no—
225#392—611no—
226#392—1221no—
227C4×C22⋊C4—1221no—
228C4×C22⋊C4—1221no—
229C4×C22⋊C4#692311yescharacteristic, complemented
230#342—612no—
231#323—612no—
232#323—1221no—
233C61#1172511yescharacteristic, complemented, Sylow
234C2×#41—2441no—
235C2×#41—2441no—
236C2×#41—2444no—
237C22×Q8—611no—
238C22×D4—611no—
239C22×D4—611no—
240C22×D4—1221no—
241C22×D4—1221no—
242C23×C4—611no—
243C23×C4—1221no—
244C23×C4C2×#692311yescharacteristic
245C4×D4—2444no—
246C4×D4—2441no—
247C4×D4—2441no—
248C2×C4⋊C4—611no—
249C2×C4⋊C4—1221no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—611no—
252C2×C22⋊C4—611no—
253C2×C22⋊C4—1222no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C42—21no—
259C2×C42—611no—
260C2×C42—2441no—
261C4⋊C8—2441no—
262#99—1224no—
263C22⋊C8—1222no—
264C4×C8—2441no—
265#95—1221no—
266#95—1221no—
267#95—2441no—
268#95C2×#692311yescharacteristic
269#95C2×#692311yescharacteristic
270C24—611no—
271C24—1221no—
272C24C22⋊#692311yescharacteristic
273#41—2444no—
274#41—2444no—
275#41—2444no—
276#41—2444no—
277C2×Q8—2441no—
278C2×Q8—2442no—
279C2×D4—1222no—
280C2×D4—1222no—
281C2×D4—2441no—
282C2×D4—2442no—
283C2×D4—2442no—
284C2×D4—2442no—
285C2×D4—2442no—
286C2×D4—2441no—
287C2×D4—2442no—
288C2×D4—2442no—
289C2×D4—2442no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—42no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—1224no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—2442no—
303C22×C4—2442no—
304C22×C4—2442no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4C22⋊#692311yescharacteristic
308C22×C4C22×#692311yescharacteristic
309C2×C8—2442no—
310C4⋊C4—2441no—
311C4⋊C4—2442no—
312C22⋊C4—42no—
313C22⋊C4—1224no—
314C22⋊C4—2441no—
315C22⋊C4—2442no—
316C22⋊C4—2442no—
317C22⋊C4—2442no—
318C22⋊C4—2442no—
319C22⋊C4—2441no—
320C22⋊C4—2442no—
321C42—42no—
322C42—1221no—
323C42—1221no—
324C42—4882no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23—612no—
331C23—1222no—
332C23—1221no—
333C23—1221no—
334C23—2441no—
335C23—2441no—
336C23—2441no—
337C23—2441no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23C2×C22⋊#692311yescharacteristic
343Q8—2442no—
344Q8—2442no—
345D4—2442no—
346D4—2448no—
347D4—2442no—
348D4—2444no—
349D4—2448no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—612no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1222no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—4881no—
368C2×C4—4882no—
369C2×C4—4882no—
370C2×C4—2444no—
371C2×C4—2444no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2442no—
375C2×C4—2444no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4#1451983611yescharacteristic
379C2×C4#1451983611yescharacteristic
380C8—4882no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—81no—
387C22—81no—
388C22—1222no—
389C22—4881no—
390C22—4881no—
391C22—4881no—
392C22—4881no—
393C22—4881no—
394C22—2442no—
395C22—2442no—
396C22—2442no—
397C22—2442no—
398C22—2441no—
399C22—2441no—
400C22C2×#1451983611yescharacteristic
401C22#1684075211yescharacteristic
402C22D61⋊#10411yescharacteristic
403C4—21no—
404C4—42no—
405C4—41no—
406C4—81no—
407C4—1222no—
408C4—4884no—
409C4—2441no—
410C4—2442no—
411C4—2441no—
412C4#1684066312yes—
413C2—21no—
414C2—21no—
415C2—81no—
416C2—4882no—
417C2—2442no—
418C2#2146119611yescharacteristic
419C2C2×#1684066311yescharacteristic
420C2#2146209211yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#99
prime radical#21449035C2
cosocleC2×#11758198C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#11725
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C4×#14519835C2semidirect
2. #21461058C2semidirect
3. #21460813C2semidirect
4. #21460798C2semidirect
12. C22×#11758222C4semidirect
15. #16839683C4semidirect
16. #16839680C4semidirect
22. C4×C22⋊C4×C61C4semidirect
229. C4×C22⋊C4#6923semidirect
233. C61#11725semidirect

Maximal subgroups

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

subgroupindex
C4×#145198352
#214610582
#214608132
#214607982
#214490352
#1172561