Finite Group Databasebeta

← #30606821

Subgroups — #30606821

Order 15616.

1098 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 1098 conjugacy classes of subgroups — too many to draw. Only its 100 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×#16840669C212yesmaximal, complemented
2C2×#16840667C212yesmaximal, complemented
3#21461648C212yesmaximal, complemented
4C2×#16840312C211yesmaximal, characteristic
5C2×#14519836C2214yes—
6C2×#14519835—22no—
7#16840705—22no—
8#16840669—24no—
9#16840667—24no—
10C22×#11758222C411yescharacteristic, complemented
11C22×#11758222C2211yescharacteristic
12#16840312—24no—
13#16840312—24no—
14C2×#14519777C411yescharacteristic, complemented
15C2×#14519774C2211yescharacteristic
16C2×#14519765C411yescharacteristic, complemented
17C2×#14519765C2211yescharacteristic
18C2×#14519751—22no—
19C2×C4×D244—22no—
20C22×C42×C61C411yescharacteristic, complemented
21C2×C22⋊#6923—24no—
22#14519836—24no—
23#14519836—24no—
24#14519835—44no—
25(C2×#6923)⋊C4—44no—
26C2×#11758222—22no—
27C2×#11758222—22no—
28C2×#11758222—22no—
29C2×#11758222—22no—
30C2×#11758222—42no—
31C2×#11758222—42no—
32C2×#11758222—42no—
33C2×#11758222—42no—
34C22×Dic122C2×C411yescharacteristic
35C22×Dic122C2×C411yescharacteristic
36C22×D244—22no—
37C22×D244C2×C411yescharacteristic
38C22×D244C2311yescharacteristic
39C22×C22⋊D61—21no—
40C22×C22⋊D61D412yes—
41C22×C4×D61—21no—
42C22×C4×D61D412yes—
43#14519777—22no—
44#14519777—22no—
45#14519774—22no—
46#14519774D414yes—
47#14519765—22no—
48#14519765—22no—
49#14519765—22no—
50#14519765D414yes—
51#14519751—216no—
52C4×D244—216no—
53C2×C4⋊Dic61—22no—
54C2×#11758198—22no—
55C2×#11758198—22no—
56C23×C4×C61—21no—
57C23×C4×C61C2×C411yescharacteristic
58C2×C42×C61—21no—
59C2×C42×C61—22no—
60C2×C42×C61—22no—
61C2×C42×C61C2×C411yescharacteristic
62C2×C42×C61C2×C411yescharacteristic
63C24×C61C22⋊C411yescharacteristic
64C23×D61—21no—
65C23×D61C2×D412yes—
66C22×#6923—44no—
67C22×C4×C61—22no—
68C22×C4×C61—21no—
69C22×C4×C61—22no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—24no—
73C22×C4×C61—21no—
74C22×C4×C61—44no—
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C2×C22⋊D61—24no—
78C2×C22⋊D61—24no—
79C2×C22⋊D61—24no—
80C2×C22⋊D61—42no—
81C2×C22⋊D61—42no—
82C2×C22⋊D61—42no—
83C22×Dic61—21no—
84C22×Dic61C22⋊C412yes—
85#11758222—48no—
86#11758222—48no—
87#11758222—48no—
88#11758222—48no—
89C2×D244—28no—
90C2×D244—21no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—48no—
94C2×D244—41no—
95C2×D244—41no—
96C2×D244C22⋊C412yes—
97C2×D244C2×D412yes—
98C2×D244C2×D412yes—
99C2×C4×D61—24no—
100C2×C4×D61—24no—
101C2×C4×D61—24no—
102C2×C4×D61—42no—
103C2×C4×D61—42no—
104C2×C4×D61—42no—
105C2×Dic122—21no—
106C2×Dic122—21no—
107C2×Dic122—21no—
108C2×Dic122—41no—
109C2×Dic122—41no—
110C2×Dic122—41no—
111C2×Dic122—41no—
112C2×Dic122C22⋊C412yes—
113C22⋊#6923—44no—
114C22⋊#6923—44no—
115C42×C61—24no—
116C42×C61—21no—
117C42×C61—21no—
118C42×C61C22⋊C412yes—
119C42×C61C22⋊C412yes—
120#11758198—28no—
121#11758198—28no—
122C4⋊Dic61—28no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—42no—
126C23×C61#9912yes—
127C23×C61C2×C22⋊C411yescharacteristic
128C22×D61—22no—
129C22×D61—22no—
130C22×D61—22no—
131C22×D61—44no—
132C22×D61—44no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61#12014yes—
136C2×#6923—84no—
137C2×#6923—88no—
138C2×C4×C61—24no—
139C2×C4×C61—24no—
140C2×C4×C61—24no—
141C2×C4×C61—22no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—22no—
147C2×C4×C61—48no—
148C2×C4×C61—42no—
149C2×C4×C61#9912yes—
150C2×C4×C61C2×C22⋊C411yescharacteristic
151C2×C4×C61C2×C22⋊C411yescharacteristic
152C22⋊D61—48no—
153C22⋊D61—48no—
154C2×Dic61—22no—
155C2×Dic61—22no—
156C2×Dic61—22no—
157C2×Dic61—22no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160D244—42no—
161D244—42no—
162D244—42no—
163D244—416no—
164D244—42no—
165C4×D61—48no—
166C4×D61—48no—
167Dic122—42no—
168Dic122—42no—
169Dic122—42no—
170Dic122—42no—
171#12695—611nomaximal, Sylow
172C22×C61—22no—
173C22×C61—22no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—42no—
177C22×C61#37911yescharacteristic
178C22×C61C2×#9911yescharacteristic
179C22×C61C2×#9911yescharacteristic
180C2×D61—24no—
181C2×D61—44no—
182C2×D61—44no—
183C2×D61—44no—
184C2×D61—42no—
185C2×D61—82no—
186C2×D61—82no—
187C2×D61—82no—
188#6923—164no—
189C4×C61—24no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—22no—
193C4×C61—42no—
194Dic61—42no—
195Dic61—42no—
196C2×#532—611no—
197C2×#354—612no—
198C2×#353—612no—
199#1782—612no—
200C2×C61—21no—
201C2×C61—21no—
202C2×C61—42no—
203C2×C61#178111yescharacteristic
204C2×C61#212612yes—
205D61—44no—
206D61—82no—
207C22×#41—611no—
208C22×#41—611no—
209#532—1224no—
210#532—1224no—
211C2×C4⋊Q8—611no—
212C2×#127—611no—
213C2×#124—611no—
214C2×#124—611no—
215C2×#121—1222no—
216C2×C4×D4—1222no—
217C22×C42#692311yescharacteristic, complemented
218C2×#99—614no—
219C2×#99—1222no—
220#381—1222no—
221#354—1224no—
222#353—1224no—
223C61#1269511yescharacteristic, complemented, Sylow
224C2×#41—1222no—
225C2×#41—1222no—
226C2×#41—1222no—
227C2×#41—1222no—
228C2×#41—2442no—
229C2×#41—2442no—
230C2×#41—2442no—
231C2×#41—2442no—
232C22×Q8—611no—
233C22×Q8—611no—
234C22×D4—612no—
235C22×D4—611no—
236C22×D4—611no—
237C22×D4—1222no—
238C22×D4—1221no—
239C23×C4—21no—
240C23×C4—612no—
241C23×C4—1221no—
242C23×C4C2×#692311yescharacteristic
243C4⋊Q8—1222no—
244C4⋊Q8—1222no—
245#127—614no—
246#127—1222no—
247#124—614no—
248#124—1222no—
249#124—1222no—
250#124—1222no—
251#121—12216no—
252C4×D4—12216no—
253C2×C4⋊C4—1222no—
254C2×C22⋊C4—1222no—
255C2×C22⋊C4—1222no—
256C2×C22⋊C4—1224no—
257C2×C42—21no—
258C2×C42—22no—
259C2×C42—22no—
260C2×C42C2×#692311yescharacteristic
261C2×C42C2×#692311yescharacteristic
262#99—1224no—
263#99—1224no—
264#99—2444no—
265#95—2444no—
266C24—612no—
267C24—1221no—
268C24C22⋊#692311yescharacteristic
269#41—2448no—
270#41—2448no—
271#41—2448no—
272#41—2448no—
273C2×Q8—612no—
274C2×Q8—1221no—
275C2×Q8—1221no—
276C2×Q8—1221no—
277C2×Q8—2441no—
278C2×Q8—2441no—
279C2×Q8—2441no—
280C2×Q8—2441no—
281C2×D4—612no—
282C2×D4—612no—
283C2×D4—612no—
284C2×D4—1228no—
285C2×D4—1224no—
286C2×D4—1224no—
287C2×D4—1224no—
288C2×D4—1221no—
289C2×D4—2441no—
290C2×D4—2441no—
291C2×D4—2441no—
292C2×D4—2441no—
293C2×D4—2448no—
294C2×D4—2442no—
295C2×D4—2442no—
296C2×D4—2442no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—24no—
303C22×C4—21no—
304C22×C4—44no—
305C22×C4—612no—
306C22×C4—1224no—
307C22×C4—1224no—
308C22×C4—1221no—
309C22×C4—1224no—
310C22×C4—2442no—
311C22×C4—2442no—
312C22×C4—2444no—
313C22×C4—2442no—
314C22×C4C22⋊#692311yescharacteristic
315C22×C4C22×#692311yescharacteristic
316C4⋊C4—1228no—
317C22⋊C4—1228no—
318C22⋊C4—1228no—
319C22⋊C4—2444no—
320C22⋊C4—2444no—
321C42—24no—
322C42—21no—
323C42—21no—
324C42C22⋊#692312yes—
325C42C22⋊#692312yes—
326C23—21no—
327C23—21no—
328C23—42no—
329C23—614no—
330C23—1222no—
331C23—1222no—
332C23—1222no—
333C23—2444no—
334C23—2444no—
335C23—2441no—
336C23—2441no—
337C23#1451983612yes—
338C23C2×C22⋊#692311yescharacteristic
339Q8—2442no—
340Q8—2442no—
341Q8—2442no—
342Q8—2442no—
343D4—2442no—
344D4—2442no—
345D4—2442no—
346D4—24416no—
347D4—2442no—
348D4—2448no—
349D4—2448no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—48no—
360C2×C4—42no—
361C2×C4—1222no—
362C2×C4—1222no—
363C2×C4—1222no—
364C2×C4—1222no—
365C2×C4—4884no—
366C2×C4—4888no—
367C2×C4—2448no—
368C2×C4—2448no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4#1451983612yes—
372C2×C4C2×C22⋊#692311yescharacteristic
373C2×C4C2×C22⋊#692311yescharacteristic
374C22—22no—
375C22—22no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—1224no—
380C22—4882no—
381C22—4882no—
382C22—4882no—
383C22—2444no—
384C22—2444no—
385C22—2442no—
386C22—2444no—
387C22#1684070311yescharacteristic
388C22C2×#1451983611yescharacteristic
389C22C2×#1451983611yescharacteristic
390C4—24no—
391C4—22no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—9764no—
396C4—2442no—
397C4—2442no—
398C2—21no—
399C2—21no—
400C2—42no—
401C2—4882no—
402C2—2444no—
403C2#2146164711yescharacteristic
404C2#2146209212yes—
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C42×C61C4
socleC22×C61C2×#99
prime radicalC2×#16840312C2
cosocleC22×D244C23
hypercenterC22×C42#6923
hypocenterC61#12695
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C2×#16840669C2semidirect
2. C2×#16840667C2semidirect
3. #21461648C2semidirect
10. C22×#11758222C4semidirect
14. C2×#14519777C4semidirect
16. C2×#14519765C4semidirect
20. C22×C42×C61C4semidirect
217. C22×C42#6923semidirect
223. C61#12695semidirect

Maximal subgroups

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

subgroupindex
C2×#168406692
C2×#168406672
#214616482
C2×#168403122
#1269561