Finite Group Databasebeta

← #30606841

Subgroups — #30606841

Order 15616.

1070 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 1070 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×#16840673C212yesmaximal, complemented
2C2×#16840671C212yesmaximal, complemented
3#21461655C212yesmaximal, complemented
4C2×#16840312C211yesmaximal, characteristic
5C2×#14519838C2214yes—
6C2×#14519837—22no—
7#16840734—22no—
8#16840673—24no—
9#16840671—24no—
10C22×#11758222C411yescharacteristic
11C22×#11758222C2211yescharacteristic
12#16840312—24no—
13#16840312—24no—
14C2×#14519777C2211yescharacteristic
15C2×#14519774C411yescharacteristic
16C2×#14519765C411yescharacteristic
17C2×#14519765C2211yescharacteristic
18C2×#14519751—22no—
19C2×C4×D244—22no—
20C22×C42×C61C411yescharacteristic
21C2×#11758217—24no—
22#14519838—24no—
23#14519838—24no—
24#14519837—44no—
25#14519834—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×Dic122C2311yescharacteristic
36C22×D244—22no—
37C22×D244C2×C411yescharacteristic
38C22×D244C2×C411yescharacteristic
39C22×C22⋊D61—21no—
40C22×C22⋊D61D412yes—
41C22×C4×D61—21no—
42C22×C4×D61D412yes—
43#14519777—22no—
44#14519777D414yes—
45#14519774—22no—
46#14519774—22no—
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×D61C22⋊C412yes—
66C22×C4×C61—22no—
67C22×C4×C61—21no—
68C22×C4×C61—22no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—24no—
72C22×C4×C61—21no—
73C22×C4×C61—44no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22×C411yescharacteristic
76C2×C22⋊D61—24no—
77C2×C22⋊D61—24no—
78C2×C22⋊D61—24no—
79C2×C22⋊D61—42no—
80C2×C22⋊D61—42no—
81C2×C22⋊D61—42no—
82C22×Dic61—21no—
83C22×Dic61C2×D412yes—
84#11758222—48no—
85#11758222—48no—
86#11758222—48no—
87#11758222—48no—
88C2×D244—28no—
89C2×D244—21no—
90C2×D244—21no—
91C2×D244—21no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—48no—
95C2×D244—41no—
96C2×D244—41no—
97C2×D244C22⋊C412yes—
98C2×C4×D61—24no—
99C2×C4×D61—24no—
100C2×C4×D61—24no—
101C2×C4×D61—42no—
102C2×C4×D61—42no—
103C2×C4×D61—42no—
104C2×Dic122—21no—
105C2×Dic122—41no—
106C2×Dic122—41no—
107C2×Dic122—41no—
108C2×Dic122—41no—
109C2×Dic122C22⋊C412yes—
110C2×Dic122C2×D412yes—
111C2×Dic122C2×D412yes—
112#11758217—44no—
113#11758217—44no—
114C2×#92420—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—22no—
132C22×D61—44no—
133C22×D61—44no—
134C22×D61—41no—
135C22×D61—41no—
136C2×C4×C61—24no—
137C2×C4×C61—24no—
138C2×C4×C61—24no—
139C2×C4×C61—22no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—22no—
145C2×C4×C61—48no—
146C2×C4×C61—42no—
147C2×C4×C61#9912yes—
148C2×C4×C61C2×C22⋊C411yescharacteristic
149C2×C4×C61C2×C22⋊C411yescharacteristic
150C22⋊D61—48no—
151C22⋊D61—48no—
152C2×Dic61—22no—
153C2×Dic61—22no—
154C2×Dic61—22no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61#12014yes—
158D244—42no—
159D244—416no—
160D244—42no—
161D244—42no—
162D244—42no—
163C4×D61—48no—
164C4×D61—48no—
165Dic122—42no—
166Dic122—42no—
167Dic122—42no—
168Dic122—42no—
169#92420—84no—
170#12701—611nomaximal, Sylow
171C22×C61—22no—
172C22×C61—22no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61#37911yescharacteristic
177C22×C61C2×#9911yescharacteristic
178C22×C61C2×#9911yescharacteristic
179C2×D61—44no—
180C2×D61—44no—
181C2×D61—44no—
182C2×D61—42no—
183C2×D61—42no—
184C2×D61—82no—
185C2×D61—82no—
186C2×D61—82no—
187C4×C61—24no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—22no—
191C4×C61—42no—
192Dic61—24no—
193Dic61—42no—
194C2×#532—611no—
195C2×#356—612no—
196C2×#355—612no—
197#1785—612no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61—42no—
201C2×C61#178111yescharacteristic
202C2×C61#213212yes—
203D61—82no—
204D61—82no—
205C22×#41—611no—
206C22×#41—611no—
207#532—1224no—
208#532—1224no—
209C2×C4⋊Q8—611no—
210C2×#127—611no—
211C2×#124—611no—
212C2×#124—611no—
213C2×#121—1222no—
214C2×C4×D4—1222no—
215C22×C42#692311yescharacteristic
216C2×#101—614no—
217C2×#100—1222no—
218#407—1222no—
219#356—1224no—
220#355—1224no—
221C61#1270111yescharacteristic, complemented, Sylow
222C2×#41—1222no—
223C2×#41—1222no—
224C2×#41—1222no—
225C2×#41—1222no—
226C2×#41—2442no—
227C2×#41—2442no—
228C2×#41—2442no—
229C2×#41—2442no—
230C22×Q8—611no—
231C22×Q8—611no—
232C22×D4—612no—
233C22×D4—611no—
234C22×D4—611no—
235C22×D4—1222no—
236C22×D4—1221no—
237C23×C4—21no—
238C23×C4—612no—
239C23×C4—1221no—
240C23×C4C2×#692311yescharacteristic
241C2×M16—1224no—
242C4⋊Q8—614no—
243C4⋊Q8—1222no—
244#127—1222no—
245#127—1222no—
246#124—614no—
247#124—1222no—
248#124—1222no—
249#124—1222no—
250#121—12216no—
251C4×D4—12216no—
252C2×C4⋊C4—1222no—
253C2×C22⋊C4—1222no—
254C2×C22⋊C4—1222no—
255C2×C42—21no—
256C2×C42—22no—
257C2×C42—22no—
258C2×C42C2×#692311yescharacteristic
259C2×C42C2×#692311yescharacteristic
260#101—1224no—
261#101—1224no—
262#100—2444no—
263C22⋊C8—2444no—
264C24—612no—
265C24—1221no—
266C24C22⋊#692311yescharacteristic
267#41—2448no—
268#41—2448no—
269#41—2448no—
270#41—2448no—
271C2×Q8—612no—
272C2×Q8—612no—
273C2×Q8—612no—
274C2×Q8—1221no—
275C2×Q8—2441no—
276C2×Q8—2441no—
277C2×Q8—2441no—
278C2×Q8—2441no—
279C2×D4—612no—
280C2×D4—1228no—
281C2×D4—1224no—
282C2×D4—1224no—
283C2×D4—1224no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—2441no—
288C2×D4—2441no—
289C2×D4—2441no—
290C2×D4—2441no—
291C2×D4—2448no—
292C2×D4—2442no—
293C2×D4—2442no—
294C2×D4—2442no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—24no—
301C22×C4—21no—
302C22×C4—44no—
303C22×C4—612no—
304C22×C4—1224no—
305C22×C4—1224no—
306C22×C4—1221no—
307C22×C4—1224no—
308C22×C4—2442no—
309C22×C4—2442no—
310C22×C4—2442no—
311C22×C4C22⋊#692311yescharacteristic
312C22×C4C22×#692311yescharacteristic
313M16—2444no—
314M16—2444no—
315C2×C8—2444no—
316C4⋊C4—1228no—
317C22⋊C4—1228no—
318C22⋊C4—1228no—
319C42—24no—
320C42—21no—
321C42—21no—
322C42C22⋊#692312yes—
323C42C22⋊#692312yes—
324C23—21no—
325C23—21no—
326C23—42no—
327C23—1222no—
328C23—1222no—
329C23—1222no—
330C23—1222no—
331C23—2444no—
332C23—2444no—
333C23—2441no—
334C23—2441no—
335C23#1451983612yes—
336C23C2×C22⋊#692311yescharacteristic
337Q8—2442no—
338Q8—2442no—
339Q8—2442no—
340Q8—2442no—
341D4—2442no—
342D4—24416no—
343D4—2442no—
344D4—2442no—
345D4—2442no—
346D4—2448no—
347D4—2448no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—48no—
358C2×C4—42no—
359C2×C4—614no—
360C2×C4—1222no—
361C2×C4—1222no—
362C2×C4—1222no—
363C2×C4—2448no—
364C2×C4—2448no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4#1451983612yes—
368C2×C4C2×C22⋊#692311yescharacteristic
369C2×C4C2×C22⋊#692311yescharacteristic
370C8—4884no—
371C22—22no—
372C22—22no—
373C22—42no—
374C22—42no—
375C22—42no—
376C22—4882no—
377C22—4882no—
378C22—4882no—
379C22—2444no—
380C22—2444no—
381C22—2444no—
382C22—2442no—
383C22—2442no—
384C22#1684070311yescharacteristic
385C22C2×#1451983611yescharacteristic
386C22C2×#1451983611yescharacteristic
387C4—24no—
388C4—22no—
389C4—21no—
390C4—21no—
391C4—42no—
392C4—1224no—
393C4—2442no—
394C2—21no—
395C2—21no—
396C2—42no—
397C2—4882no—
398C2—4882no—
399C2#2146164711yescharacteristic
400C2#2146211212yes—
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C42×C61C4
socleC22×C61C2×#99
prime radicalC2×#16840312C2
cosocleC22×Dic122C23
hypercenterC22×C42#6923
hypocenterC61#12701
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×#16840673C2semidirect
2. C2×#16840671C2semidirect
3. #21461655C2semidirect
221. C61#12701semidirect

Maximal subgroups

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

subgroupindex
C2×#168406732
C2×#168406712
#214616552
C2×#168403122
#1270161