Finite Group Databasebeta

← #30606839

Subgroups — #30606839

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×#16840672C212yesmaximal, complemented
2C2×#16840670C212yesmaximal, complemented
3#21461655C212yesmaximal, complemented
4C2×#16840308C211yesmaximal, characteristic
5C2×#14519838C2214yes—
6C2×#14519837—22no—
7#16840734—22no—
8#16840672—24no—
9#16840670—24no—
10C22×#11758222C2211yescharacteristic
11#16840308—24no—
12#16840308—24no—
13C2×#14519775C2211yescharacteristic
14C2×#14519773C411yescharacteristic
15C2×#14519766C411yescharacteristic
16C2×#14519764C2211yescharacteristic
17C2×#14519749—22no—
18C2×C4×C22⋊D61—22no—
19C22×C4×Dic61C411yescharacteristic
20C22×#41×C61C411yescharacteristic
21C2×#11758217—24no—
22#14519838—24no—
23#14519838—24no—
24#14519837—44no—
25#14519834—44no—
26C2×#11758222—22no—
27C2×#11758222—22no—
28C2×#11758222—42no—
29C2×#11758222—42no—
30C22×Dic122C2311yescharacteristic
31C22×D244C2×C411yescharacteristic
32C22×C22⋊D61—22no—
33C22×C22⋊D61D412yes—
34C23×Dic61—21no—
35C22×C4×D61D412yes—
36#14519775—22no—
37#14519775D414yes—
38#14519773—22no—
39#14519773—22no—
40#14519766—22no—
41#14519766—22no—
42#14519764—22no—
43#14519764D414yes—
44#14519749—216no—
45C4×C22⋊D61—216no—
46C2×#11758196—22no—
47C2×C22⋊Dic61—22no—
48C2×#11758198—22no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61—22no—
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61C2×C411yescharacteristic
54C2×#41×C61—22no—
55C2×#41×C61—22no—
56C2×#41×C61—42no—
57C2×#41×C61—42no—
58C22×Q8×C61C2×C411yescharacteristic
59C22×D4×C61—21no—
60C22×D4×C61C2×C411yescharacteristic
61C23×C4×C61—21no—
62C23×C4×C61C2×C411yescharacteristic
63C24×C61—21no—
64C24×C61C22⋊C411yescharacteristic
65C23×D61C22⋊C412yes—
66#41×C61—48no—
67#41×C61—48no—
68C2×Q8×C61—21no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61C22⋊C412yes—
72C2×D4×C61—24no—
73C2×D4×C61—21no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61—42no—
77C2×D4×C61—42no—
78C2×D4×C61C22⋊C412yes—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—24no—
84C22×C4×C61—21no—
85C22×C4×C61—42no—
86C22×C4×C61—42no—
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C22×C411yescharacteristic
89C2×C22⋊D61—28no—
90C2×C22⋊D61—24no—
91C2×C22⋊D61—24no—
92C2×C22⋊D61—42no—
93C2×C22⋊D61—48no—
94C22×Dic61—21no—
95C22×Dic61—24no—
96C22×Dic61—21no—
97C22×Dic61—44no—
98C22×Dic61C2×D412yes—
99#11758222—48no—
100#11758222—48no—
101C2×D244—21no—
102C2×D244—21no—
103C2×D244—41no—
104C2×D244—41no—
105C2×C4×D61—24no—
106C2×C4×D61—24no—
107C2×C4×D61—42no—
108C2×Dic122—41no—
109C2×Dic122—41no—
110C2×Dic122C2×D412yes—
111C2×Dic122C2×D412yes—
112#11758217—44no—
113#11758217—44no—
114C2×#92420—44no—
115C22⋊Dic61—28no—
116#11758198—28no—
117#11758196—28no—
118C4×Dic61—24no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C4×Dic61C22⋊C412yes—
122C4×Dic61C22⋊C412yes—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—22no—
126C23×C61—42no—
127C23×C61—44no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61#9912yes—
131C23×C61C2×C22⋊C411yescharacteristic
132C22×D61—22no—
133C22×D61—22no—
134C22×D61—22no—
135C22×D61—44no—
136Q8×C61—42no—
137Q8×C61—42no—
138D4×C61—42no—
139D4×C61—42no—
140D4×C61—48no—
141C2×C4×C61—24no—
142C2×C4×C61—24no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—22no—
148C2×C4×C61—48no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61#9912yes—
152C2×C4×C61C2×C22⋊C411yescharacteristic
153C2×C4×C61C2×C22⋊C411yescharacteristic
154C22⋊D61—48no—
155C22⋊D61—416no—
156C2×Dic61—24no—
157C2×Dic61—22no—
158C2×Dic61—22no—
159C2×Dic61—22no—
160C2×Dic61—22no—
161C2×Dic61—48no—
162C2×Dic61—42no—
163C2×Dic61#12014yes—
164D244—42no—
165D244—42no—
166C4×D61—48no—
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—44no—
176C22×C61—42no—
177C22×C61—42no—
178C22×C61—82no—
179C22×C61—82no—
180C22×C61#37911yescharacteristic
181C22×C61C2×#9911yescharacteristic
182C22×C61C2×#9911yescharacteristic
183C2×D61—44no—
184C2×D61—44no—
185C2×D61—42no—
186C2×D61—82no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—22no—
190C4×C61—42no—
191Dic61—24no—
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—82no—
202C2×C61#178111yescharacteristic
203C2×C61#213212yes—
204D61—82no—
205C22×#41—611no—
206C22×#41#692311yescharacteristic
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—611no—
216C2×#101—614no—
217C2×#100—1222no—
218#407—1222no—
219#356—1224no—
220#355—1224no—
221C61#1270111yescharacteristic, complemented, Sylow
222C2×#41—22no—
223C2×#41—22no—
224C2×#41—42no—
225C2×#41—42no—
226C2×#41—1222no—
227C2×#41—1222no—
228C2×#41—2442no—
229C2×#41—2442no—
230C22×Q8—611no—
231C22×Q8C2×#692311yescharacteristic
232C22×D4—21no—
233C22×D4—612no—
234C22×D4—611no—
235C22×D4—1222no—
236C22×D4C2×#692311yescharacteristic
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—611no—
256C2×C42—611no—
257C2×C42—1222no—
258C2×C42—1222no—
259C2×C42—1221no—
260#101—1224no—
261#101—1224no—
262#100—2444no—
263C22⋊C8—2444no—
264C24—21no—
265C24—612no—
266C24C22⋊#692311yescharacteristic
267#41—48no—
268#41—48no—
269#41—2448no—
270#41—2448no—
271C2×Q8—21no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—612no—
275C2×Q8—612no—
276C2×Q8—2441no—
277C2×Q8—2441no—
278C2×Q8C22⋊#692312yes—
279C2×D4—24no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—1224no—
286C2×D4—1228no—
287C2×D4—1224no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4—2441no—
291C2×D4—2441no—
292C2×D4—2442no—
293C2×D4—2448no—
294C2×D4C22⋊#692312yes—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—24no—
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—612no—
304C22×C4—1224no—
305C22×C4—1221no—
306C22×C4—1224no—
307C22×C4—1221no—
308C22×C4—1224no—
309C22×C4—2442no—
310C22×C4—2444no—
311C22×C4C22⋊#692311yescharacteristic
312C22×C4C22×#692311yescharacteristic
313M16—2444no—
314M16—2444no—
315C2×C8—2444no—
316C4⋊C4—1228no—
317C22⋊C4—1228no—
318C22⋊C4—1228no—
319C42—612no—
320C42—612no—
321C42—1224no—
322C42—1221no—
323C42—1221no—
324C23—21no—
325C23—21no—
326C23—22no—
327C23—42no—
328C23—44no—
329C23—41no—
330C23—41no—
331C23—1222no—
332C23—1222no—
333C23—1222no—
334C23—2444no—
335C23#1451983512yes—
336C23C2×C22⋊#692311yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—2442no—
340Q8—2442no—
341D4—42no—
342D4—42no—
343D4—48no—
344D4—2442no—
345D4—2442no—
346D4—2448no—
347D4—24416no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—48no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—614no—
359C2×C4—1224no—
360C2×C4—1222no—
361C2×C4—1222no—
362C2×C4—1222no—
363C2×C4—1222no—
364C2×C4—2448no—
365C2×C4—2448no—
366C2×C4—2442no—
367C2×C4#1451983512yes—
368C2×C4C2×C22⋊#692311yescharacteristic
369C2×C4C2×C22⋊#692311yescharacteristic
370C8—4884no—
371C22—22no—
372C22—22no—
373C22—42no—
374C22—42no—
375C22—44no—
376C22—42no—
377C22—42no—
378C22—82no—
379C22—82no—
380C22—4882no—
381C22—2444no—
382C22—2444no—
383C22—2442no—
384C22#1684070311yescharacteristic
385C22C2×#1451983511yescharacteristic
386C22C2×#1451983511yescharacteristic
387C4—22no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—1224no—
392C4—1224no—
393C4—2442no—
394C2—21no—
395C2—21no—
396C2—42no—
397C2—82no—
398C2—4882no—
399C2#2146164511yescharacteristic
400C2#2146211012yes—
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×#41×C61C4
socleC22×C61C2×#99
prime radicalC2×#16840308C2
cosocleC22×Dic122C23
hypercenterC22×#41#6923
hypocenterC61#12701
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16840672C2semidirect
2. C2×#16840670C2semidirect
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×#168406722
C2×#168406702
#214616552
C2×#168403082
#1270161