Finite Group Databasebeta

← #30598167

Subgroups — #30598167

Order 15616.

1116 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 146 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#21461674C211yesmaximal, characteristic, complemented
2C4×#14519834C211yesmaximal, characteristic, complemented
3C2×#16840610C214yesmaximal, complemented
4C2×#16840313C211yesmaximal, characteristic
5C2×C4⋊#92420C2212yes—
6C2×#14519834—21no—
7C2×#14519834—21no—
8C2×C4×#92420C2212yes—
9#16840628—21no—
10#16840628—21no—
11#16840610—28no—
12C22×#11758226—21no—
13#16840313—28no—
14C2×#14519774C411yescharacteristic
15C2×#14519766—21no—
16C2×#14519752—21no—
17C2×#14519752C412yes—
18C2×#14519739—21no—
19C2×#14519739C2212yes—
20C2×C42×D61C2211yescharacteristic
21C2×C4⋊Q8×C61C411yescharacteristic
22C22×#92420—22no—
23C22×#92420—22no—
24C4⋊#92420—24no—
25#14519834—24no—
26#14519834—42no—
27C4×#92420—24no—
28C2×#11758226—28no—
29C2×#11758226—44no—
30C2×#11758226—42no—
31C2×#11758226—42no—
32C22×D244—22no—
33C22×D244—21no—
34C22×D244—21no—
35C22×D244C2×C412yes—
36C22×C4×D61—22no—
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40#14519774—24no—
41#14519766—28no—
42#14519752—28no—
43#14519752—24no—
44#14519752—24no—
45#14519739—28no—
46#14519739—24no—
47#14519739D418yes—
48C2×#11758198—22no—
49C2×#11758198—22no—
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61C2311yescharacteristic
53C42×D61—24no—
54C22×Q8×C61—21no—
55C4⋊Q8×C61—24no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61C2×C412yes—
58C2×C42×C61C2×C411yescharacteristic
59C23×D61—22no—
60C23×D61C22⋊C411yescharacteristic
61C2×Q8×C61—24no—
62C2×Q8×C61—42no—
63C2×Q8×C61—42no—
64C22×C4×C61—22no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71#11758226—416no—
72#11758226—416no—
73C2×D244—24no—
74C2×D244—24no—
75C2×D244—28no—
76C2×D244—24no—
77C2×D244—24no—
78C2×D244—22no—
79C2×D244—42no—
80C2×D244—42no—
81C2×D244—44no—
82C2×D244—44no—
83C2×D244—42no—
84C2×D244—42no—
85C2×D244C22⋊C414yes—
86C2×C4×D61—22no—
87C2×C4×D61—22no—
88C2×C4×D61—22no—
89C2×C4×D61—22no—
90C2×C4×D61—22no—
91C2×C4×D61—22no—
92C2×C4×D61—28no—
93C2×C4×D61—22no—
94C2×C4×D61—41no—
95C2×C4×D61—42no—
96C2×C4×D61—42no—
97C2×C4×D61—44no—
98C2×C4×D61D812yes—
99C2×C4×D61SD1612yes—
100C2×#92420—24no—
101C2×#92420—42no—
102C2×#92420—42no—
103C2×#92420—42no—
104C2×#92420—42no—
105C2×#92420—42no—
106C4⋊C4×C61—24no—
107C4⋊C4×C61—22no—
108C4⋊C4×C61C22⋊C414yes—
109C42×C61—22no—
110#11758198—28no—
111#11758198—28no—
112C4×Dic61—22no—
113C4×Dic61—22no—
114C4×Dic61C2×D414yes—
115C23×C61C2×C22⋊C411yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—24no—
123C22×D61—42no—
124C22×D61—42no—
125C22×D61—42no—
126C22×D61—42no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61#10212yes—
130Q8×C61—48no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—24no—
136C2×C4×C61—42no—
137C2×C4×C61—42no—
138C2×C4×C61#10212yes—
139C2×C4×C61#10412yes—
140C2×C4×C61C2×C22⋊C412yes—
141C2×C4×C61#13112yes—
142C2×C4×C61#13112yes—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61#12012yes—
149C2×Dic61#12012yes—
150C2×Dic61C2×D811yescharacteristic
151C2×Dic61C2×SD1611yescharacteristic
152C2×Dic61AGL(1,ℤ/8)12yes—
153D244—28no—
154D244—48no—
155D244—48no—
156D244—416no—
157D244—44no—
158C4×D61—24no—
159C4×D61—24no—
160C4×D61—44no—
161C4×D61—44no—
162C4×D61—48no—
163C4×D61—48no—
164#92420—44no—
165#92420—82no—
166#8313—611nomaximal, Sylow
167C22×C61#37911yescharacteristic
168C22×C61#40811yescharacteristic
169C22×C61#40811yescharacteristic
170C22×C61C2×#10211yescharacteristic
171C22×C61#41811yescharacteristic
172C22×C61C2×#10411yescharacteristic
173C22×C61#42111yescharacteristic
174C2×D61—22no—
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—44no—
182C2×D61—44no—
183C2×D61—44no—
184C2×D61—82no—
185C2×D61—82no—
186C2×D61—82no—
187C2×D61—82no—
188C4×C61—22no—
189C4×C61—22no—
190C4×C61—44no—
191C4×C61#40814yes—
192Dic61—22no—
193Dic61—41no—
194Dic61#44712yes—
195Dic61#45012yes—
196C2×#532—611no—
197#1797—611no—
198C4×C22⋊C8—611no—
199C2×D4⋊C8—614no—
200C2×C61#148011yescharacteristic
201C2×C61#148411yescharacteristic
202C2×C61#149211yescharacteristic
203C2×C61#149611yescharacteristic
204C2×C61#178011yescharacteristic
205C2×C61#178611yescharacteristic
206C2×C61#178911yescharacteristic
207D61—42no—
208D61—84no—
209C22×#41—1221no—
210#532—1228no—
211C2×C4⋊Q8#692311yescharacteristic
212C2×#127—611no—
213C2×#124—1221no—
214C2×#121—612no—
215C2×#121—1221no—
216C2×C4×D4—612no—
217C2×C4×D4—1221no—
218C22×C42—611no—
219C2×C4⋊C8—612no—
220C2×C22⋊C8—1221no—
221C2×C22⋊C8—1221no—
222C2×C4×C8—612no—
223#336—1221no—
224#336—1221no—
225D4⋊C8—1228no—
226C61#831311yescharacteristic, complemented, Sylow
227C2×#41—1228no—
228C2×#41—2442no—
229C2×#41—2442no—
230C2×#41—2444no—
231C22×Q8—21no—
232C22×D4—612no—
233C22×D4—1222no—
234C22×D4—1221no—
235C22×D4—1221no—
236C23×C4—611no—
237C23×C4—611no—
238C23×C4—611no—
239C23×C4—1222no—
240C22×C8—1222no—
241C22×C8—1222no—
242C4⋊Q8—24no—
243#127—1224no—
244#124—1228no—
245#121—1224no—
246#121—1228no—
247#121—1224no—
248C4×D4—618no—
249C4×D4—1224no—
250C4×D4—1228no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C2×#692312yes—
253C2×C22⋊C4—1222no—
254C2×C22⋊C4—1222no—
255C2×C42—611no—
256C2×C42—611no—
257C2×C42—611no—
258C2×C42—1224no—
259C2×C42C2×#692311yescharacteristic
260C4⋊C8—1224no—
261C22⋊C8—1224no—
262C22⋊C8—2442no—
263C4×C8—1224no—
264C24—611no—
265C24—1222no—
266#41—24416no—
267#41—24416no—
268C2×Q8—24no—
269C2×Q8—42no—
270C2×Q8—42no—
271C2×D4—614no—
272C2×D4—1224no—
273C2×D4—1228no—
274C2×D4—1224no—
275C2×D4—1222no—
276C2×D4—1224no—
277C2×D4—1224no—
278C2×D4—2442no—
279C2×D4—2442no—
280C2×D4—2444no—
281C2×D4—2444no—
282C2×D4—2442no—
283C2×D4—2442no—
284C22×C4—22no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—612no—
288C22×C4—612no—
289C22×C4—611no—
290C22×C4—1222no—
291C22×C4—1222no—
292C22×C4—1222no—
293C22×C4—1228no—
294C22×C4—1222no—
295C22×C4—1222no—
296C22×C4—1222no—
297C22×C4—1222no—
298C22×C4—2441no—
299C22×C4—2442no—
300C22×C4—2442no—
301C22×C4—2444no—
302C22×C4C22⋊#692311yescharacteristic
303C22×C4C22⋊#692311yescharacteristic
304C22×C4C22×#692311yescharacteristic
305C2×C8—1224no—
306C2×C8—2442no—
307C2×C8—2442no—
308C2×C8—2442no—
309C2×C8—2442no—
310C2×C8—2442no—
311C4⋊C4—24no—
312C4⋊C4—22no—
313C4⋊C4C22⋊#692314yes—
314C22⋊C4—1228no—
315C22⋊C4—1228no—
316C42—22no—
317C42—614no—
318C42—1222no—
319C42—1222no—
320C23—612no—
321C23—1221no—
322C23—1221no—
323C23—1221no—
324C23—1221no—
325C23—1221no—
326C23—1221no—
327C23—1224no—
328C23—2442no—
329C23—2442no—
330C23—2442no—
331C23—2442no—
332C23—2442no—
333C23—2442no—
334C23C2×C22⋊#692311yescharacteristic
335Q8—48no—
336D4—1228no—
337D4—2448no—
338D4—2448no—
339D4—24416no—
340D4—2444no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—24no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—612no—
351C2×C4—612no—
352C2×C4—612no—
353C2×C4—1224no—
354C2×C4—1224no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—2444no—
361C2×C4—2448no—
362C2×C4—2448no—
363C2×C4—2444no—
364C2×C4#1451983912yes—
365C2×C4#1451984212yes—
366C2×C4C2×C22⋊#692312yes—
367C2×C4#1451986512yes—
368C2×C4#1451986512yes—
369C8—4882no—
370C8—2444no—
371C22—1222no—
372C22—1222no—
373C22—1222no—
374C22—4882no—
375C22—4882no—
376C22—4882no—
377C22—4882no—
378C22—2444no—
379C22—2444no—
380C22—2444no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22#1684070311yescharacteristic
386C22#1684073711yescharacteristic
387C22#1684073711yescharacteristic
388C22C2×#1451983911yescharacteristic
389C22#1684075411yescharacteristic
390C22C2×#1451984211yescharacteristic
391C22#1684076111yescharacteristic
392C4—22no—
393C4—22no—
394C4—44no—
395C4—612no—
396C4—612no—
397C4—1222no—
398C4—2441no—
399C4#1684073714yes—
400C2—4884no—
401C2—2442no—
402C2#2146112611yescharacteristic
403C2#2146114011yescharacteristic
404C2#2146116611yescharacteristic
405C2#2146118011yescharacteristic
406C2#2146164411yescharacteristic
407C2#2146165711yescharacteristic
408C2#2146166211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840313C2
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#8313
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21461674C2semidirect
2. C4×#14519834C2semidirect
3. C2×#16840610C2semidirect
226. C61#8313semidirect

Maximal subgroups

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

subgroupindex
#214616742
C4×#145198342
C2×#168406102
C2×#168403132
#831361