Finite Group Databasebeta

← #30598195

Subgroups — #30598195

Order 15616.

930 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461123C212yesmaximal, complemented
2#21461121C212yesmaximal, complemented
3#21461052C211yesmaximal, characteristic
4#21461052C211yesmaximal, characteristic
5C2×#16840238C211yesmaximal, characteristic
6#16840778C2212yes—
7#16840778C2212yes—
8#16840612—24no—
9Q8⋊#92420—24no—
10#16840608—21no—
11#16840608—21no—
12#16840606—21no—
13#16840606—21no—
14C22×Q8×D61C411yescharacteristic
15#16840238—24no—
16#16840238—24no—
17C2×Q8×Dic61C2211yescharacteristic
18C2×C4×Dic122—21no—
19C2×C4×Dic122C411yescharacteristic
20C2×#14519742—21no—
21C2×#14519742C2211yescharacteristic
22C2×#14519735—21no—
23C2×#14519735C411yescharacteristic
24C2×#14519734—21no—
25C2×#14519734C2211yescharacteristic
26C2×C4×Q8×C61C411yescharacteristic
27C4⋊#92420—22no—
28C4⋊#92420—22no—
29C22⋊#92420—22no—
30C22⋊#92420—22no—
31C4×#92420—22no—
32C4×#92420—22no—
33C22×Dic122—21no—
34C22×Dic122C2×C411yescharacteristic
35C2×Q8×D61—22no—
36C2×Q8×D61—22no—
37C2×Q8×D61—22no—
38C2×Q8×D61—22no—
39C2×Q8×D61—22no—
40C2×Q8×D61C814yescomplemented
41C22×C4×D61—21no—
42C22×C4×D61C2×C411yescharacteristic
43Q8×Dic61—22no—
44Q8×Dic61D414yes—
45C4×Dic122—28no—
46C4×Dic122—22no—
47C4×Dic122—22no—
48#14519742—28no—
49#14519742—22no—
50#14519742D414yes—
51#14519735—28no—
52#14519735—22no—
53#14519735—22no—
54#14519734—28no—
55#14519734—22no—
56#14519734—22no—
57C2×C4⋊Dic61—21no—
58C2×C4⋊Dic61C2×C411yescharacteristic
59C2×#11758196—21no—
60C2×#11758196—21no—
61C2×#11758196D411yescharacteristic
62C2×#11758196D411yescharacteristic
63C2×#11758198—21no—
64C2×#11758198D411yescharacteristic
65C2×#11758198D411yescharacteristic
66C2×C4×Dic61—21no—
67C2×C4×Dic61—21no—
68C2×C4×Dic61—21no—
69C2×C4×Dic61—21no—
70C2×C4×Dic61C2311yescharacteristic
71C22×Q8×C61C2×C411yescharacteristic
72C4×Q8×C61—22no—
73C4×Q8×C61—22no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61C2×C411yescharacteristic
76C2×C42×C61—21no—
77C2×C42×C61C2×C411yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C2×Q8×C61—21no—
80C2×Q8×C61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61C22⋊C412yes—
83C2×Q8×C61C2×C812yes—
84C2×Q8×C61M1612yes—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C22⋊C411yescharacteristic
89C22×C4×C61C22×C411yescharacteristic
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C2×D411yescharacteristic
94C22×Dic61C2×D411yescharacteristic
95Q8×D61—28no—
96Q8×D61—28no—
97Q8×D61—28no—
98Q8×D61—28no—
99C2×C4×D61—24no—
100C2×C4×D61—24no—
101C2×C4×D61—24no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61C2×C812yes—
107C2×C4×D61M1612yes—
108C2×Dic122—24no—
109C2×Dic122—24no—
110C2×Dic122—21no—
111C2×Dic122—21no—
112C2×Dic122—21no—
113C2×Dic122—24no—
114C2×Dic122C22⋊C412yes—
115C2×Dic122C2×C812yes—
116C2×Dic122M1612yes—
117C2×#92420—42no—
118C2×#92420—42no—
119C4⋊C4×C61—24no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61C22⋊C412yes—
122C42×C61—24no—
123C42×C61—21no—
124C42×C61—21no—
125#11758198—24no—
126#11758198—22no—
127#11758198—22no—
128C4⋊Dic61—21no—
129C4⋊Dic61—24no—
130C4⋊Dic61C22⋊C412yes—
131#11758196—24no—
132#11758196—24no—
133#11758196—22no—
134#11758196—22no—
135C4×Dic61—24no—
136C4×Dic61—24no—
137C4×Dic61—24no—
138C4×Dic61—24no—
139C4×Dic61C2×D412yes—
140C4×Dic61C2×D412yes—
141C23×C61C2×C22⋊C411yescharacteristic
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61C22⋊C812yes—
147Q8×C61—22no—
148Q8×C61—22no—
149Q8×C61—22no—
150Q8×C61C22⋊C814yes—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—22no—
154C2×C4×C61—21no—
155C2×C4×C61—22no—
156C2×C4×C61—21no—
157C2×C4×C61—42no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61C2×C22⋊C411yescharacteristic
161C2×C4×C61C2×C22⋊C411yescharacteristic
162C2×C4×C61C22×C811yescharacteristic
163C2×C4×C61C2×M1611yescharacteristic
164C2×C4×C61C2×M1611yescharacteristic
165C2×C4×C61C2×M1611yescharacteristic
166C2×Dic61—21no—
167C2×Dic61—22no—
168C2×Dic61—22no—
169C2×Dic61—21no—
170C2×Dic61—22no—
171C2×Dic61—22no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—42no—
175C2×Dic61C22⋊C812yes—
176C2×Dic61#12012yes—
177C2×Dic61#12012yes—
178C4×D61—216no—
179C4×D61—22no—
180C4×D61—22no—
181C4×D61—22no—
182C4×D61—22no—
183Dic122—216no—
184Dic122—22no—
185Dic122—22no—
186Dic122—22no—
187Dic122C22⋊C814yes—
188#92420—82no—
189#92420—82no—
190#8323—611nomaximal, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61#37911yescharacteristic
194C22×C61C2×C22⋊C811yescharacteristic
195C22×C61#40711yescharacteristic
196C2×D61—22no—
197C2×D61—42no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—42no—
201C4×C61—24no—
202C4×C61—41no—
203C4×C61—41no—
204C4×C61—42no—
205C4×C61C2×C22⋊C811yescharacteristic
206C4×C61C2×C22⋊C811yescharacteristic
207C4×C61#40711yescharacteristic
208C4×C61#40711yescharacteristic
209Dic61—22no—
210Dic61—22no—
211Dic61—22no—
212Dic61—24no—
213Dic61—42no—
214C2×#519—611no—
215#1479—612no—
216#1479—612no—
217#1458—611no—
218#1458—611no—
219C2×C61—21no—
220C2×C61—21no—
221C2×C61#177911yescharacteristic
222C2×C61#179611yescharacteristic
223C2×C61#179611yescharacteristic
224D61—42no—
225C23×Q8—611no—
226#519—1224no—
227#519—1224no—
228C2×C4×Q8—611no—
229C2×C4×Q8—611no—
230C2×C4×Q8—611no—
231C2×C4×Q8—1221no—
232C2×C4×Q8—1221no—
233C2×C4×Q8#692311yescharacteristic
234C2×#117—611no—
235C2×#117—611no—
236C2×#117—1221no—
237C2×#117—1221no—
238#431—612no—
239#431—612no—
240Q8⋊C8—1224no—
241Q8⋊C8—1224no—
242#324—1221no—
243#324—1221no—
244#323—1221no—
245#323—1221no—
246C61#832311yescharacteristic, complemented, Sylow
247C22×Q8—614no—
248C22×Q8—611no—
249C22×Q8—1221no—
250C22×Q8—1222no—
251C22×Q8—1222no—
252C22×Q8—1222no—
253C22×Q8—1222no—
254C22×Q8—1222no—
255C22×Q8C2×#692311yescharacteristic
256C23×C4—611no—
257C23×C4—1221no—
258C4×Q8—22no—
259C4×Q8—22no—
260C4×Q8—614no—
261C4×Q8—614no—
262C4×Q8—1222no—
263C4×Q8—1222no—
264C4×Q8—1228no—
265C4×Q8—1222no—
266C4×Q8—1222no—
267C4×Q8—1228no—
268#117—1222no—
269#117—1222no—
270#117—1228no—
271#117—1222no—
272#117—1228no—
273#117—1222no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4C2×#692311yescharacteristic
282C2×C22⋊C4—611no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—1221no—
285C2×C42—21no—
286C2×C42—611no—
287C2×C42—1221no—
288C2×C42—1221no—
289C2×C42—1221no—
290C2×C42—1221no—
291C2×C42C2×#692311yescharacteristic
292C4⋊C8—1222no—
293C4⋊C8—1222no—
294C22⋊C8—1222no—
295C22⋊C8—1222no—
296C4×C8—1222no—
297C4×C8—1222no—
298C24—611no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8—612no—
303C2×Q8—612no—
304C2×Q8—612no—
305C2×Q8—1224no—
306C2×Q8—1224no—
307C2×Q8—1224no—
308C2×Q8—1228no—
309C2×Q8—1228no—
310C2×Q8—1228no—
311C2×Q8—1228no—
312C2×Q8—1221no—
313C2×Q8—1221no—
314C2×Q8—1221no—
315C2×Q8D61⋊C812yes—
316C2×Q8#1175821312yes—
317C2×Q8C22⋊#692312yes—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—611no—
321C22×C4—611no—
322C22×C4—611no—
323C22×C4—612no—
324C22×C4—612no—
325C22×C4—1224no—
326C22×C4—1224no—
327C22×C4—1224no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4—1221no—
334C22×C4C22⋊#692311yescharacteristic
335C22×C4C22⋊#692311yescharacteristic
336C22×C4C22×#692311yescharacteristic
337C2×C8—2442no—
338C2×C8—2442no—
339C4⋊C4—24no—
340C4⋊C4—21no—
341C4⋊C4—612no—
342C4⋊C4—1222no—
343C4⋊C4—1222no—
344C4⋊C4—1224no—
345C4⋊C4—1224no—
346C4⋊C4—1224no—
347C4⋊C4—1221no—
348C4⋊C4C22⋊#692312yes—
349C22⋊C4—1222no—
350C22⋊C4—1222no—
351C22⋊C4—1224no—
352C42—24no—
353C42—21no—
354C42—21no—
355C42—612no—
356C42—612no—
357C42—1224no—
358C42—1224no—
359C42—1224no—
360C42—1224no—
361C23—612no—
362C23—1221no—
363C23—1221no—
364C23—2441no—
365C23—2441no—
366C23C2×C22⋊#692311yescharacteristic
367Q8—22no—
368Q8—22no—
369Q8—22no—
370Q8—614no—
371Q8—12216no—
372Q8—1222no—
373Q8—1222no—
374Q8—1222no—
375Q8#1451983414yes—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—612no—
386C2×C4—612no—
387C2×C4—612no—
388C2×C4—12216no—
389C2×C4—1222no—
390C2×C4—1221no—
391C2×C4—1222no—
392C2×C4—1221no—
393C2×C4—1222no—
394C2×C4—1222no—
395C2×C4—1222no—
396C2×C4—1222no—
397C2×C4—1222no—
398C2×C4—1222no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2442no—
402C2×C4C2×C22⋊#692311yescharacteristic
403C2×C4C2×C22⋊#692311yescharacteristic
404C2×C4C2×D61⋊C811yescharacteristic
405C2×C4D61⋊M1611yescharacteristic
406C2×C4D61⋊M1611yescharacteristic
407C2×C4C2×#1175821311yescharacteristic
408C8—4882no—
409C8—4882no—
410C22—21no—
411C22—21no—
412C22—1222no—
413C22—2442no—
414C22—2442no—
415C22—2441no—
416C22—2441no—
417C22#1684070311yescharacteristic
418C22D61⋊(C22⋊C8)11yescharacteristic
419C22#1684073311yescharacteristic
420C4—24no—
421C4—41no—
422C4—41no—
423C4—42no—
424C4—1222no—
425C4—1224no—
426C4—1222no—
427C4—1222no—
428C4—2442no—
429C4D61⋊(C22⋊C8)11yescharacteristic
430C4C2×#1451983411yescharacteristic
431C4#1684073311yescharacteristic
432C4#1684073411yescharacteristic
433C2—21no—
434C2—21no—
435C2—2442no—
436C2#2146164211yescharacteristic
437C2#2146167111yescharacteristic
438C2#2146167211yescharacteristic
subgroupG/H
centerC22#16840703
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61#379
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×Q8#6923
hypocenterC61#8323
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #21461123C2semidirect
2. #21461121C2semidirect
40. C2×Q8×D61C8semidirect
246. C61#8323semidirect

Maximal subgroups

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

subgroupindex
#214611232
#214611212
#214610522
C2×#168402382
#832361