Finite Group Databasebeta

← #30601680

Subgroups — #30601680

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461941C211yesmaximal, characteristic, complemented
2#21461940C211yesmaximal, characteristic, complemented
3C2×#16840624C211yesmaximal, characteristic, complemented
4C2×#16840610C211yesmaximal, characteristic, complemented
5C2×D4⋊#92420C211yesmaximal, characteristic, complemented
6C2×#16840603C211yesmaximal, characteristic, complemented
7C2×#16839842C211yesmaximal, characteristic
8C2×C4⋊#92420C2211yescharacteristic
9C2×C4⋊#92420C2211yescharacteristic
10C2×#14519834—22no—
11C2×C22⋊#92420—22no—
12C2×C4×#92420C2211yescharacteristic
13C2×C4×#92420C2211yescharacteristic
14#16840624—22no—
15#16840610—22no—
16D4⋊#92420—22no—
17#16840603—22no—
18C22×#11758199C411yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21#16839842—22no—
22#16839842—22no—
23C2×#14519710C411yescharacteristic
24C2×#14519699C411yescharacteristic
25C2×C8×Dic61C2211yescharacteristic
26C2×#102×C61C411yescharacteristic
27C22×#92420—21no—
28C22×#92420—21no—
29C22×#92420—21no—
30C22×#92420D412yes—
31C4⋊#92420—21no—
32C4⋊#92420—21no—
33C4⋊#92420—21no—
34C4⋊#92420—21no—
35#14519834—44no—
36C22⋊#92420—44no—
37C4×#92420—21no—
38C4×#92420—21no—
39C4×#92420—21no—
40C4×#92420D412yes—
41C22×D244C2×C411yescharacteristic
42C23×Dic61—21no—
43C22×C4×D61—21no—
44C2×#11758199—22no—
45C2×#11758199—22no—
46C2×#11758199C814yescomplemented
47C22×#92418C2×C411yescharacteristic
48D4×Dic61—21no—
49D4×Dic61—21no—
50D4×Dic61—21no—
51D4×Dic61—21no—
52#14519739—21no—
53#14519739—21no—
54#14519739—21no—
55#14519739—21no—
56C2×C4⋊Dic61C2×C411yescharacteristic
57C2×C22⋊Dic61—21no—
58C2×#11758198—21no—
59C2×C4×Dic61C2311yescharacteristic
60#14519710—22no—
61#14519699—22no—
62C8×Dic61D412yes—
63C8×Dic61D412yes—
64C22×D4×C61C2×C411yescharacteristic
65C22×C8×C61C2×C411yescharacteristic
66C2×C4⋊C4×C61C2×C411yescharacteristic
67#102×C61—22no—
68C24×C61—21no—
69C23×D61—21no—
70C2×D4×C61—21no—
71C2×D4×C61—21no—
72C2×D4×C61—21no—
73C2×D4×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61C2×C812yes—
76C22×C4×C61—21no—
77C22×C4×C61C22×C411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61—42no—
82C22×Dic61—42no—
83C22×Dic61C2×D411yescharacteristic
84C22×Dic61#4111yescharacteristic
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244C2×C812yes—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C2×#92420—22no—
96C2×#92420—22no—
97C2×#92420—22no—
98C2×#92420—22no—
99C2×#92420—42no—
100C2×#92420—41no—
101C2×#92420—41no—
102C2×#92420—42no—
103C2×#92420—42no—
104C2×C8×C61—21no—
105C2×C8×C61—21no—
106C2×C8×C61C22⋊C412yes—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C22⋊Dic61—41no—
110C22⋊Dic61—41no—
111#11758199—28no—
112#11758198—41no—
113#11758198—41no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4×Dic61C2×D411yescharacteristic
117C4×Dic61C2×D411yescharacteristic
118C4×Dic61C2×D411yescharacteristic
119C4×Dic61#4111yescharacteristic
120C2×#92418C22⋊C412yes—
121C2×#92418C2×C812yes—
122C2×#92418M1612yes—
123C23×C61—22no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—42no—
127C23×C61—42no—
128C23×C61C4×D411yescharacteristic
129C22×D61—22no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—42no—
133C22×D61—42no—
134D4×C61—22no—
135D4×C61—22no—
136D4×C61—41no—
137D4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61C22×C811yescharacteristic
143C2×C4×C61C2×M1611yescharacteristic
144C2×C4×C61#13111yescharacteristic
145C2×C4×C61#13111yescharacteristic
146C2×Dic61—22no—
147C2×Dic61—41no—
148C2×Dic61—42no—
149C2×Dic61—82no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152C2×Dic61#12111yescharacteristic
153C2×Dic61#12111yescharacteristic
154C2×Dic61#12411yescharacteristic
155C2×Dic61#12711yescharacteristic
156C2×Dic61AGL(1,ℤ/8)12yes—
157C2×Dic61AGL(1,ℤ/8)12yes—
158D244—22no—
159D244—22no—
160D244—41no—
161D244—41no—
162C4×D61—82no—
163C4×D61—81no—
164C4×D61—81no—
165#92420—42no—
166#92420—42no—
167#92420—81no—
168#92420—81no—
169C8×C61—22no—
170#92418C22⋊C814yescomplemented
171#9659—611nomaximal, Sylow
172C22×C61—44no—
173C22×C61—42no—
174C22×C61—82no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61#39011yescharacteristic
178C22×C61C8×D411yescharacteristic
179C22×C61#43611yescharacteristic
180C22×C61#44212yes—
181C22×C61#44412yes—
182C2×D61—44no—
183C2×D61—42no—
184C2×D61—82no—
185C2×D61—81no—
186C2×D61—81no—
187C4×C61—81no—
188C4×C61C2×C22⋊C811yescharacteristic
189C4×C61#40811yescharacteristic
190C4×C61C8×D411yescharacteristic
191C4×C61#43611yescharacteristic
192Dic61—21no—
193Dic61—21no—
194Dic61—81no—
195Dic61#46912yes—
196Dic61#49611yescharacteristic
197Dic61#49611yescharacteristic
198C2×C4×D8—611no—
199#1954—611no—
200#1954—611no—
201C2×#334—611no—
202C2×D4⋊C8—611no—
203C2×D4⋊C8—611no—
204C2×#322—611no—
205C2×C61—82no—
206C2×C61#158012yes—
207C2×C61#159412yes—
208C2×C61#195411yescharacteristic
209C2×C61#197211yescharacteristic
210C2×C61#197511yescharacteristic
211D61—82no—
212C22×D8—611no—
213C2×C4×D4—611no—
214C2×C4×D4—611no—
215C4×D8—1222no—
216C4×D8—1222no—
217C2×#107—611no—
218C2×C4⋊C8—611no—
219C2×C4⋊C8—611no—
220C2×#102—611no—
221C2×#102#692311yescharacteristic
222C2×C22⋊C8—1222no—
223C2×C22⋊C8—1222no—
224C2×C4×C8—611no—
225C2×C4×C8—611no—
226C2×C4×C8—611no—
227#334—1222no—
228D4⋊C8—1222no—
229D4⋊C8—1222no—
230#322—1222no—
231C61#965911yescharacteristic, complemented, Sylow
232C22×D4—611no—
233C22×D4C2×#692311yescharacteristic
234C23×C4—1221no—
235C23×C4—1221no—
236C2×D8—614no—
237C2×D8—1222no—
238C2×D8—1222no—
239C22×C8—611no—
240C22×C8—612no—
241C22×C8—1221no—
242C22×C8—1221no—
243C22×C8—1221no—
244C22×C8C2×#692311yescharacteristic
245C4×D4—1221no—
246C4×D4—1221no—
247C4×D4—1221no—
248C4×D4—1221no—
249C4×D4—1221no—
250C4×D4—1221no—
251C4×D4—1221no—
252C4×D4—1221no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4C2×#692311yescharacteristic
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C42—611no—
258#107—1222no—
259C4⋊C8—1221no—
260C4⋊C8—1221no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263#102—22no—
264#102—1222no—
265C22⋊C8—2444no—
266C22⋊C8—2444no—
267C4×C8—612no—
268C4×C8—612no—
269C4×C8—612no—
270C4×C8—1221no—
271C4×C8—1221no—
272C4×C8—1221no—
273C24—21no—
274C24—1221no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—612no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4D61⋊C812yes—
287C22×C4—21no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—1221no—
291C22×C4—2442no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4—2442no—
295C22×C4—2442no—
296C22×C4—2441no—
297C22×C4—2441no—
298C22×C4—2442no—
299C22×C4C22×#692311yescharacteristic
300D8—1228no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—612no—
304C2×C8—612no—
305C2×C8—612no—
306C2×C8—1222no—
307C2×C8—1222no—
308C2×C8—1222no—
309C2×C8—1222no—
310C2×C8—2442no—
311C2×C8—2442no—
312C2×C8—2441no—
313C2×C8—2441no—
314C2×C8—2442no—
315C2×C8C22⋊#692312yes—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C22⋊C4—2441no—
323C22⋊C4—2441no—
324C42—611no—
325C42—611no—
326C42—611no—
327C42—611no—
328C23—22no—
329C23—41no—
330C23—41no—
331C23—42no—
332C23—42no—
333C23—1222no—
334C23—2441no—
335C23—2441no—
336C23—2442no—
337C23—2442no—
338C23D4×#692311yescharacteristic
339D4—22no—
340D4—22no—
341D4—41no—
342D4—41no—
343D4—1222no—
344D4—1222no—
345D4—2441no—
346D4—2441no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—612no—
352C2×C4—612no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—1222no—
356C2×C4—4882no—
357C2×C4—4881no—
358C2×C4—4881no—
359C2×C4—4882no—
360C2×C4—4881no—
361C2×C4—4881no—
362C2×C4—2441no—
363C2×C4—2442no—
364C2×C4C2×C22⋊#692311yescharacteristic
365C2×C4D4×#692311yescharacteristic
366C2×C4C2×D61⋊C811yescharacteristic
367C2×C4D61⋊M1611yescharacteristic
368C2×C4#1451986411yescharacteristic
369C2×C4#1451986411yescharacteristic
370C8—22no—
371C8—614no—
372C8—4881no—
373C8—4881no—
374C8—2442no—
375C8—2442no—
376C22—44no—
377C22—42no—
378C22—81no—
379C22—81no—
380C22—82no—
381C22—4881no—
382C22—4881no—
383C22—4882no—
384C22—2444no—
385C22—2442no—
386C22#1684071411yescharacteristic
387C22#1684078911yescharacteristic
388C22#1684079511yescharacteristic
389C22#1684080312yes—
390C22#1684080712yes—
391C4—81no—
392C4—612no—
393C4—611no—
394C4—611no—
395C4—1221no—
396C4—1221no—
397C4—4881no—
398C4D61⋊(C22⋊C8)11yescharacteristic
399C4#1684073511yescharacteristic
400C4#1684078911yescharacteristic
401C4#1684079511yescharacteristic
402C2—82no—
403C2—4882no—
404C2#2146141612yes—
405C2#2146146712yes—
406C2#2146194211yescharacteristic
407C2#2146196811yescharacteristic
408C2#2146197511yescharacteristic
subgroupG/H
centerC23D4×#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#102×C61C4
socleC23×C61C4×D4
prime radicalC22×#11758199C4
cosocleC2×C4×Dic61C23
hypercenterC2×#102#6923
hypocenterC61#9659
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #21461941C2semidirect
2. #21461940C2semidirect
3. C2×#16840624C2semidirect
4. C2×#16840610C2semidirect
5. C2×D4⋊#92420C2semidirect
6. C2×#16840603C2semidirect
46. C2×#11758199C8semidirect
170. #92418C22⋊C8semidirect
231. C61#9659semidirect

Maximal subgroups

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

subgroupindex
#214619412
#214619402
C2×#168406242
C2×#168406102
C2×D4⋊#924202
C2×#168406032
C2×#168398422
#965961