Finite Group Databasebeta

← #29582575

Subgroups — #29582575

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840109C211yesmaximal, characteristic
2C2×#16840057C211yesmaximal, characteristic, complemented
3C2×#16839962C211yesmaximal, characteristic
4C2×#16839510C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6#21443654C211yesmaximal, characteristic, complemented
7C61×#1984C211yesmaximal, characteristic, complemented
8C22×#11758201—21no—
9C2×#14519777C2211yescharacteristic
10C2×#14519774C2211yescharacteristic
11#16840109—22no—
12#16840109—22no—
13#16840057—22no—
14#16840057—22no—
15#16839962—22no—
16#16839962—22no—
17C2×#14519710—21no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519701—21no—
21C2×#14519699—22no—
22C2×#14519697—21no—
23#16839510—22no—
24#16839505—22no—
25C2×C4×Q8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4×C8×C61C2211yescharacteristic
28C61×#336—22no—
29C22×Dic122—21no—
30C22×D244—21no—
31C22×D244—21no—
32C22×D244—21no—
33C2×#11758201—24no—
34C2×#11758201—42no—
35C2×#11758201—42no—
36C22×#92418—21no—
37C22×#92418—21no—
38#14519777—21no—
39#14519777—21no—
40#14519777—21no—
41#14519777D412yes—
42#14519774—21no—
43#14519774—21no—
44#14519774—21no—
45#14519774D412yes—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48#14519710—24no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418D412yes—
52C4⋊#92418D412yes—
53#14519701—24no—
54#14519699—28no—
55#14519697—24no—
56C22×Q8×C61D411yescharacteristic
57C22×C8×C61—21no—
58C22×C8×C61D412yes—
59C4×Q8×C61—21no—
60C4×Q8×C61—21no—
61C4×Q8×C61—21no—
62C4×Q8×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61D411yescharacteristic
65C2×C42×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4×C8×C61—21no—
70C4×C8×C61—21no—
71C23×D61—41no—
72C2×Q8×C61—21no—
73C2×Q8×C61—21no—
74C2×Q8×C61—21no—
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61SD1612yes—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C22×Dic61—41no—
84C2×D244—22no—
85C2×D244—22no—
86C2×D244—22no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—42no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—42no—
93C2×D244—41no—
94C2×D244—41no—
95C2×D244—41no—
96C2×D244—82no—
97C2×Dic122—22no—
98C2×Dic122—41no—
99C2×Dic122—82no—
100C2×C8×C61—22no—
101C2×C8×C61—22no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C2×C8×C61—42no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C42×C61—41no—
110C42×C61—41no—
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115#11758201—48no—
116C4⋊Dic61—22no—
117C4⋊Dic61—22no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120C2×#92418—22no—
121C2×#92418—22no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C23×C61#12111yescharacteristic
127C22×D61—42no—
128C22×D61—82no—
129C22×D61—81no—
130C22×D61—81no—
131C22×D61—82no—
132Q8×C61—22no—
133Q8×C61—22no—
134Q8×C61—41no—
135Q8×C61—41no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61#12011yescharacteristic
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12011yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12711yescharacteristic
148C2×C4×C61C2×SD1611yescharacteristic
149C2×C4×C61#13511yescharacteristic
150C2×C4×C61#13512yes—
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C2×C4×C61#13712yes—
154C2×Dic61—42no—
155C2×Dic61—82no—
156D244—42no—
157D244—44no—
158D244—42no—
159D244—82no—
160D244—82no—
161D244—81no—
162D244—81no—
163D244—81no—
164D244—81no—
165Dic122—82no—
166Dic122—82no—
167C8×C61—42no—
168C8×C61—81no—
169#92418—42no—
170#92418—42no—
171#10269—611nomaximal, Sylow
172C22×C61#39211yescharacteristic
173C22×C61#46412yes—
174C22×C61#46511yescharacteristic
175C22×C61#46811yescharacteristic
176C22×C61#47212yes—
177C2×D61—82no—
178C2×D61—82no—
179C2×D61—82no—
180C2×D61—162no—
181C2×D61—162no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—42no—
185C4×C61—81no—
186C4×C61#44811yescharacteristic
187C4×C61#44911yescharacteristic
188C4×C61#45011yescharacteristic
189C4×C61#45212yes—
190C4×C61#45211yescharacteristic
191C4×C61#49511yescharacteristic
192C4×C61#49711yescharacteristic
193Dic61—82no—
194C2×#486—611no—
195C2×#477—611no—
196C2×#460—611no—
197#1984D6111yescharacteristic, complemented
198C2×#333—611no—
199C2×#331—611no—
200#1277—611no—
201C2×C61#167812yes—
202C2×C61#169812yes—
203C2×C61#200011yescharacteristic
204C2×C61#201511yescharacteristic
205C2×C61#201811yescharacteristic
206D61—162no—
207C22×SD16—1221no—
208C2×C4⋊Q8—611no—
209C2×#127—611no—
210C2×C4×Q8C2×D6111yescharacteristic
211#486—1222no—
212#486—1222no—
213#477—1222no—
214#477—1222no—
215#460—1222no—
216#460—1222no—
217C2×#107—1221no—
218C2×C4⋊C8—611no—
219C2×C4⋊C8—611no—
220C2×C4⋊C8C2×D6111yescharacteristic
221C2×#103—1221no—
222C2×#102—1222no—
223C2×#102—1221no—
224C2×C4×C8C2×D6111yescharacteristic
225#336—22no—
226#333—1222no—
227#331—1222no—
228C61#1026911yescharacteristic, complemented, Sylow
229C22×Q8—1221no—
230C22×Q8D24411yescharacteristic
231C22×D4—1221no—
232C22×D4—1221no—
233C22×D4—1221no—
234C2×SD16—1224no—
235C2×SD16—2442no—
236C2×SD16—2442no—
237C22×C8—21no—
238C22×C8—1221no—
239C22×C8—1221no—
240C22×C8C22⋊D6112yes—
241C4⋊Q8—612no—
242C4⋊Q8—1221no—
243C4⋊Q8—1221no—
244C4⋊Q8—1221no—
245#127—612no—
246#127—1221no—
247#127—1221no—
248#127—1221no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4D24411yescharacteristic
257C2×C42—21no—
258C2×C42C22×D6111yescharacteristic
259#107—1224no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—612no—
263C4⋊C8—612no—
264C4⋊C8—1221no—
265C4⋊C8—1221no—
266#103—1224no—
267#102—1224no—
268#102—1228no—
269C4×C8—21no—
270C4×C8—21no—
271C24—2441no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—1222no—
278C2×Q8—4882no—
279C2×Q8—2441no—
280C2×Q8#1175819012yes—
281C2×D4—1222no—
282C2×D4—1222no—
283C2×D4—1222no—
284C2×D4—4882no—
285C2×D4—2442no—
286C2×D4—2441no—
287C2×D4—2441no—
288C2×D4—2441no—
289C2×D4—2441no—
290C2×D4—2441no—
291C2×D4—2442no—
292C2×D4—2441no—
293C2×D4—2441no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—2441no—
297C22×C4C2×D24411yescharacteristic
298C22×C4#1175822211yescharacteristic
299C22×C4C2×C22⋊D6111yescharacteristic
300SD16—2448no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—41no—
305C2×C8—42no—
306C2×C8—1222no—
307C2×C8—1222no—
308C2×C8—2441no—
309C2×C8—2441no—
310C2×C8—2441no—
311C2×C8—2441no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—1222no—
317C4⋊C4—1222no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C42—41no—
321C42—41no—
322C42D4×D6111yescharacteristic
323C42D4×D6111yescharacteristic
324C42D4×D6111yescharacteristic
325C42D4×D6111yescharacteristic
326C23—4882no—
327C23—4881no—
328C23—4881no—
329C23—4882no—
330C23—2442no—
331C23#1451975111yescharacteristic
332Q8—22no—
333Q8—22no—
334Q8—41no—
335Q8—41no—
336Q8—4882no—
337Q8—4882no—
338D4—4882no—
339D4—4882no—
340D4—4881no—
341D4—4881no—
342D4—4881no—
343D4—4881no—
344D4—2442no—
345D4—2444no—
346D4—2442no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—4882no—
354C2×C4—2442no—
355C2×C4#1451974511yescharacteristic
356C2×C4#1451974711yescharacteristic
357C2×C4#1451974711yescharacteristic
358C2×C4#1451975011yescharacteristic
359C2×C4#1451975011yescharacteristic
360C2×C4#1451977311yescharacteristic
361C2×C4C2×#1175819011yescharacteristic
362C2×C4#1451979712yes—
363C2×C4#1451979911yescharacteristic
364C2×C4#1451980511yescharacteristic
365C2×C4#1451980812yes—
366C2×C4#1451981011yescharacteristic
367C8—42no—
368C8—81no—
369C8—2442no—
370C8—2442no—
371C22—9762no—
372C22—9762no—
373C22—4882no—
374C22—4882no—
375C22—4882no—
376C22#1683967111yescharacteristic
377C22#1683998412yes—
378C22#1683999111yescharacteristic
379C22#1684000811yescharacteristic
380C22#1684003212yes—
381C4—21no—
382C4—21no—
383C4—42no—
384C4—81no—
385C4—4882no—
386C4#1683990311yescharacteristic
387C4#1683990911yescharacteristic
388C4#1683991511yescharacteristic
389C4#1683992212yes—
390C4#1683992611yescharacteristic
391C4#1684014411yescharacteristic
392C4#1684015411yescharacteristic
393C2—9762no—
394C2#2144523512yes—
395C2#2144535912yes—
396C2#2144682411yescharacteristic
397C2#2144691211yescharacteristic
398C2#2144692811yescharacteristic
subgroupG/H
centerC23#14519751
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1984C2
socleC23×C61#121
prime radicalC2×#14519774C22
hypercenter#1984D61
hypocenterC61#10269
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
2. C2×#16840057C2semidirect
4. C2×#16839510C2semidirect
6. #21443654C2semidirect
7. C61×#1984C2semidirect
197. #1984D61semidirect
228. C61#10269semidirect

Maximal subgroups

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

subgroupindex
C2×#168401092
C2×#168400572
C2×#168399622
C2×#168395102
C2×#168395052
#214436542
C61×#19842
#1026961