Finite Group Databasebeta

← #29582573

Subgroups — #29582573

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×#16840110C211yesmaximal, characteristic
2C2×#16840054C211yesmaximal, characteristic, complemented
3C2×#16839963C211yesmaximal, characteristic
4#21446754C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6#21443653C211yesmaximal, characteristic, complemented
7C2×C61×#333C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C2×#14519774C2211yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11#16840110—22no—
12#16840110—22no—
13#16840054—22no—
14#16840054—22no—
15#16839963—22no—
16#16839963—22no—
17C2×#14519710—21no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×#14519700—21no—
20C2×#14519699—21no—
21C2×#14519697—22no—
22C2×C4×#92418C2211yescharacteristic
23#16839516—22no—
24#16839505—22no—
25C2×C4⋊Q8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C61×#333—22no—
29C22×Dic122D411yescharacteristic
30C22×D244—21no—
31C22×D244—21no—
32C22×D244—21no—
33C2×#11758190—24no—
34C2×#11758190—42no—
35C2×#11758190—42no—
36C22×#92418—21no—
37C22×#92418D412yes—
38#14519774—21no—
39#14519774—21no—
40#14519774—21no—
41#14519774D412yes—
42C4×Dic122—21no—
43C4×Dic122—21no—
44C4×Dic122—21no—
45C4×Dic122—21no—
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758196—21no—
48C2×C4×Dic61—21no—
49#14519710—24no—
50C4⋊#92418—21no—
51C4⋊#92418D412yes—
52#14519700—24no—
53#14519699—24no—
54#14519697—28no—
55C4×#92418—21no—
56C4×#92418—21no—
57C22×Q8×C61—21no—
58C22×C8×C61—21no—
59C22×C8×C61—21no—
60C4⋊Q8×C61—21no—
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61D412yes—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61D412yes—
71C23×D61—41no—
72C2×Q8×C61—22no—
73C2×Q8×C61—41no—
74C2×Q8×C61—82no—
75C22×C4×C61—41no—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C22×Dic61—21no—
80C22×Dic61—21no—
81C2×D244—22no—
82C2×D244—22no—
83C2×D244—22no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—42no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—42no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—82no—
94C2×Dic122—21no—
95C2×Dic122—21no—
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—21no—
99C2×Dic122SD1612yes—
100C2×C8×C61—22no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61—42no—
105C4⋊C4×C61—22no—
106C4⋊C4×C61—22no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115#11758196—41no—
116#11758196—41no—
117C4×Dic61—41no—
118C4×Dic61—41no—
119C2×#92418—22no—
120C2×#92418—22no—
121C2×#92418—22no—
122C2×#92418—22no—
123C2×#92418—41no—
124C2×#92418—41no—
125#11758190—48no—
126C23×C61#12111yescharacteristic
127C22×D61—42no—
128C22×D61—82no—
129C22×D61—81no—
130C22×D61—81no—
131C22×D61—82no—
132Q8×C61—82no—
133Q8×C61—82no—
134C2×C4×C61—22no—
135C2×C4×C61—42no—
136C2×C4×C61—82no—
137C2×C4×C61#12011yescharacteristic
138C2×C4×C61#12011yescharacteristic
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12711yescharacteristic
143C2×C4×C61C2×SD1611yescharacteristic
144C2×C4×C61#13511yescharacteristic
145C2×C4×C61#13512yes—
146C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C61#13711yescharacteristic
148C2×C4×C61#13712yes—
149C2×Dic61—22no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—42no—
154D244—42no—
155D244—42no—
156D244—44no—
157D244—82no—
158D244—82no—
159D244—81no—
160D244—81no—
161D244—81no—
162D244—81no—
163Dic122—22no—
164Dic122—22no—
165Dic122—41no—
166Dic122—41no—
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—82no—
185C4×C61#44811yescharacteristic
186C4×C61#44911yescharacteristic
187C4×C61#45011yescharacteristic
188C4×C61#45211yescharacteristic
189C4×C61#45212yes—
190C4×C61#49511yescharacteristic
191C4×C61#49711yescharacteristic
192Dic61—42no—
193Dic61—81no—
194C2×#486—611no—
195C2×#477—611no—
196C2×#460—611no—
197#1984—611no—
198C2×#333D6111yescharacteristic, complemented
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⋊Q8C2×D6111yescharacteristic
209C2×#127—611no—
210C2×C4×Q8—611no—
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⋊C8C2×D6111yescharacteristic
220C2×C4⋊C8C2×D6111yescharacteristic
221C2×#103—1221no—
222C2×#102—1222no—
223C2×#102—1221no—
224C2×C4×C8—611no—
225#336—1222no—
226#333—22no—
227#331—1222no—
228C61#1026911yescharacteristic, complemented, Sylow
229C22×Q8—21no—
230C22×Q8—611no—
231C22×D4—1221no—
232C22×D4—1221no—
233C22×D4—1221no—
234C2×SD16—1224no—
235C2×SD16—2442no—
236C2×SD16—2442no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—612no—
240C22×C8—1221no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8D24412yes—
245#127—612no—
246#127—1221no—
247#127—1221no—
248#127—1221no—
249C4×Q8—1221no—
250C4×Q8—1221no—
251C4×Q8—1221no—
252C4×Q8—1221no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—1221no—
257C2×C42—1221no—
258C2×C42C22×D6111yescharacteristic
259#107—1224no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—612no—
264C4⋊C8—1221no—
265C4⋊C8C22⋊D6112yes—
266#103—1224no—
267#102—1228no—
268#102—1224no—
269C4×C8—1221no—
270C4×C8—1221no—
271C24—2441no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—82no—
275C2×Q8—612no—
276C2×Q8—1221no—
277C2×Q8—1221no—
278C2×Q8—1221no—
279C2×Q8—1221no—
280C2×Q8—1221no—
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—41no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4#1175822211yescharacteristic
298C22×C4D4×D6111yescharacteristic
299C22×C4D4×D6111yescharacteristic
300SD16—2448no—
301C2×C8—22no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—42no—
306C2×C8—1222no—
307C2×C8—1222no—
308C2×C8—1222no—
309C2×C8—1222no—
310C2×C8—2441no—
311C2×C8—2441no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C42—2441no—
321C42—2441no—
322C42C2×D24411yescharacteristic
323C42D4×D6111yescharacteristic
324C42D4×D6111yescharacteristic
325C42C2×C22⋊D6111yescharacteristic
326C23—4882no—
327C23—4881no—
328C23—4881no—
329C23—4882no—
330C23—2442no—
331C23#1451975011yescharacteristic
332Q8—82no—
333Q8—82no—
334Q8—1222no—
335Q8—1222no—
336Q8—2441no—
337Q8—2441no—
338D4—4882no—
339D4—4882no—
340D4—4881no—
341D4—4881no—
342D4—4881no—
343D4—4881no—
344D4—2442no—
345D4—2442no—
346D4—2444no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—82no—
350C2×C4—1222no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4#1451974511yescharacteristic
356C2×C4#1451974711yescharacteristic
357C2×C4#1451974711yescharacteristic
358C2×C4#1451975011yescharacteristic
359C2×C4#1451975111yescharacteristic
360C2×C4#1451977311yescharacteristic
361C2×C4SD16×D6111yescharacteristic
362C2×C4#1451979812yes—
363C2×C4#1451980011yescharacteristic
364C2×C4#1451980411yescharacteristic
365C2×C4#1451980912yes—
366C2×C4#1451980911yescharacteristic
367C8—42no—
368C8—81no—
369C8—2442no—
370C8—2442no—
371C22—9762no—
372C22—9762no—
373C22—4882no—
374C22—4882no—
375C22—4882no—
376C22#1683967111yescharacteristic
377C22#1683998712yes—
378C22#1683999411yescharacteristic
379C22#1684001111yescharacteristic
380C22#1684003112yes—
381C4—21no—
382C4—21no—
383C4—82no—
384C4—4881no—
385C4—2442no—
386C4#1683990211yescharacteristic
387C4#1683991011yescharacteristic
388C4#1683991111yescharacteristic
389C4#1683992311yescharacteristic
390C4#1683992712yes—
391C4#1684014311yescharacteristic
392C4#1684015511yescharacteristic
393C2—9762no—
394C2#2144523812yes—
395C2#2144536212yes—
396C2#2144682111yescharacteristic
397C2#2144691411yescharacteristic
398C2#2144692711yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#333C2
socleC23×C61#121
prime radicalC2×#14519774C22
hypercenterC2×#333D61
hypocenterC61#10269
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
2. C2×#16840054C2semidirect
4. #21446754C2semidirect
6. #21443653C2semidirect
7. C2×C61×#333C2semidirect
198. C2×#333D61semidirect
228. C61#10269semidirect

Maximal subgroups

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

subgroupindex
C2×#168401102
C2×#168400542
C2×#168399632
#214467542
C2×#168395052
#214436532
C2×C61×#3332
#1026961