Finite Group Databasebeta

← #30603234

Subgroups — #30603234

Order 15616.

850 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462461C211yesmaximal, characteristic
2C22×#14519838C212yesmaximal
3C2×#16840643C212yesmaximal
4#21461525C211yesmaximal, characteristic
5#21448404C211yesmaximal, characteristic
6C22×#11758217C2212yes—
7C22×#11758217C2212yes—
8#16840768—24no—
9#16840765—22no—
10C2×#14519838—24no—
11C2×#14519838—24no—
12C2×#14519838—24no—
13#16840643—24no—
14#16840642—22no—
15C23×Dic122C2211yescharacteristic
16C2×#14519733C2211yescharacteristic
17C2×#14519733C2211yescharacteristic
18#16839666—22no—
19#16839666—22no—
20#16839625C411yescharacteristic
21#16839623C411yescharacteristic
22#16839623C411yescharacteristic
23C61×#381C411yescharacteristic
24C2×#11758217—22no—
25C2×#11758217—22no—
26C2×#11758217—22no—
27C2×#11758217—22no—
28C2×#11758217—22no—
29C2×#11758217—22no—
30C2×#11758217—22no—
31C2×#11758217—22no—
32C2×#11758217—22no—
33C2×#11758217—22no—
34C2×#11758217D414yes—
35C2×#11758217D414yes—
36C22×#92420—22no—
37C22×#92420—22no—
38#14519844—24no—
39C4⋊#92420—24no—
40#14519838—216no—
41C22×Dic122—22no—
42C22×Dic122—22no—
43C22×Dic122—21no—
44C22×Dic122—21no—
45C22×Dic122—21no—
46C22×Dic122—21no—
47C22×Dic122—22no—
48C22×Dic122—22no—
49C22×Dic122D412yes—
50C22×Dic122Q812yes—
51C23×Dic61C2×C411yescharacteristic
52C23×Dic61C2311yescharacteristic
53#14519733—22no—
54#14519733—22no—
55#14519733—22no—
56#14519733—22no—
57C2×#11758196—21no—
58C2×#11758196D412yes—
59C2×C22⋊Dic61C2×C411yescharacteristic
60C2×C22⋊Dic61C2×C411yescharacteristic
61C2×C4×Dic61—21no—
62C2×C4×Dic61D412yes—
63#14519684—22no—
64#14519684—22no—
65#14519684—22no—
66C23×C4×C61C2×C411yescharacteristic
67C2×C22⋊C4×C61C2×C411yescharacteristic
68C2×C22⋊C4×C61C2×C411yescharacteristic
69#95×C61—22no—
70C24×C61C22×C411yescharacteristic
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—22no—
74C22×C4×C61—22no—
75C22×C4×C61—21no—
76C22×C4×C61C22⋊C412yes—
77C22×C4×C61C4⋊C412yes—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—22no—
81C22×Dic61—22no—
82C22×Dic61—21no—
83C22×Dic61C22⋊C412yes—
84C22×Dic61C4⋊C412yes—
85C22×Dic61C2×D412yes—
86C22×Dic61C2×D411yescharacteristic
87C22×Dic61C2×D412yes—
88C22×Dic61C2×D411yescharacteristic
89C22×Dic61C2×D411yescharacteristic
90C22×Dic61C2×Q811yescharacteristic
91C22×Dic61#4111yescharacteristic
92C22×Dic61#4112yes—
93C22×Dic61#4111yescharacteristic
94C22×Dic61#4112yes—
95C2×Dic122—24no—
96C2×Dic122—22no—
97C2×Dic122—22no—
98C2×Dic122—24no—
99C2×Dic122—22no—
100C2×Dic122—22no—
101C2×Dic122—24no—
102C2×Dic122—24no—
103C2×Dic122—41no—
104C2×Dic122—42no—
105C2×Dic122—42no—
106C2×Dic122—42no—
107C2×Dic122—42no—
108C2×Dic122—41no—
109C2×Dic122—42no—
110C2×Dic122—41no—
111C2×Dic122—42no—
112C2×Dic122—41no—
113#11758217—24no—
114#11758217—24no—
115#11758217—24no—
116#11758217—24no—
117#11758217—42no—
118#11758217—42no—
119#11758217—42no—
120#11758217—42no—
121C2×#92420—24no—
122C2×#92420—24no—
123C2×#92420—42no—
124C2×#92420—42no—
125C2×#92420—42no—
126C2×#92420—42no—
127C22⋊C4×C61—22no—
128C22⋊C4×C61—22no—
129C22⋊Dic61—22no—
130C22⋊Dic61—22no—
131#11758196—24no—
132#11758196—41no—
133#11758196—41no—
134C4×Dic61—22no—
135C4×Dic61—22no—
136C4×Dic61—42no—
137C23×C61—42no—
138C23×C61C2×C22⋊C411yescharacteristic
139C23×C61C2×C4⋊C411yescharacteristic
140C23×C61#11711yescharacteristic
141C23×C61C4×D412yes—
142C23×C61C4×D412yes—
143C2×C4×C61—22no—
144C2×C4×C61—24no—
145C2×C4×C61—22no—
146C2×C4×C61—41no—
147C2×C4×C61—42no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—42no—
151C2×C4×C61—41no—
152C2×Dic61—22no—
153C2×Dic61—24no—
154C2×Dic61—22no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61—41no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160C2×Dic61—41no—
161C2×Dic61#12011yescharacteristic
162C2×Dic61#12012yes—
163C2×Dic61#12112yes—
164C2×Dic61#12111yescharacteristic
165C2×Dic61#12111yescharacteristic
166C2×Dic61#12112yes—
167C2×Dic61#12112yes—
168C2×Dic61C22⋊Q812yes—
169C2×Dic61C22⋊Q811yescharacteristic
170C2×Dic61C22⋊Q811yescharacteristic
171C2×Dic61C22⋊Q812yes—
172C2×Dic61#12312yes—
173C2×Dic61#12312yes—
174C2×Dic61#12311yescharacteristic
175C2×Dic61#12412yes—
176C2×Dic61#12411yescharacteristic
177C2×Dic61#12612yes—
178C2×Dic61#12711yescharacteristic
179Dic122—42no—
180Dic122—42no—
181Dic122—44no—
182Dic122—44no—
183Dic122—42no—
184Dic122—42no—
185#92420—44no—
186#92420—44no—
187#11048—611nomaximal, Sylow
188C22×C61—22no—
189C22×C61—24no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—42no—
193C22×C61#38011yescharacteristic
194C22×C61#38512yes—
195C22×C61#38611yescharacteristic
196C22×C61#38812yes—
197C22×C61#39011yescharacteristic
198C4×C61—42no—
199C4×C61—42no—
200C4×C61—81no—
201Dic61—42no—
202Dic61—42no—
203Dic61—81no—
204Dic61#39211yescharacteristic
205Dic61#39311yescharacteristic
206Dic61#39412yes—
207Dic61#39612yes—
208Dic61#39711yescharacteristic
209Dic61#39911yescharacteristic
210#2905—611no—
211C22×#101—612no—
212#2310—611no—
213C2×#344—612no—
214#1742—611no—
215C2×C61—21no—
216C2×C61—21no—
217C2×C61—22no—
218C2×C61—22no—
219C2×C61#143911yescharacteristic
220C2×C61#191512yes—
221C23×Q8—611no—
222C22×M16—612no—
223C22×M16—612no—
224C2×#117—611no—
225C2×#117—611no—
226#424—1224no—
227#423—1222no—
228C2×#101—1224no—
229C2×#101—1224no—
230C2×#101—1224no—
231#391—1222no—
232#391—1222no—
233#381—611no—
234#381—611no—
235#381—611no—
236#381#692311yescharacteristic
237#344—1224no—
238#343—1222no—
239C61#1104811yescharacteristic, complemented, Sylow
240C22×Q8—612no—
241C22×Q8—612no—
242C22×Q8—1221no—
243C22×Q8—1221no—
244C22×Q8—1222no—
245C22×Q8—1222no—
246C22×Q8—1221no—
247C22×Q8—1221no—
248C22×Q8—1222no—
249C22×Q8—1222no—
250C23×C4—611no—
251C23×C4—611no—
252C23×C4C2×#692311yescharacteristic
253C2×M16—614no—
254C2×M16—614no—
255C2×M16—1222no—
256C2×M16—1222no—
257C2×M16—1222no—
258C2×M16—1222no—
259C2×M16—1222no—
260C2×M16—1222no—
261C2×M16—1222no—
262C2×M16—1222no—
263C2×M16—1222no—
264C2×M16—1222no—
265C22×C8—1222no—
266C22×C8—1222no—
267#117—1222no—
268#117—1222no—
269#117—1222no—
270#117—1222no—
271C2×C4⋊C4—612no—
272C2×C4⋊C4—1221no—
273C2×C22⋊C4—611no—
274C2×C22⋊C4—611no—
275C2×C22⋊C4C2×#692311yescharacteristic
276C2×C22⋊C4C2×#692311yescharacteristic
277C2×C42—612no—
278C2×C42—1221no—
279C4⋊C8—1224no—
280C4⋊C8—1224no—
281#101—12216no—
282#95—22no—
283#95—1222no—
284#95—1222no—
285#95—1222no—
286C24C22×#692311yescharacteristic
287C2×Q8—1224no—
288C2×Q8—1222no—
289C2×Q8—1222no—
290C2×Q8—1222no—
291C2×Q8—1222no—
292C2×Q8—1224no—
293C2×Q8—1224no—
294C2×Q8—1224no—
295C2×Q8—2441no—
296C2×Q8—2442no—
297C2×Q8—2441no—
298C2×Q8—2442no—
299C2×Q8—2442no—
300C2×Q8—2442no—
301C2×Q8—2442no—
302C2×Q8—2442no—
303C2×Q8—2441no—
304C2×Q8—2441no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—611no—
311C22×C4—611no—
312C22×C4—611no—
313C22×C4—611no—
314C22×C4—611no—
315C22×C4—611no—
316C22×C4—612no—
317C22×C4—612no—
318C22×C4—612no—
319C22×C4—612no—
320C22×C4—612no—
321C22×C4—612no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1222no—
325C22×C4—1222no—
326C22×C4—1221no—
327C22×C4C4⋊#692312yes—
328C22×C4C22⋊#692312yes—
329M16—1224no—
330M16—1224no—
331M16—1224no—
332M16—1224no—
333M16—2442no—
334M16—2442no—
335M16—2442no—
336M16—2442no—
337C2×C8—1224no—
338C2×C8—1224no—
339C2×C8—2442no—
340C2×C8—2442no—
341C2×C8—2442no—
342C2×C8—2442no—
343C4⋊C4—1224no—
344C4⋊C4—2441no—
345C4⋊C4—2441no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—1222no—
349C22⋊C4—1222no—
350C42—1222no—
351C42—1222no—
352C42—2442no—
353C23—42no—
354C23C2×C22⋊#692311yescharacteristic
355C23C2×C4⋊#692311yescharacteristic
356C23#1451985611yescharacteristic
357C23D4×#692312yes—
358C23D4×#692312yes—
359Q8—2442no—
360Q8—2442no—
361Q8—2444no—
362Q8—2444no—
363Q8—2442no—
364Q8—2442no—
365C2×C4—22no—
366C2×C4—24no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—611no—
375C2×C4—611no—
376C2×C4—611no—
377C2×C4—611no—
378C2×C4—612no—
379C2×C4—612no—
380C2×C4—612no—
381C2×C4—612no—
382C2×C4—611no—
383C2×C4—612no—
384C2×C4—611no—
385C2×C4—612no—
386C2×C4—612no—
387C2×C4—612no—
388C2×C4—612no—
389C2×C4—612no—
390C2×C4—611no—
391C2×C4—611no—
392C2×C4—1222no—
393C2×C4—1224no—
394C2×C4—1222no—
395C2×C4—2442no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2442no—
399C2×C4—2441no—
400C2×C4—2442no—
401C8—2444no—
402C8—2444no—
403C22—22no—
404C22—24no—
405C22—41no—
406C22—41no—
407C22—42no—
408C22#1684070411yescharacteristic
409C22#1684070912yes—
410C22#1684071011yescharacteristic
411C22#1684071212yes—
412C22#1684071411yescharacteristic
413C4—42no—
414C4—42no—
415C4—81no—
416C4—611no—
417C4—611no—
418C4—612no—
419C4—612no—
420C4—611no—
421C4—611no—
422C4—4881no—
423C4—2442no—
424C4—2442no—
425C2—21no—
426C2—21no—
427C2—22no—
428C2—22no—
429C2#2146100211yescharacteristic
430C2#2146187112yes—
subgroupG/H
centerC22#16840710
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#381C4
socleC22×C61#386
cosocleC23×Dic61C23
hypercenter#381#6923
hypocenterC61#11048
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
239. C61#11048semidirect

Maximal subgroups

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

subgroupindex
#214624612
C22×#145198382
C2×#168406432
#214615252
#214484042
#1104861