Finite Group Databasebeta

← #30603435

Subgroups — #30603435

Order 15616.

670 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462461C211yesmaximal, characteristic
2C2×#16840643C212yesmaximal
3#21461525C211yesmaximal, characteristic
4C2×#16840642C212yesmaximal
5#21448438C211yesmaximal, characteristic
6C22×#11758217C2212yes—
7C22×#11758217C2212yes—
8#16840768—24no—
9#16840765—21no—
10#16840765—21no—
11#16840643—24no—
12#16840642—21no—
13#16840642—21no—
14#16840642—24no—
15C2×#14519733C2211yescharacteristic
16C2×#14519733C2211yescharacteristic
17C22×#11758196C2211yescharacteristic
18#16839659—21no—
19#16839657—21no—
20#16839637C411yescharacteristic
21#16839635C411yescharacteristic
22#16839634C411yescharacteristic
23#16839631—21no—
24#16839626—21no—
25C61×#385C411yescharacteristic
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×#11758217—22no—
35C2×#11758217—22no—
36C2×#11758217D414yes—
37C2×#11758217Q814yes—
38C22×#92420—22no—
39C22×#92420—22no—
40#14519844—22no—
41#14519844—22no—
42C4⋊#92420—22no—
43C4⋊#92420—22no—
44C23×Dic61C2×C411yescharacteristic
45C23×Dic61C2311yescharacteristic
46#14519733—22no—
47#14519733—21no—
48#14519733—21no—
49#14519733—22no—
50#14519733D412yes—
51#14519733Q812yes—
52C2×C4⋊Dic61—21no—
53C2×#11758196—21no—
54C2×#11758196—22no—
55C2×#11758196—21no—
56C2×#11758196—21no—
57C2×#11758196—22no—
58C2×#11758196—21no—
59C2×#11758196—21no—
60C2×#11758196D411yescharacteristic
61C2×#11758196D411yescharacteristic
62C2×C22⋊Dic61C2×C411yescharacteristic
63C2×C22⋊Dic61C2×C411yescharacteristic
64C2×C4×Dic61—21no—
65C2×C4×Dic61D411yescharacteristic
66C2×C4×Dic61D411yescharacteristic
67#14519684—21no—
68#14519684—21no—
69#14519684—21no—
70C23×C4×C61C2×C411yescharacteristic
71C2×C4⋊C4×C61—21no—
72C2×C22⋊C4×C61C2×C411yescharacteristic
73C2×C22⋊C4×C61C2×C411yescharacteristic
74#95×C61—21no—
75C24×C61C22×C411yescharacteristic
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—22no—
79C22×C4×C61—81no—
80C22×C4×C61C22⋊C411yescharacteristic
81C22×C4×C61C22⋊C411yescharacteristic
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—22no—
85C22×Dic61—81no—
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C2×D412yes—
89C22×Dic61C2×D411yescharacteristic
90C22×Dic61C2×D411yescharacteristic
91C22×Dic61C2×D411yescharacteristic
92C22×Dic61C2×Q812yes—
93C22×Dic61C2×Q811yescharacteristic
94C22×Dic61#4111yescharacteristic
95C22×Dic61#4111yescharacteristic
96C22×Dic61#4112yes—
97C22×Dic61#4112yes—
98#11758217—24no—
99#11758217—24no—
100#11758217—24no—
101#11758217—24no—
102#11758217—42no—
103#11758217—42no—
104#11758217—42no—
105#11758217—42no—
106C2×#92420—24no—
107C2×#92420—24no—
108C2×#92420—42no—
109C2×#92420—42no—
110C2×#92420—42no—
111C2×#92420—42no—
112C4⋊C4×C61—81no—
113C22⋊C4×C61—21no—
114C22⋊C4×C61—22no—
115C22⋊C4×C61C4⋊C412yes—
116C22⋊Dic61—21no—
117C22⋊Dic61—22no—
118C22⋊Dic61C4⋊C412yes—
119C4⋊Dic61—81no—
120#11758196—22no—
121#11758196—22no—
122#11758196—22no—
123#11758196—22no—
124#11758196—41no—
125#11758196—42no—
126#11758196—41no—
127#11758196—81no—
128#11758196—81no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61—22no—
132C4×Dic61—22no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61C2×C22⋊C411yescharacteristic
138C23×C61C2×C4⋊C411yescharacteristic
139C23×C61#11711yescharacteristic
140C23×C61C4×D412yes—
141C23×C61C4×Q812yes—
142C2×C4×C61—22no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—82no—
153C2×Dic61—22no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—82no—
164C2×Dic61#12011yescharacteristic
165C2×Dic61#12112yes—
166C2×Dic61#12111yescharacteristic
167C2×Dic61#12111yescharacteristic
168C2×Dic61#12112yes—
169C2×Dic61C22⋊Q812yes—
170C2×Dic61C22⋊Q811yescharacteristic
171C2×Dic61C22⋊Q812yes—
172C2×Dic61C22⋊Q812yes—
173C2×Dic61C22⋊Q811yescharacteristic
174C2×Dic61#12312yes—
175C2×Dic61#12311yescharacteristic
176C2×Dic61#12411yescharacteristic
177C2×Dic61#12512yes—
178C2×Dic61#12512yes—
179C2×Dic61#12612yes—
180C2×Dic61C4⋊Q812yes—
181C2×Dic61C4⋊Q811yescharacteristic
182#92420—44no—
183#92420—44no—
184#11206—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—22no—
187C22×C61—21no—
188C22×C61—22no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—42no—
192C22×C61#38011yescharacteristic
193C22×C61#38611yescharacteristic
194C22×C61#38712yes—
195C22×C61#38912yes—
196C22×C61#39111yescharacteristic
197C4×C61—42no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61—81no—
201Dic61—42no—
202Dic61—41no—
203Dic61—41no—
204Dic61—81no—
205Dic61#39411yescharacteristic
206Dic61#39511yescharacteristic
207Dic61#39612yes—
208Dic61#39811yescharacteristic
209Dic61#39812yes—
210Dic61#40011yescharacteristic
211#2905—611no—
212#2317—611no—
213C2×#344—612no—
214#1742—611no—
215C2×#343—612no—
216C2×C61—21no—
217C2×C61—22no—
218C2×C61—22no—
219C2×C61—21no—
220C2×C61#144111yescharacteristic
221C2×C61#191411yescharacteristic
222C2×C61#191511yescharacteristic
223C22×M16—612no—
224C22×M16—612no—
225C2×#117—611no—
226C2×#117—611no—
227C22×C4⋊C4—611no—
228#424—1224no—
229#423—1221no—
230#423—1221no—
231#389—1221no—
232#389—1221no—
233#385—611no—
234#385—611no—
235#385—611no—
236#385#692311yescharacteristic
237#384—1221no—
238#382—1221no—
239#344—1224no—
240#343—1221no—
241#343—1221no—
242#343—1224no—
243C61#1120611yescharacteristic, complemented, Sylow
244C23×C4—611no—
245C23×C4—611no—
246C23×C4C2×#692311yescharacteristic
247C2×M16—614no—
248C2×M16—614no—
249C2×M16—1222no—
250C2×M16—1222no—
251C2×M16—1222no—
252C2×M16—1222no—
253C2×M16—1222no—
254C2×M16—1222no—
255C2×M16—1222no—
256C2×M16—1222no—
257C2×M16—1222no—
258C2×M16—1222no—
259C22×C8—1222no—
260C22×C8—1222no—
261#117—612no—
262#117—612no—
263#117—1222no—
264#117—1222no—
265#117—1221no—
266#117—1221no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4—611no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4—1221no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—1222no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4—1222no—
278C2×C22⋊C4—611no—
279C2×C22⋊C4—611no—
280C2×C22⋊C4C2×#692311yescharacteristic
281C2×C22⋊C4C2×#692311yescharacteristic
282C2×C42—611no—
283C2×C42—611no—
284C2×C42—1221no—
285C4⋊C8—1222no—
286C4⋊C8—1222no—
287C4⋊C8—1222no—
288C4⋊C8—1222no—
289#95—21no—
290#95—1221no—
291#95—1221no—
292#95—1221no—
293C24C22×#692311yescharacteristic
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—81no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—612no—
305C22×C4—612no—
306C22×C4—612no—
307C22×C4—612no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—1221no—
311C22×C4—1222no—
312C22×C4—1221no—
313C22×C4—4881no—
314C22×C4C22⋊#692311yescharacteristic
315C22×C4C22⋊#692311yescharacteristic
316M16—1224no—
317M16—1224no—
318M16—1224no—
319M16—1224no—
320M16—2442no—
321M16—2442no—
322M16—2442no—
323M16—2442no—
324C2×C8—1224no—
325C2×C8—1224no—
326C2×C8—2442no—
327C2×C8—2442no—
328C2×C8—2442no—
329C2×C8—2442no—
330C4⋊C4—81no—
331C4⋊C4—1222no—
332C4⋊C4—1222no—
333C4⋊C4—1222no—
334C4⋊C4—1222no—
335C4⋊C4—4881no—
336C4⋊C4—4881no—
337C4⋊C4—4881no—
338C4⋊C4—2441no—
339C4⋊C4—2442no—
340C4⋊C4—2441no—
341C22⋊C4—21no—
342C22⋊C4—22no—
343C22⋊C4—612no—
344C22⋊C4—1221no—
345C22⋊C4—1222no—
346C22⋊C4C4⋊#692312yes—
347C42—1221no—
348C42—1221no—
349C42—1221no—
350C42—1221no—
351C42—1222no—
352C42—1222no—
353C23—41no—
354C23—41no—
355C23C2×C22⋊#692311yescharacteristic
356C23C2×C4⋊#692311yescharacteristic
357C23#1451985611yescharacteristic
358C23D4×#692312yes—
359C23Q8×#692312yes—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—82no—
371C2×C4—611no—
372C2×C4—611no—
373C2×C4—611no—
374C2×C4—611no—
375C2×C4—611no—
376C2×C4—612no—
377C2×C4—611no—
378C2×C4—612no—
379C2×C4—612no—
380C2×C4—612no—
381C2×C4—612no—
382C2×C4—612no—
383C2×C4—612no—
384C2×C4—612no—
385C2×C4—612no—
386C2×C4—612no—
387C2×C4—611no—
388C2×C4—611no—
389C2×C4—1222no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—4882no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C8—2444no—
401C8—2444no—
402C22—21no—
403C22—22no—
404C22—21no—
405C22—22no—
406C22—41no—
407C22—41no—
408C22—42no—
409C22#1684070411yescharacteristic
410C22#1684071011yescharacteristic
411C22#1684071112yes—
412C22#1684071312yes—
413C22(C2×#6923)⋊Q811yescharacteristic
414C4—42no—
415C4—41no—
416C4—41no—
417C4—81no—
418C4—611no—
419C4—611no—
420C4—612no—
421C4—611no—
422C4—612no—
423C4—611no—
424C4—4881no—
425C4—2442no—
426C4—2441no—
427C4—2441no—
428C2—21no—
429C2—22no—
430C2—22no—
431C2—21no—
432C2#2146100411yescharacteristic
433C2#2146187011yescharacteristic
434C2#2146187111yescharacteristic
subgroupG/H
centerC22#16840710
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#385C4
socleC22×C61#386
cosocleC23×Dic61C23
hypercenter#385#6923
hypocenterC61#11206
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #385

Complements

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

NH ≅ G/Ntype
243. C61#11206semidirect

Maximal subgroups

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

subgroupindex
#214624612
C2×#168406432
#214615252
C2×#168406422
#214484382
#1120661