Finite Group Databasebeta

← #30600987

Subgroups — #30600987

Order 15616.

640 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462668C211yesmaximal, characteristic, complemented
2#21461681C211yesmaximal, characteristic, complemented
3#21461255C212yesmaximal, complemented
4#21460693C212yesmaximal, complemented
5#21450774C211yesmaximal, characteristic
6#16840789—24no—
7#16840779—21no—
8C2×#14519835—21no—
9D61⋊(C22⋊C8)C2212yes—
10C2×C22⋊#92420—21no—
11#16840704C2212yes—
12#16840640—21no—
13#16840613—24no—
14C2×#14519748—21no—
15C2×#14519748C2211yescharacteristic
16C2×#14519737C2211yescharacteristic
17#16839694C411yescharacteristic, complemented
18#16839687C411yescharacteristic, complemented
19#16839676C411yescharacteristic, complemented
20#16839655—21no—
21#16839642—21no—
22#16839638—21no—
23#95×D61C2211yescharacteristic
24C61×#392C411yescharacteristic, complemented
25C2×D61⋊C8—22no—
26C22×#92420—22no—
27C2×C4⋊#6923—22no—
28C2×C22⋊#6923—22no—
29#14519844—22no—
30#14519835—42no—
31#14519834D414yescomplemented
32C22⋊#92420—22no—
33C22⋊#92420—22no—
34C4×#92420—22no—
35(C2×#6923)⋊C4—22no—
36C22×C22⋊D61—21no—
37C22×C22⋊D61D411yescharacteristic
38C23×Dic61D411yescharacteristic
39C22×C4×D61—21no—
40C22×C4×D61C2311yescharacteristic
41#14519748—22no—
42#14519748—22no—
43#14519748—42no—
44#14519748—42no—
45#14519737—22no—
46#14519737—22no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×#11758196C2×C411yescharacteristic
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61—21no—
52C2×C22⋊Dic61—21no—
53C2×C22⋊Dic61—21no—
54C2×#11758198D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684C2×C411yescharacteristic
60C22×D4×C61—21no—
61C22×D4×C61C2×C411yescharacteristic
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61C2×C411yescharacteristic
64#95×C61C2×C411yescharacteristic
65C24×C61—21no—
66C24×C61C22⋊C411yescharacteristic
67C23×D61C2×D411yescharacteristic
68C22×#6923—42no—
69C2×D4×C61—22no—
70C2×D4×C61—42no—
71C2×D4×C61—42no—
72C2×D4×C61—81no—
73C2×D4×C61—81no—
74C22×C4×C61—21no—
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C2×C22⋊D61—22no—
78C2×C22⋊D61—22no—
79C2×C22⋊D61—42no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—42no—
83C2×C22⋊D61D812yes—
84C2×C22⋊D61SD1612yes—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—81no—
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C2×D411yescharacteristic
93C2×C4×D61—42no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—81no—
97C2×C4×D61—81no—
98C2×C4×D61C2×D412yes—
99C2×C4×D61#4112yes—
100C22⋊#6923—42no—
101C22⋊#6923—42no—
102C2×#92420—24no—
103C2×#92420—82no—
104C4⋊#6923—82no—
105D61⋊C8—82no—
106C22⋊C4×C61—22no—
107C22⋊C4×C61—42no—
108C22⋊Dic61—42no—
109C22⋊Dic61—42no—
110C22⋊Dic61—41no—
111C22⋊Dic61—41no—
112C22⋊Dic61—81no—
113#11758198—22no—
114C4⋊Dic61—22no—
115C4⋊Dic61—42no—
116#11758196—22no—
117C4×Dic61—21no—
118C4×Dic61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61#10212yes—
131C23×C61C2×C22⋊C411yescharacteristic
132C22×D61—41no—
133C22×D61—41no—
134C22×D61#12112yes—
135C22×D61C2×D811yescharacteristic
136C22×D61C2×SD1611yescharacteristic
137C22×D61#13512yes—
138C2×#6923—82no—
139C2×#6923—82no—
140C2×#6923—82no—
141D4×C61—82no—
142D4×C61—84no—
143C2×C4×C61—22no—
144C2×C4×C61—21no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61C4×D412yes—
150C22⋊D61—24no—
151C22⋊D61—24no—
152C22⋊D61—82no—
153C22⋊D61—82no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—41no—
158C2×Dic61—42no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—81no—
167C2×Dic61#10212yes—
168C2×Dic61#12011yescharacteristic
169C2×Dic61#12311yescharacteristic
170C4×D61—42no—
171C4×D61—42no—
172C4×D61—82no—
173C4×D61—82no—
174#92420—44no—
175#9384—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—22no—
179C22×C61—42no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61#38611yescharacteristic
191C22×C61C2×#10211yescharacteristic
192C22×C61#41611yescharacteristic
193C2×D61—22no—
194C2×D61—22no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—42no—
198C2×D61#46512yes—
199C2×D61#46612yes—
200#6923—162no—
201C4×C61—22no—
202C4×C61—42no—
203C4×C61—41no—
204Dic61—22no—
205Dic61—21no—
206Dic61—21no—
207Dic61—41no—
208Dic61—81no—
209Dic61—81no—
210#2972—611no—
211#2543—611no—
212#1799—611no—
213#1519—612no—
214#1294—612no—
215C2×C61—21no—
216C2×C61—21no—
217C2×C61—42no—
218C2×C61—161no—
219C2×C61#188411yescharacteristic
220C2×C61#189311yescharacteristic
221C2×C61#191311yescharacteristic
222D61—22no—
223D61—22no—
224C2×#121—611no—
225C2×#121—1221no—
226C2×C4×D4—611no—
227C8×D4—1224no—
228#431—1221no—
229C2×#99—1221no—
230C2×C22⋊C8—612no—
231C2×C22⋊C8—1221no—
232#398—611no—
233#397—611no—
234#394—611no—
235#392#692311yescharacteristic, complemented
236#388—1221no—
237#386—1221no—
238#386—1221no—
239#380—612no—
240C2×#95—611no—
241#342—1221no—
242#327—1224no—
243C61#938411yescharacteristic, complemented, Sylow
244C22×D4—21no—
245C22×D4—611no—
246C22×D4—1221no—
247C22×D4C2×#692311yescharacteristic
248C23×C4—611no—
249C23×C4—611no—
250C23×C4—1221no—
251C22×C8—1222no—
252C22×C8—1222no—
253#121—1222no—
254#121—1222no—
255#121—2442no—
256#121—2442no—
257C4×D4—1222no—
258C4×D4—1222no—
259C2×C4⋊C4—611no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4—1222no—
262C2×C4⋊C4—1221no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—611no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1222no—
270C2×C22⋊C4C2×#692311yescharacteristic
271C2×C42—611no—
272C4⋊C8—1222no—
273#99—2442no—
274C22⋊C8—614no—
275C22⋊C8—1222no—
276C22⋊C8—1222no—
277C4×C8—1222no—
278#95—611no—
279#95—1221no—
280#95—1221no—
281#95—1222no—
282#95—1221no—
283#95C2×#692311yescharacteristic
284C24—21no—
285C24—611no—
286C24C22⋊#692311yescharacteristic
287C2×D4—22no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—81no—
291C2×D4—81no—
292C2×D4—612no—
293C2×D4—612no—
294C2×D4—1222no—
295C2×D4—1222no—
296C2×D4—2442no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2442no—
300C22×C4—21no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—612no—
304C22×C4—612no—
305C22×C4—611no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—4881no—
311C22×C4—4881no—
312C22×C4—4881no—
313C22×C4—2442no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2442no—
317C22×C4C22⋊#692311yescharacteristic
318C22×C4C22×#692311yescharacteristic
319C2×C8—1224no—
320C2×C8—4882no—
321C2×C8—4882no—
322C4⋊C4—1222no—
323C4⋊C4—1222no—
324C4⋊C4—4882no—
325C4⋊C4—2442no—
326C22⋊C4—22no—
327C22⋊C4—42no—
328C22⋊C4—1222no—
329C22⋊C4—4881no—
330C22⋊C4—2441no—
331C22⋊C4—2441no—
332C22⋊C4—2442no—
333C22⋊C4—2442no—
334C22⋊C4—2442no—
335C22⋊C4—2442no—
336C42—1221no—
337C42—1221no—
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—612no—
350C23—611no—
351C23—611no—
352C23—612no—
353C23—2441no—
354C23—2441no—
355C23#1451983912yes—
356C23C2×C22⋊#692311yescharacteristic
357D4—82no—
358D4—84no—
359D4—1224no—
360D4—1224no—
361D4—4882no—
362D4—4882no—
363C2×C4—22no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—611no—
370C2×C4—611no—
371C2×C4—612no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—4882no—
376C2×C4—4882no—
377C2×C4—4881no—
378C2×C4—4882no—
379C2×C4—4882no—
380C2×C4—4882no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4—2441no—
384C2×C4—2442no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4D4×#692312yes—
393C8—2444no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—612no—
409C22—612no—
410C22—1222no—
411C22—1222no—
412C22—2441no—
413C22—2441no—
414C22—2442no—
415C22#1684071011yescharacteristic
416C22C2×#1451983911yescharacteristic
417C22#1684075211yescharacteristic
418C4—22no—
419C4—42no—
420C4—41no—
421C4—1222no—
422C4—1221no—
423C4—1221no—
424C4—9762no—
425C4—4881no—
426C4—4881no—
427C4—2441no—
428C2—21no—
429C2—21no—
430C2—42no—
431C2—161no—
432C2—1222no—
433C2—1222no—
434C2#2146182211yescharacteristic
435C2#2146183311yescharacteristic
436C2#2146186811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#392C4
socleC22×C61#386
prime radical#21450774C2
cosocleC22×C4×D61C23
hypercenter#392#6923
hypocenterC61#9384
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #21462668C2semidirect
2. #21461681C2semidirect
3. #21461255C2semidirect
4. #21460693C2semidirect
17. #16839694C4semidirect
18. #16839687C4semidirect
19. #16839676C4semidirect
24. C61×#392C4semidirect
31. #14519834D4semidirect
235. #392#6923semidirect
243. C61#9384semidirect

Maximal subgroups

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

subgroupindex
#214626682
#214616812
#214612552
#214606932
#214507742
#938461