Finite Group Databasebeta

← #29583503

Subgroups — #29583503

Order 15616.

460 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 89 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#21453871C211yesmaximal, characteristic
2#21446788C211yesmaximal, characteristic, complemented
3#21446635C211yesmaximal, characteristic
4#21445988C211yesmaximal, characteristic, complemented
5C2×#16839503C211yesmaximal, characteristic, complemented
6C2×#16839501C211yesmaximal, characteristic
7C61×#1295C211yesmaximal, characteristic, complemented
8C2×#14519769C2211yescharacteristic
9C2×#14519765C2211yescharacteristic
10C2×#14519710—21no—
11C2×#14519708—21no—
12C2×#14519702—21no—
13C2×#14519699—21no—
14C2×#14519688C2211yescharacteristic
15#16839699—21no—
16#16839689—21no—
17#16839684—21no—
18#16839684—21no—
19#16839683—21no—
20#16839680—21no—
21#16839632C2211yescharacteristic
22#16839525—21no—
23#16839525—21no—
24#16839503—22no—
25#16839501—22no—
26C2×#97×C61C2211yescharacteristic
27C2×#97×C61C2211yescharacteristic
28C61×#382C2211yescharacteristic
29C22×Dic122D411yescharacteristic
30C22×D244D411yescharacteristic
31C22×#92418—21no—
32#14519769—21no—
33#14519769—21no—
34#14519769—21no—
35#14519769—21no—
36#14519765—21no—
37#14519765—21no—
38#14519765—21no—
39#14519765—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61D411yescharacteristic
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198—21no—
55#14519710—42no—
56#14519708—42no—
57#14519702—42no—
58#14519699—42no—
59#14519688—21no—
60#14519688D412yes—
61#14519684—21no—
62#14519684—21no—
63C22×C8×C61—21no—
64C22×C8×C61—21no—
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C42×C61C2311yescharacteristic
68#97×C61—21no—
69#97×C61—21no—
70#97×C61—21no—
71#97×C61—21no—
72#95×C61—21no—
73#95×C61—21no—
74C23×D61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—41no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—41no—
87C2×D244—41no—
88C2×Dic122—21no—
89C2×Dic122—21no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×C8×C61—22no—
93C2×C8×C61—22no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C42×C61C2×D411yescharacteristic
101C42×C61#4111yescharacteristic
102C42×C61#4111yescharacteristic
103C42×C61#4111yescharacteristic
104#11758198—41no—
105#11758198—41no—
106#11758198—41no—
107#11758198—41no—
108#11758198—81no—
109#11758198—81no—
110#11758198—81no—
111#11758198—81no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—41no—
117C4⋊Dic61—41no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120C4⋊Dic61—42no—
121C4⋊Dic61—81no—
122C4⋊Dic61—81no—
123#11758196—41no—
124#11758196—41no—
125#11758196—41no—
126#11758196—41no—
127C2×#92418—22no—
128C2×#92418—22no—
129C2×#92418—22no—
130C23×C61#12011yescharacteristic
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12311yescharacteristic
154C2×C4×C61#12311yescharacteristic
155C2×C4×C61#12411yescharacteristic
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—81no—
166C2×Dic61—81no—
167C2×Dic61—81no—
168D244—42no—
169D244—81no—
170Dic122—42no—
171Dic122—81no—
172C8×C61—42no—
173C8×C61—42no—
174#92418—24no—
175#10427—611nomaximal, Sylow
176C22×C61#39411yescharacteristic
177C22×C61#45311yescharacteristic
178C22×C61#45311yescharacteristic
179C22×C61#45411yescharacteristic
180C22×C61#45511yescharacteristic
181C22×C61#45611yescharacteristic
182C22×C61#45611yescharacteristic
183C2×D61—81no—
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—81no—
197C4×C61—81no—
198Dic61—81no—
199Dic61—81no—
200Dic61—81no—
201Dic61—161no—
202#2820—611no—
203#1992—611no—
204#1959—611no—
205#1847—611no—
206C2×#330—611no—
207C2×#329—611no—
208#1295D6111yescharacteristic, complemented
209C2×C61#165611yescharacteristic
210C2×C61#166011yescharacteristic
211C2×C61#166111yescharacteristic
212C2×C61#166411yescharacteristic
213C2×C61#203711yescharacteristic
214C2×C61#203811yescharacteristic
215C2×C61#203911yescharacteristic
216D61—161no—
217C2×#125—611no—
218C2×#124—611no—
219C2×#107—1221no—
220C2×#106—1221no—
221C2×#103—1221no—
222C2×#102—1221no—
223C2×#97—611no—
224C2×#97C2×D6111yescharacteristic
225C2×#97C2×D6111yescharacteristic
226#399—1221no—
227#397—1221no—
228#396—1221no—
229#396—1221no—
230#395—1221no—
231#394—1221no—
232#384—611no—
233#382C2×D6111yescharacteristic
234#340—1221no—
235#340—1221no—
236#330—1222no—
237#329—1222no—
238C61#1042711yescharacteristic, complemented, Sylow
239C22×Q8—611no—
240C22×D4—611no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—1221no—
244#125—1221no—
245#125—1221no—
246#125—1221no—
247#125—1221no—
248#124—1221no—
249#124—1221no—
250#124—1221no—
251#124—1221no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4D24411yescharacteristic
262C2×C4⋊C4D24411yescharacteristic
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C42C22×D6111yescharacteristic
270#107—2442no—
271#106—2442no—
272#103—2442no—
273#102—2442no—
274#97—21no—
275#97—21no—
276#97—21no—
277#97—21no—
278#97—612no—
279#97—1221no—
280#95—21no—
281#95—21no—
282#95—1221no—
283#95—1221no—
284C24—1221no—
285C2×Q8—1221no—
286C2×Q8—1221no—
287C2×Q8—2441no—
288C2×Q8—2441no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—2441no—
292C2×D4—2441no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—2441no—
299C22×C4C2×D24411yescharacteristic
300C22×C4D4×D6111yescharacteristic
301C22×C4D4×D6111yescharacteristic
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—1222no—
309C2×C8—1222no—
310C2×C8—1222no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4—1221no—
317C4⋊C4—4881no—
318C4⋊C4—4881no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4—2441no—
322C4⋊C4—2441no—
323C4⋊C4—2442no—
324C4⋊C4—2441no—
325C4⋊C4—2441no—
326C4⋊C4—2441no—
327C4⋊C4—2441no—
328C22⋊C4—4881no—
329C22⋊C4—4881no—
330C22⋊C4—4881no—
331C22⋊C4—4881no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C42#1175822211yescharacteristic
337C42#1175822211yescharacteristic
338C42D4×D6111yescharacteristic
339C42#1175822611yescharacteristic
340C23—2441no—
341C23—2441no—
342C23—2441no—
343C23—2441no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23#1451974711yescharacteristic
348Q8—4881no—
349Q8—2442no—
350D4—4881no—
351D4—2442no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—4881no—
365C2×C4—4881no—
366C2×C4—4881no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4#1451975011yescharacteristic
377C2×C4#1451975011yescharacteristic
378C2×C4#1451975211yescharacteristic
379C2×C4#1451976211yescharacteristic
380C2×C4#1451976211yescharacteristic
381C2×C4#1451976511yescharacteristic
382C8—42no—
383C8—42no—
384C8—1224no—
385C22—4881no—
386C22—4881no—
387C22—4881no—
388C22—4881no—
389C22—4881no—
390C22—4881no—
391C22—4881no—
392C22#1683968011yescharacteristic
393C22#1683993111yescharacteristic
394C22#1683993211yescharacteristic
395C22#1683993611yescharacteristic
396C22#1683994111yescharacteristic
397C22#1683994611yescharacteristic
398C22#1683994711yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—81no—
406C4—81no—
407C4—9761no—
408C4—4881no—
409C4—4881no—
410C4—4881no—
411C2—9761no—
412C2#2144511311yescharacteristic
413C2#2144513211yescharacteristic
414C2#2144513711yescharacteristic
415C2#2144515511yescharacteristic
416C2#2144703211yescharacteristic
417C2#2144703911yescharacteristic
418C2#2144704411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1295D61
hypocenterC61#10427
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #21446788C2semidirect
4. #21445988C2semidirect
5. C2×#16839503C2semidirect
7. C61×#1295C2semidirect
208. #1295D61semidirect
238. C61#10427semidirect

Maximal subgroups

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

subgroupindex
#214538712
#214467882
#214466352
#214459882
C2×#168395032
C2×#168395012
C61×#12952
#1042761