Finite Group Databasebeta

← #29583496

Subgroups — #29583496

Order 15616.

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

normal subgroups only

This group has 444 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#21445952C211yesmaximal, characteristic, complemented
5C2×#16839503C211yesmaximal, characteristic, complemented
6C2×#16839501C211yesmaximal, characteristic
7C61×#1295C211yesmaximal, characteristic, complemented
8C2×#14519769C2211yescharacteristic
9C2×#14519765C2211yescharacteristic
10C2×#14519702—21no—
11C2×#14519699—21no—
12C2×#14519688C2211yescharacteristic
13#16839699—21no—
14#16839689—21no—
15#16839684—21no—
16#16839684—21no—
17#16839683—21no—
18#16839680—21no—
19#16839632C2211yescharacteristic
20#16839525—21no—
21#16839525—21no—
22#16839524—21no—
23#16839524—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#14519702—42no—
56#14519699—42no—
57#14519688—21no—
58#14519688D412yes—
59#14519684—21no—
60#14519684—21no—
61C22×C8×C61—21no—
62C22×C8×C61—21no—
63C2×C4⋊C4×C61D411yescharacteristic
64C2×C4⋊C4×C61D411yescharacteristic
65C2×C42×C61C2311yescharacteristic
66#97×C61—21no—
67#97×C61—21no—
68#97×C61—21no—
69#97×C61—21no—
70#95×C61—21no—
71#95×C61—21no—
72C23×D61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—41no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—41no—
85C2×D244—41no—
86C2×Dic122—21no—
87C2×Dic122—21no—
88C2×Dic122—41no—
89C2×Dic122—41no—
90C2×C8×C61—22no—
91C2×C8×C61—22no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C42×C61C2×D411yescharacteristic
99C42×C61#4111yescharacteristic
100C42×C61#4111yescharacteristic
101C42×C61#4111yescharacteristic
102#11758198—41no—
103#11758198—41no—
104#11758198—41no—
105#11758198—41no—
106#11758198—81no—
107#11758198—81no—
108#11758198—81no—
109#11758198—81no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—41no—
115C4⋊Dic61—41no—
116C4⋊Dic61—42no—
117C4⋊Dic61—42no—
118C4⋊Dic61—81no—
119C4⋊Dic61—81no—
120#11758196—41no—
121#11758196—41no—
122#11758196—41no—
123#11758196—41no—
124C2×#92418—22no—
125C2×#92418—41no—
126C2×#92418—41no—
127C23×C61#12011yescharacteristic
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12311yescharacteristic
151C2×C4×C61#12311yescharacteristic
152C2×C4×C61#12411yescharacteristic
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—81no—
163C2×Dic61—81no—
164C2×Dic61—81no—
165D244—42no—
166D244—81no—
167Dic122—42no—
168Dic122—81no—
169C8×C61—42no—
170C8×C61—42no—
171#92418—42no—
172#10426—611nomaximal, Sylow
173C22×C61#39411yescharacteristic
174C22×C61#45311yescharacteristic
175C22×C61#45411yescharacteristic
176C22×C61#45411yescharacteristic
177C22×C61#45511yescharacteristic
178C22×C61#45511yescharacteristic
179C22×C61#45611yescharacteristic
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—81no—
183C2×D61—81no—
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—81no—
194C4×C61—81no—
195Dic61—81no—
196Dic61—81no—
197Dic61—81no—
198Dic61—161no—
199#2820—611no—
200#1992—611no—
201#1959—611no—
202#1836—611no—
203C2×#330—611no—
204C2×#329—611no—
205#1295D6111yescharacteristic, complemented
206C2×C61#165711yescharacteristic
207C2×C61#166111yescharacteristic
208C2×C61#166211yescharacteristic
209C2×C61#166411yescharacteristic
210C2×C61#203711yescharacteristic
211C2×C61#203811yescharacteristic
212C2×C61#204011yescharacteristic
213D61—161no—
214C2×#125—611no—
215C2×#124—611no—
216C2×#103—1221no—
217C2×#102—1221no—
218C2×#97—611no—
219C2×#97C2×D6111yescharacteristic
220C2×#97C2×D6111yescharacteristic
221#399—1221no—
222#397—1221no—
223#396—1221no—
224#396—1221no—
225#395—1221no—
226#394—1221no—
227#384—611no—
228#382C2×D6111yescharacteristic
229#340—1221no—
230#340—1221no—
231#340—1221no—
232#340—1221no—
233#330—1222no—
234#329—1222no—
235C61#1042611yescharacteristic, complemented, Sylow
236C22×Q8—611no—
237C22×D4—611no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—1221no—
241#125—1221no—
242#125—1221no—
243#125—1221no—
244#125—1221no—
245#124—1221no—
246#124—1221no—
247#124—1221no—
248#124—1221no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4D24411yescharacteristic
259C2×C4⋊C4D24411yescharacteristic
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C42C22×D6111yescharacteristic
267#103—2442no—
268#102—2442no—
269#97—21no—
270#97—21no—
271#97—21no—
272#97—21no—
273#97—612no—
274#97—1221no—
275#95—21no—
276#95—21no—
277#95—1221no—
278#95—1221no—
279C24—1221no—
280C2×Q8—1221no—
281C2×Q8—1221no—
282C2×Q8—2441no—
283C2×Q8—2441no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—2441no—
287C2×D4—2441no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—2441no—
294C22×C4C2×D24411yescharacteristic
295C22×C4D4×D6111yescharacteristic
296C22×C4D4×D6111yescharacteristic
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—1222no—
304C2×C8—2441no—
305C2×C8—2441no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—4881no—
313C4⋊C4—4881no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C4⋊C4—2442no—
317C4⋊C4—2442no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4—2441no—
322C22⋊C4—4881no—
323C22⋊C4—4881no—
324C22⋊C4—4881no—
325C22⋊C4—4881no—
326C22⋊C4—2441no—
327C22⋊C4—2441no—
328C22⋊C4—2441no—
329C22⋊C4—2441no—
330C42#1175822211yescharacteristic
331C42#1175822211yescharacteristic
332C42D4×D6111yescharacteristic
333C42#1175822611yescharacteristic
334C23—2441no—
335C23—2441no—
336C23—2441no—
337C23—2441no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23#1451974711yescharacteristic
342Q8—4881no—
343Q8—2442no—
344D4—4881no—
345D4—2442no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—4881no—
359C2×C4—4881no—
360C2×C4—4881no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4#1451975011yescharacteristic
371C2×C4#1451975011yescharacteristic
372C2×C4#1451975211yescharacteristic
373C2×C4#1451976211yescharacteristic
374C2×C4#1451976211yescharacteristic
375C2×C4#1451976511yescharacteristic
376C8—42no—
377C8—42no—
378C8—2442no—
379C22—4881no—
380C22—4881no—
381C22—4881no—
382C22—4881no—
383C22—4881no—
384C22—4881no—
385C22—4881no—
386C22#1683968011yescharacteristic
387C22#1683993111yescharacteristic
388C22#1683993611yescharacteristic
389C22#1683993711yescharacteristic
390C22#1683994111yescharacteristic
391C22#1683994211yescharacteristic
392C22#1683994611yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—81no—
401C4—9761no—
402C4—4881no—
403C4—4881no—
404C4—4881no—
405C2—9761no—
406C2#2144511911yescharacteristic
407C2#2144513911yescharacteristic
408C2#2144514411yescharacteristic
409C2#2144515411yescharacteristic
410C2#2144703211yescharacteristic
411C2#2144703911yescharacteristic
412C2#2144704911yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1295D61
hypocenterC61#10426
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. #21445952C2semidirect
5. C2×#16839503C2semidirect
7. C61×#1295C2semidirect
205. #1295D61semidirect
235. C61#10426semidirect

Maximal subgroups

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

subgroupindex
#214538712
#214467882
#214466352
#214459522
C2×#168395032
C2×#168395012
C61×#12952
#1042661