Finite Group Databasebeta

← #29577350

Subgroups — #29577350

Order 15616.

532 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 93 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#21454236C211yesmaximal, characteristic
2#21451519C211yesmaximal, characteristic
3#21444421C211yesmaximal, characteristic, complemented
4#21444151C211yesmaximal, characteristic
5#21443713C211yesmaximal, characteristic, complemented
6#21443711C211yesmaximal, characteristic, complemented
7C61×#1528C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519734C2211yescharacteristic
10#16839819C2211yescharacteristic
11#16839719—22no—
12#16839716—22no—
13C4×#11758194C2211yescharacteristic
14M16×Dic61—21no—
15#16839700C411yescharacteristic
16#16839697C411yescharacteristic
17#16839693C411yescharacteristic
18#16839688C411yescharacteristic
19#16839657—21no—
20#16839652—21no—
21#16839643—21no—
22#16839633—21no—
23#16839608C2211yescharacteristic
24#16839504—22no—
25#16839487—21no—
26#16839485—21no—
27C2×#125×C61C2211yescharacteristic
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#330—22no—
31C22×C4×D61D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758189—22no—
34M16×D61—24no—
35M16×D61—24no—
36C2×C8×D61—22no—
37#14519734—21no—
38#14519734—21no—
39#14519734—21no—
40#14519734—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196C2×C411yescharacteristic
44C2×#11758196D411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198C2×C411yescharacteristic
48C2×#11758198D411yescharacteristic
49C2×C4×Dic61—21no—
50C2×C4×Dic61D411yescharacteristic
51C4⋊#92418—21no—
52C22⋊#92418—21no—
53#14519688—21no—
54#14519688D412yes—
55#14519687—22no—
56C4×#92418—21no—
57C8×Dic61—22no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63#14519684C2×C411yescharacteristic
64#14519684C2×C411yescharacteristic
65C2×M16×C61—21no—
66#125×C61—21no—
67#125×C61—21no—
68#125×C61—21no—
69#125×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C4⋊C4×C61C2×C411yescharacteristic
74C2×C42×C61C2311yescharacteristic
75C4⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77#97×C61—21no—
78#97×C61D412yes—
79C4×C8×C61—21no—
80C23×D61C22⋊C411yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61C22×C411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C2×C4×D61—22no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—22no—
95M16×C61—22no—
96M16×C61—22no—
97C2×C8×C61—22no—
98C2×C8×C61—41no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61#4111yescharacteristic
110C42×C61#4111yescharacteristic
111#11758198—21no—
112#11758198—21no—
113#11758198—21no—
114#11758198—21no—
115#11758198—42no—
116#11758198—42no—
117#11758196—21no—
118#11758196—21no—
119#11758196—21no—
120#11758196—21no—
121#11758196—42no—
122#11758196—42no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61—42no—
126#11758194—22no—
127#11758194—22no—
128C2×#92418—22no—
129C2×#92418—41no—
130#11758189—28no—
131C8×D61—28no—
132C23×C61C2×C22⋊C411yescharacteristic
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61#10412yes—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
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—41no—
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12311yescharacteristic
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—22no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61#10412yes—
167C4×D61—22no—
168C4×D61—22no—
169C4×D61—24no—
170C8×C61—24no—
171C8×C61—81no—
172#92418—24no—
173#92418—81no—
174#9388—611nomaximal, Sylow
175C22×C61—21no—
176C22×C61—21no—
177C22×C61#38611yescharacteristic
178C22×C61C2×#10411yescharacteristic
179C22×C61C2×#10411yescharacteristic
180C2×D61—22no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—42no—
184C2×D61—81no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—81no—
192C4×C61—81no—
193Dic61—22no—
194Dic61—42no—
195Dic61—41no—
196Dic61—41no—
197Dic61—81no—
198#2873—611no—
199#2611—611no—
200#1528—611no—
201#1528D6111yescharacteristic, complemented
202#1464—611no—
203#1300—611no—
204#1300—611no—
205C2×C61—21no—
206C2×C61—21no—
207C2×C61#188411yescharacteristic
208C2×C61#189611yescharacteristic
209C2×C61#191511yescharacteristic
210D61—42no—
211C22×M16—1221no—
212C2×#125C2×D6111yescharacteristic
213C2×#117—611no—
214#432—611no—
215#432C2×D6111yescharacteristic
216#405—1222no—
217#405—1222no—
218C4×M16—611no—
219C4×M16—1221no—
220C4×M16C2×D6111yescharacteristic
221#400—611no—
222#399—611no—
223#398—611no—
224#397—611no—
225#389—1221no—
226#388—1221no—
227#387—1221no—
228#385—1221no—
229#376—611no—
230#330—22no—
231#330—1222no—
232#324—1221no—
233#323—1221no—
234C61#938811yescharacteristic, complemented, Sylow
235C23×C4—611no—
236C2×M16—21no—
237C2×M16—1222no—
238C2×M16—1224no—
239C2×M16—1224no—
240C2×M16—1221no—
241C22×C8—1222no—
242#125—21no—
243#125—21no—
244#125—21no—
245#125—21no—
246#117—1221no—
247#117—1221no—
248#117—1221no—
249#117—1221no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4C4×D6111yescharacteristic
257C2×C4⋊C4C4×D6111yescharacteristic
258C2×C22⋊C4—611no—
259C2×C22⋊C4—611no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C42—611no—
263C2×C42—1221no—
264C2×C42C22×D6111yescharacteristic
265C4⋊C8—21no—
266C4⋊C8—1221no—
267C22⋊C8—21no—
268C22⋊C8—1221no—
269#97—21no—
270#97—612no—
271#97—1222no—
272#97—1221no—
273#97C22⋊D6112yes—
274C4×C8—21no—
275C4×C8—1222no—
276C4×C8—1221no—
277#95—611no—
278#95—611no—
279#95—1221no—
280#95—1221no—
281#95—1221no—
282#95—1221no—
283#95—1221no—
284C24—611no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—1222no—
291C22×C4—1222no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4C2×C4×D6111yescharacteristic
297C22×C4D4×D6111yescharacteristic
298C22×C4D4×D6111yescharacteristic
299M16—22no—
300M16—22no—
301M16—1228no—
302M16—1222no—
303M16—1222no—
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—1228no—
307C2×C8—1222no—
308C2×C8—2441no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—1221no—
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C4⋊C4—1221no—
321C4⋊C4—2442no—
322C4⋊C4—2442no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—2442no—
328C22⋊C4—2442no—
329C42—1221no—
330C42—1221no—
331C42—2442no—
332C42#1175822211yescharacteristic
333C42D4×D6111yescharacteristic
334C42#1175822411yescharacteristic
335C42C2×C22⋊D6111yescharacteristic
336C23—612no—
337C23—1221no—
338C23—1221no—
339C23—2441no—
340C23—2441no—
341C23C22⋊C4×D6111yescharacteristic
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—612no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—1224no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1222no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4#1451973711yescharacteristic
369C2×C4C4×C22⋊D6111yescharacteristic
370C2×C4#1451974511yescharacteristic
371C2×C4#1451974811yescharacteristic
372C2×C4#1451975011yescharacteristic
373C2×C4#1451975911yescharacteristic
374C8—24no—
375C8—81no—
376C8—1224no—
377C8—4881no—
378C22—21no—
379C22—21no—
380C22—1222no—
381C22—4881no—
382C22—2442no—
383C22—2441no—
384C22—2441no—
385C22#1683963811yescharacteristic
386C22#104×D6111yescharacteristic
387C22#104×D6111yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—1222no—
397C4—4881no—
398C4—2442no—
399C4—2441no—
400C4—2441no—
401C2—21no—
402C2—21no—
403C2—2442no—
404C2#2144619911yescharacteristic
405C2#2144625911yescharacteristic
406C2#2144636811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1528C2
socleC22×C61#386
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1528D61
hypocenterC61#9388
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
3. #21444421C2semidirect
5. #21443713C2semidirect
6. #21443711C2semidirect
7. C61×#1528C2semidirect
201. #1528D61semidirect
234. C61#9388semidirect

Maximal subgroups

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

subgroupindex
#214542362
#214515192
#214444212
#214441512
#214437132
#214437112
C61×#15282
#938861