Finite Group Databasebeta

← #29590786

Subgroups — #29590786

Order 15616.

446 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 71 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#21449104C211yesmaximal, characteristic
2#21445806C211yesmaximal, characteristic
3#21444154C211yesmaximal, characteristic
4#21443841C211yesmaximal, characteristic, complemented
5#21443839C211yesmaximal, characteristic, complemented
6#21443819C211yesmaximal, characteristic, complemented
7C61×#1344C211yesmaximal, characteristic, complemented
8C2×#14519742C411yescharacteristic, complemented
9C2×#14519737C2211yescharacteristic
10C2×#14519691—21no—
11#16839724—21no—
12#16839703—21no—
13#16839688C411yescharacteristic, complemented
14#16839677—21no—
15#16839675C411yescharacteristic, complemented
16#16839674C2211yescharacteristic
17#16839620—21no—
18C22⋊C4×Dic61—21no—
19#16839609—21no—
20#16839607C411yescharacteristic, complemented
21#16839529C2211yescharacteristic
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#397C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×C22⋊D61D411yescharacteristic
29C23×Dic61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758189—41no—
32#14519742—41no—
33#14519742—41no—
34#14519737—41no—
35#14519737—41no—
36C2×#11758196—21no—
37C2×#11758196—41no—
38C2×#11758196D411yescharacteristic
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198C2×C411yescharacteristic
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47#14519691—42no—
48C22⋊#92418—21no—
49#14519689—41no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—41no—
55#14519684C2×C411yescharacteristic
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C24×C61C2×D411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—42no—
79C22×Dic61—41no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—42no—
86C2×Dic122—41no—
87C2×Dic122—42no—
88C2×C8×C61—41no—
89C4⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C22⋊Dic61—42no—
96C22⋊Dic61—41no—
97C22⋊Dic61—41no—
98#11758198—41no—
99#11758198—42no—
100#11758198—42no—
101#11758196—41no—
102#11758196—42no—
103#11758196—82no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—42no—
107C4×Dic61—41no—
108C4×Dic61—41no—
109C2×#92418—41no—
110#11758189—82no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61C2×C22⋊C411yescharacteristic
116C23×C61AGL(1,ℤ/8)11yescharacteristic
117C23×C61#13711yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—41no—
122C22×D61—41no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C22⋊D61—42no—
137C22⋊D61—42no—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—42no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155C2×Dic61#9911yescharacteristic
156C2×Dic61#9911yescharacteristic
157C4×D61—42no—
158C4×D61—81no—
159Dic122—42no—
160Dic122—42no—
161C8×C61—81no—
162#92418—81no—
163#11823—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—81no—
173C22×C61C2×#9911yescharacteristic
174C22×C61#41711yescharacteristic
175C22×C61#42111yescharacteristic
176C2×D61—42no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—81no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—81no—
184C4×C61—81no—
185C4×C61—161no—
186Dic61—21no—
187Dic61—42no—
188Dic61—41no—
189Dic61—41no—
190Dic61—81no—
191Dic61—161no—
192Dic61#35412yes—
193#2398—611no—
194#1799—611no—
195#1465—611no—
196#1351—611no—
197#1351—611no—
198#1344—611no—
199#1344D6111yescharacteristic, complemented
200C2×C61—21no—
201C2×C61—21no—
202C2×C61—41no—
203C2×C61—41no—
204C2×C61#151311yescharacteristic
205C2×C61#212011yescharacteristic
206C2×C61C2×#35411yescharacteristic
207D61—81no—
208C2×C4×Q8—611no—
209C2×C4×D4—611no—
210C2×#99—1221no—
211#407—1221no—
212#400—1221no—
213#397—611no—
214#397C2×D6111yescharacteristic
215#394—1221no—
216#393—611no—
217#393—611no—
218#380—1221no—
219C4×C22⋊C4—1221no—
220C4×C22⋊C4—1221no—
221#376—611no—
222#342—611no—
223#342C2×D6111yescharacteristic
224#324—1221no—
225#323—611no—
226#323C2×D6111yescharacteristic
227C61#1182311yescharacteristic, complemented, Sylow
228C22×Q8—611no—
229C22×D4—611no—
230C23×C4—611no—
231C23×C4—611no—
232C2×M16—2441no—
233C4×Q8—2441no—
234C4×Q8—2441no—
235C4×D4—2441no—
236C4×D4—2441no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—2441no—
240C2×C4⋊C4C4×D6111yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—611no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4C22×D6111yescharacteristic
249C2×C42—611no—
250C2×C42—1221no—
251C2×C42—1221no—
252#99—2442no—
253C22⋊C8—21no—
254C22⋊C8—1221no—
255C22⋊C8—2441no—
256#95—21no—
257#95—611no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95—2441no—
263#95C4×D6111yescharacteristic
264C24—611no—
265C24D4×D6111yescharacteristic
266C2×Q8—2441no—
267C2×Q8—2442no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—2441no—
271C2×D4—2441no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—2442no—
285C22×C4—2442no—
286C22×C4—2441no—
287C22×C4C2×C4×D6111yescharacteristic
288C22×C4D4×D6111yescharacteristic
289M16—4882no—
290C2×C8—41no—
291C2×C8—2441no—
292C4⋊C4—41no—
293C4⋊C4—4882no—
294C4⋊C4—2441no—
295C4⋊C4—2442no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—2441no—
302C22⋊C4—2442no—
303C22⋊C4—2442no—
304C22⋊C4—2442no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C42—1221no—
308C42—1221no—
309C42—2441no—
310C42—2441no—
311C42—2442no—
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—1221no—
317C23—1221no—
318C23—1221no—
319C23—2441no—
320C23—2441no—
321C23C22⋊C4×D6111yescharacteristic
322C23#1451980111yescharacteristic
323C23#1451980611yescharacteristic
324Q8—2442no—
325Q8—2442no—
326D4—2442no—
327D4—2442no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—4881no—
350C2×C4—4881no—
351C2×C4—4881no—
352C2×C4—4881no—
353C2×C4—4881no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C8—81no—
363C8—4881no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—4881no—
374C22—2442no—
375C22—2441no—
376C22—2441no—
377C22—2441no—
378C22#99×D6111yescharacteristic
379C22#1683976011yescharacteristic
380C22#1683977711yescharacteristic
381C4—41no—
382C4—41no—
383C4—81no—
384C4—81no—
385C4—161no—
386C4—612no—
387C4—1221no—
388C4—9761no—
389C4—4881no—
390C4—2441no—
391C4—2442no—
392C4—2441no—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—4881no—
398C2#2144435911yescharacteristic
399C2#2144745911yescharacteristic
400C2#354×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1344C2
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1344D61
hypocenterC61#11823
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
4. #21443841C2semidirect
5. #21443839C2semidirect
6. #21443819C2semidirect
7. C61×#1344C2semidirect
8. C2×#14519742C4semidirect
13. #16839688C4semidirect
15. #16839675C4semidirect
20. #16839607C4semidirect
199. #1344D61semidirect
227. C61#11823semidirect

Maximal subgroups

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

subgroupindex
#214491042
#214458062
#214441542
#214438412
#214438392
#214438192
C61×#13442
#1182361