Finite Group Databasebeta

← #29575086

Subgroups — #29575086

Order 15616.

484 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 95 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#21454903C211yesmaximal, characteristic
2#21449112C211yesmaximal, characteristic
3C4×#14519695C211yesmaximal, characteristic
4#21444267C211yesmaximal, characteristic
5#21444265C211yesmaximal, characteristic
6#21443712C211yesmaximal, characteristic
7C61×#1300C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16839891—22no—
11#16839890—22no—
12#16839819C2211yescharacteristic
13#16839816—21no—
14#16839812—21no—
15C2×#14519695—21no—
16C4×#11758194C2211yescharacteristic
17#16839694—21no—
18#16839694C411yescharacteristic
19#16839694C411yescharacteristic
20#16839683—21no—
21#16839683C411yescharacteristic
22#16839683C411yescharacteristic
23C4×C4⋊Dic61—21no—
24C4×C4⋊Dic61—21no—
25#16839530—21no—
26#16839494—22no—
27#16839492—22no—
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#376C2211yescharacteristic
31C22×Dic122C2×C411yescharacteristic
32C22×Dic122D411yescharacteristic
33C2×#11758194—21no—
34C4×Dic122—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×C4⋊Dic61D411yescharacteristic
48C2×#11758196—21no—
49C2×#11758196C2×C411yescharacteristic
50C2×#11758196C2×C411yescharacteristic
51C2×C4×Dic61—21no—
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C4⋊#92418D412yes—
55#14519706—22no—
56#14519706—22no—
57#14519695—24no—
58C22⋊#92418—21no—
59#14519688—21no—
60#14519688—21no—
61#14519687—22no—
62C4×#92418—21no—
63C8×Dic61—22no—
64#14519684—21no—
65#14519684—21no—
66#14519684—21no—
67#14519684—21no—
68C2×M16×C61—21no—
69C2×C42×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61D412yes—
72C22⋊C8×C61—21no—
73#97×C61—21no—
74#97×C61—21no—
75C4×C8×C61—21no—
76#95×C61—21no—
77#95×C61C2×C411yescharacteristic
78#95×C61C2×C411yescharacteristic
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61C22×C411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C2×Dic122—21no—
91C2×Dic122—21no—
92C2×Dic122—21no—
93C2×Dic122—21no—
94C2×Dic122—22no—
95C2×Dic122—42no—
96C2×Dic122—41no—
97M16×C61—22no—
98M16×C61—41no—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C42×C61—24no—
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105C42×C61#4111yescharacteristic
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—42no—
111C4⋊Dic61—42no—
112C4⋊Dic61—42no—
113C4⋊Dic61—42no—
114#11758196—21no—
115#11758196—21no—
116#11758196—21no—
117#11758196—21no—
118#11758196—41no—
119#11758196—41no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124C4×Dic61—41no—
125C4×Dic61—41no—
126#11758194—22no—
127#11758194—41no—
128C2×#92418—22no—
129C2×#92418—41no—
130C23×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—22no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12311yescharacteristic
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—22no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61#10412yes—
163Dic122—22no—
164Dic122—22no—
165Dic122—42no—
166Dic122—42no—
167Dic122—41no—
168Dic122—41no—
169C8×C61—42no—
170C8×C61—42no—
171#92418—42no—
172#92418—42no—
173#9030—611nomaximal, Sylow
174C22×C61—21no—
175C22×C61—21no—
176C22×C61#38611yescharacteristic
177C22×C61C2×#10411yescharacteristic
178C22×C61#42111yescharacteristic
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—42no—
185C4×C61—42no—
186C4×C61#45612yes—
187Dic61—22no—
188Dic61—41no—
189Dic61—42no—
190Dic61—41no—
191Dic61—41no—
192Dic61—81no—
193#2983—611no—
194#2399—611no—
195C4×#101—611no—
196#1491—611no—
197#1491—611no—
198#1300—611no—
199#1300D6111yescharacteristic
200C2×C61—21no—
201C2×C61—21no—
202C2×C61#187111yescharacteristic
203C2×C61#188611yescharacteristic
204C2×C61#189111yescharacteristic
205C2×C4×Q8—611no—
206C2×C4×Q8—611no—
207#446—1222no—
208#446—1222no—
209#432—611no—
210#432—1221no—
211#432C2×D6111yescharacteristic
212#431—1221no—
213C2×#101—1221no—
214C4×M16—611no—
215C4×M16C2×D6111yescharacteristic
216#398—611no—
217#398—611no—
218#398—1221no—
219#395—611no—
220#395—611no—
221#395—1221no—
222C4×C4⋊C4—1221no—
223C4×C4⋊C4—1221no—
224#376C2×D6111yescharacteristic
225#343—1221no—
226Q8⋊C8—1222no—
227Q8⋊C8—1222no—
228C61#903011yescharacteristic, complemented, Sylow
229C22×Q8—611no—
230C22×Q8—611no—
231C2×M16—21no—
232C2×M16—1221no—
233C4×Q8—1221no—
234C4×Q8—1221no—
235C4×Q8—1221no—
236C4×Q8—1221no—
237C4×Q8—1221no—
238C4×Q8—1221no—
239C4×Q8—1221no—
240C4×Q8—1221no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—1221no—
250C2×C42—21no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—1221no—
254C2×C42C22×D6111yescharacteristic
255C4⋊C8—612no—
256C4⋊C8—1222no—
257C4⋊C8—1222no—
258C4⋊C8D24412yes—
259#101—1224no—
260C22⋊C8—21no—
261C22⋊C8—1221no—
262#97—21no—
263#97—21no—
264#97—1222no—
265#97—1221no—
266#97—1221no—
267C4×C8—21no—
268C4×C8—1222no—
269C4×C8—1221no—
270#95—21no—
271#95—1221no—
272#95—1221no—
273#95—1221no—
274#95—1221no—
275#95C4×D6111yescharacteristic
276#95C4×D6111yescharacteristic
277C2×Q8—1222no—
278C2×Q8—1221no—
279C2×Q8—1221no—
280C2×Q8—1221no—
281C2×Q8—1221no—
282C2×Q8—2441no—
283C2×Q8—2442no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4C2×C4×D6111yescharacteristic
293C22×C4D4×D6111yescharacteristic
294C22×C4D4×D6111yescharacteristic
295M16—22no—
296M16—41no—
297M16—1222no—
298M16—2441no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—1222no—
302C2×C8—2441no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—2442no—
312C4⋊C4—2442no—
313C4⋊C4—2442no—
314C4⋊C4—2442no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C42—24no—
318C42—1221no—
319C42—1221no—
320C42—1221no—
321C42—1221no—
322C42—2441no—
323C42—2441no—
324C42C2×D24411yescharacteristic
325C42#1175822211yescharacteristic
326C42D4×D6111yescharacteristic
327C42#1175822611yescharacteristic
328C23C22⋊C4×D6111yescharacteristic
329Q8—1222no—
330Q8—1222no—
331Q8—2442no—
332Q8—2442no—
333Q8—2441no—
334Q8—2441no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—612no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1222no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4#1451973911yescharacteristic
362C2×C4C4×D24411yescharacteristic
363C2×C4#1451974711yescharacteristic
364C2×C4#1451975011yescharacteristic
365C2×C4#1451975211yescharacteristic
366C2×C4#1451976211yescharacteristic
367C8—42no—
368C8—42no—
369C8—2442no—
370C8—2442no—
371C22—21no—
372C22—21no—
373C22#1683964011yescharacteristic
374C22#104×D6111yescharacteristic
375C22#1683977711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—42no—
383C4—1222no—
384C4—4881no—
385C4—2441no—
386C4—2441no—
387C4—2442no—
388C4—2441no—
389C4#1683994612yes—
390C2—21no—
391C2—21no—
392C2#2144612011yescharacteristic
393C2#2144621111yescharacteristic
394C2#2144623611yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1300C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1300D61
hypocenterC61#9030
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
228. C61#9030semidirect

Maximal subgroups

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

subgroupindex
#214549032
#214491122
C4×#145196952
#214442672
#214442652
#214437122
C61×#13002
#903061