Finite Group Databasebeta

← #29583511

Subgroups — #29583511

Order 15616.

402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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#21453886C211yesmaximal, characteristic
2#21446789C211yesmaximal, characteristic
3#21446788C211yesmaximal, characteristic
4#21445987C211yesmaximal, characteristic
5C2×#16839503C211yesmaximal, characteristic
6#21443701C211yesmaximal, characteristic
7C2×C61×#330C211yesmaximal, characteristic
8C2×#14519769C2211yescharacteristic
9C2×#14519711—21no—
10C2×#14519709—21no—
11C2×#14519688C2211yescharacteristic
12#16839701—21no—
13#16839700—21no—
14#16839695—21no—
15#16839695—21no—
16#16839693—21no—
17#16839692—21no—
18#16839632C2211yescharacteristic
19#16839628C2211yescharacteristic
20#16839525—21no—
21#16839525—21no—
22#16839524—21no—
23#16839524—21no—
24#16839503—22no—
25C2×#125×C61C2211yescharacteristic
26C2×#97×C61C2211yescharacteristic
27C2×#97×C61C2211yescharacteristic
28C61×#330—22no—
29C22×#92418—21no—
30#14519769—21no—
31#14519769—21no—
32#14519769—21no—
33#14519769—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45#14519711—42no—
46#14519709—42no—
47#14519688—21no—
48#14519688—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59#125×C61—21no—
60#125×C61—21no—
61#125×C61—21no—
62#125×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×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×C61D412yes—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—41no—
82C2×C8×C61—22no—
83C2×C8×C61—22no—
84C2×C8×C61—22no—
85C2×C8×C61—22no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C42×C61C2×D411yescharacteristic
97C42×C61#4111yescharacteristic
98C42×C61#4111yescharacteristic
99C42×C61#4111yescharacteristic
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107C4⋊Dic61—41no—
108C4⋊Dic61—42no—
109C4⋊Dic61—42no—
110#11758196—41no—
111#11758196—41no—
112#11758196—41no—
113#11758196—41no—
114#11758196—81no—
115#11758196—81no—
116C2×#92418—22no—
117C2×#92418—41no—
118C2×#92418—41no—
119C23×C61#12011yescharacteristic
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
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#12111yescharacteristic
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12311yescharacteristic
136C2×C4×C61#12311yescharacteristic
137C2×C4×C61#12411yescharacteristic
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153C8×C61—24no—
154C8×C61—42no—
155#92418—42no—
156#10429—611nomaximal, Sylow
157C22×C61#39411yescharacteristic
158C22×C61#45311yescharacteristic
159C22×C61#45411yescharacteristic
160C22×C61#45411yescharacteristic
161C22×C61#45611yescharacteristic
162C22×C61#45611yescharacteristic
163C22×C61#45611yescharacteristic
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—81no—
171C4×C61—81no—
172Dic61—81no—
173Dic61—81no—
174Dic61—81no—
175Dic61—81no—
176Dic61—161no—
177#2822—611no—
178#1992—611no—
179#1992—611no—
180#1847—611no—
181C2×#330—611no—
182C2×#330D6111yescharacteristic
183#1295—611no—
184C2×C61#165711yescharacteristic
185C2×C61#166011yescharacteristic
186C2×C61#166311yescharacteristic
187C2×C61#166311yescharacteristic
188C2×C61#203811yescharacteristic
189C2×C61#203811yescharacteristic
190C2×C61#203911yescharacteristic
191C2×#125—611no—
192C2×#125C2×D6111yescharacteristic
193C2×#107—1221no—
194C2×#106—1221no—
195C2×#97—611no—
196C2×#97C2×D6111yescharacteristic
197C2×#97C2×D6111yescharacteristic
198#400—1221no—
199#400—1221no—
200#398—1221no—
201#398—1221no—
202#398—1221no—
203#398—1221no—
204#384—611no—
205#382—611no—
206#340—1221no—
207#340—1221no—
208#340—1221no—
209#340—1221no—
210#330—22no—
211#330—1222no—
212C61#1042911yescharacteristic, complemented, Sylow
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—1221no—
216#125—21no—
217#125—21no—
218#125—21no—
219#125—21no—
220#125—1221no—
221#125—1221no—
222#125—1221no—
223#125—1221no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4D24411yescharacteristic
238C2×C4⋊C4D24411yescharacteristic
239C2×C42C22×D6111yescharacteristic
240#107—2442no—
241#106—2442no—
242#97—21no—
243#97—21no—
244#97—21no—
245#97—1221no—
246#97—1221no—
247#97C22⋊D6112yes—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255#95—1221no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—2441no—
263C22×C4C2×D24411yescharacteristic
264C22×C4D4×D6111yescharacteristic
265C22×C4D4×D6111yescharacteristic
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—1222no—
273C2×C8—2441no—
274C2×C8—2441no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—4881no—
288C4⋊C4—4881no—
289C4⋊C4—2441no—
290C4⋊C4—2441no—
291C4⋊C4—2442no—
292C4⋊C4—2442no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C42#1175822211yescharacteristic
300C42#1175822411yescharacteristic
301C42#1175822411yescharacteristic
302C42C2×C22⋊D6111yescharacteristic
303C23#1451974711yescharacteristic
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4#1451974811yescharacteristic
332C2×C4#1451974911yescharacteristic
333C2×C4#1451975111yescharacteristic
334C2×C4#1451975911yescharacteristic
335C2×C4#1451976111yescharacteristic
336C2×C4#1451976311yescharacteristic
337C8—24no—
338C8—42no—
339C8—2442no—
340C22#1683967811yescharacteristic
341C22#1683993111yescharacteristic
342C22#1683993611yescharacteristic
343C22#1683993711yescharacteristic
344C22#1683994611yescharacteristic
345C22#1683994611yescharacteristic
346C22#1683994711yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—81no—
354C4—81no—
355C4—9761no—
356C4—4881no—
357C4—4881no—
358C4—4881no—
359C4—4881no—
360C2#2144511911yescharacteristic
361C2#2144513211yescharacteristic
362C2#2144514811yescharacteristic
363C2#2144514911yescharacteristic
364C2#2144703511yescharacteristic
365C2#2144703711yescharacteristic
366C2#2144704211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#330C2
socle, prime radicalC23×C61#120
hypercenterC2×#330D61
hypocenterC61#10429
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
212. C61#10429semidirect

Maximal subgroups

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

subgroupindex
#214538862
#214467892
#214467882
#214459872
C2×#168395032
#214437012
C2×C61×#3302
#1042961