Finite Group Databasebeta

← #29583501

Subgroups — #29583501

Order 15616.

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

normal subgroups only

This group has 460 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#21453869C211yesmaximal, characteristic
2#21446789C211yesmaximal, characteristic, complemented
3#21446635C211yesmaximal, characteristic
4#21445987C211yesmaximal, characteristic, complemented
5C2×#16839501C211yesmaximal, characteristic
6#21443701C211yesmaximal, characteristic, complemented
7C2×C61×#330C211yesmaximal, characteristic, complemented
8C2×#14519765C2211yescharacteristic
9C2×#14519711—21no—
10C2×#14519709—21no—
11C2×#14519702—21no—
12C2×#14519699—21no—
13C2×#14519688C2211yescharacteristic
14#16839697—21no—
15#16839688—21no—
16#16839684—21no—
17#16839684—21no—
18#16839682—21no—
19#16839679—21no—
20#16839632C2211yescharacteristic
21#16839628C2211yescharacteristic
22#16839524—21no—
23#16839524—21no—
24#16839501—22no—
25C2×#125×C61C2211yescharacteristic
26C2×#97×C61C2211yescharacteristic
27C2×#97×C61C2211yescharacteristic
28C61×#330—22no—
29C22×Dic122D411yescharacteristic
30C22×D244D411yescharacteristic
31C22×#92418—21no—
32#14519765—21no—
33#14519765—21no—
34#14519765—21no—
35#14519765—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49#14519711—42no—
50#14519709—42no—
51#14519702—42no—
52#14519699—42no—
53#14519688—21no—
54#14519688—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59C22×C8×C61—21no—
60C22×C8×C61—21no—
61#125×C61—21no—
62#125×C61—21no—
63#125×C61—21no—
64#125×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61D411yescharacteristic
68C2×C4⋊C4×C61D411yescharacteristic
69C2×C42×C61C2311yescharacteristic
70#97×C61—21no—
71#97×C61—21no—
72#97×C61—21no—
73#97×C61D412yes—
74C23×D61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—41no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—41no—
87C2×D244—41no—
88C2×Dic122—21no—
89C2×Dic122—21no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×C8×C61—22no—
93C2×C8×C61—22no—
94C2×C8×C61—22no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C42×C61C2×D411yescharacteristic
107C42×C61#4111yescharacteristic
108C42×C61#4111yescharacteristic
109C42×C61#4111yescharacteristic
110#11758198—41no—
111#11758198—41no—
112#11758198—41no—
113#11758198—41no—
114#11758198—81no—
115#11758198—81no—
116#11758198—81no—
117#11758198—81no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124C4⋊Dic61—42no—
125#11758196—81no—
126#11758196—81no—
127C2×#92418—22no—
128C2×#92418—41no—
129C2×#92418—41no—
130C23×C61#12011yescharacteristic
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12311yescharacteristic
154C2×C4×C61#12311yescharacteristic
155C2×C4×C61#12411yescharacteristic
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—81no—
166C2×Dic61—81no—
167C2×Dic61—81no—
168D244—42no—
169D244—81no—
170Dic122—42no—
171Dic122—81no—
172C8×C61—24no—
173C8×C61—42no—
174#92418—42no—
175#10427—611nomaximal, Sylow
176C22×C61#39411yescharacteristic
177C22×C61#45311yescharacteristic
178C22×C61#45311yescharacteristic
179C22×C61#45411yescharacteristic
180C22×C61#45511yescharacteristic
181C22×C61#45611yescharacteristic
182C22×C61#45611yescharacteristic
183C2×D61—81no—
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—81no—
197C4×C61—81no—
198Dic61—81no—
199Dic61—81no—
200Dic61—81no—
201Dic61—161no—
202#2820—611no—
203#1992—611no—
204#1959—611no—
205#1847—611no—
206C2×#330D6111yescharacteristic, complemented
207C2×#329—611no—
208#1295—611no—
209C2×C61#165611yescharacteristic
210C2×C61#166011yescharacteristic
211C2×C61#166111yescharacteristic
212C2×C61#166411yescharacteristic
213C2×C61#203711yescharacteristic
214C2×C61#203811yescharacteristic
215C2×C61#203911yescharacteristic
216D61—161no—
217C2×#125C2×D6111yescharacteristic
218C2×#124—611no—
219C2×#107—1221no—
220C2×#106—1221no—
221C2×#103—1221no—
222C2×#102—1221no—
223C2×#97—611no—
224C2×#97C2×D6111yescharacteristic
225C2×#97C2×D6111yescharacteristic
226#399—1221no—
227#397—1221no—
228#396—1221no—
229#396—1221no—
230#395—1221no—
231#394—1221no—
232#384—611no—
233#382—611no—
234#340—1221no—
235#340—1221no—
236#330—22no—
237#329—1222no—
238C61#1042711yescharacteristic, complemented, Sylow
239C22×Q8—611no—
240C22×D4—611no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—1221no—
244#125—21no—
245#125—21no—
246#125—21no—
247#125—21no—
248#124—1221no—
249#124—1221no—
250#124—1221no—
251#124—1221no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—611no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4D24411yescharacteristic
262C2×C4⋊C4D24411yescharacteristic
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C42C22×D6111yescharacteristic
270#107—2442no—
271#106—2442no—
272#103—2442no—
273#102—2442no—
274#97—21no—
275#97—21no—
276#97—21no—
277#97—1221no—
278#97—1221no—
279#97C22⋊D6112yes—
280#95—1221no—
281#95—1221no—
282#95—1221no—
283#95—1221no—
284C24—1221no—
285C2×Q8—1221no—
286C2×Q8—1221no—
287C2×Q8—2441no—
288C2×Q8—2441no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—2441no—
292C2×D4—2441no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—2441no—
299C22×C4C2×D24411yescharacteristic
300C22×C4D4×D6111yescharacteristic
301C22×C4D4×D6111yescharacteristic
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—1222no—
309C2×C8—2441no—
310C2×C8—2441no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—4881no—
320C4⋊C4—4881no—
321C4⋊C4—2441no—
322C4⋊C4—2441no—
323C4⋊C4—2441no—
324C4⋊C4—2441no—
325C4⋊C4—2442no—
326C4⋊C4—2441no—
327C4⋊C4—2441no—
328C22⋊C4—4881no—
329C22⋊C4—4881no—
330C22⋊C4—4881no—
331C22⋊C4—4881no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C42#1175822211yescharacteristic
337C42#1175822411yescharacteristic
338C42#1175822411yescharacteristic
339C42C2×C22⋊D6111yescharacteristic
340C23—2441no—
341C23—2441no—
342C23—2441no—
343C23—2441no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23#1451974711yescharacteristic
348Q8—4881no—
349Q8—2442no—
350D4—4881no—
351D4—2442no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—4881no—
365C2×C4—4881no—
366C2×C4—4881no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4#1451974811yescharacteristic
377C2×C4#1451974911yescharacteristic
378C2×C4#1451975111yescharacteristic
379C2×C4#1451975911yescharacteristic
380C2×C4#1451976111yescharacteristic
381C2×C4#1451976311yescharacteristic
382C8—24no—
383C8—42no—
384C8—2442no—
385C22—4881no—
386C22—4881no—
387C22—4881no—
388C22—4881no—
389C22—4881no—
390C22—4881no—
391C22—4881no—
392C22#1683967811yescharacteristic
393C22#1683993111yescharacteristic
394C22#1683993111yescharacteristic
395C22#1683993711yescharacteristic
396C22#1683994111yescharacteristic
397C22#1683994611yescharacteristic
398C22#1683994711yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—81no—
406C4—81no—
407C4—9761no—
408C4—4881no—
409C4—4881no—
410C4—4881no—
411C2—9761no—
412C2#2144511411yescharacteristic
413C2#2144513211yescharacteristic
414C2#2144513811yescharacteristic
415C2#2144515411yescharacteristic
416C2#2144702811yescharacteristic
417C2#2144703711yescharacteristic
418C2#2144704211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#330C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenterC2×#330D61
hypocenterC61#10427
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
2. #21446789C2semidirect
4. #21445987C2semidirect
6. #21443701C2semidirect
7. C2×C61×#330C2semidirect
206. C2×#330D61semidirect
238. C61#10427semidirect

Maximal subgroups

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

subgroupindex
#214538692
#214467892
#214466352
#214459872
C2×#168395012
#214437012
C2×C61×#3302
#1042761