Finite Group Databasebeta

← #30600099

Subgroups — #30600099

Order 15616.

424 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 86 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#21462610C211yesmaximal, characteristic
2#21461993C211yesmaximal, characteristic
3#21461321C211yesmaximal, characteristic
4#21461147C211yesmaximal, characteristic
5#21460710C211yesmaximal, characteristic
6#21460658C211yesmaximal, characteristic
7#21455853C211yesmaximal, characteristic
8#16840814—21no—
9#16840814—21no—
10#16840813—21no—
11#16840812—21no—
12#16840779C2211yescharacteristic
13#16840768—21no—
14#16840765C2211yescharacteristic
15C2×#14519844C2211yescharacteristic
16#16840726—21no—
17C2×#14519832C2211yescharacteristic
18#16840628—21no—
19#16840628—21no—
20#16840622—21no—
21#16840621—21no—
22Q8⋊#92420—21no—
23Q8⋊#92420—21no—
24#16840314C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26#16840098C411yescharacteristic
27#16840095C411yescharacteristic
28#16840055—21no—
29#16839970—21no—
30#16839918C411yescharacteristic
31Q16×Dic61—21no—
32#16839854—21no—
33#16839812C2211yescharacteristic
34C61×#451C411yescharacteristic
35C2×#11758217—21no—
36C22×#92420—21no—
37C22×#92420D411yescharacteristic
38C22×#92420D411yescharacteristic
39#14519844—21no—
40#14519844—21no—
41#14519844—21no—
42#14519844—21no—
43#14519844—21no—
44#14519844—21no—
45C4⋊#92420—21no—
46C4⋊#92420—21no—
47C4⋊#92420D411yescharacteristic
48C4⋊#92420D411yescharacteristic
49C22⋊#92420—21no—
50#14519832—21no—
51#14519832—21no—
52#14519832—21no—
53#14519832—21no—
54C4×#92420—21no—
55C4×#92420—21no—
56C4×#92420—21no—
57C2×#11758202—21no—
58#14519776D411yescharacteristic
59#14519775D411yescharacteristic
60#14519767—21no—
61#14519756C2×C411yescharacteristic
62#14519754—21no—
63Q8×Dic61—21no—
64Q8×Dic61—21no—
65Q8×Dic61—21no—
66Q8×Dic61—21no—
67Q8×Dic61D411yescharacteristic
68#14519742—21no—
69#14519742D411yescharacteristic
70#14519733—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2×C411yescharacteristic
73C2×C4×Dic61—21no—
74C2×C4×Dic61C2311yescharacteristic
75#14519711—21no—
76#14519710—21no—
77#14519706—21no—
78#14519702—21no—
79#14519701—21no—
80#14519701—21no—
81C22⋊#92418C2×C411yescharacteristic
82C8×Dic61—21no—
83C22×Q8×C61C2×C411yescharacteristic
84C2×Q16×C61—21no—
85C22⋊Q8×C61C2×C411yescharacteristic
86#103×C61—21no—
87C22⋊C8×C61C2×C411yescharacteristic
88C2×Q8×C61—21no—
89C2×Q8×C61—21no—
90C2×Q8×C61—42no—
91C2×Q8×C61C22⋊C411yescharacteristic
92C22×C4×C61—21no—
93C22×C4×C61C22×C411yescharacteristic
94C22×Dic61—21no—
95C22×Dic61C2×D411yescharacteristic
96C22×Dic61#4111yescharacteristic
97C2×Dic122—21no—
98C2×Dic122C22⋊C411yescharacteristic
99#11758217—41no—
100#11758217—41no—
101C2×#92420—21no—
102C2×#92420—21no—
103C2×#92420—21no—
104C2×#92420—21no—
105C2×#92420—21no—
106C2×#92420—21no—
107C2×#92420—21no—
108C2×#92420—41no—
109C2×#92420—41no—
110C2×#92420—41no—
111C2×#92420—41no—
112C2×#92420Q1612yescomplemented
113Q16×C61—42no—
114C2×C8×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61C22⋊C411yescharacteristic
117C22⋊C4×C61—21no—
118C22⋊Dic61—21no—
119#11758202—42no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—41no—
124C4⋊Dic61—41no—
125C4⋊Dic61C22⋊C411yescharacteristic
126#11758196—21no—
127#11758196—21no—
128#11758196—21no—
129#11758196—21no—
130#11758196—21no—
131C4×Dic61—21no—
132C4×Dic61—21no—
133C4×Dic61—41no—
134C4×Dic61—41no—
135C4×Dic61C2×D411yescharacteristic
136C4×Dic61C2×D411yescharacteristic
137C4×Dic61C2×D411yescharacteristic
138C4×Dic61#4111yescharacteristic
139C2×#92418—21no—
140C23×C61C4×D411yescharacteristic
141Q8×C61—22no—
142Q8×C61—22no—
143Q8×C61—41no—
144Q8×C61—41no—
145Q8×C61—41no—
146C2×C4×C61—22no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61C2×C22⋊C411yescharacteristic
153C2×C4×C61C4×D411yescharacteristic
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—41no—
157C2×Dic61—42no—
158C2×Dic61—41no—
159C2×Dic61#12011yescharacteristic
160C2×Dic61#12111yescharacteristic
161C2×Dic61#12111yescharacteristic
162C2×Dic61#12311yescharacteristic
163C2×Dic61C2×Q1611yescharacteristic
164C2×Dic61#13511yescharacteristic
165C2×Dic61#13711yescharacteristic
166C2×Dic61#13711yescharacteristic
167Dic122—41no—
168Dic122—81no—
169#92420—22no—
170#92420—41no—
171#92420—41no—
172#92420—41no—
173#92420—81no—
174#92420—81no—
175C8×C61—41no—
176#92418—41no—
177#9048—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61#38611yescharacteristic
181C22×C61C4×Q1611yescharacteristic
182C22×C61#44111yescharacteristic
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—41no—
186C4×C61—42no—
187C4×C61—41no—
188Dic61—21no—
189Dic61—21no—
190Dic61—41no—
191Dic61—41no—
192Dic61—81no—
193Dic61#45111yescharacteristic
194Dic61#45211yescharacteristic
195Dic61#46211yescharacteristic
196Dic61#46411yescharacteristic
197#3104—611no—
198#2961—611no—
199#1985—611no—
200#1542—611no—
201#1487—611no—
202#1301—611no—
203#1281—611no—
204C2×C61—21no—
205C2×C61—21no—
206C2×C61#187811yescharacteristic
207C2×C61#188111yescharacteristic
208C2×C61#189111yescharacteristic
209#533—611no—
210C2×C4×Q8—611no—
211#484—611no—
212#484—611no—
213#477—1221no—
214#462—1221no—
215#451—611no—
216#451#692311yescharacteristic
217#446—1221no—
218#446—1221no—
219#446—1221no—
220#446—1221no—
221C4×Q16—1221no—
222C4×Q16—1221no—
223#431—611no—
224#431—611no—
225#424—1221no—
226#423—611no—
227C2×C4⋊C8—611no—
228#405—1221no—
229C2×#97—611no—
230#336—1221no—
231#336—1221no—
232#333—1221no—
233#332—1221no—
234Q8⋊C8—1221no—
235Q8⋊C8—1221no—
236C61#904811yescharacteristic, complemented, Sylow
237C22×Q8C2×#692311yescharacteristic
238C2×Q16—21no—
239C2×Q16—1221no—
240C2×M16—1221no—
241C22×C8—611no—
242C22×C8—611no—
243C22×C8—1221no—
244C4⋊Q8—611no—
245C4⋊Q8—611no—
246#125—1221no—
247C22⋊Q8—611no—
248C22⋊Q8—1221no—
249C22⋊Q8C2×#692311yescharacteristic
250C4×Q8—611no—
251C4×Q8—611no—
252C4×Q8—1221no—
253C4×Q8—1221no—
254C4×Q8—1221no—
255C4×Q8—1221no—
256C4×Q8—1221no—
257#117—1221no—
258C2×C4⋊C4—611no—
259C2×C4⋊C4—1221no—
260C2×C42—611no—
261C2×C42—1221no—
262#107—1221no—
263#107—1221no—
264C4⋊C8—611no—
265C4⋊C8—611no—
266C4⋊C8—1221no—
267C4⋊C8—1221no—
268C4⋊C8—1221no—
269C4⋊C8—1221no—
270C4⋊C8—1221no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274C4⋊C8—1221no—
275#103—21no—
276#103—1221no—
277#103—1221no—
278#103—1221no—
279C22⋊C8—611no—
280C22⋊C8—1221no—
281C22⋊C8C2×#692311yescharacteristic
282#97—1221no—
283#97—1221no—
284#97—1221no—
285#97—1221no—
286C4×C8—1221no—
287C4×C8—1221no—
288C4×C8—1221no—
289C4×C8—1221no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—42no—
293C2×Q8—611no—
294C2×Q8—1221no—
295C2×Q8C22⋊#692311yescharacteristic
296C22×C4—21no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—1221no—
300C22×C4C22×#692311yescharacteristic
301Q16—42no—
302Q16—2442no—
303M16—2441no—
304M16—2441no—
305C2×C8—21no—
306C2×C8—612no—
307C2×C8—1221no—
308C2×C8—1221no—
309C2×C8—1221no—
310C2×C8—1221no—
311C2×C8—1221no—
312C2×C8—1221no—
313C2×C8—1221no—
314C2×C8—1221no—
315C2×C8—2441no—
316C2×C8—2441no—
317C2×C8—2441no—
318C2×C8—2441no—
319C4⋊C4—21no—
320C4⋊C4—611no—
321C4⋊C4—1221no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C4⋊C4—1221no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4—2441no—
330C4⋊C4—2441no—
331C4⋊C4C22⋊#692311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—1221no—
334C42—611no—
335C42—611no—
336C42—611no—
337C42—611no—
338C42—1221no—
339C42—1221no—
340C42—2441no—
341C42—2441no—
342C23D4×#692311yescharacteristic
343Q8—22no—
344Q8—22no—
345Q8—41no—
346Q8—41no—
347Q8—41no—
348Q8—4881no—
349Q8—2441no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—611no—
359C2×C4—611no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—611no—
363C2×C4—611no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—2441no—
367C2×C4—2442no—
368C2×C4—2441no—
369C2×C4C2×C22⋊#692311yescharacteristic
370C2×C4D4×#692311yescharacteristic
371C8—41no—
372C8—1222no—
373C8—4881no—
374C8—4881no—
375C8—2441no—
376C8—2441no—
377C8—2441no—
378C8—2441no—
379C22—21no—
380C22—21no—
381C22#1684071011yescharacteristic
382C22Q16×#692311yescharacteristic
383C22#1684080211yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—42no—
388C4—41no—
389C4—611no—
390C4—611no—
391C4—611no—
392C4—611no—
393C4—1221no—
394C4—1221no—
395C4—4881no—
396C4—2441no—
397C4—2441no—
398C2—21no—
399C2—21no—
400C2#2146181311yescharacteristic
401C2#2146181611yescharacteristic
402C2#2146183011yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#451C4
socleC22×C61#386
prime radicalC23×C61C4×D4
cosocleC2×C4×Dic61C23
hypercenter#451#6923
hypocenterC61#9048
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
112. C2×#92420Q16semidirect
236. C61#9048semidirect

Maximal subgroups

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

subgroupindex
#214626102
#214619932
#214613212
#214611472
#214607102
#214606582
#214558532
#904861