Finite Group Databasebeta

← #30600663

Subgroups — #30600663

Order 15616.

466 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 92 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#21462620C211yesmaximal, characteristic
2#21462011C211yesmaximal, characteristic
3#21461332C211yesmaximal, characteristic
4#21461149C211yesmaximal, characteristic
5#21460689C211yesmaximal, characteristic
6#21460664C211yesmaximal, characteristic
7C2×#16839971C211yesmaximal, characteristic
8#16840814—22no—
9#16840812—21no—
10#16840811—21no—
11#16840779C2211yescharacteristic
12#16840765—21no—
13#16840765C2211yescharacteristic
14#16840765C2211yescharacteristic
15C4×#11758217—21no—
16C4×#11758217C2211yescharacteristic
17#16840642—21no—
18#16840642—21no—
19#16840622—22no—
20#16840612—21no—
21#16840612—21no—
22C22×Dic244C411yescharacteristic
23C22×#11758202C411yescharacteristic
24C2×#14519775C2211yescharacteristic
25C2×#14519742C2211yescharacteristic
26#16839971—21no—
27#16839971—21no—
28#16839971—21no—
29#16839971—21no—
30C2×#14519706C2211yescharacteristic
31C2×#14519700C411yescharacteristic
32C2×#103×C61C411yescharacteristic
33C2×#11758217—21no—
34C2×#11758217—21no—
35C2×#11758217D411yescharacteristic
36C2×#11758217D411yescharacteristic
37#14519844—22no—
38#14519844—21no—
39#14519844—21no—
40#14519844D412yes—
41C4⋊#92420—22no—
42C4⋊#92420—21no—
43C4⋊#92420—21no—
44C22⋊#92420—21no—
45#14519832—22no—
46#14519832—21no—
47C4×#92420—22no—
48C4×#92420—21no—
49C4×#92420—21no—
50C22×Dic122C2×C411yescharacteristic
51C22×Dic122C2×C411yescharacteristic
52C2×Dic244—21no—
53C2×Dic244—21no—
54C2×Dic244—42no—
55C2×#11758202—21no—
56C2×#11758202—21no—
57C2×#11758202—42no—
58C22×#92418C2×C411yescharacteristic
59#14519775—21no—
60#14519775—21no—
61#14519775—21no—
62#14519775—21no—
63#14519742—21no—
64#14519742—21no—
65#14519742D411yescharacteristic
66#14519742D411yescharacteristic
67#14519742D411yescharacteristic
68#14519742D411yescharacteristic
69C2×#11758196—21no—
70C2×#11758196—21no—
71C2×#11758196—21no—
72C2×C4×Dic61—21no—
73C2×C4×Dic61C2311yescharacteristic
74#14519706—21no—
75#14519706—21no—
76#14519700—21no—
77#14519700—21no—
78C22×Q8×C61C2×C411yescharacteristic
79C22×C8×C61C2×C411yescharacteristic
80C2×C4⋊C4×C61C2×C411yescharacteristic
81#103×C61—21no—
82#103×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—41no—
86C2×Q8×C61—41no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61C22×C411yescharacteristic
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61C2×D411yescharacteristic
93C22×Dic61#4111yescharacteristic
94C2×Dic122—22no—
95C2×Dic122—21no—
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—41no—
99C2×Dic122—41no—
100C2×Dic122—41no—
101C2×Dic122C22⋊C411yescharacteristic
102C2×Dic122C22⋊C411yescharacteristic
103#11758217—21no—
104#11758217—21no—
105#11758217—21no—
106#11758217—41no—
107#11758217—41no—
108#11758217—41no—
109#11758217—41no—
110#11758217Q1612yescomplemented
111C2×#92420—21no—
112C2×#92420—21no—
113C2×#92420—22no—
114C2×#92420—41no—
115C2×#92420—41no—
116C2×C8×C61—21no—
117C2×C8×C61—41no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61C22⋊C411yescharacteristic
120C4⋊C4×C61C22⋊C411yescharacteristic
121#11758202—42no—
122#11758202—42no—
123#11758196—21no—
124#11758196—21no—
125#11758196—21no—
126#11758196—21no—
127#11758196—41no—
128#11758196—41no—
129#11758196—41no—
130#11758196—41no—
131C4×Dic61—21no—
132C4×Dic61—21no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135C4×Dic61C2×D411yescharacteristic
136C4×Dic61C2×D411yescharacteristic
137C4×Dic61C2×D411yescharacteristic
138C4×Dic61#4111yescharacteristic
139C2×#92418—21no—
140C2×#92418—41no—
141Dic244—42no—
142Dic244—42no—
143C23×C61C4×D411yescharacteristic
144Q8×C61—41no—
145Q8×C61—41no—
146Q8×C61—81no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—41no—
152C2×C4×C61—81no—
153C2×C4×C61—81no—
154C2×C4×C61C2×C22⋊C411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—41no—
159C2×Dic61—42no—
160C2×Dic61—41no—
161C2×Dic61—81no—
162C2×Dic61#12011yescharacteristic
163C2×Dic61#12111yescharacteristic
164C2×Dic61#12111yescharacteristic
165C2×Dic61#12311yescharacteristic
166C2×Dic61C2×Q1611yescharacteristic
167C2×Dic61#13511yescharacteristic
168C2×Dic61#13711yescharacteristic
169C2×Dic61#13711yescharacteristic
170Dic122—21no—
171Dic122—21no—
172Dic122—21no—
173Dic122—42no—
174Dic122—41no—
175Dic122—41no—
176Dic122—81no—
177Dic122#10012yes—
178#92420—22no—
179#92420—41no—
180#92420—42no—
181#92420—81no—
182#92420—81no—
183C8×C61—41no—
184#92418—41no—
185#9248—611nomaximal, Sylow
186C22×C61—21no—
187C22×C61—21no—
188C22×C61#38611yescharacteristic
189C22×C61C4×Q1611yescharacteristic
190C22×C61#44111yescharacteristic
191C4×C61—21no—
192C4×C61—41no—
193C4×C61—41no—
194C4×C61—81no—
195C4×C61C2×#10011yescharacteristic
196C4×C61#41311yescharacteristic
197Dic61—22no—
198Dic61—21no—
199Dic61—21no—
200Dic61—41no—
201Dic61—81no—
202Dic61#45111yescharacteristic
203Dic61#45211yescharacteristic
204Dic61#46211yescharacteristic
205Dic61#46411yescharacteristic
206C2×#462—611no—
207Q8×M16—611no—
208#1997—611no—
209#1548—611no—
210#1487—611no—
211#1292—611no—
212#1283—611no—
213C2×C61—21no—
214C2×C61—21no—
215C2×C61#187811yescharacteristic
216C2×C61#190011yescharacteristic
217C2×C61#190211yescharacteristic
218C22×Q16—611no—
219C22×Q16—611no—
220C2×C4⋊Q8—611no—
221C2×C4×Q8—611no—
222#462—1221no—
223#462—1221no—
224#462—1221no—
225#462—1221no—
226#446—1222no—
227#446—1221no—
228C8×Q8—1221no—
229#431—611no—
230#423—611no—
231#423—611no—
232#423—1221no—
233C2×C4⋊C8—611no—
234C2×#103—611no—
235C2×#103#692311yescharacteristic
236C4×M16—611no—
237C4×M16—1221no—
238#343—1221no—
239#343—1221no—
240#333—1222no—
241Q8⋊C8—1221no—
242Q8⋊C8—1221no—
243C61#924811yescharacteristic, complemented, Sylow
244C22×Q8—611no—
245C22×Q8—611no—
246C22×Q8C2×#692311yescharacteristic
247C2×Q16—1221no—
248C2×Q16—1221no—
249C2×Q16—1221no—
250C2×Q16—1221no—
251C2×Q16—2442no—
252C2×Q16—2442no—
253C2×M16—611no—
254C2×M16—611no—
255C2×M16—1221no—
256C2×M16—1221no—
257C22×C8—611no—
258C22×C8C2×#692311yescharacteristic
259C4⋊Q8—1221no—
260C4⋊Q8—1221no—
261C4⋊Q8—1221no—
262C4⋊Q8—1221no—
263C4×Q8—611no—
264C4×Q8—611no—
265C4×Q8—611no—
266C4×Q8—611no—
267C4×Q8—1221no—
268C4×Q8—1221no—
269C2×C4⋊C4—1221no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4—1221no—
272C2×C4⋊C4C2×#692311yescharacteristic
273C2×C42—611no—
274C2×C42—1221no—
275C4⋊C8—612no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278C4⋊C8—1221no—
279C4⋊C8—1221no—
280C4⋊C8—1221no—
281C4⋊C8—1221no—
282C4⋊C8—1222no—
283C4⋊C8—1222no—
284#103—21no—
285#103—21no—
286#103—1221no—
287#103—1221no—
288C22⋊C8—1221no—
289#97—1221no—
290#97—1222no—
291C4×C8—1221no—
292C4×C8—1221no—
293C4×C8—1222no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—611no—
299C2×Q8—611no—
300C2×Q8—1222no—
301C2×Q8—1221no—
302C2×Q8—1221no—
303C2×Q8—1221no—
304C2×Q8—2441no—
305C2×Q8—2441no—
306C2×Q8—2441no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4C22×#692311yescharacteristic
314Q16—2442no—
315Q16—2442no—
316Q16—2442no—
317Q16—2442no—
318M16—612no—
319M16—1221no—
320M16—1221no—
321M16—1221no—
322M16—2441no—
323M16—2441no—
324M16—2441no—
325M16—2441no—
326C2×C8—21no—
327C2×C8—41no—
328C2×C8—1221no—
329C2×C8—1222no—
330C2×C8—1221no—
331C2×C8—1221no—
332C2×C8—2441no—
333C2×C8—2441no—
334C2×C8—2441no—
335C4⋊C4—21no—
336C4⋊C4—1221no—
337C4⋊C4—1221no—
338C4⋊C4—1221no—
339C4⋊C4—1221no—
340C4⋊C4—2441no—
341C4⋊C4—2441no—
342C4⋊C4—2441no—
343C4⋊C4—2441no—
344C4⋊C4C22⋊#692311yescharacteristic
345C4⋊C4C22⋊#692311yescharacteristic
346C42—611no—
347C42—611no—
348C42—611no—
349C42—611no—
350C42—1221no—
351C42—1221no—
352C42—1221no—
353C42—1221no—
354C23D4×#692311yescharacteristic
355Q8—41no—
356Q8—41no—
357Q8—81no—
358Q8—612no—
359Q8—1221no—
360Q8—1221no—
361Q8—1221no—
362Q8—4881no—
363Q8—2442no—
364Q8—2441no—
365Q8—2441no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—611no—
374C2×C4—611no—
375C2×C4—611no—
376C2×C4—611no—
377C2×C4—611no—
378C2×C4—611no—
379C2×C4—611no—
380C2×C4—611no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—4881no—
384C2×C4—2441no—
385C2×C4—2442no—
386C2×C4—2441no—
387C2×C4C2×C22⋊#692311yescharacteristic
388C2×C4D4×#692311yescharacteristic
389C8—41no—
390C8—1222no—
391C8—4881no—
392C8—4881no—
393C8—2441no—
394C8—2442no—
395C8—2441no—
396C22—21no—
397C22—21no—
398C22#1684071011yescharacteristic
399C22Q16×#692311yescharacteristic
400C22#1684080211yescharacteristic
401C4—21no—
402C4—41no—
403C4—41no—
404C4—81no—
405C4—611no—
406C4—611no—
407C4—611no—
408C4—611no—
409C4—1222no—
410C4—1221no—
411C4—1221no—
412C4—4881no—
413C4—2441no—
414C4D61⋊#10011yescharacteristic
415C4#1684074811yescharacteristic
416C2—21no—
417C2—21no—
418C2#2146181311yescharacteristic
419C2#2146184511yescharacteristic
420C2#2146184811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#103×C61C4
socleC22×C61#386
prime radicalC23×C61C4×D4
cosocleC2×C4×Dic61C23
hypercenterC2×#103#6923
hypocenterC61#9248
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
110. #11758217Q16semidirect
243. C61#9248semidirect

Maximal subgroups

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

subgroupindex
#214626202
#214620112
#214613322
#214611492
#214606892
#214606642
C2×#168399712
#924861