Finite Group Databasebeta

← #30600668

Subgroups — #30600668

Order 15616.

434 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Q8×#11758217C211yesmaximal, characteristic
2#21462012C211yesmaximal, characteristic
3#21461334C211yesmaximal, characteristic
4#21461147C211yesmaximal, characteristic
5#21460689C211yesmaximal, characteristic
6#21460664C211yesmaximal, characteristic
7C2×#16840055C211yesmaximal, characteristic
8#16840813—21no—
9#16840813—22no—
10Q8×#92420—21no—
11#16840779C2211yescharacteristic
12#16840765—21no—
13#16840765C2211yescharacteristic
14#16840765C2211yescharacteristic
15C4×#11758217—21no—
16C4×#11758217C2211yescharacteristic
17#16840642—21no—
18#16840642—21no—
19#16840621—22no—
20Q8⋊#92420—21no—
21Q8⋊#92420—21no—
22C2×#14519776C2211yescharacteristic
23C2×Q8×Dic61C2211yescharacteristic
24#16840055—21no—
25#16840055—21no—
26#16840055—21no—
27#16840055—21no—
28C2×#14519711C411yescharacteristic
29C2×#14519710C411yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519701C411yescharacteristic
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×Dic122—21no—
51C22×#92418C2×C411yescharacteristic
52#14519776—21no—
53#14519776—21no—
54#14519776—21no—
55#14519776—21no—
56Q8×Dic61—21no—
57Q8×Dic61—21no—
58Q8×Dic61D411yescharacteristic
59Q8×Dic61D411yescharacteristic
60Q8×Dic61D411yescharacteristic
61Q8×Dic61D411yescharacteristic
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61C2×C411yescharacteristic
64C2×C4⋊Dic61C2×C411yescharacteristic
65C2×#11758196—21no—
66C2×C4×Dic61—21no—
67C2×C4×Dic61C2311yescharacteristic
68#14519711—21no—
69#14519711—21no—
70#14519710—21no—
71#14519710—21no—
72#14519706—21no—
73#14519706—21no—
74#14519701—21no—
75#14519701—21no—
76C22×Q8×C61C2×C411yescharacteristic
77C22×C8×C61C2×C411yescharacteristic
78C2×C4⋊C4×C61C2×C411yescharacteristic
79#103×C61—21no—
80#103×C61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61—22no—
83C2×Q8×C61—41no—
84C2×Q8×C61C22⋊C411yescharacteristic
85C2×Q8×C61C22⋊C411yescharacteristic
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61C22×C411yescharacteristic
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61C2×D411yescharacteristic
92C22×Dic61#4111yescharacteristic
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×Dic122—82no—
96#11758217—21no—
97#11758217—21no—
98#11758217—21no—
99#11758217—41no—
100#11758217—41no—
101#11758217—41no—
102#11758217—41no—
103#11758217Q1612yes—
104C2×#92420—21no—
105C2×#92420—21no—
106C2×#92420—22no—
107C2×#92420—41no—
108C2×#92420—41no—
109C2×C8×C61—21no—
110C2×C8×C61—41no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61C22⋊C411yescharacteristic
121C4⋊Dic61C22⋊C411yescharacteristic
122#11758196—41no—
123#11758196—41no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61C2×D411yescharacteristic
129C4×Dic61C2×D411yescharacteristic
130C4×Dic61C2×D411yescharacteristic
131C4×Dic61#4111yescharacteristic
132C2×#92418—21no—
133C2×#92418—41no—
134C23×C61C4×D411yescharacteristic
135Q8×C61—21no—
136Q8×C61—21no—
137Q8×C61—21no—
138Q8×C61—42no—
139Q8×C61#10112yes—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—81no—
147C2×C4×C61C2×C22⋊C411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155C2×Dic61#12011yescharacteristic
156C2×Dic61#12111yescharacteristic
157C2×Dic61#12111yescharacteristic
158C2×Dic61#12311yescharacteristic
159C2×Dic61C2×Q1611yescharacteristic
160C2×Dic61#13511yescharacteristic
161C2×Dic61#13711yescharacteristic
162C2×Dic61#13711yescharacteristic
163Dic122—82no—
164Dic122—82no—
165#92420—22no—
166#92420—41no—
167#92420—42no—
168#92420—81no—
169#92420—81no—
170C8×C61—41no—
171#92418—41no—
172#9250—611nomaximal, Sylow
173C22×C61—21no—
174C22×C61—21no—
175C22×C61#38611yescharacteristic
176C22×C61C4×Q1611yescharacteristic
177C22×C61#44111yescharacteristic
178C4×C61—21no—
179C4×C61—22no—
180C4×C61—41no—
181C4×C61—81no—
182C4×C61C2×#10111yescharacteristic
183C4×C61#41311yescharacteristic
184Dic61—21no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61—81no—
189Dic61#45111yescharacteristic
190Dic61#45211yescharacteristic
191Dic61#46211yescharacteristic
192Dic61#46411yescharacteristic
193C2×#477—611no—
194Q8×M16—611no—
195#1997—611no—
196#1549—611no—
197#1487—611no—
198#1292—611no—
199#1283—611no—
200C2×C61—21no—
201C2×C61—21no—
202C2×C61#187811yescharacteristic
203C2×C61#190111yescharacteristic
204C2×C61#190311yescharacteristic
205C2×C4⋊Q8—611no—
206C2×C4×Q8—611no—
207#477—1221no—
208#477—1221no—
209#477—1221no—
210#477—1221no—
211#446—1222no—
212#446—1221no—
213C8×Q8—1221no—
214#431—611no—
215C2×#107—611no—
216C2×#107—611no—
217#423—611no—
218#423—611no—
219#423—1221no—
220C2×C4⋊C8—611no—
221C2×#103—611no—
222C2×#103#692311yescharacteristic
223C4×M16—611no—
224C4×M16—1221no—
225#343—1221no—
226#343—1221no—
227#332—1222no—
228Q8⋊C8—1221no—
229Q8⋊C8—1221no—
230C61#925011yescharacteristic, complemented, Sylow
231C22×Q8—1221no—
232C22×Q8C2×#692311yescharacteristic
233C2×M16—611no—
234C2×M16—611no—
235C2×M16—1221no—
236C2×M16—1221no—
237C22×C8—611no—
238C22×C8C2×#692311yescharacteristic
239C4⋊Q8—1221no—
240C4⋊Q8—1221no—
241C4⋊Q8—1221no—
242C4⋊Q8—1221no—
243C4×Q8—611no—
244C4×Q8—611no—
245C4×Q8—611no—
246C4×Q8—611no—
247C4×Q8—1221no—
248C4×Q8—1221no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4C2×#692311yescharacteristic
254C2×C42—611no—
255C2×C42—1221no—
256#107—1221no—
257#107—1221no—
258#107—1221no—
259#107—1221no—
260C4⋊C8—612no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263C4⋊C8—1221no—
264C4⋊C8—1221no—
265C4⋊C8—1221no—
266C4⋊C8—1221no—
267C4⋊C8—1222no—
268C4⋊C8—1222no—
269#103—21no—
270#103—21no—
271#103—1221no—
272#103—1221no—
273C22⋊C8—1221no—
274#97—1221no—
275#97—1222no—
276C4×C8—1221no—
277C4×C8—1221no—
278C4×C8—1222no—
279C2×Q8—21no—
280C2×Q8—22no—
281C2×Q8—41no—
282C2×Q8—4882no—
283C2×Q8—2441no—
284C2×Q8—2441no—
285C2×Q8C22⋊#692311yescharacteristic
286C2×Q8C22⋊#692311yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4C22×#692311yescharacteristic
294M16—612no—
295M16—1221no—
296M16—1221no—
297M16—1221no—
298M16—2441no—
299M16—2441no—
300M16—2441no—
301M16—2441no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8—1221no—
305C2×C8—1222no—
306C2×C8—1221no—
307C2×C8—1221no—
308C2×C8—2441no—
309C2×C8—2441no—
310C2×C8—2441no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—611no—
314C4⋊C4—611no—
315C4⋊C4—1221no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C4⋊C4—1221no—
321C4⋊C4—1221no—
322C4⋊C4—2441no—
323C4⋊C4—2441no—
324C42—611no—
325C42—611no—
326C42—611no—
327C42—611no—
328C42—1221no—
329C42—1221no—
330C42—1221no—
331C42—1221no—
332C23D4×#692311yescharacteristic
333Q8—21no—
334Q8—21no—
335Q8—21no—
336Q8—42no—
337Q8—4882no—
338Q8—4882no—
339Q8#1451983812yes—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—4881no—
358C2×C4—4881no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4C2×C22⋊#692311yescharacteristic
362C2×C4D4×#692311yescharacteristic
363C8—41no—
364C8—1222no—
365C8—4881no—
366C8—4881no—
367C8—2441no—
368C8—2442no—
369C8—2441no—
370C22—21no—
371C22—21no—
372C22#1684071011yescharacteristic
373C22Q16×#692311yescharacteristic
374C22#1684080211yescharacteristic
375C4—21no—
376C4—22no—
377C4—41no—
378C4—81no—
379C4—611no—
380C4—611no—
381C4—611no—
382C4—611no—
383C4—1221no—
384C4—1221no—
385C4—4881no—
386C4—2441no—
387C4—2441no—
388C4C2×#1451983811yescharacteristic
389C4#1684074911yescharacteristic
390C2—21no—
391C2—21no—
392C2#2146181311yescharacteristic
393C2#2146184611yescharacteristic
394C2#2146185111yescharacteristic
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#9250
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
230. C61#9250semidirect

Maximal subgroups

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

subgroupindex
Q8×#117582172
#214620122
#214613342
#214611472
#214606892
#214606642
C2×#168400552
#925061