Finite Group Databasebeta

← #30599677

Subgroups — #30599677

Order 15616.

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

normal subgroups only

This group has 432 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#21462547C211yesmaximal, characteristic
2#21461919C211yesmaximal, characteristic, complemented
3#21461388C211yesmaximal, characteristic, complemented
4#21461124C211yesmaximal, characteristic
5#21460717C211yesmaximal, characteristic, complemented
6#21460658C211yesmaximal, characteristic, complemented
7#21444312C211yesmaximal, characteristic
8C2×#14519864—21no—
9#16840794—21no—
10#16840793—21no—
11#16840792—21no—
12#16840791—21no—
13#16840779C2211yescharacteristic
14#16840765C2211yescharacteristic
15C2×C4⋊#92420—21no—
16C2×C4⋊#92420C2211yescharacteristic
17#16840735—21no—
18C2×#14519832C2211yescharacteristic
19#16840628—21no—
20#16840626—21no—
21#16840625—21no—
22#16840610—21no—
23D4⋊#92420—21no—
24#16840307C2211yescharacteristic
25#16839812C2211yescharacteristic
26#16839613C2211yescharacteristic
27#16839497C411yescharacteristic
28#16839496C411yescharacteristic
29#16839495C411yescharacteristic
30C61×#327C411yescharacteristic
31#14519864—42no—
32#14519864—42no—
33C2×#11758213—21no—
34C2×#11758217—21no—
35C2×#11758217—21no—
36C2×D61⋊C8—21no—
37C22×#92420—21no—
38C22×#92420—21no—
39C22×#92420D411yescharacteristic
40C22×#92420D411yescharacteristic
41#14519844—21no—
42#14519844—21no—
43C4⋊#92420—21no—
44C4⋊#92420—21no—
45C4⋊#92420—42no—
46C4⋊#92420D411yescharacteristic
47C4⋊#92420D411yescharacteristic
48#14519834—21no—
49#14519834—21no—
50C22⋊#92420—21no—
51C22⋊#92420—21no—
52C22⋊#92420—21no—
53#14519832—21no—
54#14519832—21no—
55C4×#92420—21no—
56C2×#11758224—21no—
57#14519776Q811yescharacteristic
58#14519773Q811yescharacteristic
59#14519763—21no—
60#14519751C2×C411yescharacteristic
61#14519749—21no—
62D4×Dic61D411yescharacteristic
63#14519739D411yescharacteristic
64#14519737—21no—
65C2×#11758196—21no—
66C2×C4×Dic61—21no—
67C2×C4×Dic61C2311yescharacteristic
68#14519706—21no—
69C22⋊#92418C2×C411yescharacteristic
70C8×Dic61—21no—
71#14519684C2×C411yescharacteristic
72#121×C61C2×C411yescharacteristic
73C22⋊C8×C61C2×C411yescharacteristic
74#95×C61C2×C411yescharacteristic
75C2×D4×C61—21no—
76C2×D4×C61C4⋊C411yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61C22×C411yescharacteristic
79C2×C22⋊D61—21no—
80C2×C22⋊D61—21no—
81C2×C22⋊D61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61C2×D411yescharacteristic
85C22×Dic61#4111yescharacteristic
86#11758224—41no—
87#11758224—41no—
88#11758224—41no—
89#11758224—41no—
90C2×D244C4⋊C411yescharacteristic
91C2×C4×D61—21no—
92C2×Dic122—21no—
93#11758217—42no—
94#11758217—41no—
95#11758217—41no—
96C2×#92420—21no—
97C2×#92420—21no—
98C2×#92420—21no—
99C2×#92420—21no—
100C2×#92420—21no—
101C2×#92420—21no—
102C2×#92420—21no—
103C2×#92420—42no—
104C2×#92420—41no—
105C2×#92420—41no—
106C2×#92420—41no—
107C2×#92420—41no—
108C2×#92420D812yes—
109#11758213—42no—
110D61⋊C8—42no—
111C2×C8×C61—21no—
112C4⋊C4×C61C4⋊C411yescharacteristic
113C22⋊C4×C61—21no—
114C22⋊Dic61—21no—
115#11758198—21no—
116#11758198—21no—
117C4⋊Dic61C4⋊C411yescharacteristic
118#11758196—21no—
119#11758196—42no—
120C4×Dic61—41no—
121C4×Dic61—41no—
122C4×Dic61C2×D411yescharacteristic
123C4×Dic61C2×D411yescharacteristic
124C4×Dic61C2×Q811yescharacteristic
125C4×Dic61#4111yescharacteristic
126C2×#92418—21no—
127C23×C61—21no—
128C23×C61C4×D411yescharacteristic
129C22×D61—21no—
130D4×C61—41no—
131D4×C61—41no—
132D4×C61—41no—
133C2×C4×C61—22no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61C2×C4⋊C411yescharacteristic
139C2×C4×C61C4×D411yescharacteristic
140C22⋊D61—41no—
141C22⋊D61—41no—
142C22⋊D61—41no—
143C22⋊D61—41no—
144C22⋊D61—81no—
145C2×Dic61—21no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61#12011yescharacteristic
153C2×Dic61C22⋊Q811yescharacteristic
154C2×Dic61C22⋊Q811yescharacteristic
155C2×Dic61#12311yescharacteristic
156C2×Dic61C2×D811yescharacteristic
157C2×Dic61#13511yescharacteristic
158C2×Dic61AGL(1,ℤ/8)11yescharacteristic
159C2×Dic61#13711yescharacteristic
160D244—41no—
161C4×D61—41no—
162C4×D61—41no—
163Dic122—41no—
164Dic122—41no—
165#92420—22no—
166#92420—41no—
167#92420—41no—
168#92420—41no—
169#92420—81no—
170#92420—81no—
171C8×C61—41no—
172#92418—41no—
173#8878—611nomaximal, Sylow
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61#38511yescharacteristic
180C22×C61C4×D811yescharacteristic
181C22×C61#44011yescharacteristic
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—42no—
188C4×C61—41no—
189Dic61—21no—
190Dic61—21no—
191Dic61—41no—
192Dic61—81no—
193Dic61#44711yescharacteristic
194Dic61#45211yescharacteristic
195Dic61#47411yescharacteristic
196Dic61#47811yescharacteristic
197#2932—611no—
198#1940—611no—
199#1571—611no—
200#1502—611no—
201#1480—611no—
202#1303—611no—
203#1281—611no—
204C2×C61—21no—
205C2×C61—21no—
206C2×C61—81no—
207C2×C61#186111yescharacteristic
208C2×C61#186211yescharacteristic
209C2×C61#186811yescharacteristic
210D61—81no—
211C2×#131—1221no—
212#532—611no—
213#435—1221no—
214#435—1221no—
215#435—1221no—
216#435—1221no—
217#431—611no—
218#431—611no—
219#423—611no—
220C2×C4⋊C8—611no—
221C2×C4⋊C8—1221no—
222#408—1221no—
223C2×#97—611no—
224C4×C4⋊C4—611no—
225#336—1221no—
226#335—1221no—
227#335—1221no—
228#327—611no—
229#327—611no—
230#327—611no—
231#327#692311yescharacteristic
232D4⋊C8—1221no—
233D4⋊C8—1221no—
234C61#887811yescharacteristic, complemented, Sylow
235C2×#41—1221no—
236#131—2442no—
237#131—2442no—
238C2×M16—1221no—
239C2×M16—1221no—
240C2×M16—1221no—
241C22×C8—611no—
242C22×C8—611no—
243C22×C8—1221no—
244C22×C8—1221no—
245C22×C8—1221no—
246C4⋊Q8—611no—
247#127—611no—
248#124—1221no—
249#121—611no—
250#121—1221no—
251#121C2×#692311yescharacteristic
252C4×D4—611no—
253C4×D4—611no—
254C4×D4—1221no—
255C2×C4⋊C4—1221no—
256C2×C42—611no—
257C2×C42—1221no—
258C4⋊C8—611no—
259C4⋊C8—611no—
260C4⋊C8—1221no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263C4⋊C8—1221no—
264C4⋊C8—1221no—
265C4⋊C8—2442no—
266C22⋊C8—611no—
267C22⋊C8—1221no—
268C22⋊C8—1221no—
269C22⋊C8—1221no—
270C22⋊C8—1221no—
271C22⋊C8—1221no—
272C22⋊C8C2×#692311yescharacteristic
273#97—1221no—
274#97—1221no—
275C4×C8—1221no—
276C4×C8—1221no—
277#95—611no—
278#95C2×#692311yescharacteristic
279#41—2441no—
280#41—2441no—
281#41—2441no—
282#41—2441no—
283C2×Q8—1221no—
284C2×D4—21no—
285C2×D4—611no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4C4⋊#692311yescharacteristic
290C22×C4—21no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4C22×#692311yescharacteristic
297M16—2442no—
298M16—2442no—
299M16—2441no—
300M16—2441no—
301C2×C8—21no—
302C2×C8—612no—
303C2×C8—1221no—
304C2×C8—1221no—
305C2×C8—1221no—
306C2×C8—1221no—
307C2×C8—1221no—
308C2×C8—1221no—
309C2×C8—1221no—
310C2×C8—1221no—
311C2×C8—2442no—
312C2×C8—2442no—
313C2×C8—2441no—
314C2×C8—2441no—
315C2×C8—2441no—
316C2×C8—2441no—
317C4⋊C4—611no—
318C4⋊C4—1221no—
319C4⋊C4—2442no—
320C4⋊C4C4⋊#692311yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C42—611no—
326C42—611no—
327C42—611no—
328C42—611no—
329C42—2441no—
330C42—2441no—
331C23—21no—
332C23—1221no—
333C23D4×#692311yescharacteristic
334Q8—2441no—
335Q8—2441no—
336D4—41no—
337D4—41no—
338D4—41no—
339D4—4881no—
340D4—2441no—
341D4—2441no—
342D4—2441no—
343D4—2441no—
344D4—2441no—
345C2×C4—22no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—611no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—1221no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4C2×C4⋊#692311yescharacteristic
368C2×C4D4×#692311yescharacteristic
369C8—41no—
370C8—1222no—
371C8—4881no—
372C8—4881no—
373C8—2441no—
374C8—2441no—
375C8—2441no—
376C8—2441no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22#1684070911yescharacteristic
386C22D8×#692311yescharacteristic
387C22#1684080111yescharacteristic
388C4—21no—
389C4—21no—
390C4—42no—
391C4—41no—
392C4—611no—
393C4—611no—
394C4—611no—
395C4—611no—
396C4—1221no—
397C4—1221no—
398C4—4881no—
399C4—2441no—
400C2—21no—
401C2—21no—
402C2—81no—
403C2—4881no—
404C2#2146178011yescharacteristic
405C2#2146178211yescharacteristic
406C2#2146179111yescharacteristic
subgroupG/H
centerC22#16840709
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#327C4
socleC22×C61#385
prime radical#16840307C22
cosocleC2×C4×Dic61C23
hypercenter#327#6923
hypocenterC61#8878
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #21461919C2semidirect
3. #21461388C2semidirect
5. #21460717C2semidirect
6. #21460658C2semidirect
234. C61#8878semidirect

Maximal subgroups

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

subgroupindex
#214625472
#214619192
#214613882
#214611242
#214607172
#214606582
#214443122
#887861