Finite Group Databasebeta

← #30600106

Subgroups — #30600106

Order 15616.

436 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 78 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#21462758C211yesmaximal, characteristic
2#21461993C211yesmaximal, characteristic, complemented
3#21461272C211yesmaximal, characteristic
4#21461161C211yesmaximal, characteristic, complemented
5#21460714C211yesmaximal, characteristic, complemented
6#21460663C211yesmaximal, characteristic, complemented
7#21455900C211yesmaximal, characteristic
8#16840813—21no—
9#16840792—21no—
10#16840791—21no—
11#16840789—21no—
12#16840787—21no—
13#16840783C2211yescharacteristic
14#16840769—21no—
15C2×#14519844C2211yescharacteristic
16C4×#11758217C2211yescharacteristic
17C2×#14519832C2211yescharacteristic
18#16840628—21no—
19#16840628—21no—
20#16840619—21no—
21#16840618—21no—
22Q8⋊#92420—21no—
23Q8⋊#92420—21no—
24#16840298C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26#16840090C411yescharacteristic
27#16840076C411yescharacteristic
28#16840071—21no—
29#16839986—21no—
30#16839901C411yescharacteristic
31Q16×Dic61—21no—
32#16839847—21no—
33#16839812C2211yescharacteristic
34C61×#451C411yescharacteristic
35C2×#11758213—21no—
36C2×#11758217—21no—
37C2×D61⋊C8—21no—
38C22×#92420—21no—
39C22×#92420D411yescharacteristic
40C22×#92420D411yescharacteristic
41#14519844—21no—
42#14519844—21no—
43#14519844—21no—
44C4⋊#92420—21no—
45C4⋊#92420D411yescharacteristic
46C4⋊#92420D411yescharacteristic
47#14519834—21no—
48#14519834—21no—
49C22⋊#92420—21no—
50#14519832—21no—
51#14519832—21no—
52#14519832—21no—
53#14519832—21no—
54#14519832—21no—
55C4×#92420—21no—
56C4×#92420—21no—
57C2×#11758201—21no—
58#14519772—21no—
59#14519768D411yescharacteristic
60#14519766D411yescharacteristic
61#14519761—21no—
62#14519751C2×C411yescharacteristic
63Q8×Dic61—21no—
64Q8×Dic61—21no—
65Q8×Dic61—21no—
66Q8×Dic61—21no—
67Q8×Dic61D411yescharacteristic
68#14519739D411yescharacteristic
69#14519737—21no—
70#14519735—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2×C411yescharacteristic
73C2×C4×Dic61—21no—
74C2×C4×Dic61C2311yescharacteristic
75#14519711—21no—
76#14519708—21no—
77#14519706—21no—
78#14519701—21no—
79#14519701—21no—
80#14519699—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
94C2×C22⋊D61—21no—
95C22×Dic61—21no—
96C22×Dic61C2×D411yescharacteristic
97C22×Dic61#4111yescharacteristic
98C2×D244C22⋊C411yescharacteristic
99C2×C4×D61—21no—
100#11758217—22no—
101#11758217—41no—
102C2×#92420—22no—
103C2×#92420—21no—
104C2×#92420—21no—
105C2×#92420—21no—
106C2×#92420—21no—
107C2×#92420—41no—
108C2×#92420—41no—
109C2×#92420—41no—
110C2×#92420—41no—
111C2×#92420—41no—
112#11758213—81no—
113D61⋊C8—81no—
114Q16×C61—42no—
115C2×C8×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61C22⋊C411yescharacteristic
118C22⋊C4×C61—21no—
119#11758201—42no—
120#11758198—21no—
121#11758198—21no—
122#11758198—21no—
123#11758198—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128C4⋊Dic61—41no—
129C4⋊Dic61—41no—
130C4⋊Dic61C22⋊C411yescharacteristic
131#11758196—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
141C22×D61—21no—
142Q8×C61—22no—
143Q8×C61—22no—
144Q8×C61—41no—
145Q8×C61—41no—
146Q8×C61—41no—
147C2×C4×C61—22no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61C2×C22⋊C411yescharacteristic
154C2×C4×C61C4×D411yescharacteristic
155C22⋊D61—41no—
156C22⋊D61—41no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61#12011yescharacteristic
166C2×Dic61#12111yescharacteristic
167C2×Dic61#12111yescharacteristic
168C2×Dic61#12311yescharacteristic
169D244—41no—
170C4×D61—41no—
171C4×D61—41no—
172#92420—42no—
173#92420—42no—
174#92420—41no—
175#92420—41no—
176#92420—41no—
177#92420—41no—
178C8×C61—41no—
179#92418—41no—
180#9051—611nomaximal, Sylow
181C22×C61—21no—
182C22×C61—21no—
183C22×C61#38611yescharacteristic
184C22×C61#44311yescharacteristic
185C22×C61#44411yescharacteristic
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—42no—
193C4×C61—41no—
194Dic61—21no—
195Dic61—21no—
196Dic61—21no—
197Dic61—41no—
198Dic61—81no—
199Dic61#45511yescharacteristic
200Dic61#45611yescharacteristic
201#3108—611no—
202#2992—611no—
203#1985—611no—
204#1524—611no—
205#1491—611no—
206#1302—611no—
207#1283—611no—
208C2×C61—21no—
209C2×C61—21no—
210C2×C61#187611yescharacteristic
211C2×C61#188211yescharacteristic
212C2×C61#189111yescharacteristic
213D61—81no—
214#529—611no—
215C2×C4×Q8—611no—
216#483—611no—
217#480—611no—
218#479—1221no—
219#464—1221no—
220#451#692311yescharacteristic
221#448—611no—
222#446—1221no—
223C4×Q16—1221no—
224C4×SD16—1221no—
225#435—1221no—
226#435—1221no—
227C8×D4—1221no—
228#433—1221no—
229#432—611no—
230#431—611no—
231#424—1221no—
232C2×C4⋊C8—611no—
233C4×M16—611no—
234C2×#97—611no—
235#336—1221no—
236#336—1221no—
237#330—1221no—
238#329—1221no—
239Q8⋊C8—1221no—
240Q8⋊C8—1221no—
241C61#905111yescharacteristic, complemented, Sylow
242C22×Q8C2×#692311yescharacteristic
243C2×Q16—21no—
244C2×SD16—1221no—
245C2×M16—1221no—
246C2×M16—1221no—
247C22×C8—611no—
248C22×C8—611no—
249C22×C8—1221no—
250C22×C8—1221no—
251#126—1221no—
252#125—611no—
253#124—611no—
254#123—1221no—
255C22⋊Q8C2×#692311yescharacteristic
256#121—611no—
257C4×Q8—611no—
258C4×Q8—1221no—
259C4×Q8—1221no—
260C4×Q8—1221no—
261C4×Q8—1221no—
262C4×D4—611no—
263C4×D4—1221no—
264#117—1221no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—1221no—
267C2×C42—611no—
268C2×C42—1221no—
269#107—1221no—
270#106—1221no—
271C4⋊C8—611no—
272C4⋊C8—611no—
273C4⋊C8—1221no—
274C4⋊C8—1221no—
275C4⋊C8—1221no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278#103—21no—
279#103—1221no—
280#103—1221no—
281#102—1221no—
282C22⋊C8—611no—
283C22⋊C8—1221no—
284C22⋊C8—1221no—
285C22⋊C8—1221no—
286C22⋊C8C2×#692311yescharacteristic
287#97—1221no—
288#97—1221no—
289#97—1221no—
290#97—1221no—
291#97—1221no—
292C4×C8—1221no—
293C4×C8—1221no—
294C4×C8—1221no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—42no—
298C2×Q8C22⋊#692311yescharacteristic
299C2×D4—611no—
300C2×D4—1221no—
301C22×C4—21no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4C22×#692311yescharacteristic
307Q16—42no—
308SD16—2442no—
309M16—1222no—
310M16—4881no—
311M16—2441no—
312C2×C8—21no—
313C2×C8—1221no—
314C2×C8—1221no—
315C2×C8—1221no—
316C2×C8—1221no—
317C2×C8—1222no—
318C2×C8—1221no—
319C2×C8—4881no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8—2441no—
325C4⋊C4—21no—
326C4⋊C4—611no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—2441no—
333C4⋊C4—2441no—
334C4⋊C4C22⋊#692311yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C42—611no—
341C42—611no—
342C42—611no—
343C42—611no—
344C42—1221no—
345C42—2441no—
346C42—2441no—
347C23—1221no—
348C23D4×#692311yescharacteristic
349Q8—22no—
350Q8—22no—
351Q8—41no—
352Q8—41no—
353Q8—41no—
354D4—2441no—
355D4—2441no—
356D4—2441no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—611no—
364C2×C4—611no—
365C2×C4—611no—
366C2×C4—611no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4C2×C22⋊#692311yescharacteristic
378C2×C4D4×#692311yescharacteristic
379C8—41no—
380C8—2441no—
381C8—2441no—
382C8—2441no—
383C8—2441no—
384C8—2441no—
385C8—2442no—
386C8—2442no—
387C22—21no—
388C22—21no—
389C22—2441no—
390C22—2441no—
391C22—2441no—
392C22#1684071011yescharacteristic
393C22#1684080611yescharacteristic
394C22#1684080811yescharacteristic
395C4—21no—
396C4—21no—
397C4—41no—
398C4—42no—
399C4—41no—
400C4—611no—
401C4—611no—
402C4—1221no—
403C4—1221no—
404C4—1221no—
405C4—4881no—
406C4—2441no—
407C2—21no—
408C2—21no—
409C2—4881no—
410C2#2146180911yescharacteristic
411C2#2146181811yescharacteristic
412C2#2146183011yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#451C4
socleC22×C61#386
prime radical#14519751C2×C4
cosocleC2×C4×Dic61C23
hypercenter#451#6923
hypocenterC61#9051
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
2. #21461993C2semidirect
4. #21461161C2semidirect
5. #21460714C2semidirect
6. #21460663C2semidirect
241. C61#9051semidirect

Maximal subgroups

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

subgroupindex
#214627582
#214619932
#214612722
#214611612
#214607142
#214606632
#214559002
#905161