Finite Group Databasebeta

← #29595949

Subgroups — #29595949

Order 15616.

450 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454241C211yesmaximal, characteristic
2#21447574C211yesmaximal, characteristic, complemented
3C2×#16839580C211yesmaximal, characteristic, complemented
4C2×#16839547C211yesmaximal, characteristic
5C2×#16839545C211yesmaximal, characteristic
6#21443908C211yesmaximal, characteristic, complemented
7C61×#1379C211yesmaximal, characteristic, complemented
8C2×#14519785C411yescharacteristic
9C2×#14519783C2211yescharacteristic
10#16840230C411yescharacteristic
11C2×#14519717C2211yescharacteristic
12C22×#11758185C2211yescharacteristic
13#16839719—21no—
14#16839718C411yescharacteristic
15#16839716—21no—
16#16839714—21no—
17M16×Dic61C411yescharacteristic
18C2×C8×Dic61C2211yescharacteristic
19C4×C8×D61—21no—
20#16839580—21no—
21#16839580—21no—
22#16839580—21no—
23#16839580—21no—
24#16839547—22no—
25#16839545—22no—
26C2×M32×C61C2211yescharacteristic
27C22×C16×C61C2211yescharacteristic
28C61×#405C2211yescharacteristic
29C2×#11758222C2×C411yescharacteristic
30#14519785—22no—
31#14519785—22no—
32#14519783—21no—
33#14519783—21no—
34#14519783D412yes—
35#14519783Q812yes—
36C2×#11758194C2×C411yescharacteristic
37C2×#11758189—21no—
38C2×#11758189—21no—
39C22×#92418C2×C411yescharacteristic
40C2×C8×D61—21no—
41C2×C8×D61—21no—
42#14519742C811yescharacteristic
43#14519742C811yescharacteristic
44#14519739C811yescharacteristic
45#14519739C811yescharacteristic
46#14519737—21no—
47#14519737—21no—
48#14519734—21no—
49C2×C4×Dic61C2×C411yescharacteristic
50C42×D61—21no—
51#14519717—21no—
52#14519717—21no—
53C2×#11758185—21no—
54C2×#11758185—21no—
55C2×#11758185—21no—
56C2×#11758185—21no—
57#14519688—21no—
58#14519687—21no—
59C4×#92418—21no—
60C8×Dic61—21no—
61C8×Dic61D411yescharacteristic
62C8×Dic61D411yescharacteristic
63C8×Dic61D411yescharacteristic
64C8×Dic61D411yescharacteristic
65C2×M16×C61C2×C411yescharacteristic
66C22×C8×C61C2311yescharacteristic
67#117×C61C2×C411yescharacteristic
68M32×C61—21no—
69M32×C61—21no—
70C2×C16×C61—21no—
71C2×C16×C61—21no—
72C2×C16×C61—21no—
73C2×C16×C61—21no—
74#97×C61—21no—
75C4×C8×C61—21no—
76C22×C4×C61C22×C411yescharacteristic
77C2×C22⋊D61—21no—
78C22×Dic61M1611yescharacteristic
79C22×Dic61M1611yescharacteristic
80#11758222—21no—
81#11758222—21no—
82#11758222C4⋊C412yes—
83#11758222M1612yes—
84C2×D244C2×C811yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×Dic122C2×C811yescharacteristic
89M16×C61—21no—
90M16×C61M1612yes—
91C2×C8×C61—21no—
92C2×C8×C61C2×D411yescharacteristic
93C2×C8×C61C2×D411yescharacteristic
94C2×C8×C61C2×D411yescharacteristic
95C2×C8×C61C2×Q811yescharacteristic
96C2×C8×C61#4111yescharacteristic
97C2×C8×C61#4111yescharacteristic
98C4⋊C4×C61C2×C811yescharacteristic
99C4⋊C4×C61C2×C811yescharacteristic
100C22⋊C4×C61—21no—
101C42×C61—21no—
102#11758198—21no—
103#11758198—21no—
104#11758196—21no—
105#11758196—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61C22⋊C411yescharacteristic
109C4×Dic61C22⋊C411yescharacteristic
110C4×Dic61C2×C811yescharacteristic
111C4×Dic61C2×C811yescharacteristic
112#11758194—21no—
113#11758194C4⋊C412yes—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—21no—
117C2×#92418C22⋊C411yescharacteristic
118C2×#92418C22⋊C411yescharacteristic
119#11758189—24no—
120#11758189—22no—
121#11758189—22no—
122C8×D61—24no—
123C8×D61—22no—
124C8×D61—22no—
125C16×C61—41no—
126C16×C61—41no—
127#11758185—41no—
128#11758185—41no—
129C23×C61C2×M1611yescharacteristic
130C22×D61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61C2×C4⋊C411yescharacteristic
135C2×C4×C61#11711yescharacteristic
136C2×C4×C61C22×C811yescharacteristic
137C2×C4×C61C2×M1611yescharacteristic
138C2×C4×C61C2×M1611yescharacteristic
139C22⋊D61—22no—
140C22⋊D61—22no—
141C2×Dic61—21no—
142C2×Dic61—22no—
143C2×Dic61—41no—
144C2×Dic61C22⋊C811yescharacteristic
145C2×Dic61C22⋊C811yescharacteristic
146C2×Dic61C22⋊C811yescharacteristic
147C2×Dic61C22⋊C811yescharacteristic
148D244—21no—
149D244C4⋊C812yes—
150C4×D61—22no—
151C4×D61—22no—
152C4×D61—42no—
153C4×D61—42no—
154Dic122—21no—
155Dic122C4⋊C812yes—
156C8×C61—22no—
157C8×C61#12111yescharacteristic
158C8×C61#12111yescharacteristic
159C8×C61C22⋊Q811yescharacteristic
160C8×C61C22⋊Q811yescharacteristic
161#92418—22no—
162#92418—21no—
163#92418—21no—
164#12787—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61C2×C22⋊C811yescharacteristic
168C22×C61#42311yescharacteristic
169C22×C61#43211yescharacteristic
170C2×D61—22no—
171C2×D61—41no—
172C2×D61—41no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61#38011yescharacteristic
176C4×C61#40711yescharacteristic
177C4×C61C2×C4⋊C811yescharacteristic
178C4×C61#43111yescharacteristic
179Dic61—22no—
180Dic61—21no—
181Dic61—21no—
182Dic61—21no—
183Dic61#35012yescomplemented
184C4×#131—611no—
185#2150—611no—
186C2×C4⋊C16—611no—
187C2×#350—611no—
188C2×#350—611no—
189#1379—611no—
190#1379D6111yescharacteristic, complemented
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#179711yescharacteristic
194C2×C61C2×#35011yescharacteristic
195C2×C61#211711yescharacteristic
196D61—42no—
197C2×#131—611no—
198C2×#131—611no—
199C4×#41—611no—
200C2×M32—611no—
201C2×M32C2×D6111yescharacteristic
202C22×C16—611no—
203C22×C16C2×D6111yescharacteristic
204#405—611no—
205#405—1221no—
206#405—1221no—
207#405C2×D6111yescharacteristic
208C4×M16—611no—
209C4×M16—1221no—
210C2×C4×C8—611no—
211C2×C4×C8—1221no—
212C4⋊C16—1221no—
213C4⋊C16—1221no—
214C4⋊C16—1221no—
215C4⋊C16—1221no—
216#350—1222no—
217#350—1222no—
218C61#1278711yescharacteristic, complemented, Sylow
219C2×#41—611no—
220#131—612no—
221#131—612no—
222#131—1222no—
223#131—1222no—
224#131—1221no—
225#131—1221no—
226C2×M16—611no—
227C2×M16—1221no—
228C2×M16—1221no—
229C2×M16C4×D6111yescharacteristic
230C22×C8—611no—
231C22×C8—1221no—
232C22×C8—1221no—
233C22×C8C22×D6111yescharacteristic
234C4×Q8—611no—
235C4×Q8—611no—
236C4×D4—611no—
237C4×D4—611no—
238C4×D4—1221no—
239C4×D4—1221no—
240#117—1221no—
241#117C4×D6111yescharacteristic
242C2×C42—611no—
243C2×C42—1221no—
244M32—21no—
245M32—21no—
246M32—1221no—
247M32—1221no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—1221no—
253C2×C16—1221no—
254C2×C16—1221no—
255C2×C16—1221no—
256#97—21no—
257#97—1221no—
258#97—1221no—
259C4×C8—21no—
260C4×C8—611no—
261C4×C8—611no—
262C4×C8—611no—
263C4×C8—611no—
264C4×C8—1221no—
265C4×C8—1221no—
266#41—612no—
267#41—612no—
268#41—1221no—
269#41—1221no—
270C2×Q8—611no—
271C2×D4—611no—
272C2×D4—1221no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4C2×C4×D6111yescharacteristic
279M16—21no—
280M16—612no—
281M16—1224no—
282M16—1221no—
283M16—1222no—
284M16—1222no—
285M16#1175818912yes—
286C2×C8—21no—
287C2×C8—611no—
288C2×C8—611no—
289C2×C8—1224no—
290C2×C8—1221no—
291C2×C8—1221no—
292C2×C8—1221no—
293C2×C8—1222no—
294C2×C8—1222no—
295C2×C8#1175822211yescharacteristic
296C2×C8#1175822211yescharacteristic
297C2×C8D4×D6111yescharacteristic
298C2×C8D4×D6111yescharacteristic
299C2×C8D4×D6111yescharacteristic
300C2×C8Q8×D6111yescharacteristic
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4C8×D6111yescharacteristic
304C4⋊C4C8×D6111yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C42—21no—
309C42—611no—
310C42—611no—
311C42—611no—
312C42—611no—
313C42—1221no—
314C42—1221no—
315C16—41no—
316C16—41no—
317C16—2441no—
318C16—2441no—
319C23—1221no—
320C23M16×D6111yescharacteristic
321Q8—612no—
322Q8—1221no—
323D4—612no—
324D4—1222no—
325D4—1222no—
326D4—1221no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—611no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—1222no—
334C2×C4—1221no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2441no—
340C2×C4C22⋊C4×D6111yescharacteristic
341C2×C4C4⋊C4×D6111yescharacteristic
342C2×C4#1451973411yescharacteristic
343C2×C4C2×C8×D6111yescharacteristic
344C2×C4M16×D6111yescharacteristic
345C2×C4C2×#1175818911yescharacteristic
346C8—22no—
347C8—1221no—
348C8—1221no—
349C8—1222no—
350C8#1451975011yescharacteristic
351C8#1451975011yescharacteristic
352C8#1451975511yescharacteristic
353C8#1451975511yescharacteristic
354C22—21no—
355C22—21no—
356C22—1222no—
357C22—2441no—
358C22—2441no—
359C22C22⋊C8×D6111yescharacteristic
360C22#1683978411yescharacteristic
361C22#1683981711yescharacteristic
362C4—41no—
363C4—41no—
364C4—612no—
365C4—1221no—
366C4—1221no—
367C4—1221no—
368C4—1222no—
369C4#1683962111yescharacteristic
370C4#1683972411yescharacteristic
371C4C4⋊C8×D6111yescharacteristic
372C4#1683981311yescharacteristic
373C2—21no—
374C2—21no—
375C2—2442no—
376C2#2144579811yescharacteristic
377C2#350×D6111yescharacteristic
378C2#2144744511yescharacteristic
subgroupG/H
centerC2×C8D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#1379C2
socleC22×C61C2×C22⋊C8
prime radicalC2×#11758222C2×C4
cosocleC22×C8×C61C23
hypercenter#1379D61
hypocenterC61#12787
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1379

Complements

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

NH ≅ G/Ntype
2. #21447574C2semidirect
3. C2×#16839580C2semidirect
6. #21443908C2semidirect
7. C61×#1379C2semidirect
183. Dic61#350semidirect
190. #1379D61semidirect
218. C61#12787semidirect

Maximal subgroups

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

subgroupindex
#214542412
#214475742
C2×#168395802
C2×#168395472
C2×#168395452
#214439082
C61×#13792
#1278761