Finite Group Databasebeta

← #30615380

Subgroups — #30615380

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840777C212yesmaximal
2C22×#14519848C211yesmaximal, characteristic
3C2×D61⋊#108C211yesmaximal, characteristic
4#21462462C212yesmaximal
5#21461761C214yesmaximal, complemented
6#21461760C212yesmaximal, complemented
7#21461759C212yesmaximal, complemented
8#405×D61C211yesmaximal, characteristic
9C22×#11758213C2212yes—
10C2×D61⋊M16C2212yes—
11#16840777—28no—
12C2×#14519848—24no—
13C2×#14519848C2211yescharacteristic
14C2×#14519848C2214yes—
15C2×#14519848C2212yes—
16C2×#14519848C2212yes—
17C2×#14519848C2211yescharacteristic
18D61⋊#108—24no—
19C2×#14519847C2212yes—
20C2×#14519847C2214yes—
21#16840769—24no—
22#16840768—24no—
23#16840767C2214yes—
24#16840766C2214yes—
25C2×M16×D61C2211yescharacteristic
26C22×C8×D61C2211yescharacteristic
27#117×D61C2211yescharacteristic
28#16839720C411yescharacteristic
29#16839719C412yes—
30#16839718C411yescharacteristic
31#16839717C411yescharacteristic
32#16839716C412yes—
33#97×D61C2212yes—
34C4×C8×D61C2212yes—
35C61×#405C411yescharacteristic
36C2×#11758213—24no—
37C2×#11758213—24no—
38C2×#11758213—22no—
39C2×#11758213C2312yes—
40C2×#11758213C2314yes—
41C2×#11758213C2312yes—
42D61⋊M16—24no—
43D61⋊M16—24no—
44C2×#11758217—22no—
45C2×D61⋊C8—22no—
46C22×#92420—22no—
47#14519848—22no—
48#14519848—22no—
49#14519848—24no—
50#14519848—24no—
51#14519848—28no—
52#14519847—24no—
53#14519847—28no—
54#14519844—28no—
55C4⋊#92420—28no—
56C22×C4×D61C2311yescharacteristic
57C2×#11758194C2×C411yescharacteristic
58C2×#11758189C2×C412yes—
59M16×D61D414yes—
60M16×D61Q814yes—
61C22×#92418C2×C411yescharacteristic
62C2×C8×D61C2×C411yescharacteristic
63C2×C8×D61C2×C411yescharacteristic
64C2×C8×D61D414yes—
65C2×C8×D61Q814yes—
66C2×C8×D61C2311yescharacteristic
67C2×C8×D61C2312yes—
68C2×C8×D61C2311yescharacteristic
69#14519736C2×C411yescharacteristic
70#14519735D412yes—
71#14519734C2×C412yes—
72#14519733D412yes—
73C4⋊C4×D61Q812yes—
74C22⋊C4×D61Q812yes—
75C42×D61C2312yes—
76#14519688C2×C412yes—
77#14519687C2×C412yes—
78#14519687C2×C412yes—
79C4×#92418C2×C412yes—
80C8×Dic61C2×C412yes—
81C8×Dic61C2×C412yes—
82C2×M16×C61C2×C411yescharacteristic
83C22×C8×C61C2×C411yescharacteristic
84#117×C61C2×C411yescharacteristic
85#97×C61C2×C412yes—
86C4×C8×C61C2×C412yes—
87C23×D61C2×Q811yescharacteristic
88C22×C4×C61C22×C411yescharacteristic
89C22×Dic61C2×D411yescharacteristic
90C2×C4×D61C22×C411yescharacteristic
91C2×C4×D61C2×D412yes—
92C2×C4×D61C2×D412yes—
93C2×C4×D61C2×D411yescharacteristic
94C2×C4×D61C2×Q814yes—
95C2×C4×D61C2×Q812yes—
96C2×C4×D61C2×Q812yes—
97C2×C4×D61C2×Q811yescharacteristic
98C2×C4×D61C2411yescharacteristic
99#11758217—44no—
100C2×#92420—22no—
101C2×#92420—24no—
102C2×#92420—22no—
103C2×#92420—44no—
104#11758213—22no—
105#11758213—22no—
106#11758213—22no—
107#11758213—24no—
108#11758213—22no—
109#11758213—24no—
110#11758213—44no—
111D61⋊C8—44no—
112M16×C61C4⋊C414yes—
113C2×C8×C61C4⋊C414yes—
114C2×C8×C61C22×C411yescharacteristic
115C2×C8×C61C22×C412yes—
116C2×C8×C61C22×C411yescharacteristic
117C4⋊C4×C61C4⋊C412yes—
118C22⋊C4×C61C4⋊C412yes—
119C42×C61C22×C412yes—
120C22⋊Dic61C4⋊C412yes—
121#11758198C4⋊C414yes—
122C4⋊Dic61C4⋊C412yes—
123#11758196C4⋊C414yes—
124C4×Dic61C22×C412yes—
125C4×Dic61C2×D414yes—
126#11758194C4⋊C414yes—
127C2×#92418C4⋊C414yes—
128C2×#92418C22×C411yescharacteristic
129C2×#92418C22×C412yes—
130C2×#92418C22×C411yescharacteristic
131#11758189C4⋊C418yes—
132C8×D61C4⋊C414yes—
133C8×D61C4⋊C414yes—
134C8×D61C2×D412yes—
135C8×D61C2×D414yes—
136C8×D61C2×D412yes—
137C8×D61C2×Q812yes—
138C8×D61C2×Q812yes—
139C8×D61C2×Q814yes—
140C23×C61C2×C4⋊C411yescharacteristic
141C22×D61—42no—
142C22×D61C2×C4⋊C411yescharacteristic
143C22×D61C4⋊Q812yes—
144C22×D61C4⋊Q812yes—
145C22×D61C22×Q811yescharacteristic
146C2×C4×C61C2×C4⋊C414yes—
147C2×C4×C61C2×C4⋊C412yes—
148C2×C4×C61C2×C4⋊C412yes—
149C2×C4×C61C2×C4⋊C411yescharacteristic
150C2×C4×C61C23×C411yescharacteristic
151C2×Dic61C2×C4⋊C414yes—
152C2×Dic61C2×C4⋊C411yescharacteristic
153C2×Dic61#12712yes—
154C2×Dic61C4⋊Q812yes—
155C2×Dic61C22×D411yescharacteristic
156C4×D61—44no—
157C4×D61C2×C4⋊C412yes—
158C4×D61C2×C4⋊C412yes—
159C4×D61#12712yes—
160C4×D61C4⋊Q812yes—
161C4×D61C4⋊Q812yes—
162C4×D61C4⋊Q812yes—
163C4×D61C22×D411yescharacteristic
164C4×D61C22×D411yescharacteristic
165C4×D61C22×Q811yescharacteristic
166C4×D61C22×Q811yescharacteristic
167#92420—42no—
168#92420—42no—
169#92420—44no—
170C8×C61C2×C4⋊C412yes—
171C8×C61C2×C4⋊C412yes—
172C8×C61C2×C4⋊C414yes—
173#92418C2×C4⋊C412yes—
174#92418C2×C4⋊C412yes—
175#92418C2×C4⋊C414yes—
176#20807—611nomaximal, Sylow
177C22×C61—22no—
178C22×C61#38412yes—
179C22×C61C22×C4⋊C411yescharacteristic
180C2×D61—22no—
181C2×D61—22no—
182C2×D61—42no—
183C2×D61—42no—
184C2×D61#38412yes—
185C2×D61C2×C4⋊Q811yescharacteristic
186C2×D61C2×C4⋊Q811yescharacteristic
187C4×C61—24no—
188C4×C61#38412yes—
189C4×C61C22×C4⋊C411yescharacteristic
190C4×C61C22×C4⋊C411yescharacteristic
191Dic61—24no—
192Dic61#38412yes—
193Dic61C2×#12711yescharacteristic
194Dic61C2×C4⋊Q811yescharacteristic
195C2×#430—612no—
196C22×#108—611no—
197C22×#108—611no—
198#2905—612no—
199C2×#405—611no—
200#1849—614no—
201#1848—612no—
202#1848—612no—
203C2×C61—22no—
204C2×C61C2×#38411yescharacteristic
205C2×C61#291612yes—
206D61—21no—
207D61—21no—
208D61—22no—
209C22×M16—611no—
210C22×M16—612no—
211C22×M16—612no—
212C23×C8—611no—
213C2×#117—611no—
214#430—1228no—
215C2×#108—611no—
216C2×#108—612no—
217C2×#108—611no—
218C2×#108—614no—
219C2×#108—614no—
220C2×#108—612no—
221C2×#108—612no—
222C2×#108—1224no—
223C2×#108—1224no—
224#424—1224no—
225#424—1224no—
226#423—614no—
227#423—614no—
228#405—611no—
229#405—611no—
230#405—611no—
231#405—612no—
232#405—612no—
233#405#692311yescharacteristic
234C2×#97—612no—
235C2×C4×C8—612no—
236C61#2080711yescharacteristic, complemented, Sylow
237C23×C4—611no—
238C2×M16—611no—
239C2×M16—614no—
240C2×M16—614no—
241C2×M16—612no—
242C2×M16—612no—
243C2×M16—612no—
244C2×M16—614no—
245C2×M16—1222no—
246C2×M16—1222no—
247C2×M16—1224no—
248C2×M16—1224no—
249C2×M16—1224no—
250C2×M16—1224no—
251C2×M16C2×#692311yescharacteristic
252C22×C8—611no—
253C22×C8—614no—
254C22×C8—614no—
255C22×C8—611no—
256C22×C8—611no—
257C22×C8—611no—
258C22×C8—611no—
259C22×C8—612no—
260C22×C8—1222no—
261C22×C8—1222no—
262C22×C8C2×#692311yescharacteristic
263#117—611no—
264#117—612no—
265#117—612no—
266#117—612no—
267#117C2×#692311yescharacteristic
268C2×C4⋊C4—612no—
269C2×C22⋊C4—612no—
270C2×C42—612no—
271#108—1224no—
272#108—1228no—
273#108—1222no—
274#108—1222no—
275#108—1224no—
276#108—1224no—
277#108—1228no—
278C4⋊C8—1228no—
279C4⋊C8—1228no—
280#97—612no—
281#97—612no—
282#97—612no—
283#97C2×#692312yes—
284C4×C8—612no—
285C4×C8—612no—
286C4×C8—612no—
287C4×C8C2×#692312yes—
288C24—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—612no—
295C22×C4—612no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—614no—
299C22×C4C22×#692311yescharacteristic
300M16—614no—
301M16—618no—
302M16—1222no—
303M16—1222no—
304M16—1222no—
305M16—1224no—
306M16—1224no—
307M16—1222no—
308M16—2444no—
309M16—2444no—
310M16C4⋊#692314yes—
311C2×C8—614no—
312C2×C8—611no—
313C2×C8—612no—
314C2×C8—611no—
315C2×C8—612no—
316C2×C8—612no—
317C2×C8—614no—
318C2×C8—614no—
319C2×C8—614no—
320C2×C8—612no—
321C2×C8—612no—
322C2×C8—614no—
323C2×C8—1222no—
324C2×C8—1224no—
325C2×C8—1222no—
326C2×C8—2444no—
327C2×C8—2444no—
328C2×C8C4⋊#692314yes—
329C2×C8C22×#692311yescharacteristic
330C2×C8C22×#692312yes—
331C2×C8C22×#692311yescharacteristic
332C4⋊C4—614no—
333C4⋊C4—612no—
334C4⋊C4C4⋊#692312yes—
335C22⋊C4—612no—
336C22⋊C4—614no—
337C22⋊C4C4⋊#692312yes—
338C42—614no—
339C42—612no—
340C42C22×#692312yes—
341C23—611no—
342C23—611no—
343C23—612no—
344C23—612no—
345C23—2442no—
346C23C2×C4⋊#692311yescharacteristic
347C2×C4—612no—
348C2×C4—612no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—612no—
352C2×C4—612no—
353C2×C4—612no—
354C2×C4—612no—
355C2×C4—612no—
356C2×C4—612no—
357C2×C4—611no—
358C2×C4—611no—
359C2×C4—611no—
360C2×C4—611no—
361C2×C4—614no—
362C2×C4—2444no—
363C2×C4C2×C4⋊#692314yes—
364C2×C4C2×C4⋊#692311yescharacteristic
365C2×C4C2×C4⋊#692312yes—
366C2×C4C2×C4⋊#692312yes—
367C2×C4C23×#692311yescharacteristic
368C8—612no—
369C8—612no—
370C8—614no—
371C8—2442no—
372C8—2442no—
373C8—2444no—
374C8C2×C4⋊#692312yes—
375C8C2×C4⋊#692312yes—
376C8C2×C4⋊#692314yes—
377C22—22no—
378C22—611no—
379C22—611no—
380C22—612no—
381C22—1222no—
382C22—1222no—
383C22—2442no—
384C22—2442no—
385C22#1684070812yes—
386C22C22×C4⋊#692311yescharacteristic
387C4—24no—
388C4—611no—
389C4—611no—
390C4—612no—
391C4—1224no—
392C4#1684070812yes—
393C4C22×C4⋊#692311yescharacteristic
394C4C22×C4⋊#692311yescharacteristic
395C2—22no—
396C2—1221no—
397C2—1221no—
398C2—1222no—
399C2C2×#1684070811yescharacteristic
400C2#2146248112yes—
subgroupG/H
centerC22C22×C4⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#405C4
socleC22×C61C22×C4⋊C4
prime radicalC23×D61C2×Q8
cosocleC2×C4×D61C24
hypercenter#405#6923
hypocenterC61#20807
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
5. #21461761C2semidirect
6. #21461760C2semidirect
7. #21461759C2semidirect
236. C61#20807semidirect

Maximal subgroups

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

subgroupindex
C2×#168407772
C22×#145198482
C2×D61⋊#1082
#214624622
#214617612
#214617602
#214617592
#405×D612
#2080761