Finite Group Databasebeta

← #29575875

Subgroups — #29575875

Order 15616.

478 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455628C211yesmaximal, characteristic
2#21454388C211yesmaximal, characteristic
3C2×#16839511C211yesmaximal, characteristic, complemented
4#21444207C211yesmaximal, characteristic
5#21443715C211yesmaximal, characteristic, complemented
6#21443693C211yesmaximal, characteristic, complemented
7C61×#1549C211yesmaximal, characteristic, complemented
8C2×#14519785—21no—
9C4×#11758222C2211yescharacteristic
10#16840054—21no—
11#16840049—21no—
12#16840044C412yes—
13#16840039C412yes—
14#16839802—21no—
15#16839790—21no—
16#16839787—22no—
17#16839786C2211yescharacteristic
18#16839784—21no—
19C2×C4⋊#92418C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C4⋊C8×D61—21no—
22#16839761—21no—
23#16839511—21no—
24#16839511—21no—
25#16839494—21no—
26#16839491—21no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C61×#332—22no—
31C2×#11758222D411yescharacteristic
32#14519785—42no—
33#14519785—42no—
34C2×#11758194—21no—
35C2×#11758189—22no—
36C22×#92418—21no—
37C22×#92418—21no—
38C2×C8×D61—22no—
39C4×Dic122C2×C411yescharacteristic
40C4×Dic122D411yescharacteristic
41C4×D244C2×C411yescharacteristic
42C4×D244D411yescharacteristic
43C4×C22⋊D61—21no—
44C4×C22⋊D61—21no—
45#14519736D411yescharacteristic
46#14519734—21no—
47C42×D61—21no—
48#14519710—22no—
49#14519708—22no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418C2×C412yes—
55C4⋊#92418D411yescharacteristic
56C4⋊#92418D411yescharacteristic
57#14519706—22no—
58#14519706—22no—
59#14519700—22no—
60#14519697—22no—
61C22×Q8×C61—21no—
62C2×M16×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61C2×C412yes—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61D412yes—
73C22⋊C8×C61—21no—
74C4×C8×C61—21no—
75C2×Q8×C61—22no—
76C2×Q8×C61—41no—
77C2×Q8×C61—82no—
78C22×C4×C61—41no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C2×C22⋊D61—21no—
83#11758222—21no—
84#11758222—21no—
85#11758222SD1612yes—
86#11758222Q1612yes—
87C2×D244C22⋊C411yescharacteristic
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×Dic122C22⋊C411yescharacteristic
92M16×C61—41no—
93M16×C61—41no—
94C2×C8×C61—22no—
95C2×C8×C61—41no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C42×C61C22×C411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C22⋊Dic61—21no—
105#11758198—21no—
106#11758198—21no—
107C4⋊Dic61C22⋊C411yescharacteristic
108C4⋊Dic61C22⋊C411yescharacteristic
109#11758196—21no—
110#11758196—21no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114#11758194—41no—
115#11758194—41no—
116C2×#92418—22no—
117C2×#92418—21no—
118C2×#92418—21no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—81no—
123#11758189—44no—
124C8×D61—44no—
125C23×C61#12311yescharacteristic
126C22×D61—21no—
127Q8×C61—82no—
128Q8×C61—82no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—42no—
133C2×C4×C61—82no—
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61#12011yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61C2×SD1611yescharacteristic
141C2×C4×C61C2×Q1611yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C22⋊D61—22no—
145C22⋊D61—22no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149D244—21no—
150D244#10312yes—
151C4×D61—22no—
152C4×D61—22no—
153C4×D61—41no—
154C4×D61—41no—
155C4×D61—81no—
156Dic122—21no—
157Dic122#10312yes—
158C8×C61—42no—
159C8×C61—81no—
160#92418—42no—
161#92418—41no—
162#92418—41no—
163#92418—81no—
164#9169—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61#38611yescharacteristic
168C22×C61#48311yescharacteristic
169C22×C61#48411yescharacteristic
170C2×D61—22no—
171C2×D61—41no—
172C2×D61—41no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—82no—
177C4×C61C2×#10311yescharacteristic
178C4×C61#41711yescharacteristic
179C4×C61#45011yescharacteristic
180C4×C61#45111yescharacteristic
181C4×C61#47111yescharacteristic
182C4×C61#47311yescharacteristic
183Dic61—22no—
184Dic61—41no—
185Dic61—41no—
186#3079—611no—
187#2906—611no—
188#1549D6111yescharacteristic, complemented
189C2×#333—611no—
190#1477—611no—
191#1301—611no—
192#1292—611no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61#187211yescharacteristic
196C2×C61#190311yescharacteristic
197C2×C61#190811yescharacteristic
198D61—42no—
199C2×#131—1221no—
200C2×C4⋊Q8C2×D6111yescharacteristic
201C4×#41—611no—
202#477—1221no—
203#476—1221no—
204#475—612no—
205#474—612no—
206#431C2×D6111yescharacteristic
207#428—1221no—
208#424—1221no—
209#424—1222no—
210#423—611no—
211#423—1221no—
212#423C2×D6111yescharacteristic
213C2×C4⋊C8—611no—
214C2×C4⋊C8—611no—
215C2×C4⋊C8—1221no—
216#417—1221no—
217#333—1221no—
218#333—1221no—
219#332—22no—
220Q8⋊C8—1221no—
221D4⋊C8—1221no—
222C61#916911yescharacteristic, complemented, Sylow
223C2×#41—611no—
224C22×Q8—21no—
225#131—2442no—
226#131—2442no—
227C2×M16—21no—
228C2×M16—1222no—
229C2×M16—1221no—
230C22×C8—1222no—
231C22×C8—1221no—
232C22×C8—1221no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8C4×D6112yes—
237C4×Q8—611no—
238C4×Q8—611no—
239C4×D4—611no—
240C4×D4—611no—
241C4×D4—1221no—
242C4×D4—1221no—
243#117—611no—
244#117—1221no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42—1221no—
248C2×C42C22×D6111yescharacteristic
249#107—1222no—
250#106—1222no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—612no—
254C4⋊C8—611no—
255C4⋊C8—611no—
256C4⋊C8—1222no—
257C4⋊C8—1222no—
258C4⋊C8—1221no—
259C4⋊C8—1221no—
260C4⋊C8—1221no—
261C4⋊C8—1221no—
262C4⋊C8C22⋊D6112yes—
263#103—1222no—
264#102—1222no—
265C22⋊C8—21no—
266C4×C8—21no—
267#41—612no—
268#41—612no—
269#41—1221no—
270#41—1221no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—82no—
274C2×Q8—611no—
275C2×D4—611no—
276C2×D4—1221no—
277C22×C4—41no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4#1175822211yescharacteristic
282C22×C4D4×D6111yescharacteristic
283C22×C4#1175822411yescharacteristic
284M16—41no—
285M16—41no—
286M16—2444no—
287M16—2441no—
288M16—2441no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—1222no—
292C2×C8—1221no—
293C2×C8—1221no—
294C2×C8—4881no—
295C2×C8—2444no—
296C2×C8—2441no—
297C2×C8—2441no—
298C2×C8—2441no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—611no—
304C4⋊C4—611no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C42—1221no—
311C42—1221no—
312C42—1221no—
313C42C2×C4×D6111yescharacteristic
314C42D4×D6111yescharacteristic
315C42D4×D6111yescharacteristic
316C42C2×C22⋊D6111yescharacteristic
317C23—1221no—
318C23#1451975911yescharacteristic
319Q8—82no—
320Q8—82no—
321Q8—612no—
322Q8—1221no—
323D4—612no—
324D4—1222no—
325D4—1222no—
326D4—1221no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—82no—
332C2×C4—1221no—
333C2×C4—1222no—
334C2×C4—1222no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—4881no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4C22⋊C4×D6111yescharacteristic
341C2×C4#1451973711yescharacteristic
342C2×C4C4×C22⋊D6111yescharacteristic
343C2×C4#1451974511yescharacteristic
344C2×C4#1451974811yescharacteristic
345C2×C4#1451975011yescharacteristic
346C2×C4SD16×D6111yescharacteristic
347C2×C4Q16×D6111yescharacteristic
348C2×C4#1451980411yescharacteristic
349C2×C4#1451980911yescharacteristic
350C8—42no—
351C8—81no—
352C8—4881no—
353C8—2442no—
354C8—2441no—
355C8—2441no—
356C22—21no—
357C22—21no—
358C22—1222no—
359C22—2441no—
360C22—2441no—
361C22#1683963811yescharacteristic
362C22#1684009111yescharacteristic
363C22#1684009611yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—82no—
368C4—1222no—
369C4—2441no—
370C4—2441no—
371C4#103×D6111yescharacteristic
372C4#1683976211yescharacteristic
373C4#1683991111yescharacteristic
374C4#1683991611yescharacteristic
375C4#1684002811yescharacteristic
376C4#1684003611yescharacteristic
377C2—21no—
378C2—21no—
379C2—2442no—
380C2#2144612311yescharacteristic
381C2#2144629611yescharacteristic
382C2#2144633111yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1549C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1549D61
hypocenterC61#9169
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
3. C2×#16839511C2semidirect
5. #21443715C2semidirect
6. #21443693C2semidirect
7. C61×#1549C2semidirect
188. #1549D61semidirect
222. C61#9169semidirect

Maximal subgroups

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

subgroupindex
#214556282
#214543882
C2×#168395112
#214442072
#214437152
#214436932
C61×#15492
#916961