Finite Group Databasebeta

← #30605216

Subgroups — #30605216

Order 15616.

612 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461683C211yesmaximal, characteristic, complemented
2#21461074C211yesmaximal, characteristic, complemented
3#21460820C212yesmaximal, complemented
4#21460801C212yesmaximal, complemented
5#21449032C211yesmaximal, characteristic
6#16840765—21no—
7C2×#14519837—21no—
8#16840733—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840605—21no—
12C2×C4×C22⋊D61—21no—
13C2×C4×C22⋊D61C2211yescharacteristic
14#16839681C2211yescharacteristic
15#16839676—21no—
16#16839676C2211yescharacteristic
17#16839673C411yescharacteristic
18#16839670—21no—
19#16839670C411yescharacteristic
20C4×C22⋊Dic61—21no—
21C4×C22⋊Dic61C411yescharacteristic
22C22×#41×C61C411yescharacteristic
23C2×#11758213—41no—
24C2×#11758217—22no—
25#14519844—41no—
26C4⋊#92420—41no—
27#14519837—42no—
28#14519834—41no—
29C22⋊#92420—22no—
30C22×C22⋊D61—21no—
31C22×C22⋊D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C4×C22⋊D61—41no—
34C4×C22⋊D61—41no—
35C4×C22⋊D61—44no—
36C2×#11758196—21no—
37C2×#11758196C2311yescharacteristic
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61D411yescharacteristic
43C2×#11758198—21no—
44C2×#11758198C2×C411yescharacteristic
45C2×C4×Dic61—21no—
46C2×C4×Dic61D411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684C2×C411yescharacteristic
50#14519684C2×C411yescharacteristic
51C2×#41×C61—44no—
52C2×#41×C61—41no—
53C2×#41×C61—41no—
54C22×Q8×C61C2×C411yescharacteristic
55C22×D4×C61—21no—
56C22×D4×C61C2×C411yescharacteristic
57C23×C4×C61—21no—
58C23×C4×C61C2×C411yescharacteristic
59C24×C61—21no—
60C24×C61C22⋊C411yescharacteristic
61C23×D61C22⋊C411yescharacteristic
62#41×C61—44no—
63#41×C61—44no—
64#41×C61—44no—
65#41×C61—44no—
66C2×Q8×C61—42no—
67C2×Q8×C61—41no—
68C2×D4×C61—42no—
69C2×D4×C61—41no—
70C2×D4×C61—42no—
71C2×D4×C61—42no—
72C2×D4×C61—42no—
73C22×C4×C61—24no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—42no—
78C22×C4×C61—42no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61C22⋊C411yescharacteristic
82C22×C4×C61C22×C411yescharacteristic
83C2×C22⋊D61—21no—
84C2×C22⋊D61—21no—
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—42no—
88C2×C22⋊D61—42no—
89C2×C22⋊D61—42no—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C2×D411yescharacteristic
94C22×Dic61C2×D411yescharacteristic
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61—42no—
98#11758217—42no—
99#11758217—42no—
100C2×#92420—42no—
101C2×#92420—42no—
102#11758213—82no—
103C22⋊Dic61—41no—
104C22⋊Dic61—42no—
105C22⋊Dic61—42no—
106C22⋊Dic61—42no—
107C22⋊Dic61—41no—
108C22⋊Dic61—41no—
109#11758198—41no—
110#11758198—42no—
111#11758196—41no—
112#11758196—42no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—42no—
116C23×C61—22no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61C2×C22⋊C411yescharacteristic
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—41no—
133C22×D61—41no—
134Q8×C61—42no—
135Q8×C61—42no—
136D4×C61—42no—
137D4×C61—48no—
138D4×C61—42no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—21no—
142C2×C4×C61—44no—
143C2×C4×C61—42no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—44no—
147C2×C4×C61—42no—
148C2×C4×C61—41no—
149C2×C4×C61#9911yescharacteristic
150C2×C4×C61#9911yescharacteristic
151C22⋊D61—42no—
152C22⋊D61—42no—
153C22⋊D61—48no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—22no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61AGL(1,ℤ/8)11yescharacteristic
167C2×Dic61#13711yescharacteristic
168C4×D61—42no—
169C4×D61—81no—
170#92420—82no—
171#92420—82no—
172#11828—611nomaximal, Sylow
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—42no—
176C22×C61—42no—
177C22×C61—41no—
178C22×C61—42no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61C2×#9911yescharacteristic
188C22×C61#41711yescharacteristic
189C22×C61#42111yescharacteristic
190C2×D61—42no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—81no—
195C4×C61—21no—
196C4×C61—42no—
197C4×C61—41no—
198C4×C61AΣL(1,𝔽16)12yes—
199Dic61—21no—
200Dic61—21no—
201Dic61—42no—
202Dic61—41no—
203Dic61—41no—
204Dic61—81no—
205#2388—611no—
206#1800—611no—
207#1465—611no—
208#1354—612no—
209#1345—612no—
210C2×C61—21no—
211C2×C61—21no—
212C2×C61—81no—
213C2×C61—82no—
214C2×C61#151311yescharacteristic
215C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
216C2×C61#213211yescharacteristic
217D61—81no—
218C22×#41#692311yescharacteristic
219C2×C4×D4—611no—
220C2×C4×D4—1221no—
221#423—1221no—
222C2×#100—1221no—
223#407—1221no—
224#395—611no—
225#394—611no—
226#394—1221no—
227#393—611no—
228#392—611no—
229#392—1221no—
230C4×C22⋊C4—611no—
231C4×C22⋊C4—1221no—
232#343—612no—
233#324—612no—
234#323—1221no—
235C61#1182811yescharacteristic, complemented, Sylow
236C2×#41—44no—
237C2×#41—41no—
238C2×#41—41no—
239C22×Q8C2×#692311yescharacteristic
240C22×D4—21no—
241C22×D4—611no—
242C22×D4—1221no—
243C22×D4C2×#692311yescharacteristic
244C23×C4—21no—
245C23×C4—611no—
246C23×C4C2×#692311yescharacteristic
247C2×M16—1222no—
248C2×M16—2441no—
249C4×D4—2441no—
250C4×D4—2441no—
251C4×D4—2444no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—1221no—
254C2×C22⋊C4—611no—
255C2×C22⋊C4—611no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C42—611no—
262C2×C42—1221no—
263C4⋊C8—2441no—
264C4⋊C8—2441no—
265#100—2442no—
266C22⋊C8—1222no—
267C22⋊C8—2441no—
268#95—611no—
269#95—611no—
270#95—1221no—
271#95—1221no—
272C24—21no—
273C24—611no—
274C24C22⋊#692311yescharacteristic
275#41—44no—
276#41—44no—
277#41—44no—
278#41—44no—
279C2×Q8—42no—
280C2×Q8—41no—
281C2×D4—41no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—2441no—
289C2×D4—2441no—
290C2×D4—2442no—
291C2×D4—2442no—
292C2×D4—2442no—
293C22×C4—24no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—2442no—
309C22×C4C22⋊#692311yescharacteristic
310C22×C4C22×#692311yescharacteristic
311M16—4882no—
312M16—2442no—
313M16—2442no—
314C2×C8—2442no—
315C2×C8—2442no—
316C4⋊C4—2441no—
317C4⋊C4—2442no—
318C22⋊C4—2441no—
319C22⋊C4—2442no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C22⋊C4—2441no—
323C22⋊C4—2442no—
324C22⋊C4—2442no—
325C22⋊C4—2442no—
326C42—1221no—
327C42—1221no—
328C42—2442no—
329C23—22no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—1221no—
342C23—1221no—
343C23—1221no—
344C23—2441no—
345C23—2441no—
346C23C2×C22⋊#692311yescharacteristic
347Q8—42no—
348Q8—42no—
349D4—42no—
350D4—48no—
351D4—42no—
352D4—2442no—
353D4—2442no—
354D4—2448no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—21no—
358C2×C4—44no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—44no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—611no—
366C2×C4—611no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1222no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—4881no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2442no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4#1451983511yescharacteristic
382C2×C4#1451983511yescharacteristic
383C8—4882no—
384C8—4882no—
385C22—21no—
386C22—21no—
387C22—42no—
388C22—42no—
389C22—41no—
390C22—42no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—4881no—
400C22—2442no—
401C22—2441no—
402C22—2441no—
403C22—2441no—
404C22C2×#1451983511yescharacteristic
405C22#1684075311yescharacteristic
406C22#1684075911yescharacteristic
407C4—21no—
408C4—42no—
409C4—41no—
410C4—1221no—
411C4—1221no—
412C4—4881no—
413C4—2442no—
414C4—2441no—
415C4—2441no—
416C4#1684066212yes—
417C2—21no—
418C2—21no—
419C2—82no—
420C2—81no—
421C2—4881no—
422C2#2146123411yescharacteristic
423C2C2×#1684066211yescharacteristic
424C2#2146211011yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×#41×C61C4
socleC22×C61C2×#99
prime radical#21449032C2
cosocleC2×#11758196C23
hypercenterC22×#41#6923
hypocenterC61#11828
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. #21461683C2semidirect
2. #21461074C2semidirect
3. #21460820C2semidirect
4. #21460801C2semidirect
235. C61#11828semidirect

Maximal subgroups

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

subgroupindex
#214616832
#214610742
#214608202
#214608012
#214490322
#1182861