Finite Group Databasebeta

← #29590394

Subgroups — #29590394

Order 15616.

470 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 71 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#21451711C211yesmaximal, characteristic
2#21445610C211yesmaximal, characteristic, complemented
3#21444136C211yesmaximal, characteristic, complemented
4#21443847C211yesmaximal, characteristic, complemented
5#21443845C211yesmaximal, characteristic, complemented
6#21443822C211yesmaximal, characteristic, complemented
7C61×#1345C211yesmaximal, characteristic, complemented
8C2×#14519748C411yescharacteristic
9C2×#14519739C2211yescharacteristic
10C2×#14519693—21no—
11C22⋊C8×D61—21no—
12M16×Dic61—21no—
13#16839701C2211yescharacteristic
14#16839699C411yescharacteristic
15#16839678—21no—
16#16839671—21no—
17#16839670C411yescharacteristic
18#16839655—21no—
19#16839638—21no—
20#16839624C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#394C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×D244D411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C22⋊D61—21no—
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×#11758194—21no—
33C2×C8×D61—41no—
34#14519748—41no—
35#14519748—41no—
36#14519739—41no—
37#14519739—41no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198C2×C411yescharacteristic
45C2×#11758198D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519693—24no—
48C22⋊#92418—21no—
49#14519689—41no—
50#14519687—41no—
51C8×Dic61—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C22×D4×C61C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61C2311yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C22⋊C8×C61—21no—
62#95×C61C2×C411yescharacteristic
63C24×C61—21no—
64C23×D61C22⋊C411yescharacteristic
65C23×D61C22⋊C411yescharacteristic
66C2×D4×C61—41no—
67C2×D4×C61—81no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—42no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61—81no—
75C2×C22⋊D61—81no—
76C2×C22⋊D61—81no—
77C2×C22⋊D61—81no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C2×D244—22no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—41no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—81no—
91C2×C4×D61—81no—
92M16×C61—22no—
93M16×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C4⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—81no—
100C22⋊Dic61—41no—
101C22⋊Dic61—41no—
102C22⋊Dic61—81no—
103#11758198—41no—
104#11758198—41no—
105#11758198—81no—
106#11758198—81no—
107C4⋊Dic61—41no—
108C4⋊Dic61—81no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111#11758194—22no—
112#11758194—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C8×D61—82no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61C2×C22⋊C411yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61#10412yes—
134D4×C61—82no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61#13511yescharacteristic
145C2×C4×C61#13511yescharacteristic
146C22⋊D61—84no—
147C22⋊D61—84no—
148C2×Dic61—21no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61#9911yescharacteristic
158C2×Dic61#9911yescharacteristic
159D244—42no—
160D244—42no—
161C4×D61—42no—
162C4×D61—81no—
163C4×D61—81no—
164C4×D61—81no—
165C8×C61—42no—
166C8×C61—81no—
167#92418—42no—
168#92418—81no—
169#11737—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61C2×#9911yescharacteristic
180C22×C61#41611yescharacteristic
181C22×C61C2×#10411yescharacteristic
182C2×D61—22no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—42no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—41no—
195C4×C61—41no—
196C4×C61—81no—
197Dic61—21no—
198Dic61—21no—
199Dic61—41no—
200Dic61—81no—
201Dic61—81no—
202#2635—611no—
203C4×#100—611no—
204#1459—611no—
205#1353—611no—
206#1353—611no—
207#1345—611no—
208#1345D6111yescharacteristic, complemented
209C2×C61—21no—
210C2×C61—21no—
211C2×C61—161no—
212C2×C61#150111yescharacteristic
213C2×C61#212111yescharacteristic
214C2×C61#213411yescharacteristic
215D61—42no—
216D61—81no—
217C2×#121—611no—
218C2×C4×D4—611no—
219C2×#100—1221no—
220C2×C22⋊C8—1221no—
221C4×M16—1221no—
222#400—611no—
223#399—611no—
224#394—1221no—
225#394C2×D6111yescharacteristic
226#392—611no—
227#392—1221no—
228#388—1221no—
229#386—1221no—
230#381—611no—
231#343—611no—
232#343C2×D6111yescharacteristic
233#324—611no—
234#324C2×D6111yescharacteristic
235#323—1221no—
236C61#1173711yescharacteristic, complemented, Sylow
237C22×D4—611no—
238C22×D4—1221no—
239C22×D4—1221no—
240C22×D4C4×D6111yescharacteristic
241C23×C4—611no—
242C23×C4—611no—
243C2×M16—21no—
244C2×M16—1221no—
245C22×C8—2441no—
246#121—2441no—
247#121—2441no—
248C4×D4—2441no—
249C4×D4—2441no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4C22×D6111yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—611no—
256C2×C22⋊C4—611no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C42—611no—
262#100—1224no—
263C22⋊C8—21no—
264C22⋊C8—1221no—
265C22⋊C8—2441no—
266#97—2441no—
267C4×C8—2441no—
268#95—611no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272#95C4×D6111yescharacteristic
273C24—21no—
274C24—611no—
275C24—611no—
276C2×D4—41no—
277C2×D4—81no—
278C2×D4—1222no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—4881no—
282C2×D4—4881no—
283C2×D4—4881no—
284C2×D4—4881no—
285C2×D4—2441no—
286C2×D4—2442no—
287C2×D4—2442no—
288C22×C4—21no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—4881no—
298C22×C4—4881no—
299C22×C4C2×C4×D6111yescharacteristic
300C22×C4D4×D6111yescharacteristic
301C22×C4D4×D6111yescharacteristic
302M16—22no—
303M16—41no—
304M16—1222no—
305M16—2441no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—4882no—
309C2×C8—2441no—
310C2×C8—2441no—
311C4⋊C4—41no—
312C4⋊C4—4881no—
313C4⋊C4—2441no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—81no—
317C22⋊C4—4881no—
318C22⋊C4—4881no—
319C22⋊C4—4881no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C22⋊C4—2441no—
323C22⋊C4—2441no—
324C42—1221no—
325C42—1221no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—612no—
334C23—1221no—
335C23—1221no—
336C23—1221no—
337C23—1221no—
338C23—1221no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23—2441no—
343C23C22⋊C4×D6111yescharacteristic
344D4—82no—
345D4—4884no—
346D4—4884no—
347D4—2442no—
348D4—2442no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—611no—
359C2×C4—611no—
360C2×C4—1221no—
361C2×C4—4881no—
362C2×C4—4881no—
363C2×C4—4881no—
364C2×C4—2442no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4#1451979611yescharacteristic
374C2×C4#1451979811yescharacteristic
375C8—42no—
376C8—81no—
377C8—4881no—
378C8—2442no—
379C22—21no—
380C22—21no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—1222no—
389C22—4881no—
390C22—4881no—
391C22—4881no—
392C22—2442no—
393C22—2441no—
394C22—2441no—
395C22—2441no—
396C22—2441no—
397C22—2441no—
398C22#99×D6111yescharacteristic
399C22#1683975511yescharacteristic
400C22#104×D6111yescharacteristic
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—81no—
406C4—1221no—
407C4—1221no—
408C4—4881no—
409C4—4881no—
410C4—2441no—
411C2—21no—
412C2—21no—
413C2—161no—
414C2—4881no—
415C2—2442no—
416C2#2144430711yescharacteristic
417C2#2144746211yescharacteristic
418C2#2144750911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1345C2
socleC22×C61C2×#99
prime radical#21451711C2
cosocleC2×C4⋊C4×C61C23
hypercenter#1345D61
hypocenterC61#11737
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #21445610C2semidirect
3. #21444136C2semidirect
4. #21443847C2semidirect
5. #21443845C2semidirect
6. #21443822C2semidirect
7. C61×#1345C2semidirect
208. #1345D61semidirect
236. C61#11737semidirect

Maximal subgroups

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

subgroupindex
#214517112
#214456102
#214441362
#214438472
#214438452
#214438222
C61×#13452
#1173761