Finite Group Databasebeta

← #29577839

Subgroups — #29577839

Order 15616.

614 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 93 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#21450089C211yesmaximal, characteristic
2#21448414C211yesmaximal, characteristic
3#21445918C211yesmaximal, characteristic, complemented
4#21444145C211yesmaximal, characteristic
5#21443673C211yesmaximal, characteristic, complemented
6#21443672C211yesmaximal, characteristic, complemented
7C61×#1826C211yesmaximal, characteristic, complemented
8C22×#11758198C2211yescharacteristic
9#16839726C2211yescharacteristic
10#16839697C412yescomplemented
11#16839688C412yescomplemented
12#16839653—22no—
13#16839653—22no—
14#16839651—22no—
15#16839634—21no—
16#16839625C2211yescharacteristic
17#16839620—21no—
18#16839617—21no—
19#16839617—21no—
20C4×C22⋊Dic61C2211yescharacteristic
21#16839521—22no—
22#16839485—22no—
23C2×#117×C61C2211yescharacteristic
24C61×#407C2211yescharacteristic
25C4×C22⋊C4×C61C2211yescharacteristic
26C61×#339—22no—
27C24×D61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C2×#11758194—21no—
30C2×#11758196—22no—
31C2×#11758196—22no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—22no—
39C2×#11758198—22no—
40C2×#11758198—22no—
41C2×#11758198—22no—
42C2×#11758198C2×C412yes—
43C2×#11758198D412yes—
44C2×C4×Dic61D412yes—
45C22⋊#92418—21no—
46C22⋊#92418—21no—
47#14519684—22no—
48#14519684—21no—
49#14519684—21no—
50#14519684—22no—
51#14519684C2×C412yes—
52C23×C4×C61C2311yescharacteristic
53C2×M16×C61—21no—
54#117×C61—21no—
55#117×C61—21no—
56#117×C61—21no—
57#117×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C42×C61—21no—
63C2×C42×C61D412yes—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66#95×C61—21no—
67C24×C61C2×D411yescharacteristic
68C23×D61—21no—
69C23×D61—21no—
70C23×D61—42no—
71C23×D61—42no—
72C23×D61—81no—
73C23×D61C22⋊C412yes—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—22no—
77C22×C4×C61—42no—
78C22×C4×C61C22×C411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C22×C4×C61#4111yescharacteristic
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—22no—
87C22×Dic61—22no—
88C22×Dic61—81no—
89C22×Dic61C22⋊C412yes—
90M16×C61—42no—
91C2×C8×C61—41no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—21no—
96C22⋊C4×C61—42no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C42×C61—42no—
100C42×C61—41no—
101C42×C61—41no—
102C22⋊Dic61—42no—
103C22⋊Dic61—42no—
104#11758198—22no—
105#11758198—22no—
106#11758198—22no—
107#11758198—22no—
108#11758198—44no—
109#11758198—82no—
110#11758198—82no—
111#11758198—82no—
112#11758196—82no—
113#11758196—82no—
114C4×Dic61—42no—
115#11758194—42no—
116C2×#92418—41no—
117C23×C61—22no—
118C23×C61—22no—
119C23×C61—41no—
120C23×C61C2×C22⋊C411yescharacteristic
121C23×C61#12011yescharacteristic
122C23×C61#12311yescharacteristic
123C22×D61—22no—
124C22×D61—22no—
125C22×D61—22no—
126C22×D61—42no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—81no—
133C22×D61—81no—
134C22×D61—88no—
135C2×C4×C61—22no—
136C2×C4×C61—22no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—42no—
147C2×C4×C61—42no—
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×Dic61—22no—
153C2×Dic61—42no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160C2×Dic61—42no—
161C2×Dic61—81no—
162C8×C61—81no—
163#92418—81no—
164#9481—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—44no—
173C22×C61#38611yescharacteristic
174C22×C61#42112yes—
175C22×C61#45812yes—
176C2×D61—44no—
177C2×D61—42no—
178C2×D61—42no—
179C2×D61—42no—
180C2×D61—84no—
181C2×D61—84no—
182C2×D61—82no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—82no—
188C4×C61—81no—
189C4×C61—81no—
190Dic61—42no—
191Dic61—82no—
192Dic61—82no—
193#2482—611no—
194#2312—611no—
195#1826—611no—
196#1826D6111yescharacteristic, complemented
197#1462—611no—
198#1284—611no—
199#1284—611no—
200C2×C61—22no—
201C2×C61—22no—
202C2×C61—41no—
203C2×C61#189011yescharacteristic
204C2×C61#189711yescharacteristic
205C2×C61#191111yescharacteristic
206D61—82no—
207C2×#117C2×D6111yescharacteristic
208C22×C22⋊C4—611no—
209#407—611no—
210#407C2×D6111yescharacteristic
211#399—612no—
212#397—612no—
213#388—1222no—
214#388—1222no—
215#388—1222no—
216#385—1221no—
217#381—611no—
218#380—1221no—
219#379—1221no—
220#379—1221no—
221C4×C22⋊C4—611no—
222C4×C22⋊C4C2×D6111yescharacteristic
223#339—22no—
224#339—1222no—
225#323—1222no—
226C61#948111yescharacteristic, complemented, Sylow
227C25—611no—
228C23×C4—611no—
229C23×C4C22×D6111yescharacteristic
230C2×M16—21no—
231C2×M16—1221no—
232#117—21no—
233#117—21no—
234#117—21no—
235#117—21no—
236C2×C4⋊C4—1222no—
237C2×C4⋊C4—1222no—
238C2×C4⋊C4C4×D6111yescharacteristic
239C2×C4⋊C4C4×D6111yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—612no—
243C2×C22⋊C4—612no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1222no—
249C2×C22⋊C4—1222no—
250C2×C22⋊C4—1222no—
251C2×C22⋊C4—1222no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C42—21no—
255C2×C42—612no—
256C2×C42C22⋊D6112yes—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—1221no—
260C22⋊C8—1221no—
261#95—21no—
262#95—612no—
263#95—1222no—
264#95—1222no—
265#95—1221no—
266#95—1221no—
267C24—612no—
268C24—1221no—
269C24—1221no—
270C24—4881no—
271C24—2442no—
272C24—2442no—
273C24D4×D6111yescharacteristic
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—42no—
278C22×C4—612no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1222no—
282C22×C4—1222no—
283C22×C4—4881no—
284C22×C4C2×C4×D6111yescharacteristic
285C22×C4#1175822211yescharacteristic
286C22×C4D4×D6111yescharacteristic
287C22×C4D4×D6111yescharacteristic
288C22×C4#1175822411yescharacteristic
289C22×C4C2×C22⋊D6111yescharacteristic
290M16—42no—
291M16—2442no—
292C2×C8—41no—
293C2×C8—2441no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—4882no—
299C4⋊C4—4882no—
300C22⋊C4—42no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—1222no—
304C22⋊C4—1222no—
305C22⋊C4—1222no—
306C22⋊C4—1222no—
307C22⋊C4—4882no—
308C22⋊C4—4882no—
309C22⋊C4—4882no—
310C22⋊C4—2444no—
311C22⋊C4—2442no—
312C22⋊C4—2442no—
313C42—42no—
314C42—41no—
315C42—41no—
316C42—2442no—
317C23—22no—
318C23—22no—
319C23—41no—
320C23—1222no—
321C23—1222no—
322C23—1222no—
323C23—4881no—
324C23—4881no—
325C23—4888no—
326C23—2442no—
327C23—2442no—
328C23—2442no—
329C23—2442no—
330C23—2442no—
331C23—2442no—
332C23C22⋊C4×D6111yescharacteristic
333C23#1451974511yescharacteristic
334C23#1451975911yescharacteristic
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—1222no—
349C2×C4—4881no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2442no—
358C2×C4#1451973711yescharacteristic
359C2×C4C4×C22⋊D6111yescharacteristic
360C2×C4#1451974811yescharacteristic
361C2×C4#1451975011yescharacteristic
362C8—81no—
363C8—4881no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—44no—
372C22—4882no—
373C22—4884no—
374C22—4884no—
375C22—2444no—
376C22—2442no—
377C22—2442no—
378C22—2442no—
379C22#1683963811yescharacteristic
380C22#1683977712yes—
381C22#1683995112yes—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—82no—
387C4—81no—
388C4—81no—
389C4—4882no—
390C4—4882no—
391C4—2442no—
392C2—22no—
393C2—22no—
394C2—41no—
395C2—4882no—
396C2#2144622911yescharacteristic
397C2#2144626411yescharacteristic
398C2#2144634811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1826C2
socleC22×C61#386
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenter#1826D61
hypocenterC61#9481
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
3. #21445918C2semidirect
5. #21443673C2semidirect
6. #21443672C2semidirect
7. C61×#1826C2semidirect
10. #16839697C4semidirect
11. #16839688C4semidirect
196. #1826D61semidirect
226. C61#9481semidirect

Maximal subgroups

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

subgroupindex
#214500892
#214484142
#214459182
#214441452
#214436732
#214436722
C61×#18262
#948161