Finite Group Databasebeta

← #29577981

Subgroups — #29577981

Order 15616.

524 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 95 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#21454846C211yesmaximal, characteristic
2#21450137C211yesmaximal, characteristic
3#21445897C211yesmaximal, characteristic, complemented
4#21445897C211yesmaximal, characteristic, complemented
5#21444155C211yesmaximal, characteristic
6#21443725C211yesmaximal, characteristic, complemented
7C61×#1305C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D61C2211yescharacteristic
9C22×C4⋊Dic61C2211yescharacteristic
10#16839836—22no—
11#16839831—22no—
12#16839816—21no—
13#16839726C2211yescharacteristic
14#16839726C2211yescharacteristic
15C22⋊C8×D61—21no—
16#16839702—21no—
17#16839699—21no—
18#16839661—21no—
19#16839639C412yes—
20#16839637C412yes—
21#16839619—21no—
22#16839530—22no—
23#16839530—22no—
24#16839487—21no—
25#16839485—21no—
26C61×#407C2211yescharacteristic
27C61×#407C2211yescharacteristic
28C61×#380C2211yescharacteristic
29C22×C22⋊D61C2×C411yescharacteristic
30C23×Dic61C2×C412yes—
31C22×C4×D61D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758194D412yes—
34C2×C8×D61—22no—
35C4×C22⋊D61—21no—
36C4×C22⋊D61—21no—
37C4×C22⋊D61—21no—
38C4×C22⋊D61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—22no—
46C2×#11758196D411yescharacteristic
47C2×C22⋊Dic61C2×C411yescharacteristic
48C2×#11758198—22no—
49C2×#11758198D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51#14519706—22no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56#14519689—22no—
57#14519687—22no—
58#14519684—22no—
59#14519684—22no—
60C23×C4×C61C2311yescharacteristic
61C2×M16×C61—21no—
62C2×M16×C61D412yes—
63C2×C4⋊C4×C61—21no—
64C2×C22⋊C4×C61C2×C412yes—
65C22⋊C8×C61—21no—
66C22⋊C8×C61—21no—
67C22⋊C8×C61—21no—
68C22⋊C8×C61—21no—
69#95×C61—21no—
70C24×C61C22×C411yescharacteristic
71C23×D61C22⋊C411yescharacteristic
72C22×C4×C61—22no—
73C22×C4×C61—42no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C2×C22⋊D61—21no—
81C2×C22⋊D61—21no—
82C2×C22⋊D61—22no—
83C2×C22⋊D61—41no—
84C22×Dic61—22no—
85C22×Dic61—22no—
86C22×Dic61—22no—
87C22×Dic61—82no—
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—42no—
94M16×C61—42no—
95M16×C61—42no—
96C2×C8×C61—22no—
97C2×C8×C61—41no—
98C4⋊C4×C61—42no—
99C22⋊C4×C61—42no—
100C22⋊Dic61—21no—
101C22⋊Dic61—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—82no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107C4⋊Dic61—41no—
108C4⋊Dic61—41no—
109C4⋊Dic61—82no—
110#11758196—21no—
111#11758196—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114#11758194—42no—
115#11758194—42no—
116C2×#92418—22no—
117C2×#92418—41no—
118C8×D61—82no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61C2×C22⋊C411yescharacteristic
124C23×C61C4×D411yescharacteristic
125C23×C61C4×D411yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61#10112yes—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12311yescharacteristic
144C22⋊D61—42no—
145C22⋊D61—42no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—42no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156C2×Dic61—82no—
157C2×Dic61—82no—
158C4×D61—42no—
159C4×D61—81no—
160C8×C61—42no—
161C8×C61—81no—
162#92418—42no—
163#92418—81no—
164#9509—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—21no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61#38611yescharacteristic
176C22×C61C2×#10111yescharacteristic
177C22×C61#41311yescharacteristic
178C2×D61—22no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—42no—
182C2×D61—81no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—82no—
187C4×C61#45812yes—
188Dic61—41no—
189Dic61—41no—
190Dic61—41no—
191Dic61—82no—
192#2973—611no—
193#2487—611no—
194#1821—611no—
195#1821—611no—
196#1465—611no—
197#1305—611no—
198#1305D6111yescharacteristic, complemented
199C2×C61—21no—
200C2×C61—21no—
201C2×C61—41no—
202C2×C61—41no—
203C2×C61#189011yescharacteristic
204C2×C61#190111yescharacteristic
205C2×C61#191411yescharacteristic
206D61—42no—
207C2×C4×D4—611no—
208C22×C4⋊C4—611no—
209#435—1222no—
210#435—1222no—
211#432—1221no—
212#407—611no—
213#407—611no—
214#407C2×D6111yescharacteristic
215#407C2×D6111yescharacteristic
216C2×C22⋊C8—1221no—
217#400—1221no—
218#399—1221no—
219#389—1221no—
220#386—612no—
221#385—612no—
222#380—1221no—
223#380C2×D6111yescharacteristic
224#343—1222no—
225#343—1222no—
226#324—1221no—
227#323—1221no—
228C61#950911yescharacteristic, complemented, Sylow
229C22×D4—611no—
230C23×C4—611no—
231C23×C4—612no—
232C23×C4C22×D6111yescharacteristic
233C2×M16—21no—
234C2×M16—612no—
235C2×M16—1221no—
236C2×M16D24412yes—
237C22×C8—1222no—
238C4×D4—1221no—
239C4×D4—1221no—
240C4×D4—1221no—
241C4×D4—1221no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—1222no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—1221no—
250C2×C4⋊C4—1221no—
251C2×C22⋊C4—611no—
252C2×C22⋊C4—611no—
253C2×C22⋊C4—1222no—
254C2×C22⋊C4C4×D6112yes—
255C2×C42—611no—
256C4⋊C8—1222no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—1222no—
262C22⋊C8—1221no—
263C22⋊C8—1221no—
264C22⋊C8—1221no—
265C22⋊C8—1221no—
266#97—1222no—
267#95—21no—
268#95—1222no—
269#95—1222no—
270C24—611no—
271C24C2×C4×D6111yescharacteristic
272C2×D4—1222no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—2441no—
276C22×C4—22no—
277C22×C4—42no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1222no—
284C22×C4—1222no—
285C22×C4—1222no—
286C22×C4—4882no—
287C22×C4—2442no—
288C22×C4C2×D24411yescharacteristic
289C22×C4#1175822211yescharacteristic
290C22×C4D4×D6111yescharacteristic
291C22×C4D4×D6111yescharacteristic
292C22×C4D4×D6111yescharacteristic
293C22×C4#1175822611yescharacteristic
294M16—42no—
295M16—42no—
296M16—2442no—
297M16—2442no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—1222no—
301C2×C8—4882no—
302C2×C8—2441no—
303C4⋊C4—42no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—4882no—
307C4⋊C4—2441no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C4⋊C4—2441no—
311C22⋊C4—42no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—4882no—
317C42—1221no—
318C42—1221no—
319C23—21no—
320C23—21no—
321C23—41no—
322C23—41no—
323C23—612no—
324C23—1221no—
325C23—1221no—
326C23—2441no—
327C23—2441no—
328C23C22⋊C4×D6111yescharacteristic
329C23#1451973911yescharacteristic
330C23C4×D24411yescharacteristic
331D4—2442no—
332D4—2442no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—4881no—
348C2×C4—4882no—
349C2×C4—4882no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4#1451974711yescharacteristic
357C2×C4#1451975011yescharacteristic
358C2×C4#1451975211yescharacteristic
359C2×C4#1451976211yescharacteristic
360C8—42no—
361C8—81no—
362C8—4881no—
363C8—2442no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22—1222no—
375C22—4881no—
376C22—2442no—
377C22—2441no—
378C22—2441no—
379C22#1683964011yescharacteristic
380C22#101×D6111yescharacteristic
381C22#1683974311yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—82no—
386C4—4882no—
387C4—2441no—
388C4—2441no—
389C4—2441no—
390C4#1683995312yes—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—2442no—
396C2#2144623111yescharacteristic
397C2#2144628611yescharacteristic
398C2#2144636511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1305C2
socleC22×C61#386
prime radicalC22×C22⋊D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1305D61
hypocenterC61#9509
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
3. #21445897C2semidirect
4. #21445897C2semidirect
6. #21443725C2semidirect
7. C61×#1305C2semidirect
198. #1305D61semidirect
228. C61#9509semidirect

Maximal subgroups

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

subgroupindex
#214548462
#214501372
#214458972
#214441552
#214437252
C61×#13052
#950961