Finite Group Databasebeta

← #29577979

Subgroups — #29577979

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#21450130C211yesmaximal, characteristic
3#21445899C211yesmaximal, characteristic, complemented
4#21444155C211yesmaximal, characteristic
5#21443726C211yesmaximal, characteristic, complemented
6#21443724C211yesmaximal, characteristic, complemented
7C61×#1821C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D61C2211yescharacteristic
9#16839836—22no—
10#16839831—22no—
11#16839816—21no—
12#16839726C2211yescharacteristic
13#16839726C2211yescharacteristic
14C22⋊C8×D61—21no—
15#16839700—21no—
16#16839697—21no—
17#16839658—21no—
18#16839641C412yes—
19#16839635C412yes—
20#16839622C2211yescharacteristic
21#16839619—21no—
22#16839531—22no—
23#16839487—21no—
24#16839485—21no—
25C22×C4⋊C4×C61C2211yescharacteristic
26C61×#407C2211yescharacteristic
27C61×#407C2211yescharacteristic
28C61×#343—22no—
29C22×C22⋊D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758194—21no—
32C2×#11758194D412yes—
33C2×C8×D61—22no—
34C4×C22⋊D61—21no—
35C4×C22⋊D61—21no—
36C4×C22⋊D61—21no—
37C4×C22⋊D61—21no—
38C2×C4⋊Dic61—21no—
39C2×#11758196—22no—
40C2×#11758196D411yescharacteristic
41C2×C22⋊Dic61C2×C411yescharacteristic
42C2×C22⋊Dic61C2×C412yes—
43C2×#11758198—22no—
44C2×#11758198D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519706—22no—
47C22⋊#92418—21no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51#14519689—22no—
52#14519687—22no—
53#14519684—21no—
54#14519684—22no—
55#14519684—22no—
56C23×C4×C61C2×C412yes—
57C23×C4×C61C2311yescharacteristic
58C2×M16×C61—21no—
59C2×M16×C61D412yes—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C22⋊C8×C61—21no—
67C22⋊C8×C61—21no—
68C22⋊C8×C61—21no—
69C22⋊C8×C61—21no—
70C24×C61C22×C411yescharacteristic
71C23×D61C22⋊C411yescharacteristic
72C22×C4×C61—22no—
73C22×C4×C61—22no—
74C22×C4×C61—22no—
75C22×C4×C61—42no—
76C22×C4×C61—82no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C2×C22⋊D61—21no—
84C2×C22⋊D61—21no—
85C2×C22⋊D61—22no—
86C2×C22⋊D61—41no—
87C22×Dic61—22no—
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—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C22⋊Dic61—21no—
103C22⋊Dic61—21no—
104C22⋊Dic61—42no—
105#11758198—21no—
106#11758198—21no—
107#11758198—82no—
108C4⋊Dic61—42no—
109#11758196—21no—
110#11758196—21no—
111#11758196—82no—
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—82no—
141C2×C4×C61—82no—
142C2×C4×C61#12011yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C22⋊D61—42no—
147C22⋊D61—42no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61—42no—
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#1821D6111yescharacteristic, complemented
196#1465—611no—
197#1305—611no—
198#1305—611no—
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⋊C4C2×D6111yescharacteristic
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—611no—
223#380—1221no—
224#343—22no—
225#343—1222no—
226#324—1221no—
227#323—1221no—
228C61#950911yescharacteristic, complemented, Sylow
229C22×D4—611no—
230C23×C4—611no—
231C23×C4C4×D6112yes—
232C23×C4C22×D6111yescharacteristic
233C2×M16—21no—
234C2×M16—612no—
235C2×M16—1221no—
236C2×M16C22⋊D6112yes—
237C22×C8—1222no—
238C4×D4—1221no—
239C4×D4—1221no—
240C4×D4—1221no—
241C4×D4—1221no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—611no—
249C2×C4⋊C4—1222no—
250C2×C4⋊C4—1221no—
251C2×C22⋊C4—611no—
252C2×C22⋊C4—611no—
253C2×C22⋊C4—612no—
254C2×C22⋊C4—1222no—
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—1222no—
268#95—1222no—
269#95—1221no—
270C24—611no—
271C24C2×C4×D6111yescharacteristic
272C2×D4—1222no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—2441no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—42no—
280C22×C4—82no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1222no—
287C22×C4—2442no—
288C22×C4#1175822211yescharacteristic
289C22×C4D4×D6111yescharacteristic
290C22×C4D4×D6111yescharacteristic
291C22×C4D4×D6111yescharacteristic
292C22×C4#1175822411yescharacteristic
293C22×C4C2×C22⋊D6111yescharacteristic
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—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—4882no—
310C4⋊C4—2442no—
311C22⋊C4—1221no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—4882no—
316C22⋊C4—2442no—
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#1451973711yescharacteristic
330C23C4×C22⋊D6111yescharacteristic
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—82no—
343C2×C4—82no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—4881no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4#1451974511yescharacteristic
357C2×C4#1451974811yescharacteristic
358C2×C4#1451975011yescharacteristic
359C2×C4#1451975911yescharacteristic
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#1683963811yescharacteristic
380C22#101×D6111yescharacteristic
381C22#1683974511yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—82no—
386C4—4882no—
387C4—2441no—
388C4—2441no—
389C4—2441no—
390C4#1683995112yes—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—2442no—
396C2#2144622911yescharacteristic
397C2#2144628411yescharacteristic
398C2#2144636311yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1821C2
socleC22×C61#386
prime radicalC22×C22⋊D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1821D61
hypocenterC61#9509
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #21445899C2semidirect
5. #21443726C2semidirect
6. #21443724C2semidirect
7. C61×#1821C2semidirect
195. #1821D61semidirect
228. C61#9509semidirect

Maximal subgroups

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

subgroupindex
#214548462
#214501302
#214458992
#214441552
#214437262
#214437242
C61×#18212
#950961