Finite Group Databasebeta

← #29572999

Subgroups — #29572999

Order 15616.

456 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 97 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#21454509C211yesmaximal, characteristic
2#21445855C211yesmaximal, characteristic, complemented
3#21445842C211yesmaximal, characteristic, complemented
4#21444363C211yesmaximal, characteristic
5#21444360C211yesmaximal, characteristic
6#21443724C211yesmaximal, characteristic, complemented
7C61×#1305C211yesmaximal, characteristic, complemented
8C2×#14519785C411yescharacteristic, complemented
9C23×#92418C2211yescharacteristic
10#16840273C2211yescharacteristic
11#16839830—21no—
12#16839830—21no—
13#16839825—21no—
14#16839825—21no—
15C2×#14519712—21no—
16C2×#14519708—21no—
17#16839790C411yescharacteristic, complemented
18#16839730C411yescharacteristic, complemented
19#16839726C2211yescharacteristic
20#16839720C411yescharacteristic, complemented
21#16839622C2211yescharacteristic
22#16839526—21no—
23#16839524—21no—
24#16839500—21no—
25#16839498—21no—
26#16839497—21no—
27#16839495—21no—
28C61×#407C2211yescharacteristic
29C61×#407C2211yescharacteristic
30C61×#380C2211yescharacteristic
31C2×#11758222C2×C411yescharacteristic
32#14519785—42no—
33C2×#11758194—21no—
34C2×#11758189—21no—
35C22×#92418—42no—
36C22×#92418C2×C411yescharacteristic
37C22×#92418C2×C411yescharacteristic
38C22×#92418D411yescharacteristic
39C22×#92418D411yescharacteristic
40C22×#92418D411yescharacteristic
41C22×#92418D411yescharacteristic
42C2×C8×D61—21no—
43#14519760—21no—
44#14519756D411yescharacteristic
45#14519756Q811yescharacteristic
46#14519751D411yescharacteristic
47#14519751Q811yescharacteristic
48#14519746—21no—
49C4×C22⋊D61—21no—
50C4×C22⋊D61—21no—
51#14519736C2×C411yescharacteristic
52C2×C4⋊Dic61—21no—
53C2×C22⋊Dic61—21no—
54#14519712—42no—
55#14519708—42no—
56#14519706—21no—
57#14519706—21no—
58C22⋊#92418—21no—
59C22⋊#92418—21no—
60#14519689—21no—
61#14519689—21no—
62#14519687—21no—
63C8×Dic61—21no—
64#14519684—21no—
65C23×C4×C61C2311yescharacteristic
66C2×M16×C61—21no—
67C2×M16×C61C2×C411yescharacteristic
68C2×M16×C61C2×C411yescharacteristic
69C2×C4⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75#95×C61—21no—
76C24×C61#4111yescharacteristic
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×Q811yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C2×C22⋊D61—21no—
87C2×C22⋊D61—21no—
88C2×C22⋊D61—21no—
89C22×Dic61—41no—
90#11758222—41no—
91#11758222—41no—
92C2×D244C4⋊C411yescharacteristic
93C2×C4×D61—21no—
94C2×Dic122C4⋊C411yescharacteristic
95M16×C61—41no—
96M16×C61—41no—
97M16×C61—41no—
98M16×C61—41no—
99C2×C8×C61—21no—
100C2×C8×C61—21no—
101C2×C8×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C22⋊C4×C61—81no—
105C22⋊Dic61—21no—
106C22⋊Dic61—21no—
107C22⋊Dic61—21no—
108C22⋊Dic61—81no—
109#11758198—21no—
110#11758198—21no—
111C4⋊Dic61—41no—
112C4⋊Dic61—41no—
113C4⋊Dic61C4⋊C411yescharacteristic
114C4⋊Dic61C4⋊C411yescharacteristic
115#11758196—21no—
116#11758196—21no—
117C4×Dic61—21no—
118#11758194—41no—
119#11758194—41no—
120C2×#92418—22no—
121C2×#92418—22no—
122C2×#92418—22no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418C22⋊C411yescharacteristic
128C2×#92418C22⋊C411yescharacteristic
129C2×#92418C22⋊C411yescharacteristic
130C2×#92418C22⋊C411yescharacteristic
131#11758189—42no—
132C8×D61—42no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61#11711yescharacteristic
138C23×C61#12111yescharacteristic
139C23×C61C22⋊Q811yescharacteristic
140C22×D61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—81no—
151C2×C4×C61—81no—
152C2×C4×C61—81no—
153C2×C4×C61C2×C22⋊C411yescharacteristic
154C2×C4×C61C2×C4⋊C411yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61C22⋊Q811yescharacteristic
157C22⋊D61—42no—
158C22⋊D61—42no—
159C22⋊D61—41no—
160C22⋊D61—41no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—81no—
165C2×Dic61—81no—
166C2×Dic61—81no—
167D244—41no—
168C4×D61—41no—
169C4×D61—41no—
170Dic122—41no—
171C8×C61—41no—
172C8×C61—41no—
173C8×C61—81no—
174#92418—21no—
175#92418—21no—
176#92418—21no—
177#92418—81no—
178#92418#9912yes—
179#8629—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—42no—
189C22×C61—42no—
190C22×C61#38011yescharacteristic
191C22×C61#47111yescharacteristic
192C22×C61#47111yescharacteristic
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—161no—
200C4×C61C2×#9911yescharacteristic
201C4×C61#41011yescharacteristic
202Dic61—41no—
203Dic61—41no—
204Dic61—41no—
205Dic61—161no—
206#2929—611no—
207#1810—611no—
208#1807—611no—
209#1513—611no—
210#1513—611no—
211#1305—611no—
212#1305D6111yescharacteristic, complemented
213C2×C61—21no—
214C2×C61—21no—
215C2×C61—41no—
216C2×C61—41no—
217C2×C61#179911yescharacteristic
218C2×C61#181411yescharacteristic
219C2×C61#181511yescharacteristic
220D61—81no—
221C2×#131—611no—
222C23×C8—611no—
223#525—611no—
224#435—1221no—
225#435—1221no—
226C8×D4—1221no—
227C8×D4—1221no—
228C2×#108—1221no—
229C2×#106—1221no—
230#424—611no—
231#408—611no—
232#407—611no—
233#407C2×D6111yescharacteristic
234#407C2×D6111yescharacteristic
235#405—611no—
236#380—611no—
237#380C2×D6111yescharacteristic
238#341—1221no—
239#340—1221no—
240#328—1221no—
241#328—1221no—
242#327—1221no—
243#327—1221no—
244C61#862911yescharacteristic, complemented, Sylow
245C2×#41—611no—
246C23×C4C22×D6111yescharacteristic
247#131—2442no—
248C2×M16—21no—
249C2×M16—1221no—
250C2×M16—1221no—
251C2×M16C4×D6111yescharacteristic
252C2×M16C4×D6111yescharacteristic
253C22×C8—611no—
254C22×C8—611no—
255C22×C8—611no—
256C22×C8—611no—
257C22×C8—611no—
258C22×C8—611no—
259C22×C8—1221no—
260C22×C8—2442no—
261#123—1221no—
262C22⋊Q8—611no—
263C22⋊Q8—611no—
264#121—611no—
265#121—611no—
266#120—1221no—
267C4×D4—1221no—
268C4×D4—1221no—
269#117—611no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—1221no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—1221no—
274#108—2442no—
275#106—2442no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—1221no—
283C22⋊C8—1221no—
284C22⋊C8—1221no—
285C22⋊C8—1221no—
286#97—1221no—
287C4×C8—1221no—
288#95—21no—
289#95—1221no—
290C24#1175822211yescharacteristic
291#41—2441no—
292#41—2441no—
293C2×Q8—611no—
294C2×D4—611no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—1221no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—1221no—
302C22×C4—2441no—
303C22×C4C2×C4×D6111yescharacteristic
304C22×C4#1175822211yescharacteristic
305C22×C4D4×D6111yescharacteristic
306C22×C4D4×D6111yescharacteristic
307C22×C4D4×D6111yescharacteristic
308C22×C4Q8×D6111yescharacteristic
309M16—41no—
310M16—41no—
311M16—41no—
312M16—41no—
313M16—2442no—
314M16—2441no—
315M16—2441no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—41no—
319C2×C8—611no—
320C2×C8—611no—
321C2×C8—611no—
322C2×C8—611no—
323C2×C8—1222no—
324C2×C8—1222no—
325C2×C8—1222no—
326C2×C8—2442no—
327C2×C8—2441no—
328C2×C8—2441no—
329C2×C8—2441no—
330C2×C8—2441no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—611no—
334C4⋊C4—611no—
335C4⋊C4—1221no—
336C4⋊C4—1221no—
337C4⋊C4—2441no—
338C4⋊C4—2441no—
339C22⋊C4—81no—
340C22⋊C4—1221no—
341C22⋊C4—1221no—
342C22⋊C4—1221no—
343C22⋊C4—1221no—
344C22⋊C4—1221no—
345C22⋊C4—4881no—
346C42—1221no—
347C23—21no—
348C23—21no—
349C23—41no—
350C23—41no—
351C23—1221no—
352C23#1451973411yescharacteristic
353C23#1451975011yescharacteristic
354C23#1451975511yescharacteristic
355Q8—2441no—
356D4—2441no—
357D4—2442no—
358D4—2442no—
359D4—2441no—
360D4—2441no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—4881no—
377C2×C4—4881no—
378C2×C4—4881no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4C22⋊C4×D6111yescharacteristic
382C2×C4C4⋊C4×D6111yescharacteristic
383C2×C4#1451975011yescharacteristic
384C2×C4#1451975511yescharacteristic
385C8—41no—
386C8—41no—
387C8—81no—
388C8—612no—
389C8—1221no—
390C8—1221no—
391C8—1221no—
392C8—4881no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—2441no—
404C22—2441no—
405C22—2441no—
406C22#1683962111yescharacteristic
407C22#1684002411yescharacteristic
408C22#1684002811yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—161no—
413C4—9761no—
414C4—2441no—
415C4—2441no—
416C4—2441no—
417C4#99×D6111yescharacteristic
418C4#1683973411yescharacteristic
419C2—21no—
420C2—21no—
421C2—41no—
422C2—41no—
423C2—4881no—
424C2#2144580611yescharacteristic
425C2#2144587211yescharacteristic
426C2#2144587711yescharacteristic
subgroupG/H
centerC22#16839621
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1305C2
socleC22×C61#380
prime radical#16840273C22
cosocleC23×C4×C61C23
hypercenter#1305D61
hypocenterC61#8629
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
2. #21445855C2semidirect
3. #21445842C2semidirect
6. #21443724C2semidirect
7. C61×#1305C2semidirect
8. C2×#14519785C4semidirect
17. #16839790C4semidirect
18. #16839730C4semidirect
20. #16839720C4semidirect
212. #1305D61semidirect
244. C61#8629semidirect

Maximal subgroups

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

subgroupindex
#214545092
#214458552
#214458422
#214443632
#214443602
#214437242
C61×#13052
#862961