Finite Group Databasebeta

← #29577357

Subgroups — #29577357

Order 15616.

496 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 89 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#21454455C211yesmaximal, characteristic, complemented
2#21451500C211yesmaximal, characteristic
3#21444418C211yesmaximal, characteristic, complemented
4#21444416C211yesmaximal, characteristic, complemented
5#21444151C211yesmaximal, characteristic, complemented
6#21443712C211yesmaximal, characteristic, complemented
7C61×#1300C211yesmaximal, characteristic, complemented
8C2×#14519765C2211yescharacteristic
9C2×#14519734C2211yescharacteristic
10#16839824—22no—
11#16839821—22no—
12#16839819C2211yescharacteristic
13#16839785—21no—
14#16839725—21no—
15C4×#11758194C2211yescharacteristic
16#16839683C411yescharacteristic
17#16839680C411yescharacteristic
18#16839675C411yescharacteristic
19#16839672C411yescharacteristic
20#16839664—21no—
21#16839654—21no—
22#16839653—21no—
23#16839640—21no—
24#16839501—22no—
25#16839501—22no—
26#16839487—21no—
27#16839485—21no—
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#376C2211yescharacteristic
31C22×Dic122C2×C411yescharacteristic
32C22×D244—21no—
33C22×D244C2×C411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C2×#11758194—21no—
36#14519765—21no—
37#14519765—21no—
38#14519765—21no—
39#14519765—21no—
40#14519734—21no—
41#14519734—21no—
42#14519734—21no—
43#14519734—21no—
44C2×C4⋊Dic61—21no—
45C2×#11758196C2×C411yescharacteristic
46C2×#11758196D411yescharacteristic
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198C2×C411yescharacteristic
54C2×#11758198D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C4⋊#92418—21no—
57#14519706—24no—
58C22⋊#92418—21no—
59#14519689—24no—
60#14519688—21no—
61#14519688D412yescomplemented
62C4×#92418—21no—
63#14519684—21no—
64#14519684—21no—
65C2×M16×C61—21no—
66C2×C42×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C22⋊C8×C61—21no—
70#97×C61—21no—
71#97×C61D412yescomplemented
72C4×C8×C61—21no—
73#95×C61—21no—
74#95×C61C2×C411yescharacteristic
75#95×C61C2×C411yescharacteristic
76C23×D61—21no—
77C23×D61C22⋊C411yescharacteristic
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×Dic61—21no—
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—42no—
90C2×D244—42no—
91C2×D244—81no—
92C2×D244—81no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×Dic122—21no—
98C2×Dic122—21no—
99C2×Dic122—81no—
100M16×C61—41no—
101M16×C61—41no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C42×C61—42no—
105C42×C61C2×D411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61#4111yescharacteristic
108C42×C61#4111yescharacteristic
109#11758198—21no—
110#11758198—21no—
111#11758198—21no—
112#11758198—21no—
113#11758198—42no—
114#11758198—42no—
115#11758198—41no—
116#11758198—41no—
117#11758198—41no—
118#11758198—41no—
119#11758198—81no—
120#11758198—81no—
121C4⋊Dic61—81no—
122#11758196—21no—
123#11758196—21no—
124#11758196—21no—
125#11758196—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128#11758194—41no—
129#11758194—41no—
130C2×#92418—22no—
131C2×#92418—41no—
132C23×C61C2×C22⋊C411yescharacteristic
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—41no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—22no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61#12011yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12311yescharacteristic
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171D244—81no—
172D244—81no—
173D244—84no—
174C4×D61—42no—
175C4×D61—42no—
176Dic122—81no—
177Dic122—81no—
178C8×C61—42no—
179C8×C61—81no—
180#92418—42no—
181#92418—81no—
182#9389—611nomaximal, Sylow
183C22×C61—21no—
184C22×C61—21no—
185C22×C61#38611yescharacteristic
186C22×C61#42111yescharacteristic
187C22×C61#42111yescharacteristic
188C2×D61—42no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—81no—
193C2×D61—81no—
194C2×D61—81no—
195C2×D61—81no—
196C2×D61—81no—
197C2×D61—81no—
198C2×D61—81no—
199C2×D61—81no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—42no—
207C4×C61—81no—
208Dic61—41no—
209Dic61—41no—
210Dic61—41no—
211Dic61—81no—
212#2921—611no—
213#2610—611no—
214#1527—611no—
215#1527—611no—
216#1464—611no—
217#1300—611no—
218#1300D6111yescharacteristic, complemented
219C2×C61—21no—
220C2×C61—21no—
221C2×C61#188411yescharacteristic
222C2×C61#189711yescharacteristic
223C2×C61#191411yescharacteristic
224D61—81no—
225D61—161no—
226C2×#124—611no—
227C2×#117—611no—
228#433—1222no—
229#433—1222no—
230#432—611no—
231#432C2×D6111yescharacteristic
232#423—1221no—
233#407—1221no—
234C4×M16—611no—
235C4×M16C2×D6111yescharacteristic
236#395—611no—
237#394—611no—
238#393—611no—
239#392—611no—
240#390—1221no—
241#388—1221no—
242#388—1221no—
243#386—1221no—
244#376C2×D6111yescharacteristic
245#329—1222no—
246#329—1222no—
247#324—1221no—
248#323—1221no—
249C61#938911yescharacteristic, complemented, Sylow
250C22×Q8—611no—
251C22×D4—611no—
252C22×D4—1221no—
253C23×C4—611no—
254C2×M16—21no—
255C2×M16—1221no—
256#124—1221no—
257#124—1221no—
258#124—1221no—
259#124—1221no—
260#117—1221no—
261#117—1221no—
262#117—1221no—
263#117—1221no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—1221no—
267C2×C22⋊C4—611no—
268C2×C22⋊C4—611no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C42—21no—
276C2×C42—611no—
277C2×C42C22×D6111yescharacteristic
278C4⋊C8—21no—
279C4⋊C8—1224no—
280C4⋊C8—1221no—
281C22⋊C8—21no—
282C22⋊C8—1224no—
283C22⋊C8—1221no—
284#97—21no—
285#97—612no—
286#97—1221no—
287#97D24412yescomplemented
288C4×C8—21no—
289C4×C8—1221no—
290#95—21no—
291#95—1221no—
292#95—1221no—
293#95C4×D6111yescharacteristic
294#95C4×D6111yescharacteristic
295C24—611no—
296C24—1221no—
297C2×Q8—1221no—
298C2×Q8—1221no—
299C2×Q8—4881no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—4881no—
303C2×D4—4881no—
304C2×D4—2442no—
305C2×D4—2442no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4C2×C4×D6111yescharacteristic
317C22×C4D4×D6111yescharacteristic
318C22×C4D4×D6111yescharacteristic
319M16—41no—
320M16—41no—
321M16—2441no—
322M16—2441no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—1222no—
326C2×C8—2441no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C4⋊C4—4881no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C22⋊C4—4881no—
337C22⋊C4—4881no—
338C22⋊C4—2442no—
339C22⋊C4—2442no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C42—42no—
345C42—1221no—
346C42—1221no—
347C42C2×D24411yescharacteristic
348C42#1175822211yescharacteristic
349C42D4×D6111yescharacteristic
350C42#1175822611yescharacteristic
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—2441no—
355C23—2441no—
356C23—2441no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23C22⋊C4×D6111yescharacteristic
364Q8—4881no—
365Q8—4881no—
366D4—4881no—
367D4—4881no—
368D4—4884no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—2442no—
385C2×C4—2442no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4#1451973911yescharacteristic
392C2×C4C4×D24411yescharacteristic
393C2×C4#1451974711yescharacteristic
394C2×C4#1451975011yescharacteristic
395C2×C4#1451975211yescharacteristic
396C2×C4#1451976211yescharacteristic
397C8—42no—
398C8—81no—
399C8—4881no—
400C8—2442no—
401C22—21no—
402C22—21no—
403C22—4881no—
404C22—4881no—
405C22—4881no—
406C22—4881no—
407C22—4881no—
408C22—4881no—
409C22—4881no—
410C22—4881no—
411C22—2442no—
412C22—2441no—
413C22—2441no—
414C22—2441no—
415C22#1683964011yescharacteristic
416C22#1683977711yescharacteristic
417C22#1683977711yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—42no—
425C4—81no—
426C4—4881no—
427C4—2441no—
428C4—2441no—
429C4—2441no—
430C2—21no—
431C2—21no—
432C2—9761no—
433C2—4881no—
434C2#2144620111yescharacteristic
435C2#2144626611yescharacteristic
436C2#2144636511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1300C2
socleC22×C61#386
prime radical#16839672C4
cosocleC2×C42×C61C23
hypercenter#1300D61
hypocenterC61#9389
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
1. #21454455C2semidirect
3. #21444418C2semidirect
4. #21444416C2semidirect
5. #21444151C2semidirect
6. #21443712C2semidirect
7. C61×#1300C2semidirect
61. #14519688D4semidirect
71. #97×C61D4semidirect
218. #1300D61semidirect
249. C61#9389semidirect
287. #97D244semidirect

Maximal subgroups

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

subgroupindex
#214544552
#214515002
#214444182
#214444162
#214441512
#214437122
C61×#13002
#938961