Finite Group Databasebeta

← #29577355

Subgroups — #29577355

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#21451508C211yesmaximal, characteristic
3#21444417C211yesmaximal, characteristic, complemented
4#21444151C211yesmaximal, characteristic, complemented
5#21443713C211yesmaximal, characteristic, complemented
6#21443711C211yesmaximal, characteristic, complemented
7C61×#1527C211yesmaximal, characteristic, complemented
8C2×#14519734C2211yescharacteristic
9#16839824—22no—
10#16839821—22no—
11#16839819C2211yescharacteristic
12#16839785—21no—
13#16839725—21no—
14C4×#11758194C2211yescharacteristic
15#16839681C411yescharacteristic
16#16839676C411yescharacteristic
17#16839673C411yescharacteristic
18#16839670C411yescharacteristic
19#16839662—21no—
20#16839656—21no—
21#16839650—21no—
22#16839638—21no—
23#16839608C2211yescharacteristic
24#16839502—22no—
25#16839487—21no—
26#16839485—21no—
27C2×#124×C61C2211yescharacteristic
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#329—22no—
31C22×C22⋊D61—21no—
32C22×C4×D61D411yescharacteristic
33C2×#11758194—21no—
34#14519734—21no—
35#14519734—21no—
36#14519734—21no—
37#14519734—21no—
38C2×#11758196—21no—
39C2×#11758196C2×C411yescharacteristic
40C2×#11758196D411yescharacteristic
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198C2×C411yescharacteristic
46C2×#11758198D411yescharacteristic
47C2×C4×Dic61—21no—
48C2×C4×Dic61D411yescharacteristic
49C4⋊#92418—21no—
50#14519706—24no—
51C22⋊#92418—21no—
52#14519689—24no—
53#14519688—21no—
54#14519688D412yescomplemented
55C4×#92418—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684C2×C411yescharacteristic
60#14519684C2×C411yescharacteristic
61C22×Q8×C61C2×C411yescharacteristic
62C22×D4×C61C2×C411yescharacteristic
63C2×M16×C61—21no—
64#124×C61—21no—
65#124×C61—21no—
66#124×C61—21no—
67#124×C61—21no—
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73#97×C61—21no—
74#97×C61D412yescomplemented
75C4×C8×C61—21no—
76C24×C61—21no—
77C23×D61C22⋊C411yescharacteristic
78C2×Q8×C61—21no—
79C2×Q8×C61—21no—
80C2×Q8×C61—81no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—81no—
84C22×C4×C61—21no—
85C22×C4×C61C22×C411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C2×C22⋊D61—42no—
89C2×C22⋊D61—42no—
90C2×C22⋊D61—81no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61C22⋊C411yescharacteristic
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C22⋊C411yescharacteristic
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100M16×C61—41no—
101M16×C61—41no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61#4111yescharacteristic
111C42×C61#4111yescharacteristic
112C22⋊Dic61—42no—
113C22⋊Dic61—42no—
114C22⋊Dic61—81no—
115#11758198—21no—
116#11758198—21no—
117#11758198—21no—
118#11758198—21no—
119#11758198—81no—
120#11758196—21no—
121#11758196—21no—
122#11758196—21no—
123#11758196—21no—
124#11758196—81no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—42no—
128#11758194—41no—
129#11758194—41no—
130C2×#92418—22no—
131C2×#92418—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61C2×C22⋊C411yescharacteristic
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—41no—
144C22×D61—41no—
145Q8×C61—81no—
146Q8×C61—81no—
147D4×C61—81no—
148D4×C61—81no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C2×C4×C61#12011yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12311yescharacteristic
162C22⋊D61—84no—
163C2×Dic61—22no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C4×D61—42no—
177C4×D61—42no—
178C8×C61—42no—
179C8×C61—81no—
180#92418—42no—
181#92418—81no—
182#9389—611nomaximal, Sylow
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61#38611yescharacteristic
193C22×C61#42111yescharacteristic
194C22×C61#42111yescharacteristic
195C2×D61—42no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—81no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—81no—
207Dic61—42no—
208Dic61—41no—
209Dic61—41no—
210Dic61—41no—
211Dic61—81no—
212#2921—611no—
213#2610—611no—
214#1527—611no—
215#1527D6111yescharacteristic, complemented
216#1464—611no—
217#1300—611no—
218#1300—611no—
219C2×C61—21no—
220C2×C61—21no—
221C2×C61—161no—
222C2×C61#188411yescharacteristic
223C2×C61#189711yescharacteristic
224C2×C61#191411yescharacteristic
225D61—81no—
226C2×#124C2×D6111yescharacteristic
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#376—611no—
245#329—22no—
246#329—1222no—
247#324—1221no—
248#323—1221no—
249C61#938911yescharacteristic, complemented, Sylow
250C22×Q8C4×D6111yescharacteristic
251C22×D4—1221no—
252C22×D4C4×D6111yescharacteristic
253C23×C4—611no—
254C2×M16—21no—
255C2×M16—1221no—
256#124—21no—
257#124—21no—
258#124—21no—
259#124—21no—
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—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—611no—
270C2×C22⋊C4—611no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C42—611no—
276C2×C42—1221no—
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#97C22⋊D6112yescomplemented
288C4×C8—21no—
289C4×C8—1221no—
290#95—611no—
291#95—611no—
292#95—1221no—
293#95—1221no—
294#95—1221no—
295C24—21no—
296C24—611no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—81no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—81no—
303C2×D4—4881no—
304C2×D4—2442no—
305C2×D4—2442no—
306C22×C4—21no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—1221no—
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—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—4881no—
341C22⋊C4—4881no—
342C22⋊C4—2442no—
343C22⋊C4—2442no—
344C42—1221no—
345C42—1221no—
346C42—2442no—
347C42#1175822211yescharacteristic
348C42D4×D6111yescharacteristic
349C42#1175822411yescharacteristic
350C42C2×C22⋊D6111yescharacteristic
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—1221no—
359C23—1221no—
360C23—1221no—
361C23—2441no—
362C23—2441no—
363C23C22⋊C4×D6111yescharacteristic
364Q8—81no—
365Q8—81no—
366D4—81no—
367D4—81no—
368D4—4884no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—1222no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4#1451973711yescharacteristic
392C2×C4C4×C22⋊D6111yescharacteristic
393C2×C4#1451974511yescharacteristic
394C2×C4#1451974811yescharacteristic
395C2×C4#1451975011yescharacteristic
396C2×C4#1451975911yescharacteristic
397C8—42no—
398C8—81no—
399C8—4881no—
400C8—2442no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—4881no—
411C22—2442no—
412C22—2441no—
413C22—2441no—
414C22—2441no—
415C22#1683963811yescharacteristic
416C22#1683977711yescharacteristic
417C22#1683977711yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—81no—
425C4—4881no—
426C4—2442no—
427C4—2441no—
428C4—2441no—
429C4—2441no—
430C2—21no—
431C2—21no—
432C2—161no—
433C2—4881no—
434C2#2144619911yescharacteristic
435C2#2144626411yescharacteristic
436C2#2144636311yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1527C2
socleC22×C61#386
prime radical#16839670C4
cosocleC2×C42×C61C23
hypercenter#1527D61
hypocenterC61#9389
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1527

Complements

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

NH ≅ G/Ntype
1. #21454455C2semidirect
3. #21444417C2semidirect
4. #21444151C2semidirect
5. #21443713C2semidirect
6. #21443711C2semidirect
7. C61×#1527C2semidirect
54. #14519688D4semidirect
74. #97×C61D4semidirect
215. #1527D61semidirect
249. C61#9389semidirect
287. #97C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214544552
#214515082
#214444172
#214441512
#214437132
#214437112
C61×#15272
#938961