Finite Group Databasebeta

← #29577345

Subgroups — #29577345

Order 15616.

582 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 93 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#21454236C211yesmaximal, 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×M16×D61—21no—
9C2×#14519734C2211yescharacteristic
10#16839819C2211yescharacteristic
11#16839719—22no—
12#16839716—22no—
13C4×#11758194C2211yescharacteristic
14M16×Dic61—21no—
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—
34C2×#11758189—22no—
35M16×D61—24no—
36M16×D61—24no—
37C2×C8×D61—22no—
38#14519734—21no—
39#14519734—21no—
40#14519734—21no—
41#14519734—21no—
42C2×#11758196—21no—
43C2×#11758196C2×C411yescharacteristic
44C2×#11758196D411yescharacteristic
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×#11758198—21no—
49C2×#11758198C2×C411yescharacteristic
50C2×#11758198D411yescharacteristic
51C2×C4×Dic61—21no—
52C2×C4×Dic61D411yescharacteristic
53C4⋊#92418—21no—
54C22⋊#92418—21no—
55#14519688—21no—
56#14519688D412yescomplemented
57#14519687—22no—
58C4×#92418—21no—
59C8×Dic61—22no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63#14519684C2×C411yescharacteristic
64#14519684C2×C411yescharacteristic
65C22×Q8×C61C2×C411yescharacteristic
66C22×D4×C61C2×C411yescharacteristic
67C2×M16×C61—21no—
68#124×C61—21no—
69#124×C61—21no—
70#124×C61—21no—
71#124×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C42×C61C2311yescharacteristic
75C4⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77#97×C61—21no—
78#97×C61D412yescomplemented
79C4×C8×C61—21no—
80C24×C61—21no—
81C23×D61C22⋊C411yescharacteristic
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—81no—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—81no—
88C22×C4×C61—21no—
89C22×C4×C61C22×C411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C2×C22⋊D61—42no—
93C2×C22⋊D61—42no—
94C2×C22⋊D61—81no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C2×C4×D61—22no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—22no—
104M16×C61—22no—
105M16×C61—22no—
106C2×C8×C61—22no—
107C2×C8×C61—41no—
108C22⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61#4111yescharacteristic
115C42×C61#4111yescharacteristic
116C22⋊Dic61—42no—
117C22⋊Dic61—42no—
118C22⋊Dic61—81no—
119#11758198—21no—
120#11758198—21no—
121#11758198—21no—
122#11758198—21no—
123#11758198—81no—
124#11758196—21no—
125#11758196—21no—
126#11758196—21no—
127#11758196—21no—
128#11758196—81no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61—42no—
132#11758194—22no—
133#11758194—22no—
134C2×#92418—22no—
135C2×#92418—41no—
136#11758189—28no—
137C8×D61—28no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61C2×C22⋊C411yescharacteristic
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61#10412yes—
151Q8×C61—81no—
152Q8×C61—81no—
153D4×C61—81no—
154D4×C61—81no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61C4×D411yescharacteristic
163C2×C4×C61C4×D411yescharacteristic
164C2×C4×C61#12011yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12311yescharacteristic
168C22⋊D61—84no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—22no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61#10412yes—
182C4×D61—22no—
183C4×D61—22no—
184C4×D61—24no—
185C8×C61—24no—
186C8×C61—81no—
187#92418—24no—
188#92418—81no—
189#9387—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61—81no—
198C22×C61—81no—
199C22×C61#38611yescharacteristic
200C22×C61C2×#10411yescharacteristic
201C22×C61C2×#10411yescharacteristic
202C2×D61—22no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—42no—
206C2×D61—81no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—81no—
214Dic61—22no—
215Dic61—42no—
216Dic61—41no—
217Dic61—41no—
218Dic61—81no—
219#2873—611no—
220#2610—611no—
221#1527—611no—
222#1527D6111yescharacteristic, complemented
223#1464—611no—
224#1300—611no—
225#1300—611no—
226C2×C61—21no—
227C2×C61—21no—
228C2×C61—161no—
229C2×C61#188411yescharacteristic
230C2×C61#189611yescharacteristic
231C2×C61#191411yescharacteristic
232D61—42no—
233C22×M16—1221no—
234C2×#124C2×D6111yescharacteristic
235C2×#117—611no—
236#432—611no—
237#432C2×D6111yescharacteristic
238#405—1222no—
239#405—1222no—
240C4×M16—611no—
241C4×M16—1221no—
242C4×M16C2×D6111yescharacteristic
243#395—611no—
244#394—611no—
245#393—611no—
246#392—611no—
247#390—1221no—
248#388—1221no—
249#388—1221no—
250#386—1221no—
251#376—611no—
252#329—22no—
253#329—1222no—
254#324—1221no—
255#323—1221no—
256C61#938711yescharacteristic, complemented, Sylow
257C22×Q8C4×D6111yescharacteristic
258C22×D4—1221no—
259C22×D4C4×D6111yescharacteristic
260C23×C4—611no—
261C2×M16—21no—
262C2×M16—1222no—
263C2×M16—1224no—
264C2×M16—1224no—
265C2×M16—1221no—
266C22×C8—1222no—
267#124—21no—
268#124—21no—
269#124—21no—
270#124—21no—
271#117—1221no—
272#117—1221no—
273#117—1221no—
274#117—1221no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—1221no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—611no—
282C2×C22⋊C4—1221no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—1221no—
286C2×C42—611no—
287C2×C42—1221no—
288C2×C42C22×D6111yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—1221no—
291C22⋊C8—21no—
292C22⋊C8—1221no—
293#97—21no—
294#97—612no—
295#97—1222no—
296#97—1221no—
297#97C22⋊D6112yescomplemented
298C4×C8—21no—
299C4×C8—1222no—
300C4×C8—1221no—
301#95—611no—
302#95—611no—
303#95—1221no—
304#95—1221no—
305#95—1221no—
306C24—21no—
307C24—611no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—81no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—81no—
314C2×D4—4881no—
315C2×D4—2442no—
316C2×D4—2442no—
317C22×C4—21no—
318C22×C4—611no—
319C22×C4—611no—
320C22×C4—611no—
321C22×C4—1222no—
322C22×C4—1222no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4C2×C4×D6111yescharacteristic
328C22×C4D4×D6111yescharacteristic
329C22×C4D4×D6111yescharacteristic
330M16—22no—
331M16—22no—
332M16—1228no—
333M16—1222no—
334M16—1222no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—1228no—
338C2×C8—1222no—
339C2×C8—2441no—
340C4⋊C4—1221no—
341C4⋊C4—1221no—
342C4⋊C4—1221no—
343C4⋊C4—1221no—
344C4⋊C4—4881no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—1221no—
350C22⋊C4—1221no—
351C22⋊C4—1221no—
352C22⋊C4—1221no—
353C22⋊C4—4881no—
354C22⋊C4—4881no—
355C22⋊C4—2442no—
356C22⋊C4—2442no—
357C42—1221no—
358C42—1221no—
359C42—2442no—
360C42#1175822211yescharacteristic
361C42D4×D6111yescharacteristic
362C42#1175822411yescharacteristic
363C42C2×C22⋊D6111yescharacteristic
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—612no—
372C23—1221no—
373C23—1221no—
374C23—2441no—
375C23—2441no—
376C23C22⋊C4×D6111yescharacteristic
377Q8—81no—
378Q8—81no—
379D4—81no—
380D4—81no—
381D4—4884no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—612no—
390C2×C4—1222no—
391C2×C4—1222no—
392C2×C4—1224no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1222no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4#1451973711yescharacteristic
406C2×C4C4×C22⋊D6111yescharacteristic
407C2×C4#1451974511yescharacteristic
408C2×C4#1451974811yescharacteristic
409C2×C4#1451975011yescharacteristic
410C2×C4#1451975911yescharacteristic
411C8—24no—
412C8—81no—
413C8—1224no—
414C8—4881no—
415C22—21no—
416C22—21no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—1222no—
425C22—4881no—
426C22—2442no—
427C22—2441no—
428C22—2441no—
429C22#1683963811yescharacteristic
430C22#104×D6111yescharacteristic
431C22#104×D6111yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—81no—
439C4—1222no—
440C4—4881no—
441C4—2442no—
442C4—2441no—
443C4—2441no—
444C2—21no—
445C2—21no—
446C2—161no—
447C2—2442no—
448C2#2144619911yescharacteristic
449C2#2144625911yescharacteristic
450C2#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#9387
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. #21454236C2semidirect
3. #21444417C2semidirect
4. #21444151C2semidirect
5. #21443713C2semidirect
6. #21443711C2semidirect
7. C61×#1527C2semidirect
56. #14519688D4semidirect
78. #97×C61D4semidirect
222. #1527D61semidirect
256. C61#9387semidirect
297. #97C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214542362
#214515082
#214444172
#214441512
#214437132
#214437112
C61×#15272
#938761