Finite Group Databasebeta

← #29584358

Subgroups — #29584358

Order 15616.

474 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 79 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#21456572C211yesmaximal, characteristic
2#21446288C211yesmaximal, characteristic, complemented
3#21446280C211yesmaximal, characteristic
4#21446004C211yesmaximal, characteristic, complemented
5#21444334C211yesmaximal, characteristic
6#21443695C211yesmaximal, characteristic, complemented
7C61×#1508C211yesmaximal, characteristic, complemented
8C22×#11758194C2211yescharacteristic
9C2×#14519751C2211yescharacteristic
10#16840090—21no—
11#16840080—21no—
12#16839993—21no—
13#16839993—21no—
14#16839912—21no—
15#16839901—21no—
16C2×C4⋊#92418—21no—
17C2×#14519696—21no—
18C2×#14519693—21no—
19#16839726C2211yescharacteristic
20C2×C22⋊#92418C2211yescharacteristic
21#16839531—21no—
22#16839530—21no—
23#16839517—21no—
24#16839495—21no—
25#16839495—21no—
26C2×C22⋊Q8×C61C2211yescharacteristic
27C61×#407C2211yescharacteristic
28C4×C22⋊C4×C61C2211yescharacteristic
29C61×#328—21no—
30C61×#328—21no—
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C2×#11758201—21no—
34C2×#11758201—21no—
35C2×#11758194—21no—
36C2×#11758194—21no—
37C2×#11758194—21no—
38C2×#11758194—42no—
39C22×#92418—21no—
40C22×#92418D411yescharacteristic
41C22×#92418D411yescharacteristic
42#14519751—21no—
43#14519751—21no—
44#14519751—21no—
45#14519751—21no—
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758198—21no—
48#14519708—21no—
49#14519708—21no—
50C4⋊#92418—42no—
51#14519701—21no—
52#14519701—21no—
53#14519697—21no—
54#14519697—21no—
55#14519696—42no—
56#14519693—42no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59C22⋊#92418—21no—
60C22⋊#92418—21no—
61C22×Q8×C61D411yescharacteristic
62C23×C4×C61C2311yescharacteristic
63C2×M16×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C22⋊Q8×C61—21no—
67C22⋊Q8×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61D411yescharacteristic
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C42×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75#95×C61D411yescharacteristic
76#95×C61D411yescharacteristic
77C24×C61#4111yescharacteristic
78C23×D61—21no—
79C2×Q8×C61—21no—
80C2×Q8×C61—21no—
81C2×Q8×C61—41no—
82C2×Q8×C61—41no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C2×C22⋊D61—41no—
96C2×C22⋊D61—41no—
97C2×C22⋊D61—81no—
98C2×C22⋊D61—81no—
99C22×Dic61—21no—
100C2×D244—21no—
101C2×D244—21no—
102C2×D244—41no—
103C2×D244—41no—
104M16×C61—41no—
105M16×C61—41no—
106C2×C8×C61—41no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C22⋊C4×C61—42no—
112C22⋊C4×C61—41no—
113C22⋊C4×C61—41no—
114C42×C61—41no—
115C42×C61—41no—
116#11758201—81no—
117#11758201—81no—
118#11758198—41no—
119#11758198—41no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122#11758194—22no—
123#11758194—22no—
124#11758194—41no—
125#11758194—41no—
126#11758194—41no—
127#11758194—41no—
128C2×#92418—22no—
129C2×#92418—21no—
130C2×#92418—21no—
131C2×#92418—41no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418—41no—
135C2×#92418—41no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61#12111yescharacteristic
141C23×C61#12311yescharacteristic
142C23×C61#12311yescharacteristic
143C22×D61—41no—
144C22×D61—42no—
145C22×D61—81no—
146C22×D61—81no—
147Q8×C61—41no—
148Q8×C61—41no—
149Q8×C61—81no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—22no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—42no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—81no—
169C2×C4×C61#12011yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12411yescharacteristic
173C22⋊D61—82no—
174C22⋊D61—81no—
175C22⋊D61—81no—
176C2×Dic61—41no—
177C2×Dic61—81no—
178D244—41no—
179D244—41no—
180D244—81no—
181C8×C61—81no—
182#92418—42no—
183#92418—41no—
184#92418—41no—
185#92418—81no—
186#10558—611nomaximal, Sylow
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61#39411yescharacteristic
198C22×C61#47111yescharacteristic
199C22×C61#47111yescharacteristic
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—162no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—42no—
208C4×C61—81no—
209C4×C61—81no—
210C4×C61—81no—
211C4×C61B(4,𝔽2)11yescharacteristic
212C4×C61#45811yescharacteristic
213Dic61—81no—
214#3187—611no—
215#1901—611no—
216#1900—611no—
217#1851—611no—
218#1508D6111yescharacteristic, complemented
219#1507—611no—
220#1293—611no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61—41no—
224C2×C61—41no—
225C2×C61#204411yescharacteristic
226C2×C61#204611yescharacteristic
227C2×C61#205011yescharacteristic
228D61—161no—
229C22×M16—611no—
230C2×C22⋊Q8C2×D6111yescharacteristic
231C2×#121—611no—
232#483—1221no—
233#481—1221no—
234#465—1221no—
235#465—1221no—
236#450—1221no—
237#448—1221no—
238C2×C4⋊C8—1221no—
239C2×#101—1221no—
240C2×#100—1221no—
241#407—611no—
242#407C2×D6111yescharacteristic
243C2×C22⋊C8—611no—
244C4×C22⋊C4C2×D6111yescharacteristic
245#343—1221no—
246#343—1221no—
247#336—1221no—
248#328—21no—
249#328—21no—
250#327—1221no—
251#327—1221no—
252C61#1055811yescharacteristic, complemented, Sylow
253C22×Q8D24411yescharacteristic
254C22×D4—611no—
255C22×D4—1221no—
256C23×C4C22×D6111yescharacteristic
257C2×SD16—1221no—
258C2×SD16—1221no—
259C2×M16—21no—
260C2×M16—1221no—
261C2×M16—1221no—
262C2×M16—1221no—
263C2×M16—2442no—
264C22×C8—611no—
265C22×C8—611no—
266C22×C8—1221no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271#121—1221no—
272#121—1221no—
273#121—1221no—
274#121—1221no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4D24411yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—1221no—
281C2×C42—21no—
282#106—1221no—
283#106—1221no—
284C4⋊C8—2442no—
285#103—1221no—
286#103—1221no—
287#102—1221no—
288#102—1221no—
289#101—2442no—
290#100—2442no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—1221no—
294C22⋊C8—1221no—
295C22⋊C8—1221no—
296C22⋊C8—1221no—
297#95C22⋊D6111yescharacteristic
298#95C22⋊D6111yescharacteristic
299C24—1221no—
300C24#1175822411yescharacteristic
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×D4—1221no—
306C2×D4—1221no—
307C2×D4—4881no—
308C2×D4—4881no—
309C2×D4—2441no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—1221no—
320C22×C4C2×D24411yescharacteristic
321C22×C4#1175822211yescharacteristic
322C22×C4D4×D6111yescharacteristic
323C22×C4D4×D6111yescharacteristic
324C22×C4#1175822411yescharacteristic
325C22×C4C2×C22⋊D6111yescharacteristic
326SD16—4881no—
327SD16—4881no—
328M16—41no—
329M16—41no—
330M16—1222no—
331M16—1222no—
332M16—2441no—
333M16—2441no—
334M16—2441no—
335M16—2441no—
336C2×C8—41no—
337C2×C8—1222no—
338C2×C8—1221no—
339C2×C8—1221no—
340C2×C8—2441no—
341C2×C8—2441no—
342C2×C8—2441no—
343C2×C8—2441no—
344C2×C8—2441no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—1221no—
350C4⋊C4—1221no—
351C22⋊C4—42no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—2441no—
355C22⋊C4—2441no—
356C42—41no—
357C42—41no—
358C23—21no—
359C23—21no—
360C23—41no—
361C23—41no—
362C23—4881no—
363C23—4881no—
364C23—2442no—
365C23—2441no—
366C23#1451974911yescharacteristic
367C23#1451975911yescharacteristic
368C23#1451976111yescharacteristic
369Q8—41no—
370Q8—41no—
371Q8—81no—
372D4—4881no—
373D4—4882no—
374D4—4881no—
375D4—4881no—
376D4—2441no—
377D4—2441no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—4881no—
398C2×C4—2441no—
399C2×C4#1451974711yescharacteristic
400C2×C4#1451974811yescharacteristic
401C2×C4#1451975111yescharacteristic
402C2×C4#1451976311yescharacteristic
403C8—81no—
404C8—4881no—
405C8—2442no—
406C8—2441no—
407C8—2441no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—81no—
417C22—81no—
418C22—9762no—
419C22—4881no—
420C22—4881no—
421C22—4881no—
422C22#1683967811yescharacteristic
423C22#1684002711yescharacteristic
424C22#1684002711yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—42no—
429C4—81no—
430C4—81no—
431C4—81no—
432C4—4881no—
433C4#1683995011yescharacteristic
434C4#1683995311yescharacteristic
435C2—21no—
436C2—21no—
437C2—41no—
438C2—41no—
439C2—9761no—
440C2#2144706911yescharacteristic
441C2#2144707911yescharacteristic
442C2#2144710511yescharacteristic
subgroupG/H
centerC22#16839678
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1508C2
socleC22×C61#394
prime radicalC2×#14519751C22
hypercenter#1508D61
hypocenterC61#10558
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
2. #21446288C2semidirect
4. #21446004C2semidirect
6. #21443695C2semidirect
7. C61×#1508C2semidirect
218. #1508D61semidirect
252. C61#10558semidirect

Maximal subgroups

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

subgroupindex
#214565722
#214462882
#214462802
#214460042
#214443342
#214436952
C61×#15082
#1055861