Finite Group Databasebeta

← #29599693

Subgroups — #29599693

Order 15616.

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

normal subgroups only

This group has 484 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#21453762C211yesmaximal, characteristic
2#21446100C211yesmaximal, characteristic
3#21446029C211yesmaximal, characteristic
4#21443943C211yesmaximal, characteristic
5#21443937C211yesmaximal, characteristic
6#21443936C211yesmaximal, characteristic
7C61×#1867C211yesmaximal, characteristic
8#16839805—21no—
9C2×#14519694C2211yescharacteristic
10C2×#14519692C2211yescharacteristic
11#16839704—21no—
12#16839674—21no—
13#16839674—21no—
14#16839666—21no—
15#16839665C2211yescharacteristic
16#16839642C2211yescharacteristic
17#16839635—21no—
18#16839634—21no—
19#16839634—21no—
20#16839529—21no—
21#16839521—21no—
22C61×#518C2211yescharacteristic
23C2×#99×C61C2211yescharacteristic
24C61×#386C2211yescharacteristic
25C61×#385—21no—
26C61×#342—21no—
27C22×Dic122—21no—
28C23×Dic61D411yescharacteristic
29C2×#11758194—21no—
30C2×C4⋊Dic61D411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—41no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40#14519710—41no—
41#14519708—41no—
42#14519694—21no—
43#14519694Q812yescomplemented
44#14519692—21no—
45#14519692Q812yescomplemented
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—41no—
53C22×D4×C61C2311yescharacteristic
54C23×C4×C61D411yescharacteristic
55C4×D4×C61—41no—
56C4×D4×C61—41no—
57#117×C61—21no—
58C2×C4⋊C4×C61—41no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61D411yescharacteristic
64#99×C61—21no—
65#99×C61Q812yescomplemented
66#95×C61—21no—
67#95×C61—41no—
68C24×C61C2×D411yescharacteristic
69C24×C61C2×D411yescharacteristic
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61C2×Q811yescharacteristic
73C2×D4×C61C2×Q811yescharacteristic
74C2×D4×C61C2×Q811yescharacteristic
75C2×D4×C61#4111yescharacteristic
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—81no—
85C22×C4×C61C2×D411yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61—81no—
93C2×Dic122—42no—
94C2×Dic122—81no—
95C2×Dic122—81no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—82no—
99C22⋊C4×C61—22no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—81no—
106C42×C61—41no—
107C22⋊Dic61—22no—
108C22⋊Dic61—42no—
109C22⋊Dic61—42no—
110C22⋊Dic61—41no—
111C22⋊Dic61—41no—
112C22⋊Dic61—81no—
113C4⋊Dic61—41no—
114#11758196—81no—
115#11758196—81no—
116#11758196—82no—
117C4×Dic61—41no—
118#11758194—22no—
119#11758194—41no—
120C2×#92418—41no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61#12011yescharacteristic
130C23×C61C22⋊Q811yescharacteristic
131C23×C61C22⋊Q811yescharacteristic
132C23×C61C4⋊Q811yescharacteristic
133C23×C61C4⋊Q811yescharacteristic
134D4×C61—41no—
135D4×C61—41no—
136D4×C61—41no—
137D4×C61—41no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—41no—
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×C61—81no—
154C2×C4×C61—81no—
155C2×C4×C61—81no—
156C2×C4×C61—81no—
157C2×C4×C61C22⋊Q811yescharacteristic
158C2×C4×C61C4⋊Q811yescharacteristic
159C2×Dic61—22no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—42no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—42no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—81no—
174C2×Dic61—81no—
175C2×Dic61—81no—
176Dic122—84no—
177#92418—42no—
178#13463—611nomaximal, Sylow
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61#39511yescharacteristic
196C22×C61B(4,𝔽2)11yescharacteristic
197C22×C61#45811yescharacteristic
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—81no—
201C4×C61—82no—
202C4×C61—81no—
203C4×C61—81no—
204C4×C61—81no—
205Dic61—42no—
206Dic61—81no—
207Dic61—82no—
208Dic61—81no—
209Dic61—81no—
210#2804—611no—
211#1867—611no—
212#1867D6111yescharacteristic
213#1856—611no—
214#1393—611no—
215#1390—611no—
216#1390—611no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—41no—
220C2×C61—41no—
221C2×C61—41no—
222C2×C61—41no—
223C2×C61#206211yescharacteristic
224C2×C61#219811yescharacteristic
225C2×C61#219911yescharacteristic
226#518C2×D6111yescharacteristic
227#428—1221no—
228C2×#100—611no—
229C2×#99—611no—
230C2×#99C2×D6111yescharacteristic
231#400—1221no—
232#393—1221no—
233#393—1221no—
234#391—1221no—
235#390—611no—
236#386—611no—
237#386C2×D6111yescharacteristic
238#385—21no—
239#385—1221no—
240#385—1221no—
241#385—1221no—
242#342—21no—
243#342—1221no—
244#339—1221no—
245C61#1346311yescharacteristic, complemented, Sylow
246C22×Q8—1221no—
247C22×D4C22×D6111yescharacteristic
248C23×C4—611no—
249C23×C4C22⋊D6111yescharacteristic
250C2×M16—1221no—
251C4×D4—41no—
252C4×D4—41no—
253#117—21no—
254C2×C4⋊C4—41no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—2441no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—611no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4C22⋊D6111yescharacteristic
269C2×C42—611no—
270#107—2441no—
271#106—2441no—
272#100—612no—
273#100—1221no—
274#99—21no—
275#99—612no—
276#99—1221no—
277#99Dic12212yescomplemented
278#95—21no—
279#95—41no—
280#95—1221no—
281#95—1221no—
282#95—1221no—
283#95—1221no—
284#95—1221no—
285#95—1221no—
286#95—2441no—
287C24D4×D6111yescharacteristic
288C24C2×C22⋊D6111yescharacteristic
289C2×Q8—4881no—
290C2×Q8—4881no—
291C2×Q8—2442no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4C2×Dic12211yescharacteristic
295C2×D4#1175822211yescharacteristic
296C2×D4Q8×D6111yescharacteristic
297C2×D4Q8×D6111yescharacteristic
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—81no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—4881no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4D4×D6111yescharacteristic
315M16—1222no—
316M16—2441no—
317C2×C8—2441no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—82no—
321C4⋊C4—4881no—
322C4⋊C4—4881no—
323C4⋊C4—4882no—
324C4⋊C4—2441no—
325C22⋊C4—22no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—1222no—
333C22⋊C4—4881no—
334C22⋊C4—2442no—
335C22⋊C4—2442no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C42—41no—
339C42—2441no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23#1451974511yescharacteristic
349C23#1451975511yescharacteristic
350C23#1451975611yescharacteristic
351C23#1451977511yescharacteristic
352C23#1451977611yescharacteristic
353Q8—4884no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—41no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—1222no—
378C2×C4—4881no—
379C2×C4—4881no—
380C2×C4—4881no—
381C2×C4—2442no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2442no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4#1451975511yescharacteristic
395C2×C4#1451977611yescharacteristic
396C8—2442no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22#1683968211yescharacteristic
414C22#1683994811yescharacteristic
415C22#1683995111yescharacteristic
416C4—21no—
417C4—21no—
418C4—81no—
419C4—82no—
420C4—81no—
421C4—81no—
422C4—81no—
423C4—4881no—
424C4—4882no—
425C4—4881no—
426C4—4881no—
427C4—2442no—
428C2—21no—
429C2—21no—
430C2—41no—
431C2—41no—
432C2—41no—
433C2—41no—
434C2#2144717211yescharacteristic
435C2#2144781311yescharacteristic
436C2#2144781811yescharacteristic
subgroupG/H
centerC22#16839948
commutator, prime radical, cosocleC22×D4×C61C23
FrattiniC22×D4C22×D61
FittingC61×#1867C2
socleC22×C61B(4,𝔽2)
hypercenter#1867D61
hypocenterC61#13463
LCSG ▷ C22×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1867

Complements

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

NH ≅ G/Ntype
43. #14519694Q8semidirect
45. #14519692Q8semidirect
65. #99×C61Q8semidirect
245. C61#13463semidirect
277. #99Dic122semidirect

Maximal subgroups

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

subgroupindex
#214537622
#214461002
#214460292
#214439432
#214439372
#214439362
C61×#18672
#1346361