Finite Group Databasebeta

← #29573653

Subgroups — #29573653

Order 15616.

466 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 85 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#21448793C211yesmaximal, characteristic
2C4×#14519691C211yesmaximal, characteristic
3#21444155C211yesmaximal, characteristic
4#21443705C211yesmaximal, characteristic, complemented
5#21443673C211yesmaximal, characteristic, complemented
6#21443672C211yesmaximal, characteristic, complemented
7C61×#1297C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D61C2211yescharacteristic
9C2×#14519691—21no—
10#16839726C2211yescharacteristic
11#16839662—21no—
12#16839656—21no—
13#16839653—21no—
14#16839626C411yescharacteristic, complemented
15#16839625C2211yescharacteristic
16#16839624C411yescharacteristic, complemented
17C4×#11758196—21no—
18#16839613C411yescharacteristic, complemented
19C4×C22⋊Dic61C2211yescharacteristic
20#16839609C411yescharacteristic, complemented
21#16839528—21no—
22#16839487—21no—
23#16839485—21no—
24C61×#407C2211yescharacteristic
25C4×C22⋊C4×C61C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C22×C22⋊D61D411yescharacteristic
28C22×C4×D61C2×C411yescharacteristic
29C2×#11758194—21no—
30C4×C22⋊D61—21no—
31C4×C22⋊D61—21no—
32C4×C22⋊D61—21no—
33C4×C22⋊D61—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196D411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61D411yescharacteristic
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198D411yescharacteristic
43C2×C4×Dic61—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47#14519691—24no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55#14519684C2×C411yescharacteristic
56C23×C4×C61C2311yescharacteristic
57C2×M16×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C42×C61—21no—
61C2×C42×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64#95×C61—21no—
65#95×C61C2×C411yescharacteristic
66#95×C61C2×C411yescharacteristic
67C24×C61C2×D411yescharacteristic
68C23×D61C22⋊C411yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61—81no—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C2×C22⋊D61—21no—
80C2×C22⋊D61—21no—
81C2×C22⋊D61—22no—
82C2×C22⋊D61—41no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—41no—
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—81no—
92M16×C61—81no—
93C2×C8×C61—41no—
94C22⋊C4×C61—22no—
95C22⋊C4×C61—42no—
96C22⋊C4×C61—41no—
97C42×C61—81no—
98C42×C61—81no—
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101C22⋊Dic61—22no—
102C22⋊Dic61—41no—
103C22⋊Dic61—81no—
104#11758198—21no—
105#11758198—21no—
106#11758198—42no—
107#11758198—81no—
108#11758196—21no—
109#11758196—21no—
110#11758196—42no—
111#11758196—42no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61—42no—
115C4×Dic61—81no—
116C4×Dic61—81no—
117#11758194—81no—
118C2×#92418—41no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61C2×C22⋊C411yescharacteristic
124C23×C61#12311yescharacteristic
125C23×C61#12311yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—41no—
130C22×D61—41no—
131C2×C4×C61—22no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—81no—
145C2×C4×C61—81no—
146C2×C4×C61#11711yescharacteristic
147C2×C4×C61#11711yescharacteristic
148C2×C4×C61#12311yescharacteristic
149C2×C4×C61#12311yescharacteristic
150C22⋊D61—42no—
151C22⋊D61—42no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—42no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—81no—
166C2×Dic61—81no—
167C2×Dic61#10412yes—
168C4×D61—81no—
169C4×D61—81no—
170C8×C61—81no—
171#92418—81no—
172#8779—611nomaximal, Sylow
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61#38111yescharacteristic
184C22×C61C2×#10411yescharacteristic
185C22×C61#42111yescharacteristic
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—81no—
190C2×D61—81no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—42no—
196C4×C61—81no—
197C4×C61—82no—
198Dic61—22no—
199Dic61—41no—
200Dic61—41no—
201Dic61—81no—
202Dic61—81no—
203Dic61—82no—
204#2357—611no—
205C4×#99—611no—
206#1465—611no—
207#1297—611no—
208#1297D6111yescharacteristic, complemented
209#1284—611no—
210#1284—611no—
211C2×C61—21no—
212C2×C61—21no—
213C2×C61—41no—
214C2×C61—41no—
215C2×C61#182611yescharacteristic
216C2×C61#182711yescharacteristic
217C2×C61#182811yescharacteristic
218D61—81no—
219C2×C4×D4—611no—
220C2×#99—1221no—
221#407—611no—
222#407C2×D6111yescharacteristic
223#390—1221no—
224#388—1221no—
225#388—1221no—
226#382—611no—
227#381—611no—
228#381—611no—
229C4×C4⋊C4—611no—
230C4×C4⋊C4—1221no—
231C4×C22⋊C4—611no—
232C4×C22⋊C4—611no—
233C4×C22⋊C4C2×D6111yescharacteristic
234C4×C22⋊C4C2×D6111yescharacteristic
235#342—1221no—
236#324—1221no—
237#323—1221no—
238C61#877911yescharacteristic, complemented, Sylow
239C22×D4—611no—
240C23×C4—611no—
241C23×C4C22×D6111yescharacteristic
242C2×M16—21no—
243C2×M16—1221no—
244C4×D4—1221no—
245C4×D4—1221no—
246C4×D4—1221no—
247C4×D4—1221no—
248C2×C4⋊C4—611no—
249C2×C4⋊C4—1221no—
250C2×C4⋊C4—1221no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—611no—
254C2×C22⋊C4—611no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C42—21no—
260C2×C42—21no—
261C2×C42—611no—
262C2×C42—1221no—
263C2×C42—1221no—
264C2×C42—1221no—
265#99—1224no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C22⋊C8—1221no—
269C22⋊C8—1221no—
270#95—21no—
271#95—611no—
272#95—611no—
273#95—1221no—
274#95—1221no—
275#95—1221no—
276#95—1221no—
277#95C4×D6111yescharacteristic
278#95C4×D6111yescharacteristic
279C24—611no—
280C24D4×D6111yescharacteristic
281C2×D4—1222no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—2441no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—81no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—4881no—
297C22×C4—2441no—
298C22×C4C2×C4×D6111yescharacteristic
299C22×C4#1175822211yescharacteristic
300C22×C4#1175822211yescharacteristic
301C22×C4D4×D6111yescharacteristic
302C22×C4#1175822411yescharacteristic
303C22×C4#1175822611yescharacteristic
304M16—81no—
305M16—4881no—
306C2×C8—41no—
307C2×C8—2441no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—2442no—
311C4⋊C4—2442no—
312C22⋊C4—22no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C22⋊C4—1222no—
320C22⋊C4—4881no—
321C22⋊C4—4881no—
322C22⋊C4—2442no—
323C22⋊C4—2441no—
324C42—81no—
325C42—81no—
326C42—1221no—
327C42—1221no—
328C42—4881no—
329C42—4881no—
330C42—2442no—
331C23—21no—
332C23—21no—
333C23—41no—
334C23—41no—
335C23—1221no—
336C23—1221no—
337C23—1221no—
338C23—2441no—
339C23—2441no—
340C23C22⋊C4×D6111yescharacteristic
341C23#1451975911yescharacteristic
342C23#1451976211yescharacteristic
343D4—2442no—
344D4—2442no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—612no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—4881no—
366C2×C4—4881no—
367C2×C4—4881no—
368C2×C4—4881no—
369C2×C4—2441no—
370C2×C4—2442no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4#1451973411yescharacteristic
379C2×C4#1451973511yescharacteristic
380C2×C4#1451975911yescharacteristic
381C2×C4#1451976211yescharacteristic
382C8—81no—
383C8—4881no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—81no—
393C22—81no—
394C22—4881no—
395C22—4881no—
396C22—2441no—
397C22—2441no—
398C22—2441no—
399C22#1683962411yescharacteristic
400C22#104×D6111yescharacteristic
401C22#1683977711yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—42no—
407C4—81no—
408C4—82no—
409C4—1222no—
410C4—4881no—
411C4—4881no—
412C4—4882no—
413C4—2441no—
414C4—2441no—
415C2—21no—
416C2—21no—
417C2—41no—
418C2—41no—
419C2—4881no—
420C2#2144591711yescharacteristic
421C2#2144592211yescharacteristic
422C2#2144592611yescharacteristic
subgroupG/H
centerC22#16839624
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1297C2
socleC22×C61#381
prime radicalC22×C22⋊D61D4
cosocleC23×C4×C61C23
hypercenter#1297D61
hypocenterC61#8779
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
4. #21443705C2semidirect
5. #21443673C2semidirect
6. #21443672C2semidirect
7. C61×#1297C2semidirect
14. #16839626C4semidirect
16. #16839624C4semidirect
18. #16839613C4semidirect
20. #16839609C4semidirect
208. #1297D61semidirect
238. C61#8779semidirect

Maximal subgroups

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

subgroupindex
#214487932
C4×#145196912
#214441552
#214437052
#214436732
#214436722
C61×#12972
#877961