Finite Group Databasebeta

← #30603907

Subgroups — #30603907

Order 15616.

562 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 90 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
1D61⋊#323C211yesmaximal, characteristic
2D61⋊#323C211yesmaximal, characteristic
3#21460764C212yesmaximal, complemented
4#21460763C212yesmaximal, complemented
5#21448430C211yesmaximal, characteristic
6D61⋊(C22⋊C8)—21no—
7D61⋊(C22⋊C8)—21no—
8#16840606—21no—
9#16840606—21no—
10#16840605C2212yes—
11#16840605C2212yes—
12C22×#11758198C411yescharacteristic
13C2×C22⋊C4×D61C411yescharacteristic
14C2×C22⋊C4×D61C2211yescharacteristic
15#16839637C2211yescharacteristic
16#16839636—21no—
17#16839635C2211yescharacteristic
18#16839634C411yescharacteristic
19#16839633—21no—
20#16839621—21no—
21#16839619—21no—
22C61×#385C411yescharacteristic
23C2×D61⋊C8—41no—
24C2×D61⋊C8—41no—
25#14519834—41no—
26#14519834—41no—
27C22⋊#92420—22no—
28C22⋊#92420—22no—
29C24×D61C2×C411yescharacteristic
30C23×Dic61C2×C411yescharacteristic
31C22×C4×D61—21no—
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C2×C4⋊Dic61—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×C22⋊Dic61C2×C411yescharacteristic
38C2×C22⋊Dic61C2311yescharacteristic
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—41no—
43C2×#11758198—41no—
44C2×#11758198D411yescharacteristic
45C2×#11758198D411yescharacteristic
46C22⋊C4×D61—22no—
47C22⋊C4×D61—41no—
48C22⋊C4×D61—41no—
49C22⋊C4×D61C814yescomplemented
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C23×C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C22⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61C2×C411yescharacteristic
57#95×C61—21no—
58C24×C61C22×C411yescharacteristic
59C23×D61—21no—
60C23×D61—21no—
61C23×D61—22no—
62C23×D61—81no—
63C23×D61—81no—
64C23×D61C22⋊C411yescharacteristic
65C23×D61C22⋊C411yescharacteristic
66C23×D61C2×C812yes—
67C23×D61M1612yes—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—41no—
71C22×C4×C61—81no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—41no—
77C22×Dic61—81no—
78C22×Dic61C2×D411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—24no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—81no—
86C2×C4×D61—81no—
87C2×C4×D61—81no—
88C2×C4×D61—81no—
89C2×#92420—42no—
90C2×#92420—42no—
91D61⋊C8—82no—
92D61⋊C8—82no—
93C4⋊C4×C61—81no—
94C22⋊C4×C61—21no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61C2×C812yescomplemented
97C22⋊Dic61—21no—
98C22⋊Dic61—41no—
99C22⋊Dic61C2×C812yescomplemented
100#11758198—24no—
101#11758198—41no—
102#11758198—41no—
103#11758198—42no—
104#11758198—41no—
105#11758198—41no—
106C4⋊Dic61—81no—
107#11758196—81no—
108#11758196—81no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61C2×C22⋊C411yescharacteristic
114C23×C61C22×C811yescharacteristic
115C23×C61C2×M1611yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—22no—
119C22×D61—22no—
120C22×D61—22no—
121C22×D61—22no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—81no—
127C22×D61—81no—
128C22×D61—81no—
129C22×D61—81no—
130C22×D61—84no—
131C22×D61—82no—
132C22×D61—82no—
133C22×D61C22⋊C812yes—
134C22×D61C22⋊C812yes—
135C22×D61#9911yescharacteristic
136C22×D61#9911yescharacteristic
137C22×D61#10112yes—
138C2×C4×C61—22no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—82no—
149C2×Dic61—22no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—82no—
160C4×D61—42no—
161C4×D61—42no—
162C4×D61—81no—
163C4×D61—81no—
164C4×D61—84no—
165#92420—82no—
166#92420—82no—
167#11453—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—42no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61C2×C22⋊C811yescharacteristic
178C22×C61C2×#9911yescharacteristic
179C22×C61C2×#10111yescharacteristic
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—22no—
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—42no—
191C2×D61—82no—
192C2×D61—82no—
193C2×D61—82no—
194C2×D61—82no—
195C2×D61#32412yes—
196C2×D61#32412yes—
197C4×C61—42no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61—81no—
201Dic61—42no—
202Dic61—41no—
203Dic61—41no—
204Dic61—81no—
205#2315—611no—
206C2×#323—611no—
207C2×#323—611no—
208#1326—612no—
209#1326—612no—
210C2×C61—21no—
211C2×C61—21no—
212C2×C61—41no—
213C2×C61—41no—
214C2×C61C2×#32411yescharacteristic
215C2×C61#212111yescharacteristic
216C2×C61#212111yescharacteristic
217D61—22no—
218D61—22no—
219D61—42no—
220C22×C22⋊C4—611no—
221C22×C22⋊C4—611no—
222C22×C22⋊C4—611no—
223C2×C22⋊C8—1221no—
224C2×C22⋊C8—1221no—
225#385—611no—
226#385—611no—
227#385—611no—
228#385—1221no—
229#385—1221no—
230#385#692311yescharacteristic
231#380—1221no—
232#380—1221no—
233#323—612no—
234#323—612no—
235#323—1221no—
236#323—1221no—
237C61#1145311yescharacteristic, complemented, Sylow
238C25—611no—
239C23×C4—611no—
240C23×C4—611no—
241C23×C4—611no—
242C23×C4—1221no—
243C23×C4C2×#692311yescharacteristic
244C22×C8—2441no—
245C22×C8—2441no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—1221no—
250C2×C22⋊C4—611no—
251C2×C22⋊C4—614no—
252C2×C22⋊C4—611no—
253C2×C22⋊C4—611no—
254C2×C22⋊C4—611no—
255C2×C22⋊C4—1222no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—2441no—
260C2×C22⋊C4—2441no—
261C2×C22⋊C4—2441no—
262C2×C22⋊C4—2441no—
263C2×C22⋊C4C2×#692311yescharacteristic
264C2×C22⋊C4C2×#692311yescharacteristic
265C22⋊C8—1222no—
266C22⋊C8—1222no—
267C22⋊C8—2441no—
268C22⋊C8—2441no—
269#95—21no—
270#95—1221no—
271#95—1221no—
272#95—1221no—
273C24—611no—
274C24—612no—
275C24—612no—
276C24—611no—
277C24—1221no—
278C24—1221no—
279C24—1222no—
280C24—4881no—
281C24—4881no—
282C24C22×#692311yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—81no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1224no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—4881no—
297C22×C4—4881no—
298C22×C4—4881no—
299C22×C4—4881no—
300C22×C4—4881no—
301C22×C4—2441no—
302C22×C4C22⋊#692311yescharacteristic
303C22×C4C22⋊#692311yescharacteristic
304C2×C8—4882no—
305C2×C8—4882no—
306C2×C8—2442no—
307C2×C8—2442no—
308C4⋊C4—81no—
309C4⋊C4—4881no—
310C4⋊C4—4881no—
311C4⋊C4—4881no—
312C22⋊C4—21no—
313C22⋊C4—41no—
314C22⋊C4—612no—
315C22⋊C4—1224no—
316C22⋊C4—1221no—
317C22⋊C4—2441no—
318C22⋊C4—2441no—
319C22⋊C4—2441no—
320C22⋊C4—2441no—
321C22⋊C4—2442no—
322C22⋊C4—2441no—
323C22⋊C4D61⋊C812yescomplemented
324C23—21no—
325C23—21no—
326C23—41no—
327C23—41no—
328C23—611no—
329C23—611no—
330C23—612no—
331C23—612no—
332C23—612no—
333C23—1222no—
334C23—1222no—
335C23—1222no—
336C23—1222no—
337C23—1221no—
338C23—1221no—
339C23—4881no—
340C23—4881no—
341C23—4881no—
342C23—4881no—
343C23—4884no—
344C23—4882no—
345C23—4882no—
346C23—2441no—
347C23—2441no—
348C23—2441no—
349C23—2441no—
350C23C2×C22⋊#692311yescharacteristic
351C23C2×D61⋊C811yescharacteristic
352C23D61⋊M1611yescharacteristic
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—82no—
364C2×C4—1222no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—4881no—
368C2×C4—4881no—
369C2×C4—4884no—
370C2×C4—4882no—
371C2×C4—2442no—
372C2×C4—2442no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C8—4882no—
381C8—4882no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—42no—
389C22—41no—
390C22—41no—
391C22—612no—
392C22—612no—
393C22—1221no—
394C22—1221no—
395C22—1221no—
396C22—1221no—
397C22—1222no—
398C22—4882no—
399C22—4882no—
400C22—4882no—
401C22—4882no—
402C22—2442no—
403C22—2442no—
404C22—2442no—
405C22—2442no—
406C22—2441no—
407C22—2441no—
408C22D61⋊(C22⋊C8)11yescharacteristic
409C22D61⋊#9911yescharacteristic
410C22D61⋊#10111yescharacteristic
411C4—42no—
412C4—41no—
413C4—41no—
414C4—81no—
415C4—4881no—
416C4—2442no—
417C4—2441no—
418C4—2441no—
419C2—21no—
420C2—21no—
421C2—41no—
422C2—41no—
423C2—1222no—
424C2—1222no—
425C2—2442no—
426C2D61⋊#32411yescharacteristic
427C2#2146207511yescharacteristic
428C2#2146207711yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC61×#385C4
socleC22×C61C2×#99
prime radicalC24×D61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenter#385#6923
hypocenterC61#11453
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #21460764C2semidirect
4. #21460763C2semidirect
49. C22⋊C4×D61C8semidirect
96. C22⋊C4×C61C2×C8semidirect
99. C22⋊Dic61C2×C8semidirect
237. C61#11453semidirect
323. C22⋊C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3232
#214607642
#214607632
#214484302
#1145361