Finite Group Databasebeta

← #29590779

Subgroups — #29590779

Order 15616.

582 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 91 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#21445807C211yesmaximal, characteristic, complemented
2#21444157C211yesmaximal, characteristic, complemented
3#21443843C212yesmaximal, complemented
4#21443816C212yesmaximal, complemented
5C61×#2397C211yesmaximal, characteristic
6C2×#14519692—21no—
7#16839726—21no—
8#16839622—21no—
9#16839529C2212yes—
10#16839488—21no—
11#16839486C2212yes—
12C2×C4×D4×C61—21no—
13C2×C4×D4×C61—21no—
14C2×C4×D4×C61C411yescharacteristic, complemented
15C2×C4×D4×C61C2211yescharacteristic
16C61×#399—21no—
17C61×#399C411yescharacteristic, complemented
18C61×#399C2211yescharacteristic
19C61×#392—21no—
20C61×#392C411yescharacteristic, complemented
21C61×#392C2211yescharacteristic
22C61×#376C411yescharacteristic, complemented
23C2×#11758194—41no—
24C2×C4⋊Dic61—41no—
25C2×C22⋊Dic61—22no—
26#14519692—42no—
27C22⋊#92418—22no—
28C22⋊#92418—41no—
29#14519684—41no—
30C22×D4×C61—21no—
31C22×D4×C61—21no—
32C22×D4×C61C2×C411yescharacteristic
33C22×D4×C61D411yescharacteristic
34C23×C4×C61—21no—
35C23×C4×C61D411yescharacteristic
36C23×C4×C61D411yescharacteristic
37C4×D4×C61—41no—
38C4×D4×C61—41no—
39C4×D4×C61—44no—
40C4×D4×C61—44no—
41C4×D4×C61—41no—
42C4×D4×C61—41no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61D411yescharacteristic
47C2×C22⋊C4×C61—21no—
48C2×C22⋊C4×C61—21no—
49C2×C22⋊C4×C61—21no—
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61C2311yescharacteristic
54C2×C42×C61—21no—
55C2×C42×C61C2×C411yescharacteristic
56#95×C61—21no—
57#95×C61C2×C411yescharacteristic
58#95×C61C2×C411yescharacteristic
59C24×C61—21no—
60C24×C61C22⋊C411yescharacteristic
61C24×C61C2×D411yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61—41no—
65C2×D4×C61—41no—
66C2×D4×C61—42no—
67C2×D4×C61—42no—
68C2×D4×C61—41no—
69C2×D4×C61—42no—
70C2×D4×C61—42no—
71C2×D4×C61—42no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61—42no—
75C22×C4×C61—21no—
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—42no—
83C22×C4×C61—42no—
84C22×C4×C61—42no—
85C22×C4×C61—42no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61C22⋊C411yescharacteristic
89C22×C4×C61C22⋊C411yescharacteristic
90C22×C4×C61C22⋊C411yescharacteristic
91C22×C4×C61C22×C411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×Dic61—42no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—42no—
96C4⋊C4×C61—42no—
97C4⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—42no—
101C22⋊C4×C61—42no—
102C22⋊C4×C61—42no—
103C22⋊C4×C61—42no—
104C22⋊C4×C61—42no—
105C42×C61—24no—
106C42×C61—21no—
107C42×C61—21no—
108C22⋊Dic61—42no—
109C22⋊Dic61—42no—
110C4⋊Dic61—82no—
111#11758194—82no—
112C2×#92418—42no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—22no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61C2×C22⋊C411yescharacteristic
130C23×C61AGL(1,ℤ/8)11yescharacteristic
131C23×C61#13711yescharacteristic
132D4×C61—42no—
133D4×C61—42no—
134D4×C61—42no—
135D4×C61—44no—
136D4×C61—44no—
137D4×C61—48no—
138D4×C61—42no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—81no—
161C2×C4×C61—81no—
162C2×C4×C61—82no—
163C2×C4×C61—82no—
164C2×C4×C61#9911yescharacteristic
165C2×C4×C61#9911yescharacteristic
166C2×Dic61—82no—
167C2×Dic61—82no—
168C2×Dic61—82no—
169#92418—82no—
170#11821—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—42no—
178C22×C61—42no—
179C22×C61—42no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—42no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61C2×#9911yescharacteristic
193C22×C61#41711yescharacteristic
194C22×C61#42111yescharacteristic
195C4×C61—21no—
196C4×C61—42no—
197C4×C61—42no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61—41no—
201C4×C61—41no—
202C4×C61—81no—
203C4×C61#35312yes—
204Dic61—162no—
205#2397D6111yescharacteristic
206#1799—611no—
207#1465—611no—
208#1352—612no—
209#1343—612no—
210C2×C61—21no—
211C2×C61—21no—
212C2×C61—41no—
213C2×C61—41no—
214C2×C61—81no—
215C2×C61—82no—
216C2×C61#151311yescharacteristic
217C2×C61#212011yescharacteristic
218C2×C61C2×#35311yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4—21no—
221C2×C4×D4Dic6111yescharacteristic, complemented
222C2×C4×D4C2×D6111yescharacteristic
223C2×#99—1221no—
224#407—1221no—
225#399—21no—
226#399Dic6111yescharacteristic, complemented
227#399C2×D6111yescharacteristic
228#392—21no—
229#392Dic6111yescharacteristic, complemented
230#392C2×D6111yescharacteristic
231#380—1221no—
232#376Dic6111yescharacteristic, complemented
233#342—612no—
234#324—1221no—
235#323—612no—
236C61#1182111yescharacteristic, complemented, Sylow
237C22×D4—21no—
238C22×D4—21no—
239C22×D4C2×Dic6111yescharacteristic
240C22×D4C22⋊D6111yescharacteristic
241C23×C4—21no—
242C23×C4C22⋊D6111yescharacteristic
243C23×C4C22⋊D6111yescharacteristic
244C2×M16—2441no—
245C4×D4—41no—
246C4×D4—41no—
247C4×D4—44no—
248C4×D4—44no—
249C4×D4—41no—
250C4×D4—41no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—2441no—
254C2×C4⋊C4C2×Dic6111yescharacteristic
255C2×C4⋊C4C22⋊D6111yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—1222no—
262C2×C22⋊C4C2×Dic6111yescharacteristic
263C2×C22⋊C4C22×D6111yescharacteristic
264C2×C42—21no—
265C2×C42C2×Dic6111yescharacteristic
266#99—2442no—
267C22⋊C8—1222no—
268C22⋊C8—2441no—
269#95—21no—
270#95—2441no—
271#95C2×Dic6111yescharacteristic
272#95C2×Dic6111yescharacteristic
273C24—21no—
274C24C22⋊Dic6111yescharacteristic
275C24C2×C22⋊D6111yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—42no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—2442no—
303C22×C4C22⋊Dic6111yescharacteristic
304C22×C4C22⋊Dic6111yescharacteristic
305C22×C4C22⋊Dic6111yescharacteristic
306C22×C4C22×Dic6111yescharacteristic
307C22×C4C2×C22⋊D6111yescharacteristic
308M16—4882no—
309C2×C8—2442no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—4882no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—2442no—
323C22⋊C4—2442no—
324C42—24no—
325C42—21no—
326C42—21no—
327C23—21no—
328C23—21no—
329C23—22no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23C2×C22⋊Dic6111yescharacteristic
344C23#1451980211yescharacteristic
345C23#1451980711yescharacteristic
346D4—42no—
347D4—42no—
348D4—42no—
349D4—44no—
350D4—44no—
351D4—48no—
352D4—42no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—4882no—
379C2×C4—4882no—
380C2×C4—4882no—
381C2×C4#1451969211yescharacteristic
382C2×C4#1451969211yescharacteristic
383C8—4882no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—42no—
397C22—41no—
398C22—41no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22C2×#1451969211yescharacteristic
406C22#1683976311yescharacteristic
407C22#1683977911yescharacteristic
408C4—21no—
409C4—42no—
410C4—42no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—81no—
416C4—9762no—
417C4#1683955512yes—
418C2—21no—
419C2—21no—
420C2—41no—
421C2—41no—
422C2—81no—
423C2—82no—
424C2#2144436211yescharacteristic
425C2#2144746011yescharacteristic
426C2C2×#1683955511yescharacteristic
subgroupG/H
centerC22C2×#14519692
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
Fitting, prime radicalC61×#2397C2
socleC22×C61C2×#99
cosocleC2×C22⋊C4×C61C23
hypercenter#2397D61
hypocenterC61#11821
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. #21445807C2semidirect
2. #21444157C2semidirect
3. #21443843C2semidirect
4. #21443816C2semidirect
14. C2×C4×D4×C61C4semidirect
17. C61×#399C4semidirect
20. C61×#392C4semidirect
22. C61×#376C4semidirect
221. C2×C4×D4Dic61semidirect
226. #399Dic61semidirect
229. #392Dic61semidirect
232. #376Dic61semidirect
236. C61#11821semidirect

Maximal subgroups

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

subgroupindex
#214458072
#214441572
#214438432
#214438162
C61×#23972
#1182161