Finite Group Databasebeta

← #29590777

Subgroups — #29590777

Order 15616.

582 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 83 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#21449098C211yesmaximal, characteristic
2#21444157C211yesmaximal, characteristic, complemented
3#21443842C212yesmaximal, complemented
4#21443815C212yesmaximal, complemented
5C61×#1799C211yesmaximal, characteristic, complemented
6C2×C4×D244C411yescharacteristic, complemented
7C2×C4×C22⋊D61—21no—
8C2×C4×C22⋊D61—21no—
9#16839726—21no—
10#16839698C411yescharacteristic, complemented
11#16839698C2211yescharacteristic
12#16839697—21no—
13#16839671C411yescharacteristic, complemented
14#16839671C2211yescharacteristic
15#16839670—21no—
16#16839608C411yescharacteristic, complemented
17#16839488—21no—
18#16839486C2212yes—
19C2×C4×D4×C61C2211yescharacteristic
20C2×#99×C61—21no—
21C61×#380—21no—
22C61×#342C2212yes—
23C22×D244C2×C411yescharacteristic
24C22×C22⋊D61—21no—
25C22×C22⋊D61—21no—
26C22×C4×D61—21no—
27C2×#11758194—41no—
28C4×D244—41no—
29C4×D244—41no—
30C4×C22⋊D61—44no—
31C4×C22⋊D61—44no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×C4×Dic61—21no—
41C22⋊#92418—22no—
42C22⋊#92418—41no—
43#14519684—21no—
44#14519684C2×C411yescharacteristic
45#14519684C2×C411yescharacteristic
46C22×D4×C61D411yescharacteristic
47C23×C4×C61D411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C4×D4×C61—41no—
50C4×D4×C61—41no—
51C2×C4⋊C4×C61—41no—
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C22⋊C4×C61—22no—
54C2×C22⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61C2311yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57#99×C61—42no—
58#95×C61—41no—
59C24×C61C22⋊C411yescharacteristic
60C24×C61C2×D411yescharacteristic
61C23×D61—21no—
62C2×D4×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61—41no—
65C2×D4×C61—41no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—42no—
71C22×C4×C61—42no—
72C22×C4×C61—42no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C2×C22⋊D61—42no—
79C2×C22⋊D61—42no—
80C2×C22⋊D61—42no—
81C2×C22⋊D61—42no—
82C2×C22⋊D61—42no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C2×D244—41no—
89C2×D244—42no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—82no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—42no—
99C22⋊C4×C61—42no—
100C42×C61—21no—
101C42×C61—21no—
102C22⋊Dic61—42no—
103C22⋊Dic61—42no—
104#11758198—42no—
105#11758198—42no—
106#11758198—42no—
107C4⋊Dic61—41no—
108#11758196—42no—
109#11758196—42no—
110C4×Dic61—24no—
111#11758194—82no—
112C2×#92418—42no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61C2×C22⋊C411yescharacteristic
123C23×C61AGL(1,ℤ/8)11yescharacteristic
124C23×C61#13711yescharacteristic
125C22×D61—22no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132D4×C61—42no—
133D4×C61—42no—
134C2×C4×C61—22no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—42no—
142C2×C4×C61—42no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—81no—
147C2×C4×C61—81no—
148C2×C4×C61—82no—
149C2×C4×C61—82no—
150C2×C4×C61—82no—
151C2×C4×C61#9911yescharacteristic
152C2×C4×C61#9911yescharacteristic
153C22⋊D61—44no—
154C22⋊D61—44no—
155C22⋊D61—48no—
156C2×Dic61—22no—
157C2×Dic61—22no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165D244—42no—
166D244—42no—
167C4×D61—82no—
168C4×D61—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—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61C2×#9911yescharacteristic
186C22×C61#41711yescharacteristic
187C22×C61#42111yescharacteristic
188C2×D61—42no—
189C2×D61—42no—
190C2×D61—42no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—81no—
194C2×D61—81no—
195C4×C61—21no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61—162no—
201C4×C61#35312yes—
202Dic61—42no—
203Dic61—42no—
204Dic61—81no—
205#2397—611no—
206#1799D6111yescharacteristic, complemented
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#151311yescharacteristic
216C2×C61#212011yescharacteristic
217C2×C61C2×#35311yescharacteristic
218D61—82no—
219C2×C4×D4—611no—
220C2×C4×D4—1221no—
221C2×C4×D4—1221no—
222C2×C4×D4C2×D6111yescharacteristic
223C2×#99—21no—
224#407—1221no—
225#399—611no—
226#399—611no—
227#399—1221no—
228#392—611no—
229#392—611no—
230#392—1221no—
231#380—21no—
232#376—611no—
233#342C2×D6112yes—
234#324—1221no—
235#323—612no—
236C61#1182111yescharacteristic, complemented, Sylow
237C22×D4—611no—
238C22×D4—1221no—
239C22×D4—1221no—
240C22×D4C22⋊D6111yescharacteristic
241C23×C4—1221no—
242C23×C4D24411yescharacteristic
243C23×C4C22⋊D6111yescharacteristic
244C2×M16—2441no—
245C4×D4—41no—
246C4×D4—41no—
247C4×D4—2441no—
248C4×D4—2441no—
249C4×D4—2444no—
250C4×D4—2444no—
251C2×C4⋊C4—41no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4D24411yescharacteristic
256C2×C22⋊C4—22no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4C4×D6111yescharacteristic
263C2×C22⋊C4C22×D6111yescharacteristic
264C2×C42—1221no—
265C2×C42C4×D6111yescharacteristic
266#99—42no—
267C22⋊C8—1222no—
268C22⋊C8—2441no—
269#95—41no—
270#95—611no—
271#95—611no—
272#95—1221no—
273C24—1221no—
274C24#1175819811yescharacteristic
275C24C2×C22⋊D6111yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—2441no—
281C2×D4—2442no—
282C2×D4—2442no—
283C2×D4—2442no—
284C2×D4—2442no—
285C2×D4—2442no—
286C2×D4—2442no—
287C2×D4—2441no—
288C2×D4—2441no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—2442no—
300C22×C4—2442no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4#1175819811yescharacteristic
304C22×C4#1175819811yescharacteristic
305C22×C4#1175819811yescharacteristic
306C22×C4C2×C4×D6111yescharacteristic
307C22×C4C2×D24411yescharacteristic
308M16—4882no—
309C2×C8—2442no—
310C4⋊C4—41no—
311C4⋊C4—82no—
312C4⋊C4—2441no—
313C4⋊C4—2442no—
314C4⋊C4—2442no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—2442no—
320C22⋊C4—2442no—
321C22⋊C4—2442no—
322C22⋊C4—2442no—
323C22⋊C4—2442no—
324C42—21no—
325C42—21no—
326C42—1224no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—1222no—
337C23—2441no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23—2441no—
343C23C2×#1175819811yescharacteristic
344C23#1451980311yescharacteristic
345C23#1451980811yescharacteristic
346D4—42no—
347D4—42no—
348D4—2442no—
349D4—2442no—
350D4—2444no—
351D4—2444no—
352D4—2448no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—1222no—
371C2×C4—1222no—
372C2×C4—4882no—
373C2×C4—4882no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4#1451969111yescharacteristic
382C2×C4#1451969111yescharacteristic
383C8—4882no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—81no—
397C22—81no—
398C22—4881no—
399C22—4881no—
400C22—4881no—
401C22—4881no—
402C22—2442no—
403C22—2442no—
404C22—2442no—
405C22C2×#1451969111yescharacteristic
406C22#1683976111yescharacteristic
407C22#1683978011yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—162no—
414C4—4881no—
415C4—2442no—
416C4—2442no—
417C4#1683955412yes—
418C2—21no—
419C2—21no—
420C2—41no—
421C2—41no—
422C2—81no—
423C2—4882no—
424C2#2144436011yescharacteristic
425C2#2144745811yescharacteristic
426C2C2×#1683955411yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1799C2
socleC22×C61C2×#99
prime radical#21449098C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1799D61
hypocenterC61#11821
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #21444157C2semidirect
3. #21443842C2semidirect
4. #21443815C2semidirect
5. C61×#1799C2semidirect
6. C2×C4×D244C4semidirect
10. #16839698C4semidirect
13. #16839671C4semidirect
16. #16839608C4semidirect
206. #1799D61semidirect
236. C61#11821semidirect

Maximal subgroups

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

subgroupindex
#214490982
#214441572
#214438422
#214438152
C61×#17992
#1182161