Finite Group Databasebeta

← #29568610

Subgroups — #29568610

Order 15616.

426 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 93 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#21454187C211yesmaximal, characteristic
2#21445961C211yesmaximal, characteristic, complemented
3#21445671C211yesmaximal, characteristic, complemented
4#21443642C211yesmaximal, characteristic, complemented
5#21443639C211yesmaximal, characteristic
6#21443639C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic, complemented
8C2×#14519772—21no—
9C2×#14519706—21no—
10C2×#14519687—21no—
11#16839664C2211yescharacteristic
12#16839663C411yescharacteristic
13#16839663C411yescharacteristic
14#16839661C411yescharacteristic
15#16839658C411yescharacteristic
16#16839654—21no—
17#16839652—21no—
18#16839651—21no—
19C42×Dic61C2211yescharacteristic
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22#16839516—21no—
23#16839516—21no—
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×#92418—21no—
29C22×#92418—21no—
30#14519772—42no—
31#14519772—42no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519706—24no—
48#14519687—42no—
49#14519684—21no—
50#14519684—21no—
51C22×C8×C61—21no—
52C22×C8×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57#95×C61—21no—
58C23×D61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22×C411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C22⋊C411yescharacteristic
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—41no—
72C2×D244—41no—
73C2×C8×C61—22no—
74C2×C8×C61—41no—
75C2×C8×C61—41no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C42×C61—41no—
85#11758198—42no—
86#11758198—42no—
87#11758198—42no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91#11758198—41no—
92#11758198—42no—
93C4⋊Dic61—42no—
94C4⋊Dic61—41no—
95#11758196—42no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—22no—
103C4×Dic61—41no—
104C4×Dic61—41no—
105C2×#92418—22no—
106C2×#92418—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61#13111yescharacteristic
132C2×C4×C61#13111yescharacteristic
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C61#13711yescharacteristic
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61#10412yes—
152D244—81no—
153D244—81no—
154C8×C61—42no—
155C8×C61—81no—
156#92418—42no—
157#92418—81no—
158#7712—611nomaximal, Sylow
159C22×C61#40811yescharacteristic
160C22×C61#41011yescharacteristic
161C22×C61#41311yescharacteristic
162C22×C61#41711yescharacteristic
163C22×C61#41811yescharacteristic
164C22×C61C2×#10411yescharacteristic
165C22×C61#42111yescharacteristic
166C2×D61—81no—
167C2×D61—81no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—81no—
180C4×C61—81no—
181Dic61—22no—
182Dic61—41no—
183Dic61—41no—
184Dic61—41no—
185Dic61—81no—
186#2860—611no—
187#1839—611no—
188#1767—611no—
189#1271—611no—
190#1271D6111yescharacteristic, complemented
191#1270—611no—
192#1270—611no—
193C2×C61#147311yescharacteristic
194C2×C61#148411yescharacteristic
195C2×C61#149511yescharacteristic
196C2×C61#150911yescharacteristic
197C2×C61#151411yescharacteristic
198C2×C61#153211yescharacteristic
199C2×C61#155711yescharacteristic
200D61—161no—
201C2×#126—1221no—
202C2×C4⋊C8—1221no—
203C2×#97—1221no—
204#390—611no—
205#390—611no—
206#390—611no—
207#389—611no—
208#389—611no—
209#389C2×D6111yescharacteristic
210#388—1221no—
211#388—1221no—
212#388—1221no—
213C43—611no—
214#336—611no—
215#336—611no—
216#336—1221no—
217#336—1221no—
218#336C2×D6111yescharacteristic
219#336C2×D6111yescharacteristic
220C61#771211yescharacteristic, complemented, Sylow
221C22×D4—611no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—1221no—
225C22×C8—1221no—
226#126—2442no—
227#126—2442no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4C4×D6111yescharacteristic
233C2×C4⋊C4C4×D6111yescharacteristic
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42C22×D6111yescharacteristic
247C4⋊C8—1224no—
248#97—2442no—
249#95—21no—
250#95—1221no—
251#95—1221no—
252C24—1221no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4—2441no—
256C2×D4—2441no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—1221no—
264C22×C4C2×C4×D6111yescharacteristic
265C22×C4D4×D6111yescharacteristic
266C22×C4D4×D6111yescharacteristic
267C2×C8—22no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—1222no—
274C2×C8—2441no—
275C2×C8—2441no—
276C2×C8—2441no—
277C2×C8—2441no—
278C2×C8—2441no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—2441no—
285C4⋊C4—2442no—
286C4⋊C4—2442no—
287C22⋊C4—2442no—
288C22⋊C4—2442no—
289C22⋊C4—2442no—
290C22⋊C4—2442no—
291C22⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C42—41no—
296C42—1222no—
297C42—1221no—
298C42—1221no—
299C42—1221no—
300C42—1221no—
301C42—1221no—
302C42—1221no—
303C42—2441no—
304C42—2441no—
305C23—2441no—
306C23—2441no—
307C23—2441no—
308C23—2441no—
309C23—2441no—
310C23—2441no—
311C23—2441no—
312C23C22⋊C4×D6111yescharacteristic
313D4—4881no—
314D4—4881no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—612no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4#1451978311yescharacteristic
343C2×C4#1451978511yescharacteristic
344C2×C4#1451980111yescharacteristic
345C2×C4#1451980411yescharacteristic
346C2×C4#1451980411yescharacteristic
347C2×C4#1451980911yescharacteristic
348C8—42no—
349C8—81no—
350C8—4881no—
351C8—2442no—
352C22—4881no—
353C22—4881no—
354C22—4881no—
355C22—4881no—
356C22—4881no—
357C22—4881no—
358C22—4881no—
359C22#1683972711yescharacteristic
360C22#1683973411yescharacteristic
361C22#1683974511yescharacteristic
362C22#1683976211yescharacteristic
363C22#1683976511yescharacteristic
364C22#104×D6111yescharacteristic
365C22#1683977711yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—81no—
373C4—81no—
374C4—1222no—
375C4—4881no—
376C4—2441no—
377C4—2441no—
378C4—2441no—
379C2—9761no—
380C2#2144418711yescharacteristic
381C2#2144423411yescharacteristic
382C2#2144428311yescharacteristic
383C2#2144434311yescharacteristic
384C2#2144436411yescharacteristic
385C2#2144443811yescharacteristic
386C2#2144454011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61#7712
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
2. #21445961C2semidirect
3. #21445671C2semidirect
4. #21443642C2semidirect
7. C61×#1271C2semidirect
190. #1271D61semidirect
220. C61#7712semidirect

Maximal subgroups

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

subgroupindex
#214541872
#214459612
#214456712
#214436422
#214436392
C61×#12712
#771261