Finite Group Databasebeta

← #29573418

Subgroups — #29573418

Order 15616.

482 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448212C211yesmaximal, characteristic
2#21445582C211yesmaximal, characteristic
3#21445582C211yesmaximal, characteristic
4#21443701C211yesmaximal, characteristic, complemented
5#21443701C211yesmaximal, characteristic, complemented
6#21443700C211yesmaximal, characteristic, complemented
7C61×#1295C211yesmaximal, characteristic, complemented
8C2×C42×D61C2211yescharacteristic
9C2×#14519689—21no—
10C2×#14519689—21no—
11C2×#14519688C2211yescharacteristic
12C2×#14519688C2211yescharacteristic
13#16839629—21no—
14#16839628C2211yescharacteristic
15#16839624—21no—
16#16839619C411yescharacteristic
17#16839619C411yescharacteristic
18C4⋊C4×Dic61C411yescharacteristic
19C4⋊C4×Dic61C411yescharacteristic
20#16839609—21no—
21#16839607—21no—
22#16839516—21no—
23#16839516—21no—
24C2×#97×C61C2211yescharacteristic
25C2×#97×C61C2211yescharacteristic
26C61×#382C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×#92418—21no—
31C22×#92418—21no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C42×D61—21no—
42C42×D61—21no—
43C42×D61—21no—
44C42×D61—21no—
45#14519689—24no—
46#14519689—24no—
47#14519688—21no—
48#14519688—21no—
49#14519688—21no—
50#14519688—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C42×C61C2311yescharacteristic
62#97×C61—21no—
63#97×C61—21no—
64#97×C61—21no—
65#97×C61—21no—
66#95×C61—21no—
67#95×C61—21no—
68C23×D61C22⋊C411yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—22no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C8×C61—22no—
92C2×C8×C61—22no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C42×C61#4111yescharacteristic
100C42×C61#4111yescharacteristic
101C42×C61#4111yescharacteristic
102C42×C61#4111yescharacteristic
103#11758198—42no—
104#11758198—42no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61—42no—
114C4×Dic61—42no—
115C2×#92418—22no—
116C2×#92418—22no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C23×C61C2×C22⋊C411yescharacteristic
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61#10412yes—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
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#11711yescharacteristic
142C2×C4×C61#11711yescharacteristic
143C2×C4×C61#12311yescharacteristic
144C2×C4×C61#12311yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C2×C4×C61#12311yescharacteristic
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61#10412yes—
162C4×D61—42no—
163C4×D61—42no—
164C4×D61—42no—
165C4×D61—42no—
166C4×D61—42no—
167C4×D61—42no—
168C8×C61—42no—
169C8×C61—42no—
170#92418—42no—
171#92418—42no—
172#8720—611nomaximal, Sylow
173C22×C61#38111yescharacteristic
174C22×C61#41311yescharacteristic
175C22×C61#41311yescharacteristic
176C22×C61C2×#10411yescharacteristic
177C22×C61C2×#10411yescharacteristic
178C22×C61#42111yescharacteristic
179C22×C61#42111yescharacteristic
180C2×D61—22no—
181C2×D61—22no—
182C2×D61—22no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—81no—
194C4×C61—81no—
195Dic61—22no—
196Dic61—41no—
197Dic61—41no—
198Dic61—81no—
199Dic61—81no—
200#2283—611no—
201#1749—611no—
202#1749—611no—
203#1295—611no—
204#1295—611no—
205#1295—611no—
206#1295D6111yescharacteristic, complemented
207C2×C61#152411yescharacteristic
208C2×C61#152911yescharacteristic
209C2×C61#153211yescharacteristic
210C2×C61#153511yescharacteristic
211C2×C61#182211yescharacteristic
212C2×C61#182611yescharacteristic
213C2×C61#182611yescharacteristic
214D61—42no—
215C22×C42—611no—
216C2×C22⋊C8—1221no—
217C2×C22⋊C8—1221no—
218C2×#97—611no—
219C2×#97—611no—
220C2×#97C2×D6111yescharacteristic
221C2×#97C2×D6111yescharacteristic
222#383—1221no—
223#382—611no—
224#382C2×D6111yescharacteristic
225#381—1221no—
226#380—611no—
227#380—611no—
228C4×C4⋊C4—611no—
229C4×C4⋊C4—611no—
230C4×C22⋊C4—1221no—
231#376—1221no—
232#336—1221no—
233#336—1221no—
234C61#872011yescharacteristic, complemented, Sylow
235C23×C4—611no—
236C23×C4—611no—
237C23×C4—611no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—1221no—
241C22×C8—1221no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4C4×D6111yescharacteristic
245C2×C4⋊C4C4×D6111yescharacteristic
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—1221no—
252C2×C42—1221no—
253C2×C42—1221no—
254C2×C42—1221no—
255C2×C42—1221no—
256C2×C42—1221no—
257C2×C42C22×D6111yescharacteristic
258C22⋊C8—1224no—
259C22⋊C8—1224no—
260#97—21no—
261#97—21no—
262#97—21no—
263#97—21no—
264#97—1221no—
265#97—1221no—
266#97—1221no—
267#97—1221no—
268#95—21no—
269#95—21no—
270#95—1221no—
271#95—1221no—
272#95—1221no—
273#95—1221no—
274#95—1221no—
275#95—1221no—
276C24—611no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—1222no—
283C22×C4—1222no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4—2441no—
296C22×C4C2×C4×D6111yescharacteristic
297C22×C4D4×D6111yescharacteristic
298C22×C4D4×D6111yescharacteristic
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—1222no—
306C2×C8—1222no—
307C2×C8—2441no—
308C2×C8—2441no—
309C2×C8—2441no—
310C2×C8—2441no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—2441no—
314C4⋊C4—2441no—
315C22⋊C4—2442no—
316C22⋊C4—2442no—
317C42—1221no—
318C42—1221no—
319C42—1221no—
320C42—1221no—
321C42—1221no—
322C42—1221no—
323C42—2442no—
324C42—2442no—
325C42#1175822211yescharacteristic
326C42#1175822211yescharacteristic
327C42#1175822411yescharacteristic
328C42#1175822611yescharacteristic
329C23—612no—
330C23—1221no—
331C23—1221no—
332C23—1221no—
333C23—1221no—
334C23—1221no—
335C23—1221no—
336C23C22⋊C4×D6111yescharacteristic
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—612no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4—2442no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4#1451973411yescharacteristic
371C2×C4#1451973511yescharacteristic
372C2×C4#1451975911yescharacteristic
373C2×C4#1451975911yescharacteristic
374C2×C4#1451976211yescharacteristic
375C2×C4#1451976211yescharacteristic
376C8—42no—
377C8—42no—
378C8—2442no—
379C8—2442no—
380C22—1222no—
381C22—1222no—
382C22—1222no—
383C22—2441no—
384C22—2441no—
385C22—2441no—
386C22—2441no—
387C22#1683962411yescharacteristic
388C22#1683974311yescharacteristic
389C22#1683974511yescharacteristic
390C22#104×D6111yescharacteristic
391C22#104×D6111yescharacteristic
392C22#1683977711yescharacteristic
393C22#1683977711yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—81no—
401C4—81no—
402C4—1222no—
403C4—4881no—
404C4—4881no—
405C4—2441no—
406C4—2441no—
407C2—2442no—
408C2#2144440611yescharacteristic
409C2#2144442311yescharacteristic
410C2#2144443611yescharacteristic
411C2#2144444911yescharacteristic
412C2#2144590111yescharacteristic
413C2#2144591711yescharacteristic
414C2#2144591711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1295D61
hypocenterC61#8720
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
4. #21443701C2semidirect
5. #21443701C2semidirect
6. #21443700C2semidirect
7. C61×#1295C2semidirect
206. #1295D61semidirect
234. C61#8720semidirect

Maximal subgroups

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

subgroupindex
#214482122
#214455822
#214437012
#214437002
C61×#12952
#872061