Finite Group Databasebeta

← #29568484

Subgroups — #29568484

Order 15616.

562 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454170C211yesmaximal, characteristic
2#21445576C211yesmaximal, characteristic
3#21445511C211yesmaximal, characteristic
4#21443643C211yesmaximal, characteristic, complemented
5#21443642C211yesmaximal, characteristic, complemented
6#21443641C211yesmaximal, characteristic, complemented
7C61×#1271C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C2×#14519776C411yescharacteristic
10C2×#14519755—21no—
11C2×C42×D61C2211yescharacteristic
12C2×#14519689—21no—
13C2×C8×Dic61—21no—
14#16839666—21no—
15#16839660C2211yescharacteristic
16#16839657—21no—
17#16839631C411yescharacteristic
18#16839621—21no—
19#16839619C411yescharacteristic
20#16839619C411yescharacteristic
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×C4×D61C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×#11758189—24no—
32C2×#11758189—42no—
33C2×#11758189—42no—
34C22×#92418—21no—
35C22×#92418—21no—
36#14519776—42no—
37#14519755—42no—
38#14519755—42no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C42×D61—42no—
51#14519689—24no—
52C8×Dic61—42no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56C22×C8×C61—21no—
57C22×C8×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C42×C61C2311yescharacteristic
62#95×C61—21no—
63C23×D61C22⋊C411yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—22no—
81C2×C4×D61—22no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61D812yes—
85C2×C4×D61SD1612yes—
86C2×Dic122—42no—
87C2×Dic122—42no—
88C2×Dic122—42no—
89C2×C8×C61—22no—
90C2×C8×C61—22no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C42×C61—41no—
101#11758198—42no—
102#11758198—42no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—41no—
106#11758196—42no—
107#11758196—41no—
108#11758196—41no—
109#11758196—42no—
110#11758196—42no—
111C4×Dic61—22no—
112C4×Dic61—22no—
113C4×Dic61—41no—
114C2×#92418—22no—
115C2×#92418—22no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120#11758189—48no—
121C23×C61C2×C22⋊C411yescharacteristic
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61#10212yes—
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#13111yescharacteristic
142C2×C4×C61#13111yescharacteristic
143C2×C4×C61C2×D811yescharacteristic
144C2×C4×C61C2×SD1611yescharacteristic
145C2×C4×C61#13711yescharacteristic
146C2×C4×C61#13711yescharacteristic
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61#9912yes—
158C2×Dic61#10112yes—
159C2×Dic61#10212yes—
160C2×Dic61#10412yes—
161C2×Dic61#10412yes—
162C4×D61—24no—
163C4×D61—24no—
164C4×D61—42no—
165C4×D61—42no—
166C4×D61—42no—
167C4×D61—42no—
168Dic122—84no—
169C8×C61—42no—
170C8×C61—42no—
171#92418—42no—
172#92418—42no—
173#7685—611nomaximal, Sylow
174C22×C61#40811yescharacteristic
175C22×C61C2×#9911yescharacteristic
176C22×C61C2×#10111yescharacteristic
177C22×C61C2×#10211yescharacteristic
178C22×C61#41911yescharacteristic
179C22×C61C2×#10411yescharacteristic
180C22×C61C2×#10411yescharacteristic
181C2×D61—22no—
182C2×D61—22no—
183C2×D61—22no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—81no—
195C4×C61—81no—
196Dic61—22no—
197Dic61—22no—
198Dic61—81no—
199Dic61—81no—
200Dic61#32714yes—
201#2857—611no—
202C4×C22⋊C8—611no—
203#1728—611no—
204#1271—611no—
205#1271—611no—
206#1271—611no—
207#1271D6111yescharacteristic, complemented
208C2×C61#147211yescharacteristic
209C2×C61#148511yescharacteristic
210C2×C61#149211yescharacteristic
211C2×C61C2×#32711yescharacteristic
212C2×C61#150811yescharacteristic
213C2×C61#152611yescharacteristic
214C2×C61#154611yescharacteristic
215D61—42no—
216C22×M16—1221no—
217C2×C4⋊Q8—611no—
218C2×C22⋊Q8—1221no—
219C22×C42—611no—
220C2×C22⋊C8—1221no—
221C2×C4×C8—1221no—
222#391—1221no—
223#389—611no—
224#389—1221no—
225#389C2×D6111yescharacteristic
226#384—611no—
227#380—611no—
228#380—611no—
229#380—1221no—
230#336—611no—
231#336—611no—
232#336—1221no—
233#336C2×D6111yescharacteristic
234#336C2×D6111yescharacteristic
235C61#768511yescharacteristic, complemented, Sylow
236C22×Q8—1221no—
237C23×C4—611no—
238C23×C4—611no—
239C23×C4—611no—
240C2×M16—1224no—
241C2×M16—2442no—
242C2×M16—2442no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—1221no—
246C22×C8—1221no—
247C4⋊Q8—2442no—
248C22⋊Q8—2442no—
249C22⋊Q8—2442no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4C4×D6111yescharacteristic
258C2×C4⋊C4C4×D6111yescharacteristic
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C42—611no—
262C2×C42—611no—
263C2×C42—611no—
264C2×C42—2442no—
265C2×C42C22×D6111yescharacteristic
266C22⋊C8—1224no—
267C4×C8—2442no—
268#95—21no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272C24—611no—
273C2×Q8—2442no—
274C2×Q8—2442no—
275C2×Q8—2442no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—612no—
282C22×C4—612no—
283C22×C4—1222no—
284C22×C4—1222no—
285C22×C4—1222no—
286C22×C4—1222no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4C2×C4×D6111yescharacteristic
296C22×C4D4×D6111yescharacteristic
297C22×C4D4×D6111yescharacteristic
298M16—2448no—
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—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4—2441no—
319C4⋊C4—2442no—
320C4⋊C4—2442no—
321C4⋊C4—2442no—
322C4⋊C4—2441no—
323C4⋊C4—2441no—
324C22⋊C4—2442no—
325C22⋊C4—2442no—
326C42—41no—
327C42—1222no—
328C42—1222no—
329C42—2441no—
330C23—612no—
331C23—1221no—
332C23—1221no—
333C23—1221no—
334C23—1221no—
335C23—1221no—
336C23—1221no—
337C23C22⋊C4×D6111yescharacteristic
338Q8—4884no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—612no—
352C2×C4—612no—
353C2×C4—612no—
354C2×C4—612no—
355C2×C4—612no—
356C2×C4—1224no—
357C2×C4—1224no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—2442no—
363C2×C4—2442no—
364C2×C4—2442no—
365C2×C4—2442no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4#1451978311yescharacteristic
373C2×C4#1451978511yescharacteristic
374C2×C4D8×D6111yescharacteristic
375C2×C4SD16×D6111yescharacteristic
376C2×C4#1451980611yescharacteristic
377C2×C4#1451980911yescharacteristic
378C8—42no—
379C8—42no—
380C8—2442no—
381C8—2442no—
382C22—1222no—
383C22—1222no—
384C22—1222no—
385C22—2441no—
386C22—2441no—
387C22—2441no—
388C22—2441no—
389C22#1683972711yescharacteristic
390C22#99×D6111yescharacteristic
391C22#101×D6111yescharacteristic
392C22#102×D6111yescharacteristic
393C22#1683976911yescharacteristic
394C22#104×D6111yescharacteristic
395C22#104×D6111yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—81no—
403C4—81no—
404C4—614no—
405C4—1222no—
406C4—1222no—
407C4—4881no—
408C4—4881no—
409C2—2442no—
410C2#2144418111yescharacteristic
411C2#2144423811yescharacteristic
412C2#2144426811yescharacteristic
413C2#327×D6111yescharacteristic
414C2#2144433711yescharacteristic
415C2#2144441211yescharacteristic
416C2#2144448911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61#7685
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
4. #21443643C2semidirect
5. #21443642C2semidirect
6. #21443641C2semidirect
7. C61×#1271C2semidirect
207. #1271D61semidirect
235. C61#7685semidirect

Maximal subgroups

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

subgroupindex
#214541702
#214455762
#214455112
#214436432
#214436422
#214436412
C61×#12712
#768561