Finite Group Databasebeta

← #29568115

Subgroups — #29568115

Order 15616.

588 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448335C211yesmaximal, characteristic
2#21445886C211yesmaximal, characteristic, complemented
3#21445798C211yesmaximal, characteristic, complemented
4#21443643C211yesmaximal, characteristic, complemented
5#21443641C211yesmaximal, characteristic, complemented
6#21443640C211yesmaximal, characteristic, complemented
7C61×#1270C211yesmaximal, characteristic, complemented
8C2×#14519748C411yescharacteristic
9C2×D4×Dic61C411yescharacteristic
10C2×#14519737—21no—
11C2×C42×D61C2211yescharacteristic
12C2×#14519706—21no—
13C2×#14519689—21no—
14C2×#14519689—21no—
15#16839660C2211yescharacteristic
16#16839656—21no—
17#16839638—21no—
18#16839619C411yescharacteristic
19C4⋊C4×Dic61C411yescharacteristic
20C22⋊C4×Dic61—21no—
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×C22⋊D61—21no—
28C23×Dic61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×#92418—21no—
33C22×#92418—21no—
34#14519748—22no—
35#14519748C814yescomplemented
36D4×Dic61—42no—
37#14519737—42no—
38#14519737—42no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C42×D61—42no—
50#14519706—42no—
51#14519689—42no—
52#14519689—42no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56C22×D4×C61C2×C411yescharacteristic
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C42×C61C2311yescharacteristic
63C24×C61—21no—
64C23×D61C22⋊C411yescharacteristic
65C2×D4×C61—21no—
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C2×D4×C61C2×C812yes—
69C22×C4×C61—21no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C2×C22⋊D61—24no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—42no—
79C22×Dic61—42no—
80C22×Dic61—42no—
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—22no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61C2×C812yes—
95C2×C4×D61M1612yes—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C4⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C42×C61—41no—
108C22⋊Dic61—24no—
109C22⋊Dic61—42no—
110#11758198—42no—
111C4⋊Dic61—21no—
112C4⋊Dic61—41no—
113C4⋊Dic61C2×C812yes—
114#11758196—41no—
115#11758196—41no—
116C4×Dic61—22no—
117C4×Dic61—22no—
118C4×Dic61—41no—
119C4×Dic61—42no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C23×C61—22no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61C2×C22⋊C411yescharacteristic
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61C22⋊C812yes—
141D4×C61—42no—
142D4×C61—42no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61C22×C811yescharacteristic
153C2×C4×C61C2×M1611yescharacteristic
154C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61#13711yescharacteristic
158C22⋊D61—48no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—22no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—84no—
173C2×Dic61C22⋊C812yes—
174C2×Dic61#9912yes—
175C4×D61—42no—
176C4×D61—42no—
177C4×D61—42no—
178C4×D61—42no—
179C4×D61—42no—
180C4×D61—42no—
181C8×C61—81no—
182C8×C61—81no—
183#92418—81no—
184#92418—81no—
185#7599—611nomaximal, Sylow
186C22×C61—42no—
187C22×C61—42no—
188C22×C61—42no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61C2×C22⋊C811yescharacteristic
194C22×C61C2×#9911yescharacteristic
195C22×C61#41311yescharacteristic
196C22×C61#41711yescharacteristic
197C22×C61#41811yescharacteristic
198C22×C61#42111yescharacteristic
199C22×C61#42111yescharacteristic
200C2×D61—22no—
201C2×D61—22no—
202C2×D61—22no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—41no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—81no—
214Dic61—22no—
215Dic61—22no—
216Dic61—42no—
217Dic61—41no—
218Dic61—81no—
219C4×#121—611no—
220#1817—611no—
221#1797—611no—
222#1271—611no—
223#1271—611no—
224#1270—611no—
225#1270D6111yescharacteristic, complemented
226C2×C61—82no—
227C2×C61#145911yescharacteristic
228C2×C61#147711yescharacteristic
229C2×C61#147811yescharacteristic
230C2×C61#151011yescharacteristic
231C2×C61#151311yescharacteristic
232C2×C61#153511yescharacteristic
233C2×C61#155711yescharacteristic
234D61—42no—
235C2×#121—611no—
236C2×C4×D4—611no—
237C2×C4×D4—1221no—
238C22×C42—611no—
239C2×C4⋊C8—1221no—
240C2×C22⋊C8—1221no—
241C2×C22⋊C8—1221no—
242#390C2×D6111yescharacteristic
243#389—611no—
244#388—1221no—
245#386—1221no—
246#380—611no—
247C4×C4⋊C4—611no—
248C4×C22⋊C4—1221no—
249#336—611no—
250#336—611no—
251#336—1221no—
252#336C2×D6111yescharacteristic
253#336C2×D6111yescharacteristic
254C61#759911yescharacteristic, complemented, Sylow
255C22×D4—1221no—
256C22×D4C4×D6111yescharacteristic
257C23×C4—611no—
258C23×C4—611no—
259C23×C4—611no—
260C23×C4—1221no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—1221no—
264C22×C8—1221no—
265#121—614no—
266#121—1222no—
267C4×D4—2442no—
268C4×D4—2442no—
269C4×D4—2442no—
270C2×C4⋊C4—611no—
271C2×C4⋊C4—611no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4C4×D6111yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C42—611no—
280C2×C42—611no—
281C2×C42—611no—
282C2×C42—1221no—
283C2×C42—2442no—
284C2×C42C22×D6111yescharacteristic
285C4⋊C8—2442no—
286C22⋊C8—2442no—
287C22⋊C8—2442no—
288#95—1221no—
289#95—1221no—
290#95—1221no—
291C24—21no—
292C24—611no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—1224no—
297C2×D4—2442no—
298C2×D4—2442no—
299C2×D4C8×D6112yes—
300C22×C4—21no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—612no—
304C22×C4—612no—
305C22×C4—611no—
306C22×C4—1222no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—2441no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4—2441no—
318C22×C4—2442no—
319C22×C4—2442no—
320C22×C4—2442no—
321C22×C4C2×C4×D6111yescharacteristic
322C22×C4D4×D6111yescharacteristic
323C22×C4D4×D6111yescharacteristic
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—2441no—
331C2×C8—2441no—
332C2×C8—2441no—
333C2×C8—2441no—
334C2×C8—2441no—
335C2×C8—2441no—
336C4⋊C4—41no—
337C4⋊C4—612no—
338C4⋊C4—1221no—
339C4⋊C4—2441no—
340C4⋊C4—2441no—
341C4⋊C4—2441no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—1224no—
347C22⋊C4—2442no—
348C22⋊C4—2442no—
349C42—41no—
350C42—1222no—
351C42—1222no—
352C42—2441no—
353C42—2442no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—612no—
362C23—1221no—
363C23—1221no—
364C23—1221no—
365C23—1221no—
366C23—1221no—
367C23—1221no—
368C23C22⋊C4×D6111yescharacteristic
369D4—42no—
370D4—42no—
371D4—2448no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—612no—
382C2×C4—612no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1222no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—4884no—
392C2×C4—2442no—
393C2×C4—2442no—
394C2×C4—2442no—
395C2×C4—2442no—
396C2×C4—2442no—
397C2×C4—2442no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4C2×C8×D6111yescharacteristic
404C2×C4M16×D6111yescharacteristic
405C2×C4#1451980111yescharacteristic
406C2×C4#1451980111yescharacteristic
407C2×C4#1451980411yescharacteristic
408C2×C4#1451980611yescharacteristic
409C8—81no—
410C8—81no—
411C8—4881no—
412C8—4881no—
413C22—42no—
414C22—42no—
415C22—42no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—1222no—
421C22—1222no—
422C22—1222no—
423C22—2441no—
424C22—2441no—
425C22—2441no—
426C22—2441no—
427C22C22⋊C8×D6111yescharacteristic
428C22#99×D6111yescharacteristic
429C22#1683974311yescharacteristic
430C22#1683976011yescharacteristic
431C22#1683976511yescharacteristic
432C22#1683977711yescharacteristic
433C22#1683977711yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—81no—
441C4—1222no—
442C4—1222no—
443C4—4881no—
444C4—2441no—
445C4—2442no—
446C2—82no—
447C2—2442no—
448C2#2144413411yescharacteristic
449C2#2144420311yescharacteristic
450C2#2144420811yescharacteristic
451C2#2144434611yescharacteristic
452C2#2144435911yescharacteristic
453C2#2144444711yescharacteristic
454C2#2144453811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC2×C42×C61C23
hypercenter#1270D61
hypocenterC61#7599
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #21445886C2semidirect
3. #21445798C2semidirect
4. #21443643C2semidirect
5. #21443641C2semidirect
6. #21443640C2semidirect
7. C61×#1270C2semidirect
35. #14519748C8semidirect
225. #1270D61semidirect
254. C61#7599semidirect

Maximal subgroups

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

subgroupindex
#214483352
#214458862
#214457982
#214436432
#214436412
#214436402
C61×#12702
#759961