Finite Group Databasebeta

← #29567971

Subgroups — #29567971

Order 15616.

680 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448327C211yesmaximal, characteristic
2#21445576C211yesmaximal, characteristic, complemented
3#336×D61C211yesmaximal, characteristic, complemented
4#21443642C211yesmaximal, characteristic, complemented
5#21443639C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic, complemented
7C61×#1271C211yesmaximal, characteristic, complemented
8C22×C8×D61—21no—
9C2×#14519752C411yescharacteristic
10C2×#14519739—21no—
11C2×#14519739C411yescharacteristic
12C2×C42×D61C2211yescharacteristic
13C2×#14519689—21no—
14C2×C8×Dic61—21no—
15#16839664C2211yescharacteristic
16#16839652—21no—
17#16839640—21no—
18#16839619C411yescharacteristic
19C4⋊C4×Dic61C411yescharacteristic
20#16839609—21no—
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×D244—21no—
28C22×D244C2×C411yescharacteristic
29C22×C4×D61—21no—
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×#92418—21no—
34C22×#92418—21no—
35C2×C8×D61—24no—
36C2×C8×D61—42no—
37C2×C8×D61—42no—
38#14519752—22no—
39#14519752C814yescomplemented
40#14519739—42no—
41#14519739—42no—
42#14519739—42no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C42×D61—42no—
54#14519689—24no—
55C8×Dic61—42no—
56#14519684—21no—
57#14519684—21no—
58C22×C8×C61—21no—
59C22×C8×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C42×C61C2311yescharacteristic
64#95×C61—21no—
65C23×D61—21no—
66C23×D61C22⋊C411yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C2×D244—24no—
77C2×D244—21no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—42no—
81C2×D244—42no—
82C2×D244C2×C812yescomplemented
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—22no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C4×D61C2×C812yes—
95C2×C4×D61M1612yes—
96C2×C4×D61D812yes—
97C2×C4×D61SD1612yes—
98C2×C8×C61—22no—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61C2×C812yescomplemented
109C42×C61—41no—
110#11758198—24no—
111#11758198—42no—
112#11758198—42no—
113#11758198—41no—
114#11758198—41no—
115#11758198—41no—
116#11758198—41no—
117C4⋊Dic61—41no—
118C4×Dic61—22no—
119C4×Dic61—22no—
120C4×Dic61—41no—
121C4×Dic61—42no—
122C2×#92418—22no—
123C2×#92418—22no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128C8×D61—48no—
129C23×C61C2×C22⋊C411yescharacteristic
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—22no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61C22⋊C812yes—
142C22×D61#10212yes—
143C22×D61#10412yes—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—22no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61C22×C811yescharacteristic
157C2×C4×C61C2×M1611yescharacteristic
158C2×C4×C61C2×D811yescharacteristic
159C2×C4×C61C2×SD1611yescharacteristic
160C2×C4×C61#13511yescharacteristic
161C2×C4×C61#13511yescharacteristic
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61C22⋊C812yes—
171C2×Dic61#9912yes—
172C2×Dic61#10212yes—
173C2×Dic61#10412yes—
174D244—42no—
175D244—42no—
176D244—48no—
177C4×D61—24no—
178C4×D61—24no—
179C4×D61—42no—
180C4×D61—42no—
181C4×D61—42no—
182C4×D61—42no—
183C4×D61—84no—
184C8×C61—42no—
185C8×C61—42no—
186#92418—42no—
187#92418—42no—
188#7565—611nomaximal, Sylow
189C22×C61C2×C22⋊C811yescharacteristic
190C22×C61C2×#9911yescharacteristic
191C22×C61#41311yescharacteristic
192C22×C61C2×#10211yescharacteristic
193C22×C61#41611yescharacteristic
194C22×C61C2×#10411yescharacteristic
195C22×C61C2×#10411yescharacteristic
196C2×D61—22no—
197C2×D61—22no—
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—22no—
201C2×D61—22no—
202C2×D61—42no—
203C2×D61—42no—
204C2×D61—42no—
205C2×D61—81no—
206C2×D61—81no—
207C2×D61—81no—
208C2×D61—81no—
209C2×D61D4⋊C814yes—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—42no—
217C4×C61—81no—
218Dic61—22no—
219Dic61—41no—
220Dic61—81no—
221Dic61#32714yes—
222C4×#121—611no—
223C4×C22⋊C8—611no—
224C2×#336—611no—
225#1271—611no—
226#1271D6111yescharacteristic, complemented
227#1270—611no—
228#1270—611no—
229C2×C61#145911yescharacteristic
230C2×C61C2×D4⋊C811yescharacteristic
231C2×C61#147611yescharacteristic
232C2×C61C2×#32711yescharacteristic
233C2×C61#150111yescharacteristic
234C2×C61#152411yescharacteristic
235C2×C61#154011yescharacteristic
236D61—24no—
237D61—82no—
238C23×C8—1221no—
239C2×#121—611no—
240C2×C4×D4—611no—
241C2×C4×D4—1221no—
242C22×C42—611no—
243C2×C22⋊C8—1221no—
244C2×C4×C8—1221no—
245#390—611no—
246#389C2×D6111yescharacteristic
247#388—1221no—
248#386—1221no—
249#380—611no—
250C4×C4⋊C4—611no—
251C4×C22⋊C4—1221no—
252#336—611no—
253#336—611no—
254#336—1221no—
255#336C2×D6111yescharacteristic
256#336C2×D6111yescharacteristic
257C61#756511yescharacteristic, complemented, Sylow
258C22×D4—611no—
259C22×D4—1221no—
260C23×C4—611no—
261C23×C4—611no—
262C23×C4—611no—
263C23×C4—1221no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—1224no—
267C22×C8—1221no—
268C22×C8—1221no—
269C22×C8—2442no—
270C22×C8—2442no—
271#121—614no—
272#121—1222no—
273C4×D4—2442no—
274C4×D4—2442no—
275C4×D4—2442no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4C4×D6111yescharacteristic
279C2×C4⋊C4C4×D6111yescharacteristic
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1221no—
282C2×C22⋊C4—1221no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—1221no—
285C2×C42—611no—
286C2×C42—611no—
287C2×C42—611no—
288C2×C42—1221no—
289C2×C42—2442no—
290C2×C42C22×D6111yescharacteristic
291C22⋊C8—1224no—
292C4×C8—2442no—
293#95—21no—
294#95—1221no—
295#95—1221no—
296C24—611no—
297C24—1221no—
298C2×D4—612no—
299C2×D4—1224no—
300C2×D4—1221no—
301C2×D4—2441no—
302C2×D4—2441no—
303C2×D4—2442no—
304C2×D4—2442no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—612no—
310C22×C4—612no—
311C22×C4—612no—
312C22×C4—612no—
313C22×C4—611no—
314C22×C4—1222no—
315C22×C4—1222no—
316C22×C4—1222no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4—2441no—
323C22×C4—2442no—
324C22×C4—2442no—
325C22×C4—2442no—
326C22×C4C2×C4×D6111yescharacteristic
327C22×C4D4×D6111yescharacteristic
328C22×C4D4×D6111yescharacteristic
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—1222no—
336C2×C8—1222no—
337C2×C8—2448no—
338C2×C8—2441no—
339C2×C8—2441no—
340C2×C8—2441no—
341C2×C8—2441no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—2441no—
347C4⋊C4C8×D6112yescomplemented
348C22⋊C4—1224no—
349C22⋊C4—2442no—
350C22⋊C4—2442no—
351C22⋊C4—2441no—
352C22⋊C4—2441no—
353C22⋊C4—2441no—
354C22⋊C4—2441no—
355C42—41no—
356C42—1222no—
357C42—1222no—
358C42—2441no—
359C42—2442no—
360C23—612no—
361C23—612no—
362C23—612no—
363C23—1221no—
364C23—1221no—
365C23—1221no—
366C23—1221no—
367C23—1222no—
368C23—2441no—
369C23—2441no—
370C23—2441no—
371C23—2441no—
372C23—2441no—
373C23—2441no—
374C23C22⋊C4×D6111yescharacteristic
375D4—2442no—
376D4—2442no—
377D4—2448no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—612no—
391C2×C4—612no—
392C2×C4—612no—
393C2×C4—612no—
394C2×C4—1224no—
395C2×C4—1224no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—4884no—
402C2×C4—2442no—
403C2×C4—2442no—
404C2×C4—2442no—
405C2×C4—2442no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4C2×C8×D6111yescharacteristic
410C2×C4M16×D6111yescharacteristic
411C2×C4D8×D6111yescharacteristic
412C2×C4SD16×D6111yescharacteristic
413C2×C4#1451979811yescharacteristic
414C2×C4#1451980011yescharacteristic
415C8—42no—
416C8—42no—
417C8—2442no—
418C8—2442no—
419C22—614no—
420C22—1222no—
421C22—1222no—
422C22—1222no—
423C22—1222no—
424C22—1222no—
425C22—1222no—
426C22—4881no—
427C22—4881no—
428C22—4881no—
429C22—4881no—
430C22—2442no—
431C22—2442no—
432C22—2442no—
433C22C22⋊C8×D6111yescharacteristic
434C22#99×D6111yescharacteristic
435C22#1683974511yescharacteristic
436C22#102×D6111yescharacteristic
437C22#1683975711yescharacteristic
438C22#104×D6111yescharacteristic
439C22#104×D6111yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—42no—
447C4—81no—
448C4—614no—
449C4—1222no—
450C4—4881no—
451C4—2441no—
452C2—1224no—
453C2—4882no—
454C2#2144413611yescharacteristic
455C2D4⋊C8×D6111yescharacteristic
456C2#2144420011yescharacteristic
457C2#327×D6111yescharacteristic
458C2#2144430911yescharacteristic
459C2#2144440611yescharacteristic
460C2#2144446711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61#7565
LCSG ▷ C2×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. #21445576C2semidirect
3. #336×D61C2semidirect
4. #21443642C2semidirect
5. #21443639C2semidirect
6. #21443639C2semidirect
7. C61×#1271C2semidirect
39. #14519752C8semidirect
82. C2×D244C2×C8semidirect
108. C4⋊C4×C61C2×C8semidirect
226. #1271D61semidirect
257. C61#7565semidirect
347. C4⋊C4C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214483272
#214455762
#336×D612
#214436422
#214436392
C61×#12712
#756561