Finite Group Databasebeta

← #29568367

Subgroups — #29568367

Order 15616.

566 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454173C211yesmaximal, characteristic
2#21445934C211yesmaximal, characteristic, complemented
3#21445667C211yesmaximal, characteristic, complemented
4#21443640C211yesmaximal, characteristic, complemented
5#21443639C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic, complemented
7C61×#1270C211yesmaximal, characteristic, complemented
8C2×#14519776C411yescharacteristic
9C2×#14519773C411yescharacteristic
10C2×#14519763—21no—
11C2×#14519763—21no—
12C2×#14519706—21no—
13C2×#14519706—21no—
14C2×C8×Dic61—21no—
15#16839665C411yescharacteristic
16#16839664C2211yescharacteristic
17#16839663C411yescharacteristic
18#16839662—21no—
19#16839662—21no—
20C42×Dic61C2211yescharacteristic
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244C2×C411yescharacteristic
29C22×C22⋊D61—21no—
30C22×C22⋊D61—21no—
31C22×#92418—21no—
32C22×#92418—21no—
33#14519776—42no—
34#14519773—42no—
35#14519763—42no—
36#14519763—42no—
37#14519763—42no—
38#14519763—42no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53#14519706—24no—
54#14519706—42no—
55C8×Dic61—42no—
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×D61—21no—
65C2×D4×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C22×C4×C61—21no—
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C22×Dic61—21no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—41no—
87C2×D244—41no—
88C2×Dic122—42no—
89C2×Dic122—42no—
90C2×Dic122—42no—
91C2×C8×C61—22no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C4⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C42×C61—41no—
103C22⋊Dic61—42no—
104C22⋊Dic61—42no—
105#11758198—41no—
106#11758198—41no—
107#11758198—41no—
108#11758198—41no—
109#11758198—42no—
110#11758198—42no—
111C4⋊Dic61—41no—
112#11758196—42no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—22no—
116C4×Dic61—22no—
117C4×Dic61—41no—
118C4×Dic61D812yes—
119C4×Dic61D812yes—
120C4×Dic61SD1612yes—
121C4×Dic61SD1612yes—
122C2×#92418—22no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61C2×C22⋊C411yescharacteristic
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143D4×C61—81no—
144D4×C61—81no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61#13111yescharacteristic
155C2×C4×C61#13111yescharacteristic
156C2×C4×C61C2×D811yescharacteristic
157C2×C4×C61C2×D811yescharacteristic
158C2×C4×C61C2×SD1611yescharacteristic
159C2×C4×C61C2×SD1611yescharacteristic
160C22⋊D61—84no—
161C22⋊D61—84no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61#10012yes—
172C2×Dic61#10212yes—
173C2×Dic61#10212yes—
174C2×Dic61#10212yes—
175C2×Dic61#10212yes—
176C2×Dic61#10412yes—
177D244—81no—
178D244—81no—
179Dic122—84no—
180C8×C61—42no—
181C8×C61—81no—
182#92418—42no—
183#92418—81no—
184#7659—611nomaximal, Sylow
185C22×C61—81no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61#40811yescharacteristic
193C22×C61#41011yescharacteristic
194C22×C61C2×#10011yescharacteristic
195C22×C61C2×#10211yescharacteristic
196C22×C61C2×#10211yescharacteristic
197C22×C61C2×#10411yescharacteristic
198C22×C61#42111yescharacteristic
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—81no—
213Dic61—22no—
214Dic61—22no—
215Dic61—22no—
216Dic61—81no—
217Dic61#33114yes—
218#2858—611no—
219#1831—611no—
220C4×C4⋊C8—611no—
221#1270—611no—
222#1270—611no—
223#1270—611no—
224#1270D6111yescharacteristic, complemented
225C2×C61—161no—
226C2×C61#146911yescharacteristic
227C2×C61#148011yescharacteristic
228C2×C61#149211yescharacteristic
229C2×C61#150211yescharacteristic
230C2×C61#151711yescharacteristic
231C2×C61#152711yescharacteristic
232C2×C61C2×#33111yescharacteristic
233D61—161no—
234C2×C4⋊Q8—611no—
235C2×#127—611no—
236C2×#124—1221no—
237C2×#124—1221no—
238C2×C4⋊C8—1221no—
239C2×C4⋊C8—1221no—
240C2×C4×C8—1221no—
241#390—611no—
242#390—611no—
243#390—611no—
244#390—1221no—
245#390—1221no—
246#390C2×D6111yescharacteristic
247C43—611no—
248#336—611no—
249#336—611no—
250#336—1221no—
251#336C2×D6111yescharacteristic
252#336C2×D6111yescharacteristic
253C61#765911yescharacteristic, complemented, Sylow
254C22×Q8—1221no—
255C22×D4—611no—
256C22×D4—1221no—
257C22×D4—1221no—
258C22×D4C4×D6111yescharacteristic
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—1221no—
262C22×C8—1221no—
263C4⋊Q8—2442no—
264#127—2442no—
265#124—2442no—
266#124—2442no—
267#124—2442no—
268#124—2442no—
269C2×C4⋊C4—611no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4C4×D6111yescharacteristic
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C42—611no—
281C2×C42—611no—
282C2×C42—611no—
283C2×C42—611no—
284C2×C42—611no—
285C2×C42—611no—
286C2×C42C22×D6111yescharacteristic
287C4⋊C8—1224no—
288C4⋊C8—2442no—
289C4×C8—2442no—
290C24—21no—
291C24—1221no—
292C2×Q8—2442no—
293C2×Q8—2442no—
294C2×Q8—2442no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—2441no—
302C2×D4—2441no—
303C2×D4—2442no—
304C2×D4—2442no—
305C2×D4—2442no—
306C2×D4—2442no—
307C2×D4—2442no—
308C2×D4—2442no—
309C22×C4—21no—
310C22×C4—611no—
311C22×C4—611no—
312C22×C4—611no—
313C22×C4—611no—
314C22×C4—1221no—
315C22×C4C2×C4×D6111yescharacteristic
316C22×C4D4×D6111yescharacteristic
317C22×C4D4×D6111yescharacteristic
318C2×C8—22no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—1222no—
325C2×C8—2441no—
326C2×C8—2441no—
327C2×C8—2441no—
328C2×C8—2441no—
329C2×C8—2441no—
330C4⋊C4—41no—
331C4⋊C4—2441no—
332C4⋊C4—2442no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—2442no—
338C22⋊C4—2442no—
339C22⋊C4—2442no—
340C22⋊C4—2442no—
341C22⋊C4—2441no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C22⋊C4—2441no—
345C42—41no—
346C42—612no—
347C42—612no—
348C42—612no—
349C42—612no—
350C42—1222no—
351C42—1222no—
352C42—1221no—
353C42—1221no—
354C42—2441no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—2441no—
363C23—2441no—
364C23—2441no—
365C23—2441no—
366C23—2441no—
367C23—2441no—
368C23—2441no—
369C23C22⋊C4×D6111yescharacteristic
370Q8—4884no—
371D4—81no—
372D4—81no—
373D4—4881no—
374D4—4881no—
375D4—4884no—
376D4—4884no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—612no—
387C2×C4—612no—
388C2×C4—612no—
389C2×C4—612no—
390C2×C4—612no—
391C2×C4—612no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4#1451978311yescharacteristic
402C2×C4#1451978511yescharacteristic
403C2×C4D8×D6111yescharacteristic
404C2×C4D8×D6111yescharacteristic
405C2×C4SD16×D6111yescharacteristic
406C2×C4SD16×D6111yescharacteristic
407C8—42no—
408C8—81no—
409C8—4881no—
410C8—2442no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—4881no—
419C22—4881no—
420C22—4881no—
421C22—4881no—
422C22—4881no—
423C22—4881no—
424C22—4881no—
425C22#1683972711yescharacteristic
426C22#1683973411yescharacteristic
427C22#100×D6111yescharacteristic
428C22#102×D6111yescharacteristic
429C22#102×D6111yescharacteristic
430C22#104×D6111yescharacteristic
431C22#1683977711yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—81no—
439C4—614no—
440C4—1222no—
441C4—1222no—
442C4—1222no—
443C4—4881no—
444C2—161no—
445C2—9761no—
446C2#2144416911yescharacteristic
447C2#2144421611yescharacteristic
448C2#2144426811yescharacteristic
449C2#2144431211yescharacteristic
450C2#2144437711yescharacteristic
451C2#2144441511yescharacteristic
452C2#331×D6111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519773C4
cosocleC2×C42×C61C23
hypercenter#1270D61
hypocenterC61#7659
LCSG ▷ C22×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. #21445934C2semidirect
3. #21445667C2semidirect
4. #21443640C2semidirect
5. #21443639C2semidirect
6. #21443639C2semidirect
7. C61×#1270C2semidirect
224. #1270D61semidirect
253. C61#7659semidirect

Maximal subgroups

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

subgroupindex
#214541732
#214459342
#214456672
#214436402
#214436392
C61×#12702
#765961