Finite Group Databasebeta

← #29576898

Subgroups — #29576898

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455295C211yesmaximal, characteristic
2#21454932C211yesmaximal, characteristic, complemented
3#21446747C211yesmaximal, characteristic, complemented
4#21445836C211yesmaximal, characteristic, complemented
5#21443721C211yesmaximal, characteristic, complemented
6#21443693C211yesmaximal, characteristic, complemented
7C61×#1545C211yesmaximal, characteristic, complemented
8C2×#14519803—21no—
9C4×#11758222C2211yescharacteristic
10#16839959—21no—
11#16839959C412yescomplemented
12#16839954—21no—
13#16839954C412yescomplemented
14#16839892—21no—
15#16839841—21no—
16#16839830—22no—
17#16839818—21no—
18#16839786C2211yescharacteristic
19#16839784—21no—
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519703—21no—
22#16839767—21no—
23C2×#14519698—22no—
24C4×C4⋊Dic61C2211yescharacteristic
25#16839523—21no—
26C2×#127×C61C2211yescharacteristic
27C61×#431C2211yescharacteristic
28C61×#423C2211yescharacteristic
29C61×#331—21no—
30C61×#331—21no—
31C2×#11758222D411yescharacteristic
32#14519803—42no—
33#14519803—42no—
34C2×#11758200—22no—
35C2×#11758199—22no—
36C2×#11758194—21no—
37C2×#11758189—22no—
38C22×#92418D412yes—
39C4×Dic122C2×C411yescharacteristic
40C4×Dic122D411yescharacteristic
41C4×D244C2×C411yescharacteristic
42C4×D244D411yescharacteristic
43C4×C22⋊D61—21no—
44C4×C22⋊D61—21no—
45#14519736D411yescharacteristic
46#14519734—21no—
47C2×C4⋊Dic61—21no—
48C2×C4×Dic61—21no—
49C42×D61—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53C4⋊#92418C2×C412yes—
54#14519706—22no—
55#14519703—42no—
56#14519698—22no—
57#14519698—22no—
58#14519698—44no—
59#14519689—22no—
60#14519687—22no—
61#14519684—21no—
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C2×M16×C61—21no—
66#127×C61—21no—
67#127×C61—21no—
68#127×C61—21no—
69#127×C61C2×C412yes—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C4⋊C8×C61D411yescharacteristic
74C4⋊C8×C61D411yescharacteristic
75C22⋊C8×C61—21no—
76C4×C8×C61—21no—
77C24×C61—41no—
78C2×D4×C61—22no—
79C2×D4×C61—22no—
80C2×D4×C61—22no—
81C2×D4×C61—42no—
82C2×D4×C61—42no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—82no—
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C2×C22⋊D61—21no—
95C22×Dic61—41no—
96#11758222—21no—
97#11758222—21no—
98#11758222—21no—
99#11758222—21no—
100C2×D244C22⋊C411yescharacteristic
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×Dic122C22⋊C411yescharacteristic
105M16×C61—41no—
106M16×C61—41no—
107C2×C8×C61—21no—
108C2×C8×C61—21no—
109C2×C8×C61—41no—
110C42×C61C22×C411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61#4111yescharacteristic
114C22⋊Dic61—21no—
115#11758200—44no—
116#11758199—44no—
117#11758198—21no—
118#11758198—21no—
119C4⋊Dic61—22no—
120C4⋊Dic61—41no—
121C4⋊Dic61C22⋊C411yescharacteristic
122C4⋊Dic61C22⋊C411yescharacteristic
123#11758196—21no—
124#11758196—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—41no—
129C4×Dic61—41no—
130#11758194—41no—
131#11758194—41no—
132C2×#92418—22no—
133C2×#92418—22no—
134C2×#92418—42no—
135#11758189—82no—
136C23×C61—42no—
137C23×C61—82no—
138C23×C61—82no—
139C23×C61—81no—
140C23×C61—81no—
141C23×C61#12111yescharacteristic
142C22×D61—21no—
143D4×C61—44no—
144D4×C61—42no—
145D4×C61—42no—
146D4×C61—82no—
147D4×C61—82no—
148D4×C61—81no—
149D4×C61—81no—
150D4×C61—81no—
151D4×C61—81no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—41no—
155C2×C4×C61C2×C22⋊C411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C2×C4×C61#12011yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12311yescharacteristic
161C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C61#13711yescharacteristic
165C22⋊D61—41no—
166C22⋊D61—41no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—42no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173D244—21no—
174D244—21no—
175C4×D61—41no—
176C4×D61—41no—
177C4×D61—41no—
178C4×D61—41no—
179C4×D61—81no—
180Dic122—21no—
181Dic122—21no—
182C8×C61—41no—
183C8×C61—41no—
184C8×C61—81no—
185#92418—42no—
186#92418—42no—
187#9322—611nomaximal, Sylow
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—82no—
191C22×C61—82no—
192C22×C61—82no—
193C22×C61—162no—
194C22×C61—162no—
195C22×C61#38611yescharacteristic
196C22×C61#46811yescharacteristic
197C22×C61#46911yescharacteristic
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61#41711yescharacteristic
205C4×C61#41811yescharacteristic
206C4×C61#45311yescharacteristic
207C4×C61#45411yescharacteristic
208C4×C61#46811yescharacteristic
209C4×C61#46911yescharacteristic
210Dic61—41no—
211Dic61—41no—
212Dic61—41no—
213Dic61—82no—
214#3038—611no—
215#2989—611no—
216#1982—611no—
217#1806—611no—
218#1545D6111yescharacteristic, complemented
219#1303—611no—
220#1292—611no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61—162no—
224C2×C61#188311yescharacteristic
225C2×C61#189511yescharacteristic
226C2×C61#190311yescharacteristic
227D61—81no—
228C2×AGL(1,ℤ/8)—1221no—
229C2×#127C2×D6111yescharacteristic
230C4×#41—611no—
231#460—612no—
232#460—1221no—
233#459—612no—
234#459—1221no—
235#446—1221no—
236#436—1221no—
237#435—1222no—
238#432—1221no—
239#431C2×D6111yescharacteristic
240#423—611no—
241#423—1221no—
242#423C2×D6111yescharacteristic
243C2×C4⋊C8—611no—
244C2×#104—1221no—
245#418—1221no—
246C2×#102—1222no—
247C4×C4⋊C4—611no—
248#339—1221no—
249#331—21no—
250#331—21no—
251C61#932211yescharacteristic, complemented, Sylow
252C2×#41—611no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—21no—
256AGL(1,ℤ/8)—2442no—
257AGL(1,ℤ/8)—2442no—
258C2×SD16—1222no—
259C2×D8—1222no—
260C2×M16—21no—
261C2×M16—1222no—
262C2×M16—1221no—
263C22×C8—612no—
264#127—21no—
265#127—21no—
266#127—21no—
267#127C4×D6112yes—
268C4×Q8—611no—
269C4×Q8—611no—
270C4×D4—611no—
271C4×D4—611no—
272C4×D4—1221no—
273C4×D4—1221no—
274#117—611no—
275#117—1221no—
276C2×C4⋊C4—1221no—
277C2×C42—1221no—
278C2×C42—1221no—
279C2×C42C22×D6111yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—612no—
283C4⋊C8—1222no—
284C4⋊C8—1221no—
285C4⋊C8—1221no—
286C4⋊C8—1221no—
287C4⋊C8C22⋊D6111yescharacteristic
288C4⋊C8C22⋊D6111yescharacteristic
289#104—2442no—
290#102—1222no—
291#102—1222no—
292#102—2444no—
293C22⋊C8—21no—
294C22⋊C8—1222no—
295#97—1222no—
296C4×C8—21no—
297#95—1221no—
298C24—41no—
299#41—1221no—
300#41—1221no—
301#41—1221no—
302#41—1221no—
303C2×Q8—611no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—42no—
308C2×D4—42no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—82no—
317C2×D4—611no—
318C2×D4—1221no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—2441no—
323C22×C4#1175822211yescharacteristic
324C22×C4D4×D6111yescharacteristic
325C22×C4D4×D6111yescharacteristic
326SD16—2444no—
327D8—2444no—
328M16—41no—
329M16—41no—
330M16—4882no—
331M16—2441no—
332M16—2441no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—41no—
336C2×C8—1222no—
337C2×C8—1222no—
338C2×C8—2442no—
339C4⋊C4—611no—
340C4⋊C4—611no—
341C4⋊C4—1222no—
342C4⋊C4—1221no—
343C4⋊C4—1221no—
344C4⋊C4—2441no—
345C22⋊C4—1221no—
346C22⋊C4—1221no—
347C22⋊C4—1221no—
348C42—1221no—
349C42—1221no—
350C42—1221no—
351C42—2441no—
352C42—2441no—
353C42C2×C4×D6111yescharacteristic
354C42D4×D6111yescharacteristic
355C42#1175822411yescharacteristic
356C42C2×C22⋊D6111yescharacteristic
357C23—42no—
358C23—82no—
359C23—82no—
360C23—81no—
361C23—81no—
362C23—1221no—
363C23#1451975011yescharacteristic
364Q8—1221no—
365Q8—1221no—
366D4—44no—
367D4—42no—
368D4—42no—
369D4—82no—
370D4—82no—
371D4—81no—
372D4—81no—
373D4—81no—
374D4—81no—
375D4—1221no—
376D4—1221no—
377D4—2441no—
378D4—2441no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—4881no—
386C2×C4—4881no—
387C2×C4—4881no—
388C2×C4—2442no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4C22⋊C4×D6111yescharacteristic
394C2×C4#1451973711yescharacteristic
395C2×C4C4×C22⋊D6111yescharacteristic
396C2×C4#1451974511yescharacteristic
397C2×C4#1451974811yescharacteristic
398C2×C4#1451975911yescharacteristic
399C2×C4#1451980111yescharacteristic
400C2×C4#1451980111yescharacteristic
401C2×C4#1451980411yescharacteristic
402C2×C4#1451980611yescharacteristic
403C8—41no—
404C8—41no—
405C8—81no—
406C8—2442no—
407C8—2442no—
408C22—21no—
409C22—21no—
410C22—82no—
411C22—82no—
412C22—82no—
413C22—162no—
414C22—162no—
415C22—2441no—
416C22—2441no—
417C22—2441no—
418C22#1683963811yescharacteristic
419C22#1684000711yescharacteristic
420C22#1684001411yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—4882no—
425C4—2441no—
426C4—2441no—
427C4—2441no—
428C4#1683976011yescharacteristic
429C4#1683976511yescharacteristic
430C4#1683992811yescharacteristic
431C4#1683993311yescharacteristic
432C4#1684000511yescharacteristic
433C4#1684001211yescharacteristic
434C2—21no—
435C2—21no—
436C2—162no—
437C2—4881no—
438C2#2144619211yescharacteristic
439C2#2144625411yescharacteristic
440C2#2144630211yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1545C2
socleC22×C61#386
prime radical#21455295C2
cosocleC2×C42×C61C23
hypercenter#1545D61
hypocenterC61#9322
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
2. #21454932C2semidirect
3. #21446747C2semidirect
4. #21445836C2semidirect
5. #21443721C2semidirect
6. #21443693C2semidirect
7. C61×#1545C2semidirect
11. #16839959C4semidirect
13. #16839954C4semidirect
218. #1545D61semidirect
251. C61#9322semidirect

Maximal subgroups

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

subgroupindex
#214552952
#214549322
#214467472
#214458362
#214437212
#214436932
C61×#15452
#932261