Finite Group Databasebeta

← #29575910

Subgroups — #29575910

Order 15616.

516 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455295C211yesmaximal, characteristic
2#21454487C211yesmaximal, characteristic, complemented
3C2×#16839506C211yesmaximal, characteristic, complemented
4#21444207C211yesmaximal, characteristic, complemented
5#21443715C211yesmaximal, characteristic, complemented
6#21443693C211yesmaximal, characteristic, complemented
7C61×#1545C211yesmaximal, characteristic, complemented
8C2×#14519803—21no—
9C4×#11758222C2211yescharacteristic
10#16839959—21no—
11#16839959C412yes—
12#16839954—21no—
13#16839954C412yes—
14#16839822—22no—
15#16839818—21no—
16#16839814—21no—
17#16839786C2211yescharacteristic
18C2×C4⋊#92418C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20#16839767—21no—
21#16839730—21no—
22#16839720—21no—
23#16839506—21no—
24#16839506—21no—
25#16839494—21no—
26#16839491—21no—
27C2×#127×C61C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C61×#331—22no—
31C2×#11758222D411yescharacteristic
32#14519803—42no—
33#14519803—42no—
34C2×#11758200—22no—
35C2×#11758199—22no—
36C2×#11758194—21no—
37C22×#92418—21no—
38C22×#92418—21no—
39C4×Dic122C2×C411yescharacteristic
40C4×Dic122D411yescharacteristic
41C4×D244C2×C411yescharacteristic
42C4×D244D411yescharacteristic
43C4×C22⋊D61—21no—
44C4×C22⋊D61—21no—
45#14519736D411yescharacteristic
46#14519734—21no—
47C42×D61—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418C2×C412yes—
53C4⋊#92418D411yescharacteristic
54C4⋊#92418D411yescharacteristic
55#14519698—22no—
56#14519698—22no—
57#14519689—22no—
58#14519689—22no—
59#14519687—22no—
60C8×Dic61—22no—
61C22×D4×C61—21no—
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C2×M16×C61—21no—
65#127×C61—21no—
66#127×C61—21no—
67#127×C61—21no—
68#127×C61C2×C412yes—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61D412yes—
73C22⋊C8×C61—21no—
74C4×C8×C61—21no—
75C24×C61—41no—
76C2×D4×C61—22no—
77C2×D4×C61—22no—
78C2×D4×C61—22no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—81no—
87C2×D4×C61—81no—
88C2×D4×C61—82no—
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C22×C4×C61#4111yescharacteristic
92C2×C22⋊D61—21no—
93#11758222—21no—
94#11758222—21no—
95#11758222—21no—
96#11758222—21no—
97C2×D244C22⋊C411yescharacteristic
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×Dic122C22⋊C411yescharacteristic
102M16×C61—41no—
103M16×C61—41no—
104C2×C8×C61—22no—
105C2×C8×C61—41no—
106C42×C61C22×C411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C22⋊Dic61—21no—
111#11758200—44no—
112#11758199—44no—
113#11758198—21no—
114#11758198—21no—
115C4⋊Dic61C22⋊C411yescharacteristic
116C4⋊Dic61C22⋊C411yescharacteristic
117#11758196—21no—
118#11758196—21no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122#11758194—41no—
123#11758194—41no—
124C2×#92418—22no—
125C2×#92418—21no—
126C2×#92418—21no—
127C2×#92418—41no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418—81no—
131C23×C61—42no—
132C23×C61—82no—
133C23×C61—82no—
134C23×C61—81no—
135C23×C61—81no—
136C23×C61#12311yescharacteristic
137C22×D61—21no—
138D4×C61—42no—
139D4×C61—42no—
140D4×C61—82no—
141D4×C61—82no—
142D4×C61—82no—
143D4×C61—81no—
144D4×C61—81no—
145D4×C61—81no—
146D4×C61—81no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—41no—
150C2×C4×C61C2×C22⋊C411yescharacteristic
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61C4×D411yescharacteristic
153C2×C4×C61#12011yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#13511yescharacteristic
157C2×C4×C61#13511yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C22⋊D61—41no—
161C22⋊D61—41no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165D244—21no—
166D244—21no—
167C4×D61—41no—
168C4×D61—41no—
169C4×D61—41no—
170C4×D61—41no—
171C4×D61—81no—
172Dic122—21no—
173Dic122—21no—
174C8×C61—42no—
175C8×C61—81no—
176#92418—42no—
177#92418—41no—
178#92418—41no—
179#92418—81no—
180#9174—611nomaximal, Sylow
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—82no—
184C22×C61—82no—
185C22×C61—82no—
186C22×C61—162no—
187C22×C61—162no—
188C22×C61#38611yescharacteristic
189C22×C61#48211yescharacteristic
190C22×C61#48211yescharacteristic
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61#41611yescharacteristic
198C4×C61#41811yescharacteristic
199C4×C61#44911yescharacteristic
200C4×C61#44911yescharacteristic
201C4×C61#47111yescharacteristic
202C4×C61#47211yescharacteristic
203Dic61—41no—
204Dic61—41no—
205Dic61—41no—
206#3038—611no—
207#2925—611no—
208#1545D6111yescharacteristic, complemented
209C2×#331—611no—
210#1477—611no—
211#1301—611no—
212#1292—611no—
213C2×C61—21no—
214C2×C61—21no—
215C2×C61—162no—
216C2×C61#187511yescharacteristic
217C2×C61#190311yescharacteristic
218C2×C61#190711yescharacteristic
219D61—81no—
220C2×AGL(1,ℤ/8)—1221no—
221C2×#127C2×D6111yescharacteristic
222C4×#41—611no—
223#460—612no—
224#460—1221no—
225#459—612no—
226#459—1221no—
227#433—1222no—
228#432—1221no—
229#431—1221no—
230#431C2×D6111yescharacteristic
231#423—611no—
232#423C2×D6111yescharacteristic
233C2×C4⋊C8—611no—
234C2×C4⋊C8—611no—
235#418—1221no—
236#408—1221no—
237#405—1221no—
238#331—22no—
239#331—1221no—
240#331—1221no—
241Q8⋊C8—1221no—
242D4⋊C8—1221no—
243C61#917411yescharacteristic, complemented, Sylow
244C2×#41—611no—
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—21no—
248AGL(1,ℤ/8)—2442no—
249AGL(1,ℤ/8)—2442no—
250C2×SD16—1222no—
251C2×D8—1222no—
252C2×M16—21no—
253C2×M16—1221no—
254C22×C8—1221no—
255C22×C8—1221no—
256#127—21no—
257#127—21no—
258#127—21no—
259#127C4×D6112yes—
260C4×Q8—611no—
261C4×Q8—611no—
262C4×D4—611no—
263C4×D4—611no—
264C4×D4—1221no—
265C4×D4—1221no—
266#117—611no—
267#117—1221no—
268C2×C42—1221no—
269C2×C42C22×D6111yescharacteristic
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—612no—
273C4⋊C8—611no—
274C4⋊C8—611no—
275C4⋊C8—1221no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278C4⋊C8—1221no—
279C4⋊C8C22⋊D6112yes—
280#102—1222no—
281#102—1222no—
282C22⋊C8—21no—
283C22⋊C8—1222no—
284C22⋊C8—1222no—
285#97—1222no—
286C4×C8—21no—
287C4×C8—1222no—
288C24—41no—
289#41—1221no—
290#41—1221no—
291#41—1221no—
292#41—1221no—
293C2×Q8—611no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—81no—
305C2×D4—81no—
306C2×D4—82no—
307C2×D4—611no—
308C2×D4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4#1175822211yescharacteristic
313C22×C4D4×D6111yescharacteristic
314C22×C4#1175822411yescharacteristic
315SD16—2444no—
316D8—2444no—
317M16—41no—
318M16—41no—
319M16—2441no—
320M16—2441no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—1222no—
324C2×C8—1221no—
325C2×C8—1221no—
326C2×C8—4881no—
327C2×C8—2441no—
328C2×C8—2441no—
329C2×C8—2441no—
330C4⋊C4—611no—
331C4⋊C4—611no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C22⋊C4—1221no—
337C42—1221no—
338C42—1221no—
339C42—1221no—
340C42C2×C4×D6111yescharacteristic
341C42D4×D6111yescharacteristic
342C42D4×D6111yescharacteristic
343C42C2×C22⋊D6111yescharacteristic
344C23—42no—
345C23—82no—
346C23—82no—
347C23—81no—
348C23—81no—
349C23—1221no—
350C23#1451975911yescharacteristic
351Q8—1221no—
352Q8—1221no—
353D4—42no—
354D4—42no—
355D4—82no—
356D4—82no—
357D4—82no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—1221no—
363D4—1221no—
364D4—2441no—
365D4—2441no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—4881no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4C22⋊C4×D6111yescharacteristic
378C2×C4#1451973711yescharacteristic
379C2×C4C4×C22⋊D6111yescharacteristic
380C2×C4#1451974511yescharacteristic
381C2×C4#1451974811yescharacteristic
382C2×C4#1451975011yescharacteristic
383C2×C4#1451979611yescharacteristic
384C2×C4#1451979811yescharacteristic
385C2×C4#1451980111yescharacteristic
386C2×C4#1451980411yescharacteristic
387C8—42no—
388C8—81no—
389C8—4881no—
390C8—2442no—
391C8—2441no—
392C8—2441no—
393C22—21no—
394C22—21no—
395C22—82no—
396C22—82no—
397C22—82no—
398C22—162no—
399C22—162no—
400C22—2441no—
401C22—2441no—
402C22—2441no—
403C22#1683963811yescharacteristic
404C22#1684008411yescharacteristic
405C22#1684008511yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—2441no—
410C4—2441no—
411C4—2441no—
412C4#1683975511yescharacteristic
413C4#1683976511yescharacteristic
414C4#1683990411yescharacteristic
415C4#1683990611yescharacteristic
416C4#1684002411yescharacteristic
417C4#1684003111yescharacteristic
418C2—21no—
419C2—21no—
420C2—162no—
421C2—4881no—
422C2#2144613811yescharacteristic
423C2#2144629611yescharacteristic
424C2#2144632411yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1545C2
socleC22×C61#386
prime radical#21455295C2
cosocleC2×C42×C61C23
hypercenter#1545D61
hypocenterC61#9174
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. #21454487C2semidirect
3. C2×#16839506C2semidirect
4. #21444207C2semidirect
5. #21443715C2semidirect
6. #21443693C2semidirect
7. C61×#1545C2semidirect
208. #1545D61semidirect
243. C61#9174semidirect

Maximal subgroups

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

subgroupindex
#214552952
#214544872
C2×#168395062
#214442072
#214437152
#214436932
C61×#15452
#917461