Finite Group Databasebeta

← #14909149

Subgroups — #14909149

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622491C211yesmaximal, characteristic, complemented
2#13079040C211yesmaximal, characteristic
3#13070860C212yesmaximal, complemented
4#13070856C212yesmaximal, complemented
5#13070849C212yesmaximal, complemented
6#13070846C212yesmaximal, complemented
7#13070329C211yesmaximal, characteristic, complemented
8#13070328C211yesmaximal, characteristic, complemented
9#13070326C211yesmaximal, characteristic, complemented
10M32×Dic11C211yesmaximal, characteristic, complemented
11C11×#2139C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13#10623363—21no—
14C2×#67003—21no—
15C2×#66957C2211yescharacteristic
16C2×#66943—21no—
17C2×C11×M32C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622804C2211yescharacteristic
20#10622794C2211yescharacteristic
21#10622788—21no—
22#10622781—21no—
23#10622768C2211yescharacteristic
24#10622764C2211yescharacteristic
25C2×#66882C2211yescharacteristic
26C2×C8×Dic11C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28C2×#66872—21no—
29#10622491—21no—
30#10622491—21no—
31#10622491C2212yes—
32#10622491C2212yes—
33C11×#358C2212yes—
34C11×#357C2212yes—
35#10622202C2212yes—
36#10622200C2212yes—
37#10622147C2212yes—
38#10622141C2212yes—
39#10622140C2212yes—
40C16×Dic11C2212yes—
41#10622130C2212yes—
42#10622129C2212yes—
43C2×C11×#41—21no—
44C2×#4339—21no—
45C11×#135—22no—
46C11×#135—22no—
47C2×C11×Q16C2311yescharacteristic
48C2×C11×SD16—21no—
49C2×C11×D8C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C2×C11×C4⋊C4—21no—
52#67003—44no—
53#67000—21no—
54#66997—21no—
55C2×#4326—21no—
56C2×#4325—21no—
57#66993—21no—
58#66992—41no—
59#66992—41no—
60#66989—21no—
61C2×#4324—21no—
62C2×#4323—21no—
63C4×C22⋊D11—41no—
64C4×C22⋊D11—41no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—41no—
67C2×Dic11⋊C4—41no—
68C2×C4×Dic11D411yescharacteristic
69C22×C11⋊C8D411yescharacteristic
70C2×Dic44C2311yescharacteristic
71#66957—22no—
72#66957—22no—
73C2×D88C2311yescharacteristic
74C2×#4314—21no—
75#66943—22no—
76#66943—22no—
77#66943—41no—
78#66943—41no—
79C11×M32—22no—
80C2×C11×C16C2312yes—
81C11×#107—21no—
82C11×#107C2312yes—
83#66882—21no—
84#66882C2312yes—
85C8×Dic11D411yescharacteristic
86C8×Dic11D411yescharacteristic
87C8×Dic11C2311yescharacteristic
88C8×Dic11C2311yescharacteristic
89#66876—22no—
90C2×C11⋊C16C2312yes—
91#66872—22no—
92#66872—22no—
93#33708—111nomaximal, Sylow
94C11×#41—42no—
95C11×#41—42no—
96C2×Q8×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C22×Dic11—41no—
106C22×Dic11D811yescharacteristic
107C22×Dic11D811yescharacteristic
108#4339—42no—
109#4339—42no—
110C2×D44—21no—
111C2×C4×D11—41no—
112C2×Dic22—21no—
113C11×Q16—21no—
114C11×Q16—21no—
115C11×SD16—42no—
116C11×D8—21no—
117C11×D8—21no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11#4112yes—
120C2×C8×C11#4112yes—
121C2×C8×C11C2411yescharacteristic
122C11×C4⋊C4—22no—
123C11×C4⋊C4—41no—
124C22⋊Dic11—41no—
125C22⋊Dic11—41no—
126#4326—42no—
127#4325—42no—
128#4324—42no—
129#4323—42no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—41no—
132C4⋊Dic11—22no—
133C4⋊Dic11—42no—
134C4⋊Dic11—42no—
135C4⋊Dic11—41no—
136Dic11⋊C4—42no—
137Dic11⋊C4—42no—
138Dic11⋊C4—41no—
139Dic11⋊C4—41no—
140C4×Dic11D811yescharacteristic
141C4×Dic11D811yescharacteristic
142C4×Dic11C2×D411yescharacteristic
143C4×Dic11C2×D411yescharacteristic
144C2×C11⋊C8SD1614yes—
145C2×C11⋊C8C2×D411yescharacteristic
146C2×C11⋊C8C2×D411yescharacteristic
147Dic44—21no—
148Dic44—21no—
149D88—21no—
150D88—21no—
151#4314—42no—
152C11×C16—22no—
153C11⋊C16—22no—
154C2×#499—111no—
155#3147—111no—
156#2245—112no—
157#2244—112no—
158#2242—112no—
159#2242—112no—
160#2139—111no—
161#2139—111no—
162#2139—111no—
163#2139D1111yescharacteristic, complemented
164C4×M32—111no—
165C23×C11—41no—
166C23×C11C2×D811yescharacteristic
167C22×D11—41no—
168Q8×C11—41no—
169Q8×C11—41no—
170D4×C11—41no—
171D4×C11—41no—
172D4×C11—82no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—82no—
176C2×C4×C11—82no—
177C2×C4×C11#12412yes—
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11C2×SD1612yes—
180C2×C4×C11C22×D411yescharacteristic
181C22⋊D11—82no—
182C22⋊D11—82no—
183C22⋊D11—82no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—42no—
187C2×Dic11—41no—
188C2×Dic11—82no—
189C2×Dic11C2×D811yescharacteristic
190C2×Dic11C2×D811yescharacteristic
191C2×Dic11C2×D811yescharacteristic
192C2×Dic11C2×D811yescharacteristic
193D44—41no—
194D44—41no—
195C4×D11—82no—
196Dic22—41no—
197Dic22—41no—
198C8×C11#12412yes—
199C8×C11C2×#4111yescharacteristic
200C8×C11C2×#4111yescharacteristic
201C11⋊C8C2×SD1612yes—
202C11⋊C8C2×SD1612yes—
203C2×#135—111no—
204C2×#135—221no—
205C2×#135C2×D1111yescharacteristic
206#532—221no—
207C2×#125—221no—
208C2×M32—111no—
209C2×M32C2×D1111yescharacteristic
210#499—112no—
211#499—112no—
212#499—221no—
213#499—221no—
214#495—111no—
215#495—111no—
216#495—221no—
217#494—111no—
218#493—111no—
219#492—221no—
220C2×#107—111no—
221C2×#107C2×D1111yescharacteristic
222C2×#106—221no—
223C2×C4×C8—111no—
224#358—112no—
225#358—112no—
226#358—112no—
227#358C2×D1112yes—
228#357—112no—
229#357—112no—
230#357—112no—
231#357C2×D1112yes—
232#346—112no—
233C4×C16—112no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11#48612yes—
240C22×C11C22×D811yescharacteristic
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C4×C11—81no—
245C4×C11—82no—
246C4×C11#48612yes—
247C4×C11C2×#12411yescharacteristic
248C4×C11C22×SD1611yescharacteristic
249Dic11—21no—
250Dic11—21no—
251Dic11—21no—
252Dic11—21no—
253Dic11—81no—
254Dic11—82no—
255C2×#41—21no—
256C2×#41—221no—
257#135—22no—
258#135—22no—
259#135—222no—
260#135—222no—
261#135—444no—
262C2×Q16—111no—
263C2×Q16—221no—
264C2×Q16C22×D1111yescharacteristic
265C2×SD16—21no—
266C2×SD16—221no—
267C2×SD16—221no—
268C2×SD16—221no—
269C2×D8—111no—
270C2×D8—221no—
271C2×D8C22×D1111yescharacteristic
272C22×C8—111no—
273C22×C8C22×D1111yescharacteristic
274C4⋊Q8—221no—
275#127—221no—
276#125—222no—
277#125—222no—
278#125—441no—
279#125—441no—
280#124—221no—
281#124—221no—
282#121—441no—
283#121—441no—
284C4×D4—441no—
285C4×D4—441no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—441no—
289C2×C4⋊C4—441no—
290C2×C42—111no—
291M32—22no—
292M32—222no—
293C2×C16—112no—
294C2×C16C22×D1112yes—
295#107—21no—
296#107—112no—
297#107—221no—
298#107C22×D1112yes—
299#106—222no—
300#106—222no—
301C4×C8—111no—
302C4×C8—111no—
303C4×C8—111no—
304C4×C8—111no—
305C2×C11—22no—
306C2×C11—161no—
307C2×C11C2×#48611yescharacteristic
308C2×C11#341411yescharacteristic
309C2×C11#341411yescharacteristic
310D11—161no—
311#41—42no—
312#41—42no—
313#41—442no—
314#41—442no—
315C2×Q8—21no—
316C2×Q8—221no—
317C2×D4—21no—
318C2×D4—41no—
319C2×D4—221no—
320C2×D4—441no—
321C2×D4—441no—
322C2×D4—441no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—111no—
326C22×C4—111no—
327C22×C4—441no—
328C22×C4—441no—
329C22×C4D4×D1111yescharacteristic
330Q16—21no—
331Q16—21no—
332Q16—221no—
333Q16—221no—
334Q16—442no—
335SD16—42no—
336SD16—442no—
337SD16—442no—
338SD16—442no—
339D8—21no—
340D8—21no—
341D8—221no—
342D8—221no—
343D8—442no—
344C2×C8—114no—
345C2×C8—111no—
346C2×C8—111no—
347C2×C8#433912yes—
348C2×C8D4×D1111yescharacteristic
349C2×C8#434112yes—
350C2×C8C23×D1111yescharacteristic
351C4⋊C4—22no—
352C4⋊C4—41no—
353C4⋊C4—222no—
354C4⋊C4—442no—
355C4⋊C4—442no—
356C4⋊C4—442no—
357C4⋊C4—442no—
358C4⋊C4—441no—
359C4⋊C4—441no—
360C4⋊C4—441no—
361C22⋊C4—441no—
362C22⋊C4—441no—
363C22⋊C4—441no—
364C22⋊C4—441no—
365C42—111no—
366C42—111no—
367C42—111no—
368C42—111no—
369C16—22no—
370C16—222no—
371C11#3370811yescharacteristic, complemented, Sylow
372C23—41no—
373C23—441no—
374C23D8×D1111yescharacteristic
375Q8—41no—
376Q8—41no—
377Q8—441no—
378Q8—441no—
379D4—41no—
380D4—41no—
381D4—82no—
382D4—441no—
383D4—441no—
384D4—882no—
385D4—882no—
386D4—882no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—111no—
392C2×C4—111no—
393C2×C4—111no—
394C2×C4—111no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—442no—
399C2×C4—882no—
400C2×C4—882no—
401C2×C4#6693812yes—
402C2×C4D8×D1111yescharacteristic
403C2×C4SD16×D1112yes—
404C2×C4C2×D4×D1111yescharacteristic
405C8—112no—
406C8—112no—
407C8#6693812yes—
408C8C2×#433911yescharacteristic
409C8C2×#434111yescharacteristic
410C22—21no—
411C22—21no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—881no—
416C22—881no—
417C22—881no—
418C22#1062237312yes—
419C22C2×D8×D1111yescharacteristic
420C4—81no—
421C4—82no—
422C4—221no—
423C4—221no—
424C4—221no—
425C4—221no—
426C4—881no—
427C4—882no—
428C4#1062237312yes—
429C4C2×#6693811yescharacteristic
430C4C2×SD16×D1111yescharacteristic
431C2—22no—
432C2—161no—
433C2—1761no—
434C2C2×#1062237311yescharacteristic
435C2#1308174811yescharacteristic
436C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2139C2
socleC22×C11C22×D8
prime radical#13079040C2
hypercenter#2139D11
hypocenterC11#33708
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2139

Complements

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

NH ≅ G/Ntype
1. C2×#10622491C2semidirect
3. #13070860C2semidirect
4. #13070856C2semidirect
5. #13070849C2semidirect
6. #13070846C2semidirect
7. #13070329C2semidirect
8. #13070328C2semidirect
9. #13070326C2semidirect
10. M32×Dic11C2semidirect
11. C11×#2139C2semidirect
163. #2139D11semidirect
371. C11#33708semidirect

Maximal subgroups

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

subgroupindex
C2×#106224912
#130790402
#130708602
#130708562
#130708492
#130708462
#130703292
#130703282
#130703262
M32×Dic112
C11×#21392
#3370811