Finite Group Databasebeta

← #14909330

Subgroups — #14909330

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079197C211yesmaximal, characteristic, complemented
2#13079190C211yesmaximal, characteristic
3#13070897C211yesmaximal, characteristic, complemented
4#13070870C211yesmaximal, characteristic, complemented
5#13070842C211yesmaximal, characteristic, complemented
6#13070838C211yesmaximal, characteristic, complemented
7#13070714C211yesmaximal, characteristic, complemented
8#13070712C211yesmaximal, characteristic, complemented
9#13070710C211yesmaximal, characteristic, complemented
10#13070471C211yesmaximal, characteristic, complemented
11SD32×Dic11C211yesmaximal, characteristic, complemented
12#13070467C211yesmaximal, characteristic, complemented
13#13070465C211yesmaximal, characteristic, complemented
14C2×C16×Dic11C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16#10623153—21no—
17#10623127—21no—
18C2×C11×SD32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C11×#467C2211yescharacteristic
21C11×#466C2211yescharacteristic
22Q16×Dic11C2211yescharacteristic
23#10622794C2211yescharacteristic
24C2×#66892C2211yescharacteristic
25#10622764C2211yescharacteristic
26D8×Dic11C2211yescharacteristic
27C2×#66891C2211yescharacteristic
28#10622729C2211yescharacteristic
29#10622728C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C22×C11⋊C16C2211yescharacteristic
32#10622664—21no—
33#10622651—21no—
34C2×#66864C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622487C2211yescharacteristic
37#10622486C2211yescharacteristic
38#10622485C2211yescharacteristic
39#10622405—21no—
40#10622403—21no—
41#10622373—21no—
42#10622369—21no—
43C11×#367C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#357C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622141C2211yescharacteristic
51C16×Dic11C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622128C2211yescharacteristic
59C2×#4341—41no—
60C2×C11×Q16C2311yescharacteristic
61C2×C11×D8C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×C22⋊Q8—21no—
64C11×#121—21no—
65Q8×Dic11—21no—
66#66997—21no—
67C2×#4326—21no—
68#66993—21no—
69#66992—41no—
70D4×Dic11—21no—
71C2×#4323—21no—
72#66983—21no—
73#66977—21no—
74C2×C4×Dic11D411yescharacteristic
75C22×C11⋊C8D411yescharacteristic
76C2×Dic44C2311yescharacteristic
77C2×D88C2311yescharacteristic
78#66946—21no—
79#66942—41no—
80#66941—21no—
81#66941—21no—
82#66940—21no—
83#66940—41no—
84#66938—41no—
85(C22⋊D11)⋊C4—41no—
86#66931—41no—
87#66930—41no—
88C11×SD32—22no—
89C2×C11×C16—22no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#103—21no—
95C11×#102—21no—
96#66899—21no—
97#66896—21no—
98#66892—22no—
99#66891—22no—
100#66885—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66880—21no—
104C8×Dic11D411yescharacteristic
105C8×Dic11D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16—22no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111#66874—21no—
112#66873—21no—
113#66871—21no—
114#66871—21no—
115#66864—22no—
116#33736—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C22×Dic11—41no—
125C22×Dic11D811yescharacteristic
126C22×Dic11D811yescharacteristic
127#4341—84no—
128C2×D44—21no—
129C2×C4×D11—41no—
130C2×Dic22—21no—
131C2×Dic22—41no—
132C2×Dic22—41no—
133C11×Q16—21no—
134C11×Q16—21no—
135C11×D8—21no—
136C11×D8—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2411yescharacteristic
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—41no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C22⋊Dic11—41no—
147C22⋊Dic11—41no—
148#4326—42no—
149#4323—42no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163C4×Dic11D811yescharacteristic
164C4×Dic11D811yescharacteristic
165C4×Dic11C2×D411yescharacteristic
166C4×Dic11C2×D411yescharacteristic
167C2×C11⋊C8—22no—
168C2×C11⋊C8C2×D411yescharacteristic
169C2×C11⋊C8C2×D411yescharacteristic
170Dic44—21no—
171Dic44—21no—
172D88—21no—
173D88—21no—
174C11×C16—21no—
175C11×C16#4112yescomplemented
176C11⋊C16—21no—
177C11⋊C16#4112yescomplemented
178#3170—111no—
179#3169—111no—
180#2254—111no—
181#2248—111no—
182#2241—111no—
183#2240—111no—
184#2217—111no—
185#2217—111no—
186#2217—111no—
187#2217D1111yescharacteristic, complemented
188C4×SD32—111no—
189C4×SD32—111no—
190C4×SD32—111no—
191C4×SD32—111no—
192C2×C4×C16—111no—
193C23×C11—41no—
194C23×C11C2×D811yescharacteristic
195C22×D11—41no—
196Q8×C11—41no—
197Q8×C11—41no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11—82no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C22⋊D11—82no—
209C22⋊D11—82no—
210C22⋊D11—82no—
211C2×Dic11—22no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—82no—
216C2×Dic11SD3214yescomplemented
217C2×Dic11C2×D811yescharacteristic
218C2×Dic11C2×D811yescharacteristic
219C2×Dic11C2×D811yescharacteristic
220C2×Dic11C2×D811yescharacteristic
221D44—41no—
222D44—41no—
223C4×D11—82no—
224Dic22—41no—
225Dic22—41no—
226Dic22—82no—
227Dic22—82no—
228C8×C11—21no—
229C8×C11C2×#4111yescharacteristic
230C8×C11C2×#4111yescharacteristic
231C11⋊C8—21no—
232C11⋊C8#13512yes—
233#533—221no—
234#532—221no—
235C2×SD32—111no—
236C2×SD32—111no—
237C2×SD32—111no—
238C2×SD32C2×D1111yescharacteristic
239C22×C16—111no—
240C22×C16C2×D1111yescharacteristic
241#500—111no—
242#500—111no—
243#494—111no—
244#493—111no—
245#487—221no—
246#486—221no—
247#467—111no—
248#467—221no—
249#467C2×D1111yescharacteristic
250#466—111no—
251#466—221no—
252#466C2×D1111yescharacteristic
253C4×Q16—111no—
254C4×Q16—111no—
255C4×Q16—221no—
256C4×D8—111no—
257C4×D8—111no—
258C4×D8—221no—
259C2×C4×C8—111no—
260#367—111no—
261#367—111no—
262#367—111no—
263#367C2×D1111yescharacteristic
264#358—111no—
265#358—111no—
266#358—111no—
267#358C2×D1111yescharacteristic
268#357—111no—
269#357—111no—
270#357—111no—
271#357C2×D1111yescharacteristic
272C4×C16—111no—
273C4×C16—111no—
274C4×C16—111no—
275C4×C16—111no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11C2×SD3212yes—
282C22×C11C22×D811yescharacteristic
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—81no—
286C4×C11—21no—
287C4×C11—81no—
288C4×C11—81no—
289C4×C11—81no—
290C4×C11#53211yescharacteristic
291C4×C11C2×#13511yescharacteristic
292Dic11—21no—
293Dic11—81no—
294Dic11—81no—
295Dic11—81no—
296Dic11C2×SD3212yes—
297Dic11C2×SD3212yes—
298Dic11#50812yes—
299C2×#41—441no—
300C2×Q16—111no—
301C2×Q16—221no—
302C2×Q16C22×D1111yescharacteristic
303C2×D8—111no—
304C2×D8—221no—
305C2×D8C22×D1111yescharacteristic
306C22×C8—111no—
307C22×C8C22×D1111yescharacteristic
308C4⋊Q8—221no—
309C4⋊Q8—221no—
310C4⋊Q8—221no—
311#127—221no—
312#125—441no—
313#124—441no—
314C22⋊Q8—21no—
315C22⋊Q8—221no—
316C22⋊Q8—441no—
317#121—21no—
318#121—221no—
319#121—441no—
320C4×Q8—221no—
321C4×Q8—221no—
322C4×Q8—441no—
323C4×D4—221no—
324C4×D4—221no—
325C4×D4—441no—
326#117—441no—
327C2×C42—111no—
328SD32—22no—
329SD32—222no—
330SD32—222no—
331SD32—222no—
332C2×C16—22no—
333C2×C16—111no—
334C2×C16—111no—
335C2×C16—222no—
336C2×C16C22×D1111yescharacteristic
337C2×C16C22×D1111yescharacteristic
338#107—111no—
339#107—111no—
340#107—221no—
341#107—221no—
342#107C22×D1111yescharacteristic
343#107C22×D1111yescharacteristic
344#103—21no—
345#103—221no—
346#103—221no—
347#103—221no—
348#102—21no—
349#102—221no—
350#102—221no—
351#102—221no—
352C4×C8—111no—
353C4×C8—111no—
354C4×C8—111no—
355C4×C8—111no—
356C2×C11—22no—
357C2×C11—161no—
358C2×C11#316911yescharacteristic
359C2×C11C22×SD3211yescharacteristic
360C2×C11C2×#50811yescharacteristic
361D11—161no—
362#41—884no—
363C2×Q8—21no—
364C2×Q8—221no—
365C2×Q8—441no—
366C2×Q8—441no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4—221no—
370C2×D4—441no—
371C2×D4—441no—
372C2×D4—441no—
373C22×C4—111no—
374C22×C4—111no—
375C22×C4—441no—
376C22×C4—441no—
377C22×C4D4×D1111yescharacteristic
378Q16—21no—
379Q16—21no—
380Q16—221no—
381Q16—221no—
382Q16—442no—
383D8—21no—
384D8—21no—
385D8—221no—
386D8—221no—
387D8—442no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—111no—
391C2×C8—111no—
392C2×C8—222no—
393C2×C8D4×D1111yescharacteristic
394C2×C8C23×D1111yescharacteristic
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—221no—
399C4⋊C4—221no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C4⋊C4—441no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C4⋊C4—441no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—441no—
410C22⋊C4—441no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C42—111no—
414C42—111no—
415C42—111no—
416C42—111no—
417C42—441no—
418C42—441no—
419C16—21no—
420C16—112no—
421C16—221no—
422C16#434112yescomplemented
423C11#3373611yescharacteristic, complemented, Sylow
424C23—41no—
425C23—441no—
426C23D8×D1111yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—441no—
430Q8—441no—
431Q8—882no—
432Q8—882no—
433D4—41no—
434D4—41no—
435D4—82no—
436D4—441no—
437D4—441no—
438D4—882no—
439D4—882no—
440D4—882no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—111no—
447C2×C4—111no—
448C2×C4—111no—
449C2×C4—114no—
450C2×C4—111no—
451C2×C4—222no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—882no—
456C2×C4—882no—
457C2×C4D8×D1111yescharacteristic
458C2×C4C2×D4×D1111yescharacteristic
459C8—21no—
460C8—112no—
461C8—221no—
462C8C2×#434111yescharacteristic
463C8#41×D1111yescharacteristic
464C22—21no—
465C22—21no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—881no—
470C22—881no—
471C22—881no—
472C22D11×SD3212yes—
473C22C2×D8×D1111yescharacteristic
474C4—21no—
475C4—81no—
476C4—81no—
477C4—81no—
478C4—112no—
479C4—112no—
480C4—112no—
481C4—221no—
482C4—881no—
483C4—881no—
484C4—881no—
485C4#1062312711yescharacteristic
486C4D11×#13511yescharacteristic
487C2—22no—
488C2—161no—
489C2—1761no—
490C2#1307919011yescharacteristic
491C2C2×D11×SD3211yescharacteristic
492C2D11×#50811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
prime radical#13079190C2
hypercenter#2217D11
hypocenterC11#33736
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. #13079197C2semidirect
3. #13070897C2semidirect
4. #13070870C2semidirect
5. #13070842C2semidirect
6. #13070838C2semidirect
7. #13070714C2semidirect
8. #13070712C2semidirect
9. #13070710C2semidirect
10. #13070471C2semidirect
11. SD32×Dic11C2semidirect
12. #13070467C2semidirect
13. #13070465C2semidirect
14. C2×C16×Dic11C2semidirect
15. C11×#2217C2semidirect
175. C11×C16#41semidirect
177. C11⋊C16#41semidirect
187. #2217D11semidirect
216. C2×Dic11SD32semidirect
422. C16#4341semidirect
423. C11#33736semidirect

Maximal subgroups

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

subgroupindex
#130791972
#130791902
#130708972
#130708702
#130708422
#130708382
#130707142
#130707122
#130707102
#130704712
SD32×Dic112
#130704672
#130704652
C2×C16×Dic112
C11×#22172
#3373611