Finite Group Databasebeta

← #14909332

Subgroups — #14909332

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#13079199C211yesmaximal, characteristic, complemented
2#13079192C211yesmaximal, characteristic
3#13070897C211yesmaximal, characteristic, complemented
4#13070870C211yesmaximal, characteristic, complemented
5#13070842C211yesmaximal, characteristic, complemented
6#13070838C211yesmaximal, characteristic, complemented
7#13070715C211yesmaximal, characteristic, complemented
8#13070713C211yesmaximal, characteristic, complemented
9#13070711C211yesmaximal, characteristic, complemented
10#13070709C211yesmaximal, characteristic, complemented
11C4×#66864C211yesmaximal, characteristic, complemented
12C4×#66892C211yesmaximal, characteristic, complemented
13C4×#66891C211yesmaximal, characteristic, complemented
14C4×C16×D11C211yesmaximal, characteristic, complemented
15C4×C11×SD32C211yesmaximal, characteristic, complemented
16#10623109—21no—
17#10623079—21no—
18C2×C11×SD32C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21#10622801C2211yescharacteristic
22#10622794C2211yescharacteristic
23C2×#66892C2211yescharacteristic
24#10622770C2211yescharacteristic
25#10622764C2211yescharacteristic
26C2×#66891C2211yescharacteristic
27C4×#4326—21no—
28C4×#4323—21no—
29C2×#66864C2211yescharacteristic
30C2×C16×D11C2211yescharacteristic
31C2×C16×D11C2211yescharacteristic
32#10622500C2211yescharacteristic
33#10622496C2211yescharacteristic
34#10622487C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622426—21no—
37#10622405—21no—
38#10622388—21no—
39#10622373—21no—
40C4×Dic44C2211yescharacteristic
41C4×D88C2211yescharacteristic
42C4×C8×D11C2211yescharacteristic
43C11×#367C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#357C2211yescharacteristic
46C4×C11×C16C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622141C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622128C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×#4339—41no—
60C2×C11×Q16C2311yescharacteristic
61C2×C11×D8C2311yescharacteristic
62C4×Q8×C11—21no—
63C4×D4×C11—21no—
64#66999—21no—
65#66997—21no—
66C2×#4326—21no—
67#66993—21no—
68#66991—21no—
69C2×#4323—21no—
70C4×C22⋊D11—41no—
71C2×Dic44C2311yescharacteristic
72C2×D88C2311yescharacteristic
73C2×C8×D11D411yescharacteristic
74C2×C8×D11C2311yescharacteristic
75#66950—21no—
76#66949—41no—
77#66948—21no—
78#66942—41no—
79#66941—21no—
80#66941—21no—
81#66938—41no—
82#66937—41no—
83C4×D44—21no—
84#66925—41no—
85C42×D11D411yescharacteristic
86C4×Dic22—21no—
87C4×Dic22—41no—
88C11×SD32—22no—
89C2×C11×C16C2311yescharacteristic
90C2×C11×C16C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#103—21no—
94C11×#102—21no—
95C4×C8×C11C2311yescharacteristic
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×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66873—21no—
110#66871—21no—
111#66871—21no—
112C4×C11⋊C8D411yescharacteristic
113#66864—22no—
114C16×D11—22no—
115C16×D11—22no—
116#33736—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C22×C4×C11—41no—
120C2×C22⋊D11—41no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123#4339—84no—
124C2×D44—21no—
125C2×D44—41no—
126C2×C4×D11—41no—
127C2×C4×D11D811yescharacteristic
128C2×C4×D11D811yescharacteristic
129C2×C4×D11C2×D411yescharacteristic
130C2×Dic22—21no—
131C2×Dic22—41no—
132C2×Dic22—41no—
133C11×Q16—21no—
134C11×Q16—21no—
135C11×D8—21no—
136C11×D8—21no—
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2411yescharacteristic
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—41no—
142C11×C22⋊C4—41no—
143C42×C11—41no—
144C42×C11C2×D411yescharacteristic
145C22⋊Dic11—41no—
146#4326—42no—
147#4323—42no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
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×Dic11D811yescharacteristic
163C4×Dic11D811yescharacteristic
164C4×Dic11C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167Dic44—21no—
168Dic44—21no—
169D88—21no—
170D88—21no—
171C8×D11—21no—
172C8×D11—21no—
173C8×D11—22no—
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#2217—111no—
188C4×SD32—111no—
189C4×SD32—111no—
190C4×SD32—111no—
191C4×SD32D1111yescharacteristic, complemented
192C2×C4×C16—111no—
193C23×C11—41no—
194C22×D11—41no—
195C22×D11C2×D811yescharacteristic
196Q8×C11—41no—
197Q8×C11—41no—
198D4×C11—41no—
199D4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—82no—
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C22⋊D11—82no—
208C22⋊D11—82no—
209C22⋊D11—82no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11C2×D811yescharacteristic
214C2×Dic11C2×D811yescharacteristic
215C2×Dic11C2×D811yescharacteristic
216D44—41no—
217D44—41no—
218D44—82no—
219C4×D11—21no—
220C4×D11—21no—
221C4×D11—22no—
222C4×D11—82no—
223C4×D11SD3214yescomplemented
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×C16—111no—
241#500—111no—
242#500—111no—
243#494—111no—
244#493—111no—
245#487—221no—
246#486—221no—
247#467—111no—
248#467—111no—
249#467—221no—
250#466—111no—
251#466—111no—
252#466—221no—
253C4×Q16—111no—
254C4×Q16—221no—
255C4×Q16C2×D1111yescharacteristic
256C4×D8—111no—
257C4×D8—221no—
258C4×D8C2×D1111yescharacteristic
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×C16C2×D1111yescharacteristic
276C22×C11—81no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11C22×D811yescharacteristic
280C2×D11—21no—
281C2×D11—21no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C2×D11C2×SD3212yes—
286C4×C11—21no—
287C4×C11—81no—
288C4×C11—81no—
289C4×C11—81no—
290C4×C11C2×SD3212yes—
291C4×C11#53211yescharacteristic
292C4×C11C2×#13511yescharacteristic
293Dic11—21no—
294Dic11—81no—
295Dic11—81no—
296Dic11—81no—
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×C8—111no—
308C4⋊Q8—221no—
309C4⋊Q8—221no—
310C4⋊Q8—221no—
311#127—221no—
312#125—441no—
313#124—441no—
314C22⋊Q8—221no—
315C22⋊Q8—221no—
316C22⋊Q8—441no—
317#121—221no—
318#121—221no—
319#121—441no—
320C4×Q8—21no—
321C4×Q8—221no—
322C4×Q8—441no—
323C4×D4—21no—
324C4×D4—221no—
325C4×D4—441no—
326#117—441no—
327C2×C42—111no—
328SD32—22no—
329SD32—222no—
330SD32—222no—
331SD32—222no—
332C2×C16—111no—
333C2×C16—111no—
334C2×C16—222no—
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×C8C22×D1111yescharacteristic
356C2×C11—161no—
357C2×C11#316911yescharacteristic
358C2×C11C22×SD3211yescharacteristic
359C2×C11C2×#50811yescharacteristic
360D11—22no—
361D11—161no—
362#41—884no—
363C2×Q8—21no—
364C2×Q8—221no—
365C2×Q8—441no—
366C2×Q8—441no—
367C2×D4—21no—
368C2×D4—221no—
369C2×D4—441no—
370C2×D4—441no—
371C2×D4—441no—
372C2×D4—441no—
373C22×C4—41no—
374C22×C4—111no—
375C22×C4—111no—
376C22×C4—111no—
377C22×C4—441no—
378Q16—21no—
379Q16—21no—
380Q16—221no—
381Q16—221no—
382Q16—442no—
383D8—21no—
384D8—21no—
385D8—221no—
386D8—221no—
387D8—442no—
388C2×C8—111no—
389C2×C8—111no—
390C2×C8—222no—
391C2×C8—221no—
392C2×C8—221no—
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—441no—
409C22⋊C4—441no—
410C22⋊C4—441no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C42—41no—
414C42—111no—
415C42—111no—
416C42—111no—
417C42—441no—
418C42D4×D1111yescharacteristic
419C16—21no—
420C16—112no—
421C16—221no—
422C16#433912yescomplemented
423C11#3373611yescharacteristic, complemented, Sylow
424C23—41no—
425C23—111no—
426C23—441no—
427Q8—41no—
428Q8—41no—
429Q8—441no—
430Q8—441no—
431Q8—882no—
432Q8—882no—
433D4—41no—
434D4—41no—
435D4—441no—
436D4—441no—
437D4—882no—
438D4—882no—
439D4—882no—
440D4—882no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—82no—
445C2×C4—111no—
446C2×C4—111no—
447C2×C4—114no—
448C2×C4—111no—
449C2×C4—222no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—882no—
456C2×C4D8×D1111yescharacteristic
457C2×C4D8×D1111yescharacteristic
458C2×C4C2×D4×D1111yescharacteristic
459C8—21no—
460C8—112no—
461C8—221no—
462C8C2×#433911yescharacteristic
463C8#41×D1111yescharacteristic
464C22—81no—
465C22—81no—
466C22—81no—
467C22—112no—
468C22—221no—
469C22—221no—
470C22—881no—
471C22—881no—
472C22—881no—
473C22C2×D8×D1111yescharacteristic
474C4—21no—
475C4—81no—
476C4—81no—
477C4—81no—
478C4—112no—
479C4—112no—
480C4—221no—
481C4—881no—
482C4—881no—
483C4—881no—
484C4D11×SD3212yes—
485C4#1062307911yescharacteristic
486C4D11×#13511yescharacteristic
487C2—161no—
488C2—222no—
489C2—1761no—
490C2#1307919211yescharacteristic
491C2C2×D11×SD3211yescharacteristic
492C2D11×#50811yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radical#13079192C2
hypercenterC4×SD32D11
hypocenterC11#33736
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #13079199C2semidirect
3. #13070897C2semidirect
4. #13070870C2semidirect
5. #13070842C2semidirect
6. #13070838C2semidirect
7. #13070715C2semidirect
8. #13070713C2semidirect
9. #13070711C2semidirect
10. #13070709C2semidirect
11. C4×#66864C2semidirect
12. C4×#66892C2semidirect
13. C4×#66891C2semidirect
14. C4×C16×D11C2semidirect
15. C4×C11×SD32C2semidirect
175. C11×C16#41semidirect
177. C11⋊C16#41semidirect
191. C4×SD32D11semidirect
223. C4×D11SD32semidirect
422. C16#4339semidirect
423. C11#33736semidirect

Maximal subgroups

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

subgroupindex
#130791992
#130791922
#130708972
#130708702
#130708422
#130708382
#130707152
#130707132
#130707112
#130707092
C4×#668642
C4×#668922
C4×#668912
C4×C16×D112
C4×C11×SD322
#3373611