Finite Group Databasebeta

← #14908808

Subgroups — #14908808

Order 2816.

554 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic, complemented
2C4×#66957C211yesmaximal, characteristic, complemented
3#13070825C211yesmaximal, characteristic, complemented
4#13070808C211yesmaximal, characteristic, complemented
5#13070781C211yesmaximal, characteristic, complemented
6#13070774C211yesmaximal, characteristic, complemented
7#13070679C211yesmaximal, characteristic, complemented
8#13070672C211yesmaximal, characteristic, complemented
9#13070558C211yesmaximal, characteristic, complemented
10#13070541C211yesmaximal, characteristic
11#13070493C211yesmaximal, characteristic, complemented
12#13070488C211yesmaximal, characteristic, complemented
13#13070482C211yesmaximal, characteristic, complemented
14#13070482C211yesmaximal, characteristic, complemented
15C11×#2163C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17#10623010—21no—
18C4×#4339—21no—
19C2×C4×C8×C11C2211yescharacteristic
20#10622729C2211yescharacteristic
21#10622728C2211yescharacteristic
22#10622727—21no—
23#10622726—21no—
24#10622719C2211yescharacteristic
25C2×Dic88C2211yescharacteristic
26C2×#66864C2211yescharacteristic
27C2×#66864C2211yescharacteristic
28C2×D176C2211yescharacteristic
29C4×Dic44C2211yescharacteristic
30C4×Dic44C2211yescharacteristic
31C4×Dic44C2211yescharacteristic
32#10622310—21no—
33#10622309C2211yescharacteristic
34C4×D88C2211yescharacteristic
35C4×D88C2211yescharacteristic
36C4×D88C2211yescharacteristic
37C4×#4314—21no—
38C4×#4314—21no—
39C4×#4314—21no—
40#10622296C2211yescharacteristic
41C11×C4⋊C16C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45C11×#346C2211yescharacteristic
46C11×#346C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622143C2211yescharacteristic
53#10622142C2211yescharacteristic
54#10622142C2211yescharacteristic
55#10622141C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C2×#4339—21no—
60C22×C8×C11D411yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C2×C42×C11D411yescharacteristic
63#66983—21no—
64#66982—41no—
65C4×C22⋊D11—41no—
66C4×C22⋊D11—41no—
67C4×C22⋊D11—41no—
68#66979—21no—
69#66977—21no—
70C2×Dic44C2311yescharacteristic
71C2×Dic44C2311yescharacteristic
72#66957—22no—
73#66957—22no—
74C2×D88C2311yescharacteristic
75C2×D88C2311yescharacteristic
76C2×#4314—21no—
77C2×#4314—21no—
78#66929—41no—
79#66928—21no—
80C4×D44—21no—
81C4×D44—21no—
82C4×D44—21no—
83#66925—41no—
84#66925—41no—
85C42×D11—41no—
86#66923—21no—
87C4×Dic22—21no—
88C4×Dic22—21no—
89C4×Dic22—21no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C4×C8×C11D411yescharacteristic
95C4×C8×C11D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97C4×C8×C11C2311yescharacteristic
98#66885—21no—
99#66885—21no—
100#66885—21no—
101#66885—21no—
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66881—21no—
107#66881—21no—
108#66880—21no—
109#66880—21no—
110#66880—21no—
111#66880—21no—
112Dic88—22no—
113#66864—22no—
114#66864—22no—
115D176—22no—
116#33671—111nomaximal, Sylow
117C22×C4×C11D811yescharacteristic
118C22×C4×C11D811yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C2×C22⋊D11—41no—
121C2×C22⋊D11—41no—
122#4339—24no—
123#4339—42no—
124C2×D44—21no—
125C2×D44—21no—
126C2×C4×D11—41no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×C4×D11—41no—
130C2×Dic22—21no—
131C2×Dic22—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—41no—
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2411yescharacteristic
139C42×C11D811yescharacteristic
140C42×C11D811yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C22⋊Dic11—41no—
144C22⋊Dic11—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
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×Dic11—41no—
164C4×Dic11—41no—
165Dic44—21no—
166Dic44—21no—
167Dic44—21no—
168Dic44#4112yes—
169D88—21no—
170D88—21no—
171D88—21no—
172D88#4112yes—
173#4314—24no—
174#4314—42no—
175C11×C16—21no—
176C11×C16—21no—
177C11×C16—21no—
178C11×C16—21no—
179#3168—111no—
180C4×#135—111no—
181#2237—111no—
182#2234—111no—
183#2229—111no—
184#2228—111no—
185#2211—111no—
186#2210—111no—
187#2189—111no—
188#2186—111no—
189#2177—111no—
190#2176—111no—
191#2175—111no—
192#2175—111no—
193#2163D1111yescharacteristic, complemented
194C23×C11C2×D811yescharacteristic
195C22×D11—41no—
196C22×D11—41no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C22⋊D11—44no—
208C22⋊D11—82no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215D44—22no—
216D44—41no—
217D44—41no—
218D44—41no—
219C4×D11—44no—
220C4×D11—82no—
221C4×D11—82no—
222C4×D11—82no—
223Dic22—22no—
224Dic22—41no—
225Dic22—41no—
226Dic22—41no—
227C8×C11—21no—
228C8×C11—21no—
229C8×C11—21no—
230C8×C11C2×#4111yescharacteristic
231C8×C11C2×#4111yescharacteristic
232C2×#135—111no—
233#529—221no—
234C4×#41—221no—
235C2×Q32—111no—
236C2×SD32—111no—
237C2×SD32—111no—
238C2×D16—111no—
239#499—111no—
240#495—111no—
241#488—221no—
242#467—111no—
243#466—111no—
244#465—221no—
245C4×Q16—111no—
246C4×Q16—111no—
247C4×Q16—111no—
248C4×SD16—221no—
249C4×SD16—221no—
250C4×SD16—221no—
251C4×D8—111no—
252C4×D8—111no—
253C4×D8—111no—
254#427—111no—
255#416—221no—
256C2×C4×C8C2×D1111yescharacteristic
257#367—111no—
258#367—111no—
259#366—111no—
260#366—111no—
261C4⋊C16C2×D1111yescharacteristic
262C4⋊C16C2×D1111yescharacteristic
263#358—111no—
264#358—111no—
265#358—111no—
266#358—111no—
267#357—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271C22⋊C16C2×D1111yescharacteristic
272C22⋊C16C2×D1111yescharacteristic
273#346C2×D1111yescharacteristic
274#346C2×D1111yescharacteristic
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11C22×D811yescharacteristic
279C2×D11—42no—
280C2×D11—81no—
281C2×D11—81no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11#52511yescharacteristic
291C4×C11#57511yescharacteristic
292Dic11—42no—
293Dic11—81no—
294Dic11—81no—
295Dic11—81no—
296Dic11—81no—
297Dic11—81no—
298C2×#41—221no—
299#135—222no—
300#135—222no—
301C2×Q16—111no—
302C2×Q16—111no—
303C2×SD16—221no—
304C2×SD16—221no—
305C2×D8—111no—
306C2×D8—111no—
307C22×C8D4411yescharacteristic
308C22×C8C22×D1111yescharacteristic
309#126—441no—
310#125—221no—
311#124—221no—
312#123—441no—
313C22⋊Q8—221no—
314#121—221no—
315C4×Q8—221no—
316C4×Q8—221no—
317C4×Q8—221no—
318C4×D4—221no—
319C4×D4—221no—
320C4×D4—221no—
321C4×D4—441no—
322C4×D4—441no—
323C4×D4—441no—
324#117—221no—
325#117—441no—
326#117—441no—
327C2×C42—441no—
328C2×C42D4411yescharacteristic
329Q32—222no—
330SD32—222no—
331SD32—222no—
332D16—222no—
333C2×C16C22×D1111yescharacteristic
334C2×C16C22×D1111yescharacteristic
335C2×C16C22×D1111yescharacteristic
336C2×C16C22×D1111yescharacteristic
337#107—111no—
338#107—111no—
339#107—111no—
340#107—111no—
341#106—221no—
342#106—221no—
343#103—221no—
344#103—221no—
345#103—221no—
346#103—221no—
347#102—221no—
348#102—221no—
349#102—221no—
350#102—221no—
351C4×C8D4411yescharacteristic
352C4×C8D4411yescharacteristic
353C4×C8C22×D1111yescharacteristic
354C4×C8C22×D1111yescharacteristic
355C2×C11—41no—
356C2×C11#310011yescharacteristic
357C2×C11#341411yescharacteristic
358C2×C11#341411yescharacteristic
359D11—82no—
360D11—161no—
361#41—224no—
362#41—442no—
363C2×Q8—221no—
364C2×Q8—221no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—441no—
368C2×D4—441no—
369C22×C4—441no—
370C22×C4—441no—
371C22×C4—441no—
372C22×C4—441no—
373C22×C4D8811yescharacteristic
374C22×C4D8811yescharacteristic
375C22×C4C2×D4411yescharacteristic
376Q16—112no—
377Q16—221no—
378Q16—221no—
379Q16—221no—
380SD16—224no—
381SD16—442no—
382D8—112no—
383D8—221no—
384D8—221no—
385D8—221no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—41no—
389C2×C8C2×D4411yescharacteristic
390C2×C8C2×D4411yescharacteristic
391C2×C8C2×D4411yescharacteristic
392C2×C8C23×D1111yescharacteristic
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4—221no—
396C4⋊C4—221no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C22⋊C4—441no—
408C22⋊C4—441no—
409C22⋊C4—441no—
410C22⋊C4—441no—
411C42—441no—
412C42—441no—
413C42—441no—
414C42—441no—
415C42D8811yescharacteristic
416C42D8811yescharacteristic
417C42C2×D4411yescharacteristic
418C42C2×D4411yescharacteristic
419C16—21no—
420C16—21no—
421C16—21no—
422C16—21no—
423C11#3367111yescharacteristic, complemented, Sylow
424C23—441no—
425C23—441no—
426C23C2×D8811yescharacteristic
427Q8—222no—
428Q8—441no—
429Q8—441no—
430Q8—441no—
431D4—222no—
432D4—444no—
433D4—441no—
434D4—441no—
435D4—441no—
436D4—882no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—444no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—882no—
449C2×C4—882no—
450C2×C4—882no—
451C2×C4C2×D8811yescharacteristic
452C2×C4C2×D8811yescharacteristic
453C2×C4C2×D8811yescharacteristic
454C2×C4C2×D8811yescharacteristic
455C2×C4C2×D8811yescharacteristic
456C2×C4C22×D4411yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8#41×D1111yescharacteristic
461C8#41×D1111yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—442no—
466C22—881no—
467C22—881no—
468C22—881no—
469C22—881no—
470C22—881no—
471C22C22×D8811yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—442no—
478C4—881no—
479C4—881no—
480C4—881no—
481C4—881no—
482C4—881no—
483C4#1062305511yescharacteristic
484C4#1062327911yescharacteristic
485C2—41no—
486C2—882no—
487C2—1761no—
488C2#1307861711yescharacteristic
489C2#1308175211yescharacteristic
490C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2163C2
socleC22×C11C22×D8
prime radical#13070541C2
hypercenter#2163D11
hypocenterC11#33671
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. C4×#66957C2semidirect
3. #13070825C2semidirect
4. #13070808C2semidirect
5. #13070781C2semidirect
6. #13070774C2semidirect
7. #13070679C2semidirect
8. #13070672C2semidirect
9. #13070558C2semidirect
11. #13070493C2semidirect
12. #13070488C2semidirect
13. #13070482C2semidirect
14. #13070482C2semidirect
15. C11×#2163C2semidirect
193. #2163D11semidirect
423. C11#33671semidirect

Maximal subgroups

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

subgroupindex
#130791862
C4×#669572
#130708252
#130708082
#130707812
#130707742
#130706792
#130706722
#130705582
#130705412
#130704932
#130704882
#130704822
C11×#21632
#3367111