Finite Group Databasebeta

← #14909324

Subgroups — #14909324

Order 2816.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079189C211yesmaximal, characteristic, complemented
2#13079184C211yesmaximal, characteristic, complemented
3#13070894C211yesmaximal, characteristic, complemented
4#13070876C211yesmaximal, characteristic, complemented
5#13070849C211yesmaximal, characteristic, complemented
6#13070846C211yesmaximal, characteristic, complemented
7#13070713C211yesmaximal, characteristic, complemented
8#13070709C211yesmaximal, characteristic, complemented
9#13070706C211yesmaximal, characteristic, complemented
10#13070701C211yesmaximal, characteristic
11C4×#66893C211yesmaximal, characteristic, complemented
12C4×#66864C211yesmaximal, characteristic, complemented
13C4×#66890C211yesmaximal, characteristic, complemented
14C4×C16×D11C211yesmaximal, characteristic, complemented
15C4×C11×SD32C211yesmaximal, characteristic, complemented
16#10623111—21no—
17#10623088—21no—
18C2×C11×SD32C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21#10622804C2211yescharacteristic
22#10622801C2211yescharacteristic
23C2×#66893C2211yescharacteristic
24#10622770C2211yescharacteristic
25#10622768C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27C4×#4325—21no—
28C4×#4324—21no—
29C2×#66864C2211yescharacteristic
30C2×C16×D11C2211yescharacteristic
31C2×C16×D11C2211yescharacteristic
32#10622500C2211yescharacteristic
33#10622496C2211yescharacteristic
34#10622491C2211yescharacteristic
35#10622491C2211yescharacteristic
36#10622420—21no—
37#10622413—21no—
38#10622391—21no—
39#10622381—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#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×D8C2311yescharacteristic
61C4×Q8×C11—21no—
62C4×D4×C11—21no—
63#67000—21no—
64#66999—21no—
65C2×#4325—21no—
66#66991—21no—
67#66989—21no—
68C2×#4324—21no—
69C4×C22⋊D11—41no—
70#66979—41no—
71C2×Dic44C2311yescharacteristic
72C2×D88C2311yescharacteristic
73C2×C8×D11D411yescharacteristic
74C2×C8×D11C2311yescharacteristic
75#66951—41no—
76#66950—21no—
77#66948—21no—
78#66947—41no—
79#66943—21no—
80#66943—21no—
81#66936—41no—
82#66932—41no—
83C4×D44—21no—
84C4×D44—41no—
85#66925—41no—
86C42×D11D411yescharacteristic
87C4×Dic22—21no—
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#66893—22no—
99#66890—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#66872—21no—
111#66872—21no—
112C4×C11⋊C8D411yescharacteristic
113#66864—22no—
114C16×D11—22no—
115C16×D11—22no—
116#33735—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C22×C4×C11—41no—
120C2×C22⋊D11—41no—
121C2×D44—21no—
122C2×D44—41no—
123C2×C4×D11—41no—
124C2×C4×D11D811yescharacteristic
125C2×C4×D11D811yescharacteristic
126C2×C4×D11C2×D411yescharacteristic
127C2×Dic22—21no—
128C11×Q16—21no—
129C11×Q16—21no—
130C11×D8—21no—
131C11×D8—21no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2411yescharacteristic
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—41no—
137C11×C22⋊C4—41no—
138C42×C11—41no—
139C42×C11C2×D411yescharacteristic
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143#4325—42no—
144#4324—42no—
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—41no—
154C4⋊Dic11—41no—
155C4⋊Dic11—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160C4×Dic11—41no—
161C4×Dic11D811yescharacteristic
162C4×Dic11D811yescharacteristic
163C4×Dic11C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166Dic44—21no—
167Dic44—21no—
168D88—21no—
169D88—21no—
170C8×D11—21no—
171C8×D11—21no—
172C8×D11—22no—
173C11×C16—21no—
174C11×C16#4112yes—
175C11⋊C16—21no—
176C11⋊C16#4112yes—
177#3168—111no—
178#3168—111no—
179#2253—111no—
180#2249—111no—
181#2242—111no—
182#2242—111no—
183#2217—111no—
184#2217—111no—
185#2216—111no—
186#2215—111no—
187C4×Q32—111no—
188C4×SD32—111no—
189C4×SD32D1111yescharacteristic, complemented
190C4×D16—111no—
191C2×C4×C16—111no—
192C23×C11—41no—
193C22×D11—41no—
194C22×D11C2×D811yescharacteristic
195Q8×C11—41no—
196Q8×C11—41no—
197D4×C11—41no—
198D4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—82no—
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C22⋊D11—82no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11C2×D811yescharacteristic
211C2×Dic11C2×D811yescharacteristic
212C2×Dic11C2×D811yescharacteristic
213D44—41no—
214D44—41no—
215D44—82no—
216C4×D11—22no—
217C4×D11—21no—
218C4×D11—21no—
219C4×D11—22no—
220C4×D11—82no—
221Dic22—41no—
222Dic22—41no—
223C8×C11—21no—
224C8×C11C2×#4111yescharacteristic
225C8×C11C2×#4111yescharacteristic
226C11⋊C8—21no—
227C11⋊C8#13512yes—
228#529—221no—
229#529—221no—
230C2×Q32—111no—
231C2×SD32—111no—
232C2×SD32C2×D1111yescharacteristic
233C2×D16—111no—
234C22×C16—111no—
235C22×C16—111no—
236#499—111no—
237#499—111no—
238#495—111no—
239#495—111no—
240#488—221no—
241#488—221no—
242#467—111no—
243#467—111no—
244#466—111no—
245#466—111no—
246#465—221no—
247#465—221no—
248C4×Q16—111no—
249C4×Q16C2×D1111yescharacteristic
250C4×SD16—221no—
251C4×SD16—221no—
252C4×D8—111no—
253C4×D8C2×D1111yescharacteristic
254C2×C4×C8—111no—
255#367—111no—
256#367C2×D1111yescharacteristic
257#366—111no—
258#366—111no—
259#358—111no—
260#358—111no—
261#358—111no—
262#358C2×D1111yescharacteristic
263#357—111no—
264#357—111no—
265#357—111no—
266#357C2×D1111yescharacteristic
267C4×C16—111no—
268C4×C16—111no—
269C4×C16—111no—
270C4×C16C2×D1111yescharacteristic
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11C22×D811yescharacteristic
275C2×D11—21no—
276C2×D11—21no—
277C2×D11—81no—
278C2×D11—81no—
279C2×D11—81no—
280C2×D11#50812yes—
281C4×C11—21no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11#50812yes—
286C4×C11#53211yescharacteristic
287C4×C11C2×#13511yescharacteristic
288Dic11—21no—
289Dic11—21no—
290Dic11—21no—
291Dic11—81no—
292Dic11—81no—
293Dic11—81no—
294C2×Q16—111no—
295C2×Q16C22×D1111yescharacteristic
296C2×SD16—221no—
297C2×SD16—221no—
298C2×D8—111no—
299C2×D8C22×D1111yescharacteristic
300C22×C8—111no—
301C22×C8—111no—
302#126—441no—
303#126—441no—
304#125—221no—
305#125—221no—
306#124—221no—
307#124—221no—
308#123—441no—
309#123—441no—
310C22⋊Q8—221no—
311C22⋊Q8—221no—
312#121—221no—
313#121—221no—
314C4×Q8—21no—
315C4×Q8—221no—
316C4×D4—21no—
317C4×D4—221no—
318C4×D4—441no—
319C4×D4—441no—
320#117—441no—
321#117—441no—
322C2×C42—111no—
323Q32—222no—
324SD32—22no—
325SD32—222no—
326D16—222no—
327C2×C16—111no—
328C2×C16—111no—
329C2×C16—222no—
330C2×C16—222no—
331C2×C16C22×D1111yescharacteristic
332C2×C16C22×D1111yescharacteristic
333#107—111no—
334#107—111no—
335#107C22×D1111yescharacteristic
336#107C22×D1111yescharacteristic
337#106—221no—
338#106—221no—
339#103—21no—
340#103—221no—
341#103—221no—
342#103—221no—
343#102—21no—
344#102—221no—
345#102—221no—
346#102—221no—
347C4×C8—111no—
348C4×C8—111no—
349C4×C8—111no—
350C4×C8C22×D1111yescharacteristic
351C2×C11—161no—
352C2×C11#316911yescharacteristic
353C2×C11C2×#50811yescharacteristic
354C2×C11C2×#50811yescharacteristic
355D11—22no—
356D11—161no—
357C2×Q8—21no—
358C2×Q8—221no—
359C2×D4—21no—
360C2×D4—221no—
361C2×D4—441no—
362C2×D4—441no—
363C22×C4—41no—
364C22×C4—111no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—441no—
368Q16—21no—
369Q16—21no—
370Q16—221no—
371Q16—221no—
372SD16—442no—
373SD16—442no—
374D8—21no—
375D8—21no—
376D8—221no—
377D8—221no—
378C2×C8—111no—
379C2×C8—111no—
380C2×C8—222no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8D4×D1111yescharacteristic
384C2×C8C23×D1111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C22⋊C4—41no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C22⋊C4—441no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C42—41no—
408C42—111no—
409C42—111no—
410C42—111no—
411C42—441no—
412C42D4×D1111yescharacteristic
413C16—21no—
414C16—112no—
415C16—221no—
416C16#433912yes—
417C11#3373511yescharacteristic, complemented, Sylow
418C23—41no—
419C23—111no—
420C23—441no—
421Q8—41no—
422Q8—41no—
423Q8—441no—
424Q8—441no—
425D4—41no—
426D4—41no—
427D4—441no—
428D4—441no—
429D4—882no—
430D4—882no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—82no—
435C2×C4—111no—
436C2×C4—111no—
437C2×C4—111no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—882no—
446C2×C4D8×D1111yescharacteristic
447C2×C4D8×D1111yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C8—21no—
450C8—112no—
451C8—221no—
452C8C2×#433911yescharacteristic
453C8#41×D1111yescharacteristic
454C22—81no—
455C22—81no—
456C22—81no—
457C22—112no—
458C22—221no—
459C22—221no—
460C22—881no—
461C22—881no—
462C22—881no—
463C22C2×D8×D1111yescharacteristic
464C4—21no—
465C4—81no—
466C4—81no—
467C4—81no—
468C4—221no—
469C4—221no—
470C4—221no—
471C4—881no—
472C4—881no—
473C4—881no—
474C4#1062252912yes—
475C4#1062307911yescharacteristic
476C4D11×#13511yescharacteristic
477C2—161no—
478C2—222no—
479C2—1761no—
480C2#1307919211yescharacteristic
481C2D11×#50811yescharacteristic
482C2C2×#1062252911yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radical#13070701C2
hypercenterC4×SD32D11
hypocenterC11#33735
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. #13079189C2semidirect
2. #13079184C2semidirect
3. #13070894C2semidirect
4. #13070876C2semidirect
5. #13070849C2semidirect
6. #13070846C2semidirect
7. #13070713C2semidirect
8. #13070709C2semidirect
9. #13070706C2semidirect
11. C4×#66893C2semidirect
12. C4×#66864C2semidirect
13. C4×#66890C2semidirect
14. C4×C16×D11C2semidirect
15. C4×C11×SD32C2semidirect
189. C4×SD32D11semidirect
417. C11#33735semidirect

Maximal subgroups

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

subgroupindex
#130791892
#130791842
#130708942
#130708762
#130708492
#130708462
#130707132
#130707092
#130707062
#130707012
C4×#668932
C4×#668642
C4×#668902
C4×C16×D112
C4×C11×SD322
#3373511