Finite Group Databasebeta

← #14723698

Subgroups — #14723698

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078653C211yesmaximal, characteristic
2#13077547C211yesmaximal, characteristic
3C8×Q8×D11C211yesmaximal, characteristic
4#13067489C211yesmaximal, characteristic, complemented
5#13067487C211yesmaximal, characteristic, complemented
6#13067485C211yesmaximal, characteristic, complemented
7#13067435C211yesmaximal, characteristic, complemented
8#13067434C211yesmaximal, characteristic, complemented
9#13067432C211yesmaximal, characteristic, complemented
10#13067432C211yesmaximal, characteristic, complemented
11#13067385C211yesmaximal, characteristic
12#13067043C211yesmaximal, characteristic
13#13067017C211yesmaximal, characteristic
14#13066907C211yesmaximal, characteristic
15C11×#1587C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17C4×Q8×D11C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21#10622799C411yescharacteristic
22#10622795C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4326C2211yescharacteristic
25Q8×C11⋊C8C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622497C411yescharacteristic
28#10622488C411yescharacteristic
29#10622452—21no—
30#10622450C2211yescharacteristic
31D11×C4⋊C8—21no—
32D11×C4⋊C8C2211yescharacteristic
33#10622443—21no—
34#10622443—21no—
35#10622443C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622422C411yescharacteristic
38#10622421C411yescharacteristic
39#10622407C411yescharacteristic
40#10622406C411yescharacteristic
41#10622321—21no—
42#10622314—21no—
43C4×Dic44C2211yescharacteristic
44#10622298C2211yescharacteristic
45#10622298C2211yescharacteristic
46C4×C8×D11—21no—
47C4×C8×D11C2211yescharacteristic
48#10622292C2211yescharacteristic
49C8×Dic22—21no—
50C8×Dic22C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71#66999C2×C411yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73#66997C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4326C2×C411yescharacteristic
76C2×Dic44C2×C411yescharacteristic
77C2×#4313—21no—
78C2×C8×D11—21no—
79C2×C8×D11D411yescharacteristic
80C2×C8×D11D411yescharacteristic
81#66950C2×C411yescharacteristic
82#66949—21no—
83C4⋊C4×D11—21no—
84C4⋊C4×D11C2×C411yescharacteristic
85#66942—21no—
86#66941C2×C411yescharacteristic
87#66940—21no—
88#66940C2×C411yescharacteristic
89#66925—21no—
90C42×D11—21no—
91C42×D11C2311yescharacteristic
92C4×Dic22—21no—
93C4×Dic22—21no—
94C4×Dic22C2311yescharacteristic
95C4×Dic22C2311yescharacteristic
96C11×#107C2×C411yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×#103C2×C411yescharacteristic
102C11×#103C2×C411yescharacteristic
103C11×#97—21no—
104C4×C8×C11—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108#66899C2×C411yescharacteristic
109#66899C2×C411yescharacteristic
110(C2×D11)⋊C8—21no—
111(C2×D11)⋊C8C2×C411yescharacteristic
112(C2×D11)⋊C8C2×C411yescharacteristic
113#66882C2×C411yescharacteristic
114#66880C2×C411yescharacteristic
115#66880C2×C411yescharacteristic
116#66879—21no—
117Dic11⋊C8—21no—
118Dic11⋊C8—21no—
119Dic11⋊C8—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8C2×C411yescharacteristic
125Dic11⋊C8C2×C411yescharacteristic
126C8×Dic11—21no—
127C8×Dic11—21no—
128C8×Dic11—21no—
129C8×Dic11D411yescharacteristic
130C8×Dic11D411yescharacteristic
131#66874C2×C411yescharacteristic
132#66874C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17906—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147Q8×D11—22no—
148Q8×D11—22no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11C22×C411yescharacteristic
152C2×C4×D11C2×D411yescharacteristic
153C2×C4×D11#4111yescharacteristic
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22C22×C411yescharacteristic
157C2×Dic22C22×C411yescharacteristic
158C11×Q16—22no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C22×C411yescharacteristic
169C11×C4⋊C4C22×C411yescharacteristic
170C42×C11—21no—
171C42×C11—21no—
172C42×C11C2411yescharacteristic
173#4326—22no—
174#4326—22no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11C22×C411yescharacteristic
180C4⋊Dic11C22×C411yescharacteristic
181Dic11⋊C4—21no—
182Dic11⋊C4—21no—
183Dic11⋊C4—21no—
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11C22×C411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11#4111yescharacteristic
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203Dic44—22no—
204#4313—42no—
205C8×D11—22no—
206C8×D11—22no—
207C8×D11—42no—
208#3104—111no—
209#2960—111no—
210C2×C8×Q8—111no—
211#1587—111no—
212#1587—111no—
213#1587—111no—
214#1587D1111yescharacteristic, complemented
215#1579—111no—
216#1579—111no—
217#1579—111no—
218#1579—111no—
219#1570—111no—
220#1487—111no—
221#1481—111no—
222#1452—111no—
223C22×D11C4×D411yescharacteristic
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11#13112yes—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11C23×C411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11C4×D411yescharacteristic
240C2×Dic11C4×D411yescharacteristic
241C2×Dic11C4×D411yescharacteristic
242C4×D11—24no—
243C4×D11—21no—
244C4×D11—21no—
245C4×D11—41no—
246C4×D11—42no—
247C4×D11#13712yes—
248C4×D11#13712yes—
249Dic22—24no—
250Dic22—21no—
251Dic22—21no—
252Dic22—21no—
253Dic22—42no—
254Dic22#13112yes—
255C8×C11—21no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—41no—
260C8×C11—41no—
261C8×C11—41no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269#533—111no—
270C2×C4×Q8—111no—
271#484—111no—
272#484—111no—
273#477—111no—
274#477—111no—
275#462—111no—
276#462—111no—
277#451—111no—
278#451—111no—
279#446—111no—
280#446—221no—
281#446C2×D1111yescharacteristic
282C8×Q8—111no—
283C8×Q8—111no—
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—111no—
287C8×Q8—221no—
288C8×Q8—221no—
289C8×Q8—221no—
290C8×Q8C2×D1111yescharacteristic
291C4×Q16—111no—
292C4×Q16—111no—
293C4×Q16—111no—
294C4×Q16C2×D1111yescharacteristic
295#431—111no—
296#431—111no—
297#424—221no—
298#423—111no—
299C2×C4⋊C8—111no—
300C2×C4⋊C8—221no—
301#405—221no—
302C2×C4×C8—111no—
303C2×C4×C8—221no—
304#334—111no—
305#334—111no—
306#334—111no—
307#334C2×D1111yescharacteristic
308Q8⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8C2×D1111yescharacteristic
315Q8⋊C8C2×D1111yescharacteristic
316#322—111no—
317#322—111no—
318#322—111no—
319#322C2×D1111yescharacteristic
320C22×C11C2×C4×D411yescharacteristic
321C2×D11—21no—
322C2×D11—21no—
323C2×D11#44112yes—
324C4×C11—22no—
325C4×C11—21no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11C2×#13111yescharacteristic
330C4×C11C2×#13111yescharacteristic
331C4×C11C2×#13711yescharacteristic
332C4×C11C2×#13711yescharacteristic
333Dic11—21no—
334Dic11—22no—
335Dic11—21no—
336Dic11—41no—
337Dic11—41no—
338Dic11—41no—
339Dic11#44112yes—
340C22×Q8—111no—
341C2×Q16—111no—
342C2×Q16—111no—
343C2×Q16—111no—
344C2×Q16C4×D1111yescharacteristic
345C2×M16—221no—
346C22×C8—111no—
347C22×C8—111no—
348C22×C8—221no—
349C4⋊Q8—111no—
350C4⋊Q8—111no—
351#125—221no—
352C22⋊Q8—111no—
353C22⋊Q8—111no—
354C22⋊Q8—221no—
355C4×Q8—111no—
356C4×Q8—111no—
357C4×Q8—111no—
358C4×Q8—111no—
359C4×Q8—221no—
360C4×Q8—221no—
361C4×Q8—221no—
362C4×Q8C22×D1111yescharacteristic
363C4×Q8C22×D1111yescharacteristic
364#117—221no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—221no—
367C2×C42—111no—
368C2×C42—221no—
369#107—111no—
370#107—111no—
371#107—111no—
372#107C4×D1111yescharacteristic
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—111no—
376C4⋊C8—111no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—221no—
380C4⋊C8—221no—
381C4⋊C8—221no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8C22×D1111yescharacteristic
389C4⋊C8C22×D1111yescharacteristic
390#103—111no—
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103C4×D1111yescharacteristic
397#103C4×D1111yescharacteristic
398C22⋊C8—111no—
399C22⋊C8—111no—
400C22⋊C8—221no—
401#97—21no—
402#97—221no—
403C4×C8—21no—
404C4×C8—111no—
405C4×C8—111no—
406C4×C8—111no—
407C4×C8—111no—
408C4×C8—111no—
409C4×C8—221no—
410C4×C8—221no—
411C4×C8—221no—
412C4×C8—221no—
413C4×C8—221no—
414C4×C8C22×D1111yescharacteristic
415C4×C8C22×D1111yescharacteristic
416C4×C8C22×D1111yescharacteristic
417C2×C11#292911yescharacteristic
418C2×C11C2×#44111yescharacteristic
419C2×C11#295511yescharacteristic
420D11—22no—
421C2×Q8—111no—
422C2×Q8—111no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8—222no—
426C2×Q8—222no—
427C2×Q8C2×C4×D1111yescharacteristic
428C2×Q8C2×C4×D1111yescharacteristic
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—221no—
433C22×C4—221no—
434Q16—22no—
435Q16—222no—
436Q16—222no—
437Q16—222no—
438M16—442no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—111no—
443C2×C8—111no—
444C2×C8—111no—
445C2×C8—111no—
446C2×C8—222no—
447C2×C8—222no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—442no—
452C2×C8C2×C4×D1111yescharacteristic
453C2×C8C2×C4×D1111yescharacteristic
454C2×C8D4×D1111yescharacteristic
455C2×C8D4×D1111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—111no—
459C4⋊C4—111no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4C2×C4×D1111yescharacteristic
471C4⋊C4C2×C4×D1111yescharacteristic
472C22⋊C4—221no—
473C22⋊C4—221no—
474C42—21no—
475C42—21no—
476C42—111no—
477C42—111no—
478C42—111no—
479C42—221no—
480C42—221no—
481C42—221no—
482C42—221no—
483C42C23×D1111yescharacteristic
484C11#1790611yescharacteristic, complemented, Sylow
485C23—111no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—112no—
490Q8—224no—
491Q8—221no—
492Q8—221no—
493Q8—221no—
494Q8—442no—
495Q8#6696012yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—111no—
501C2×C4—112no—
502C2×C4—112no—
503C2×C4—111no—
504C2×C4—111no—
505C2×C4—224no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—441no—
513C2×C4—442no—
514C2×C4C22×C4×D1111yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4#41×D1111yescharacteristic
517C8—21no—
518C8—21no—
519C8—21no—
520C8—21no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—221no—
525C8—221no—
526C8—221no—
527C8—221no—
528C8—441no—
529C8—441no—
530C8—441no—
531C22—112no—
532C22—221no—
533C22—221no—
534C22C4×D4×D1111yescharacteristic
535C4—21no—
536C4—22no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—112no—
541C4—221no—
542C4—221no—
543C4—222no—
544C4—441no—
545C4—441no—
546C4—441no—
547C4C2×#6696011yescharacteristic
548C4D11×#13111yescharacteristic
549C4D11×#13711yescharacteristic
550C4D11×#13711yescharacteristic
551C2—222no—
552C2#1307730711yescharacteristic
553C2D11×#44111yescharacteristic
554C2#1307751411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1587C2
socleC22×C11C2×C4×D4
prime radicalC22×D11C4×D4
cosocleC42×C11C24
hypercenter#1587D11
hypocenterC11#17906
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
4. #13067489C2semidirect
5. #13067487C2semidirect
6. #13067485C2semidirect
7. #13067435C2semidirect
8. #13067434C2semidirect
9. #13067432C2semidirect
10. #13067432C2semidirect
15. C11×#1587C2semidirect
214. #1587D11semidirect
484. C11#17906semidirect

Maximal subgroups

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

subgroupindex
#130786532
#130775472
C8×Q8×D112
#130674892
#130674872
#130674852
#130674352
#130674342
#130674322
#130673852
#130670432
#130670172
#130669072
C11×#15872
#1790611