Finite Group Databasebeta

← #14764406

Subgroups — #14764406

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077251C211yesmaximal, characteristic
2C2×#10622333C211yesmaximal, characteristic
3#13077179C211yesmaximal, characteristic
4#13069390C211yesmaximal, characteristic, complemented
5#13069390C211yesmaximal, characteristic, complemented
6#13069388C211yesmaximal, characteristic, complemented
7#13069388C211yesmaximal, characteristic, complemented
8#13068823C211yesmaximal, characteristic
9#13068821C211yesmaximal, characteristic
10#13068820C211yesmaximal, characteristic
11#13068789C211yesmaximal, characteristic, complemented
12#13068786C211yesmaximal, characteristic, complemented
13#13068755C211yesmaximal, characteristic, complemented
14#13068752C211yesmaximal, characteristic, complemented
15C11×#1855C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C2×C11×#108C2211yescharacteristic
20C2×C11×#108C2211yescharacteristic
21C11×#407C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23#10622820C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×#66886C2211yescharacteristic
26C2×#66886C2211yescharacteristic
27C2×#66886C2211yescharacteristic
28C2×#66886C2211yescharacteristic
29#10622732—21no—
30#10622732—21no—
31#10622731C2211yescharacteristic
32#10622731C2211yescharacteristic
33#10622731C2211yescharacteristic
34#10622731C2211yescharacteristic
35#10622731C2211yescharacteristic
36#10622731C2211yescharacteristic
37M16×Dic11C2211yescharacteristic
38M16×Dic11C2211yescharacteristic
39C2×#66883C2211yescharacteristic
40C2×#66883C2211yescharacteristic
41#10622715—21no—
42#10622715—21no—
43C2×#66879C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45C2×Dic11⋊C8C2211yescharacteristic
46C2×C8×Dic11C2211yescharacteristic
47#10622333—21no—
48#10622333—21no—
49#10622333—21no—
50#10622333—21no—
51#10622333C412yes—
52#10622333C412yes—
53#10622333C412yes—
54#10622333C412yes—
55C11×#341C2211yescharacteristic
56C11×#341C2211yescharacteristic
57#10622196C2211yescharacteristic
58#10622196C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622196C2211yescharacteristic
61#10622190C2211yescharacteristic
62#10622190C2211yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C2×C11×M16—21no—
65C2×C11×M16—41no—
66C2×C11×M16—41no—
67C2×C11×M16C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C2×C11×M16C2311yescharacteristic
71C22×C8×C11—21no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C2×C22⋊Dic11Q811yescharacteristic
75C2×C22⋊Dic11Q811yescharacteristic
76#66979C2×C411yescharacteristic
77#66979C2×C411yescharacteristic
78#66979C2×C411yescharacteristic
79#66979C2×C411yescharacteristic
80#66979D411yescharacteristic
81#66979D411yescharacteristic
82#66979D411yescharacteristic
83#66979D411yescharacteristic
84C2×C4⋊Dic11Q811yescharacteristic
85C2×C4⋊Dic11Q811yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C2×#4318—21no—
89C2×#4318—41no—
90C2×#4318—41no—
91C2×#4318C2311yescharacteristic
92C2×#4318C2311yescharacteristic
93C2×#4318C2311yescharacteristic
94C2×#4318C2311yescharacteristic
95C22×C11⋊C8—21no—
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C11×#108—41no—
99C11×#108—41no—
100C11×C22⋊C8—21no—
101C11×C22⋊C8—21no—
102C11×C22⋊C8C2×C412yes—
103C11×C22⋊C8C2×C412yes—
104C22⋊(C11⋊C8)—21no—
105C22⋊(C11⋊C8)—21no—
106C22⋊(C11⋊C8)C2×C412yes—
107C22⋊(C11⋊C8)C2×C412yes—
108#66886—41no—
109#66886—41no—
110#66886—41no—
111#66886—41no—
112#66883—41no—
113#66883—41no—
114#66879—21no—
115#66879—21no—
116#66879C2×C412yes—
117#66879C2×C412yes—
118Dic11⋊C8—21no—
119Dic11⋊C8—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8C2×C412yes—
131Dic11⋊C8C2×C412yes—
132Dic11⋊C8C2×C412yes—
133Dic11⋊C8C2×C412yes—
134C8×Dic11—21no—
135C8×Dic11—21no—
136C8×Dic11C2×C412yes—
137C8×Dic11C2×C412yes—
138#21995—111nomaximal, Sylow
139C24×C11C2×Q811yescharacteristic
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×Q811yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11C2×Q811yescharacteristic
151C22×Dic11C2×Q811yescharacteristic
152C22×Dic11C2×Q811yescharacteristic
153C22×Dic11C2×Q811yescharacteristic
154C11×M16—21no—
155C11×M16—21no—
156C11×M16—21no—
157C11×M16—21no—
158C11×M16—21no—
159C11×M16—21no—
160C11×M16—21no—
161C11×M16—21no—
162C11×M16—42no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—42no—
172C2×C8×C11C22×C412yes—
173C2×C8×C11C22×C412yes—
174C22⋊Dic11C4⋊C411yescharacteristic
175C22⋊Dic11C4⋊C411yescharacteristic
176C22⋊Dic11C4⋊C411yescharacteristic
177C22⋊Dic11C4⋊C411yescharacteristic
178C22⋊Dic11C4⋊C411yescharacteristic
179C22⋊Dic11C4⋊C411yescharacteristic
180C22⋊Dic11C4⋊C411yescharacteristic
181C22⋊Dic11C4⋊C411yescharacteristic
182C4⋊Dic11C4⋊C411yescharacteristic
183C4⋊Dic11C4⋊C411yescharacteristic
184C4⋊Dic11C4⋊C411yescharacteristic
185C4⋊Dic11C4⋊C411yescharacteristic
186C4⋊Dic11C4⋊C411yescharacteristic
187C4⋊Dic11C4⋊C411yescharacteristic
188C4⋊Dic11C4⋊C411yescharacteristic
189C4⋊Dic11C4⋊C411yescharacteristic
190C4×Dic11C22×C411yescharacteristic
191C4×Dic11C22×C411yescharacteristic
192C4×Dic11C22×C411yescharacteristic
193C4×Dic11C22×C411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11C2×D411yescharacteristic
196C4×Dic11C2×D411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198#4318—21no—
199#4318—21no—
200#4318—21no—
201#4318—21no—
202#4318—21no—
203#4318—21no—
204#4318—21no—
205#4318—21no—
206#4318—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—42no—
216C2×C11⋊C8C22×C412yes—
217C2×C11⋊C8C22×C412yes—
218#2921—111no—
219C2×#433—111no—
220#2905—111no—
221#1950—111no—
222#1950—111no—
223#1950—111no—
224#1950—111no—
225#1855—111no—
226#1855—111no—
227#1855—111no—
228#1855D1111yescharacteristic
229#1849—111no—
230#1848—111no—
231#1838—111no—
232#1837—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11C2×C4⋊C411yescharacteristic
238C23×C11C2×C4⋊C411yescharacteristic
239C23×C11C22×Q811yescharacteristic
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11C2×C4⋊C411yescharacteristic
251C2×C4×C11C2×C4⋊C411yescharacteristic
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11C2×C4⋊C411yescharacteristic
263C2×Dic11C2×C4⋊C411yescharacteristic
264C2×Dic11C2×C4⋊C411yescharacteristic
265C2×Dic11C2×C4⋊C411yescharacteristic
266C2×Dic11C2×C4⋊C411yescharacteristic
267C2×Dic11C2×C4⋊C411yescharacteristic
268C2×Dic11C2×C4⋊C411yescharacteristic
269C2×Dic11C2×C4⋊C411yescharacteristic
270C8×C11—22no—
271C8×C11—22no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276C11⋊C8—22no—
277C11⋊C8—22no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C22×M16—111no—
283C22×M16C2×D1111yescharacteristic
284C2×#117—111no—
285#433—112no—
286#433—112no—
287#433—112no—
288#433—112no—
289#433—221no—
290#433—221no—
291#433—221no—
292#433—221no—
293C2×#108—111no—
294C2×#108—111no—
295C2×#108—111no—
296C2×#108—111no—
297C2×#108—111no—
298C2×#108—111no—
299C2×#108C2×D1111yescharacteristic
300C2×#108C2×D1111yescharacteristic
301#424—221no—
302#424—221no—
303#424—221no—
304#424—221no—
305#423—111no—
306#423—111no—
307#423—111no—
308#423—111no—
309#423—111no—
310#423—111no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8—111no—
313#407—111no—
314#407C2×D1111yescharacteristic
315C2×C22⋊C8—111no—
316C2×C22⋊C8C2×D1111yescharacteristic
317C4×M16—111no—
318C4×M16—111no—
319C2×#97—111no—
320C2×C4×C8—111no—
321#341—111no—
322#341—111no—
323#341—111no—
324#341—111no—
325#341—111no—
326#341—111no—
327#341C2×D1111yescharacteristic
328#341C2×D1111yescharacteristic
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11C22×C4⋊C411yescharacteristic
340C22×C11#54411yescharacteristic
341C22×C11#54411yescharacteristic
342C4×C11—21no—
343C4×C11—21no—
344C4×C11#52011yescharacteristic
345C4×C11#52011yescharacteristic
346C4×C11#53511yescharacteristic
347C4×C11#53611yescharacteristic
348Dic11—21no—
349Dic11—21no—
350Dic11—21no—
351Dic11—21no—
352Dic11—21no—
353Dic11—21no—
354Dic11—21no—
355Dic11—21no—
356C23×C4C22×D1111yescharacteristic
357C2×M16—21no—
358C2×M16—41no—
359C2×M16—41no—
360C2×M16—111no—
361C2×M16—111no—
362C2×M16—111no—
363C2×M16—111no—
364C2×M16—221no—
365C2×M16—441no—
366C2×M16—441no—
367C2×M16C22×D1111yescharacteristic
368C2×M16C22×D1111yescharacteristic
369C2×M16C22×D1111yescharacteristic
370C2×M16C22×D1111yescharacteristic
371C22×C8—21no—
372C22×C8—111no—
373C22×C8—111no—
374C22×C8—221no—
375C22×C8C22×D1111yescharacteristic
376C22×C8C22×D1111yescharacteristic
377#117—111no—
378#117—111no—
379#117—111no—
380#117—111no—
381#117—111no—
382#117—111no—
383#117—111no—
384#117—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C22⋊C4—111no—
388C2×C22⋊C4—111no—
389C2×C42—111no—
390C2×C42—111no—
391#108—41no—
392#108—41no—
393#108—441no—
394#108—441no—
395#108—441no—
396#108—441no—
397#108—441no—
398#108—441no—
399C4⋊C8—112no—
400C4⋊C8—112no—
401C4⋊C8—112no—
402C4⋊C8—112no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8—221no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412C4⋊C8—221no—
413C4⋊C8—221no—
414C4⋊C8—221no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—112no—
418C22⋊C8—112no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8C4×D1112yes—
422C22⋊C8C4×D1112yes—
423#97—112no—
424#97—112no—
425#97—221no—
426#97—221no—
427C4×C8—112no—
428C4×C8—112no—
429C4×C8—221no—
430C4×C8—221no—
431C2×C11—21no—
432C2×C11—21no—
433C2×C11—41no—
434C2×C11—41no—
435C2×C11#231711yescharacteristic
436C2×C11#291611yescharacteristic
437C2×C11#291611yescharacteristic
438C24Q8×D1111yescharacteristic
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4C2×C4×D1111yescharacteristic
448C22×C4C2×C4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4D4×D1111yescharacteristic
451C22×C4Q8×D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453M16—21no—
454M16—21no—
455M16—21no—
456M16—21no—
457M16—21no—
458M16—21no—
459M16—21no—
460M16—21no—
461M16—42no—
462M16—221no—
463M16—221no—
464M16—221no—
465M16—221no—
466M16—221no—
467M16—221no—
468M16—221no—
469M16—221no—
470M16—442no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—112no—
481C2×C8—112no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—442no—
491C2×C8C2×C4×D1112yes—
492C2×C8C2×C4×D1112yes—
493C4⋊C4—111no—
494C4⋊C4—111no—
495C4⋊C4—111no—
496C4⋊C4—111no—
497C4⋊C4—111no—
498C4⋊C4—111no—
499C4⋊C4—111no—
500C4⋊C4—111no—
501C22⋊C4—111no—
502C22⋊C4—111no—
503C22⋊C4—111no—
504C22⋊C4—111no—
505C22⋊C4—111no—
506C22⋊C4—111no—
507C22⋊C4—111no—
508C22⋊C4—111no—
509C42—111no—
510C42—111no—
511C42—111no—
512C42—111no—
513C42—111no—
514C42—111no—
515C42—111no—
516C42—111no—
517C11#2199511yescharacteristic, complemented, Sylow
518C23—21no—
519C23—21no—
520C23—41no—
521C23—41no—
522C23C4⋊C4×D1111yescharacteristic
523C23C4⋊C4×D1111yescharacteristic
524C23C2×Q8×D1111yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—111no—
536C2×C4—111no—
537C2×C4—111no—
538C2×C4—111no—
539C2×C4—111no—
540C2×C4—111no—
541C2×C4—111no—
542C2×C4—111no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4C4⋊C4×D1111yescharacteristic
548C2×C4C4⋊C4×D1111yescharacteristic
549C2×C4C22×C4×D1111yescharacteristic
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4#6703711yescharacteristic
552C2×C4#6703711yescharacteristic
553C2×C4#6704311yescharacteristic
554C2×C4#6704311yescharacteristic
555C8—22no—
556C8—22no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—222no—
562C8—222no—
563C8—441no—
564C8—441no—
565C8—441no—
566C8—441no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—81no—
576C22—81no—
577C22C2×C4⋊C4×D1111yescharacteristic
578C22#1062315411yescharacteristic
579C22#1062315411yescharacteristic
580C4—21no—
581C4—21no—
582C4—221no—
583C4—221no—
584C4—221no—
585C4—221no—
586C4—221no—
587C4—221no—
588C4—221no—
589C4—221no—
590C4#1062307711yescharacteristic
591C4#1062307711yescharacteristic
592C4#1062312311yescharacteristic
593C4#1062317911yescharacteristic
594C2—21no—
595C2—21no—
596C2—41no—
597C2—41no—
598C2#1307123511yescharacteristic
599C2#1307722411yescharacteristic
600C2#1307722611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1855C2
socleC22×C11C22×C4⋊C4
prime radicalC24×C11C2×Q8
cosocleC22×C4×C11C24
hypercenter#1855D11
hypocenterC11#21995
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
4. #13069390C2semidirect
5. #13069390C2semidirect
6. #13069388C2semidirect
7. #13069388C2semidirect
11. #13068789C2semidirect
12. #13068786C2semidirect
13. #13068755C2semidirect
14. #13068752C2semidirect
517. C11#21995semidirect

Maximal subgroups

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

subgroupindex
#130772512
C2×#106223332
#130771792
#130693902
#130693882
#130688232
#130688212
#130688202
#130687892
#130687862
#130687552
#130687522
C11×#18552
#2199511