Finite Group Databasebeta

← #14769941

Subgroups — #14769941

Order 2816.

1068 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4318C212yesmaximal
2#13069610C212yesmaximal, complemented
3#13069085C212yesmaximal, complemented
4#13069085C212yesmaximal, complemented
5#13068699C211yesmaximal, characteristic, complemented
6#13068696C211yesmaximal, characteristic, complemented
7#13068612C211yesmaximal, characteristic, complemented
8C4×#66900C211yesmaximal, characteristic, complemented
9#13068355C211yesmaximal, characteristic, complemented
10C2×#10622168C211yesmaximal, characteristic, complemented
11C2×C11×#552C211yesmaximal, characteristic
12C11×#552—22no—
13C11×#552—22no—
14C11×#552—22no—
15C11×#552—22no—
16C2×C11×#126C412yes—
17C2×C11×#125C412yes—
18C2×C11×#125C2211yescharacteristic
19C2×C11×#123C412yes—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117C412yes—
25C2×C11×#117C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×#4318C2212yes—
28C22×#4318C2212yes—
29C2×#66900C2212yes—
30C2×#66900C2212yes—
31#10622820C2212yes—
32#10622820C2212yes—
33#10622625—22no—
34#10622624—22no—
35#10622624—22no—
36D4×C11⋊C8—22no—
37#10622537C2212yes—
38C4×#4318C2212yes—
39#10622168C2212yes—
40#10622168C2212yes—
41#10622168C2212yes—
42#10622168C2212yes—
43#10622168C2211yescharacteristic
44#10622168C2211yescharacteristic
45#10622168C2211yescharacteristic
46#10622168C2211yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11C2×C411yescharacteristic
49C23×C4×C11C2×C412yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C11×#126—24no—
53C11×#126—24no—
54C11×#125—24no—
55C11×#125—24no—
56C11×#125—22no—
57C11×#125—22no—
58C11×#123—24no—
59C11×#123—24no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×D4×C11D412yes—
67C4×D4×C11D412yes—
68C4×D4×C11D412yes—
69C4×D4×C11D412yes—
70C11×#117—22no—
71C11×#117—22no—
72C11×#117—22no—
73C11×#117—22no—
74C11×#117—22no—
75C11×#117—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4C2×C412yes—
79C2×C11×C4⋊C4C2×C412yes—
80C2×C11×C4⋊C4C2×C412yes—
81C2×C11×C4⋊C4C2×C412yes—
82C2×C11×C4⋊C4C2×C412yes—
83C2×C11×C4⋊C4C2×C412yes—
84C2×C11×C4⋊C4C2×C411yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4C2×C412yes—
89C2×C11×C22⋊C4C2×C412yes—
90C2×C11×C22⋊C4C2×C412yes—
91C2×C11×C22⋊C4C2×C411yescharacteristic
92C2×C11×C22⋊C4C2×C411yescharacteristic
93C2×C42×C11C2×C412yes—
94C2×C42×C11C2×C412yes—
95C2×C42×C11C2311yescharacteristic
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318—24no—
99C2×#4318—24no—
100C2×#4318—42no—
101C2×#4318—42no—
102C2×#4318C2312yes—
103C2×#4318C2312yes—
104C2×#4318C2312yes—
105C2×#4318C2312yes—
106C22×C11⋊C8—22no—
107C22×C11⋊C8—22no—
108#66900—24no—
109#66900—42no—
110C22⋊(C11⋊C8)—22no—
111C22⋊(C11⋊C8)—22no—
112C22⋊(C11⋊C8)—22no—
113C22⋊(C11⋊C8)—22no—
114C4⋊(C11⋊C8)—22no—
115C4⋊(C11⋊C8)—22no—
116#66867—22no—
117C4×C11⋊C8—22no—
118#22480—111nomaximal, Sylow
119C24×C11C22×C411yescharacteristic
120C24×C11C22×C411yescharacteristic
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×D4×C11—42no—
126C2×D4×C11C22⋊C412yes—
127C2×D4×C11C22⋊C412yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—44no—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C412yes—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2411yescharacteristic
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4C22⋊C412yes—
162C11×C4⋊C4C22⋊C412yes—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4C22⋊C411yescharacteristic
168C11×C22⋊C4C22⋊C411yescharacteristic
169C11×C22⋊C4C22⋊C411yescharacteristic
170C11×C22⋊C4C22⋊C411yescharacteristic
171C11×C22⋊C4C22⋊C412yes—
172C11×C22⋊C4C22⋊C412yes—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11C2×D412yes—
178C42×C11C2×D412yes—
179#4318—22no—
180#4318—22no—
181#4318—22no—
182#4318—22no—
183#4318—22no—
184#4318—22no—
185#4318—22no—
186#4318—44no—
187#4318—44no—
188#4318#4114yes—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—44no—
194C2×C11⋊C8—44no—
195C2×#552D1111yescharacteristic
196D4×M16—112no—
197#1998—112no—
198#1901—112no—
199#1901—112no—
200#1822—111no—
201#1821—111no—
202#1801—111no—
203C4×#101—111no—
204#1742—111no—
205C2×#343—111no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—22no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11C2×C22⋊C412yes—
215C23×C11C2×C22⋊C411yescharacteristic
216C23×C11C2×C22⋊C411yescharacteristic
217C23×C11C23×C411yescharacteristic
218Q8×C11—42no—
219Q8×C11—42no—
220D4×C11—24no—
221D4×C11—42no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—44no—
243C2×C4×C11—44no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11C2×C22⋊C411yescharacteristic
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11C2×C22⋊C411yescharacteristic
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C2×#4112yes—
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C11⋊C8—24no—
258C11⋊C8—42no—
259C11⋊C8—42no—
260C11⋊C8—42no—
261C22×M16—112no—
262C22×M16—112no—
263#552—22no—
264#552—22no—
265#552—22no—
266#552—22no—
267C2×#126Dic1112yes—
268C2×#125Dic1112yes—
269C2×#125C2×D1111yescharacteristic
270C2×#123Dic1112yes—
271C2×C22⋊Q8C2×D1111yescharacteristic
272C2×C22⋊Q8C2×D1111yescharacteristic
273C2×C4×Q8C2×D1111yescharacteristic
274C2×C4×D4C2×D1111yescharacteristic
275C2×#117Dic1112yes—
276C2×#117C2×D1111yescharacteristic
277C22×C4⋊C4C2×D1111yescharacteristic
278#436—222no—
279#435—222no—
280#435—222no—
281C8×D4—222no—
282#423—112no—
283C2×#101—112no—
284C2×#101—112no—
285#407—112no—
286#407—112no—
287C4×M16—112no—
288#343—111no—
289#343—111no—
290#343—111no—
291#343—112no—
292#343—112no—
293#343—112no—
294#343—112no—
295#343—111no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—22no—
302C22×C11—21no—
303C22×C11—22no—
304C22×C11—21no—
305C22×C11—22no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11#41312yes—
311C22×C11C22×C22⋊C411yescharacteristic
312C22×C11C4×#4111yescharacteristic
313C22×C11#52011yescharacteristic
314C4×C11—21no—
315C4×C11—22no—
316C4×C11—21no—
317C4×C11—22no—
318C4×C11—21no—
319C4×C11—21no—
320C4×C11—42no—
321C4×C11—42no—
322C4×C11—42no—
323C4×C11—42no—
324C4×C11#54612yes—
325C4×C11#54712yes—
326C22×Q8C22×D1111yescharacteristic
327C22×D4C2×Dic1111yescharacteristic
328C23×C4C2×Dic1112yes—
329C23×C4C22×D1111yescharacteristic
330C23×C4C22×D1111yescharacteristic
331C2×M16—112no—
332C2×M16—112no—
333C2×M16—112no—
334C2×M16—112no—
335C2×M16—222no—
336C2×M16—222no—
337C2×M16—224no—
338C2×M16—224no—
339C2×M16—442no—
340C2×M16—442no—
341C22×C8—222no—
342C22×C8—222no—
343#126—24no—
344#126—24no—
345#125—24no—
346#125—24no—
347#125—22no—
348#125—22no—
349#123—24no—
350#123—24no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C4×Q8—22no—
356C4×Q8—22no—
357C4×D4C22⋊D1112yes—
358C4×D4C22⋊D1112yes—
359C4×D4C22⋊D1112yes—
360C4×D4C22⋊D1112yes—
361#117—22no—
362#117—22no—
363#117—22no—
364#117—22no—
365#117—22no—
366#117—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4C2×Dic1112yes—
370C2×C4⋊C4C2×Dic1112yes—
371C2×C4⋊C4C2×Dic1112yes—
372C2×C4⋊C4C2×Dic1112yes—
373C2×C4⋊C4C2×Dic1112yes—
374C2×C4⋊C4C2×Dic1112yes—
375C2×C4⋊C4C2×Dic1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C22⋊C4C2×Dic1112yes—
380C2×C22⋊C4C2×Dic1112yes—
381C2×C22⋊C4C2×Dic1112yes—
382C2×C22⋊C4C2×Dic1111yescharacteristic
383C2×C22⋊C4C2×Dic1111yescharacteristic
384C2×C42C2×Dic1112yes—
385C2×C42C2×Dic1112yes—
386C2×C42C22×D1111yescharacteristic
387C4⋊C8—222no—
388C4⋊C8—222no—
389#101—224no—
390#101—442no—
391C22⋊C8—222no—
392C22⋊C8—222no—
393C22⋊C8—222no—
394C22⋊C8—222no—
395#97—222no—
396C4×C8—222no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—22no—
400C2×C11—41no—
401C2×C11—42no—
402C2×C11#233911yescharacteristic
403C2×C11C2×#41311yescharacteristic
404C2×C11#288911yescharacteristic
405C24C22×Dic1111yescharacteristic
406C24C22×Dic1111yescharacteristic
407C2×Q8—22no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—22no—
411C2×D4—42no—
412C2×D4C22⋊Dic1112yes—
413C2×D4C22⋊Dic1112yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—44no—
423C22×C4C22×Dic1112yes—
424C22×C4C22×Dic1111yescharacteristic
425C22×C4C22×Dic1111yescharacteristic
426C22×C4C22×Dic1112yes—
427C22×C4C22×Dic1112yes—
428C22×C4C22×Dic1112yes—
429C22×C4C22×Dic1111yescharacteristic
430C22×C4C22×Dic1111yescharacteristic
431C22×C4C2×C22⋊D1112yes—
432C22×C4C2×C22⋊D1112yes—
433C22×C4C2×C22⋊D1112yes—
434C22×C4C2×C22⋊D1112yes—
435C22×C4C23×D1111yescharacteristic
436M16—114no—
437M16—222no—
438M16—222no—
439M16—222no—
440M16—222no—
441M16—222no—
442M16—222no—
443M16—222no—
444M16—444no—
445M16—444no—
446C2×C8—222no—
447C2×C8—222no—
448C2×C8—222no—
449C2×C8—222no—
450C2×C8—444no—
451C2×C8—444no—
452C4⋊C4—24no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4C22⋊Dic1112yes—
464C4⋊C4C22⋊Dic1112yes—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4C22⋊Dic1111yescharacteristic
470C22⋊C4C22⋊Dic1111yescharacteristic
471C22⋊C4C22⋊Dic1111yescharacteristic
472C22⋊C4C22⋊Dic1111yescharacteristic
473C22⋊C4C22⋊Dic1112yes—
474C22⋊C4C22⋊Dic1112yes—
475C42—22no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42C2×C22⋊D1112yes—
480C42C2×C22⋊D1112yes—
481C11#2248011yescharacteristic, complemented, Sylow
482C23—21no—
483C23—21no—
484C23—22no—
485C23—21no—
486C23—21no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C2×C22⋊Dic1112yes—
491C23C2×C22⋊Dic1111yescharacteristic
492C23C2×C22⋊Dic1111yescharacteristic
493C23C23×Dic1111yescharacteristic
494Q8—42no—
495Q8—42no—
496D4—24no—
497D4—42no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4C2×C22⋊Dic1111yescharacteristic
524C2×C4C2×C22⋊Dic1111yescharacteristic
525C2×C4C2×C22⋊Dic1111yescharacteristic
526C2×C4C2×C22⋊Dic1111yescharacteristic
527C2×C4C2×C22⋊Dic1112yes—
528C2×C4C2×C22⋊Dic1112yes—
529C2×C4#41×D1112yes—
530C2×C4#6704211yescharacteristic
531C2×C4#6704311yescharacteristic
532C2×C4C22×C22⋊D1112yes—
533C8—224no—
534C8—442no—
535C8—442no—
536C8—442no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—22no—
543C22—21no—
544C22—22no—
545C22—21no—
546C22—22no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22#1062285012yes—
552C22#41×Dic1111yescharacteristic
553C22#1062335811yescharacteristic
554C22C22×C22⋊Dic1111yescharacteristic
555C4—21no—
556C4—22no—
557C4—21no—
558C4—22no—
559C4—21no—
560C4—21no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4#1062335512yes—
566C4#1062336012yes—
567C2—21no—
568C2—21no—
569C2—22no—
570C2—41no—
571C2—42no—
572C2#1307144611yescharacteristic
573C2C2×#1062285011yescharacteristic
574C2#1307709911yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#552C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC2×#552D11
hypocenterC11#22480
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #13069610C2semidirect
3. #13069085C2semidirect
4. #13069085C2semidirect
5. #13068699C2semidirect
6. #13068696C2semidirect
7. #13068612C2semidirect
8. C4×#66900C2semidirect
9. #13068355C2semidirect
10. C2×#10622168C2semidirect
481. C11#22480semidirect

Maximal subgroups

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

subgroupindex
D4×#43182
#130696102
#130690852
#130686992
#130686962
#130686122
C4×#669002
#130683552
C2×#106221682
C2×C11×#5522
#2248011