Finite Group Databasebeta

← #14792609

Subgroups — #14792609

Order 2816.

944 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622660C211yesmaximal, characteristic
2C2×#10622333C211yesmaximal, characteristic, complemented
3#13074414C211yesmaximal, characteristic, complemented
4#13071209C211yesmaximal, characteristic
5#13070012C211yesmaximal, characteristic, complemented
6#13070005C211yesmaximal, characteristic, complemented
7#13069937C211yesmaximal, characteristic, complemented
8#13069930C211yesmaximal, characteristic, complemented
9#13069494C211yesmaximal, characteristic, complemented
10#13069474C211yesmaximal, characteristic, complemented
11#13069304C211yesmaximal, characteristic, complemented
12#13069297C211yesmaximal, characteristic, complemented
13#13068804C211yesmaximal, characteristic, complemented
14#13068557C211yesmaximal, characteristic
15C11×#1872C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622843C2211yescharacteristic
26#10622843C2211yescharacteristic
27#10622826—21no—
28#10622826—21no—
29#10622825C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622660—24no—
40#10622601C2211yescharacteristic
41#10622601C2211yescharacteristic
42#10622600—21no—
43#10622600—21no—
44#10622599—21no—
45#10622596—21no—
46#10622587C2211yescharacteristic
47#10622587C2211yescharacteristic
48#10622586C2211yescharacteristic
49#10622586C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54#10622565—21no—
55#10622565—21no—
56#10622333—24no—
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C2×#4339—22no—
66C2×#4339—22no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—41no—
70C2×#4339—41no—
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C22×Dic22C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4—41no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11D411yescharacteristic
88C2×C22⋊Dic11D411yescharacteristic
89C2×#4326—22no—
90C2×#4326—22no—
91C2×#4326—41no—
92C2×#4325—22no—
93C2×#4325—22no—
94C2×#4325—41no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99#66979—22no—
100#66979—22no—
101C2×C4⋊Dic11D411yescharacteristic
102C2×C4⋊Dic11D411yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C11×#103—41no—
112C11×#103—41no—
113C11×C22⋊C8—22no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C22⋊(C11⋊C8)D414yes—
126#66885—22no—
127#66885—41no—
128#66880—22no—
129#66880—41no—
130#66879—22no—
131Dic11⋊C8—22no—
132Dic11⋊C8—22no—
133C8×Dic11—22no—
134#66874—22no—
135#66873—22no—
136#66871—41no—
137#66871—41no—
138#24515—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—42no—
156C22×C4×C11—81no—
157C22×C4×C11—81no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11#4112yes—
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—24no—
163C2×C22⋊D11—42no—
164C2×C22⋊D11—42no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172#4339—44no—
173#4339—44no—
174#4339—44no—
175#4339—44no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44#4112yes—
182C2×C4×D11—24no—
183C2×C4×D11—42no—
184C2×C4×D11—42no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22#4112yes—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—42no—
204C11×C4⋊C4—42no—
205C11×C22⋊C4—42no—
206C22⋊Dic11—22no—
207C22⋊Dic11—22no—
208C22⋊Dic11—81no—
209#4326—44no—
210#4325—44no—
211(C2×D11)⋊C4—81no—
212(C2×D11)⋊C4—81no—
213(C2×D11)⋊C4—81no—
214(C2×D11)⋊C4—81no—
215C4⋊Dic11—22no—
216C4⋊Dic11—22no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221Dic11⋊C4—81no—
222Dic11⋊C4—81no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8C2×D412yes—
232C2×C11⋊C8C2×D412yes—
233C2×#452—111no—
234C2×#433—111no—
235#2625—111no—
236#2311—111no—
237#2068—111no—
238#2067—111no—
239#2056—111no—
240#2055—111no—
241#1973—111no—
242#1969—111no—
243#1935—111no—
244#1934—111no—
245#1872D1111yescharacteristic, complemented
246#1852—111no—
247#1788—111no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11#12112yes—
255C23×C11C22×D411yescharacteristic
256C22×D11—22no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263Q8×C11—41no—
264Q8×C11—41no—
265Q8×C11—41no—
266Q8×C11—41no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—84no—
286C2×C4×C11#12112yes—
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×C4×C11H(5,𝔽2)11yescharacteristic
293C22⋊D11—48no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—22no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—21no—
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315D44—22no—
316D44—22no—
317D44—41no—
318D44—41no—
319C4×D11—48no—
320Dic22—22no—
321Dic22—22no—
322Dic22—41no—
323Dic22—41no—
324C8×C11—41no—
325C8×C11—41no—
326C11⋊C8—22no—
327C11⋊C8—22no—
328C22×#41—111no—
329C22×Q16—111no—
330C22×SD16—111no—
331C2×C22⋊Q8C2×D1111yescharacteristic
332C2×#117—111no—
333C22×C4⋊C4C2×D1111yescharacteristic
334#452—224no—
335#433—224no—
336C2×#107—111no—
337C2×#107—111no—
338C2×C4⋊C8—111no—
339C2×C4⋊C8—111no—
340C2×#103—111no—
341C2×#103—111no—
342C2×#103—111no—
343C2×#103C2×D1111yescharacteristic
344C2×#103C2×D1111yescharacteristic
345C2×#102—111no—
346C2×#102—111no—
347C2×#102—111no—
348C2×C22⋊C8—111no—
349C2×C22⋊C8C2×D1111yescharacteristic
350C2×#97—111no—
351C2×C4×C8—111no—
352#400—221no—
353#398—221no—
354#397—221no—
355#397—221no—
356#391—111no—
357#391—111no—
358#391—111no—
359#391—111no—
360#390—111no—
361#390—111no—
362#389—111no—
363#389—111no—
364#386—221no—
365#386—221no—
366#380—111no—
367#380—221no—
368#380—221no—
369#340—111no—
370#340—111no—
371#340C2×D1111yescharacteristic
372#340C2×D1111yescharacteristic
373C22×C11—22no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11C2×#12111yescharacteristic
381C22×C11#52511yescharacteristic
382C22×C11#53511yescharacteristic
383C22×C11#57611yescharacteristic
384C22×C11#57711yescharacteristic
385C22×C11#57811yescharacteristic
386C22×C11#57811yescharacteristic
387C2×D11—42no—
388C2×D11—42no—
389C2×D11—42no—
390C2×D11—81no—
391C2×D11—81no—
392C2×D11—81no—
393C2×D11—81no—
394C4×C11—22no—
395C4×C11—81no—
396C4×C11—81no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11#54611yescharacteristic
400C4×C11#54611yescharacteristic
401C4×C11#55111yescharacteristic
402C4×C11#55111yescharacteristic
403Dic11—42no—
404Dic11—41no—
405Dic11—41no—
406Dic11—41no—
407Dic11—41no—
408Dic11—81no—
409Dic11—81no—
410C2×#41—222no—
411C2×#41—222no—
412C2×#41—222no—
413C2×#41—222no—
414C2×#41—441no—
415C2×#41—441no—
416C22×Q8—111no—
417C22×Q8C22×D1111yescharacteristic
418C22×D4—111no—
419C22×D4—221no—
420C23×C4—21no—
421C23×C4—221no—
422C23×C4C22×D1111yescharacteristic
423C2×Q16—222no—
424C2×Q16—222no—
425C2×Q16—441no—
426C2×SD16—222no—
427C2×SD16—222no—
428C2×SD16—441no—
429C22×C8—111no—
430C22×C8—111no—
431C22×C8C22×D1111yescharacteristic
432C22×C8C22×D1111yescharacteristic
433C22⋊Q8—22no—
434C22⋊Q8—22no—
435#117—222no—
436#117—222no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—41no—
440C2×C4⋊C4—41no—
441C2×C4⋊C4—111no—
442C2×C4⋊C4—111no—
443C2×C4⋊C4—111no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—221no—
446C2×C4⋊C4—221no—
447C2×C4⋊C4C22×D1111yescharacteristic
448C2×C4⋊C4C22×D1111yescharacteristic
449C2×C4⋊C4C22×D1111yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—111no—
452C2×C22⋊C4—111no—
453C2×C22⋊C4—221no—
454C2×C22⋊C4—221no—
455C2×C22⋊C4—221no—
456C2×C22⋊C4—221no—
457C2×C22⋊C4—221no—
458C2×C42—111no—
459C2×C42—111no—
460#107—441no—
461#107—441no—
462C4⋊C8—222no—
463C4⋊C8—222no—
464#103—41no—
465#103—41no—
466#103—222no—
467#103—222no—
468#103—441no—
469#102—222no—
470#102—222no—
471#102—441no—
472C22⋊C8—22no—
473C22⋊C8—114no—
474#97—222no—
475C4×C8—222no—
476#95—221no—
477#95—221no—
478#95—221no—
479#95—221no—
480#95—221no—
481#95—221no—
482#95—221no—
483#95—221no—
484#95—221no—
485#95—221no—
486#95—221no—
487C2×C11—42no—
488C2×C11#241111yescharacteristic
489C2×C11#306111yescharacteristic
490C2×C11#306311yescharacteristic
491C2×C11#312011yescharacteristic
492C2×C11#312411yescharacteristic
493C2×C11#322311yescharacteristic
494C2×C11#322411yescharacteristic
495D11—82no—
496C24—221no—
497C24D4×D1111yescharacteristic
498#41—444no—
499#41—444no—
500#41—444no—
501#41—444no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—112no—
509C2×Q8—221no—
510C2×Q8—221no—
511C2×Q8—221no—
512C2×Q8—221no—
513C2×Q8—221no—
514C2×D4—112no—
515C2×D4—224no—
516C2×D4—221no—
517C2×D4—221no—
518C2×D4—221no—
519C2×D4—221no—
520C2×D4—221no—
521C2×D4—442no—
522C2×D4—442no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—111no—
535C22×C4—111no—
536C22×C4—111no—
537C22×C4—111no—
538C22×C4—224no—
539C22×C4—221no—
540C22×C4—221no—
541C22×C4—221no—
542C22×C4—442no—
543C22×C4—442no—
544C22×C4#433912yes—
545C22×C4D4×D1111yescharacteristic
546C22×C4D4×D1112yes—
547C22×C4C23×D1111yescharacteristic
548Q16—444no—
549SD16—444no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—112no—
557C2×C8—112no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8—221no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—222no—
571C4⋊C4—222no—
572C4⋊C4—221no—
573C4⋊C4—221no—
574C4⋊C4—221no—
575C4⋊C4—221no—
576C4⋊C4—881no—
577C4⋊C4—881no—
578C22⋊C4—42no—
579C22⋊C4—222no—
580C22⋊C4—222no—
581C22⋊C4—881no—
582C22⋊C4—881no—
583C22⋊C4—881no—
584C22⋊C4—881no—
585C22⋊C4—881no—
586C42—221no—
587C42—221no—
588C42—221no—
589C42—221no—
590C11#2451511yescharacteristic, complemented, Sylow
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—222no—
598C23—441no—
599C23—441no—
600C23—441no—
601C23—441no—
602C23—441no—
603C23—441no—
604C23#6693712yes—
605C23C2×D4×D1111yescharacteristic
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610Q8—222no—
611Q8—222no—
612Q8—441no—
613Q8—441no—
614D4—222no—
615D4—222no—
616D4—448no—
617D4—441no—
618D4—441no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—84no—
638C2×C4—221no—
639C2×C4—221no—
640C2×C4—221no—
641C2×C4—221no—
642C2×C4—221no—
643C2×C4—221no—
644C2×C4—221no—
645C2×C4—221no—
646C2×C4—221no—
647C2×C4—221no—
648C2×C4—221no—
649C2×C4—221no—
650C2×C4—222no—
651C2×C4—448no—
652C2×C4—441no—
653C2×C4—441no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4#6693712yes—
661C2×C4C2×#433911yescharacteristic
662C2×C4C2×D4×D1111yescharacteristic
663C2×C4#6703711yescharacteristic
664C2×C4#6703711yescharacteristic
665C2×C4#41×D1111yescharacteristic
666C2×C4#41×D1111yescharacteristic
667C8—41no—
668C8—41no—
669C8—222no—
670C8—222no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—442no—
679C22—442no—
680C22—442no—
681C22—881no—
682C22—881no—
683C22—881no—
684C22—881no—
685C22C2×#6693711yescharacteristic
686C22#1062312311yescharacteristic
687C22#1062318711yescharacteristic
688C22#1062329311yescharacteristic
689C22#1062329711yescharacteristic
690C22#1062330511yescharacteristic
691C22#1062331011yescharacteristic
692C4—22no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4—441no—
698C4—441no—
699C4—441no—
700C4—441no—
701C4—442no—
702C4—881no—
703C4—881no—
704C4#1062308711yescharacteristic
705C4#1062308711yescharacteristic
706C4#1062314111yescharacteristic
707C4#1062314111yescharacteristic
708C2—42no—
709C2—882no—
710C2#1307200411yescharacteristic
711C2#1307828511yescharacteristic
712C2#1307830511yescharacteristic
713C2#1307883311yescharacteristic
714C2#1307888111yescharacteristic
715C2#1307969511yescharacteristic
716C2#1307971411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenter#1872D11
hypocenterC11#24515
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#10622333C2semidirect
3. #13074414C2semidirect
5. #13070012C2semidirect
6. #13070005C2semidirect
7. #13069937C2semidirect
8. #13069930C2semidirect
9. #13069494C2semidirect
10. #13069474C2semidirect
11. #13069304C2semidirect
12. #13069297C2semidirect
13. #13068804C2semidirect
15. C11×#1872C2semidirect
245. #1872D11semidirect
590. C11#24515semidirect

Maximal subgroups

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

subgroupindex
C2×#106226602
C2×#106223332
#130744142
#130712092
#130700122
#130700052
#130699372
#130699302
#130694942
#130694742
#130693042
#130692972
#130688042
#130685572
C11×#18722
#2451511