Finite Group Databasebeta

← #14792597

Subgroups — #14792597

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×#10622346C211yesmaximal, characteristic
2#13074413C211yesmaximal, characteristic, complemented
3#13071204C211yesmaximal, characteristic
4#13070010C211yesmaximal, characteristic, complemented
5#13070003C211yesmaximal, characteristic, complemented
6#13069939C211yesmaximal, characteristic, complemented
7#13069934C211yesmaximal, characteristic, complemented
8#13069497C211yesmaximal, characteristic, complemented
9#13069477C211yesmaximal, characteristic, complemented
10#13069306C211yesmaximal, characteristic, complemented
11#13069299C211yesmaximal, characteristic, complemented
12#13068921C211yesmaximal, characteristic, complemented
13#13068806C211yesmaximal, characteristic, complemented
14#13068557C211yesmaximal, characteristic
15C2×C11×#433C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C22×Dic44C2211yescharacteristic
21C22×#4314C2211yescharacteristic
22C11×#433—24no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29#10622825C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40#10622600—21no—
41#10622600—21no—
42#10622595—21no—
43#10622593—21no—
44#10622571—21no—
45#10622571—21no—
46#10622565—21no—
47#10622565—21no—
48#10622552C2211yescharacteristic
49#10622552C2211yescharacteristic
50#10622542C2211yescharacteristic
51#10622542C2211yescharacteristic
52#10622542C2211yescharacteristic
53#10622542C2211yescharacteristic
54#10622541C2211yescharacteristic
55#10622541C2211yescharacteristic
56#10622346—24no—
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C2×#4339—22no—
65C2×#4339—22no—
66C2×#4339—22no—
67C2×#4339—22no—
68C2×#4339—41no—
69C2×#4339—41no—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×Dic22C2311yescharacteristic
73C22×Dic22C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×#117—22no—
79C11×#117—22no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—41no—
94C2×C4⋊Dic11—41no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100#66977—22no—
101#66977—22no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic44—22no—
106C2×Dic44—22no—
107C2×Dic44—41no—
108C2×#4314—22no—
109C2×#4314—22no—
110C2×#4314—41no—
111C11×C4⋊C8—22no—
112C11×C4⋊C8—22no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8D414yes—
115C11×#97—22no—
116C4×C8×C11—22no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128#66885—22no—
129#66885—22no—
130#66885—41no—
131#66882—41no—
132#66882—41no—
133#66880—22no—
134#66880—22no—
135#66880—41no—
136#66880—41no—
137#66880—41no—
138#24515—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11#4112yes—
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—24no—
154C2×C22⋊D11—42no—
155C2×C22⋊D11—42no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—42no—
164C22×Dic11—81no—
165C22×Dic11—81no—
166#4339—44no—
167#4339—44no—
168#4339—44no—
169#4339—44no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44#4112yes—
176C2×C4×D11—24no—
177C2×C4×D11—42no—
178C2×C4×D11—42no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
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—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11C2×D412yes—
202C2×C8×C11C2×D412yes—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C22⋊Dic11—42no—
212C22⋊Dic11—81no—
213(C2×D11)⋊C4—81no—
214(C2×D11)⋊C4—81no—
215(C2×D11)⋊C4—81no—
216(C2×D11)⋊C4—81no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—42no—
228Dic11⋊C4—42no—
229Dic11⋊C4—81no—
230Dic11⋊C4—81no—
231Dic44—44no—
232#4314—44no—
233C2×#452—111no—
234C2×#433D1111yescharacteristic, complemented
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#1872—111no—
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—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11#12112yes—
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C22⋊D11—48no—
289C2×Dic11—22no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—84no—
311D44—22no—
312D44—22no—
313D44—41no—
314D44—41no—
315C4×D11—48no—
316Dic22—22no—
317Dic22—22no—
318Dic22—41no—
319Dic22—41no—
320Dic22—41no—
321Dic22—41no—
322Dic22—41no—
323Dic22—41no—
324C8×C11—22no—
325C8×C11—22no—
326C8×C11—41no—
327C8×C11—41no—
328C22×#41—111no—
329C22×Q16—111no—
330C22×SD16—111no—
331C2×C22⋊Q8—111no—
332C2×#117C2×D1111yescharacteristic
333C22×C4⋊C4—111no—
334#452—224no—
335#433—24no—
336C2×#107—111no—
337C2×#107—111no—
338C2×C4⋊C8C2×D1111yescharacteristic
339C2×C4⋊C8C2×D1111yescharacteristic
340C2×#103—111no—
341C2×#103—111no—
342C2×#103—111no—
343C2×#103—111no—
344C2×#103—111no—
345C2×#102—111no—
346C2×#102—111no—
347C2×#102—111no—
348C2×C22⋊C8C2×D1111yescharacteristic
349C2×C22⋊C8C2×D1111yescharacteristic
350C2×#97C2×D1111yescharacteristic
351C2×C4×C8C2×D1111yescharacteristic
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#340—111no—
372#340—111no—
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—41no—
396C4×C11—41no—
397C4×C11—41no—
398C4×C11—41no—
399C4×C11#54611yescharacteristic
400C4×C11#54611yescharacteristic
401C4×C11#55111yescharacteristic
402C4×C11#55111yescharacteristic
403Dic11—42no—
404Dic11—81no—
405Dic11—81no—
406Dic11—81no—
407Dic11—81no—
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×Q8—111no—
418C22×D4—111no—
419C22×D4—221no—
420C23×C4—221no—
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×C8C22×D1111yescharacteristic
430C22×C8C22×D1111yescharacteristic
431C22×C8C22×D1111yescharacteristic
432C22×C8C22×D1111yescharacteristic
433C22⋊Q8—222no—
434C22⋊Q8—222no—
435#117—22no—
436#117—22no—
437C2×C4⋊C4—111no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—111no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—111no—
442C2×C4⋊C4—221no—
443C2×C4⋊C4—221no—
444C2×C4⋊C4—221no—
445C2×C4⋊C4—221no—
446C2×C4⋊C4—441no—
447C2×C4⋊C4—441no—
448C2×C4⋊C4D4411yescharacteristic
449C2×C4⋊C4D4411yescharacteristic
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C22⋊C4—221no—
455C2×C22⋊C4—221no—
456C2×C22⋊C4D4411yescharacteristic
457C2×C22⋊C4D4411yescharacteristic
458C2×C42C22×D1111yescharacteristic
459C2×C42C22×D1111yescharacteristic
460#107—441no—
461#107—441no—
462C4⋊C8—22no—
463C4⋊C8—22no—
464#103—222no—
465#103—222no—
466#103—441no—
467#103—441no—
468#103—441no—
469#102—222no—
470#102—222no—
471#102—441no—
472C22⋊C8—22no—
473C22⋊C8C22⋊D1114yes—
474#97—22no—
475C4×C8—22no—
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—
497C24C2×D4411yescharacteristic
498#41—444no—
499#41—444no—
500#41—444no—
501#41—444no—
502C2×Q8—112no—
503C2×Q8—221no—
504C2×Q8—221no—
505C2×Q8—221no—
506C2×Q8—221no—
507C2×Q8—221no—
508C2×Q8—221no—
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—224no—
528C22×C4—221no—
529C22×C4—221no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—221no—
534C22×C4—221no—
535C22×C4—442no—
536C22×C4—442no—
537C22×C4—442no—
538C22×C4—881no—
539C22×C4—881no—
540C22×C4C2×D4411yescharacteristic
541C22×C4C2×D4411yescharacteristic
542C22×C4C2×D4411yescharacteristic
543C22×C4C2×D4411yescharacteristic
544C22×C4C2×D4411yescharacteristic
545C22×C4#433912yes—
546C22×C4C2×C22⋊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—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8C2×C22⋊D1112yes—
561C2×C8C2×C22⋊D1112yes—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—221no—
565C4⋊C4—221no—
566C4⋊C4—221no—
567C4⋊C4—221no—
568C4⋊C4—221no—
569C4⋊C4—221no—
570C4⋊C4—221no—
571C4⋊C4—221no—
572C4⋊C4—221no—
573C4⋊C4—221no—
574C4⋊C4—442no—
575C4⋊C4—442no—
576C4⋊C4—881no—
577C4⋊C4—881no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—442no—
581C22⋊C4—881no—
582C22⋊C4—881no—
583C22⋊C4—881no—
584C22⋊C4—881no—
585C22⋊C4—881no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
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#6698312yes—
605C23C22×D4411yescharacteristic
606Q8—222no—
607Q8—222no—
608Q8—441no—
609Q8—441no—
610Q8—441no—
611Q8—441no—
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—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—222no—
638C2×C4—448no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—441no—
648C2×C4—441no—
649C2×C4—441no—
650C2×C4—441no—
651C2×C4—441no—
652C2×C4—441no—
653C2×C4—441no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—884no—
660C2×C4#6698312yes—
661C2×C4C2×#433911yescharacteristic
662C2×C4#41×D1111yescharacteristic
663C2×C4#41×D1111yescharacteristic
664C2×C4#6704211yescharacteristic
665C2×C4#6704211yescharacteristic
666C2×C4C22×C22⋊D1111yescharacteristic
667C8—22no—
668C8—22no—
669C8—41no—
670C8—41no—
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—
685C22#1062305511yescharacteristic
686C22#1062305611yescharacteristic
687C22#1062328211yescharacteristic
688C22#1062328311yescharacteristic
689C22#1062328411yescharacteristic
690C22#1062328411yescharacteristic
691C22C2×#6698311yescharacteristic
692C4—22no—
693C4—41no—
694C4—41no—
695C4—41no—
696C4—41no—
697C4—442no—
698C4—881no—
699C4—881no—
700C4—881no—
701C4—881no—
702C4—881no—
703C4—881no—
704C4#1062305811yescharacteristic
705C4#1062305811yescharacteristic
706C4#1062336011yescharacteristic
707C4#1062336011yescharacteristic
708C2—42no—
709C2—882no—
710C2#1307199511yescharacteristic
711C2#1307828611yescharacteristic
712C2#1307830711yescharacteristic
713C2#1307883211yescharacteristic
714C2#1307888011yescharacteristic
715C2#1307970111yescharacteristic
716C2#1307971211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#433C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#433D11
hypocenterC11#24515
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #13074413C2semidirect
4. #13070010C2semidirect
5. #13070003C2semidirect
6. #13069939C2semidirect
7. #13069934C2semidirect
8. #13069497C2semidirect
9. #13069477C2semidirect
10. #13069306C2semidirect
11. #13069299C2semidirect
12. #13068921C2semidirect
13. #13068806C2semidirect
15. C2×C11×#433C2semidirect
234. C2×#433D11semidirect
590. C11#24515semidirect

Maximal subgroups

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

subgroupindex
C2×#106223462
#130744132
#130712042
#130700102
#130700032
#130699392
#130699342
#130694972
#130694772
#130693062
#130692992
#130689212
#130688062
#130685572
C2×C11×#4332
#2451511