Finite Group Databasebeta

← #35414767

Subgroups — #35414767

Order 21248.

790 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127761C211yesmaximal, characteristic
2C2×#19127760C211yesmaximal, characteristic
3#24909943C211yesmaximal, characteristic
4#24908187C211yesmaximal, characteristic, complemented
5#24908185C211yesmaximal, characteristic, complemented
6#24908184C211yesmaximal, characteristic, complemented
7#24908183C211yesmaximal, characteristic, complemented
8#24908181C211yesmaximal, characteristic, complemented
9#24908180C211yesmaximal, characteristic, complemented
10#24908178C211yesmaximal, characteristic, complemented
11#24907446C211yesmaximal, characteristic
12#24907444C211yesmaximal, characteristic
13#24907442C211yesmaximal, characteristic
14#24907440C211yesmaximal, characteristic
15C83×#1939C211yesmaximal, characteristic, complemented
16C2×#14581749C2211yescharacteristic
17C2×#14581749C2211yescharacteristic
18C2×C42×D83C2211yescharacteristic
19#19127761—24no—
20#19127760—24no—
21C2×C4⋊(C83⋊C8)C2211yescharacteristic
22C2×C4⋊(C83⋊C8)C2211yescharacteristic
23C2×C4⋊(C83⋊C8)C2211yescharacteristic
24C2×Dic83⋊C8C2211yescharacteristic
25C2×Dic83⋊C8C2211yescharacteristic
26C2×Dic83⋊C8C2211yescharacteristic
27C2×Dic83⋊C8C2211yescharacteristic
28C2×Dic83⋊C8C2211yescharacteristic
29C2×Dic83⋊C8C2211yescharacteristic
30C2×(C2×D83)⋊C8C2211yescharacteristic
31C2×(C2×D83)⋊C8C2211yescharacteristic
32C2×(C2×D83)⋊C8C2211yescharacteristic
33C2×(C2×D83)⋊C8C2211yescharacteristic
34C2×#14581703C2211yescharacteristic
35C2×#14581702C2211yescharacteristic
36C2×C8×Dic83C2211yescharacteristic
37#19127598C411yescharacteristic
38#19127598C411yescharacteristic
39#19127596C411yescharacteristic
40#19127596C411yescharacteristic
41#19127575C411yescharacteristic
42#19127575C411yescharacteristic
43#19127572C411yescharacteristic
44#19127572C411yescharacteristic
45C4×Dic83⋊C4C2211yescharacteristic
46C4×Dic83⋊C4C2211yescharacteristic
47C4×C4⋊Dic83C2211yescharacteristic
48#19127456C2211yescharacteristic
49#19127456C2211yescharacteristic
50#19127455C2211yescharacteristic
51#19127455C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54C2×C4⋊C8×C83C2211yescharacteristic
55C2×C4⋊C8×C83C2211yescharacteristic
56C2×C4⋊C8×C83C2211yescharacteristic
57C2×C4×C8×C83C2211yescharacteristic
58C4×C4⋊C4×C83C2211yescharacteristic
59#336×C83C2211yescharacteristic
60#336×C83C2211yescharacteristic
61C22×C4×D83C2×C411yescharacteristic
62C22×C4×D83C2×C411yescharacteristic
63C22×C4×D83C2311yescharacteristic
64C22×C83⋊C8C2311yescharacteristic
65C22×C83⋊C8C2311yescharacteristic
66C22×C83⋊C8C2311yescharacteristic
67C22×C83⋊C8C2311yescharacteristic
68#14581749—41no—
69#14581749—41no—
70#14581749D414yes—
71#14581749Q814yes—
72C2×C4⋊Dic83C2×C411yescharacteristic
73C2×C4⋊Dic83C2×C411yescharacteristic
74C2×Dic83⋊C4C2×C411yescharacteristic
75C2×Dic83⋊C4C2×C411yescharacteristic
76C2×Dic83⋊C4C2×C411yescharacteristic
77C2×Dic83⋊C4C2×C411yescharacteristic
78C2×Dic83⋊C4C2×C411yescharacteristic
79C2×Dic83⋊C4C2×C411yescharacteristic
80C2×Dic83⋊C4C2×C411yescharacteristic
81C2×Dic83⋊C4C2×C411yescharacteristic
82C2×(C2×D83)⋊C4C2×C411yescharacteristic
83C2×(C2×D83)⋊C4C2×C411yescharacteristic
84C2×(C2×D83)⋊C4C2×C411yescharacteristic
85C2×(C2×D83)⋊C4C2×C411yescharacteristic
86C2×C4×Dic83C2×C411yescharacteristic
87C2×C4×Dic83C2×C411yescharacteristic
88C2×C4×Dic83C2311yescharacteristic
89C2×C4×Dic83C2311yescharacteristic
90C2×C4×Dic83C2311yescharacteristic
91C42×D83—41no—
92C42×D83—41no—
93C4⋊(C83⋊C8)—22no—
94C4⋊(C83⋊C8)—41no—
95C4⋊(C83⋊C8)—41no—
96Dic83⋊C8—22no—
97Dic83⋊C8—22no—
98Dic83⋊C8—41no—
99Dic83⋊C8—41no—
100Dic83⋊C8—41no—
101Dic83⋊C8—41no—
102(C2×D83)⋊C8—22no—
103(C2×D83)⋊C8—22no—
104(C2×D83)⋊C8—22no—
105(C2×D83)⋊C8—22no—
106#14581703—22no—
107#14581702—22no—
108C8×Dic83—22no—
109C83⋊#95C2×C411yescharacteristic
110C83⋊#95C2×C411yescharacteristic
111C83⋊#95C2×C411yescharacteristic
112C83⋊#95C2×C411yescharacteristic
113C83⋊#95C2×C411yescharacteristic
114C83⋊#95C2×C411yescharacteristic
115C22×C8×C83C2311yescharacteristic
116C22×C8×C83C2311yescharacteristic
117C22×C8×C83C2311yescharacteristic
118C22×C8×C83C2311yescharacteristic
119C2×C4⋊C4×C83C2×C411yescharacteristic
120C2×C4⋊C4×C83C2×C411yescharacteristic
121C2×C42×C83C2311yescharacteristic
122C2×C42×C83C2311yescharacteristic
123C2×C42×C83C2311yescharacteristic
124C4⋊C8×C83—22no—
125C4⋊C8×C83—41no—
126C4⋊C8×C83—41no—
127C4×C8×C83—22no—
128#95×C83C2×C411yescharacteristic
129#95×C83C2×C411yescharacteristic
130C23×D83C22×C411yescharacteristic
131C22×Dic83C22×C411yescharacteristic
132C22×Dic83C22×C411yescharacteristic
133C22×Dic83C22×C411yescharacteristic
134C22×Dic83C22×C411yescharacteristic
135C22×Dic83C22×C411yescharacteristic
136C22×Dic83C22×C411yescharacteristic
137C22×Dic83C22×C411yescharacteristic
138C2×C4×D83—21no—
139C2×C4×D83—21no—
140C2×C4×D83—21no—
141C2×C4×D83—21no—
142C2×C4×D83—22no—
143C2×C4×D83—22no—
144C2×C4×D83—41no—
145C2×C4×D83—41no—
146C2×C4×D83—41no—
147C2×C4×D83—41no—
148C2×C4×D83C2×D412yes—
149C2×C4×D83C2×Q812yes—
150C2×C83⋊C8—21no—
151C2×C83⋊C8—21no—
152C2×C83⋊C8—21no—
153C2×C83⋊C8—21no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C4⋊Dic83—22no—
163C4⋊Dic83—41no—
164Dic83⋊C4—22no—
165Dic83⋊C4—22no—
166Dic83⋊C4—41no—
167Dic83⋊C4—41no—
168Dic83⋊C4—41no—
169Dic83⋊C4—41no—
170Dic83⋊C4C4⋊C414yes—
171Dic83⋊C4C4⋊C414yes—
172(C2×D83)⋊C4—41no—
173(C2×D83)⋊C4—41no—
174(C2×D83)⋊C4C4⋊C414yes—
175(C2×D83)⋊C4C4⋊C414yes—
176C4×Dic83—21no—
177C4×Dic83—21no—
178C4×Dic83—21no—
179C4×Dic83—21no—
180C4×Dic83—41no—
181C4×Dic83—41no—
182C4×Dic83C2×D412yes—
183C4×Dic83C2×Q812yes—
184C22×C4×C83C22×C411yescharacteristic
185C22×C4×C83C22×C411yescharacteristic
186C22×C4×C83C22×C411yescharacteristic
187C22×C4×C83C22×C411yescharacteristic
188C22×C4×C83C22×C411yescharacteristic
189C22×C4×C83C22×C411yescharacteristic
190C22×C4×C83C2411yescharacteristic
191C2×C8×C83—21no—
192C2×C8×C83—21no—
193C2×C8×C83—21no—
194C2×C8×C83—21no—
195C2×C8×C83—21no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83—21no—
199C2×C8×C83—21no—
200C2×C8×C83—21no—
201C2×C8×C83—21no—
202C2×C8×C83—21no—
203C4⋊C4×C83—22no—
204C4⋊C4×C83—41no—
205C42×C83—21no—
206C42×C83—21no—
207C42×C83—21no—
208C42×C83—21no—
209C42×C83C2×D412yes—
210C42×C83C2×Q812yes—
211C23×C83C23×C411yescharacteristic
212C22×D83—21no—
213C22×D83—21no—
214C22×D83—21no—
215C22×D83—21no—
216C22×D83—21no—
217C22×D83—21no—
218C22×D83C2×C4⋊C412yes—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—21no—
225C2×C4×C83—21no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—21no—
232C2×C4×C83—21no—
233C2×C4×C83—21no—
234C2×C4×C83C2×C4⋊C412yes—
235C2×C4×C83C2×C4⋊C412yes—
236C2×C4×C83#13112yes—
237C2×C4×C83C22×D411yescharacteristic
238C2×C4×C83C22×Q811yescharacteristic
239C2×C4×C83H(5,𝔽2)11yescharacteristic
240C2×C4×C83H(5,𝔽2)11yescharacteristic
241C2×C4×C832−1+411yescharacteristic
242C2×C4×C832−1+411yescharacteristic
243C2×Dic83—21no—
244C2×Dic83—21no—
245C2×Dic83—21no—
246C2×Dic83—21no—
247C2×Dic83—21no—
248C2×Dic83—21no—
249C2×Dic83—21no—
250C2×Dic83—21no—
251C2×Dic83—21no—
252C2×Dic83—21no—
253C2×Dic83—21no—
254C2×Dic83—21no—
255C2×Dic83—21no—
256C2×Dic83—21no—
257C2×Dic83—21no—
258C2×Dic83—21no—
259C2×Dic83—21no—
260C2×Dic83C2×C4⋊C412yes—
261C2×Dic83C2×C4⋊C412yes—
262C2×Dic83C2×C4⋊C412yes—
263C2×Dic83#13112yes—
264C4×D83—22no—
265C4×D83—22no—
266C4×D83—22no—
267C4×D83—22no—
268C4×D83—44no—
269C4×D83—44no—
270C8×C83—41no—
271C8×C83—41no—
272C8×C83—41no—
273C8×C83—41no—
274C83⋊C8—41no—
275C83⋊C8—41no—
276C83⋊C8—41no—
277C83⋊C8—41no—
278C22×C83C22×C4⋊C411yescharacteristic
279C22×C83#51811yescharacteristic
280C22×C83#51911yescharacteristic
281C22×C83C2×#13111yescharacteristic
282C22×C83C2×#13111yescharacteristic
283C22×C83#56811yescharacteristic
284C22×C83#56811yescharacteristic
285C2×D83—22no—
286C2×D83—22no—
287C2×D83—22no—
288C2×D83—41no—
289C2×D83—41no—
290C2×D83—41no—
291C2×D83—41no—
292C4×C83—22no—
293C4×C83—22no—
294C4×C83—22no—
295C4×C83—41no—
296C4×C83—41no—
297C4×C83—41no—
298C4×C83#53711yescharacteristic
299C4×C83#53711yescharacteristic
300C4×C83#54411yescharacteristic
301C4×C83#54411yescharacteristic
302Dic83—22no—
303Dic83—22no—
304Dic83—22no—
305Dic83—22no—
306Dic83—41no—
307Dic83—41no—
308Dic83—41no—
309#21958—831nomaximal, Sylow
310C2×C83#231611yescharacteristic
311C2×C83#290611yescharacteristic
312C2×C83#290611yescharacteristic
313C2×C83#297711yescharacteristic
314C2×C83#297811yescharacteristic
315C2×C83#298511yescharacteristic
316C2×C83#298511yescharacteristic
317D83—42no—
318C2×#433—831no—
319C2×#433—831no—
320#2296—831no—
321#1940—831no—
322#1940—831no—
323#1940—831no—
324#1940—831no—
325#1939—831no—
326#1939—831no—
327#1939—831no—
328#1939D8311yescharacteristic, complemented
329#1798—831no—
330#1798—831no—
331#1797—831no—
332#1797—831no—
333C83#2195811yescharacteristic, complemented, Sylow
334C2×#117—831no—
335C2×#117—831no—
336C22×C42—831no—
337#433—1664no—
338#433—1664no—
339C2×C4⋊C8—831no—
340C2×C4⋊C8—831no—
341C2×C4⋊C8—831no—
342C2×C4⋊C8—831no—
343C2×C4⋊C8—831no—
344C2×C4⋊C8—831no—
345C2×C4⋊C8—831no—
346C2×C4⋊C8—831no—
347C2×C4⋊C8—831no—
348C2×C4⋊C8C2×D8311yescharacteristic
349C2×C4⋊C8C2×D8311yescharacteristic
350C2×C4⋊C8C2×D8311yescharacteristic
351C2×C22⋊C8—831no—
352C2×C22⋊C8—831no—
353C2×C22⋊C8—831no—
354C2×C22⋊C8—831no—
355C2×#97—831no—
356C2×#97—831no—
357C2×C4×C8—831no—
358C2×C4×C8C2×D8311yescharacteristic
359#389—831no—
360#389—831no—
361#389—831no—
362#389—831no—
363#385—831no—
364#385—831no—
365#385—831no—
366#385—831no—
367C4×C4⋊C4—831no—
368C4×C4⋊C4—831no—
369C4×C4⋊C4—831no—
370C4×C4⋊C4C2×D8311yescharacteristic
371#336—831no—
372#336—831no—
373#336—831no—
374#336—831no—
375#336—831no—
376#336—831no—
377#336C2×D8311yescharacteristic
378#336C2×D8311yescharacteristic
379C23×C4—831no—
380C23×C4—831no—
381C23×C4—831no—
382C22×C8—831no—
383C22×C8—831no—
384C22×C8—831no—
385C22×C8—831no—
386C22×C8C22×D8311yescharacteristic
387C22×C8C22×D8311yescharacteristic
388C22×C8C22×D8311yescharacteristic
389C22×C8C22×D8311yescharacteristic
390#117—3321no—
391#117—3321no—
392#117—834no—
393#117—834no—
394C2×C4⋊C4—831no—
395C2×C4⋊C4—831no—
396C2×C4⋊C4—831no—
397C2×C4⋊C4—831no—
398C2×C4⋊C4—831no—
399C2×C4⋊C4—831no—
400C2×C4⋊C4—831no—
401C2×C4⋊C4—831no—
402C2×C4⋊C4—831no—
403C2×C4⋊C4—831no—
404C2×C4⋊C4C4×D8311yescharacteristic
405C2×C4⋊C4C4×D8311yescharacteristic
406C2×C22⋊C4—831no—
407C2×C22⋊C4—831no—
408C2×C22⋊C4—831no—
409C2×C22⋊C4—831no—
410C2×C42—3321no—
411C2×C42—3321no—
412C2×C42—831no—
413C2×C42—831no—
414C2×C42—831no—
415C2×C42—831no—
416C2×C42—831no—
417C2×C42C22×D8311yescharacteristic
418C2×C42C22×D8311yescharacteristic
419C2×C42C22×D8311yescharacteristic
420C4⋊C8—22no—
421C4⋊C8—41no—
422C4⋊C8—41no—
423C4⋊C8—3321no—
424C4⋊C8—3321no—
425C4⋊C8—3321no—
426C4⋊C8—3321no—
427C4⋊C8—3321no—
428C4⋊C8—3321no—
429C4⋊C8—1662no—
430C4⋊C8—1662no—
431C4⋊C8—1662no—
432C22⋊C8—1662no—
433C22⋊C8—1662no—
434C22⋊C8—1662no—
435C22⋊C8—1662no—
436#97—1662no—
437#97—1662no—
438C4×C8—22no—
439C4×C8—1662no—
440#95—831no—
441#95—831no—
442#95—831no—
443#95—831no—
444#95—831no—
445#95—831no—
446#95C4×D8311yescharacteristic
447#95C4×D8311yescharacteristic
448C24—831no—
449C22×C4—3321no—
450C22×C4—3321no—
451C22×C4—3321no—
452C22×C4—3321no—
453C22×C4—831no—
454C22×C4—831no—
455C22×C4—831no—
456C22×C4—831no—
457C22×C4—832no—
458C22×C4—832no—
459C22×C4—831no—
460C22×C4—831no—
461C22×C4—831no—
462C22×C4—1662no—
463C22×C4—1662no—
464C22×C4—1661no—
465C22×C4—1661no—
466C22×C4—1661no—
467C22×C4—1661no—
468C22×C4C2×C4×D8311yescharacteristic
469C22×C4C2×C4×D8311yescharacteristic
470C22×C4C2×C4×D8311yescharacteristic
471C22×C4C2×C4×D8311yescharacteristic
472C22×C4C2×C4×D8311yescharacteristic
473C22×C4C2×C4×D8311yescharacteristic
474C22×C4C23×D8311yescharacteristic
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—1661no—
488C2×C8—1661no—
489C2×C8—1661no—
490C2×C8—1661no—
491C2×C8—1661no—
492C2×C8—1661no—
493C2×C8—1661no—
494C2×C8—1661no—
495C2×C8—1661no—
496C2×C8—1661no—
497C2×C8—1661no—
498C2×C8—1661no—
499C4⋊C4—22no—
500C4⋊C4—41no—
501C4⋊C4—3321no—
502C4⋊C4—3321no—
503C4⋊C4—3321no—
504C4⋊C4—3321no—
505C4⋊C4—3321no—
506C4⋊C4—834no—
507C4⋊C4—834no—
508C4⋊C4—1662no—
509C4⋊C4—1662no—
510C4⋊C4—1662no—
511C22⋊C4—3321no—
512C22⋊C4—3321no—
513C22⋊C4—834no—
514C22⋊C4—834no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—3321no—
520C42—3321no—
521C42—832no—
522C42—832no—
523C42—1661no—
524C42—1661no—
525C42—1661no—
526C42—1661no—
527C42D4×D8312yes—
528C42Q8×D8312yes—
529C23—832no—
530C23—1661no—
531C23—1661no—
532C23—1661no—
533C23—1661no—
534C23—1661no—
535C23—1661no—
536C23C22×C4×D8311yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—3324no—
553C2×C4—3324no—
554C2×C4—832no—
555C2×C4—832no—
556C2×C4—832no—
557C2×C4—832no—
558C2×C4—1661no—
559C2×C4—1661no—
560C2×C4—1661no—
561C2×C4—1661no—
562C2×C4—1661no—
563C2×C4—1661no—
564C2×C4—1661no—
565C2×C4—1661no—
566C2×C4—1661no—
567C2×C4—1661no—
568C2×C4—1661no—
569C2×C4—1661no—
570C2×C4—1661no—
571C2×C4—1661no—
572C2×C4—1661no—
573C2×C4—1661no—
574C2×C4—1661no—
575C2×C4—1662no—
576C2×C4—1662no—
577C2×C4—1662no—
578C2×C4—1662no—
579C2×C4C4⋊C4×D8312yes—
580C2×C4C4⋊C4×D8312yes—
581C2×C4#1458179812yes—
582C2×C4C2×D4×D8311yescharacteristic
583C2×C4C2×Q8×D8311yescharacteristic
584C2×C4#1458183711yescharacteristic
585C2×C4#1458183811yescharacteristic
586C2×C4#1458183911yescharacteristic
587C2×C4#1458184011yescharacteristic
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—3321no—
593C8—3321no—
594C8—3321no—
595C8—3321no—
596C22—3321no—
597C22—3321no—
598C22—3321no—
599C22—3321no—
600C22—1662no—
601C22—1662no—
602C22—1662no—
603C22C2×C4⋊C4×D8311yescharacteristic
604C22#1912817311yescharacteristic
605C22#1912817711yescharacteristic
606C22#131×D8311yescharacteristic
607C22C2×#1458179811yescharacteristic
608C22#1912846611yescharacteristic
609C22#1912846711yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—3321no—
617C4—3321no—
618C4—3321no—
619C4—1662no—
620C4—1662no—
621C4—1662no—
622C4—1662no—
623C4#1912828011yescharacteristic
624C4#1912828111yescharacteristic
625C4#1912832811yescharacteristic
626C4#1912833111yescharacteristic
627C2—3322no—
628C2#2491007811yescharacteristic
629C2#2491602811yescharacteristic
630C2#2491603011yescharacteristic
631C2#2491651611yescharacteristic
632C2#2491652011yescharacteristic
633C2#2491655411yescharacteristic
634C2#2491655611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1939C2
prime radicalC23×D83C22×C4
cosocleC22×C4×C83C24
hypercenter#1939D83
hypocenterC83#21958
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
4. #24908187C2semidirect
5. #24908185C2semidirect
6. #24908184C2semidirect
7. #24908183C2semidirect
8. #24908181C2semidirect
9. #24908180C2semidirect
10. #24908178C2semidirect
15. C83×#1939C2semidirect
328. #1939D83semidirect
333. C83#21958semidirect

Maximal subgroups

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

subgroupindex
C2×#191277612
C2×#191277602
#249099432
#249081872
#249081852
#249081842
#249081832
#249081812
#249081802
#249081782
#249074462
#249074442
#249074422
#249074402
C83×#19392
#2195883