Finite Group Databasebeta

← #35373298

Subgroups — #35373298

Order 21248.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916588C211yesmaximal, characteristic, complemented
2#24916588C211yesmaximal, characteristic, complemented
3#24906193C211yesmaximal, characteristic, complemented
4#24906185C211yesmaximal, characteristic, complemented
5#24906180C211yesmaximal, characteristic, complemented
6#24906173C211yesmaximal, characteristic, complemented
7#24906168C211yesmaximal, characteristic, complemented
8#24906158C211yesmaximal, characteristic, complemented
9#24906158C211yesmaximal, characteristic, complemented
10#24906153C211yesmaximal, characteristic, complemented
11#24906140C211yesmaximal, characteristic, complemented
12#24906120C211yesmaximal, characteristic, complemented
13#24906112C211yesmaximal, characteristic, complemented
14C2×#19127447C211yesmaximal, characteristic, complemented
15C83×#3511C211yesmaximal, characteristic
16#19127832—21no—
17#19127832—21no—
18#19127773—21no—
19#19127773—21no—
20#19127773—21no—
21#19127773—21no—
22D4×C83⋊C8—21no—
23D4×C83⋊C8—21no—
24#19127758C2211yescharacteristic
25#19127758C2211yescharacteristic
26#19127758C2211yescharacteristic
27#19127758C2211yescharacteristic
28#19127754C2211yescharacteristic
29#19127754C2211yescharacteristic
30#19127725C2211yescharacteristic
31#19127725C2211yescharacteristic
32C2×C4⋊(C83⋊C8)C2211yescharacteristic
33C2×C4⋊(C83⋊C8)C2211yescharacteristic
34C2×C4⋊(C83⋊C8)C2211yescharacteristic
35C2×C4⋊(C83⋊C8)C2211yescharacteristic
36#19127450C2211yescharacteristic
37#19127450C2211yescharacteristic
38#19127450C2211yescharacteristic
39#19127450C2211yescharacteristic
40#19127447C2211yescharacteristic
41#19127447C2211yescharacteristic
42#19127447C2211yescharacteristic
43#19127447C2211yescharacteristic
44#19127447C2211yescharacteristic
45#19127447C2211yescharacteristic
46#19127447C2211yescharacteristic
47#19127447C2211yescharacteristic
48#19127445C2211yescharacteristic
49#19127445C2211yescharacteristic
50#19127445C2211yescharacteristic
51#19127445C2211yescharacteristic
52#556×C83—21no—
53#555×C83—21no—
54#554×C83—21no—
55#553×C83—21no—
56#553×C83—21no—
57#548×C83—21no—
58#548×C83—21no—
59#547×C83—21no—
60#542×C83C412yes—
61#542×C83C412yes—
62#537×C83C412yes—
63#533×C83C2211yescharacteristic
64#533×C83C2211yescharacteristic
65#532×C83C2211yescharacteristic
66#532×C83C2211yescharacteristic
67#532×C83C2211yescharacteristic
68C2×C4⋊Q8×C83C2211yescharacteristic
69#520×C83C412yes—
70C4×#41×C83C2211yescharacteristic
71C2×#13050574—21no—
72C2×#13050574—21no—
73C22×C83⋊C8—21no—
74C22×C83⋊C8—21no—
75C22×C83⋊C8—21no—
76C22×C83⋊C8—21no—
77C4⋊(C83⋊C8)—21no—
78C4⋊(C83⋊C8)—21no—
79C4⋊(C83⋊C8)—21no—
80C4⋊(C83⋊C8)—21no—
81C4⋊(C83⋊C8)—21no—
82C4⋊(C83⋊C8)—21no—
83C4⋊(C83⋊C8)C2311yescharacteristic
84C4⋊(C83⋊C8)C2311yescharacteristic
85C4⋊(C83⋊C8)C2311yescharacteristic
86C4⋊(C83⋊C8)C2311yescharacteristic
87C4⋊(C83⋊C8)C2311yescharacteristic
88C4⋊(C83⋊C8)C2311yescharacteristic
89C4⋊(C83⋊C8)C2311yescharacteristic
90C4⋊(C83⋊C8)C2311yescharacteristic
91C22⋊(C83⋊C8)—21no—
92C22⋊(C83⋊C8)—21no—
93C22⋊(C83⋊C8)—21no—
94C22⋊(C83⋊C8)—21no—
95C22⋊(C83⋊C8)—21no—
96C22⋊(C83⋊C8)—21no—
97#14581703—21no—
98#14581703—21no—
99#14581703—21no—
100#14581703—21no—
101C4×C83⋊C8—21no—
102C4×C83⋊C8—21no—
103C2×#41×C83—21no—
104C2×#41×C83—21no—
105C2×#41×C83C2×C412yes—
106C2×#41×C83C2×C411yescharacteristic
107C22×Q8×C83—21no—
108C4⋊Q8×C83—21no—
109C4⋊Q8×C83—21no—
110C4⋊Q8×C83C2×C412yes—
111C4⋊Q8×C83C2311yescharacteristic
112C4⋊Q8×C83C2311yescharacteristic
113C4⋊Q8×C83C2311yescharacteristic
114#127×C83C2311yescharacteristic
115#126×C83—22no—
116#126×C83—22no—
117#125×C83—21no—
118#125×C83—21no—
119#124×C83—22no—
120#124×C83—22no—
121#124×C83—21no—
122#124×C83—21no—
123#124×C83C2×C412yes—
124#123×C83—22no—
125#123×C83—22no—
126C22⋊Q8×C83—22no—
127C22⋊Q8×C83—21no—
128C22⋊Q8×C83—21no—
129C22⋊Q8×C83—22no—
130C22⋊Q8×C83—22no—
131C22⋊Q8×C83C2×C412yes—
132C22⋊Q8×C83C2×C412yes—
133#121×C83—22no—
134#121×C83—22no—
135#121×C83—22no—
136#121×C83—21no—
137#121×C83—21no—
138#121×C83—21no—
139#121×C83—21no—
140#121×C83C2×C412yes—
141#121×C83C2×C412yes—
142C4×Q8×C83—21no—
143C4×Q8×C83—21no—
144C4×Q8×C83C2×C412yes—
145C4×Q8×C83C2×C412yes—
146C4×Q8×C83D411yescharacteristic
147C4×Q8×C83D411yescharacteristic
148C4×D4×C83—22no—
149C4×D4×C83—22no—
150C4×D4×C83—21no—
151C4×D4×C83—21no—
152C4×D4×C83—21no—
153C4×D4×C83—21no—
154C4×D4×C83C2×C412yes—
155C4×D4×C83C2×C412yes—
156C4×D4×C83D411yescharacteristic
157C4×D4×C83D411yescharacteristic
158C4×D4×C83D411yescharacteristic
159C4×D4×C83D411yescharacteristic
160C4×D4×C83D411yescharacteristic
161C4×D4×C83D411yescharacteristic
162#117×C83—21no—
163#117×C83—21no—
164#117×C83—22no—
165#117×C83C2×C411yescharacteristic
166#117×C83C2×C411yescharacteristic
167#117×C83C2×C411yescharacteristic
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83—22no—
170C2×C4⋊C4×C83C2×C412yes—
171C2×C42×C83C2311yescharacteristic
172C2×C42×C83C2311yescharacteristic
173C2×C42×C83C2311yescharacteristic
174#13050574—81no—
175#13050574—81no—
176C2×C83⋊C8—21no—
177C2×C83⋊C8—21no—
178C2×C83⋊C8—21no—
179C2×C83⋊C8—21no—
180C2×C83⋊C8—21no—
181C2×C83⋊C8—21no—
182C2×C83⋊C8—21no—
183C2×C83⋊C8—21no—
184C2×C83⋊C8—81no—
185C2×C83⋊C8—81no—
186C2×C83⋊C8—81no—
187C2×C83⋊C8—81no—
188#41×C83—42no—
189#41×C83—44no—
190#41×C83—81no—
191#41×C83—81no—
192#41×C83—81no—
193#41×C83—81no—
194C2×Q8×C83—22no—
195C2×Q8×C83—21no—
196C2×Q8×C83—21no—
197C2×Q8×C83—81no—
198C2×Q8×C83—81no—
199C2×Q8×C83C22⋊C411yescharacteristic
200C2×Q8×C83C22×C412yes—
201C2×D4×C83—22no—
202C2×D4×C83—22no—
203C2×D4×C83—22no—
204C2×D4×C83—21no—
205C2×D4×C83—21no—
206C2×D4×C83C22⋊C411yescharacteristic
207C2×D4×C83C22⋊C411yescharacteristic
208C2×D4×C83C22⋊C411yescharacteristic
209C2×D4×C83C22×C412yes—
210C22×C4×C83—22no—
211C22×C4×C83—22no—
212C22×C4×C83—22no—
213C22×C4×C83—22no—
214C22×C4×C83C22×C411yescharacteristic
215C22×C4×C83C22×C411yescharacteristic
216C22×C4×C83C22×C411yescharacteristic
217C22×C4×C83C2×D411yescharacteristic
218C22×C4×C83C2×D411yescharacteristic
219C22×C4×C83C2×D411yescharacteristic
220C22×C4×C83C2×D411yescharacteristic
221C22×C4×C83C2×D411yescharacteristic
222C22×C4×C83C2×D411yescharacteristic
223C4⋊C4×C83—22no—
224C4⋊C4×C83—22no—
225C4⋊C4×C83—22no—
226C4⋊C4×C83—22no—
227C4⋊C4×C83—22no—
228C4⋊C4×C83—22no—
229C4⋊C4×C83—21no—
230C4⋊C4×C83—21no—
231C4⋊C4×C83—21no—
232C4⋊C4×C83—21no—
233C4⋊C4×C83C22⋊C411yescharacteristic
234C4⋊C4×C83C22⋊C411yescharacteristic
235C4⋊C4×C83C22⋊C411yescharacteristic
236C4⋊C4×C83C22⋊C411yescharacteristic
237C4⋊C4×C83C22⋊C411yescharacteristic
238C4⋊C4×C83C22⋊C411yescharacteristic
239C4⋊C4×C83C22×C412yes—
240C4⋊C4×C83C22×C412yes—
241C22⋊C4×C83—22no—
242C22⋊C4×C83—22no—
243C22⋊C4×C83—22no—
244C22⋊C4×C83—22no—
245C22⋊C4×C83—22no—
246C22⋊C4×C83—22no—
247C22⋊C4×C83—22no—
248C22⋊C4×C83—22no—
249C22⋊C4×C83C22⋊C411yescharacteristic
250C22⋊C4×C83C22⋊C411yescharacteristic
251C22⋊C4×C83C22⋊C411yescharacteristic
252C22⋊C4×C83C22⋊C411yescharacteristic
253C22⋊C4×C83C22⋊C411yescharacteristic
254C22⋊C4×C83C22⋊C411yescharacteristic
255C42×C83—22no—
256C42×C83—22no—
257C42×C83C22×C411yescharacteristic
258C42×C83C22×C411yescharacteristic
259C42×C83C22×C411yescharacteristic
260C42×C83C2×D411yescharacteristic
261C42×C83C2×D411yescharacteristic
262C42×C83C2×D411yescharacteristic
263C42×C83C2×D411yescharacteristic
264C42×C83C2×D411yescharacteristic
265C42×C83C2×D411yescharacteristic
266C42×C83C2411yescharacteristic
267C23×C83—22no—
268C23×C83C2×C22⋊C411yescharacteristic
269C23×C83C2×C22⋊C411yescharacteristic
270C23×C83C2×C22⋊C411yescharacteristic
271Q8×C83—41no—
272Q8×C83—42no—
273Q8×C83—41no—
274Q8×C83—41no—
275Q8×C83—41no—
276Q8×C83—41no—
277Q8×C83—82no—
278D4×C83—22no—
279D4×C83—22no—
280D4×C83—41no—
281D4×C83—42no—
282D4×C83—44no—
283D4×C83—41no—
284D4×C83—41no—
285D4×C83—41no—
286D4×C83—41no—
287D4×C83—82no—
288D4×C83—82no—
289C2×C4×C83—22no—
290C2×C4×C83—21no—
291C2×C4×C83—21no—
292C2×C4×C83—21no—
293C2×C4×C83—21no—
294C2×C4×C83—21no—
295C2×C4×C83—21no—
296C2×C4×C83—21no—
297C2×C4×C83—21no—
298C2×C4×C83—21no—
299C2×C4×C83—21no—
300C2×C4×C83—21no—
301C2×C4×C83—21no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—22no—
305C2×C4×C83—41no—
306C2×C4×C83—41no—
307C2×C4×C83—44no—
308C2×C4×C83—82no—
309C2×C4×C83—82no—
310C2×C4×C83—82no—
311C2×C4×C83C2×C22⋊C411yescharacteristic
312C2×C4×C83C2×C22⋊C411yescharacteristic
313C2×C4×C83C2×C22⋊C411yescharacteristic
314C2×C4×C83C2×C22⋊C411yescharacteristic
315C2×C4×C83C2×C22⋊C411yescharacteristic
316C2×C4×C83C2×C22⋊C411yescharacteristic
317C2×C4×C83C2×C22⋊C411yescharacteristic
318C2×C4×C83C2×C22⋊C411yescharacteristic
319C2×C4×C83C2×C22⋊C411yescharacteristic
320C2×C4×C83C23×C411yescharacteristic
321C2×C4×C83C22×D411yescharacteristic
322C2×C4×C83C22×D411yescharacteristic
323C83⋊C8—41no—
324C83⋊C8—41no—
325C83⋊C8—41no—
326C83⋊C8—41no—
327C83⋊C8—41no—
328C83⋊C8—41no—
329C83⋊C8—41no—
330C83⋊C8—41no—
331C22×C83—21no—
332C22×C83—21no—
333C22×C83—21no—
334C22×C83—21no—
335C22×C83—21no—
336C22×C83—21no—
337C22×C83—21no—
338C22×C83—21no—
339C22×C83—42no—
340C22×C83—42no—
341C22×C83—42no—
342C22×C83#41312yes—
343C22×C83C22×C22⋊C411yescharacteristic
344C4×C83—21no—
345C4×C83—21no—
346C4×C83—21no—
347C4×C83—21no—
348C4×C83—21no—
349C4×C83—21no—
350C4×C83—21no—
351C4×C83—21no—
352C4×C83—21no—
353C4×C83—21no—
354C4×C83—42no—
355C4×C83—42no—
356C4×C83—42no—
357C4×C83#57611yescharacteristic
358C4×C83#57711yescharacteristic
359C4×C83#57711yescharacteristic
360C4×C83#57811yescharacteristic
361#17775—831nomaximal, Sylow
362C2×C83—22no—
363C2×C83—41no—
364C2×C83—41no—
365C2×C83—82no—
366C2×C83C2×#41311yescharacteristic
367C2×C83#289711yescharacteristic
368C2×C83#289811yescharacteristic
369#3511D8311yescharacteristic
370#2990—831no—
371#2990—831no—
372#1559—831no—
373#1557—831no—
374#1556—831no—
375#1554—831no—
376#1553—831no—
377#1551—831no—
378#1551—831no—
379#1550—831no—
380#1547—831no—
381#1542—831no—
382#1540—831no—
383C2×#332—831no—
384C83#1777511yescharacteristic, complemented, Sylow
385#556—21no—
386#555—21no—
387#554—21no—
388#553—21no—
389#553—21no—
390#548—21no—
391#548—21no—
392#547—21no—
393#542Dic8312yes—
394#542Dic8312yes—
395#537Dic8312yes—
396#533C2×D8311yescharacteristic
397#533C2×D8311yescharacteristic
398#532C2×D8311yescharacteristic
399#532C2×D8311yescharacteristic
400#532C2×D8311yescharacteristic
401C2×C4⋊Q8C2×D8311yescharacteristic
402#520Dic8312yes—
403C4×#41C2×D8311yescharacteristic
404#446—1661no—
405#446—1661no—
406#435—1661no—
407#435—1661no—
408#435—1661no—
409#435—1661no—
410C8×D4—1661no—
411C8×D4—1661no—
412#432—831no—
413#432—831no—
414#432—831no—
415#432—831no—
416#431—831no—
417#431—831no—
418#423—831no—
419#423—831no—
420C2×C4⋊C8—831no—
421C2×C4⋊C8—831no—
422C2×C4⋊C8—831no—
423C2×C4⋊C8—831no—
424#333—831no—
425#333—831no—
426#333—831no—
427#333—831no—
428#332—831no—
429#332—831no—
430#332—831no—
431#332—831no—
432#332—831no—
433#332—831no—
434#332—831no—
435#332—831no—
436#331—831no—
437#331—831no—
438#331—831no—
439#331—831no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41C2×Dic8312yes—
443C2×#41C2×Dic8311yescharacteristic
444C22×Q8—21no—
445C2×M16—1661no—
446C2×M16—1661no—
447C22×C8—1661no—
448C22×C8—1661no—
449C22×C8—1661no—
450C22×C8—1661no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8C2×Dic8312yes—
454C4⋊Q8C22×D8311yescharacteristic
455C4⋊Q8C22×D8311yescharacteristic
456C4⋊Q8C22×D8311yescharacteristic
457#127C22×D8311yescharacteristic
458#126—22no—
459#126—22no—
460#125—21no—
461#125—21no—
462#124—22no—
463#124—22no—
464#124—21no—
465#124—21no—
466#124C2×Dic8312yes—
467#123—22no—
468#123—22no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8C2×Dic8312yes—
475C22⋊Q8C2×Dic8312yes—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121C2×Dic8312yes—
484#121C2×Dic8312yes—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8C2×Dic8312yes—
488C4×Q8C2×Dic8312yes—
489C4×Q8C22⋊D8311yescharacteristic
490C4×Q8C22⋊D8311yescharacteristic
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4C2×Dic8312yes—
498C4×D4C2×Dic8312yes—
499C4×D4C22⋊D8311yescharacteristic
500C4×D4C22⋊D8311yescharacteristic
501C4×D4C22⋊D8311yescharacteristic
502C4×D4C22⋊D8311yescharacteristic
503C4×D4C22⋊D8311yescharacteristic
504C4×D4C22⋊D8311yescharacteristic
505#117—21no—
506#117—21no—
507#117—22no—
508#117C2×Dic8311yescharacteristic
509#117C2×Dic8311yescharacteristic
510#117C2×Dic8311yescharacteristic
511C2×C4⋊C4—21no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4C2×Dic8312yes—
514C2×C42C22×D8311yescharacteristic
515C2×C42C22×D8311yescharacteristic
516C2×C42C22×D8311yescharacteristic
517C4⋊C8—831no—
518C4⋊C8—831no—
519C4⋊C8—831no—
520C4⋊C8—831no—
521C4⋊C8—831no—
522C4⋊C8—831no—
523C4⋊C8—831no—
524C4⋊C8—831no—
525C4⋊C8—1661no—
526C4⋊C8—1661no—
527C4⋊C8—1661no—
528C4⋊C8—1661no—
529C4⋊C8—1661no—
530C4⋊C8—1661no—
531C22⋊C8—1661no—
532C22⋊C8—1661no—
533C22⋊C8—1661no—
534C22⋊C8—1661no—
535C22⋊C8—1661no—
536C22⋊C8—1661no—
537#97—1661no—
538#97—1661no—
539#97—1661no—
540#97—1661no—
541C4×C8—1661no—
542C4×C8—1661no—
543#41—42no—
544#41—44no—
545#41—81no—
546#41—81no—
547#41—81no—
548#41—81no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—81no—
553C2×Q8—81no—
554C2×Q8C22⋊Dic8311yescharacteristic
555C2×Q8C22×Dic8312yes—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4C22⋊Dic8311yescharacteristic
562C2×D4C22⋊Dic8311yescharacteristic
563C2×D4C22⋊Dic8311yescharacteristic
564C2×D4C22×Dic8312yes—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4C22×Dic8311yescharacteristic
570C22×C4C22×Dic8311yescharacteristic
571C22×C4C22×Dic8311yescharacteristic
572C22×C4C2×C22⋊D8311yescharacteristic
573C22×C4C2×C22⋊D8311yescharacteristic
574C22×C4C2×C22⋊D8311yescharacteristic
575C22×C4C2×C22⋊D8311yescharacteristic
576C22×C4C2×C22⋊D8311yescharacteristic
577C22×C4C2×C22⋊D8311yescharacteristic
578M16—6641no—
579M16—6641no—
580C2×C8—6641no—
581C2×C8—6641no—
582C2×C8—6641no—
583C2×C8—6641no—
584C2×C8—1661no—
585C2×C8—1661no—
586C2×C8—1661no—
587C2×C8—1661no—
588C2×C8—1661no—
589C2×C8—1661no—
590C2×C8—1661no—
591C2×C8—1661no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4C22⋊Dic8311yescharacteristic
603C4⋊C4C22⋊Dic8311yescharacteristic
604C4⋊C4C22⋊Dic8311yescharacteristic
605C4⋊C4C22⋊Dic8311yescharacteristic
606C4⋊C4C22⋊Dic8311yescharacteristic
607C4⋊C4C22⋊Dic8311yescharacteristic
608C4⋊C4C22×Dic8312yes—
609C4⋊C4C22×Dic8312yes—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4C22⋊Dic8311yescharacteristic
619C22⋊C4C22⋊Dic8311yescharacteristic
620C22⋊C4C22⋊Dic8311yescharacteristic
621C22⋊C4C22⋊Dic8311yescharacteristic
622C22⋊C4C22⋊Dic8311yescharacteristic
623C22⋊C4C22⋊Dic8311yescharacteristic
624C42—22no—
625C42—22no—
626C42C22×Dic8311yescharacteristic
627C42C22×Dic8311yescharacteristic
628C42C22×Dic8311yescharacteristic
629C42C2×C22⋊D8311yescharacteristic
630C42C2×C22⋊D8311yescharacteristic
631C42C2×C22⋊D8311yescharacteristic
632C42C2×C22⋊D8311yescharacteristic
633C42C2×C22⋊D8311yescharacteristic
634C42C2×C22⋊D8311yescharacteristic
635C42C23×D8311yescharacteristic
636C23—22no—
637C23C2×C22⋊Dic8311yescharacteristic
638C23C2×C22⋊Dic8311yescharacteristic
639C23C2×C22⋊Dic8311yescharacteristic
640Q8—41no—
641Q8—42no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—82no—
647D4—22no—
648D4—22no—
649D4—41no—
650D4—42no—
651D4—44no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—82no—
657D4—82no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—44no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4C2×C22⋊Dic8311yescharacteristic
681C2×C4C2×C22⋊Dic8311yescharacteristic
682C2×C4C2×C22⋊Dic8311yescharacteristic
683C2×C4C2×C22⋊Dic8311yescharacteristic
684C2×C4C2×C22⋊Dic8311yescharacteristic
685C2×C4C2×C22⋊Dic8311yescharacteristic
686C2×C4C2×C22⋊Dic8311yescharacteristic
687C2×C4C2×C22⋊Dic8311yescharacteristic
688C2×C4C2×C22⋊Dic8311yescharacteristic
689C2×C4C23×Dic8311yescharacteristic
690C2×C4C22×C22⋊D8311yescharacteristic
691C2×C4C22×C22⋊D8311yescharacteristic
692C8—3321no—
693C8—3321no—
694C8—3321no—
695C8—3321no—
696C8—3321no—
697C8—3321no—
698C8—3321no—
699C8—3321no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22#1912768512yes—
712C22C22×C22⋊Dic8311yescharacteristic
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4#1912850411yescharacteristic
727C4#1912850911yescharacteristic
728C4#1912851211yescharacteristic
729C4#1912851611yescharacteristic
730C2—22no—
731C2—41no—
732C2—41no—
733C2—82no—
734C2C2×#1912768511yescharacteristic
735C2#2491598911yescharacteristic
736C2#2491599611yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
Fitting, prime radicalC83×#3511C2
socleC22×C83C22×C22⋊C4
cosocleC42×C83C24
hypercenter#3511D83
hypocenterC83#17775
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #24916588C2semidirect
2. #24916588C2semidirect
3. #24906193C2semidirect
4. #24906185C2semidirect
5. #24906180C2semidirect
6. #24906173C2semidirect
7. #24906168C2semidirect
8. #24906158C2semidirect
9. #24906158C2semidirect
10. #24906153C2semidirect
11. #24906140C2semidirect
12. #24906120C2semidirect
13. #24906112C2semidirect
14. C2×#19127447C2semidirect
384. C83#17775semidirect

Maximal subgroups

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

subgroupindex
#249165882
#249061932
#249061852
#249061802
#249061732
#249061682
#249061582
#249061532
#249061402
#249061202
#249061122
C2×#191274472
C83×#35112
#1777583