Finite Group Databasebeta

← #35423435

Subgroups — #35423435

Order 21248.

984 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127751C211yesmaximal, characteristic, complemented
2C2×#19127723C211yesmaximal, characteristic, complemented
3C4×(C22⋊D83)⋊C4C211yesmaximal, characteristic
4#24908078C211yesmaximal, characteristic, complemented
5#24908023C211yesmaximal, characteristic, complemented
6#24908017C211yesmaximal, characteristic, complemented
7#24907757C211yesmaximal, characteristic
8#24907757C211yesmaximal, characteristic
9#24907578C211yesmaximal, characteristic, complemented
10#24907442C211yesmaximal, characteristic, complemented
11#24907441C211yesmaximal, characteristic, complemented
12#24907317C211yesmaximal, characteristic, complemented
13#24907248C211yesmaximal, characteristic, complemented
14#24907245C211yesmaximal, characteristic, complemented
15C83×#1924C211yesmaximal, characteristic, complemented
16C22×#13050573C2211yescharacteristic
17C22×#13050573C2211yescharacteristic
18C2×C4×C22⋊D83C2211yescharacteristic
19C2×(C22⋊D83)⋊C4C411yescharacteristic
20C2×(C22⋊D83)⋊C4C411yescharacteristic
21C22×C4×Dic83C2211yescharacteristic
22C2×C42×D83C2211yescharacteristic
23#19127751—24no—
24#19127723—24no—
25C2×C4⋊(C83⋊C8)C2211yescharacteristic
26C2×Dic83⋊C8C2211yescharacteristic
27C2×Dic83⋊C8C2211yescharacteristic
28C2×Dic83⋊C8C2211yescharacteristic
29C2×Dic83⋊C8C2211yescharacteristic
30C2×C22⋊(C83⋊C8)C2211yescharacteristic
31C2×C22⋊(C83⋊C8)C2211yescharacteristic
32C2×(C2×D83)⋊C8C2211yescharacteristic
33C2×(C2×D83)⋊C8C2211yescharacteristic
34C2×#14581703C2211yescharacteristic
35C2×C8×Dic83C2211yescharacteristic
36C2×C8×Dic83C2211yescharacteristic
37C4×Dic83⋊C4C2211yescharacteristic
38#19127552C411yescharacteristic
39#19127552C411yescharacteristic
40C22⋊C4×Dic83C411yescharacteristic
41C22⋊C4×Dic83C411yescharacteristic
42C4×(C2×D83)⋊C4C2211yescharacteristic
43#19127548C411yescharacteristic
44#19127548C411yescharacteristic
45C42×Dic83C2211yescharacteristic
46#19127456C2211yescharacteristic
47#19127456C2211yescharacteristic
48#19127455C2211yescharacteristic
49#19127455C2211yescharacteristic
50#19127455C2211yescharacteristic
51#19127455C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54C2×C4⋊C8×C83C2211yescharacteristic
55C2×C22⋊C8×C83C2211yescharacteristic
56C2×C22⋊C8×C83C2211yescharacteristic
57C2×#97×C83C2211yescharacteristic
58C4×C22⋊C4×C83C2211yescharacteristic
59#336×C83C2211yescharacteristic
60#336×C83C2211yescharacteristic
61C22×C22⋊D83C2×C411yescharacteristic
62C23×Dic83C2×C411yescharacteristic
63C23×Dic83C2×C411yescharacteristic
64C22×C4×D83C2×C411yescharacteristic
65C22×C4×D83C2×C411yescharacteristic
66C22×C4×D83C2311yescharacteristic
67C2×#13050573—22no—
68C2×#13050573—22no—
69C2×#13050573—22no—
70C2×#13050573—22no—
71C2×#13050573—41no—
72C2×#13050573—41no—
73C22×C83⋊C8C2311yescharacteristic
74C22×C83⋊C8C2311yescharacteristic
75C22×C83⋊C8C2311yescharacteristic
76C22×C83⋊C8C2311yescharacteristic
77C4×C22⋊D83—22no—
78C4×C22⋊D83—22no—
79(C22⋊D83)⋊C4—24no—
80(C22⋊D83)⋊C4—24no—
81C2×Dic83⋊C4C2×C411yescharacteristic
82C2×Dic83⋊C4C2×C411yescharacteristic
83C2×Dic83⋊C4C2×C411yescharacteristic
84C2×C22⋊Dic83C2×C411yescharacteristic
85C2×(C2×D83)⋊C4C2×C411yescharacteristic
86C2×(C2×D83)⋊C4C2×C411yescharacteristic
87C2×(C2×D83)⋊C4C2×C411yescharacteristic
88C2×C4×Dic83—22no—
89C2×C4×Dic83—22no—
90C2×C4×Dic83C2×C411yescharacteristic
91C2×C4×Dic83C2×C411yescharacteristic
92C2×C4×Dic83C2×C411yescharacteristic
93C2×C4×Dic83C2×C411yescharacteristic
94C2×C4×Dic83C2×C411yescharacteristic
95C2×C4×Dic83C2×C411yescharacteristic
96C2×C4×Dic83C2×C411yescharacteristic
97C2×C4×Dic83C2×C411yescharacteristic
98C2×C4×Dic83C2311yescharacteristic
99C2×C4×Dic83C2311yescharacteristic
100C2×C4×Dic83C2311yescharacteristic
101C42×D83—22no—
102C42×D83—22no—
103C4⋊(C83⋊C8)—22no—
104Dic83⋊C8—22no—
105Dic83⋊C8—22no—
106Dic83⋊C8—22no—
107Dic83⋊C8D414yescomplemented
108C22⋊(C83⋊C8)—22no—
109C22⋊(C83⋊C8)—41no—
110(C2×D83)⋊C8—22no—
111(C2×D83)⋊C8—22no—
112#14581703—41no—
113C8×Dic83—22no—
114C8×Dic83—22no—
115C83⋊#95C2×C411yescharacteristic
116C83⋊#95C2×C411yescharacteristic
117C83⋊#95C2×C411yescharacteristic
118C83⋊#95C2×C411yescharacteristic
119C23×C4×C83C2311yescharacteristic
120C22×C8×C83C2311yescharacteristic
121C22×C8×C83C2311yescharacteristic
122C22×C8×C83C2311yescharacteristic
123C22×C8×C83C2311yescharacteristic
124C2×C22⋊C4×C83C2×C411yescharacteristic
125C2×C22⋊C4×C83C2×C411yescharacteristic
126C2×C42×C83C2311yescharacteristic
127C2×C42×C83C2311yescharacteristic
128C4⋊C8×C83—22no—
129C22⋊C8×C83—22no—
130C22⋊C8×C83—41no—
131#97×C83—41no—
132#95×C83C2×C411yescharacteristic
133#95×C83C2×C411yescharacteristic
134C23×D83C22×C411yescharacteristic
135C2×C22⋊D83—22no—
136C2×C22⋊D83—22no—
137C2×C22⋊D83—22no—
138C22×Dic83—22no—
139C22×Dic83—22no—
140C22×Dic83—22no—
141C22×Dic83—22no—
142C22×Dic83—41no—
143C22×Dic83M1614yescomplemented
144C22×Dic83C22×C411yescharacteristic
145C22×Dic83C22×C411yescharacteristic
146C22×Dic83C22×C411yescharacteristic
147C22×Dic83C22×C411yescharacteristic
148C22×Dic83C22×C411yescharacteristic
149C22×Dic83C22×C411yescharacteristic
150C22×Dic83C22×C411yescharacteristic
151C2×C4×D83—21no—
152C2×C4×D83—21no—
153C2×C4×D83—21no—
154C2×C4×D83—21no—
155C2×C4×D83—22no—
156C2×C4×D83—22no—
157C2×C4×D83—22no—
158C2×C4×D83—22no—
159C2×C4×D83—22no—
160C2×C4×D83—41no—
161C2×C4×D83#4112yes—
162C2×C4×D83#4112yes—
163#13050573—44no—
164#13050573—44no—
165C2×C83⋊C8—21no—
166C2×C83⋊C8—21no—
167C2×C83⋊C8—21no—
168C2×C83⋊C8—21no—
169C2×C83⋊C8—21no—
170C2×C83⋊C8—21no—
171C2×C83⋊C8—21no—
172C2×C83⋊C8—21no—
173C2×C83⋊C8—21no—
174C2×C83⋊C8—21no—
175C2×C83⋊C8—21no—
176C2×C83⋊C8C2×D412yes—
177Dic83⋊C4—22no—
178Dic83⋊C4—22no—
179Dic83⋊C4M1614yescomplemented
180C22⋊Dic83—22no—
181(C2×D83)⋊C4—22no—
182(C2×D83)⋊C4—22no—
183(C2×D83)⋊C4—22no—
184C4×Dic83—21no—
185C4×Dic83—21no—
186C4×Dic83—21no—
187C4×Dic83—21no—
188C4×Dic83—22no—
189C4×Dic83—22no—
190C4×Dic83—22no—
191C4×Dic83—22no—
192C4×Dic83—22no—
193C4×Dic83—22no—
194C4×Dic83—22no—
195C4×Dic83—41no—
196C4×Dic83C2×D412yes—
197C4×Dic83#4112yes—
198C24×C83C22×C411yescharacteristic
199C22×C4×C83—21no—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—21no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83C22×C411yescharacteristic
206C22×C4×C83C22×C411yescharacteristic
207C22×C4×C83C22×C411yescharacteristic
208C22×C4×C83C22×C411yescharacteristic
209C22×C4×C83C22×C411yescharacteristic
210C22×C4×C83C2411yescharacteristic
211C2×C8×C83—21no—
212C2×C8×C83—21no—
213C2×C8×C83—21no—
214C2×C8×C83—21no—
215C2×C8×C83—21no—
216C2×C8×C83—21no—
217C2×C8×C83—21no—
218C2×C8×C83—21no—
219C2×C8×C83—21no—
220C2×C8×C83—21no—
221C2×C8×C83—21no—
222C2×C8×C83C2×D412yes—
223C22⋊C4×C83—22no—
224C22⋊C4×C83—22no—
225C42×C83—21no—
226C42×C83—21no—
227C42×C83—21no—
228C42×C83—21no—
229C23×C83—21no—
230C23×C83—21no—
231C23×C83—21no—
232C23×C83—21no—
233C23×C83—21no—
234C23×C83—21no—
235C23×C83C2×M1612yes—
236C23×C83C23×C411yescharacteristic
237C22×D83—21no—
238C22×D83—21no—
239C22×D83—21no—
240C22×D83—21no—
241C22×D83—21no—
242C22×D83—21no—
243C22×D83#11712yes—
244C2×C4×C83—21no—
245C2×C4×C83—21no—
246C2×C4×C83—21no—
247C2×C4×C83—21no—
248C2×C4×C83—21no—
249C2×C4×C83—21no—
250C2×C4×C83—21no—
251C2×C4×C83—21no—
252C2×C4×C83—21no—
253C2×C4×C83—21no—
254C2×C4×C83—21no—
255C2×C4×C83—21no—
256C2×C4×C83—21no—
257C2×C4×C83—21no—
258C2×C4×C83—41no—
259C2×C4×C83—41no—
260C2×C4×C83—41no—
261C2×C4×C83—41no—
262C2×C4×C83C2×M1612yes—
263C2×C4×C83C22×D411yescharacteristic
264C2×C4×C83C2×#4111yescharacteristic
265C2×C4×C83C2×#4111yescharacteristic
266C2×C4×C83C2×#4111yescharacteristic
267C2×C4×C83H(5,𝔽2)11yescharacteristic
268C2×C4×C832−1+411yescharacteristic
269C22⋊D83—28no—
270C2×Dic83—21no—
271C2×Dic83—21no—
272C2×Dic83—21no—
273C2×Dic83—21no—
274C2×Dic83—21no—
275C2×Dic83—21no—
276C2×Dic83—21no—
277C2×Dic83—21no—
278C2×Dic83—21no—
279C2×Dic83—21no—
280C2×Dic83—28no—
281C2×Dic83—21no—
282C2×Dic83—21no—
283C2×Dic83—21no—
284C2×Dic83—44no—
285C2×Dic83#11712yes—
286C2×Dic83C4×D412yes—
287C2×Dic83C4×D412yes—
288C2×Dic83C2×M1612yes—
289C2×Dic83C2×M1612yes—
290C2×Dic83C2×M1612yes—
291C2×Dic83C2×M1612yes—
292C2×Dic83#13112yes—
293C4×D83—22no—
294C4×D83—22no—
295C4×D83—22no—
296C4×D83—22no—
297C4×D83—44no—
298C4×D83—44no—
299C8×C83—22no—
300C8×C83—41no—
301C8×C83—41no—
302C8×C83—41no—
303C83⋊C8—22no—
304C83⋊C8—41no—
305C83⋊C8—41no—
306C83⋊C8—41no—
307C22×C83—22no—
308C22×C83—22no—
309C22×C83—22no—
310C22×C83—41no—
311C22×C83—41no—
312C22×C83—41no—
313C22×C83—41no—
314C22×C83C2×#11711yescharacteristic
315C22×C83C2×C4×D411yescharacteristic
316C22×C83#52011yescharacteristic
317C22×C83C22×M1611yescharacteristic
318C22×C83C22×M1611yescharacteristic
319C22×C83C2×#13111yescharacteristic
320C22×C83#56811yescharacteristic
321C2×D83—22no—
322C2×D83—22no—
323C2×D83—22no—
324C2×D83—41no—
325C2×D83—41no—
326C2×D83—41no—
327C2×D83—41no—
328C4×C83—22no—
329C4×C83—41no—
330C4×C83—41no—
331C4×C83—41no—
332C4×C83—41no—
333C4×C83#54611yescharacteristic
334C4×C83#54811yescharacteristic
335C4×C83#55211yescharacteristic
336C4×C83#55311yescharacteristic
337Dic83—22no—
338Dic83—22no—
339Dic83—22no—
340Dic83—22no—
341Dic83—22no—
342Dic83—41no—
343Dic83#43514yes—
344#22749—831nomaximal, Sylow
345C2×C83—42no—
346C2×C83#235211yescharacteristic
347C2×C83#292011yescharacteristic
348C2×C83#292511yescharacteristic
349C2×C83C2×#43511yescharacteristic
350C2×C83D4×M1611yescharacteristic
351C2×C83#298911yescharacteristic
352C2×C83#299111yescharacteristic
353D83—42no—
354C2×#431—831no—
355C2×#423—831no—
356C42×D4—831no—
357#1924—831no—
358#1924D8311yescharacteristic, complemented
359#1916—831no—
360#1916—831no—
361#1870—831no—
362#1870—831no—
363#1831—831no—
364#1797—831no—
365#1797—831no—
366#1767—831no—
367#1753—831no—
368#1753—831no—
369C83#2274911yescharacteristic, complemented, Sylow
370C22×M16—831no—
371C22×M16—831no—
372C2×C4×D4—831no—
373C2×C4×D4—831no—
374C2×C4×D4—831no—
375C22×C42—831no—
376C22×C42—831no—
377#431—1664no—
378#423—1664no—
379C2×C4⋊C8—831no—
380C2×C4⋊C8—831no—
381C2×C4⋊C8—831no—
382C2×C4⋊C8—831no—
383C2×C4⋊C8—831no—
384C2×C4⋊C8C2×D8311yescharacteristic
385C2×C22⋊C8—831no—
386C2×C22⋊C8—831no—
387C2×C22⋊C8—831no—
388C2×C22⋊C8—831no—
389C2×C22⋊C8C2×D8311yescharacteristic
390C2×C22⋊C8C2×D8311yescharacteristic
391C2×#97—831no—
392C2×#97C2×D8311yescharacteristic
393C2×C4×C8—831no—
394C2×C4×C8—831no—
395C4×C4⋊C4—831no—
396C4×C4⋊C4—831no—
397C4×C4⋊C4—831no—
398C4×C22⋊C4—831no—
399C4×C22⋊C4—831no—
400C4×C22⋊C4—831no—
401C4×C22⋊C4—831no—
402C4×C22⋊C4—831no—
403C4×C22⋊C4C2×D8311yescharacteristic
404C43—831no—
405#336—831no—
406#336—831no—
407#336—831no—
408#336—831no—
409#336—831no—
410#336—831no—
411#336—831no—
412#336—831no—
413#336C2×D8311yescharacteristic
414#336C2×D8311yescharacteristic
415C22×D4—831no—
416C23×C4—831no—
417C23×C4—831no—
418C23×C4—831no—
419C23×C4—831no—
420C23×C4—831no—
421C23×C4C22×D8311yescharacteristic
422C2×M16—3321no—
423C2×M16—3321no—
424C2×M16—1662no—
425C2×M16—1662no—
426C2×M16—1662no—
427C2×M16—1662no—
428C22×C8—831no—
429C22×C8—831no—
430C22×C8—831no—
431C22×C8—831no—
432C22×C8C22×D8311yescharacteristic
433C22×C8C22×D8311yescharacteristic
434C22×C8C22×D8311yescharacteristic
435C22×C8C22×D8311yescharacteristic
436C4×D4—1664no—
437C4×D4—1664no—
438C4×D4—1662no—
439C4×D4—1662no—
440C2×C4⋊C4—831no—
441C2×C4⋊C4—831no—
442C2×C4⋊C4—831no—
443C2×C22⋊C4—831no—
444C2×C22⋊C4—831no—
445C2×C22⋊C4—831no—
446C2×C22⋊C4—831no—
447C2×C22⋊C4C4×D8311yescharacteristic
448C2×C22⋊C4C4×D8311yescharacteristic
449C2×C42—831no—
450C2×C42—831no—
451C2×C42—831no—
452C2×C42—831no—
453C2×C42—831no—
454C2×C42—831no—
455C2×C42—831no—
456C2×C42—831no—
457C2×C42—831no—
458C2×C42—831no—
459C2×C42—831no—
460C2×C42—1662no—
461C2×C42—1662no—
462C2×C42—1662no—
463C2×C42—1662no—
464C2×C42C22×D8311yescharacteristic
465C2×C42C22×D8311yescharacteristic
466C4⋊C8—22no—
467C4⋊C8—834no—
468C4⋊C8—1662no—
469C4⋊C8—1662no—
470C4⋊C8—1662no—
471C4⋊C8—1662no—
472C22⋊C8—22no—
473C22⋊C8—41no—
474C22⋊C8—3321no—
475C22⋊C8—1662no—
476C22⋊C8—1662no—
477C22⋊C8—1662no—
478#97—41no—
479#97—3321no—
480C4×C8—1662no—
481C4×C8—1662no—
482#95—831no—
483#95—831no—
484#95—831no—
485#95—831no—
486#95C4×D8311yescharacteristic
487#95C4×D8311yescharacteristic
488C24—831no—
489C24C2×C4×D8311yescharacteristic
490C2×D4—1662no—
491C2×D4—1662no—
492C2×D4—1662no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—3321no—
500C22×C4—3321no—
501C22×C4—831no—
502C22×C4—834no—
503C22×C4—831no—
504C22×C4—831no—
505C22×C4—831no—
506C22×C4—831no—
507C22×C4—831no—
508C22×C4—832no—
509C22×C4—832no—
510C22×C4—831no—
511C22×C4—1662no—
512C22×C4—1662no—
513C22×C4—1662no—
514C22×C4—1662no—
515C22×C4—1662no—
516C22×C4—1662no—
517C22×C4—1662no—
518C22×C4—1662no—
519C22×C4—1662no—
520C22×C4—1661no—
521C22×C4—1661no—
522C22×C4—1661no—
523C22×C4—1661no—
524C22×C4C2×C4×D8311yescharacteristic
525C22×C4C2×C4×D8311yescharacteristic
526C22×C4C2×C4×D8311yescharacteristic
527C22×C4C2×C4×D8311yescharacteristic
528C22×C4C2×C4×D8311yescharacteristic
529C22×C4C23×D8311yescharacteristic
530M16—3324no—
531M16—3324no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—832no—
544C2×C8—1661no—
545C2×C8—1661no—
546C2×C8—1661no—
547C2×C8—1661no—
548C2×C8—1661no—
549C2×C8—1661no—
550C2×C8—1661no—
551C2×C8—1661no—
552C2×C8—1661no—
553C2×C8—1661no—
554C2×C8—1661no—
555C2×C8D4×D8312yes—
556C4⋊C4—834no—
557C4⋊C4—1662no—
558C4⋊C4—1662no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—1662no—
562C22⋊C4—1662no—
563C22⋊C4—1662no—
564C22⋊C4—1662no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—3321no—
570C42—832no—
571C42—832no—
572C42—1662no—
573C42—1662no—
574C42—1662no—
575C42—1662no—
576C42—1662no—
577C42—1662no—
578C42—1662no—
579C42—1661no—
580C42—1661no—
581C42—1661no—
582C42—1661no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—832no—
590C23—1661no—
591C23—1661no—
592C23—1661no—
593C23—1661no—
594C23—1661no—
595C23—1661no—
596C23M16×D8312yes—
597C23C22×C4×D8311yescharacteristic
598D4—1668no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—3324no—
618C2×C4—3324no—
619C2×C4—3324no—
620C2×C4—832no—
621C2×C4—832no—
622C2×C4—832no—
623C2×C4—832no—
624C2×C4—832no—
625C2×C4—832no—
626C2×C4—832no—
627C2×C4—832no—
628C2×C4—1661no—
629C2×C4—1661no—
630C2×C4—1661no—
631C2×C4—1668no—
632C2×C4—1661no—
633C2×C4—1661no—
634C2×C4—1661no—
635C2×C4—1661no—
636C2×C4—1661no—
637C2×C4—1661no—
638C2×C4—1661no—
639C2×C4—1661no—
640C2×C4—1661no—
641C2×C4—1661no—
642C2×C4—1662no—
643C2×C4—1662no—
644C2×C4—1662no—
645C2×C4—1662no—
646C2×C4M16×D8312yes—
647C2×C4C2×D4×D8311yescharacteristic
648C2×C4#41×D8311yescharacteristic
649C2×C4#41×D8311yescharacteristic
650C2×C4#41×D8311yescharacteristic
651C2×C4#1458183711yescharacteristic
652C2×C4#1458183911yescharacteristic
653C8—22no—
654C8—41no—
655C8—41no—
656C8—41no—
657C8—3321no—
658C8—3321no—
659C8—3321no—
660C8—1662no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—3321no—
669C22—3321no—
670C22—3321no—
671C22—3321no—
672C22—1662no—
673C22—1662no—
674C22—1662no—
675C22#117×D8311yescharacteristic
676C22C4×D4×D8311yescharacteristic
677C22#1912818011yescharacteristic
678C22C2×M16×D8311yescharacteristic
679C22C2×M16×D8311yescharacteristic
680C22#131×D8311yescharacteristic
681C22#1912846611yescharacteristic
682C4—22no—
683C4—41no—
684C4—41no—
685C4—41no—
686C4—41no—
687C4—3321no—
688C4—834no—
689C4—1662no—
690C4—1662no—
691C4—1662no—
692C4—1662no—
693C4—1662no—
694C4#1912834011yescharacteristic
695C4#1912835911yescharacteristic
696C4#1912838711yescharacteristic
697C4#1912839611yescharacteristic
698C2—42no—
699C2—3322no—
700C2#2491039111yescharacteristic
701C2#2491609311yescharacteristic
702C2#2491612611yescharacteristic
703C2#435×D8311yescharacteristic
704C2#2491619611yescharacteristic
705C2#2491657511yescharacteristic
706C2#2491659111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1924C2
prime radicalC22×C22⋊D83C2×C4
cosocleC22×C4×C83C24
hypercenter#1924D83
hypocenterC83#22749
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#19127751C2semidirect
2. C2×#19127723C2semidirect
4. #24908078C2semidirect
5. #24908023C2semidirect
6. #24908017C2semidirect
9. #24907578C2semidirect
10. #24907442C2semidirect
11. #24907441C2semidirect
12. #24907317C2semidirect
13. #24907248C2semidirect
14. #24907245C2semidirect
15. C83×#1924C2semidirect
107. Dic83⋊C8D4semidirect
143. C22×Dic83M16semidirect
179. Dic83⋊C4M16semidirect
358. #1924D83semidirect
369. C83#22749semidirect

Maximal subgroups

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

subgroupindex
C2×#191277512
C2×#191277232
C4×(C22⋊D83)⋊C42
#249080782
#249080232
#249080172
#249077572
#249075782
#249074422
#249074412
#249073172
#249072482
#249072452
C83×#19242
#2274983