Finite Group Databasebeta

← #35415048

Subgroups — #35415048

Order 21248.

930 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×(C22⋊D83)⋊C4C211yesmaximal, characteristic
2#24908070C211yesmaximal, characteristic, complemented
3#24908068C211yesmaximal, characteristic, complemented
4#24908023C211yesmaximal, characteristic, complemented
5#24908017C211yesmaximal, characteristic, complemented
6#24907755C211yesmaximal, characteristic
7#24907753C211yesmaximal, characteristic
8#24907643C211yesmaximal, characteristic, complemented
9#24907605C211yesmaximal, characteristic, complemented
10#24907579C211yesmaximal, characteristic, complemented
11#24907530C211yesmaximal, characteristic, complemented
12#24907440C211yesmaximal, characteristic, complemented
13C22⋊C8×Dic83C211yesmaximal, characteristic, complemented
14C2×#19127455C211yesmaximal, characteristic, complemented
15C83×#1850C211yesmaximal, characteristic, complemented
16C23×C83⋊C8C2211yescharacteristic
17C2×C4×C22⋊D83C2211yescharacteristic
18C2×(C22⋊D83)⋊C4C411yescharacteristic
19C2×(C22⋊D83)⋊C4C411yescharacteristic
20C22×C4×Dic83C2211yescharacteristic
21C2×C42×D83C2211yescharacteristic
22C2×C4⋊(C83⋊C8)C2211yescharacteristic
23C2×C4⋊(C83⋊C8)C2211yescharacteristic
24C2×C22⋊(C83⋊C8)C2211yescharacteristic
25C2×(C2×D83)⋊C8C2211yescharacteristic
26C2×(C2×D83)⋊C8C2211yescharacteristic
27C2×(C2×D83)⋊C8C2211yescharacteristic
28C2×(C2×D83)⋊C8C2211yescharacteristic
29C2×C8×Dic83C2211yescharacteristic
30C2×C8×Dic83C2211yescharacteristic
31C4×Dic83⋊C4C2211yescharacteristic
32#19127552C411yescharacteristic
33#19127552C411yescharacteristic
34C22⋊C4×Dic83C411yescharacteristic
35C22⋊C4×Dic83C411yescharacteristic
36C4×(C2×D83)⋊C4C2211yescharacteristic
37#19127548C411yescharacteristic
38#19127548C411yescharacteristic
39C42×Dic83C2211yescharacteristic
40#19127456C2211yescharacteristic
41#19127456C2211yescharacteristic
42#19127455C2211yescharacteristic
43#19127455C2211yescharacteristic
44#19127455C2211yescharacteristic
45#19127455C2211yescharacteristic
46#19127455C2211yescharacteristic
47#19127455C2211yescharacteristic
48#19127455C2211yescharacteristic
49#19127455C2211yescharacteristic
50#19127455C2211yescharacteristic
51#19127455C2211yescharacteristic
52C23×C8×C83C2211yescharacteristic
53C2×C4⋊C8×C83C2211yescharacteristic
54C2×C4⋊C8×C83C2211yescharacteristic
55C2×C22⋊C8×C83C2211yescharacteristic
56C4×C22⋊C4×C83C2211yescharacteristic
57#336×C83C2211yescharacteristic
58#336×C83C2211yescharacteristic
59C22×C22⋊D83C2×C411yescharacteristic
60C23×Dic83C2×C411yescharacteristic
61C23×Dic83C2×C411yescharacteristic
62C22×C4×D83C2×C411yescharacteristic
63C22×C4×D83C2×C411yescharacteristic
64C22×C4×D83C2311yescharacteristic
65C22×C83⋊C8—22no—
66C22×C83⋊C8—41no—
67C22×C83⋊C8—41no—
68C22×C83⋊C8C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C22×C83⋊C8C2311yescharacteristic
71C22×C83⋊C8C2311yescharacteristic
72C4×C22⋊D83—22no—
73C4×C22⋊D83—22no—
74(C22⋊D83)⋊C4—24no—
75(C22⋊D83)⋊C4C818yescomplemented
76C2×Dic83⋊C4C2×C411yescharacteristic
77C2×Dic83⋊C4C2×C411yescharacteristic
78C2×Dic83⋊C4C2×C411yescharacteristic
79C2×C22⋊Dic83C2×C411yescharacteristic
80C2×(C2×D83)⋊C4C2×C411yescharacteristic
81C2×(C2×D83)⋊C4C2×C411yescharacteristic
82C2×(C2×D83)⋊C4C2×C411yescharacteristic
83C2×C4×Dic83—41no—
84C2×C4×Dic83—41no—
85C2×C4×Dic83C2×C411yescharacteristic
86C2×C4×Dic83C2×C411yescharacteristic
87C2×C4×Dic83C2×C411yescharacteristic
88C2×C4×Dic83C2×C411yescharacteristic
89C2×C4×Dic83C2×C411yescharacteristic
90C2×C4×Dic83C2×C411yescharacteristic
91C2×C4×Dic83C2×C411yescharacteristic
92C2×C4×Dic83C2×C411yescharacteristic
93C2×C4×Dic83C2311yescharacteristic
94C2×C4×Dic83C2311yescharacteristic
95C2×C4×Dic83C2311yescharacteristic
96C42×D83—41no—
97C42×D83—41no—
98C4⋊(C83⋊C8)—41no—
99C4⋊(C83⋊C8)—41no—
100C22⋊(C83⋊C8)—22no—
101(C2×D83)⋊C8—41no—
102(C2×D83)⋊C8—41no—
103(C2×D83)⋊C8—41no—
104(C2×D83)⋊C8—41no—
105C8×Dic83—41no—
106C8×Dic83—41no—
107C83⋊#95C2×C411yescharacteristic
108C83⋊#95C2×C411yescharacteristic
109C83⋊#95C2×C411yescharacteristic
110C83⋊#95C2×C411yescharacteristic
111C23×C4×C83C2311yescharacteristic
112C22×C8×C83—22no—
113C22×C8×C83—41no—
114C22×C8×C83—41no—
115C22×C8×C83C2311yescharacteristic
116C22×C8×C83C2311yescharacteristic
117C22×C8×C83C2311yescharacteristic
118C22×C8×C83C2311yescharacteristic
119C2×C22⋊C4×C83C2×C411yescharacteristic
120C2×C22⋊C4×C83C2×C411yescharacteristic
121C2×C42×C83C2311yescharacteristic
122C2×C42×C83C2311yescharacteristic
123C4⋊C8×C83—41no—
124C4⋊C8×C83—41no—
125C22⋊C8×C83—22no—
126#95×C83C2×C411yescharacteristic
127#95×C83C2×C411yescharacteristic
128C23×D83C22×C411yescharacteristic
129C2×C22⋊D83—22no—
130C2×C22⋊D83—22no—
131C2×C22⋊D83C2×C814yes—
132C22×Dic83—41no—
133C22×Dic83—41no—
134C22×Dic83—41no—
135C22×Dic83—41no—
136C22×Dic83C2×C814yes—
137C22×Dic83M1614yes—
138C22×Dic83C22×C411yescharacteristic
139C22×Dic83C22×C411yescharacteristic
140C22×Dic83C22×C411yescharacteristic
141C22×Dic83C22×C411yescharacteristic
142C22×Dic83C22×C411yescharacteristic
143C22×Dic83C22×C411yescharacteristic
144C22×Dic83C22×C411yescharacteristic
145C2×C4×D83—21no—
146C2×C4×D83—21no—
147C2×C4×D83—21no—
148C2×C4×D83—21no—
149C2×C4×D83—21no—
150C2×C4×D83—21no—
151C2×C4×D83—22no—
152C2×C4×D83—41no—
153C2×C4×D83—41no—
154C2×C4×D83—41no—
155C2×C4×D83—41no—
156C2×C4×D83C2×C814yescomplemented
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8—21no—
165C2×C83⋊C8—21no—
166C2×C83⋊C8—21no—
167C2×C83⋊C8—21no—
168C2×C83⋊C8—21no—
169C2×C83⋊C8—44no—
170Dic83⋊C4—22no—
171Dic83⋊C4—22no—
172Dic83⋊C4C2×C814yescomplemented
173C22⋊Dic83—22no—
174(C2×D83)⋊C4—22no—
175(C2×D83)⋊C4—22no—
176(C2×D83)⋊C4C2×C814yescomplemented
177C4×Dic83—21no—
178C4×Dic83—21no—
179C4×Dic83—21no—
180C4×Dic83—21no—
181C4×Dic83—21no—
182C4×Dic83—21no—
183C4×Dic83—22no—
184C4×Dic83—41no—
185C4×Dic83—41no—
186C4×Dic83—41no—
187C4×Dic83—41no—
188C4×Dic83—41no—
189C4×Dic83—41no—
190C4×Dic83C2×C814yescomplemented
191C24×C83C22×C411yescharacteristic
192C22×C4×C83—21no—
193C22×C4×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83C22×C411yescharacteristic
197C22×C4×C83C22×C411yescharacteristic
198C22×C4×C83C22×C411yescharacteristic
199C22×C4×C83C22×C411yescharacteristic
200C22×C4×C83C22×C411yescharacteristic
201C22×C4×C83#4112yes—
202C22×C4×C83#4112yes—
203C22×C4×C83C2411yescharacteristic
204C2×C8×C83—21no—
205C2×C8×C83—21no—
206C2×C8×C83—21no—
207C2×C8×C83—21no—
208C2×C8×C83—21no—
209C2×C8×C83—21no—
210C2×C8×C83—21no—
211C2×C8×C83—21no—
212C2×C8×C83—21no—
213C2×C8×C83—21no—
214C2×C8×C83—21no—
215C2×C8×C83—21no—
216C2×C8×C83—44no—
217C22⋊C4×C83—22no—
218C22⋊C4×C83C2×C814yes—
219C42×C83—21no—
220C42×C83—21no—
221C42×C83—21no—
222C42×C83—21no—
223C23×C83—21no—
224C23×C83—21no—
225C23×C83—21no—
226C23×C83—21no—
227C23×C83#11712yes—
228C23×C83C22×C812yes—
229C23×C83C2×M1612yes—
230C23×C83C23×C411yescharacteristic
231C22×D83—21no—
232C22×D83—21no—
233C22×D83—21no—
234C22×D83—21no—
235C22×D83—21no—
236C22×D83—21no—
237C22×D83C22×C812yes—
238C2×C4×C83—21no—
239C2×C4×C83—21no—
240C2×C4×C83—21no—
241C2×C4×C83—21no—
242C2×C4×C83—21no—
243C2×C4×C83—21no—
244C2×C4×C83—22no—
245C2×C4×C83—22no—
246C2×C4×C83—22no—
247C2×C4×C83—22no—
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#11712yes—
255C2×C4×C83C22×C812yes—
256C2×C4×C83C22×C812yes—
257C2×C4×C83C2×#4111yescharacteristic
258C2×C4×C83C2×#4111yescharacteristic
259C2×C4×C83H(5,𝔽2)11yescharacteristic
260C2×C4×C83H(5,𝔽2)11yescharacteristic
261C2×C4×C83H(5,𝔽2)11yescharacteristic
262C2×C4×C832−1+411yescharacteristic
263C22⋊D83—28no—
264C2×Dic83—21no—
265C2×Dic83—21no—
266C2×Dic83—21no—
267C2×Dic83—21no—
268C2×Dic83—21no—
269C2×Dic83—21no—
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—44no—
281C2×Dic83—44no—
282C2×Dic83C22×C812yes—
283C2×Dic83C22×C812yes—
284C2×Dic83C22×C812yes—
285C2×Dic83C2×M1612yes—
286C2×Dic83C2×M1612yes—
287C4×D83—44no—
288C4×D83—44no—
289C4×D83—41no—
290C4×D83—41no—
291C4×D83—41no—
292C4×D83—41no—
293C8×C83—41no—
294C8×C83—41no—
295C8×C83—41no—
296C8×C83—41no—
297C83⋊C8—41no—
298C83⋊C8—41no—
299C83⋊C8—41no—
300C83⋊C8—41no—
301C22×C83—22no—
302C22×C83—22no—
303C22×C83—22no—
304C22×C83—22no—
305C22×C83—22no—
306C22×C83—22no—
307C22×C83#43114yes—
308C22×C83C2×#11711yescharacteristic
309C22×C83#51811yescharacteristic
310C22×C83#52011yescharacteristic
311C22×C83C23×C811yescharacteristic
312C22×C83C22×M1611yescharacteristic
313C22×C83#56811yescharacteristic
314C22×C83#56811yescharacteristic
315C2×D83—22no—
316C2×D83—22no—
317C2×D83—22no—
318C2×D83—41no—
319C2×D83—41no—
320C2×D83—41no—
321C2×D83—41no—
322C4×C83—22no—
323C4×C83—22no—
324C4×C83—22no—
325C4×C83—41no—
326C4×C83—41no—
327C4×C83#53811yescharacteristic
328C4×C83#53811yescharacteristic
329C4×C83#53911yescharacteristic
330C4×C83#53911yescharacteristic
331Dic83—22no—
332Dic83—22no—
333Dic83—22no—
334Dic83—22no—
335Dic83—22no—
336Dic83—41no—
337Dic83—41no—
338#21996—831nomaximal, Sylow
339C2×C83—24no—
340C2×C83#231811yescharacteristic
341C2×C83C2×#43111yescharacteristic
342C2×C83#292311yescharacteristic
343C2×C83#297211yescharacteristic
344C2×C83#297311yescharacteristic
345C2×C83#298811yescharacteristic
346C2×C83#298911yescharacteristic
347D83—42no—
348C42×D4—831no—
349#1923—831no—
350#1923—831no—
351#1916—831no—
352#1916—831no—
353#1869—831no—
354#1869—831no—
355#1850—831no—
356#1850D8311yescharacteristic, complemented
357#1839—831no—
358#1831—831no—
359#1817—831no—
360#1797—831no—
361C4×C22⋊C8—831no—
362C2×#336—831no—
363C83#2199611yescharacteristic, complemented, Sylow
364C23×C8—831no—
365C23×C8C2×D8311yescharacteristic
366C2×C4×D4—831no—
367C2×C4×D4—831no—
368C2×C4×D4—831no—
369C22×C42—831no—
370C22×C42—831no—
371C2×C4⋊C8—831no—
372C2×C4⋊C8—831no—
373C2×C4⋊C8C2×D8311yescharacteristic
374C2×C4⋊C8C2×D8311yescharacteristic
375C2×C22⋊C8—831no—
376C2×C22⋊C8—831no—
377C2×C22⋊C8—831no—
378C2×C22⋊C8—831no—
379C2×C22⋊C8—831no—
380C2×C22⋊C8C2×D8311yescharacteristic
381C2×C4×C8—831no—
382C2×C4×C8—831no—
383C4×C4⋊C4—831no—
384C4×C4⋊C4—831no—
385C4×C4⋊C4—831no—
386C4×C22⋊C4—831no—
387C4×C22⋊C4—831no—
388C4×C22⋊C4—831no—
389C4×C22⋊C4—831no—
390C4×C22⋊C4—831no—
391C4×C22⋊C4C2×D8311yescharacteristic
392C43—831no—
393#336—831no—
394#336—831no—
395#336—831no—
396#336—831no—
397#336—831no—
398#336—831no—
399#336—831no—
400#336—831no—
401#336—831no—
402#336—831no—
403#336—831no—
404#336—831no—
405#336C2×D8311yescharacteristic
406#336C2×D8311yescharacteristic
407C22×D4—831no—
408C23×C4—831no—
409C23×C4—831no—
410C23×C4—831no—
411C23×C4—831no—
412C23×C4—831no—
413C23×C4C22×D8311yescharacteristic
414C22×C8—22no—
415C22×C8—41no—
416C22×C8—41no—
417C22×C8—3321no—
418C22×C8—3321no—
419C22×C8—831no—
420C22×C8—831no—
421C22×C8—831no—
422C22×C8—831no—
423C22×C8—1662no—
424C22×C8C22×D8311yescharacteristic
425C22×C8C22×D8311yescharacteristic
426C22×C8C22×D8311yescharacteristic
427C22×C8C22×D8311yescharacteristic
428C4×D4—838no—
429C4×D4—1664no—
430C4×D4—1662no—
431C4×D4—1662no—
432C2×C4⋊C4—831no—
433C2×C4⋊C4—831no—
434C2×C4⋊C4—831no—
435C2×C22⋊C4—831no—
436C2×C22⋊C4—831no—
437C2×C22⋊C4—831no—
438C2×C22⋊C4—831no—
439C2×C22⋊C4C4×D8311yescharacteristic
440C2×C22⋊C4C4×D8311yescharacteristic
441C2×C42—3321no—
442C2×C42—3321no—
443C2×C42—3321no—
444C2×C42—3321no—
445C2×C42—831no—
446C2×C42—831no—
447C2×C42—831no—
448C2×C42—831no—
449C2×C42—831no—
450C2×C42—831no—
451C2×C42—831no—
452C2×C42—831no—
453C2×C42—831no—
454C2×C42—831no—
455C2×C42—831no—
456C2×C42C22×D8311yescharacteristic
457C2×C42C22×D8311yescharacteristic
458C4⋊C8—41no—
459C4⋊C8—41no—
460C4⋊C8—3321no—
461C4⋊C8—3321no—
462C22⋊C8—22no—
463C22⋊C8—3321no—
464C22⋊C8—3321no—
465C22⋊C8—3321no—
466C22⋊C8—3321no—
467C22⋊C8—1662no—
468C4×C8—3321no—
469C4×C8—3321no—
470#95—831no—
471#95—831no—
472#95—831no—
473#95—831no—
474#95C4×D8311yescharacteristic
475#95C4×D8311yescharacteristic
476C24—831no—
477C24C2×C4×D8311yescharacteristic
478C2×D4—834no—
479C2×D4—1662no—
480C2×D4—1662no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—3321no—
486C22×C4—3321no—
487C22×C4—3321no—
488C22×C4—3321no—
489C22×C4—3321no—
490C22×C4—3321no—
491C22×C4—3321no—
492C22×C4—3321no—
493C22×C4—834no—
494C22×C4—834no—
495C22×C4—834no—
496C22×C4—831no—
497C22×C4—831no—
498C22×C4—831no—
499C22×C4—831no—
500C22×C4—831no—
501C22×C4—831no—
502C22×C4—831no—
503C22×C4—1662no—
504C22×C4—1661no—
505C22×C4—1661no—
506C22×C4—1661no—
507C22×C4—1661no—
508C22×C4—1661no—
509C22×C4—1661no—
510C22×C4C2×C4×D8311yescharacteristic
511C22×C4C2×C4×D8311yescharacteristic
512C22×C4C2×C4×D8311yescharacteristic
513C22×C4C2×C4×D8311yescharacteristic
514C22×C4C2×C4×D8311yescharacteristic
515C22×C4#1305058912yes—
516C22×C4#1305059112yes—
517C22×C4C23×D8311yescharacteristic
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—44no—
531C2×C8—3324no—
532C2×C8—1661no—
533C2×C8—1661no—
534C2×C8—1661no—
535C2×C8—1661no—
536C2×C8—1661no—
537C2×C8—1661no—
538C2×C8—1661no—
539C2×C8—1661no—
540C2×C8—1661no—
541C2×C8—1661no—
542C2×C8—1661no—
543C2×C8—1661no—
544C4⋊C4—834no—
545C4⋊C4—1662no—
546C4⋊C4—1662no—
547C22⋊C4—22no—
548C22⋊C4—834no—
549C22⋊C4—1662no—
550C22⋊C4—1662no—
551C22⋊C4—1662no—
552C22⋊C4C8×D8314yes—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—3321no—
558C42—3321no—
559C42—3321no—
560C42—3321no—
561C42—3321no—
562C42—3321no—
563C42—834no—
564C42—1662no—
565C42—1661no—
566C42—1661no—
567C42—1661no—
568C42—1661no—
569C42—1661no—
570C42—1661no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—832no—
576C23—1661no—
577C23—1661no—
578C23—1661no—
579C23—1661no—
580C23—1661no—
581C23—1661no—
582C23#1458175012yes—
583C23C2×C8×D8312yes—
584C23M16×D8312yes—
585C23C22×C4×D8311yescharacteristic
586D4—1668no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—3324no—
604C2×C4—3324no—
605C2×C4—3321no—
606C2×C4—3321no—
607C2×C4—3321no—
608C2×C4—3321no—
609C2×C4—3324no—
610C2×C4—3324no—
611C2×C4—832no—
612C2×C4—832no—
613C2×C4—832no—
614C2×C4—832no—
615C2×C4—832no—
616C2×C4—1661no—
617C2×C4—1661no—
618C2×C4—1661no—
619C2×C4—1661no—
620C2×C4—1661no—
621C2×C4—1661no—
622C2×C4—1661no—
623C2×C4—1661no—
624C2×C4—1661no—
625C2×C4—1661no—
626C2×C4—1661no—
627C2×C4—1661no—
628C2×C4—1661no—
629C2×C4—1661no—
630C2×C4—1661no—
631C2×C4—1661no—
632C2×C4#1458175012yes—
633C2×C4C2×C8×D8312yes—
634C2×C4C2×C8×D8312yes—
635C2×C4C2×#1305058911yescharacteristic
636C2×C4C2×#1305059111yescharacteristic
637C2×C4#1458183711yescharacteristic
638C2×C4#1458183711yescharacteristic
639C2×C4#1458183811yescharacteristic
640C2×C4#1458183911yescharacteristic
641C8—41no—
642C8—41no—
643C8—41no—
644C8—41no—
645C8—3321no—
646C8—3321no—
647C8—3321no—
648C8—3321no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—3321no—
656C22—3321no—
657C22—3321no—
658C22—3321no—
659C22—1662no—
660C22—1662no—
661C22—1662no—
662C22#1912775314yes—
663C22C2×#1458175011yescharacteristic
664C22#1912817311yescharacteristic
665C22#1912818011yescharacteristic
666C22C22×C8×D8311yescharacteristic
667C22C2×M16×D8311yescharacteristic
668C22#1912846611yescharacteristic
669C22#1912846611yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—41no—
674C4—41no—
675C4—3321no—
676C4—3321no—
677C4—1662no—
678C4—1662no—
679C4—1662no—
680C4—1662no—
681C4—1662no—
682C4#1912828611yescharacteristic
683C4#1912829111yescharacteristic
684C4#1912829511yescharacteristic
685C4#1912830011yescharacteristic
686C2—24no—
687C2—3322no—
688C2#2491009111yescharacteristic
689C2C2×#1912775311yescharacteristic
690C2#2491611311yescharacteristic
691C2#2491648411yescharacteristic
692C2#2491648811yescharacteristic
693C2#2491657011yescharacteristic
694C2#2491657511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutatorC22×C83C23×C8
FittingC83×#1850C2
socleC23×C83C23×C4
prime radicalC22×C22⋊D83C2×C4
cosocleC22×C4×C83C24
hypercenter#1850D83
hypocenterC83#21996
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
2. #24908070C2semidirect
3. #24908068C2semidirect
4. #24908023C2semidirect
5. #24908017C2semidirect
8. #24907643C2semidirect
9. #24907605C2semidirect
10. #24907579C2semidirect
11. #24907530C2semidirect
12. #24907440C2semidirect
13. C22⋊C8×Dic83C2semidirect
14. C2×#19127455C2semidirect
15. C83×#1850C2semidirect
75. (C22⋊D83)⋊C4C8semidirect
156. C2×C4×D83C2×C8semidirect
172. Dic83⋊C4C2×C8semidirect
176. (C2×D83)⋊C4C2×C8semidirect
190. C4×Dic83C2×C8semidirect
356. #1850D83semidirect
363. C83#21996semidirect

Maximal subgroups

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

subgroupindex
C4×(C22⋊D83)⋊C42
#249080702
#249080682
#249080232
#249080172
#249077552
#249077532
#249076432
#249076052
#249075792
#249075302
#249074402
C22⋊C8×Dic832
C2×#191274552
C83×#18502
#2199683