Finite Group Databasebeta

← #35423457

Subgroups — #35423457

Order 21248.

976 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×#19127755C211yesmaximal, characteristic, complemented
2C2×#19127723C211yesmaximal, characteristic, complemented
3C4×(C22⋊D83)⋊C4C211yesmaximal, characteristic
4#24908071C211yesmaximal, characteristic, complemented
5#24908030C211yesmaximal, characteristic, complemented
6#24908024C211yesmaximal, characteristic, complemented
7#24907757C211yesmaximal, characteristic
8#24907757C211yesmaximal, characteristic
9#24907578C211yesmaximal, characteristic, complemented
10#24907442C211yesmaximal, characteristic, complemented
11#24907441C211yesmaximal, characteristic, complemented
12C4×Dic83⋊C8C211yesmaximal, characteristic, complemented
13#24907246C211yesmaximal, characteristic, complemented
14#24907243C211yesmaximal, characteristic, complemented
15C83×#1923C211yesmaximal, 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#19127755—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×#14581702C2211yescharacteristic
35C2×#14581702C2211yescharacteristic
36C2×C4×C83⋊C8C2211yescharacteristic
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×C4×C8×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#14581702—22no—
113#14581702—22no—
114C4×C83⋊C8—41no—
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—
131C4×C8×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—22no—
143C22×Dic83—41no—
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⋊C4—22no—
180C22⋊Dic83—22no—
181(C2×D83)⋊C4—22no—
182(C2×D83)⋊C4—22no—
183(C2×D83)⋊C4—22no—
184C4×Dic83—22no—
185C4×Dic83—21no—
186C4×Dic83—21no—
187C4×Dic83—21no—
188C4×Dic83—21no—
189C4×Dic83—22no—
190C4×Dic83—22no—
191C4×Dic83—22no—
192C4×Dic83—22no—
193C4×Dic83—22no—
194C4×Dic83—41no—
195C4×Dic83M1614yescomplemented
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×C83M1614yescomplemented
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—41no—
257C2×C4×C83—41no—
258C2×C4×C83—41no—
259C2×C4×C83—41no—
260C2×C4×C83C2×M1612yes—
261C2×C4×C83C2×M1612yes—
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—21no—
281C2×Dic83—21no—
282C2×Dic83—21no—
283C2×Dic83—21no—
284C2×Dic83—21no—
285C2×Dic83—44no—
286C2×Dic83—44no—
287C2×Dic83#11712yes—
288C2×Dic83C4×D412yes—
289C2×Dic83C4×D412yes—
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—22no—
330C4×C83—22no—
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—41no—
341Dic83—41no—
342Dic83—41no—
343Dic83#43614yes—
344#22751—831nomaximal, Sylow
345C2×C83—42no—
346C2×C83#235211yescharacteristic
347C2×C83#292011yescharacteristic
348C2×C83#292511yescharacteristic
349C2×C83C2×#43611yescharacteristic
350C2×C83D4×M1611yescharacteristic
351C2×C83#298911yescharacteristic
352C2×C83#299011yescharacteristic
353D83—42no—
354C2×#432—831no—
355C2×#423—831no—
356C42×D4—831no—
357#1923—831no—
358#1923D8311yescharacteristic, complemented
359#1917—831no—
360#1917—831no—
361#1870—831no—
362#1870—831no—
363#1831—831no—
364#1797—831no—
365#1797—831no—
366C4×C4⋊C8—831no—
367#1753—831no—
368#1753—831no—
369C83#2275111yescharacteristic, 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#432—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×#97—831no—
393C2×C4×C8—831no—
394C2×C4×C8C2×D8311yescharacteristic
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—1662no—
438C4×D4—1662no—
439C4×D4—1664no—
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—1662no—
479#97—1662no—
480C4×C8—41no—
481C4×C8—3321no—
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—831no—
503C22×C4—831no—
504C22×C4—831no—
505C22×C4—832no—
506C22×C4—832no—
507C22×C4—831no—
508C22×C4—831no—
509C22×C4—831no—
510C22×C4—1662no—
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—1662no—
557C4⋊C4—1662no—
558C4⋊C4—1662no—
559C22⋊C4—22no—
560C22⋊C4—1662no—
561C22⋊C4—1662no—
562C22⋊C4—1662no—
563C22⋊C4—1662no—
564C22⋊C4#1305057314yescomplemented
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—3321no—
570C42—834no—
571C42—832no—
572C42—832no—
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—
596C23C2×#1305057312yes—
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—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—3324no—
616C2×C4—3324no—
617C2×C4—3324no—
618C2×C4—3324no—
619C2×C4—832no—
620C2×C4—832no—
621C2×C4—832no—
622C2×C4—832no—
623C2×C4—832no—
624C2×C4—832no—
625C2×C4—1661no—
626C2×C4—1661no—
627C2×C4—1661no—
628C2×C4—1661no—
629C2×C4—1661no—
630C2×C4—1661no—
631C2×C4—1661no—
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—1662no—
641C2×C4—1662no—
642C2×C4—1662no—
643C2×C4—1662no—
644C2×C4M16×D8312yes—
645C2×C4C2×#1305057312yes—
646C2×C4C2×#1305057312yes—
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
679C22C22×#1305057311yescharacteristic
680C22#131×D8311yescharacteristic
681C22#1912846611yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—41no—
686C4—41no—
687C4—3321no—
688C4—3321no—
689C4—3321no—
690C4—834no—
691C4—1662no—
692C4—1662no—
693C4—1662no—
694C4#1912834011yescharacteristic
695C4#1912835911yescharacteristic
696C4#1912838711yescharacteristic
697C4#1912839611yescharacteristic
698C2—42no—
699C2—3322no—
700C2#2491039111yescharacteristic
701C2#2491609111yescharacteristic
702C2#2491612611yescharacteristic
703C2#436×D8311yescharacteristic
704C2D4×#1305057311yescharacteristic
705C2#2491657511yescharacteristic
706C2#2491658611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1923C2
prime radicalC22×C22⋊D83C2×C4
cosocleC22×C4×C83C24
hypercenter#1923D83
hypocenterC83#22751
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#19127755C2semidirect
2. C2×#19127723C2semidirect
4. #24908071C2semidirect
5. #24908030C2semidirect
6. #24908024C2semidirect
9. #24907578C2semidirect
10. #24907442C2semidirect
11. #24907441C2semidirect
12. C4×Dic83⋊C8C2semidirect
13. #24907246C2semidirect
14. #24907243C2semidirect
15. C83×#1923C2semidirect
107. Dic83⋊C8D4semidirect
195. C4×Dic83M16semidirect
224. C22⋊C4×C83M16semidirect
358. #1923D83semidirect
369. C83#22751semidirect
564. C22⋊C4#13050573semidirect

Maximal subgroups

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

subgroupindex
C2×#191277552
C2×#191277232
C4×(C22⋊D83)⋊C42
#249080712
#249080302
#249080242
#249077572
#249075782
#249074422
#249074412
C4×Dic83⋊C82
#249072462
#249072432
C83×#19232
#2275183