Finite Group Databasebeta

← #25107722

Subgroups — #25107722

Order 11008.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582978C211yesmaximal, characteristic, complemented
2C2×#14582864C211yesmaximal, characteristic, complemented
3#19137811C211yesmaximal, characteristic
4#19135392C211yesmaximal, characteristic, complemented
5#19135387C211yesmaximal, characteristic, complemented
6#19135210C211yesmaximal, characteristic, complemented
7#19135202C211yesmaximal, characteristic, complemented
8#19135201C211yesmaximal, characteristic, complemented
9#19134891C211yesmaximal, characteristic, complemented
10#19134889C211yesmaximal, characteristic, complemented
11#19134886C211yesmaximal, characteristic, complemented
12#19134771C211yesmaximal, characteristic, complemented
13#19134506C211yesmaximal, characteristic, complemented
14#19134377C211yesmaximal, characteristic, complemented
15C43×#1923C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×C22⋊D43C2211yescharacteristic
23#14582978—24no—
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26#14582864—24no—
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×#13063236C2211yescharacteristic
39C2×C8×Dic43C2211yescharacteristic
40#14582820C411yescharacteristic
41#14582817C411yescharacteristic
42#14582815C411yescharacteristic
43#14582815C411yescharacteristic
44#14582812C411yescharacteristic
45#14582809C411yescharacteristic
46#14582808C411yescharacteristic
47#14582808C411yescharacteristic
48C4×(C2×D43)⋊C4C2211yescharacteristic
49C4×(C2×D43)⋊C4C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#10621898—22no—
62C2×#10621898—22no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C22×Dic86C2×C411yescharacteristic
68C22×D172C2×C411yescharacteristic
69C22×D172C2×C411yescharacteristic
70C22×D172C2×C411yescharacteristic
71C22×C22⋊D43C2×C411yescharacteristic
72C22×C22⋊D43C2×C411yescharacteristic
73C22×C22⋊D43C2×C411yescharacteristic
74C22×C4×D43C2311yescharacteristic
75C22×C4×D43C2311yescharacteristic
76C22×C4×D43C2311yescharacteristic
77C2×#10621872—22no—
78C2×#10621872—41no—
79C2×#10621872—41no—
80C2×#10621872—41no—
81C2×#10621872—41no—
82C2×#10621872D414yescomplemented
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C2×C8×D43—22no—
88C2×C8×D43—41no—
89C2×C8×D43—41no—
90C4×D172—22no—
91C4×D172—22no—
92C4×D172—41no—
93C4×D172—41no—
94C4×C22⋊D43—41no—
95C4×C22⋊D43—41no—
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×C4⋊Dic43C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×C22⋊Dic43C2×C411yescharacteristic
100C2×(C2×D43)⋊C4C2×C411yescharacteristic
101C2×(C2×D43)⋊C4C2×C411yescharacteristic
102C2×(C2×D43)⋊C4C2×C411yescharacteristic
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
110C4⋊(C43⋊C8)—22no—
111Dic43⋊C8—41no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)—41no—
114(C2×D43)⋊C8—22no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—41no—
120(C2×D43)⋊C8—41no—
121(C2×D43)⋊C8—41no—
122(C2×D43)⋊C8—41no—
123#13063236—41no—
124C8×Dic43—41no—
125C43⋊#95C2×C411yescharacteristic
126C43⋊#95C2×C411yescharacteristic
127C43⋊#95C2×C411yescharacteristic
128C43⋊#95C2×C411yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C2×C22⋊C4×C43C2×C411yescharacteristic
135C2×C22⋊C4×C43C2×C411yescharacteristic
136C2×C42×C43C2311yescharacteristic
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—41no—
139C22⋊C8×C43—22no—
140C22⋊C8×C43—41no—
141C4×C8×C43—22no—
142#95×C43C2×C411yescharacteristic
143#95×C43C2×C411yescharacteristic
144C24×C43C22×C411yescharacteristic
145C23×D43C22×C411yescharacteristic
146C23×D43C22×C411yescharacteristic
147C23×D43C22×C411yescharacteristic
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C22×C411yescharacteristic
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C22×C411yescharacteristic
157C22×C4×C43C22×C411yescharacteristic
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C2411yescharacteristic
160C2×C22⋊D43—22no—
161C2×C22⋊D43—22no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43—41no—
164C2×C22⋊D43—41no—
165C2×C22⋊D43—41no—
166C2×C22⋊D43—41no—
167C2×C22⋊D43—41no—
168C2×C22⋊D43—41no—
169C22×Dic43C22×C411yescharacteristic
170C22×Dic43C22×C411yescharacteristic
171C22×Dic43C22×C411yescharacteristic
172C22×Dic43C22×C411yescharacteristic
173C22×Dic43C22×C411yescharacteristic
174#10621898—44no—
175#10621898—44no—
176#10621898—44no—
177#10621898—44no—
178C2×D172—22no—
179C2×D172—22no—
180C2×D172—22no—
181C2×D172—41no—
182C2×D172—41no—
183C2×D172—41no—
184C2×D172—41no—
185C2×D172—41no—
186C2×D172—41no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43C2×D412yes—
204C2×C4×D43#4112yes—
205C2×Dic86—22no—
206C2×Dic86—41no—
207C2×Dic86—41no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43C2×D412yes—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—41no—
222C42×C43—21no—
223C42×C43—21no—
224C42×C43—21no—
225C42×C43—21no—
226C22⋊Dic43—41no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—22no—
231(C2×D43)⋊C4—22no—
232(C2×D43)⋊C4—41no—
233(C2×D43)⋊C4—41no—
234(C2×D43)⋊C4—41no—
235(C2×D43)⋊C4—41no—
236C4⋊Dic43—22no—
237C4⋊Dic43—41no—
238Dic43⋊C4—41no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8C2×D412yes—
253#10621872—44no—
254#10621872—44no—
255C8×D43—44no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43C23×C411yescharacteristic
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43C4×D412yes—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43#13112yes—
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C43H(5,𝔽2)11yescharacteristic
308C2×C4×C43H(5,𝔽2)11yescharacteristic
309C2×C4×C43H(5,𝔽2)11yescharacteristic
310C22⋊D43—44no—
311C22⋊D43—44no—
312C22⋊D43—44no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43C4×D412yes—
327C2×Dic43#13112yes—
328D172—44no—
329D172—44no—
330D172—44no—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—41no—
336C4×D43—41no—
337C4×D43—41no—
338C4×D43—41no—
339C4×D43—41no—
340C4×D43—41no—
341C4×D43—41no—
342C4×D43—41no—
343Dic86—44no—
344C8×C43—22no—
345C8×C43—41no—
346C8×C43—41no—
347C8×C43—41no—
348C43⋊C8—22no—
349C43⋊C8—41no—
350C43⋊C8—41no—
351C43⋊C8—41no—
352#22039—431nomaximal, Sylow
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43C2×C4×D411yescharacteristic
361C22×C43#51811yescharacteristic
362C22×C43#51811yescharacteristic
363C22×C43C2×#13111yescharacteristic
364C22×C43C2×#13111yescharacteristic
365C22×C43#56811yescharacteristic
366C22×C43#56811yescharacteristic
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—41no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43—41no—
375C2×D43—41no—
376C2×D43—41no—
377C2×D43—41no—
378C2×D43—41no—
379C2×D43—41no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—41no—
383C2×D43—41no—
384C2×D43—41no—
385C2×D43—41no—
386C2×D43—41no—
387C2×D43—41no—
388C4×C43—22no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43—41no—
393C4×C43#53411yescharacteristic
394C4×C43#53511yescharacteristic
395C4×C43#53811yescharacteristic
396C4×C43#53811yescharacteristic
397Dic43—22no—
398Dic43—22no—
399Dic43—41no—
400Dic43—41no—
401Dic43—41no—
402C2×#436—431no—
403C2×#408—431no—
404#2388—431no—
405#1955—431no—
406#1954—431no—
407#1924—431no—
408#1923—431no—
409#1923—431no—
410#1923D4311yescharacteristic, complemented
411#1870—431no—
412#1870—431no—
413#1869—431no—
414#1850—431no—
415#1780—431no—
416#1753—431no—
417C2×C43—81no—
418C2×C43#232111yescharacteristic
419C2×C43#293311yescharacteristic
420C2×C43#293511yescharacteristic
421C2×C43#297611yescharacteristic
422C2×C43#297811yescharacteristic
423C2×C43#297911yescharacteristic
424C2×C43#298111yescharacteristic
425D43—42no—
426D43—81no—
427D43—81no—
428C22×#41—431no—
429C22×M16—431no—
430C22×M16—431no—
431C23×C8—431no—
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4—431no—
435#436—864no—
436C2×C4⋊C8—431no—
437C2×C4⋊C8—431no—
438C2×C4⋊C8C2×D4311yescharacteristic
439#408—864no—
440C2×C22⋊C8—431no—
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8—431no—
446C2×C22⋊C8—431no—
447C2×C22⋊C8—431no—
448C2×C22⋊C8—431no—
449C2×C22⋊C8—431no—
450C2×C22⋊C8—431no—
451C2×C22⋊C8C2×D4311yescharacteristic
452C2×C22⋊C8C2×D4311yescharacteristic
453C2×#97—431no—
454C2×C4×C8—431no—
455C2×C4×C8C2×D4311yescharacteristic
456#395—431no—
457#394—431no—
458#394—431no—
459#394—431no—
460#393—431no—
461#392—431no—
462#392—431no—
463#392—431no—
464C4×C22⋊C4—431no—
465C4×C22⋊C4—431no—
466C4×C22⋊C4C2×D4311yescharacteristic
467#336—431no—
468#336—431no—
469#336—431no—
470#336—431no—
471#336C2×D4311yescharacteristic
472#336C2×D4311yescharacteristic
473C43#2203911yescharacteristic, complemented, Sylow
474C2×#41—862no—
475C2×#41—862no—
476C2×#41—1721no—
477C2×#41—1721no—
478C2×#41—1721no—
479C2×#41—1721no—
480C22×Q8—431no—
481C22×D4—431no—
482C22×D4—431no—
483C22×D4—431no—
484C22×D4—431no—
485C22×D4—431no—
486C22×D4—431no—
487C23×C4—431no—
488C23×C4—431no—
489C23×C4—431no—
490C23×C4C22×D4311yescharacteristic
491C2×M16—434no—
492C2×M16—862no—
493C2×M16—1721no—
494C2×M16—1721no—
495C2×M16—1721no—
496C2×M16—1721no—
497C22×C8—431no—
498C22×C8—431no—
499C22×C8—431no—
500C22×C8—431no—
501C22×C8—862no—
502C22×C8—1721no—
503C22×C8—1721no—
504C22×C8C22×D4311yescharacteristic
505C22×C8C22×D4311yescharacteristic
506C22×C8C22×D4311yescharacteristic
507C22×C8C22×D4311yescharacteristic
508C4×D4—862no—
509C4×D4—862no—
510C4×D4—1721no—
511C4×D4—1721no—
512C4×D4—1721no—
513C4×D4—1721no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C22⋊C4—431no—
518C2×C22⋊C4—431no—
519C2×C22⋊C4—431no—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—431no—
524C2×C22⋊C4—431no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4—431no—
527C2×C22⋊C4C4×D4311yescharacteristic
528C2×C22⋊C4C4×D4311yescharacteristic
529C2×C42—431no—
530C2×C42C22×D4311yescharacteristic
531C2×C42C22×D4311yescharacteristic
532C4⋊C8—41no—
533C4⋊C8—862no—
534C4⋊C8—1721no—
535C22⋊C8—22no—
536C22⋊C8—41no—
537C22⋊C8—862no—
538C22⋊C8—862no—
539C22⋊C8—862no—
540C22⋊C8—862no—
541C22⋊C8—862no—
542C22⋊C8—862no—
543C22⋊C8—1721no—
544C22⋊C8—1721no—
545C22⋊C8—1721no—
546C22⋊C8—1721no—
547C22⋊C8—1721no—
548#97—1721no—
549C4×C8—22no—
550C4×C8—1721no—
551#95—431no—
552#95—431no—
553#95—431no—
554#95—431no—
555#95C4×D4311yescharacteristic
556#95C4×D4311yescharacteristic
557C24—431no—
558C24—431no—
559C24—431no—
560C24C2×C4×D4311yescharacteristic
561#41—1724no—
562#41—1724no—
563#41—1724no—
564#41—1724no—
565C2×Q8—862no—
566C2×Q8—1721no—
567C2×Q8—1721no—
568C2×D4—862no—
569C2×D4—862no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—1721no—
575C2×D4—1721no—
576C2×D4—1721no—
577C2×D4—1721no—
578C2×D4—1721no—
579C2×D4—1721no—
580C2×D4—1721no—
581C2×D4—1721no—
582C2×D4—1721no—
583C2×D4—1721no—
584C2×D4—1721no—
585C2×D4—1721no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—431no—
593C22×C4—431no—
594C22×C4—432no—
595C22×C4—432no—
596C22×C4—431no—
597C22×C4—431no—
598C22×C4—431no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4C2×C4×D4311yescharacteristic
616C22×C4C2×C4×D4311yescharacteristic
617C22×C4C2×C4×D4311yescharacteristic
618C22×C4C2×C4×D4311yescharacteristic
619C22×C4C2×C4×D4311yescharacteristic
620C22×C4C23×D4311yescharacteristic
621M16—1724no—
622M16—1724no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—432no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—861no—
644C2×C8—861no—
645C2×C8—861no—
646C2×C8—1724no—
647C2×C8D4×D4312yes—
648C4⋊C4—862no—
649C4⋊C4—1721no—
650C4⋊C4—1721no—
651C22⋊C4—22no—
652C22⋊C4—41no—
653C22⋊C4—862no—
654C22⋊C4—862no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—862no—
658C22⋊C4—1721no—
659C22⋊C4—1721no—
660C22⋊C4—1721no—
661C22⋊C4—1721no—
662C22⋊C4—1721no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—861no—
668C42—861no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—432no—
677C23—861no—
678C23—861no—
679C23—861no—
680C23—861no—
681C23—861no—
682C23—861no—
683C23—861no—
684C23—861no—
685C23—861no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—861no—
690C23—861no—
691C23—861no—
692C23—861no—
693C23—861no—
694C23—861no—
695C23—861no—
696C23—861no—
697C23C22×C4×D4311yescharacteristic
698Q8—1724no—
699D4—1724no—
700D4—1724no—
701D4—1724no—
702D4—1724no—
703D4—1724no—
704D4—1724no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—432no—
724C2×C4—432no—
725C2×C4—861no—
726C2×C4—861no—
727C2×C4—861no—
728C2×C4—861no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—861no—
738C2×C4—861no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4#1306333112yes—
751C2×C4C2×D4×D4311yescharacteristic
752C2×C4#41×D4311yescharacteristic
753C2×C4#1306337011yescharacteristic
754C2×C4#1306337111yescharacteristic
755C2×C4#1306337111yescharacteristic
756C2×C4#1306337111yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—862no—
762C8—1721no—
763C8—1721no—
764C8—1721no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—862no—
773C22—862no—
774C22—862no—
775C22—1721no—
776C22—1721no—
777C22—1721no—
778C22—1721no—
779C22—1721no—
780C22—1721no—
781C22—1721no—
782C22—1721no—
783C22—1721no—
784C22—1721no—
785C22—1721no—
786C22—1721no—
787C22—1721no—
788C22—1721no—
789C22—1721no—
790C22—1721no—
791C22—1721no—
792C22—1721no—
793C22C4×D4×D4311yescharacteristic
794C22#1458337111yescharacteristic
795C22#1458337311yescharacteristic
796C22#131×D4311yescharacteristic
797C22C2×#1306333111yescharacteristic
798C22#1458366411yescharacteristic
799C22#1458366511yescharacteristic
800C4—22no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—862no—
806C4—862no—
807C4—1721no—
808C4—1721no—
809C4—1721no—
810C4#1458346011yescharacteristic
811C4#1458346511yescharacteristic
812C4#1458348311yescharacteristic
813C4#1458348811yescharacteristic
814C2—81no—
815C2—3441no—
816C2—3441no—
817C2—1722no—
818C2#1913725711yescharacteristic
819C2#1914331511yescharacteristic
820C2#1914333611yescharacteristic
821C2#1914364111yescharacteristic
822C2#1914365211yescharacteristic
823C2#1914365811yescharacteristic
824C2#1914367011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1923C2
prime radical#19137811C2
cosocleC22×C4×C43C24
hypercenter#1923D43
hypocenterC43#22039
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#14582978C2semidirect
2. C2×#14582864C2semidirect
4. #19135392C2semidirect
5. #19135387C2semidirect
6. #19135210C2semidirect
7. #19135202C2semidirect
8. #19135201C2semidirect
9. #19134891C2semidirect
10. #19134889C2semidirect
11. #19134886C2semidirect
12. #19134771C2semidirect
13. #19134506C2semidirect
14. #19134377C2semidirect
15. C43×#1923C2semidirect
82. C2×#10621872D4semidirect
410. #1923D43semidirect
473. C43#22039semidirect

Maximal subgroups

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

subgroupindex
C2×#145829782
C2×#145828642
#191378112
#191353922
#191353872
#191352102
#191352022
#191352012
#191348912
#191348892
#191348862
#191347712
#191345062
#191343772
C43×#19232
#2203943