Finite Group Databasebeta

← #25107940

Subgroups — #25107940

Order 11008.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583035C211yesmaximal, characteristic
2#19137288C211yesmaximal, characteristic, complemented
3#19137175C211yesmaximal, characteristic, complemented
4#19135471C211yesmaximal, characteristic, complemented
5#19135461C211yesmaximal, characteristic, complemented
6#19135292C211yesmaximal, characteristic, complemented
7#19135278C211yesmaximal, characteristic, complemented
8#19135223C211yesmaximal, characteristic, complemented
9#19135216C211yesmaximal, characteristic, complemented
10#19134942C211yesmaximal, characteristic, complemented
11#19134942C211yesmaximal, characteristic, complemented
12#19134915C211yesmaximal, characteristic, complemented
13#19134796C211yesmaximal, characteristic, complemented
14#19134527C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic, complemented
21C2×#13063284C2211yescharacteristic
22#14583035C418yescomplemented
23C2×#13063259C2211yescharacteristic, complemented
24C2×#13063257C2211yescharacteristic, complemented
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic, complemented
32C2×#13063247C2211yescharacteristic, complemented
33#14582801C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582801C2211yescharacteristic, complemented
38#14582800—21no—
39#14582800—21no—
40#14582799—21no—
41#14582797C2211yescharacteristic, complemented
42#14582789—21no—
43#14582775—21no—
44#14582770—21no—
45#14582759C2211yescharacteristic
46#14582754—21no—
47#14582754—21no—
48C4×C4⋊Dic43C2211yescharacteristic, complemented
49#14582662C2211yescharacteristic, complemented
50#14582662C2211yescharacteristic, complemented
51#14582662C2211yescharacteristic, complemented
52#14582662C2211yescharacteristic, complemented
53C2×#117×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic, complemented
57C2×C4×C8×C43C2211yescharacteristic, complemented
58C43×#336C2211yescharacteristic, complemented
59C43×#336C2211yescharacteristic, complemented
60C24×D43—21no—
61C22×D172—21no—
62C22×D172—22no—
63C22×D172—41no—
64C22×D172—41no—
65C22×D172—41no—
66C22×D172—41no—
67C22×D172C2×C414yescomplemented
68C22×D172C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C4×D43—21no—
73C2×D344—41no—
74C2×D344—41no—
75C2×D344—41no—
76C2×D344—41no—
77C2×D344C2×C414yes—
78C2×D344C2×C414yes—
79#13063299—22no—
80#13063299C2×C414yes—
81C4×D172—41no—
82C4×D172—41no—
83#13063284—41no—
84#13063284—41no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107#13063259—41no—
108#13063257—41no—
109#13063247—41no—
110#13063247—41no—
111#13063247—41no—
112#13063247—41no—
113#13063247—41no—
114#13063247—41no—
115#13063247C2×C414yescomplemented
116#13063247C2×C414yescomplemented
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C23×C4×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125#117×C43—41no—
126#117×C43—41no—
127C2×C4⋊C4×C43D411yescharacteristic
128C2×C4⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C42×C43C2311yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C22⋊C8×C43—22no—
134C22⋊C8×C43C2×C414yescomplemented
135#97×C43—41no—
136C4×C8×C43—41no—
137C24×C43C2×D411yescharacteristic
138C23×D43—21no—
139C23×D43—21no—
140C23×D43—21no—
141C23×D43—24no—
142C23×D43—42no—
143C23×D43—42no—
144C23×D43—81no—
145C23×D43—81no—
146C23×D43—81no—
147C23×D43—81no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C22×C412yes—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4112yes—
159C22×C4×C43C2411yescharacteristic
160C2×C22⋊D43—24no—
161C2×C22⋊D43—81no—
162C2×C22⋊D43—81no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C2×D172—24no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—44no—
185C2×D172—44no—
186C2×D172—44no—
187C2×D172—44no—
188C2×D172—42no—
189C2×D172—42no—
190C2×D172C22×C412yes—
191C2×D172C22×C412yes—
192C2×D172C22×C412yes—
193C2×C4×D43—42no—
194C2×C4×D43—81no—
195C2×C4×D43—81no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43C22×C412yes—
207C2×C8×C43C22×C412yes—
208C4⋊C4×C43—41no—
209C4⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—21no—
216C22⋊Dic43—42no—
217C22⋊Dic43—81no—
218(C2×D43)⋊C4—24no—
219(C2×D43)⋊C4—42no—
220(C2×D43)⋊C4—81no—
221(C2×D43)⋊C4—81no—
222(C2×D43)⋊C4—81no—
223(C2×D43)⋊C4—81no—
224(C2×D43)⋊C4—81no—
225(C2×D43)⋊C4—81no—
226(C2×D43)⋊C4—81no—
227(C2×D43)⋊C4—81no—
228(C2×D43)⋊C4—81no—
229(C2×D43)⋊C4—81no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43C22×C412yes—
240Dic43⋊C4—81no—
241C4×Dic43—42no—
242C4×Dic43—81no—
243D344—44no—
244D344—44no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43C4×D412yes—
252C23×C43C22×D411yescharacteristic
253C22×D43—22no—
254C22×D43—22no—
255C22×D43—22no—
256C22×D43—48no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—84no—
276C22×D43—84no—
277C22×D43—84no—
278C22×D43—84no—
279C22×D43—84no—
280C22×D43—84no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
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×C43C4×D412yes—
300C2×C4×C43C23×C411yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C22⋊D43—84no—
307C2×Dic43—22no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322D172—22no—
323D172—22no—
324D172—22no—
325D172—22no—
326D172—22no—
327D172—22no—
328D172—48no—
329D172—41no—
330D172—41no—
331D172—41no—
332D172—41no—
333D172—41no—
334D172—41no—
335C4×D43—84no—
336C8×C43—22no—
337C8×C43—22no—
338C8×C43—41no—
339C8×C43—41no—
340#22056—431nomaximal, Sylow
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43C2×C4×D411yescharacteristic
349C22×C43#53411yescharacteristic
350C22×C43#53511yescharacteristic
351C22×C43#57611yescharacteristic
352C22×C43#57611yescharacteristic
353C22×C43#57611yescharacteristic
354C22×C43#57711yescharacteristic
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—816no—
365C2×D43—81no—
366C2×D43—81no—
367C2×D43—81no—
368C2×D43—81no—
369C2×D43—81no—
370C2×D43—81no—
371C2×D43—81no—
372C2×D43—81no—
373C2×D43—81no—
374C2×D43—81no—
375C2×D43—81no—
376C2×D43—81no—
377C4×C43—22no—
378C4×C43—41no—
379C4×C43—41no—
380C4×C43—41no—
381C4×C43—41no—
382C4×C43#51811yescharacteristic
383C4×C43#51811yescharacteristic
384C4×C43#53811yescharacteristic
385C4×C43#53811yescharacteristic
386Dic43—42no—
387Dic43—81no—
388Dic43—81no—
389Dic43—81no—
390Dic43—81no—
391C2×#447—431no—
392#2324—431no—
393#2309—431no—
394#1972—431no—
395#1970—431no—
396#1936—431no—
397#1934—431no—
398#1926—431no—
399#1925—431no—
400#1879—431no—
401#1879—431no—
402#1875—431no—
403#1854—431no—
404#1786—431no—
405#1750D4311yescharacteristic, complemented
406C2×C43—42no—
407C2×C43#232111yescharacteristic
408C2×C43#294611yescharacteristic
409C2×C43#294811yescharacteristic
410C2×C43#319811yescharacteristic
411C2×C43#319911yescharacteristic
412C2×C43#322011yescharacteristic
413C2×C43#322411yescharacteristic
414D43—82no—
415D43—82no—
416D43—82no—
417C23×D4—431no—
418C22×D8—431no—
419C22×D8—431no—
420C2×#121—431no—
421C2×C4×D4—431no—
422C2×#117—431no—
423C2×#117C2×D4311yescharacteristic
424#447—438no—
425C2×#107—431no—
426C2×#106—431no—
427C2×#102—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×#102—431no—
435C2×C22⋊C8C2×D4311yescharacteristic
436C2×C22⋊C8C2×D4311yescharacteristic
437C2×#97C2×D4311yescharacteristic, complemented
438C2×C4×C8C2×D4311yescharacteristic, complemented
439#390—431no—
440#390—431no—
441#390—431no—
442#390—431no—
443#390—431no—
444#390—861no—
445#390—861no—
446#390—861no—
447#389—431no—
448#388—861no—
449#386—861no—
450#385—861no—
451#380—431no—
452#379—861no—
453#379—861no—
454C4×C4⋊C4—431no—
455#340—431no—
456#340—431no—
457#340—431no—
458#340—431no—
459#336C2×D4311yescharacteristic, complemented
460#336C2×D4311yescharacteristic, complemented
461C43#2205611yescharacteristic, complemented, Sylow
462C25—861no—
463C22×D4—434no—
464C22×D4—431no—
465C22×D4—431no—
466C22×D4—431no—
467C22×D4—861no—
468C22×D4—861no—
469C22×D4—862no—
470C22×D4—1721no—
471C22×D4—1721no—
472C22×D4—1721no—
473C22×D4—1721no—
474C23×C4—861no—
475C23×C4C22×D4311yescharacteristic
476C2×D8—434no—
477C2×D8—434no—
478C2×D8—1721no—
479C2×D8—1721no—
480C2×D8—1721no—
481C2×D8—1721no—
482C22×C8C22×D4311yescharacteristic
483C22×C8C22×D4311yescharacteristic
484C22×C8C22×D4311yescharacteristic
485C22×C8C22×D4311yescharacteristic
486#121—434no—
487#121—862no—
488C4×D4—1721no—
489C4×D4—1721no—
490#117—41no—
491#117—41no—
492#117—1721no—
493#117—1721no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4D17211yescharacteristic
501C2×C4⋊C4D17211yescharacteristic
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4D17211yescharacteristic
517C2×C22⋊C4D17211yescharacteristic
518C2×C42—861no—
519C2×C42—861no—
520C2×C42C22×D4311yescharacteristic
521C2×C42C22×D4311yescharacteristic
522#107—1721no—
523#106—1721no—
524#102—434no—
525#102—434no—
526#102—1721no—
527#102—1721no—
528#102—1721no—
529#102—1721no—
530#102—1721no—
531#102—1721no—
532C22⋊C8—22no—
533C22⋊C8C4×D4314yescomplemented
534#97—41no—
535C4×C8—41no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—864no—
540C24—861no—
541C24—861no—
542C24—861no—
543C24—3441no—
544C24—3441no—
545C24—3441no—
546C24—3441no—
547C24—1722no—
548C24—1722no—
549C24C2×D17211yescharacteristic
550C2×D4—432no—
551C2×D4—432no—
552C2×D4—432no—
553C2×D4—864no—
554C2×D4—864no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—861no—
559C2×D4—861no—
560C2×D4—861no—
561C2×D4—861no—
562C2×D4—861no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—3441no—
571C2×D4—3441no—
572C2×D4—1724no—
573C2×D4—1724no—
574C2×D4—1722no—
575C2×D4—1722no—
576C2×D4—1724no—
577C2×D4—1724no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—3441no—
588C22×C4—3441no—
589C22×C4—1722no—
590C22×C4C2×C4×D4312yes—
591C22×C4C2×D17211yescharacteristic
592C22×C4C2×D17211yescharacteristic
593C22×C4C2×D17211yescharacteristic
594C22×C4C2×D17211yescharacteristic
595C22×C4C2×D17211yescharacteristic
596C22×C4#1062189812yes—
597C22×C4C23×D4311yescharacteristic
598D8—1724no—
599D8—1724no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C2×C4×D4312yes—
611C2×C8C2×C4×D4312yes—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4—432no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—3441no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—864no—
628C22⋊C4—3441no—
629C22⋊C4—3441no—
630C22⋊C4—3441no—
631C22⋊C4—3441no—
632C22⋊C4—3441no—
633C22⋊C4—3441no—
634C22⋊C4—3441no—
635C22⋊C4—3441no—
636C22⋊C4—3441no—
637C22⋊C4—3441no—
638C22⋊C4—3441no—
639C22⋊C4—1722no—
640C22⋊C4—1722no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—3441no—
646C42—1722no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—862no—
654C23—862no—
655C23—862no—
656C23—3444no—
657C23—3444no—
658C23—3444no—
659C23—3444no—
660C23—3444no—
661C23—3444no—
662C23—1728no—
663C23—1721no—
664C23—1721no—
665C23—1721no—
666C23—1721no—
667C23—1721no—
668C23—1721no—
669C23—1721no—
670C23—1721no—
671C23—1721no—
672C23—1721no—
673C23—1721no—
674C23—1721no—
675C23—1721no—
676C23—1721no—
677C23—1721no—
678C23—1721no—
679C23—1721no—
680C23—1721no—
681C23C4×D17212yes—
682C23C22×D17211yescharacteristic
683D4—862no—
684D4—862no—
685D4—862no—
686D4—862no—
687D4—862no—
688D4—862no—
689D4—3444no—
690D4—1728no—
691D4—1721no—
692D4—1721no—
693D4—1721no—
694D4—1721no—
695D4—1721no—
696D4—1721no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
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—862no—
716C2×C4—3444no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4C4×D17212yes—
732C2×C4C22×C4×D4311yescharacteristic
733C2×C4C2×#1062189811yescharacteristic
734C2×C4#1306337011yescharacteristic
735C2×C4#1306337011yescharacteristic
736C2×C4#1306337111yescharacteristic
737C2×C4#1306337111yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—34416no—
750C22—3441no—
751C22—3441no—
752C22—3441no—
753C22—3441no—
754C22—3441no—
755C22—3441no—
756C22—3441no—
757C22—3441no—
758C22—3441no—
759C22—3441no—
760C22—3441no—
761C22—3441no—
762C22—1722no—
763C22—1722no—
764C22—1722no—
765C22—1722no—
766C22—1722no—
767C22—1722no—
768C22—1722no—
769C22—1722no—
770C22—1722no—
771C22C2×C4×D17211yescharacteristic
772C22#1458346111yescharacteristic
773C22#1458346811yescharacteristic
774C22#1458370411yescharacteristic
775C22#1458370411yescharacteristic
776C22#1458370411yescharacteristic
777C22#1458371111yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—3441no—
784C4—3441no—
785C4—3441no—
786C4—3441no—
787C4—1722no—
788C4#1458337111yescharacteristic
789C4#1458337111yescharacteristic
790C4#1458348211yescharacteristic
791C4#1458348211yescharacteristic
792C2—42no—
793C2—3442no—
794C2—3442no—
795C2—3442no—
796C2#1913725511yescharacteristic
797C2#1914342911yescharacteristic
798C2#1914344811yescharacteristic
799C2#1914544911yescharacteristic
800C2#1914546011yescharacteristic
801C2#1914564711yescharacteristic
802C2#1914569111yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1750C2
socleC23×C43C22×D4
prime radicalC2×#14583035C2
cosocleC22×C4×C43C24
hypercenter#1750D43
hypocenterC43#22056
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. #19137288C2semidirect
3. #19137175C2semidirect
4. #19135471C2semidirect
5. #19135461C2semidirect
6. #19135292C2semidirect
7. #19135278C2semidirect
8. #19135223C2semidirect
9. #19135216C2semidirect
10. #19134942C2semidirect
11. #19134942C2semidirect
12. #19134915C2semidirect
13. #19134796C2semidirect
14. #19134527C2semidirect
15. C43×#1750C2semidirect
20. C2×C4×D172C22semidirect
22. #14583035C4semidirect
23. C2×#13063259C22semidirect
24. C2×#13063257C22semidirect
31. C2×#13063247C22semidirect
32. C2×#13063247C22semidirect
37. #14582801C22semidirect
41. #14582797C22semidirect
48. C4×C4⋊Dic43C22semidirect
49. #14582662C22semidirect
50. #14582662C22semidirect
51. #14582662C22semidirect
52. #14582662C22semidirect
56. C2×#97×C43C22semidirect
57. C2×C4×C8×C43C22semidirect
58. C43×#336C22semidirect
59. C43×#336C22semidirect
67. C22×D172C2×C4semidirect
115. #13063247C2×C4semidirect
116. #13063247C2×C4semidirect
134. C22⋊C8×C43C2×C4semidirect
405. #1750D43semidirect
437. C2×#97C2×D43semidirect
438. C2×C4×C8C2×D43semidirect
459. #336C2×D43semidirect
460. #336C2×D43semidirect
461. C43#22056semidirect
533. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830352
#191372882
#191371752
#191354712
#191354612
#191352922
#191352782
#191352232
#191352162
#191349422
#191349152
#191347962
#191345272
C43×#17502
#2205643