Finite Group Databasebeta

← #25107936

Subgroups — #25107936

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#19137284C211yesmaximal, characteristic, complemented
3#19137175C211yesmaximal, characteristic, complemented
4#19135469C211yesmaximal, characteristic, complemented
5#19135459C211yesmaximal, characteristic, complemented
6#19135290C211yesmaximal, characteristic, complemented
7#19135276C211yesmaximal, characteristic, complemented
8#19135221C211yesmaximal, characteristic, complemented
9#19135214C211yesmaximal, characteristic, complemented
10#19134944C211yesmaximal, characteristic, complemented
11#19134944C211yesmaximal, characteristic, complemented
12#19134917C211yesmaximal, characteristic, complemented
13#19134525C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1854C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063287C2211yescharacteristic, complemented
21C2×#13063284C2211yescharacteristic
22#14583035C418yescomplemented
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic, complemented
30C2×#13063245C2211yescharacteristic, complemented
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063235C2211yescharacteristic, complemented
33C2×C8×Dic43C2211yescharacteristic, complemented
34#14582801—21no—
35#14582801—21no—
36#14582800C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582800C2211yescharacteristic
40#14582800C2211yescharacteristic, complemented
41#14582799—21no—
42#14582795C2211yescharacteristic, complemented
43#14582791—21no—
44#14582775—21no—
45#14582773—21no—
46#14582754—21no—
47#14582754—21no—
48C4⋊C4×Dic43C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C2×#117×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic, complemented
55C2×#106×C43C2211yescharacteristic, complemented
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic, complemented
59C43×#340C2211yescharacteristic, 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—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81#13063299—22no—
82#13063299C2×C414yes—
83#13063287—41no—
84#13063287—41no—
85#13063284—41no—
86#13063284—41no—
87C2×C4⋊Dic43D411yescharacteristic
88C2×C4⋊Dic43D411yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×C22⋊Dic43D411yescharacteristic
92C2×C22⋊Dic43D411yescharacteristic
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×Dic43C2311yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108#13063247C2×C414yescomplemented
109#13063247C2×C414yescomplemented
110#13063245—41no—
111#13063245—41no—
112#13063245—41no—
113#13063245—41no—
114#13063245—41no—
115#13063245—41no—
116C22⋊(C43⋊C8)—22no—
117#13063235—41no—
118C8×Dic43—41no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C23×C4×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124#117×C43—41no—
125#117×C43—41no—
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C42×C43—21no—
133#107×C43—41no—
134#106×C43—41no—
135C22⋊C8×C43C2×C414yescomplemented
136#95×C43—21no—
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×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43C22×C412yes—
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×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
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×C43C22×C412yes—
201C2×C8×C43C22×C412yes—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C22⋊C4×C43—42no—
211C22⋊C4×C43—81no—
212C42×C43—42no—
213C22⋊Dic43—41no—
214C22⋊Dic43—41no—
215(C2×D43)⋊C4—24no—
216(C2×D43)⋊C4—42no—
217(C2×D43)⋊C4—81no—
218(C2×D43)⋊C4—81no—
219(C2×D43)⋊C4—81no—
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—
227C4⋊Dic43—21no—
228C4⋊Dic43—41no—
229C4⋊Dic43—41no—
230C4⋊Dic43C22×C412yes—
231Dic43⋊C4—81no—
232C4×Dic43—21no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43—81no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
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—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
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—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
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—
338C43⋊C8—41no—
339C43⋊C8—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—81no—
379C4×C43—81no—
380C4×C43—81no—
381C4×C43—81no—
382C4×C43#51811yescharacteristic
383C4×C43#51811yescharacteristic
384C4×C43#53811yescharacteristic
385C4×C43#53811yescharacteristic
386Dic43—41no—
387Dic43—41no—
388Dic43—41no—
389Dic43—41no—
390Dic43—42no—
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#1854D4311yescharacteristic, complemented
404#1786—431no—
405#1750—431no—
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×#107C2×D4311yescharacteristic, complemented
426C2×#106C2×D4311yescharacteristic, complemented
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⋊C8—431no—
436C2×C22⋊C8C2×D4311yescharacteristic
437C2×#97—431no—
438C2×C4×C8—431no—
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#380C2×D4311yescharacteristic
452#379—861no—
453#379—861no—
454C4×C4⋊C4—431no—
455#340—431no—
456#340—431no—
457#340C2×D4311yescharacteristic, complemented
458#340C2×D4311yescharacteristic, complemented
459#336—431no—
460#336—431no—
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×C8—431no—
483C22×C8—431no—
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—861no—
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—431no—
505C2×C22⋊C4—431no—
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⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C42—21no—
519C2×C42—431no—
520C2×C42—431no—
521C2×C42—861no—
522#107—41no—
523#106—41no—
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—862no—
533C22⋊C8C4×D4314yescomplemented
534#97—1721no—
535C4×C8—1721no—
536#95—21no—
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—
549C24D4×D4311yescharacteristic
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—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—431no—
589C22×C4—431no—
590C22×C4—861no—
591C22×C4—3441no—
592C22×C4—3441no—
593C22×C4—1722no—
594C22×C4C2×C4×D4312yes—
595C22×C4D4×D4311yescharacteristic
596C22×C4#1062190212yes—
597C22×C4C23×D4311yescharacteristic
598D8—1724no—
599D8—1724no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8C2×C4×D4312yes—
611C2×C8C2×C4×D4312yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—432no—
621C4⋊C4—861no—
622C4⋊C4—3441no—
623C4⋊C4—1721no—
624C4⋊C4—1721no—
625C22⋊C4—42no—
626C22⋊C4—81no—
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—1722no—
639C22⋊C4—1721no—
640C22⋊C4—1721no—
641C42—42no—
642C42—861no—
643C42—861no—
644C42—861no—
645C42—861no—
646C42—3441no—
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—
681C23#1306328712yes—
682C23C2×D4×D4311yescharacteristic
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—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—862no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—861no—
724C2×C4—861no—
725C2×C4—861no—
726C2×C4—861no—
727C2×C4—861no—
728C2×C4—3444no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4#1306328712yes—
732C2×C4C22×C4×D4311yescharacteristic
733C2×C4C2×#1062190211yescharacteristic
734C2×C4#1306337011yescharacteristic
735C2×C4#1306337011yescharacteristic
736C2×C4#1306337111yescharacteristic
737C2×C4#1306337111yescharacteristic
738C8—22no—
739C8—22no—
740C8—1721no—
741C8—1721no—
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×#1306328711yescharacteristic
772C22#1458346011yescharacteristic
773C22#1458346411yescharacteristic
774C22#1458370111yescharacteristic
775C22#1458370111yescharacteristic
776C22#1458370311yescharacteristic
777C22#1458370811yescharacteristic
778C4—22no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—1722no—
784C4—1721no—
785C4—1721no—
786C4—1721no—
787C4—1721no—
788C4#1458337111yescharacteristic
789C4#1458337111yescharacteristic
790C4#1458348911yescharacteristic
791C4#1458348911yescharacteristic
792C2—42no—
793C2—3442no—
794C2—3442no—
795C2—3442no—
796C2#1913725211yescharacteristic
797C2#1914342511yescharacteristic
798C2#1914344611yescharacteristic
799C2#1914545311yescharacteristic
800C2#1914545911yescharacteristic
801C2#1914564311yescharacteristic
802C2#1914569511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC2×#14583035C2
cosocleC22×C4×C43C24
hypercenter#1854D43
hypocenterC43#22056
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. #19137284C2semidirect
3. #19137175C2semidirect
4. #19135469C2semidirect
5. #19135459C2semidirect
6. #19135290C2semidirect
7. #19135276C2semidirect
8. #19135221C2semidirect
9. #19135214C2semidirect
10. #19134944C2semidirect
11. #19134944C2semidirect
12. #19134917C2semidirect
13. #19134525C2semidirect
14. #19134363C2semidirect
15. C43×#1854C2semidirect
20. C2×#13063287C22semidirect
22. #14583035C4semidirect
29. C2×#13063245C22semidirect
30. C2×#13063245C22semidirect
32. C2×#13063235C22semidirect
33. C2×C8×Dic43C22semidirect
40. #14582800C22semidirect
42. #14582795C22semidirect
48. C4⋊C4×Dic43C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582653C22semidirect
52. #14582653C22semidirect
54. C2×#107×C43C22semidirect
55. C2×#106×C43C22semidirect
58. C43×#340C22semidirect
59. C43×#340C22semidirect
67. C22×D172C2×C4semidirect
108. #13063247C2×C4semidirect
109. #13063247C2×C4semidirect
135. C22⋊C8×C43C2×C4semidirect
403. #1854D43semidirect
425. C2×#107C2×D43semidirect
426. C2×#106C2×D43semidirect
457. #340C2×D43semidirect
458. #340C2×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
#191372842
#191371752
#191354692
#191354592
#191352902
#191352762
#191352212
#191352142
#191349442
#191349172
#191345252
#191343632
C43×#18542
#2205643