Finite Group Databasebeta

← #25105979

Subgroups — #25105979

Order 11008.

1250 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583469C211yesmaximal, characteristic
2C2×#14582959C211yesmaximal, characteristic, complemented
3#19137200C211yesmaximal, characteristic, complemented
4#19135528C211yesmaximal, characteristic, complemented
5#19135518C211yesmaximal, characteristic, complemented
6#19135517C211yesmaximal, characteristic, complemented
7#19135413C211yesmaximal, characteristic, complemented
8#19135410C211yesmaximal, characteristic, complemented
9#19135405C211yesmaximal, characteristic, complemented
10#19135395C211yesmaximal, characteristic, complemented
11#19134532C211yesmaximal, characteristic
12#19134532C211yesmaximal, characteristic
13#19134528C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic, complemented
15C43×#1983C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18#14583469—24no—
19#14583469C418yescomplemented
20C2×#13063325C2211yescharacteristic
21C2×#13063323C2211yescharacteristic
22C2×#13063312C2211yescharacteristic
23C2×#13063307—21no—
24C2×#13063307—21no—
25C2×#13063302—21no—
26C2×#13063302—21no—
27C2×#13063282C2211yescharacteristic
28#14582959—24no—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×#13063235C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic
46#14582790—21no—
47#14582788—21no—
48#14582783—21no—
49#14582781—21no—
50#14582768C2211yescharacteristic
51#14582764C2211yescharacteristic
52#14582756C2211yescharacteristic
53#14582756C2211yescharacteristic
54C4×C4⋊Dic43C2211yescharacteristic
55C2×#124×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C2×#10621900—22no—
63C2×#10621900—41no—
64C2×#10621900—41no—
65C2×#10621900—41no—
66C2×#10621900—41no—
67C2×#10621900C2×C414yes—
68C22×Dic86—21no—
69C22×Dic86C2311yescharacteristic
70C22×Dic86C2311yescharacteristic
71C2×Q8×D43—22no—
72C2×Q8×D43—41no—
73C2×Q8×D43—41no—
74C2×Q8×D43—41no—
75C2×Q8×D43—41no—
76C2×Q8×D43C2×C414yes—
77C22×C22⋊D43—21no—
78C23×Dic43—21no—
79C22×C4×D43—21no—
80C22×C4×D43C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063325—22no—
84#13063325C2×C414yes—
85#13063323—22no—
86#13063323C2×C414yes—
87#13063312—22no—
88#13063312C2×C414yes—
89#13063307—28no—
90#13063307—28no—
91#13063302—28no—
92#13063302—28no—
93#13063282C2×C414yes—
94#13063282D414yes—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4D411yescharacteristic
104C2×Dic43⋊C4D411yescharacteristic
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4D411yescharacteristic
110C2×(C2×D43)⋊C4D411yescharacteristic
111C2×C4×Dic43—21no—
112C2×C4×Dic43C2311yescharacteristic
113C4⋊(C43⋊C8)—22no—
114#13063250—41no—
115#13063250—41no—
116#13063250—41no—
117#13063250—41no—
118#13063249—41no—
119#13063249—41no—
120#13063248—41no—
121#13063248—41no—
122#13063248—41no—
123#13063248—41no—
124#13063246—41no—
125#13063246—41no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—22no—
128#13063235—22no—
129C8×Dic43—22no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C22×Q8×C43C2311yescharacteristic
136C22×D4×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139#124×C43—22no—
140#124×C43C2×C414yes—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C42×C43—21no—
146C2×C42×C43C2311yescharacteristic
147C4⋊C8×C43—22no—
148#103×C43—41no—
149#103×C43—41no—
150#102×C43—41no—
151#102×C43—41no—
152#95×C43—21no—
153C24×C43—21no—
154C23×D43C2×D411yescharacteristic
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43C22×C412yes—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43C22×C412yes—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2411yescharacteristic
173C2×C22⋊D43—24no—
174C2×C22⋊D43—42no—
175C2×C22⋊D43—42no—
176C22×Dic43—24no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—42no—
182C22×Dic43—42no—
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186Q8×D43—44no—
187Q8×D43—44no—
188Q8×D43—44no—
189Q8×D43—44no—
190#10621900—44no—
191#10621900—44no—
192#10621900—44no—
193#10621900—44no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—24no—
199C2×C4×D43—42no—
200C2×C4×D43—42no—
201C2×C4×D43C22×C412yes—
202C2×C4×D43C2×D412yes—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—24no—
214C2×Dic86—42no—
215C2×Dic86—42no—
216C2×Dic86C22×C412yes—
217C2×Dic86C22×C412yes—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C22⋊C4×C43—24no—
229C22⋊C4×C43—24no—
230C42×C43—81no—
231C42×C43C22×C412yes—
232C42×C43C2×D412yes—
233C22⋊Dic43—24no—
234C22⋊Dic43—24no—
235(C2×D43)⋊C4—81no—
236(C2×D43)⋊C4—81no—
237(C2×D43)⋊C4C22⋊C414yes—
238(C2×D43)⋊C4C22⋊C414yes—
239C4⋊Dic43—24no—
240C4⋊Dic43—24no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245Dic43⋊C4—24no—
246Dic43⋊C4—24no—
247Dic43⋊C4—81no—
248Dic43⋊C4—81no—
249Dic43⋊C4C22⋊C414yes—
250Dic43⋊C4C22⋊C414yes—
251C4×Dic43—81no—
252C4×Dic43C22×C412yes—
253C4×Dic43C2×D412yes—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C23×C43—22no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43C22×D411yescharacteristic
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43C2×C22⋊C412yes—
275Q8×C43—22no—
276Q8×C43—22no—
277Q8×C43—41no—
278Q8×C43—41no—
279D4×C43—22no—
280D4×C43—22no—
281D4×C43—41no—
282D4×C43—41no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—22no—
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×C43C2×C22⋊C412yes—
297C2×C4×C43C2×C22⋊C412yes—
298C2×C4×C43C23×C411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43H(5,𝔽2)11yescharacteristic
301C2×C4×C43H(5,𝔽2)11yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C22⋊D43—48no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—48no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43C2×C22⋊C412yes—
325C2×Dic43C2×C22⋊C412yes—
326C2×Dic43C2×C22⋊C412yes—
327C4×D43—22no—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—22no—
331C4×D43—48no—
332Dic86—22no—
333Dic86—22no—
334Dic86—22no—
335Dic86—22no—
336Dic86—48no—
337Dic86—41no—
338Dic86—41no—
339Dic86—41no—
340Dic86—41no—
341C8×C43—41no—
342C8×C43—41no—
343C43⋊C8—41no—
344C43⋊C8—41no—
345#21814—431nomaximal, Sylow
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43C22×C22⋊C411yescharacteristic
354C22×C43#53511yescharacteristic
355C22×C43#53511yescharacteristic
356C22×C43#57711yescharacteristic
357C22×C43#57711yescharacteristic
358C22×C43#57811yescharacteristic
359C22×C43#57811yescharacteristic
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—41no—
364C2×D43—41no—
365C2×D43—41no—
366C2×D43—41no—
367C4×C43—22no—
368C4×C43—22no—
369C4×C43—42no—
370C4×C43—81no—
371C4×C43—81no—
372C4×C43#51811yescharacteristic
373C4×C43#51811yescharacteristic
374C4×C43#53511yescharacteristic
375C4×C43#53511yescharacteristic
376Dic43—22no—
377Dic43—22no—
378Dic43—22no—
379Dic43—42no—
380Dic43—42no—
381Dic43—81no—
382Dic43—81no—
383C2×#536—431no—
384C2×#433—431no—
385#2314—431no—
386#1983—431no—
387#1983D4311yescharacteristic, complemented
388#1981—431no—
389#1981—431no—
390#1960—431no—
391#1959—431no—
392#1958—431no—
393#1956—431no—
394#1788—431no—
395#1788—431no—
396#1787—431no—
397#1787—431no—
398C2×C43—82no—
399C2×C43#230911yescharacteristic
400C2×C43#289811yescharacteristic
401C2×C43#289811yescharacteristic
402C2×C43#322111yescharacteristic
403C2×C43#322311yescharacteristic
404C2×C43#322511yescharacteristic
405C2×C43#322511yescharacteristic
406D43—42no—
407C22×#41—431no—
408C23×Q8—431no—
409#536—438no—
410#536—864no—
411C2×C4⋊Q8—431no—
412C2×C4⋊Q8—431no—
413C2×#124—431no—
414C2×#124C2×D4311yescharacteristic
415C2×#123—861no—
416C2×#123—861no—
417C2×C22⋊Q8—861no—
418C2×C22⋊Q8—861no—
419C2×#117—431no—
420#433—864no—
421C2×C4⋊C8—431no—
422C2×C4⋊C8C2×D4311yescharacteristic
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103C2×D4311yescharacteristic
434C2×#103C2×D4311yescharacteristic
435C2×#102—431no—
436C2×#102—431no—
437C2×#102C2×D4311yescharacteristic
438C2×#102C2×D4311yescharacteristic
439C2×C22⋊C8—431no—
440C2×C22⋊C8—431no—
441C2×#97—431no—
442C2×C4×C8—431no—
443#388—861no—
444#388—861no—
445#387—861no—
446#387—861no—
447#384—431no—
448#382—431no—
449#380—431no—
450#380—431no—
451C4×C4⋊C4—431no—
452C4×C4⋊C4C2×D4311yescharacteristic
453C43#2181411yescharacteristic, complemented, Sylow
454C2×#41—434no—
455C2×#41—862no—
456C2×#41—1721no—
457C2×#41—1721no—
458C2×#41—1721no—
459C2×#41—1721no—
460C22×Q8—434no—
461C22×Q8—431no—
462C22×Q8—431no—
463C22×Q8—861no—
464C22×Q8—862no—
465C22×Q8—1721no—
466C22×Q8—1721no—
467C22×Q8—1721no—
468C22×Q8—1721no—
469C22×Q8C22×D4311yescharacteristic
470C22×D4—861no—
471C22×D4C22×D4311yescharacteristic
472C23×C4—431no—
473C23×C4—861no—
474C23×C4—861no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479C4⋊Q8—434no—
480C4⋊Q8—434no—
481C4⋊Q8—862no—
482C4⋊Q8—862no—
483#124—22no—
484#124—434no—
485#124—862no—
486#124C4×D4314yes—
487#123—868no—
488#123—868no—
489C22⋊Q8—868no—
490C22⋊Q8—868no—
491#117—434no—
492#117—434no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—431no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C42—21no—
514C2×C42—431no—
515C2×C42—861no—
516C2×C42C22×D4311yescharacteristic
517C4⋊C8—22no—
518C4⋊C8—862no—
519#103—41no—
520#103—41no—
521#103—1721no—
522#103—1721no—
523#103—1721no—
524#103—1721no—
525#103—1721no—
526#103—1721no—
527#103—1721no—
528#103—1721no—
529#103—1721no—
530#103—1721no—
531#102—41no—
532#102—41no—
533#102—1721no—
534#102—1721no—
535C22⋊C8—862no—
536C22⋊C8—862no—
537#97—862no—
538C4×C8—862no—
539#95—21no—
540#95—861no—
541#95—861no—
542#95—861no—
543#95—861no—
544#95—861no—
545C24—21no—
546C24—431no—
547#41—1724no—
548#41—1724no—
549#41—1724no—
550#41—1724no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—432no—
557C2×Q8—432no—
558C2×Q8—864no—
559C2×Q8—861no—
560C2×Q8—861no—
561C2×Q8—861no—
562C2×Q8—861no—
563C2×Q8—861no—
564C2×Q8—861no—
565C2×Q8—861no—
566C2×Q8—861no—
567C2×Q8—861no—
568C2×Q8—861no—
569C2×Q8—1722no—
570C2×Q8—1722no—
571C2×Q8—1724no—
572C2×Q8—1724no—
573C2×Q8—1724no—
574C2×Q8—1724no—
575C2×Q8C2×C4×D4312yes—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—864no—
582C2×D4—1722no—
583C2×D4—1722no—
584C2×D4C2×C4×D4312yes—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—431no—
589C22×C4—431no—
590C22×C4—431no—
591C22×C4—432no—
592C22×C4—432no—
593C22×C4—864no—
594C22×C4—864no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—1722no—
604C22×C4—1722no—
605C22×C4—1722no—
606C22×C4—1722no—
607C22×C4D4×D4311yescharacteristic
608C22×C4D4×D4311yescharacteristic
609C22×C4C23×D4311yescharacteristic
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—434no—
627C4⋊C4—434no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—861no—
636C4⋊C4—3441no—
637C4⋊C4—3441no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—434no—
641C22⋊C4—434no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—3441no—
645C22⋊C4—3441no—
646C42—81no—
647C42—432no—
648C42—432no—
649C42—3441no—
650C42C2×C4×D4312yes—
651C42D4×D4312yes—
652C23—22no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—432no—
660C23—861no—
661C23—861no—
662C23—861no—
663C23—861no—
664C23—861no—
665C23—861no—
666C23C2×D4×D4311yescharacteristic
667Q8—22no—
668Q8—22no—
669Q8—41no—
670Q8—41no—
671Q8—862no—
672Q8—862no—
673Q8—862no—
674Q8—862no—
675Q8—1728no—
676Q8—1721no—
677Q8—1721no—
678Q8—1721no—
679Q8—1721no—
680D4—22no—
681D4—22no—
682D4—41no—
683D4—41no—
684D4—1728no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—432no—
699C2×C4—432no—
700C2×C4—432no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—1728no—
714C2×C4—1728no—
715C2×C4—1721no—
716C2×C4—1721no—
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×C4C22⋊C4×D4312yes—
726C2×C4C22⋊C4×D4312yes—
727C2×C4C22×C4×D4311yescharacteristic
728C2×C4C2×D4×D4311yescharacteristic
729C2×C4#1306337011yescharacteristic
730C2×C4#1306337011yescharacteristic
731C2×C4#1306337111yescharacteristic
732C2×C4#1306337111yescharacteristic
733C8—41no—
734C8—41no—
735C8—1721no—
736C8—1721no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—862no—
745C22—862no—
746C22—862no—
747C22—1721no—
748C22—1721no—
749C22—1721no—
750C22—1721no—
751C22C2×C22⋊C4×D4311yescharacteristic
752C22#1458346511yescharacteristic
753C22#1458346511yescharacteristic
754C22#1458370611yescharacteristic
755C22#1458370911yescharacteristic
756C22#1458371311yescharacteristic
757C22#1458371511yescharacteristic
758C4—22no—
759C4—22no—
760C4—42no—
761C4—81no—
762C4—81no—
763C4—862no—
764C4—862no—
765C4—862no—
766C4—3441no—
767C4—3441no—
768C4—1722no—
769C4—1722no—
770C4#1458337111yescharacteristic
771C4#1458337111yescharacteristic
772C4#1458346211yescharacteristic
773C4#1458346711yescharacteristic
774C2—82no—
775C2—1722no—
776C2#1913717411yescharacteristic
777C2#1914312411yescharacteristic
778C2#1914312611yescharacteristic
779C2#1914565311yescharacteristic
780C2#1914567511yescharacteristic
781C2#1914570111yescharacteristic
782C2#1914570911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1983C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenter#1983D43
hypocenterC43#21814
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#14582959C2semidirect
3. #19137200C2semidirect
4. #19135528C2semidirect
5. #19135518C2semidirect
6. #19135517C2semidirect
7. #19135413C2semidirect
8. #19135410C2semidirect
9. #19135405C2semidirect
10. #19135395C2semidirect
13. #19134528C2semidirect
14. #19134528C2semidirect
15. C43×#1983C2semidirect
19. #14583469C4semidirect
387. #1983D43semidirect
453. C43#21814semidirect

Maximal subgroups

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

subgroupindex
C2×#145834692
C2×#145829592
#191372002
#191355282
#191355182
#191355172
#191354132
#191354102
#191354052
#191353952
#191345322
#191345282
C43×#19832
#2181443