Finite Group Databasebeta

← #25128570

Subgroups — #25128570

Order 11008.

1206 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×#14583509C211yesmaximal, characteristic, complemented
2C2×#14583061C211yesmaximal, characteristic
3#19137187C211yesmaximal, characteristic
4#19135744C211yesmaximal, characteristic, complemented
5#19135739C211yesmaximal, characteristic, complemented
6#19135693C211yesmaximal, characteristic, complemented
7#19135676C211yesmaximal, characteristic, complemented
8#19134952C211yesmaximal, characteristic, complemented
9#19134947C211yesmaximal, characteristic, complemented
10#19134938C211yesmaximal, characteristic, complemented
11#19134933C211yesmaximal, characteristic, complemented
12#19134903C211yesmaximal, characteristic, complemented
13#19134900C211yesmaximal, characteristic, complemented
14#19134664C211yesmaximal, characteristic, complemented
15C2×C43×#452C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18#14583509—24no—
19#14583509—24no—
20C2×#13063323C2211yescharacteristic
21C2×#13063318—21no—
22C2×#13063318—21no—
23C2×#13063316—21no—
24C2×#13063316C2211yescharacteristic
25C2×#13063315—21no—
26C2×#13063304C2211yescharacteristic
27C2×Q8×Dic43C2211yescharacteristic
28C2×#13063290C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31#14583061—24no—
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39#14582806C2211yescharacteristic
40#14582806C2211yescharacteristic
41#14582802C2211yescharacteristic
42#14582802C2211yescharacteristic
43#14582779—21no—
44#14582779—21no—
45#14582759—21no—
46#14582759—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×#41×C43C2211yescharacteristic
56C22×Q16×C43C2211yescharacteristic
57C22×SD16×C43C2211yescharacteristic
58C2×C22⋊Q8×C43C2211yescharacteristic
59C43×#452—24no—
60C2×#103×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C23×Dic43—21no—
65C2×#10621885—22no—
66C2×#10621885—22no—
67C2×#10621885—41no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063323—22no—
74#13063323—22no—
75#13063318—28no—
76#13063318—28no—
77#13063316—28no—
78#13063316—22no—
79#13063316—22no—
80#13063315—28no—
81#13063304—22no—
82#13063304D414yes—
83Q8×Dic43—22no—
84Q8×Dic43—22no—
85#13063290—22no—
86#13063290—22no—
87#13063284—22no—
88#13063284—22no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—41no—
93C2×C4⋊Dic43—41no—
94C2×C4⋊Dic43D411yescharacteristic
95C2×C4⋊Dic43D411yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43D411yescharacteristic
110C2×C22⋊Dic43D411yescharacteristic
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115#13063250—41no—
116#13063250—41no—
117#13063249—22no—
118#13063249—41no—
119#13063249—41no—
120#13063246—22no—
121C22⋊(C43⋊C8)—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C2×#41×C43—22no—
127C2×#41×C43—22no—
128C2×#41×C43—22no—
129C2×#41×C43—22no—
130C2×#41×C43—41no—
131C2×#41×C43—41no—
132C22×Q8×C43C2311yescharacteristic
133C22×Q8×C43C2311yescharacteristic
134C22×D4×C43—21no—
135C22×D4×C43C2311yescharacteristic
136C23×C4×C43—21no—
137C23×C4×C43C2311yescharacteristic
138C2×Q16×C43—22no—
139C2×Q16×C43—22no—
140C2×Q16×C43—41no—
141C2×SD16×C43—22no—
142C2×SD16×C43—22no—
143C2×SD16×C43—41no—
144C22×C8×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146C22⋊Q8×C43—22no—
147C22⋊Q8×C43D414yes—
148C2×C4⋊C4×C43—21no—
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C22⋊C4×C43—21no—
151#103×C43—22no—
152#102×C43—22no—
153C22⋊C8×C43—22no—
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156#41×C43—44no—
157#41×C43—44no—
158#41×C43—44no—
159#41×C43—44no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43C2×D412yes—
171C2×Q8×C43#4112yes—
172C2×D4×C43—24no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43#4112yes—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—24no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—42no—
190C22×C4×C43—42no—
191C22×C4×C43C2×D412yes—
192C22×C4×C43C2×D412yes—
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—42no—
200C22×Dic43—81no—
201C22×Dic43—81no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86C2×D412yes—
212Q16×C43—44no—
213SD16×C43—44no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C4⋊C4×C43—24no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43C2×D412yes—
223C22⋊C4×C43—24no—
224C22⋊Dic43—24no—
225C22⋊Dic43—22no—
226C22⋊Dic43—22no—
227C22⋊Dic43—81no—
228C22⋊Dic43—81no—
229C22⋊Dic43—81no—
230C22⋊Dic43—81no—
231#10621885—44no—
232#10621883—44no—
233C4⋊Dic43—24no—
234C4⋊Dic43—24no—
235C4⋊Dic43—22no—
236C4⋊Dic43—22no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—42no—
243C4⋊Dic43C2×D412yes—
244Dic43⋊C4—24no—
245Dic43⋊C4—24no—
246Dic43⋊C4—24no—
247Dic43⋊C4—24no—
248Dic43⋊C4—24no—
249C4×Dic43—24no—
250C4×Dic43—24no—
251C4×Dic43—21no—
252C4×Dic43—21no—
253C4×Dic43—21no—
254C4×Dic43—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—22no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43#12012yes—
275C23×C43C22×D411yescharacteristic
276Q8×C43—22no—
277Q8×C43—22no—
278Q8×C43—22no—
279Q8×C43—22no—
280Q8×C43—41no—
281Q8×C43—41no—
282Q8×C43—41no—
283Q8×C43—41no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—48no—
287D4×C43—41no—
288D4×C43—41no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—48no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43#12012yes—
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—22no—
316C2×Dic43—21no—
317C2×Dic43—22no—
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×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—84no—
337Dic86—22no—
338Dic86—22no—
339Dic86—41no—
340Dic86—41no—
341C8×C43—41no—
342C8×C43—41no—
343C43⋊C8—41no—
344C43⋊C8—41no—
345#23944—431nomaximal, Sylow
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43C2×#12011yescharacteristic
361C22×C43#52511yescharacteristic
362C22×C43#53511yescharacteristic
363C22×C43#57711yescharacteristic
364C22×C43#57711yescharacteristic
365C22×C43#57811yescharacteristic
366C22×C43#57811yescharacteristic
367C4×C43—22no—
368C4×C43—42no—
369C4×C43—42no—
370C4×C43—42no—
371C4×C43#54611yescharacteristic
372C4×C43#54611yescharacteristic
373C4×C43#54611yescharacteristic
374C4×C43#54611yescharacteristic
375Dic43—42no—
376Dic43—41no—
377Dic43—41no—
378Dic43—41no—
379Dic43—41no—
380Dic43—42no—
381Dic43—81no—
382Dic43—81no—
383C2×#541—431no—
384C2×#452—431no—
385C2×#452D4311yescharacteristic
386#2311—431no—
387#2026—431no—
388#2025—431no—
389#2016—431no—
390#2013—431no—
391#1880—431no—
392#1880—431no—
393#1878—431no—
394#1878—431no—
395#1872—431no—
396#1872—431no—
397#1818—431no—
398C2×C43—42no—
399C2×C43—82no—
400C2×C43#240411yescharacteristic
401C2×C43#301311yescharacteristic
402C2×C43#301311yescharacteristic
403C2×C43#312011yescharacteristic
404C2×C43#312011yescharacteristic
405C2×C43#322211yescharacteristic
406C2×C43#322311yescharacteristic
407C22×#41C2×D4311yescharacteristic
408C22×Q16—431no—
409C22×Q16C2×D4311yescharacteristic
410C22×SD16—431no—
411C22×SD16C2×D4311yescharacteristic
412#541—864no—
413#541—864no—
414C2×C4⋊Q8—431no—
415C2×#126—861no—
416C2×#126—861no—
417C2×#125—431no—
418C2×#125—861no—
419C2×#125—861no—
420C2×C22⋊Q8—431no—
421C2×C22⋊Q8C2×D4311yescharacteristic
422C2×C4×Q8—431no—
423C2×C4×Q8—431no—
424C2×#117—431no—
425C22×C4⋊C4—431no—
426#452—24no—
427#452—864no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103C2×D4311yescharacteristic
434C2×#102—431no—
435C2×#102C2×D4311yescharacteristic
436C2×C22⋊C8—431no—
437C2×C22⋊C8C2×D4311yescharacteristic
438#391—431no—
439#391—431no—
440#390—431no—
441#390—431no—
442#386—861no—
443#386—861no—
444#380—861no—
445#380—861no—
446#340—431no—
447#340—431no—
448#340—431no—
449#340—431no—
450#336—431no—
451#336—431no—
452#336—431no—
453#336—431no—
454C43#2394411yescharacteristic, complemented, Sylow
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41—22no—
459C2×#41—41no—
460C2×#41—41no—
461C22×Q8—431no—
462C22×Q8C22×D4311yescharacteristic
463C22×Q8C22×D4311yescharacteristic
464C22×D4—21no—
465C22×D4C22×D4311yescharacteristic
466C23×C4—21no—
467C23×C4—861no—
468C23×C4C22×D4311yescharacteristic
469C2×Q16—22no—
470C2×Q16—22no—
471C2×Q16—41no—
472C2×Q16—862no—
473C2×Q16—862no—
474C2×Q16—1721no—
475C2×SD16—22no—
476C2×SD16—22no—
477C2×SD16—41no—
478C2×SD16—862no—
479C2×SD16—862no—
480C2×SD16—1721no—
481C22×C8—431no—
482C22×C8—431no—
483C22×C8C22×D4311yescharacteristic
484C22×C8C22×D4311yescharacteristic
485C4⋊Q8—862no—
486C4⋊Q8—862no—
487#126—868no—
488#126—868no—
489#125—862no—
490#125—868no—
491#125—868no—
492#125—862no—
493C22⋊Q8—22no—
494C22⋊Q8—434no—
495C22⋊Q8—862no—
496C22⋊Q8C22⋊D4314yes—
497C4×Q8—862no—
498C4×Q8—862no—
499C4×Q8—862no—
500C4×Q8—862no—
501#117—862no—
502#117—862no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—1721no—
518C2×C4⋊C4—1721no—
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C42—431no—
529C2×C42—431no—
530C2×C42—861no—
531C2×C42—861no—
532#103—22no—
533#103—862no—
534#103—1721no—
535#103—1721no—
536#103—1721no—
537#103—1721no—
538#102—22no—
539#102—862no—
540C22⋊C8—22no—
541C22⋊C8—862no—
542#95—861no—
543#95—861no—
544#95—861no—
545#95—861no—
546C24—21no—
547C24D4×D4311yescharacteristic
548#41—44no—
549#41—44no—
550#41—44no—
551#41—44no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—432no—
563C2×Q8—861no—
564C2×Q8—861no—
565C2×Q8—861no—
566C2×Q8—861no—
567C2×Q8—861no—
568C2×Q8#1062190012yes—
569C2×Q8C2×C22⋊D4312yes—
570C2×D4—24no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4#1062190012yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—431no—
590C22×C4—431no—
591C22×C4—431no—
592C22×C4—431no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—3441no—
598C22×C4—3441no—
599C22×C4—1722no—
600C22×C4D4×D4311yescharacteristic
601C22×C4D4×D4312yes—
602C22×C4C2×C22⋊D4312yes—
603C22×C4C23×D4311yescharacteristic
604Q16—44no—
605Q16—1724no—
606SD16—44no—
607SD16—1724no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—432no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—862no—
630C4⋊C4—862no—
631C4⋊C4—864no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—861no—
636C4⋊C4—861no—
637C4⋊C4—1722no—
638C4⋊C4C2×C22⋊D4312yes—
639C22⋊C4—24no—
640C22⋊C4—862no—
641C22⋊C4—862no—
642C22⋊C4—864no—
643C22⋊C4—3441no—
644C22⋊C4—3441no—
645C22⋊C4—3441no—
646C22⋊C4—3441no—
647C42—864no—
648C42—864no—
649C42—861no—
650C42—861no—
651C42—861no—
652C42—861no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—22no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23#1306329312yes—
667C23C2×D4×D4311yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—862no—
677Q8—862no—
678Q8—1721no—
679Q8—1721no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—41no—
684D4—41no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—48no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—862no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—862no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—3444no—
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×C4—1721no—
726C2×C4#1306329312yes—
727C2×C4C2×D4×D4311yescharacteristic
728C2×C4C22×C22⋊D4311yescharacteristic
729C2×C4C2×#1062190011yescharacteristic
730C2×C4C2×#1062190011yescharacteristic
731C2×C4#1306337011yescharacteristic
732C2×C4#1306337011yescharacteristic
733C8—41no—
734C8—41no—
735C8—1721no—
736C8—1721no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×#1306329311yescharacteristic
752C22#1458340511yescharacteristic
753C22#1458346411yescharacteristic
754C22#1458370611yescharacteristic
755C22#1458370811yescharacteristic
756C22#1458371311yescharacteristic
757C22#1458371511yescharacteristic
758C4—22no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—3441no—
763C4—3441no—
764C4—1722no—
765C4—1721no—
766C4—1721no—
767C4—1721no—
768C4—1721no—
769C4—1722no—
770C4#1458353611yescharacteristic
771C4#1458353611yescharacteristic
772C4#1458354311yescharacteristic
773C4#1458354311yescharacteristic
774C2—42no—
775C2—82no—
776C2#1913791111yescharacteristic
777C2#1914390611yescharacteristic
778C2#1914390911yescharacteristic
779C2#1914480211yescharacteristic
780C2#1914481011yescharacteristic
781C2#1914566511yescharacteristic
782C2#1914567611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
hypercenterC2×#452D43
hypocenterC43#23944
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#14583509C2semidirect
4. #19135744C2semidirect
5. #19135739C2semidirect
6. #19135693C2semidirect
7. #19135676C2semidirect
8. #19134952C2semidirect
9. #19134947C2semidirect
10. #19134938C2semidirect
11. #19134933C2semidirect
12. #19134903C2semidirect
13. #19134900C2semidirect
14. #19134664C2semidirect
454. C43#23944semidirect

Maximal subgroups

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

subgroupindex
C2×#145835092
C2×#145830612
#191371872
#191357442
#191357392
#191356932
#191356762
#191349522
#191349472
#191349382
#191349332
#191349032
#191349002
#191346642
C2×C43×#4522
#2394443