Finite Group Databasebeta

← #25102380

Subgroups — #25102380

Order 11008.

1400 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583376C211yesmaximal, characteristic, complemented
2C2×#14583040C211yesmaximal, characteristic
3C2×#14583001C211yesmaximal, characteristic, complemented
4C2×C4×#10621873C211yesmaximal, characteristic, complemented
5#19137288C211yesmaximal, characteristic
6#19134949C211yesmaximal, characteristic, complemented
7#19134949C211yesmaximal, characteristic, complemented
8#19134915C211yesmaximal, characteristic
9#19134866C211yesmaximal, characteristic, complemented
10#19134852C211yesmaximal, characteristic, complemented
11#19134796C211yesmaximal, characteristic, complemented
12#19134531C211yesmaximal, characteristic, complemented
13#19134426C211yesmaximal, characteristic, complemented
14C4×#13063250C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20#14583376—24no—
21#14583376—24no—
22C2×C4×Dic86C2211yescharacteristic
23C2×C4×Dic86C2211yescharacteristic
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×#13063290—21no—
27C2×#13063290—21no—
28C2×C4×D172C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30C2×#13063281—21no—
31C2×#13063281—21no—
32#14583040C418yescomplemented
33#14583001—24no—
34C4×#10621873—24no—
35C2×#13063259C2211yescharacteristic
36C2×#13063257C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40C2×#13063250C2211yescharacteristic
41C2×#13063250C2211yescharacteristic
42C2×#13063250C2211yescharacteristic
43C2×#13063247C2211yescharacteristic
44C2×#13063247C2211yescharacteristic
45#14582801C2211yescharacteristic
46#14582799—21no—
47#14582797C2211yescharacteristic
48#14582789—21no—
49#14582775—21no—
50#14582770—21no—
51#14582759C2211yescharacteristic
52C4×C4⋊Dic43C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582662C2211yescharacteristic
56#14582662C2211yescharacteristic
57C2×#117×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C2×C4×C8×C43C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C43×#336C2211yescharacteristic
64C22×Dic86—21no—
65C22×Dic86—22no—
66C22×Dic86—22no—
67C22×Dic86—22no—
68C22×Dic86—22no—
69C22×Dic86—22no—
70C22×Dic86C2×C414yescomplemented
71C22×Dic86C2311yescharacteristic
72C22×Dic86C2311yescharacteristic
73C22×D172C2311yescharacteristic
74C22×C22⋊D43—21no—
75C23×Dic43—21no—
76C22×C4×D43—21no—
77C2×#10621873—22no—
78C2×#10621873—22no—
79C2×#10621873—22no—
80C2×#10621873—22no—
81C2×#10621873C2×C414yes—
82C2×#10621873C2×C414yes—
83#13063299—22no—
84#13063299C2×C414yes—
85C4×Dic86—22no—
86C4×Dic86—22no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×Dic86—22no—
91C4×Dic86D414yescomplemented
92C4×Dic86D414yescomplemented
93#13063290—28no—
94#13063290—28no—
95C4×D172—22no—
96C4×D172—22no—
97#13063284—22no—
98#13063284—22no—
99#13063281—28no—
100#13063281—28no—
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43—21no—
123#13063259—22no—
124#13063257—22no—
125#13063250—22no—
126#13063250—22no—
127#13063250—22no—
128#13063250—22no—
129#13063250C2×C414yescomplemented
130#13063250C2×C414yescomplemented
131#13063247—22no—
132#13063247—22no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C23×C4×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141#117×C43—22no—
142#117×C43—22no—
143C2×C4⋊C4×C43D411yescharacteristic
144C2×C4⋊C4×C43D411yescharacteristic
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C42×C43C2311yescharacteristic
148C2×C42×C43C2311yescharacteristic
149C22⋊C8×C43—22no—
150C22⋊C8×C43C2×C414yescomplemented
151#97×C43—22no—
152C4×C8×C43—22no—
153C24×C43C2×D411yescharacteristic
154C23×D43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43C22×C412yes—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43#4112yes—
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—24no—
168C2×C22⋊D43—81no—
169C2×C22⋊D43—81no—
170C22×Dic43—24no—
171C22×Dic43—24no—
172C22×Dic43—24no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172C22×C412yes—
186C2×C4×D43—42no—
187C2×C4×D43—81no—
188C2×C4×D43—81no—
189C2×Dic86—24no—
190C2×Dic86—24no—
191C2×Dic86—28no—
192C2×Dic86—28no—
193C2×Dic86—24no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—28no—
201C2×Dic86—28no—
202C2×Dic86C22×C412yes—
203C2×Dic86C22×C412yes—
204C2×Dic86C2×D412yes—
205C2×Dic86C2×D412yes—
206C2×Dic86#4112yes—
207C2×Dic86#4112yes—
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×C43C22×C412yes—
219C2×C8×C43C22×C412yes—
220C4⋊C4×C43—22no—
221C4⋊C4×C43—22no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—22no—
224C42×C43—21no—
225C42×C43—21no—
226C42×C43C2×D412yes—
227C42×C43C2×D412yes—
228C22⋊Dic43—24no—
229C22⋊Dic43—81no—
230(C2×D43)⋊C4—24no—
231(C2×D43)⋊C4—42no—
232(C2×D43)⋊C4—81no—
233(C2×D43)⋊C4—81no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43C22×C412yes—
242C4⋊Dic43C2×D412yes—
243C4⋊Dic43C2×D412yes—
244Dic43⋊C4—24no—
245Dic43⋊C4—24no—
246Dic43⋊C4—24no—
247Dic43⋊C4—24no—
248Dic43⋊C4—81no—
249C4×Dic43—24no—
250C4×Dic43—24no—
251C4×Dic43—24no—
252C4×Dic43—24no—
253C4×Dic43—24no—
254C4×Dic43—81no—
255#10621873—28no—
256#10621873—28no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43C4×D412yes—
264C23×C43C22×D411yescharacteristic
265C22×D43—22no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43C4×D412yes—
289C2×C4×C43#12012yes—
290C2×C4×C43#12012yes—
291C2×C4×C43C23×C411yescharacteristic
292C2×C4×C43C22×D411yescharacteristic
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C22⋊D43—84no—
298C2×Dic43—216no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
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—
320D172—22no—
321D172—22no—
322D172—41no—
323D172—41no—
324C4×D43—84no—
325Dic86—216no—
326Dic86—22no—
327Dic86—22no—
328Dic86—22no—
329Dic86—22no—
330Dic86—22no—
331Dic86—22no—
332Dic86C4×D414yes—
333Dic86C4×D414yes—
334C8×C43—22no—
335C8×C43—22no—
336C8×C43—41no—
337C8×C43—41no—
338#21462—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43C2×C4×D411yescharacteristic
347C22×C43C2×#12011yescharacteristic
348C22×C43#52511yescharacteristic
349C22×C43#57711yescharacteristic
350C22×C43#57711yescharacteristic
351C22×C43#57711yescharacteristic
352C22×C43#57811yescharacteristic
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—81no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C4×C43—22no—
361C4×C43—22no—
362C4×C43—22no—
363C4×C43—41no—
364C4×C43—41no—
365C4×C43C2×C4×D411yescharacteristic
366C4×C43C2×C4×D411yescharacteristic
367C4×C43#52511yescharacteristic
368C4×C43#52511yescharacteristic
369Dic43—24no—
370Dic43—24no—
371Dic43—42no—
372Dic43—42no—
373Dic43—42no—
374Dic43—81no—
375Dic43—81no—
376C2×#519—431no—
377C2×#448—431no—
378C2×#440—431no—
379C2×C4×SD16—431no—
380#2324—431no—
381#1880—431no—
382#1880—431no—
383#1875—431no—
384#1865—431no—
385#1863—431no—
386#1854—431no—
387#1787—431no—
388#1763—431no—
389C4×#103—431no—
390#1750D4311yescharacteristic, complemented
391C2×C43—42no—
392C2×C43C4×#12011yescharacteristic
393C2×C43#294711yescharacteristic
394C2×C43#294911yescharacteristic
395C2×C43#301011yescharacteristic
396C2×C43#301311yescharacteristic
397C2×C43#312111yescharacteristic
398C2×C43#312611yescharacteristic
399D43—82no—
400C23×Q8—431no—
401C22×SD16—431no—
402C22×SD16—431no—
403C2×#121—431no—
404#519—864no—
405#519—864no—
406C2×C4×Q8—431no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—861no—
411C2×C4×Q8—861no—
412C2×C4×D4—431no—
413C2×#117—431no—
414C2×#117—861no—
415C2×#117—861no—
416C2×#117C2×D4311yescharacteristic
417#448—438no—
418#440—864no—
419C4×SD16—864no—
420C2×#107—431no—
421C2×#106—431no—
422C2×#103—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×C22⋊C8C2×D4311yescharacteristic
431C2×C22⋊C8C2×D4311yescharacteristic
432C2×#97C2×D4311yescharacteristic
433C2×C4×C8C2×D4311yescharacteristic
434#390—431no—
435#390—861no—
436#389—431no—
437#388—861no—
438#386—861no—
439#385—861no—
440#380—431no—
441C4×C4⋊C4—431no—
442#340—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446#336C2×D4311yescharacteristic
447#336C2×D4311yescharacteristic
448C43#2146211yescharacteristic, complemented, Sylow
449C22×Q8—434no—
450C22×Q8—431no—
451C22×Q8—431no—
452C22×Q8—862no—
453C22×Q8—862no—
454C22×Q8—862no—
455C22×Q8—862no—
456C22×Q8—861no—
457C22×Q8—862no—
458C22×D4—431no—
459C22×D4—861no—
460C23×C4—861no—
461C23×C4—861no—
462C23×C4C22×D4311yescharacteristic
463C2×SD16—434no—
464C2×SD16—434no—
465C2×SD16—862no—
466C2×SD16—862no—
467C2×SD16—862no—
468C2×SD16—862no—
469C22×C8C22×D4311yescharacteristic
470C22×C8C22×D4311yescharacteristic
471C22×C8C22×D4311yescharacteristic
472C22×C8C22×D4311yescharacteristic
473#121—434no—
474#121—862no—
475C4×Q8—434no—
476C4×Q8—434no—
477C4×Q8—862no—
478C4×Q8—862no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—868no—
482C4×Q8—868no—
483C4×Q8—862no—
484C4×Q8—862no—
485C4×D4—862no—
486C4×D4—862no—
487#117—22no—
488#117—22no—
489#117—868no—
490#117—868no—
491#117—862no—
492#117—862no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4D17211yescharacteristic
504C2×C4⋊C4D17211yescharacteristic
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⋊C4D17211yescharacteristic
512C2×C22⋊C4D17211yescharacteristic
513C2×C42—861no—
514C2×C42—861no—
515C2×C42—861no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42C22×D4311yescharacteristic
520C2×C42C22×D4311yescharacteristic
521#107—862no—
522#106—862no—
523#103—434no—
524#103—434no—
525#103—862no—
526#103—862no—
527#103—862no—
528#103—862no—
529#102—862no—
530#102—862no—
531C22⋊C8—22no—
532C22⋊C8C4×D4314yescomplemented
533#97—22no—
534C4×C8—22no—
535#95—861no—
536#95—861no—
537#95—861no—
538C24—861no—
539C24C2×D17211yescharacteristic
540C2×Q8—432no—
541C2×Q8—432no—
542C2×Q8—432no—
543C2×Q8—432no—
544C2×Q8—432no—
545C2×Q8—432no—
546C2×Q8—868no—
547C2×Q8—868no—
548C2×Q8—864no—
549C2×Q8—864no—
550C2×Q8—868no—
551C2×Q8—868no—
552C2×Q8—864no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×D4—432no—
560C2×D4—864no—
561C2×D4—861no—
562C2×D4—861no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—3441no—
567C2×D4—3441no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—864no—
573C22×C4—864no—
574C22×C4—864no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—3441no—
583C22×C4—3441no—
584C22×C4—1722no—
585C22×C4C2×C4×D4312yes—
586C22×C4C2×D17211yescharacteristic
587C22×C4C2×D17211yescharacteristic
588C22×C4C2×D17211yescharacteristic
589C22×C4C2×D17211yescharacteristic
590C22×C4C2×D17211yescharacteristic
591C22×C4#1062189812yes—
592C22×C4C23×D4311yescharacteristic
593SD16—868no—
594SD16—868no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8C2×C4×D4312yes—
606C2×C8C2×C4×D4312yes—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—432no—
610C4⋊C4—432no—
611C4⋊C4—432no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—3441no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—864no—
627C22⋊C4—864no—
628C22⋊C4—3441no—
629C22⋊C4—3441no—
630C22⋊C4—3441no—
631C22⋊C4—1722no—
632C42—21no—
633C42—21no—
634C42—864no—
635C42—864no—
636C42—864no—
637C42—864no—
638C42—864no—
639C42—3441no—
640C42D4×D4312yes—
641C42D4×D4312yes—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—862no—
649C23—1721no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23C4×D17212yes—
656C23C22×D17211yescharacteristic
657Q8—434no—
658Q8—434no—
659Q8—8616no—
660Q8—862no—
661Q8—862no—
662Q8—862no—
663Q8—862no—
664Q8—862no—
665Q8—862no—
666D4—862no—
667D4—862no—
668D4—3444no—
669D4—1721no—
670D4—1721no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—8616no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—3444no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4C4×D17212yes—
711C2×C4#1306329512yes—
712C2×C4#1306329512yes—
713C2×C4C22×C4×D4311yescharacteristic
714C2×C4C2×D4×D4311yescharacteristic
715C2×C4C2×D4×D4311yescharacteristic
716C2×C4#41×D4311yescharacteristic
717C2×C4#41×D4311yescharacteristic
718C2×C4C2×#1062189811yescharacteristic
719C8—22no—
720C8—22no—
721C8—41no—
722C8—41no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—3441no—
731C22—3441no—
732C22—3441no—
733C22—3441no—
734C22—1722no—
735C22—1722no—
736C22—1722no—
737C22C2×C4×D17211yescharacteristic
738C22C2×#1306329511yescharacteristic
739C22#1458341111yescharacteristic
740C22#1458371111yescharacteristic
741C22#1458371111yescharacteristic
742C22#1458371111yescharacteristic
743C22#1458371611yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—41no—
748C4—41no—
749C4—864no—
750C4—864no—
751C4—3441no—
752C4—3441no—
753C4—1722no—
754C4—1722no—
755C4—1722no—
756C4C4×D4×D4311yescharacteristic
757C4C4×D4×D4311yescharacteristic
758C4#1458340811yescharacteristic
759C4#1458340811yescharacteristic
760C2—42no—
761C2—3442no—
762C2C4×#1306329511yescharacteristic
763C2#1914344011yescharacteristic
764C2#1914345611yescharacteristic
765C2#1914388311yescharacteristic
766C2#1914391311yescharacteristic
767C2#1914482611yescharacteristic
768C2#1914488711yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1750C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
cosocleC22×C4×C43C24
hypercenter#1750D43
hypocenterC43#21462
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
1. C2×#14583376C2semidirect
3. C2×#14583001C2semidirect
4. C2×C4×#10621873C2semidirect
6. #19134949C2semidirect
7. #19134949C2semidirect
9. #19134866C2semidirect
10. #19134852C2semidirect
11. #19134796C2semidirect
12. #19134531C2semidirect
13. #19134426C2semidirect
14. C4×#13063250C2semidirect
15. C43×#1750C2semidirect
32. #14583040C4semidirect
70. C22×Dic86C2×C4semidirect
91. C4×Dic86D4semidirect
92. C4×Dic86D4semidirect
129. #13063250C2×C4semidirect
130. #13063250C2×C4semidirect
150. C22⋊C8×C43C2×C4semidirect
390. #1750D43semidirect
448. C43#21462semidirect
532. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833762
C2×#145830402
C2×#145830012
C2×C4×#106218732
#191372882
#191349492
#191349152
#191348662
#191348522
#191347962
#191345312
#191344262
C4×#130632502
C43×#17502
#2146243