Finite Group Databasebeta

← #25102425

Subgroups — #25102425

Order 11008.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583379C211yesmaximal, characteristic
2C2×#14583063C211yesmaximal, characteristic
3C2×#14583001C211yesmaximal, characteristic, complemented
4C2×C4×Dic172C211yesmaximal, characteristic, complemented
5#19137277C211yesmaximal, characteristic, complemented
6#19134935C211yesmaximal, characteristic, complemented
7#19134928C211yesmaximal, characteristic, complemented
8#19134900C211yesmaximal, characteristic, complemented
9#19134852C211yesmaximal, characteristic, complemented
10#19134845C211yesmaximal, characteristic, complemented
11#19134785C211yesmaximal, characteristic, complemented
12#19134536C211yesmaximal, characteristic
13#19134426C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20#14583379—24no—
21#14583379—24no—
22C2×C4×Dic86C2211yescharacteristic
23C2×C4×Dic86C2211yescharacteristic
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27C2×(C22⋊D43)⋊C4—21no—
28C2×(C22⋊D43)⋊C4—21no—
29C2×#13063283—21no—
30C22×C4⋊Dic43C2211yescharacteristic
31C2×C4⋊C4×D43—21no—
32#14583063C418yescomplemented
33#14583001—24no—
34C4×Dic172—24no—
35C2×#13063259C2211yescharacteristic
36C2×#13063259C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40C2×#13063250C2211yescharacteristic
41C2×#13063250C2211yescharacteristic
42C2×#13063247C2211yescharacteristic
43C2×#13063247C2211yescharacteristic
44C2×#13063247C2211yescharacteristic
45#14582805C2211yescharacteristic
46#14582797C2211yescharacteristic
47#14582794—21no—
48#14582793—21no—
49#14582787—21no—
50#14582780—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
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898C2×C414yes—
70C22×Dic86C2311yescharacteristic
71C22×Dic86C2311yescharacteristic
72C22×D172C2311yescharacteristic
73C22×C22⋊D43—21no—
74C23×Dic43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C2×Dic172—22no—
79C2×Dic172—22no—
80C2×Dic172C2×C414yescomplemented
81C2×#10621873—22no—
82C2×#10621873—22no—
83C2×#10621873C2×C414yescomplemented
84#13063304—22no—
85#13063304C2×C414yescomplemented
86C4×Dic86—22no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×Dic86—22no—
91C4×Dic86D414yes—
92C4×D172—22no—
93C4×D172—22no—
94C4×D172—22no—
95C4×D172D414yes—
96(C22⋊D43)⋊C4—28no—
97(C22⋊D43)⋊C4—28no—
98#13063283—28no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43—22no—
101C2×C4⋊Dic43—22no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4—21no—
112C4⋊C4×D43—28no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43—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—
121#13063259—22no—
122#13063259—22no—
123#13063250—22no—
124#13063250—22no—
125#13063250—22no—
126#13063250—22no—
127#13063250C2×C414yescomplemented
128#13063247—22no—
129#13063247—22no—
130#13063247C2×C414yescomplemented
131C43⋊#95—21no—
132C43⋊#95—21no—
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—24no—
169C2×C22⋊D43—24no—
170C22×Dic43—24no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—81no—
179C22×Dic43—81no—
180#10621898—28no—
181#10621898—28no—
182#10621898—28no—
183#10621898—28no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172C22×C412yes—
188C2×D172C2×D412yes—
189C2×D172#4112yes—
190C2×C4×D43—24no—
191C2×C4×D43—24no—
192C2×C4×D43—24no—
193C2×C4×D43—24no—
194C2×C4×D43—24no—
195C2×C4×D43—81no—
196C2×C4×D43—81no—
197C2×C4×D43—81no—
198C2×C4×D43—81no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86C22×C412yes—
208C2×Dic86C22×C412yes—
209C2×Dic86C2×D412yes—
210C2×Dic86#4112yes—
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×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43C22×C412yes—
222C2×C8×C43C22×C412yes—
223C4⋊C4×C43—22no—
224C4⋊C4×C43—22no—
225C22⋊C4×C43—22no—
226C22⋊C4×C43—22no—
227C42×C43—21no—
228C42×C43—21no—
229C42×C43C2×D412yes—
230C42×C43C2×D412yes—
231C22⋊Dic43—24no—
232C22⋊Dic43—81no—
233(C2×D43)⋊C4—24no—
234(C2×D43)⋊C4—24no—
235C4⋊Dic43—24no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43C22×C412yes—
244C4⋊Dic43C2×D412yes—
245C4⋊Dic43C2×D412yes—
246Dic43⋊C4—24no—
247Dic43⋊C4—24no—
248Dic43⋊C4—24no—
249Dic43⋊C4—42no—
250Dic43⋊C4—81no—
251C4×Dic43—24no—
252C4×Dic43—24no—
253C4×Dic43—42no—
254C4×Dic43—81no—
255Dic172—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—22no—
267C22×D43—22no—
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—216no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
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—84no—
320D172—22no—
321D172—22no—
322D172—22no—
323D172C4×D414yes—
324C4×D43—216no—
325C4×D43—84no—
326C4×D43—84no—
327Dic86—22no—
328Dic86—22no—
329Dic86—22no—
330Dic86—22no—
331Dic86—22no—
332Dic86—41no—
333Dic86—41no—
334Dic86C4×D414yes—
335C8×C43—22no—
336C8×C43—22no—
337C8×C43—41no—
338C8×C43—41no—
339#21465—431nomaximal, Sylow
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43C2×C4×D411yescharacteristic
348C22×C43C2×#12011yescharacteristic
349C22×C43#52511yescharacteristic
350C22×C43#57611yescharacteristic
351C22×C43#57711yescharacteristic
352C22×C43#57811yescharacteristic
353C22×C43#57811yescharacteristic
354C2×D43—24no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C4×C43—22no—
362C4×C43—22no—
363C4×C43—22no—
364C4×C43—41no—
365C4×C43—41no—
366C4×C43C2×C4×D411yescharacteristic
367C4×C43C2×C4×D411yescharacteristic
368C4×C43#52511yescharacteristic
369C4×C43#52511yescharacteristic
370Dic43—24no—
371Dic43—42no—
372Dic43—42no—
373Dic43—42no—
374Dic43—42no—
375Dic43—81no—
376Dic43—81no—
377C2×#520—431no—
378C2×#452—431no—
379C2×#440—431no—
380C2×C4×Q16—431no—
381#2323—431no—
382#1878—431no—
383#1877—431no—
384#1872—431no—
385#1863—431no—
386#1862—431no—
387#1852—431no—
388#1788—431no—
389#1763—431no—
390C4×#102—431no—
391#1750D4311yescharacteristic, complemented
392C2×C43—42no—
393C2×C43C4×#12011yescharacteristic
394C2×C43#294711yescharacteristic
395C2×C43#295111yescharacteristic
396C2×C43#301111yescharacteristic
397C2×C43#301211yescharacteristic
398C2×C43#312011yescharacteristic
399C2×C43#312411yescharacteristic
400D43—44no—
401C22×#41—431no—
402C22×Q16—431no—
403C22×SD16—431no—
404C2×C22⋊Q8—431no—
405#520—864no—
406#520—864no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×D4—431no—
411C2×C4×D4—431no—
412C2×C4×D4—861no—
413C2×C4×D4—861no—
414C2×#117—861no—
415C2×#117C2×D4311yescharacteristic
416C22×C4⋊C4—431no—
417C22×C4⋊C4—861no—
418#452—438no—
419#440—864no—
420C4×Q16—864no—
421C2×#107—431no—
422C2×#107—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×C22⋊C8C2×D4311yescharacteristic
432C2×C22⋊C8C2×D4311yescharacteristic
433C2×#97C2×D4311yescharacteristic
434C2×C4×C8C2×D4311yescharacteristic
435#391—431no—
436#389—431no—
437#389—861no—
438#388—861no—
439#388—861no—
440#387—861no—
441#380—431no—
442C4×C4⋊C4—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#336C2×D4311yescharacteristic
448#336C2×D4311yescharacteristic
449C43#2146511yescharacteristic, complemented, Sylow
450C2×#41—434no—
451C2×#41—862no—
452C2×#41—862no—
453C2×#41—862no—
454C2×#41—862no—
455C2×#41—862no—
456C22×Q8—431no—
457C22×Q8—431no—
458C22×D4—431no—
459C22×D4—861no—
460C23×C4—861no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4—861no—
464C23×C4C22×D4311yescharacteristic
465C2×Q16—434no—
466C2×Q16—862no—
467C2×Q16—862no—
468C2×SD16—434no—
469C2×SD16—862no—
470C2×SD16—862no—
471C22×C8C22×D4311yescharacteristic
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C22⋊Q8—434no—
476C22⋊Q8—862no—
477C4×Q8—434no—
478C4×Q8—862no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—862no—
482C4×Q8—862no—
483C4×D4—434no—
484C4×D4—862no—
485C4×D4—862no—
486C4×D4—868no—
487C4×D4—868no—
488C4×D4—862no—
489#117—22no—
490#117—22no—
491#117—868no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—868no—
498C2×C4⋊C4—862no—
499C2×C4⋊C4—862no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4D17211yescharacteristic
507C2×C4⋊C4D17211yescharacteristic
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4D17211yescharacteristic
513C2×C22⋊C4D17211yescharacteristic
514C2×C42—861no—
515C2×C42—861no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42C22×D4311yescharacteristic
519C2×C42C22×D4311yescharacteristic
520#107—862no—
521#107—862no—
522#103—434no—
523#103—862no—
524#103—862no—
525#103—862no—
526#103—862no—
527#102—434no—
528#102—862no—
529#102—862no—
530C22⋊C8—22no—
531C22⋊C8C4×D4314yescomplemented
532#97—22no—
533C4×C8—22no—
534#95—861no—
535#95—861no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—861no—
540C24C2×D17211yescharacteristic
541#41—868no—
542#41—868no—
543#41—868no—
544#41—868no—
545C2×Q8—432no—
546C2×Q8—432no—
547C2×Q8—432no—
548C2×Q8—432no—
549C2×Q8—861no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×D4—432no—
558C2×D4—432no—
559C2×D4—432no—
560C2×D4—864no—
561C2×D4—864no—
562C2×D4—864no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—864no—
571C22×C4—864no—
572C22×C4—864no—
573C22×C4—861no—
574C22×C4—864no—
575C22×C4—864no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—864no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—3441no—
584C22×C4—3441no—
585C22×C4—3441no—
586C22×C4—3441no—
587C22×C4—3441no—
588C22×C4—3441no—
589C22×C4C2×C4×D4312yes—
590C22×C4C2×D17211yescharacteristic
591C22×C4C2×D17211yescharacteristic
592C22×C4C2×D17211yescharacteristic
593C22×C4C2×D17211yescharacteristic
594C22×C4C2×D17211yescharacteristic
595C22×C4#1062189812yes—
596C22×C4C23×D4311yescharacteristic
597Q16—868no—
598SD16—868no—
599C2×C8—21no—
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×C8C2×C4×D4312yes—
610C2×C8C2×C4×D4312yes—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—432no—
614C4⋊C4—432no—
615C4⋊C4—432no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—3441no—
628C4⋊C4—1722no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—864no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C22⋊C4—3441no—
635C42—21no—
636C42—21no—
637C42—864no—
638C42—864no—
639C42—3441no—
640C42—1722no—
641C42D4×D4312yes—
642C42D4×D4312yes—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—862no—
650C23—862no—
651C23—862no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23C4×D17212yes—
657C23C22×D17211yescharacteristic
658Q8—434no—
659Q8—862no—
660Q8—862no—
661Q8—862no—
662Q8—862no—
663Q8—862no—
664Q8—1721no—
665Q8—1721no—
666D4—434no—
667D4—8616no—
668D4—862no—
669D4—862no—
670D4—862no—
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—3444no—
696C2×C4—3444no—
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×C4—1721no—
711C2×C4—1721no—
712C2×C4C4×D17212yes—
713C2×C4#1306329512yes—
714C2×C4#1306329512yes—
715C2×C4C22×C4×D4311yescharacteristic
716C2×C4C2×D4×D4311yescharacteristic
717C2×C4C2×D4×D4311yescharacteristic
718C2×C4#41×D4311yescharacteristic
719C2×C4#41×D4311yescharacteristic
720C2×C4C2×#1062189811yescharacteristic
721C8—22no—
722C8—22no—
723C8—41no—
724C8—41no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—864no—
733C22—1722no—
734C22—1722no—
735C22—1722no—
736C22—1722no—
737C22—1722no—
738C22—1722no—
739C22C2×C4×D17211yescharacteristic
740C22C2×#1306329511yescharacteristic
741C22#1458341111yescharacteristic
742C22#1458370411yescharacteristic
743C22#1458371111yescharacteristic
744C22#1458371611yescharacteristic
745C22#1458371611yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—864no—
752C4—3441no—
753C4—3441no—
754C4—1722no—
755C4—1722no—
756C4—1722no—
757C4—1722no—
758C4C4×D4×D4311yescharacteristic
759C4C4×D4×D4311yescharacteristic
760C4#1458340811yescharacteristic
761C4#1458340811yescharacteristic
762C2—42no—
763C2—1724no—
764C2C4×#1306329511yescharacteristic
765C2#1914344011yescharacteristic
766C2#1914347211yescharacteristic
767C2#1914389211yescharacteristic
768C2#1914390211yescharacteristic
769C2#1914481111yescharacteristic
770C2#1914485911yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1750C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1750D43
hypocenterC43#21465
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
3. C2×#14583001C2semidirect
4. C2×C4×Dic172C2semidirect
5. #19137277C2semidirect
6. #19134935C2semidirect
7. #19134928C2semidirect
8. #19134900C2semidirect
9. #19134852C2semidirect
10. #19134845C2semidirect
11. #19134785C2semidirect
13. #19134426C2semidirect
14. C4×#13063247C2semidirect
15. C43×#1750C2semidirect
32. #14583063C4semidirect
80. C2×Dic172C2×C4semidirect
83. C2×#10621873C2×C4semidirect
85. #13063304C2×C4semidirect
127. #13063250C2×C4semidirect
130. #13063247C2×C4semidirect
150. C22⋊C8×C43C2×C4semidirect
391. #1750D43semidirect
449. C43#21465semidirect
531. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833792
C2×#145830632
C2×#145830012
C2×C4×Dic1722
#191372772
#191349352
#191349282
#191349002
#191348522
#191348452
#191347852
#191345362
#191344262
C4×#130632472
C43×#17502
#2146543