Finite Group Databasebeta

← #25102350

Subgroups — #25102350

Order 11008.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583379C211yesmaximal, characteristic, complemented
2C2×#14583046C211yesmaximal, characteristic
3C2×#14583001C211yesmaximal, characteristic, complemented
4C2×C4×D344C211yesmaximal, characteristic, complemented
5#19137288C211yesmaximal, characteristic, complemented
6#19134949C211yesmaximal, characteristic, complemented
7#19134942C211yesmaximal, characteristic, complemented
8#19134910C211yesmaximal, characteristic, complemented
9#19134852C211yesmaximal, characteristic, complemented
10#19134845C211yesmaximal, characteristic, complemented
11#19134785C211yesmaximal, characteristic, complemented
12#19134536C211yesmaximal, characteristic, complemented
13#19134421C211yesmaximal, characteristic, complemented
14C4×#13063250C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20#14583379—24no—
21#14583379—24no—
22C2×C4×Dic86C2211yescharacteristic
23C2×C4×Dic86C2211yescharacteristic
24C2×C4×D172C2211yescharacteristic
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#14583046C418yescomplemented
33#14583001—24no—
34C4×D344—24no—
35C2×#13063259C2211yescharacteristic
36C2×#13063259C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063247C2211yescharacteristic
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
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898C2×C414yescomplemented
70C22×Dic86C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×D172C2311yescharacteristic
73C22×C22⋊D43—21no—
74C22×C22⋊D43—21no—
75C23×Dic43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C22×C4×D43—21no—
79C22×C4×D43—21no—
80C2×#10621873—22no—
81C2×#10621873—22no—
82C2×#10621873C2×C414yescomplemented
83C2×D344—22no—
84C2×D344—22no—
85C2×D344C2×C414yescomplemented
86#13063299—22no—
87#13063299C2×C414yescomplemented
88C4×Dic86—22no—
89C4×Dic86—22no—
90C4×Dic86—22no—
91C4×Dic86D414yescomplemented
92C4×D172—22no—
93C4×D172—22no—
94C4×D172—22no—
95C4×D172—22no—
96C4×D172—22no—
97C4×D172D414yescomplemented
98(C22⋊D43)⋊C4—28no—
99(C22⋊D43)⋊C4—28no—
100#13063283—28no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43—22no—
103C2×C4⋊Dic43—22no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4—21no—
112C4⋊C4×D43—28no—
113C2×C22⋊Dic43—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43—21no—
123#13063259—22no—
124#13063259—22no—
125#13063250—22no—
126#13063250—22no—
127#13063250C2×C414yescomplemented
128#13063247—22no—
129#13063247—22no—
130#13063247—22no—
131#13063247—22no—
132#13063247C2×C414yescomplemented
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—
155C23×D43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C22×C412yes—
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43#4112yes—
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43—24no—
169C2×C22⋊D43—24no—
170C2×C22⋊D43—24no—
171C2×C22⋊D43—24no—
172C2×C22⋊D43—81no—
173C2×C22⋊D43—81no—
174C22×Dic43—24no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—81no—
182C22×Dic43—81no—
183#10621898—28no—
184#10621898—28no—
185#10621898—28no—
186#10621898—28no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172C22×C412yes—
196C2×D172C22×C412yes—
197C2×D172C2×D412yes—
198C2×D172#4112yes—
199C2×C4×D43—24no—
200C2×C4×D43—24no—
201C2×C4×D43—24no—
202C2×C4×D43—24no—
203C2×C4×D43—24no—
204C2×C4×D43—42no—
205C2×C4×D43—81no—
206C2×C4×D43—81no—
207C2×C4×D43—81no—
208C2×C4×D43—81no—
209C2×C4×D43—81no—
210C2×C4×D43—81no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86C22×C412yes—
215C2×Dic86C2×D412yes—
216C2×Dic86#4112yes—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43C22×C412yes—
228C2×C8×C43C22×C412yes—
229C4⋊C4×C43—22no—
230C4⋊C4×C43—22no—
231C22⋊C4×C43—22no—
232C22⋊C4×C43—22no—
233C42×C43—21no—
234C42×C43—21no—
235C42×C43C2×D412yes—
236C42×C43C2×D412yes—
237C22⋊Dic43—81no—
238(C2×D43)⋊C4—24no—
239(C2×D43)⋊C4—24no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—42no—
242(C2×D43)⋊C4—81no—
243(C2×D43)⋊C4—81no—
244C4⋊Dic43—24no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43C22×C412yes—
253C4⋊Dic43C2×D412yes—
254C4⋊Dic43C2×D412yes—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—81no—
258C4×Dic43—24no—
259C4×Dic43—24no—
260C4×Dic43—81no—
261D344—28no—
262#10621873—28no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43C4×D412yes—
270C23×C43C22×D411yescharacteristic
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
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—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43C4×D412yes—
302C2×C4×C43#12012yes—
303C2×C4×C43#12012yes—
304C2×C4×C43C23×C411yescharacteristic
305C2×C4×C43C22×D411yescharacteristic
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C22⋊D43—216no—
311C22⋊D43—84no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—84no—
331D172—22no—
332D172—22no—
333D172—22no—
334D172—22no—
335D172—22no—
336D172—41no—
337D172—41no—
338D172C4×D414yes—
339C4×D43—216no—
340C4×D43—84no—
341C4×D43—84no—
342C4×D43—84no—
343Dic86—22no—
344Dic86—22no—
345Dic86—22no—
346Dic86C4×D414yes—
347C8×C43—22no—
348C8×C43—22no—
349C8×C43—41no—
350C8×C43—41no—
351#21460—431nomaximal, Sylow
352C22×C43—22no—
353C22×C43—22no—
354C22×C43—22no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43C2×C4×D411yescharacteristic
360C22×C43C2×#12011yescharacteristic
361C22×C43#52511yescharacteristic
362C22×C43#57611yescharacteristic
363C22×C43#57611yescharacteristic
364C22×C43#57711yescharacteristic
365C22×C43#57811yescharacteristic
366C2×D43—24no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—81no—
377C2×D43—81no—
378C2×D43—81no—
379C2×D43—81no—
380C4×C43—22no—
381C4×C43—22no—
382C4×C43—22no—
383C4×C43—41no—
384C4×C43—41no—
385C4×C43C2×C4×D411yescharacteristic
386C4×C43C2×C4×D411yescharacteristic
387C4×C43#52511yescharacteristic
388C4×C43#52511yescharacteristic
389Dic43—24no—
390Dic43—42no—
391Dic43—42no—
392Dic43—42no—
393Dic43—81no—
394Dic43—81no—
395C2×#520—431no—
396C2×#449—431no—
397C2×#440—431no—
398C2×C4×D8—431no—
399#2324—431no—
400#1880—431no—
401#1879—431no—
402#1874—431no—
403#1863—431no—
404#1862—431no—
405#1852—431no—
406#1788—431no—
407#1762—431no—
408C4×#103—431no—
409#1750D4311yescharacteristic, complemented
410C2×C43—42no—
411C2×C43C4×#12011yescharacteristic
412C2×C43#294611yescharacteristic
413C2×C43#295111yescharacteristic
414C2×C43#300811yescharacteristic
415C2×C43#301311yescharacteristic
416C2×C43#311911yescharacteristic
417C2×C43#312411yescharacteristic
418D43—44no—
419D43—82no—
420C22×#41—431no—
421C22×SD16—431no—
422C22×D8—431no—
423C2×#121—431no—
424#520—864no—
425#520—864no—
426C2×C4×Q8—431no—
427C2×C4×Q8—431no—
428C2×C4×D4—431no—
429C2×C4×D4—431no—
430C2×C4×D4—431no—
431C2×C4×D4—861no—
432C2×C4×D4—861no—
433C2×#117—861no—
434C2×#117C2×D4311yescharacteristic
435C22×C4⋊C4—431no—
436C22×C4⋊C4—861no—
437#449—438no—
438#440—864no—
439C4×D8—864no—
440C2×#107—431no—
441C2×#107—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#103—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—431no—
450C2×C22⋊C8C2×D4311yescharacteristic
451C2×C22⋊C8C2×D4311yescharacteristic
452C2×#97C2×D4311yescharacteristic
453C2×C4×C8C2×D4311yescharacteristic
454#390—431no—
455#390—861no—
456#389—431no—
457#388—861no—
458#386—861no—
459#385—861no—
460#380—431no—
461C4×C4⋊C4—431no—
462#340—431no—
463#340—431no—
464#340—431no—
465#340—431no—
466#336C2×D4311yescharacteristic
467#336C2×D4311yescharacteristic
468C43#2146011yescharacteristic, complemented, Sylow
469C2×#41—434no—
470C2×#41—862no—
471C2×#41—862no—
472C2×#41—862no—
473C2×#41—862no—
474C2×#41—862no—
475C22×Q8—431no—
476C22×D4—431no—
477C22×D4—431no—
478C22×D4—861no—
479C22×D4—861no—
480C23×C4—861no—
481C23×C4—861no—
482C23×C4—861no—
483C23×C4—861no—
484C23×C4—861no—
485C23×C4C22×D4311yescharacteristic
486C2×SD16—434no—
487C2×SD16—862no—
488C2×SD16—862no—
489C2×D8—434no—
490C2×D8—862no—
491C2×D8—862no—
492C22×C8C22×D4311yescharacteristic
493C22×C8C22×D4311yescharacteristic
494C22×C8C22×D4311yescharacteristic
495C22×C8C22×D4311yescharacteristic
496#121—434no—
497#121—862no—
498C4×Q8—434no—
499C4×Q8—862no—
500C4×Q8—862no—
501C4×Q8—862no—
502C4×D4—434no—
503C4×D4—862no—
504C4×D4—862no—
505C4×D4—868no—
506C4×D4—868no—
507C4×D4—862no—
508C4×D4—862no—
509C4×D4—862no—
510#117—22no—
511#117—22no—
512#117—868no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—868no—
519C2×C4⋊C4—862no—
520C2×C4⋊C4—862no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4D17211yescharacteristic
526C2×C4⋊C4D17211yescharacteristic
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4D17211yescharacteristic
535C2×C22⋊C4D17211yescharacteristic
536C2×C42—861no—
537C2×C42—861no—
538C2×C42—861no—
539C2×C42C22×D4311yescharacteristic
540C2×C42C22×D4311yescharacteristic
541#107—862no—
542#107—862no—
543#103—434no—
544#103—862no—
545#103—862no—
546#102—434no—
547#102—862no—
548#102—862no—
549#102—862no—
550#102—862no—
551C22⋊C8—22no—
552C22⋊C8C4×D4314yescomplemented
553#97—22no—
554C4×C8—22no—
555#95—861no—
556#95—861no—
557#95—861no—
558C24—861no—
559C24—861no—
560C24C2×D17211yescharacteristic
561#41—868no—
562#41—868no—
563#41—868no—
564#41—868no—
565C2×Q8—432no—
566C2×Q8—432no—
567C2×Q8—432no—
568C2×Q8—861no—
569C2×Q8—861no—
570C2×Q8—861no—
571C2×D4—432no—
572C2×D4—432no—
573C2×D4—432no—
574C2×D4—432no—
575C2×D4—864no—
576C2×D4—864no—
577C2×D4—864no—
578C2×D4—864no—
579C2×D4—861no—
580C2×D4—861no—
581C2×D4—861no—
582C2×D4—861no—
583C2×D4—861no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—3441no—
588C2×D4—3441no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—864no—
594C22×C4—864no—
595C22×C4—864no—
596C22×C4—861no—
597C22×C4—864no—
598C22×C4—864no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—864no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—3441no—
606C22×C4—3441no—
607C22×C4—3441no—
608C22×C4—3441no—
609C22×C4—3441no—
610C22×C4—3441no—
611C22×C4—3441no—
612C22×C4—3441no—
613C22×C4—1722no—
614C22×C4C2×C4×D4312yes—
615C22×C4C2×D17211yescharacteristic
616C22×C4C2×D17211yescharacteristic
617C22×C4C2×D17211yescharacteristic
618C22×C4C2×D17211yescharacteristic
619C22×C4C2×D17211yescharacteristic
620C22×C4#1062189812yes—
621C22×C4C23×D4311yescharacteristic
622SD16—868no—
623D8—868no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8C2×C4×D4312yes—
635C2×C8C2×C4×D4312yes—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—432no—
639C4⋊C4—432no—
640C4⋊C4—432no—
641C4⋊C4—864no—
642C4⋊C4—864no—
643C4⋊C4—864no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—861no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—3441no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—864no—
655C22⋊C4—864no—
656C22⋊C4—864no—
657C22⋊C4—3441no—
658C22⋊C4—3441no—
659C22⋊C4—3441no—
660C22⋊C4—1722no—
661C42—21no—
662C42—21no—
663C42—864no—
664C42—864no—
665C42—3441no—
666C42D4×D4312yes—
667C42D4×D4312yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—862no—
678C23—1721no—
679C23—1721no—
680C23—1721no—
681C23—1721no—
682C23—1721no—
683C23—1721no—
684C23—1721no—
685C23—1721no—
686C23—1721no—
687C23—1721no—
688C23C4×D17212yes—
689C23C22×D17211yescharacteristic
690Q8—434no—
691Q8—862no—
692Q8—862no—
693Q8—862no—
694D4—434no—
695D4—8616no—
696D4—862no—
697D4—862no—
698D4—862no—
699D4—862no—
700D4—862no—
701D4—3444no—
702D4—1721no—
703D4—1721no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—8616no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—3444no—
728C2×C4—3444no—
729C2×C4—3444no—
730C2×C4—3444no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4C4×D17212yes—
744C2×C4#1306329512yes—
745C2×C4#1306329512yes—
746C2×C4C22×C4×D4311yescharacteristic
747C2×C4C2×D4×D4311yescharacteristic
748C2×C4C2×D4×D4311yescharacteristic
749C2×C4#41×D4311yescharacteristic
750C2×C4#41×D4311yescharacteristic
751C2×C4C2×#1062189811yescharacteristic
752C8—22no—
753C8—22no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—864no—
764C22—3441no—
765C22—3441no—
766C22—3441no—
767C22—3441no—
768C22—1722no—
769C22—1722no—
770C22—1722no—
771C22—1722no—
772C22—1722no—
773C22—1722no—
774C22—1722no—
775C22—1722no—
776C22—1722no—
777C22C2×C4×D17211yescharacteristic
778C22C2×#1306329511yescharacteristic
779C22#1458341111yescharacteristic
780C22#1458370411yescharacteristic
781C22#1458370411yescharacteristic
782C22#1458371111yescharacteristic
783C22#1458371611yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—41no—
788C4—41no—
789C4—864no—
790C4—3441no—
791C4—3441no—
792C4—1722no—
793C4—1722no—
794C4—1722no—
795C4C4×D4×D4311yescharacteristic
796C4C4×D4×D4311yescharacteristic
797C4#1458340811yescharacteristic
798C4#1458340811yescharacteristic
799C2—42no—
800C2—3442no—
801C2—1724no—
802C2C4×#1306329511yescharacteristic
803C2#1914342911yescharacteristic
804C2#1914347211yescharacteristic
805C2#1914386511yescharacteristic
806C2#1914391311yescharacteristic
807C2#1914479611yescharacteristic
808C2#1914485911yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1750C2
socleC23×C43C22×D4
prime radicalC2×#14583046C2
cosocleC22×C4×C43C24
hypercenter#1750D43
hypocenterC43#21460
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×#14583379C2semidirect
3. C2×#14583001C2semidirect
4. C2×C4×D344C2semidirect
5. #19137288C2semidirect
6. #19134949C2semidirect
7. #19134942C2semidirect
8. #19134910C2semidirect
9. #19134852C2semidirect
10. #19134845C2semidirect
11. #19134785C2semidirect
12. #19134536C2semidirect
13. #19134421C2semidirect
14. C4×#13063250C2semidirect
15. C43×#1750C2semidirect
32. #14583046C4semidirect
69. C2×#10621898C2×C4semidirect
82. C2×#10621873C2×C4semidirect
85. C2×D344C2×C4semidirect
87. #13063299C2×C4semidirect
91. C4×Dic86D4semidirect
97. C4×D172D4semidirect
127. #13063250C2×C4semidirect
132. #13063247C2×C4semidirect
150. C22⋊C8×C43C2×C4semidirect
409. #1750D43semidirect
468. C43#21460semidirect
552. 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×#145830462
C2×#145830012
C2×C4×D3442
#191372882
#191349492
#191349422
#191349102
#191348522
#191348452
#191347852
#191345362
#191344212
C4×#130632502
C43×#17502
#2146043