Finite Group Databasebeta

← #25102313

Subgroups — #25102313

Order 11008.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583373C211yesmaximal, characteristic, complemented
2C2×#14583035C211yesmaximal, characteristic
3C2×#14583010C211yesmaximal, characteristic, complemented
4C2×#14582981C211yesmaximal, characteristic, complemented
5#19137284C211yesmaximal, characteristic, complemented
6#19134944C211yesmaximal, characteristic, complemented
7#19134944C211yesmaximal, characteristic, complemented
8#19134917C211yesmaximal, characteristic, complemented
9#19134853C211yesmaximal, characteristic, complemented
10#19134839C211yesmaximal, characteristic, complemented
11#19134525C211yesmaximal, characteristic, complemented
12#19134419C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1854C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20#14583373—24no—
21#14583373—24no—
22C2×C4×D172—21no—
23C2×C4×D172—21no—
24C2×#13063287C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×#13063287C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28C2×#13063287C2211yescharacteristic, complemented
29C2×#13063284C2211yescharacteristic
30C2×C22⋊C4×D43—21no—
31C2×C22⋊C4×D43—21no—
32#14583035C418yescomplemented
33#14583010—24no—
34#14582981—24no—
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic, complemented
42C2×#13063245C2211yescharacteristic, complemented
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×#13063235C2211yescharacteristic, complemented
45C2×C8×Dic43C2211yescharacteristic, complemented
46#14582800C2211yescharacteristic, complemented
47#14582799—21no—
48#14582795C2211yescharacteristic, complemented
49#14582791—21no—
50#14582775—21no—
51#14582773—21no—
52C4⋊C4×Dic43C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57C2×#117×C43C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic, complemented
59C2×#106×C43C2211yescharacteristic, complemented
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172—21no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172—22no—
69C22×D172—22no—
70C22×D172—22no—
71C22×D172C2×C414yescomplemented
72C22×D172C2311yescharacteristic
73C22×D172C2311yescharacteristic
74C22×D172C2311yescharacteristic
75C22×C22⋊D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C22×C4×D43—21no—
79C22×C4×D43—21no—
80C22×C4×D43—21no—
81C2×D344—22no—
82C2×D344—22no—
83C2×D344—22no—
84C2×D344—22no—
85C2×D344C2×C414yescomplemented
86C2×D344C2×C414yescomplemented
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89#13063299—22no—
90#13063299C2×C414yescomplemented
91C4×D172—28no—
92C4×D172—28no—
93#13063287—22no—
94#13063287—22no—
95#13063287—22no—
96#13063287—22no—
97#13063287—22no—
98#13063287—22no—
99#13063287—22no—
100#13063287—22no—
101#13063287D414yescomplemented
102#13063287D414yescomplemented
103#13063284—22no—
104#13063284—22no—
105C2×C4⋊Dic43D411yescharacteristic
106C2×C4⋊Dic43D411yescharacteristic
107C2×C4⋊Dic43C2311yescharacteristic
108C2×Dic43⋊C4—21no—
109C2×C22⋊Dic43D411yescharacteristic
110C2×C22⋊Dic43D411yescharacteristic
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—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—
119C22⋊C4×D43—28no—
120C22⋊C4×D43—28no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43C2311yescharacteristic
123C2×C4×Dic43C2311yescharacteristic
124#13063247C2×C414yescomplemented
125#13063247C2×C414yescomplemented
126#13063245—22no—
127#13063245—22no—
128#13063245—22no—
129#13063245—22no—
130#13063245—22no—
131#13063245—22no—
132C22⋊(C43⋊C8)—22no—
133#13063235—22no—
134C8×Dic43—22no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C23×C4×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140#117×C43—22no—
141#117×C43—22no—
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C42×C43—21no—
149#107×C43—22no—
150#106×C43—22no—
151C22⋊C8×C43C2×C414yescomplemented
152#95×C43—21no—
153C24×C43C2×D411yescharacteristic
154C23×D43—21no—
155C23×D43—21no—
156C23×D43—24no—
157C23×D43—24no—
158C23×D43—24no—
159C23×D43—21no—
160C23×D43—81no—
161C23×D43—81no—
162C23×D43—81no—
163C23×D43—81no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43C22×C412yes—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43#4112yes—
175C22×C4×C43C2411yescharacteristic
176C2×C22⋊D43—24no—
177C2×C22⋊D43—81no—
178C2×C22⋊D43—81no—
179C22×Dic43—21no—
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183C22×Dic43C2×D411yescharacteristic
184C2×D172—24no—
185C2×D172—24no—
186C2×D172—28no—
187C2×D172—28no—
188C2×D172—24no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—28no—
196C2×D172—28no—
197C2×D172—21no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172C22×C412yes—
203C2×D172C22×C412yes—
204C2×D172C22×C412yes—
205C2×D172C2×D412yes—
206C2×D172C2×D412yes—
207C2×D172#4112yes—
208C2×D172#4112yes—
209C2×C4×D43—24no—
210C2×C4×D43—24no—
211C2×C4×D43—24no—
212C2×C4×D43—24no—
213C2×C4×D43—42no—
214C2×C4×D43—81no—
215C2×C4×D43—81no—
216C2×C4×D43—81no—
217C2×C4×D43—81no—
218C2×C4×D43—81no—
219C2×C4×D43—81no—
220C2×C4×D43—81no—
221C2×C4×D43—81no—
222C2×C4×D43—81no—
223C2×C4×D43—81no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43C22×C412yes—
229C2×C8×C43C22×C412yes—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43C2×D412yes—
237C4⋊C4×C43C2×D412yes—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—81no—
240C42×C43—24no—
241C22⋊Dic43—22no—
242C22⋊Dic43—22no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—42no—
249(C2×D43)⋊C4—81no—
250(C2×D43)⋊C4—81no—
251C4⋊Dic43—21no—
252C4⋊Dic43—22no—
253C4⋊Dic43—22no—
254C4⋊Dic43C22×C412yes—
255Dic43⋊C4—81no—
256C4×Dic43—21no—
257C4×Dic43—21no—
258C4×Dic43—81no—
259C4×Dic43C2×D412yes—
260C4×Dic43C2×D412yes—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267D344—28no—
268D344—28no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43C4×D412yes—
276C23×C43C22×D411yescharacteristic
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—216no—
284C22×D43—22no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—41no—
289C22×D43—41no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—84no—
300C22×D43—84no—
301C22×D43—84no—
302C22×D43—84no—
303C22×D43—84no—
304C22×D43—84no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43C4×D412yes—
324C2×C4×C43C23×C411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43C2×#4111yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C22⋊D43—84no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—22no—
336C2×Dic43—21no—
337C2×Dic43—21no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43#12012yes—
345C2×Dic43#12012yes—
346D172—216no—
347D172—22no—
348D172—22no—
349D172—22no—
350D172—22no—
351D172—22no—
352D172—22no—
353D172—22no—
354D172—22no—
355D172—41no—
356D172—41no—
357D172C4×D414yes—
358D172C4×D414yes—
359C4×D43—84no—
360C4×D43—84no—
361C4×D43—84no—
362C4×D43—84no—
363C4×D43—84no—
364C8×C43—22no—
365C8×C43—22no—
366C43⋊C8—41no—
367C43⋊C8—41no—
368#21458—431nomaximal, Sylow
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43C2×C4×D411yescharacteristic
377C22×C43C2×#12011yescharacteristic
378C22×C43#52511yescharacteristic
379C22×C43#57611yescharacteristic
380C22×C43#57611yescharacteristic
381C22×C43#57611yescharacteristic
382C22×C43#57711yescharacteristic
383C2×D43—24no—
384C2×D43—24no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—42no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—816no—
401C2×D43—81no—
402C2×D43—81no—
403C2×D43—81no—
404C2×D43—81no—
405C4×C43—22no—
406C4×C43—42no—
407C4×C43—42no—
408C4×C43—81no—
409C4×C43—81no—
410C4×C43C2×C4×D411yescharacteristic
411C4×C43C2×C4×D411yescharacteristic
412C4×C43#52511yescharacteristic
413C4×C43#52511yescharacteristic
414Dic43—22no—
415Dic43—22no—
416Dic43—42no—
417Dic43—41no—
418Dic43—41no—
419C2×#518—431no—
420C2×#447—431no—
421C2×#442—431no—
422C2×C4×D8—431no—
423#2324—431no—
424#1879—431no—
425#1879—431no—
426#1875—431no—
427#1864—431no—
428#1862—431no—
429#1854D4311yescharacteristic, complemented
430#1786—431no—
431#1762—431no—
432C4×#102—431no—
433#1750—431no—
434C2×C43—42no—
435C2×C43C4×#12011yescharacteristic
436C2×C43#294611yescharacteristic
437C2×C43#294811yescharacteristic
438C2×C43#300811yescharacteristic
439C2×C43#301211yescharacteristic
440C2×C43#311811yescharacteristic
441C2×C43#312211yescharacteristic
442D43—44no—
443D43—44no—
444D43—82no—
445C23×D4—431no—
446C22×D8—431no—
447C22×D8—431no—
448C2×#121—431no—
449#518—864no—
450#518—864no—
451C2×C4×D4—431no—
452C2×C4×D4—431no—
453C2×C4×D4—431no—
454C2×C4×D4—431no—
455C2×C4×D4—431no—
456C2×C4×D4—861no—
457C2×C4×D4—861no—
458C2×#117—431no—
459C2×#117C2×D4311yescharacteristic
460C22×C22⋊C4—861no—
461C22×C22⋊C4—861no—
462#447—438no—
463#442—864no—
464C4×D8—864no—
465C2×#107C2×D4311yescharacteristic, complemented
466C2×#106C2×D4311yescharacteristic, complemented
467C2×#102—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×#102—431no—
472C2×#102—431no—
473C2×#102—431no—
474C2×#102—431no—
475C2×C22⋊C8—431no—
476C2×C22⋊C8C2×D4311yescharacteristic
477C2×#97—431no—
478C2×C4×C8—431no—
479#390—431no—
480#390—861no—
481#389—431no—
482#388—861no—
483#386—861no—
484#385—861no—
485#380C2×D4311yescharacteristic
486C4×C4⋊C4—431no—
487#340—431no—
488#340—431no—
489#340C2×D4311yescharacteristic, complemented
490#340C2×D4311yescharacteristic, complemented
491#336—431no—
492#336—431no—
493C43#2145811yescharacteristic, complemented, Sylow
494C25—861no—
495C22×D4—434no—
496C22×D4—431no—
497C22×D4—431no—
498C22×D4—431no—
499C22×D4—862no—
500C22×D4—862no—
501C22×D4—862no—
502C22×D4—862no—
503C22×D4—861no—
504C22×D4—861no—
505C22×D4—862no—
506C23×C4—861no—
507C23×C4—861no—
508C23×C4—861no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4C22×D4311yescharacteristic
512C2×D8—434no—
513C2×D8—434no—
514C2×D8—862no—
515C2×D8—862no—
516C2×D8—862no—
517C2×D8—862no—
518C22×C8—431no—
519C22×C8—431no—
520C22×C8C22×D4311yescharacteristic
521C22×C8C22×D4311yescharacteristic
522#121—434no—
523#121—862no—
524C4×D4—434no—
525C4×D4—434no—
526C4×D4—868no—
527C4×D4—868no—
528C4×D4—862no—
529C4×D4—862no—
530C4×D4—862no—
531C4×D4—862no—
532C4×D4—862no—
533C4×D4—862no—
534C4×D4—862no—
535C4×D4—862no—
536#117—22no—
537#117—22no—
538#117—862no—
539#117—862no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4C22×D4311yescharacteristic
545C2×C4⋊C4C22×D4311yescharacteristic
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—431no—
551C2×C22⋊C4—431no—
552C2×C22⋊C4—868no—
553C2×C22⋊C4—868no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C42—21no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—861no—
566#107—22no—
567#106—22no—
568#102—434no—
569#102—434no—
570#102—862no—
571#102—862no—
572#102—862no—
573#102—862no—
574#102—862no—
575#102—862no—
576C22⋊C8—862no—
577C22⋊C8C4×D4314yescomplemented
578#97—862no—
579C4×C8—862no—
580#95—21no—
581#95—861no—
582#95—861no—
583C24—864no—
584C24—864no—
585C24—864no—
586C24—861no—
587C24—861no—
588C24—861no—
589C24—3441no—
590C24—3441no—
591C24—3441no—
592C24—3441no—
593C24D4×D4311yescharacteristic
594C2×D4—432no—
595C2×D4—432no—
596C2×D4—432no—
597C2×D4—432no—
598C2×D4—432no—
599C2×D4—432no—
600C2×D4—432no—
601C2×D4—868no—
602C2×D4—868no—
603C2×D4—864no—
604C2×D4—864no—
605C2×D4—868no—
606C2×D4—868no—
607C2×D4—864no—
608C2×D4—864no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—3441no—
621C2×D4—3441no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—864no—
635C22×C4—864no—
636C22×C4—864no—
637C22×C4—864no—
638C22×C4—861no—
639C22×C4—3441no—
640C22×C4—3441no—
641C22×C4—3441no—
642C22×C4—3441no—
643C22×C4—3441no—
644C22×C4—3441no—
645C22×C4—3441no—
646C22×C4—3441no—
647C22×C4—3441no—
648C22×C4—3441no—
649C22×C4—1722no—
650C22×C4C2×C4×D4312yes—
651C22×C4D4×D4311yescharacteristic
652C22×C4#1062190212yes—
653C22×C4C23×D4311yescharacteristic
654D8—868no—
655D8—868no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8C2×C4×D4312yes—
667C2×C8C2×C4×D4312yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—432no—
675C4⋊C4—862no—
676C4⋊C4—862no—
677C4⋊C4—861no—
678C4⋊C4—3441no—
679C4⋊C4D4×D4312yes—
680C4⋊C4D4×D4312yes—
681C22⋊C4—24no—
682C22⋊C4—81no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—864no—
687C22⋊C4—862no—
688C22⋊C4—862no—
689C22⋊C4—864no—
690C22⋊C4—3441no—
691C22⋊C4—3441no—
692C22⋊C4—1722no—
693C42—24no—
694C42—432no—
695C42—432no—
696C42—861no—
697C42—861no—
698C42—3441no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—8616no—
706C23—862no—
707C23—862no—
708C23—862no—
709C23—862no—
710C23—862no—
711C23—862no—
712C23—862no—
713C23—3444no—
714C23—3444no—
715C23—3444no—
716C23—3444no—
717C23—3444no—
718C23—3444no—
719C23—1721no—
720C23—1721no—
721C23—1721no—
722C23—1721no—
723C23—1721no—
724C23—1721no—
725C23—1721no—
726C23—1721no—
727C23—1721no—
728C23—1721no—
729C23—1721no—
730C23—1721no—
731C23—1721no—
732C23—1721no—
733C23#1306328712yes—
734C23C2×D4×D4311yescharacteristic
735D4—434no—
736D4—434no—
737D4—8616no—
738D4—862no—
739D4—862no—
740D4—862no—
741D4—862no—
742D4—862no—
743D4—862no—
744D4—862no—
745D4—862no—
746D4—3444no—
747D4—1721no—
748D4—1721no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—432no—
768C2×C4—432no—
769C2×C4—861no—
770C2×C4—861no—
771C2×C4—861no—
772C2×C4—861no—
773C2×C4—862no—
774C2×C4—861no—
775C2×C4—861no—
776C2×C4—861no—
777C2×C4—861no—
778C2×C4—861no—
779C2×C4—861no—
780C2×C4—3444no—
781C2×C4—3444no—
782C2×C4—3444no—
783C2×C4—3444no—
784C2×C4—3444no—
785C2×C4—1721no—
786C2×C4—1721no—
787C2×C4#1306328712yes—
788C2×C4C22×C4×D4311yescharacteristic
789C2×C4C2×D4×D4311yescharacteristic
790C2×C4C2×D4×D4311yescharacteristic
791C2×C4#41×D4311yescharacteristic
792C2×C4#41×D4311yescharacteristic
793C2×C4C2×#1062190211yescharacteristic
794C8—22no—
795C8—22no—
796C8—1721no—
797C8—1721no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—864no—
806C22—864no—
807C22—34416no—
808C22—3441no—
809C22—3441no—
810C22—3441no—
811C22—3441no—
812C22—1722no—
813C22—1722no—
814C22—1722no—
815C22—1722no—
816C22—1722no—
817C22—1722no—
818C22—1722no—
819C22—1722no—
820C22—1722no—
821C22—1722no—
822C22—1722no—
823C22—1722no—
824C22—1722no—
825C22—1722no—
826C22—1722no—
827C22C2×#1306328711yescharacteristic
828C22#120×D4311yescharacteristic
829C22#1458340711yescharacteristic
830C22#1458370111yescharacteristic
831C22#1458370111yescharacteristic
832C22#1458370311yescharacteristic
833C22#1458370811yescharacteristic
834C4—22no—
835C4—42no—
836C4—42no—
837C4—81no—
838C4—81no—
839C4—862no—
840C4—862no—
841C4—1722no—
842C4—1721no—
843C4—1721no—
844C4C4×D4×D4311yescharacteristic
845C4C4×D4×D4311yescharacteristic
846C4#1458341211yescharacteristic
847C4#1458341211yescharacteristic
848C2—42no—
849C2—3442no—
850C2—1724no—
851C2—1724no—
852C2#1913709611yescharacteristic
853C2#1914342511yescharacteristic
854C2#1914344611yescharacteristic
855C2#1914386011yescharacteristic
856C2#1914390311yescharacteristic
857C2#1914478211yescharacteristic
858C2#1914483411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC2×#14583035C2
cosocleC22×C4×C43C24
hypercenter#1854D43
hypocenterC43#21458
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
1. C2×#14583373C2semidirect
3. C2×#14583010C2semidirect
4. C2×#14582981C2semidirect
5. #19137284C2semidirect
6. #19134944C2semidirect
7. #19134944C2semidirect
8. #19134917C2semidirect
9. #19134853C2semidirect
10. #19134839C2semidirect
11. #19134525C2semidirect
12. #19134419C2semidirect
13. #19134409C2semidirect
14. #19134363C2semidirect
15. C43×#1854C2semidirect
28. C2×#13063287C22semidirect
32. #14583035C4semidirect
41. C2×#13063245C22semidirect
42. C2×#13063245C22semidirect
44. C2×#13063235C22semidirect
45. C2×C8×Dic43C22semidirect
46. #14582800C22semidirect
48. #14582795C22semidirect
52. C4⋊C4×Dic43C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
58. C2×#107×C43C22semidirect
59. C2×#106×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
71. C22×D172C2×C4semidirect
85. C2×D344C2×C4semidirect
86. C2×D344C2×C4semidirect
90. #13063299C2×C4semidirect
101. #13063287D4semidirect
102. #13063287D4semidirect
124. #13063247C2×C4semidirect
125. #13063247C2×C4semidirect
151. C22⋊C8×C43C2×C4semidirect
429. #1854D43semidirect
465. C2×#107C2×D43semidirect
466. C2×#106C2×D43semidirect
489. #340C2×D43semidirect
490. #340C2×D43semidirect
493. C43#21458semidirect
577. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833732
C2×#145830352
C2×#145830102
C2×#145829812
#191372842
#191349442
#191349172
#191348532
#191348392
#191345252
#191344192
#191344092
#191343632
C43×#18542
#2145843