Finite Group Databasebeta

← #25112403

Subgroups — #25112403

Order 11008.

1406 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063356C211yesmaximal, characteristic
2C2×#14583004C211yesmaximal, characteristic, complemented
3C2×C4×#10621885C211yesmaximal, characteristic, complemented
4#19137435C211yesmaximal, characteristic
5#19135479C211yesmaximal, characteristic, complemented
6#19135452C211yesmaximal, characteristic, complemented
7#19134950C211yesmaximal, characteristic, complemented
8#19134950C211yesmaximal, characteristic, complemented
9#19134939C211yesmaximal, characteristic, complemented
10#19134939C211yesmaximal, characteristic, complemented
11#19134626C211yesmaximal, characteristic, complemented
12#19134533C211yesmaximal, characteristic
13#19134530C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063356—24no—
18C2×#13063356—24no—
19C2×#13063356C418yescomplemented
20C22×#10621885C2211yescharacteristic
21C22×#10621885C2211yescharacteristic
22C22×#10621884C2211yescharacteristic
23C22×#10621884C2211yescharacteristic
24C22×#10621877C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27#14583004—24no—
28C4×#10621885—24no—
29C2×#13063258C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×#13063236C2211yescharacteristic
41C2×C4×C43⋊C8C2211yescharacteristic
42#14582801C2211yescharacteristic
43#14582801C2211yescharacteristic
44#14582799—21no—
45#14582799—21no—
46#14582759C2211yescharacteristic
47#14582758—21no—
48#14582746—21no—
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582654C2211yescharacteristic
53C23×Q8×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C43×#391—21no—
57C43×#391—21no—
58C43×#391C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#380—21no—
61C43×#380C2211yescharacteristic
62C4×C22⋊C4×C43—21no—
63C4×C22⋊C4×C43C2211yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C2×#10621898C2×C414yes—
70C22×Dic86C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C22×C4×D43—21no—
74#13063356—232no—
75C2×#10621885—22no—
76C2×#10621885—22no—
77C2×#10621885C2×C414yes—
78C2×#10621885C2×C414yes—
79C2×#10621885D414yes—
80C2×#10621885D414yes—
81C2×#10621884—22no—
82C2×#10621884—22no—
83C2×#10621884—22no—
84C2×#10621884—22no—
85C2×#10621884C2×C414yes—
86C2×#10621884C2×C414yes—
87C2×#10621877—22no—
88C2×#10621877—22no—
89C2×#10621877C2×C414yes—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94C4×Dic86—22no—
95C4×Dic86—22no—
96C4×Dic86—41no—
97C4×Dic86—41no—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109#13063258—22no—
110#13063256—22no—
111#13063249—22no—
112#13063249—22no—
113#13063249—41no—
114#13063249—41no—
115#13063248—22no—
116#13063248—22no—
117#13063245—41no—
118#13063245—41no—
119C22⋊(C43⋊C8)—22no—
120#13063236—22no—
121C4×C43⋊C8—22no—
122C43⋊#95—21no—
123C22×Q8×C43—21no—
124C22×Q8×C43—22no—
125C22×Q8×C43—22no—
126C22×Q8×C43—22no—
127C22×Q8×C43—41no—
128C22×Q8×C43—41no—
129C22×Q8×C43C2×C414yes—
130C22×Q8×C43C2311yescharacteristic
131C22×Q8×C43C2311yescharacteristic
132C23×C4×C43—21no—
133C23×C4×C43C2311yescharacteristic
134C4×Q8×C43—22no—
135C4×Q8×C43—22no—
136C4×Q8×C43—41no—
137C4×Q8×C43—41no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43D411yescharacteristic
144C2×C22⋊C4×C43D411yescharacteristic
145C2×C42×C43—21no—
146C2×C42×C43—21no—
147C2×C42×C43C2311yescharacteristic
148C2×C42×C43C2311yescharacteristic
149#95×C43—21no—
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
154#95×C43D411yescharacteristic
155#95×C43D411yescharacteristic
156C24×C43C2×D411yescharacteristic
157C23×D43—21no—
158C2×Q8×C43—24no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—28no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—42no—
169C2×Q8×C43—42no—
170C2×Q8×C43—44no—
171C2×Q8×C43—44no—
172C2×Q8×C43—44no—
173C2×Q8×C43C22×C412yes—
174C2×Q8×C43C22×C412yes—
175C2×Q8×C43C2×D412yes—
176C2×Q8×C43C2×D412yes—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—24no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—42no—
187C22×C4×C43—42no—
188C22×C4×C43C22×C412yes—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43#4112yes—
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—24no—
197C2×C22⋊D43—42no—
198C2×C22⋊D43—42no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202#10621898—28no—
203#10621898—44no—
204#10621898—44no—
205#10621898—44no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172C22×C412yes—
212C2×C4×D43—24no—
213C2×C4×D43—42no—
214C2×C4×D43—42no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86C22×C412yes—
219C2×Dic86C2×D412yes—
220C2×Dic86C2×D412yes—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—42no—
226C4⋊C4×C43—42no—
227C22⋊C4×C43—22no—
228C22⋊C4×C43—41no—
229C22⋊C4×C43—42no—
230C42×C43—21no—
231C42×C43—21no—
232C42×C43—21no—
233C42×C43—21no—
234C42×C43—42no—
235C42×C43—42no—
236C22⋊Dic43—81no—
237#10621885—28no—
238#10621885C22⋊C4116yescomplemented
239#10621884—28no—
240#10621884—28no—
241(C2×D43)⋊C4—42no—
242(C2×D43)⋊C4—42no—
243(C2×D43)⋊C4—81no—
244(C2×D43)⋊C4—81no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249Dic43⋊C4—42no—
250Dic43⋊C4—42no—
251C4×Dic43—42no—
252C4×Dic43—42no—
253#10621877—28no—
254C2×C43⋊C8—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—
261C2×C43⋊C8—21no—
262C2×C43⋊C8C22×C412yes—
263C2×C43⋊C8C22×C412yes—
264C2×C43⋊C8C2×D412yes—
265C2×C43⋊C8C2×D412yes—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43C4×D412yes—
273C23×C43C22×D411yescharacteristic
274C22×D43—22no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281Q8×C43—22no—
282Q8×C43—22no—
283Q8×C43—22no—
284Q8×C43—22no—
285Q8×C43—22no—
286Q8×C43—48no—
287Q8×C43—41no—
288Q8×C43—41no—
289Q8×C43C2×C22⋊C414yes—
290C2×C4×C43—22no—
291C2×C4×C43—21no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—48no—
312C2×C4×C43—41no—
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×C43C4×D412yes—
321C2×C4×C43#13712yescomplemented
322C2×C4×C43C23×C411yescharacteristic
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C2×#4111yescharacteristic
326C2×C4×C43H(5,𝔽2)11yescharacteristic
327C2×C4×C43H(5,𝔽2)11yescharacteristic
328C22⋊D43—48no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338D172—22no—
339D172—22no—
340D172—41no—
341D172—41no—
342C4×D43—48no—
343Dic86—22no—
344Dic86—22no—
345Dic86—22no—
346Dic86C2×C22⋊C414yes—
347C43⋊C8—22no—
348C43⋊C8—41no—
349C43⋊C8—41no—
350C43⋊C8C2×C22⋊C414yes—
351#22445—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×C43D4211yescharacteristic
361C22×C43D4211yescharacteristic
362C22×C43C2×#13711yescharacteristic
363C22×C43#57511yescharacteristic
364C22×C43#57711yescharacteristic
365C22×C43#57811yescharacteristic
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—81no—
370C2×D43—81no—
371C2×D43—81no—
372C2×D43—81no—
373C4×C43—22no—
374C4×C43—24no—
375C4×C43—22no—
376C4×C43—42no—
377C4×C43—41no—
378C4×C43—41no—
379C4×C43—41no—
380C4×C43—81no—
381C4×C43—81no—
382C4×C43C22×C22⋊C411yescharacteristic
383C4×C43#51811yescharacteristic
384C4×C43#54611yescharacteristic
385C4×C43#54611yescharacteristic
386Dic43—24no—
387Dic43—81no—
388Dic43—81no—
389C22×#137—431no—
390C2×#441—431no—
391C2×C4×Q16—431no—
392#2341—431no—
393Q8×C22⋊C4D4311yescharacteristic, complemented
394#1973—431no—
395#1968—431no—
396#1880—431no—
397#1880—431no—
398#1878—431no—
399#1878—431no—
400#1809—431no—
401#1788—431no—
402#1787—431no—
403#1753—431no—
404C2×C43—42no—
405C2×C43D4×C22⋊C411yescharacteristic
406C2×C43C4×#13711yescharacteristic
407C2×C43#294711yescharacteristic
408C2×C43#327011yescharacteristic
409C2×C43#327111yescharacteristic
410C2×C43#327711yescharacteristic
411C2×C43#327811yescharacteristic
412D43—82no—
413C22×#41—431no—
414C23×Q8C2×D4311yescharacteristic
415C2×#137—438no—
416C2×#137—864no—
417C2×#137—864no—
418C22×Q16—431no—
419C22×Q16—431no—
420C22×SD16—431no—
421C22×SD16—431no—
422C22×M16—431no—
423C2×C4×Q8—431no—
424C2×C4×Q8—431no—
425C2×C4×Q8C2×D4311yescharacteristic
426C2×C4×Q8C2×D4311yescharacteristic
427#441—864no—
428C4×Q16—864no—
429C2×#107—431no—
430C2×#106—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×C22⋊C8—431no—
440C2×#97—431no—
441C2×C4×C8—431no—
442#391—21no—
443#391—21no—
444#391C2×D4311yescharacteristic
445#391C2×D4311yescharacteristic
446#390—431no—
447#390—431no—
448#390—861no—
449#390—861no—
450#380—21no—
451#380—431no—
452#380—861no—
453#380C2×D4311yescharacteristic
454C4×C22⋊C4—21no—
455C4×C22⋊C4—861no—
456C4×C22⋊C4C2×D4311yescharacteristic
457#340—431no—
458#340—431no—
459#336—431no—
460#336—431no—
461C43#2244511yescharacteristic, complemented, Sylow
462C2×#41—434no—
463C2×#41—862no—
464C2×#41—862no—
465C2×#41—862no—
466C2×#41—1721no—
467C2×#41—1721no—
468C22×Q8—22no—
469C22×Q8—21no—
470C22×Q8—22no—
471C22×Q8—22no—
472C22×Q8—41no—
473C22×Q8—41no—
474C22×Q8—431no—
475C22×Q8C4×D4314yes—
476C22×Q8C22×D4311yescharacteristic
477C22×Q8C22×D4311yescharacteristic
478C22×D4—431no—
479C22×D4—861no—
480C23×C4—21no—
481C23×C4—861no—
482C23×C4C22×D4311yescharacteristic
483#137—8632no—
484C2×Q16—434no—
485C2×Q16—434no—
486C2×Q16—434no—
487C2×Q16—434no—
488C2×Q16—862no—
489C2×Q16—862no—
490C2×SD16—434no—
491C2×SD16—434no—
492C2×SD16—862no—
493C2×SD16—862no—
494C2×SD16—862no—
495C2×SD16—862no—
496C2×M16—434no—
497C2×M16—862no—
498C2×M16—862no—
499C22×C8—431no—
500C22×C8—431no—
501C22×C8—431no—
502C22×C8—431no—
503C4×Q8—22no—
504C4×Q8—22no—
505C4×Q8—41no—
506C4×Q8—41no—
507C4×Q8—862no—
508C4×Q8—862no—
509C4×Q8—1721no—
510C4×Q8—1721no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4C22×D4311yescharacteristic
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4C22⋊D4311yescharacteristic
526C2×C22⋊C4C22⋊D4311yescharacteristic
527C2×C42—21no—
528C2×C42—21no—
529C2×C42—861no—
530C2×C42—861no—
531C2×C42C22×D4311yescharacteristic
532C2×C42C22×D4311yescharacteristic
533#107—862no—
534#106—862no—
535#103—862no—
536#103—862no—
537#103—862no—
538#103—862no—
539#103—1721no—
540#103—1721no—
541#102—1721no—
542#102—1721no—
543C22⋊C8—862no—
544#97—862no—
545C4×C8—862no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—861no—
552#95C22⋊D4311yescharacteristic
553#95C22⋊D4311yescharacteristic
554C24—861no—
555C24C2×C22⋊D4311yescharacteristic
556#41—868no—
557#41—1724no—
558#41—1724no—
559#41—1724no—
560C2×Q8—24no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—28no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—44no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—432no—
576C2×Q8—432no—
577C2×Q8—432no—
578C2×Q8—861no—
579C2×Q8—861no—
580C2×Q8—861no—
581C2×Q8C2×C4×D4312yes—
582C2×Q8C2×C4×D4312yes—
583C2×Q8D4×D4312yes—
584C2×Q8D4×D4312yes—
585C2×D4—432no—
586C2×D4—864no—
587C2×D4—861no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—1722no—
593C2×D4—1722no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—861no—
606C22×C4—864no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—1722no—
610C22×C4—1722no—
611C22×C4C2×C4×D4312yes—
612C22×C4#1062189812yes—
613C22×C4C2×C22⋊D4311yescharacteristic
614C22×C4C2×C22⋊D4311yescharacteristic
615C22×C4C2×C22⋊D4311yescharacteristic
616C22×C4C2×C22⋊D4311yescharacteristic
617C22×C4C2×C22⋊D4311yescharacteristic
618C22×C4C23×D4311yescharacteristic
619Q16—4316no—
620Q16—868no—
621SD16—868no—
622SD16—868no—
623M16—868no—
624C2×C8—432no—
625C2×C8—432no—
626C2×C8—432no—
627C2×C8—432no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—1722no—
647C4⋊C4—1722no—
648C22⋊C4—22no—
649C22⋊C4—41no—
650C22⋊C4—42no—
651C22⋊C4—3441no—
652C22⋊C4—3441no—
653C22⋊C4—3441no—
654C22⋊C4—1722no—
655C22⋊C4—1722no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—42no—
661C42—42no—
662C42—1722no—
663C42—1722no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—862no—
671C23—1721no—
672C23—1721no—
673C23—1721no—
674C23—1721no—
675C23—1721no—
676C23—1721no—
677C23C4×C22⋊D4312yes—
678C23C22×C22⋊D4311yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—48no—
685Q8—41no—
686Q8—41no—
687Q8—434no—
688Q8—862no—
689Q8—862no—
690Q8—862no—
691Q8C22⋊C4×D4314yes—
692D4—862no—
693D4—862no—
694D4—1728no—
695D4—1721no—
696D4—1721no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—48no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—1728no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4C4×C22⋊D4312yes—
738C2×C4#1306335612yescomplemented
739C2×C4C22×C4×D4311yescharacteristic
740C2×C4C2×D4×D4311yescharacteristic
741C2×C4C2×D4×D4311yescharacteristic
742C2×C4C2×#1062189811yescharacteristic
743C2×C4#1306337011yescharacteristic
744C2×C4#1306337011yescharacteristic
745C8—434no—
746C8—862no—
747C8—1721no—
748C8—1721no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—3441no—
757C22—3441no—
758C22—3441no—
759C22—3441no—
760C22—1722no—
761C22—1722no—
762C22—1722no—
763C22C2×C4×C22⋊D4311yescharacteristic
764C22D4×C22⋊D4311yescharacteristic
765C22D4×C22⋊D4311yescharacteristic
766C22C2×#1306335611yescharacteristic
767C22#1458369711yescharacteristic
768C22#1458370711yescharacteristic
769C22#1458371411yescharacteristic
770C4—22no—
771C4—24no—
772C4—22no—
773C4—41no—
774C4—41no—
775C4—42no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—864no—
780C4—3441no—
781C4—3441no—
782C4C2×C22⋊C4×D4311yescharacteristic
783C4#1458337211yescharacteristic
784C4#1458353911yescharacteristic
785C4#1458353911yescharacteristic
786C2—42no—
787C2—3442no—
788C2C22⋊C4×C22⋊D4311yescharacteristic
789C2C4×#1306335611yescharacteristic
790C2#1914343811yescharacteristic
791C2#1914616611yescharacteristic
792C2#1914618111yescharacteristic
793C2#1914624811yescharacteristic
794C2#1914625711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingQ8×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterQ8×C22⋊C4D43
hypocenterC43#22445
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14583004C2semidirect
3. C2×C4×#10621885C2semidirect
5. #19135479C2semidirect
6. #19135452C2semidirect
7. #19134950C2semidirect
8. #19134950C2semidirect
9. #19134939C2semidirect
10. #19134939C2semidirect
11. #19134626C2semidirect
13. #19134530C2semidirect
14. #19134379C2semidirect
15. Q8×C22⋊C4×C43C2semidirect
19. C2×#13063356C4semidirect
238. #10621885C22⋊C4semidirect
321. C2×C4×C43#137semidirect
393. Q8×C22⋊C4D43semidirect
461. C43#22445semidirect
738. C2×C4#13063356semidirect

Maximal subgroups

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

subgroupindex
C22×#130633562
C2×#145830042
C2×C4×#106218852
#191374352
#191354792
#191354522
#191349502
#191349392
#191346262
#191345332
#191345302
#191343792
Q8×C22⋊C4×C432
#2244543