Finite Group Databasebeta

← #25096201

Subgroups — #25096201

Order 11008.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063333C211yesmaximal, characteristic
2C2×#14582940C211yesmaximal, characteristic, complemented
3C2×#14582938C211yesmaximal, characteristic, complemented
4#19137184C211yesmaximal, characteristic
5#19137184C211yesmaximal, characteristic
6#19134628C211yesmaximal, characteristic, complemented
7#19134627C211yesmaximal, characteristic, complemented
8#19134627C211yesmaximal, characteristic, complemented
9#19134622C211yesmaximal, characteristic, complemented
10#19134621C211yesmaximal, characteristic, complemented
11#19134618C211yesmaximal, characteristic, complemented
12#19134617C211yesmaximal, characteristic, complemented
13#19134310C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#1809C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063333—24no—
18C2×#13063333—24no—
19C2×#13063333C418yescomplemented
20C22×#10621872C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22C23×C43⋊C8C2211yescharacteristic
23C22×C8×D43C2211yescharacteristic
24C22×C8×D43C2211yescharacteristic
25C2×#13063283C2211yescharacteristic
26C2×#13063283C2211yescharacteristic
27C2×C4⋊C4×D43C2211yescharacteristic
28C2×C4⋊C4×D43C2211yescharacteristic
29#14582940—24no—
30#14582938—24no—
31C2×#13063259C2211yescharacteristic
32C2×#13063258C2211yescharacteristic
33C2×#13063258C2211yescharacteristic
34C2×#13063257C2211yescharacteristic
35C2×#13063256C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37#14582803—21no—
38#14582803—21no—
39#14582799—21no—
40#14582799—21no—
41#14582777—21no—
42#14582777—21no—
43#14582775—21no—
44#14582775—21no—
45#14582759C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49#14582756C2211yescharacteristic
50#14582756C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57C22×M16×C43C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic
59C2×#106×C43C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898C2×C414yes—
69C2×#10621898Q814yes—
70C22×Dic86D411yescharacteristic
71C22×D172D411yescharacteristic
72C22×C22⋊D43D411yescharacteristic
73C22×C22⋊D43D411yescharacteristic
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43C2311yescharacteristic
77C22×C4×D43C2311yescharacteristic
78#13063333—232no—
79C2×#10621872—22no—
80C2×#10621872—22no—
81C2×#10621872C2×C414yes—
82C2×#10621872C2×C414yescomplemented
83C2×#10621872D414yes—
84C2×#10621872D414yes—
85C22×C43⋊C8—22no—
86C22×C43⋊C8—22no—
87C22×C43⋊C8C2×C414yescomplemented
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C2×C8×D43—22no—
91C2×C8×D43—22no—
92C2×C8×D43—22no—
93C2×C8×D43—22no—
94C2×C8×D43C2×C414yes—
95C2×C8×D43C2×C414yescomplemented
96#13063283—22no—
97#13063283—22no—
98#13063283—22no—
99#13063283—22no—
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C4⋊C4×D43—22no—
107C4⋊C4×D43—22no—
108C4⋊C4×D43—22no—
109C4⋊C4×D43—22no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—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×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120#13063259—22no—
121#13063258—22no—
122#13063258—22no—
123#13063257—22no—
124#13063256—22no—
125#13063256—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C23×C4×C43C2311yescharacteristic
133C2×M16×C43—22no—
134C2×M16×C43—22no—
135C2×M16×C43C2×C414yescomplemented
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144#107×C43—22no—
145#106×C43—22no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43C2×D411yescharacteristic
149C23×D43C2×D411yescharacteristic
150C23×D43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—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×Q812yes—
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43C4⋊C414yes—
168C2×C22⋊D43C4⋊C414yes—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175#10621898—28no—
176#10621898—28no—
177#10621898—28no—
178#10621898—28no—
179C2×D172—22no—
180C2×D172—22no—
181C2×D172C4⋊C414yes—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43—81no—
189C2×C4×D43—81no—
190C2×C4×D43—81no—
191C2×C4×D43—81no—
192C2×C4×D43C22×C412yes—
193C2×C4×D43C22×C412yes—
194C2×C4×D43C2×D412yes—
195C2×C4×D43C2×D412yes—
196C2×C4×D43C2×Q812yes—
197C2×C4×D43C2×Q812yes—
198C2×C4×D43#4112yes—
199C2×C4×D43#4112yes—
200C2×Dic86—22no—
201C2×Dic86—22no—
202C2×Dic86C4⋊C414yes—
203M16×C43—28no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43C22×C412yes—
207C2×C8×C43C22×C412yes—
208C2×C8×C43C2×D412yes—
209C2×C8×C43C2×D412yes—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C22⋊C4×C43—81no—
219C22⋊C4×C43—81no—
220C22⋊Dic43—81no—
221C22⋊Dic43—81no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—42no—
224(C2×D43)⋊C4—81no—
225(C2×D43)⋊C4—81no—
226(C2×D43)⋊C4—81no—
227(C2×D43)⋊C4—81no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236Dic43⋊C4—42no—
237Dic43⋊C4—42no—
238C4×Dic43—42no—
239C4×Dic43—42no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—28no—
243C2×C43⋊C8C22×C412yes—
244C2×C43⋊C8C22×C412yes—
245C2×C43⋊C8C2×D412yes—
246C2×C43⋊C8C2×D412yes—
247#10621872—28no—
248#10621872C22⋊C4116yescomplemented
249C8×D43—28no—
250C8×D43—28no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43C2×C4⋊C412yes—
258C23×C43C22×D411yescharacteristic
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43C2×C4⋊C412yes—
270C22×D43C2×C4⋊C412yes—
271C22×D43#12112yes—
272C22×D43#12112yes—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43C2×C4⋊C412yes—
292C2×C4×C43C23×C411yescharacteristic
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C22×Q811yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C22⋊D43—28no—
299C22⋊D43—28no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
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×Dic43C2×C4⋊C412yes—
315C2×Dic43C2×C4⋊C412yes—
316C2×Dic43#12112yes—
317C2×Dic43#12112yes—
318D172—28no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—84no—
324C4×D43—84no—
325C4×D43C2×C22⋊C414yes—
326C4×D43#11714yes—
327C4×D43C22⋊Q814yes—
328C4×D43C22⋊Q814yes—
329Dic86—28no—
330C8×C43—22no—
331C8×C43C2×C22⋊C414yes—
332C43⋊C8—22no—
333C43⋊C8C2×C22⋊C414yes—
334#20664—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43C22×C4⋊C411yescharacteristic
343C22×C43C2×#12111yescharacteristic
344C22×C43C2×#12111yescharacteristic
345C22×C43#57611yescharacteristic
346C22×C43#57711yescharacteristic
347C22×C43#57711yescharacteristic
348C22×C43#57811yescharacteristic
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—22no—
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C2×D43—41no—
362C2×D43#38014yes—
363C4×C43—22no—
364C4×C43—81no—
365C4×C43—81no—
366C4×C43—81no—
367C4×C43—81no—
368C4×C43C22×C22⋊C411yescharacteristic
369C4×C43C2×#11711yescharacteristic
370C4×C43C2×C22⋊Q811yescharacteristic
371C4×C43C2×C22⋊Q811yescharacteristic
372Dic43—22no—
373Dic43—81no—
374Dic43—81no—
375Dic43—81no—
376Dic43—81no—
377Dic43#38014yes—
378C22×#131—431no—
379C2×#428—431no—
380C2×#428—431no—
381#2311—431no—
382#2311—431no—
383#1809—431no—
384#1809—431no—
385#1809—431no—
386#1809D4311yescharacteristic, complemented
387#1808—431no—
388#1808—431no—
389#1807—431no—
390#1807—431no—
391#1735—431no—
392C2×#340—431no—
393C2×C43—42no—
394C2×C43C2×#38011yescharacteristic
395C2×C43#291211yescharacteristic
396C2×C43#291311yescharacteristic
397C2×C43#306211yescharacteristic
398C2×C43#306211yescharacteristic
399C2×C43#306311yescharacteristic
400C2×C43#306311yescharacteristic
401D43—24no—
402D43—42no—
403C22×#41—431no—
404C2×#131—438no—
405C2×#131—864no—
406C2×#131—864no—
407C22×M16—431no—
408C22×M16—431no—
409C22×M16C2×D4311yescharacteristic
410C23×C8—431no—
411C23×C8—431no—
412C23×C8—431no—
413C2×#117—431no—
414C2×#117—431no—
415C22×C4⋊C4—431no—
416C22×C4⋊C4—431no—
417#428—864no—
418#428—864no—
419C2×#107—431no—
420C2×#107—431no—
421C2×#107—431no—
422C2×#107C2×D4311yescharacteristic
423C2×#106—431no—
424C2×#106—431no—
425C2×#106—431no—
426C2×#106C2×D4311yescharacteristic
427#391—861no—
428#391—861no—
429#390—861no—
430#390—861no—
431#386—861no—
432#386—861no—
433#386—861no—
434#386—861no—
435#380—431no—
436#380—431no—
437#380—431no—
438#380—431no—
439#380—431no—
440#380—431no—
441#380C2×D4311yescharacteristic
442#380C2×D4311yescharacteristic
443#340—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#340—431no—
448#340—431no—
449#340C2×D4311yescharacteristic
450#340C2×D4311yescharacteristic
451C43#2066411yescharacteristic, complemented, Sylow
452C2×#41—434no—
453C2×#41—434no—
454C2×#41—862no—
455C2×#41—862no—
456C2×#41—862no—
457C2×#41—862no—
458C22×Q8—431no—
459C22×D4—431no—
460C22×D4—431no—
461C22×D4—431no—
462C23×C4—431no—
463C23×C4—431no—
464C23×C4—861no—
465C23×C4—861no—
466C23×C4C22×D4311yescharacteristic
467#131—8632no—
468C2×M16—22no—
469C2×M16—22no—
470C2×M16—434no—
471C2×M16—434no—
472C2×M16—434no—
473C2×M16—434no—
474C2×M16—862no—
475C2×M16—862no—
476C2×M16C4×D4314yescomplemented
477C22×C8—431no—
478C22×C8—434no—
479C22×C8—431no—
480C22×C8—434no—
481C22×C8—434no—
482C22×C8—862no—
483C22×C8—862no—
484C22×C8—862no—
485C22×C8—862no—
486C22×C8—862no—
487C22×C8—862no—
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490#117—862no—
491#117—862no—
492#117—862no—
493#117—862no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—862no—
499C2×C4⋊C4—862no—
500C2×C4⋊C4—862no—
501C2×C4⋊C4—862no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C42—861no—
519C2×C42—861no—
520#107—22no—
521#107—862no—
522#107—862no—
523#107—862no—
524#106—22no—
525#106—862no—
526#106—862no—
527#106—862no—
528#95—21no—
529#95—21no—
530#95—861no—
531#95—861no—
532#95—861no—
533#95—861no—
534#95—861no—
535#95—861no—
536C24—431no—
537C24—431no—
538C24D4×D4311yescharacteristic
539#41—868no—
540#41—868no—
541#41—868no—
542#41—868no—
543C2×Q8—434no—
544C2×Q8—862no—
545C2×Q8—862no—
546C2×D4—434no—
547C2×D4—434no—
548C2×D4—434no—
549C2×D4—862no—
550C2×D4—862no—
551C2×D4—862no—
552C2×D4—862no—
553C2×D4—862no—
554C2×D4—862no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—431no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—432no—
567C22×C4—432no—
568C22×C4—432no—
569C22×C4—432no—
570C22×C4—431no—
571C22×C4—432no—
572C22×C4—432no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—3441no—
582C22×C4—3441no—
583C22×C4—3441no—
584C22×C4—3441no—
585C22×C4—1722no—
586C22×C4—1722no—
587C22×C4C2×C4×D4312yes—
588C22×C4D4×D4311yescharacteristic
589C22×C4Q8×D4312yes—
590C22×C4C23×D4311yescharacteristic
591M16—28no—
592M16—4316no—
593M16—868no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—432no—
597C2×C8—432no—
598C2×C8—432no—
599C2×C8—432no—
600C2×C8—868no—
601C2×C8—868no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—868no—
605C2×C8C2×C4×D4312yes—
606C2×C8C2×C4×D4312yes—
607C2×C8D4×D4312yes—
608C2×C8D4×D4312yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—1722no—
626C4⋊C4—1722no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—3441no—
630C22⋊C4—3441no—
631C22⋊C4—3441no—
632C22⋊C4—3441no—
633C22⋊C4—3441no—
634C22⋊C4—3441no—
635C22⋊C4—1722no—
636C22⋊C4—1722no—
637C42—1722no—
638C42—1722no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—432no—
646C23—432no—
647C23—432no—
648C23—432no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23—861no—
656C23—861no—
657C23—861no—
658C23—861no—
659C23C4⋊C4×D4312yes—
660C23C2×D4×D4311yescharacteristic
661Q8—868no—
662D4—868no—
663D4—868no—
664D4—868no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—432no—
684C2×C4—432no—
685C2×C4—432no—
686C2×C4—434no—
687C2×C4—434no—
688C2×C4—434no—
689C2×C4—434no—
690C2×C4—432no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—3444no—
698C2×C4—3444no—
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×C4C4⋊C4×D4312yes—
712C2×C4C22×C4×D4311yescharacteristic
713C2×C4C2×D4×D4311yescharacteristic
714C2×C4C2×D4×D4311yescharacteristic
715C2×C4C2×Q8×D4311yescharacteristic
716C2×C4#41×D4311yescharacteristic
717C2×C4#41×D4311yescharacteristic
718C8—22no—
719C8—434no—
720C8—862no—
721C8C22⋊C4×D4314yes—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—434no—
730C22—862no—
731C22—862no—
732C22—862no—
733C22—862no—
734C22—862no—
735C22—862no—
736C22—862no—
737C22—862no—
738C22—862no—
739C22—1721no—
740C22—1721no—
741C22—1721no—
742C22—1721no—
743C22C2×C4⋊C4×D4311yescharacteristic
744C22#121×D4311yescharacteristic
745C22#121×D4311yescharacteristic
746C22#1458370311yescharacteristic
747C22#1458370811yescharacteristic
748C22#1458370911yescharacteristic
749C22#1458371511yescharacteristic
750C4—22no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—434no—
756C4—862no—
757C4—3441no—
758C4—3441no—
759C4—3441no—
760C4—3441no—
761C4C2×C22⋊C4×D4311yescharacteristic
762C4#117×D4311yescharacteristic
763C4C22⋊Q8×D4311yescharacteristic
764C4C22⋊Q8×D4311yescharacteristic
765C2—42no—
766C2—864no—
767C2—1722no—
768C2#380×D4311yescharacteristic
769C2#1914318911yescharacteristic
770C2#1914319411yescharacteristic
771C2#1914427011yescharacteristic
772C2#1914427211yescharacteristic
773C2#1914428111yescharacteristic
774C2#1914428311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1809C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1809D43
hypocenterC43#20664
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#14582940C2semidirect
3. C2×#14582938C2semidirect
6. #19134628C2semidirect
7. #19134627C2semidirect
8. #19134627C2semidirect
9. #19134622C2semidirect
10. #19134621C2semidirect
11. #19134618C2semidirect
12. #19134617C2semidirect
13. #19134310C2semidirect
14. #340×D43C2semidirect
15. C43×#1809C2semidirect
19. C2×#13063333C4semidirect
82. C2×#10621872C2×C4semidirect
87. C22×C43⋊C8C2×C4semidirect
95. C2×C8×D43C2×C4semidirect
135. C2×M16×C43C2×C4semidirect
248. #10621872C22⋊C4semidirect
386. #1809D43semidirect
451. C43#20664semidirect
476. C2×M16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633332
C2×#145829402
C2×#145829382
#191371842
#191346282
#191346272
#191346222
#191346212
#191346182
#191346172
#191343102
#340×D432
C43×#18092
#2066443