Finite Group Databasebeta

← #25003780

Subgroups — #25003780

Order 11008.

1478 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063239C211yesmaximal, characteristic
2#19137170C211yesmaximal, characteristic
3C2×#14582778C211yesmaximal, characteristic
4C2×#14582666C211yesmaximal, characteristic, complemented
5C2×#14582665C211yesmaximal, characteristic, complemented
6#19132818C211yesmaximal, characteristic, complemented
7C2×C43×#385C211yesmaximal, characteristic, complemented
8C23×C22⋊D43C2211yescharacteristic
9C22×C22⋊Dic43C2211yescharacteristic
10C22×C22⋊Dic43C2211yescharacteristic
11C22×C22⋊Dic43C2211yescharacteristic
12C22×(C2×D43)⋊C4—21no—
13C2×#13063239—22no—
14C2×#13063239—22no—
15C2×#13063239C414yescomplemented
16#14582778—22no—
17#14582778—21no—
18#14582778—21no—
19#14582778—22no—
20#14582776—22no—
21#14582760—21no—
22#14582754—21no—
23C2×C43⋊#95—21no—
24C2×C43⋊#95—22no—
25#14582666—22no—
26#14582665—22no—
27C24×C4×C43C2211yescharacteristic
28C22×C4⋊C4×C43—21no—
29C22×C22⋊C4×C43C2211yescharacteristic
30C22×C22⋊C4×C43C2211yescharacteristic
31C43×#385—22no—
32C43×#385—22no—
33C2×#95×C43—21no—
34C24×D43D411yescharacteristic
35C22×C22⋊D43—21no—
36C22×C22⋊D43—21no—
37C22×C22⋊D43—21no—
38C22×C22⋊D43—21no—
39C22×C22⋊D43—21no—
40C22×C22⋊D43—21no—
41C22×C22⋊D43—21no—
42C22×C22⋊D43—21no—
43C22×C22⋊D43—21no—
44C22×C22⋊D43—21no—
45C22×C22⋊D43—21no—
46C22×C22⋊D43—21no—
47C22×C22⋊D43C2×C412yes—
48C22×C22⋊D43Q812yes—
49C23×Dic43—21no—
50C23×Dic43—21no—
51C23×Dic43D411yescharacteristic
52C23×Dic43D412yes—
53C2×C22⋊Dic43—21no—
54C2×C22⋊Dic43—21no—
55C2×C22⋊Dic43—21no—
56C2×C22⋊Dic43—21no—
57C2×C22⋊Dic43—21no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—21no—
60C2×C22⋊Dic43—21no—
61C2×C22⋊Dic43—21no—
62C2×C22⋊Dic43—21no—
63C2×C22⋊Dic43—21no—
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C22⋊Dic43—21no—
67C2×C22⋊Dic43—21no—
68C2×C22⋊Dic43—21no—
69C2×C22⋊Dic43C2×C412yes—
70C2×C22⋊Dic43D412yes—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4—44no—
75#13063239—28no—
76C43⋊#95—24no—
77C43⋊#95—22no—
78C43⋊#95—22no—
79C43⋊#95—44no—
80C25×C43C2311yescharacteristic
81C23×C4×C43—21no—
82C23×C4×C43—21no—
83C23×C4×C43—21no—
84C23×C4×C43—21no—
85C23×C4×C43—21no—
86C23×C4×C43—21no—
87C23×C4×C43—21no—
88C23×C4×C43—44no—
89C23×C4×C43D411yescharacteristic
90C23×C4×C43D411yescharacteristic
91C23×C4×C43D412yes—
92C2×C4⋊C4×C43—24no—
93C2×C4⋊C4×C43—44no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43C2×C412yes—
104C2×C22⋊C4×C43D412yes—
105C2×C22⋊C4×C43D412yes—
106#95×C43—24no—
107C24×C43—42no—
108C24×C43—42no—
109C24×C43C22×C411yescharacteristic
110C24×C43C2×D411yescharacteristic
111C24×C43C2×D411yescharacteristic
112C24×C43C2×D411yescharacteristic
113C24×C43C2×D411yescharacteristic
114C24×C43C2×D411yescharacteristic
115C24×C43C2×D411yescharacteristic
116C24×C43C2×D411yescharacteristic
117C24×C43C2×Q811yescharacteristic
118C24×C43#4111yescharacteristic
119C24×C43#4111yescharacteristic
120C24×C43#4111yescharacteristic
121C24×C43#4111yescharacteristic
122C24×C43#4111yescharacteristic
123C24×C43#4111yescharacteristic
124C23×D43—21no—
125C23×D43—21no—
126C23×D43—21no—
127C23×D43—21no—
128C23×D43—21no—
129C23×D43—21no—
130C23×D43—42no—
131C23×D43—42no—
132C23×D43C4⋊C412yescomplemented
133C22×C4×C43—24no—
134C22×C4×C43—24no—
135C22×C4×C43—24no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—42no—
149C22×C4×C43—42no—
150C22×C4×C43—42no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—42no—
154C22×C4×C43—42no—
155C22×C4×C43—44no—
156C22×C4×C43—44no—
157C22×C4×C43—44no—
158C22×C4×C43—44no—
159C22×C4×C43—41no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C22×C4×C43—41no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—22no—
171C2×C22⋊D43—22no—
172C2×C22⋊D43—22no—
173C2×C22⋊D43—22no—
174C2×C22⋊D43—22no—
175C2×C22⋊D43—41no—
176C2×C22⋊D43—41no—
177C2×C22⋊D43—41no—
178C2×C22⋊D43—41no—
179C2×C22⋊D43—41no—
180C2×C22⋊D43—41no—
181C2×C22⋊D43—41no—
182C2×C22⋊D43—41no—
183C2×C22⋊D43—41no—
184C2×C22⋊D43—41no—
185C2×C22⋊D43—41no—
186C2×C22⋊D43—41no—
187C2×C22⋊D43—41no—
188C2×C22⋊D43—41no—
189C2×C22⋊D43—41no—
190C2×C22⋊D43—41no—
191C22×Dic43—22no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—22no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—22no—
202C22×Dic43—42no—
203C22×Dic43—42no—
204C22×Dic43—42no—
205C22×Dic43—42no—
206C22×Dic43—42no—
207C22×Dic43—42no—
208C22×Dic43—41no—
209C22×Dic43—41no—
210C22×Dic43—41no—
211C22×Dic43—41no—
212C22×Dic43C4⋊C412yescomplemented
213C4⋊C4×C43—48no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—22no—
217C22⋊C4×C43—41no—
218C22⋊C4×C43—41no—
219C22⋊C4×C43—41no—
220C22⋊C4×C43—41no—
221C22⋊C4×C43C22⋊C414yescomplemented
222C22⋊Dic43—22no—
223C22⋊Dic43—22no—
224C22⋊Dic43—22no—
225C22⋊Dic43—22no—
226C22⋊Dic43—41no—
227C22⋊Dic43—41no—
228C22⋊Dic43—41no—
229C22⋊Dic43—41no—
230C22⋊Dic43—41no—
231C22⋊Dic43—41no—
232C22⋊Dic43—41no—
233C22⋊Dic43—41no—
234(C2×D43)⋊C4—48no—
235(C2×D43)⋊C4—82no—
236(C2×D43)⋊C4—82no—
237C23×C43—22no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—42no—
248C23×C43—42no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—42no—
253C23×C43—42no—
254C23×C43—42no—
255C23×C43—41no—
256C23×C43—42no—
257C23×C43—42no—
258C23×C43—42no—
259C23×C43C2×C22⋊C411yescharacteristic
260C23×C43C2×C4⋊C411yescharacteristic
261C23×C43#11711yescharacteristic
262C23×C43C4×D411yescharacteristic
263C23×C43C4×D411yescharacteristic
264C23×C43C4×D411yescharacteristic
265C23×C43C4×D411yescharacteristic
266C23×C43#12011yescharacteristic
267C23×C43#12011yescharacteristic
268C23×C43#12011yescharacteristic
269C23×C43#12111yescharacteristic
270C23×C43#12111yescharacteristic
271C23×C43#12111yescharacteristic
272C23×C43#12111yescharacteristic
273C23×C43#12111yescharacteristic
274C23×C43#12111yescharacteristic
275C23×C43#12111yescharacteristic
276C23×C43#12111yescharacteristic
277C23×C43C22⋊Q811yescharacteristic
278C23×C43C22⋊Q811yescharacteristic
279C23×C43C22⋊Q811yescharacteristic
280C23×C43C22⋊Q811yescharacteristic
281C23×C43C22⋊Q811yescharacteristic
282C23×C43C22⋊Q811yescharacteristic
283C23×C43#12311yescharacteristic
284C23×C43#12311yescharacteristic
285C23×C43#12311yescharacteristic
286C23×C43#12311yescharacteristic
287C23×C43#12311yescharacteristic
288C23×C43#12411yescharacteristic
289C23×C43#12411yescharacteristic
290C23×C43#12411yescharacteristic
291C23×C43#12611yescharacteristic
292C23×C43#12611yescharacteristic
293C23×C43#12711yescharacteristic
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—44no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—44no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43—82no—
308C22×D43—81no—
309C22×D43—81no—
310C22×D43—82no—
311C2×C4×C43—24no—
312C2×C4×C43—24no—
313C2×C4×C43—24no—
314C2×C4×C43—24no—
315C2×C4×C43—42no—
316C2×C4×C43—44no—
317C2×C4×C43—42no—
318C2×C4×C43—44no—
319C2×C4×C43—42no—
320C2×C4×C43—44no—
321C2×C4×C43—42no—
322C2×C4×C43—42no—
323C2×C4×C43—44no—
324C2×C4×C43—44no—
325C2×C4×C43—42no—
326C2×C4×C43—44no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—42no—
332C2×C4×C43—42no—
333C2×C4×C43—81no—
334C2×C4×C43—81no—
335C22⋊D43—42no—
336C22⋊D43—42no—
337C22⋊D43—42no—
338C22⋊D43—42no—
339C22⋊D43—42no—
340C22⋊D43—42no—
341C22⋊D43—42no—
342C22⋊D43—42no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—42no—
351C2×Dic43—44no—
352C2×Dic43—42no—
353C2×Dic43—44no—
354C2×Dic43—42no—
355C2×Dic43—42no—
356C2×Dic43—42no—
357C2×Dic43—42no—
358C2×Dic43—42no—
359C2×Dic43—82no—
360C2×Dic43—81no—
361C2×Dic43—81no—
362C2×Dic43—82no—
363C2×Dic43—82no—
364C2×Dic43—82no—
365#11087—431nomaximal, Sylow
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—21no—
373C22×C43—21no—
374C22×C43—21no—
375C22×C43—21no—
376C22×C43—21no—
377C22×C43—21no—
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—21no—
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43—41no—
405C22×C43—41no—
406C22×C43#38011yescharacteristic
407C22×C43#38511yescharacteristic
408C22×C43#38511yescharacteristic
409C22×C43#38611yescharacteristic
410C22×C43#38811yescharacteristic
411C22×C43#38811yescharacteristic
412C22×C43#39011yescharacteristic
413C22×C43#39211yescharacteristic
414C22×C43#39311yescharacteristic
415C22×C43#39411yescharacteristic
416C22×C43#39411yescharacteristic
417C22×C43#39611yescharacteristic
418C22×C43#39611yescharacteristic
419C22×C43#39711yescharacteristic
420C22×C43#39911yescharacteristic
421C22×C43B(4,𝔽2)12yes—
422C22×C43#45812yes—
423C2×D43—44no—
424C2×D43—44no—
425C2×D43—42no—
426C2×D43—82no—
427C2×D43—82no—
428C2×D43—81no—
429C2×D43—81no—
430C2×D43—82no—
431C2×D43—82no—
432C4×C43—44no—
433C4×C43—44no—
434C4×C43—81no—
435C4×C43—81no—
436Dic43—42no—
437Dic43—82no—
438Dic43—82no—
439Dic43—82no—
440C22×#99—431no—
441#2308—431no—
442C2×#386—431no—
443C2×#385D4311yescharacteristic, complemented
444C2×#342—431no—
445C2×#342—431no—
446C22⋊#95—431no—
447C2×C43—21no—
448C2×C43—21no—
449C2×C43—21no—
450C2×C43—21no—
451C2×C43—21no—
452C2×C43—21no—
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—21no—
456C2×C43—21no—
457C2×C43—21no—
458C2×C43—21no—
459C2×C43#143911yescharacteristic
460C2×C43#186712yes—
461C2×C43#202111yescharacteristic
462C2×C43#202211yescharacteristic
463C2×C43#204412yes—
464D43—82no—
465C23×D4—431no—
466C24×C4C2×D4311yescharacteristic
467C22×C4⋊C4—21no—
468C22×C22⋊C4—431no—
469C22×C22⋊C4—431no—
470C22×C22⋊C4—431no—
471C22×C22⋊C4—861no—
472C22×C22⋊C4C2×D4311yescharacteristic
473C22×C22⋊C4C2×D4311yescharacteristic
474C2×#99—434no—
475C2×#99—862no—
476C2×#99—862no—
477#386—862no—
478#386—862no—
479#386—861no—
480#386—861no—
481#386—862no—
482#385—22no—
483#385—22no—
484#381—861no—
485#379—861no—
486C2×#95—21no—
487C2×#95—861no—
488C2×#95—862no—
489#342—862no—
490#342—862no—
491C43#1108711yescharacteristic, complemented, Sylow
492C25—431no—
493C25C22×D4311yescharacteristic
494C22×D4—432no—
495C22×D4—432no—
496C22×D4—861no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4—861no—
500C22×D4—861no—
501C22×D4—861no—
502C22×D4—861no—
503C22×D4—861no—
504C22×D4—861no—
505C22×D4—861no—
506C22×D4—861no—
507C22×D4—861no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—44no—
516C23×C4—431no—
517C23×C4—432no—
518C23×C4—861no—
519C23×C4—861no—
520C23×C4C22⋊D4311yescharacteristic
521C23×C4C22⋊D4311yescharacteristic
522C23×C4C22⋊D4312yes—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—44no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—432no—
535C2×C22⋊C4—432no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—862no—
545C2×C22⋊C4—862no—
546C2×C22⋊C4—864no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—1724no—
556C2×C22⋊C4C4×D4312yes—
557C2×C22⋊C4D17212yes—
558C2×C22⋊C4C22⋊D4312yes—
559#99—868no—
560#95—24no—
561#95—864no—
562#95—862no—
563#95—862no—
564#95—1724no—
565C24—42no—
566C24—42no—
567C24—432no—
568C24—861no—
569C24—861no—
570C24—861no—
571C24—861no—
572C24—861no—
573C24—861no—
574C24—1722no—
575C24—1722no—
576C24C2×C4×D4311yescharacteristic
577C24C2×D17211yescharacteristic
578C24#1062189811yescharacteristic
579C24#1062189811yescharacteristic
580C24D4×D4311yescharacteristic
581C24D4×D4311yescharacteristic
582C24D4×D4311yescharacteristic
583C24#1062190011yescharacteristic
584C24Q8×D4311yescharacteristic
585C24#1062190211yescharacteristic
586C24#1062190211yescharacteristic
587C24#1062190211yescharacteristic
588C24C2×C22⋊D4311yescharacteristic
589C24C2×C22⋊D4311yescharacteristic
590C24C2×C22⋊D4311yescharacteristic
591C2×D4—862no—
592C2×D4—862no—
593C2×D4—862no—
594C2×D4—862no—
595C2×D4—862no—
596C2×D4—862no—
597C2×D4—862no—
598C2×D4—862no—
599C2×D4—862no—
600C2×D4—862no—
601C2×D4—862no—
602C2×D4—862no—
603C2×D4—1721no—
604C2×D4—1721no—
605C2×D4—1721no—
606C2×D4—1721no—
607C2×D4—1721no—
608C2×D4—1721no—
609C2×D4—1721no—
610C2×D4—1721no—
611C2×D4—1721no—
612C2×D4—1721no—
613C2×D4—1721no—
614C2×D4—1721no—
615C2×D4—1721no—
616C2×D4—1721no—
617C2×D4—1721no—
618C2×D4—1721no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—432no—
650C22×C4—861no—
651C22×C4—861no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—862no—
657C22×C4—862no—
658C22×C4—862no—
659C22×C4—862no—
660C22×C4—862no—
661C22×C4—1722no—
662C22×C4—1722no—
663C22×C4—1722no—
664C22×C4—1722no—
665C22×C4—1721no—
666C22×C4—1721no—
667C22×C4—1721no—
668C22×C4—1721no—
669C22×C4—1722no—
670C22×C4—1722no—
671C4⋊C4—48no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C22⋊C4—862no—
680C22⋊C4—862no—
681C22⋊C4—862no—
682C22⋊C4—862no—
683C22⋊C4—3442no—
684C22⋊C4—3442no—
685C22⋊C4—1728no—
686C22⋊C4—1721no—
687C22⋊C4—1721no—
688C22⋊C4—1721no—
689C22⋊C4—1721no—
690C22⋊C4—1721no—
691C22⋊C4—1721no—
692C22⋊C4—1721no—
693C22⋊C4—1721no—
694C22⋊C4(C2×D43)⋊C414yescomplemented
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—41no—
710C23—41no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—41no—
716C23—41no—
717C23—862no—
718C23—862no—
719C23—862no—
720C23—3442no—
721C23—3441no—
722C23—3441no—
723C23—3442no—
724C23—1722no—
725C23—1724no—
726C23—1722no—
727C23—1724no—
728C23—1721no—
729C23—1721no—
730C23—1721no—
731C23—1721no—
732C23—1722no—
733C23—1722no—
734C23C2×(C2×D43)⋊C411yescharacteristic
735C23C4⋊C4×D4311yescharacteristic
736C23#1306328311yescharacteristic
737C23C4×C22⋊D4311yescharacteristic
738C23C4×C22⋊D4311yescharacteristic
739C23#1306328711yescharacteristic
740C23#1306328711yescharacteristic
741C23#1306329311yescharacteristic
742C23#1306329311yescharacteristic
743C23#1306329411yescharacteristic
744C23#1306329611yescharacteristic
745C23#1306329711yescharacteristic
746C23#1306329711yescharacteristic
747C23#1306329911yescharacteristic
748C23#1306329911yescharacteristic
749C23#1306330011yescharacteristic
750C23#1306330011yescharacteristic
751C23#1306330011yescharacteristic
752C23#1306330111yescharacteristic
753C23#1306330111yescharacteristic
754C23#1306330111yescharacteristic
755C23#1306330311yescharacteristic
756C23#1306330311yescharacteristic
757C23#1306330511yescharacteristic
758C23#1306330811yescharacteristic
759C23#1306331011yescharacteristic
760C23#1306331011yescharacteristic
761C23#1306331011yescharacteristic
762C23#1306331011yescharacteristic
763C23#1306331411yescharacteristic
764C23#1306331411yescharacteristic
765C23#1306331411yescharacteristic
766C23#1306332011yescharacteristic
767C23#1306332011yescharacteristic
768C23#1306332111yescharacteristic
769D4—1722no—
770D4—1722no—
771D4—1722no—
772D4—1722no—
773D4—1722no—
774D4—1722no—
775D4—1722no—
776D4—1722no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—3442no—
805C2×C4—3442no—
806C2×C4—3442no—
807C2×C4—3441no—
808C2×C4—3441no—
809C2×C4—3442no—
810C2×C4—1722no—
811C2×C4—1724no—
812C2×C4—1722no—
813C2×C4—1724no—
814C2×C4—1722no—
815C2×C4—1722no—
816C2×C4—1722no—
817C2×C4—1722no—
818C2×C4—1722no—
819C2×C4—1721no—
820C2×C4—1721no—
821C2×C4—1721no—
822C2×C4—1721no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—3442no—
864C22—3442no—
865C22—3442no—
866C22—3442no—
867C22—3441no—
868C22—3441no—
869C22—1724no—
870C22—1724no—
871C22—1722no—
872C22#1458275611yescharacteristic
873C22#1458277011yescharacteristic
874C22#1458277011yescharacteristic
875C22#1458277811yescharacteristic
876C22#1458278911yescharacteristic
877C22#1458278911yescharacteristic
878C22#1458280011yescharacteristic
879C22#1458280711yescharacteristic
880C22#1458281011yescharacteristic
881C22#1458281611yescharacteristic
882C22#1458281611yescharacteristic
883C22#1458282111yescharacteristic
884C22#1458282111yescharacteristic
885C22#1458282511yescharacteristic
886C22#1458283411yescharacteristic
887C22#1458308512yes—
888C22#1458308812yes—
889C4—44no—
890C4—44no—
891C4—81no—
892C4—81no—
893C4—3442no—
894C4—3442no—
895C4—3442no—
896C4—1722no—
897C2—21no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—21no—
903C2—21no—
904C2—21no—
905C2—21no—
906C2—21no—
907C2—21no—
908C2—21no—
909C2—3442no—
910C2#1913283711yescharacteristic
911C2#1913487412yes—
912C2#1913571811yescharacteristic
913C2#1913572311yescharacteristic
914C2#1913584612yes—
subgroupG/H
centerC23#13063293
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC2×C43×#385C2
socleC23×C43#120
prime radicalC23×C22⋊D43C22
cosocleC25×C43C23
hypercenterC2×#385D43
hypocenterC43#11087
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#14582666C2semidirect
5. C2×#14582665C2semidirect
6. #19132818C2semidirect
7. C2×C43×#385C2semidirect
15. C2×#13063239C4semidirect
132. C23×D43C4⋊C4semidirect
212. C22×Dic43C4⋊C4semidirect
221. C22⋊C4×C43C22⋊C4semidirect
443. C2×#385D43semidirect
491. C43#11087semidirect
694. C22⋊C4(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130632392
#191371702
C2×#145827782
C2×#145826662
C2×#145826652
#191328182
C2×C43×#3852
#1108743