Finite Group Databasebeta

← #25003211

Subgroups — #25003211

Order 11008.

1658 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063308C211yesmaximal, characteristic
2C22×#13063239C211yesmaximal, characteristic
3#19137170C211yesmaximal, characteristic
4C2×#14582762C211yesmaximal, characteristic, complemented
5C2×#14582666C211yesmaximal, characteristic, complemented
6C2×#14582665C211yesmaximal, characteristic, complemented
7C2×C43×#381C211yesmaximal, characteristic, complemented
8C23×C22⋊D43C2211yescharacteristic
9C2×#13063308—22no—
10C2×#13063308—22no—
11C2×#13063308—22no—
12C2×#13063308—22no—
13C2×#13063308—22no—
14C2×#13063308C414yescomplemented
15C22×Dic43⋊C4—21no—
16C22×C22⋊Dic43C2211yescharacteristic
17C22×C22⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2211yescharacteristic
19C22×(C2×D43)⋊C4—21no—
20C2×#13063239—22no—
21C2×#13063239—22no—
22C2×#13063239—22no—
23#14582778—22no—
24#14582776—22no—
25#14582762—22no—
26#14582762—22no—
27#14582760—21no—
28#14582754—21no—
29C2×C43⋊#95—22no—
30#14582666—22no—
31#14582665—22no—
32C24×C4×C43C2211yescharacteristic
33C22×C22⋊C4×C43C2211yescharacteristic
34C22×C22⋊C4×C43C2211yescharacteristic
35C43×#381—22no—
36C43×#381—22no—
37C2×#95×C43—22no—
38C24×D43D411yescharacteristic
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⋊D43—21no—
48C22×C22⋊D43—21no—
49C22×C22⋊D43—21no—
50C22×C22⋊D43—21no—
51C22×C22⋊D43C2×C412yes—
52C22×C22⋊D43D412yes—
53C23×Dic43—21no—
54C23×Dic43—21no—
55C23×Dic43D411yescharacteristic
56C23×Dic43D412yes—
57#13063308—28no—
58#13063308—28no—
59#13063308—28no—
60#13063308—28no—
61C2×Dic43⋊C4—24no—
62C2×Dic43⋊C4—24no—
63C2×Dic43⋊C4—24no—
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C22⋊Dic43—21no—
67C2×C22⋊Dic43—21no—
68C2×C22⋊Dic43—21no—
69C2×C22⋊Dic43—21no—
70C2×C22⋊Dic43—21no—
71C2×C22⋊Dic43—21no—
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43C2×C412yes—
79C2×C22⋊Dic43D412yes—
80C2×C22⋊Dic43D412yes—
81C2×C22⋊Dic43D412yes—
82C2×(C2×D43)⋊C4—24no—
83C2×(C2×D43)⋊C4—24no—
84C2×(C2×D43)⋊C4—24no—
85C2×(C2×D43)⋊C4—24no—
86#13063239—28no—
87C43⋊#95—28no—
88C43⋊#95—24no—
89C25×C43C2311yescharacteristic
90C23×C4×C43—21no—
91C23×C4×C43—21no—
92C23×C4×C43—21no—
93C23×C4×C43—21no—
94C23×C4×C43—21no—
95C23×C4×C43—21no—
96C23×C4×C43—21no—
97C23×C4×C43—21no—
98C23×C4×C43—21no—
99C23×C4×C43—21no—
100C23×C4×C43—21no—
101C23×C4×C43—21no—
102C23×C4×C43—21no—
103C23×C4×C43C2×C412yes—
104C23×C4×C43D412yes—
105C23×C4×C43D412yes—
106C23×C4×C43D412yes—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43D412yes—
119#95×C43—28no—
120C24×C43—44no—
121C24×C43C22×C411yescharacteristic
122C24×C43C2×D411yescharacteristic
123C24×C43C2×D411yescharacteristic
124C24×C43C2×D411yescharacteristic
125C24×C43C2×D411yescharacteristic
126C24×C43C2×D411yescharacteristic
127C24×C43C2×D411yescharacteristic
128C24×C43C2×D411yescharacteristic
129C24×C43C2×D411yescharacteristic
130C24×C43C2×D411yescharacteristic
131C24×C43C2×D411yescharacteristic
132C24×C43#4111yescharacteristic
133C24×C43#4111yescharacteristic
134C24×C43#4111yescharacteristic
135C24×C43#4111yescharacteristic
136C23×D43—21no—
137C23×D43—21no—
138C23×D43—21no—
139C23×D43—21no—
140C23×D43—21no—
141C23×D43—21no—
142C23×D43—44no—
143C23×D43C22⋊C412yes—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—44no—
167C22×C4×C43—44no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170C22×C4×C43—41no—
171C22×C4×C43—41no—
172C22×C4×C43—41no—
173C22×C4×C43—41no—
174C22×C4×C43—41no—
175C22×C4×C43—41no—
176C22×C4×C43—41no—
177C22×C4×C43—41no—
178C22×C4×C43—41no—
179C22×C4×C43—41no—
180C22×C4×C43—41no—
181C22×C4×C43—41no—
182C22×C4×C43—41no—
183C22×C4×C43—41no—
184C22×C4×C43—41no—
185C22×C4×C43—41no—
186C22×C4×C43C22⋊C414yescomplemented
187C2×C22⋊D43—22no—
188C2×C22⋊D43—22no—
189C2×C22⋊D43—22no—
190C2×C22⋊D43—22no—
191C2×C22⋊D43—22no—
192C2×C22⋊D43—22no—
193C2×C22⋊D43—22no—
194C2×C22⋊D43—22no—
195C2×C22⋊D43—22no—
196C2×C22⋊D43—22no—
197C2×C22⋊D43—22no—
198C2×C22⋊D43—22no—
199C2×C22⋊D43—41no—
200C2×C22⋊D43—41no—
201C2×C22⋊D43—41no—
202C2×C22⋊D43—41no—
203C2×C22⋊D43—41no—
204C2×C22⋊D43—41no—
205C2×C22⋊D43—41no—
206C2×C22⋊D43—41no—
207C2×C22⋊D43—41no—
208C2×C22⋊D43—41no—
209C2×C22⋊D43—41no—
210C2×C22⋊D43—41no—
211C2×C22⋊D43—41no—
212C2×C22⋊D43—41no—
213C2×C22⋊D43—41no—
214C2×C22⋊D43—41no—
215C22×Dic43—22no—
216C22×Dic43—21no—
217C22×Dic43—22no—
218C22×Dic43—22no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—22no—
222C22×Dic43—22no—
223C22×Dic43—22no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—22no—
227C22×Dic43—21no—
228C22×Dic43—44no—
229C22×Dic43—44no—
230C22×Dic43—44no—
231C22×Dic43—41no—
232C22×Dic43—41no—
233C22×Dic43C22⋊C412yes—
234C22⋊C4×C43—22no—
235C22⋊C4×C43—22no—
236C22⋊C4×C43—41no—
237C22⋊C4×C43—41no—
238C22⋊C4×C43—41no—
239C22⋊C4×C43—41no—
240C22⋊C4×C43—41no—
241C22⋊C4×C43—41no—
242C22⋊Dic43—22no—
243C22⋊Dic43—22no—
244C22⋊Dic43—22no—
245C22⋊Dic43—22no—
246C22⋊Dic43—22no—
247C22⋊Dic43—41no—
248C22⋊Dic43—41no—
249C22⋊Dic43—41no—
250C22⋊Dic43—41no—
251C22⋊Dic43—41no—
252C22⋊Dic43—41no—
253C22⋊Dic43C22⋊C414yescomplemented
254(C2×D43)⋊C4—216no—
255(C2×D43)⋊C4—84no—
256Dic43⋊C4—216no—
257C23×C43—24no—
258C23×C43—24no—
259C23×C43—24no—
260C23×C43—42no—
261C23×C43—42no—
262C23×C43—42no—
263C23×C43—42no—
264C23×C43—42no—
265C23×C43—42no—
266C23×C43—42no—
267C23×C43—42no—
268C23×C43—42no—
269C23×C43—42no—
270C23×C43—42no—
271C23×C43—42no—
272C23×C43C2×C22⋊C411yescharacteristic
273C23×C43C2×C22⋊C411yescharacteristic
274C23×C43C2×C22⋊C411yescharacteristic
275C23×C43C4×D411yescharacteristic
276C23×C43C4×D411yescharacteristic
277C23×C43C4×D411yescharacteristic
278C23×C43C4×D411yescharacteristic
279C23×C43#12011yescharacteristic
280C23×C43#12011yescharacteristic
281C23×C43#12011yescharacteristic
282C23×C43#12011yescharacteristic
283C23×C43#12011yescharacteristic
284C23×C43#12011yescharacteristic
285C23×C43#12011yescharacteristic
286C23×C43#12011yescharacteristic
287C23×C43#12111yescharacteristic
288C23×C43#12111yescharacteristic
289C23×C43#12111yescharacteristic
290C23×C43#12111yescharacteristic
291C23×C43#12111yescharacteristic
292C23×C43#12111yescharacteristic
293C23×C43#12111yescharacteristic
294C23×C43#12111yescharacteristic
295C23×C43#12111yescharacteristic
296C23×C43#12111yescharacteristic
297C23×C43#12111yescharacteristic
298C23×C43#12111yescharacteristic
299C23×C43#12311yescharacteristic
300C23×C43#12311yescharacteristic
301C23×C43#12311yescharacteristic
302C23×C43#12311yescharacteristic
303C23×C43#12411yescharacteristic
304C23×C43#12411yescharacteristic
305C23×C43#12711yescharacteristic
306C23×C43#12711yescharacteristic
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—44no—
311C22×D43—44no—
312C22×D43—44no—
313C22×D43—41no—
314C22×D43—41no—
315C22×D43—41no—
316C22×D43—41no—
317C22×D43—44no—
318C22×D43—82no—
319C22×D43—82no—
320C22×D43—82no—
321C2×C4×C43—24no—
322C2×C4×C43—24no—
323C2×C4×C43—24no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43—42no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43—42no—
332C2×C4×C43—42no—
333C2×C4×C43—42no—
334C2×C4×C43—42no—
335C2×C4×C43—42no—
336C2×C4×C43—44no—
337C2×C4×C43—44no—
338C2×C4×C43—42no—
339C2×C4×C43—42no—
340C2×C4×C43—44no—
341C2×C4×C43—82no—
342C2×C4×C43—82no—
343C2×C4×C43—82no—
344C22⋊D43—42no—
345C22⋊D43—42no—
346C22⋊D43—42no—
347C22⋊D43—42no—
348C22⋊D43—42no—
349C22⋊D43—42no—
350C22⋊D43—42no—
351C22⋊D43—42no—
352C2×Dic43—22no—
353C2×Dic43—24no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—44no—
357C2×Dic43—44no—
358C2×Dic43—44no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—44no—
364C2×Dic43—44no—
365C2×Dic43—42no—
366C2×Dic43—42no—
367C2×Dic43—44no—
368C2×Dic43—82no—
369C2×Dic43—82no—
370C2×Dic43—82no—
371#10992—431nomaximal, Sylow
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
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#37911yescharacteristic
407C22×C43#38611yescharacteristic
408C22×C43#38611yescharacteristic
409C22×C43#38611yescharacteristic
410C22×C43#38611yescharacteristic
411C22×C43#39011yescharacteristic
412C22×C43#39011yescharacteristic
413C22×C43#39211yescharacteristic
414C22×C43#39211yescharacteristic
415C22×C43#39211yescharacteristic
416C22×C43#39211yescharacteristic
417C22×C43#39411yescharacteristic
418C22×C43#39411yescharacteristic
419C22×C43#39411yescharacteristic
420C22×C43#39411yescharacteristic
421C22×C43#45814yes—
422C2×D43—44no—
423C2×D43—44no—
424C2×D43—42no—
425C2×D43—82no—
426C2×D43—82no—
427C2×D43—82no—
428C2×D43—82no—
429C2×D43—82no—
430C4×C43—44no—
431C4×C43—82no—
432C4×C43—82no—
433Dic43—44no—
434Dic43—42no—
435Dic43—82no—
436Dic43—82no—
437C22×#123—431no—
438C22×#99—431no—
439#2308—431no—
440C2×#381—431no—
441C2×#381D4311yescharacteristic, complemented
442C2×#342—431no—
443C2×#342—431no—
444C2×C43—21no—
445C2×C43—21no—
446C2×C43—21no—
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#143811yescharacteristic
457C2×C43#189012yes—
458C2×C43#202212yes—
459C2×C43#202212yes—
460D43—82no—
461C23×D4—431no—
462C24×C4C2×D4311yescharacteristic
463C2×#123—434no—
464C2×#123—862no—
465C2×#123—862no—
466C2×#123—862no—
467C2×#123—862no—
468C2×#123—862no—
469C22×C4⋊C4—861no—
470C22×C22⋊C4—431no—
471C22×C22⋊C4—431no—
472C22×C22⋊C4—431no—
473C22×C22⋊C4—861no—
474C22×C22⋊C4C2×D4311yescharacteristic
475C22×C22⋊C4C2×D4311yescharacteristic
476C2×#99—862no—
477C2×#99—862no—
478C2×#99—862no—
479#386—862no—
480#386—862no—
481#381—22no—
482#381—22no—
483#381—861no—
484#381—862no—
485#381—862no—
486#379—861no—
487C2×#95—22no—
488C2×#95—862no—
489#342—862no—
490#342—862no—
491C43#1099211yescharacteristic, 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—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—431no—
522C23×C4—432no—
523C23×C4—861no—
524C23×C4—861no—
525C23×C4C4×D4312yes—
526C23×C4D17212yes—
527C23×C4C22⋊D4312yes—
528C23×C4C22⋊D4312yes—
529#123—868no—
530#123—868no—
531#123—868no—
532#123—868no—
533C2×C4⋊C4—864no—
534C2×C4⋊C4—864no—
535C2×C4⋊C4—864no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—432no—
548C2×C22⋊C4—432no—
549C2×C22⋊C4—432no—
550C2×C22⋊C4—432no—
551C2×C22⋊C4—864no—
552C2×C22⋊C4—864no—
553C2×C22⋊C4—864no—
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—864no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4C22⋊D4312yes—
570#99—868no—
571#95—28no—
572#95—868no—
573#95—864no—
574C24—44no—
575C24—432no—
576C24—861no—
577C24—861no—
578C24—861no—
579C24—861no—
580C24—861no—
581C24—861no—
582C24—1724no—
583C24C2×C4×D4311yescharacteristic
584C24C2×D17211yescharacteristic
585C24#1062189811yescharacteristic
586C24#1062189811yescharacteristic
587C24D4×D4311yescharacteristic
588C24D4×D4311yescharacteristic
589C24D4×D4311yescharacteristic
590C24D4×D4311yescharacteristic
591C24D4×D4311yescharacteristic
592C24D4×D4311yescharacteristic
593C24#1062190011yescharacteristic
594C24#1062190011yescharacteristic
595C24C2×C22⋊D4311yescharacteristic
596C24C2×C22⋊D4311yescharacteristic
597C24C2×C22⋊D4311yescharacteristic
598C2×D4—862no—
599C2×D4—862no—
600C2×D4—862no—
601C2×D4—862no—
602C2×D4—862no—
603C2×D4—862no—
604C2×D4—862no—
605C2×D4—862no—
606C2×D4—862no—
607C2×D4—862no—
608C2×D4—862no—
609C2×D4—862no—
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—
619C2×D4—1721no—
620C2×D4—1721no—
621C2×D4—1721no—
622C2×D4—1721no—
623C2×D4—1721no—
624C2×D4—1721no—
625C2×D4—1721no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—432no—
669C22×C4—862no—
670C22×C4—862no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—862no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—862no—
679C22×C4—862no—
680C22×C4—862no—
681C22×C4—862no—
682C22×C4—1724no—
683C22×C4—1721no—
684C22×C4—1721no—
685C22×C4—1724no—
686C22×C4—1724no—
687C22×C4(C2×D43)⋊C414yescomplemented
688C4⋊C4—8616no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—41no—
692C22⋊C4—41no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—434no—
698C22⋊C4—8616no—
699C22⋊C4—862no—
700C22⋊C4—862no—
701C22⋊C4—862no—
702C22⋊C4—862no—
703C22⋊C4—862no—
704C22⋊C4—3444no—
705C22⋊C4—1721no—
706C22⋊C4—1721no—
707C22⋊C4—1721no—
708C22⋊C4—1721no—
709C22⋊C4—1721no—
710C22⋊C4—1721no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—862no—
727C23—862no—
728C23—862no—
729C23—3442no—
730C23—3442no—
731C23—3442no—
732C23—1724no—
733C23—1724no—
734C23—1724no—
735C23—1721no—
736C23—1721no—
737C23—1721no—
738C23—1721no—
739C23—1724no—
740C23C22⋊C4×D4311yescharacteristic
741C23C22⋊C4×D4311yescharacteristic
742C23C2×(C2×D43)⋊C411yescharacteristic
743C23(C22⋊D43)⋊C411yescharacteristic
744C23(C22⋊D43)⋊C411yescharacteristic
745C23C4×C22⋊D4311yescharacteristic
746C23C4×C22⋊D4311yescharacteristic
747C23#1306329311yescharacteristic
748C23#1306329311yescharacteristic
749C23#1306329311yescharacteristic
750C23#1306329311yescharacteristic
751C23#1306329411yescharacteristic
752C23#1306329511yescharacteristic
753C23#1306329511yescharacteristic
754C23#1306329511yescharacteristic
755C23#1306329611yescharacteristic
756C23#1306329611yescharacteristic
757C23#1306329711yescharacteristic
758C23#1306329711yescharacteristic
759C23#1306329711yescharacteristic
760C23#1306329711yescharacteristic
761C23#1306329811yescharacteristic
762C23#1306329811yescharacteristic
763C23#1306329811yescharacteristic
764C23#1306329811yescharacteristic
765C23#1306329911yescharacteristic
766C23#1306329911yescharacteristic
767C23#1306330711yescharacteristic
768C23#1306330711yescharacteristic
769C23#1306330811yescharacteristic
770C23#1306330911yescharacteristic
771C23#1306331111yescharacteristic
772C23#1306331111yescharacteristic
773C23#1306332111yescharacteristic
774C23#1306332111yescharacteristic
775D4—1722no—
776D4—1722no—
777D4—1722no—
778D4—1722no—
779D4—1722no—
780D4—1722no—
781D4—1722no—
782D4—1722no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—82no—
806C2×C4—864no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—3442no—
811C2×C4—3442no—
812C2×C4—3442no—
813C2×C4—1724no—
814C2×C4—1724no—
815C2×C4—1722no—
816C2×C4—1722no—
817C2×C4—1724no—
818C2×C4—1724no—
819C2×C4—1724no—
820C2×C4—1724no—
821C2×C4—1721no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4—1721no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
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—3442no—
860C22—3442no—
861C22—3442no—
862C22—3442no—
863C22—3442no—
864C22—1724no—
865C22—1724no—
866C22—1722no—
867C22#1458275411yescharacteristic
868C22#1458277511yescharacteristic
869C22#1458277511yescharacteristic
870C22#1458277611yescharacteristic
871C22#1458277811yescharacteristic
872C22#1458279911yescharacteristic
873C22#1458279911yescharacteristic
874C22#1458280711yescharacteristic
875C22#1458280711yescharacteristic
876C22#1458280811yescharacteristic
877C22#1458280811yescharacteristic
878C22#1458281411yescharacteristic
879C22#1458281411yescharacteristic
880C22#1458281511yescharacteristic
881C22#1458281511yescharacteristic
882C22#1458308814yes—
883C4—44no—
884C4—82no—
885C4—82no—
886C4—3442no—
887C4—3442no—
888C4—1724no—
889C4—1722no—
890C2—21no—
891C2—21no—
892C2—21no—
893C2—21no—
894C2—21no—
895C2—21no—
896C2—21no—
897C2—21no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—3442no—
903C2#1913283411yescharacteristic
904C2#1913500512yes—
905C2#1913572312yes—
906C2#1913572612yes—
subgroupG/H
centerC23#13063293
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC2×C43×#381C2
socleC23×C43#120
prime radicalC23×C22⋊D43C22
cosocleC25×C43C23
hypercenterC2×#381D43
hypocenterC43#10992
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
4. C2×#14582762C2semidirect
5. C2×#14582666C2semidirect
6. C2×#14582665C2semidirect
7. C2×C43×#381C2semidirect
14. C2×#13063308C4semidirect
186. C22×C4×C43C22⋊C4semidirect
253. C22⋊Dic43C22⋊C4semidirect
441. C2×#381D43semidirect
491. C43#10992semidirect
687. 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×#130633082
C22×#130632392
#191371702
C2×#145827622
C2×#145826662
C2×#145826652
C2×C43×#3812
#1099243