Finite Group Databasebeta

← #25018972

Subgroups — #25018972

Order 11008.

2458 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D43C211yesmaximal, characteristic
2C2×#14582799C212yesmaximal
3C2×#14582796C212yesmaximal, complemented
4C2×#14582759C211yesmaximal, characteristic, complemented
5C2×#14582758C211yesmaximal, characteristic, complemented
6#19132841C212yesmaximal, complemented
7#19132838C212yesmaximal, complemented
8Dic43⋊#95C211yesmaximal, characteristic, complemented
9(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
10#95×Dic43C211yesmaximal, characteristic, complemented
11C43×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C2×C4×C22⋊D43—28no—
15C2×C4×C22⋊D43C418yescomplemented
16C22×C4⋊Dic43C2212yes—
17C22×Dic43⋊C4C2212yes—
18C22×Dic43⋊C4C2212yes—
19C22×Dic43⋊C4C2211yescharacteristic
20C22×C22⋊Dic43C2212yes—
21C22×C22⋊Dic43C2211yescharacteristic
22C22×(C2×D43)⋊C4C2212yes—
23C22×(C2×D43)⋊C4C2212yes—
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×C4×Dic43C2212yes—
26C22×C4×Dic43C2211yescharacteristic
27#14582799—28no—
28#14582796—28no—
29#14582759—24no—
30#14582758—24no—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2211yescharacteristic
36C24×C4×C43C2211yescharacteristic
37C22×C22⋊C4×C43C2212yes—
38C2×#95×C43C2212yes—
39C2×#95×C43C2211yescharacteristic
40C2×#95×C43C2211yescharacteristic
41C24×D43C2311yescharacteristic
42C22×C22⋊D43—24no—
43C22×C22⋊D43—24no—
44C22×C22⋊D43C2×C414yes—
45C22×C22⋊D43D414yes—
46C22×C22⋊D43Q814yes—
47C23×Dic43C2312yes—
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2312yes—
50C23×Dic43C2311yescharacteristic
51C23×Dic43C2311yescharacteristic
52C22×C4×D43—22no—
53C22×C4×D43—22no—
54C22×C4×D43—24no—
55C22×C4×D43—42no—
56C22×C4×D43C2×C414yes—
57C4×C22⋊D43—232no—
58C2×C4⋊Dic43—24no—
59C2×C4⋊Dic43—24no—
60C2×C4⋊Dic43—42no—
61C2×Dic43⋊C4—24no—
62C2×Dic43⋊C4—24no—
63C2×Dic43⋊C4—24no—
64C2×Dic43⋊C4—24no—
65C2×Dic43⋊C4—24no—
66C2×Dic43⋊C4—42no—
67C2×Dic43⋊C4C2×C414yes—
68C2×Dic43⋊C4D418yes—
69C2×C22⋊Dic43—24no—
70C2×C22⋊Dic43—24no—
71C2×C22⋊Dic43—24no—
72C2×C22⋊Dic43—42no—
73C2×C22⋊Dic43C2×C414yes—
74C2×(C2×D43)⋊C4—24no—
75C2×(C2×D43)⋊C4—24no—
76C2×(C2×D43)⋊C4—24no—
77C2×(C2×D43)⋊C4—24no—
78C2×(C2×D43)⋊C4—24no—
79C2×(C2×D43)⋊C4—42no—
80C2×(C2×D43)⋊C4—42no—
81C2×(C2×D43)⋊C4C2×C414yes—
82C2×C4×Dic43—24no—
83C2×C4×Dic43—24no—
84C2×C4×Dic43—24no—
85C2×C4×Dic43—24no—
86C2×C4×Dic43C2×C414yes—
87C43⋊#95—22no—
88C43⋊#95—24no—
89C43⋊#95—24no—
90C43⋊#95—42no—
91C43⋊#95D414yescomplemented
92C25×C43C2311yescharacteristic
93C23×C4×C43—24no—
94C23×C4×C43—22no—
95C23×C4×C43—22no—
96C23×C4×C43—42no—
97C23×C4×C43C2×C414yes—
98C23×C4×C43C2312yes—
99C23×C4×C43C2312yes—
100C23×C4×C43C2311yescharacteristic
101C23×C4×C43C2311yescharacteristic
102C2×C22⋊C4×C43—24no—
103C2×C22⋊C4×C43—24no—
104C2×C22⋊C4×C43—42no—
105#95×C43—24no—
106#95×C43—22no—
107#95×C43—22no—
108C24×C43—21no—
109C24×C43—22no—
110C24×C43—22no—
111C24×C43—21no—
112C24×C43—22no—
113C24×C43—22no—
114C24×C43—21no—
115C24×C43—21no—
116C24×C43C22×C412yes—
117C24×C43C2×D412yes—
118C24×C43C2×Q812yes—
119C24×C43C2411yescharacteristic
120C23×D43—21no—
121C23×D43—22no—
122C23×D43—22no—
123C23×D43—21no—
124C23×D43—22no—
125C23×D43—21no—
126C23×D43—22no—
127C23×D43—21no—
128C23×D43C22×C412yes—
129C23×D43C2×D412yes—
130C23×D43C2×Q812yes—
131C22×C4×C43—28no—
132C22×C4×C43—28no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—21no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
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—44no—
152C22×C4×C43—48no—
153C22×C4×C43—48no—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C22×C412yes—
156C22×C4×C43C2×D414yes—
157C22×C4×C43C2×D412yes—
158C22×C4×C43#4114yes—
159C22×C4×C43#4112yes—
160C2×C22⋊D43—28no—
161C2×C22⋊D43—28no—
162C2×C22⋊D43—216no—
163C2×C22⋊D43—216no—
164C2×C22⋊D43C4⋊C4116yescomplemented
165C22×Dic43—21no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—21no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—21no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—21no—
185C22×Dic43C22×C412yes—
186C22×Dic43C22×C412yes—
187C22×Dic43C22×C412yes—
188C22×Dic43C2×D414yes—
189C22×Dic43C2×D414yes—
190C22×Dic43C2×D414yes—
191C22×Dic43C2×D412yes—
192C22×Dic43C2×Q812yes—
193C22×Dic43#4114yes—
194C2×C4×D43—28no—
195C2×C4×D43—28no—
196C2×C4×D43—44no—
197C2×C4×D43—48no—
198C2×C4×D43—48no—
199C22⋊C4×C43—48no—
200C22⋊Dic43—28no—
201C22⋊Dic43—48no—
202(C2×D43)⋊C4—28no—
203(C2×D43)⋊C4—48no—
204(C2×D43)⋊C4—48no—
205C4⋊Dic43—48no—
206Dic43⋊C4—48no—
207Dic43⋊C4—48no—
208Dic43⋊C4C22⋊C4116yescomplemented
209C4×Dic43—28no—
210C4×Dic43—48no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43—24no—
218C23×C43—24no—
219C23×C43—22no—
220C23×C43—24no—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43—24no—
224C23×C43—22no—
225C23×C43—42no—
226C23×C43—42no—
227C23×C43—42no—
228C23×C43—42no—
229C23×C43—42no—
230C23×C43—42no—
231C23×C43—42no—
232C23×C43—42no—
233C23×C43C2×C4⋊C414yes—
234C23×C43C23×C411yescharacteristic
235C23×C43C22×D412yes—
236C23×C43C22×D411yescharacteristic
237C23×C43C22×D411yescharacteristic
238C23×C43C22×Q811yescharacteristic
239C23×C43C2×#4112yes—
240C23×C43C2×#4111yescharacteristic
241C23×C43C2×#4112yes—
242C23×C43H(5,𝔽2)12yes—
243C23×C43H(5,𝔽2)11yescharacteristic
244C23×C432−1+411yescharacteristic
245C22×D43—22no—
246C22×D43—22no—
247C22×D43—22no—
248C22×D43—22no—
249C22×D43—22no—
250C22×D43—22no—
251C22×D43—24no—
252C22×D43—24no—
253C22×D43—22no—
254C22×D43—24no—
255C22×D43—22no—
256C22×D43—22no—
257C22×D43—24no—
258C22×D43—22no—
259C22×D43—42no—
260C22×D43—42no—
261C22×D43—42no—
262C22×D43—42no—
263C22×D43—42no—
264C22×D43—42no—
265C22×D43—42no—
266C22×D43—42no—
267C22×D43C2×C4⋊C414yes—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—24no—
273C2×C4×C43—24no—
274C2×C4×C43—24no—
275C2×C4×C43—24no—
276C2×C4×C43—24no—
277C2×C4×C43—24no—
278C2×C4×C43—24no—
279C2×C4×C43—416no—
280C2×C4×C43—42no—
281C2×C4×C43—42no—
282C2×C4×C43—42no—
283C2×C4×C43—42no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43C2×C22⋊C414yes—
292C2×C4×C43C4×D414yes—
293C22⋊D43—232no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—24no—
297C2×Dic43—24no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—24no—
302C2×Dic43—24no—
303C2×Dic43—24no—
304C2×Dic43—42no—
305C2×Dic43—42no—
306C2×Dic43—42no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43C2×C22⋊C414yes—
318C2×Dic43C2×C22⋊C414yes—
319C2×Dic43C2×C4⋊C414yes—
320C2×Dic43#11714yes—
321C2×Dic43#12118yes—
322C2×Dic43C22⋊Q818yes—
323C4×D43—416no—
324#13920—431nomaximal, Sylow
325C22×C43—24no—
326C22×C43—24no—
327C22×C43—24no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—44no—
332C22×C43—44no—
333C22×C43—44no—
334C22×C43—44no—
335C22×C43—42no—
336C22×C43C22×C22⋊C411yescharacteristic
337C22×C43C22×C4⋊C411yescharacteristic
338C22×C43C2×#11711yescharacteristic
339C22×C43C2×C4×D411yescharacteristic
340C22×C43C4×#4111yescharacteristic
341C22×C43#51811yescharacteristic
342C22×C43#52011yescharacteristic
343C22×C43C2×#12112yes—
344C22×C43C2×C22⋊Q812yes—
345C22×C43#52912yes—
346C22×C43#53212yes—
347C22×C43#54012yes—
348C22×C43#54212yes—
349C22×C43D4212yes—
350C22×C43D4211yescharacteristic
351C22×C43#54612yes—
352C22×C43#54612yes—
353C22×C43#54711yescharacteristic
354C22×C43#54812yes—
355C22×C43D4×Q811yescharacteristic
356C22×C43#55012yes—
357C22×C43#55412yes—
358C22×C43#55411yescharacteristic
359C2×D43—24no—
360C2×D43—24no—
361C2×D43—24no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—44no—
366C2×D43—44no—
367C2×D43—44no—
368C2×D43—44no—
369C2×D43—42no—
370C4×C43—24no—
371C4×C43—24no—
372C4×C43—44no—
373C4×C43—82no—
374Dic43—24no—
375Dic43—42no—
376Dic43—44no—
377Dic43—82no—
378Dic43#38018yescomplemented
379C22×C4×D4—431no—
380C2×#390—432no—
381C2×#389—432no—
382C2×#380—431no—
383C2×#380—431no—
384#1439—432no—
385#1439—432no—
386C4⋊#95—431no—
387C22⋊#95—431no—
388C22⋊#95D4311yescharacteristic, complemented
389C4×#95—431no—
390C2×C43—44no—
391C2×C43C2×#38011yescharacteristic
392C2×C43#229311yescharacteristic
393C2×C43#231911yescharacteristic
394C2×C43D4×C22⋊C411yescharacteristic
395C2×C43#234111yescharacteristic
396C2×C43D4×C4⋊C411yescharacteristic
397C2×C43#234911yescharacteristic
398C2×C43#242712yes—
399C2×C43#242812yes—
400C2×C43#245212yes—
401C2×C43#245412yes—
402D43—44no—
403C23×D4—431no—
404C24×C4—431no—
405C24×C4C2×D4311yescharacteristic
406C2×C4×D4—438no—
407C2×C4×D4—868no—
408C22×C4⋊C4—431no—
409C22×C4⋊C4—432no—
410C22×C4⋊C4—432no—
411C22×C4⋊C4—432no—
412C22×C22⋊C4—431no—
413C22×C22⋊C4—431no—
414C22×C22⋊C4—432no—
415C22×C22⋊C4—432no—
416C22×C22⋊C4—432no—
417C22×C22⋊C4C2×D4312yes—
418C22×C42—431no—
419C22×C42—432no—
420#390—868no—
421#389—868no—
422#380—864no—
423#380—864no—
424C2×#95—431no—
425C2×#95—432no—
426C2×#95—431no—
427C2×#95—432no—
428C2×#95—432no—
429C2×#95C2×D4311yescharacteristic
430C2×#95C2×D4311yescharacteristic
431C2×#95C2×D4312yes—
432C43#1392011yescharacteristic, complemented, Sylow
433C25—431no—
434C25C22×D4311yescharacteristic
435C22×D4—434no—
436C22×D4—434no—
437C22×D4—434no—
438C22×D4—864no—
439C22×D4—864no—
440C23×C4—24no—
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—42no—
444C23×C4—431no—
445C23×C4—431no—
446C23×C4—432no—
447C23×C4—431no—
448C23×C4—434no—
449C23×C4—432no—
450C23×C4—864no—
451C23×C4—862no—
452C23×C4—862no—
453C23×C4—1722no—
454C23×C4C4×D4314yes—
455C23×C4C22×D4312yes—
456C23×C4C22×D4312yes—
457C23×C4C22×D4311yescharacteristic
458C23×C4C22×D4311yescharacteristic
459C4×D4—8632no—
460C2×C4⋊C4—434no—
461C2×C4⋊C4—438no—
462C2×C4⋊C4—864no—
463C2×C4⋊C4—864no—
464C2×C4⋊C4—864no—
465C2×C4⋊C4—864no—
466C2×C4⋊C4—864no—
467C2×C4⋊C4—864no—
468C2×C4⋊C4—864no—
469C2×C4⋊C4—1722no—
470C2×C4⋊C4—1722no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—434no—
475C2×C22⋊C4—434no—
476C2×C22⋊C4—864no—
477C2×C22⋊C4—864no—
478C2×C22⋊C4—864no—
479C2×C22⋊C4—864no—
480C2×C22⋊C4—864no—
481C2×C22⋊C4—864no—
482C2×C22⋊C4—864no—
483C2×C22⋊C4—864no—
484C2×C22⋊C4—1722no—
485C2×C22⋊C4—1722no—
486C2×C22⋊C4—1722no—
487C2×C42—434no—
488C2×C42—864no—
489C2×C42—864no—
490C2×C42—864no—
491C2×C42—864no—
492#95—22no—
493#95—24no—
494#95—22no—
495#95—434no—
496#95—864no—
497#95—864no—
498#95—862no—
499#95—1722no—
500C24—21no—
501C24—22no—
502C24—22no—
503C24—21no—
504C24—22no—
505C24—22no—
506C24—21no—
507C24—21no—
508C24—432no—
509C24—432no—
510C24—432no—
511C24—861no—
512C24—862no—
513C24—862no—
514C24—861no—
515C24—862no—
516C24—862no—
517C24—861no—
518C24—861no—
519C24C2×C4×D4312yes—
520C24D4×D4312yes—
521C24Q8×D4312yes—
522C24C23×D4311yescharacteristic
523C2×D4—4316no—
524C2×D4—868no—
525C2×D4—868no—
526C2×D4—8616no—
527C2×D4—8616no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—44no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—432no—
552C22×C4—434no—
553C22×C4—432no—
554C22×C4—432no—
555C22×C4—434no—
556C22×C4—432no—
557C22×C4—434no—
558C22×C4—432no—
559C22×C4—434no—
560C22×C4—868no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—861no—
572C22×C4—862no—
573C22×C4—861no—
574C22×C4—868no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—1724no—
583C22×C4—1728no—
584C22×C4—1728no—
585C22×C4C2×C4×D4312yes—
586C22×C4C2×C4×D4312yes—
587C22×C4#1062189814yes—
588C22×C4D4×D4314yes—
589C22×C4D4×D4312yes—
590C22×C4#1062190012yes—
591C4⋊C4—4316no—
592C4⋊C4—1728no—
593C4⋊C4—1728no—
594C4⋊C4—1728no—
595C22⋊C4—48no—
596C22⋊C4—868no—
597C22⋊C4—868no—
598C22⋊C4—1728no—
599C22⋊C4—1728no—
600C22⋊C4—1728no—
601C42—868no—
602C42—1728no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—24no—
613C23—24no—
614C23—22no—
615C23—24no—
616C23—22no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—434no—
626C23—862no—
627C23—862no—
628C23—864no—
629C23—862no—
630C23—862no—
631C23—862no—
632C23—862no—
633C23—862no—
634C23—862no—
635C23—864no—
636C23—864no—
637C23—862no—
638C23—864no—
639C23—862no—
640C23—1722no—
641C23—1722no—
642C23—1722no—
643C23—1722no—
644C23—1722no—
645C23—1722no—
646C23—1722no—
647C23—1722no—
648C23C4⋊C4×D4314yes—
649C23C22×C4×D4311yescharacteristic
650C23C2×D4×D4312yes—
651C23C2×D4×D4311yescharacteristic
652C23C2×D4×D4311yescharacteristic
653C23C2×Q8×D4311yescharacteristic
654C23#41×D4312yes—
655C23C2×#1062190011yescharacteristic
656C23C2×#1062189812yes—
657C23#1306337012yes—
658C23#1306337111yescharacteristic
659C23#1306337211yescharacteristic
660D4—8632no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—416no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—434no—
685C2×C4—434no—
686C2×C4—434no—
687C2×C4—438no—
688C2×C4—438no—
689C2×C4—434no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—864no—
693C2×C4—864no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—864no—
698C2×C4—864no—
699C2×C4—864no—
700C2×C4—17216no—
701C2×C4—1722no—
702C2×C4—1722no—
703C2×C4—1722no—
704C2×C4—1722no—
705C2×C4—1722no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4—1722no—
711C2×C4—1722no—
712C2×C4—1722no—
713C2×C4—1722no—
714C2×C4C22⋊C4×D4314yes—
715C2×C4(C22⋊D43)⋊C414yes—
716C22—24no—
717C22—24no—
718C22—24no—
719C22—42no—
720C22—44no—
721C22—42no—
722C22—44no—
723C22—44no—
724C22—42no—
725C22—44no—
726C22—42no—
727C22—864no—
728C22—864no—
729C22—864no—
730C22—1722no—
731C22—1724no—
732C22—1722no—
733C22—1724no—
734C22—1724no—
735C22—1722no—
736C22—1724no—
737C22—1722no—
738C22C2×C22⋊C4×D4311yescharacteristic
739C22C2×C4⋊C4×D4311yescharacteristic
740C22#117×D4311yescharacteristic
741C22C2×(C22⋊D43)⋊C411yescharacteristic
742C22C4×#1062189811yescharacteristic
743C22#1458337211yescharacteristic
744C22#1458337911yescharacteristic
745C22#121×D4312yes—
746C22C22⋊Q8×D4312yes—
747C22#1458342912yes—
748C22#1458344612yes—
749C22#1458350112yes—
750C22#1458351712yes—
751C22#1458353112yes—
752C22#1458353311yescharacteristic
753C22#1458353612yes—
754C22#1458353912yes—
755C22#1458354911yescharacteristic
756C22#1458355812yes—
757C22#1458356211yescharacteristic
758C22#1458357012yes—
759C22#1458360412yes—
760C22#1458360711yescharacteristic
761C4—24no—
762C4—24no—
763C4—44no—
764C4—82no—
765C4—438no—
766C4—864no—
767C4—3442no—
768C4—1724no—
769C4—1722no—
770C2—44no—
771C2—1724no—
772C2#380×D4311yescharacteristic
773C2#1913705811yescharacteristic
774C2#1913723511yescharacteristic
775C2#1913741111yescharacteristic
776C2#1913743511yescharacteristic
777C2#1913749111yescharacteristic
778C2#1913750211yescharacteristic
779C2#1913816912yes—
780C2#1913818212yes—
781C2#1913844212yes—
782C2#1913846412yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC22⋊#95D43
hypocenterC43#13920
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#14582796C2semidirect
4. C2×#14582759C2semidirect
5. C2×#14582758C2semidirect
6. #19132841C2semidirect
7. #19132838C2semidirect
8. Dic43⋊#95C2semidirect
9. (C2×D43)⋊#95C2semidirect
10. #95×Dic43C2semidirect
11. C43×C22⋊#95C2semidirect
15. C2×C4×C22⋊D43C4semidirect
91. C43⋊#95D4semidirect
164. C2×C22⋊D43C4⋊C4semidirect
208. Dic43⋊C4C22⋊C4semidirect
378. Dic43#380semidirect
388. C22⋊#95D43semidirect
432. C43#13920semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C2×#145827992
C2×#145827962
C2×#145827592
C2×#145827582
#191328412
#191328382
Dic43⋊#952
(C2×D43)⋊#952
#95×Dic432
C43×C22⋊#952
#1392043