Finite Group Databasebeta

← #25113348

Subgroups — #25113348

Order 11008.

1172 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
1C2×#14583597C211yesmaximal, characteristic
2#19137472C211yesmaximal, characteristic, complemented
3#19135431C211yesmaximal, characteristic, complemented
4#19135431C212yesmaximal, complemented
5#19135430C211yesmaximal, characteristic, complemented
6#19135430C212yesmaximal, complemented
7#19134580C211yesmaximal, characteristic, complemented
8#19134580C212yesmaximal, complemented
9C4×#13063239C211yesmaximal, characteristic, complemented
10C4×#13063239C212yesmaximal, complemented
11C43×#2345C211yesmaximal, characteristic, complemented
12#14583597—22no—
13#14583597—21no—
14#14583597—21no—
15#14583597—21no—
16#14583597—22no—
17#14583597—21no—
18C2×#13063320C412yescomplemented
19C2×#13063316C411yescharacteristic, complemented
20C2×#13063310C412yescomplemented
21C2×#13063300C411yescharacteristic, complemented
22C2×#13063299C2211yescharacteristic
23C2×#13063299C2212yes—
24C2×#13063287C411yescharacteristic, complemented
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×C4×C22⋊D43C2212yes—
27C2×#13063283C411yescharacteristic, complemented
28C2×#13063239C2211yescharacteristic
29C2×#13063239C2212yes—
30C2×#13063239C2211yescharacteristic
31C2×#13063239C2212yes—
32C2×#13063239C2212yes—
33C2×#13063239C2212yes—
34C2×#13063239C2212yes—
35#14582798—21no—
36#14582785—22no—
37#14582759C2211yescharacteristic
38#14582759C2212yes—
39C4⋊C4×Dic43—21no—
40C4×C22⋊Dic43C2211yescharacteristic
41C4×C22⋊Dic43C2212yes—
42#14582665C2211yescharacteristic
43#14582665C2212yes—
44#14582665C2211yescharacteristic
45C22×C4⋊C4×C43C2211yescharacteristic
46C43×#389—21no—
47C43×#387—22no—
48C43×#380C2212yes—
49C43×#380C2211yescharacteristic
50C4×C4⋊C4×C43—21no—
51C4×C22⋊C4×C43C2211yescharacteristic
52C4×C22⋊C4×C43C2212yes—
53C22×D172C2×C411yescharacteristic
54C22×D172C2×C412yes—
55C22×C22⋊D43C2312yes—
56C22×C22⋊D43C2311yescharacteristic
57C22×C4×D43C2×C411yescharacteristic
58C22×C4×D43C2×C412yes—
59#13063320—22no—
60#13063320—22no—
61#13063320—22no—
62#13063320—22no—
63#13063316—22no—
64#13063316—21no—
65#13063316—21no—
66#13063310—22no—
67#13063310—22no—
68#13063310—22no—
69#13063310—22no—
70#13063300—22no—
71#13063300—21no—
72#13063300—21no—
73#13063299—21no—
74#13063299—21no—
75#13063299—22no—
76#13063299—22no—
77#13063299—21no—
78#13063299—21no—
79#13063299—22no—
80#13063299—22no—
81#13063287—22no—
82#13063287—21no—
83#13063287—21no—
84C4×C22⋊D43—22no—
85C4×C22⋊D43—22no—
86C4×C22⋊D43—21no—
87C4×C22⋊D43—21no—
88C4×C22⋊D43—22no—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—21no—
91C4×C22⋊D43—21no—
92#13063283—22no—
93#13063283—21no—
94#13063283—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—22no—
97C2×C4⋊Dic43C2×C411yescharacteristic
98C2×C4⋊Dic43C2×C412yes—
99C2×Dic43⋊C4C2×C412yes—
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×C22⋊Dic43C2311yescharacteristic
102C2×C22⋊Dic43C2312yes—
103C2×C22⋊Dic43C2311yescharacteristic
104C2×C22⋊Dic43C2311yescharacteristic
105C2×(C2×D43)⋊C4C2×C412yes—
106C2×(C2×D43)⋊C4C2×C412yes—
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C412yes—
109C2×(C2×D43)⋊C4C2×C412yes—
110C2×C4×Dic43—21no—
111C2×C4×Dic43—22no—
112C2×C4×Dic43C2×C412yes—
113C2×C4×Dic43C2×C411yescharacteristic
114#13063239—22no—
115#13063239—24no—
116#13063239—22no—
117#13063239—24no—
118#13063239—42no—
119#13063239—42no—
120#13063239—42no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C23×C4×C43C2311yescharacteristic
126C23×C4×C43C2312yes—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—22no—
129C2×C4⋊C4×C43C2×C411yescharacteristic
130C2×C4⋊C4×C43C2×C411yescharacteristic
131C2×C4⋊C4×C43C2×C412yes—
132C2×C4⋊C4×C43D412yes—
133C2×C4⋊C4×C43D411yescharacteristic
134C2×C4⋊C4×C43D411yescharacteristic
135C2×C4⋊C4×C43D411yescharacteristic
136C2×C4⋊C4×C43D412yes—
137C2×C4⋊C4×C43D411yescharacteristic
138C2×C22⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43C2312yes—
140C2×C22⋊C4×C43C2311yescharacteristic
141C2×C42×C43—21no—
142C2×C42×C43—22no—
143#95×C43—21no—
144#95×C43—22no—
145#95×C43—22no—
146#95×C43—21no—
147C24×C43C2411yescharacteristic
148C23×D43C22×C411yescharacteristic
149C23×D43C22×C412yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—22no—
153C22×C4×C43—42no—
154C22×C4×C43—82no—
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C22×C412yes—
157C22×C4×C43C22×C411yescharacteristic
158C22×C4×C43C22×C412yes—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D412yes—
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D412yes—
166C22×C4×C43C2×D412yes—
167C2×C22⋊D43—21no—
168C2×C22⋊D43—22no—
169C2×C22⋊D43—21no—
170C2×C22⋊D43—22no—
171C2×C22⋊D43—21no—
172C2×C22⋊D43—22no—
173C2×C22⋊D43—21no—
174C2×C22⋊D43—22no—
175C2×C22⋊D43—21no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43—21no—
178C2×C22⋊D43—22no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—22no—
182C22×Dic43C22×C412yes—
183C22×Dic43C22×C411yescharacteristic
184C22×Dic43C22×C411yescharacteristic
185C22×Dic43C22×C411yescharacteristic
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—22no—
189C2×D172—22no—
190C2×D172—42no—
191C2×D172—82no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—22no—
195C2×C4×D43—22no—
196C2×C4×D43—42no—
197C2×C4×D43—82no—
198C4⋊C4×C43—42no—
199C4⋊C4×C43—82no—
200C4⋊C4×C43C22⋊C412yes—
201C4⋊C4×C43C22⋊C411yescharacteristic
202C4⋊C4×C43C22⋊C411yescharacteristic
203C4⋊C4×C43C22⋊C412yes—
204C4⋊C4×C43C22⋊C411yescharacteristic
205C4⋊C4×C43C22⋊C411yescharacteristic
206C4⋊C4×C43C22⋊C412yes—
207C4⋊C4×C43C22⋊C412yes—
208C4⋊C4×C43C22⋊C412yes—
209C4⋊C4×C43C22⋊C412yes—
210C22⋊C4×C43—21no—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—21no—
213C22⋊C4×C43—22no—
214C22⋊C4×C43—21no—
215C22⋊C4×C43#4112yes—
216C42×C43—42no—
217C42×C43—82no—
218C22⋊Dic43—21no—
219C22⋊Dic43—21no—
220C22⋊Dic43—21no—
221C22⋊Dic43—22no—
222C22⋊Dic43—21no—
223C22⋊Dic43—22no—
224C22⋊Dic43—21no—
225C22⋊Dic43#4112yes—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—21no—
231(C2×D43)⋊C4—21no—
232(C2×D43)⋊C4—22no—
233(C2×D43)⋊C4—22no—
234(C2×D43)⋊C4—22no—
235(C2×D43)⋊C4—22no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—22no—
239C4⋊Dic43—22no—
240C4⋊Dic43—42no—
241C4⋊Dic43—82no—
242Dic43⋊C4—22no—
243Dic43⋊C4—22no—
244Dic43⋊C4—21no—
245Dic43⋊C4—21no—
246C4×Dic43—22no—
247C4×Dic43—22no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250C4×Dic43—42no—
251C4×Dic43—82no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43C23×C411yescharacteristic
255C23×C43C22×D411yescharacteristic
256C23×C43C22×D411yescharacteristic
257C23×C43C2×#4111yescharacteristic
258C23×C43C2×#4111yescharacteristic
259C23×C43H(5,𝔽2)11yescharacteristic
260C23×C432−1+411yescharacteristic
261C22×D43—21no—
262C22×D43—22no—
263C22×D43—21no—
264C22×D43—22no—
265C22×D43—21no—
266C22×D43—22no—
267C22×D43—41no—
268C22×D43—42no—
269C22×D43—42no—
270C22×D43—41no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—42no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
280C2×C4×C43—42no—
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—42no—
288C2×C4×C43—42no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—42no—
292C2×C4×C43C2×C22⋊C411yescharacteristic
293C2×C4×C43C2×C22⋊C412yes—
294C2×C4×C43C2×C22⋊C412yes—
295C2×C4×C43C2×C22⋊C412yes—
296C2×C4×C43C2×C22⋊C412yes—
297C2×C4×C43C2×C22⋊C411yescharacteristic
298C2×C4×C43C2×C22⋊C411yescharacteristic
299C2×C4×C43C2×C22⋊C411yescharacteristic
300C22⋊D43—42no—
301C22⋊D43—41no—
302C22⋊D43—42no—
303C22⋊D43—41no—
304C22⋊D43—42no—
305C22⋊D43—41no—
306C22⋊D43—42no—
307C22⋊D43—41no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—22no—
311C2×Dic43—21no—
312C2×Dic43—22no—
313C2×Dic43—21no—
314C2×Dic43—22no—
315C2×Dic43—21no—
316C2×Dic43—22no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—42no—
327D172—42no—
328D172—42no—
329D172—82no—
330D172—82no—
331C4×D43—42no—
332C4×D43—42no—
333C4×D43—82no—
334C4×D43—82no—
335#22535—431nomaximal, Sylow
336C22×C43—21no—
337C22×C43—21no—
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—21no—
341C22×C43—21no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43C22×C22⋊C411yescharacteristic
347C22×C43C4×#4111yescharacteristic
348C22×C43#52011yescharacteristic
349C22×C43#54811yescharacteristic
350C22×C43#54811yescharacteristic
351C22×C43#55011yescharacteristic
352C22×C43#55011yescharacteristic
353C2×D43—41no—
354C2×D43—42no—
355C2×D43—41no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—41no—
359C2×D43—81no—
360C2×D43—82no—
361C2×D43—81no—
362C2×D43—82no—
363C4×C43—21no—
364C4×C43—21no—
365C4×C43—21no—
366C4×C43—22no—
367C4×C43—22no—
368C4×C43—22no—
369C4×C43—22no—
370C4×C43—42no—
371C4×C43—81no—
372C4×C43—82no—
373C4×C43#41012yes—
374Dic43—42no—
375Dic43—42no—
376Dic43—41no—
377Dic43—41no—
378Dic43—41no—
379Dic43—81no—
380Dic43—82no—
381C2×#553—431no—
382#2345—431no—
383#2345D4311yescharacteristic, complemented
384#1964—432no—
385#1964—431no—
386#1964—432no—
387#1964—431no—
388#1799—432no—
389#1799—431no—
390C4×#99—432no—
391C4×#99—431no—
392C2×C43—21no—
393C2×C43—21no—
394C2×C43—21no—
395C2×C43—21no—
396C2×C43—21no—
397C2×C43—21no—
398C2×C43#234111yescharacteristic
399C2×C43C2×#41011yescharacteristic
400C2×C43#288311yescharacteristic
401D43—81no—
402D43—82no—
403#553—861no—
404#553—862no—
405#553—861no—
406#553—861no—
407#553—862no—
408#553—861no—
409C2×#126—432no—
410C2×#125—431no—
411C2×#123—432no—
412C2×#121—432no—
413C2×#121—431no—
414C2×#121—431no—
415C2×C4×D4—432no—
416C2×C4×D4—431no—
417C2×C4×D4—431no—
418C2×#117—431no—
419C22×C4⋊C4C2×D4311yescharacteristic
420C2×#99—431no—
421C2×#99—432no—
422C2×#99—432no—
423C2×#99—431no—
424C2×#99—432no—
425C2×#99—432no—
426C2×#99—432no—
427#389—21no—
428#389—861no—
429#387—22no—
430#387—862no—
431#380—432no—
432#380—431no—
433#380C2×D4312yes—
434#380C2×D4311yescharacteristic
435C4×C4⋊C4—21no—
436C4×C4⋊C4—861no—
437C4×C22⋊C4—431no—
438C4×C22⋊C4—432no—
439C4×C22⋊C4C2×D4311yescharacteristic
440C4×C22⋊C4C2×D4312yes—
441#342—432no—
442#342—431no—
443#342—431no—
444C43#2253511yescharacteristic, complemented, Sylow
445C22×D4—432no—
446C22×D4—431no—
447C22×D4—432no—
448C22×D4—431no—
449C23×C4—432no—
450C23×C4—431no—
451C23×C4C22×D4311yescharacteristic
452C23×C4C22×D4312yes—
453#126—862no—
454#126—862no—
455#126—862no—
456#126—862no—
457#125—862no—
458#125—861no—
459#125—861no—
460#123—862no—
461#123—862no—
462#123—862no—
463#123—862no—
464#121—862no—
465#121—862no—
466#121—861no—
467#121—861no—
468#121—862no—
469#121—862no—
470#121—861no—
471#121—861no—
472#121—862no—
473#121—861no—
474#121—861no—
475C4×D4—862no—
476C4×D4—862no—
477C4×D4—861no—
478C4×D4—861no—
479C4×D4—862no—
480C4×D4—862no—
481C4×D4—861no—
482C4×D4—861no—
483C4×D4—862no—
484C4×D4—861no—
485C4×D4—861no—
486#117—862no—
487#117—861no—
488#117—861no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—432no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—432no—
495C2×C4⋊C4—862no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4C4×D4311yescharacteristic
498C2×C4⋊C4C4×D4311yescharacteristic
499C2×C4⋊C4C4×D4312yes—
500C2×C4⋊C4D17211yescharacteristic
501C2×C4⋊C4D17212yes—
502C2×C4⋊C4D17211yescharacteristic
503C2×C4⋊C4C22⋊D4311yescharacteristic
504C2×C4⋊C4C22⋊D4312yes—
505C2×C4⋊C4C22⋊D4311yescharacteristic
506C2×C22⋊C4—431no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—432no—
509C2×C22⋊C4—432no—
510C2×C22⋊C4—432no—
511C2×C22⋊C4—431no—
512C2×C22⋊C4—432no—
513C2×C22⋊C4—432no—
514C2×C22⋊C4—431no—
515C2×C22⋊C4C22×D4311yescharacteristic
516C2×C22⋊C4C22×D4312yes—
517C2×C22⋊C4C22×D4311yescharacteristic
518C2×C42—21no—
519C2×C42—22no—
520C2×C42—432no—
521C2×C42—431no—
522C2×C42—862no—
523C2×C42—861no—
524#99—862no—
525#99—864no—
526#99—864no—
527#99—862no—
528#99—1722no—
529#99—1722no—
530#99—1722no—
531#95—21no—
532#95—22no—
533#95—22no—
534#95—21no—
535#95—861no—
536#95—862no—
537#95—862no—
538#95—861no—
539C24—432no—
540C24—431no—
541C24C23×D4311yescharacteristic
542C2×D4—862no—
543C2×D4—861no—
544C2×D4—862no—
545C2×D4—861no—
546C2×D4—862no—
547C2×D4—861no—
548C2×D4—862no—
549C2×D4—861no—
550C2×D4—862no—
551C2×D4—861no—
552C2×D4—862no—
553C2×D4—861no—
554C2×D4—862no—
555C2×D4—862no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—3442no—
559C2×D4—1722no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—42no—
564C22×C4—82no—
565C22×C4—432no—
566C22×C4—431no—
567C22×C4—431no—
568C22×C4—431no—
569C22×C4—861no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—862no—
575C22×C4—861no—
576C22×C4—3442no—
577C22×C4—1722no—
578C22×C4C2×C4×D4311yescharacteristic
579C22×C4C2×C4×D4312yes—
580C22×C4C2×C4×D4311yescharacteristic
581C22×C4C2×C4×D4312yes—
582C22×C4C2×D17211yescharacteristic
583C22×C4C2×D17211yescharacteristic
584C22×C4C2×D17212yes—
585C22×C4C2×D17212yes—
586C22×C4C2×C22⋊D4311yescharacteristic
587C22×C4C2×C22⋊D4311yescharacteristic
588C22×C4C2×C22⋊D4312yes—
589C22×C4C2×C22⋊D4312yes—
590C4⋊C4—42no—
591C4⋊C4—82no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—862no—
595C4⋊C4—862no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—862no—
599C4⋊C4—862no—
600C4⋊C4—3442no—
601C4⋊C4—1722no—
602C4⋊C4(C2×D43)⋊C412yes—
603C4⋊C4(C2×D43)⋊C411yescharacteristic
604C4⋊C4(C2×D43)⋊C411yescharacteristic
605C4⋊C4(C2×D43)⋊C412yes—
606C4⋊C4(C2×D43)⋊C411yescharacteristic
607C4⋊C4(C2×D43)⋊C411yescharacteristic
608C4⋊C4(C2×D43)⋊C412yes—
609C4⋊C4(C2×D43)⋊C412yes—
610C4⋊C4(C2×D43)⋊C412yes—
611C4⋊C4(C2×D43)⋊C412yes—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—21no—
616C22⋊C4—22no—
617C22⋊C4—432no—
618C22⋊C4—861no—
619C22⋊C4—861no—
620C22⋊C4—861no—
621C22⋊C4—862no—
622C22⋊C4—862no—
623C22⋊C4—862no—
624C22⋊C4—862no—
625C22⋊C4—862no—
626C22⋊C4—862no—
627C22⋊C4—861no—
628C22⋊C4—861no—
629C22⋊C4—862no—
630C22⋊C4—862no—
631C22⋊C4—862no—
632C22⋊C4—861no—
633C22⋊C4—862no—
634C22⋊C4—861no—
635C22⋊C4#1062190212yes—
636C42—42no—
637C42—82no—
638C42—862no—
639C42—862no—
640C42—861no—
641C42—861no—
642C42—3442no—
643C42—1722no—
644C23—41no—
645C23—41no—
646C23—862no—
647C23—861no—
648C23—862no—
649C23—861no—
650C23—861no—
651C23—862no—
652C23—1722no—
653C23—1721no—
654C23—1721no—
655C23—1722no—
656C23C22×C4×D4311yescharacteristic
657C23C22×C22⋊D4311yescharacteristic
658C23C22×D17211yescharacteristic
659C23#41×D4311yescharacteristic
660C23C2×#1062190211yescharacteristic
661C23#1306337111yescharacteristic
662C23#1306337311yescharacteristic
663D4—3442no—
664D4—3442no—
665D4—1722no—
666D4—1722no—
667D4—1721no—
668D4—1722no—
669D4—1721no—
670D4—1722no—
671D4—1721no—
672D4—1722no—
673D4—1721no—
674D4—1722no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—862no—
697C2×C4—861no—
698C2×C4—862no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—862no—
702C2×C4—861no—
703C2×C4—862no—
704C2×C4—861no—
705C2×C4—3442no—
706C2×C4—3442no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1722no—
712C2×C4—1722no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1722no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4C2×(C2×D43)⋊C412yes—
720C2×C4C2×(C2×D43)⋊C412yes—
721C2×C4C2×(C2×D43)⋊C411yescharacteristic
722C2×C4C2×(C2×D43)⋊C411yescharacteristic
723C2×C4C2×(C2×D43)⋊C411yescharacteristic
724C2×C4C2×(C2×D43)⋊C412yes—
725C2×C4C2×(C2×D43)⋊C412yes—
726C2×C4C2×(C2×D43)⋊C411yescharacteristic
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—3442no—
738C22—3441no—
739C22—3442no—
740C22—3441no—
741C22—1721no—
742C22—1722no—
743C22—1722no—
744C22—1721no—
745C22—1721no—
746C22—1722no—
747C22C22×(C2×D43)⋊C411yescharacteristic
748C22C4×#1062190211yescharacteristic
749C22#1458338111yescharacteristic
750C22#1458356011yescharacteristic
751C22#1458356111yescharacteristic
752C22#1458356811yescharacteristic
753C22#1458357111yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—22no—
758C4—22no—
759C4—22no—
760C4—22no—
761C4—42no—
762C4—81no—
763C4—82no—
764C4—3442no—
765C4—3441no—
766C4—1722no—
767C4—1721no—
768C4—1721no—
769C4—1722no—
770C4—1721no—
771C4#1458287212yes—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2—21no—
777C2—21no—
778C2—3441no—
779C2—3442no—
780C2#1913743311yescharacteristic
781C2C2×#1458287211yescharacteristic
782C2#1914305511yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#2345C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583597C2
cosocleC24×C43C24
hypercenter#2345D43
hypocenterC43#22535
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #19137472C2semidirect
3. #19135431C2semidirect
4. #19135431C2semidirect
5. #19135430C2semidirect
6. #19135430C2semidirect
7. #19134580C2semidirect
8. #19134580C2semidirect
9. C4×#13063239C2semidirect
10. C4×#13063239C2semidirect
11. C43×#2345C2semidirect
18. C2×#13063320C4semidirect
19. C2×#13063316C4semidirect
20. C2×#13063310C4semidirect
21. C2×#13063300C4semidirect
24. C2×#13063287C4semidirect
27. C2×#13063283C4semidirect
383. #2345D43semidirect
444. C43#22535semidirect

Maximal subgroups

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

subgroupindex
C2×#145835972
#191374722
#191354312
#191354302
#191345802
C4×#130632392
C43×#23452
#2253543