Finite Group Databasebeta

← #25003319

Subgroups — #25003319

Order 11008.

1506 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583445C211yesmaximal, characteristic
2C22×#13063253C211yesmaximal, characteristic, complemented
3C22×#13063252C211yesmaximal, characteristic, complemented
4C22×#13063251C211yesmaximal, characteristic, complemented
5#19134288C211yesmaximal, characteristic, complemented
6C4×C43⋊#95C211yesmaximal, characteristic, complemented
7C22×#104×C43C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10#14583445—22no—
11#14583445—22no—
12#14583445—22no—
13#14583445—22no—
14C2×#13063323C411yescharacteristic, complemented
15C2×#13063321C411yescharacteristic, complemented
16C2×#13063314C411yescharacteristic, complemented
17C2×#13063312C411yescharacteristic, complemented
18C2×#13063297—22no—
19C2×C4×C22⋊D43—22no—
20C22×C4×Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22C2×#13063253—22no—
23C2×#13063253—22no—
24C2×#13063253—22no—
25C2×#13063252—22no—
26C2×#13063252—22no—
27C2×#13063252—22no—
28C2×#13063251—22no—
29C2×#13063251—22no—
30C2×#13063251—22no—
31C2×C43⋊#95—22no—
32#14582653—22no—
33C22×#41×C43C2211yescharacteristic
34C22×M16×C43C2211yescharacteristic
35C22×C42×C43C2211yescharacteristic
36C2×#104×C43—22no—
37C2×#104×C43—22no—
38C2×#104×C43—22no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898D412yes—
50C2×#10621898D412yes—
51C22×Dic86C2×C411yescharacteristic
52C22×D172C2×C411yescharacteristic
53C22×C22⋊D43—21no—
54C22×C22⋊D43—22no—
55C23×Dic43—21no—
56C23×Dic43D412yes—
57C22×C4×D43—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877—21no—
61C2×#10621877—21no—
62C2×#10621877—21no—
63C2×#10621877D412yescomplemented
64C22×C43⋊C8—21no—
65#13063323—22no—
66#13063323—22no—
67#13063321—22no—
68#13063321—22no—
69#13063314—22no—
70#13063314—22no—
71#13063312—22no—
72#13063312—22no—
73#13063297—28no—
74#13063297—28no—
75C4×C22⋊D43—28no—
76C4×C22⋊D43—28no—
77C2×Dic43⋊C4—22no—
78C2×C22⋊Dic43—22no—
79C2×(C2×D43)⋊C4—22no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2×C411yescharacteristic
90C2×C4×Dic43C2×C411yescharacteristic
91C2×C4×Dic43D412yes—
92C2×C4×Dic43D412yescomplemented
93#13063253—28no—
94#13063252—28no—
95#13063251—28no—
96C43⋊#95—28no—
97C2×#41×C43—21no—
98C2×#41×C43—21no—
99C2×#41×C43—21no—
100C2×#41×C43—21no—
101C2×#41×C43—21no—
102C2×#41×C43—21no—
103C2×#41×C43—21no—
104C2×#41×C43—21no—
105C2×#41×C43—21no—
106C2×#41×C43—21no—
107C2×#41×C43D412yes—
108C2×#41×C43D412yes—
109C22×Q8×C43C2×C411yescharacteristic
110C22×D4×C43—21no—
111C22×D4×C43C2×C411yescharacteristic
112C23×C4×C43—21no—
113C23×C4×C43—21no—
114C23×C4×C43C2311yescharacteristic
115C2×M16×C43—21no—
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43—21no—
120C2×M16×C43D412yescomplemented
121C22×C8×C43—21no—
122C2×C42×C43—21no—
123C2×C42×C43—21no—
124C2×C42×C43—21no—
125C2×C42×C43—21no—
126C2×C42×C43—21no—
127C2×C42×C43D412yescomplemented
128#104×C43—28no—
129C24×C43—21no—
130C24×C43C2×D411yescharacteristic
131C23×D43—21no—
132#41×C43—22no—
133#41×C43—22no—
134#41×C43—22no—
135#41×C43—22no—
136#41×C43—22no—
137#41×C43—22no—
138#41×C43—22no—
139#41×C43—22no—
140#41×C43—41no—
141#41×C43—41no—
142#41×C43—41no—
143#41×C43—41no—
144#41×C43—41no—
145#41×C43—41no—
146#41×C43—41no—
147#41×C43—41no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43C22⋊C412yes—
154C2×D4×C43—21no—
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—41no—
162C2×D4×C43—41no—
163C2×D4×C43—41no—
164C2×D4×C43—41no—
165C2×D4×C43C22⋊C412yes—
166C22×C4×C43—24no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—21no—
170C22×C4×C43—22no—
171C22×C4×C43—42no—
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×C43C22×C411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43#4111yescharacteristic
189C22×C4×C43#4111yescharacteristic
190C22×C4×C43#4111yescharacteristic
191C22×C4×C43#4111yescharacteristic
192C2×C22⋊D43—28no—
193C2×C22⋊D43—22no—
194C2×C22⋊D43—22no—
195C2×C22⋊D43—44no—
196C2×C22⋊D43—44no—
197C2×C22⋊D43—41no—
198C2×C22⋊D43—41no—
199C2×C22⋊D43—41no—
200C2×C22⋊D43—41no—
201C22×Dic43—24no—
202C22×Dic43—24no—
203C22×Dic43—21no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—42no—
208C22×Dic43—42no—
209C22×Dic43—41no—
210C22×Dic43—41no—
211C22×Dic43C22⋊C412yes—
212C22×Dic43C22⋊C412yes—
213#10621898—22no—
214#10621898—22no—
215#10621898—22no—
216#10621898—22no—
217#10621898—22no—
218#10621898—22no—
219#10621898—22no—
220#10621898—22no—
221#10621898—41no—
222#10621898—41no—
223#10621898—41no—
224#10621898—41no—
225#10621898—41no—
226#10621898—41no—
227#10621898—41no—
228#10621898—41no—
229C2×D172—21no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172C22⋊C412yes—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—41no—
238C2×C4×D43—41no—
239C2×C4×D43—41no—
240C2×C4×D43—41no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—21no—
245C2×Dic86—21no—
246C2×Dic86C22⋊C412yes—
247M16×C43—22no—
248M16×C43—22no—
249M16×C43—41no—
250M16×C43—41no—
251C2×C8×C43—22no—
252C2×C8×C43—41no—
253C2×C8×C43—41no—
254C42×C43—22no—
255C42×C43—22no—
256C42×C43—41no—
257C42×C43—41no—
258C22⋊Dic43—28no—
259(C2×D43)⋊C4—28no—
260Dic43⋊C4—28no—
261C4×Dic43—21no—
262C4×Dic43—21no—
263C4×Dic43—21no—
264C4×Dic43—21no—
265C4×Dic43—22no—
266C4×Dic43—22no—
267C4×Dic43—22no—
268C4×Dic43—22no—
269C4×Dic43—41no—
270C4×Dic43—41no—
271#10621877—22no—
272#10621877—22no—
273#10621877—41no—
274#10621877—41no—
275C2×C43⋊C8—22no—
276C2×C43⋊C8—41no—
277C2×C43⋊C8—41no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—42no—
284C23×C43—42no—
285C23×C43C2×C22⋊C411yescharacteristic
286C23×C43#12011yescharacteristic
287C23×C43#12011yescharacteristic
288C23×C43#12111yescharacteristic
289C23×C43#12111yescharacteristic
290C23×C43#12411yescharacteristic
291C23×C43#12711yescharacteristic
292C22×D43—22no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—42no—
296C22×D43—42no—
297Q8×C43—22no—
298Q8×C43—22no—
299Q8×C43—41no—
300Q8×C43—41no—
301D4×C43—22no—
302D4×C43—22no—
303D4×C43—42no—
304D4×C43—42no—
305D4×C43—42no—
306D4×C43—42no—
307D4×C43—41no—
308D4×C43—41no—
309C2×C4×C43—24no—
310C2×C4×C43—22no—
311C2×C4×C43—42no—
312C2×C4×C43—44no—
313C2×C4×C43—44no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43C2×C22⋊C411yescharacteristic
322C2×C4×C43C2×C22⋊C411yescharacteristic
323C2×C4×C43C4×D411yescharacteristic
324C2×C4×C43C4×D411yescharacteristic
325C2×C4×C43C4×D411yescharacteristic
326C2×C4×C43C4×D411yescharacteristic
327C2×C4×C43#12011yescharacteristic
328C2×C4×C43#12011yescharacteristic
329C2×C4×C43#12011yescharacteristic
330C2×C4×C43#12011yescharacteristic
331C2×C4×C43#12011yescharacteristic
332C2×C4×C43#12011yescharacteristic
333C2×C4×C43#12111yescharacteristic
334C2×C4×C43#12111yescharacteristic
335C2×C4×C43#12111yescharacteristic
336C2×C4×C43#12111yescharacteristic
337C2×C4×C43#12111yescharacteristic
338C2×C4×C43#12111yescharacteristic
339C2×C4×C43#12111yescharacteristic
340C2×C4×C43#12111yescharacteristic
341C2×C4×C43#12111yescharacteristic
342C2×C4×C43#12111yescharacteristic
343C2×C4×C43#12311yescharacteristic
344C2×C4×C43#12311yescharacteristic
345C2×C4×C43#12311yescharacteristic
346C2×C4×C43#12311yescharacteristic
347C2×C4×C43#12411yescharacteristic
348C2×C4×C43#12711yescharacteristic
349C22⋊D43—416no—
350C22⋊D43—42no—
351C22⋊D43—42no—
352C22⋊D43—42no—
353C22⋊D43—42no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—24no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—44no—
362C2×Dic43—44no—
363C2×Dic43—42no—
364C2×Dic43—44no—
365C2×Dic43—44no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—42no—
369C2×Dic43#10414yescomplemented
370D172—22no—
371D172—22no—
372D172—41no—
373D172—41no—
374C4×D43—42no—
375C4×D43—42no—
376C4×D43—42no—
377C4×D43—42no—
378Dic86—22no—
379Dic86—22no—
380Dic86—41no—
381Dic86—41no—
382C8×C43—42no—
383C43⋊C8—42no—
384#11011—431nomaximal, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—22no—
392C22×C43—22no—
393C22×C43—42no—
394C22×C43—44no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43—82no—
398C22×C43#37911yescharacteristic
399C22×C43#39011yescharacteristic
400C22×C43#39011yescharacteristic
401C22×C43#39211yescharacteristic
402C22×C43#39211yescharacteristic
403C22×C43#39411yescharacteristic
404C22×C43#39411yescharacteristic
405C22×C43C2×#10412yes—
406C22×C43#42112yes—
407C2×D43—42no—
408C2×D43—44no—
409C2×D43—81no—
410C2×D43—81no—
411C2×D43—82no—
412C4×C43—44no—
413C4×C43—42no—
414C4×C43#38611yescharacteristic
415C4×C43#38611yescharacteristic
416C4×C43#38611yescharacteristic
417C4×C43#38611yescharacteristic
418C4×C43#39211yescharacteristic
419C4×C43#39211yescharacteristic
420C4×C43#39411yescharacteristic
421C4×C43#39411yescharacteristic
422Dic43—24no—
423Dic43—44no—
424Dic43—42no—
425Dic43—42no—
426C2×#532—431no—
427C22×#104—431no—
428C22×#104—431no—
429C22×#104—431no—
430C22×#104D4311yescharacteristic, complemented
431#1728—431no—
432C4×#95—431no—
433C2×C43—21no—
434C2×C43—21no—
435C2×C43—21no—
436C2×C43—21no—
437C2×C43—82no—
438C2×C43#143811yescharacteristic
439C2×C43#178912yes—
440C2×C43#196211yescharacteristic
441C2×C43#196311yescharacteristic
442C2×C43#198012yes—
443D43—82no—
444C22×#41—431no—
445C22×#41C2×D4311yescharacteristic
446C22×M16—431no—
447C22×M16C2×D4311yescharacteristic
448#532—862no—
449#532—862no—
450#532—862no—
451#532—862no—
452C2×C4⋊Q8—431no—
453C2×#127—431no—
454C2×#124—431no—
455C2×#124—431no—
456C2×#121—862no—
457C2×C4×D4—862no—
458C22×C42—431no—
459C22×C42—431no—
460C22×C42C2×D4311yescharacteristic
461C2×#104—22no—
462C2×#104—22no—
463C2×#104—22no—
464C2×#104—862no—
465C2×#104—862no—
466C2×#104—862no—
467C2×#104—862no—
468C2×#104—862no—
469C2×#104—862no—
470C2×#104—862no—
471C2×#104—862no—
472C2×#104—862no—
473C2×#95—862no—
474#336—862no—
475C43#1101111yescharacteristic, complemented, Sylow
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—21no—
484C2×#41—21no—
485C2×#41—21no—
486C2×#41—432no—
487C2×#41—432no—
488C2×#41—861no—
489C2×#41—861no—
490C2×#41—861no—
491C2×#41—861no—
492C2×#41—861no—
493C2×#41—861no—
494C2×#41—861no—
495C2×#41—861no—
496C2×#41—861no—
497C2×#41—861no—
498C2×#41D17212yes—
499C2×#41C22⋊D4312yes—
500C22×Q8—431no—
501C22×Q8C4×D4311yescharacteristic
502C22×D4—21no—
503C22×D4—431no—
504C22×D4—862no—
505C22×D4—861no—
506C22×D4C4×D4311yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—432no—
510C23×C4—861no—
511C23×C4—861no—
512C23×C4C22×D4311yescharacteristic
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—432no—
519C2×M16—861no—
520C2×M16—861no—
521C2×M16—861no—
522C2×M16—861no—
523C2×M16—861no—
524C2×M16C22⋊D4312yescomplemented
525C22×C8—21no—
526C22×C8—861no—
527C4⋊Q8—862no—
528C4⋊Q8—862no—
529#127—862no—
530#127—862no—
531#124—862no—
532#124—862no—
533#124—862no—
534#124—862no—
535#121—868no—
536#121—868no—
537C4×D4—868no—
538C4×D4—868no—
539C2×C4⋊C4—862no—
540C2×C22⋊C4—862no—
541C2×C22⋊C4—862no—
542C2×C42—21no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—21no—
546C2×C42—21no—
547C2×C42—431no—
548C2×C42—431no—
549C2×C42—432no—
550C2×C42—432no—
551C2×C42—861no—
552C2×C42—861no—
553C2×C42—861no—
554C2×C42—861no—
555C2×C42—861no—
556C2×C42—861no—
557C2×C42—861no—
558C2×C42—861no—
559C2×C42—861no—
560C2×C42C22⋊D4312yescomplemented
561#104—28no—
562#104—868no—
563#104—868no—
564#104—868no—
565#95—868no—
566C24—21no—
567C24—861no—
568C24D4×D4311yescharacteristic
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—41no—
578#41—41no—
579#41—41no—
580#41—41no—
581#41—41no—
582#41—41no—
583#41—41no—
584#41—41no—
585#41—862no—
586#41—862no—
587#41—862no—
588#41—862no—
589#41—862no—
590#41—862no—
591#41—862no—
592#41—862no—
593#41—1721no—
594#41—1721no—
595#41—1721no—
596#41—1721no—
597#41—1721no—
598#41—1721no—
599#41—1721no—
600#41—1721no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—432no—
607C2×Q8—861no—
608C2×Q8—861no—
609C2×Q8—861no—
610C2×Q8—861no—
611C2×Q8—861no—
612C2×Q8(C2×D43)⋊C412yes—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—432no—
625C2×D4—868no—
626C2×D4—862no—
627C2×D4—862no—
628C2×D4—861no—
629C2×D4—861no—
630C2×D4—861no—
631C2×D4—861no—
632C2×D4—861no—
633C2×D4—1724no—
634C2×D4—1724no—
635C2×D4—1721no—
636C2×D4—1721no—
637C2×D4—1721no—
638C2×D4—1721no—
639C2×D4(C2×D43)⋊C412yes—
640C22×C4—24no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—42no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—432no—
653C22×C4—432no—
654C22×C4—864no—
655C22×C4—864no—
656C22×C4—861no—
657C22×C4—862no—
658C22×C4—862no—
659C22×C4—862no—
660C22×C4—862no—
661C22×C4—862no—
662C22×C4—1722no—
663C22×C4—1722no—
664C22×C4—1721no—
665C22×C4—1721no—
666C22×C4—1721no—
667C22×C4—1721no—
668C22×C4—1721no—
669C22×C4—1721no—
670C22×C4C2×C4×D4311yescharacteristic
671C22×C4C2×D17211yescharacteristic
672C22×C4#1062189811yescharacteristic
673C22×C4#1062189811yescharacteristic
674C22×C4D4×D4311yescharacteristic
675C22×C4D4×D4311yescharacteristic
676C22×C4D4×D4311yescharacteristic
677C22×C4D4×D4311yescharacteristic
678C22×C4D4×D4311yescharacteristic
679C22×C4#1062190011yescharacteristic
680C22×C4#1062190011yescharacteristic
681C22×C4C2×C22⋊D4311yescharacteristic
682C22×C4C2×C22⋊D4311yescharacteristic
683C22×C4C2×C22⋊D4311yescharacteristic
684M16—22no—
685M16—22no—
686M16—41no—
687M16—41no—
688M16—862no—
689M16—862no—
690M16—1721no—
691M16—1721no—
692C2×C8—22no—
693C2×C8—41no—
694C2×C8—41no—
695C2×C8—862no—
696C2×C8—1721no—
697C2×C8—1721no—
698C4⋊C4—868no—
699C22⋊C4—868no—
700C22⋊C4—868no—
701C42—22no—
702C42—22no—
703C42—41no—
704C42—41no—
705C42—861no—
706C42—861no—
707C42—861no—
708C42—861no—
709C42—862no—
710C42—862no—
711C42—862no—
712C42—862no—
713C42—1721no—
714C42—1721no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—42no—
722C23—862no—
723C23—1721no—
724C23—1721no—
725C23—1722no—
726C23—1722no—
727C23C22⋊C4×D4311yescharacteristic
728C23#1306329311yescharacteristic
729C23#1306329511yescharacteristic
730C23#1306329711yescharacteristic
731C23#1306329811yescharacteristic
732C23#1306331111yescharacteristic
733C23#1306332111yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—41no—
737Q8—41no—
738Q8—862no—
739Q8—862no—
740Q8—1721no—
741Q8—1721no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—42no—
746D4—42no—
747D4—42no—
748D4—41no—
749D4—41no—
750D4—862no—
751D4—862no—
752D4—17216no—
753D4—1722no—
754D4—1722no—
755D4—1722no—
756D4—1722no—
757D4—1721no—
758D4—1721no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—434no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—864no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—1724no—
780C2×C4—1724no—
781C2×C4—1724no—
782C2×C4—1724no—
783C2×C4—1722no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4—1722no—
787C2×C4—1722no—
788C2×C4—1722no—
789C2×C4—1722no—
790C2×C4—1722no—
791C2×C4C22⋊C4×D4311yescharacteristic
792C2×C4C2×(C2×D43)⋊C411yescharacteristic
793C2×C4(C22⋊D43)⋊C411yescharacteristic
794C2×C4(C22⋊D43)⋊C411yescharacteristic
795C2×C4C4×C22⋊D4311yescharacteristic
796C2×C4C4×C22⋊D4311yescharacteristic
797C2×C4#1306329311yescharacteristic
798C2×C4#1306329311yescharacteristic
799C2×C4#1306329311yescharacteristic
800C2×C4#1306329411yescharacteristic
801C2×C4#1306329511yescharacteristic
802C2×C4#1306329511yescharacteristic
803C2×C4#1306329611yescharacteristic
804C2×C4#1306329611yescharacteristic
805C2×C4#1306329711yescharacteristic
806C2×C4#1306329711yescharacteristic
807C2×C4#1306329711yescharacteristic
808C2×C4#1306329811yescharacteristic
809C2×C4#1306329811yescharacteristic
810C2×C4#1306329811yescharacteristic
811C2×C4#1306329911yescharacteristic
812C2×C4#1306329911yescharacteristic
813C2×C4#1306330711yescharacteristic
814C2×C4#1306330711yescharacteristic
815C2×C4#1306330811yescharacteristic
816C2×C4#1306330911yescharacteristic
817C2×C4#1306331111yescharacteristic
818C2×C4#1306332111yescharacteristic
819C8—42no—
820C8—1722no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—44no—
830C22—42no—
831C22—82no—
832C22—81no—
833C22—81no—
834C22—3442no—
835C22—3441no—
836C22—3441no—
837C22—1724no—
838C22—1722no—
839C22#1458275411yescharacteristic
840C22#1458279911yescharacteristic
841C22#1458279911yescharacteristic
842C22#1458280711yescharacteristic
843C22#1458280811yescharacteristic
844C22#1458281411yescharacteristic
845C22#1458281511yescharacteristic
846C22#104×D4312yes—
847C22#1458291412yes—
848C4—44no—
849C4—42no—
850C4—864no—
851C4—1724no—
852C4—1722no—
853C4—1722no—
854C4#1458277511yescharacteristic
855C4#1458277511yescharacteristic
856C4#1458277611yescharacteristic
857C4#1458277811yescharacteristic
858C4#1458280711yescharacteristic
859C4#1458280811yescharacteristic
860C4#1458281411yescharacteristic
861C4#1458281511yescharacteristic
862C2—21no—
863C2—21no—
864C2—21no—
865C2—21no—
866C2—82no—
867C2—3442no—
868C2#1913283411yescharacteristic
869C2#1913453712yes—
870C2#1913542111yescharacteristic
871C2#1913542511yescharacteristic
872C2#1913551212yes—
subgroupG/H
centerC22×C4D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC22×#104×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#14583445C2
cosocleC23×C4×C43C23
hypercenterC22×#104D43
hypocenterC43#11011
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C22×#13063253C2semidirect
3. C22×#13063252C2semidirect
4. C22×#13063251C2semidirect
5. #19134288C2semidirect
6. C4×C43⋊#95C2semidirect
7. C22×#104×C43C2semidirect
14. C2×#13063323C4semidirect
15. C2×#13063321C4semidirect
16. C2×#13063314C4semidirect
17. C2×#13063312C4semidirect
63. C2×#10621877D4semidirect
92. C2×C4×Dic43D4semidirect
120. C2×M16×C43D4semidirect
127. C2×C42×C43D4semidirect
369. C2×Dic43#104semidirect
430. C22×#104D43semidirect
475. C43#11011semidirect
524. C2×M16C22⋊D43semidirect
560. C2×C42C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834452
C22×#130632532
C22×#130632522
C22×#130632512
#191342882
C4×C43⋊#952
C22×#104×C432
#1101143