Finite Group Databasebeta

← #25111934

Subgroups — #25111934

Order 11008.

1474 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583548C211yesmaximal, characteristic
2C2×#14582873C211yesmaximal, characteristic, complemented
3C2×#14582871C211yesmaximal, characteristic, complemented
4#19137459C212yesmaximal, complemented
5#19135429C212yesmaximal, complemented
6#19135051C212yesmaximal, complemented
7#19135050C212yesmaximal, complemented
8#19134581C211yesmaximal, characteristic, complemented
9#19134511C211yesmaximal, characteristic, complemented
10#99×Dic43C211yesmaximal, characteristic, complemented
11C43×#1782C211yesmaximal, characteristic, complemented
12C22×#10621900C2211yescharacteristic
13#14583548—22no—
14#14583548—22no—
15#14583548—22no—
16#14583548—22no—
17C2×#13063323C411yescharacteristic, complemented
18C2×#13063308C411yescharacteristic, complemented
19C2×#13063308C2211yescharacteristic
20C2×#13063306C411yescharacteristic, complemented
21C2×#13063306C2211yescharacteristic
22C2×#13063304C411yescharacteristic, complemented
23C2×#13063301C411yescharacteristic, complemented
24C2×#13063297C411yescharacteristic, complemented
25C2×#13063297C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43C411yescharacteristic, complemented
28C2×#13063284C2212yes—
29C2×#13063281C2212yes—
30C22×Dic43⋊C4C411yescharacteristic, complemented
31C22×Dic43⋊C4C2211yescharacteristic
32#14582873—24no—
33#14582871—24no—
34C2×#13063240C2211yescharacteristic
35C2×#13063240C2212yes—
36C2×#13063240C2211yescharacteristic
37C2×#13063239C2212yes—
38C2×#13063239C2212yes—
39#14582796—22no—
40#14582786—22no—
41#14582781—22no—
42#14582760C2212yes—
43#14582757C2212yes—
44#14582750—22no—
45C22⋊C4×Dic43C2212yes—
46#14582665C2212yes—
47#14582665C2212yes—
48C22×#41×C43C2211yescharacteristic
49C2×#99×C43C2211yescharacteristic
50C2×#99×C43C2211yescharacteristic
51C2×#99×C43C2212yes—
52C43×#381C2212yes—
53C2×#10621900—22no—
54C2×#10621900—22no—
55C2×#10621900—22no—
56C2×#10621900—22no—
57C2×#10621900—42no—
58C22×Dic86C2×C411yescharacteristic
59C22×C22⋊D43C2×C411yescharacteristic
60C22×C22⋊D43C2×C411yescharacteristic
61C22×C22⋊D43C2311yescharacteristic
62C23×Dic43C2×C411yescharacteristic
63C23×Dic43C2×C411yescharacteristic
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C22×C4×D43C2×C411yescharacteristic
67#13063323—22no—
68#13063323—22no—
69#13063308—22no—
70#13063308—22no—
71#13063308—22no—
72#13063308—22no—
73#13063306—22no—
74#13063306—22no—
75#13063306—22no—
76#13063306—22no—
77#13063304—22no—
78#13063304—22no—
79#13063301—22no—
80#13063301—22no—
81#13063297—22no—
82#13063297—22no—
83#13063297—22no—
84#13063297—22no—
85D4×Dic43—22no—
86D4×Dic43—22no—
87C4×C22⋊D43—21no—
88C4×C22⋊D43—21no—
89C4×C22⋊D43—21no—
90C4×C22⋊D43—21no—
91#13063284—24no—
92#13063284—42no—
93#13063281—24no—
94#13063281—42no—
95C2×C4⋊Dic43—22no—
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—22no—
102C2×Dic43⋊C4—22no—
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×Dic43⋊C4C2×C411yescharacteristic
105C2×Dic43⋊C4C2×C411yescharacteristic
106C2×Dic43⋊C4C2×C411yescharacteristic
107C2×Dic43⋊C4C2×C411yescharacteristic
108C2×Dic43⋊C4C2×C411yescharacteristic
109C2×Dic43⋊C4C2×C411yescharacteristic
110C2×Dic43⋊C4C2×C411yescharacteristic
111C2×Dic43⋊C4C2×C411yescharacteristic
112C2×Dic43⋊C4D412yes—
113C2×Dic43⋊C4D412yes—
114C2×Dic43⋊C4D412yes—
115C2×Dic43⋊C4D412yes—
116C2×C22⋊Dic43C2×C411yescharacteristic
117C2×C22⋊Dic43C2×C411yescharacteristic
118C2×C22⋊Dic43C2×C411yescharacteristic
119C2×C22⋊Dic43C2×C411yescharacteristic
120C2×C22⋊Dic43C2312yes—
121C2×C22⋊Dic43C2311yescharacteristic
122C2×C22⋊Dic43C2312yes—
123C2×(C2×D43)⋊C4C2×C411yescharacteristic
124C2×(C2×D43)⋊C4C2×C411yescharacteristic
125C2×(C2×D43)⋊C4C2×C411yescharacteristic
126C2×C4×Dic43—22no—
127C2×C4×Dic43—22no—
128C2×C4×Dic43—22no—
129C2×C4×Dic43C2×C411yescharacteristic
130#13063240—22no—
131#13063240—24no—
132#13063240D414yescomplemented
133#13063239—24no—
134#13063239—42no—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C2×#41×C43—22no—
140C2×#41×C43—22no—
141C2×#41×C43—22no—
142C2×#41×C43—22no—
143C2×#41×C43—42no—
144C22×Q8×C43C2×C411yescharacteristic
145C22×D4×C43C2×C411yescharacteristic
146C22×D4×C43C2311yescharacteristic
147C22×D4×C43C2311yescharacteristic
148C23×C4×C43C2×C411yescharacteristic
149C23×C4×C43C2×C411yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C2×C22⋊C4×C43C2312yes—
152C2×C22⋊C4×C43C2312yes—
153#99×C43—22no—
154#99×C43—22no—
155#99×C43—42no—
156#95×C43—22no—
157#95×C43—22no—
158C24×C43C22×C411yescharacteristic
159C24×C43C22×C411yescharacteristic
160C24×C43C2411yescharacteristic
161C23×D43C22×C411yescharacteristic
162#41×C43—44no—
163#41×C43—44no—
164#41×C43—44no—
165#41×C43—44no—
166C2×Q8×C43—22no—
167C2×Q8×C43—22no—
168C2×Q8×C43—41no—
169C2×D4×C43—22no—
170C2×D4×C43—22no—
171C2×D4×C43—22no—
172C2×D4×C43—21no—
173C2×D4×C43—22no—
174C2×D4×C43—21no—
175C2×D4×C43—22no—
176C2×D4×C43—22no—
177C2×D4×C43—41no—
178C2×D4×C43C2×D412yes—
179C2×D4×C43#4112yes—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—21no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—21no—
190C22×C4×C43—22no—
191C22×C4×C43—41no—
192C22×C4×C43—41no—
193C22×C4×C43C22×C411yescharacteristic
194C22×C4×C43C22×C411yescharacteristic
195C22×C4×C43C22×C411yescharacteristic
196C22×C4×C43C22×C411yescharacteristic
197C22×C4×C43C2×D412yes—
198C22×C4×C43C2×D412yes—
199C2×C22⋊D43—21no—
200C2×C22⋊D43—21no—
201C2×C22⋊D43—22no—
202C2×C22⋊D43—22no—
203C2×C22⋊D43—21no—
204C2×C22⋊D43—22no—
205C2×C22⋊D43—21no—
206C2×C22⋊D43—22no—
207C2×C22⋊D43—41no—
208C2×C22⋊D43—42no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—22no—
214C22×Dic43—21no—
215C22×Dic43—22no—
216C22×Dic43—22no—
217C22×Dic43—21no—
218C22×Dic43—22no—
219C22×Dic43—41no—
220C22×Dic43—42no—
221C22×Dic43—42no—
222C22×Dic43C22×C411yescharacteristic
223C22×Dic43C22×C411yescharacteristic
224C22×Dic43C22×C411yescharacteristic
225C22×Dic43C22×C411yescharacteristic
226C22×Dic43C22×C411yescharacteristic
227C22×Dic43C22×C411yescharacteristic
228C22×Dic43C22×C411yescharacteristic
229C22×Dic43C2×D412yes—
230C22×Dic43C2×D412yes—
231C22×Dic43C2×D412yes—
232C22×Dic43C2×D412yes—
233#10621900—44no—
234#10621900—44no—
235#10621900—44no—
236#10621900—44no—
237C2×C4×D43—22no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—41no—
241C2×Dic86—22no—
242C2×Dic86—22no—
243C2×Dic86—41no—
244C22⋊C4×C43—22no—
245C22⋊C4×C43—22no—
246C22⋊C4×C43—22no—
247C22⋊C4×C43—22no—
248C22⋊Dic43—21no—
249C22⋊Dic43—21no—
250C22⋊Dic43—22no—
251C22⋊Dic43—22no—
252C22⋊Dic43—22no—
253C22⋊Dic43—22no—
254C22⋊Dic43—22no—
255C22⋊Dic43—22no—
256C22⋊Dic43—22no—
257C22⋊Dic43C2×D414yes—
258(C2×D43)⋊C4—21no—
259(C2×D43)⋊C4—21no—
260(C2×D43)⋊C4—22no—
261(C2×D43)⋊C4—22no—
262C4⋊Dic43—22no—
263C4⋊Dic43—44no—
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—22no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—22no—
272Dic43⋊C4—44no—
273Dic43⋊C4—44no—
274Dic43⋊C4C22⋊C411yescharacteristic
275Dic43⋊C4C22⋊C411yescharacteristic
276Dic43⋊C4C22⋊C411yescharacteristic
277Dic43⋊C4C22⋊C411yescharacteristic
278Dic43⋊C4C22⋊C412yes—
279Dic43⋊C4C22⋊C412yes—
280Dic43⋊C4C22⋊C412yes—
281Dic43⋊C4C22⋊C412yes—
282Dic43⋊C4C22⋊C412yes—
283Dic43⋊C4C22⋊C412yes—
284C4×Dic43—21no—
285C4×Dic43—21no—
286C4×Dic43—44no—
287C4×Dic43—44no—
288C4×Dic43—44no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43C4×D412yes—
301C23×C43C23×C411yescharacteristic
302C23×C43C22×D412yes—
303C23×C43C22×D411yescharacteristic
304C23×C43C2×#4111yescharacteristic
305C23×C43H(5,𝔽2)12yes—
306C22×D43—21no—
307C22×D43—21no—
308C22×D43—21no—
309C22×D43—41no—
310C22×D43—41no—
311Q8×C43—44no—
312D4×C43—24no—
313D4×C43—24no—
314D4×C43—44no—
315D4×C43—42no—
316D4×C43—42no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
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—42no—
337C2×C4×C43—42no—
338C2×C4×C43—42no—
339C2×C4×C43—42no—
340C2×C4×C43C2×C22⋊C411yescharacteristic
341C2×C4×C43C2×C22⋊C411yescharacteristic
342C2×C4×C43C2×C22⋊C412yes—
343C2×C4×C43C4×D412yes—
344C22⋊D43—44no—
345C22⋊D43—42no—
346C22⋊D43—42no—
347C22⋊D43—42no—
348C22⋊D43—42no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—24no—
358C2×Dic43—22no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—24no—
365C2×Dic43—41no—
366C2×Dic43—42no—
367C2×Dic43—42no—
368C2×Dic43—42no—
369C2×Dic43—42no—
370C2×Dic43—42no—
371C2×Dic43—42no—
372C2×Dic43—42no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43—42no—
376C2×Dic43—42no—
377C2×Dic43—42no—
378C2×Dic43C2×C22⋊C411yescharacteristic
379C2×Dic43C2×C22⋊C412yes—
380C2×Dic43C2×C22⋊C411yescharacteristic
381C2×Dic43C2×C22⋊C411yescharacteristic
382C2×Dic43C2×C22⋊C412yes—
383C2×Dic43C2×C22⋊C411yescharacteristic
384C4×D43—42no—
385C4×D43—42no—
386Dic86—44no—
387#22406—431nomaximal, Sylow
388C22×C43—21no—
389C22×C43—22no—
390C22×C43—21no—
391C22×C43—22no—
392C22×C43—22no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43C22×C22⋊C411yescharacteristic
406C22×C43C2×C4×D411yescharacteristic
407C22×C43#51811yescharacteristic
408C22×C43D4212yes—
409C22×C43#54612yes—
410C2×D43—41no—
411C2×D43—41no—
412C2×D43—41no—
413C2×D43—81no—
414C2×D43—81no—
415C4×C43—22no—
416C4×C43—21no—
417C4×C43—21no—
418C4×C43—22no—
419C4×C43—41no—
420C4×C43—82no—
421C4×C43—82no—
422Dic43—22no—
423Dic43—21no—
424Dic43—21no—
425Dic43—21no—
426Dic43—22no—
427Dic43—44no—
428Dic43—41no—
429Dic43—41no—
430Dic43—41no—
431Dic43—82no—
432Dic43#41012yescomplemented
433C2×#547—431no—
434C2×#410—431no—
435C2×#410—431no—
436#2344—432no—
437#1964—432no—
438#1899—432no—
439#1899—432no—
440#1799—431no—
441#1782—431no—
442#1782D4311yescharacteristic, complemented
443C4×#99—431no—
444C2×C43—22no—
445C2×C43—22no—
446C2×C43—21no—
447C2×C43—21no—
448C2×C43—42no—
449C2×C43—81no—
450C2×C43D4×C22⋊C411yescharacteristic
451C2×C43C2×#41011yescharacteristic
452C2×C43#288411yescharacteristic
453D43—81no—
454C22×#41—431no—
455C22×#41C2×D4311yescharacteristic
456#547—862no—
457#547—862no—
458#547—862no—
459#547—862no—
460C2×C4⋊Q8—431no—
461C2×#123—431no—
462C2×#123—431no—
463C2×#123—431no—
464C2×#123—431no—
465C2×C22⋊Q8—431no—
466C2×C22⋊Q8—431no—
467C2×#121—431no—
468C2×#121—431no—
469C2×C4×D4—431no—
470C2×C4×D4—431no—
471C2×#117—432no—
472C2×#117—432no—
473C22×C4⋊C4—431no—
474C22×C4⋊C4—431no—
475#410—864no—
476#410—864no—
477C2×#99—431no—
478C2×#99—431no—
479C2×#99—432no—
480C2×#99—432no—
481C2×#99—432no—
482C2×#99C2×D4311yescharacteristic
483C2×#99C2×D4311yescharacteristic
484C2×#99C2×D4312yes—
485#389—862no—
486#387—862no—
487#387—862no—
488#381—432no—
489#381C2×D4312yes—
490#380—432no—
491C4×C4⋊C4—862no—
492C4×C22⋊C4—432no—
493#342—432no—
494#342—432no—
495C43#2240611yescharacteristic, complemented, Sylow
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—42no—
501C2×#41—862no—
502C2×#41—862no—
503C2×#41—862no—
504C2×#41—862no—
505C2×#41—1722no—
506C22×Q8—431no—
507C22×Q8C4×D4311yescharacteristic
508C22×D4—431no—
509C22×D4—431no—
510C22×D4—431no—
511C22×D4C4×D4311yescharacteristic
512C22×D4C22×D4311yescharacteristic
513C22×D4C22×D4311yescharacteristic
514C23×C4—431no—
515C23×C4—431no—
516C23×C4—431no—
517C23×C4—431no—
518C23×C4—431no—
519C23×C4C4×D4311yescharacteristic
520C23×C4C4×D4311yescharacteristic
521C23×C4C22×D4311yescharacteristic
522C4⋊Q8—862no—
523C4⋊Q8—862no—
524#123—862no—
525#123—862no—
526#123—862no—
527#123—862no—
528#123—862no—
529#123—862no—
530#123—862no—
531#123—862no—
532C22⋊Q8—862no—
533C22⋊Q8—862no—
534C22⋊Q8—862no—
535C22⋊Q8—862no—
536#121—862no—
537#121—862no—
538#121—862no—
539#121—862no—
540C4×D4—861no—
541C4×D4—861no—
542C4×D4—861no—
543C4×D4—861no—
544C4×D4—862no—
545C4×D4—862no—
546#117—864no—
547#117—864no—
548#117—1722no—
549#117—1722no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—432no—
555C2×C4⋊C4—432no—
556C2×C4⋊C4—432no—
557C2×C4⋊C4—432no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4—862no—
569C2×C4⋊C4—862no—
570C2×C4⋊C4—862no—
571C2×C22⋊C4—432no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—431no—
574C2×C22⋊C4—431no—
575C2×C22⋊C4—431no—
576C2×C22⋊C4—431no—
577C2×C22⋊C4—431no—
578C2×C22⋊C4—431no—
579C2×C22⋊C4—431no—
580C2×C22⋊C4—432no—
581C2×C22⋊C4C22×D4312yes—
582C2×C22⋊C4C22×D4312yes—
583C2×C42—431no—
584C2×C42—862no—
585C2×C42—862no—
586C2×C42—862no—
587#99—22no—
588#99—22no—
589#99—42no—
590#99—434no—
591#99—864no—
592#99—864no—
593#99—862no—
594#99—1722no—
595#95—22no—
596#95—22no—
597#95—862no—
598#95—862no—
599#95—862no—
600#95—862no—
601C24—431no—
602C24C2×C4×D4311yescharacteristic
603C24C2×C4×D4311yescharacteristic
604C24C23×D4311yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—1724no—
610#41—1724no—
611#41—1724no—
612#41—1724no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—41no—
616C2×Q8—862no—
617C2×Q8—862no—
618C2×Q8—1721no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—41no—
628C2×D4—861no—
629C2×D4—861no—
630C2×D4—862no—
631C2×D4—862no—
632C2×D4—861no—
633C2×D4—862no—
634C2×D4—861no—
635C2×D4—862no—
636C2×D4—1721no—
637C2×D4—1722no—
638C2×D4D4×D4312yes—
639C2×D4#1062190012yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—432no—
657C22×C4—432no—
658C22×C4—432no—
659C22×C4—431no—
660C22×C4—432no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—862no—
675C22×C4—862no—
676C22×C4—862no—
677C22×C4—1721no—
678C22×C4—1722no—
679C22×C4—1721no—
680C22×C4—1722no—
681C22×C4C2×C4×D4311yescharacteristic
682C22×C4C2×C4×D4311yescharacteristic
683C22×C4C2×C4×D4311yescharacteristic
684C22×C4C2×C4×D4311yescharacteristic
685C22×C4D4×D4312yes—
686C22×C4D4×D4312yes—
687C4⋊C4—431no—
688C4⋊C4—431no—
689C4⋊C4—431no—
690C4⋊C4—431no—
691C4⋊C4—432no—
692C4⋊C4—432no—
693C4⋊C4—432no—
694C4⋊C4—432no—
695C4⋊C4—432no—
696C4⋊C4—432no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—862no—
702C4⋊C4—862no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—862no—
706C4⋊C4—1724no—
707C4⋊C4—1724no—
708C4⋊C4—1724no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—434no—
714C22⋊C4—862no—
715C22⋊C4—862no—
716C22⋊C4—861no—
717C22⋊C4—861no—
718C22⋊C4—862no—
719C22⋊C4—862no—
720C22⋊C4—862no—
721C22⋊C4—862no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—862no—
725C22⋊C4—862no—
726C22⋊C4—862no—
727C42—861no—
728C42—861no—
729C42—1724no—
730C42—1724no—
731C42—1724no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—861no—
744C23—861no—
745C23—861no—
746C23—1721no—
747C23—1721no—
748C23(C22⋊D43)⋊C412yes—
749C23C22×C4×D4311yescharacteristic
750C23C2×D4×D4312yes—
751C23C2×D4×D4311yescharacteristic
752C23C2×#1062190011yescharacteristic
753C23#1306337012yes—
754Q8—44no—
755Q8—1724no—
756D4—24no—
757D4—24no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—1722no—
762D4—1724no—
763D4—1722no—
764D4—1722no—
765D4—1722no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—431no—
790C2×C4—431no—
791C2×C4—432no—
792C2×C4—431no—
793C2×C4—431no—
794C2×C4—432no—
795C2×C4—864no—
796C2×C4—862no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—861no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—861no—
809C2×C4—861no—
810C2×C4—864no—
811C2×C4—1722no—
812C2×C4—1722no—
813C2×C4—1722no—
814C2×C4—1722no—
815C2×C4—1721no—
816C2×C4—1722no—
817C2×C4—1722no—
818C2×C4—1722no—
819C2×C4—1722no—
820C2×C4—1722no—
821C2×C4—1722no—
822C2×C4—1722no—
823C2×C4—1722no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4C22⋊C4×D4311yescharacteristic
827C2×C4C22⋊C4×D4311yescharacteristic
828C2×C4C22⋊C4×D4312yes—
829C2×C4(C22⋊D43)⋊C412yes—
830C22—22no—
831C22—21no—
832C22—22no—
833C22—21no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—81no—
846C22—81no—
847C22—3441no—
848C22—3441no—
849C22—1721no—
850C22—1721no—
851C22—1721no—
852C22C2×C22⋊C4×D4311yescharacteristic
853C22C2×(C22⋊D43)⋊C411yescharacteristic
854C22#1458337211yescharacteristic
855C22#1458353112yes—
856C22#1458353612yes—
857C4—21no—
858C4—21no—
859C4—22no—
860C4—22no—
861C4—41no—
862C4—82no—
863C4—82no—
864C4—432no—
865C4—861no—
866C4—861no—
867C4—862no—
868C4—861no—
869C4—862no—
870C4—3442no—
871C4—1724no—
872C4—1721no—
873C4—1721no—
874C4—1721no—
875C2—22no—
876C2—22no—
877C2—21no—
878C2—21no—
879C2—42no—
880C2—81no—
881C2—3441no—
882C2#1913741111yescharacteristic
883C2#410×D4311yescharacteristic
884C2#1914305711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1782C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583548C2
cosocleC24×C43C24
hypercenter#1782D43
hypocenterC43#22406
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. C2×#14582873C2semidirect
3. C2×#14582871C2semidirect
4. #19137459C2semidirect
5. #19135429C2semidirect
6. #19135051C2semidirect
7. #19135050C2semidirect
8. #19134581C2semidirect
9. #19134511C2semidirect
10. #99×Dic43C2semidirect
11. C43×#1782C2semidirect
17. C2×#13063323C4semidirect
18. C2×#13063308C4semidirect
20. C2×#13063306C4semidirect
22. C2×#13063304C4semidirect
23. C2×#13063301C4semidirect
24. C2×#13063297C4semidirect
27. C2×C4×C22⋊D43C4semidirect
30. C22×Dic43⋊C4C4semidirect
132. #13063240D4semidirect
432. Dic43#410semidirect
442. #1782D43semidirect
495. C43#22406semidirect

Maximal subgroups

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

subgroupindex
C2×#145835482
C2×#145828732
C2×#145828712
#191374592
#191354292
#191350512
#191350502
#191345812
#191345112
#99×Dic432
C43×#17822
#2240643