Finite Group Databasebeta

← #25112779

Subgroups — #25112779

Order 11008.

1132 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583596C211yesmaximal, characteristic
2M16×C22⋊D43C211yesmaximal, characteristic, complemented
3#19143327C211yesmaximal, characteristic, complemented
4#19135586C211yesmaximal, characteristic, complemented
5#19135586C211yesmaximal, characteristic, complemented
6#19135059C211yesmaximal, characteristic, complemented
7#19135055C211yesmaximal, characteristic, complemented
8#19135055C211yesmaximal, characteristic, complemented
9#19134676C211yesmaximal, characteristic, complemented
10#19134674C211yesmaximal, characteristic, complemented
11#19134585C211yesmaximal, characteristic, complemented
12#100×Dic43C211yesmaximal, characteristic, complemented
13#19134333C211yesmaximal, characteristic, complemented
14#343×D43C211yesmaximal, characteristic, complemented
15C43×#1900C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19#14583596—21no—
20#14583596—21no—
21#14583596—21no—
22#14583596—21no—
23#14583596—21no—
24#14583596—21no—
25#14583596—21no—
26#14583596—21no—
27C2×#13063318C412yes—
28C2×#13063316C2211yescharacteristic
29C2×#13063306C412yes—
30C2×#13063296C412yes—
31C2×#13063296C2211yescharacteristic
32C2×D4×Dic43C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×(C22⋊D43)⋊C4C412yes—
35C2×#13063284C2211yescharacteristic
36C2×C4⋊C4×D43C2211yescharacteristic
37#14582975—21no—
38#14582974—21no—
39#14582973—21no—
40#14582970—21no—
41#14582968—21no—
42#14582967—21no—
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582922C2211yescharacteristic
46#14582922C2211yescharacteristic
47C2×#13063242C2211yescharacteristic
48C2×#13063242C2211yescharacteristic
49#14582863C2211yescharacteristic
50#14582862C2211yescharacteristic
51#14582862C2211yescharacteristic
52M16×Dic43C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582668C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60#14582667C2211yescharacteristic
61#14582667C2211yescharacteristic
62#14582667C2211yescharacteristic
63#14582667C2211yescharacteristic
64C22×M16×C43C2211yescharacteristic
65C2×#121×C43C2211yescharacteristic
66C2×#100×C43C2211yescharacteristic
67C2×#100×C43C2211yescharacteristic
68C43×#407C2211yescharacteristic
69C43×#343C2211yescharacteristic
70C43×#343C2211yescharacteristic
71C22×C22⋊D43C2×C412yes—
72C22×C22⋊D43C2×C411yescharacteristic
73C23×Dic43C2×C412yes—
74C22×C4×D43C2×C412yes—
75C22×C4×D43C2311yescharacteristic
76C2×#10621877—21no—
77C2×#10621877—22no—
78C2×#10621877—41no—
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621872—21no—
84C2×#10621872—21no—
85M16×D43—22no—
86M16×D43—22no—
87M16×D43—41no—
88M16×D43—41no—
89C22×C43⋊C8—21no—
90C2×C8×D43—21no—
91C2×C8×D43—21no—
92#13063318—22no—
93#13063318—22no—
94#13063318—22no—
95#13063318—22no—
96#13063316—21no—
97#13063316—21no—
98#13063316—21no—
99#13063316—21no—
100#13063306—22no—
101#13063306—22no—
102#13063306—22no—
103#13063306—22no—
104#13063296—22no—
105#13063296—22no—
106#13063296—22no—
107#13063296—22no—
108#13063296—21no—
109#13063296—21no—
110#13063296—21no—
111#13063296—21no—
112D4×Dic43—21no—
113D4×Dic43—21no—
114D4×Dic43—21no—
115D4×Dic43—21no—
116C4×C22⋊D43D411yescharacteristic
117C4×C22⋊D43D411yescharacteristic
118C4×C22⋊D43D411yescharacteristic
119C4×C22⋊D43D411yescharacteristic
120C4×C22⋊D43D411yescharacteristic
121C4×C22⋊D43D411yescharacteristic
122C4×C22⋊D43D411yescharacteristic
123C4×C22⋊D43D411yescharacteristic
124(C22⋊D43)⋊C4—22no—
125(C22⋊D43)⋊C4—22no—
126(C22⋊D43)⋊C4—22no—
127(C22⋊D43)⋊C4—22no—
128#13063284—21no—
129#13063284—21no—
130#13063284—21no—
131#13063284—21no—
132C2×C4⋊Dic43C2×C412yes—
133C2×C4⋊Dic43C2311yescharacteristic
134C2×C4⋊Dic43C2311yescharacteristic
135C2×Dic43⋊C4C2×C412yes—
136C2×Dic43⋊C4C2×C412yes—
137C2×Dic43⋊C4C2×C411yescharacteristic
138C4⋊C4×D43—21no—
139C4⋊C4×D43—21no—
140C4⋊C4×D43—21no—
141C4⋊C4×D43—21no—
142C2×C22⋊Dic43C2×C412yes—
143C2×C22⋊Dic43C2×C412yes—
144C2×C22⋊Dic43C2×C412yes—
145C2×C22⋊Dic43C2×C411yescharacteristic
146C2×(C2×D43)⋊C4C2×C411yescharacteristic
147C2×C4×Dic43C2×C412yes—
148C2×C4×Dic43C2311yescharacteristic
149Dic43⋊C8—21no—
150Dic43⋊C8—21no—
151Dic43⋊C8—21no—
152Dic43⋊C8—21no—
153#13063242—22no—
154#13063242—41no—
155C22⋊(C43⋊C8)—21no—
156C22⋊(C43⋊C8)—21no—
157(C2×D43)⋊C8—21no—
158(C2×D43)⋊C8—21no—
159(C2×D43)⋊C8—21no—
160(C2×D43)⋊C8—21no—
161#13063235—21no—
162#13063235—21no—
163C8×Dic43—21no—
164C8×Dic43—21no—
165C22×D4×C43C2×C412yes—
166C22×D4×C43C2311yescharacteristic
167C23×C4×C43C2311yescharacteristic
168C2×M16×C43—21no—
169C2×M16×C43—22no—
170C2×M16×C43—41no—
171C2×M16×C43C2311yescharacteristic
172C2×M16×C43C2311yescharacteristic
173C2×M16×C43C2311yescharacteristic
174C2×M16×C43C2311yescharacteristic
175C22×C8×C43—21no—
176#121×C43—21no—
177#121×C43—21no—
178#121×C43—21no—
179#121×C43—21no—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43C2×C412yes—
182#100×C43—22no—
183#100×C43—41no—
184C22⋊C8×C43—21no—
185C22⋊C8×C43—21no—
186C24×C43C22×C412yes—
187C24×C43C22×C411yescharacteristic
188C23×D43C22×C411yescharacteristic
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—82no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43C22×C411yescharacteristic
203C22×C4×C43C22×C412yes—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2411yescharacteristic
209C2×C22⋊D43—22no—
210C2×C22⋊D43—22no—
211C2×C22⋊D43—42no—
212C2×C22⋊D43—44no—
213C2×C22⋊D43C22⋊C411yescharacteristic
214C2×C22⋊D43C22⋊C411yescharacteristic
215C2×C22⋊D43C22⋊C411yescharacteristic
216C2×C22⋊D43C22⋊C411yescharacteristic
217C22×Dic43—22no—
218C22×Dic43—22no—
219C22×Dic43—82no—
220C22×Dic43C22×C411yescharacteristic
221C22×Dic43C22×C412yes—
222C22×Dic43C22×C412yes—
223C22×Dic43C22×C411yescharacteristic
224C22×Dic43C22×C411yescharacteristic
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—22no—
230C2×C4×D43—22no—
231C2×C4×D43—82no—
232C2×C4×D43C2×D411yescharacteristic
233C2×C4×D43C2×D411yescharacteristic
234C2×C4×D43C2×D411yescharacteristic
235C2×C4×D43C2×D411yescharacteristic
236M16×C43—21no—
237M16×C43—21no—
238M16×C43—21no—
239M16×C43—21no—
240M16×C43—21no—
241M16×C43—21no—
242M16×C43—21no—
243M16×C43—42no—
244M16×C43#4112yes—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—42no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C22⋊C4×C43—22no—
253C22⋊C4×C43—22no—
254C22⋊Dic43—22no—
255C22⋊Dic43—22no—
256C22⋊Dic43—22no—
257C22⋊Dic43—22no—
258C22⋊Dic43—22no—
259C22⋊Dic43—22no—
260C22⋊Dic43C22⋊C411yescharacteristic
261C22⋊Dic43C22⋊C411yescharacteristic
262C22⋊Dic43C22⋊C411yescharacteristic
263C22⋊Dic43C22⋊C411yescharacteristic
264(C2×D43)⋊C4C22⋊C411yescharacteristic
265(C2×D43)⋊C4C22⋊C411yescharacteristic
266(C2×D43)⋊C4C22⋊C411yescharacteristic
267(C2×D43)⋊C4C22⋊C411yescharacteristic
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—22no—
273C4⋊Dic43—22no—
274Dic43⋊C4—22no—
275Dic43⋊C4—22no—
276Dic43⋊C4—22no—
277Dic43⋊C4—22no—
278Dic43⋊C4C22⋊C411yescharacteristic
279Dic43⋊C4C22⋊C411yescharacteristic
280Dic43⋊C4C22⋊C411yescharacteristic
281Dic43⋊C4C22⋊C411yescharacteristic
282C4×Dic43—22no—
283C4×Dic43—22no—
284C4×Dic43C2×D411yescharacteristic
285C4×Dic43C2×D411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288#10621877—21no—
289#10621877—21no—
290#10621877—21no—
291#10621877—21no—
292#10621877—21no—
293#10621877—21no—
294#10621877—21no—
295#10621877—42no—
296#10621877#4112yes—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8—21no—
301C2×C43⋊C8—42no—
302#10621872—42no—
303#10621872—42no—
304C8×D43—42no—
305C8×D43—42no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—42no—
314C23×C43—42no—
315C23×C43C2×C22⋊C411yescharacteristic
316C23×C43C2×C22⋊C411yescharacteristic
317C23×C43C23×C411yescharacteristic
318C22×D43—21no—
319C22×D43—21no—
320C22×D43—22no—
321C22×D43—41no—
322C22×D43C2×C22⋊C411yescharacteristic
323C22×D43C2×C22⋊C411yescharacteristic
324D4×C43—41no—
325D4×C43—41no—
326D4×C43—41no—
327D4×C43—41no—
328D4×C43—82no—
329D4×C43—82no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—22no—
341C2×C4×C43—42no—
342C2×C4×C43C2×C22⋊C411yescharacteristic
343C2×C4×C43C2×C22⋊C411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C2×#4111yescharacteristic
347C2×C4×C43C2×#4111yescharacteristic
348C2×C4×C43H(5,𝔽2)11yescharacteristic
349C2×C4×C432−1+411yescharacteristic
350C22⋊D43—22no—
351C22⋊D43—22no—
352C22⋊D43—41no—
353C22⋊D43—41no—
354C22⋊D43—44no—
355C22⋊D43—44no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—42no—
363C2×Dic43—42no—
364C2×Dic43—82no—
365C2×Dic43—82no—
366C2×Dic43C2×C22⋊C411yescharacteristic
367C2×Dic43C2×C22⋊C411yescharacteristic
368C2×Dic43C2×C22⋊C411yescharacteristic
369C2×Dic43C2×C22⋊C411yescharacteristic
370C2×Dic43C2×C22⋊C411yescharacteristic
371C2×Dic43C2×C22⋊C411yescharacteristic
372C4×D43—21no—
373C4×D43—21no—
374C4×D43—21no—
375C4×D43—21no—
376C4×D43—21no—
377C4×D43—21no—
378C4×D43—21no—
379C4×D43—21no—
380C4×D43—82no—
381C4×D43—82no—
382C8×C43—22no—
383C8×C43—41no—
384C8×C43—41no—
385C8×C43—41no—
386C43⋊C8—22no—
387C43⋊C8—41no—
388C43⋊C8—41no—
389C43⋊C8—41no—
390#22482—431nomaximal, Sylow
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—21no—
394C22×C43—21no—
395C22×C43—21no—
396C22×C43—21no—
397C22×C43—21no—
398C22×C43—21no—
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—42no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—82no—
405C22×C43—82no—
406C22×C43C22×C22⋊C411yescharacteristic
407C22×C43C4×#4111yescharacteristic
408C22×C43#52011yescharacteristic
409C2×D43—21no—
410C2×D43—21no—
411C2×D43—21no—
412C2×D43—21no—
413C2×D43—21no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43#41312yes—
417C4×C43—21no—
418C4×C43—21no—
419C4×C43—42no—
420C4×C43#54611yescharacteristic
421C4×C43#54611yescharacteristic
422C4×C43#54711yescharacteristic
423C4×C43#54711yescharacteristic
424Dic43—21no—
425Dic43—21no—
426Dic43—21no—
427Dic43—21no—
428Dic43—21no—
429Dic43—21no—
430Dic43—42no—
431Dic43—42no—
432C2×#553—431no—
433D4×M16—431no—
434D4×M16—431no—
435#1998—431no—
436#1998—431no—
437#1900—431no—
438#1900—431no—
439#1900—431no—
440#1900D4311yescharacteristic, complemented
441#1822—431no—
442#1821—431no—
443#1800—431no—
444C4×#100—431no—
445#1742—431no—
446C2×#343—431no—
447C2×C43—21no—
448C2×C43—21no—
449C2×C43—41no—
450C2×C43—41no—
451C2×C43—82no—
452C2×C43#233911yescharacteristic
453C2×C43C2×#41311yescharacteristic
454C2×C43#288811yescharacteristic
455D43—22no—
456D43—41no—
457C22×M16—431no—
458C22×M16—431no—
459C22×M16—431no—
460C22×M16C2×D4311yescharacteristic
461#553—861no—
462#553—861no—
463#553—861no—
464#553—861no—
465#553—861no—
466#553—861no—
467#553—861no—
468#553—861no—
469C2×#126—432no—
470C2×#125—431no—
471C2×#123—432no—
472C2×#121—431no—
473C2×#121—432no—
474C2×#121C2×D4311yescharacteristic
475C2×C4×D4—431no—
476C2×C4×D4—431no—
477C2×C4×D4—432no—
478C2×#117—431no—
479C22×C4⋊C4—431no—
480#436—861no—
481#436—861no—
482#435—861no—
483#435—861no—
484#435—861no—
485#435—861no—
486C8×D4—861no—
487C8×D4—861no—
488#423—431no—
489#423—431no—
490C2×#100—431no—
491C2×#100—431no—
492C2×#100C2×D4311yescharacteristic
493C2×#100C2×D4311yescharacteristic
494#407—431no—
495#407—431no—
496#407—431no—
497#407C2×D4311yescharacteristic
498C4×M16—431no—
499C4×M16—431no—
500#343—431no—
501#343—431no—
502#343—431no—
503#343—431no—
504#343—431no—
505#343—431no—
506#343—431no—
507#343—431no—
508#343—431no—
509#343—431no—
510#343C2×D4311yescharacteristic
511#343C2×D4311yescharacteristic
512C43#2248211yescharacteristic, complemented, Sylow
513C22×D4—431no—
514C22×D4—432no—
515C22×D4C4×D4312yes—
516C22×D4C22×D4311yescharacteristic
517C23×C4—431no—
518C23×C4—432no—
519C23×C4—432no—
520C23×C4C22×D4311yescharacteristic
521C2×M16—21no—
522C2×M16—22no—
523C2×M16—41no—
524C2×M16—431no—
525C2×M16—431no—
526C2×M16—431no—
527C2×M16—431no—
528C2×M16—861no—
529C2×M16—861no—
530C2×M16—861no—
531C2×M16—862no—
532C2×M16—862no—
533C2×M16—862no—
534C2×M16—1721no—
535C2×M16—1721no—
536C2×M16—1721no—
537C2×M16C22×D4311yescharacteristic
538C2×M16C22×D4311yescharacteristic
539C2×M16C22×D4311yescharacteristic
540C2×M16C22×D4311yescharacteristic
541C22×C8—21no—
542C22×C8—861no—
543C22×C8—861no—
544C22×C8—861no—
545#126—862no—
546#126—862no—
547#126—862no—
548#126—862no—
549#125—861no—
550#125—861no—
551#125—861no—
552#125—861no—
553#123—862no—
554#123—862no—
555#123—862no—
556#123—862no—
557#121—21no—
558#121—21no—
559#121—21no—
560#121—21no—
561#121—861no—
562#121—861no—
563#121—861no—
564#121—861no—
565#121—862no—
566#121—862no—
567#121—862no—
568#121—862no—
569C4×D4—431no—
570C4×D4—431no—
571C4×D4—431no—
572C4×D4—431no—
573C4×D4—431no—
574C4×D4—431no—
575C4×D4—431no—
576C4×D4—431no—
577C4×D4—861no—
578C4×D4—861no—
579C4×D4—861no—
580C4×D4—861no—
581C4×D4—862no—
582C4×D4—862no—
583C4×D4—862no—
584C4×D4—862no—
585#117—861no—
586#117—861no—
587#117—861no—
588#117—861no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—432no—
591C2×C4⋊C4—432no—
592C2×C4⋊C4—432no—
593C2×C4⋊C4—431no—
594C2×C4⋊C4—431no—
595C2×C4⋊C4—861no—
596C2×C4⋊C4—861no—
597C2×C4⋊C4—861no—
598C2×C4⋊C4—861no—
599C2×C4⋊C4C22×D4311yescharacteristic
600C2×C22⋊C4—431no—
601C2×C22⋊C4—431no—
602C2×C22⋊C4—432no—
603C2×C22⋊C4—432no—
604C2×C22⋊C4—432no—
605C2×C22⋊C4C4×D4312yes—
606C2×C42—431no—
607C2×C42—432no—
608C4⋊C8—861no—
609C4⋊C8—861no—
610C4⋊C8—861no—
611C4⋊C8—861no—
612#100—22no—
613#100—41no—
614#100—862no—
615#100—1721no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—861no—
619C22⋊C8—861no—
620C22⋊C8—861no—
621C22⋊C8—861no—
622C22⋊C8—861no—
623C22⋊C8—861no—
624#97—861no—
625#97—861no—
626C4×C8—861no—
627C4×C8—861no—
628C24—431no—
629C24C2×C4×D4312yes—
630C24C2×C4×D4311yescharacteristic
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—82no—
640C2×D4—431no—
641C2×D4—431no—
642C2×D4—431no—
643C2×D4—431no—
644C2×D4—862no—
645C2×D4—862no—
646C2×D4—1722no—
647C2×D4—1724no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—431no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—432no—
660C22×C4—432no—
661C22×C4—862no—
662C22×C4—862no—
663C22×C4—862no—
664C22×C4—862no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—3442no—
670C22×C4—3442no—
671C22×C4C2×C4×D4311yescharacteristic
672C22×C4C2×C4×D4312yes—
673C22×C4D4×D4311yescharacteristic
674C22×C4D4×D4311yescharacteristic
675C22×C4D4×D4311yescharacteristic
676C22×C4D4×D4311yescharacteristic
677C22×C4C23×D4311yescharacteristic
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—432no—
687M16—861no—
688M16—861no—
689M16—861no—
690M16—861no—
691M16—861no—
692M16—861no—
693M16—861no—
694M16—1722no—
695M16—1722no—
696M16—1722no—
697M16#1062190012yes—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—42no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—1722no—
708C2×C8—1722no—
709C2×C8—1722no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—431no—
713C4⋊C4—431no—
714C4⋊C4—431no—
715C4⋊C4—431no—
716C4⋊C4—862no—
717C4⋊C4—862no—
718C4⋊C4—862no—
719C4⋊C4—862no—
720C4⋊C4—862no—
721C4⋊C4—862no—
722C4⋊C4—861no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—431no—
729C22⋊C4—431no—
730C22⋊C4—431no—
731C22⋊C4—431no—
732C22⋊C4—431no—
733C22⋊C4—431no—
734C22⋊C4—431no—
735C22⋊C4—431no—
736C22⋊C4—862no—
737C22⋊C4—862no—
738C22⋊C4—862no—
739C22⋊C4—862no—
740C22⋊C4—862no—
741C22⋊C4—862no—
742C42—431no—
743C42—431no—
744C42—431no—
745C42—431no—
746C42—862no—
747C42—862no—
748C23—21no—
749C23—21no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—41no—
754C23—41no—
755C23—42no—
756C23—42no—
757C23—431no—
758C23—431no—
759C23—862no—
760C23—861no—
761C23—861no—
762C23—1721no—
763C23C22⋊C4×D4311yescharacteristic
764C23C22⋊C4×D4311yescharacteristic
765C23C22×C4×D4311yescharacteristic
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—82no—
771D4—82no—
772D4—862no—
773D4—862no—
774D4—1721no—
775D4—1721no—
776D4—1724no—
777D4—1724no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—42no—
790C2×C4—431no—
791C2×C4—431no—
792C2×C4—431no—
793C2×C4—431no—
794C2×C4—431no—
795C2×C4—431no—
796C2×C4—861no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—3442no—
809C2×C4—3442no—
810C2×C4—3442no—
811C2×C4—3442no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1722no—
815C2×C4—1722no—
816C2×C4C22⋊C4×D4311yescharacteristic
817C2×C4C22⋊C4×D4311yescharacteristic
818C2×C4C2×D4×D4311yescharacteristic
819C2×C4C2×D4×D4311yescharacteristic
820C2×C4#41×D4311yescharacteristic
821C2×C4C2×#1062190011yescharacteristic
822C2×C4#1306337011yescharacteristic
823C2×C4#1306337211yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C8—862no—
829C8—1721no—
830C8—1721no—
831C8—1721no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—82no—
846C22—82no—
847C22—432no—
848C22—861no—
849C22—861no—
850C22—861no—
851C22—861no—
852C22—861no—
853C22—1722no—
854C22—1722no—
855C22C2×C22⋊C4×D4311yescharacteristic
856C22C4×#1062190011yescharacteristic
857C22#1458337811yescharacteristic
858C4—21no—
859C4—21no—
860C4—42no—
861C4—861no—
862C4—861no—
863C4—861no—
864C4—861no—
865C4—861no—
866C4—861no—
867C4—1722no—
868C4—1722no—
869C4#1458353611yescharacteristic
870C4#1458353811yescharacteristic
871C4#1458354711yescharacteristic
872C4#1458354911yescharacteristic
873C2—21no—
874C2—21no—
875C2—41no—
876C2—41no—
877C2—82no—
878C2—862no—
879C2—1721no—
880C2#1913742111yescharacteristic
881C2#413×D4311yescharacteristic
882C2#1914307111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1900C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583596C2
cosocleC22×C4×C43C24
hypercenter#1900D43
hypocenterC43#22482
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1900

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D43C2semidirect
3. #19143327C2semidirect
4. #19135586C2semidirect
5. #19135586C2semidirect
6. #19135059C2semidirect
7. #19135055C2semidirect
8. #19135055C2semidirect
9. #19134676C2semidirect
10. #19134674C2semidirect
11. #19134585C2semidirect
12. #100×Dic43C2semidirect
13. #19134333C2semidirect
14. #343×D43C2semidirect
15. C43×#1900C2semidirect
440. #1900D43semidirect
512. C43#22482semidirect

Maximal subgroups

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

subgroupindex
C2×#145835962
M16×C22⋊D432
#191433272
#191355862
#191350592
#191350552
#191346762
#191346742
#191345852
#100×Dic432
#191343332
#343×D432
C43×#19002
#2248243