Finite Group Databasebeta

← #25062788

Subgroups — #25062788

Order 11008.

1046 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583573C211yesmaximal, characteristic
2#19143253C211yesmaximal, characteristic, complemented
3#19132965C211yesmaximal, characteristic, complemented
4#19132962C211yesmaximal, characteristic, complemented
5#19132948C211yesmaximal, characteristic, complemented
6#19132946C211yesmaximal, characteristic, complemented
7#19132944C211yesmaximal, characteristic, complemented
8#19132941C211yesmaximal, characteristic, complemented
9#19132935C211yesmaximal, characteristic, complemented
10#19132927C211yesmaximal, characteristic, complemented
11#19132921C211yesmaximal, characteristic, complemented
12#19132915C211yesmaximal, characteristic, complemented
13#19132907C211yesmaximal, characteristic, complemented
14C2×#14582622C211yesmaximal, characteristic, complemented
15C43×#2924C211yesmaximal, characteristic, complemented
16#14583573—21no—
17#14583573—21no—
18#14583573—21no—
19#14583573—21no—
20#14583573—21no—
21#14583573—21no—
22#14583573—21no—
23#14583573—21no—
24C2×#13063320C411yescharacteristic
25C2×#13063319C2211yescharacteristic
26C2×#13063313C2211yescharacteristic
27C2×#13063310C411yescharacteristic
28C2×#13063310C411yescharacteristic
29C2×#13063308C2211yescharacteristic
30C2×#13063303C411yescharacteristic
31C2×#13063302C411yescharacteristic
32C2×#13063295C411yescharacteristic
33C2×C4×D172C2211yescharacteristic
34C2×(C22⋊D43)⋊C4C411yescharacteristic
35C2×#13063282C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C2×C22⋊C4×D43C411yescharacteristic
38#14582960—21no—
39#14582960—21no—
40#14582956C2211yescharacteristic, complemented
41#14582956C2211yescharacteristic, complemented
42#14582952C2211yescharacteristic, complemented
43#14582952C2211yescharacteristic, complemented
44#14582926—21no—
45#14582863C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47#14582855—21no—
48#14582624C2211yescharacteristic, complemented
49#14582624C2211yescharacteristic, complemented
50#14582624C2211yescharacteristic, complemented
51#14582624C2211yescharacteristic, complemented
52#14582622C2211yescharacteristic
53#14582622C2211yescharacteristic
54#14582622C2211yescharacteristic
55#14582622C2211yescharacteristic
56#14582622C2211yescharacteristic
57#14582622C2211yescharacteristic
58#14582622C2211yescharacteristic
59#14582622C2211yescharacteristic
60#14582622C2211yescharacteristic, complemented
61#14582622C2211yescharacteristic, complemented
62#14582622C2211yescharacteristic, complemented
63#14582622C2211yescharacteristic, complemented
64C2×#117×C43C2211yescharacteristic
65C43×#433—21no—
66C43×#433—21no—
67C43×#432C2211yescharacteristic, complemented
68C43×#432C2211yescharacteristic, complemented
69C43×#431C2211yescharacteristic, complemented
70C43×#431C2211yescharacteristic, complemented
71C43×#424—21no—
72C43×#407C2211yescharacteristic
73C2×C22⋊C8×C43C2211yescharacteristic
74C43×#405—21no—
75C24×D43C2×C411yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C22×D172C2×C411yescharacteristic
78C22×D172C2×C411yescharacteristic
79C22×C22⋊D43C2×C411yescharacteristic
80C23×Dic43C2×C411yescharacteristic
81C22×C4×D43C2×C411yescharacteristic
82C22×C4×D43C2×C411yescharacteristic
83C22×C4×D43C2×C411yescharacteristic
84C2×#10621877—21no—
85C22×C43⋊C8—21no—
86#13063320—21no—
87#13063320—21no—
88#13063320—21no—
89#13063320—21no—
90#13063319—21no—
91#13063319—21no—
92#13063319—21no—
93#13063319—21no—
94#13063313—21no—
95#13063313—21no—
96#13063313—21no—
97#13063313—21no—
98#13063310—21no—
99#13063310—21no—
100#13063310—21no—
101#13063310—21no—
102#13063310—21no—
103#13063310—21no—
104#13063310—21no—
105#13063310—21no—
106#13063308—21no—
107#13063308—21no—
108#13063308—21no—
109#13063308—21no—
110#13063303—21no—
111#13063303—21no—
112#13063303—21no—
113#13063303—21no—
114#13063302—21no—
115#13063302—21no—
116#13063302—21no—
117#13063302—21no—
118#13063295—21no—
119#13063295—21no—
120#13063295—21no—
121#13063295—21no—
122C4×D172—21no—
123C4×D172—21no—
124C4×D172—21no—
125C4×D172—21no—
126(C22⋊D43)⋊C4—21no—
127(C22⋊D43)⋊C4—21no—
128(C22⋊D43)⋊C4—21no—
129(C22⋊D43)⋊C4—21no—
130#13063282—21no—
131#13063282—21no—
132#13063282—21no—
133#13063282—21no—
134C2×C4⋊Dic43C2×C411yescharacteristic
135C2×Dic43⋊C4C2×C411yescharacteristic
136C2×Dic43⋊C4C2×C411yescharacteristic
137C2×Dic43⋊C4C2×C411yescharacteristic
138C2×Dic43⋊C4C2×C411yescharacteristic
139C2×Dic43⋊C4C2311yescharacteristic
140C2×C22⋊Dic43C2×C411yescharacteristic
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4C2×C411yescharacteristic
146C2×(C2×D43)⋊C4C2×C411yescharacteristic
147C2×(C2×D43)⋊C4C2×C411yescharacteristic
148C2×(C2×D43)⋊C4C2×C411yescharacteristic
149C2×(C2×D43)⋊C4C2×C411yescharacteristic
150C2×(C2×D43)⋊C4C2×C411yescharacteristic
151C2×(C2×D43)⋊C4C2×C411yescharacteristic
152C2×(C2×D43)⋊C4C2×C411yescharacteristic
153C2×(C2×D43)⋊C4C2311yescharacteristic
154C2×(C2×D43)⋊C4C2311yescharacteristic
155C2×(C2×D43)⋊C4C2311yescharacteristic
156C22⋊C4×D43—21no—
157C22⋊C4×D43—21no—
158C22⋊C4×D43—21no—
159C22⋊C4×D43—21no—
160C2×C4×Dic43C2×C411yescharacteristic
161C4⋊(C43⋊C8)—21no—
162C4⋊(C43⋊C8)—21no—
163C4⋊(C43⋊C8)—21no—
164C4⋊(C43⋊C8)—21no—
165C22⋊(C43⋊C8)—21no—
166C22⋊(C43⋊C8)—21no—
167C22⋊(C43⋊C8)C2311yescharacteristic
168C22⋊(C43⋊C8)C2311yescharacteristic
169C22⋊(C43⋊C8)C2311yescharacteristic
170C22⋊(C43⋊C8)C2311yescharacteristic
171#13063236—21no—
172#13063236—21no—
173C4×C43⋊C8—21no—
174C4×C43⋊C8—21no—
175C23×C4×C43C2311yescharacteristic
176C2×M16×C43—21no—
177C22×C8×C43—21no—
178#117×C43D411yescharacteristic
179#117×C43D411yescharacteristic
180#117×C43D411yescharacteristic
181#117×C43D411yescharacteristic
182#117×C43D411yescharacteristic
183#117×C43D411yescharacteristic
184#117×C43D411yescharacteristic
185#117×C43D411yescharacteristic
186C2×C4⋊C4×C43C2×C411yescharacteristic
187C2×C4⋊C4×C43C2×C411yescharacteristic
188C2×C22⋊C4×C43C2×C411yescharacteristic
189C2×C22⋊C4×C43C2×C411yescharacteristic
190C2×C42×C43C2311yescharacteristic
191C2×C42×C43C2311yescharacteristic
192C4⋊C8×C43—21no—
193C4⋊C8×C43—21no—
194C4⋊C8×C43—21no—
195C4⋊C8×C43—21no—
196C22⋊C8×C43—21no—
197C22⋊C8×C43—21no—
198C22⋊C8×C43C2311yescharacteristic
199C22⋊C8×C43C2311yescharacteristic
200C22⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43C2311yescharacteristic
202#97×C43—21no—
203#97×C43—21no—
204C4×C8×C43—21no—
205C4×C8×C43—21no—
206C24×C43C22×C411yescharacteristic
207C23×D43—21no—
208C23×D43—21no—
209C23×D43—22no—
210C23×D43—41no—
211C23×D43—42no—
212C23×D43—81no—
213C23×D43C22×C411yescharacteristic
214C23×D43C22×C411yescharacteristic
215C23×D43C22×C411yescharacteristic
216C22×C4×C43—42no—
217C22×C4×C43C22×C411yescharacteristic
218C22×C4×C43C22×C411yescharacteristic
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2411yescharacteristic
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—42no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—81no—
233C22×Dic43C22×C411yescharacteristic
234C22×Dic43C22×C411yescharacteristic
235C22×Dic43C22×C411yescharacteristic
236C22×Dic43C22×C411yescharacteristic
237C22×Dic43C22×C411yescharacteristic
238C2×D172—21no—
239C2×D172—21no—
240C2×D172—21no—
241C2×D172—21no—
242C2×D172—22no—
243C2×D172—41no—
244C2×D172—81no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—22no—
252C2×C4×D43—41no—
253C2×C4×D43—81no—
254C2×C4×D43—81no—
255C2×Dic86—21no—
256C2×Dic86—21no—
257C2×Dic86—81no—
258M16×C43—42no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—42no—
264C4⋊C4×C43C22⋊C411yescharacteristic
265C4⋊C4×C43C22⋊C411yescharacteristic
266C4⋊C4×C43C22⋊C411yescharacteristic
267C4⋊C4×C43C22⋊C411yescharacteristic
268C4⋊C4×C43C22⋊C411yescharacteristic
269C4⋊C4×C43C22⋊C411yescharacteristic
270C4⋊C4×C43C22⋊C411yescharacteristic
271C4⋊C4×C43C22⋊C411yescharacteristic
272C22⋊C4×C43C22⋊C411yescharacteristic
273C22⋊C4×C43C22⋊C411yescharacteristic
274C22⋊C4×C43C22⋊C411yescharacteristic
275C22⋊C4×C43C22⋊C411yescharacteristic
276C22⋊C4×C43C22⋊C411yescharacteristic
277C22⋊C4×C43C22⋊C411yescharacteristic
278C22⋊C4×C43C22⋊C411yescharacteristic
279C22⋊C4×C43C22⋊C411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2×D411yescharacteristic
282C42×C43C2×D411yescharacteristic
283C42×C43C2×D411yescharacteristic
284C42×C43C2×D411yescharacteristic
285C42×C43C2×D411yescharacteristic
286C42×C43C2×D411yescharacteristic
287C42×C43C2×D411yescharacteristic
288C22⋊Dic43—21no—
289C22⋊Dic43—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4—21no—
306(C2×D43)⋊C4—21no—
307(C2×D43)⋊C4—21no—
308(C2×D43)⋊C4—21no—
309(C2×D43)⋊C4—21no—
310(C2×D43)⋊C4—21no—
311(C2×D43)⋊C4—21no—
312C4⋊Dic43—21no—
313C4⋊Dic43—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—21no—
323Dic43⋊C4—21no—
324C4×Dic43—21no—
325C4×Dic43—21no—
326#10621877—42no—
327C2×C43⋊C8—21no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—21no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—42no—
332C23×C43—21no—
333C23×C43—21no—
334C23×C43—22no—
335C23×C43—41no—
336C23×C43C2×C22⋊C411yescharacteristic
337C23×C43C2×C22⋊C411yescharacteristic
338C23×C43C23×C411yescharacteristic
339C22×D43—21no—
340C22×D43—21no—
341C22×D43—21no—
342C22×D43—21no—
343C22×D43—21no—
344C22×D43—21no—
345C22×D43—21no—
346C22×D43—21no—
347C22×D43—42no—
348C22×D43—42no—
349C22×D43—41no—
350C22×D43—41no—
351C22×D43—42no—
352C22×D43—42no—
353C22×D43—41no—
354C22×D43—41no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—81no—
358C22×D43—81no—
359C22×D43—84no—
360C22×D43—84no—
361C22×D43#13112yes—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
364C2×C4×C43—21no—
365C2×C4×C43—21no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43C2×C22⋊C411yescharacteristic
375C2×C4×C43C2×C22⋊C411yescharacteristic
376C2×C4×C43C2×C22⋊C411yescharacteristic
377C2×C4×C43C2×C22⋊C411yescharacteristic
378C2×C4×C43C2×C22⋊C411yescharacteristic
379C2×C4×C43C2×C22⋊C411yescharacteristic
380C2×C4×C43C2×C22⋊C411yescharacteristic
381C2×C4×C43C2×C22⋊C411yescharacteristic
382C2×C4×C43C2×C22⋊C411yescharacteristic
383C2×C4×C43C2×C22⋊C411yescharacteristic
384C2×C4×C43C22×D411yescharacteristic
385C2×C4×C43C22×D411yescharacteristic
386C22⋊D43—42no—
387C22⋊D43—42no—
388C2×Dic43—21no—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43—21no—
392C2×Dic43—21no—
393C2×Dic43—21no—
394C2×Dic43—21no—
395C2×Dic43—41no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—81no—
400C2×Dic43—81no—
401D172—42no—
402D172—42no—
403D172—81no—
404D172—81no—
405C4×D43—42no—
406C4×D43—42no—
407C4×D43—81no—
408C4×D43—81no—
409C4×D43—81no—
410C4×D43—81no—
411Dic86—81no—
412Dic86—81no—
413C8×C43—41no—
414C8×C43—41no—
415C8×C43—41no—
416C8×C43—41no—
417C43⋊C8—41no—
418C43⋊C8—41no—
419C43⋊C8—41no—
420C43⋊C8—41no—
421#17412—431nomaximal, Sylow
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—21no—
425C22×C43—21no—
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—21no—
429C22×C43—42no—
430C22×C43—42no—
431C22×C43#41012yes—
432C22×C43C22×C22⋊C411yescharacteristic
433C22×C43C2×#13111yescharacteristic
434C22×C43#56811yescharacteristic
435C2×D43—22no—
436C2×D43—42no—
437C2×D43—41no—
438C2×D43—41no—
439C2×D43—42no—
440C2×D43—41no—
441C2×D43—41no—
442C2×D43—41no—
443C2×D43—41no—
444C2×D43—41no—
445C2×D43—41no—
446C2×D43—84no—
447C2×D43—84no—
448C2×D43—81no—
449C2×D43—81no—
450C2×D43—81no—
451C2×D43—81no—
452C4×C43—21no—
453C4×C43—21no—
454C4×C43—21no—
455C4×C43—21no—
456C4×C43—21no—
457C4×C43—21no—
458C4×C43—21no—
459C4×C43—21no—
460C4×C43—21no—
461C4×C43—21no—
462C4×C43—21no—
463C4×C43—21no—
464Dic43—41no—
465Dic43—41no—
466Dic43—41no—
467Dic43—41no—
468Dic43—41no—
469C2×#551—431no—
470#2924—431no—
471#2924D4311yescharacteristic, complemented
472#1473—431no—
473#1473—431no—
474#1469—431no—
475#1469—431no—
476#1468—431no—
477#1468—431no—
478#1466—431no—
479#1464—431no—
480#1462—431no—
481#1460—431no—
482#1458—431no—
483C2×#323—431no—
484C2×C43—21no—
485C2×C43—21no—
486C2×C43—22no—
487C2×C43—41no—
488C2×C43#288011yescharacteristic
489C2×C43C2×#41011yescharacteristic
490C2×C43#288811yescharacteristic
491D43—42no—
492D43—81no—
493D43—81no—
494#551—861no—
495#551—861no—
496#551—861no—
497#551—861no—
498#551—861no—
499#551—861no—
500#551—861no—
501#551—861no—
502C2×#126—431no—
503C2×#126—431no—
504C2×#124—431no—
505C2×#123—431no—
506C2×#123—431no—
507C2×#123—431no—
508C2×C22⋊Q8—431no—
509C2×C22⋊Q8—431no—
510C2×#120—431no—
511C2×C4×D4—431no—
512C2×C4×D4—431no—
513C2×#117—431no—
514C2×#117C2×D4311yescharacteristic
515C22×C22⋊C4—431no—
516C22×C22⋊C4—431no—
517#433—21no—
518#433—21no—
519#433—861no—
520#433—861no—
521#432—431no—
522#432—431no—
523#432C2×D4311yescharacteristic, complemented
524#432C2×D4311yescharacteristic, complemented
525#431—431no—
526#431—431no—
527#431C2×D4311yescharacteristic, complemented
528#431C2×D4311yescharacteristic, complemented
529#424—21no—
530#424—861no—
531#407—431no—
532#407C2×D4311yescharacteristic
533C2×C22⋊C8—431no—
534C2×C22⋊C8C2×D4311yescharacteristic
535#405—21no—
536#405—861no—
537#324—431no—
538#324—431no—
539#324—431no—
540#324—431no—
541#323—431no—
542#323—431no—
543#323—431no—
544#323—431no—
545#323—431no—
546#323—431no—
547#323—431no—
548#323—431no—
549#323—431no—
550#323—431no—
551#323—431no—
552#323—431no—
553C43#1741211yescharacteristic, complemented, Sylow
554C25—431no—
555C22×Q8—431no—
556C22×D4—431no—
557C22×D4—431no—
558C22×D4—431no—
559C23×C4—431no—
560C23×C4—431no—
561C23×C4—431no—
562C23×C4—431no—
563C23×C4C22×D4311yescharacteristic
564C2×M16—21no—
565C2×M16—861no—
566C22×C8—21no—
567C22×C8—861no—
568#126—861no—
569#126—861no—
570#126—861no—
571#126—861no—
572#126—861no—
573#126—861no—
574#126—861no—
575#126—861no—
576#124—861no—
577#124—861no—
578#124—861no—
579#124—861no—
580#123—861no—
581#123—861no—
582#123—861no—
583#123—861no—
584#123—861no—
585#123—861no—
586#123—861no—
587#123—861no—
588#123—861no—
589#123—861no—
590#123—861no—
591#123—861no—
592C22⋊Q8—861no—
593C22⋊Q8—861no—
594C22⋊Q8—861no—
595C22⋊Q8—861no—
596C22⋊Q8—861no—
597C22⋊Q8—861no—
598C22⋊Q8—861no—
599C22⋊Q8—861no—
600#120—861no—
601#120—861no—
602#120—861no—
603#120—861no—
604C4×D4—861no—
605C4×D4—861no—
606C4×D4—861no—
607C4×D4—861no—
608C4×D4—861no—
609C4×D4—861no—
610C4×D4—861no—
611C4×D4—861no—
612#117—861no—
613#117—861no—
614#117—861no—
615#117—861no—
616#117D17211yescharacteristic
617#117D17211yescharacteristic
618#117D17211yescharacteristic
619#117D17211yescharacteristic
620#117C22⋊D4311yescharacteristic
621#117C22⋊D4311yescharacteristic
622#117C22⋊D4311yescharacteristic
623#117C22⋊D4311yescharacteristic
624C2×C4⋊C4—431no—
625C2×C4⋊C4—431no—
626C2×C4⋊C4—431no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—431no—
630C2×C4⋊C4C4×D4311yescharacteristic
631C2×C4⋊C4C4×D4311yescharacteristic
632C2×C22⋊C4—431no—
633C2×C22⋊C4—431no—
634C2×C22⋊C4—431no—
635C2×C22⋊C4—431no—
636C2×C22⋊C4—431no—
637C2×C22⋊C4—431no—
638C2×C22⋊C4—431no—
639C2×C22⋊C4—431no—
640C2×C22⋊C4—431no—
641C2×C22⋊C4—431no—
642C2×C22⋊C4—431no—
643C2×C22⋊C4—431no—
644C2×C22⋊C4—861no—
645C2×C22⋊C4—861no—
646C2×C22⋊C4—861no—
647C2×C22⋊C4—861no—
648C2×C22⋊C4—861no—
649C2×C22⋊C4—861no—
650C2×C22⋊C4—861no—
651C2×C22⋊C4—861no—
652C2×C22⋊C4C4×D4311yescharacteristic
653C2×C22⋊C4C4×D4311yescharacteristic
654C2×C42—431no—
655C2×C42C22×D4311yescharacteristic
656C2×C42C22×D4311yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—21no—
660C4⋊C8—21no—
661C4⋊C8—861no—
662C4⋊C8—861no—
663C4⋊C8—861no—
664C4⋊C8—861no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—431no—
668C22⋊C8—431no—
669C22⋊C8—431no—
670C22⋊C8—431no—
671C22⋊C8—861no—
672C22⋊C8—861no—
673C22⋊C8C22×D4311yescharacteristic
674C22⋊C8C22×D4311yescharacteristic
675C22⋊C8C22×D4311yescharacteristic
676C22⋊C8C22×D4311yescharacteristic
677#97—21no—
678#97—21no—
679#97—861no—
680#97—861no—
681C4×C8—21no—
682C4×C8—21no—
683C4×C8—861no—
684C4×C8—861no—
685C24—431no—
686C24—431no—
687C24—431no—
688C24—862no—
689C24—861no—
690C24—861no—
691C24—3441no—
692C24—1721no—
693C24—1722no—
694C24C2×C4×D4311yescharacteristic
695C2×Q8—861no—
696C2×Q8—861no—
697C2×Q8—3441no—
698C2×D4—862no—
699C2×D4—861no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—861no—
704C2×D4—861no—
705C2×D4—3441no—
706C2×D4—1721no—
707C2×D4—1722no—
708C22×C4—42no—
709C22×C4—431no—
710C22×C4—431no—
711C22×C4—431no—
712C22×C4—431no—
713C22×C4—431no—
714C22×C4—862no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—3441no—
724C22×C4—3441no—
725C22×C4—3441no—
726C22×C4—1721no—
727C22×C4C2×C4×D4311yescharacteristic
728C22×C4C2×C4×D4311yescharacteristic
729C22×C4C2×C4×D4311yescharacteristic
730C22×C4C2×C4×D4311yescharacteristic
731C22×C4C2×C4×D4311yescharacteristic
732C22×C4C2×D17211yescharacteristic
733C22×C4C2×D17211yescharacteristic
734C22×C4C2×C22⋊D4311yescharacteristic
735C22×C4C2×C22⋊D4311yescharacteristic
736C22×C4C23×D4311yescharacteristic
737M16—42no—
738M16—1722no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—42no—
744C2×C8—861no—
745C2×C8—861no—
746C2×C8—861no—
747C2×C8—861no—
748C2×C8—1722no—
749C4⋊C4—861no—
750C4⋊C4—861no—
751C4⋊C4—861no—
752C4⋊C4—861no—
753C4⋊C4—861no—
754C4⋊C4—861no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4(C2×D43)⋊C411yescharacteristic
762C4⋊C4(C2×D43)⋊C411yescharacteristic
763C4⋊C4(C2×D43)⋊C411yescharacteristic
764C4⋊C4(C2×D43)⋊C411yescharacteristic
765C4⋊C4(C2×D43)⋊C411yescharacteristic
766C4⋊C4(C2×D43)⋊C411yescharacteristic
767C4⋊C4(C2×D43)⋊C411yescharacteristic
768C4⋊C4(C2×D43)⋊C411yescharacteristic
769C22⋊C4—861no—
770C22⋊C4—861no—
771C22⋊C4—861no—
772C22⋊C4—861no—
773C22⋊C4—861no—
774C22⋊C4—861no—
775C22⋊C4—861no—
776C22⋊C4—861no—
777C22⋊C4—861no—
778C22⋊C4—861no—
779C22⋊C4—861no—
780C22⋊C4—861no—
781C22⋊C4—861no—
782C22⋊C4—861no—
783C22⋊C4—861no—
784C22⋊C4—861no—
785C22⋊C4—861no—
786C22⋊C4—861no—
787C22⋊C4—861no—
788C22⋊C4—861no—
789C22⋊C4—861no—
790C22⋊C4—861no—
791C22⋊C4—861no—
792C22⋊C4—861no—
793C22⋊C4(C2×D43)⋊C411yescharacteristic
794C22⋊C4(C2×D43)⋊C411yescharacteristic
795C22⋊C4(C2×D43)⋊C411yescharacteristic
796C22⋊C4(C2×D43)⋊C411yescharacteristic
797C22⋊C4(C2×D43)⋊C411yescharacteristic
798C22⋊C4(C2×D43)⋊C411yescharacteristic
799C22⋊C4(C2×D43)⋊C411yescharacteristic
800C22⋊C4(C2×D43)⋊C411yescharacteristic
801C42—861no—
802C42—861no—
803C42C2×D17211yescharacteristic
804C42C2×D17211yescharacteristic
805C42C2×D17211yescharacteristic
806C42C2×D17211yescharacteristic
807C42C2×C22⋊D4311yescharacteristic
808C42C2×C22⋊D4311yescharacteristic
809C42C2×C22⋊D4311yescharacteristic
810C42C2×C22⋊D4311yescharacteristic
811C23—22no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—432no—
816C23—861no—
817C23—861no—
818C23—861no—
819C23—861no—
820C23—861no—
821C23—861no—
822C23—861no—
823C23—861no—
824C23—3441no—
825C23—3441no—
826C23—3444no—
827C23—3444no—
828C23—1722no—
829C23—1722no—
830C23—1721no—
831C23—1721no—
832C23—1721no—
833C23—1721no—
834C23—1722no—
835C23—1721no—
836C23—1721no—
837C23—1722no—
838C23C2×(C2×D43)⋊C411yescharacteristic
839C23C2×(C2×D43)⋊C411yescharacteristic
840C23C22×C4×D4311yescharacteristic
841Q8—3441no—
842Q8—3441no—
843D4—3441no—
844D4—3441no—
845D4—1722no—
846D4—1722no—
847D4—1722no—
848D4—1722no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—861no—
862C2×C4—861no—
863C2×C4—861no—
864C2×C4—861no—
865C2×C4—861no—
866C2×C4—861no—
867C2×C4—861no—
868C2×C4—3441no—
869C2×C4—3441no—
870C2×C4—3441no—
871C2×C4—3441no—
872C2×C4—3441no—
873C2×C4—3441no—
874C2×C4—1722no—
875C2×C4—1722no—
876C2×C4—1721no—
877C2×C4—1721no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4C2×(C2×D43)⋊C411yescharacteristic
881C2×C4C2×(C2×D43)⋊C411yescharacteristic
882C2×C4C2×(C2×D43)⋊C411yescharacteristic
883C2×C4C2×(C2×D43)⋊C411yescharacteristic
884C2×C4C2×(C2×D43)⋊C411yescharacteristic
885C2×C4C2×(C2×D43)⋊C411yescharacteristic
886C2×C4C2×(C2×D43)⋊C411yescharacteristic
887C2×C4C2×(C2×D43)⋊C411yescharacteristic
888C2×C4C2×(C2×D43)⋊C411yescharacteristic
889C2×C4C2×(C2×D43)⋊C411yescharacteristic
890C2×C4C22×C22⋊D4311yescharacteristic
891C2×C4C22×D17211yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C8—1721no—
897C8—1721no—
898C8—1721no—
899C8—1721no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—42no—
908C22—42no—
909C22—862no—
910C22—3441no—
911C22—3441no—
912C22—3441no—
913C22—3441no—
914C22—3444no—
915C22—3444no—
916C22—1722no—
917C22—1722no—
918C22—1721no—
919C22—1721no—
920C22—1721no—
921C22—1721no—
922C22—1721no—
923C22—1721no—
924C22—1721no—
925C22—1721no—
926C22#1458287212yes—
927C22C22×(C2×D43)⋊C411yescharacteristic
928C22#131×D4311yescharacteristic
929C22#1458366411yescharacteristic
930C4—21no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—1721no—
943C4—1721no—
944C4—1721no—
945C4—1721no—
946C4—1721no—
947C2—21no—
948C2—21no—
949C2—22no—
950C2—41no—
951C2—3441no—
952C2—3441no—
953C2—1722no—
954C2#1914304211yescharacteristic
955C2C2×#1458287211yescharacteristic
956C2#1914307311yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2924C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063295C4
cosocleC22×C4×C43C24
hypercenter#2924D43
hypocenterC43#17412
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #19143253C2semidirect
3. #19132965C2semidirect
4. #19132962C2semidirect
5. #19132948C2semidirect
6. #19132946C2semidirect
7. #19132944C2semidirect
8. #19132941C2semidirect
9. #19132935C2semidirect
10. #19132927C2semidirect
11. #19132921C2semidirect
12. #19132915C2semidirect
13. #19132907C2semidirect
14. C2×#14582622C2semidirect
15. C43×#2924C2semidirect
40. #14582956C22semidirect
41. #14582956C22semidirect
42. #14582952C22semidirect
43. #14582952C22semidirect
48. #14582624C22semidirect
49. #14582624C22semidirect
50. #14582624C22semidirect
51. #14582624C22semidirect
60. #14582622C22semidirect
61. #14582622C22semidirect
62. #14582622C22semidirect
63. #14582622C22semidirect
67. C43×#432C22semidirect
68. C43×#432C22semidirect
69. C43×#431C22semidirect
70. C43×#431C22semidirect
471. #2924D43semidirect
523. #432C2×D43semidirect
524. #432C2×D43semidirect
527. #431C2×D43semidirect
528. #431C2×D43semidirect
553. C43#17412semidirect

Maximal subgroups

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

subgroupindex
C2×#145835732
#191432532
#191329652
#191329622
#191329482
#191329462
#191329442
#191329412
#191329352
#191329272
#191329212
#191329152
#191329072
C2×#145826222
C43×#29242
#1741243