Finite Group Databasebeta

← #25062860

Subgroups — #25062860

Order 11008.

1346 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583538C211yesmaximal, characteristic
2#19143631C211yesmaximal, characteristic, complemented
3#19143626C211yesmaximal, characteristic, complemented
4#19132955C211yesmaximal, characteristic, complemented
5#19132953C211yesmaximal, characteristic, complemented
6#19132953C211yesmaximal, characteristic, complemented
7#19132945C211yesmaximal, characteristic, complemented
8#19132945C211yesmaximal, characteristic, complemented
9#19132934C211yesmaximal, characteristic, complemented
10#19132921C211yesmaximal, characteristic, complemented
11#19132920C211yesmaximal, characteristic, complemented
12#19132914C211yesmaximal, characteristic, complemented
13C2×#14582622C211yesmaximal, characteristic, complemented
14#323×D43C211yesmaximal, characteristic, complemented
15C43×#1471C211yesmaximal, characteristic, complemented
16C22×#10621900C411yescharacteristic
17C22×D4×D43C411yescharacteristic
18#14583538—21no—
19#14583538—21no—
20#14583538—21no—
21#14583538—21no—
22#14583538—21no—
23#14583538—21no—
24#14583538—21no—
25#14583538—21no—
26C2×#13063311C2211yescharacteristic
27C2×#13063310C411yescharacteristic
28C2×#13063306C411yescharacteristic
29C2×#13063303C411yescharacteristic
30C2×#13063298C2211yescharacteristic
31C2×#13063297C411yescharacteristic
32C2×#13063293C411yescharacteristic
33C2×#13063293C411yescharacteristic
34C2×C4×C22⋊D43C2211yescharacteristic
35C2×(C22⋊D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C2×C22⋊C4×D43C2211yescharacteristic
38#14582975—21no—
39#14582974—21no—
40#14582973—21no—
41#14582970—21no—
42#14582968—21no—
43#14582967—21no—
44C8×C22⋊D43—21no—
45(C22⋊D43)⋊C8—21no—
46#14582953C2211yescharacteristic, complemented
47#14582953C2211yescharacteristic, complemented
48#14582949C2211yescharacteristic, complemented
49#14582949C2211yescharacteristic, complemented
50#14582863C2211yescharacteristic, complemented
51#14582861C2211yescharacteristic, complemented
52#14582861C2211yescharacteristic, complemented
53C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
54C22⋊C8×D43C2211yescharacteristic, complemented
55C22⋊C8×D43C2211yescharacteristic, complemented
56#14582623C2211yescharacteristic, complemented
57#14582623C2211yescharacteristic, complemented
58#14582623C2211yescharacteristic, complemented
59#14582623C2211yescharacteristic, complemented
60#14582622C2211yescharacteristic
61#14582622C2211yescharacteristic
62#14582622C2211yescharacteristic
63#14582622C2211yescharacteristic
64#14582622C2211yescharacteristic, complemented
65#14582622C2211yescharacteristic, complemented
66#14582622C2211yescharacteristic, complemented
67#14582622C2211yescharacteristic, complemented
68C2×#121×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic, complemented
70C2×C22⋊C8×C43C2211yescharacteristic, complemented
71C43×#323C2211yescharacteristic, complemented
72C43×#323C2211yescharacteristic, complemented
73C43×#323C2211yescharacteristic, complemented
74C43×#323C2211yescharacteristic, complemented
75C24×D43C2×C411yescharacteristic
76C24×D43C2×C411yescharacteristic
77C2×#10621900—21no—
78C2×#10621900—21no—
79C2×#10621900—21no—
80C2×#10621900—21no—
81C2×#10621900—44no—
82C22×Dic86C2×C411yescharacteristic
83C22×D172C2×C411yescharacteristic
84C22×C22⋊D43C2×C411yescharacteristic
85C22×C22⋊D43C2×C411yescharacteristic
86C22×C22⋊D43C2×C411yescharacteristic
87C22×C22⋊D43C2×C411yescharacteristic
88C22×C22⋊D43C2×C411yescharacteristic
89C2×D4×D43—21no—
90C2×D4×D43—21no—
91C2×D4×D43—21no—
92C2×D4×D43—21no—
93C2×D4×D43—44no—
94C23×Dic43C2×C411yescharacteristic
95C23×Dic43C2×C411yescharacteristic
96C22×C4×D43C2×C411yescharacteristic
97C22×C4×D43C2×C411yescharacteristic
98C22×C4×D43C2311yescharacteristic
99C2×#10621877—21no—
100C2×#10621872—21no—
101C2×#10621872—21no—
102C22×C43⋊C8—21no—
103C2×C8×D43—21no—
104C2×C8×D43—21no—
105#13063311—21no—
106#13063311—21no—
107#13063311—21no—
108#13063311—21no—
109#13063310—21no—
110#13063310—21no—
111#13063310—21no—
112#13063310—21no—
113#13063306—21no—
114#13063306—21no—
115#13063306—21no—
116#13063306—21no—
117#13063303—21no—
118#13063303—21no—
119#13063303—21no—
120#13063303—21no—
121#13063298—21no—
122#13063298—21no—
123#13063298—21no—
124#13063298—21no—
125#13063297—21no—
126#13063297—21no—
127#13063297—21no—
128#13063297—21no—
129#13063293—21no—
130#13063293—21no—
131#13063293—21no—
132#13063293—21no—
133#13063293—21no—
134#13063293—21no—
135#13063293—21no—
136#13063293—21no—
137C4×C22⋊D43D411yescharacteristic
138C4×C22⋊D43D411yescharacteristic
139C4×C22⋊D43D411yescharacteristic
140C4×C22⋊D43D411yescharacteristic
141C4×C22⋊D43D411yescharacteristic
142C4×C22⋊D43D411yescharacteristic
143C4×C22⋊D43D411yescharacteristic
144C4×C22⋊D43D411yescharacteristic
145(C22⋊D43)⋊C4—21no—
146(C22⋊D43)⋊C4—21no—
147(C22⋊D43)⋊C4—21no—
148(C22⋊D43)⋊C4—21no—
149C2×Dic43⋊C4C2×C411yescharacteristic
150C2×Dic43⋊C4C2×C411yescharacteristic
151C2×Dic43⋊C4C2×C411yescharacteristic
152C2×C22⋊Dic43C2×C411yescharacteristic
153C2×C22⋊Dic43C2×C411yescharacteristic
154C2×C22⋊Dic43C2×C411yescharacteristic
155C2×(C2×D43)⋊C4—21no—
156C2×(C2×D43)⋊C4—21no—
157C2×(C2×D43)⋊C4—21no—
158C2×(C2×D43)⋊C4—21no—
159C2×(C2×D43)⋊C4C2×C411yescharacteristic
160C2×(C2×D43)⋊C4C2×C411yescharacteristic
161C2×(C2×D43)⋊C4C2×C411yescharacteristic
162C2×(C2×D43)⋊C4C2×C411yescharacteristic
163C2×(C2×D43)⋊C4C2×C411yescharacteristic
164C2×(C2×D43)⋊C4C2311yescharacteristic
165C2×(C2×D43)⋊C4C2311yescharacteristic
166C22⋊C4×D43—21no—
167C22⋊C4×D43—21no—
168C22⋊C4×D43—21no—
169C22⋊C4×D43—21no—
170C2×C4×Dic43C2311yescharacteristic
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175C22⋊(C43⋊C8)—21no—
176C22⋊(C43⋊C8)—21no—
177C22⋊(C43⋊C8)C2311yescharacteristic
178C22⋊(C43⋊C8)C2311yescharacteristic
179C22⋊(C43⋊C8)C2311yescharacteristic
180C22⋊(C43⋊C8)C2311yescharacteristic
181(C2×D43)⋊C8—21no—
182(C2×D43)⋊C8—21no—
183(C2×D43)⋊C8—21no—
184(C2×D43)⋊C8—21no—
185#13063235—21no—
186#13063235—21no—
187C8×Dic43—21no—
188C8×Dic43—21no—
189C22×D4×C43C2×C411yescharacteristic
190C22×D4×C43C2×C411yescharacteristic
191C22×D4×C43C2×C411yescharacteristic
192C23×C4×C43C2311yescharacteristic
193C2×M16×C43—21no—
194C22×C8×C43—21no—
195#121×C43—21no—
196#121×C43—21no—
197#121×C43—21no—
198#121×C43—21no—
199C2×C4⋊C4×C43C2×C411yescharacteristic
200C2×C22⋊C4×C43C2311yescharacteristic
201C2×C22⋊C4×C43C2311yescharacteristic
202C22⋊C8×C43—21no—
203C22⋊C8×C43—21no—
204C22⋊C8×C43C2311yescharacteristic
205C22⋊C8×C43C2311yescharacteristic
206C22⋊C8×C43C2311yescharacteristic
207C22⋊C8×C43C2311yescharacteristic
208C24×C43C22×C411yescharacteristic
209C24×C43C22×C411yescharacteristic
210C24×C43C22×C411yescharacteristic
211C23×D43—21no—
212C23×D43—21no—
213C23×D43—21no—
214C23×D43—21no—
215C23×D43—22no—
216C23×D43—22no—
217C23×D43—41no—
218C23×D43—41no—
219C23×D43—42no—
220C23×D43—42no—
221C23×D43—81no—
222C23×D43—81no—
223C23×D43C22×C411yescharacteristic
224C23×D43C22×C411yescharacteristic
225C23×D43C22×C411yescharacteristic
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—21no—
229C2×D4×C43—21no—
230C2×D4×C43—21no—
231C2×D4×C43—21no—
232C2×D4×C43—42no—
233C2×D4×C43—42no—
234C2×D4×C43—81no—
235C22×C4×C43—81no—
236C22×C4×C43C22×C411yescharacteristic
237C22×C4×C43C22×C411yescharacteristic
238C22×C4×C43C22×C411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43C2×D411yescharacteristic
242C22×C4×C43C2×D411yescharacteristic
243C22×C4×C43C2411yescharacteristic
244C2×C22⋊D43—24no—
245C2×C22⋊D43—21no—
246C2×C22⋊D43—21no—
247C2×C22⋊D43—21no—
248C2×C22⋊D43—21no—
249C2×C22⋊D43—21no—
250C2×C22⋊D43—21no—
251C2×C22⋊D43—21no—
252C2×C22⋊D43—21no—
253C2×C22⋊D43—22no—
254C2×C22⋊D43—41no—
255C2×C22⋊D43—42no—
256C2×C22⋊D43—42no—
257C2×C22⋊D43—81no—
258C2×C22⋊D43C22⋊C411yescharacteristic
259C2×C22⋊D43C22⋊C411yescharacteristic
260C2×C22⋊D43C22⋊C411yescharacteristic
261C2×C22⋊D43C22⋊C411yescharacteristic
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—42no—
267C22×Dic43—42no—
268C22×Dic43C22×C411yescharacteristic
269C22×Dic43C22×C411yescharacteristic
270C22×Dic43C22×C411yescharacteristic
271C22×Dic43C22×C411yescharacteristic
272C22×Dic43C22×C411yescharacteristic
273#10621900—44no—
274#10621900—44no—
275#10621900—44no—
276#10621900—44no—
277D4×D43—44no—
278D4×D43—44no—
279D4×D43—44no—
280D4×D43—44no—
281C2×D172—21no—
282C2×D172—21no—
283C2×D172—42no—
284C2×C4×D43—21no—
285C2×C4×D43—21no—
286C2×C4×D43—21no—
287C2×C4×D43—21no—
288C2×C4×D43—42no—
289C2×C4×D43—42no—
290C2×C4×D43—81no—
291C2×C4×D43C2×D411yescharacteristic
292C2×C4×D43C2×D411yescharacteristic
293C2×C4×D43C2×D411yescharacteristic
294C2×C4×D43C2×D411yescharacteristic
295C2×Dic86—21no—
296C2×Dic86—21no—
297C2×Dic86—42no—
298M16×C43—81no—
299C2×C8×C43—21no—
300C2×C8×C43—21no—
301C2×C8×C43—21no—
302C2×C8×C43—21no—
303C2×C8×C43—81no—
304C4⋊C4×C43—21no—
305C4⋊C4×C43—21no—
306C22⋊C4×C43—21no—
307C22⋊C4×C43—21no—
308C22⋊C4×C43—21no—
309C22⋊C4×C43—21no—
310C22⋊Dic43—21no—
311C22⋊Dic43—21no—
312C22⋊Dic43—21no—
313C22⋊Dic43—21no—
314C22⋊Dic43C22⋊C411yescharacteristic
315C22⋊Dic43C22⋊C411yescharacteristic
316C22⋊Dic43C22⋊C411yescharacteristic
317C22⋊Dic43C22⋊C411yescharacteristic
318(C2×D43)⋊C4—21no—
319(C2×D43)⋊C4—21no—
320(C2×D43)⋊C4—21no—
321(C2×D43)⋊C4—21no—
322(C2×D43)⋊C4—21no—
323(C2×D43)⋊C4—21no—
324(C2×D43)⋊C4—21no—
325(C2×D43)⋊C4—21no—
326(C2×D43)⋊C4—21no—
327(C2×D43)⋊C4—21no—
328(C2×D43)⋊C4—21no—
329(C2×D43)⋊C4—21no—
330(C2×D43)⋊C4C22⋊C411yescharacteristic
331(C2×D43)⋊C4C22⋊C411yescharacteristic
332(C2×D43)⋊C4C22⋊C411yescharacteristic
333(C2×D43)⋊C4C22⋊C411yescharacteristic
334Dic43⋊C4—21no—
335Dic43⋊C4—21no—
336Dic43⋊C4—21no—
337Dic43⋊C4—21no—
338Dic43⋊C4C22⋊C411yescharacteristic
339Dic43⋊C4C22⋊C411yescharacteristic
340Dic43⋊C4C22⋊C411yescharacteristic
341Dic43⋊C4C22⋊C411yescharacteristic
342C4×Dic43C2×D411yescharacteristic
343C4×Dic43C2×D411yescharacteristic
344C4×Dic43C2×D411yescharacteristic
345C4×Dic43C2×D411yescharacteristic
346#10621877—81no—
347C2×C43⋊C8—21no—
348C2×C43⋊C8—21no—
349C2×C43⋊C8—21no—
350C2×C43⋊C8—21no—
351C2×C43⋊C8—81no—
352#10621872—81no—
353#10621872—81no—
354C8×D43—81no—
355C8×D43—81no—
356C23×C43—21no—
357C23×C43—21no—
358C23×C43—22no—
359C23×C43—21no—
360C23×C43—21no—
361C23×C43—21no—
362C23×C43—21no—
363C23×C43—21no—
364C23×C43—21no—
365C23×C43—41no—
366C23×C43—41no—
367C23×C43—41no—
368C23×C43—41no—
369C23×C43—41no—
370C23×C43C2×C22⋊C411yescharacteristic
371C23×C43C2×C22⋊C411yescharacteristic
372C23×C43C23×C411yescharacteristic
373C22×D43—21no—
374C22×D43—21no—
375C22×D43—21no—
376C22×D43—21no—
377C22×D43—22no—
378C22×D43—21no—
379C22×D43—21no—
380C22×D43—21no—
381C22×D43—41no—
382C22×D43—42no—
383C22×D43—42no—
384C22×D43—42no—
385C22×D43—42no—
386C22×D43—42no—
387C22×D43—41no—
388C22×D43—41no—
389C22×D43—42no—
390C22×D43—42no—
391C22×D43—42no—
392C22×D43—41no—
393C22×D43—41no—
394C22×D43—81no—
395C22×D43—81no—
396C22×D43—81no—
397C22×D43—81no—
398C22×D43—84no—
399C22×D43—84no—
400C22×D43—84no—
401C22×D43—84no—
402C22×D43C2×C22⋊C411yescharacteristic
403C22×D43C2×C22⋊C411yescharacteristic
404C22×D43#13112yes—
405D4×C43—42no—
406D4×C43—42no—
407D4×C43—42no—
408D4×C43—42no—
409D4×C43—81no—
410D4×C43—81no—
411C2×C4×C43—21no—
412C2×C4×C43—21no—
413C2×C4×C43—41no—
414C2×C4×C43—41no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43C2×C22⋊C411yescharacteristic
422C2×C4×C43C2×C22⋊C411yescharacteristic
423C2×C4×C43C22×D411yescharacteristic
424C2×C4×C43C22×D411yescharacteristic
425C22⋊D43—22no—
426C22⋊D43—22no—
427C22⋊D43—22no—
428C22⋊D43—42no—
429C22⋊D43—42no—
430C22⋊D43—42no—
431C22⋊D43—42no—
432C22⋊D43—42no—
433C22⋊D43—42no—
434C22⋊D43—81no—
435C22⋊D43—81no—
436C22⋊D43#10014yes—
437C2×Dic43—21no—
438C2×Dic43—21no—
439C2×Dic43—22no—
440C2×Dic43—21no—
441C2×Dic43—21no—
442C2×Dic43—41no—
443C2×Dic43—42no—
444C2×Dic43—42no—
445C2×Dic43—42no—
446C2×Dic43—42no—
447C2×Dic43—41no—
448C2×Dic43—41no—
449C2×Dic43C2×C22⋊C411yescharacteristic
450C2×Dic43C2×C22⋊C411yescharacteristic
451C2×Dic43C2×C22⋊C411yescharacteristic
452C2×Dic43C2×C22⋊C411yescharacteristic
453C2×Dic43C2×C22⋊C411yescharacteristic
454C2×Dic43C2×C22⋊C411yescharacteristic
455D172—42no—
456D172—42no—
457C4×D43—41no—
458C4×D43—41no—
459C4×D43—41no—
460C4×D43—41no—
461C4×D43—42no—
462C4×D43—42no—
463C4×D43—42no—
464C4×D43—42no—
465Dic86—42no—
466Dic86—42no—
467C8×C43—41no—
468C8×C43—41no—
469C8×C43—41no—
470C8×C43—41no—
471C43⋊C8—41no—
472C43⋊C8—41no—
473C43⋊C8—41no—
474C43⋊C8—41no—
475#17421—431nomaximal, Sylow
476C22×C43—21no—
477C22×C43—21no—
478C22×C43—21no—
479C22×C43—21no—
480C22×C43—21no—
481C22×C43—21no—
482C22×C43—21no—
483C22×C43—42no—
484C22×C43—42no—
485C22×C43—41no—
486C22×C43—41no—
487C22×C43—41no—
488C22×C43—41no—
489C22×C43—41no—
490C22×C43—41no—
491C22×C43—81no—
492C22×C43—81no—
493C22×C43—81no—
494C22×C43—81no—
495C22×C43C2×#10012yes—
496C22×C43C22×C22⋊C411yescharacteristic
497C22×C43C2×#13111yescharacteristic
498C22×C43#56811yescharacteristic
499C2×D43—21no—
500C2×D43—21no—
501C2×D43—22no—
502C2×D43—21no—
503C2×D43—21no—
504C2×D43—21no—
505C2×D43—42no—
506C2×D43—42no—
507C2×D43—42no—
508C2×D43—41no—
509C2×D43—41no—
510C2×D43—42no—
511C2×D43—41no—
512C2×D43—41no—
513C2×D43—41no—
514C2×D43—84no—
515C2×D43—84no—
516C2×D43—84no—
517C2×D43—84no—
518C2×D43—81no—
519C2×D43—81no—
520C2×D43C2×#10012yes—
521C4×C43—21no—
522C4×C43—21no—
523C4×C43—21no—
524C4×C43—21no—
525C4×C43—41no—
526C4×C43—41no—
527Dic43—21no—
528Dic43—21no—
529Dic43—21no—
530Dic43—21no—
531Dic43—21no—
532Dic43—41no—
533Dic43—41no—
534Dic43C2×#10012yes—
535C2×#546—431no—
536#2974—431no—
537#2974—431no—
538#1471—431no—
539#1471—431no—
540#1471—431no—
541#1471D4311yescharacteristic, complemented
542#1469—431no—
543#1469—431no—
544#1466—431no—
545#1462—431no—
546#1462—431no—
547#1460—431no—
548C2×#323—431no—
549C2×#323—431no—
550C2×C43—21no—
551C2×C43—21no—
552C2×C43—22no—
553C2×C43—41no—
554C2×C43—81no—
555C2×C43—81no—
556C2×C43#288011yescharacteristic
557C2×C43#288311yescharacteristic
558C2×C43C22×#10011yescharacteristic
559D43—22no—
560D43—41no—
561D43—42no—
562D43—81no—
563C22×#41—431no—
564C23×D4—431no—
565#546—861no—
566#546—861no—
567#546—861no—
568#546—861no—
569#546—861no—
570#546—861no—
571#546—861no—
572#546—861no—
573C2×#124—431no—
574C2×#123—431no—
575C2×#123—431no—
576C2×C22⋊Q8—431no—
577C2×#121—431no—
578C2×#121—431no—
579C2×#121C2×D4311yescharacteristic
580C2×#120—431no—
581C2×#120—431no—
582C2×C4×D4—431no—
583C2×C4×D4—431no—
584C22×C22⋊C4—431no—
585C22×C22⋊C4—431no—
586#436—861no—
587#436—861no—
588#435—861no—
589#435—861no—
590#435—861no—
591#435—861no—
592C8×D4—861no—
593C8×D4—861no—
594#432—431no—
595#432—431no—
596#431—431no—
597#431—431no—
598#407—431no—
599#407—431no—
600#407—431no—
601#407C2×D4311yescharacteristic, complemented
602C2×C22⋊C8—431no—
603C2×C22⋊C8—431no—
604C2×C22⋊C8—431no—
605C2×C22⋊C8C2×D4311yescharacteristic, complemented
606#323—431no—
607#323—431no—
608#323—431no—
609#323—431no—
610#323—431no—
611#323—431no—
612#323—431no—
613#323—431no—
614#323—431no—
615#323—431no—
616#323—431no—
617#323—431no—
618#323C2×D4311yescharacteristic, complemented
619#323C2×D4311yescharacteristic, complemented
620#323C2×D4311yescharacteristic, complemented
621#323C2×D4311yescharacteristic, complemented
622C43#1742111yescharacteristic, complemented, Sylow
623C25—431no—
624C25—431no—
625C2×#41—861no—
626C2×#41—861no—
627C2×#41—861no—
628C2×#41—861no—
629C2×#41—1724no—
630C22×Q8—431no—
631C22×D4—431no—
632C22×D4—431no—
633C22×D4—431no—
634C22×D4—431no—
635C22×D4—431no—
636C22×D4—431no—
637C22×D4—861no—
638C22×D4—861no—
639C22×D4—861no—
640C22×D4—861no—
641C22×D4—1724no—
642C22×D4C4×D4311yescharacteristic
643C22×D4C4×D4311yescharacteristic
644C22×D4C4×D4311yescharacteristic
645C23×C4—431no—
646C23×C4—431no—
647C23×C4—431no—
648C23×C4—431no—
649C23×C4—431no—
650C23×C4C22×D4311yescharacteristic
651C2×M16—21no—
652C2×M16—861no—
653C2×M16—861no—
654C2×M16—861no—
655C22×C8—21no—
656C22×C8—861no—
657C22×C8—861no—
658C22×C8—861no—
659#124—861no—
660#124—861no—
661#124—861no—
662#124—861no—
663#123—861no—
664#123—861no—
665#123—861no—
666#123—861no—
667#123—861no—
668#123—861no—
669#123—861no—
670#123—861no—
671C22⋊Q8—861no—
672C22⋊Q8—861no—
673C22⋊Q8—861no—
674C22⋊Q8—861no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—861no—
680#121—861no—
681#121—861no—
682#121—861no—
683#121—861no—
684#121—861no—
685#121—861no—
686#121—861no—
687#120—861no—
688#120—861no—
689#120—861no—
690#120—861no—
691#120—861no—
692#120—861no—
693#120—861no—
694#120—861no—
695C4×D4—431no—
696C4×D4—431no—
697C4×D4—431no—
698C4×D4—431no—
699C4×D4—431no—
700C4×D4—431no—
701C4×D4—431no—
702C4×D4—431no—
703C4×D4—861no—
704C4×D4—861no—
705C4×D4—861no—
706C4×D4—861no—
707C2×C4⋊C4—431no—
708C2×C4⋊C4—431no—
709C2×C4⋊C4—431no—
710C2×C4⋊C4C4×D4311yescharacteristic
711C2×C22⋊C4—431no—
712C2×C22⋊C4—431no—
713C2×C22⋊C4—431no—
714C2×C22⋊C4—431no—
715C2×C22⋊C4—431no—
716C2×C22⋊C4—431no—
717C2×C22⋊C4—431no—
718C2×C22⋊C4—431no—
719C2×C22⋊C4—431no—
720C2×C22⋊C4—431no—
721C2×C22⋊C4—861no—
722C2×C22⋊C4—861no—
723C2×C22⋊C4—861no—
724C2×C22⋊C4—861no—
725C2×C22⋊C4—861no—
726C2×C22⋊C4—861no—
727C2×C22⋊C4—861no—
728C2×C22⋊C4—861no—
729C2×C22⋊C4C22×D4311yescharacteristic
730C2×C22⋊C4C22×D4311yescharacteristic
731C2×C42—431no—
732C4⋊C8—861no—
733C4⋊C8—861no—
734C4⋊C8—861no—
735C4⋊C8—861no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738C22⋊C8—431no—
739C22⋊C8—431no—
740C22⋊C8—431no—
741C22⋊C8—431no—
742C22⋊C8—861no—
743C22⋊C8—861no—
744C22⋊C8—861no—
745C22⋊C8—861no—
746C22⋊C8—861no—
747C22⋊C8—861no—
748C22⋊C8C22×D4311yescharacteristic
749C22⋊C8C22×D4311yescharacteristic
750C22⋊C8C22×D4311yescharacteristic
751C22⋊C8C22×D4311yescharacteristic
752#97—861no—
753#97—861no—
754C4×C8—861no—
755C4×C8—861no—
756C24—431no—
757C24—431no—
758C24—431no—
759C24—862no—
760C24—862no—
761C24—861no—
762C24—861no—
763C24—861no—
764C24—861no—
765C24—3441no—
766C24—3441no—
767C24—1721no—
768C24—1721no—
769C24—1722no—
770C24—1722no—
771C24C2×C4×D4311yescharacteristic
772C24C2×C4×D4311yescharacteristic
773C24C2×C4×D4311yescharacteristic
774#41—1724no—
775#41—1724no—
776#41—1724no—
777#41—1724no—
778C2×Q8—861no—
779C2×Q8—861no—
780C2×Q8—1722no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—81no—
790C2×D4—431no—
791C2×D4—431no—
792C2×D4—431no—
793C2×D4—431no—
794C2×D4—861no—
795C2×D4—861no—
796C2×D4—861no—
797C2×D4—861no—
798C2×D4—861no—
799C2×D4—861no—
800C2×D4—861no—
801C2×D4—861no—
802C2×D4—864no—
803C2×D4—861no—
804C2×D4—861no—
805C2×D4—862no—
806C2×D4—3441no—
807C2×D4—1722no—
808C2×D4—1721no—
809C2×D4—1722no—
810C2×D4—1724no—
811C2×D4—1724no—
812C2×D4—1724no—
813C2×D4—1724no—
814C2×D4—1722no—
815C22×C4—81no—
816C22×C4—431no—
817C22×C4—431no—
818C22×C4—431no—
819C22×C4—431no—
820C22×C4—431no—
821C22×C4—431no—
822C22×C4—431no—
823C22×C4—431no—
824C22×C4—431no—
825C22×C4—861no—
826C22×C4—861no—
827C22×C4—861no—
828C22×C4—861no—
829C22×C4—861no—
830C22×C4—861no—
831C22×C4—861no—
832C22×C4—861no—
833C22×C4—3441no—
834C22×C4—1722no—
835C22×C4—1722no—
836C22×C4—1722no—
837C22×C4—1722no—
838C22×C4C2×C4×D4311yescharacteristic
839C22×C4C2×C4×D4311yescharacteristic
840C22×C4C2×C4×D4311yescharacteristic
841C22×C4D4×D4311yescharacteristic
842C22×C4D4×D4311yescharacteristic
843C22×C4D4×D4311yescharacteristic
844C22×C4D4×D4311yescharacteristic
845C22×C4C23×D4311yescharacteristic
846M16—81no—
847M16—3441no—
848M16—3441no—
849M16—3441no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—81no—
855C2×C8—861no—
856C2×C8—861no—
857C2×C8—861no—
858C2×C8—861no—
859C2×C8—3441no—
860C2×C8—3441no—
861C2×C8—3441no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—431no—
865C4⋊C4—431no—
866C4⋊C4—431no—
867C4⋊C4—431no—
868C4⋊C4—861no—
869C4⋊C4—861no—
870C4⋊C4—861no—
871C4⋊C4—861no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—431no—
877C22⋊C4—431no—
878C22⋊C4—431no—
879C22⋊C4—431no—
880C22⋊C4—431no—
881C22⋊C4—431no—
882C22⋊C4—431no—
883C22⋊C4—431no—
884C22⋊C4—861no—
885C22⋊C4—861no—
886C22⋊C4—861no—
887C22⋊C4—861no—
888C22⋊C4—861no—
889C22⋊C4—861no—
890C22⋊C4—861no—
891C22⋊C4—861no—
892C22⋊C4—861no—
893C22⋊C4—861no—
894C22⋊C4—861no—
895C22⋊C4—861no—
896C22⋊C4—861no—
897C22⋊C4—861no—
898C22⋊C4—861no—
899C22⋊C4—861no—
900C42—431no—
901C42—431no—
902C42—431no—
903C42—431no—
904C23—22no—
905C23—21no—
906C23—21no—
907C23—21no—
908C23—21no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—431no—
919C23—431no—
920C23—432no—
921C23—862no—
922C23—861no—
923C23—861no—
924C23—861no—
925C23—861no—
926C23—861no—
927C23—861no—
928C23—861no—
929C23—3441no—
930C23—3441no—
931C23—3441no—
932C23—3441no—
933C23—3444no—
934C23—3444no—
935C23—3444no—
936C23—3444no—
937C23—1721no—
938C23—1722no—
939C23—1722no—
940C23—1721no—
941C23—1721no—
942C23—1722no—
943C23—1721no—
944C23—1721no—
945C23—1722no—
946C23—1722no—
947C23—1722no—
948C23—1722no—
949C23—1722no—
950C23C22⋊C4×D4311yescharacteristic
951C23C22⋊C4×D4311yescharacteristic
952C23C22×C4×D4311yescharacteristic
953Q8—1722no—
954Q8—1722no—
955D4—42no—
956D4—42no—
957D4—42no—
958D4—42no—
959D4—81no—
960D4—81no—
961D4—434no—
962D4—862no—
963D4—862no—
964D4—862no—
965D4—3441no—
966D4—3441no—
967D4—1722no—
968D4—1722no—
969D4—1722no—
970D4—1722no—
971D4—1722no—
972D4—1722no—
973D4—1722no—
974D4—1722no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—431no—
986C2×C4—431no—
987C2×C4—431no—
988C2×C4—431no—
989C2×C4—431no—
990C2×C4—431no—
991C2×C4—862no—
992C2×C4—861no—
993C2×C4—861no—
994C2×C4—861no—
995C2×C4—861no—
996C2×C4—1721no—
997C2×C4—1721no—
998C2×C4—1721no—
999C2×C4—1721no—
1000C2×C4—1722no—
1001C2×C4—1722no—
1002C2×C4—1722no—
1003C2×C4—1722no—
1004C2×C4—1722no—
1005C2×C4—1721no—
1006C2×C4—1722no—
1007C2×C4—1722no—
1008C2×C4—1722no—
1009C2×C4—1721no—
1010C2×C4—1721no—
1011C2×C4C22⋊C4×D4311yescharacteristic
1012C2×C4C22⋊C4×D4311yescharacteristic
1013C2×C4C2×D4×D4311yescharacteristic
1014C2×C4C2×D4×D4311yescharacteristic
1015C8—41no—
1016C8—41no—
1017C8—41no—
1018C8—41no—
1019C8—1721no—
1020C8—1721no—
1021C8—1721no—
1022C8—1721no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—21no—
1030C22—42no—
1031C22—42no—
1032C22—41no—
1033C22—41no—
1034C22—41no—
1035C22—41no—
1036C22—41no—
1037C22—41no—
1038C22—81no—
1039C22—81no—
1040C22—81no—
1041C22—81no—
1042C22—432no—
1043C22—861no—
1044C22—861no—
1045C22—862no—
1046C22—861no—
1047C22—861no—
1048C22—861no—
1049C22—3441no—
1050C22—3441no—
1051C22—3444no—
1052C22—3444no—
1053C22—3444no—
1054C22—3444no—
1055C22—1722no—
1056C22—1722no—
1057C22—1722no—
1058C22—1722no—
1059C22—1721no—
1060C22—1721no—
1061C22—1721no—
1062C22—1721no—
1063C22—1721no—
1064C22#100×D4312yes—
1065C22C2×C22⋊C4×D4311yescharacteristic
1066C22#131×D4311yescharacteristic
1067C22#1458366411yescharacteristic
1068C4—21no—
1069C4—21no—
1070C4—21no—
1071C4—21no—
1072C4—41no—
1073C4—41no—
1074C4—432no—
1075C4—861no—
1076C4—861no—
1077C4—861no—
1078C4—861no—
1079C4—861no—
1080C4—1721no—
1081C4—1721no—
1082C2—21no—
1083C2—21no—
1084C2—22no—
1085C2—41no—
1086C2—81no—
1087C2—81no—
1088C2—862no—
1089C2—3441no—
1090C2—1721no—
1091C2—1722no—
1092C2#1914304311yescharacteristic
1093C2#1914305311yescharacteristic
1094C2C2×#100×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1471C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583538C2
cosocleC22×C4×C43C24
hypercenter#1471D43
hypocenterC43#17421
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1471

Complements

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

NH ≅ G/Ntype
2. #19143631C2semidirect
3. #19143626C2semidirect
4. #19132955C2semidirect
5. #19132953C2semidirect
6. #19132953C2semidirect
7. #19132945C2semidirect
8. #19132945C2semidirect
9. #19132934C2semidirect
10. #19132921C2semidirect
11. #19132920C2semidirect
12. #19132914C2semidirect
13. C2×#14582622C2semidirect
14. #323×D43C2semidirect
15. C43×#1471C2semidirect
46. #14582953C22semidirect
47. #14582953C22semidirect
48. #14582949C22semidirect
49. #14582949C22semidirect
50. #14582863C22semidirect
51. #14582861C22semidirect
52. #14582861C22semidirect
53. C2×C22⋊(C43⋊C8)C22semidirect
54. C22⋊C8×D43C22semidirect
55. C22⋊C8×D43C22semidirect
56. #14582623C22semidirect
57. #14582623C22semidirect
58. #14582623C22semidirect
59. #14582623C22semidirect
64. #14582622C22semidirect
65. #14582622C22semidirect
66. #14582622C22semidirect
67. #14582622C22semidirect
69. C43×#407C22semidirect
70. C2×C22⋊C8×C43C22semidirect
71. C43×#323C22semidirect
72. C43×#323C22semidirect
73. C43×#323C22semidirect
74. C43×#323C22semidirect
541. #1471D43semidirect
601. #407C2×D43semidirect
605. C2×C22⋊C8C2×D43semidirect
618. #323C2×D43semidirect
619. #323C2×D43semidirect
620. #323C2×D43semidirect
621. #323C2×D43semidirect
622. C43#17421semidirect

Maximal subgroups

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

subgroupindex
C2×#145835382
#191436312
#191436262
#191329552
#191329532
#191329452
#191329342
#191329212
#191329202
#191329142
C2×#145826222
#323×D432
C43×#14712
#1742143