Finite Group Databasebeta

← #25112732

Subgroups — #25112732

Order 11008.

1294 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583575C211yesmaximal, characteristic
2#19137444C211yesmaximal, characteristic, complemented
3#19135580C211yesmaximal, characteristic, complemented
4#19135579C211yesmaximal, characteristic, complemented
5#19135053C211yesmaximal, characteristic, complemented
6#19135051C211yesmaximal, characteristic, complemented
7#19135048C211yesmaximal, characteristic
8#19135046C211yesmaximal, characteristic
9#19134670C211yesmaximal, characteristic, complemented
10#19134667C211yesmaximal, characteristic, complemented
11#19134580C211yesmaximal, characteristic, complemented
12C4×#13063239C211yesmaximal, characteristic, complemented
13#19134327C211yesmaximal, characteristic, complemented
14C2×#14582665C211yesmaximal, characteristic, complemented
15C43×#2342C211yesmaximal, characteristic, complemented
16#14583575—21no—
17#14583575—21no—
18#14583575—21no—
19#14583575—21no—
20#14583575—21no—
21#14583575—21no—
22#14583575—21no—
23#14583575—21no—
24C2×#13063318C411yescharacteristic, complemented
25C2×#13063318C411yescharacteristic, complemented
26C2×#13063311C411yescharacteristic, complemented
27C2×#13063309C411yescharacteristic, complemented
28C2×#13063308C2211yescharacteristic
29C2×#13063307C411yescharacteristic, complemented
30C2×#13063304C2211yescharacteristic
31C2×#13063302C411yescharacteristic, complemented
32C2×#13063294C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×(C22⋊D43)⋊C4C411yescharacteristic, complemented
35C2×#13063284C2211yescharacteristic
36C2×#13063284C2211yescharacteristic
37C2×#13063281C411yescharacteristic, complemented
38C22×C22⋊Dic43C2211yescharacteristic
39C22×C22⋊Dic43C2211yescharacteristic
40C2×#13063239C2211yescharacteristic
41C2×#13063239C2211yescharacteristic
42C2×#13063239C2211yescharacteristic
43C2×#13063239C2211yescharacteristic
44#14582792—21no—
45#14582792—21no—
46#14582774—21no—
47#14582762C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582755C2211yescharacteristic
50C22⋊C4×Dic43—21no—
51C4×C22⋊Dic43C2211yescharacteristic
52#14582665C2211yescharacteristic
53#14582665C2211yescharacteristic
54#14582665C2211yescharacteristic
55#14582665C2211yescharacteristic
56#14582665C2211yescharacteristic
57#14582665C2211yescharacteristic
58#14582665C2211yescharacteristic
59#14582665C2211yescharacteristic
60#14582665C2211yescharacteristic
61#14582665C2211yescharacteristic
62#14582665C2211yescharacteristic
63#14582665C2211yescharacteristic
64C2×#117×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C43×#388—21no—
68C43×#388—21no—
69C43×#385—21no—
70C43×#381C2211yescharacteristic
71C43×#380C2211yescharacteristic
72C43×#379C2211yescharacteristic
73C4×C22⋊C4×C43—21no—
74C4×C22⋊C4×C43C2211yescharacteristic
75C22×Dic86C2×C411yescharacteristic, complemented
76C22×C22⋊D43C2×C411yescharacteristic
77C22×C22⋊D43C2×C411yescharacteristic
78C22×C22⋊D43C2311yescharacteristic
79C23×Dic43—21no—
80C23×Dic43C2×C411yescharacteristic
81C23×Dic43C2×C411yescharacteristic
82C22×C4×D43C2×C411yescharacteristic, complemented
83#13063318—21no—
84#13063318—21no—
85#13063318—21no—
86#13063318—21no—
87#13063318—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063311—21no—
92#13063311—21no—
93#13063311—21no—
94#13063311—21no—
95#13063309—21no—
96#13063309—21no—
97#13063309—21no—
98#13063309—21no—
99#13063308—21no—
100#13063308—21no—
101#13063308—21no—
102#13063308—21no—
103#13063307—21no—
104#13063307—21no—
105#13063307—21no—
106#13063307—21no—
107#13063304—21no—
108#13063304—21no—
109#13063304—21no—
110#13063304—21no—
111#13063302—21no—
112#13063302—21no—
113#13063302—21no—
114#13063302—21no—
115#13063294—21no—
116#13063294—21no—
117#13063294—21no—
118#13063294—21no—
119C4×C22⋊D43—21no—
120C4×C22⋊D43—21no—
121C4×C22⋊D43—21no—
122C4×C22⋊D43—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125(C22⋊D43)⋊C4—21no—
126(C22⋊D43)⋊C4—21no—
127#13063284—21no—
128#13063284—21no—
129#13063284—21no—
130#13063284—21no—
131#13063284—22no—
132#13063284—41no—
133#13063281—21no—
134#13063281—21no—
135#13063281—21no—
136#13063281—21no—
137C2×C4⋊Dic43—21no—
138C2×C4⋊Dic43—21no—
139C2×C4⋊Dic43C2×C411yescharacteristic, complemented
140C2×C4⋊Dic43C2×C411yescharacteristic, complemented
141C2×C4⋊Dic43C2×C411yescharacteristic, complemented
142C2×Dic43⋊C4C2×C411yescharacteristic, complemented
143C2×Dic43⋊C4C2×C411yescharacteristic, complemented
144C2×Dic43⋊C4C2×C411yescharacteristic, complemented
145C2×Dic43⋊C4C2×C411yescharacteristic, complemented
146C2×Dic43⋊C4C2×C411yescharacteristic, complemented
147C2×C22⋊Dic43—21no—
148C2×C22⋊Dic43—21no—
149C2×C22⋊Dic43—21no—
150C2×C22⋊Dic43—21no—
151C2×C22⋊Dic43—22no—
152C2×C22⋊Dic43—21no—
153C2×C22⋊Dic43—21no—
154C2×C22⋊Dic43—21no—
155C2×C22⋊Dic43—41no—
156C2×C22⋊Dic43C2×C411yescharacteristic
157C2×C22⋊Dic43C2×C411yescharacteristic
158C2×C22⋊Dic43C2×C411yescharacteristic
159C2×C22⋊Dic43C2×C411yescharacteristic
160C2×C22⋊Dic43C2311yescharacteristic
161C2×C22⋊Dic43C2311yescharacteristic
162C2×C22⋊Dic43C2311yescharacteristic
163C2×C22⋊Dic43C2311yescharacteristic
164C2×C22⋊Dic43C2311yescharacteristic
165C2×C22⋊Dic43C2311yescharacteristic
166C2×C22⋊Dic43C2311yescharacteristic
167C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
168C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
169C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
170C2×C4×Dic43—21no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43C2×C411yescharacteristic, complemented
173C2×C4×Dic43C2×C411yescharacteristic, complemented
174C2×C4×Dic43C2×C411yescharacteristic, complemented
175#13063239—22no—
176#13063239—22no—
177#13063239—41no—
178#13063239—41no—
179C43⋊#95—21no—
180C43⋊#95—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C25×C43C2311yescharacteristic
184C23×C4×C43—21no—
185C23×C4×C43C2311yescharacteristic
186C23×C4×C43C2311yescharacteristic
187#117×C43—22no—
188#117×C43—41no—
189C2×C4⋊C4×C43—21no—
190C2×C4⋊C4×C43—21no—
191C2×C22⋊C4×C43—22no—
192C2×C22⋊C4×C43—21no—
193C2×C22⋊C4×C43—21no—
194C2×C22⋊C4×C43—21no—
195C2×C22⋊C4×C43—41no—
196C2×C22⋊C4×C43C2×C411yescharacteristic
197C2×C22⋊C4×C43C2×C411yescharacteristic
198C2×C22⋊C4×C43C2×C411yescharacteristic
199C2×C22⋊C4×C43C2×C411yescharacteristic
200C2×C22⋊C4×C43D411yescharacteristic
201C2×C22⋊C4×C43D411yescharacteristic
202C2×C22⋊C4×C43D411yescharacteristic
203C2×C22⋊C4×C43D411yescharacteristic
204C2×C22⋊C4×C43D411yescharacteristic
205C2×C22⋊C4×C43D411yescharacteristic
206C2×C22⋊C4×C43D411yescharacteristic
207C2×C22⋊C4×C43D411yescharacteristic
208C2×C22⋊C4×C43C2311yescharacteristic
209C2×C22⋊C4×C43C2311yescharacteristic
210C2×C22⋊C4×C43C2311yescharacteristic
211C2×C22⋊C4×C43C2311yescharacteristic
212C2×C42×C43—21no—
213C2×C42×C43—21no—
214#95×C43—21no—
215#95×C43—21no—
216#95×C43—21no—
217#95×C43—21no—
218C24×C43—21no—
219C24×C43—21no—
220C24×C43—21no—
221C24×C43—21no—
222C24×C43—42no—
223C24×C43—81no—
224C24×C43C22×C411yescharacteristic
225C24×C43C22×C411yescharacteristic
226C24×C43C2×D411yescharacteristic
227C24×C43C2×D411yescharacteristic
228C24×C43C2×D411yescharacteristic
229C24×C43C2×D411yescharacteristic
230C24×C43C2411yescharacteristic
231C23×D43C22×C411yescharacteristic
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—42no—
241C22×C4×C43—42no—
242C22×C4×C43—81no—
243C22×C4×C43—81no—
244C22×C4×C43C22×C411yescharacteristic
245C22×C4×C43C22×C411yescharacteristic
246C22×C4×C43C22×C411yescharacteristic
247C22×C4×C43C22×C411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2×D411yescharacteristic
251C22×C4×C43C2×D411yescharacteristic
252C22×C4×C43C2×D411yescharacteristic
253C22×C4×C43C2×D411yescharacteristic
254C22×C4×C43C2×D411yescharacteristic
255C22×C4×C43C2×D411yescharacteristic
256C2×C22⋊D43—21no—
257C2×C22⋊D43—21no—
258C2×C22⋊D43—21no—
259C2×C22⋊D43—21no—
260C2×C22⋊D43—21no—
261C2×C22⋊D43—21no—
262C2×C22⋊D43—21no—
263C2×C22⋊D43—21no—
264C2×C22⋊D43—21no—
265C2×C22⋊D43—21no—
266C2×C22⋊D43—42no—
267C2×C22⋊D43—81no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—42no—
277C22×Dic43—42no—
278C22×Dic43—42no—
279C22×Dic43—81no—
280C22×Dic43—81no—
281C22×Dic43C22×C411yescharacteristic
282C22×Dic43C22×C411yescharacteristic
283C22×Dic43C22×C411yescharacteristic
284C22×Dic43C22×C411yescharacteristic
285C22×Dic43C22×C411yescharacteristic
286C22×Dic43C22×C411yescharacteristic
287C22×Dic43C22×C411yescharacteristic
288C2×C4×D43—21no—
289C2×C4×D43—21no—
290C2×C4×D43—81no—
291C2×Dic86—21no—
292C2×Dic86—21no—
293C2×Dic86—81no—
294C4⋊C4×C43—42no—
295C4⋊C4×C43—81no—
296C22⋊C4×C43—21no—
297C22⋊C4×C43—21no—
298C22⋊C4×C43—21no—
299C22⋊C4×C43—21no—
300C22⋊C4×C43—21no—
301C22⋊C4×C43—21no—
302C22⋊C4×C43—21no—
303C22⋊C4×C43—42no—
304C22⋊C4×C43—42no—
305C22⋊C4×C43—81no—
306C22⋊C4×C43C22⋊C411yescharacteristic
307C22⋊C4×C43C22⋊C411yescharacteristic
308C22⋊C4×C43C22⋊C411yescharacteristic
309C22⋊C4×C43C22⋊C411yescharacteristic
310C22⋊C4×C43C22⋊C411yescharacteristic
311C22⋊C4×C43C22⋊C411yescharacteristic
312C22⋊C4×C43C22⋊C411yescharacteristic
313C22⋊C4×C43C22⋊C411yescharacteristic
314C22⋊C4×C43C22⋊C411yescharacteristic
315C22⋊C4×C43C22⋊C411yescharacteristic
316C22⋊C4×C43C22⋊C411yescharacteristic
317C22⋊C4×C43C22⋊C411yescharacteristic
318C22⋊C4×C43C22⋊C411yescharacteristic
319C22⋊C4×C43C22⋊C411yescharacteristic
320C22⋊C4×C43C22⋊C411yescharacteristic
321C22⋊C4×C43C22⋊C411yescharacteristic
322C22⋊C4×C43#4112yes—
323C42×C43—42no—
324C42×C43—81no—
325C22⋊Dic43—21no—
326C22⋊Dic43—21no—
327C22⋊Dic43—21no—
328C22⋊Dic43—21no—
329C22⋊Dic43—21no—
330C22⋊Dic43—21no—
331C22⋊Dic43—21no—
332C22⋊Dic43—21no—
333C22⋊Dic43—21no—
334C22⋊Dic43—21no—
335C22⋊Dic43—21no—
336C22⋊Dic43—21no—
337C22⋊Dic43—21no—
338C22⋊Dic43—21no—
339C22⋊Dic43—21no—
340C22⋊Dic43—21no—
341C22⋊Dic43—21no—
342C22⋊Dic43—21no—
343C22⋊Dic43—21no—
344C22⋊Dic43—21no—
345C22⋊Dic43—21no—
346C22⋊Dic43—42no—
347C22⋊Dic43—42no—
348C22⋊Dic43—81no—
349C22⋊Dic43#4112yes—
350(C2×D43)⋊C4—21no—
351(C2×D43)⋊C4—21no—
352(C2×D43)⋊C4—21no—
353(C2×D43)⋊C4—21no—
354(C2×D43)⋊C4—21no—
355(C2×D43)⋊C4—21no—
356C4⋊Dic43—21no—
357C4⋊Dic43—21no—
358C4⋊Dic43—21no—
359C4⋊Dic43—21no—
360C4⋊Dic43—21no—
361C4⋊Dic43—21no—
362C4⋊Dic43—42no—
363C4⋊Dic43—81no—
364Dic43⋊C4—21no—
365Dic43⋊C4—21no—
366Dic43⋊C4—21no—
367Dic43⋊C4—21no—
368Dic43⋊C4—21no—
369Dic43⋊C4—21no—
370Dic43⋊C4—21no—
371Dic43⋊C4—21no—
372Dic43⋊C4—21no—
373Dic43⋊C4—21no—
374C4×Dic43—21no—
375C4×Dic43—21no—
376C4×Dic43—21no—
377C4×Dic43—21no—
378C4×Dic43—21no—
379C4×Dic43—21no—
380C4×Dic43—42no—
381C4×Dic43—81no—
382C23×C43—21no—
383C23×C43—21no—
384C23×C43—21no—
385C23×C43—21no—
386C23×C43—21no—
387C23×C43—21no—
388C23×C43—22no—
389C23×C43—22no—
390C23×C43—22no—
391C23×C43—21no—
392C23×C43—21no—
393C23×C43—21no—
394C23×C43—21no—
395C23×C43—21no—
396C23×C43—21no—
397C23×C43—41no—
398C23×C43—41no—
399C23×C43—41no—
400C23×C43—41no—
401C23×C43—41no—
402C23×C43—41no—
403C23×C43—41no—
404C23×C43—41no—
405C23×C43—41no—
406C23×C43—41no—
407C23×C43—41no—
408C23×C43—82no—
409C23×C43—82no—
410C23×C43—82no—
411C23×C43—82no—
412C23×C43C2×C22⋊C411yescharacteristic
413C23×C43C2×C22⋊C411yescharacteristic
414C23×C43C2×C22⋊C411yescharacteristic
415C23×C43C2×C22⋊C411yescharacteristic
416C23×C43C23×C411yescharacteristic
417C23×C43C22×D411yescharacteristic
418C23×C43C22×D411yescharacteristic
419C23×C43C2×#4111yescharacteristic
420C23×C43C2×#4111yescharacteristic
421C23×C43H(5,𝔽2)11yescharacteristic
422C23×C432−1+411yescharacteristic
423C22×D43—21no—
424C22×D43—21no—
425C22×D43—21no—
426C22×D43—41no—
427C22×D43—41no—
428C2×C4×C43—21no—
429C2×C4×C43—21no—
430C2×C4×C43—21no—
431C2×C4×C43—21no—
432C2×C4×C43—21no—
433C2×C4×C43—21no—
434C2×C4×C43—21no—
435C2×C4×C43—21no—
436C2×C4×C43—21no—
437C2×C4×C43—21no—
438C2×C4×C43—21no—
439C2×C4×C43—21no—
440C2×C4×C43—22no—
441C2×C4×C43—41no—
442C2×C4×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—41no—
454C2×C4×C43—41no—
455C2×C4×C43—41no—
456C2×C4×C43—41no—
457C2×C4×C43—41no—
458C2×C4×C43—84no—
459C2×C4×C43C2×C22⋊C411yescharacteristic
460C2×C4×C43C2×C22⋊C411yescharacteristic
461C2×C4×C43C2×C22⋊C411yescharacteristic
462C2×C4×C43C2×C22⋊C411yescharacteristic
463C2×C4×C43C2×C22⋊C411yescharacteristic
464C2×C4×C43C2×C22⋊C411yescharacteristic
465C2×C4×C43C2×C22⋊C411yescharacteristic
466C2×C4×C43C2×C22⋊C411yescharacteristic
467C22⋊D43—42no—
468C22⋊D43—41no—
469C22⋊D43—41no—
470C22⋊D43—41no—
471C22⋊D43—41no—
472C22⋊D43—42no—
473C22⋊D43—81no—
474C22⋊D43—81no—
475C2×Dic43—21no—
476C2×Dic43—21no—
477C2×Dic43—21no—
478C2×Dic43—21no—
479C2×Dic43—21no—
480C2×Dic43—21no—
481C2×Dic43—21no—
482C2×Dic43—21no—
483C2×Dic43—21no—
484C2×Dic43—22no—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—42no—
488C2×Dic43—42no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43—41no—
496C2×Dic43—41no—
497C2×Dic43—41no—
498C2×Dic43—41no—
499C2×Dic43—41no—
500C2×Dic43—41no—
501C2×Dic43—41no—
502C2×Dic43—41no—
503C2×Dic43—41no—
504C2×Dic43—81no—
505C2×Dic43—81no—
506C2×Dic43—84no—
507C4×D43—81no—
508C4×D43—81no—
509Dic86—81no—
510Dic86—81no—
511#22477—431nomaximal, Sylow
512C22×C43—21no—
513C22×C43—21no—
514C22×C43—21no—
515C22×C43—21no—
516C22×C43—21no—
517C22×C43—21no—
518C22×C43—21no—
519C22×C43—21no—
520C22×C43—21no—
521C22×C43—21no—
522C22×C43—21no—
523C22×C43—21no—
524C22×C43—21no—
525C22×C43—21no—
526C22×C43—21no—
527C22×C43—21no—
528C22×C43—21no—
529C22×C43—41no—
530C22×C43—41no—
531C22×C43—41no—
532C22×C43—41no—
533C22×C43—42no—
534C22×C43—42no—
535C22×C43—42no—
536C22×C43—42no—
537C22×C43—42no—
538C22×C43—42no—
539C22×C43—81no—
540C22×C43—81no—
541C22×C43—81no—
542C22×C43—81no—
543C22×C43—81no—
544C22×C43—81no—
545C22×C43#41012yes—
546C22×C43C22×C22⋊C411yescharacteristic
547C22×C43C4×#4111yescharacteristic
548C22×C43#52011yescharacteristic
549C22×C43#54611yescharacteristic
550C22×C43#54611yescharacteristic
551C22×C43#54711yescharacteristic
552C22×C43#54711yescharacteristic
553C2×D43—41no—
554C2×D43—41no—
555C2×D43—41no—
556C2×D43—81no—
557C2×D43—81no—
558C4×C43—21no—
559C4×C43—21no—
560C4×C43—21no—
561C4×C43—21no—
562C4×C43—21no—
563C4×C43—21no—
564C4×C43—21no—
565C4×C43—21no—
566C4×C43—42no—
567C4×C43—81no—
568C4×C43—81no—
569C4×C43—81no—
570Dic43—42no—
571Dic43—41no—
572Dic43—41no—
573Dic43—41no—
574Dic43—41no—
575Dic43—41no—
576Dic43—41no—
577Dic43—41no—
578Dic43—81no—
579Dic43—81no—
580Dic43—81no—
581C2×#551—431no—
582#2342—431no—
583#2342D4311yescharacteristic, complemented
584#1996—431no—
585#1996—431no—
586#1899—431no—
587#1899—431no—
588#1898—431no—
589#1898—431no—
590#1820—431no—
591#1819—431no—
592#1799—431no—
593C4×#99—431no—
594#1740—431no—
595C2×#342—431no—
596C2×C43—21no—
597C2×C43—21no—
598C2×C43—21no—
599C2×C43—21no—
600C2×C43—21no—
601C2×C43—21no—
602C2×C43—22no—
603C2×C43—41no—
604C2×C43—41no—
605C2×C43—41no—
606C2×C43#233911yescharacteristic
607C2×C43C2×#41011yescharacteristic
608C2×C43#288311yescharacteristic
609D43—81no—
610#551—861no—
611#551—861no—
612#551—861no—
613#551—861no—
614#551—861no—
615#551—861no—
616#551—861no—
617#551—861no—
618C2×#126—431no—
619C2×#126—431no—
620C2×#124—431no—
621C2×#123—431no—
622C2×#123—431no—
623C2×#123—431no—
624C2×C22⋊Q8—431no—
625C2×C22⋊Q8—431no—
626C2×#120—431no—
627C2×C4×D4—431no—
628C2×C4×D4—431no—
629C2×#117—431no—
630C2×#117—431no—
631C2×#117—431no—
632C2×#117C2×D4311yescharacteristic
633C22×C22⋊C4—431no—
634C22×C22⋊C4—431no—
635C22×C22⋊C4C2×D4311yescharacteristic
636C22×C22⋊C4C2×D4311yescharacteristic
637C2×#99—431no—
638C2×#99—431no—
639C2×#99—431no—
640C2×#99—431no—
641#388—21no—
642#388—21no—
643#388—861no—
644#388—861no—
645#385—21no—
646#385—861no—
647#381—431no—
648#381C2×D4311yescharacteristic
649#380—431no—
650#380C2×D4311yescharacteristic
651#379—431no—
652#379C2×D4311yescharacteristic
653C4×C22⋊C4—21no—
654C4×C22⋊C4—431no—
655C4×C22⋊C4—861no—
656C4×C22⋊C4C2×D4311yescharacteristic
657#342—431no—
658#342—431no—
659#342—431no—
660#342—431no—
661#342—431no—
662#342—431no—
663#342—431no—
664#342—431no—
665#342—431no—
666#342—431no—
667#342—431no—
668#342—431no—
669C43#2247711yescharacteristic, complemented, Sylow
670C25C22×D4311yescharacteristic
671C22×Q8—431no—
672C22×D4—431no—
673C22×D4—431no—
674C22×D4—431no—
675C23×C4—21no—
676C23×C4—431no—
677C23×C4—431no—
678C23×C4—431no—
679C23×C4—861no—
680C23×C4C22×D4311yescharacteristic
681C23×C4C22×D4311yescharacteristic
682#126—861no—
683#126—861no—
684#126—861no—
685#126—861no—
686#126—861no—
687#126—861no—
688#126—861no—
689#126—861no—
690#124—861no—
691#124—861no—
692#124—861no—
693#124—861no—
694#123—861no—
695#123—861no—
696#123—861no—
697#123—861no—
698#123—861no—
699#123—861no—
700#123—861no—
701#123—861no—
702#123—861no—
703#123—861no—
704#123—861no—
705#123—861no—
706C22⋊Q8—861no—
707C22⋊Q8—861no—
708C22⋊Q8—861no—
709C22⋊Q8—861no—
710C22⋊Q8—861no—
711C22⋊Q8—861no—
712C22⋊Q8—861no—
713C22⋊Q8—861no—
714#120—861no—
715#120—861no—
716#120—861no—
717#120—861no—
718C4×D4—861no—
719C4×D4—861no—
720C4×D4—861no—
721C4×D4—861no—
722C4×D4—861no—
723C4×D4—861no—
724C4×D4—861no—
725C4×D4—861no—
726#117—22no—
727#117—41no—
728#117—861no—
729#117—861no—
730#117—861no—
731#117—861no—
732#117—861no—
733#117—861no—
734#117—861no—
735#117—861no—
736#117—862no—
737#117—1721no—
738C2×C4⋊C4—21no—
739C2×C4⋊C4—21no—
740C2×C4⋊C4—431no—
741C2×C4⋊C4—431no—
742C2×C4⋊C4—431no—
743C2×C4⋊C4—431no—
744C2×C4⋊C4—431no—
745C2×C4⋊C4—431no—
746C2×C4⋊C4—431no—
747C2×C4⋊C4—431no—
748C2×C4⋊C4—861no—
749C2×C4⋊C4—861no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—21no—
754C2×C22⋊C4—41no—
755C2×C22⋊C4—431no—
756C2×C22⋊C4—431no—
757C2×C22⋊C4—431no—
758C2×C22⋊C4—431no—
759C2×C22⋊C4—431no—
760C2×C22⋊C4—431no—
761C2×C22⋊C4—431no—
762C2×C22⋊C4—431no—
763C2×C22⋊C4—431no—
764C2×C22⋊C4—431no—
765C2×C22⋊C4—431no—
766C2×C22⋊C4—431no—
767C2×C22⋊C4—431no—
768C2×C22⋊C4—431no—
769C2×C22⋊C4—862no—
770C2×C22⋊C4—861no—
771C2×C22⋊C4—861no—
772C2×C22⋊C4—861no—
773C2×C22⋊C4—861no—
774C2×C22⋊C4—861no—
775C2×C22⋊C4—861no—
776C2×C22⋊C4—861no—
777C2×C22⋊C4—1721no—
778C2×C22⋊C4C4×D4311yescharacteristic
779C2×C22⋊C4C4×D4311yescharacteristic
780C2×C22⋊C4C4×D4311yescharacteristic
781C2×C22⋊C4C4×D4311yescharacteristic
782C2×C22⋊C4D17211yescharacteristic
783C2×C22⋊C4D17211yescharacteristic
784C2×C22⋊C4D17211yescharacteristic
785C2×C22⋊C4D17211yescharacteristic
786C2×C22⋊C4C22⋊D4311yescharacteristic
787C2×C22⋊C4C22⋊D4311yescharacteristic
788C2×C22⋊C4C22⋊D4311yescharacteristic
789C2×C22⋊C4C22⋊D4311yescharacteristic
790C2×C22⋊C4C22×D4311yescharacteristic
791C2×C22⋊C4C22×D4311yescharacteristic
792C2×C22⋊C4C22×D4311yescharacteristic
793C2×C22⋊C4C22×D4311yescharacteristic
794C2×C42—21no—
795C2×C42—21no—
796C2×C42—431no—
797C2×C42—431no—
798C2×C42—431no—
799C2×C42—861no—
800C2×C42—861no—
801#99—862no—
802#99—862no—
803#99—1721no—
804#99—1721no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—861no—
810#95—861no—
811#95—861no—
812#95—861no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—42no—
818C24—81no—
819C24—431no—
820C24C2×C4×D4311yescharacteristic
821C24C2×C4×D4311yescharacteristic
822C24C2×D17211yescharacteristic
823C24C2×D17211yescharacteristic
824C24C2×C22⋊D4311yescharacteristic
825C24C2×C22⋊D4311yescharacteristic
826C24C23×D4311yescharacteristic
827C2×Q8—861no—
828C2×Q8—861no—
829C2×Q8—3441no—
830C2×D4—861no—
831C2×D4—861no—
832C2×D4—861no—
833C2×D4—861no—
834C2×D4—861no—
835C2×D4—861no—
836C2×D4—861no—
837C2×D4—861no—
838C2×D4—861no—
839C2×D4—861no—
840C2×D4—3441no—
841C2×D4—1722no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—431no—
855C22×C4—431no—
856C22×C4—431no—
857C22×C4—431no—
858C22×C4—431no—
859C22×C4—431no—
860C22×C4—431no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—861no—
870C22×C4—861no—
871C22×C4—3441no—
872C22×C4—3441no—
873C22×C4—3441no—
874C22×C4—1722no—
875C22×C4—1722no—
876C22×C4—1722no—
877C22×C4C2×C4×D4311yescharacteristic
878C22×C4C2×C4×D4311yescharacteristic
879C22×C4C2×C4×D4311yescharacteristic
880C22×C4C2×C4×D4311yescharacteristic
881C22×C4C2×D17211yescharacteristic
882C22×C4C2×D17211yescharacteristic
883C22×C4C2×D17211yescharacteristic
884C22×C4C2×D17211yescharacteristic
885C22×C4C2×C22⋊D4311yescharacteristic
886C22×C4C2×C22⋊D4311yescharacteristic
887C22×C4C2×C22⋊D4311yescharacteristic
888C22×C4C2×C22⋊D4311yescharacteristic
889C4⋊C4—42no—
890C4⋊C4—81no—
891C4⋊C4—861no—
892C4⋊C4—861no—
893C4⋊C4—861no—
894C4⋊C4—861no—
895C4⋊C4—861no—
896C4⋊C4—861no—
897C4⋊C4—861no—
898C4⋊C4—861no—
899C4⋊C4—861no—
900C4⋊C4—861no—
901C4⋊C4—861no—
902C4⋊C4—861no—
903C4⋊C4—861no—
904C4⋊C4—861no—
905C4⋊C4—861no—
906C4⋊C4—861no—
907C4⋊C4—3441no—
908C4⋊C4—1722no—
909C22⋊C4—21no—
910C22⋊C4—21no—
911C22⋊C4—21no—
912C22⋊C4—21no—
913C22⋊C4—21no—
914C22⋊C4—21no—
915C22⋊C4—21no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—81no—
919C22⋊C4—432no—
920C22⋊C4—861no—
921C22⋊C4—861no—
922C22⋊C4—861no—
923C22⋊C4—861no—
924C22⋊C4—861no—
925C22⋊C4—861no—
926C22⋊C4—861no—
927C22⋊C4—861no—
928C22⋊C4—861no—
929C22⋊C4—861no—
930C22⋊C4—861no—
931C22⋊C4—861no—
932C22⋊C4—861no—
933C22⋊C4—861no—
934C22⋊C4—861no—
935C22⋊C4—861no—
936C22⋊C4—861no—
937C22⋊C4—861no—
938C22⋊C4—861no—
939C22⋊C4—861no—
940C22⋊C4—861no—
941C22⋊C4—861no—
942C22⋊C4—861no—
943C22⋊C4—861no—
944C22⋊C4—861no—
945C22⋊C4—861no—
946C22⋊C4—861no—
947C22⋊C4—3441no—
948C22⋊C4—1722no—
949C22⋊C4—1722no—
950C22⋊C4(C2×D43)⋊C411yescharacteristic
951C22⋊C4(C2×D43)⋊C411yescharacteristic
952C22⋊C4(C2×D43)⋊C411yescharacteristic
953C22⋊C4(C2×D43)⋊C411yescharacteristic
954C22⋊C4(C2×D43)⋊C411yescharacteristic
955C22⋊C4(C2×D43)⋊C411yescharacteristic
956C22⋊C4(C2×D43)⋊C411yescharacteristic
957C22⋊C4(C2×D43)⋊C411yescharacteristic
958C22⋊C4(C2×D43)⋊C411yescharacteristic
959C22⋊C4(C2×D43)⋊C411yescharacteristic
960C22⋊C4(C2×D43)⋊C411yescharacteristic
961C22⋊C4(C2×D43)⋊C411yescharacteristic
962C22⋊C4(C2×D43)⋊C411yescharacteristic
963C22⋊C4(C2×D43)⋊C411yescharacteristic
964C22⋊C4(C2×D43)⋊C411yescharacteristic
965C22⋊C4(C2×D43)⋊C411yescharacteristic
966C22⋊C4#1062190012yes—
967C42—42no—
968C42—81no—
969C42—861no—
970C42—861no—
971C42—861no—
972C42—861no—
973C42—861no—
974C42—861no—
975C42—3441no—
976C42—1722no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—82no—
1004C23—82no—
1005C23—82no—
1006C23—82no—
1007C23—861no—
1008C23—861no—
1009C23—861no—
1010C23—1721no—
1011C23—1721no—
1012C23C2×(C2×D43)⋊C411yescharacteristic
1013C23C2×(C2×D43)⋊C411yescharacteristic
1014C23C2×(C2×D43)⋊C411yescharacteristic
1015C23C2×(C2×D43)⋊C411yescharacteristic
1016C23C22×C4×D4311yescharacteristic
1017C23C22×C22⋊D4311yescharacteristic
1018C23C22×D17211yescharacteristic
1019C23#41×D4311yescharacteristic
1020C23C2×#1062190011yescharacteristic
1021C23#1306337011yescharacteristic
1022C23#1306337211yescharacteristic
1023Q8—3441no—
1024Q8—3441no—
1025D4—3441no—
1026D4—3441no—
1027D4—1722no—
1028D4—1721no—
1029D4—1722no—
1030D4—1721no—
1031D4—1721no—
1032D4—1721no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—84no—
1064C2×C4—861no—
1065C2×C4—861no—
1066C2×C4—861no—
1067C2×C4—861no—
1068C2×C4—861no—
1069C2×C4—861no—
1070C2×C4—861no—
1071C2×C4—861no—
1072C2×C4—861no—
1073C2×C4—862no—
1074C2×C4—3441no—
1075C2×C4—3441no—
1076C2×C4—3444no—
1077C2×C4—3441no—
1078C2×C4—3441no—
1079C2×C4—1721no—
1080C2×C4—1721no—
1081C2×C4—1721no—
1082C2×C4—1721no—
1083C2×C4—1721no—
1084C2×C4—1721no—
1085C2×C4—1721no—
1086C2×C4—1721no—
1087C2×C4—1721no—
1088C2×C4—1721no—
1089C2×C4—1721no—
1090C2×C4—1722no—
1091C2×C4—1722no—
1092C2×C4—1721no—
1093C2×C4—1721no—
1094C2×C4—1721no—
1095C2×C4—1721no—
1096C2×C4—1721no—
1097C2×C4—1721no—
1098C2×C4C2×(C2×D43)⋊C411yescharacteristic
1099C2×C4C2×(C2×D43)⋊C411yescharacteristic
1100C2×C4C2×(C2×D43)⋊C411yescharacteristic
1101C2×C4C2×(C2×D43)⋊C411yescharacteristic
1102C2×C4C2×(C2×D43)⋊C411yescharacteristic
1103C2×C4C2×(C2×D43)⋊C411yescharacteristic
1104C2×C4C2×(C2×D43)⋊C411yescharacteristic
1105C2×C4C2×(C2×D43)⋊C411yescharacteristic
1106C22—21no—
1107C22—21no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—3441no—
1140C22—3441no—
1141C22—1721no—
1142C22—1721no—
1143C22—1721no—
1144C22#1458287212yes—
1145C22C22×(C2×D43)⋊C411yescharacteristic
1146C22C4×#1062190011yescharacteristic
1147C22#1458337811yescharacteristic
1148C22#1458354311yescharacteristic
1149C22#1458354411yescharacteristic
1150C22#1458354811yescharacteristic
1151C22#1458355311yescharacteristic
1152C4—21no—
1153C4—21no—
1154C4—21no—
1155C4—21no—
1156C4—21no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—42no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—3441no—
1165C4—3441no—
1166C4—3441no—
1167C4—1722no—
1168C4—1721no—
1169C4—1721no—
1170C4—1721no—
1171C4—1721no—
1172C4—1721no—
1173C4—1721no—
1174C4—1721no—
1175C2—21no—
1176C2—21no—
1177C2—21no—
1178C2—21no—
1179C2—22no—
1180C2—21no—
1181C2—21no—
1182C2—41no—
1183C2—41no—
1184C2—41no—
1185C2—3441no—
1186C2#1913742011yescharacteristic
1187C2C2×#1458287211yescharacteristic
1188C2#1914305511yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#2342C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063294C22
cosocleC24×C43C24
hypercenter#2342D43
hypocenterC43#22477
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. #19137444C2semidirect
3. #19135580C2semidirect
4. #19135579C2semidirect
5. #19135053C2semidirect
6. #19135051C2semidirect
9. #19134670C2semidirect
10. #19134667C2semidirect
11. #19134580C2semidirect
12. C4×#13063239C2semidirect
13. #19134327C2semidirect
14. C2×#14582665C2semidirect
15. C43×#2342C2semidirect
24. C2×#13063318C4semidirect
25. C2×#13063318C4semidirect
26. C2×#13063311C4semidirect
27. C2×#13063309C4semidirect
29. C2×#13063307C4semidirect
31. C2×#13063302C4semidirect
34. C2×(C22⋊D43)⋊C4C4semidirect
37. C2×#13063281C4semidirect
75. C22×Dic86C2×C4semidirect
82. C22×C4×D43C2×C4semidirect
139. C2×C4⋊Dic43C2×C4semidirect
140. C2×C4⋊Dic43C2×C4semidirect
141. C2×C4⋊Dic43C2×C4semidirect
142. C2×Dic43⋊C4C2×C4semidirect
143. C2×Dic43⋊C4C2×C4semidirect
144. C2×Dic43⋊C4C2×C4semidirect
145. C2×Dic43⋊C4C2×C4semidirect
146. C2×Dic43⋊C4C2×C4semidirect
167. C2×(C2×D43)⋊C4C2×C4semidirect
168. C2×(C2×D43)⋊C4C2×C4semidirect
169. C2×(C2×D43)⋊C4C2×C4semidirect
172. C2×C4×Dic43C2×C4semidirect
173. C2×C4×Dic43C2×C4semidirect
174. C2×C4×Dic43C2×C4semidirect
583. #2342D43semidirect
669. C43#22477semidirect

Maximal subgroups

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

subgroupindex
C2×#145835752
#191374442
#191355802
#191355792
#191350532
#191350512
#191350482
#191350462
#191346702
#191346672
#191345802
C4×#130632392
#191343272
C2×#145826652
C43×#23422
#2247743