Finite Group Databasebeta

← #25063789

Subgroups — #25063789

Order 11008.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148621C211yesmaximal, characteristic
2#19143626C211yesmaximal, characteristic, complemented
3#19136953C211yesmaximal, characteristic, complemented
4#19133117C211yesmaximal, characteristic, complemented
5#19133111C211yesmaximal, characteristic, complemented
6#19133109C211yesmaximal, characteristic, complemented
7#19133101C211yesmaximal, characteristic, complemented
8#19133097C211yesmaximal, characteristic, complemented
9#19133096C211yesmaximal, characteristic, complemented
10#19133088C211yesmaximal, characteristic, complemented
11#19133087C211yesmaximal, characteristic, complemented
12#19133083C211yesmaximal, characteristic, complemented
13#19133078C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C2×C43×#327C211yesmaximal, characteristic, complemented
16#14583613C411yescharacteristic, complemented
17#14583604C411yescharacteristic, complemented
18#14583597C411yescharacteristic, complemented
19#14583596C411yescharacteristic, complemented
20#14583592—21no—
21#14583567C411yescharacteristic, complemented
22#14583546C411yescharacteristic, complemented
23#14583543—21no—
24#14583543C411yescharacteristic, complemented
25#14583538—21no—
26D4×C22⋊D43—21no—
27D4×C22⋊D43C411yescharacteristic, complemented
28#14583499—21no—
29#14583487—21no—
30#14583481—21no—
31#14583444C2211yescharacteristic
32#14583430C2211yescharacteristic
33#14583410C2211yescharacteristic
34#14583409C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583372—21no—
37C2×C4×C22⋊D43—21no—
38C2×C4×C22⋊D43C2211yescharacteristic
39#14582974—21no—
40#14582973—21no—
41#14582970—21no—
42C8×C22⋊D43—21no—
43#14582953C2211yescharacteristic, complemented
44#14582949C2211yescharacteristic, complemented
45#14582863C2211yescharacteristic, complemented
46#14582861C2211yescharacteristic, complemented
47C22⋊C8×D43C2211yescharacteristic, complemented
48#14582750—21no—
49#14582750C2211yescharacteristic, complemented
50C4×C22⋊Dic43—21no—
51C4×C22⋊Dic43C2211yescharacteristic, complemented
52#14582746—21no—
53#14582746C2211yescharacteristic, complemented
54#14582744C2211yescharacteristic, complemented
55#95×D43C2211yescharacteristic, complemented
56#14582637C2211yescharacteristic, complemented
57#14582637C2211yescharacteristic, complemented
58#14582635C2211yescharacteristic, complemented
59#14582635C2211yescharacteristic, complemented
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582633C2211yescharacteristic
63#14582633C2211yescharacteristic
64#14582633C2211yescharacteristic, complemented
65#14582633C2211yescharacteristic, complemented
66#14582632C2211yescharacteristic, complemented
67#14582632C2211yescharacteristic, complemented
68C2×#121×C43C2211yescharacteristic
69C2×C22⋊C8×C43C2211yescharacteristic, complemented
70C2×#95×C43C2211yescharacteristic, complemented
71C43×#327C2211yescharacteristic
72C43×#327C2211yescharacteristic
73C43×#327C2211yescharacteristic, complemented
74C43×#327C2211yescharacteristic, complemented
75C2×#10621898C2×C411yescharacteristic, complemented
76C2×#10621900—21no—
77C2×#10621900C2×C411yescharacteristic, complemented
78C22×C22⋊D43—21no—
79C22×C22⋊D43D411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43C2×C411yescharacteristic, complemented
82C22×C4×D43—21no—
83C22×C4×D43C2311yescharacteristic
84C2×#10621877—21no—
85C2×#10621872—21no—
86C2×C8×D43—21no—
87#13063324C2×C411yescharacteristic, complemented
88#13063321—21no—
89#13063321C2×C411yescharacteristic, complemented
90#13063320—21no—
91#13063318—21no—
92#13063318—21no—
93#13063316C2×C411yescharacteristic, complemented
94#13063315—21no—
95#13063312—21no—
96#13063312C2×C411yescharacteristic, complemented
97#13063311—21no—
98#13063311—21no—
99#13063310—21no—
100#13063308—21no—
101#13063307—21no—
102#13063307—21no—
103#13063306—21no—
104#13063306—21no—
105#13063306—21no—
106#13063305C2×C411yescharacteristic, complemented
107#13063304—21no—
108#13063304C2×C411yescharacteristic, complemented
109#13063304C2311yescharacteristic
110#13063303—21no—
111#13063300C2×C411yescharacteristic, complemented
112#13063299—21no—
113#13063299C2×C411yescharacteristic, complemented
114#13063299C2311yescharacteristic
115#13063298—21no—
116#13063298—21no—
117#13063297—21no—
118#13063297—21no—
119#13063297—21no—
120#13063297—21no—
121#13063297—21no—
122#13063297—21no—
123#13063296—21no—
124#13063296—21no—
125#13063296C2×C411yescharacteristic, complemented
126#13063296C2×C411yescharacteristic, complemented
127#13063294—21no—
128#13063294—21no—
129#13063294—21no—
130#13063293—21no—
131#13063293—21no—
132#13063293—21no—
133#13063290C2×C411yescharacteristic, complemented
134D4×Dic43—21no—
135D4×Dic43—21no—
136D4×Dic43C2×C411yescharacteristic, complemented
137D4×Dic43C2×C411yescharacteristic, complemented
138#13063287C2×C411yescharacteristic, complemented
139C4×C22⋊D43—28no—
140C4×C22⋊D43—21no—
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43—21no—
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43C2×C411yescharacteristic
146C4×C22⋊D43C2×C411yescharacteristic
147C4×C22⋊D43C2×C411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149C4×C22⋊D43D411yescharacteristic
150C4×C22⋊D43D411yescharacteristic
151C4×C22⋊D43D411yescharacteristic
152(C22⋊D43)⋊C4—21no—
153(C22⋊D43)⋊C4—21no—
154(C22⋊D43)⋊C4—21no—
155(C22⋊D43)⋊C4—21no—
156#13063284C2×C411yescharacteristic, complemented
157#13063283C2×C411yescharacteristic, complemented
158#13063281—21no—
159#13063281—21no—
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4D411yescharacteristic
162C4⋊C4×D43C2×C411yescharacteristic, complemented
163C2×C22⋊Dic43—21no—
164C2×C22⋊Dic43—21no—
165C2×C22⋊Dic43D411yescharacteristic
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4D411yescharacteristic
168C22⋊C4×D43—21no—
169C22⋊C4×D43—21no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43—21no—
174C2×C4×Dic43C2311yescharacteristic
175Dic43⋊C8—21no—
176Dic43⋊C8—21no—
177C22⋊(C43⋊C8)—21no—
178C22⋊(C43⋊C8)C2311yescharacteristic
179C22⋊(C43⋊C8)C2311yescharacteristic
180(C2×D43)⋊C8—21no—
181(C2×D43)⋊C8—21no—
182#13063235—21no—
183C8×Dic43—21no—
184C43⋊#95—21no—
185C43⋊#95—21no—
186C43⋊#95C2311yescharacteristic
187C43⋊#95C2311yescharacteristic
188C22×D4×C43—21no—
189C22×D4×C43C2×C411yescharacteristic, complemented
190C23×C4×C43—21no—
191C23×C4×C43C2311yescharacteristic
192C22×C8×C43—21no—
193#121×C43—21no—
194#121×C43—21no—
195#121×C43C2×C411yescharacteristic, complemented
196#121×C43C2×C411yescharacteristic, complemented
197#121×C43C2311yescharacteristic
198#121×C43C2311yescharacteristic
199C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
200C2×C22⋊C4×C43—21no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204#95×C43—21no—
205#95×C43C2311yescharacteristic
206#95×C43C2311yescharacteristic
207C24×C43—21no—
208C24×C43C2×D411yescharacteristic
209C23×D43—21no—
210C23×D43C2×D411yescharacteristic
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—21no—
216C2×D4×C43—81no—
217C2×D4×C43—81no—
218C2×D4×C43—81no—
219C2×D4×C43C22×C411yescharacteristic
220C2×D4×C43C22×C411yescharacteristic
221C22×C4×C43—24no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—81no—
226C22×C4×C43—81no—
227C22×C4×C43—81no—
228C22×C4×C43C22×C411yescharacteristic
229C22×C4×C43C22×C411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2411yescharacteristic
234C2×C22⋊D43—24no—
235C2×C22⋊D43—21no—
236C2×C22⋊D43—21no—
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C2×C22⋊D43—21no—
240C2×C22⋊D43—21no—
241C2×C22⋊D43—21no—
242C2×C22⋊D43—21no—
243C2×C22⋊D43—21no—
244C2×C22⋊D43—44no—
245C2×C22⋊D43C22⋊C411yescharacteristic
246C2×C22⋊D43C22⋊C411yescharacteristic
247C2×C22⋊D43C22⋊C411yescharacteristic
248C2×C22⋊D43C22⋊C411yescharacteristic
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43C2×D411yescharacteristic
255C22×Dic43C2×D411yescharacteristic
256C22×Dic43C2×D411yescharacteristic
257#10621900—81no—
258#10621900—81no—
259#10621900—81no—
260D4×D43—81no—
261D4×D43—81no—
262D4×D43—81no—
263#10621898—81no—
264C2×D172—21no—
265C2×D172C22×C411yescharacteristic
266C2×C4×D43—24no—
267C2×C4×D43—21no—
268C2×C4×D43—21no—
269C2×C4×D43—21no—
270C2×C4×D43—81no—
271C2×C4×D43—81no—
272C2×C4×D43—81no—
273C2×C4×D43C22×C411yescharacteristic
274C2×C4×D43C22×C411yescharacteristic
275C2×C4×D43C2×D411yescharacteristic
276C2×C4×D43C2×D411yescharacteristic
277C2×Dic86—21no—
278C2×Dic86C22×C411yescharacteristic
279C2×C8×C43—21no—
280C2×C8×C43—21no—
281C2×C8×C43—81no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43C22×C411yescharacteristic
284C4⋊C4×C43C22×C411yescharacteristic
285C22⋊C4×C43—21no—
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊Dic43—24no—
290C22⋊Dic43—21no—
291C22⋊Dic43—21no—
292C22⋊Dic43—21no—
293C22⋊Dic43—21no—
294C22⋊Dic43—21no—
295C22⋊Dic43—21no—
296C22⋊Dic43—21no—
297C22⋊Dic43—21no—
298C22⋊Dic43—21no—
299C22⋊Dic43C22⋊C411yescharacteristic
300C22⋊Dic43C22⋊C411yescharacteristic
301C22⋊Dic43C22⋊C411yescharacteristic
302C22⋊Dic43C22⋊C411yescharacteristic
303(C2×D43)⋊C4—24no—
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)⋊C4C22⋊C411yescharacteristic
311(C2×D43)⋊C4C22⋊C411yescharacteristic
312(C2×D43)⋊C4C22⋊C411yescharacteristic
313(C2×D43)⋊C4C22⋊C411yescharacteristic
314C4⋊Dic43—21no—
315C4⋊Dic43—21no—
316C4⋊Dic43C22×C411yescharacteristic
317C4⋊Dic43C22×C411yescharacteristic
318Dic43⋊C4—24no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—21no—
323Dic43⋊C4—21no—
324Dic43⋊C4—21no—
325Dic43⋊C4C22⋊C411yescharacteristic
326Dic43⋊C4C22⋊C411yescharacteristic
327Dic43⋊C4C22⋊C411yescharacteristic
328Dic43⋊C4C22⋊C411yescharacteristic
329C4×Dic43—24no—
330C4×Dic43—21no—
331C4×Dic43—21no—
332C4×Dic43—21no—
333C4×Dic43—81no—
334C4×Dic43—81no—
335C4×Dic43—81no—
336C4×Dic43C22×C411yescharacteristic
337C4×Dic43C22×C411yescharacteristic
338C4×Dic43C2×D411yescharacteristic
339C4×Dic43C2×D411yescharacteristic
340#10621877—81no—
341C2×C43⋊C8—21no—
342C2×C43⋊C8—21no—
343#10621872—81no—
344C8×D43—81no—
345C23×C43—21no—
346C23×C43—21no—
347C23×C43—22no—
348C23×C43—21no—
349C23×C43—21no—
350C23×C43—41no—
351C23×C43—42no—
352C23×C43—81no—
353C23×C43—81no—
354C23×C43C2×C22⋊C411yescharacteristic
355C23×C43C2×C22⋊C411yescharacteristic
356C23×C43C22×D411yescharacteristic
357C22×D43—21no—
358C22×D43—21no—
359C22×D43—22no—
360C22×D43—21no—
361C22×D43—41no—
362C22×D43—42no—
363C22×D43—81no—
364C22×D43—81no—
365C22×D43C2×C22⋊C411yescharacteristic
366C22×D43C2×C22⋊C411yescharacteristic
367D4×C43—41no—
368D4×C43—41no—
369D4×C43—41no—
370D4×C43—41no—
371D4×C43—41no—
372D4×C43—41no—
373D4×C43—81no—
374D4×C43—81no—
375D4×C43—81no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—21no—
379C2×C4×C43—21no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—81no—
391C2×C4×C43—84no—
392C2×C4×C43C2×C22⋊C411yescharacteristic
393C2×C4×C43C2×C22⋊C411yescharacteristic
394C2×C4×C43C23×C411yescharacteristic
395C2×C4×C43C22×D411yescharacteristic
396C22⋊D43—22no—
397C22⋊D43—22no—
398C22⋊D43—22no—
399C22⋊D43—41no—
400C22⋊D43—41no—
401C22⋊D43—42no—
402C22⋊D43—42no—
403C22⋊D43—42no—
404C22⋊D43—81no—
405C22⋊D43—81no—
406C22⋊D43—81no—
407C22⋊D43—81no—
408C22⋊D43—81no—
409C22⋊D43#10414yes—
410C2×Dic43—21no—
411C2×Dic43—21no—
412C2×Dic43—22no—
413C2×Dic43—22no—
414C2×Dic43—22no—
415C2×Dic43—21no—
416C2×Dic43—21no—
417C2×Dic43—21no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—41no—
423C2×Dic43—42no—
424C2×Dic43—81no—
425C2×Dic43—81no—
426C2×Dic43C2×C22⋊C411yescharacteristic
427C2×Dic43C2×C22⋊C411yescharacteristic
428C2×Dic43C2×C22⋊C411yescharacteristic
429C2×Dic43C2×C22⋊C411yescharacteristic
430C2×Dic43C2×C22⋊C411yescharacteristic
431C2×Dic43C2×C22⋊C411yescharacteristic
432D172—41no—
433D172—81no—
434C4×D43—41no—
435C4×D43—41no—
436C4×D43—41no—
437C4×D43—41no—
438C4×D43—81no—
439C4×D43—81no—
440C4×D43—81no—
441C4×D43—84no—
442Dic86—41no—
443Dic86—81no—
444C8×C43—41no—
445C8×C43—41no—
446C43⋊C8—41no—
447C43⋊C8—41no—
448#17547—431nomaximal, Sylow
449C22×C43—21no—
450C22×C43—21no—
451C22×C43—21no—
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—21no—
456C22×C43—42no—
457C22×C43—42no—
458C22×C43—41no—
459C22×C43—41no—
460C22×C43—41no—
461C22×C43—41no—
462C22×C43—41no—
463C22×C43—41no—
464C22×C43—162no—
465C22×C43C2×#10412yes—
466C22×C43C22×C22⋊C411yescharacteristic
467C22×C43#57611yescharacteristic
468C22×C43#57711yescharacteristic
469C2×D43—21no—
470C2×D43—21no—
471C2×D43—21no—
472C2×D43—21no—
473C2×D43—21no—
474C2×D43—42no—
475C2×D43—42no—
476C2×D43—41no—
477C2×D43—41no—
478C2×D43—41no—
479C2×D43—162no—
480C2×D43C2×#10412yes—
481C4×C43—21no—
482C4×C43—21no—
483C4×C43—21no—
484C4×C43—21no—
485C4×C43—42no—
486C4×C43—42no—
487C4×C43—41no—
488C4×C43—41no—
489Dic43—21no—
490Dic43—21no—
491Dic43—21no—
492Dic43—21no—
493Dic43—21no—
494Dic43—42no—
495Dic43—42no—
496Dic43—41no—
497Dic43—41no—
498Dic43—41no—
499Dic43C2×#10412yes—
500#3519—431no—
501#2974—431no—
502#2275—431no—
503#1509—431no—
504#1507—431no—
505#1507—431no—
506#1505—431no—
507#1504—431no—
508#1504—431no—
509#1502—431no—
510#1501—431no—
511#1501—431no—
512#1500—431no—
513C2×#327—431no—
514C2×#327D4311yescharacteristic, complemented
515C2×C43—21no—
516C2×C43—21no—
517C2×C43—22no—
518C2×C43—41no—
519C2×C43—81no—
520C2×C43—81no—
521C2×C43#288311yescharacteristic
522C2×C43#289711yescharacteristic
523C2×C43C22×#10411yescharacteristic
524D43—22no—
525D43—41no—
526D43—81no—
527#555—431no—
528#554—431no—
529#553—431no—
530#553—431no—
531#553—861no—
532#550—431no—
533#546—431no—
534#546—431no—
535#546—861no—
536#546—861no—
537D42—431no—
538D42—861no—
539#540—861no—
540#538—861no—
541#538—861no—
542#532—431no—
543#529—431no—
544#525—431no—
545#525—431no—
546C2×#121—431no—
547C2×#121C2×D4311yescharacteristic
548#518—861no—
549C2×C4×D4—431no—
550C2×C4×D4—861no—
551#436—861no—
552#435—861no—
553#435—861no—
554C8×D4—861no—
555#432—431no—
556#431—431no—
557#407—431no—
558#407—431no—
559C2×C22⋊C8—431no—
560C2×C22⋊C8C2×D4311yescharacteristic, complemented
561C4×C4⋊C4—431no—
562C4×C4⋊C4—861no—
563C4×C22⋊C4—431no—
564C4×C22⋊C4—431no—
565C4×C22⋊C4—861no—
566C4×C22⋊C4—861no—
567#376—431no—
568C2×#95—431no—
569C2×#95C2×D4311yescharacteristic, complemented
570#328—431no—
571#328—431no—
572#328—431no—
573#328—431no—
574#327—431no—
575#327—431no—
576#327—431no—
577#327—431no—
578#327—431no—
579#327—431no—
580#327—431no—
581#327—431no—
582#327C2×D4311yescharacteristic
583#327C2×D4311yescharacteristic
584#327C2×D4311yescharacteristic, complemented
585#327C2×D4311yescharacteristic, complemented
586C43#1754711yescharacteristic, complemented, Sylow
587C2×#41—431no—
588C2×#41—431no—
589C2×#41—861no—
590C22×D4—21no—
591C22×D4—431no—
592C22×D4—431no—
593C22×D4—861no—
594C22×D4—861no—
595C22×D4C4×D4311yescharacteristic, complemented
596C23×C4—21no—
597C23×C4—431no—
598C23×C4—861no—
599C23×C4C22×D4311yescharacteristic
600C2×M16—861no—
601C2×M16—861no—
602C22×C8—21no—
603C22×C8—861no—
604C4⋊Q8—431no—
605#127—431no—
606#127—861no—
607#126—861no—
608#126—861no—
609#126—861no—
610#125—431no—
611#125—861no—
612#124—431no—
613#124—861no—
614#124—861no—
615#124—861no—
616#123—861no—
617#123—861no—
618#123—861no—
619#123—861no—
620#123—861no—
621#123—861no—
622#123—861no—
623C22⋊Q8—431no—
624C22⋊Q8—431no—
625C22⋊Q8—431no—
626C22⋊Q8—861no—
627C22⋊Q8—861no—
628#121—21no—
629#121—21no—
630#121—431no—
631#121—431no—
632#121—431no—
633#121—431no—
634#121—431no—
635#121—861no—
636#121—861no—
637#121—861no—
638#121—861no—
639#121—861no—
640#121—861no—
641#121—861no—
642#121—861no—
643#121—861no—
644#121—861no—
645#121—861no—
646#121C4×D4311yescharacteristic, complemented
647#121C4×D4311yescharacteristic, complemented
648#121C22×D4311yescharacteristic
649#121C22×D4311yescharacteristic
650#120—861no—
651#120—861no—
652#120—861no—
653#120—861no—
654#120—861no—
655#120—861no—
656C4×Q8—431no—
657C4×D4—431no—
658C4×D4—431no—
659C4×D4—431no—
660C4×D4—431no—
661C4×D4—431no—
662C4×D4—431no—
663C4×D4—431no—
664C4×D4—431no—
665C4×D4—431no—
666C4×D4—431no—
667C4×D4—431no—
668C4×D4—861no—
669C4×D4—861no—
670C4×D4—861no—
671C4×D4—861no—
672C4×D4—861no—
673C4×D4—861no—
674C4×D4—868no—
675C4×D4—861no—
676C4×D4—861no—
677C4×D4—861no—
678C4×D4—861no—
679#117—431no—
680#117—431no—
681#117—861no—
682#117—861no—
683C2×C4⋊C4—431no—
684C2×C4⋊C4—431no—
685C2×C4⋊C4—861no—
686C2×C4⋊C4C4×D4311yescharacteristic, complemented
687C2×C22⋊C4—21no—
688C2×C22⋊C4—431no—
689C2×C22⋊C4—431no—
690C2×C22⋊C4—861no—
691C2×C22⋊C4—861no—
692C2×C22⋊C4—861no—
693C2×C22⋊C4—861no—
694C2×C22⋊C4—861no—
695C2×C42—431no—
696C2×C42—861no—
697C2×C42—861no—
698C2×C42—861no—
699C2×C42—861no—
700C4⋊C8—861no—
701C4⋊C8—861no—
702C22⋊C8—21no—
703C22⋊C8—431no—
704C22⋊C8—431no—
705C22⋊C8—861no—
706C22⋊C8—861no—
707C22⋊C8—861no—
708C22⋊C8C22×D4311yescharacteristic
709C22⋊C8C22×D4311yescharacteristic
710#97—861no—
711C4×C8—861no—
712#95—21no—
713#95—431no—
714#95—431no—
715#95—861no—
716#95—861no—
717#95C22×D4311yescharacteristic
718#95C22×D4311yescharacteristic
719C24—21no—
720C24—431no—
721C24—861no—
722C24D4×D4311yescharacteristic
723#41—3441no—
724#41—3441no—
725#41—3441no—
726#41—3441no—
727C2×Q8—431no—
728C2×Q8—861no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—431no—
738C2×D4—431no—
739C2×D4—431no—
740C2×D4—431no—
741C2×D4—431no—
742C2×D4—861no—
743C2×D4—861no—
744C2×D4—861no—
745C2×D4—861no—
746C2×D4—864no—
747C2×D4—861no—
748C2×D4—861no—
749C2×D4—861no—
750C2×D4—861no—
751C2×D4—861no—
752C2×D4—861no—
753C2×D4—3441no—
754C2×D4—3441no—
755C2×D4—3441no—
756C2×D4—1724no—
757C2×D4C2×C4×D4311yescharacteristic
758C2×D4C2×C4×D4311yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—24no—
762C22×C4—21no—
763C22×C4—81no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—431no—
767C22×C4—431no—
768C22×C4—431no—
769C22×C4—431no—
770C22×C4—431no—
771C22×C4—431no—
772C22×C4—431no—
773C22×C4—861no—
774C22×C4—861no—
775C22×C4—864no—
776C22×C4—861no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—3441no—
783C22×C4—3441no—
784C22×C4—3441no—
785C22×C4C2×C4×D4311yescharacteristic
786C22×C4C2×C4×D4311yescharacteristic
787C22×C4D4×D4311yescharacteristic
788C22×C4D4×D4311yescharacteristic
789C22×C4D4×D4311yescharacteristic
790C22×C4C23×D4311yescharacteristic
791M16—3441no—
792M16—3441no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—81no—
796C2×C8—861no—
797C2×C8—861no—
798C2×C8—3441no—
799C4⋊C4—21no—
800C4⋊C4—431no—
801C4⋊C4—431no—
802C4⋊C4—431no—
803C4⋊C4—431no—
804C4⋊C4—431no—
805C4⋊C4—431no—
806C4⋊C4—861no—
807C4⋊C4—861no—
808C4⋊C4—861no—
809C4⋊C4—861no—
810C4⋊C4—861no—
811C4⋊C4—861no—
812C4⋊C4—864no—
813C4⋊C4—861no—
814C4⋊C4—861no—
815C4⋊C4C2×C4×D4311yescharacteristic
816C4⋊C4C2×C4×D4311yescharacteristic
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—431no—
822C22⋊C4—431no—
823C22⋊C4—431no—
824C22⋊C4—431no—
825C22⋊C4—431no—
826C22⋊C4—431no—
827C22⋊C4—431no—
828C22⋊C4—431no—
829C22⋊C4—861no—
830C22⋊C4—861no—
831C22⋊C4—861no—
832C22⋊C4—861no—
833C22⋊C4—864no—
834C22⋊C4—861no—
835C22⋊C4—861no—
836C22⋊C4—861no—
837C22⋊C4—861no—
838C22⋊C4—861no—
839C22⋊C4—861no—
840C22⋊C4—864no—
841C22⋊C4—861no—
842C22⋊C4—861no—
843C22⋊C4—861no—
844C22⋊C4—861no—
845C22⋊C4—861no—
846C42—431no—
847C42—431no—
848C42—431no—
849C42—431no—
850C42—861no—
851C42—861no—
852C42—864no—
853C42—861no—
854C42—3441no—
855C42—3441no—
856C42—3441no—
857C23—22no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—41no—
863C23—42no—
864C23—81no—
865C23—81no—
866C23—431no—
867C23—431no—
868C23—862no—
869C23—861no—
870C23—861no—
871C23—861no—
872C23—3441no—
873C23—3441no—
874C23—1721no—
875C23—1722no—
876C23C22⋊C4×D4311yescharacteristic
877C23C22⋊C4×D4311yescharacteristic
878C23C2×D4×D4311yescharacteristic
879Q8—3441no—
880Q8—1721no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—434no—
891D4—862no—
892D4—862no—
893D4—862no—
894D4—3441no—
895D4—3441no—
896D4—3441no—
897D4—3441no—
898D4—3441no—
899D4—3441no—
900D4—1721no—
901D4—1722no—
902D4—1722no—
903D4—1722no—
904D4—1721no—
905D4—1721no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—81no—
921C2×C4—84no—
922C2×C4—431no—
923C2×C4—431no—
924C2×C4—431no—
925C2×C4—431no—
926C2×C4—431no—
927C2×C4—431no—
928C2×C4—862no—
929C2×C4—861no—
930C2×C4—861no—
931C2×C4—862no—
932C2×C4—862no—
933C2×C4—861no—
934C2×C4—861no—
935C2×C4—861no—
936C2×C4—3441no—
937C2×C4—3441no—
938C2×C4—3441no—
939C2×C4—3444no—
940C2×C4—3441no—
941C2×C4—3441no—
942C2×C4—1721no—
943C2×C4—1721no—
944C2×C4—1721no—
945C2×C4—1721no—
946C2×C4—1722no—
947C2×C4—1721no—
948C2×C4—1721no—
949C2×C4—1721no—
950C2×C4—1721no—
951C2×C4—1721no—
952C2×C4C22⋊C4×D4311yescharacteristic
953C2×C4C22⋊C4×D4311yescharacteristic
954C2×C4C22×C4×D4311yescharacteristic
955C2×C4C2×D4×D4311yescharacteristic
956C8—41no—
957C8—41no—
958C8—1721no—
959C8—1721no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—42no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—162no—
976C22—432no—
977C22—861no—
978C22—861no—
979C22—861no—
980C22—861no—
981C22—861no—
982C22—1722no—
983C22—1722no—
984C22—1721no—
985C22—1721no—
986C22—1721no—
987C22—6882no—
988C22#104×D4312yes—
989C22C2×C22⋊C4×D4311yescharacteristic
990C22#1458370011yescharacteristic
991C22#1458370511yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—432no—
1001C4—861no—
1002C4—861no—
1003C4—861no—
1004C4—861no—
1005C4—861no—
1006C4—1722no—
1007C4—1722no—
1008C4—1721no—
1009C4—1721no—
1010C4—1721no—
1011C2—21no—
1012C2—21no—
1013C2—22no—
1014C2—41no—
1015C2—81no—
1016C2—81no—
1017C2—862no—
1018C2—3441no—
1019C2—1721no—
1020C2#1914305311yescharacteristic
1021C2#1914311611yescharacteristic
1022C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#327C2
socleC22×C43C22×C22⋊C4
prime radical#19148621C2
cosocleC22×C4×C43C24
hypercenterC2×#327D43
hypocenterC43#17547
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #19143626C2semidirect
3. #19136953C2semidirect
4. #19133117C2semidirect
5. #19133111C2semidirect
6. #19133109C2semidirect
7. #19133101C2semidirect
8. #19133097C2semidirect
9. #19133096C2semidirect
10. #19133088C2semidirect
11. #19133087C2semidirect
12. #19133083C2semidirect
13. #19133078C2semidirect
14. #327×D43C2semidirect
15. C2×C43×#327C2semidirect
16. #14583613C4semidirect
17. #14583604C4semidirect
18. #14583597C4semidirect
19. #14583596C4semidirect
21. #14583567C4semidirect
22. #14583546C4semidirect
24. #14583543C4semidirect
27. D4×C22⋊D43C4semidirect
43. #14582953C22semidirect
44. #14582949C22semidirect
45. #14582863C22semidirect
46. #14582861C22semidirect
47. C22⋊C8×D43C22semidirect
49. #14582750C22semidirect
51. C4×C22⋊Dic43C22semidirect
53. #14582746C22semidirect
54. #14582744C22semidirect
55. #95×D43C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582635C22semidirect
59. #14582635C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
64. #14582633C22semidirect
65. #14582633C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
69. C2×C22⋊C8×C43C22semidirect
70. C2×#95×C43C22semidirect
73. C43×#327C22semidirect
74. C43×#327C22semidirect
75. C2×#10621898C2×C4semidirect
77. C2×#10621900C2×C4semidirect
81. C2×D4×D43C2×C4semidirect
87. #13063324C2×C4semidirect
89. #13063321C2×C4semidirect
93. #13063316C2×C4semidirect
96. #13063312C2×C4semidirect
106. #13063305C2×C4semidirect
108. #13063304C2×C4semidirect
111. #13063300C2×C4semidirect
113. #13063299C2×C4semidirect
125. #13063296C2×C4semidirect
126. #13063296C2×C4semidirect
133. #13063290C2×C4semidirect
136. D4×Dic43C2×C4semidirect
137. D4×Dic43C2×C4semidirect
138. #13063287C2×C4semidirect
156. #13063284C2×C4semidirect
157. #13063283C2×C4semidirect
162. C4⋊C4×D43C2×C4semidirect
189. C22×D4×C43C2×C4semidirect
195. #121×C43C2×C4semidirect
196. #121×C43C2×C4semidirect
199. C2×C4⋊C4×C43C2×C4semidirect
514. C2×#327D43semidirect
560. C2×C22⋊C8C2×D43semidirect
569. C2×#95C2×D43semidirect
584. #327C2×D43semidirect
585. #327C2×D43semidirect
586. C43#17547semidirect
595. C22×D4C4×D43semidirect
646. #121C4×D43semidirect
647. #121C4×D43semidirect
686. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191486212
#191436262
#191369532
#191331172
#191331112
#191331092
#191331012
#191330972
#191330962
#191330882
#191330872
#191330832
#191330782
#327×D432
C2×C43×#3272
#1754743