Finite Group Databasebeta

← #25064244

Subgroups — #25064244

Order 11008.

1298 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148271C211yesmaximal, characteristic
2#19143041C211yesmaximal, characteristic, complemented
3#19137422C211yesmaximal, characteristic, complemented
4#19133165C211yesmaximal, characteristic, complemented
5#19133152C211yesmaximal, characteristic, complemented
6#19133150C211yesmaximal, characteristic, complemented
7#19133137C211yesmaximal, characteristic, complemented
8#19133128C211yesmaximal, characteristic, complemented
9#19133126C211yesmaximal, characteristic, complemented
10#19133113C211yesmaximal, characteristic, complemented
11#19133098C211yesmaximal, characteristic, complemented
12#19133097C211yesmaximal, characteristic, complemented
13#19133085C211yesmaximal, characteristic, complemented
14#328×D43C211yesmaximal, characteristic, complemented
15C2×C43×#328C211yesmaximal, characteristic, complemented
16C2×#13063373C411yescharacteristic, complemented
17C22×#10621898C2211yescharacteristic
18C2×#13063331—21no—
19#14583562—21no—
20#14583559—21no—
21#14583551—21no—
22#14583550—21no—
23#14583550—21no—
24#14583540—21no—
25#14583539—21no—
26#14583539—21no—
27#14583480C411yescharacteristic, complemented
28#14583479C411yescharacteristic, complemented
29#14583479C411yescharacteristic, complemented
30#14583473C411yescharacteristic, complemented
31#14583472C411yescharacteristic, complemented
32#14583472C411yescharacteristic, complemented
33#14583412C2211yescharacteristic
34#14583412C2211yescharacteristic
35#14583410C2211yescharacteristic
36C22⋊Q8×D43C2211yescharacteristic
37C22⋊Q8×D43C2211yescharacteristic
38#14583380C411yescharacteristic, complemented
39C2×C4×C22⋊D43—21no—
40#14582865—21no—
41#14582864—21no—
42#14582864—21no—
43#14582863C2211yescharacteristic
44#14582861C2211yescharacteristic
45#14582861C2211yescharacteristic
46C22⋊C8×D43C2211yescharacteristic
47C22⋊C8×D43C2211yescharacteristic
48#14582803—21no—
49#14582778—21no—
50#14582777—21no—
51#14582762C2211yescharacteristic
52#14582761C2211yescharacteristic
53#14582758C2211yescharacteristic
54#14582746C2211yescharacteristic
55#95×D43C2211yescharacteristic
56#14582637C2211yescharacteristic
57#14582637C2211yescharacteristic
58#14582636C2211yescharacteristic
59#14582636C2211yescharacteristic
60#14582636C2211yescharacteristic
61#14582636C2211yescharacteristic
62#14582635C2211yescharacteristic
63#14582635C2211yescharacteristic
64#14582634C2211yescharacteristic
65#14582634C2211yescharacteristic
66#14582632C2211yescharacteristic
67#14582632C2211yescharacteristic
68C2×C22⋊Q8×C43C2211yescharacteristic
69C2×C22⋊C8×C43C2211yescharacteristic
70C2×#95×C43C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#328C2211yescharacteristic
74C43×#328C2211yescharacteristic
75#13063373—44no—
76C2×#10621902—21no—
77C2×#10621902C2×C411yescharacteristic, complemented
78C2×#10621902C2×C411yescharacteristic, complemented
79C2×#10621898—21no—
80C2×#10621898—21no—
81C2×#10621898—44no—
82C2×#10621898C2×C411yescharacteristic
83C2×#10621898C2×C411yescharacteristic
84C2×#10621898C2×C411yescharacteristic
85C2×#10621898C2×C411yescharacteristic
86C2×#10621898C2×C411yescharacteristic, complemented
87C2×#10621898D411yescharacteristic
88C2×#10621898D411yescharacteristic
89C2×#10621898D411yescharacteristic
90C2×#10621898D411yescharacteristic
91C22×Dic86D411yescharacteristic
92C2×Q8×D43—21no—
93C2×Q8×D43C2×C411yescharacteristic, complemented
94C2×Q8×D43C2×C411yescharacteristic, complemented
95C22×D172D411yescharacteristic
96C22×C22⋊D43D411yescharacteristic
97C22×C22⋊D43D411yescharacteristic
98C22×C4×D43—21no—
99C22×C4×D43C2311yescharacteristic
100C22×C4×D43C2311yescharacteristic
101#13063331—44no—
102C2×#10621877—21no—
103C2×#10621872—21no—
104C2×#10621872—21no—
105C2×C8×D43—21no—
106C2×C8×D43—21no—
107#13063324—21no—
108#13063324—21no—
109#13063323—21no—
110#13063314—21no—
111#13063311—21no—
112#13063311—21no—
113#13063310—21no—
114#13063310—21no—
115#13063310—21no—
116#13063310—21no—
117#13063308—21no—
118#13063308—21no—
119#13063308—21no—
120#13063307—21no—
121#13063307—21no—
122#13063305—21no—
123#13063305C2×C411yescharacteristic, complemented
124#13063305C2×C411yescharacteristic, complemented
125#13063304C2×C411yescharacteristic, complemented
126#13063304C2311yescharacteristic
127#13063303—21no—
128#13063303—21no—
129#13063303—21no—
130#13063303—21no—
131#13063302—21no—
132#13063302—21no—
133#13063301C2×C411yescharacteristic, complemented
134#13063301C2×C411yescharacteristic, complemented
135#13063301C2×C411yescharacteristic, complemented
136#13063301C2×C411yescharacteristic, complemented
137#13063300—21no—
138#13063300—21no—
139#13063300—21no—
140#13063300C2×C411yescharacteristic, complemented
141#13063300C2×C411yescharacteristic, complemented
142#13063299—21no—
143#13063299—21no—
144#13063299C2×C411yescharacteristic, complemented
145#13063299C2311yescharacteristic
146#13063298—21no—
147#13063298—21no—
148#13063298—21no—
149#13063298—21no—
150#13063295—21no—
151#13063295—21no—
152#13063294—21no—
153#13063290—21no—
154#13063287—21no—
155#13063287—21no—
156#13063287—21no—
157C4×C22⋊D43—21no—
158C4×C22⋊D43—21no—
159C4×C22⋊D43—21no—
160C4×C22⋊D43—21no—
161C4×C22⋊D43—44no—
162(C22⋊D43)⋊C4—21no—
163(C22⋊D43)⋊C4—21no—
164#13063284C2×C411yescharacteristic, complemented
165#13063283C2×C411yescharacteristic, complemented
166#13063283C2×C411yescharacteristic, complemented
167C2×Dic43⋊C4—21no—
168C4⋊C4×D43—21no—
169C4⋊C4×D43—21no—
170C4⋊C4×D43C2×C411yescharacteristic, complemented
171C4⋊C4×D43C2×C411yescharacteristic, complemented
172C2×C22⋊Dic43—21no—
173C2×(C2×D43)⋊C4—21no—
174C2×(C2×D43)⋊C4—21no—
175C2×(C2×D43)⋊C4—21no—
176C22⋊C4×D43—21no—
177C22⋊C4×D43—21no—
178C2×C4×Dic43—21no—
179C22⋊(C43⋊C8)—21no—
180C22⋊(C43⋊C8)C2311yescharacteristic
181C22⋊(C43⋊C8)C2311yescharacteristic
182(C2×D43)⋊C8—21no—
183(C2×D43)⋊C8—21no—
184(C2×D43)⋊C8—21no—
185(C2×D43)⋊C8—21no—
186C43⋊#95—21no—
187C43⋊#95—21no—
188C43⋊#95—21no—
189C43⋊#95C2311yescharacteristic
190C43⋊#95C2311yescharacteristic
191C22×Q8×C43C2×C411yescharacteristic, complemented
192C23×C4×C43—21no—
193C23×C4×C43C2311yescharacteristic
194C22×C8×C43—21no—
195C22⋊Q8×C43—21no—
196C22⋊Q8×C43—21no—
197C22⋊Q8×C43C2×C411yescharacteristic, complemented
198C22⋊Q8×C43C2×C411yescharacteristic, complemented
199C22⋊Q8×C43C2311yescharacteristic
200C22⋊Q8×C43C2311yescharacteristic
201C2×C4⋊C4×C43—21no—
202C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
203C2×C22⋊C4×C43—21no—
204C22⋊C8×C43—21no—
205C22⋊C8×C43C2311yescharacteristic
206C22⋊C8×C43C2311yescharacteristic
207#95×C43—21no—
208#95×C43C2311yescharacteristic
209#95×C43C2311yescharacteristic
210C24×C43C2×D411yescharacteristic
211C23×D43C2×D411yescharacteristic
212C23×D43C2×D411yescharacteristic
213C2×Q8×C43—21no—
214C2×Q8×C43—42no—
215C2×Q8×C43C22×C411yescharacteristic
216C2×Q8×C43C22×C411yescharacteristic
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—42no—
222C22×C4×C43—42no—
223C22×C4×C43—42no—
224C22×C4×C43—81no—
225C22×C4×C43C22×C411yescharacteristic
226C22×C4×C43C22×C411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2411yescharacteristic
231C2×C22⋊D43—24no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43—21no—
235C2×C22⋊D43—42no—
236C2×C22⋊D43C22⋊C411yescharacteristic
237C2×C22⋊D43C22⋊C411yescharacteristic
238C2×C22⋊D43C22⋊C411yescharacteristic
239C2×C22⋊D43C22⋊C411yescharacteristic
240C2×C22⋊D43C22⋊C411yescharacteristic
241C2×C22⋊D43C22⋊C411yescharacteristic
242C2×C22⋊D43C22⋊C411yescharacteristic
243C2×C22⋊D43C22⋊C411yescharacteristic
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43C2×D411yescharacteristic
247C22×Dic43C2×D411yescharacteristic
248#10621902—42no—
249#10621902—42no—
250#10621902—44no—
251Q8×D43—44no—
252Q8×D43—42no—
253Q8×D43—42no—
254#10621898—24no—
255#10621898—24no—
256#10621898—42no—
257#10621898—42no—
258#10621898—42no—
259#10621898—42no—
260#10621898—42no—
261#10621898—42no—
262#10621898—44no—
263#10621898—44no—
264#10621898—42no—
265C2×D172—21no—
266C2×D172—21no—
267C2×D172—21no—
268C2×D172—21no—
269C2×D172—42no—
270C2×D172C22⋊C411yescharacteristic
271C2×D172C22⋊C411yescharacteristic
272C2×D172C22⋊C411yescharacteristic
273C2×D172C22⋊C411yescharacteristic
274C2×D172C22×C411yescharacteristic
275C2×C4×D43—21no—
276C2×C4×D43—21no—
277C2×C4×D43—21no—
278C2×C4×D43—21no—
279C2×C4×D43—21no—
280C2×C4×D43—21no—
281C2×C4×D43—21no—
282C2×C4×D43—42no—
283C2×C4×D43—42no—
284C2×C4×D43—42no—
285C2×C4×D43—42no—
286C2×C4×D43—81no—
287C2×C4×D43C22×C411yescharacteristic
288C2×C4×D43C22×C411yescharacteristic
289C2×C4×D43C22×C411yescharacteristic
290C2×C4×D43C22×C411yescharacteristic
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—
298C2×Dic86C22⋊C411yescharacteristic
299C2×Dic86C22⋊C411yescharacteristic
300C2×Dic86C22⋊C411yescharacteristic
301C2×Dic86C22⋊C411yescharacteristic
302C2×Dic86C22×C411yescharacteristic
303C2×C8×C43—21no—
304C2×C8×C43—21no—
305C2×C8×C43—42no—
306C4⋊C4×C43—21no—
307C4⋊C4×C43—21no—
308C4⋊C4×C43—21no—
309C4⋊C4×C43—21no—
310C4⋊C4×C43—21no—
311C4⋊C4×C43C22×C411yescharacteristic
312C4⋊C4×C43C22×C411yescharacteristic
313C22⋊C4×C43—21no—
314C22⋊C4×C43—21no—
315C22⋊C4×C43—21no—
316C22⋊C4×C43—21no—
317C22⋊Dic43—21no—
318C22⋊Dic43—21no—
319C22⋊Dic43—21no—
320C22⋊Dic43—42no—
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)⋊C4—21no—
331(C2×D43)⋊C4—21no—
332(C2×D43)⋊C4—21no—
333(C2×D43)⋊C4—42no—
334(C2×D43)⋊C4—42no—
335(C2×D43)⋊C4—81no—
336C4⋊Dic43—21no—
337C4⋊Dic43—21no—
338C4⋊Dic43C22×C411yescharacteristic
339C4⋊Dic43C22×C411yescharacteristic
340Dic43⋊C4—21no—
341Dic43⋊C4—21no—
342Dic43⋊C4—21no—
343Dic43⋊C4—21no—
344Dic43⋊C4—21no—
345Dic43⋊C4—21no—
346Dic43⋊C4—21no—
347Dic43⋊C4—21no—
348Dic43⋊C4—42no—
349C4×Dic43—21no—
350C4×Dic43—21no—
351C4×Dic43—21no—
352C4×Dic43—42no—
353#10621877—42no—
354C2×C43⋊C8—21no—
355C2×C43⋊C8—21no—
356#10621872—42no—
357#10621872—42no—
358C8×D43—42no—
359C8×D43—42no—
360C23×C43—21no—
361C23×C43—21no—
362C23×C43—22no—
363C23×C43—41no—
364C23×C43C2×C22⋊C411yescharacteristic
365C23×C43C2×C22⋊C411yescharacteristic
366C23×C43C22×D411yescharacteristic
367C22×D43—21no—
368C22×D43—21no—
369C22×D43—21no—
370C22×D43—21no—
371C22×D43—22no—
372C22×D43—21no—
373C22×D43—41no—
374C22×D43—41no—
375C22×D43—41no—
376C22×D43C2×C22⋊C411yescharacteristic
377C22×D43C2×C22⋊C411yescharacteristic
378C22×D43C2×C22⋊C411yescharacteristic
379C22×D43C2×C22⋊C411yescharacteristic
380Q8×C43—41no—
381Q8×C43—41no—
382Q8×C43—42no—
383C2×C4×C43—22no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—21no—
387C2×C4×C43—21no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—42no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—81no—
401C2×C4×C43—84no—
402C2×C4×C43C2×C22⋊C411yescharacteristic
403C2×C4×C43C2×C22⋊C411yescharacteristic
404C2×C4×C43C23×C411yescharacteristic
405C2×C4×C43C22×D411yescharacteristic
406C22⋊D43—22no—
407C22⋊D43—22no—
408C22⋊D43—22no—
409C22⋊D43—22no—
410C22⋊D43—22no—
411C22⋊D43—41no—
412C22⋊D43—41no—
413C22⋊D43—41no—
414C22⋊D43—41no—
415C22⋊D43—42no—
416C22⋊D43—81no—
417C22⋊D43#9914yes—
418C2×Dic43—22no—
419C2×Dic43—21no—
420C2×Dic43—21no—
421C2×Dic43—21no—
422C2×Dic43—41no—
423C2×Dic43—41no—
424C2×Dic43—41no—
425C2×Dic43—41no—
426C2×Dic43—41no—
427C2×Dic43—41no—
428C2×Dic43—41no—
429C2×Dic43C2×C22⋊C411yescharacteristic
430C2×Dic43C2×C22⋊C411yescharacteristic
431C2×Dic43C2×C22⋊C411yescharacteristic
432C2×Dic43C2×C22⋊C411yescharacteristic
433D172—22no—
434D172—22no—
435D172—41no—
436D172—41no—
437D172—41no—
438D172—42no—
439D172—42no—
440D172—81no—
441D172—81no—
442C4×D43—22no—
443C4×D43—22no—
444C4×D43—22no—
445C4×D43—22no—
446C4×D43—41no—
447C4×D43—41no—
448C4×D43—41no—
449C4×D43—41no—
450C4×D43—42no—
451C4×D43—42no—
452C4×D43—42no—
453C4×D43—42no—
454C4×D43—42no—
455C4×D43—81no—
456C4×D43—81no—
457C4×D43—84no—
458Dic86—22no—
459Dic86—22no—
460Dic86—41no—
461Dic86—41no—
462Dic86—42no—
463Dic86—42no—
464Dic86—41no—
465C8×C43—41no—
466C8×C43—41no—
467C43⋊C8—41no—
468C43⋊C8—41no—
469#17608—431nomaximal, Sylow
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—21no—
474C22×C43—21no—
475C22×C43—21no—
476C22×C43—21no—
477C22×C43—42no—
478C22×C43—42no—
479C22×C43C2×#9912yes—
480C22×C43C22×C22⋊C411yescharacteristic
481C22×C43#57711yescharacteristic
482C22×C43#57811yescharacteristic
483C2×D43—21no—
484C2×D43—21no—
485C2×D43—21no—
486C2×D43—21no—
487C2×D43—21no—
488C2×D43—21no—
489C2×D43—21no—
490C2×D43—21no—
491C2×D43—21no—
492C2×D43—21no—
493C2×D43—21no—
494C2×D43—42no—
495C2×D43—42no—
496C2×D43—41no—
497C2×D43—41no—
498C2×D43—41no—
499C2×D43—81no—
500C2×D43—81no—
501C2×D43C2×#9912yes—
502C4×C43—21no—
503C4×C43—21no—
504C4×C43—21no—
505C4×C43—21no—
506C4×C43—42no—
507C4×C43—41no—
508C4×C43—41no—
509C4×C43—41no—
510C4×C43—41no—
511C4×C43—81no—
512Dic43—21no—
513Dic43—21no—
514Dic43—21no—
515Dic43—41no—
516Dic43—41no—
517Dic43—41no—
518Dic43—81no—
519Dic43—81no—
520Dic43C2×#9912yes—
521#3489—431no—
522#2880—431no—
523#2339—431no—
524#1520—431no—
525#1516—431no—
526#1516—431no—
527#1513—431no—
528#1511—431no—
529#1511—431no—
530#1508—431no—
531#1504—431no—
532#1504—431no—
533#1501—431no—
534C2×#328—431no—
535C2×#328D4311yescharacteristic, complemented
536C2×C43—21no—
537C2×C43—21no—
538C2×C43—22no—
539C2×C43—41no—
540C2×C43C22×#9911yescharacteristic
541C2×C43#289811yescharacteristic
542C2×C43#290111yescharacteristic
543D43—22no—
544D43—41no—
545D43—41no—
546D43—41no—
547D43—81no—
548C2×2−1+4—431no—
549C22×#41—431no—
550C2×#131—861no—
551D4×Q8—861no—
552#548—861no—
553#547—861no—
554#547—861no—
555#547—861no—
556#546—861no—
557#546—861no—
558#546—861no—
559#537—431no—
560#537—431no—
561#537—431no—
562#536—431no—
563#536—431no—
564#536—431no—
565#525—431no—
566#525—431no—
567#525—431no—
568C2×C22⋊Q8—431no—
569C2×C22⋊Q8—431no—
570C2×C22⋊Q8C2×D4311yescharacteristic
571#520—431no—
572C2×C4×D4—861no—
573#408—861no—
574#408—861no—
575#408—861no—
576#407—431no—
577#407—431no—
578#407—431no—
579C2×C22⋊C8—431no—
580C2×C22⋊C8—431no—
581C2×C22⋊C8C2×D4311yescharacteristic
582#391—861no—
583#386—861no—
584#386—861no—
585#381—431no—
586#381—431no—
587#380—431no—
588C4×C22⋊C4—431no—
589C2×#95—431no—
590C2×#95C2×D4311yescharacteristic
591#328—431no—
592#328—431no—
593#328—431no—
594#328—431no—
595#328—431no—
596#328—431no—
597#328—431no—
598#328—431no—
599#328C2×D4311yescharacteristic
600#328C2×D4311yescharacteristic
601#328C2×D4311yescharacteristic
602#328C2×D4311yescharacteristic
603#327—431no—
604#327—431no—
605#327—431no—
606#327—431no—
607C43#1760811yescharacteristic, complemented, Sylow
6082−1+4—1724no—
609C2×#41—431no—
610C2×#41—431no—
611C2×#41—431no—
612C2×#41—431no—
613C2×#41—431no—
614C2×#41—431no—
615C2×#41—431no—
616C2×#41—431no—
617C2×#41—431no—
618C2×#41—431no—
619C2×#41—431no—
620C2×#41—861no—
621C2×#41—861no—
622C2×#41—861no—
623C2×#41—1724no—
624C22×Q8—431no—
625C22×Q8—431no—
626C22×Q8—431no—
627C22×Q8—861no—
628C22×Q8C4×D4311yescharacteristic, complemented
629C22×D4—431no—
630C22×D4—431no—
631C22×D4—431no—
632C23×C4—21no—
633C23×C4—431no—
634C23×C4—431no—
635C23×C4—861no—
636C23×C4C22×D4311yescharacteristic
637#131—1724no—
638C2×M16—861no—
639C2×M16—861no—
640C2×M16—861no—
641C22×C8—21no—
642C22×C8—861no—
643C22×C8—861no—
644C4⋊Q8—861no—
645C4⋊Q8—861no—
646C4⋊Q8—861no—
647#124—861no—
648#124—861no—
649#124—861no—
650#123—861no—
651#123—861no—
652#123—861no—
653#123—861no—
654#123—861no—
655#123—861no—
656#123—861no—
657#123—861no—
658#123—861no—
659C22⋊Q8—21no—
660C22⋊Q8—21no—
661C22⋊Q8—431no—
662C22⋊Q8—431no—
663C22⋊Q8—431no—
664C22⋊Q8—431no—
665C22⋊Q8—431no—
666C22⋊Q8—431no—
667C22⋊Q8—431no—
668C22⋊Q8—431no—
669C22⋊Q8—861no—
670C22⋊Q8—861no—
671C22⋊Q8—861no—
672C22⋊Q8—861no—
673C22⋊Q8—861no—
674C22⋊Q8—861no—
675C22⋊Q8—861no—
676C22⋊Q8C4×D4311yescharacteristic, complemented
677C22⋊Q8C4×D4311yescharacteristic, complemented
678C22⋊Q8C22×D4311yescharacteristic
679C22⋊Q8C22×D4311yescharacteristic
680#121—431no—
681#121—431no—
682#121—431no—
683#121—431no—
684#121—861no—
685#121—861no—
686#121—861no—
687#121—861no—
688#121—861no—
689#121—861no—
690#121—861no—
691#121—861no—
692#121—861no—
693#120—861no—
694#120—861no—
695#120—861no—
696C4×Q8—861no—
697C4×D4—861no—
698C4×D4—861no—
699C4×D4—861no—
700C4×D4—861no—
701C4×D4—861no—
702C4×D4—861no—
703C4×D4—861no—
704C4×D4—861no—
705C4×D4—861no—
706C4×D4—1724no—
707#117—431no—
708#117—431no—
709#117—431no—
710C2×C4⋊C4—21no—
711C2×C4⋊C4—431no—
712C2×C4⋊C4—431no—
713C2×C4⋊C4—861no—
714C2×C4⋊C4—861no—
715C2×C4⋊C4—861no—
716C2×C4⋊C4C4×D4311yescharacteristic, complemented
717C2×C22⋊C4—21no—
718C2×C22⋊C4—861no—
719C2×C22⋊C4—861no—
720C2×C22⋊C4—861no—
721C2×C22⋊C4—861no—
722C2×C22⋊C4—861no—
723C2×C22⋊C4—861no—
724C2×C42—861no—
725C22⋊C8—21no—
726C22⋊C8—431no—
727C22⋊C8—431no—
728C22⋊C8—861no—
729C22⋊C8—861no—
730C22⋊C8—861no—
731C22⋊C8—861no—
732C22⋊C8—861no—
733C22⋊C8C22×D4311yescharacteristic
734C22⋊C8C22×D4311yescharacteristic
735#95—21no—
736#95—431no—
737#95—431no—
738#95—861no—
739#95—861no—
740#95—861no—
741#95C22×D4311yescharacteristic
742#95C22×D4311yescharacteristic
743C24—431no—
744C24—431no—
745C24D4×D4311yescharacteristic
746#41—864no—
747#41—864no—
748#41—1722no—
749#41—1722no—
750#41—1722no—
751#41—1722no—
752#41—1722no—
753#41—1722no—
754#41—1722no—
755#41—1724no—
756#41—1724no—
757#41—1722no—
758#41—1722no—
759#41—1724no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8—431no—
763C2×Q8—431no—
764C2×Q8—431no—
765C2×Q8—431no—
766C2×Q8—431no—
767C2×Q8—861no—
768C2×Q8—861no—
769C2×Q8—1722no—
770C2×Q8—1722no—
771C2×Q8—1722no—
772C2×Q8—1724no—
773C2×Q8C2×C4×D4311yescharacteristic
774C2×Q8C2×C4×D4311yescharacteristic
775C2×D4—431no—
776C2×D4—431no—
777C2×D4—431no—
778C2×D4—431no—
779C2×D4—431no—
780C2×D4—431no—
781C2×D4—431no—
782C2×D4—431no—
783C2×D4—431no—
784C2×D4—431no—
785C2×D4—431no—
786C2×D4—431no—
787C2×D4—431no—
788C2×D4—861no—
789C2×D4—861no—
790C2×D4—861no—
791C2×D4—861no—
792C2×D4—864no—
793C2×D4—861no—
794C2×D4—861no—
795C2×D4—861no—
796C2×D4—1722no—
797C2×D4—1722no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—81no—
806C22×C4—431no—
807C22×C4—431no—
808C22×C4—431no—
809C22×C4—431no—
810C22×C4—431no—
811C22×C4—431no—
812C22×C4—431no—
813C22×C4—431no—
814C22×C4—431no—
815C22×C4—431no—
816C22×C4—861no—
817C22×C4—861no—
818C22×C4—861no—
819C22×C4—861no—
820C22×C4—861no—
821C22×C4—861no—
822C22×C4—861no—
823C22×C4—861no—
824C22×C4—861no—
825C22×C4—3441no—
826C22×C4—1722no—
827C22×C4—1722no—
828C22×C4—1722no—
829C22×C4—1722no—
830C22×C4C2×C4×D4311yescharacteristic
831C22×C4C2×C4×D4311yescharacteristic
832C22×C4D4×D4311yescharacteristic
833C22×C4D4×D4311yescharacteristic
834C22×C4D4×D4311yescharacteristic
835C22×C4C23×D4311yescharacteristic
836M16—1722no—
837M16—1722no—
838M16—1722no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—42no—
842C2×C8—861no—
843C2×C8—861no—
844C2×C8—1722no—
845C2×C8—1722no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—431no—
852C4⋊C4—431no—
853C4⋊C4—861no—
854C4⋊C4—861no—
855C4⋊C4—861no—
856C4⋊C4—861no—
857C4⋊C4—861no—
858C4⋊C4—861no—
859C4⋊C4—861no—
860C4⋊C4—861no—
861C4⋊C4—861no—
862C4⋊C4—861no—
863C4⋊C4—1722no—
864C4⋊C4C2×C4×D4311yescharacteristic
865C4⋊C4C2×C4×D4311yescharacteristic
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—861no—
871C22⋊C4—861no—
872C22⋊C4—861no—
873C22⋊C4—861no—
874C22⋊C4—861no—
875C22⋊C4—861no—
876C22⋊C4—861no—
877C22⋊C4—861no—
878C22⋊C4—861no—
879C22⋊C4—861no—
880C22⋊C4—861no—
881C22⋊C4—861no—
882C22⋊C4—861no—
883C22⋊C4—861no—
884C22⋊C4—861no—
885C22⋊C4—3441no—
886C22⋊C4—1722no—
887C22⋊C4—1722no—
888C22⋊C4—1722no—
889C42—861no—
890C42—861no—
891C42—861no—
892C42—1722no—
893C23—22no—
894C23—21no—
895C23—21no—
896C23—41no—
897C23—431no—
898C23—431no—
899C23—431no—
900C23—431no—
901C23—862no—
902C23—861no—
903C23—861no—
904C23—861no—
905C23—861no—
906C23—861no—
907C23—1721no—
908C23—1721no—
909C23—1721no—
910C23C22⋊C4×D4311yescharacteristic
911C23C22⋊C4×D4311yescharacteristic
912C23C2×D4×D4311yescharacteristic
913Q8—41no—
914Q8—41no—
915Q8—42no—
916Q8—862no—
917Q8—862no—
918Q8—1721no—
919Q8—1721no—
920Q8—1721no—
921Q8—1722no—
922Q8—1722no—
923D4—434no—
924D4—862no—
925D4—862no—
926D4—862no—
927D4—862no—
928D4—862no—
929D4—862no—
930D4—862no—
931D4—3441no—
932D4—3441no—
933D4—3441no—
934D4—1721no—
935D4—1721no—
936D4—1721no—
937D4—1722no—
938D4—1722no—
939D4—1721no—
940D4—1721no—
941D4—1722no—
942D4—1721no—
943D4—1721no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—42no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—81no—
962C2×C4—84no—
963C2×C4—431no—
964C2×C4—431no—
965C2×C4—431no—
966C2×C4—431no—
967C2×C4—862no—
968C2×C4—862no—
969C2×C4—862no—
970C2×C4—862no—
971C2×C4—862no—
972C2×C4—861no—
973C2×C4—861no—
974C2×C4—861no—
975C2×C4—3444no—
976C2×C4—3441no—
977C2×C4—3441no—
978C2×C4—1721no—
979C2×C4—1721no—
980C2×C4—1721no—
981C2×C4—1721no—
982C2×C4—1722no—
983C2×C4—1722no—
984C2×C4—1722no—
985C2×C4—1722no—
986C2×C4—1722no—
987C2×C4—1721no—
988C2×C4—1721no—
989C2×C4—1721no—
990C2×C4—1721no—
991C2×C4—1721no—
992C2×C4—1721no—
993C2×C4—1721no—
994C2×C4C22⋊C4×D4311yescharacteristic
995C2×C4C22⋊C4×D4311yescharacteristic
996C2×C4C22×C4×D4311yescharacteristic
997C2×C4C2×D4×D4311yescharacteristic
998C8—41no—
999C8—41no—
1000C8—1721no—
1001C8—1721no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—42no—
1010C22—42no—
1011C22—432no—
1012C22—861no—
1013C22—861no—
1014C22—861no—
1015C22—861no—
1016C22—861no—
1017C22—861no—
1018C22—861no—
1019C22—861no—
1020C22—861no—
1021C22—861no—
1022C22—861no—
1023C22—3441no—
1024C22—3441no—
1025C22—1722no—
1026C22—1722no—
1027C22—1721no—
1028C22—1721no—
1029C22—1721no—
1030C22#99×D4312yes—
1031C22C2×C22⋊C4×D4311yescharacteristic
1032C22#1458370511yescharacteristic
1033C22#1458371211yescharacteristic
1034C4—21no—
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—42no—
1039C4—41no—
1040C4—41no—
1041C4—41no—
1042C4—41no—
1043C4—81no—
1044C4—432no—
1045C4—861no—
1046C4—861no—
1047C4—861no—
1048C4—3441no—
1049C4—3441no—
1050C4—1721no—
1051C4—1721no—
1052C4—1721no—
1053C2—21no—
1054C2—21no—
1055C2—22no—
1056C2—41no—
1057C2—862no—
1058C2—3441no—
1059C2—1721no—
1060C2—1721no—
1061C2—1721no—
1062C2C2×#99×D4311yescharacteristic
1063C2#1914312311yescharacteristic
1064C2#1914313911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#328C2
socleC22×C43C22×C22⋊C4
prime radical#19148271C2
cosocleC22×C4×C43C24
hypercenterC2×#328D43
hypocenterC43#17608
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. #19143041C2semidirect
3. #19137422C2semidirect
4. #19133165C2semidirect
5. #19133152C2semidirect
6. #19133150C2semidirect
7. #19133137C2semidirect
8. #19133128C2semidirect
9. #19133126C2semidirect
10. #19133113C2semidirect
11. #19133098C2semidirect
12. #19133097C2semidirect
13. #19133085C2semidirect
14. #328×D43C2semidirect
15. C2×C43×#328C2semidirect
16. C2×#13063373C4semidirect
27. #14583480C4semidirect
28. #14583479C4semidirect
29. #14583479C4semidirect
30. #14583473C4semidirect
31. #14583472C4semidirect
32. #14583472C4semidirect
38. #14583380C4semidirect
77. C2×#10621902C2×C4semidirect
78. C2×#10621902C2×C4semidirect
86. C2×#10621898C2×C4semidirect
93. C2×Q8×D43C2×C4semidirect
94. C2×Q8×D43C2×C4semidirect
123. #13063305C2×C4semidirect
124. #13063305C2×C4semidirect
125. #13063304C2×C4semidirect
133. #13063301C2×C4semidirect
134. #13063301C2×C4semidirect
135. #13063301C2×C4semidirect
136. #13063301C2×C4semidirect
140. #13063300C2×C4semidirect
141. #13063300C2×C4semidirect
144. #13063299C2×C4semidirect
164. #13063284C2×C4semidirect
165. #13063283C2×C4semidirect
166. #13063283C2×C4semidirect
170. C4⋊C4×D43C2×C4semidirect
171. C4⋊C4×D43C2×C4semidirect
191. C22×Q8×C43C2×C4semidirect
197. C22⋊Q8×C43C2×C4semidirect
198. C22⋊Q8×C43C2×C4semidirect
202. C2×C4⋊C4×C43C2×C4semidirect
535. C2×#328D43semidirect
607. C43#17608semidirect
628. C22×Q8C4×D43semidirect
676. C22⋊Q8C4×D43semidirect
677. C22⋊Q8C4×D43semidirect
716. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191482712
#191430412
#191374222
#191331652
#191331522
#191331502
#191331372
#191331282
#191331262
#191331132
#191330982
#191330972
#191330852
#328×D432
C2×C43×#3282
#1760843