Finite Group Databasebeta

← #25064253

Subgroups — #25064253

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#19148267C211yesmaximal, characteristic
2#19143041C211yesmaximal, characteristic, complemented
3#19137419C211yesmaximal, characteristic, complemented
4#19133165C211yesmaximal, characteristic, complemented
5#19133148C211yesmaximal, characteristic, complemented
6#19133135C211yesmaximal, characteristic, complemented
7#19133127C211yesmaximal, characteristic, complemented
8#19133126C211yesmaximal, characteristic, complemented
9#19133113C211yesmaximal, characteristic, complemented
10#19133099C211yesmaximal, characteristic, complemented
11#19133096C211yesmaximal, characteristic, complemented
12#19133083C211yesmaximal, characteristic, complemented
13C2×#14582637C211yesmaximal, characteristic, complemented
14#328×D43C211yesmaximal, characteristic, complemented
15C43×#1516C211yesmaximal, characteristic, complemented
16C2×#13063372C411yescharacteristic, complemented
17C22×#10621898C2211yescharacteristic
18C2×#13063331—21no—
19D4×Dic86—21no—
20#14583558—21no—
21#14583554—21no—
22#14583547—21no—
23#14583547—21no—
24#14583545—21no—
25#14583536—21no—
26#14583536—21no—
27#14583478C411yescharacteristic, complemented
28#14583478C411yescharacteristic, complemented
29#14583477C411yescharacteristic, complemented
30#14583475C411yescharacteristic, complemented
31#14583472C411yescharacteristic, complemented
32#14583472C411yescharacteristic, complemented
33#14583409C2211yescharacteristic
34#14583409C2211yescharacteristic
35C2×#13063304C2211yescharacteristic
36C22⋊Q8×D43C2211yescharacteristic
37C22⋊Q8×D43C2211yescharacteristic
38#14583379C411yescharacteristic, complemented
39C2×(C22⋊D43)⋊C4—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#14582777—21no—
50#14582776—21no—
51#14582761C2211yescharacteristic
52#14582758C2211yescharacteristic
53#14582746C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55#95×D43C2211yescharacteristic
56#14582637C2211yescharacteristic
57#14582637C2211yescharacteristic
58#14582637C2211yescharacteristic
59#14582637C2211yescharacteristic
60#14582636C2211yescharacteristic
61#14582636C2211yescharacteristic
62#14582635C2211yescharacteristic
63#14582635C2211yescharacteristic
64#14582635C2211yescharacteristic
65#14582635C2211yescharacteristic
66#14582633C2211yescharacteristic
67#14582633C2211yescharacteristic
68C43×#525C2211yescharacteristic
69C2×C22⋊C8×C43C2211yescharacteristic
70C43×#381C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75#13063372—44no—
76C2×#10621898—21no—
77C2×#10621898—44no—
78C2×#10621898C2×C411yescharacteristic
79C2×#10621898C2×C411yescharacteristic
80C2×#10621898C2×C411yescharacteristic
81C2×#10621898C2×C411yescharacteristic
82C2×#10621898D411yescharacteristic
83C2×#10621898D411yescharacteristic
84C2×#10621898D411yescharacteristic
85C2×#10621898D411yescharacteristic
86C2×#10621900—21no—
87C2×#10621900—21no—
88C2×#10621900C2×C411yescharacteristic, complemented
89C2×#10621900C2×C411yescharacteristic, complemented
90C22×Dic86—21no—
91C22×Dic86C2×C411yescharacteristic, complemented
92C22×Dic86D411yescharacteristic
93C2×Q8×D43C2×C411yescharacteristic, complemented
94C2×Q8×D43C2×C411yescharacteristic, complemented
95C22×D172D411yescharacteristic
96C22×C22⋊D43D411yescharacteristic
97C22×C22⋊D43D411yescharacteristic
98C23×Dic43—21no—
99C22×C4×D43—21no—
100C22×C4×D43C2311yescharacteristic
101C22×C4×D43C2311yescharacteristic
102#13063331—44no—
103C2×#10621877—21no—
104C2×#10621872—21no—
105C2×#10621872—21no—
106C2×C8×D43—21no—
107C2×C8×D43—21no—
108#13063325—21no—
109#13063324—21no—
110#13063324—21no—
111#13063313—21no—
112#13063311—21no—
113#13063311—21no—
114#13063310—21no—
115#13063310—21no—
116#13063309—21no—
117#13063309—21no—
118#13063307—21no—
119#13063307—21no—
120#13063307—21no—
121#13063307—21no—
122#13063305C2×C411yescharacteristic, complemented
123#13063305C2×C411yescharacteristic, complemented
124#13063305C2×C411yescharacteristic, complemented
125#13063305C2×C411yescharacteristic, complemented
126#13063304—21no—
127#13063304—21no—
128#13063304—21no—
129#13063304C2×C411yescharacteristic, complemented
130#13063304C2×C411yescharacteristic, complemented
131#13063304C2311yescharacteristic
132#13063304C2311yescharacteristic
133#13063303—21no—
134#13063303—21no—
135#13063302—21no—
136#13063302—21no—
137#13063302—21no—
138#13063302—21no—
139#13063301C2×C411yescharacteristic, complemented
140#13063301C2×C411yescharacteristic, complemented
141#13063299—21no—
142#13063298—21no—
143#13063298—21no—
144#13063297—21no—
145#13063297—21no—
146#13063297—21no—
147#13063297—21no—
148#13063296—21no—
149#13063296—21no—
150#13063296C2×C411yescharacteristic, complemented
151#13063296C2×C411yescharacteristic, complemented
152#13063293—21no—
153#13063293—21no—
154C4×Dic86—21no—
155C4×D172—21no—
156D4×Dic43—21no—
157D4×Dic43—21no—
158(C22⋊D43)⋊C4—21no—
159(C22⋊D43)⋊C4—21no—
160(C22⋊D43)⋊C4—21no—
161(C22⋊D43)⋊C4—21no—
162(C22⋊D43)⋊C4—44no—
163#13063283C2×C411yescharacteristic, complemented
164#13063283C2×C411yescharacteristic, complemented
165C2×C4⋊Dic43C2×C411yescharacteristic, complemented
166C2×Dic43⋊C4—21no—
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
191C2×#41×C43C2×C411yescharacteristic, complemented
192C23×C4×C43C2311yescharacteristic
193C22×C8×C43—21no—
194#123×C43—21no—
195C22⋊Q8×C43C2×C411yescharacteristic, complemented
196C22⋊Q8×C43C2311yescharacteristic
197#121×C43C2×C411yescharacteristic, complemented
198#121×C43C2311yescharacteristic
199#120×C43—21no—
200C4×D4×C43—21no—
201C4×D4×C43—21no—
202#117×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
213#41×C43—42no—
214C2×Q8×C43C22×C411yescharacteristic
215C2×D4×C43—21no—
216C2×D4×C43—21no—
217C2×D4×C43—21no—
218C2×D4×C43C22×C411yescharacteristic
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—42no—
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C22×C411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2411yescharacteristic
229C2×C22⋊D43—24no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43—42no—
235C2×C22⋊D43C22⋊C411yescharacteristic
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
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—42no—
250C22×Dic43—42no—
251C22×Dic43—81no—
252C22×Dic43C2×D411yescharacteristic
253C22×Dic43C2×D411yescharacteristic
254Q8×D43—42no—
255Q8×D43—42no—
256#10621900—42no—
257#10621900—42no—
258#10621900—44no—
259#10621900—44no—
260#10621898—24no—
261#10621898—24no—
262#10621898—42no—
263#10621898—42no—
264#10621898—42no—
265#10621898—42no—
266#10621898—44no—
267#10621898—42no—
268#10621898—42no—
269C2×D172—42no—
270C2×D172C22⋊C411yescharacteristic
271C2×D172C22⋊C411yescharacteristic
272C2×D172C22⋊C411yescharacteristic
273C2×D172C22⋊C411yescharacteristic
274C2×C4×D43—21no—
275C2×C4×D43—21no—
276C2×C4×D43—21no—
277C2×C4×D43—21no—
278C2×C4×D43—42no—
279C2×C4×D43—42no—
280C2×C4×D43—42no—
281C2×C4×D43—42no—
282C2×C4×D43—81no—
283C2×C4×D43C22×C411yescharacteristic
284C2×C4×D43C22×C411yescharacteristic
285C2×C4×D43C22×C411yescharacteristic
286C2×C4×D43C22×C411yescharacteristic
287C2×C4×D43C2×D411yescharacteristic
288C2×C4×D43C2×D411yescharacteristic
289C2×C4×D43C2×D411yescharacteristic
290C2×C4×D43C2×D411yescharacteristic
291C2×Dic86—21no—
292C2×Dic86—21no—
293C2×Dic86—21no—
294C2×Dic86—42no—
295C2×Dic86—44no—
296C2×Dic86—42no—
297C2×Dic86C22⋊C411yescharacteristic
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×C43C22×C411yescharacteristic
309C4⋊C4×C43C22×C411yescharacteristic
310C22⋊C4×C43—21no—
311C22⋊C4×C43—21no—
312C22⋊C4×C43—21no—
313C22⋊C4×C43—21no—
314C22⋊C4×C43—21no—
315C22⋊C4×C43—42no—
316C42×C43—21no—
317C22⋊Dic43—21no—
318C22⋊Dic43—21no—
319C22⋊Dic43—21no—
320C22⋊Dic43—21no—
321C22⋊Dic43—21no—
322C22⋊Dic43—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—42no—
332(C2×D43)⋊C4—42no—
333(C2×D43)⋊C4—81no—
334C4⋊Dic43—21no—
335C4⋊Dic43—21no—
336C4⋊Dic43—21no—
337C4⋊Dic43—21no—
338C4⋊Dic43—21no—
339C4⋊Dic43C22×C411yescharacteristic
340C4⋊Dic43C22×C411yescharacteristic
341Dic43⋊C4—21no—
342Dic43⋊C4—21no—
343Dic43⋊C4—21no—
344Dic43⋊C4—21no—
345Dic43⋊C4—21no—
346Dic43⋊C4—21no—
347Dic43⋊C4—21no—
348Dic43⋊C4—21no—
349Dic43⋊C4—42no—
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—21no—
364C23×C43—41no—
365C23×C43C2×C22⋊C411yescharacteristic
366C23×C43C2×C22⋊C411yescharacteristic
367C23×C43C22×D411yescharacteristic
368C22×D43—21no—
369C22×D43—21no—
370C22×D43—21no—
371C22×D43—21no—
372C22×D43—22no—
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—
381D4×C43—41no—
382D4×C43—41no—
383D4×C43—41no—
384D4×C43—42no—
385D4×C43—81no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—42no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
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—42no—
414C22⋊D43—42no—
415C22⋊D43—81no—
416C22⋊D43—81no—
417C22⋊D43#9914yes—
418C2×Dic43—22no—
419C2×Dic43—22no—
420C2×Dic43—21no—
421C2×Dic43—21no—
422C2×Dic43—21no—
423C2×Dic43—21no—
424C2×Dic43—41no—
425C2×Dic43—42no—
426C2×Dic43—41no—
427C2×Dic43—41no—
428C2×Dic43—42no—
429C2×Dic43—42no—
430C2×Dic43—41no—
431C2×Dic43—41no—
432C2×Dic43—41no—
433C2×Dic43—81no—
434C2×Dic43—84no—
435C2×Dic43C2×C22⋊C411yescharacteristic
436C2×Dic43C2×C22⋊C411yescharacteristic
437C2×Dic43C2×C22⋊C411yescharacteristic
438C2×Dic43C2×C22⋊C411yescharacteristic
439D172—22no—
440D172—22no—
441D172—41no—
442D172—41no—
443C4×D43—22no—
444C4×D43—22no—
445C4×D43—22no—
446C4×D43—22no—
447C4×D43—41no—
448C4×D43—41no—
449C4×D43—41no—
450C4×D43—41no—
451C4×D43—42no—
452C4×D43—42no—
453C4×D43—81no—
454C4×D43—81no—
455C4×D43—84no—
456Dic86—22no—
457Dic86—22no—
458Dic86—41no—
459Dic86—41no—
460Dic86—42no—
461Dic86—42no—
462Dic86—42no—
463Dic86—41no—
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×C43—41no—
480C22×C43—41no—
481C22×C43—41no—
482C22×C43C2×#9912yes—
483C22×C43C22×C22⋊C411yescharacteristic
484C22×C43#57711yescharacteristic
485C22×C43#57811yescharacteristic
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—21no—
495C2×D43—21no—
496C2×D43—21no—
497C2×D43—42no—
498C2×D43—42no—
499C2×D43—81no—
500C2×D43—81no—
501C2×D43C2×#9912yes—
502C4×C43—21no—
503C4×C43—21no—
504C4×C43—21no—
505C4×C43—21no—
506C4×C43—41no—
507C4×C43—41no—
508C4×C43—41no—
509C4×C43—81no—
510C4×C43—81no—
511Dic43—21no—
512Dic43—21no—
513Dic43—21no—
514Dic43—42no—
515Dic43—41no—
516Dic43—41no—
517Dic43—41no—
518Dic43—41no—
519Dic43—81no—
520Dic43C2×#9912yes—
521#3489—431no—
522#2880—431no—
523#2339—431no—
524#1520—431no—
525#1516—431no—
526#1516D4311yescharacteristic, complemented
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×#328—431no—
536C2×C43—21no—
537C2×C43—21no—
538C2×C43—22no—
539C2×C43—41no—
540C2×C43—81no—
541C2×C43C22×#9911yescharacteristic
542C2×C43#289811yescharacteristic
543C2×C43#290111yescharacteristic
544D43—22no—
545D43—41no—
546D43—41no—
547D43—41no—
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#525C2×D4311yescharacteristic
568C2×C22⋊Q8—431no—
569C2×C22⋊Q8—431no—
570C2×C22⋊Q8—431no—
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#381C2×D4311yescharacteristic
587#380—431no—
588C4×C22⋊C4—431no—
589C2×#95—431no—
590C2×#95—431no—
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#328—431no—
600#328—431no—
601#328C2×D4311yescharacteristic
602#328C2×D4311yescharacteristic
603#327—431no—
604#327—431no—
605#327C2×D4311yescharacteristic
606#327C2×D4311yescharacteristic
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—861no—
620C2×#41—861no—
621C2×#41—861no—
622C2×#41—1724no—
623C2×#41C4×D4311yescharacteristic, complemented
624C22×Q8—431no—
625C22×Q8—431no—
626C22×Q8—431no—
627C22×Q8—431no—
628C22×Q8—861no—
629C22×D4—431no—
630C22×D4—431no—
631C22×D4—431no—
632C23×C4—431no—
633C23×C4—431no—
634C23×C4—861no—
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—21no—
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—431no—
660C22⋊Q8—431no—
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⋊Q8—861no—
677C22⋊Q8—861no—
678C22⋊Q8C4×D4311yescharacteristic, complemented
679C22⋊Q8C22×D4311yescharacteristic
680#121—431no—
681#121—431no—
682#121—861no—
683#121—861no—
684#121—861no—
685#121—861no—
686#121—861no—
687#121—861no—
688#121—861no—
689#121—861no—
690#121—861no—
691#121C4×D4311yescharacteristic, complemented
692#121C22×D4311yescharacteristic
693#120—21no—
694#120—861no—
695#120—861no—
696C4×Q8—861no—
697C4×D4—21no—
698C4×D4—21no—
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#117C4×D4311yescharacteristic, complemented
710C2×C4⋊C4—431no—
711C2×C4⋊C4—431no—
712C2×C4⋊C4—431no—
713C2×C4⋊C4—861no—
714C2×C4⋊C4—861no—
715C2×C4⋊C4—861no—
716C2×C4⋊C4—861no—
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—42no—
747#41—864no—
748#41—864no—
749#41—1722no—
750#41—1722no—
751#41—1722no—
752#41—1722no—
753#41—1722no—
754#41—1722no—
755#41—1724no—
756#41—1722no—
757#41—1722no—
758#41—1724no—
759#41—1724no—
760C2×Q8—431no—
761C2×Q8—431no—
762C2×Q8—431no—
763C2×Q8—431no—
764C2×Q8—431no—
765C2×Q8—431no—
766C2×Q8—861no—
767C2×Q8—861no—
768C2×Q8—861no—
769C2×Q8—1722no—
770C2×Q8—1722no—
771C2×Q8—1724no—
772C2×Q8—1722no—
773C2×Q8—1722no—
774C2×Q8C2×C4×D4311yescharacteristic
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
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—431no—
789C2×D4—431no—
790C2×D4—864no—
791C2×D4—861no—
792C2×D4—861no—
793C2×D4—861no—
794C2×D4—861no—
795C2×D4—1722no—
796C2×D4—1722no—
797C2×D4C2×C4×D4311yescharacteristic
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—42no—
802C22×C4—431no—
803C22×C4—431no—
804C22×C4—431no—
805C22×C4—431no—
806C22×C4—431no—
807C22×C4—431no—
808C22×C4—431no—
809C22×C4—431no—
810C22×C4—431no—
811C22×C4—431no—
812C22×C4—861no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—861no—
816C22×C4—861no—
817C22×C4—861no—
818C22×C4—861no—
819C22×C4—861no—
820C22×C4—861no—
821C22×C4—861no—
822C22×C4—3441no—
823C22×C4—3441no—
824C22×C4—1722no—
825C22×C4—1722no—
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—431no—
849C4⋊C4—431no—
850C4⋊C4—861no—
851C4⋊C4—861no—
852C4⋊C4—861no—
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—21no—
871C22⋊C4—42no—
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—861no—
886C22⋊C4—3441no—
887C22⋊C4—1722no—
888C22⋊C4—1722no—
889C42—21no—
890C42—861no—
891C42—861no—
892C42—1722no—
893C23—22no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—41no—
898C23—431no—
899C23—431no—
900C23—431no—
901C23—431no—
902C23—862no—
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—862no—
915Q8—862no—
916Q8—1721no—
917Q8—1721no—
918Q8—1721no—
919Q8—1721no—
920Q8—1722no—
921Q8—1722no—
922Q8—1722no—
923D4—41no—
924D4—42no—
925D4—41no—
926D4—41no—
927D4—81no—
928D4—434no—
929D4—862no—
930D4—862no—
931D4—862no—
932D4—862no—
933D4—862no—
934D4—862no—
935D4—862no—
936D4—3441no—
937D4—3441no—
938D4—1721no—
939D4—1721no—
940D4—1721no—
941D4—1721no—
942D4—1722no—
943D4—1722no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—431no—
961C2×C4—431no—
962C2×C4—431no—
963C2×C4—431no—
964C2×C4—862no—
965C2×C4—862no—
966C2×C4—862no—
967C2×C4—862no—
968C2×C4—862no—
969C2×C4—862no—
970C2×C4—861no—
971C2×C4—861no—
972C2×C4—861no—
973C2×C4—861no—
974C2×C4—3441no—
975C2×C4—3441no—
976C2×C4—3444no—
977C2×C4—3444no—
978C2×C4—3441no—
979C2×C4—1721no—
980C2×C4—1721no—
981C2×C4—1721no—
982C2×C4—1721no—
983C2×C4—1722no—
984C2×C4—1722no—
985C2×C4—1722no—
986C2×C4—1721no—
987C2×C4—1722no—
988C2×C4—1721no—
989C2×C4—1721no—
990C2×C4—1721no—
991C2×C4—1721no—
992C2×C4—1722no—
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—41no—
1012C22—41no—
1013C22—41no—
1014C22—432no—
1015C22—861no—
1016C22—861no—
1017C22—861no—
1018C22—861no—
1019C22—861no—
1020C22—861no—
1021C22—861no—
1022C22—861no—
1023C22—861no—
1024C22—861no—
1025C22—861no—
1026C22—3441no—
1027C22—3441no—
1028C22—1722no—
1029C22—1722no—
1030C22#99×D4312yes—
1031C22C2×C22⋊C4×D4311yescharacteristic
1032C22#1458370611yescharacteristic
1033C22#1458371311yescharacteristic
1034C4—21no—
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—41no—
1039C4—41no—
1040C4—41no—
1041C4—81no—
1042C4—81no—
1043C4—432no—
1044C4—861no—
1045C4—861no—
1046C4—861no—
1047C4—3441no—
1048C4—1722no—
1049C4—1721no—
1050C4—1721no—
1051C4—1721no—
1052C4—1721no—
1053C2—21no—
1054C2—21no—
1055C2—22no—
1056C2—41no—
1057C2—81no—
1058C2—862no—
1059C2—1721no—
1060C2—1721no—
1061C2—1721no—
1062C2C2×#99×D4311yescharacteristic
1063C2#1914312411yescharacteristic
1064C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1516C2
socleC22×C43C22×C22⋊C4
prime radical#19148267C2
cosocleC22×C4×C43C24
hypercenter#1516D43
hypocenterC43#17608
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. #19143041C2semidirect
3. #19137419C2semidirect
4. #19133165C2semidirect
5. #19133148C2semidirect
6. #19133135C2semidirect
7. #19133127C2semidirect
8. #19133126C2semidirect
9. #19133113C2semidirect
10. #19133099C2semidirect
11. #19133096C2semidirect
12. #19133083C2semidirect
13. C2×#14582637C2semidirect
14. #328×D43C2semidirect
15. C43×#1516C2semidirect
16. C2×#13063372C4semidirect
27. #14583478C4semidirect
28. #14583478C4semidirect
29. #14583477C4semidirect
30. #14583475C4semidirect
31. #14583472C4semidirect
32. #14583472C4semidirect
38. #14583379C4semidirect
88. C2×#10621900C2×C4semidirect
89. C2×#10621900C2×C4semidirect
91. C22×Dic86C2×C4semidirect
93. C2×Q8×D43C2×C4semidirect
94. C2×Q8×D43C2×C4semidirect
122. #13063305C2×C4semidirect
123. #13063305C2×C4semidirect
124. #13063305C2×C4semidirect
125. #13063305C2×C4semidirect
129. #13063304C2×C4semidirect
130. #13063304C2×C4semidirect
139. #13063301C2×C4semidirect
140. #13063301C2×C4semidirect
150. #13063296C2×C4semidirect
151. #13063296C2×C4semidirect
163. #13063283C2×C4semidirect
164. #13063283C2×C4semidirect
165. C2×C4⋊Dic43C2×C4semidirect
170. C4⋊C4×D43C2×C4semidirect
171. C4⋊C4×D43C2×C4semidirect
191. C2×#41×C43C2×C4semidirect
195. C22⋊Q8×C43C2×C4semidirect
197. #121×C43C2×C4semidirect
202. #117×C43C2×C4semidirect
526. #1516D43semidirect
607. C43#17608semidirect
623. C2×#41C4×D43semidirect
678. C22⋊Q8C4×D43semidirect
691. #121C4×D43semidirect
709. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191482672
#191430412
#191374192
#191331652
#191331482
#191331352
#191331272
#191331262
#191331132
#191330992
#191330962
#191330832
C2×#145826372
#328×D432
C43×#15162
#1760843