Finite Group Databasebeta

← #25064208

Subgroups — #25064208

Order 11008.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148318C211yesmaximal, characteristic
2#19143254C211yesmaximal, characteristic, complemented
3#19137448C211yesmaximal, characteristic, complemented
4#19133171C211yesmaximal, characteristic, complemented
5#19133154C211yesmaximal, characteristic, complemented
6#19133150C211yesmaximal, characteristic, complemented
7#19133140C211yesmaximal, characteristic, complemented
8#19133122C211yesmaximal, characteristic, complemented
9#19133119C211yesmaximal, characteristic, complemented
10#19133104C211yesmaximal, characteristic, complemented
11#19133098C211yesmaximal, characteristic, complemented
12#19133088C211yesmaximal, characteristic, complemented
13#19133081C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C43×#1512C211yesmaximal, characteristic, complemented
16#14583612—21no—
17#14583600—21no—
18#14583598—21no—
19#14583574—21no—
20#14583573—21no—
21#14583547—21no—
22#14583544—21no—
23#14583541—21no—
24#14583529C411yescharacteristic, complemented
25#14583521C411yescharacteristic, complemented
26#14583518C411yescharacteristic, complemented
27#14583505C411yescharacteristic, complemented
28#14583500C411yescharacteristic, complemented
29#14583467C411yescharacteristic, complemented
30#14583449C2211yescharacteristic
31#14583444C2211yescharacteristic
32#14583435C2211yescharacteristic
33#14583412C2211yescharacteristic
34#121×D43C2211yescharacteristic
35#14583381C411yescharacteristic, complemented
36#14583371C411yescharacteristic, complemented
37C2×#13063282C2211yescharacteristic
38#14582961—21no—
39#14582959—21no—
40#14582953C2211yescharacteristic, complemented
41#14582952C2211yescharacteristic, complemented
42#14582949C2211yescharacteristic, complemented
43#14582924—21no—
44#14582861C2211yescharacteristic
45C22⋊C8×D43C2211yescharacteristic
46#14582856—21no—
47#14582781—21no—
48#14582780—21no—
49#14582770—21no—
50#14582766C2211yescharacteristic, complemented
51#14582761C2211yescharacteristic
52#14582750C2211yescharacteristic, complemented
53#14582746—21no—
54#14582745C2211yescharacteristic, complemented
55#95×D43C2211yescharacteristic
56#14582636C2211yescharacteristic, complemented
57#14582636C2211yescharacteristic, complemented
58#14582634C2211yescharacteristic
59#14582634C2211yescharacteristic
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582633C2211yescharacteristic
63#14582633C2211yescharacteristic
64#14582632C2211yescharacteristic
65#14582632C2211yescharacteristic
66#14582632C2211yescharacteristic, complemented
67#14582632C2211yescharacteristic, complemented
68C43×#529C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C43×#382C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic
76C2×#10621898—21no—
77C2×#10621900—21no—
78C2×D4×D43—21no—
79C2×D4×D43C2×C411yescharacteristic
80C22×C4×D43—21no—
81C22×C4×D43C2311yescharacteristic
82C2×#10621872—21no—
83C2×C8×D43—21no—
84#13063325C2×C411yescharacteristic, complemented
85#13063324—21no—
86#13063324C2×C411yescharacteristic, complemented
87#13063322C2×C411yescharacteristic, complemented
88#13063321C2×C411yescharacteristic, complemented
89#13063320—21no—
90#13063319—21no—
91#13063318—21no—
92#13063316C2×C411yescharacteristic, complemented
93#13063315—21no—
94#13063314C2×C411yescharacteristic, complemented
95#13063313—21no—
96#13063313—21no—
97#13063311—21no—
98#13063311—21no—
99#13063310—21no—
100#13063310—21no—
101#13063310—21no—
102#13063310—21no—
103#13063309—21no—
104#13063309—21no—
105#13063308—21no—
106#13063307—21no—
107#13063305—21no—
108#13063303—21no—
109#13063303—21no—
110#13063302—21no—
111#13063301C2×C411yescharacteristic
112#13063300—21no—
113#13063300—21no—
114#13063300C2×C411yescharacteristic
115#13063300C2×C411yescharacteristic
116#13063299—21no—
117#13063299—21no—
118#13063299C2311yescharacteristic
119#13063299C2311yescharacteristic
120#13063298—21no—
121#13063298—21no—
122#13063298—21no—
123#13063298—21no—
124#13063297—21no—
125#13063297—21no—
126#13063296C2×C411yescharacteristic
127#13063295—21no—
128#13063295—21no—
129#13063295—21no—
130Q8×Dic43C2×C411yescharacteristic, complemented
131C4×D172—21no—
132C4×D172—21no—
133C4×D172C2×C411yescharacteristic, complemented
134C4×D172C2×C411yescharacteristic, complemented
135D4×Dic43C2×C411yescharacteristic, complemented
136#13063287—21no—
137#13063287—21no—
138#13063287C2×C411yescharacteristic, complemented
139#13063287C2×C411yescharacteristic, complemented
140C4×C22⋊D43—21no—
141(C22⋊D43)⋊C4—21no—
142(C22⋊D43)⋊C4—21no—
143(C22⋊D43)⋊C4—21no—
144(C22⋊D43)⋊C4—21no—
145#13063283—21no—
146#13063283C2×C411yescharacteristic
147#13063282—21no—
148#13063282C2×C411yescharacteristic
149#13063282C2×C411yescharacteristic
150#13063282C2×C411yescharacteristic
151#13063282C2×C411yescharacteristic
152#13063282D411yescharacteristic
153#13063282D411yescharacteristic
154#13063282D411yescharacteristic
155#13063282D411yescharacteristic
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4D411yescharacteristic
158C2×Dic43⋊C4D411yescharacteristic
159C4⋊C4×D43—21no—
160C4⋊C4×D43C2×C411yescharacteristic
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4D411yescharacteristic
164C2×(C2×D43)⋊C4D411yescharacteristic
165C22⋊C4×D43—21no—
166C22⋊C4×D43—21no—
167C2×C4×Dic43—21no—
168C2×C4×Dic43—21no—
169C2×C4×Dic43C2311yescharacteristic
170C4⋊(C43⋊C8)—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)C2311yescharacteristic
174C22⋊(C43⋊C8)C2311yescharacteristic
175(C2×D43)⋊C8—21no—
176(C2×D43)⋊C8—21no—
177#13063235—21no—
178C4×C43⋊C8—21no—
179C8×Dic43—21no—
180C43⋊#95—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187#126×C43—21no—
188#125×C43C2×C411yescharacteristic, complemented
189#124×C43C2×C411yescharacteristic, complemented
190#123×C43—21no—
191C22⋊Q8×C43C2311yescharacteristic
192#121×C43C2311yescharacteristic
193C4×Q8×C43C2×C411yescharacteristic, complemented
194C4×D4×C43—21no—
195C4×D4×C43C2×C411yescharacteristic, complemented
196#117×C43—21no—
197C2×C4⋊C4×C43—21no—
198C2×C42×C43C2311yescharacteristic
199C4⋊C8×C43—21no—
200C22⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43C2311yescharacteristic
202#97×C43—21no—
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C23×D43—21no—
207C23×D43C2×D411yescharacteristic
208C2×Q8×C43C22×C411yescharacteristic
209C2×D4×C43—21no—
210C2×D4×C43C22×C411yescharacteristic
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229#10621902—42no—
230#10621900—81no—
231#10621900—81no—
232D4×D43—42no—
233D4×D43—81no—
234D4×D43—81no—
235#10621898—81no—
236#10621898—81no—
237C2×D172—21no—
238C2×D172—21no—
239C2×D172—21no—
240C2×D172—21no—
241C2×D172—21no—
242C2×D172C22×C411yescharacteristic
243C2×D172C22×C411yescharacteristic
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—42no—
251C2×C4×D43—42no—
252C2×C4×D43—42no—
253C2×C4×D43—81no—
254C2×C4×D43C22×C411yescharacteristic
255C2×C4×D43C22×C411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×Dic86—21no—
259C2×Dic86—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—81no—
267C4⋊C4×C43C22×C411yescharacteristic
268C4⋊C4×C43C22×C411yescharacteristic
269C22⋊C4×C43—21no—
270C22⋊C4×C43—21no—
271C22⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C42×C43—21no—
275C42×C43C22×C411yescharacteristic
276C42×C43C22×C411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C42×C43C2×D411yescharacteristic
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281(C2×D43)⋊C4—21no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—42no—
294(C2×D43)⋊C4C22⋊C411yescharacteristic
295(C2×D43)⋊C4C22⋊C411yescharacteristic
296(C2×D43)⋊C4C22⋊C411yescharacteristic
297(C2×D43)⋊C4C22⋊C411yescharacteristic
298(C2×D43)⋊C4C22⋊C411yescharacteristic
299(C2×D43)⋊C4C22⋊C411yescharacteristic
300(C2×D43)⋊C4C22⋊C411yescharacteristic
301(C2×D43)⋊C4C22⋊C411yescharacteristic
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43—21no—
305C4⋊Dic43C22×C411yescharacteristic
306C4⋊Dic43C22×C411yescharacteristic
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—42no—
312Dic43⋊C4C22⋊C411yescharacteristic
313Dic43⋊C4C22⋊C411yescharacteristic
314Dic43⋊C4C22⋊C411yescharacteristic
315Dic43⋊C4C22⋊C411yescharacteristic
316Dic43⋊C4C22⋊C411yescharacteristic
317Dic43⋊C4C22⋊C411yescharacteristic
318Dic43⋊C4C22⋊C411yescharacteristic
319Dic43⋊C4C22⋊C411yescharacteristic
320C4×Dic43—21no—
321C4×Dic43—21no—
322C4×Dic43—42no—
323C4×Dic43—81no—
324C4×Dic43C22×C411yescharacteristic
325C4×Dic43C22×C411yescharacteristic
326C4×Dic43C2×D411yescharacteristic
327C4×Dic43C2×D411yescharacteristic
328C2×C43⋊C8—21no—
329C2×C43⋊C8—21no—
330#10621872—42no—
331C8×D43—42no—
332C23×C43—21no—
333C23×C43C22×D411yescharacteristic
334C22×D43—21no—
335C22×D43—21no—
336C22×D43—22no—
337C22×D43—21no—
338C22×D43—21no—
339C22×D43—41no—
340C22×D43—42no—
341C22×D43—81no—
342C22×D43—81no—
343C22×D43C2×C22⋊C411yescharacteristic
344C22×D43C2×C22⋊C411yescharacteristic
345Q8×C43—41no—
346D4×C43—41no—
347D4×C43—41no—
348D4×C43—41no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—81no—
363C2×C4×C43C2×C22⋊C411yescharacteristic
364C2×C4×C43C2×C22⋊C411yescharacteristic
365C2×C4×C43C2×C22⋊C411yescharacteristic
366C2×C4×C43C2×C22⋊C411yescharacteristic
367C2×C4×C43C23×C411yescharacteristic
368C2×C4×C43C22×D411yescharacteristic
369C22⋊D43—42no—
370C22⋊D43—41no—
371C22⋊D43—41no—
372C22⋊D43—41no—
373C22⋊D43—41no—
374C22⋊D43—81no—
375C22⋊D43—81no—
376C22⋊D43—81no—
377C2×Dic43—21no—
378C2×Dic43—21no—
379C2×Dic43—22no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—41no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43—81no—
390C2×Dic43C2×C22⋊C411yescharacteristic
391C2×Dic43C2×C22⋊C411yescharacteristic
392C2×Dic43C2×C22⋊C411yescharacteristic
393C2×Dic43C2×C22⋊C411yescharacteristic
394C2×Dic43C2×C22⋊C411yescharacteristic
395C2×Dic43C2×C22⋊C411yescharacteristic
396D172—41no—
397D172—41no—
398D172—42no—
399D172—81no—
400D172—81no—
401D172—81no—
402D172—81no—
403C4×D43—22no—
404C4×D43—22no—
405C4×D43—41no—
406C4×D43—41no—
407C4×D43—42no—
408C4×D43—81no—
409C4×D43—81no—
410C4×D43—81no—
411C4×D43—81no—
412C4×D43—81no—
413C4×D43—84no—
414Dic86—81no—
415Dic86—81no—
416C8×C43—41no—
417C8×C43—41no—
418C43⋊C8—41no—
419C43⋊C8—41no—
420#17604—431nomaximal, Sylow
421C22×C43—21no—
422C22×C43—21no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43C22×C22⋊C411yescharacteristic
427C22×C43#57611yescharacteristic
428C22×C43#57711yescharacteristic
429C2×D43—21no—
430C2×D43—21no—
431C2×D43—21no—
432C2×D43—21no—
433C2×D43—21no—
434C2×D43—42no—
435C2×D43—42no—
436C2×D43—41no—
437C2×D43—41no—
438C2×D43—41no—
439C2×D43—41no—
440C2×D43—41no—
441C2×D43—41no—
442C2×D43—162no—
443C2×D43#41012yes—
444C4×C43—21no—
445C4×C43—21no—
446C4×C43—21no—
447C4×C43—21no—
448C4×C43—21no—
449C4×C43—21no—
450C4×C43—41no—
451C4×C43—41no—
452C4×C43—41no—
453C4×C43—81no—
454C4×C43—81no—
455Dic43—21no—
456Dic43—21no—
457Dic43—21no—
458Dic43—21no—
459Dic43—21no—
460Dic43—21no—
461Dic43—42no—
462Dic43—41no—
463Dic43—41no—
464Dic43—81no—
465#3494—431no—
466#2924—431no—
467#2343—431no—
468#1521—431no—
469#1517—431no—
470#1516—431no—
471#1514—431no—
472#1512D4311yescharacteristic, complemented
473#1510—431no—
474#1509—431no—
475#1505—431no—
476#1504—431no—
477#1502—431no—
478#1500—431no—
479C2×#327—431no—
480C2×C43—21no—
481C2×C43—21no—
482C2×C43—81no—
483C2×C43C2×#41011yescharacteristic
484C2×C43#289711yescharacteristic
485C2×C43#290111yescharacteristic
486D43—22no—
487D43—41no—
488D43—81no—
489D43—81no—
490#555—861no—
491#553—861no—
492#553—861no—
493#551—861no—
494#551—861no—
495#547—861no—
496#546—861no—
497#546—861no—
498#544—431no—
499#542—431no—
500#542—431no—
501#540—431no—
502#540—431no—
503#535—431no—
504#532—431no—
505#532—431no—
506#529—431no—
507#529C2×D4311yescharacteristic
508#525—431no—
509C2×#121—431no—
510#520—431no—
511#518—431no—
512C2×#117—431no—
513#433—861no—
514#433—861no—
515#432—431no—
516#432C2×D4311yescharacteristic, complemented
517#431—431no—
518#431—431no—
519#424—861no—
520#407—431no—
521C2×C22⋊C8—431no—
522#405—861no—
523#387—861no—
524#387—861no—
525#385—861no—
526#383—431no—
527#382C2×D4311yescharacteristic, complemented
528#381—431no—
529C4×C4⋊C4—431no—
530C4×C22⋊C4—861no—
531#376—431no—
532C2×#95—431no—
533#328—431no—
534#328—431no—
535#328C2×D4311yescharacteristic, complemented
536#328C2×D4311yescharacteristic, complemented
537#327—431no—
538#327—431no—
539#327—431no—
540#327—431no—
541#327—431no—
542#327—431no—
543#327—431no—
544#327—431no—
545#327—431no—
546#327—431no—
547#327C2×D4311yescharacteristic
548#327C2×D4311yescharacteristic
549C43#1760411yescharacteristic, complemented, Sylow
550C2×#41—431no—
551C2×#41—861no—
552C2×#41—861no—
553C22×D4—431no—
554C22×D4—861no—
555C23×C4—431no—
556C23×C4—861no—
557C2×M16—861no—
558C22×C8—861no—
559C4⋊Q8—431no—
560C4⋊Q8—431no—
561C4⋊Q8—861no—
562#127—431no—
563#127—431no—
564#126—21no—
565#126—861no—
566#126—861no—
567#126—861no—
568#125—431no—
569#125—861no—
570#125C4×D4311yescharacteristic, complemented
571#124—431no—
572#124—861no—
573#124—861no—
574#124—861no—
575#124—861no—
576#124C4×D4311yescharacteristic, complemented
577#123—21no—
578#123—861no—
579#123—861no—
580#123—861no—
581#123—861no—
582#123—861no—
583#123—861no—
584#123—861no—
585#123—861no—
586C22⋊Q8—431no—
587C22⋊Q8—861no—
588C22⋊Q8—861no—
589C22⋊Q8—861no—
590C22⋊Q8—861no—
591C22⋊Q8C22×D4311yescharacteristic
592#121—431no—
593#121—431no—
594#121—431no—
595#121—431no—
596#121—431no—
597#121—861no—
598#121—861no—
599#121—861no—
600#121—861no—
601#121—861no—
602#121—861no—
603#121—861no—
604#121—861no—
605#121—861no—
606#121—861no—
607#121C22×D4311yescharacteristic
608#120—861no—
609#120—861no—
610#120—861no—
611C4×Q8—431no—
612C4×Q8C4×D4311yescharacteristic, complemented
613C4×D4—21no—
614C4×D4—431no—
615C4×D4—431no—
616C4×D4—431no—
617C4×D4—431no—
618C4×D4—431no—
619C4×D4—861no—
620C4×D4—861no—
621C4×D4—861no—
622C4×D4—861no—
623C4×D4—861no—
624C4×D4—861no—
625C4×D4—861no—
626C4×D4—861no—
627C4×D4—861no—
628C4×D4C4×D4311yescharacteristic, complemented
629#117—21no—
630#117—431no—
631#117—431no—
632#117—431no—
633#117—431no—
634#117—431no—
635#117—431no—
636#117—431no—
637#117—431no—
638#117—431no—
639#117—861no—
640#117—861no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—431no—
643C2×C4⋊C4—431no—
644C2×C4⋊C4—431no—
645C2×C4⋊C4—861no—
646C2×C4⋊C4—861no—
647C2×C22⋊C4—431no—
648C2×C22⋊C4—431no—
649C2×C22⋊C4—861no—
650C2×C22⋊C4—861no—
651C2×C22⋊C4—861no—
652C2×C22⋊C4—861no—
653C2×C42—431no—
654C2×C42—861no—
655C2×C42—861no—
656C2×C42C22×D4311yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—861no—
659C4⋊C8—861no—
660C4⋊C8—861no—
661C22⋊C8—431no—
662C22⋊C8—431no—
663C22⋊C8—861no—
664C22⋊C8—861no—
665C22⋊C8C22×D4311yescharacteristic
666C22⋊C8C22×D4311yescharacteristic
667#97—21no—
668#97—861no—
669C4×C8—861no—
670C4×C8—861no—
671#95—21no—
672#95—431no—
673#95—431no—
674#95—861no—
675#95—861no—
676#95—861no—
677#95—861no—
678#95—861no—
679#95C22×D4311yescharacteristic
680#95C22×D4311yescharacteristic
681C24—431no—
682C24—861no—
683#41—3441no—
684#41—3441no—
685#41—3441no—
686#41—3441no—
687#41—1722no—
688C2×Q8—861no—
689C2×Q8—861no—
690C2×Q8C2×C4×D4311yescharacteristic
691C2×D4—21no—
692C2×D4—431no—
693C2×D4—431no—
694C2×D4—861no—
695C2×D4—861no—
696C2×D4—861no—
697C2×D4—861no—
698C2×D4—861no—
699C2×D4—861no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—861no—
704C2×D4—861no—
705C2×D4—3441no—
706C2×D4—3441no—
707C2×D4—1722no—
708C2×D4C2×C4×D4311yescharacteristic
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—431no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—431no—
717C22×C4—431no—
718C22×C4—431no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—3441no—
729C22×C4—1722no—
730C22×C4—1722no—
731C22×C4—1722no—
732C22×C4D4×D4311yescharacteristic
733C22×C4D4×D4311yescharacteristic
734C22×C4C23×D4311yescharacteristic
735M16—1722no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—861no—
739C2×C8—861no—
740C2×C8—1722no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—81no—
746C4⋊C4—431no—
747C4⋊C4—431no—
748C4⋊C4—431no—
749C4⋊C4—431no—
750C4⋊C4—431no—
751C4⋊C4—431no—
752C4⋊C4—431no—
753C4⋊C4—431no—
754C4⋊C4—431no—
755C4⋊C4—431no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—861no—
762C4⋊C4—861no—
763C4⋊C4—1722no—
764C4⋊C4C2×C4×D4311yescharacteristic
765C4⋊C4C2×C4×D4311yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—431no—
772C22⋊C4—431no—
773C22⋊C4—431no—
774C22⋊C4—431no—
775C22⋊C4—431no—
776C22⋊C4—431no—
777C22⋊C4—431no—
778C22⋊C4—431no—
779C22⋊C4—861no—
780C22⋊C4—861no—
781C22⋊C4—861no—
782C22⋊C4—861no—
783C22⋊C4—861no—
784C22⋊C4—861no—
785C22⋊C4—861no—
786C22⋊C4—861no—
787C22⋊C4—861no—
788C22⋊C4—861no—
789C22⋊C4—861no—
790C22⋊C4—861no—
791C22⋊C4—861no—
792C22⋊C4—861no—
793C22⋊C4—1722no—
794C42—21no—
795C42—431no—
796C42—431no—
797C42—431no—
798C42—431no—
799C42—861no—
800C42—861no—
801C42—3441no—
802C42—1722no—
803C42C2×C4×D4311yescharacteristic
804C42C2×C4×D4311yescharacteristic
805C42D4×D4311yescharacteristic
806C42D4×D4311yescharacteristic
807C23—21no—
808C23—431no—
809C23—431no—
810C23—862no—
811C23—861no—
812C23—861no—
813C23—861no—
814C23—861no—
815C23—3441no—
816C23—3441no—
817C23—1721no—
818C23—1722no—
819C23C2×D4×D4311yescharacteristic
820Q8—41no—
821Q8—3441no—
822Q8—3441no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—3441no—
827D4—3441no—
828D4—3441no—
829D4—3441no—
830D4—3441no—
831D4—3441no—
832D4—3441no—
833D4—1721no—
834D4—1721no—
835D4—1722no—
836D4—1722no—
837D4—1721no—
838D4—1721no—
839D4—1721no—
840D4—1721no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—81no—
855C2×C4—431no—
856C2×C4—431no—
857C2×C4—431no—
858C2×C4—431no—
859C2×C4—431no—
860C2×C4—431no—
861C2×C4—862no—
862C2×C4—862no—
863C2×C4—861no—
864C2×C4—861no—
865C2×C4—862no—
866C2×C4—861no—
867C2×C4—861no—
868C2×C4—3441no—
869C2×C4—3441no—
870C2×C4—3441no—
871C2×C4—3441no—
872C2×C4—3441no—
873C2×C4—3444no—
874C2×C4—3441no—
875C2×C4—1721no—
876C2×C4—1721no—
877C2×C4—1722no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4—1721no—
881C2×C4—1721no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4C22⋊C4×D4311yescharacteristic
886C2×C4C22⋊C4×D4311yescharacteristic
887C2×C4C22⋊C4×D4311yescharacteristic
888C2×C4C22⋊C4×D4311yescharacteristic
889C2×C4C22×C4×D4311yescharacteristic
890C2×C4C2×D4×D4311yescharacteristic
891C8—41no—
892C8—41no—
893C8—1721no—
894C8—1721no—
895C22—21no—
896C22—21no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—432no—
901C22—861no—
902C22—861no—
903C22—861no—
904C22—861no—
905C22—861no—
906C22—1722no—
907C22—1722no—
908C22—1721no—
909C22—1721no—
910C22—1721no—
911C22—1721no—
912C22—1721no—
913C22—1721no—
914C22—6882no—
915C22C2×C22⋊C4×D4311yescharacteristic
916C22#1458370311yescharacteristic
917C22#1458370811yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—41no—
925C4—41no—
926C4—41no—
927C4—81no—
928C4—81no—
929C4—861no—
930C4—861no—
931C4—861no—
932C4—861no—
933C4—861no—
934C4—861no—
935C4—3441no—
936C4—1722no—
937C4—1721no—
938C4—1721no—
939C2—21no—
940C2—21no—
941C2—81no—
942C2—862no—
943C2—3441no—
944C2—3441no—
945C2—1721no—
946C2#410×D4311yescharacteristic
947C2#1914311911yescharacteristic
948C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1512C2
socleC22×C43C22×C22⋊C4
prime radical#19148318C2
cosocleC22×C4×C43C24
hypercenter#1512D43
hypocenterC43#17604
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1512

Complements

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

NH ≅ G/Ntype
2. #19143254C2semidirect
3. #19137448C2semidirect
4. #19133171C2semidirect
5. #19133154C2semidirect
6. #19133150C2semidirect
7. #19133140C2semidirect
8. #19133122C2semidirect
9. #19133119C2semidirect
10. #19133104C2semidirect
11. #19133098C2semidirect
12. #19133088C2semidirect
13. #19133081C2semidirect
14. #327×D43C2semidirect
15. C43×#1512C2semidirect
24. #14583529C4semidirect
25. #14583521C4semidirect
26. #14583518C4semidirect
27. #14583505C4semidirect
28. #14583500C4semidirect
29. #14583467C4semidirect
35. #14583381C4semidirect
36. #14583371C4semidirect
40. #14582953C22semidirect
41. #14582952C22semidirect
42. #14582949C22semidirect
50. #14582766C22semidirect
52. #14582750C22semidirect
54. #14582745C22semidirect
56. #14582636C22semidirect
57. #14582636C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
69. C43×#432C22semidirect
70. C43×#382C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
84. #13063325C2×C4semidirect
86. #13063324C2×C4semidirect
87. #13063322C2×C4semidirect
88. #13063321C2×C4semidirect
92. #13063316C2×C4semidirect
94. #13063314C2×C4semidirect
130. Q8×Dic43C2×C4semidirect
133. C4×D172C2×C4semidirect
134. C4×D172C2×C4semidirect
135. D4×Dic43C2×C4semidirect
138. #13063287C2×C4semidirect
139. #13063287C2×C4semidirect
188. #125×C43C2×C4semidirect
189. #124×C43C2×C4semidirect
193. C4×Q8×C43C2×C4semidirect
195. C4×D4×C43C2×C4semidirect
472. #1512D43semidirect
516. #432C2×D43semidirect
527. #382C2×D43semidirect
535. #328C2×D43semidirect
536. #328C2×D43semidirect
549. C43#17604semidirect
570. #125C4×D43semidirect
576. #124C4×D43semidirect
612. C4×Q8C4×D43semidirect
628. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191483182
#191432542
#191374482
#191331712
#191331542
#191331502
#191331402
#191331222
#191331192
#191331042
#191330982
#191330882
#191330812
#327×D432
C43×#15122
#1760443