Finite Group Databasebeta

← #25113084

Subgroups — #25113084

Order 11008.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148153C211yesmaximal, characteristic
2#19137040C211yesmaximal, characteristic, complemented
3#19135575C211yesmaximal, characteristic, complemented
4#19135539C211yesmaximal, characteristic, complemented
5#19135041C211yesmaximal, characteristic, complemented
6#19135036C211yesmaximal, characteristic, complemented
7#19134897C211yesmaximal, characteristic, complemented
8#19134897C211yesmaximal, characteristic, complemented
9#19134692C211yesmaximal, characteristic, complemented
10#19134692C211yesmaximal, characteristic, complemented
11#19134612C211yesmaximal, characteristic, complemented
12#19134408C211yesmaximal, characteristic, complemented
13#19134306C211yesmaximal, characteristic, complemented
14C2×#14582660C211yesmaximal, characteristic, complemented
15D4×M16×C43C211yesmaximal, characteristic, complemented
16#14583619C411yescharacteristic, complemented
17#14583614C411yescharacteristic, complemented
18#14583606C411yescharacteristic, complemented
19#14583595C411yescharacteristic, complemented
20#14583595C411yescharacteristic, complemented
21#14583589C411yescharacteristic, complemented
22#14583589C411yescharacteristic, complemented
23#14583584—21no—
24#14583575—21no—
25#14583575—21no—
26#14583553C411yescharacteristic, complemented
27#14583543—21no—
28#14583456C2211yescharacteristic
29#14583431—21no—
30#14583429—21no—
31#14583429—21no—
32#14583410C2211yescharacteristic
33#14583410C2211yescharacteristic
34C4×#10621898C2211yescharacteristic
35C4×#10621900—21no—
36C2×#13063284C2211yescharacteristic
37C2×#13063284C2211yescharacteristic
38C2×#13063284C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C2×#13063251C2211yescharacteristic
41C2×#13063251C2211yescharacteristic
42C2×#13063251C2211yescharacteristic
43C2×#13063251C2211yescharacteristic
44#14582792—21no—
45#14582785—21no—
46#14582779—21no—
47#14582774—21no—
48C4×C4⋊Dic43C2211yescharacteristic
49C4×C22⋊Dic43C2211yescharacteristic
50C4×C22⋊Dic43C2211yescharacteristic
51#14582745C2211yescharacteristic
52#14582660C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582660C2211yescharacteristic
55#14582660C2211yescharacteristic
56#14582660C2211yescharacteristic
57#14582660C2211yescharacteristic
58#14582660C2211yescharacteristic
59#14582660C2211yescharacteristic
60#14582660C2211yescharacteristic
61#14582660C2211yescharacteristic
62#14582660C2211yescharacteristic
63#14582660C2211yescharacteristic
64C22×M16×C43C2211yescharacteristic
65C22×M16×C43C2211yescharacteristic
66C2×C4×D4×C43C2211yescharacteristic
67C43×#436—21no—
68C43×#435—21no—
69C43×#435—21no—
70C8×D4×C43—21no—
71C43×#423C2211yescharacteristic
72C43×#407C2211yescharacteristic
73C43×#407C2211yescharacteristic
74C4×M16×C43C2211yescharacteristic
75C2×#10621898C2311yescharacteristic
76C2×#10621900—21no—
77C23×Dic43—21no—
78#13063325C2×C411yescharacteristic, complemented
79#13063325C2×C411yescharacteristic, complemented
80#13063320—21no—
81#13063320—21no—
82#13063318—21no—
83#13063318—21no—
84#13063318—21no—
85#13063318—21no—
86#13063317C2×C411yescharacteristic, complemented
87#13063317C2×C411yescharacteristic, complemented
88#13063316—21no—
89#13063315—21no—
90#13063315—21no—
91#13063312—21no—
92#13063311—21no—
93#13063311—21no—
94#13063309—21no—
95#13063309—21no—
96#13063308—21no—
97#13063308—21no—
98#13063307—21no—
99#13063307—21no—
100#13063306—21no—
101#13063306—21no—
102#13063305—21no—
103#13063304—21no—
104#13063304—21no—
105#13063304C2×C411yescharacteristic
106#13063304C2×C411yescharacteristic
107#13063304C2×C411yescharacteristic, complemented
108#13063304C2×C411yescharacteristic, complemented
109#13063302—21no—
110#13063302—21no—
111#13063299C2×C411yescharacteristic
112#13063299C2×C411yescharacteristic
113#13063299C2×C411yescharacteristic, complemented
114#13063299C2×C411yescharacteristic, complemented
115#13063297—21no—
116#13063297—21no—
117#13063296—21no—
118#13063294—21no—
119#13063294—21no—
120C4×Dic86—21no—
121C4×Dic86—21no—
122C4×Dic86C2×C411yescharacteristic, complemented
123C4×Dic86C2×C411yescharacteristic, complemented
124#13063290—21no—
125C4×D172C2×C411yescharacteristic, complemented
126C4×D172C2×C411yescharacteristic, complemented
127D4×Dic43—21no—
128C4×C22⋊D43—21no—
129C4×C22⋊D43—21no—
130C4×C22⋊D43—21no—
131C4×C22⋊D43—21no—
132C4×C22⋊D43—21no—
133C4×C22⋊D43—21no—
134(C22⋊D43)⋊C4—21no—
135(C22⋊D43)⋊C4—21no—
136#13063284—21no—
137#13063284—21no—
138#13063284—21no—
139#13063284—21no—
140#13063284—22no—
141#13063284—41no—
142#13063284C2×C411yescharacteristic
143#13063284C2×C411yescharacteristic
144#13063284C2×C411yescharacteristic, complemented
145#13063284C2×C411yescharacteristic, complemented
146#13063284C2311yescharacteristic
147#13063284C2311yescharacteristic
148#13063284C2311yescharacteristic
149#13063283—21no—
150#13063282—21no—
151#13063281—21no—
152#13063281—21no—
153C2×C4⋊Dic43—21no—
154C2×C4⋊Dic43—21no—
155C2×C4⋊Dic43C2×C411yescharacteristic
156C2×C4⋊Dic43C2×C411yescharacteristic
157C2×C4⋊Dic43C2×C411yescharacteristic, complemented
158C2×C4⋊Dic43C2×C411yescharacteristic, complemented
159C2×C22⋊Dic43—21no—
160C2×C22⋊Dic43—21no—
161C2×C22⋊Dic43—21no—
162C2×C22⋊Dic43—21no—
163C2×C22⋊Dic43—21no—
164C2×C4×Dic43—21no—
165C2×C4×Dic43—21no—
166C2×C4×Dic43—22no—
167C2×C4×Dic43—21no—
168C2×C4×Dic43—41no—
169C2×C4×Dic43C2311yescharacteristic
170C2×C4×Dic43C2311yescharacteristic
171C2×C4×Dic43C2311yescharacteristic
172C2×C4×Dic43C2311yescharacteristic
173C42×D43—21no—
174#13063251—22no—
175#13063251—22no—
176#13063251—41no—
177#13063251—41no—
178C43⋊#95—21no—
179C43⋊#95—21no—
180C43⋊#95—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C22×D4×C43D411yescharacteristic
184C23×C4×C43C2311yescharacteristic
185C23×C4×C43C2311yescharacteristic
186C2×M16×C43—21no—
187C2×M16×C43—21no—
188C2×M16×C43—22no—
189C2×M16×C43—22no—
190C2×M16×C43—41no—
191C2×M16×C43—41no—
192C2×M16×C43C2311yescharacteristic
193C2×M16×C43C2311yescharacteristic
194C2×M16×C43C2311yescharacteristic
195C2×M16×C43C2311yescharacteristic
196C22×C8×C43—21no—
197C22×C8×C43—21no—
198C4×D4×C43C2×C411yescharacteristic
199C4×D4×C43C2×C411yescharacteristic
200C4×D4×C43C2×C411yescharacteristic
201C4×D4×C43C2×C411yescharacteristic
202C4×D4×C43D411yescharacteristic
203C4×D4×C43D411yescharacteristic
204C4×D4×C43D411yescharacteristic
205C4×D4×C43D411yescharacteristic
206C2×C4⋊C4×C43D411yescharacteristic
207C2×C22⋊C4×C43D411yescharacteristic
208C2×C22⋊C4×C43D411yescharacteristic
209C2×C42×C43C2311yescharacteristic
210C4⋊C8×C43—21no—
211C4⋊C8×C43—21no—
212C22⋊C8×C43—21no—
213C22⋊C8×C43—21no—
214C22⋊C8×C43—21no—
215C22⋊C8×C43—21no—
216#97×C43—21no—
217C4×C8×C43—21no—
218C24×C43C2×D411yescharacteristic
219C24×C43C2×D411yescharacteristic
220C2×D4×C43—42no—
221C2×D4×C43C22⋊C411yescharacteristic
222C2×D4×C43C22⋊C411yescharacteristic
223C2×D4×C43C22⋊C411yescharacteristic
224C2×D4×C43C22⋊C411yescharacteristic
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43C22×C411yescharacteristic
234C22×C4×C43C22×C411yescharacteristic
235C22×C4×C43C22×C411yescharacteristic
236C22×C4×C43C22×C411yescharacteristic
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43C2×D411yescharacteristic
242C22×C4×C43C2×D411yescharacteristic
243C22×C4×C43C2×D411yescharacteristic
244C22×C4×C43C2×D411yescharacteristic
245C22×C4×C43C2411yescharacteristic
246C2×C22⋊D43—21no—
247C2×C22⋊D43—21no—
248C2×C22⋊D43—21no—
249C2×C22⋊D43—21no—
250C2×C22⋊D43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—42no—
260C22×Dic43—42no—
261C22×Dic43—42no—
262#10621900—44no—
263#10621898—21no—
264#10621898—21no—
265#10621898—21no—
266#10621898—21no—
267C2×D172C22×C411yescharacteristic
268C2×C4×D43—21no—
269C2×C4×D43—21no—
270C2×C4×D43—21no—
271C2×Dic86—21no—
272C2×Dic86—21no—
273C2×Dic86C22×C411yescharacteristic
274M16×C43—21no—
275M16×C43—21no—
276M16×C43—21no—
277M16×C43—21no—
278M16×C43—21no—
279M16×C43—21no—
280M16×C43—21no—
281M16×C43—42no—
282M16×C43—42no—
283M16×C43#4112yescomplemented
284C2×C8×C43—21no—
285C2×C8×C43—21no—
286C2×C8×C43—21no—
287C2×C8×C43—21no—
288C2×C8×C43—42no—
289C2×C8×C43—42no—
290C4⋊C4×C43C22⋊C411yescharacteristic
291C4⋊C4×C43C22⋊C411yescharacteristic
292C4⋊C4×C43C22⋊C411yescharacteristic
293C4⋊C4×C43C22⋊C411yescharacteristic
294C22⋊C4×C43C22⋊C411yescharacteristic
295C22⋊C4×C43C22⋊C411yescharacteristic
296C22⋊C4×C43C22⋊C411yescharacteristic
297C22⋊C4×C43C22⋊C411yescharacteristic
298C22⋊C4×C43C22⋊C411yescharacteristic
299C22⋊C4×C43C22⋊C411yescharacteristic
300C22⋊C4×C43C22⋊C411yescharacteristic
301C22⋊C4×C43C22⋊C411yescharacteristic
302C42×C43C22×C411yescharacteristic
303C42×C43C22×C411yescharacteristic
304C42×C43C2×D411yescharacteristic
305C42×C43C2×D411yescharacteristic
306C22⋊Dic43—21no—
307C22⋊Dic43—21no—
308C22⋊Dic43—21no—
309C22⋊Dic43—21no—
310C22⋊Dic43—21no—
311C22⋊Dic43—21no—
312C22⋊Dic43—21no—
313C22⋊Dic43—21no—
314C22⋊Dic43—21no—
315C22⋊Dic43—21no—
316C22⋊Dic43—21no—
317C22⋊Dic43—42no—
318C22⋊Dic43—42no—
319C22⋊Dic43—42no—
320(C2×D43)⋊C4—21no—
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—
326C4⋊Dic43—21no—
327C4⋊Dic43—21no—
328C4⋊Dic43—21no—
329C4⋊Dic43—21no—
330C4⋊Dic43—21no—
331C4⋊Dic43—21no—
332C4⋊Dic43—42no—
333C4⋊Dic43—42no—
334C4⋊Dic43C22×C411yescharacteristic
335C4⋊Dic43C22×C411yescharacteristic
336C4⋊Dic43C22×C411yescharacteristic
337C4⋊Dic43C22×C411yescharacteristic
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—21no—
349Dic43⋊C4—21no—
350C4×Dic43—21no—
351C4×Dic43—21no—
352C4×Dic43—21no—
353C4×Dic43—21no—
354C4×Dic43—21no—
355C4×Dic43—21no—
356C4×Dic43—21no—
357C4×Dic43—21no—
358C4×Dic43—21no—
359C4×Dic43—21no—
360C4×Dic43—21no—
361C4×Dic43—21no—
362C4×Dic43—21no—
363C4×Dic43—21no—
364C4×Dic43—21no—
365C4×Dic43—21no—
366C4×Dic43—42no—
367C4×Dic43#4112yescomplemented
368C23×C43—21no—
369C23×C43—21no—
370C23×C43—22no—
371C23×C43—21no—
372C23×C43—21no—
373C23×C43—41no—
374C23×C43—41no—
375C23×C43—41no—
376C23×C43C2×C22⋊C411yescharacteristic
377C23×C43C2×C22⋊C411yescharacteristic
378C23×C43C2×C22⋊C411yescharacteristic
379C23×C43C2×C22⋊C411yescharacteristic
380C23×C43C22×D411yescharacteristic
381C22×D43—21no—
382D4×C43—22no—
383D4×C43—22no—
384D4×C43—41no—
385D4×C43—41no—
386C2×C4×C43—21no—
387C2×C4×C43—21no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—21no—
392C2×C4×C43—21no—
393C2×C4×C43—21no—
394C2×C4×C43—21no—
395C2×C4×C43—21no—
396C2×C4×C43—21no—
397C2×C4×C43—21no—
398C2×C4×C43—21no—
399C2×C4×C43—21no—
400C2×C4×C43—21no—
401C2×C4×C43—21no—
402C2×C4×C43—21no—
403C2×C4×C43—21no—
404C2×C4×C43—21no—
405C2×C4×C43—21no—
406C2×C4×C43—41no—
407C2×C4×C43—41no—
408C2×C4×C43C2×C22⋊C411yescharacteristic
409C2×C4×C43C2×C22⋊C411yescharacteristic
410C2×C4×C43C2×C22⋊C411yescharacteristic
411C2×C4×C43C2×C22⋊C411yescharacteristic
412C2×C4×C43C2×C22⋊C411yescharacteristic
413C2×C4×C43C2×C22⋊C411yescharacteristic
414C2×C4×C43C2×C22⋊C411yescharacteristic
415C2×C4×C43C2×C22⋊C411yescharacteristic
416C2×C4×C43C23×C411yescharacteristic
417C2×C4×C43C22×D411yescharacteristic
418C2×C4×C43C2×#4111yescharacteristic
419C2×C4×C43C2×#4111yescharacteristic
420C2×C4×C43H(5,𝔽2)11yescharacteristic
421C2×C4×C432−1+411yescharacteristic
422C22⋊D43—42no—
423C22⋊D43—41no—
424C22⋊D43—41no—
425C22⋊D43—42no—
426C22⋊D43—81no—
427C22⋊D43—81no—
428C2×Dic43—22no—
429C2×Dic43—21no—
430C2×Dic43—21no—
431C2×Dic43—21no—
432C2×Dic43—21no—
433C2×Dic43—21no—
434C2×Dic43—21no—
435C2×Dic43—21no—
436C2×Dic43—22no—
437C2×Dic43—42no—
438C2×Dic43—41no—
439C2×Dic43—41no—
440C2×Dic43—41no—
441C2×Dic43—48no—
442C2×Dic43—41no—
443C2×Dic43—42no—
444C2×Dic43—41no—
445C2×Dic43—41no—
446C2×Dic43—41no—
447C2×Dic43—41no—
448C2×Dic43—41no—
449C2×Dic43—41no—
450C2×Dic43—81no—
451C2×Dic43—81no—
452D172—21no—
453D172—21no—
454C4×D43—42no—
455C4×D43—41no—
456C4×D43—41no—
457C4×D43—81no—
458Dic86—21no—
459Dic86—21no—
460Dic86—42no—
461Dic86—81no—
462C8×C43—22no—
463C8×C43—41no—
464C8×C43—41no—
465C8×C43—41no—
466#22506—431nomaximal, Sylow
467C22×C43—21no—
468C22×C43—21no—
469C22×C43—21no—
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—21no—
474C22×C43—21no—
475C22×C43—21no—
476C22×C43—21no—
477C22×C43—21no—
478C22×C43—21no—
479C22×C43—21no—
480C22×C43—42no—
481C22×C43—42no—
482C22×C43—81no—
483C22×C43—81no—
484C22×C43#42112yes—
485C22×C43C22×C22⋊C411yescharacteristic
486C22×C43#54611yescharacteristic
487C22×C43#54711yescharacteristic
488C2×D43—41no—
489C2×D43—41no—
490C2×D43—41no—
491C4×C43—21no—
492C4×C43—21no—
493C4×C43—21no—
494C4×C43—21no—
495C4×C43—21no—
496C4×C43—21no—
497C4×C43—21no—
498C4×C43—21no—
499C4×C43C4×#4111yescharacteristic
500C4×C43#52011yescharacteristic
501C4×C43#54611yescharacteristic
502C4×C43#54711yescharacteristic
503Dic43—42no—
504Dic43—42no—
505Dic43—41no—
506Dic43—41no—
507Dic43—41no—
508Dic43—41no—
509Dic43—41no—
510Dic43—41no—
511Dic43—41no—
512Dic43—81no—
513Dic43—81no—
514#3475—431no—
515D4×M16D4311yescharacteristic, complemented
516#2290—431no—
517#1995—431no—
518#1986—431no—
519#1897—431no—
520#1896—431no—
521#1871—431no—
522#1871—431no—
523#1826—431no—
524#1826—431no—
525#1806—431no—
526#1759—431no—
527#1733—431no—
528C2×#339—431no—
529C2×C43—21no—
530C2×C43—21no—
531C2×C43—22no—
532C2×C43—41no—
533C2×C43—41no—
534C2×C43—41no—
535C2×C43#233911yescharacteristic
536C2×C43C2×#42111yescharacteristic
537C2×C43#290111yescharacteristic
538D43—81no—
539C22×M16C2×D4311yescharacteristic
540C22×M16C2×D4311yescharacteristic
541#556—431no—
542#555—431no—
543#554—431no—
544#553—431no—
545#553—431no—
546#552—431no—
547#552—431no—
548#552—861no—
549#551—861no—
550#551—861no—
551#547—431no—
552#546—861no—
553#533—431no—
554#529—861no—
555#529—861no—
556#529—861no—
557#525—431no—
558#525—431no—
559C4×#41—431no—
560C4×#41—861no—
561C2×C4×D4C2×D4311yescharacteristic
562C2×#117—431no—
563C2×#117—431no—
564C2×#117—431no—
565C22×C42—431no—
566#436—21no—
567#435—21no—
568#435—21no—
569C8×D4—21no—
570#423C2×D4311yescharacteristic
571C2×#104—431no—
572C2×#104—431no—
573C2×#104—431no—
574C2×#104—431no—
575#407C2×D4311yescharacteristic
576#407C2×D4311yescharacteristic
577C4×M16C2×D4311yescharacteristic
578#388—861no—
579#387—861no—
580#386—861no—
581#385—861no—
582C4×C4⋊C4—431no—
583C4×C22⋊C4—431no—
584C4×C22⋊C4—431no—
585#376—431no—
586#339—431no—
587#339—431no—
588#339—431no—
589#339—431no—
590#339—431no—
591#339—431no—
592#339—431no—
593#339—431no—
594#339—431no—
595#339—431no—
596#339—431no—
597#339—431no—
598C43#2250611yescharacteristic, complemented, Sylow
599C2×#41—431no—
600C2×#41—861no—
601C22×D4D17211yescharacteristic
602C23×C4—861no—
603C23×C4C22×D4311yescharacteristic
604C23×C4C22×D4311yescharacteristic
605C2×M16—21no—
606C2×M16—21no—
607C2×M16—22no—
608C2×M16—22no—
609C2×M16—41no—
610C2×M16—41no—
611C2×M16C22×D4311yescharacteristic
612C2×M16C22×D4311yescharacteristic
613C2×M16C22×D4311yescharacteristic
614C2×M16C22×D4311yescharacteristic
615C22×C8—21no—
616C22×C8—21no—
617C4⋊Q8—431no—
618C4⋊Q8—431no—
619#126—861no—
620#126—861no—
621#126—861no—
622#126—861no—
623#126—861no—
624#126—861no—
625#125—431no—
626#125—431no—
627#125—861no—
628#125—861no—
629#125—861no—
630#124—861no—
631#124—861no—
632#124—861no—
633#123—861no—
634#123—861no—
635#123—861no—
636#123—861no—
637#123—861no—
638#123—861no—
639#123—861no—
640#123—861no—
641C22⋊Q8—431no—
642C22⋊Q8—431no—
643C22⋊Q8—431no—
644C22⋊Q8—431no—
645C22⋊Q8—861no—
646C22⋊Q8—861no—
647C22⋊Q8—861no—
648C22⋊Q8—861no—
649C22⋊Q8—861no—
650#121—431no—
651#121—431no—
652#121—431no—
653#121—431no—
654#121—861no—
655#121—861no—
656#121—861no—
657#120—861no—
658#120—861no—
659C4×Q8—431no—
660C4×Q8—431no—
661C4×Q8—861no—
662C4×Q8—861no—
663C4×Q8—861no—
664C4×D4—431no—
665C4×D4—431no—
666C4×D4—861no—
667C4×D4—861no—
668C4×D4—861no—
669C4×D4—861no—
670C4×D4—861no—
671C4×D4—861no—
672C4×D4—861no—
673C4×D4—861no—
674C4×D4—861no—
675C4×D4C4×D4311yescharacteristic
676C4×D4C4×D4311yescharacteristic
677C4×D4C4×D4311yescharacteristic
678C4×D4C4×D4311yescharacteristic
679C4×D4C22⋊D4311yescharacteristic
680C4×D4C22⋊D4311yescharacteristic
681C4×D4C22⋊D4311yescharacteristic
682C4×D4C22⋊D4311yescharacteristic
683#117—431no—
684#117—431no—
685#117—431no—
686#117—431no—
687#117—431no—
688#117—431no—
689#117—431no—
690#117—862no—
691#117—861no—
692#117—861no—
693#117—861no—
694#117—861no—
695#117—861no—
696#117—861no—
697#117—861no—
698#117—861no—
699#117—1721no—
700C2×C4⋊C4—431no—
701C2×C4⋊C4—431no—
702C2×C4⋊C4—431no—
703C2×C4⋊C4—431no—
704C2×C4⋊C4—861no—
705C2×C4⋊C4—861no—
706C2×C4⋊C4D17211yescharacteristic
707C2×C22⋊C4—861no—
708C2×C22⋊C4—861no—
709C2×C22⋊C4—861no—
710C2×C22⋊C4—861no—
711C2×C22⋊C4—861no—
712C2×C22⋊C4D17211yescharacteristic
713C2×C22⋊C4D17211yescharacteristic
714C2×C42—431no—
715C2×C42—431no—
716C2×C42—431no—
717C2×C42—431no—
718C2×C42—862no—
719C2×C42—861no—
720C2×C42—861no—
721C2×C42—861no—
722C2×C42—861no—
723C2×C42—1721no—
724C2×C42C22×D4311yescharacteristic
725C4⋊C8—21no—
726C4⋊C8—21no—
727#104—862no—
728#104—862no—
729#104—1721no—
730#104—1721no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8—21no—
734C22⋊C8—21no—
735#97—21no—
736C4×C8—21no—
737#95—861no—
738#95—861no—
739#95—861no—
740#95—861no—
741#95—861no—
742C24C2×D17211yescharacteristic
743C24C2×D17211yescharacteristic
744#41—861no—
745#41—861no—
746#41—861no—
747#41—861no—
748#41—1724no—
749C2×Q8—431no—
750C2×Q8—861no—
751C2×Q8—861no—
752C2×D4—42no—
753C2×D4—431no—
754C2×D4—861no—
755C2×D4—861no—
756C2×D4—861no—
757C2×D4—861no—
758C2×D4—861no—
759C2×D4(C2×D43)⋊C411yescharacteristic
760C2×D4(C2×D43)⋊C411yescharacteristic
761C2×D4(C2×D43)⋊C411yescharacteristic
762C2×D4(C2×D43)⋊C411yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—861no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—861no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—1722no—
783C22×C4—1722no—
784C22×C4—1722no—
785C22×C4C2×C4×D4311yescharacteristic
786C22×C4C2×C4×D4311yescharacteristic
787C22×C4C2×C4×D4311yescharacteristic
788C22×C4C2×C4×D4311yescharacteristic
789C22×C4C2×D17211yescharacteristic
790C22×C4C2×D17211yescharacteristic
791C22×C4C2×D17211yescharacteristic
792C22×C4C2×D17211yescharacteristic
793C22×C4C2×C22⋊D4311yescharacteristic
794C22×C4C2×C22⋊D4311yescharacteristic
795C22×C4C2×C22⋊D4311yescharacteristic
796C22×C4C2×C22⋊D4311yescharacteristic
797C22×C4C23×D4311yescharacteristic
798M16—21no—
799M16—21no—
800M16—21no—
801M16—21no—
802M16—21no—
803M16—21no—
804M16—21no—
805M16—42no—
806M16—42no—
807M16#1062190012yescomplemented
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—42no—
813C2×C8—42no—
814C4⋊C4—431no—
815C4⋊C4—431no—
816C4⋊C4—431no—
817C4⋊C4—431no—
818C4⋊C4—431no—
819C4⋊C4—431no—
820C4⋊C4—861no—
821C4⋊C4—861no—
822C4⋊C4—861no—
823C4⋊C4—861no—
824C4⋊C4—861no—
825C4⋊C4—861no—
826C4⋊C4—861no—
827C4⋊C4—861no—
828C4⋊C4—861no—
829C4⋊C4—861no—
830C4⋊C4—861no—
831C4⋊C4—861no—
832C4⋊C4—861no—
833C4⋊C4—861no—
834C4⋊C4—861no—
835C4⋊C4—861no—
836C4⋊C4—1722no—
837C4⋊C4—1722no—
838C4⋊C4(C2×D43)⋊C411yescharacteristic
839C4⋊C4(C2×D43)⋊C411yescharacteristic
840C4⋊C4(C2×D43)⋊C411yescharacteristic
841C4⋊C4(C2×D43)⋊C411yescharacteristic
842C22⋊C4—861no—
843C22⋊C4—861no—
844C22⋊C4—861no—
845C22⋊C4—861no—
846C22⋊C4—861no—
847C22⋊C4—861no—
848C22⋊C4—861no—
849C22⋊C4—861no—
850C22⋊C4—861no—
851C22⋊C4—861no—
852C22⋊C4—861no—
853C22⋊C4—861no—
854C22⋊C4—861no—
855C22⋊C4—861no—
856C22⋊C4—861no—
857C22⋊C4—861no—
858C22⋊C4—861no—
859C22⋊C4—1722no—
860C22⋊C4—1722no—
861C22⋊C4—1722no—
862C22⋊C4(C2×D43)⋊C411yescharacteristic
863C22⋊C4(C2×D43)⋊C411yescharacteristic
864C22⋊C4(C2×D43)⋊C411yescharacteristic
865C22⋊C4(C2×D43)⋊C411yescharacteristic
866C22⋊C4(C2×D43)⋊C411yescharacteristic
867C22⋊C4(C2×D43)⋊C411yescharacteristic
868C22⋊C4(C2×D43)⋊C411yescharacteristic
869C22⋊C4(C2×D43)⋊C411yescharacteristic
870C42—432no—
871C42—861no—
872C42—861no—
873C42—861no—
874C42—861no—
875C42—861no—
876C42—861no—
877C42—861no—
878C42—861no—
879C42—861no—
880C42—861no—
881C42—861no—
882C42—861no—
883C42—861no—
884C42—861no—
885C42—861no—
886C42—861no—
887C42—1722no—
888C42C2×C4×D4311yescharacteristic
889C42C2×C4×D4311yescharacteristic
890C42C2×C22⋊D4311yescharacteristic
891C42C2×C22⋊D4311yescharacteristic
892C23—21no—
893C23—22no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—861no—
901C23C2×(C2×D43)⋊C411yescharacteristic
902C23C2×(C2×D43)⋊C411yescharacteristic
903C23C2×(C2×D43)⋊C411yescharacteristic
904C23C2×(C2×D43)⋊C411yescharacteristic
905C23C22×D17211yescharacteristic
906Q8—861no—
907Q8—861no—
908Q8—3441no—
909Q8—1722no—
910D4—22no—
911D4—22no—
912D4—41no—
913D4—41no—
914D4—861no—
915D4—861no—
916D4—3441no—
917D4—3441no—
918D4—1722no—
919D4—1721no—
920D4—1722no—
921D4—1721no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—862no—
945C2×C4—861no—
946C2×C4—861no—
947C2×C4—861no—
948C2×C4—861no—
949C2×C4—861no—
950C2×C4—861no—
951C2×C4—861no—
952C2×C4—862no—
953C2×C4—3441no—
954C2×C4—3441no—
955C2×C4—3441no—
956C2×C4—1722no—
957C2×C4—1721no—
958C2×C4—1721no—
959C2×C4—1721no—
960C2×C4—1721no—
961C2×C4—1721no—
962C2×C4—1721no—
963C2×C4—1721no—
964C2×C4—1721no—
965C2×C4—1721no—
966C2×C4—1722no—
967C2×C4—1728no—
968C2×C4—1722no—
969C2×C4—1721no—
970C2×C4—1721no—
971C2×C4—1721no—
972C2×C4C2×(C2×D43)⋊C411yescharacteristic
973C2×C4C2×(C2×D43)⋊C411yescharacteristic
974C2×C4C2×(C2×D43)⋊C411yescharacteristic
975C2×C4C2×(C2×D43)⋊C411yescharacteristic
976C2×C4C2×(C2×D43)⋊C411yescharacteristic
977C2×C4C2×(C2×D43)⋊C411yescharacteristic
978C2×C4C2×(C2×D43)⋊C411yescharacteristic
979C2×C4C2×(C2×D43)⋊C411yescharacteristic
980C2×C4C22×C4×D4311yescharacteristic
981C2×C4C22×C22⋊D4311yescharacteristic
982C2×C4#41×D4311yescharacteristic
983C2×C4C2×#1062190011yescharacteristic
984C2×C4#1306337011yescharacteristic
985C2×C4#1306337211yescharacteristic
986C8—22no—
987C8—41no—
988C8—41no—
989C8—41no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—81no—
1006C22—81no—
1007C22—1721no—
1008C22—1721no—
1009C22—1721no—
1010C22#1458291512yes—
1011C22C22×(C2×D43)⋊C411yescharacteristic
1012C22#1458354411yescharacteristic
1013C22#1458355311yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—3441no—
1023C4—3441no—
1024C4—1722no—
1025C4—1722no—
1026C4—1721no—
1027C4—1721no—
1028C4—1721no—
1029C4—1721no—
1030C4—1721no—
1031C4—1721no—
1032C4—1721no—
1033C4C4×#1062190011yescharacteristic
1034C4#1458337811yescharacteristic
1035C4#1458354311yescharacteristic
1036C4#1458354811yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—3441no—
1044C2#1913742011yescharacteristic
1045C2C2×#1458291511yescharacteristic
1046C2#1914314011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×M16×C43C2
socleC22×C43C22×C22⋊C4
prime radical#19148153C2
cosocleC22×C4×C43C24
hypercenterD4×M16D43
hypocenterC43#22506
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. #19137040C2semidirect
3. #19135575C2semidirect
4. #19135539C2semidirect
5. #19135041C2semidirect
6. #19135036C2semidirect
7. #19134897C2semidirect
8. #19134897C2semidirect
9. #19134692C2semidirect
10. #19134692C2semidirect
11. #19134612C2semidirect
12. #19134408C2semidirect
13. #19134306C2semidirect
14. C2×#14582660C2semidirect
15. D4×M16×C43C2semidirect
16. #14583619C4semidirect
17. #14583614C4semidirect
18. #14583606C4semidirect
19. #14583595C4semidirect
20. #14583595C4semidirect
21. #14583589C4semidirect
22. #14583589C4semidirect
26. #14583553C4semidirect
78. #13063325C2×C4semidirect
79. #13063325C2×C4semidirect
86. #13063317C2×C4semidirect
87. #13063317C2×C4semidirect
107. #13063304C2×C4semidirect
108. #13063304C2×C4semidirect
113. #13063299C2×C4semidirect
114. #13063299C2×C4semidirect
122. C4×Dic86C2×C4semidirect
123. C4×Dic86C2×C4semidirect
125. C4×D172C2×C4semidirect
126. C4×D172C2×C4semidirect
144. #13063284C2×C4semidirect
145. #13063284C2×C4semidirect
157. C2×C4⋊Dic43C2×C4semidirect
158. C2×C4⋊Dic43C2×C4semidirect
283. M16×C43#41semidirect
367. C4×Dic43#41semidirect
515. D4×M16D43semidirect
598. C43#22506semidirect
807. M16#10621900semidirect

Maximal subgroups

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

subgroupindex
#191481532
#191370402
#191355752
#191355392
#191350412
#191350362
#191348972
#191346922
#191346122
#191344082
#191343062
C2×#145826602
D4×M16×C432
#2250643