Finite Group Databasebeta

← #25112759

Subgroups — #25112759

Order 11008.

1068 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic
2D4×#10621877C211yesmaximal, characteristic
3#19135588C211yesmaximal, characteristic, complemented
4#19135587C211yesmaximal, characteristic, complemented
5#19135063C211yesmaximal, characteristic, complemented
6#19135063C211yesmaximal, characteristic, complemented
7#19135061C211yesmaximal, characteristic, complemented
8#19135061C211yesmaximal, characteristic, complemented
9#19134676C211yesmaximal, characteristic, complemented
10#19134673C211yesmaximal, characteristic, complemented
11#19134588C211yesmaximal, characteristic, complemented
12C4×#13063243C211yesmaximal, characteristic, complemented
13#19134333C211yesmaximal, characteristic, complemented
14C2×#14582667C211yesmaximal, characteristic, complemented
15D4×M16×C43C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18#14583589—21no—
19#14583589—21no—
20#14583589—21no—
21#14583589—21no—
22#14583589—21no—
23#14583589—21no—
24#14583589—21no—
25#14583589—21no—
26C2×#13063318C412yes—
27C2×#13063317C2211yescharacteristic
28C2×#13063315C412yes—
29C2×#13063306C412yes—
30C2×#13063304C2211yescharacteristic
31C2×#13063304C2211yescharacteristic
32C2×C4×Dic86C2211yescharacteristic
33C2×#13063284C2211yescharacteristic
34C2×#13063281C412yes—
35C22×C4⋊Dic43C2211yescharacteristic
36#14582977—21no—
37#14582971—21no—
38#14582971—21no—
39D4×C43⋊C8—21no—
40#14582923C2211yescharacteristic
41C2×#13063243C2211yescharacteristic
42C2×#13063243C2211yescharacteristic
43C2×#13063243C2211yescharacteristic
44C2×#13063243C2211yescharacteristic
45#14582863C2211yescharacteristic
46#14582863C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48#14582667C2211yescharacteristic
49#14582667C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582667C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60C22×M16×C43C2211yescharacteristic
61C22×M16×C43C2211yescharacteristic
62C2×C4×D4×C43C2211yescharacteristic
63C43×#436—21no—
64C43×#435—21no—
65C43×#435—21no—
66C8×D4×C43—21no—
67C43×#423C2211yescharacteristic
68C43×#407C2211yescharacteristic
69C43×#407C2211yescharacteristic
70C4×M16×C43C2211yescharacteristic
71C22×Dic86C2311yescharacteristic
72C23×Dic43C2×C412yes—
73C2×#10621877—21no—
74C2×#10621877—21no—
75C2×#10621877—22no—
76C2×#10621877—22no—
77C2×#10621877—41no—
78C2×#10621877—41no—
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C22×C43⋊C8—21no—
84C22×C43⋊C8—21no—
85#13063318—22no—
86#13063318—22no—
87#13063318—22no—
88#13063318—22no—
89#13063317—21no—
90#13063317—21no—
91#13063317—21no—
92#13063317—21no—
93#13063315—22no—
94#13063315—22no—
95#13063315—22no—
96#13063315—22no—
97#13063306—22no—
98#13063306—22no—
99#13063306—22no—
100#13063306—22no—
101#13063304—21no—
102#13063304—21no—
103#13063304—21no—
104#13063304—21no—
105#13063304—21no—
106#13063304—21no—
107#13063304—21no—
108#13063304—21no—
109C4×Dic86—21no—
110C4×Dic86—21no—
111C4×Dic86—21no—
112C4×Dic86—21no—
113#13063284—21no—
114#13063284—21no—
115#13063284—21no—
116#13063284—21no—
117#13063281—22no—
118#13063281—22no—
119#13063281—22no—
120#13063281—22no—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43C2×C412yes—
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×Dic43⋊C4C2×C412yes—
130C2×Dic43⋊C4C2×C412yes—
131C2×Dic43⋊C4C2×C412yes—
132C2×Dic43⋊C4C2×C412yes—
133C2×Dic43⋊C4C2×C412yes—
134C2×C22⋊Dic43C2×C412yes—
135C2×C22⋊Dic43C2×C412yes—
136C2×C22⋊Dic43C2×C412yes—
137C2×C4×Dic43C2×C412yes—
138C2×C4×Dic43C2×C412yes—
139C4⋊(C43⋊C8)—21no—
140C4⋊(C43⋊C8)—21no—
141#13063243—22no—
142#13063243—22no—
143#13063243—41no—
144#13063243—41no—
145C22⋊(C43⋊C8)—21no—
146C22⋊(C43⋊C8)—21no—
147C22⋊(C43⋊C8)—21no—
148C22⋊(C43⋊C8)—21no—
149#13063236—21no—
150C4×C43⋊C8—21no—
151C22×D4×C43C2×C411yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C2×M16×C43—21no—
155C2×M16×C43—21no—
156C2×M16×C43—22no—
157C2×M16×C43—22no—
158C2×M16×C43—41no—
159C2×M16×C43—41no—
160C2×M16×C43C2311yescharacteristic
161C2×M16×C43C2311yescharacteristic
162C2×M16×C43C2311yescharacteristic
163C2×M16×C43C2311yescharacteristic
164C22×C8×C43—21no—
165C22×C8×C43—21no—
166C4×D4×C43D411yescharacteristic
167C4×D4×C43D411yescharacteristic
168C4×D4×C43D411yescharacteristic
169C4×D4×C43D411yescharacteristic
170C4×D4×C43D411yescharacteristic
171C4×D4×C43D411yescharacteristic
172C4×D4×C43D411yescharacteristic
173C4×D4×C43D411yescharacteristic
174C2×C4⋊C4×C43C2×C411yescharacteristic
175C2×C22⋊C4×C43C2×C411yescharacteristic
176C2×C22⋊C4×C43C2×C411yescharacteristic
177C2×C42×C43C2311yescharacteristic
178C4⋊C8×C43—21no—
179C4⋊C8×C43—21no—
180C22⋊C8×C43—21no—
181C22⋊C8×C43—21no—
182C22⋊C8×C43—21no—
183C22⋊C8×C43—21no—
184#97×C43—21no—
185C4×C8×C43—21no—
186C24×C43C22×C411yescharacteristic
187C24×C43C22×C411yescharacteristic
188C2×D4×C43—42no—
189C2×D4×C43C22⋊C411yescharacteristic
190C2×D4×C43C22⋊C411yescharacteristic
191C2×D4×C43C22⋊C411yescharacteristic
192C2×D4×C43C22⋊C411yescharacteristic
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43C22×C411yescharacteristic
202C22×C4×C43C22×C411yescharacteristic
203C22×C4×C43C22×C411yescharacteristic
204C22×C4×C43C22×C411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2411yescharacteristic
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—44no—
217C22×Dic43C22×C412yes—
218C22×Dic43C22×C412yes—
219C22×Dic43C22×C412yes—
220C22×Dic43C22×C412yes—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227M16×C43—21no—
228M16×C43—21no—
229M16×C43—21no—
230M16×C43—21no—
231M16×C43—21no—
232M16×C43—21no—
233M16×C43—21no—
234M16×C43—42no—
235M16×C43—42no—
236M16×C43#4112yes—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—42no—
242C2×C8×C43—42no—
243C4⋊C4×C43C22⋊C411yescharacteristic
244C4⋊C4×C43C22⋊C411yescharacteristic
245C4⋊C4×C43C22⋊C411yescharacteristic
246C4⋊C4×C43C22⋊C411yescharacteristic
247C22⋊C4×C43C22⋊C411yescharacteristic
248C22⋊C4×C43C22⋊C411yescharacteristic
249C22⋊C4×C43C22⋊C411yescharacteristic
250C22⋊C4×C43C22⋊C411yescharacteristic
251C22⋊C4×C43C22⋊C411yescharacteristic
252C22⋊C4×C43C22⋊C411yescharacteristic
253C22⋊C4×C43C22⋊C411yescharacteristic
254C22⋊C4×C43C22⋊C411yescharacteristic
255C42×C43C2×D411yescharacteristic
256C42×C43C2×D411yescharacteristic
257C42×C43C2×D411yescharacteristic
258C42×C43C2×D411yescharacteristic
259C22⋊Dic43—22no—
260C22⋊Dic43—22no—
261C22⋊Dic43—22no—
262C22⋊Dic43—22no—
263C22⋊Dic43—22no—
264C22⋊Dic43—22no—
265C4⋊Dic43—22no—
266C4⋊Dic43—22no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273Dic43⋊C4—22no—
274Dic43⋊C4—22no—
275Dic43⋊C4—22no—
276Dic43⋊C4—22no—
277Dic43⋊C4—22no—
278Dic43⋊C4—22no—
279Dic43⋊C4—22no—
280Dic43⋊C4—22no—
281Dic43⋊C4—22no—
282Dic43⋊C4—22no—
283C4×Dic43—22no—
284C4×Dic43—22no—
285C4×Dic43—22no—
286C4×Dic43—22no—
287#10621877—21no—
288#10621877—21no—
289#10621877—21no—
290#10621877—21no—
291#10621877—21no—
292#10621877—21no—
293#10621877—21no—
294#10621877—42no—
295#10621877—42no—
296#10621877#4112yes—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8—21no—
301C2×C43⋊C8—42no—
302C2×C43⋊C8—42no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—22no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43C2×C22⋊C411yescharacteristic
312C23×C43C2×C22⋊C411yescharacteristic
313C23×C43C2×C22⋊C411yescharacteristic
314C23×C43C2×C22⋊C411yescharacteristic
315C23×C43C23×C411yescharacteristic
316D4×C43—22no—
317D4×C43—22no—
318D4×C43—41no—
319D4×C43—41no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43C2×C22⋊C411yescharacteristic
343C2×C4×C43C2×C22⋊C411yescharacteristic
344C2×C4×C43C2×C22⋊C411yescharacteristic
345C2×C4×C43C2×C22⋊C411yescharacteristic
346C2×C4×C43C2×C22⋊C411yescharacteristic
347C2×C4×C43C2×C22⋊C411yescharacteristic
348C2×C4×C43C2×C22⋊C411yescharacteristic
349C2×C4×C43C2×C22⋊C411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C2×#4111yescharacteristic
353C2×C4×C43C2×#4111yescharacteristic
354C2×C4×C43H(5,𝔽2)11yescharacteristic
355C2×C4×C432−1+411yescharacteristic
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—44no—
363C2×Dic43—44no—
364C2×Dic43—42no—
365C2×Dic43—42no—
366C2×Dic43—42no—
367Dic86—41no—
368Dic86—41no—
369Dic86—41no—
370Dic86—41no—
371C8×C43—22no—
372C8×C43—41no—
373C8×C43—41no—
374C8×C43—41no—
375C43⋊C8—22no—
376C43⋊C8—41no—
377C43⋊C8—41no—
378C43⋊C8—41no—
379#22480—431nomaximal, Sylow
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—21no—
384C22×C43—21no—
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43#41312yes—
398C22×C43C22×C22⋊C411yescharacteristic
399C22×C43C4×#4111yescharacteristic
400C22×C43#52011yescharacteristic
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—21no—
404C4×C43—21no—
405C4×C43—21no—
406C4×C43—21no—
407C4×C43—21no—
408C4×C43—21no—
409C4×C43#54611yescharacteristic
410C4×C43#54611yescharacteristic
411C4×C43#54711yescharacteristic
412C4×C43#54711yescharacteristic
413Dic43—42no—
414Dic43—42no—
415Dic43—42no—
416Dic43—42no—
417C2×#552—431no—
418D4×M16—431no—
419D4×M16D4311yescharacteristic
420#1998—431no—
421#1998—431no—
422#1901—431no—
423#1901—431no—
424#1901—431no—
425#1901—431no—
426#1822—431no—
427#1821—431no—
428#1801—431no—
429C4×#101—431no—
430#1742—431no—
431C2×#343—431no—
432C2×C43—21no—
433C2×C43—21no—
434C2×C43—22no—
435C2×C43—41no—
436C2×C43—41no—
437C2×C43—41no—
438C2×C43#233911yescharacteristic
439C2×C43C2×#41311yescharacteristic
440C2×C43#288911yescharacteristic
441C22×M16—431no—
442C22×M16—431no—
443C22×M16C2×D4311yescharacteristic
444C22×M16C2×D4311yescharacteristic
445#552—861no—
446#552—861no—
447#552—861no—
448#552—861no—
449#552—861no—
450#552—861no—
451#552—861no—
452#552—861no—
453C2×#126—432no—
454C2×#125—432no—
455C2×#125—431no—
456C2×#123—432no—
457C2×C22⋊Q8—431no—
458C2×C22⋊Q8—431no—
459C2×C4×Q8—431no—
460C2×C4×D4C2×D4311yescharacteristic
461C2×#117—431no—
462C2×#117—432no—
463C22×C4⋊C4—431no—
464#436—21no—
465#436—861no—
466#435—21no—
467#435—21no—
468#435—861no—
469#435—861no—
470C8×D4—21no—
471C8×D4—861no—
472#423—431no—
473#423C2×D4311yescharacteristic
474C2×#101—431no—
475C2×#101—431no—
476C2×#101—431no—
477C2×#101—431no—
478#407—431no—
479#407—431no—
480#407C2×D4311yescharacteristic
481#407C2×D4311yescharacteristic
482C4×M16—431no—
483C4×M16C2×D4311yescharacteristic
484#343—431no—
485#343—431no—
486#343—431no—
487#343—431no—
488#343—431no—
489#343—431no—
490#343—431no—
491#343—431no—
492#343—431no—
493#343—431no—
494#343—431no—
495#343—431no—
496C43#2248011yescharacteristic, complemented, Sylow
497C22×Q8—431no—
498C22×D4C4×D4311yescharacteristic
499C23×C4—432no—
500C23×C4C22×D4311yescharacteristic
501C23×C4C22×D4311yescharacteristic
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C2×M16—41no—
508C2×M16—431no—
509C2×M16—431no—
510C2×M16—431no—
511C2×M16—431no—
512C2×M16—861no—
513C2×M16—861no—
514C2×M16—862no—
515C2×M16—862no—
516C2×M16—1721no—
517C2×M16—1721no—
518C2×M16C22×D4311yescharacteristic
519C2×M16C22×D4311yescharacteristic
520C2×M16C22×D4311yescharacteristic
521C2×M16C22×D4311yescharacteristic
522C22×C8—21no—
523C22×C8—21no—
524C22×C8—861no—
525C22×C8—861no—
526#126—862no—
527#126—862no—
528#126—862no—
529#126—862no—
530#125—862no—
531#125—862no—
532#125—862no—
533#125—862no—
534#125—861no—
535#125—861no—
536#125—861no—
537#125—861no—
538#123—862no—
539#123—862no—
540#123—862no—
541#123—862no—
542C22⋊Q8—861no—
543C22⋊Q8—861no—
544C22⋊Q8—861no—
545C22⋊Q8—861no—
546C22⋊Q8—861no—
547C22⋊Q8—861no—
548C22⋊Q8—861no—
549C22⋊Q8—861no—
550C4×Q8—861no—
551C4×Q8—861no—
552C4×Q8—861no—
553C4×Q8—861no—
554C4×D4D17211yescharacteristic
555C4×D4D17211yescharacteristic
556C4×D4D17211yescharacteristic
557C4×D4D17211yescharacteristic
558C4×D4C22⋊D4311yescharacteristic
559C4×D4C22⋊D4311yescharacteristic
560C4×D4C22⋊D4311yescharacteristic
561C4×D4C22⋊D4311yescharacteristic
562#117—861no—
563#117—861no—
564#117—861no—
565#117—861no—
566#117—862no—
567#117—862no—
568#117—862no—
569#117—862no—
570C2×C4⋊C4—432no—
571C2×C4⋊C4—432no—
572C2×C4⋊C4—432no—
573C2×C4⋊C4—432no—
574C2×C4⋊C4—432no—
575C2×C4⋊C4—432no—
576C2×C4⋊C4—431no—
577C2×C4⋊C4—431no—
578C2×C4⋊C4—431no—
579C2×C4⋊C4—861no—
580C2×C4⋊C4—861no—
581C2×C4⋊C4—861no—
582C2×C4⋊C4—861no—
583C2×C4⋊C4C4×D4311yescharacteristic
584C2×C22⋊C4—432no—
585C2×C22⋊C4—432no—
586C2×C22⋊C4—432no—
587C2×C22⋊C4C4×D4311yescharacteristic
588C2×C22⋊C4C4×D4311yescharacteristic
589C2×C42—432no—
590C2×C42—432no—
591C2×C42C22×D4311yescharacteristic
592C4⋊C8—21no—
593C4⋊C8—21no—
594C4⋊C8—861no—
595C4⋊C8—861no—
596#101—862no—
597#101—862no—
598#101—1721no—
599#101—1721no—
600C22⋊C8—21no—
601C22⋊C8—21no—
602C22⋊C8—21no—
603C22⋊C8—21no—
604C22⋊C8—861no—
605C22⋊C8—861no—
606C22⋊C8—861no—
607C22⋊C8—861no—
608#97—21no—
609#97—861no—
610C4×C8—21no—
611C4×C8—861no—
612C24C2×C4×D4311yescharacteristic
613C24C2×C4×D4311yescharacteristic
614C2×Q8—861no—
615C2×Q8—861no—
616C2×Q8—861no—
617C2×Q8—861no—
618C2×Q8—861no—
619C2×Q8—861no—
620C2×D4—42no—
621C2×D4(C2×D43)⋊C411yescharacteristic
622C2×D4(C2×D43)⋊C411yescharacteristic
623C2×D4(C2×D43)⋊C411yescharacteristic
624C2×D4(C2×D43)⋊C411yescharacteristic
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—432no—
634C22×C4—432no—
635C22×C4—432no—
636C22×C4—432no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—1724no—
640C22×C4C2×C4×D4311yescharacteristic
641C22×C4C2×C4×D4311yescharacteristic
642C22×C4C2×C4×D4311yescharacteristic
643C22×C4C2×C4×D4311yescharacteristic
644C22×C4C2×D17211yescharacteristic
645C22×C4C2×D17211yescharacteristic
646C22×C4C2×D17211yescharacteristic
647C22×C4C2×D17211yescharacteristic
648C22×C4C2×C22⋊D4311yescharacteristic
649C22×C4C2×C22⋊D4311yescharacteristic
650C22×C4C2×C22⋊D4311yescharacteristic
651C22×C4C2×C22⋊D4311yescharacteristic
652C22×C4C23×D4311yescharacteristic
653M16—21no—
654M16—21no—
655M16—21no—
656M16—21no—
657M16—21no—
658M16—21no—
659M16—21no—
660M16—42no—
661M16—42no—
662M16—432no—
663M16—861no—
664M16—861no—
665M16—861no—
666M16—861no—
667M16—861no—
668M16—861no—
669M16—861no—
670M16—1722no—
671M16—1722no—
672M16#1062190012yes—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—42no—
678C2×C8—42no—
679C2×C8—861no—
680C2×C8—861no—
681C2×C8—861no—
682C2×C8—861no—
683C2×C8—1722no—
684C2×C8—1722no—
685C4⋊C4—862no—
686C4⋊C4—862no—
687C4⋊C4—862no—
688C4⋊C4—862no—
689C4⋊C4—862no—
690C4⋊C4—862no—
691C4⋊C4—862no—
692C4⋊C4—862no—
693C4⋊C4—862no—
694C4⋊C4—862no—
695C4⋊C4—862no—
696C4⋊C4—862no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4(C2×D43)⋊C411yescharacteristic
704C4⋊C4(C2×D43)⋊C411yescharacteristic
705C4⋊C4(C2×D43)⋊C411yescharacteristic
706C4⋊C4(C2×D43)⋊C411yescharacteristic
707C22⋊C4—862no—
708C22⋊C4—862no—
709C22⋊C4—862no—
710C22⋊C4—862no—
711C22⋊C4—862no—
712C22⋊C4—862no—
713C22⋊C4(C2×D43)⋊C411yescharacteristic
714C22⋊C4(C2×D43)⋊C411yescharacteristic
715C22⋊C4(C2×D43)⋊C411yescharacteristic
716C22⋊C4(C2×D43)⋊C411yescharacteristic
717C22⋊C4(C2×D43)⋊C411yescharacteristic
718C22⋊C4(C2×D43)⋊C411yescharacteristic
719C22⋊C4(C2×D43)⋊C411yescharacteristic
720C22⋊C4(C2×D43)⋊C411yescharacteristic
721C42—862no—
722C42—862no—
723C42—862no—
724C42—862no—
725C42C2×D17211yescharacteristic
726C42C2×D17211yescharacteristic
727C42C2×C22⋊D4311yescharacteristic
728C42C2×C22⋊D4311yescharacteristic
729C23—21no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×(C2×D43)⋊C411yescharacteristic
738C23C2×(C2×D43)⋊C411yescharacteristic
739C23C2×(C2×D43)⋊C411yescharacteristic
740C23C2×(C2×D43)⋊C411yescharacteristic
741C23C22×C4×D4311yescharacteristic
742Q8—1721no—
743Q8—1721no—
744Q8—1721no—
745Q8—1721no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—41no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—1724no—
779C2×C4—1724no—
780C2×C4—1722no—
781C2×C4—1722no—
782C2×C4—1722no—
783C2×C4C2×(C2×D43)⋊C411yescharacteristic
784C2×C4C2×(C2×D43)⋊C411yescharacteristic
785C2×C4C2×(C2×D43)⋊C411yescharacteristic
786C2×C4C2×(C2×D43)⋊C411yescharacteristic
787C2×C4C2×(C2×D43)⋊C411yescharacteristic
788C2×C4C2×(C2×D43)⋊C411yescharacteristic
789C2×C4C2×(C2×D43)⋊C411yescharacteristic
790C2×C4C2×(C2×D43)⋊C411yescharacteristic
791C2×C4C22×C22⋊D4311yescharacteristic
792C2×C4C22×D17211yescharacteristic
793C2×C4#41×D4311yescharacteristic
794C2×C4C2×#1062190011yescharacteristic
795C2×C4#1306337011yescharacteristic
796C2×C4#1306337211yescharacteristic
797C8—22no—
798C8—41no—
799C8—41no—
800C8—41no—
801C8—862no—
802C8—1721no—
803C8—1721no—
804C8—1721no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—42no—
819C22—42no—
820C22—81no—
821C22—81no—
822C22#1458288112yes—
823C22C22×(C2×D43)⋊C411yescharacteristic
824C22C4×#1062190011yescharacteristic
825C22#1458337811yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—1722no—
835C4—1722no—
836C4—1722no—
837C4—1722no—
838C4#1458354311yescharacteristic
839C4#1458354411yescharacteristic
840C4#1458354811yescharacteristic
841C4#1458355311yescharacteristic
842C2—21no—
843C2—21no—
844C2—22no—
845C2—41no—
846C2—41no—
847C2—41no—
848C2#1913742011yescharacteristic
849C2C2×#1458288111yescharacteristic
850C2#1914307711yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×M16×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC22×D4×C43C2×C4
cosocleC22×C4×C43C24
hypercenterD4×M16D43
hypocenterC43#22480
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
3. #19135588C2semidirect
4. #19135587C2semidirect
5. #19135063C2semidirect
6. #19135063C2semidirect
7. #19135061C2semidirect
8. #19135061C2semidirect
9. #19134676C2semidirect
10. #19134673C2semidirect
11. #19134588C2semidirect
12. C4×#13063243C2semidirect
13. #19134333C2semidirect
14. C2×#14582667C2semidirect
496. C43#22480semidirect

Maximal subgroups

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

subgroupindex
C2×#145835892
D4×#106218772
#191355882
#191355872
#191350632
#191350612
#191346762
#191346732
#191345882
C4×#130632432
#191343332
C2×#145826672
D4×M16×C432
#2248043