Finite Group Databasebeta

← #25062676

Subgroups — #25062676

Order 11008.

992 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583427C211yesmaximal, characteristic
2#19143225C211yesmaximal, characteristic, complemented
3#432×D43C211yesmaximal, characteristic, complemented
4#19132949C212yesmaximal, complemented
5#19132945C212yesmaximal, complemented
6#19132942C212yesmaximal, complemented
7#19132940C212yesmaximal, complemented
8#19132929C211yesmaximal, characteristic, complemented
9#19132927C211yesmaximal, characteristic, complemented
10#19132927C211yesmaximal, characteristic, complemented
11C43×#1464C211yesmaximal, characteristic, complemented
12#14583427—21no—
13#14583427—21no—
14#14583427—21no—
15#14583427—21no—
16#14583427—21no—
17#14583427—21no—
18#14583427—21no—
19#14583427—21no—
20C2×#13063320C411yescharacteristic
21C2×#13063318C411yescharacteristic
22C2×#13063315C2211yescharacteristic
23C2×#13063311C2211yescharacteristic
24C2×#13063310C2211yescharacteristic
25C2×#13063307C2211yescharacteristic
26C2×#13063303C411yescharacteristic
27C2×#13063298C411yescharacteristic
28C2×C4×Dic86C411yescharacteristic
29C2×C4×D172C411yescharacteristic
30C2×C4×C22⋊D43C411yescharacteristic
31C2×C4×C22⋊D43C411yescharacteristic
32C2×#13063282C2211yescharacteristic
33C2×C42×D43C2211yescharacteristic
34#14582956C2211yescharacteristic
35#14582956C2211yescharacteristic
36#14582955—21no—
37#14582954—21no—
38#14582954—21no—
39#14582953C2212yes—
40#14582951—21no—
41#14582949C2212yes—
42#14582921—21no—
43C4⋊C8×D43—21no—
44#14582861C2212yes—
45C22⋊C8×D43C2212yes—
46#14582851—21no—
47#97×D43—21no—
48#14582625C2212yes—
49#14582624C2212yes—
50#14582624C2212yes—
51#14582623C2212yes—
52#14582622C2212yes—
53#14582622C2212yes—
54C2×#117×C43C2211yescharacteristic
55C43×#432C2211yescharacteristic
56C43×#432C2211yescharacteristic
57C43×#324C2212yes—
58C43×#323C2212yes—
59C22×Dic86C2×C411yescharacteristic
60C22×D172C2×C411yescharacteristic
61C22×C22⋊D43C2×C411yescharacteristic
62C22×C22⋊D43C2×C411yescharacteristic
63C22×C4×D43C2×C411yescharacteristic
64C22×C4×D43C2×C411yescharacteristic
65C22×C4×D43C2×C411yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C2×#10621872—22no—
68C2×C8×D43—22no—
69#13063320—21no—
70#13063320—21no—
71#13063320—21no—
72#13063320—21no—
73#13063318—21no—
74#13063318—21no—
75#13063318—21no—
76#13063318—21no—
77#13063315—21no—
78#13063315—21no—
79#13063315—21no—
80#13063315—21no—
81#13063311—21no—
82#13063311—21no—
83#13063311—21no—
84#13063311—21no—
85#13063310—21no—
86#13063310—21no—
87#13063310—21no—
88#13063310—21no—
89#13063307—21no—
90#13063307—21no—
91#13063307—21no—
92#13063307—21no—
93#13063303—21no—
94#13063303—21no—
95#13063303—21no—
96#13063303—21no—
97#13063298—21no—
98#13063298—21no—
99#13063298—21no—
100#13063298—21no—
101C4×Dic86—21no—
102C4×Dic86—21no—
103C4×Dic86—21no—
104C4×Dic86—21no—
105C4×D172—21no—
106C4×D172—21no—
107C4×D172—21no—
108C4×D172—21no—
109C4×C22⋊D43—21no—
110C4×C22⋊D43—21no—
111C4×C22⋊D43—21no—
112C4×C22⋊D43—21no—
113C4×C22⋊D43—21no—
114C4×C22⋊D43—21no—
115C4×C22⋊D43—21no—
116C4×C22⋊D43—21no—
117#13063282—21no—
118#13063282—21no—
119#13063282—21no—
120#13063282—21no—
121C2×C4⋊Dic43C2×C411yescharacteristic
122C2×C4⋊Dic43C2×C411yescharacteristic
123C2×Dic43⋊C4C2×C411yescharacteristic
124C2×Dic43⋊C4C2×C411yescharacteristic
125C2×Dic43⋊C4C2×C411yescharacteristic
126C2×Dic43⋊C4C2×C411yescharacteristic
127C2×Dic43⋊C4C2×C411yescharacteristic
128C2×Dic43⋊C4C2311yescharacteristic
129C2×C22⋊Dic43C2×C411yescharacteristic
130C2×C22⋊Dic43C2×C411yescharacteristic
131C2×(C2×D43)⋊C4C2×C411yescharacteristic
132C2×(C2×D43)⋊C4C2×C411yescharacteristic
133C2×(C2×D43)⋊C4C2×C411yescharacteristic
134C2×(C2×D43)⋊C4C2×C411yescharacteristic
135C2×(C2×D43)⋊C4C2×C411yescharacteristic
136C2×(C2×D43)⋊C4C2311yescharacteristic
137C2×C4×Dic43C2×C411yescharacteristic
138C2×C4×Dic43C2×C411yescharacteristic
139C2×C4×Dic43C2×C411yescharacteristic
140C2×C4×Dic43C2311yescharacteristic
141C42×D43D411yescharacteristic
142C42×D43D411yescharacteristic
143C42×D43D411yescharacteristic
144C42×D43D411yescharacteristic
145C42×D43D411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43D411yescharacteristic
148C42×D43D411yescharacteristic
149C4⋊(C43⋊C8)—21no—
150C4⋊(C43⋊C8)—21no—
151Dic43⋊C8—22no—
152Dic43⋊C8—22no—
153C22⋊(C43⋊C8)C2312yes—
154C22⋊(C43⋊C8)C2312yes—
155(C2×D43)⋊C8—22no—
156(C2×D43)⋊C8—22no—
157#13063236—21no—
158#13063236—21no—
159#13063235—22no—
160C8×Dic43—22no—
161C23×C4×C43C2×C411yescharacteristic
162#117×C43—21no—
163#117×C43—21no—
164#117×C43—21no—
165#117×C43—21no—
166C2×C4⋊C4×C43C2×C411yescharacteristic
167C2×C4⋊C4×C43C2311yescharacteristic
168C2×C22⋊C4×C43C2×C411yescharacteristic
169C2×C22⋊C4×C43C2311yescharacteristic
170C2×C42×C43C2×C411yescharacteristic
171C2×C42×C43C2311yescharacteristic
172C4⋊C8×C43—21no—
173C4⋊C8×C43—21no—
174C22⋊C8×C43C2312yes—
175C22⋊C8×C43C2312yes—
176#97×C43—21no—
177#97×C43—21no—
178C24×C43C22×C411yescharacteristic
179C23×D43C22×C411yescharacteristic
180C23×D43C22×C411yescharacteristic
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—42no—
184C22×C4×C43C22×C411yescharacteristic
185C22×C4×C43C22×C411yescharacteristic
186C22×C4×C43C22×C411yescharacteristic
187C22×C4×C43C22×C411yescharacteristic
188C22×C4×C43C22×C411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C2×C22⋊D43—21no—
194C2×C22⋊D43—42no—
195C2×C22⋊D43—42no—
196C22×Dic43C22×C411yescharacteristic
197C22×Dic43C22×C411yescharacteristic
198C22×Dic43C22×C411yescharacteristic
199C22×Dic43C22×C411yescharacteristic
200C22×Dic43C22×C411yescharacteristic
201C22×Dic43C22×C411yescharacteristic
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—42no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—42no—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
211C2×C4×D43C22⋊C411yescharacteristic
212C2×C4×D43C22⋊C411yescharacteristic
213C2×C4×D43C22⋊C411yescharacteristic
214C2×C4×D43C22⋊C411yescharacteristic
215C2×C4×D43C22⋊C411yescharacteristic
216C2×C4×D43C22⋊C411yescharacteristic
217C2×C4×D43C22⋊C411yescharacteristic
218C2×C4×D43C22⋊C411yescharacteristic
219C2×C4×D43C2×D411yescharacteristic
220C2×C4×D43C2×D411yescharacteristic
221C2×C4×D43C2×D411yescharacteristic
222C2×C4×D43C2×D411yescharacteristic
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—42no—
226C2×C8×C43—22no—
227C2×C8×C43—22no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C22⋊C4×C43—21no—
233C22⋊C4×C43—21no—
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C42×C43—21no—
237C42×C43—21no—
238C42×C43C2×D411yescharacteristic
239C42×C43C2×D411yescharacteristic
240C42×C43C2×D411yescharacteristic
241C42×C43C2×D411yescharacteristic
242C22⋊Dic43—21no—
243C22⋊Dic43—21no—
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246(C2×D43)⋊C4—21no—
247(C2×D43)⋊C4—21no—
248(C2×D43)⋊C4—21no—
249(C2×D43)⋊C4—21no—
250(C2×D43)⋊C4—21no—
251(C2×D43)⋊C4—21no—
252(C2×D43)⋊C4—21no—
253(C2×D43)⋊C4—21no—
254(C2×D43)⋊C4—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257(C2×D43)⋊C4—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262Dic43⋊C4—21no—
263Dic43⋊C4—21no—
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274C4×Dic43—21no—
275C4×Dic43—21no—
276C4×Dic43C22⋊C411yescharacteristic
277C4×Dic43C22⋊C411yescharacteristic
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C2×D411yescharacteristic
285C4×Dic43C2×D411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288C2×C43⋊C8—22no—
289C2×C43⋊C8—22no—
290#10621872—44no—
291C8×D43—44no—
292C23×C43—21no—
293C23×C43—22no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43C23×C411yescharacteristic
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—21no—
300C22×D43—22no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43C2×C22⋊C411yescharacteristic
305C22×D43C2×C22⋊C411yescharacteristic
306C2×C4×C43—22no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—22no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43C2×C22⋊C411yescharacteristic
318C2×C4×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C2×C22⋊C411yescharacteristic
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C22×D411yescharacteristic
323C22⋊D43—42no—
324C22⋊D43—42no—
325C22⋊D43—42no—
326C22⋊D43—42no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—22no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43C2×C22⋊C411yescharacteristic
337C2×Dic43C2×C22⋊C411yescharacteristic
338C2×Dic43C2×C22⋊C411yescharacteristic
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341C2×Dic43C2×C22⋊C411yescharacteristic
342D172—42no—
343D172—42no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—41no—
349C4×D43—41no—
350C4×D43—41no—
351C4×D43—41no—
352C4×D43—41no—
353C4×D43—41no—
354C4×D43—41no—
355C4×D43—41no—
356C4×D43—42no—
357C4×D43—42no—
358Dic86—42no—
359Dic86—42no—
360C8×C43—42no—
361C8×C43—42no—
362C43⋊C8—42no—
363C43⋊C8—42no—
364#17395—431nomaximal, Sylow
365C22×C43—21no—
366C22×C43—21no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—82no—
371C22×C43C22×C22⋊C411yescharacteristic
372C22×C43#56812yes—
373C2×D43—21no—
374C2×D43—21no—
375C2×D43—21no—
376C2×D43—21no—
377C2×D43—21no—
378C2×D43—44no—
379C2×D43—41no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—82no—
383C2×D43#41012yes—
384C4×C43—21no—
385C4×C43—21no—
386C4×C43—21no—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—21no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43—41no—
393Dic43—21no—
394Dic43—21no—
395Dic43—21no—
396Dic43—21no—
397Dic43—21no—
398Dic43—41no—
399Dic43—41no—
400Dic43—41no—
401Dic43#41312yes—
402C2×#529—431no—
403#2920—431no—
404C2×#432—431no—
405#1470—432no—
406#1469—432no—
407#1468—432no—
408#1468—432no—
409#1464—431no—
410#1464—431no—
411#1464—431no—
412#1464D4311yescharacteristic, complemented
413C2×C43—22no—
414C2×C43—81no—
415C2×C43#287911yescharacteristic
416C2×C43C2×#41011yescharacteristic
417C2×C43C2×#41311yescharacteristic
418D43—22no—
419D43—41no—
420D43—81no—
421#529—861no—
422#529—861no—
423#529—861no—
424#529—861no—
425#529—861no—
426#529—861no—
427#529—861no—
428#529—861no—
429C2×#126—431no—
430C2×#126—431no—
431C2×#125—431no—
432C2×#124—431no—
433C2×#123—431no—
434C2×#123—431no—
435C2×C22⋊Q8—431no—
436C2×#121—431no—
437C2×C4×Q8—431no—
438C2×C4×D4—431no—
439C2×C4×D4—431no—
440C2×C4×D4—431no—
441C2×#117—431no—
442C2×#117C2×D4311yescharacteristic
443C22×C42—431no—
444#432—431no—
445#432—431no—
446#432—432no—
447#432—861no—
448#432—861no—
449#432—861no—
450#432C2×D4311yescharacteristic
451#432C2×D4311yescharacteristic
452#431—432no—
453#431—861no—
454#423—861no—
455C2×C4⋊C8—861no—
456#407—432no—
457C2×C22⋊C8—432no—
458C4×M16—861no—
459C2×#97—861no—
460#324—432no—
461#324—432no—
462#324—432no—
463#324C2×D4312yes—
464#323—432no—
465#323—432no—
466#323—432no—
467#323C2×D4312yes—
468C43#1739511yescharacteristic, complemented, Sylow
469C22×Q8—431no—
470C22×D4—431no—
471C22×D4—431no—
472C22×D4—431no—
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4C4×D4311yescharacteristic
478C2×M16—862no—
479C22×C8—862no—
480#126—861no—
481#126—861no—
482#126—861no—
483#126—861no—
484#126—861no—
485#126—861no—
486#126—861no—
487#126—861no—
488#125—861no—
489#125—861no—
490#125—861no—
491#125—861no—
492#124—861no—
493#124—861no—
494#124—861no—
495#124—861no—
496#123—861no—
497#123—861no—
498#123—861no—
499#123—861no—
500#123—861no—
501#123—861no—
502#123—861no—
503#123—861no—
504C22⋊Q8—861no—
505C22⋊Q8—861no—
506C22⋊Q8—861no—
507C22⋊Q8—861no—
508#121—861no—
509#121—861no—
510#121—861no—
511#121—861no—
512C4×Q8—861no—
513C4×Q8—861no—
514C4×Q8—861no—
515C4×Q8—861no—
516C4×D4—861no—
517C4×D4—861no—
518C4×D4—861no—
519C4×D4—861no—
520C4×D4—861no—
521C4×D4—861no—
522C4×D4—861no—
523C4×D4—861no—
524C4×D4—861no—
525C4×D4—861no—
526C4×D4—861no—
527C4×D4—861no—
528#117—21no—
529#117—21no—
530#117—21no—
531#117—21no—
532#117—861no—
533#117—861no—
534#117—861no—
535#117—861no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4C4×D4311yescharacteristic
545C2×C4⋊C4C22×D4311yescharacteristic
546C2×C22⋊C4—431no—
547C2×C22⋊C4—431no—
548C2×C22⋊C4—431no—
549C2×C22⋊C4—431no—
550C2×C22⋊C4—431no—
551C2×C22⋊C4—431no—
552C2×C22⋊C4—431no—
553C2×C22⋊C4—431no—
554C2×C22⋊C4C4×D4311yescharacteristic
555C2×C22⋊C4C22×D4311yescharacteristic
556C2×C42—431no—
557C2×C42—431no—
558C2×C42—431no—
559C2×C42—431no—
560C2×C42—431no—
561C2×C42—431no—
562C2×C42—431no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—431no—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42C4×D4311yescharacteristic
569C2×C42C22×D4311yescharacteristic
570C4⋊C8—21no—
571C4⋊C8—21no—
572C4⋊C8—862no—
573C4⋊C8—862no—
574C4⋊C8—861no—
575C4⋊C8—861no—
576C22⋊C8—432no—
577C22⋊C8—432no—
578C22⋊C8—862no—
579C22⋊C8—862no—
580C22⋊C8C22×D4312yes—
581C22⋊C8C22×D4312yes—
582#97—21no—
583#97—21no—
584#97—862no—
585#97—861no—
586#97—861no—
587C4×C8—862no—
588C24—431no—
589C24—431no—
590C24C2×C4×D4311yescharacteristic
591C2×Q8—861no—
592C2×Q8—861no—
593C2×Q8—1722no—
594C2×D4—861no—
595C2×D4—861no—
596C2×D4—861no—
597C2×D4—861no—
598C2×D4—861no—
599C2×D4—861no—
600C2×D4—1722no—
601C2×D4—1722no—
602C2×D4—1722no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—42no—
606C22×C4—431no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—1722no—
627C22×C4—1722no—
628C22×C4—1722no—
629C22×C4—1722no—
630C22×C4C2×C4×D4311yescharacteristic
631C22×C4C2×C4×D4311yescharacteristic
632C22×C4C2×C4×D4311yescharacteristic
633C22×C4C2×C4×D4311yescharacteristic
634C22×C4C2×C4×D4311yescharacteristic
635C22×C4C23×D4311yescharacteristic
636M16—1724no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—862no—
640C2×C8—862no—
641C2×C8—1724no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—861no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—861no—
667C22⋊C4—861no—
668C22⋊C4—861no—
669C22⋊C4—861no—
670C22⋊C4—861no—
671C22⋊C4—861no—
672C22⋊C4—861no—
673C22⋊C4—861no—
674C22⋊C4—861no—
675C22⋊C4—861no—
676C22⋊C4—861no—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C22⋊C4—861no—
682C42—21no—
683C42—21no—
684C42—431no—
685C42—431no—
686C42—431no—
687C42—431no—
688C42—431no—
689C42—431no—
690C42—431no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—861no—
697C42—861no—
698C42D4×D4311yescharacteristic
699C42D4×D4311yescharacteristic
700C42D4×D4311yescharacteristic
701C42D4×D4311yescharacteristic
702C23—21no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23—431no—
707C23—431no—
708C23—862no—
709C23—862no—
710C23—862no—
711C23—861no—
712C23—1721no—
713C23—1721no—
714C23—1721no—
715C23C22×C4×D4311yescharacteristic
716Q8—1722no—
717Q8—1722no—
718D4—1722no—
719D4—1722no—
720D4—1722no—
721D4—1722no—
722D4—1722no—
723D4—1722no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—431no—
736C2×C4—431no—
737C2×C4—431no—
738C2×C4—431no—
739C2×C4—431no—
740C2×C4—431no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—861no—
748C2×C4—861no—
749C2×C4—861no—
750C2×C4—862no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4—1721no—
764C2×C4C22⋊C4×D4311yescharacteristic
765C2×C4C22⋊C4×D4311yescharacteristic
766C2×C4C22⋊C4×D4311yescharacteristic
767C2×C4C22⋊C4×D4311yescharacteristic
768C2×C4C2×D4×D4311yescharacteristic
769C2×C4C2×D4×D4311yescharacteristic
770C8—42no—
771C8—42no—
772C8—1722no—
773C8—1722no—
774C22—21no—
775C22—21no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—82no—
780C22—432no—
781C22—861no—
782C22—861no—
783C22—861no—
784C22—861no—
785C22—861no—
786C22—3442no—
787C22—1724no—
788C22—1721no—
789C22—1721no—
790C22—1721no—
791C22C2×C22⋊C4×D4311yescharacteristic
792C22#1458366512yes—
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—432no—
803C4—861no—
804C4—861no—
805C4—861no—
806C4—861no—
807C4—861no—
808C4—1721no—
809C4—1721no—
810C4—1721no—
811C2—22no—
812C2—81no—
813C2—862no—
814C2—3441no—
815C2—1721no—
816C2#1914303811yescharacteristic
817C2#410×D4311yescharacteristic
818C2#413×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1464C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063298C4
cosocleC22×C4×C43C24
hypercenter#1464D43
hypocenterC43#17395
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #19143225C2semidirect
3. #432×D43C2semidirect
4. #19132949C2semidirect
5. #19132945C2semidirect
6. #19132942C2semidirect
7. #19132940C2semidirect
8. #19132929C2semidirect
9. #19132927C2semidirect
10. #19132927C2semidirect
11. C43×#1464C2semidirect
412. #1464D43semidirect
468. C43#17395semidirect

Maximal subgroups

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

subgroupindex
C2×#145834272
#191432252
#432×D432
#191329492
#191329452
#191329422
#191329402
#191329292
#191329272
C43×#14642
#1739543