Finite Group Databasebeta

← #25113153

Subgroups — #25113153

Order 11008.

1114 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583608C211yesmaximal, characteristic
2#19137473C212yesmaximal, complemented
3#19135580C212yesmaximal, complemented
4#19135578C212yesmaximal, complemented
5#19135578C212yesmaximal, complemented
6#19134583C211yesmaximal, characteristic
7#19134581C211yesmaximal, characteristic
8#19134581C211yesmaximal, characteristic
9#99×Dic43C211yesmaximal, characteristic
10#99×Dic43C211yesmaximal, characteristic
11C4×#99×C43C211yesmaximal, characteristic
12#14583608—22no—
13#14583608—22no—
14#14583608—22no—
15#14583608—22no—
16C2×#13063324C411yescharacteristic, complemented
17C2×#13063317C411yescharacteristic, complemented
18C2×#13063316C411yescharacteristic, complemented
19C2×#13063304C411yescharacteristic, complemented
20C2×#13063304C2211yescharacteristic
21C2×#13063302C411yescharacteristic, complemented
22C2×#13063302C411yescharacteristic, complemented
23C2×#13063302C2211yescharacteristic
24C2×#13063302C2211yescharacteristic
25C2×C4×Dic86C411yescharacteristic, complemented
26C2×D4×Dic43C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28C22×Dic43⋊C4C411yescharacteristic, complemented
29C22×Dic43⋊C4C2211yescharacteristic
30C2×#13063240C2211yescharacteristic
31C2×#13063240C2211yescharacteristic
32#14582796—22no—
33#14582786—22no—
34#14582783—22no—
35#14582759C2212yes—
36#14582757C2212yes—
37#14582757C2212yes—
38C4×Dic43⋊C4—22no—
39C22⋊C4×Dic43C2212yes—
40C22⋊C4×Dic43C2212yes—
41#14582666C2212yes—
42#14582665C2212yes—
43#14582665C2212yes—
44#14582665C2212yes—
45#14582665C2212yes—
46C2×C4×D4×C43C2211yescharacteristic
47C2×#99×C43C2211yescharacteristic
48C2×#99×C43C2211yescharacteristic
49C4×C22⋊C4×C43C2212yes—
50C43×#342C2212yes—
51C22×Dic86C2×C411yescharacteristic
52C22×Dic86C2×C411yescharacteristic
53C22×Dic86C2×C411yescharacteristic
54C23×Dic43C2×C411yescharacteristic
55C23×Dic43C2×C411yescharacteristic
56C23×Dic43C2311yescharacteristic
57C23×Dic43C2311yescharacteristic
58#13063324—22no—
59#13063324—22no—
60#13063317—22no—
61#13063317—22no—
62#13063316—22no—
63#13063316—22no—
64#13063304—22no—
65#13063304—22no—
66#13063304—22no—
67#13063304—22no—
68#13063302—22no—
69#13063302—22no—
70#13063302—22no—
71#13063302—22no—
72#13063302—22no—
73#13063302—22no—
74#13063302—22no—
75#13063302—22no—
76C4×Dic86—21no—
77C4×Dic86—21no—
78C4×Dic86—21no—
79C4×Dic86—21no—
80D4×Dic43—22no—
81D4×Dic43—22no—
82D4×Dic43—22no—
83D4×Dic43—22no—
84C2×C4⋊Dic43—22no—
85C2×C4⋊Dic43C2×C411yescharacteristic
86C2×C4⋊Dic43C2×C411yescharacteristic
87C2×C4⋊Dic43C2×C411yescharacteristic
88C2×C4⋊Dic43C2×C411yescharacteristic
89C2×C4⋊Dic43C2×C411yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C411yescharacteristic
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×Dic43⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×Dic43⋊C4C2×C411yescharacteristic
105C2×Dic43⋊C4C2×C411yescharacteristic
106C2×Dic43⋊C4D412yes—
107C2×Dic43⋊C4D412yes—
108C2×Dic43⋊C4D412yes—
109C2×Dic43⋊C4D412yes—
110C2×C22⋊Dic43C2×C411yescharacteristic
111C2×C22⋊Dic43C2×C411yescharacteristic
112C2×C22⋊Dic43C2312yes—
113C2×C22⋊Dic43C2312yes—
114C2×C22⋊Dic43C2311yescharacteristic
115C2×C22⋊Dic43C2311yescharacteristic
116C2×C4×Dic43—22no—
117C2×C4×Dic43—22no—
118C2×C4×Dic43C2×C411yescharacteristic
119C2×C4×Dic43C2×C411yescharacteristic
120#13063240—22no—
121#13063240—22no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C22×D4×C43C2311yescharacteristic
128C23×C4×C43C2×C411yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C22⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43C2312yes—
135C2×C22⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43C2312yes—
137C2×C42×C43—22no—
138C2×C42×C43C2×C411yescharacteristic
139#99×C43—22no—
140#99×C43Q814yescomplemented
141#95×C43—22no—
142C24×C43C22×C411yescharacteristic
143C24×C43C2411yescharacteristic
144C2×D4×C43—22no—
145C2×D4×C43—22no—
146C2×D4×C43C2×Q812yes—
147C2×D4×C43#4112yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—81no—
153C22×C4×C43—81no—
154C22×C4×C43C22×C411yescharacteristic
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C22×C411yescharacteristic
157C22×C4×C43C22×C411yescharacteristic
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C2×D412yes—
160C22×C4×C43C2×D412yes—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—42no—
168C22×Dic43—42no—
169C22×Dic43—81no—
170C22×Dic43—81no—
171C22×Dic43C22×C411yescharacteristic
172C22×Dic43C22×C411yescharacteristic
173C22×Dic43C22×C411yescharacteristic
174C22×Dic43C22×C411yescharacteristic
175C22×Dic43C22×C411yescharacteristic
176C22×Dic43C22×C411yescharacteristic
177C22×Dic43C22×C411yescharacteristic
178C22×Dic43C22×C411yescharacteristic
179C22×Dic43C2×D412yes—
180C22×Dic43C2×D412yes—
181C22×Dic43C2×D412yes—
182C22×Dic43C2×D412yes—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—22no—
186C2×Dic86—22no—
187C2×Dic86—42no—
188C2×Dic86—81no—
189C2×Dic86—81no—
190C4⋊C4×C43—22no—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—22no—
195C22⋊C4×C43—22no—
196C22⋊C4×C43C2×Q814yes—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—82no—
200C22⋊Dic43—22no—
201C22⋊Dic43—22no—
202C22⋊Dic43—22no—
203C22⋊Dic43—22no—
204C22⋊Dic43—22no—
205C22⋊Dic43—22no—
206C22⋊Dic43—22no—
207C22⋊Dic43—22no—
208C4⋊Dic43—22no—
209C4⋊Dic43—22no—
210C4⋊Dic43—22no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—22no—
214C4⋊Dic43—82no—
215Dic43⋊C4—21no—
216Dic43⋊C4—21no—
217Dic43⋊C4—21no—
218Dic43⋊C4—21no—
219Dic43⋊C4—21no—
220Dic43⋊C4—21no—
221Dic43⋊C4—21no—
222Dic43⋊C4—21no—
223Dic43⋊C4—22no—
224Dic43⋊C4—22no—
225Dic43⋊C4—44no—
226Dic43⋊C4—82no—
227Dic43⋊C4C22⋊C411yescharacteristic
228Dic43⋊C4C22⋊C411yescharacteristic
229Dic43⋊C4C22⋊C411yescharacteristic
230Dic43⋊C4C22⋊C411yescharacteristic
231Dic43⋊C4C22⋊C412yes—
232Dic43⋊C4C22⋊C412yes—
233Dic43⋊C4C22⋊C412yes—
234Dic43⋊C4C22⋊C412yes—
235Dic43⋊C4C22⋊C412yes—
236Dic43⋊C4C22⋊C412yes—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—44no—
242C4×Dic43—82no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43C4×Q812yes—
250C23×C43C23×C411yescharacteristic
251C23×C43C22×D412yes—
252C23×C43C22×Q811yescharacteristic
253C23×C43C2×#4111yescharacteristic
254C23×C432−1+412yes—
255D4×C43—24no—
256D4×C43—24no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—24no—
262C2×C4×C43—42no—
263C2×C4×C43—42no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—42no—
267C2×C4×C43—42no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—42no—
271C2×C4×C43—42no—
272C2×C4×C43—42no—
273C2×C4×C43—81no—
274C2×C4×C43—81no—
275C2×C4×C43C2×C22⋊C411yescharacteristic
276C2×C4×C43C2×C22⋊C411yescharacteristic
277C2×C4×C43C2×C22⋊C412yes—
278C2×C4×C43C4×Q812yes—
279C2×Dic43—24no—
280C2×Dic43—22no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—21no—
285C2×Dic43—42no—
286C2×Dic43—42no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—42no—
290C2×Dic43—41no—
291C2×Dic43—42no—
292C2×Dic43—42no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—42no—
298C2×Dic43—42no—
299C2×Dic43—42no—
300C2×Dic43—42no—
301C2×Dic43—42no—
302C2×Dic43—42no—
303C2×Dic43—81no—
304C2×Dic43—81no—
305C2×Dic43C2×C22⋊C411yescharacteristic
306C2×Dic43C2×C22⋊C411yescharacteristic
307C2×Dic43C2×C22⋊C411yescharacteristic
308C2×Dic43C2×C22⋊C412yes—
309C2×Dic43C2×C22⋊C412yes—
310C2×Dic43C2×C22⋊C411yescharacteristic
311Dic86—42no—
312Dic86—42no—
313Dic86—82no—
314Dic86—82no—
315#22513—431nomaximal, Sylow
316C22×C43—21no—
317C22×C43—22no—
318C22×C43—21no—
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43C22×C22⋊C411yescharacteristic
329C22×C43C2×C4×Q811yescharacteristic
330C22×C43#51911yescharacteristic
331C22×C43#54812yes—
332C22×C43D4×Q812yes—
333C4×C43—22no—
334C4×C43—22no—
335C4×C43—21no—
336C4×C43—21no—
337C4×C43—44no—
338C4×C43—41no—
339C4×C43—41no—
340C4×C43—82no—
341Dic43—21no—
342Dic43—22no—
343Dic43—22no—
344Dic43—21no—
345Dic43—21no—
346Dic43—41no—
347Dic43—41no—
348Dic43—41no—
349Dic43—41no—
350Dic43—82no—
351Dic43—82no—
352Dic43#41012yes—
353C2×#554—431no—
354#2345—432no—
355#1996—432no—
356#1996—432no—
357#1996—432no—
358#1799—431no—
359#1799—431no—
360#1799—431no—
361C4×#99—431no—
362C4×#99—431no—
363C4×#99D4311yescharacteristic
364C2×C43—22no—
365C2×C43—22no—
366C2×C43—21no—
367C2×C43—21no—
368C2×C43—42no—
369C2×C43Q8×C22⋊C411yescharacteristic
370C2×C43C2×#41011yescharacteristic
371C2×C43#288311yescharacteristic
372#554—862no—
373#554—862no—
374#554—862no—
375#554—862no—
376C2×C4⋊Q8—431no—
377C2×#125—431no—
378C2×#125—431no—
379C2×C22⋊Q8—431no—
380C2×C22⋊Q8—431no—
381C2×C22⋊Q8—431no—
382C2×C22⋊Q8—431no—
383C2×C22⋊Q8—431no—
384C2×C22⋊Q8—431no—
385C2×C4×Q8—431no—
386C2×C4×D4—431no—
387C2×C4×D4—431no—
388C2×C4×D4C2×D4311yescharacteristic
389C22×C4⋊C4—431no—
390C22×C4⋊C4—431no—
391C2×#99—431no—
392C2×#99—431no—
393C2×#99C2×D4311yescharacteristic
394C2×#99C2×D4311yescharacteristic
395#389—862no—
396#387—862no—
397#387—862no—
398#380—432no—
399#380—432no—
400#380—432no—
401C4×C4⋊C4—862no—
402C4×C22⋊C4—432no—
403C4×C22⋊C4—432no—
404C4×C22⋊C4C2×D4312yes—
405#342—432no—
406#342—432no—
407#342—432no—
408#342—432no—
409#342—432no—
410#342C2×D4312yes—
411C43#2251311yescharacteristic, complemented, Sylow
412C22×Q8—431no—
413C22×Q8—431no—
414C22×Q8—431no—
415C22×D4C22×D4311yescharacteristic
416C23×C4—431no—
417C23×C4—431no—
418C23×C4—431no—
419C23×C4—431no—
420C23×C4C4×D4311yescharacteristic
421C23×C4C22×D4311yescharacteristic
422C4⋊Q8—862no—
423C4⋊Q8—862no—
424#125—862no—
425#125—862no—
426#125—862no—
427#125—862no—
428C22⋊Q8—862no—
429C22⋊Q8—862no—
430C22⋊Q8—862no—
431C22⋊Q8—862no—
432C22⋊Q8—862no—
433C22⋊Q8—862no—
434C22⋊Q8—862no—
435C22⋊Q8—862no—
436C22⋊Q8—862no—
437C22⋊Q8—862no—
438C22⋊Q8—862no—
439C22⋊Q8—862no—
440C4×Q8—861no—
441C4×Q8—861no—
442C4×Q8—861no—
443C4×Q8—861no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—862no—
447C4×D4—862no—
448C4×D4—862no—
449C4×D4—862no—
450C2×C4⋊C4—431no—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—431no—
454C2×C4⋊C4—432no—
455C2×C4⋊C4—432no—
456C2×C4⋊C4—432no—
457C2×C4⋊C4—432no—
458C2×C4⋊C4—431no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—431no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4—431no—
466C2×C4⋊C4—431no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4—861no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—862no—
474C2×C4⋊C4—862no—
475C2×C4⋊C4—862no—
476C2×C4⋊C4C4×D4311yescharacteristic
477C2×C22⋊C4—431no—
478C2×C22⋊C4—431no—
479C2×C22⋊C4—431no—
480C2×C22⋊C4—431no—
481C2×C22⋊C4—432no—
482C2×C22⋊C4—432no—
483C2×C22⋊C4C4×D4311yescharacteristic
484C2×C22⋊C4C22×D4312yes—
485C2×C22⋊C4C22×D4311yescharacteristic
486C2×C22⋊C4C22×D4312yes—
487C2×C42—22no—
488C2×C42—431no—
489C2×C42—431no—
490C2×C42—862no—
491C2×C42—862no—
492C2×C42C4×D4311yescharacteristic
493#99—22no—
494#99—862no—
495#99—862no—
496#99Dic8614yescomplemented
497#95—22no—
498#95—862no—
499#95—862no—
500#95—862no—
501#95—862no—
502#95—862no—
503C24C2×C4×D4311yescharacteristic
504C24C23×D4311yescharacteristic
505C2×Q8—862no—
506C2×Q8—861no—
507C2×Q8—861no—
508C2×Q8—862no—
509C2×Q8—3441no—
510C2×Q8—3441no—
511C2×Q8—1722no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4C2×Dic8612yes—
515C2×D4#1062189812yes—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—431no—
523C22×C4—432no—
524C22×C4—431no—
525C22×C4—431no—
526C22×C4—431no—
527C22×C4—432no—
528C22×C4—432no—
529C22×C4—432no—
530C22×C4—431no—
531C22×C4—431no—
532C22×C4—431no—
533C22×C4—431no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—861no—
537C22×C4—861no—
538C22×C4—862no—
539C22×C4—862no—
540C22×C4—3441no—
541C22×C4—3441no—
542C22×C4—1722no—
543C22×C4—1722no—
544C22×C4C2×C4×D4311yescharacteristic
545C22×C4C2×C4×D4311yescharacteristic
546C22×C4C2×C4×D4311yescharacteristic
547C22×C4C2×C4×D4311yescharacteristic
548C22×C4C2×C4×D4311yescharacteristic
549C22×C4D4×D4312yes—
550C22×C4D4×D4312yes—
551C4⋊C4—22no—
552C4⋊C4—431no—
553C4⋊C4—431no—
554C4⋊C4—431no—
555C4⋊C4—431no—
556C4⋊C4—432no—
557C4⋊C4—432no—
558C4⋊C4—432no—
559C4⋊C4—432no—
560C4⋊C4—432no—
561C4⋊C4—432no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C4⋊C4—861no—
565C4⋊C4—861no—
566C4⋊C4—862no—
567C4⋊C4—862no—
568C4⋊C4—861no—
569C4⋊C4—861no—
570C4⋊C4—862no—
571C4⋊C4—862no—
572C4⋊C4—862no—
573C4⋊C4—861no—
574C4⋊C4—861no—
575C4⋊C4—861no—
576C4⋊C4—861no—
577C4⋊C4—862no—
578C4⋊C4—3442no—
579C4⋊C4—3442no—
580C4⋊C4—1724no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—862no—
587C22⋊C4—862no—
588C22⋊C4—862no—
589C22⋊C4—862no—
590C22⋊C4—862no—
591C22⋊C4—862no—
592C22⋊C4—862no—
593C22⋊C4—862no—
594C22⋊C4C2×Dic8614yes—
595C42—21no—
596C42—21no—
597C42—82no—
598C42—861no—
599C42—861no—
600C42—861no—
601C42—861no—
602C42—3442no—
603C42—1724no—
604C23—21no—
605C23—21no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C4×Dic8612yes—
611C23C22×C4×D4311yescharacteristic
612C23C2×D4×D4312yes—
613C23C22×Dic8611yescharacteristic
614C23C2×#1062189811yescharacteristic
615C23#1306337212yes—
616Q8—3442no—
617Q8—3442no—
618Q8—1722no—
619Q8—1722no—
620D4—24no—
621D4—24no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—24no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—81no—
639C2×C4—81no—
640C2×C4—431no—
641C2×C4—431no—
642C2×C4—431no—
643C2×C4—431no—
644C2×C4—432no—
645C2×C4—432no—
646C2×C4—864no—
647C2×C4—862no—
648C2×C4—861no—
649C2×C4—861no—
650C2×C4—861no—
651C2×C4—861no—
652C2×C4—3441no—
653C2×C4—3441no—
654C2×C4—1722no—
655C2×C4—1722no—
656C2×C4—1722no—
657C2×C4—1721no—
658C2×C4—1721no—
659C2×C4—1722no—
660C2×C4—1721no—
661C2×C4—1722no—
662C2×C4—1722no—
663C2×C4—1722no—
664C2×C4—1722no—
665C2×C4—1722no—
666C2×C4—1722no—
667C2×C4—1722no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4C22⋊C4×D4311yescharacteristic
673C2×C4C22⋊C4×D4311yescharacteristic
674C2×C4C22⋊C4×D4312yes—
675C2×C4C4×Dic8612yes—
676C22—22no—
677C22—21no—
678C22—22no—
679C22—21no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—41no—
687C22—41no—
688C22C2×C22⋊C4×D4311yescharacteristic
689C22C2×C4×Dic8611yescharacteristic
690C22#1458337611yescharacteristic
691C22#1458355812yes—
692C22D4×Dic8612yes—
693C4—21no—
694C4—21no—
695C4—22no—
696C4—22no—
697C4—44no—
698C4—41no—
699C4—41no—
700C4—82no—
701C4—432no—
702C4—861no—
703C4—862no—
704C4—861no—
705C4—861no—
706C4—862no—
707C4—3442no—
708C4—3442no—
709C4—1721no—
710C4—1721no—
711C4—1721no—
712C4—1721no—
713C2—22no—
714C2—22no—
715C2—21no—
716C2—21no—
717C2—42no—
718C2C22⋊C4×Dic8611yescharacteristic
719C2#410×D4311yescharacteristic
720C2#1914305311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC4×#99×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC22×D4×C43C23
cosocleC24×C43C24
hypercenterC4×#99D43
hypocenterC43#22513
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #19137473C2semidirect
3. #19135580C2semidirect
4. #19135578C2semidirect
5. #19135578C2semidirect
16. C2×#13063324C4semidirect
17. C2×#13063317C4semidirect
18. C2×#13063316C4semidirect
19. C2×#13063304C4semidirect
21. C2×#13063302C4semidirect
22. C2×#13063302C4semidirect
25. C2×C4×Dic86C4semidirect
28. C22×Dic43⋊C4C4semidirect
140. #99×C43Q8semidirect
411. C43#22513semidirect
496. #99Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145836082
#191374732
#191355802
#191355782
#191345832
#191345812
#99×Dic432
C4×#99×C432
#2251343