Finite Group Databasebeta

← #14577306

Subgroups — #14577306

Order 2432.

1522 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597436C211yesmaximal, characteristic, complemented
2C22×#64543C211yesmaximal, characteristic, complemented
3D4×Dic38C211yesmaximal, characteristic, complemented
4#11927207C211yesmaximal, characteristic, complemented
5#11927202C211yesmaximal, characteristic, complemented
6#11927200C211yesmaximal, characteristic, complemented
7#11927198C211yesmaximal, characteristic, complemented
8#11927194C212yesmaximal, complemented
9#11927193C211yesmaximal, characteristic, complemented
10#11927192C212yesmaximal, complemented
11#11927188C211yesmaximal, characteristic, complemented
12#11927184C212yesmaximal, complemented
13#11927181C212yesmaximal, complemented
14#11927123C211yesmaximal, characteristic, complemented
15#11927121C212yesmaximal, complemented
16#11927116C212yesmaximal, complemented
17#11927114C211yesmaximal, characteristic, complemented
18#11927053C211yesmaximal, characteristic, complemented
19#11927050C212yesmaximal, complemented
20C2×#10597324C212yesmaximal, complemented
21C22⋊Q8×D19C211yesmaximal, characteristic, complemented
22#11927023C211yesmaximal, characteristic, complemented
23C19×#546C211yesmaximal, characteristic, complemented
24C2×#41×C19C2211yescharacteristic, complemented
25C22×D4×C19C2211yescharacteristic
26C22×C22⋊D19C2212yes—
27C23×Dic19C2212yes—
28#10597436—28no—
29C2×Q8×D19C2211yescharacteristic, complemented
30C2×Q8×D19C2211yescharacteristic, complemented
31C2×#64543—28no—
32C2×#64543C2211yescharacteristic
33C2×#64543C2212yes—
34C2×#64543C2212yes—
35C2×#64543C2211yescharacteristic
36C2×#64543C2211yescharacteristic
37C2×#64543C2211yescharacteristic
38C2×#64543C2212yescomplemented
39C2×#64543C2212yescomplemented
40C2×#64543C2211yescharacteristic, complemented
41C2×#64541C2211yescharacteristic, complemented
42C2×#64541C2212yescomplemented
43C22×C4×D19C2211yescharacteristic
44C22×Dic38C2211yescharacteristic
45C22×Dic38C2212yescomplemented
46C22×Dic38C2211yescharacteristic, complemented
47C19×#124C2211yescharacteristic, complemented
48C19×#123C2212yescomplemented
49C19×C22⋊Q8C2211yescharacteristic
50C19×#121C2212yescomplemented
51C19×#121C2211yescharacteristic, complemented
52C19×#120C2212yes—
53C4×D4×C19C2211yescharacteristic
54C4×D4×C19C2211yescharacteristic, complemented
55C2×C22⋊C4×C19C2212yes—
56#10597399C2212yes—
57C2×C22⋊Dic19C2212yes—
58#10597392C2211yescharacteristic, complemented
59#10597390C2211yescharacteristic, complemented
60#10597385C2211yescharacteristic
61#10597385C2212yescomplemented
62#10597385C2212yescomplemented
63#10597385C2212yescomplemented
64#10597385C2212yescomplemented
65#10597384C2212yescomplemented
66#10597384C2211yescharacteristic, complemented
67#10597383C2211yescharacteristic
68#10597382C2211yescharacteristic, complemented
69#10597381C2212yescomplemented
70#10597381C2212yescomplemented
71D4×Dic19C2212yes—
72D4×Dic19C2212yescomplemented
73D4×Dic19C2211yescharacteristic, complemented
74#10597376C2212yescomplemented
75#10597375C2212yescomplemented
76C4×C22⋊D19C2211yescharacteristic
77C4×C22⋊D19C2211yescharacteristic, complemented
78C4×C22⋊D19C2212yescomplemented
79C2×C4⋊Dic19C2212yescomplemented
80#10597370C2211yescharacteristic
81#10597370C2211yescharacteristic, complemented
82C2×Dic19⋊C4C2212yescomplemented
83C2×Dic19⋊C4C2212yescomplemented
84#10597343C2211yescharacteristic, complemented
85#10597343C2211yescharacteristic, complemented
86#10597342C2211yescharacteristic, complemented
87#10597342C2212yescomplemented
88#10597342C2212yescomplemented
89#10597340C2211yescharacteristic, complemented
90C4⋊C4×D19C2211yescharacteristic, complemented
91C4⋊C4×D19C2212yescomplemented
92#10597334C2212yescomplemented
93#10597334C2212yescomplemented
94#10597333C2211yescharacteristic, complemented
95#10597332C2212yescomplemented
96#10597332C2212yescomplemented
97#10597331C2212yescomplemented
98#10597331C2212yescomplemented
99#10597330C2211yescharacteristic, complemented
100#10597330C2212yescomplemented
101#10597330C2212yescomplemented
102#10597329C2211yescharacteristic, complemented
103#10597329C2212yescomplemented
104#10597329C2212yescomplemented
105#10597328C2211yescharacteristic
106(C22⋊D19)⋊C4C2212yes—
107(C22⋊D19)⋊C4C2212yescomplemented
108(C22⋊D19)⋊C4C2212yescomplemented
109C22⋊C4×D19C2212yes—
110#10597324C2211yescharacteristic
111#10597324C2212yes—
112#10597324C2212yes—
113#10597324C2212yes—
114#10597324C2212yescomplemented
115#10597324C2212yescomplemented
116#10597324C2212yescomplemented
117#10597324C2212yescomplemented
118#10597324C2212yescomplemented
119#10597324C2212yescomplemented
120#10597323C2212yescomplemented
121C4×D76C2211yescharacteristic, complemented
122#10597318C2211yescharacteristic, complemented
123#10597315C2211yescharacteristic, complemented
124C4×Dic38C2211yescharacteristic, complemented
125C24×C19C2312yes—
126C23×D19C2311yescharacteristic
127#41×C19—24no—
128C2×Q8×C19C2311yescharacteristic
129C2×D4×C19—24no—
130C2×D4×C19C2311yescharacteristic
131C2×D4×C19C2312yes—
132C2×D4×C19C2312yes—
133C2×D4×C19C2311yescharacteristic
134C2×D4×C19C2312yes—
135C2×D4×C19C2311yescharacteristic
136C22×C4×C19C2312yes—
137C22×C4×C19C2311yescharacteristic
138C22×C4×C19C2311yescharacteristic
139C22×C4×C19C2312yes—
140C2×C22⋊D19—28no—
141C2×C22⋊D19C2312yes—
142C2×C22⋊D19C2312yes—
143C2×C22⋊D19C2311yescharacteristic
144C2×C22⋊D19C2312yes—
145C2×C22⋊D19C2311yescharacteristic
146C2×C22⋊D19C2311yescharacteristic
147C2×C22⋊D19C2312yes—
148C2×C22⋊D19C2311yescharacteristic
149C2×C22⋊D19C2312yes—
150C2×C22⋊D19C2312yes—
151C22×Dic19—28no—
152C22×Dic19C2312yes—
153C22×Dic19C2312yes—
154C22×Dic19C2312yes—
155C22×Dic19C2312yes—
156C22×Dic19C2312yes—
157C22×Dic19C2311yescharacteristic
158C22×Dic19C2312yes—
159C22×Dic19C2312yes—
160C22×Dic19C2312yes—
161Q8×D19—24no—
162Q8×D19—24no—
163#64543—24no—
164#64543—24no—
165#64543—28no—
166#64543—28no—
167#64543—28no—
168#64543—28no—
169#64543—24no—
170#64543—24no—
171#64543D418yescomplemented
172#64541—28no—
173#64541—24no—
174C2×D76C2311yescharacteristic
175C2×D76C2311yescharacteristic
176C2×C4×D19—24no—
177C2×C4×D19C2311yescharacteristic
178C2×C4×D19C2311yescharacteristic
179C2×C4×D19C2311yescharacteristic
180C2×C4×D19C2311yescharacteristic
181C2×C4×D19C2312yes—
182C2×C4×D19C2312yes—
183C2×C4×D19C2312yes—
184C2×C4×D19C2311yescharacteristic
185C2×Dic38—28no—
186C2×Dic38—24no—
187C2×Dic38—24no—
188C2×Dic38C2311yescharacteristic
189C2×Dic38C2311yescharacteristic
190C2×Dic38C2312yes—
191C2×Dic38C2311yescharacteristic
192C2×Dic38C2312yes—
193C2×Dic38C2312yes—
194C2×Dic38C2312yes—
195C2×Dic38C2311yescharacteristic
196C4⋊C4×C19C2311yescharacteristic
197C4⋊C4×C19C2311yescharacteristic
198C4⋊C4×C19C2312yes—
199C22⋊C4×C19C2311yescharacteristic
200C22⋊C4×C19C2312yes—
201C22⋊C4×C19C2312yes—
202C22⋊C4×C19C2312yes—
203C22⋊C4×C19C2311yescharacteristic
204C22⋊C4×C19C2312yes—
205C22⋊C4×C19C2312yes—
206C42×C19C2311yescharacteristic
207C22⋊Dic19C2312yes—
208C22⋊Dic19C2312yes—
209C22⋊Dic19C2311yescharacteristic
210C22⋊Dic19C2312yes—
211C22⋊Dic19C2312yes—
212C22⋊Dic19C2312yes—
213C22⋊Dic19C2312yes—
214C22⋊Dic19C2311yescharacteristic
215(C2×D19)⋊C4C2312yes—
216(C2×D19)⋊C4C2312yes—
217(C2×D19)⋊C4C2311yescharacteristic
218(C2×D19)⋊C4C2311yescharacteristic
219(C2×D19)⋊C4C2311yescharacteristic
220(C2×D19)⋊C4C2311yescharacteristic
221(C2×D19)⋊C4C2312yes—
222(C2×D19)⋊C4C2311yescharacteristic
223(C2×D19)⋊C4C2311yescharacteristic
224C4⋊Dic19C2312yes—
225C4⋊Dic19C2312yes—
226C4⋊Dic19C2311yescharacteristic
227C4⋊Dic19C2312yes—
228C4⋊Dic19C2312yes—
229C4⋊Dic19C2311yescharacteristic
230Dic19⋊C4C2311yescharacteristic
231Dic19⋊C4C2312yes—
232Dic19⋊C4C2312yes—
233Dic19⋊C4C2312yes—
234Dic19⋊C4C2311yescharacteristic
235Dic19⋊C4C2312yes—
236Dic19⋊C4C2312yes—
237Dic19⋊C4C2312yes—
238Dic19⋊C4C2312yes—
239Dic19⋊C4C2311yescharacteristic
240Dic19⋊C4C2311yescharacteristic
241Dic19⋊C4C2312yes—
242C4×Dic19C2312yes—
243C4×Dic19C2311yescharacteristic
244C4×Dic19C2312yes—
245C23×C19—24no—
246C23×C19—24no—
247C23×C19—42no—
248C23×C19C2412yes—
249C23×C19C2411yescharacteristic
250C23×C19C2412yes—
251C23×C19C2411yescharacteristic
252C22×D19—22no—
253C22×D19—22no—
254C22×D19—41no—
255C22×D19C2411yescharacteristic
256C22×D19C2411yescharacteristic
257C22×D19C2411yescharacteristic
258Q8×C19—22no—
259D4×C19—24no—
260D4×C19—24no—
261D4×C19—22no—
262D4×C19—22no—
263D4×C19—42no—
264D4×C19C2×D414yes—
265C2×C4×C19—24no—
266C2×C4×C19—22no—
267C2×C4×C19—22no—
268C2×C4×C19—42no—
269C2×C4×C19C2411yescharacteristic
270C2×C4×C19C2412yes—
271C2×C4×C19C2411yescharacteristic
272C2×C4×C19C2411yescharacteristic
273C2×C4×C19C2412yes—
274C2×C4×C19C2411yescharacteristic
275C2×C4×C19C2411yescharacteristic
276C22⋊D19—24no—
277C22⋊D19—24no—
278C22⋊D19—22no—
279C22⋊D19—22no—
280C22⋊D19—24no—
281C22⋊D19—22no—
282C22⋊D19—24no—
283C22⋊D19—42no—
284C22⋊D19—41no—
285C22⋊D19C2×D418yes—
286C2×Dic19—24no—
287C2×Dic19—24no—
288C2×Dic19—24no—
289C2×Dic19—24no—
290C2×Dic19—22no—
291C2×Dic19—24no—
292C2×Dic19—24no—
293C2×Dic19—42no—
294C2×Dic19C2×D418yes—
295C2×Dic19C2411yescharacteristic
296C2×Dic19C2411yescharacteristic
297C2×Dic19C2412yes—
298C2×Dic19C2412yes—
299C2×Dic19C2411yescharacteristic
300C2×Dic19C2411yescharacteristic
301C2×Dic19C2412yes—
302C2×Dic19C2412yes—
303C2×Dic19C2411yescharacteristic
304D76—22no—
305D76—41no—
306C4×D19—22no—
307C4×D19—24no—
308C4×D19—22no—
309C4×D19—22no—
310C4×D19—22no—
311C4×D19—24no—
312C4×D19—42no—
313C4×D19C2×D414yes—
314Dic38—22no—
315Dic38—22no—
316Dic38—24no—
317Dic38—22no—
318Dic38—24no—
319Dic38—24no—
320Dic38—24no—
321Dic38C2×D414yes—
322#3489—191nomaximal, Sylow
323C22×C19—21no—
324C22×C19—22no—
325C22×C19—22no—
326C22×C19—21no—
327C22×C19—21no—
328C22×C19—22no—
329C22×C19—21no—
330C22×C19—22no—
331C22×C19—21no—
332C22×C19—22no—
333C22×C19—48no—
334C22×C19C22×D414yes—
335C22×C192−1+412yescomplemented
336C22×C19C2511yescharacteristic
337C2×D19—21no—
338C2×D19—21no—
339C2×D19—21no—
340C2×D19—21no—
341C2×D19—21no—
342C2×D19—21no—
343C2×D19—21no—
344C2×D19—21no—
345C2×D19—44no—
346C2×D19C22×D412yes—
347C4×C19—21no—
348C4×C19—21no—
349C4×C19—22no—
350C4×C19—21no—
351C4×C19—22no—
352C4×C19—21no—
353C4×C19C22×D412yes—
354Dic19—22no—
355Dic19—21no—
356Dic19—22no—
357Dic19—21no—
358Dic19—21no—
359Dic19—22no—
360Dic19—21no—
361Dic19C22×D414yes—
362Dic19C22×D412yes—
363C2×2−1+4—191no—
364C22×#41—191no—
365D4×Q8—191no—
366D4×Q8—191no—
367#548—191no—
368#548—191no—
369#547—191no—
370#547—192no—
371#547—192no—
372#547—191no—
373#546—191no—
374#546—192no—
375#546—192no—
376#546D1911yescharacteristic, complemented
377#537—192no—
378#537—191no—
379#536—191no—
380#536—192no—
381#525—192no—
382#525—191no—
383C2×C22⋊Q8—191no—
384C2×C22⋊Q8—192no—
385#520—191no—
386C2×C19—22no—
387C2×C19—24no—
388C2×C19—41no—
389C2×C19—42no—
390C2×C19C23×D411yescharacteristic
391C2×C19C2×2−1+411yescharacteristic
392C2×C19#58511yescharacteristic
393D19—22no—
394D19—41no—
395D19—41no—
3962−1+4—388no—
397C2×#41—191no—
398C2×#41—192no—
399C2×#41—192no—
400C2×#41—191no—
401C2×#41—191no—
402C2×#41—192no—
403C2×#41—191no—
404C2×#41—192no—
405C2×#41—191no—
406C2×#41—191no—
407C2×#41—192no—
408C2×#41—388no—
409C2×#41C2×D1911yescharacteristic, complemented
410C22×Q8—191no—
411C22×Q8—191no—
412C22×Q8—192no—
413C22×Q8—191no—
414C22×Q8—191no—
415C22×D4—192no—
416C22×D4C2×D1911yescharacteristic
417C23×C4—192no—
418C23×C4—191no—
419C4⋊Q8—191no—
420C4⋊Q8—192no—
421C4⋊Q8—192no—
422C4⋊Q8—191no—
423#124—191no—
424#124—192no—
425#124—192no—
426#124C2×D1911yescharacteristic, complemented
427#123—192no—
428#123—192no—
429#123—192no—
430#123—191no—
431#123—191no—
432#123—192no—
433#123—192no—
434#123—192no—
435#123—192no—
436#123C2×D1912yescomplemented
437C22⋊Q8—191no—
438C22⋊Q8—191no—
439C22⋊Q8—191no—
440C22⋊Q8—192no—
441C22⋊Q8—191no—
442C22⋊Q8—191no—
443C22⋊Q8—192no—
444C22⋊Q8—191no—
445C22⋊Q8—192no—
446C22⋊Q8—191no—
447C22⋊Q8—192no—
448C22⋊Q8—192no—
449C22⋊Q8—192no—
450C22⋊Q8—192no—
451C22⋊Q8—192no—
452C22⋊Q8—192no—
453C22⋊Q8—192no—
454C22⋊Q8—192no—
455C22⋊Q8C2×D1911yescharacteristic
456#121—192no—
457#121—191no—
458#121—191no—
459#121—192no—
460#121—192no—
461#121—192no—
462#121—192no—
463#121—192no—
464#121—191no—
465#121—192no—
466#121—192no—
467#121C2×D1912yescomplemented
468#121C2×D1911yescharacteristic, complemented
469#120—192no—
470#120—191no—
471#120—191no—
472#120C2×D1912yes—
473C4×Q8—191no—
474C4×Q8—191no—
475C4×D4—192no—
476C4×D4—191no—
477C4×D4—192no—
478C4×D4—192no—
479C4×D4—191no—
480C4×D4—191no—
481C4×D4—192no—
482C4×D4—192no—
483C4×D4—192no—
484C4×D4—191no—
485C4×D4C2×D1911yescharacteristic
486C4×D4C2×D1911yescharacteristic, complemented
487#117—192no—
488#117—191no—
489C2×C4⋊C4—192no—
490C2×C4⋊C4—192no—
491C2×C4⋊C4—192no—
492C2×C4⋊C4—191no—
493C2×C4⋊C4—192no—
494C2×C22⋊C4—192no—
495C2×C22⋊C4—192no—
496C2×C22⋊C4C2×D1912yes—
497C19#348911yescharacteristic, complemented, Sylow
498C24—191no—
499C24C22×D1912yes—
500#41—24no—
501#41—198no—
502#41—384no—
503#41—388no—
504#41—388no—
505#41—384no—
506#41—388no—
507#41—388no—
508#41—388no—
509#41—384no—
510#41—384no—
511#41—384no—
512C2×Q8—191no—
513C2×Q8—192no—
514C2×Q8—191no—
515C2×Q8—192no—
516C2×Q8—192no—
517C2×Q8—191no—
518C2×Q8—192no—
519C2×Q8—191no—
520C2×Q8—388no—
521C2×Q8—384no—
522C2×Q8—384no—
523C2×Q8—384no—
524C2×Q8—384no—
525C2×Q8C22×D1911yescharacteristic
526C2×D4—24no—
527C2×D4—192no—
528C2×D4—191no—
529C2×D4—191no—
530C2×D4—192no—
531C2×D4—191no—
532C2×D4—192no—
533C2×D4—192no—
534C2×D4—192no—
535C2×D4—191no—
536C2×D4—192no—
537C2×D4—191no—
538C2×D4—191no—
539C2×D4—388no—
540C2×D4C22×D1911yescharacteristic
541C2×D4C22×D1912yes—
542C2×D4C22×D1912yes—
543C2×D4C22×D1911yescharacteristic
544C2×D4C22×D1912yes—
545C2×D4C22×D1911yescharacteristic
546C22×C4—192no—
547C22×C4—191no—
548C22×C4—192no—
549C22×C4—192no—
550C22×C4—192no—
551C22×C4—192no—
552C22×C4—192no—
553C22×C4—191no—
554C22×C4—192no—
555C22×C4—192no—
556C22×C4—192no—
557C22×C4—191no—
558C22×C4—192no—
559C22×C4—191no—
560C22×C4—191no—
561C22×C4—191no—
562C22×C4—192no—
563C22×C4—384no—
564C22×C4—388no—
565C22×C4C22×D1912yes—
566C22×C4C22×D1911yescharacteristic
567C22×C4C22×D1911yescharacteristic
568C22×C4C22×D1912yes—
569C4⋊C4—192no—
570C4⋊C4—191no—
571C4⋊C4—192no—
572C4⋊C4—191no—
573C4⋊C4—192no—
574C4⋊C4—192no—
575C4⋊C4—192no—
576C4⋊C4—192no—
577C4⋊C4—192no—
578C4⋊C4—191no—
579C4⋊C4—191no—
580C4⋊C4—192no—
581C4⋊C4—192no—
582C4⋊C4—191no—
583C4⋊C4—191no—
584C4⋊C4—192no—
585C4⋊C4—192no—
586C4⋊C4—192no—
587C4⋊C4C22×D1911yescharacteristic
588C4⋊C4C22×D1912yes—
589C4⋊C4C22×D1911yescharacteristic
590C22⋊C4—192no—
591C22⋊C4—191no—
592C22⋊C4—192no—
593C22⋊C4—192no—
594C22⋊C4—192no—
595C22⋊C4—191no—
596C22⋊C4—192no—
597C22⋊C4—192no—
598C22⋊C4—192no—
599C22⋊C4—192no—
600C22⋊C4—191no—
601C22⋊C4—191no—
602C22⋊C4—191no—
603C22⋊C4—191no—
604C22⋊C4—191no—
605C22⋊C4—191no—
606C22⋊C4—192no—
607C22⋊C4C22×D1912yes—
608C22⋊C4C22×D1911yescharacteristic
609C22⋊C4C22×D1912yes—
610C22⋊C4C22×D1912yes—
611C22⋊C4C22×D1912yes—
612C22⋊C4C22×D1912yes—
613C22⋊C4C22×D1911yescharacteristic
614C42—192no—
615C42—192no—
616C42—191no—
617C42C22×D1911yescharacteristic
618C23—24no—
619C23—24no—
620C23—42no—
621C23—191no—
622C23—191no—
623C23—191no—
624C23—382no—
625C23—382no—
626C23—761no—
627C23C23×D1912yes—
628C23C23×D1911yescharacteristic
629C23C23×D1912yes—
630C23C23×D1911yescharacteristic
631Q8—22no—
632Q8—194no—
633Q8—382no—
634Q8—384no—
635Q8—384no—
636Q8—384no—
637Q8—384no—
638Q8—382no—
639Q8—382no—
640D4—24no—
641D4—24no—
642D4—22no—
643D4—22no—
644D4—42no—
645D4—198no—
646D4—382no—
647D4—384no—
648D4—382no—
649D4—384no—
650D4—382no—
651D4—384no—
652D4—384no—
653D4—382no—
654D4—761no—
655D4—761no—
656D4—762no—
657D4D4×D1914yes—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—198no—
663C2×C4—192no—
664C2×C4—191no—
665C2×C4—194no—
666C2×C4—191no—
667C2×C4—191no—
668C2×C4—192no—
669C2×C4—191no—
670C2×C4—192no—
671C2×C4—191no—
672C2×C4—192no—
673C2×C4—382no—
674C2×C4—384no—
675C2×C4—382no—
676C2×C4—384no—
677C2×C4—382no—
678C2×C4—384no—
679C2×C4—384no—
680C2×C4—384no—
681C2×C4—384no—
682C2×C4—384no—
683C2×C4—384no—
684C2×C4—382no—
685C2×C4—382no—
686C2×C4—762no—
687C2×C4—762no—
688C2×C4C23×D1911yescharacteristic
689C2×C4C23×D1912yes—
690C2×C4C23×D1911yescharacteristic
691C2×C4C23×D1912yes—
692C2×C4C23×D1911yescharacteristic
693C2×C4C23×D1911yescharacteristic
694C2×C4C23×D1911yescharacteristic
695C22—21no—
696C22—22no—
697C22—22no—
698C22—21no—
699C22—21no—
700C22—22no—
701C22—21no—
702C22—22no—
703C22—21no—
704C22—22no—
705C22—48no—
706C22—192no—
707C22—381no—
708C22—381no—
709C22—381no—
710C22—381no—
711C22—381no—
712C22—381no—
713C22—381no—
714C22—381no—
715C22—764no—
716C22C2×D4×D1914yes—
717C22#1059743612yescomplemented
718C22C24×D1911yescharacteristic
719C4—21no—
720C4—21no—
721C4—22no—
722C4—21no—
723C4—21no—
724C4—22no—
725C4—192no—
726C4—194no—
727C4—381no—
728C4—382no—
729C4—382no—
730C4—381no—
731C4—381no—
732C4—382no—
733C4—381no—
734C4C2×D4×D1912yes—
735C2—22no—
736C2—24no—
737C2—42no—
738C2—41no—
739C2—382no—
740C2—761no—
741C2—761no—
742C2C22×D4×D1911yescharacteristic
743C2C2×#1059743611yescharacteristic
744C2#1192737911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#546C2
hypercenter#546D19
hypocenterC19#3489
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#10597436C2semidirect
2. C22×#64543C2semidirect
3. D4×Dic38C2semidirect
4. #11927207C2semidirect
5. #11927202C2semidirect
6. #11927200C2semidirect
7. #11927198C2semidirect
8. #11927194C2semidirect
9. #11927193C2semidirect
10. #11927192C2semidirect
11. #11927188C2semidirect
12. #11927184C2semidirect
13. #11927181C2semidirect
14. #11927123C2semidirect
15. #11927121C2semidirect
16. #11927116C2semidirect
17. #11927114C2semidirect
18. #11927053C2semidirect
19. #11927050C2semidirect
20. C2×#10597324C2semidirect
21. C22⋊Q8×D19C2semidirect
22. #11927023C2semidirect
23. C19×#546C2semidirect
24. C2×#41×C19C22semidirect
29. C2×Q8×D19C22semidirect
30. C2×Q8×D19C22semidirect
38. C2×#64543C22semidirect
39. C2×#64543C22semidirect
40. C2×#64543C22semidirect
41. C2×#64541C22semidirect
42. C2×#64541C22semidirect
45. C22×Dic38C22semidirect
46. C22×Dic38C22semidirect
47. C19×#124C22semidirect
48. C19×#123C22semidirect
50. C19×#121C22semidirect
51. C19×#121C22semidirect
54. C4×D4×C19C22semidirect
58. #10597392C22semidirect
59. #10597390C22semidirect
61. #10597385C22semidirect
62. #10597385C22semidirect
63. #10597385C22semidirect
64. #10597385C22semidirect
65. #10597384C22semidirect
66. #10597384C22semidirect
68. #10597382C22semidirect
69. #10597381C22semidirect
70. #10597381C22semidirect
72. D4×Dic19C22semidirect
73. D4×Dic19C22semidirect
74. #10597376C22semidirect
75. #10597375C22semidirect
77. C4×C22⋊D19C22semidirect
78. C4×C22⋊D19C22semidirect
79. C2×C4⋊Dic19C22semidirect
81. #10597370C22semidirect
82. C2×Dic19⋊C4C22semidirect
83. C2×Dic19⋊C4C22semidirect
84. #10597343C22semidirect
85. #10597343C22semidirect
86. #10597342C22semidirect
87. #10597342C22semidirect
88. #10597342C22semidirect
89. #10597340C22semidirect
90. C4⋊C4×D19C22semidirect
91. C4⋊C4×D19C22semidirect
92. #10597334C22semidirect
93. #10597334C22semidirect
94. #10597333C22semidirect
95. #10597332C22semidirect
96. #10597332C22semidirect
97. #10597331C22semidirect
98. #10597331C22semidirect
99. #10597330C22semidirect
100. #10597330C22semidirect
101. #10597330C22semidirect
102. #10597329C22semidirect
103. #10597329C22semidirect
104. #10597329C22semidirect
107. (C22⋊D19)⋊C4C22semidirect
108. (C22⋊D19)⋊C4C22semidirect
114. #10597324C22semidirect
115. #10597324C22semidirect
116. #10597324C22semidirect
117. #10597324C22semidirect
118. #10597324C22semidirect
119. #10597324C22semidirect
120. #10597323C22semidirect
121. C4×D76C22semidirect
122. #10597318C22semidirect
123. #10597315C22semidirect
124. C4×Dic38C22semidirect
171. #64543D4semidirect
335. C22×C192−1+4semidirect
376. #546D19semidirect
409. C2×#41C2×D19semidirect
426. #124C2×D19semidirect
436. #123C2×D19semidirect
467. #121C2×D19semidirect
468. #121C2×D19semidirect
486. C4×D4C2×D19semidirect
497. C19#3489semidirect
717. C22#10597436semidirect

Maximal subgroups

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

subgroupindex
C2×#105974362
C22×#645432
D4×Dic382
#119272072
#119272022
#119272002
#119271982
#119271942
#119271932
#119271922
#119271882
#119271842
#119271812
#119271232
#119271212
#119271162
#119271142
#119270532
#119270502
C2×#105973242
C22⋊Q8×D192
#119270232
C19×#5462
#348919