Finite Group Databasebeta

← #27084698

Subgroups — #27084698

Order 12032.

2138 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
1#20256684C211yesmaximal, characteristic
2C22×C4×Dic94C211yesmaximal, characteristic, complemented
3#20253561C214yesmaximal, complemented
4#20253519C212yesmaximal, complemented
5#20253511C212yesmaximal, complemented
6#20253470C214yesmaximal, complemented
7#20253428C212yesmaximal, complemented
8#20253420C212yesmaximal, complemented
9#20253313C212yesmaximal, complemented
10#20253195C212yesmaximal, complemented
11#20252862C212yesmaximal, complemented
12#20252625C212yesmaximal, complemented
13C4×#13094057C214yesmaximal, complemented
14C47×#2920C211yesmaximal, characteristic, complemented
15C23×Dic94C2211yescharacteristic
16C2×#13094057C2214yes—
17#15689680C2211yescharacteristic
18#15689680C2211yescharacteristic
19#15689680C2211yescharacteristic
20#15689673C2211yescharacteristic
21#15689673C2211yescharacteristic
22#15689673C2211yescharacteristic
23#15689657—21no—
24#15689657—21no—
25#15689657—21no—
26#15689657—21no—
27#15689657C2212yes—
28#15689657C2212yes—
29#15689634—21no—
30#15689634—21no—
31#15689634C2212yes—
32C4×#10625350—21no—
33C4×#10625350—21no—
34C4×#10625350C2212yes—
35C2×C4×Dic94—21no—
36C2×C4×Dic94—21no—
37C2×C4×Dic94—21no—
38C2×C4×Dic94—21no—
39C2×C4×Dic94—21no—
40C2×C4×Dic94—21no—
41C2×C4×Dic94C2212yes—
42C2×C4×Dic94C2212yes—
43C2×C4×Dic94C2212yes—
44C2×C4×Dic94C2212yes—
45C2×C4×Dic94C2212yes—
46C2×C4×Dic94C2212yes—
47C22×C4⋊Dic47C2211yescharacteristic
48C22×Dic47⋊C4—21no—
49C22×C4×Dic47—21no—
50#15689459C2214yes—
51#15689454C2214yes—
52#15689442C2214yes—
53#15689437C2214yes—
54#15689431C2218yescomplemented
55#15689419C2214yescomplemented
56#15689409C2214yescomplemented
57#15689346C2218yescomplemented
58#15689334C2214yescomplemented
59#15689324C2214yescomplemented
60#15689281C2214yes—
61#15689281C2214yes—
62#15689264C2214yes—
63#15689264C2214yes—
64#15689231C2218yescomplemented
65#15689225C2218yescomplemented
66C4×Dic188C2218yescomplemented
67C4×#10625325C2218yescomplemented
68#15689165C2214yes—
69#15689133C2214yes—
70#15689125C2214yes—
71C22×C42×C47C2211yescharacteristic
72C47×#432C2212yes—
73C47×#432C2212yes—
74C47×#431C2212yes—
75C47×#431C2212yes—
76C47×#423C2212yes—
77C47×#407C2212yes—
78C4×M16×C47C2212yes—
79C2×#10625350—21no—
80C2×#10625350—21no—
81C2×#10625350C2312yes—
82C22×Dic94—21no—
83C22×Dic94—21no—
84C22×Dic94—21no—
85C22×Dic94—28no—
86C22×Dic94C2312yes—
87C22×Dic94C2312yes—
88C22×Dic94C2312yes—
89C23×Dic47—21no—
90C23×Dic47—21no—
91#13094057—216no—
92C2×Dic188C2318yes—
93C2×#10625325C2318yes—
94#13094024C2311yescharacteristic
95#13094024C2311yescharacteristic
96#13094024C2311yescharacteristic
97#13094021C2311yescharacteristic
98#13094018—22no—
99#13094018—22no—
100#13094016—21no—
101#13094016—21no—
102#13094016C2312yes—
103#13094012—21no—
104#13094012—21no—
105#13094012C2312yes—
106#13094007—22no—
107#13094007—22no—
108#13094007—22no—
109#13094003—21no—
110#13094003—21no—
111#13094003—21no—
112#13094003—21no—
113#13094003C2312yes—
114#13094003C2312yes—
115#13093998—21no—
116#13093998—21no—
117#13093998—21no—
118#13093998—21no—
119#13093998C2312yes—
120#13093998C2312yes—
121#13093993—22no—
122C4×Dic94—22no—
123C4×Dic94—22no—
124C4×Dic94—22no—
125C4×Dic94—22no—
126C4×Dic94—22no—
127C4×Dic94—22no—
128C4×Dic94—22no—
129C4×Dic94—22no—
130C4×Dic94—22no—
131C4×Dic94—22no—
132C4×Dic94—22no—
133C4×Dic94—22no—
134C4×Dic94—21no—
135C4×Dic94—21no—
136C4×Dic94—21no—
137C4×Dic94—21no—
138C4×Dic94C2312yes—
139C4×Dic94C2314yes—
140C4×Dic94C2314yes—
141C4×Dic94C2312yes—
142C4×Dic94C2314yes—
143C4×Dic94C2314yes—
144C4×D188—21no—
145C4×D188—21no—
146C4×D188—21no—
147C4×D188—21no—
148C4×D188C2312yes—
149C4×D188C2312yes—
150C4×C22⋊D47—22no—
151C4×C22⋊D47—22no—
152C4×C22⋊D47—22no—
153C4×C22⋊D47—22no—
154C4×C22⋊D47—22no—
155C4×C22⋊D47—22no—
156#13093983—21no—
157#13093983—21no—
158#13093983C2312yes—
159#13093981—22no—
160#13093981—22no—
161#13093981—22no—
162C2×C4⋊Dic47—21no—
163C2×C4⋊Dic47—21no—
164C2×C4⋊Dic47—21no—
165C2×C4⋊Dic47C2312yes—
166C2×C4⋊Dic47C2312yes—
167C2×C4⋊Dic47C2312yes—
168C2×Dic47⋊C4—22no—
169C2×Dic47⋊C4—22no—
170C2×Dic47⋊C4—22no—
171C2×Dic47⋊C4—22no—
172C2×Dic47⋊C4—22no—
173C2×Dic47⋊C4—22no—
174C2×C4×Dic47—22no—
175C2×C4×Dic47—22no—
176C2×C4×Dic47—22no—
177C2×C4×Dic47—22no—
178C2×C4×Dic47—22no—
179C2×C4×Dic47—22no—
180C42×D47—22no—
181#13093958C2318yes—
182#13093956C2318yes—
183#13093949C2318yes—
184#13093949C2318yes—
185#13093949C2318yes—
186#13093946C2318yes—
187C23×C4×C47D411yescharacteristic
188C23×C4×C47D411yescharacteristic
189C23×C4×C47C2311yescharacteristic
190C2×M16×C47C2314yes—
191C2×C42×C47D411yescharacteristic
192C2×C42×C47D411yescharacteristic
193C2×C42×C47D411yescharacteristic
194C2×C42×C47D411yescharacteristic
195C2×C42×C47D411yescharacteristic
196C2×C42×C47D411yescharacteristic
197C2×C42×C47C2311yescharacteristic
198C2×C42×C47C2311yescharacteristic
199C2×C42×C47C2311yescharacteristic
200C2×C42×C47C2311yescharacteristic
201C2×C42×C47C2311yescharacteristic
202C2×C42×C47C2311yescharacteristic
203C4⋊C8×C47C2314yes—
204C4⋊C8×C47C2314yes—
205C22⋊C8×C47C2314yes—
206C22⋊C8×C47C2314yes—
207#97×C47C2314yes—
208C4×C8×C47C2314yes—
209C24×C47C2×D411yescharacteristic
210C22×C4×C47—24no—
211C22×C4×C47—24no—
212C22×C4×C47—42no—
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2411yescharacteristic
229C22×C4×C47C2411yescharacteristic
230C22×C4×C47C2411yescharacteristic
231C2×C22⋊D47—22no—
232C2×C22⋊D47—22no—
233C2×C22⋊D47—22no—
234C22×Dic47—28no—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—44no—
242#10625350—28no—
243#10625350—44no—
244#10625350—44no—
245C2×D188—21no—
246C2×D188—21no—
247C2×D188C2412yes—
248C2×C4×D47—22no—
249C2×C4×D47—22no—
250C2×C4×D47—22no—
251C2×Dic94—28no—
252C2×Dic94—28no—
253C2×Dic94—28no—
254C2×Dic94—22no—
255C2×Dic94—22no—
256C2×Dic94—22no—
257C2×Dic94—24no—
258C2×Dic94—28no—
259C2×Dic94—28no—
260C2×Dic94—21no—
261C2×Dic94—21no—
262C2×Dic94#4118yescomplemented
263C2×Dic94C2412yes—
264C2×Dic94C2414yes—
265M16×C47—28no—
266C2×C8×C47C2418yes—
267C42×C47C2×D411yescharacteristic
268C42×C47C2×D411yescharacteristic
269C42×C47C2×D411yescharacteristic
270C42×C47C2×D411yescharacteristic
271C42×C47C2×D411yescharacteristic
272C42×C47C2×D411yescharacteristic
273C42×C47C2×D411yescharacteristic
274C42×C47C2×D411yescharacteristic
275C42×C47C2×D411yescharacteristic
276C42×C47C2×D411yescharacteristic
277C42×C47C2×D411yescharacteristic
278C42×C47C2×D411yescharacteristic
279C42×C47C2411yescharacteristic
280C42×C47C2411yescharacteristic
281C42×C47C2411yescharacteristic
282C42×C47C2411yescharacteristic
283C22⋊Dic47—22no—
284C22⋊Dic47—22no—
285C22⋊Dic47—22no—
286(C2×D47)⋊C4—22no—
287(C2×D47)⋊C4—22no—
288(C2×D47)⋊C4—22no—
289(C2×D47)⋊C4—22no—
290(C2×D47)⋊C4—22no—
291(C2×D47)⋊C4—22no—
292C4⋊Dic47—22no—
293C4⋊Dic47—22no—
294C4⋊Dic47—22no—
295C4⋊Dic47—21no—
296C4⋊Dic47—21no—
297C4⋊Dic47—21no—
298C4⋊Dic47—21no—
299C4⋊Dic47C2414yes—
300C4⋊Dic47C2412yes—
301C4⋊Dic47C2412yes—
302Dic47⋊C4—24no—
303Dic47⋊C4—24no—
304Dic47⋊C4—24no—
305Dic47⋊C4—24no—
306Dic47⋊C4—22no—
307Dic47⋊C4—22no—
308Dic47⋊C4—22no—
309Dic47⋊C4—22no—
310Dic47⋊C4—22no—
311Dic47⋊C4—22no—
312C4×Dic47—22no—
313C4×Dic47—22no—
314C4×Dic47—22no—
315C4×Dic47—24no—
316C4×Dic47—24no—
317C4×Dic47—24no—
318C4×Dic47—24no—
319Dic188—216no—
320#10625325—216no—
321C23×C47—22no—
322C23×C47—22no—
323C23×C47—22no—
324C23×C47C22×D411yescharacteristic
325C23×C47C22×D411yescharacteristic
326C23×C47C22×D411yescharacteristic
327C22×D47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47#13714yescomplemented
345C2×C4×C47C22×D411yescharacteristic
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C22×D411yescharacteristic
349C2×C4×C47C22×D411yescharacteristic
350C2×C4×C47C22×D411yescharacteristic
351C2×C4×C47C22×D411yescharacteristic
352C2×C4×C47C22×D411yescharacteristic
353C2×C4×C47C22×D411yescharacteristic
354C2×C4×C47C22×D411yescharacteristic
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47C2×#4114yes—
357C2×C4×C47C2511yescharacteristic
358C22⋊D47—44no—
359C22⋊D47—44no—
360C22⋊D47—44no—
361C2×Dic47—28no—
362C2×Dic47—28no—
363C2×Dic47—28no—
364C2×Dic47—24no—
365C2×Dic47—24no—
366C2×Dic47—22no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—44no—
370C2×Dic47—44no—
371C2×Dic47—44no—
372D188—24no—
373D188—42no—
374D188—42no—
375C4×D47—44no—
376C4×D47—44no—
377C4×D47—44no—
378Dic94—28no—
379Dic94—28no—
380Dic94—28no—
381Dic94—24no—
382Dic94—24no—
383Dic94—42no—
384Dic94—42no—
385Dic94C2×#4118yes—
386C8×C47—28no—
387#60560—471nomaximal, Sylow
388C22×C47—28no—
389C22×C47—21no—
390C22×C47—21no—
391C22×C47—21no—
392C22×C47—21no—
393C22×C47—21no—
394C22×C47—21no—
395C22×C47#52512yes—
396C22×C47C2×#13712yes—
397C22×C47#57512yes—
398C22×C47C23×D411yescharacteristic
399C2×D47—42no—
400C2×D47—42no—
401C2×D47—42no—
402C4×C47—21no—
403C4×C47—21no—
404C4×C47—21no—
405C4×C47—21no—
406C4×C47—21no—
407C4×C47—21no—
408C4×C47—21no—
409C4×C47—21no—
410C4×C47#52512yes—
411C4×C47C2×#13712yes—
412C4×C47C2×#13712yes—
413C4×C47C22×#4112yes—
414Dic47—28no—
415Dic47—42no—
416Dic47—42no—
417Dic47—42no—
418Dic47—44no—
419#3444—471no—
420C22×C4×Q8—471no—
421#3117—474no—
422#3113—472no—
423#3112—472no—
424#3108—474no—
425#3104—472no—
426#3103—472no—
427#3092—472no—
428#3078—472no—
429#3037—472no—
430#3004—472no—
431C4×#137—474no—
432#2920D4711yescharacteristic, complemented
433C2×C47—22no—
434C2×C47—22no—
435C2×C47—22no—
436C2×C47C2×#52511yescharacteristic
437C2×C47C22×#13711yescharacteristic
438C2×C47C2×#57511yescharacteristic
439D47—82no—
440C23×Q8—471no—
441C2×#137—474no—
442#533—471no—
443#533—471no—
444#533—471no—
445#532—471no—
446#532—471no—
447#532—471no—
448#529—472no—
449#529—472no—
450#529—941no—
451#529—941no—
452#529—941no—
453#529—941no—
454#525—472no—
455#525—941no—
456#525—941no—
457C4×#41—472no—
458C4×#41—941no—
459C4×#41—941no—
460C2×C4×Q8—472no—
461C2×C4×Q8—472no—
462C2×C4×Q8—472no—
463C2×C4×Q8—472no—
464C2×C4×Q8—472no—
465C2×C4×Q8—472no—
466C2×C4×Q8—941no—
467C2×C4×Q8—941no—
468C2×C4×Q8—941no—
469C2×C4×Q8—941no—
470C2×C4×Q8—941no—
471C2×C4×Q8—941no—
472C22×C4⋊C4—471no—
473C22×C4⋊C4—941no—
474C22×C42—941no—
475C22×C42C2×D4711yescharacteristic
476#484—474no—
477#483—474no—
478#481—474no—
479#480—474no—
480#479—478no—
481#477—474no—
482#475—474no—
483#464—478no—
484#462—474no—
485#460—474no—
486#451—474no—
487#451—474no—
488#448—474no—
489#448—474no—
490#441—478no—
491#440—478no—
492C4×Q16—478no—
493C4×SD16—478no—
494#432C2×D4712yes—
495#432C2×D4712yes—
496#431C2×D4712yes—
497#431C2×D4712yes—
498#428—474no—
499#423C2×D4712yes—
500#419—474no—
501#417—474no—
502#407C2×D4712yes—
503C4×M16C2×D4712yes—
504C47#6056011yescharacteristic, complemented, Sylow
505C2×#41—472no—
506C2×#41—941no—
507C2×#41—941no—
508C22×Q8—472no—
509C22×Q8—472no—
510C22×Q8—472no—
511C22×Q8—948no—
512C22×Q8—941no—
513C22×Q8—941no—
514C22×Q8—941no—
515C23×C4—941no—
516C23×C4—941no—
517C23×C4D18811yescharacteristic
518C23×C4D18811yescharacteristic
519C23×C4C22×D4711yescharacteristic
520#137—9416no—
521C2×Q16—478no—
522C2×SD16—478no—
523C2×M16C22×D4714yes—
524C4⋊Q8—471no—
525C4⋊Q8—471no—
526C4⋊Q8—471no—
527#127—471no—
528#126—942no—
529#126—942no—
530#125—472no—
531#125—941no—
532#125—941no—
533#124—472no—
534#124—941no—
535#124—941no—
536#123—942no—
537#123—942no—
538#123—942no—
539C22⋊Q8—472no—
540C22⋊Q8—472no—
541C22⋊Q8—941no—
542C22⋊Q8—941no—
543C22⋊Q8—941no—
544C22⋊Q8—941no—
545#121—472no—
546#121—472no—
547#121—941no—
548#121—941no—
549#121—941no—
550#121—941no—
551#120—942no—
552C4×Q8—474no—
553C4×Q8—474no—
554C4×Q8—474no—
555C4×Q8—474no—
556C4×Q8—472no—
557C4×Q8—472no—
558C4×Q8—942no—
559C4×Q8—942no—
560C4×Q8—942no—
561C4×Q8—942no—
562C4×Q8—942no—
563C4×Q8—942no—
564C4×Q8—942no—
565C4×Q8—942no—
566C4×Q8—942no—
567C4×Q8—942no—
568C4×Q8—942no—
569C4×Q8—942no—
570C4×Q8—941no—
571C4×Q8—941no—
572C4×Q8—941no—
573C4×Q8—941no—
574C4×D4—472no—
575C4×D4—472no—
576C4×D4—942no—
577C4×D4—942no—
578C4×D4—942no—
579C4×D4—942no—
580C4×D4—942no—
581C4×D4—942no—
582C4×D4—941no—
583C4×D4—941no—
584C4×D4—941no—
585C4×D4—941no—
586#117—472no—
587#117—941no—
588#117—941no—
589#117—942no—
590#117—942no—
591#117—942no—
592C2×C4⋊C4—472no—
593C2×C4⋊C4—472no—
594C2×C4⋊C4—472no—
595C2×C4⋊C4—941no—
596C2×C4⋊C4—941no—
597C2×C4⋊C4—941no—
598C2×C4⋊C4—942no—
599C2×C4⋊C4—942no—
600C2×C4⋊C4—942no—
601C2×C4⋊C4—942no—
602C2×C4⋊C4—942no—
603C2×C4⋊C4—942no—
604C2×C42—942no—
605C2×C42—942no—
606C2×C42—942no—
607C2×C42—942no—
608C2×C42—942no—
609C2×C42—942no—
610C2×C42—942no—
611C2×C42D18811yescharacteristic
612C2×C42D18811yescharacteristic
613C2×C42D18811yescharacteristic
614C2×C42D18811yescharacteristic
615C2×C42D18811yescharacteristic
616C2×C42D18811yescharacteristic
617C2×C42C22×D4711yescharacteristic
618C2×C42C22×D4711yescharacteristic
619C2×C42C22×D4711yescharacteristic
620C2×C42C22×D4711yescharacteristic
621C2×C42C22×D4711yescharacteristic
622C2×C42C22×D4711yescharacteristic
623#107—478no—
624#106—478no—
625C4⋊C8C22×D4714yes—
626C4⋊C8C22×D4714yes—
627#103—478no—
628#103—478no—
629#103—478no—
630#102—478no—
631C22⋊C8C22×D4714yes—
632C22⋊C8C22×D4714yes—
633#97C22×D4714yes—
634C4×C8C22×D4714yes—
635C24C2×D18811yescharacteristic
636#41—948no—
637#41—1884no—
638#41—1884no—
639C2×Q8—478no—
640C2×Q8—474no—
641C2×Q8—472no—
642C2×Q8—948no—
643C2×Q8—948no—
644C2×Q8—948no—
645C2×Q8—948no—
646C2×Q8—948no—
647C2×Q8—942no—
648C2×Q8—942no—
649C2×Q8—942no—
650C2×Q8—941no—
651C2×Q8—941no—
652C2×Q8—944no—
653C2×D4—472no—
654C2×D4—942no—
655C2×D4—942no—
656C2×D4—942no—
657C2×D4—941no—
658C2×D4—941no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—42no—
662C22×C4—948no—
663C22×C4—942no—
664C22×C4—942no—
665C22×C4—942no—
666C22×C4—942no—
667C22×C4—942no—
668C22×C4—942no—
669C22×C4—942no—
670C22×C4—942no—
671C22×C4—942no—
672C22×C4—1884no—
673C22×C4C2×D18811yescharacteristic
674C22×C4C2×D18811yescharacteristic
675C22×C4C2×D18811yescharacteristic
676C22×C4C2×D18811yescharacteristic
677C22×C4C2×D18811yescharacteristic
678C22×C4C2×D18811yescharacteristic
679C22×C4C2×D18811yescharacteristic
680C22×C4C2×D18811yescharacteristic
681C22×C4C2×D18811yescharacteristic
682C22×C4C2×D18811yescharacteristic
683C22×C4C2×D18811yescharacteristic
684C22×C4C2×D18811yescharacteristic
685C22×C4C2×D18811yescharacteristic
686C22×C4C2×D18811yescharacteristic
687C22×C4C2×D18811yescharacteristic
688C22×C4C23×D4711yescharacteristic
689C22×C4C23×D4711yescharacteristic
690C22×C4C23×D4711yescharacteristic
691Q16—9416no—
692SD16—9416no—
693M16—28no—
694C2×C8C23×D4718yes—
695C4⋊C4—474no—
696C4⋊C4—472no—
697C4⋊C4—472no—
698C4⋊C4—944no—
699C4⋊C4—944no—
700C4⋊C4—944no—
701C4⋊C4—944no—
702C4⋊C4—942no—
703C4⋊C4—942no—
704C4⋊C4—942no—
705C4⋊C4—942no—
706C4⋊C4—942no—
707C4⋊C4—942no—
708C4⋊C4—942no—
709C4⋊C4—942no—
710C4⋊C4—942no—
711C4⋊C4—941no—
712C4⋊C4—941no—
713C4⋊C4—941no—
714C4⋊C4—941no—
715C22⋊C4—942no—
716C22⋊C4—942no—
717C22⋊C4—942no—
718C22⋊C4—942no—
719C22⋊C4—942no—
720C22⋊C4—942no—
721C22⋊C4—942no—
722C22⋊C4—942no—
723C22⋊C4—942no—
724C42—944no—
725C42—944no—
726C42—944no—
727C42—942no—
728C42—942no—
729C42—944no—
730C42—942no—
731C42C2×D18811yescharacteristic
732C42C2×D18811yescharacteristic
733C42C2×D18811yescharacteristic
734C42C2×D18811yescharacteristic
735C42C2×D18811yescharacteristic
736C42C2×D18811yescharacteristic
737C42C2×D18811yescharacteristic
738C42C2×D18811yescharacteristic
739C42C2×D18811yescharacteristic
740C42C2×D18811yescharacteristic
741C42C2×D18811yescharacteristic
742C42C2×D18811yescharacteristic
743C42C23×D4711yescharacteristic
744C42C23×D4711yescharacteristic
745C42C23×D4711yescharacteristic
746C42C23×D4711yescharacteristic
747C23—22no—
748C23—22no—
749C23—22no—
750C23—942no—
751C23C22×D18811yescharacteristic
752C23C22×D18811yescharacteristic
753C23C22×D18811yescharacteristic
754Q8—478no—
755Q8—948no—
756Q8—948no—
757Q8—948no—
758Q8—944no—
759Q8—944no—
760Q8—1882no—
761Q8—1882no—
762D4—944no—
763D4—1882no—
764D4—1884no—
765D4—1884no—
766D4—1884no—
767D4—1882no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—948no—
785C2×C4—948no—
786C2×C4—948no—
787C2×C4—944no—
788C2×C4—944no—
789C2×C4—942no—
790C2×C4—942no—
791C2×C4—942no—
792C2×C4—1884no—
793C2×C4—1884no—
794C2×C4—1884no—
795C2×C4—1884no—
796C2×C4—1884no—
797C2×C4—1884no—
798C2×C4#1309405714yescomplemented
799C2×C4C22×D18811yescharacteristic
800C2×C4C22×D18811yescharacteristic
801C2×C4C22×D18811yescharacteristic
802C2×C4C22×D18811yescharacteristic
803C2×C4C22×D18811yescharacteristic
804C2×C4C22×D18811yescharacteristic
805C2×C4C22×D18811yescharacteristic
806C2×C4C22×D18811yescharacteristic
807C2×C4C22×D18811yescharacteristic
808C2×C4C22×D18811yescharacteristic
809C2×C4C22×D18811yescharacteristic
810C2×C4#41×D4714yes—
811C2×C4C24×D4711yescharacteristic
812C8—28no—
813C22—28no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—1882no—
821C22—1882no—
822C22—1882no—
823C22#1568963512yes—
824C22C2×#1309405712yes—
825C22#1568992312yes—
826C22C23×D18811yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—948no—
836C4—1882no—
837C4—1884no—
838C4—1882no—
839C4—1882no—
840C4#1568963512yes—
841C4C2×#1309405712yes—
842C4C2×#1309405712yes—
843C4C2×#41×D4712yes—
844C2—22no—
845C2—22no—
846C2—22no—
847C2—3762no—
848C2C2×#1568963511yescharacteristic
849C2C22×#1309405711yescharacteristic
850C2C2×#1568992311yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#2920C2
socleC22×C47C23×D4
prime radical#20256684C2
hypercenter#2920D47
hypocenterC47#60560
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic94C2semidirect
3. #20253561C2semidirect
4. #20253519C2semidirect
5. #20253511C2semidirect
6. #20253470C2semidirect
7. #20253428C2semidirect
8. #20253420C2semidirect
9. #20253313C2semidirect
10. #20253195C2semidirect
11. #20252862C2semidirect
12. #20252625C2semidirect
13. C4×#13094057C2semidirect
14. C47×#2920C2semidirect
54. #15689431C22semidirect
55. #15689419C22semidirect
56. #15689409C22semidirect
57. #15689346C22semidirect
58. #15689334C22semidirect
59. #15689324C22semidirect
64. #15689231C22semidirect
65. #15689225C22semidirect
66. C4×Dic188C22semidirect
67. C4×#10625325C22semidirect
262. C2×Dic94#41semidirect
344. C2×C4×C47#137semidirect
432. #2920D47semidirect
504. C47#60560semidirect
798. C2×C4#13094057semidirect

Maximal subgroups

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

subgroupindex
#202566842
C22×C4×Dic942
#202535612
#202535192
#202535112
#202534702
#202534282
#202534202
#202533132
#202531952
#202528622
#202526252
C4×#130940572
C47×#29202
#6056047