Finite Group Databasebeta

← #25113968

Subgroups — #25113968

Order 11008.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143253C211yesmaximal, characteristic, complemented
2#19143044C211yesmaximal, characteristic
3#19135308C211yesmaximal, characteristic, complemented
4#19135301C211yesmaximal, characteristic, complemented
5#19135245C211yesmaximal, characteristic, complemented
6#19135245C211yesmaximal, characteristic, complemented
7#19134872C211yesmaximal, characteristic, complemented
8#19134872C211yesmaximal, characteristic, complemented
9#19134694C211yesmaximal, characteristic, complemented
10#19134637C211yesmaximal, characteristic, complemented
11#19134539C211yesmaximal, characteristic
12#19134442C211yesmaximal, characteristic, complemented
13#19134435C211yesmaximal, characteristic, complemented
14#19134376C211yesmaximal, characteristic, complemented
15C43×#2896C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18#14582960—21no—
19#14582960—21no—
20#14582956—21no—
21#14582952—21no—
22C2×#13063261C2211yescharacteristic, complemented
23C2×#13063261C2211yescharacteristic, complemented
24#14582926C2211yescharacteristic, complemented
25#14582926C2211yescharacteristic, complemented
26C2×#13063252C2211yescharacteristic
27C2×#13063252C2211yescharacteristic
28C2×#13063252C2211yescharacteristic
29C2×#13063252C2211yescharacteristic
30#14582866—21no—
31#14582866—21no—
32#14582866C2211yescharacteristic
33#14582866C2211yescharacteristic
34#14582863—21no—
35#14582863C2211yescharacteristic
36#14582863C2211yescharacteristic
37C2×C22⋊(C43⋊C8)—21no—
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39#14582855C2211yescharacteristic, complemented
40#14582855C2211yescharacteristic, complemented
41C2×#13063235C2211yescharacteristic, complemented
42C2×C8×Dic43C2211yescharacteristic, complemented
43C4×C22⋊Dic43C2211yescharacteristic
44#14582664C2211yescharacteristic, complemented
45#14582664C2211yescharacteristic, complemented
46#14582658C2211yescharacteristic, complemented
47#14582658C2211yescharacteristic, complemented
48#14582658C2211yescharacteristic, complemented
49#14582658C2211yescharacteristic, complemented
50#14582653C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52C22×#41×C43C2211yescharacteristic
53C22×M16×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C43×#419C411yescharacteristic, complemented
56C43×#419C411yescharacteristic, complemented
57C43×#418C411yescharacteristic, complemented
58C43×#418C411yescharacteristic, complemented
59C43×#417C411yescharacteristic, complemented
60C43×#417C411yescharacteristic, complemented
61C43×#417C411yescharacteristic, complemented
62C43×#417C411yescharacteristic, complemented
63C43×#416C2211yescharacteristic
64C43×#416C2211yescharacteristic
65C43×#416C2211yescharacteristic
66C43×#416C2211yescharacteristic
67#13063332—22no—
68#13063332—22no—
69#13063332—41no—
70#13063332—41no—
71C2×#10621877—21no—
72C2×#10621877—21no—
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C22×C43⋊C8—21no—
78C22×C43⋊C8—21no—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43C2311yescharacteristic
83C2×C4×Dic43C2311yescharacteristic
84#13063261—41no—
85#13063261—41no—
86C4⋊(C43⋊C8)—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90#13063252—22no—
91#13063252—22no—
92#13063252—41no—
93#13063252—41no—
94C22⋊(C43⋊C8)—21no—
95C22⋊(C43⋊C8)—21no—
96C22⋊(C43⋊C8)—21no—
97C22⋊(C43⋊C8)—21no—
98C22⋊(C43⋊C8)—21no—
99C22⋊(C43⋊C8)—21no—
100C22⋊(C43⋊C8)—21no—
101C22⋊(C43⋊C8)—21no—
102C22⋊(C43⋊C8)D411yescharacteristic
103C22⋊(C43⋊C8)D411yescharacteristic
104C22⋊(C43⋊C8)D411yescharacteristic
105C22⋊(C43⋊C8)D411yescharacteristic
106#13063236—21no—
107#13063236—21no—
108#13063235—41no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C8×Dic43—41no—
112C43⋊#95—21no—
113C2×#41×C43—21no—
114C2×#41×C43—21no—
115C2×#41×C43—22no—
116C2×#41×C43—22no—
117C2×#41×C43—41no—
118C2×#41×C43—41no—
119C2×#41×C43C2×C411yescharacteristic
120C2×#41×C43C2×C411yescharacteristic
121C2×#41×C43C2311yescharacteristic
122C2×#41×C43C2311yescharacteristic
123C22×Q8×C43C2×C411yescharacteristic
124C22×D4×C43—21no—
125C22×D4×C43C2×C411yescharacteristic
126C23×C4×C43—21no—
127C23×C4×C43C2311yescharacteristic
128C2×M16×C43—41no—
129C2×M16×C43—41no—
130C2×M16×C43C2×C411yescharacteristic
131C2×M16×C43C2×C411yescharacteristic
132C2×M16×C43C2×C411yescharacteristic
133C2×M16×C43C2×C411yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136#117×C43—21no—
137#117×C43—21no—
138#117×C43C2×C411yescharacteristic
139#117×C43C2×C411yescharacteristic
140#117×C43C2311yescharacteristic
141#117×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2×C411yescharacteristic
143C2×C4⋊C4×C43C2×C411yescharacteristic
144C2×C22⋊C4×C43—21no—
145C2×C42×C43—21no—
146#103×C43C2×C411yescharacteristic
147#103×C43C2×C411yescharacteristic
148#103×C43C2×C411yescharacteristic
149#103×C43C2×C411yescharacteristic
150#103×C43C2×C411yescharacteristic
151#103×C43C2×C411yescharacteristic
152#103×C43C2×C411yescharacteristic
153#103×C43C2×C411yescharacteristic
154#102×C43C2×C411yescharacteristic
155#102×C43C2×C411yescharacteristic
156#102×C43C2×C411yescharacteristic
157#102×C43C2×C411yescharacteristic
158#102×C43C2×C411yescharacteristic
159#102×C43C2×C411yescharacteristic
160#102×C43C2×C411yescharacteristic
161#102×C43C2×C411yescharacteristic
162C24×C43—21no—
163C24×C43#4111yescharacteristic
164#41×C43—21no—
165#41×C43—21no—
166#41×C43—22no—
167#41×C43—22no—
168#41×C43—21no—
169#41×C43—21no—
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—42no—
173#41×C43—42no—
174#41×C43—41no—
175#41×C43—41no—
176#41×C43—42no—
177#41×C43—42no—
178#41×C43#4112yes—
179#41×C43#4112yes—
180C2×Q8×C43—21no—
181C2×Q8×C43—22no—
182C2×Q8×C43—41no—
183C2×Q8×C43C22×C411yescharacteristic
184C2×Q8×C43C22×C411yescharacteristic
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—22no—
191C2×D4×C43—42no—
192C2×D4×C43—42no—
193C2×D4×C43—41no—
194C2×D4×C43C22×C411yescharacteristic
195C2×D4×C43C22×C411yescharacteristic
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—42no—
208C22×C4×C43—42no—
209C22×C4×C43C22×C411yescharacteristic
210C22×C4×C43C22×C411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43#4111yescharacteristic
214C22×C4×C43C2411yescharacteristic
215C22×Dic43—21no—
216C22×Dic43—21no—
217M16×C43—41no—
218M16×C43—41no—
219M16×C43—41no—
220M16×C43—41no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43C22×C411yescharacteristic
226C2×C8×C43C22×C411yescharacteristic
227C2×C8×C43C22×C411yescharacteristic
228C2×C8×C43C22×C411yescharacteristic
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43C22×C411yescharacteristic
232C4⋊C4×C43C22×C411yescharacteristic
233C4⋊C4×C43C22×C411yescharacteristic
234C4⋊C4×C43C22×C411yescharacteristic
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C42×C43—21no—
240C42×C43—21no—
241C42×C43—21no—
242C42×C43—21no—
243C22⋊Dic43—42no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—21no—
247C4×Dic43—21no—
248#10621877—21no—
249#10621877—21no—
250#10621877—21no—
251#10621877—21no—
252#10621877—21no—
253#10621877—21no—
254#10621877—21no—
255#10621877—21no—
256#10621877—42no—
257#10621877—42no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—42no—
267C2×C43⋊C8—42no—
268C2×C43⋊C8C2×D411yescharacteristic
269C2×C43⋊C8C2×D411yescharacteristic
270C2×C43⋊C8C2×D411yescharacteristic
271C2×C43⋊C8C2×D411yescharacteristic
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43—81no—
281C23×C43C4×D411yescharacteristic
282C23×C43C4×D411yescharacteristic
283C23×C43C2×#4111yescharacteristic
284Q8×C43—21no—
285Q8×C43—21no—
286Q8×C43—21no—
287Q8×C43—42no—
288Q8×C43#11712yes—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—21no—
292D4×C43—21no—
293D4×C43—21no—
294D4×C43—42no—
295D4×C43—42no—
296D4×C43—42no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43#11712yes—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—81no—
325C2×C4×C43C4×D411yescharacteristic
326C2×C4×C43C4×D411yescharacteristic
327C2×C4×C43C23×C411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C2×C4×C43H(5,𝔽2)11yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C2×Dic43—22no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C8×C43—21no—
340C8×C43—21no—
341C8×C43—21no—
342C8×C43—21no—
343C43⋊C8—21no—
344C43⋊C8—21no—
345C43⋊C8—21no—
346C43⋊C8—21no—
347C43⋊C8—41no—
348C43⋊C8—41no—
349C43⋊C8—41no—
350C43⋊C8—41no—
351#22588—431nomaximal, Sylow
352C22×C43—21no—
353C22×C43—21no—
354C22×C43—21no—
355C22×C43—21no—
356C22×C43—22no—
357C22×C43—21no—
358C22×C43—21no—
359C22×C43—21no—
360C22×C43—21no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—84no—
369C22×C43C2×C4×D411yescharacteristic
370C22×C43#55111yescharacteristic
371C22×C43#55111yescharacteristic
372C4×C43—21no—
373C4×C43—21no—
374C4×C43—22no—
375C4×C43—41no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43—41no—
379C4×C43—41no—
380C4×C43C2×#11711yescharacteristic
381C4×C43#51811yescharacteristic
382C4×C43#54611yescharacteristic
383C4×C43#54611yescharacteristic
384Dic43—42no—
385Dic43—81no—
386#2924—431no—
387#2896D4311yescharacteristic
388#2880—431no—
389#1938—431no—
390#1937—431no—
391#1929—431no—
392#1929—431no—
393#1866—431no—
394#1866—431no—
395#1826—431no—
396#1811—431no—
397#1789—431no—
398#1765—431no—
399#1764—431no—
400#1753—431no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—41no—
404C2×C43—41no—
405C2×C43—42no—
406C2×C43—81no—
407C2×C43#234211yescharacteristic
408C2×C43#295511yescharacteristic
409C2×C43#295611yescharacteristic
410C22×#41C2×D4311yescharacteristic
411C2×#131—431no—
412C2×#131—431no—
413C22×M16C2×D4311yescharacteristic
414C2×#117C2×D4311yescharacteristic
415#433—861no—
416#433—861no—
417#432—861no—
418#431—861no—
419C2×#108—431no—
420C2×#108—431no—
421#424—431no—
422#424—431no—
423C2×#104—431no—
424C2×#104—431no—
425C2×#104—431no—
426C2×#104—431no—
427#419Dic4311yescharacteristic, complemented
428#419Dic4311yescharacteristic, complemented
429#418Dic4311yescharacteristic, complemented
430#418Dic4311yescharacteristic, complemented
431#417Dic4311yescharacteristic, complemented
432#417Dic4311yescharacteristic, complemented
433#417Dic4311yescharacteristic, complemented
434#417Dic4311yescharacteristic, complemented
435#416C2×D4311yescharacteristic
436#416C2×D4311yescharacteristic
437#416C2×D4311yescharacteristic
438#416C2×D4311yescharacteristic
439#408—431no—
440#408—431no—
441#408—861no—
442#408—861no—
443#407—431no—
444#407—431no—
445#407—861no—
446C2×C22⋊C8—431no—
447C2×C22⋊C8—861no—
448#405—431no—
449#405—431no—
450C2×#97—431no—
451C2×C4×C8—431no—
452C4×C22⋊C4—431no—
453#341—431no—
454#341—431no—
455#339—431no—
456#339—431no—
457#339—431no—
458#339—431no—
459#336—431no—
460#336—431no—
461C43#2258811yescharacteristic, complemented, Sylow
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×Dic4311yescharacteristic
469C2×#41C2×Dic4311yescharacteristic
470C2×#41C22×D4311yescharacteristic
471C2×#41C22×D4311yescharacteristic
472C22×Q8C2×Dic4311yescharacteristic
473C22×D4—21no—
474C22×D4C2×Dic4311yescharacteristic
475C23×C4—21no—
476C23×C4C22×D4311yescharacteristic
477#131—862no—
478#131—862no—
479#131—1721no—
480#131—1721no—
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—431no—
484C2×M16—431no—
485C2×M16—431no—
486C2×M16—431no—
487C2×M16—861no—
488C2×M16—861no—
489C2×M16C2×Dic4311yescharacteristic
490C2×M16C2×Dic4311yescharacteristic
491C2×M16C2×Dic4311yescharacteristic
492C2×M16C2×Dic4311yescharacteristic
493C22×C8—431no—
494C22×C8—431no—
495C22×C8—861no—
496C22×C8—861no—
497C22×C8C22×D4311yescharacteristic
498C22×C8C22×D4311yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×Dic4311yescharacteristic
502#117C2×Dic4311yescharacteristic
503#117C22×D4311yescharacteristic
504#117C22×D4311yescharacteristic
505C2×C4⋊C4C2×Dic4311yescharacteristic
506C2×C4⋊C4C2×Dic4311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—861no—
509C2×C42—21no—
510C2×C42—431no—
511C2×C42—431no—
512#108—1721no—
513#108—1721no—
514C4⋊C8—861no—
515C4⋊C8—861no—
516C4⋊C8—861no—
517C4⋊C8—861no—
518#104—862no—
519#104—862no—
520#104—1721no—
521#104—1721no—
522#103C2×Dic4311yescharacteristic
523#103C2×Dic4311yescharacteristic
524#103C2×Dic4311yescharacteristic
525#103C2×Dic4311yescharacteristic
526#103C2×Dic4311yescharacteristic
527#103C2×Dic4311yescharacteristic
528#103C2×Dic4311yescharacteristic
529#103C2×Dic4311yescharacteristic
530#102C2×Dic4311yescharacteristic
531#102C2×Dic4311yescharacteristic
532#102C2×Dic4311yescharacteristic
533#102C2×Dic4311yescharacteristic
534#102C2×Dic4311yescharacteristic
535#102C2×Dic4311yescharacteristic
536#102C2×Dic4311yescharacteristic
537#102C2×Dic4311yescharacteristic
538C22⋊C8—431no—
539C22⋊C8—431no—
540C22⋊C8—431no—
541C22⋊C8—431no—
542C22⋊C8—861no—
543C22⋊C8—861no—
544C22⋊C8—861no—
545C22⋊C8—861no—
546C22⋊C8—861no—
547C22⋊C8—861no—
548C22⋊C8—861no—
549C22⋊C8—861no—
550#97—861no—
551#97—861no—
552#97—1721no—
553C4×C8—861no—
554C4×C8—861no—
555C4×C8—1721no—
556#95—861no—
557C24—21no—
558C24#1062190011yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1062189812yes—
574#41#1062189812yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×Dic4311yescharacteristic
579C2×Q8C22×Dic4311yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×Dic4311yescharacteristic
590C2×D4C22×Dic4311yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4D4×D4311yescharacteristic
607C22×C4D4×D4311yescharacteristic
608C22×C4#1062190011yescharacteristic
609C22×C4C22×Dic4311yescharacteristic
610C22×C4C22×Dic4311yescharacteristic
611C22×C4C23×D4311yescharacteristic
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616M16—861no—
617M16—861no—
618M16—861no—
619M16—861no—
620M16—861no—
621M16—861no—
622M16—861no—
623M16—861no—
624M16—1722no—
625M16—1722no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—431no—
631C2×C8—431no—
632C2×C8—431no—
633C2×C8—431no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—1722no—
643C2×C8—1722no—
644C2×C8C22×Dic4311yescharacteristic
645C2×C8C22×Dic4311yescharacteristic
646C2×C8C22×Dic4311yescharacteristic
647C2×C8C22×Dic4311yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×Dic4311yescharacteristic
651C4⋊C4C22×Dic4311yescharacteristic
652C4⋊C4C22×Dic4311yescharacteristic
653C4⋊C4C22×Dic4311yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—1722no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—861no—
664C42—861no—
665C42—861no—
666C42—861no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23D4×Dic4311yescharacteristic
677C23D4×Dic4311yescharacteristic
678C23C2×#1062190011yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1306328412yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1306328412yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—81no—
720C2×C4—862no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4D4×Dic4311yescharacteristic
727C2×C4D4×Dic4311yescharacteristic
728C2×C4C23×Dic4311yescharacteristic
729C2×C4C2×D4×D4311yescharacteristic
730C2×C4C2×#1062189811yescharacteristic
731C2×C4C2×#1062189811yescharacteristic
732C2×C4#1306337011yescharacteristic
733C2×C4#1306337011yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—861no—
739C8—861no—
740C8—861no—
741C8—861no—
742C8—1721no—
743C8—1721no—
744C8—1721no—
745C8—1721no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×D4×Dic4311yescharacteristic
764C22#1458357511yescharacteristic
765C22#1458357511yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—3441no—
775C4—1722no—
776C4C2×#1306328411yescharacteristic
777C4#1458337411yescharacteristic
778C4#1458353911yescharacteristic
779C4#1458353911yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#1913744411yescharacteristic
787C2#1914349811yescharacteristic
788C2#1914350511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2896C2
socleC22×C43C2×C4×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenter#2896D43
hypocenterC43#22588
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #19143253C2semidirect
3. #19135308C2semidirect
4. #19135301C2semidirect
5. #19135245C2semidirect
6. #19135245C2semidirect
7. #19134872C2semidirect
8. #19134872C2semidirect
9. #19134694C2semidirect
10. #19134637C2semidirect
12. #19134442C2semidirect
13. #19134435C2semidirect
14. #19134376C2semidirect
22. C2×#13063261C22semidirect
23. C2×#13063261C22semidirect
24. #14582926C22semidirect
25. #14582926C22semidirect
39. #14582855C22semidirect
40. #14582855C22semidirect
41. C2×#13063235C22semidirect
42. C2×C8×Dic43C22semidirect
44. #14582664C22semidirect
45. #14582664C22semidirect
46. #14582658C22semidirect
47. #14582658C22semidirect
48. #14582658C22semidirect
49. #14582658C22semidirect
50. #14582653C22semidirect
51. #14582653C22semidirect
55. C43×#419C4semidirect
56. C43×#419C4semidirect
57. C43×#418C4semidirect
58. C43×#418C4semidirect
59. C43×#417C4semidirect
60. C43×#417C4semidirect
61. C43×#417C4semidirect
62. C43×#417C4semidirect
427. #419Dic43semidirect
428. #419Dic43semidirect
429. #418Dic43semidirect
430. #418Dic43semidirect
431. #417Dic43semidirect
432. #417Dic43semidirect
433. #417Dic43semidirect
434. #417Dic43semidirect
461. C43#22588semidirect

Maximal subgroups

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

subgroupindex
#191432532
#191430442
#191353082
#191353012
#191352452
#191348722
#191346942
#191346372
#191345392
#191344422
#191344352
#191343762
C43×#28962
#2258843