Finite Group Databasebeta

← #25119131

Subgroups — #25119131

Order 11008.

864 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583021C211yesmaximal, characteristic, complemented
2C2×#14583016C211yesmaximal, characteristic, complemented
3#19143339C211yesmaximal, characteristic, complemented
4#19143163C211yesmaximal, characteristic, complemented
5#19135428C211yesmaximal, characteristic, complemented
6#19135371C211yesmaximal, characteristic, complemented
7#19135308C211yesmaximal, characteristic, complemented
8#19135301C211yesmaximal, characteristic, complemented
9#19134924C211yesmaximal, characteristic, complemented
10#19134924C211yesmaximal, characteristic, complemented
11#19134872C211yesmaximal, characteristic, complemented
12#19134872C211yesmaximal, characteristic, complemented
13#19134454C211yesmaximal, characteristic, complemented
14#19134405C211yesmaximal, characteristic, complemented
15C43×#3035C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C2×#13063332C2211yescharacteristic
20#14583021—24no—
21#14583016—24no—
22#14582977—21no—
23#14582971—21no—
24#14582971—21no—
25D4×C43⋊C8—21no—
26C2×#13063261C2211yescharacteristic
27C2×#13063261C2211yescharacteristic
28#14582926—21no—
29#14582926—21no—
30#14582926C2211yescharacteristic
31#14582926C2211yescharacteristic
32#14582923—21no—
33#14582923C2211yescharacteristic
34C2×C4⋊(C43⋊C8)—21no—
35C2×C4⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063252C2211yescharacteristic
37C2×#13063252C2211yescharacteristic
38C2×#13063252C2211yescharacteristic
39C2×#13063252C2211yescharacteristic
40C2×#13063252C2211yescharacteristic
41C2×#13063252C2211yescharacteristic
42#14582866C2211yescharacteristic
43#14582866C2211yescharacteristic
44C4×#10621877C2211yescharacteristic
45C2×#13063235C2211yescharacteristic
46C2×C8×Dic43C2211yescharacteristic
47#14582745C2211yescharacteristic
48#14582664C2211yescharacteristic
49#14582664C2211yescharacteristic
50#14582658C2211yescharacteristic
51#14582658C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#135×C43C2211yescharacteristic
55C2×#135×C43C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#464C411yescharacteristic, complemented
59C43×#464C411yescharacteristic, complemented
60C43×#463C411yescharacteristic, complemented
61C43×#463C411yescharacteristic, complemented
62C43×#462C411yescharacteristic, complemented
63C43×#461C411yescharacteristic, complemented
64C43×#460C411yescharacteristic, complemented
65C43×#459C411yescharacteristic, complemented
66C2×C4⋊C8×C43C2211yescharacteristic
67C43×#416C2211yescharacteristic
68C43×#416C2211yescharacteristic
69#13063332—22no—
70#13063332—22no—
71#13063332—22no—
72#13063332—22no—
73#13063332—41no—
74#13063332—41no—
75#13063332—41no—
76#13063332—41no—
77C2×#10621877—21no—
78C2×#10621877—21no—
79C2×#10621877—21no—
80C2×#10621877—21no—
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85C22×C43⋊C8—21no—
86C22×C43⋊C8—21no—
87C22×C43⋊C8—21no—
88C22×C43⋊C8—21no—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063261—22no—
94#13063261—22no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)—21no—
101C4⋊(C43⋊C8)D411yescharacteristic
102C4⋊(C43⋊C8)D411yescharacteristic
103C4⋊(C43⋊C8)D411yescharacteristic
104C4⋊(C43⋊C8)D411yescharacteristic
105#13063252—22no—
106#13063252—22no—
107#13063252—22no—
108#13063252—41no—
109#13063252—41no—
110#13063252D414yescomplemented
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113C22⋊(C43⋊C8)—21no—
114C22⋊(C43⋊C8)—21no—
115#13063236—21no—
116#13063235—22no—
117C4×C43⋊C8—21no—
118C8×Dic43—22no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C2×#41×C43C2311yescharacteristic
122C2×#41×C43C2311yescharacteristic
123C2×#41×C43C2311yescharacteristic
124#135×C43—22no—
125#135×C43—22no—
126#135×C43—22no—
127#135×C43—22no—
128C2×Q16×C43C2×C411yescharacteristic
129C2×Q16×C43C2×C411yescharacteristic
130C2×SD16×C43C2×C411yescharacteristic
131C2×SD16×C43C2×C411yescharacteristic
132C2×SD16×C43C2×C411yescharacteristic
133C2×SD16×C43C2×C411yescharacteristic
134C2×D8×C43C2×C411yescharacteristic
135C2×D8×C43C2×C411yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C4⋊Q8×C43C2×C411yescharacteristic
139#127×C43C2×C411yescharacteristic
140#124×C43C2×C411yescharacteristic
141#124×C43C2×C411yescharacteristic
142#121×C43—21no—
143#121×C43—21no—
144C4×Q8×C43C2×C411yescharacteristic
145C4×Q8×C43C2×C411yescharacteristic
146C4×D4×C43—21no—
147C4×D4×C43—21no—
148C4×D4×C43—21no—
149C4×D4×C43—21no—
150C4×D4×C43C2×C411yescharacteristic
151C4×D4×C43C2×C411yescharacteristic
152#117×C43—21no—
153#117×C43C2311yescharacteristic
154C2×C42×C43—21no—
155C2×C42×C43C2311yescharacteristic
156C4⋊C8×C43C2×C411yescharacteristic
157C4⋊C8×C43C2×C411yescharacteristic
158C4⋊C8×C43C2×C411yescharacteristic
159C4⋊C8×C43C2×C411yescharacteristic
160#103×C43C2×C411yescharacteristic
161#103×C43C2×C411yescharacteristic
162#103×C43C2×C411yescharacteristic
163#103×C43C2×C411yescharacteristic
164#102×C43C2×C411yescharacteristic
165#102×C43C2×C411yescharacteristic
166#102×C43C2×C411yescharacteristic
167#102×C43C2×C411yescharacteristic
168#41×C43—21no—
169#41×C43—21no—
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—21no—
173#41×C43—21no—
174#41×C43—21no—
175#41×C43—21no—
176#41×C43—21no—
177#41×C43—21no—
178#41×C43C2×D412yes—
179#41×C43#4112yes—
180C2×Q8×C43C22×C411yescharacteristic
181C2×Q8×C43C22×C411yescharacteristic
182C2×Q8×C43C22×C411yescharacteristic
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43C22×C411yescharacteristic
189C2×D4×C43C22×C411yescharacteristic
190C2×D4×C43C22×C411yescharacteristic
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43#4111yescharacteristic
197C22×C4×C43#4111yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C22×Dic43—21no—
200C22×Dic43—21no—
201Q16×C43—22no—
202Q16×C43—22no—
203SD16×C43—22no—
204SD16×C43—22no—
205SD16×C43—22no—
206SD16×C43—22no—
207D8×C43—22no—
208D8×C43—22no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43C22×C411yescharacteristic
214C2×C8×C43C22×C411yescharacteristic
215C2×C8×C43C22×C411yescharacteristic
216C2×C8×C43C22×C411yescharacteristic
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43C22×C411yescharacteristic
222C4⋊C4×C43C22×C411yescharacteristic
223C22⋊C4×C43—21no—
224C22⋊C4×C43—21no—
225C22⋊C4×C43—21no—
226C22⋊C4×C43—21no—
227C22⋊C4×C43—21no—
228C22⋊C4×C43—21no—
229C22⋊C4×C43—21no—
230C42×C43—21no—
231C42×C43—21no—
232C42×C43—21no—
233C42×C43C22×C411yescharacteristic
234C42×C43C22×C411yescharacteristic
235C42×C43C2×D411yescharacteristic
236C42×C43C2×D411yescharacteristic
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43C2×D412yes—
241#10621877—21no—
242#10621877—21no—
243#10621877—21no—
244#10621877—21no—
245#10621877—21no—
246#10621877—21no—
247#10621877—21no—
248#10621877—42no—
249#10621877—42no—
250#10621877—42no—
251#10621877—42no—
252#10621877C2×D412yes—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—42no—
262C2×C43⋊C8—42no—
263C2×C43⋊C8—42no—
264C2×C43⋊C8—42no—
265C2×C43⋊C8C2×D411yescharacteristic
266C2×C43⋊C8C2×D411yescharacteristic
267C2×C43⋊C8C2×D411yescharacteristic
268C2×C43⋊C8C2×D411yescharacteristic
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43C2×#4111yescharacteristic
273Q8×C43—21no—
274Q8×C43—21no—
275Q8×C43—21no—
276Q8×C43—21no—
277Q8×C43—21no—
278Q8×C43C4×D412yes—
279D4×C43—22no—
280D4×C43—22no—
281D4×C43—21no—
282D4×C43—21no—
283D4×C43—21no—
284D4×C43—21no—
285D4×C43—21no—
286D4×C43—42no—
287D4×C43—41no—
288D4×C43—41no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—81no—
292D4×C43C4×D412yes—
293C2×C4×C43—21no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—42no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—81no—
308C2×C4×C43C4×D411yescharacteristic
309C2×C4×C43C4×D411yescharacteristic
310C2×C4×C43C4×D411yescharacteristic
311C2×C4×C43C4×D411yescharacteristic
312C2×C4×C43C23×C411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43H(5,𝔽2)11yescharacteristic
317C2×C4×C432−1+411yescharacteristic
318C2×Dic43—22no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C8×C43—21no—
325C8×C43—21no—
326C8×C43—21no—
327C8×C43—21no—
328C43⋊C8—21no—
329C43⋊C8—21no—
330C43⋊C8—21no—
331C43⋊C8—21no—
332C43⋊C8—22no—
333C43⋊C8—41no—
334C43⋊C8—41no—
335C43⋊C8—41no—
336#23017—431nomaximal, Sylow
337C22×C43—21no—
338C22×C43—21no—
339C22×C43—22no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43C2×C4×D411yescharacteristic
349C22×C43#54711yescharacteristic
350C22×C43#55311yescharacteristic
351C4×C43—22no—
352C4×C43—21no—
353C4×C43—21no—
354C4×C43—21no—
355C4×C43—21no—
356C4×C43—41no—
357C4×C43—41no—
358C4×C43—41no—
359C4×C43—41no—
360C4×C43C2×C4×D411yescharacteristic
361C4×C43#52011yescharacteristic
362C4×C43D4211yescharacteristic
363C4×C43#54811yescharacteristic
364Dic43—42no—
365Dic43—81no—
366#3035D4311yescharacteristic
367C2×#444—431no—
368C2×#443—431no—
369#2935—431no—
370#2906—431no—
371#1963—431no—
372#1950—431no—
373#1938—431no—
374#1937—431no—
375#1876—431no—
376#1876—431no—
377#1866—431no—
378#1866—431no—
379#1768—431no—
380#1759—431no—
381C2×C43—21no—
382C2×C43—21no—
383C2×C43—42no—
384C2×C43—81no—
385C2×C43—81no—
386C2×C43#236111yescharacteristic
387C2×C43#295511yescharacteristic
388C2×C43#295711yescharacteristic
389C2×#135C2×D4311yescharacteristic
390C2×#135C2×D4311yescharacteristic
391C2×#131—431no—
392C2×#131—431no—
393C2×#131—431no—
394C2×#131—431no—
395#532C2×D4311yescharacteristic
396C4×#41C2×D4311yescharacteristic
397#464Dic4311yescharacteristic, complemented
398#464Dic4311yescharacteristic, complemented
399#463Dic4311yescharacteristic, complemented
400#463Dic4311yescharacteristic, complemented
401#462Dic4311yescharacteristic, complemented
402#461Dic4311yescharacteristic, complemented
403#460Dic4311yescharacteristic, complemented
404#459Dic4311yescharacteristic, complemented
405#444—864no—
406#443—864no—
407#436—861no—
408#435—861no—
409#435—861no—
410C8×D4—861no—
411C2×#108—431no—
412C2×#108—431no—
413#424—431no—
414#424—431no—
415#424—861no—
416#424—861no—
417#423—431no—
418#423—861no—
419C2×C4⋊C8—431no—
420C2×C4⋊C8—861no—
421C2×C4⋊C8C2×D4311yescharacteristic
422C2×#104—431no—
423C2×#104—431no—
424C2×#104—431no—
425C2×#104—431no—
426C2×#104—431no—
427C2×#104—431no—
428#416C2×D4311yescharacteristic
429#416C2×D4311yescharacteristic
430#408—431no—
431#408—431no—
432C4×M16—431no—
433C2×#97—431no—
434C2×C4×C8—431no—
435#376—431no—
436#341—431no—
437#341—431no—
438#339—431no—
439#339—431no—
440#336—431no—
441#336—431no—
442C43#2301711yescharacteristic, complemented, Sylow
443C2×#41C22×D4311yescharacteristic
444C2×#41C22×D4311yescharacteristic
445C2×#41C22×D4311yescharacteristic
446#135—22no—
447#135—22no—
448#135—22no—
449#135—22no—
450C2×Q16C2×Dic4311yescharacteristic
451C2×Q16C2×Dic4311yescharacteristic
452C2×SD16C2×Dic4311yescharacteristic
453C2×SD16C2×Dic4311yescharacteristic
454C2×SD16C2×Dic4311yescharacteristic
455C2×SD16C2×Dic4311yescharacteristic
456C2×D8C2×Dic4311yescharacteristic
457C2×D8C2×Dic4311yescharacteristic
458#131—862no—
459#131—862no—
460#131—862no—
461#131—862no—
462#131—1721no—
463#131—1721no—
464#131—1721no—
465#131—1721no—
466C2×M16—431no—
467C2×M16—431no—
468C2×M16—431no—
469C2×M16—431no—
470C2×M16—861no—
471C2×M16—861no—
472C2×M16—861no—
473C2×M16—861no—
474C22×C8—431no—
475C22×C8—431no—
476C22×C8—861no—
477C22×C8—861no—
478C22×C8—861no—
479C22×C8—861no—
480C22×C8C22×D4311yescharacteristic
481C22×C8C22×D4311yescharacteristic
482C4⋊Q8C2×Dic4311yescharacteristic
483#127C2×Dic4311yescharacteristic
484#124C2×Dic4311yescharacteristic
485#124C2×Dic4311yescharacteristic
486#121—21no—
487#121—21no—
488C4×Q8C2×Dic4311yescharacteristic
489C4×Q8C2×Dic4311yescharacteristic
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4C2×Dic4311yescharacteristic
495C4×D4C2×Dic4311yescharacteristic
496#117—21no—
497#117C22×D4311yescharacteristic
498C2×C42—21no—
499C2×C42—431no—
500C2×C42—431no—
501C2×C42C22×D4311yescharacteristic
502#108—862no—
503#108—862no—
504C4⋊C8—431no—
505C4⋊C8—431no—
506C4⋊C8—431no—
507C4⋊C8—431no—
508C4⋊C8—861no—
509C4⋊C8—861no—
510C4⋊C8—861no—
511C4⋊C8—861no—
512C4⋊C8—861no—
513C4⋊C8—861no—
514C4⋊C8C2×Dic4311yescharacteristic
515C4⋊C8C2×Dic4311yescharacteristic
516C4⋊C8C2×Dic4311yescharacteristic
517C4⋊C8C2×Dic4311yescharacteristic
518#104—434no—
519#104—862no—
520#104—862no—
521#104—862no—
522#104—1721no—
523#104—1721no—
524#103C2×Dic4311yescharacteristic
525#103C2×Dic4311yescharacteristic
526#103C2×Dic4311yescharacteristic
527#103C2×Dic4311yescharacteristic
528#102C2×Dic4311yescharacteristic
529#102C2×Dic4311yescharacteristic
530#102C2×Dic4311yescharacteristic
531#102C2×Dic4311yescharacteristic
532C22⋊C8—861no—
533C22⋊C8—861no—
534C22⋊C8—861no—
535C22⋊C8—861no—
536#97—862no—
537#97—861no—
538C4×C8—862no—
539C4×C8—861no—
540#95—861no—
541#95—861no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41D4×D4312yes—
553#41#1062190012yes—
554C2×Q8C22×Dic4311yescharacteristic
555C2×Q8C22×Dic4311yescharacteristic
556C2×Q8C22×Dic4311yescharacteristic
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4C22×Dic4311yescharacteristic
563C2×D4C22×Dic4311yescharacteristic
564C2×D4C22×Dic4311yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4#1062190011yescharacteristic
573C22×C4#1062190011yescharacteristic
574C22×C4C23×D4311yescharacteristic
575Q16—22no—
576Q16—22no—
577SD16—22no—
578SD16—22no—
579SD16—22no—
580SD16—22no—
581D8—22no—
582D8—22no—
583M16—432no—
584M16—861no—
585M16—861no—
586M16—861no—
587M16—861no—
588M16—861no—
589M16—861no—
590M16—861no—
591M16—1722no—
592M16—1722no—
593M16—1722no—
594M16—1722no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—431no—
600C2×C8—431no—
601C2×C8—431no—
602C2×C8—431no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—1722no—
612C2×C8—1722no—
613C2×C8—1722no—
614C2×C8—1722no—
615C2×C8C22×Dic4311yescharacteristic
616C2×C8C22×Dic4311yescharacteristic
617C2×C8C22×Dic4311yescharacteristic
618C2×C8C22×Dic4311yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C22×Dic4311yescharacteristic
624C4⋊C4C22×Dic4311yescharacteristic
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—432no—
636C42—861no—
637C42—861no—
638C42—861no—
639C42D4×D4311yescharacteristic
640C42D4×D4311yescharacteristic
641C42C22×Dic4311yescharacteristic
642C42C22×Dic4311yescharacteristic
643C23—21no—
644C23—21no—
645C23—21no—
646C23C2×#1062190011yescharacteristic
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8D4×Dic4312yes—
653D4—22no—
654D4—22no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—42no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4D4×Dic4312yes—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—81no—
682C2×C4—862no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4D4×Dic4311yescharacteristic
689C2×C4D4×Dic4311yescharacteristic
690C2×C4D4×Dic4311yescharacteristic
691C2×C4D4×Dic4311yescharacteristic
692C2×C4C23×Dic4311yescharacteristic
693C2×C4C2×D4×D4311yescharacteristic
694C2×C4C2×D4×D4311yescharacteristic
695C2×C4C2×#1062190011yescharacteristic
696C2×C4#1306337111yescharacteristic
697C2×C4#1306337211yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—861no—
703C8—861no—
704C8—861no—
705C8—861no—
706C8—862no—
707C8—1721no—
708C8—1721no—
709C8—1721no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22C2×D4×Dic4311yescharacteristic
722C22#1458354911yescharacteristic
723C22#1458360111yescharacteristic
724C4—21no—
725C4—21no—
726C4—22no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—3441no—
734C4—1722no—
735C4C2×D4×Dic4311yescharacteristic
736C4#1458338211yescharacteristic
737C4#1458353311yescharacteristic
738C4#1458355511yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—81no—
743C2—81no—
744C2#1913761511yescharacteristic
745C2#1914349811yescharacteristic
746C2#1914351211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#3035C2
socleC22×C43C2×C4×D4
cosocleC22×C4×C43C24
hypercenter#3035D43
hypocenterC43#23017
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. C2×#14583021C2semidirect
2. C2×#14583016C2semidirect
3. #19143339C2semidirect
4. #19143163C2semidirect
5. #19135428C2semidirect
6. #19135371C2semidirect
7. #19135308C2semidirect
8. #19135301C2semidirect
9. #19134924C2semidirect
10. #19134924C2semidirect
11. #19134872C2semidirect
12. #19134872C2semidirect
13. #19134454C2semidirect
14. #19134405C2semidirect
58. C43×#464C4semidirect
59. C43×#464C4semidirect
60. C43×#463C4semidirect
61. C43×#463C4semidirect
62. C43×#462C4semidirect
63. C43×#461C4semidirect
64. C43×#460C4semidirect
65. C43×#459C4semidirect
110. #13063252D4semidirect
397. #464Dic43semidirect
398. #464Dic43semidirect
399. #463Dic43semidirect
400. #463Dic43semidirect
401. #462Dic43semidirect
402. #461Dic43semidirect
403. #460Dic43semidirect
404. #459Dic43semidirect
442. C43#23017semidirect

Maximal subgroups

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

subgroupindex
C2×#145830212
C2×#145830162
#191433392
#191431632
#191354282
#191353712
#191353082
#191353012
#191349242
#191348722
#191344542
#191344052
C43×#30352
#2301743