Finite Group Databasebeta

← #25003410

Subgroups — #25003410

Order 11008.

1334 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063345C211yesmaximal, characteristic
2C22×#13063253C211yesmaximal, characteristic, complemented
3C2×#14582867C211yesmaximal, characteristic, complemented
4C2×#14582866C211yesmaximal, characteristic, complemented
5C2×#14582663C211yesmaximal, characteristic, complemented
6C2×#14582654C211yesmaximal, characteristic, complemented
7C22×#104×C43C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C2×#13063345—22no—
10C2×#13063345—22no—
11C2×#13063345—22no—
12C2×#13063345—22no—
13C2×#13063345—22no—
14C2×#13063345—22no—
15C22×#10621885C411yescharacteristic, complemented
16C22×#10621883C411yescharacteristic, complemented
17C22×#10621884C411yescharacteristic, complemented
18C22×#10621882C411yescharacteristic, complemented
19C22×#10621877C2211yescharacteristic
20C23×C43⋊C8C2211yescharacteristic
21C23×C43⋊C8C2211yescharacteristic
22C2×#13063253—22no—
23C2×#13063253—22no—
24C2×#13063253—22no—
25#14582867—22no—
26#14582867—22no—
27#14582866—22no—
28#14582866—22no—
29C2×C22⋊(C43⋊C8)—22no—
30C2×(C2×D43)⋊C8—22no—
31#14582663—22no—
32#14582654—22no—
33C22×#41×C43C2211yescharacteristic
34C22×M16×C43C2211yescharacteristic
35C22×C42×C43C2211yescharacteristic
36C2×#104×C43—22no—
37C2×#104×C43—22no—
38C2×#104×C43—22no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898D412yes—
50C2×#10621898D412yes—
51C22×Dic86C2×C411yescharacteristic
52C22×D172C2×C411yescharacteristic
53C22×C22⋊D43—21no—
54C22×C4×D43—21no—
55#13063345—28no—
56#13063345—28no—
57#13063345—28no—
58#13063345—28no—
59C2×#10621885—22no—
60C2×#10621885—22no—
61C2×#10621885—22no—
62C2×#10621883—22no—
63C2×#10621883—22no—
64C2×#10621883—22no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882—22no—
71C2×#10621877—21no—
72C2×#10621877—21no—
73C2×#10621877—21no—
74C2×#10621877—21no—
75C2×#10621877—21no—
76C2×#10621877D412yes—
77C22×C43⋊C8—21no—
78C22×C43⋊C8—21no—
79C22×C43⋊C8—21no—
80C22×C43⋊C8—21no—
81C22×C43⋊C8—21no—
82C22×C43⋊C8—21no—
83C22×C43⋊C8—21no—
84C22×C43⋊C8—21no—
85C22×C43⋊C8—21no—
86C22×C43⋊C8—21no—
87C22×C43⋊C8—21no—
88C22×C43⋊C8C2×C411yescharacteristic
89C22×C43⋊C8C2×C411yescharacteristic
90C22×C43⋊C8D412yes—
91C22×C43⋊C8D412yes—
92C22×C43⋊C8D412yes—
93#13063253—28no—
94C22⋊(C43⋊C8)—28no—
95(C2×D43)⋊C8—28no—
96C2×#41×C43—21no—
97C2×#41×C43—21no—
98C2×#41×C43—21no—
99C2×#41×C43—21no—
100C2×#41×C43—21no—
101C2×#41×C43—21no—
102C2×#41×C43—21no—
103C2×#41×C43—21no—
104C2×#41×C43—21no—
105C2×#41×C43—21no—
106C2×#41×C43D412yes—
107C2×#41×C43D412yes—
108C22×Q8×C43C2×C411yescharacteristic
109C22×D4×C43—21no—
110C22×D4×C43C2×C411yescharacteristic
111C23×C4×C43—21no—
112C23×C4×C43—21no—
113C23×C4×C43C2311yescharacteristic
114C2×M16×C43—21no—
115C2×M16×C43—21no—
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43D412yes—
120C22×C8×C43—21no—
121C2×C42×C43—21no—
122C2×C42×C43—21no—
123C2×C42×C43—21no—
124C2×C42×C43—21no—
125C2×C42×C43—21no—
126C2×C42×C43D412yes—
127#104×C43—28no—
128C24×C43—21no—
129C24×C43#4111yescharacteristic
130C23×D43—21no—
131#41×C43—22no—
132#41×C43—22no—
133#41×C43—22no—
134#41×C43—22no—
135#41×C43—22no—
136#41×C43—22no—
137#41×C43—22no—
138#41×C43—22no—
139#41×C43—41no—
140#41×C43—41no—
141#41×C43—41no—
142#41×C43—41no—
143#41×C43—41no—
144#41×C43—41no—
145#41×C43—41no—
146#41×C43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43C22⋊C412yes—
153C2×D4×C43—21no—
154C2×D4×C43—22no—
155C2×D4×C43—22no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43—41no—
163C2×D4×C43—41no—
164C2×D4×C43C22⋊C412yes—
165C22×C4×C43—24no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—21no—
169C22×C4×C43—22no—
170C22×C4×C43—42no—
171C22×C4×C43—41no—
172C22×C4×C43—41no—
173C22×C4×C43—41no—
174C22×C4×C43—41no—
175C22×C4×C43—41no—
176C22×C4×C43—41no—
177C22×C4×C43C22×C411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43#4111yescharacteristic
189C22×C4×C43#4111yescharacteristic
190C22×C4×C43#4111yescharacteristic
191C2×C22⋊D43—22no—
192C2×C22⋊D43—22no—
193C2×C22⋊D43—41no—
194C2×C22⋊D43—41no—
195C2×C22⋊D43—41no—
196C2×C22⋊D43—41no—
197C22×Dic43—21no—
198#10621898—22no—
199#10621898—22no—
200#10621898—22no—
201#10621898—22no—
202#10621898—22no—
203#10621898—22no—
204#10621898—22no—
205#10621898—22no—
206#10621898—41no—
207#10621898—41no—
208#10621898—41no—
209#10621898—41no—
210#10621898—41no—
211#10621898—41no—
212#10621898—41no—
213#10621898—41no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172C22⋊C412yes—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—41no—
223C2×C4×D43—41no—
224C2×C4×D43—41no—
225C2×C4×D43—41no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86C22⋊C412yes—
232M16×C43—22no—
233M16×C43—22no—
234M16×C43—41no—
235M16×C43—41no—
236C2×C8×C43—22no—
237C2×C8×C43—41no—
238C2×C8×C43—41no—
239C42×C43—22no—
240C42×C43—22no—
241C42×C43—41no—
242C42×C43—41no—
243#10621885—28no—
244#10621884—28no—
245#10621883—28no—
246#10621882—28no—
247#10621877—22no—
248#10621877—22no—
249#10621877—41no—
250#10621877—41no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—22no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8—22no—
259C2×C43⋊C8—22no—
260C2×C43⋊C8—22no—
261C2×C43⋊C8—22no—
262C2×C43⋊C8—22no—
263C2×C43⋊C8—41no—
264C2×C43⋊C8—41no—
265C2×C43⋊C8—41no—
266C2×C43⋊C8—41no—
267C2×C43⋊C8—41no—
268C2×C43⋊C8—41no—
269C2×C43⋊C8C22⋊C412yes—
270C2×C43⋊C8C22⋊C412yes—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—42no—
277C23×C43—42no—
278C23×C43C4×D411yescharacteristic
279C23×C43#12111yescharacteristic
280C23×C43#12111yescharacteristic
281C23×C43#12111yescharacteristic
282C23×C43#12311yescharacteristic
283C23×C43#12311yescharacteristic
284C23×C43#12411yescharacteristic
285C22×D43—22no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—42no—
289C22×D43—42no—
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43—41no—
293Q8×C43—41no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—42no—
297D4×C43—42no—
298D4×C43—42no—
299D4×C43—42no—
300D4×C43—41no—
301D4×C43—41no—
302C2×C4×C43—24no—
303C2×C4×C43—22no—
304C2×C4×C43—44no—
305C2×C4×C43—44no—
306C2×C4×C43—42no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43C2×C22⋊C411yescharacteristic
315C2×C4×C43C2×C22⋊C411yescharacteristic
316C2×C4×C43C2×C22⋊C411yescharacteristic
317C2×C4×C43C4×D411yescharacteristic
318C2×C4×C43C4×D411yescharacteristic
319C2×C4×C43C4×D411yescharacteristic
320C2×C4×C43#12011yescharacteristic
321C2×C4×C43#12011yescharacteristic
322C2×C4×C43#12011yescharacteristic
323C2×C4×C43#12011yescharacteristic
324C2×C4×C43#12011yescharacteristic
325C2×C4×C43#12011yescharacteristic
326C2×C4×C43#12011yescharacteristic
327C2×C4×C43#12011yescharacteristic
328C2×C4×C43#12111yescharacteristic
329C2×C4×C43#12111yescharacteristic
330C2×C4×C43#12111yescharacteristic
331C2×C4×C43#12111yescharacteristic
332C2×C4×C43#12111yescharacteristic
333C2×C4×C43#12111yescharacteristic
334C2×C4×C43#12111yescharacteristic
335C2×C4×C43#12111yescharacteristic
336C2×C4×C43#12111yescharacteristic
337C2×C4×C43#12311yescharacteristic
338C2×C4×C43#12311yescharacteristic
339C2×C4×C43#12411yescharacteristic
340C2×C4×C43#12711yescharacteristic
341C2×C4×C43#12711yescharacteristic
342C22⋊D43—42no—
343C22⋊D43—42no—
344C22⋊D43—42no—
345C22⋊D43—42no—
346C2×Dic43—22no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349D172—22no—
350D172—22no—
351D172—41no—
352D172—41no—
353C4×D43—42no—
354C4×D43—42no—
355C4×D43—42no—
356C4×D43—42no—
357Dic86—22no—
358Dic86—22no—
359Dic86—41no—
360Dic86—41no—
361C8×C43—42no—
362C43⋊C8—22no—
363C43⋊C8—22no—
364C43⋊C8—42no—
365C43⋊C8—42no—
366#11025—431nomaximal, Sylow
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—21no—
372C22×C43—21no—
373C22×C43—21no—
374C22×C43—21no—
375C22×C43—44no—
376C22×C43—42no—
377C22×C43—82no—
378C22×C43—81no—
379C22×C43—81no—
380C22×C43#38611yescharacteristic
381C22×C43#38611yescharacteristic
382C22×C43#39011yescharacteristic
383C22×C43#39211yescharacteristic
384C22×C43#39411yescharacteristic
385C22×C43#39411yescharacteristic
386C22×C43#39411yescharacteristic
387C22×C43#44312yes—
388C22×C43#44412yes—
389C2×D43—44no—
390C2×D43—42no—
391C2×D43—82no—
392C2×D43—81no—
393C2×D43—81no—
394C4×C43—44no—
395C4×C43—42no—
396C4×C43#37911yescharacteristic
397C4×C43#38611yescharacteristic
398C4×C43#38611yescharacteristic
399C4×C43#39011yescharacteristic
400C4×C43#39211yescharacteristic
401C4×C43#39211yescharacteristic
402C4×C43#39211yescharacteristic
403C4×C43#39411yescharacteristic
404Dic43—42no—
405C22×#135—431no—
406C22×#104—431no—
407C22×#104D4311yescharacteristic, complemented
408C2×#408—431no—
409C2×#408—431no—
410C2×#341—431no—
411C2×#336—431no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—21no—
415C2×C43—21no—
416C2×C43—82no—
417C2×C43#143811yescharacteristic
418C2×C43#187612yes—
419C2×C43#187612yes—
420C2×C43#197411yescharacteristic
421C2×C43#197511yescharacteristic
422D43—82no—
423C22×#41—431no—
424C22×#41C2×D4311yescharacteristic
425C2×#135—862no—
426C2×#135—862no—
427C2×#135—862no—
428C2×#135—862no—
429C2×#135—862no—
430C2×#135—862no—
431C22×Q16—431no—
432C22×SD16—431no—
433C22×SD16—431no—
434C22×D8—431no—
435C22×M16—431no—
436C22×M16C2×D4311yescharacteristic
437C23×C8—431no—
438C23×C8—431no—
439C22×C42C2×D4311yescharacteristic
440C2×#104—22no—
441C2×#104—22no—
442C2×#104—22no—
443C2×#104—862no—
444C2×#104—862no—
445C2×#104—862no—
446#408—862no—
447#408—862no—
448#408—862no—
449#408—862no—
450C2×C22⋊C8—862no—
451C2×C22⋊C8—862no—
452#341—862no—
453#336—862no—
454C43#1102511yescharacteristic, complemented, Sylow
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—432no—
466C2×#41—432no—
467C2×#41—861no—
468C2×#41—861no—
469C2×#41—861no—
470C2×#41—861no—
471C2×#41—861no—
472C2×#41—861no—
473C2×#41—861no—
474C2×#41—861no—
475C2×#41—861no—
476C2×#41—861no—
477C2×#41D17212yes—
478C2×#41C22⋊D4312yes—
479C22×Q8—431no—
480C22×Q8C4×D4311yescharacteristic
481C22×D4—21no—
482C22×D4—431no—
483C22×D4—861no—
484C22×D4C4×D4311yescharacteristic
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—861no—
488C23×C4C22×D4311yescharacteristic
489#135—868no—
490#135—868no—
491#135—868no—
492#135—868no—
493C2×Q16—862no—
494C2×Q16—862no—
495C2×Q16—862no—
496C2×SD16—862no—
497C2×SD16—862no—
498C2×SD16—862no—
499C2×SD16—862no—
500C2×SD16—862no—
501C2×SD16—862no—
502C2×D8—862no—
503C2×D8—862no—
504C2×D8—862no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—21no—
509C2×M16—21no—
510C2×M16—432no—
511C2×M16—861no—
512C2×M16—861no—
513C2×M16—861no—
514C2×M16—861no—
515C2×M16—861no—
516C2×M16C22⋊D4312yes—
517C22×C8—21no—
518C22×C8—431no—
519C22×C8—431no—
520C22×C8—432no—
521C22×C8—432no—
522C22×C8—432no—
523C22×C8—861no—
524C22×C8—861no—
525C22×C8—861no—
526C22×C8—861no—
527C22×C8—861no—
528C22×C8—861no—
529C22×C8—861no—
530C22×C8—861no—
531C22×C8—861no—
532C22×C8—861no—
533C22×C8—861no—
534C2×C42—21no—
535C2×C42—21no—
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—21no—
539C2×C42C22⋊D4312yes—
540#104—28no—
541#104—868no—
542C22⋊C8—868no—
543C22⋊C8—868no—
544C24—21no—
545C24—861no—
546C24#1062190011yescharacteristic
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—862no—
564#41—862no—
565#41—862no—
566#41—862no—
567#41—862no—
568#41—862no—
569#41—862no—
570#41—862no—
571#41—1721no—
572#41—1721no—
573#41—1721no—
574#41—1721no—
575#41—1721no—
576#41—1721no—
577#41—1721no—
578#41—1721no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—432no—
585C2×Q8—861no—
586C2×Q8—861no—
587C2×Q8—861no—
588C2×Q8—861no—
589C2×Q8—861no—
590C2×Q8(C2×D43)⋊C412yes—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4—432no—
603C2×D4—862no—
604C2×D4—862no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—861no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—1721no—
611C2×D4—1721no—
612C2×D4—1721no—
613C2×D4—1721no—
614C2×D4(C2×D43)⋊C412yes—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—42no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—861no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—1721no—
631C22×C4—1721no—
632C22×C4—1721no—
633C22×C4—1721no—
634C22×C4C2×C4×D4311yescharacteristic
635C22×C4C2×D17211yescharacteristic
636C22×C4#1062189811yescharacteristic
637C22×C4#1062189811yescharacteristic
638C22×C4D4×D4311yescharacteristic
639C22×C4D4×D4311yescharacteristic
640C22×C4D4×D4311yescharacteristic
641C22×C4D4×D4311yescharacteristic
642C22×C4D4×D4311yescharacteristic
643C22×C4D4×D4311yescharacteristic
644C22×C4#1062190011yescharacteristic
645C22×C4C2×C22⋊D4311yescharacteristic
646C22×C4C2×C22⋊D4311yescharacteristic
647C22×C4C2×C22⋊D4311yescharacteristic
648Q16—868no—
649SD16—868no—
650SD16—868no—
651D8—868no—
652M16—22no—
653M16—22no—
654M16—41no—
655M16—41no—
656M16—862no—
657M16—862no—
658M16—1721no—
659M16—1721no—
660C2×C8—22no—
661C2×C8—41no—
662C2×C8—41no—
663C2×C8—432no—
664C2×C8—432no—
665C2×C8—861no—
666C2×C8—861no—
667C2×C8—861no—
668C2×C8—861no—
669C2×C8—862no—
670C2×C8—862no—
671C2×C8—862no—
672C2×C8—862no—
673C2×C8—862no—
674C2×C8—862no—
675C2×C8—862no—
676C2×C8—862no—
677C2×C8—1721no—
678C2×C8—1721no—
679C2×C8—1721no—
680C2×C8—1721no—
681C2×C8—1721no—
682C2×C8—1721no—
683C42—22no—
684C42—22no—
685C42—41no—
686C42—41no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—41no—
691C23—42no—
692C23—42no—
693C23—41no—
694C23—862no—
695C23—1721no—
696C23—1722no—
697C23—1722no—
698C23—1721no—
699C23(C22⋊D43)⋊C411yescharacteristic
700C23#1306329611yescharacteristic
701C23#1306329711yescharacteristic
702C23#1306329711yescharacteristic
703C23#1306330711yescharacteristic
704C23#1306330911yescharacteristic
705C23#1306331111yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—41no—
709Q8—41no—
710Q8—862no—
711Q8—862no—
712Q8—1721no—
713Q8—1721no—
714D4—22no—
715D4—22no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—42no—
720D4—41no—
721D4—41no—
722D4—862no—
723D4—862no—
724D4—1722no—
725D4—1722no—
726D4—1722no—
727D4—1722no—
728D4—1721no—
729D4—1721no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—862no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4—1722no—
748C2×C4—1722no—
749C2×C4C22⋊C4×D4311yescharacteristic
750C2×C4C22⋊C4×D4311yescharacteristic
751C2×C4C2×(C2×D43)⋊C411yescharacteristic
752C2×C4(C22⋊D43)⋊C411yescharacteristic
753C2×C4C4×C22⋊D4311yescharacteristic
754C2×C4C4×C22⋊D4311yescharacteristic
755C2×C4#1306329311yescharacteristic
756C2×C4#1306329311yescharacteristic
757C2×C4#1306329311yescharacteristic
758C2×C4#1306329311yescharacteristic
759C2×C4#1306329411yescharacteristic
760C2×C4#1306329511yescharacteristic
761C2×C4#1306329511yescharacteristic
762C2×C4#1306329511yescharacteristic
763C2×C4#1306329611yescharacteristic
764C2×C4#1306329711yescharacteristic
765C2×C4#1306329711yescharacteristic
766C2×C4#1306329811yescharacteristic
767C2×C4#1306329811yescharacteristic
768C2×C4#1306329811yescharacteristic
769C2×C4#1306329811yescharacteristic
770C2×C4#1306329911yescharacteristic
771C2×C4#1306329911yescharacteristic
772C2×C4#1306330711yescharacteristic
773C2×C4#1306330811yescharacteristic
774C2×C4#1306331111yescharacteristic
775C2×C4#1306332111yescharacteristic
776C2×C4#1306332111yescharacteristic
777C8—42no—
778C8—862no—
779C8—862no—
780C8—1722no—
781C8—1722no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—42no—
791C22—44no—
792C22—82no—
793C22—81no—
794C22—81no—
795C22—3442no—
796C22—3441no—
797C22—3441no—
798C22—1722no—
799C22—1724no—
800C22#1458277511yescharacteristic
801C22#1458277611yescharacteristic
802C22#1458279911yescharacteristic
803C22#1458280711yescharacteristic
804C22#1458281411yescharacteristic
805C22#1458281511yescharacteristic
806C22#1458281511yescharacteristic
807C22#1458301312yes—
808C22#1458301812yes—
809C4—44no—
810C4—42no—
811C4—1722no—
812C4#1458275411yescharacteristic
813C4#1458277511yescharacteristic
814C4#1458277811yescharacteristic
815C4#1458279911yescharacteristic
816C4#1458280711yescharacteristic
817C4#1458280811yescharacteristic
818C4#1458280811yescharacteristic
819C4#1458281411yescharacteristic
820C2—21no—
821C2—21no—
822C2—21no—
823C2—21no—
824C2—82no—
825C2—3442no—
826C2#1913283411yescharacteristic
827C2#1913491912yes—
828C2#1913492012yes—
829C2#1913548011yescharacteristic
830C2#1913548511yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC22×#104×C43C2
socleC23×C43C4×D4
prime radicalC22×#13063345C2
cosocleC23×C4×C43C23
hypercenterC22×#104D43
hypocenterC43#11025
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C22×#13063253C2semidirect
3. C2×#14582867C2semidirect
4. C2×#14582866C2semidirect
5. C2×#14582663C2semidirect
6. C2×#14582654C2semidirect
7. C22×#104×C43C2semidirect
15. C22×#10621885C4semidirect
16. C22×#10621883C4semidirect
17. C22×#10621884C4semidirect
18. C22×#10621882C4semidirect
407. C22×#104D43semidirect
454. C43#11025semidirect

Maximal subgroups

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

subgroupindex
C22×#130633452
C22×#130632532
C2×#145828672
C2×#145828662
C2×#145826632
C2×#145826542
C22×#104×C432
#1102543