Finite Group Databasebeta

← #25003240

Subgroups — #25003240

Order 11008.

1630 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063252C211yesmaximal, characteristic, complemented
2C2×#14582900C211yesmaximal, characteristic, complemented
3C22×#13063242C211yesmaximal, characteristic, complemented
4C2×#14582802C211yesmaximal, characteristic, complemented
5#19134316C211yesmaximal, characteristic, complemented
6C2×#14582658C211yesmaximal, characteristic, complemented
7C2×C43×#535C211yesmaximal, characteristic
8C22×#10621877C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×C4⋊Dic43C2211yescharacteristic
11C22×C22⋊Dic43—22no—
12C22×C4×Dic43C2211yescharacteristic
13C2×#13063252—22no—
14C2×#13063252—22no—
15C2×#13063252—22no—
16#14582900—22no—
17#14582900—22no—
18C2×#13063249—21no—
19C2×#13063246—21no—
20C2×#13063242—22no—
21C2×#13063242—22no—
22C2×#13063242—22no—
23#14582802—22no—
24#14582802—22no—
25#14582661—22no—
26#14582658—22no—
27C22×#41×C43C2211yescharacteristic
28C23×D4×C43C2211yescharacteristic
29C43×#535—22no—
30C43×#535—22no—
31C43×#535—22no—
32C43×#535C414yescomplemented
33C2×#127×C43—21no—
34C2×#124×C43—21no—
35C2×#121×C43—22no—
36C2×#120×C43—22no—
37C2×#117×C43C2211yescharacteristic
38C23×Dic43—21no—
39C23×Dic43—21no—
40C2×#10621877—21no—
41C2×#10621877—21no—
42C2×#10621877—21no—
43C2×#10621877—21no—
44C2×#10621877—21no—
45C2×#10621877—21no—
46C2×#10621877—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877D412yescomplemented
51C2×#10621877D412yescomplemented
52C22×C43⋊C8—21no—
53C22×C43⋊C8—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43—21no—
58C2×C4⋊Dic43—21no—
59C2×C4⋊Dic43D412yescomplemented
60C2×C22⋊Dic43—28no—
61C2×C22⋊Dic43—48no—
62C2×C4×Dic43—21no—
63C2×C4×Dic43—21no—
64C2×C4×Dic43—21no—
65C2×C4×Dic43—21no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43D412yescomplemented
68#13063252—28no—
69#13063249—24no—
70#13063246—24no—
71#13063242—28no—
72C25×C43D412yes—
73C2×#41×C43—21no—
74C2×#41×C43—21no—
75C2×#41×C43—21no—
76C2×#41×C43—21no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—21no—
82C2×#41×C43—21no—
83C2×#41×C43C2×C412yes—
84C2×#41×C43D412yes—
85C22×Q8×C43D411yescharacteristic
86C22×D4×C43—21no—
87C22×D4×C43—24no—
88C22×D4×C43—21no—
89C22×D4×C43—21no—
90C22×D4×C43—21no—
91C22×D4×C43—21no—
92C22×D4×C43—21no—
93C22×D4×C43—21no—
94C22×D4×C43—21no—
95C22×D4×C43—21no—
96C22×D4×C43—21no—
97C22×D4×C43—21no—
98C22×D4×C43—21no—
99C22×D4×C43—21no—
100C22×D4×C43C2×C412yes—
101C22×D4×C43D412yes—
102C22×D4×C43D411yescharacteristic
103C23×C4×C43—21no—
104C23×C4×C43C2311yescharacteristic
105#127×C43—24no—
106#127×C43—24no—
107#124×C43—24no—
108#124×C43—24no—
109#121×C43—28no—
110#121×C43—28no—
111#120×C43—28no—
112#120×C43—28no—
113#117×C43—21no—
114#117×C43—21no—
115#117×C43C2×C412yes—
116#117×C43D412yes—
117C2×C4⋊C4×C43D412yes—
118C2×C22⋊C4×C43—24no—
119C2×C22⋊C4×C43—21no—
120C2×C42×C43—21no—
121C24×C43—22no—
122C24×C43—21no—
123C24×C43—22no—
124C24×C43—22no—
125C24×C43—22no—
126C24×C43—22no—
127C24×C43—22no—
128C24×C43—44no—
129C24×C43—44no—
130C24×C43C22⋊C414yes—
131C24×C43C2×D411yescharacteristic
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—22no—
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—
147#41×C43—41no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43C22⋊C412yescomplemented
154C2×D4×C43—216no—
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C2×D4×C43—22no—
159C2×D4×C43—22no—
160C2×D4×C43—22no—
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C2×D4×C43—21no—
164C2×D4×C43—22no—
165C2×D4×C43—22no—
166C2×D4×C43—22no—
167C2×D4×C43—22no—
168C2×D4×C43—22no—
169C2×D4×C43—22no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—41no—
175C2×D4×C43—41no—
176C2×D4×C43—41no—
177C2×D4×C43—41no—
178C2×D4×C43—41no—
179C2×D4×C43—41no—
180C2×D4×C43—41no—
181C2×D4×C43—41no—
182C2×D4×C43—41no—
183C2×D4×C43—41no—
184C2×D4×C43—41no—
185C2×D4×C43—41no—
186C2×D4×C43—41no—
187C2×D4×C43—41no—
188C2×D4×C43—41no—
189C2×D4×C43—41no—
190C2×D4×C43—41no—
191C2×D4×C43—41no—
192C2×D4×C43—41no—
193C2×D4×C43—41no—
194C2×D4×C43—84no—
195C2×D4×C43—84no—
196C2×D4×C43C22⋊C412yescomplemented
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—21no—
201C22×C4×C43—41no—
202C22×C4×C43—41no—
203C22×C4×C43—41no—
204C22×C4×C43—41no—
205C22×C4×C43C22×C411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43#4111yescharacteristic
216C22×C4×C43#4111yescharacteristic
217C22×C4×C43#4111yescharacteristic
218C22×C4×C43#4111yescharacteristic
219C22×Dic43—24no—
220C22×Dic43—22no—
221C22×Dic43—22no—
222C22×Dic43—42no—
223C22×Dic43—44no—
224C22×Dic43—41no—
225C22×Dic43—41no—
226C22×Dic43—41no—
227C22×Dic43—41no—
228C4⋊C4×C43—22no—
229C4⋊C4×C43C22⋊C414yescomplemented
230C22⋊C4×C43—216no—
231C22⋊C4×C43—22no—
232C22⋊C4×C43—22no—
233C42×C43—22no—
234C42×C43—22no—
235C22⋊Dic43—416no—
236C4⋊Dic43—22no—
237C4⋊Dic43—22no—
238C4⋊Dic43—41no—
239C4⋊Dic43—41no—
240C4×Dic43—22no—
241C4×Dic43—22no—
242C4×Dic43—41no—
243C4×Dic43—41no—
244#10621877—22no—
245#10621877—22no—
246#10621877—22no—
247#10621877—22no—
248#10621877—41no—
249#10621877—41no—
250#10621877—41no—
251#10621877—41no—
252C2×C43⋊C8—22no—
253C2×C43⋊C8—22no—
254C2×C43⋊C8—41no—
255C2×C43⋊C8—41no—
256C2×C43⋊C8—41no—
257C2×C43⋊C8—41no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—24no—
261C23×C43—22no—
262C23×C43—24no—
263C23×C43—24no—
264C23×C43—48no—
265C23×C43—44no—
266C23×C43—44no—
267C23×C43—48no—
268C23×C43—41no—
269C23×C43—42no—
270C23×C43—42no—
271C23×C43—41no—
272C23×C43—42no—
273C23×C43—42no—
274C23×C43—42no—
275C23×C43—44no—
276C23×C43—42no—
277C23×C43—44no—
278C23×C43—84no—
279C23×C43—82no—
280C23×C43—82no—
281C23×C43—84no—
282C23×C43C2×C22⋊C411yescharacteristic
283C23×C43#12011yescharacteristic
284C23×C43#12011yescharacteristic
285C23×C43#12011yescharacteristic
286C23×C43#12111yescharacteristic
287C23×C43#12111yescharacteristic
288C23×C43#12311yescharacteristic
289Q8×C43—22no—
290Q8×C43—22no—
291Q8×C43—41no—
292Q8×C43—41no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—42no—
296D4×C43—42no—
297D4×C43—42no—
298D4×C43—42no—
299D4×C43—42no—
300D4×C43—42no—
301D4×C43—42no—
302D4×C43—42no—
303D4×C43—42no—
304D4×C43—42no—
305D4×C43—41no—
306D4×C43—42no—
307D4×C43—42no—
308D4×C43—41no—
309D4×C43—816no—
310C2×C4×C43—24no—
311C2×C4×C43—22no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C2×C22⋊C411yescharacteristic
322C2×C4×C43C4×D411yescharacteristic
323C2×C4×C43C4×D411yescharacteristic
324C2×C4×C43C4×D411yescharacteristic
325C2×C4×C43C4×D411yescharacteristic
326C2×C4×C43#12011yescharacteristic
327C2×C4×C43#12011yescharacteristic
328C2×C4×C43#12011yescharacteristic
329C2×C4×C43#12011yescharacteristic
330C2×C4×C43#12011yescharacteristic
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#12111yescharacteristic
338C2×C4×C43#12111yescharacteristic
339C2×C4×C43#12111yescharacteristic
340C2×C4×C43#12111yescharacteristic
341C2×C4×C43#12311yescharacteristic
342C2×C4×C43#12311yescharacteristic
343C2×C4×C43#12311yescharacteristic
344C2×C4×C43#12411yescharacteristic
345C2×C4×C43#12411yescharacteristic
346C2×C4×C43#12711yescharacteristic
347C2×C4×C43#12711yescharacteristic
348C2×Dic43—24no—
349C2×Dic43—44no—
350C2×Dic43—42no—
351C2×Dic43—44no—
352C2×Dic43—42no—
353C2×Dic43—44no—
354C2×Dic43—42no—
355C2×Dic43—82no—
356C2×Dic43—82no—
357C43⋊C8—42no—
358C43⋊C8—42no—
359#10997—431nomaximal, Sylow
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—21no—
363C22×C43—21no—
364C22×C43—21no—
365C22×C43—21no—
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—48no—
369C22×C43—48no—
370C22×C43—44no—
371C22×C43—44no—
372C22×C43—42no—
373C22×C43—84no—
374C22×C43—84no—
375C22×C43—84no—
376C22×C43—81no—
377C22×C43—82no—
378C22×C43—81no—
379C22×C43—82no—
380C22×C43—82no—
381C22×C43—84no—
382C22×C43#37911yescharacteristic
383C22×C43#38611yescharacteristic
384C22×C43#38611yescharacteristic
385C22×C43#39211yescharacteristic
386C22×C43#39211yescharacteristic
387C22×C43#39411yescharacteristic
388C22×C43#39411yescharacteristic
389C22×C43#45312yes—
390C22×C43#45512yes—
391C4×C43—44no—
392C4×C43—42no—
393C4×C43#38611yescharacteristic
394C4×C43#38611yescharacteristic
395C4×C43#39011yescharacteristic
396C4×C43#39011yescharacteristic
397C4×C43#39211yescharacteristic
398C4×C43#39211yescharacteristic
399C4×C43#39411yescharacteristic
400C4×C43#39411yescharacteristic
401Dic43—44no—
402Dic43—82no—
403C2×#535D4311yescharacteristic
404C22×#104—431no—
405C2×#417—431no—
406C22×#100—431no—
407C2×#390—431no—
408#1736—431no—
409C2×#339—431no—
410C2×C43—21no—
411C2×C43—21no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—84no—
415C2×C43—82no—
416C2×C43#143811yescharacteristic
417C2×C43#179212yes—
418C2×C43#200211yescharacteristic
419C2×C43#200411yescharacteristic
420C2×C43#203712yes—
421C22×#41C2×D4311yescharacteristic
422C23×D4C2×D4311yescharacteristic
423C22×M16—431no—
424C22×M16—431no—
425#535—22no—
426#535—22no—
427#535—22no—
428#535Dic4314yescomplemented
429C2×#127—21no—
430C2×#124—21no—
431C2×#121—22no—
432C2×#120—22no—
433C2×#117C2×D4311yescharacteristic
434C22×C4⋊C4—431no—
435C22×C22⋊C4—862no—
436C22×C42—431no—
437C2×#104—862no—
438C2×#104—862no—
439C2×#104—862no—
440#417—862no—
441#417—862no—
442C2×#103—861no—
443C2×#102—861no—
444C2×#100—862no—
445C2×#100—862no—
446C2×#100—862no—
447#390—862no—
448#390—862no—
449#340—862no—
450#339—862no—
451C43#1099711yescharacteristic, complemented, Sylow
452C25C22⋊D4312yes—
453C2×#41—21no—
454C2×#41—21no—
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×#41C2×Dic4312yes—
464C2×#41C22⋊D4312yes—
465C22×Q8C22⋊D4311yescharacteristic
466C22×D4—21no—
467C22×D4—24no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4C2×Dic4312yes—
481C22×D4C22⋊D4312yes—
482C22×D4C22⋊D4311yescharacteristic
483C23×C4—21no—
484C23×C4—861no—
485C23×C4—861no—
486C23×C4C22×D4311yescharacteristic
487C2×M16—432no—
488C2×M16—432no—
489C2×M16—861no—
490C2×M16—861no—
491C2×M16—861no—
492C2×M16—861no—
493C2×M16—861no—
494C2×M16—861no—
495C2×M16—861no—
496C2×M16—861no—
497C2×M16—861no—
498C2×M16—861no—
499C22×C8—861no—
500C22×C8—861no—
501#127—24no—
502#127—24no—
503#124—24no—
504#124—24no—
505#121—28no—
506#121—28no—
507#120—28no—
508#120—28no—
509#117—21no—
510#117—21no—
511#117C2×Dic4312yes—
512#117C22⋊D4312yes—
513C2×C4⋊C4—432no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4C22⋊D4312yes—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—868no—
523C2×C22⋊C4—1728no—
524C2×C42—21no—
525C2×C42—432no—
526C2×C42—861no—
527C2×C42—861no—
528C2×C42—861no—
529C2×C42—861no—
530C2×C42—861no—
531#104—868no—
532#103—864no—
533#102—864no—
534#100—868no—
535C24—22no—
536C24—22no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—44no—
543C24—44no—
544C24C22⋊Dic4314yes—
545C24C2×C22⋊D4311yescharacteristic
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8C22⋊Dic4312yescomplemented
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—216no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—84no—
609C2×D4—84no—
610C2×D4C22⋊Dic4312yescomplemented
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—864no—
620C22×C4—862no—
621C22×C4—862no—
622C22×C4—1724no—
623C22×C4—1721no—
624C22×C4—1721no—
625C22×C4—1722no—
626C22×C4—1721no—
627C22×C4—1721no—
628C22×C4D4×D4311yescharacteristic
629C22×C4D4×D4311yescharacteristic
630C22×C4D4×D4311yescharacteristic
631C22×C4D4×D4311yescharacteristic
632C22×C4#1062190011yescharacteristic
633C22×C4#1062190011yescharacteristic
634C22×C4#1062190011yescharacteristic
635C22×C4#1062190011yescharacteristic
636C22×C4C22×Dic4311yescharacteristic
637C22×C4C2×C22⋊D4311yescharacteristic
638C22×C4C2×C22⋊D4311yescharacteristic
639C22×C4C2×C22⋊D4311yescharacteristic
640C22×C4C2×C22⋊D4311yescharacteristic
641C22×C4C2×C22⋊D4311yescharacteristic
642M16—862no—
643M16—862no—
644M16—862no—
645M16—862no—
646M16—1721no—
647M16—1721no—
648M16—1721no—
649M16—1721no—
650C2×C8—862no—
651C2×C8—862no—
652C2×C8—1721no—
653C2×C8—1721no—
654C2×C8—1721no—
655C2×C8—1721no—
656C4⋊C4—22no—
657C4⋊C4—862no—
658C4⋊C4—862no—
659C4⋊C4—1721no—
660C4⋊C4—1721no—
661C4⋊C4C22⋊Dic4314yescomplemented
662C22⋊C4—216no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—17216no—
666C42—22no—
667C42—22no—
668C42—862no—
669C42—862no—
670C42—1721no—
671C42—1721no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—48no—
679C23—44no—
680C23—48no—
681C23—44no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—44no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—44no—
692C23—84no—
693C23—84no—
694C23—82no—
695C23—82no—
696C23C2×C22⋊Dic4311yescharacteristic
697C23#1306329311yescharacteristic
698C23#1306329411yescharacteristic
699C23#1306329411yescharacteristic
700C23#1306329711yescharacteristic
701C23#1306329711yescharacteristic
702C23#1306330611yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—41no—
718D4—42no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—816no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—864no—
735C2×C4—3442no—
736C2×C4—3442no—
737C2×C4—1724no—
738C2×C4—1722no—
739C2×C4—1724no—
740C2×C4—1724no—
741C2×C4—1722no—
742C2×C4—1722no—
743C2×C4C2×C22⋊Dic4311yescharacteristic
744C2×C4C2×C22⋊Dic4311yescharacteristic
745C2×C4D4×Dic4311yescharacteristic
746C2×C4D4×Dic4311yescharacteristic
747C2×C4D4×Dic4311yescharacteristic
748C2×C4D4×Dic4311yescharacteristic
749C2×C4#1306329311yescharacteristic
750C2×C4#1306329311yescharacteristic
751C2×C4#1306329311yescharacteristic
752C2×C4#1306329411yescharacteristic
753C2×C4#1306329411yescharacteristic
754C2×C4#1306329611yescharacteristic
755C2×C4#1306329611yescharacteristic
756C2×C4#1306329611yescharacteristic
757C2×C4#1306329611yescharacteristic
758C2×C4#1306329711yescharacteristic
759C2×C4#1306329711yescharacteristic
760C2×C4#1306329711yescharacteristic
761C2×C4#1306329711yescharacteristic
762C2×C4#1306329711yescharacteristic
763C2×C4#1306329711yescharacteristic
764C2×C4#1306330611yescharacteristic
765C2×C4#1306330611yescharacteristic
766C2×C4#1306330611yescharacteristic
767C2×C4#1306331211yescharacteristic
768C2×C4#1306331211yescharacteristic
769C2×C4#1306332111yescharacteristic
770C2×C4#1306332111yescharacteristic
771C8—1722no—
772C8—1722no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—48no—
782C22—44no—
783C22—48no—
784C22—42no—
785C22—44no—
786C22—84no—
787C22—84no—
788C22—84no—
789C22—84no—
790C22—82no—
791C22—82no—
792C22—81no—
793C22—82no—
794C22—81no—
795C22#1458275511yescharacteristic
796C22#1458277911yescharacteristic
797C22#1458277911yescharacteristic
798C22#1458280711yescharacteristic
799C22#1458280711yescharacteristic
800C22#1458281311yescharacteristic
801C22#1458281311yescharacteristic
802C22#1458306712yes—
803C22#1458307712yes—
804C4—44no—
805C4—42no—
806C4—3442no—
807C4—1724no—
808C4#1458277911yescharacteristic
809C4#1458277911yescharacteristic
810C4#1458280211yescharacteristic
811C4#1458280211yescharacteristic
812C4#1458280711yescharacteristic
813C4#1458280711yescharacteristic
814C4#1458281311yescharacteristic
815C4#1458281311yescharacteristic
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—84no—
821C2—82no—
822C2#1913283611yescharacteristic
823C2#1913454912yes—
824C2#1913560811yescharacteristic
825C2#1913562211yescharacteristic
826C2#1913580212yes—
subgroupG/H
centerC23#13063294
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC2×C43×#535C2
socleC23×C43#120
cosocleC23×C4×C43C23
hypercenterC2×#535D43
hypocenterC43#10997
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C22×#13063252C2semidirect
2. C2×#14582900C2semidirect
3. C22×#13063242C2semidirect
4. C2×#14582802C2semidirect
5. #19134316C2semidirect
6. C2×#14582658C2semidirect
32. C43×#535C4semidirect
50. C2×#10621877D4semidirect
51. C2×#10621877D4semidirect
59. C2×C4⋊Dic43D4semidirect
67. C2×C4×Dic43D4semidirect
153. C2×Q8×C43C22⋊C4semidirect
196. C2×D4×C43C22⋊C4semidirect
229. C4⋊C4×C43C22⋊C4semidirect
428. #535Dic43semidirect
451. C43#10997semidirect
567. C2×Q8C22⋊Dic43semidirect
610. C2×D4C22⋊Dic43semidirect
661. C4⋊C4C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632522
C2×#145829002
C22×#130632422
C2×#145828022
#191343162
C2×#145826582
C2×C43×#5352
#1099743