Finite Group Databasebeta

← #25134227

Subgroups — #25134227

Order 11008.

1508 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
2C2×#14583128C211yesmaximal, characteristic, complemented
3C2×#14583039C211yesmaximal, characteristic, complemented
4C2×#14583038C211yesmaximal, characteristic, complemented
5#19138029C211yesmaximal, characteristic
6#19135840C211yesmaximal, characteristic, complemented
7#19135790C211yesmaximal, characteristic, complemented
8#19135679C211yesmaximal, characteristic, complemented
9#19135597C211yesmaximal, characteristic, complemented
10#19134948C211yesmaximal, characteristic, complemented
11#19134902C211yesmaximal, characteristic, complemented
12#19134887C211yesmaximal, characteristic, complemented
13#19134865C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic, complemented
15C22×#103×C43C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20Q8×C22⋊D43—24no—
21Q8×C22⋊D43—24no—
22C2×#13063323—21no—
23C2×#13063323C2211yescharacteristic
24C2×#13063304—21no—
25C2×#13063304C2211yescharacteristic
26C2×#13063301—21no—
27C2×#13063301C2211yescharacteristic
28C2×#13063300C2211yescharacteristic
29C2×#13063299—21no—
30C2×#13063299C2211yescharacteristic
31C2×Q8×Dic43C2211yescharacteristic
32C2×C4×C22⋊D43—21no—
33C2×C4×C22⋊D43C2211yescharacteristic
34#14583128—24no—
35#14583039—24no—
36#14583038—24no—
37C2×#13063257C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063247C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47#14582821—21no—
48#14582816—21no—
49#14582800C2211yescharacteristic
50#14582798C2211yescharacteristic
51#14582778—21no—
52#14582756C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C23×Q8×C43C2211yescharacteristic
58C23×C8×C43C2211yescharacteristic
59C22×C4⋊C4×C43C2211yescharacteristic
60C2×#103×C43—24no—
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C2×#103×C43C2211yescharacteristic
64C2×#103×C43C2211yescharacteristic
65C22×Dic86—21no—
66C22×Dic86C2311yescharacteristic
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43—41no—
72C2×Q8×D43—41no—
73C22×D172—21no—
74C22×D172C2311yescharacteristic
75C22×C22⋊D43—21no—
76C22×C22⋊D43D411yescharacteristic
77C22×C4×D43—21no—
78C22×C4×D43C2311yescharacteristic
79C2×#10621873—22no—
80C2×#10621873—22no—
81C2×#10621873—41no—
82C2×#10621884—22no—
83C2×#10621884—22no—
84C2×#10621884—22no—
85C2×#10621884—22no—
86C2×#10621884—41no—
87C2×#10621884—41no—
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90#13063323—28no—
91#13063323—22no—
92#13063323—22no—
93#13063304—28no—
94#13063304—22no—
95#13063304D414yescomplemented
96#13063301—28no—
97#13063301—22no—
98#13063301—22no—
99#13063300—22no—
100#13063300—41no—
101#13063299—22no—
102#13063299—22no—
103#13063299—44no—
104Q8×Dic43—22no—
105Q8×Dic43—22no—
106C4×C22⋊D43—28no—
107C4×C22⋊D43—22no—
108C4×C22⋊D43—22no—
109C2×C4⋊Dic43—21no—
110C2×C4⋊Dic43—21no—
111C2×C4⋊Dic43C2311yescharacteristic
112C2×C4⋊Dic43C2311yescharacteristic
113C2×Dic43⋊C4—21no—
114C2×Dic43⋊C4—21no—
115C2×Dic43⋊C4—21no—
116C2×Dic43⋊C4—21no—
117C2×Dic43⋊C4D411yescharacteristic
118C2×C22⋊Dic43—21no—
119C2×C22⋊Dic43D411yescharacteristic
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4—21no—
125C2×(C2×D43)⋊C4—21no—
126C2×(C2×D43)⋊C4D411yescharacteristic
127C2×C4×Dic43—21no—
128C2×C4×Dic43C2311yescharacteristic
129#13063257—22no—
130#13063250—22no—
131#13063249—22no—
132#13063249—22no—
133#13063248—22no—
134#13063248—41no—
135#13063247—22no—
136C22⋊(C43⋊C8)—22no—
137(C2×D43)⋊C8—22no—
138(C2×D43)⋊C8—41no—
139C43⋊#95—21no—
140C43⋊#95—21no—
141C22×Q8×C43—22no—
142C22×Q8×C43—21no—
143C22×Q8×C43—22no—
144C22×Q8×C43—22no—
145C22×Q8×C43—41no—
146C22×Q8×C43—41no—
147C22×Q8×C43D414yescomplemented
148C22×Q8×C43C2311yescharacteristic
149C22×Q8×C43C2311yescharacteristic
150C23×C4×C43—21no—
151C23×C4×C43—21no—
152C23×C4×C43C2311yescharacteristic
153C22×C8×C43—22no—
154C22×C8×C43—22no—
155C22×C8×C43—41no—
156C22×C8×C43C2311yescharacteristic
157C22×C8×C43C2311yescharacteristic
158C2×C4⋊C4×C43—22no—
159C2×C4⋊C4×C43—21no—
160C2×C4⋊C4×C43—41no—
161C2×C4⋊C4×C43C2311yescharacteristic
162C2×C4⋊C4×C43C2311yescharacteristic
163#103×C43—22no—
164#103×C43—22no—
165#103×C43—22no—
166#103×C43D414yescomplemented
167C24×C43C2×D411yescharacteristic
168C23×D43—21no—
169C23×D43C2×D411yescharacteristic
170C2×Q8×C43—24no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—28no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43—42no—
181C2×Q8×C43—42no—
182C2×Q8×C43—44no—
183C2×Q8×C43—44no—
184C2×Q8×C43—44no—
185C2×Q8×C43C2×D412yes—
186C2×Q8×C43C2×D412yes—
187C2×Q8×C43C2×D412yes—
188C2×Q8×C43#4112yes—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—24no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—42no—
199C22×C4×C43—42no—
200C22×C4×C43—42no—
201C22×C4×C43—42no—
202C22×C4×C43—81no—
203C22×C4×C43C2×D412yes—
204C22×C4×C43C2×D412yes—
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—22no—
208C2×C22⋊D43—22no—
209C2×C22⋊D43—42no—
210C2×C22⋊D43—42no—
211C2×C22⋊D43—42no—
212C2×C22⋊D43SD1614yescomplemented
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219Q8×D43—44no—
220Q8×D43—44no—
221Q8×D43—44no—
222Q8×D43—44no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—42no—
230C2×D172—42no—
231C2×D172—81no—
232C2×C4×D43—24no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—42no—
240C2×C4×D43—42no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—21no—
245C2×Dic86—24no—
246C2×Dic86—21no—
247C2×Dic86—42no—
248C2×Dic86—42no—
249C2×Dic86C2×D412yes—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—44no—
256C2×C8×C43C2×D412yes—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—42no—
261C4⋊C4×C43C2×D412yes—
262C22⋊Dic43—24no—
263C22⋊Dic43—22no—
264#10621884—44no—
265#10621884—44no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—22no—
268(C2×D43)⋊C4—42no—
269(C2×D43)⋊C4—42no—
270(C2×D43)⋊C4—42no—
271(C2×D43)⋊C4—42no—
272(C2×D43)⋊C4—81no—
273C4⋊Dic43—24no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—42no—
278C4⋊Dic43C2×D412yes—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4—24no—
283Dic43⋊C4—22no—
284C4×Dic43—24no—
285C4×Dic43—21no—
286C4×Dic43—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293#10621873—44no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43#12012yes—
299C23×C43C2×SD1612yes—
300C23×C43#13712yes—
301C23×C43C22×D411yescharacteristic
302C22×D43—21no—
303C22×D43—21no—
304C22×D43—21no—
305C22×D43—21no—
306C22×D43—21no—
307C22×D43—21no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43—41no—
315C22×D43C2×SD1612yes—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—22no—
320Q8×C43—22no—
321Q8×C43—48no—
322Q8×C43—41no—
323Q8×C43—41no—
324Q8×C43#12114yescomplemented
325C2×C4×C43—22no—
326C2×C4×C43—21no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—21no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—48no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—84no—
345C2×C4×C43#12012yes—
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C2×#4111yescharacteristic
350C2×C4×C43H(5,𝔽2)11yescharacteristic
351C2×C4×C43H(5,𝔽2)11yescharacteristic
352C22⋊D43—28no—
353C22⋊D43—84no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—22no—
358C2×Dic43—21no—
359C2×Dic43—22no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43C2×SD1612yes—
372D172—41no—
373D172—41no—
374D172—41no—
375D172—41no—
376D172—84no—
377C4×D43—48no—
378C4×D43—41no—
379C4×D43—41no—
380C4×D43—41no—
381C4×D43—41no—
382Dic86—22no—
383Dic86—22no—
384Dic86—48no—
385Dic86—41no—
386Dic86—41no—
387C8×C43—22no—
388C8×C43—41no—
389C43⋊C8—41no—
390C43⋊C8—41no—
391#24429—431nomaximal, Sylow
392C22×C43—22no—
393C22×C43—22no—
394C22×C43—22no—
395C22×C43—22no—
396C22×C43—22no—
397C22×C43—22no—
398C22×C43#44814yescomplemented
399C22×C43C2×#12011yescharacteristic
400C22×C43D4211yescharacteristic
401C22×C43#54611yescharacteristic
402C22×C43C22×SD1611yescharacteristic
403C22×C43C2×#13711yescharacteristic
404C22×C43#57711yescharacteristic
405C22×C43#57811yescharacteristic
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—41no—
410C2×D43—41no—
411C2×D43—41no—
412C2×D43—41no—
413C2×D43—81no—
414C2×D43—81no—
415C2×D43—81no—
416C2×D43—81no—
417C2×D43—81no—
418C2×D43—81no—
419C2×D43—81no—
420C4×C43—24no—
421C4×C43—22no—
422C4×C43—42no—
423C4×C43—42no—
424C4×C43—81no—
425C4×C43C2×#12111yescharacteristic
426C4×C43#53411yescharacteristic
427C4×C43D4211yescharacteristic
428C4×C43#54611yescharacteristic
429Dic43—22no—
430Dic43—42no—
431Dic43—41no—
432Dic43—41no—
433Dic43—42no—
434Dic43—81no—
435C2×D4×Q8—431no—
436C2×#465—431no—
437C2×#448—431no—
438C2×#448—431no—
439C22×#103D4311yescharacteristic, complemented
440#2416—431no—
441#2043—431no—
442#2035—431no—
443#2013—431no—
444#2000—431no—
445#1880—431no—
446#1872—431no—
447#1869—431no—
448#1865—431no—
449#1787—431no—
450C2×C43—24no—
451C2×C43#241011yescharacteristic
452C2×C43C2×#44811yescharacteristic
453C2×C43#301311yescharacteristic
454C2×C43#327011yescharacteristic
455C2×C43D4×SD1611yescharacteristic
456C2×C43#329811yescharacteristic
457C2×C43#332011yescharacteristic
458D43—42no—
459D43—161no—
460C23×Q8—431no—
461C23×Q8C2×D4311yescharacteristic
462C22×SD16—431no—
463C22×SD16—431no—
464C22×SD16—431no—
465C23×C8C2×D4311yescharacteristic
466D4×Q8—864no—
467D4×Q8—864no—
468C2×C4⋊Q8—431no—
469C2×C4⋊Q8—861no—
470C2×C22⋊Q8—431no—
471C2×C22⋊Q8—431no—
472C2×C22⋊Q8—861no—
473C2×C22⋊Q8—861no—
474C2×#121—431no—
475C2×#121—431no—
476C2×#121—861no—
477C2×C4×Q8—431no—
478C2×C4×D4—431no—
479C2×C4×D4—861no—
480C22×C4⋊C4C2×D4311yescharacteristic
481#465—864no—
482#448—864no—
483#448—864no—
484C2×#106—431no—
485C2×#103—24no—
486C2×#103—431no—
487C2×#103—431no—
488C2×#103—431no—
489C2×#103—431no—
490C2×#103—431no—
491C2×#103C2×D4311yescharacteristic
492C2×#103C2×D4311yescharacteristic
493C2×#103C2×D4311yescharacteristic
494C2×#103C2×D4311yescharacteristic
495C2×#102—431no—
496C2×C22⋊C8—431no—
497C2×C22⋊C8—431no—
498C2×C22⋊C8—431no—
499#396—861no—
500#394—861no—
501#390—431no—
502#389—431no—
503#386—861no—
504#380—431no—
505#340—431no—
506#340—431no—
507#336—431no—
508#336—431no—
509C43#2442911yescharacteristic, complemented, Sylow
510C22×Q8—21no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—22no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—431no—
517C22×Q8—861no—
518C22×Q8—862no—
519C22×Q8—862no—
520C22×Q8—862no—
521C22×Q8—862no—
522C22×Q8—1721no—
523C22×Q8—1721no—
524C22×Q8D17214yescomplemented
525C22×Q8C22×D4311yescharacteristic
526C22×Q8C22×D4311yescharacteristic
527C22×D4—431no—
528C22×D4—431no—
529C22×D4—861no—
530C22×D4—861no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—431no—
534C23×C4—861no—
535C23×C4C22×D4311yescharacteristic
536C2×SD16—862no—
537C2×SD16—862no—
538C2×SD16—862no—
539C2×SD16—862no—
540C2×SD16—862no—
541C2×SD16—862no—
542C2×SD16—1721no—
543C2×SD16—1721no—
544C2×SD16—1721no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8—431no—
549C22×C8—431no—
550C22×C8C22×D4311yescharacteristic
551C22×C8C22×D4311yescharacteristic
552C4⋊Q8—862no—
553C4⋊Q8—868no—
554C4⋊Q8—862no—
555C22⋊Q8—434no—
556C22⋊Q8—862no—
557C22⋊Q8—868no—
558C22⋊Q8—868no—
559C22⋊Q8—862no—
560C22⋊Q8—862no—
561#121—862no—
562#121—862no—
563#121—862no—
564#121—1721no—
565#121—1724no—
566C4×Q8—862no—
567C4×Q8—862no—
568C4×D4—868no—
569C4×D4—862no—
570C4×D4—862no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—431no—
575C2×C4⋊C4—431no—
576C2×C4⋊C4—431no—
577C2×C4⋊C4—861no—
578C2×C4⋊C4—861no—
579C2×C4⋊C4—861no—
580C2×C4⋊C4—861no—
581C2×C4⋊C4—861no—
582C2×C4⋊C4—861no—
583C2×C4⋊C4C22×D4311yescharacteristic
584C2×C4⋊C4C22×D4311yescharacteristic
585C2×C22⋊C4—431no—
586C2×C22⋊C4—431no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C22⋊C4—861no—
592C2×C22⋊C4—861no—
593C2×C22⋊C4—861no—
594C2×C42—431no—
595C2×C42—861no—
596#106—862no—
597#103—22no—
598#103—22no—
599#103—22no—
600#103—862no—
601#103—862no—
602#103—862no—
603#103—862no—
604#103—1721no—
605#103C22⋊D4314yescomplemented
606#102—862no—
607C22⋊C8—862no—
608C22⋊C8—862no—
609C22⋊C8—1721no—
610#95—861no—
611#95—861no—
612C24—431no—
613C24—861no—
614C24D4×D4311yescharacteristic
615C2×Q8—24no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—28no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—42no—
626C2×Q8—42no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—432no—
631C2×Q8—864no—
632C2×Q8—861no—
633C2×Q8—861no—
634C2×Q8—861no—
635C2×Q8—861no—
636C2×Q8—861no—
637C2×Q8—1722no—
638C2×Q8—1722no—
639C2×Q8—1724no—
640C2×Q8—1724no—
641C2×Q8—1724no—
642C2×Q8—1724no—
643C2×Q8C2×D17212yes—
644C2×Q8C2×D17212yes—
645C2×Q8#1062189812yes—
646C2×Q8C2×C22⋊D4312yes—
647C2×D4—434no—
648C2×D4—862no—
649C2×D4—862no—
650C2×D4—861no—
651C2×D4—861no—
652C2×D4—861no—
653C2×D4—861no—
654C2×D4—861no—
655C2×D4—861no—
656C2×D4—3441no—
657C2×D4—1722no—
658C2×D4—1722no—
659C2×D4—1722no—
660C2×D4—1722no—
661C2×D4—1722no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—24no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—431no—
677C22×C4—431no—
678C22×C4—431no—
679C22×C4—864no—
680C22×C4—861no—
681C22×C4—861no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—1722no—
690C22×C4—1722no—
691C22×C4C2×D17212yes—
692C22×C4D4×D4311yescharacteristic
693C22×C4D4×D4312yes—
694C22×C4C23×D4311yescharacteristic
695SD16—1724no—
696SD16—1724no—
697SD16—1724no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—44no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—861no—
710C2×C8C2×C22⋊D4312yes—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4—432no—
716C4⋊C4—864no—
717C4⋊C4—864no—
718C4⋊C4—864no—
719C4⋊C4—864no—
720C4⋊C4—862no—
721C4⋊C4—864no—
722C4⋊C4—861no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4—1722no—
726C4⋊C4C2×C22⋊D4312yes—
727C22⋊C4—864no—
728C22⋊C4—862no—
729C22⋊C4—864no—
730C22⋊C4—862no—
731C22⋊C4—3441no—
732C22⋊C4—1722no—
733C22⋊C4—1722no—
734C22⋊C4—1722no—
735C22⋊C4—1722no—
736C42—864no—
737C42—861no—
738C42—861no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—432no—
744C23—861no—
745C23—861no—
746C23—861no—
747C23—861no—
748C23—861no—
749C23—861no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23#1306329512yes—
758C23SD16×D4312yes—
759C23#1306335712yes—
760C23C2×D4×D4311yescharacteristic
761Q8—22no—
762Q8—22no—
763Q8—22no—
764Q8—22no—
765Q8—22no—
766Q8—48no—
767Q8—41no—
768Q8—41no—
769Q8—862no—
770Q8—862no—
771Q8—1728no—
772Q8—1721no—
773Q8—1721no—
774Q8#1306329914yescomplemented
775D4—868no—
776D4—3444no—
777D4—3444no—
778D4—1721no—
779D4—1721no—
780D4—1721no—
781D4—1721no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—48no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—84no—
802C2×C4—432no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—862no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—862no—
809C2×C4—861no—
810C2×C4—861no—
811C2×C4—861no—
812C2×C4—861no—
813C2×C4—1728no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4—1721no—
820C2×C4—1721no—
821C2×C4—1721no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4—1721no—
825C2×C4#1306329512yes—
826C2×C4C2×D4×D4311yescharacteristic
827C2×C4C22×C22⋊D4311yescharacteristic
828C2×C4C22×D17211yescharacteristic
829C2×C4C2×#1062189811yescharacteristic
830C2×C4#1306337011yescharacteristic
831C2×C4#1306337011yescharacteristic
832C8—22no—
833C8—41no—
834C8—1721no—
835C8—1721no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—862no—
843C22—862no—
844C22—862no—
845C22—3441no—
846C22—3441no—
847C22—3441no—
848C22—3441no—
849C22—3441no—
850C22—3441no—
851C22—3441no—
852C22—1721no—
853C22—1721no—
854C22—1721no—
855C22—1721no—
856C22#1458303914yescomplemented
857C22C2×#1306329511yescharacteristic
858C22D4×C22⋊D4311yescharacteristic
859C22#1458353911yescharacteristic
860C22C2×SD16×D4311yescharacteristic
861C22C2×#1306335711yescharacteristic
862C22#1458370511yescharacteristic
863C22#1458371211yescharacteristic
864C4—22no—
865C4—24no—
866C4—42no—
867C4—42no—
868C4—81no—
869C4—862no—
870C4—3441no—
871C4—1721no—
872C4—1722no—
873C4—1721no—
874C4—1722no—
875C4C2×#1306329911yescharacteristic
876C4#1458346111yescharacteristic
877C4D4×C22⋊D4311yescharacteristic
878C4#1458353911yescharacteristic
879C2—24no—
880C2—1722no—
881C2—6881no—
882C2#1913796311yescharacteristic
883C2C2×#1458303911yescharacteristic
884C2#1914391511yescharacteristic
885C2#1914616511yescharacteristic
886C2SD16×C22⋊D4311yescharacteristic
887C2#1914645611yescharacteristic
888C2#1914676211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×#103×C43C2
socleC23×C43C22×D4
prime radical#19138029C2
hypercenterC22×#103D43
hypocenterC43#24429
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C22⋊D43C2semidirect
2. C2×#14583128C2semidirect
3. C2×#14583039C2semidirect
4. C2×#14583038C2semidirect
6. #19135840C2semidirect
7. #19135790C2semidirect
8. #19135679C2semidirect
9. #19135597C2semidirect
10. #19134948C2semidirect
11. #19134902C2semidirect
12. #19134887C2semidirect
13. #19134865C2semidirect
14. #19134528C2semidirect
15. C22×#103×C43C2semidirect
95. #13063304D4semidirect
147. C22×Q8×C43D4semidirect
166. #103×C43D4semidirect
212. C2×C22⋊D43SD16semidirect
324. Q8×C43#121semidirect
398. C22×C43#448semidirect
439. C22×#103D43semidirect
509. C43#24429semidirect
524. C22×Q8D172semidirect
605. #103C22⋊D43semidirect
774. Q8#13063299semidirect
856. C22#14583039semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D432
C2×#145831282
C2×#145830392
C2×#145830382
#191380292
#191358402
#191357902
#191356792
#191355972
#191349482
#191349022
#191348872
#191348652
#191345282
C22×#103×C432
#2442943