Finite Group Databasebeta

← C2×#19134555 #25095888

Subgroups — C2×#19134555 #25095888

Order 11008.

3682 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063372C211yesmaximal, characteristic
2C22×#13063253C211yesmaximal, characteristic, complemented
3C2×#14582901C211yesmaximal, characteristic, complemented
4C2×#14582900C211yesmaximal, characteristic, complemented
5C22×#13063243C211yesmaximal, characteristic, complemented
6C2×#14582805C211yesmaximal, characteristic, complemented
7#19134555C218yesmaximal, direct product factor
8C22×#104×C43C211yesmaximal, characteristic, complemented
9C2×#13063372—24no—
10C2×#13063372—22no—
11C2×#13063372—22no—
12C2×#13063372—24no—
13C2×#13063372—22no—
14C2×#13063372—24no—
15C2×#13063372C418yescomplemented
16C2×#13063372C2214yes—
17C22×#10621898—21no—
18C22×#10621898C2211yescharacteristic
19C22×#10621900—22no—
20C22×#10621900—21no—
21C23×Dic86—21no—
22C23×Dic86C2211yescharacteristic
23C22×Q8×D43—21no—
24C22×#10621877C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C2×#13063253—24no—
27C2×#13063253C2214yescomplemented
28#14582901—22no—
29#14582901C2214yescomplemented
30#14582900—22no—
31#14582900C2214yescomplemented
32C2×#13063250—21no—
33C2×#13063249—21no—
34C2×#13063247—21no—
35C2×#13063246—21no—
36C2×#13063243—24no—
37C2×#13063243C2214yescomplemented
38#14582805—22no—
39#14582805C2214yescomplemented
40C2×C43⋊#95—22no—
41C22×#41×C43C2211yescharacteristic
42C22×M16×C43C2211yescharacteristic
43C22×C42×C43C2211yescharacteristic
44C2×#104×C43—24no—
45C2×#104×C43C2214yescomplemented
46#13063372—216no—
47#13063372—216no—
48#13063372—216no—
49#13063372—216no—
50#13063372—28no—
51#13063372—216no—
52#13063372—28no—
53#13063372—216no—
54#13063372—28no—
55#13063372C2×C4116yescomplemented
56C2×#10621898—28no—
57C2×#10621898—24no—
58C2×#10621898—21no—
59C2×#10621898—21no—
60C2×#10621898—22no—
61C2×#10621898—22no—
62C2×#10621898—28no—
63C2×#10621898—24no—
64C2×#10621898C2×C414yes—
65C2×#10621898D414yes—
66C2×#10621898D412yes—
67C2×#10621898C2312yes—
68C2×#10621900—216no—
69C2×#10621900—28no—
70C2×#10621900—28no—
71C2×#10621900—24no—
72C2×#10621900—28no—
73C2×#10621900—24no—
74C2×#10621900—216no—
75C2×#10621900—28no—
76C22×Dic86—22no—
77C22×Dic86—28no—
78C22×Dic86—24no—
79C22×Dic86—21no—
80C22×Dic86—21no—
81C22×Dic86—21no—
82C22×Dic86—22no—
83C22×Dic86—21no—
84C22×Dic86—22no—
85C22×Dic86—28no—
86C22×Dic86—24no—
87C22×Dic86C2×C414yes—
88C22×Dic86D412yes—
89C22×Dic86D414yes—
90C22×Dic86D411yescharacteristic
91C22×Dic86C2312yes—
92C2×Q8×D43—24no—
93C2×Q8×D43—28no—
94C2×Q8×D43—28no—
95C2×Q8×D43—24no—
96C22×D172D411yescharacteristic
97C22×C22⋊D43—22no—
98C22×C22⋊D43—21no—
99C23×Dic43—22no—
100C23×Dic43—21no—
101C23×Dic43D412yes—
102C22×C4×D43—22no—
103C22×C4×D43—21no—
104C2×#10621877—21no—
105C2×#10621877—22no—
106C2×#10621877—22no—
107C2×#10621877C2312yes—
108C22×C43⋊C8—21no—
109C2×C4⋊Dic43—21no—
110C2×C4⋊Dic43—21no—
111C2×C4⋊Dic43—21no—
112C2×C4⋊Dic43—21no—
113C2×C4⋊Dic43—21no—
114C2×C4⋊Dic43C2312yes—
115#13063253—28no—
116#13063250—24no—
117#13063249—24no—
118#13063247—24no—
119#13063246—24no—
120#13063243—28no—
121C43⋊#95—28no—
122C2×#41×C43—22no—
123C2×#41×C43—22no—
124C2×#41×C43—21no—
125C2×#41×C43—21no—
126C2×#41×C43C2×C414yes—
127C2×#41×C43D412yes—
128C2×#41×C43D414yes—
129C2×#41×C43C2312yes—
130C22×Q8×C43D411yescharacteristic
131C22×D4×C43—21no—
132C22×D4×C43D411yescharacteristic
133C23×C4×C43—21no—
134C23×C4×C43—21no—
135C23×C4×C43C2311yescharacteristic
136C2×M16×C43—21no—
137C2×M16×C43—22no—
138C2×M16×C43—22no—
139C2×M16×C43C2312yes—
140C22×C8×C43—21no—
141C2×C42×C43—22no—
142C2×C42×C43—22no—
143C2×C42×C43—21no—
144C2×C42×C43C2312yes—
145#104×C43—28no—
146C24×C43—21no—
147C24×C43C2×D411yescharacteristic
148C23×D43—21no—
149#41×C43—24no—
150#41×C43—24no—
151#41×C43—24no—
152#41×C43—24no—
153#41×C43—24no—
154#41×C43—22no—
155#41×C43—22no—
156#41×C43C22⋊C418yes—
157#41×C43C22×C414yes—
158#41×C43C2×D414yes—
159C2×Q8×C43—21no—
160C2×Q8×C43—22no—
161C2×Q8×C43C22⋊C414yes—
162C2×Q8×C43C2×D412yes—
163C2×D4×C43—21no—
164C2×D4×C43—22no—
165C2×D4×C43—24no—
166C2×D4×C43—22no—
167C2×D4×C43—24no—
168C2×D4×C43—22no—
169C2×D4×C43C22⋊C414yes—
170C2×D4×C43C2×D412yes—
171C22×C4×C43—24no—
172C22×C4×C43—22no—
173C22×C4×C43—24no—
174C22×C4×C43—22no—
175C22×C4×C43—24no—
176C22×C4×C43—21no—
177C22×C4×C43—22no—
178C22×C4×C43—42no—
179C22×C4×C43—42no—
180C22×C4×C43C22×C412yes—
181C22×C4×C43C2×D412yes—
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D412yes—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D412yes—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—28no—
191C2×C22⋊D43—216no—
192C2×C22⋊D43—24no—
193C2×C22⋊D43—22no—
194C2×C22⋊D43—24no—
195C2×C22⋊D43—22no—
196C22×Dic43—28no—
197C22×Dic43—216no—
198C22×Dic43—21no—
199C22×Dic43—22no—
200C22×Dic43—24no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—44no—
204C22×Dic43—41no—
205C22×Dic43—41no—
206C22×Dic43C22⋊C418yes—
207C22×Dic43C2×D414yes—
208Q8×D43—216no—
209Q8×D43—232no—
210Q8×D43—216no—
211#10621900—232no—
212#10621900—264no—
213#10621900—216no—
214#10621900—232no—
215#10621900—216no—
216#10621900—232no—
217#10621898—216no—
218#10621898—232no—
219#10621898—24no—
220#10621898—24no—
221#10621898—24no—
222#10621898—24no—
223#10621898—24no—
224#10621898—22no—
225#10621898—22no—
226#10621898—216no—
227#10621898C22⋊C418yes—
228#10621898C22×C414yes—
229#10621898C2×D414yes—
230C2×D172—21no—
231C2×D172—22no—
232C2×D172C22⋊C414yes—
233C2×D172C2×D412yes—
234C2×C4×D43—28no—
235C2×C4×D43—216no—
236C2×C4×D43—24no—
237C2×C4×D43—22no—
238C2×C4×D43—24no—
239C2×C4×D43—22no—
240C2×Dic86—28no—
241C2×Dic86—216no—
242C2×Dic86—216no—
243C2×Dic86—232no—
244C2×Dic86—24no—
245C2×Dic86—24no—
246C2×Dic86—24no—
247C2×Dic86—24no—
248C2×Dic86—24no—
249C2×Dic86—22no—
250C2×Dic86—24no—
251C2×Dic86—22no—
252C2×Dic86—22no—
253C2×Dic86—21no—
254C2×Dic86—24no—
255C2×Dic86—24no—
256C2×Dic86—24no—
257C2×Dic86—22no—
258C2×Dic86—22no—
259C2×Dic86—22no—
260C2×Dic86—22no—
261C2×Dic86—216no—
262C2×Dic86C22⋊C418yes—
263C2×Dic86C22⋊C414yes—
264C2×Dic86C22×C414yes—
265C2×Dic86C2×D414yes—
266C2×Dic86C2×D412yes—
267M16×C43—22no—
268M16×C43—22no—
269M16×C43—42no—
270C2×C8×C43—22no—
271C2×C8×C43—42no—
272C42×C43—22no—
273C42×C43—22no—
274C42×C43—42no—
275C4⋊Dic43—22no—
276C4⋊Dic43—22no—
277C4⋊Dic43—41no—
278C4⋊Dic43—41no—
279#10621877—22no—
280#10621877—22no—
281#10621877—42no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—42no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—22no—
287C23×C43—24no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43C2×C22⋊C412yes—
291C23×C43#12012yes—
292C23×C43#12011yescharacteristic
293C23×C43#12011yescharacteristic
294C23×C43C22×D411yescharacteristic
295C22×D43—22no—
296C22×D43—24no—
297C22×D43—42no—
298C22×D43—42no—
299Q8×C43—22no—
300Q8×C43—24no—
301Q8×C43C2×C22⋊C414yes—
302D4×C43—24no—
303D4×C43—24no—
304D4×C43—28no—
305D4×C43—22no—
306D4×C43—24no—
307D4×C43C2×C22⋊C414yes—
308C2×C4×C43—22no—
309C2×C4×C43—24no—
310C2×C4×C43—24no—
311C2×C4×C43—24no—
312C2×C4×C43—28no—
313C2×C4×C43—24no—
314C2×C4×C43—48no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43C2×C22⋊C412yes—
318C2×C4×C43C2×C22⋊C412yes—
319C2×C4×C43C2×C22⋊C412yes—
320C2×C4×C43C2×C22⋊C412yes—
321C2×C4×C43C2×C22⋊C412yes—
322C2×C4×C43#12012yes—
323C2×C4×C43#12012yes—
324C2×C4×C43#12012yes—
325C2×C4×C43#12012yes—
326C2×C4×C43#12012yes—
327C2×C4×C43#12011yescharacteristic
328C2×C4×C43#12011yescharacteristic
329C2×C4×C43C23×C411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C22⋊D43—232no—
336C22⋊D43—24no—
337C22⋊D43—24no—
338C22⋊D43—28no—
339C2×Dic43—232no—
340C2×Dic43—24no—
341C2×Dic43—22no—
342C2×Dic43—24no—
343C2×Dic43—28no—
344C2×Dic43—24no—
345C2×Dic43—28no—
346C2×Dic43—44no—
347C2×Dic43—42no—
348C2×Dic43—82no—
349C2×Dic43—82no—
350C2×Dic43C2×C22⋊C418yes—
351D172—22no—
352D172—24no—
353D172C2×C22⋊C414yes—
354C4×D43—232no—
355C4×D43—24no—
356C4×D43—24no—
357C4×D43—28no—
358Dic86—232no—
359Dic86—24no—
360Dic86—24no—
361Dic86—24no—
362Dic86—22no—
363Dic86—24no—
364Dic86—28no—
365Dic86—24no—
366Dic86—28no—
367Dic86C2×C22⋊C414yes—
368C8×C43—42no—
369C43⋊C8—42no—
370C2×#1793—431nomaximal, Sylow
371C22×C43—24no—
372C22×C43—24no—
373C22×C43—21no—
374C22×C43—21no—
375C22×C43—21no—
376C22×C43—21no—
377C22×C43—24no—
378C22×C43—48no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43#37912yes—
382C22×C43#37912yes—
383C22×C43#45412yes—
384C22×C43#45612yes—
385C22×C43C22×C22⋊C411yescharacteristic
386C22×C43C2×#12011yescharacteristic
387C22×C43C2×#12011yescharacteristic
388C2×D43—24no—
389C2×D43—48no—
390C2×D43—42no—
391C2×D43—42no—
392C4×C43—24no—
393C4×C43—44no—
394C4×C43#37912yes—
395C4×C43#37912yes—
396C4×C43C22×C22⋊C411yescharacteristic
397C4×C43C22×C22⋊C411yescharacteristic
398C4×C43C2×#12011yescharacteristic
399C4×C43C2×#12011yescharacteristic
400Dic43—28no—
401Dic43—24no—
402Dic43—82no—
403C22×2−1+4—431no—
404C22×#104—431no—
405C22×#104D4311yescharacteristic, complemented
406C2×#417—431no—
407C2×#417—431no—
408C22×#101—431no—
409C2×#391—431no—
410#1793—438no—
411C2×C43—21no—
412C2×C43—21no—
413C2×C43—22no—
414C2×C43—44no—
415C2×C43#179314yescomplemented
416C2×C43C2×#37911yescharacteristic
417C2×C43C2×#45411yescharacteristic
418C2×C43C2×#45611yescharacteristic
419D43—44no—
420C2×2−1+4—434no—
421C2×2−1+4—438no—
422C2×2−1+4—862no—
423C2×2−1+4—864no—
424C2×2−1+4—862no—
425C2×2−1+4—864no—
426C2×2−1+4—862no—
427C2×2−1+4—864no—
428C22×#41—431no—
429C22×#41—861no—
430C22×#41—862no—
431C22×#41—861no—
432C22×#41C2×D4311yescharacteristic
433C23×Q8—431no—
434C23×Q8—861no—
435C23×Q8—861no—
436C22×M16—431no—
437C22×M16C2×D4311yescharacteristic
438C22×C4⋊C4—431no—
439C22×C42C2×D4311yescharacteristic
440C2×#104—24no—
441C2×#104—434no—
442C2×#104—864no—
443C2×#104C2×D4314yescomplemented
444#417—434no—
445#417—434no—
446#417—862no—
447#417—862no—
448C2×#103—861no—
449C2×#103—861no—
450C2×#102—861no—
451C2×#102—861no—
452C2×#101—434no—
453C2×#101—864no—
454#391—434no—
455#391—862no—
456C2×#95—862no—
457C43C2×#179311yescharacteristic, complemented, Sylow
4582−1+4—4316no—
4592−1+4—8616no—
4602−1+4—868no—
4612−1+4—8616no—
4622−1+4—868no—
4632−1+4—8616no—
4642−1+4—8616no—
4652−1+4—8616no—
4662−1+4—8616no—
4672−1+4—868no—
468C2×#41—22no—
469C2×#41—22no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—434no—
473C2×#41—432no—
474C2×#41—434no—
475C2×#41—432no—
476C2×#41—868no—
477C2×#41—864no—
478C2×#41—868no—
479C2×#41—864no—
480C2×#41—8616no—
481C2×#41—868no—
482C2×#41—8616no—
483C2×#41—868no—
484C2×#41—864no—
485C2×#41—868no—
486C2×#41—868no—
487C2×#41—864no—
488C2×#41—861no—
489C2×#41—861no—
490C2×#41—862no—
491C2×#41—862no—
492C2×#41C4×D4314yes—
493C2×#41D17212yes—
494C2×#41C22⋊D4314yes—
495C2×#41C22×D4312yes—
496C22×Q8—434no—
497C22×Q8—432no—
498C22×Q8—434no—
499C22×Q8—432no—
500C22×Q8—431no—
501C22×Q8—868no—
502C22×Q8—864no—
503C22×Q8—862no—
504C22×Q8—868no—
505C22×Q8—864no—
506C22×Q8—864no—
507C22×Q8—868no—
508C22×Q8—868no—
509C22×Q8—864no—
510C22×Q8—861no—
511C22×Q8—861no—
512C22×Q8—861no—
513C22×Q8—862no—
514C22×Q8—861no—
515C22×Q8—862no—
516C22×Q8D17211yescharacteristic
517C22×D4—21no—
518C22×D4—431no—
519C22×D4—862no—
520C22×D4—861no—
521C22×D4D17211yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—432no—
525C23×C4—862no—
526C23×C4—862no—
527C23×C4—861no—
528C23×C4—861no—
529C23×C4C22×D4311yescharacteristic
530C2×M16—21no—
531C2×M16—22no—
532C2×M16—22no—
533C2×M16—432no—
534C2×M16—861no—
535C2×M16—862no—
536C2×M16—862no—
537C2×M16C22×D4312yes—
538C22×C8—21no—
539C22×C8—861no—
540C2×C4⋊C4—432no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4—861no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—21no—
549C2×C42C22×D4312yes—
550#104—28no—
551#104—868no—
552#103—864no—
553#103—864no—
554#102—864no—
555#102—864no—
556#101—868no—
557#95—868no—
558C24—21no—
559C24—861no—
560C24D4×D4311yescharacteristic
561#41—24no—
562#41—24no—
563#41—24no—
564#41—24no—
565#41—24no—
566#41—22no—
567#41—22no—
568#41—438no—
569#41—434no—
570#41—434no—
571#41—8616no—
572#41—8616no—
573#41—8632no—
574#41—8632no—
575#41—8632no—
576#41—8664no—
577#41—8616no—
578#41—8632no—
579#41—8616no—
580#41—864no—
581#41—864no—
582#41—864no—
583#41—864no—
584#41—864no—
585#41—862no—
586#41—862no—
587#41(C2×D43)⋊C418yes—
588#41C2×C4×D4314yes—
589#41C2×C22⋊D4314yes—
590C2×Q8—21no—
591C2×Q8—22no—
592C2×Q8—438no—
593C2×Q8—434no—
594C2×Q8—434no—
595C2×Q8—434no—
596C2×Q8—432no—
597C2×Q8—8616no—
598C2×Q8—868no—
599C2×Q8—8616no—
600C2×Q8—8616no—
601C2×Q8—8632no—
602C2×Q8—8616no—
603C2×Q8—8632no—
604C2×Q8—8616no—
605C2×Q8—864no—
606C2×Q8—864no—
607C2×Q8—864no—
608C2×Q8—864no—
609C2×Q8—864no—
610C2×Q8—862no—
611C2×Q8—864no—
612C2×Q8—864no—
613C2×Q8—862no—
614C2×Q8—862no—
615C2×Q8—861no—
616C2×Q8—864no—
617C2×Q8—864no—
618C2×Q8—862no—
619C2×Q8—862no—
620C2×Q8—862no—
621C2×Q8—862no—
622C2×Q8(C2×D43)⋊C414yes—
623C2×Q8C2×D17212yes—
624C2×D4—24no—
625C2×D4—24no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—21no—
630C2×D4—434no—
631C2×D4—432no—
632C2×D4—868no—
633C2×D4—8616no—
634C2×D4—864no—
635C2×D4—864no—
636C2×D4—862no—
637C2×D4—862no—
638C2×D4—862no—
639C2×D4—861no—
640C2×D4(C2×D43)⋊C414yes—
641C2×D4C2×D17212yes—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—24no—
648C22×C4—22no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—438no—
652C22×C4—434no—
653C22×C4—868no—
654C22×C4—8616no—
655C22×C4—868no—
656C22×C4—8616no—
657C22×C4—864no—
658C22×C4—862no—
659C22×C4—862no—
660C22×C4—861no—
661C22×C4—864no—
662C22×C4—862no—
663C22×C4—864no—
664C22×C4—862no—
665C22×C4—862no—
666C22×C4—1724no—
667C22×C4—1721no—
668C22×C4—1721no—
669C22×C4C2×C4×D4312yes—
670C22×C4C2×D17211yescharacteristic
671C22×C4C2×D17211yescharacteristic
672C22×C4D4×D4311yescharacteristic
673C22×C4D4×D4311yescharacteristic
674C22×C4D4×D4311yescharacteristic
675C22×C4D4×D4312yes—
676C22×C4D4×D4312yes—
677C22×C4C2×C22⋊D4312yes—
678C22×C4C23×D4311yescharacteristic
679M16—22no—
680M16—22no—
681M16—42no—
682M16—862no—
683M16—862no—
684M16—1722no—
685C2×C8—22no—
686C2×C8—42no—
687C2×C8—862no—
688C2×C8—1722no—
689C4⋊C4—862no—
690C4⋊C4—862no—
691C4⋊C4—1721no—
692C4⋊C4—1721no—
693C42—22no—
694C42—22no—
695C42—42no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—24no—
700C23—42no—
701C23—42no—
702C23—862no—
703C23—864no—
704C23—1722no—
705C23—1722no—
706C23C22⋊C4×D4312yes—
707C23#1306329312yes—
708C23#1306329511yescharacteristic
709C23#1306329511yescharacteristic
710C23C2×D4×D4311yescharacteristic
711Q8—22no—
712Q8—24no—
713Q8—434no—
714Q8—8632no—
715Q8—864no—
716Q8—864no—
717Q8—864no—
718Q8—862no—
719Q8—864no—
720Q8—868no—
721Q8—868no—
722Q8—864no—
723Q8C2×(C2×D43)⋊C414yes—
724D4—24no—
725D4—24no—
726D4—28no—
727D4—22no—
728D4—24no—
729D4—434no—
730D4—8632no—
731D4—864no—
732D4—864no—
733D4—868no—
734D4—862no—
735D4—864no—
736D4C2×(C2×D43)⋊C414yes—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—24no—
743C2×C4—48no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—438no—
747C2×C4—8632no—
748C2×C4—8632no—
749C2×C4—864no—
750C2×C4—864no—
751C2×C4—862no—
752C2×C4—868no—
753C2×C4—868no—
754C2×C4—864no—
755C2×C4—864no—
756C2×C4—864no—
757C2×C4—868no—
758C2×C4—3442no—
759C2×C4—3442no—
760C2×C4—1724no—
761C2×C4—1722no—
762C2×C4C22⋊C4×D4312yes—
763C2×C4C22⋊C4×D4312yes—
764C2×C4C22⋊C4×D4312yes—
765C2×C4C2×(C2×D43)⋊C412yes—
766C2×C4C2×(C2×D43)⋊C412yes—
767C2×C4#1306329312yes—
768C2×C4#1306329312yes—
769C2×C4#1306329312yes—
770C2×C4#1306329512yes—
771C2×C4#1306329512yes—
772C2×C4#1306329511yescharacteristic
773C2×C4#1306329511yescharacteristic
774C2×C4C22×C4×D4311yescharacteristic
775C2×C4C2×D4×D4311yescharacteristic
776C2×C4C2×D4×D4311yescharacteristic
777C2×C4C2×D4×D4311yescharacteristic
778C2×C4C22×C22⋊D4311yescharacteristic
779C2×C4C22×D17211yescharacteristic
780C8—42no—
781C8—1722no—
782C22—21no—
783C22—21no—
784C22—24no—
785C22—24no—
786C22—21no—
787C22—21no—
788C22—24no—
789C22—42no—
790C22—48no—
791C22—42no—
792C22—864no—
793C22—1722no—
794C22—1728no—
795C22—1722no—
796C22#1458275412yes—
797C22#1458275412yes—
798C22#1458307312yes—
799C22#1458308312yes—
800C22C2×C22⋊C4×D4311yescharacteristic
801C22C2×#1306329311yescharacteristic
802C22C2×#1306329511yescharacteristic
803C4—24no—
804C4—44no—
805C4—868no—
806C4—864no—
807C4—3442no—
808C4#1458275412yes—
809C4#1458275412yes—
810C4C2×C22⋊C4×D4311yescharacteristic
811C4C22×(C2×D43)⋊C411yescharacteristic
812C4C2×#1306329311yescharacteristic
813C4C2×#1306329511yescharacteristic
814C2—21no—
815C2—21no—
816C2—22no—
817C2—44no—
818C2—1724no—
819C2#1913455514yesdirect product factor
820C2C2×#1458275411yescharacteristic
821C2C2×#1458307311yescharacteristic
822C2C2×#1458308311yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#104×C43C2
socleC23×C43#120
prime radicalC22×#13063372C2
cosocleC22×C4×C43C24
hypercenterC22×#104D43
hypocenterC43C2×#1793
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C22×#13063253C2semidirect
3. C2×#14582901C2semidirect
4. C2×#14582900C2semidirect
5. C22×#13063243C2semidirect
6. C2×#14582805C2semidirect
7. #19134555C2direct (N × H)
8. C22×#104×C43C2semidirect
15. C2×#13063372C4semidirect
27. C2×#13063253C22semidirect
29. #14582901C22semidirect
31. #14582900C22semidirect
37. C2×#13063243C22semidirect
39. #14582805C22semidirect
45. C2×#104×C43C22semidirect
55. #13063372C2×C4semidirect
405. C22×#104D43semidirect
415. C2×C43#1793semidirect
443. C2×#104C2×D43semidirect
457. C43C2×#1793semidirect
819. C2#19134555direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633722
C22×#130632532
C2×#145829012
C2×#145829002
C22×#130632432
C2×#145828052
#191345552
C22×#104×C432
C2×#179343