Finite Group Databasebeta

← C2×#19135066 #25098452

Subgroups — C2×#19135066 #25098452

Order 11008.

1654 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063355C211yesmaximal, characteristic
2C2×#14583666C211yesmaximal, characteristic
3C2×#14582907C211yesmaximal, characteristic, complemented
4C22×#13063243C211yesmaximal, characteristic, complemented
5#19135066C218yesmaximal, direct product factor
6C2×#14582669C211yesmaximal, characteristic, complemented
7C2×C43⋊#338C211yesmaximal, characteristic, complemented
8C2×C43×#421C211yesmaximal, characteristic
9C23×Dic86C2211yescharacteristic
10C2×#13063355—22no—
11C2×#13063355—22no—
12C2×#13063355—22no—
13C2×#13063355—22no—
14C2×#13063355C414yescomplemented
15C2×#13063355C2214yes—
16C22×#10621885C412yescomplemented
17C22×#10621883C412yescomplemented
18#14583666—22no—
19#14583666—22no—
20#14583666—22no—
21#14583666C2214yes—
22C2×#13063332—22no—
23C2×#13063332—22no—
24C22×#10621877—22no—
25C22×#10621877C2211yescharacteristic
26C22×#10621877C2211yescharacteristic
27C22×#10621877C2211yescharacteristic
28#14582907—22no—
29#14582907C2214yescomplemented
30C2×#13063248—22no—
31C2×#13063243—22no—
32C2×#13063243—22no—
33C2×#13063243C2214yescomplemented
34#14582669C2214yescomplemented
35C43⋊#338C2214yescomplemented
36C22×#41×C43C2211yescharacteristic
37C22×M16×C43C2211yescharacteristic
38C2×#117×C43C2211yescharacteristic
39C43×#421—22no—
40C43×#421C2214yes—
41C2×#104×C43—22no—
42C22×Dic86—21no—
43C22×Dic86—21no—
44C22×Dic86—21no—
45C22×Dic86—21no—
46C22×Dic86—21no—
47C22×Dic86—21no—
48C22×Dic86—21no—
49C22×Dic86—21no—
50C22×Dic86—21no—
51C22×Dic86—21no—
52C22×Dic86—21no—
53C22×Dic86C2×C412yes—
54C22×Dic86C2×C412yes—
55C22×Dic86C2312yes—
56C23×Dic43—21no—
57#13063355—28no—
58#13063355—28no—
59#13063355—28no—
60#13063355—28no—
61C2×#10621885—24no—
62C2×#10621885—24no—
63C2×#10621885C2×C418yescomplemented
64C2×#10621883—24no—
65C2×#10621883—24no—
66C2×#10621883C2×C418yescomplemented
67#13063332—28no—
68#13063332—28no—
69#13063332—28no—
70#13063332—28no—
71C2×#10621877—24no—
72C2×#10621877—28no—
73C2×#10621877—21no—
74C2×#10621877—21no—
75C2×#10621877—21no—
76C2×#10621877—21no—
77C2×#10621877—21no—
78C2×#10621877—21no—
79C2×#10621877—21no—
80C2×#10621877—21no—
81C2×#10621877—21no—
82C2×#10621877—21no—
83C2×#10621877—21no—
84C2×#10621877—28no—
85C2×#10621877C2×C412yes—
86C2×#10621877D412yes—
87C2×#10621877D412yes—
88C2×#10621877D412yes—
89C2×#10621877C2312yes—
90C2×#10621877C2312yes—
91C2×#10621877C2312yes—
92C22×C43⋊C8—24no—
93C22×C43⋊C8—21no—
94C22×C43⋊C8C2×C412yes—
95C22×C43⋊C8D412yes—
96#13063248—28no—
97#13063243—28no—
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×C43C2×C412yes—
105C2×#41×C43D412yes—
106C2×#41×C43D412yes—
107C2×#41×C43D412yes—
108C2×#41×C43D412yes—
109C2×#41×C43C2312yes—
110C22×Q8×C43C2×C411yescharacteristic
111C22×D4×C43—21no—
112C22×D4×C43C2×C411yescharacteristic
113C23×C4×C43—21no—
114C23×C4×C43C2311yescharacteristic
115C2×M16×C43—21no—
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43—21no—
120C2×M16×C43C2312yes—
121C22×C8×C43—21no—
122#117×C43—21no—
123#117×C43—21no—
124#117×C43—21no—
125#117×C43C2312yes—
126C2×C4⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C42×C43—21no—
129#104×C43—28no—
130C24×C43—21no—
131C24×C43#4111yescharacteristic
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—22no—
141#41×C43—22no—
142#41×C43—22no—
143#41×C43—22no—
144#41×C43C22⋊C414yes—
145#41×C43C22⋊C414yes—
146#41×C43C2×D414yes—
147#41×C43C2×D414yes—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43C22⋊C412yes—
152C2×Q8×C43C22⋊C412yes—
153C2×Q8×C43C22×C412yes—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
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×C43C22⋊C412yes—
164C2×D4×C43C22⋊C412yes—
165C2×D4×C43C22×C412yes—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—21no—
173C22×C4×C43—41no—
174C22×C4×C43C22×C411yescharacteristic
175C22×C4×C43C22×C411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
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×C43#4111yescharacteristic
185C22×C4×C43#4111yescharacteristic
186C22×C4×C43#4111yescharacteristic
187C22×C4×C43C2411yescharacteristic
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—41no—
192C22×Dic43—41no—
193C22×Dic43—41no—
194C22×Dic43—41no—
195C2×Dic86—22no—
196C2×Dic86—22no—
197C2×Dic86—22no—
198C2×Dic86—22no—
199C2×Dic86—22no—
200C2×Dic86—22no—
201C2×Dic86—22no—
202C2×Dic86—22no—
203C2×Dic86—22no—
204C2×Dic86—22no—
205C2×Dic86—22no—
206C2×Dic86—22no—
207C2×Dic86—22no—
208C2×Dic86—22no—
209C2×Dic86—22no—
210C2×Dic86—41no—
211C2×Dic86—41no—
212C2×Dic86—41no—
213C2×Dic86—41no—
214C2×Dic86—41no—
215C2×Dic86—41no—
216C2×Dic86—41no—
217C2×Dic86—41no—
218C2×Dic86—41no—
219C2×Dic86—41no—
220C2×Dic86—41no—
221C2×Dic86—41no—
222C2×Dic86C22×C414yes—
223M16×C43—22no—
224M16×C43—22no—
225M16×C43—41no—
226M16×C43—41no—
227C2×C8×C43—22no—
228C2×C8×C43—41no—
229C2×C8×C43—41no—
230C4⋊C4×C43—22no—
231C4⋊C4×C43—41no—
232C22⋊C4×C43—22no—
233C22⋊C4×C43—41no—
234C42×C43—22no—
235C42×C43—41no—
236#10621885—216no—
237#10621883—216no—
238#10621877—216no—
239#10621877—22no—
240#10621877—22no—
241#10621877—22no—
242#10621877—22no—
243#10621877—22no—
244#10621877—22no—
245#10621877—22no—
246#10621877—22no—
247#10621877—22no—
248#10621877—22no—
249#10621877—22no—
250#10621877C2×D414yes—
251C2×C43⋊C8—216no—
252C2×C43⋊C8—22no—
253C2×C43⋊C8—22no—
254C2×C43⋊C8—22no—
255C2×C43⋊C8—22no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8—22no—
259C2×C43⋊C8C22×C414yes—
260C2×C43⋊C8C2×D414yes—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43—22no—
264C23×C43—42no—
265C23×C43—82no—
266C23×C43C4×D411yescharacteristic
267C23×C43C4×D411yescharacteristic
268C23×C43#12111yescharacteristic
269C23×C43#12111yescharacteristic
270C23×C43#12311yescharacteristic
271C23×C43#12311yescharacteristic
272C23×C43C2×#4111yescharacteristic
273Q8×C43—22no—
274Q8×C43—22no—
275Q8×C43—22no—
276Q8×C43C2×C22⋊C414yes—
277D4×C43—24no—
278D4×C43—24no—
279D4×C43—24no—
280D4×C43—24no—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—22no—
284D4×C43C2×C22⋊C414yes—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—24no—
289C2×C4×C43—24no—
290C2×C4×C43—24no—
291C2×C4×C43—24no—
292C2×C4×C43—42no—
293C2×C4×C43—82no—
294C2×C4×C43C2×C22⋊C411yescharacteristic
295C2×C4×C43C2×C22⋊C411yescharacteristic
296C2×C4×C43C2×C22⋊C411yescharacteristic
297C2×C4×C43C2×C22⋊C411yescharacteristic
298C2×C4×C43C4×D411yescharacteristic
299C2×C4×C43C4×D411yescharacteristic
300C2×C4×C43C4×D411yescharacteristic
301C2×C4×C43C4×D411yescharacteristic
302C2×C4×C43C4×D411yescharacteristic
303C2×C4×C43C4×D411yescharacteristic
304C2×C4×C43#12011yescharacteristic
305C2×C4×C43#12011yescharacteristic
306C2×C4×C43#12011yescharacteristic
307C2×C4×C43#12011yescharacteristic
308C2×C4×C43#12111yescharacteristic
309C2×C4×C43#12111yescharacteristic
310C2×C4×C43#12111yescharacteristic
311C2×C4×C43#12111yescharacteristic
312C2×C4×C43#12111yescharacteristic
313C2×C4×C43#12111yescharacteristic
314C2×C4×C43#12311yescharacteristic
315C2×C4×C43#12311yescharacteristic
316C2×C4×C43C23×C411yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C2×Dic43—24no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329Dic86—24no—
330Dic86—24no—
331Dic86—42no—
332Dic86—42no—
333Dic86—42no—
334Dic86—42no—
335Dic86—42no—
336Dic86—42no—
337C8×C43—42no—
338C43⋊C8—24no—
339C43⋊C8—24no—
340C43⋊C8—24no—
341C2×#1902—431nomaximal, Sylow
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—24no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—44no—
351C22×C43—82no—
352C22×C43—82no—
353C22×C43#38611yescharacteristic
354C22×C43#38611yescharacteristic
355C22×C43#38611yescharacteristic
356C22×C43#38611yescharacteristic
357C22×C43C2×C4×D411yescharacteristic
358C22×C43C2×#12111yescharacteristic
359C22×C43C2×#12311yescharacteristic
360C4×C43—24no—
361C4×C43—82no—
362C4×C43#38611yescharacteristic
363C4×C43#38611yescharacteristic
364C4×C43#38611yescharacteristic
365C4×C43#38611yescharacteristic
366C4×C43C22×C22⋊C411yescharacteristic
367C4×C43C2×C4×D411yescharacteristic
368C4×C43C2×#12011yescharacteristic
369C4×C43C2×#12111yescharacteristic
370Dic43—44no—
371C22×#137—431no—
372C2×#568—431no—
373C2×#421D4311yescharacteristic
374C2×#419—431no—
375C22×#101—431no—
376#1902—438no—
377C2×#344—431no—
378C2×#338—431no—
379C2×C43—21no—
380C2×C43—21no—
381C2×C43—21no—
382C2×C43—21no—
383C2×C43—21no—
384C2×C43—21no—
385C2×C43—44no—
386C2×C43#190212yescomplemented
387C2×C43C2×#38611yescharacteristic
388C22×#41C2×D4311yescharacteristic
389C23×Q8—431no—
390C2×#137—434no—
391C2×#137—434no—
392C2×#137—862no—
393C2×#137—862no—
394C2×#137—862no—
395C2×#137—862no—
396C22×Q16—432no—
397C22×SD16—432no—
398#568—434no—
399#568—862no—
400#568—862no—
401#568—862no—
402C2×#131—862no—
403C2×#131—862no—
404C22×M16—431no—
405C22×M16—431no—
406C22×M16—431no—
407C22×M16—862no—
408C22×M16C2×D4311yescharacteristic
409C2×#117C2×D4311yescharacteristic
410#421—22no—
411#421C2×D4314yes—
412C2×#104—22no—
413#419—434no—
414#419—862no—
415C2×#103—862no—
416C2×#101—434no—
417C2×#101—862no—
418C2×#101—862no—
419#344—434no—
420#338—434no—
421C43C2×#190211yescharacteristic, complemented, Sylow
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41C4×D4312yes—
429C2×#41D17212yes—
430C2×#41D17212yes—
431C2×#41C22⋊D4312yes—
432C2×#41C22⋊D4312yes—
433C2×#41C22×D4312yes—
434C22×Q8—432no—
435C22×Q8—432no—
436C22×Q8—432no—
437C22×Q8—861no—
438C22×Q8—861no—
439C22×Q8—861no—
440C22×Q8—861no—
441C22×Q8—861no—
442C22×Q8—861no—
443C22×Q8—861no—
444C22×Q8—861no—
445C22×Q8—861no—
446C22×Q8—861no—
447C22×Q8—861no—
448C22×Q8C4×D4311yescharacteristic
449C22×D4—21no—
450C22×D4C4×D4311yescharacteristic
451C23×C4—21no—
452C23×C4—861no—
453C23×C4C22×D4311yescharacteristic
454#137—868no—
455#137—868no—
456#137—868no—
457#137—868no—
458C2×Q16—438no—
459C2×Q16—864no—
460C2×Q16—864no—
461C2×SD16—438no—
462C2×SD16—864no—
463C2×SD16—864no—
464#131—868no—
465#131—868no—
466#131—868no—
467#131—868no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—432no—
474C2×M16—432no—
475C2×M16—432no—
476C2×M16—432no—
477C2×M16—432no—
478C2×M16—432no—
479C2×M16—432no—
480C2×M16—868no—
481C2×M16—864no—
482C2×M16—868no—
483C2×M16—861no—
484C2×M16—861no—
485C2×M16—861no—
486C2×M16—861no—
487C2×M16—861no—
488C2×M16—861no—
489C2×M16—861no—
490C2×M16—861no—
491C2×M16—861no—
492C2×M16—861no—
493C2×M16—861no—
494C2×M16C22×D4312yes—
495C22×C8—21no—
496C22×C8—432no—
497C22×C8—432no—
498C22×C8—864no—
499C22×C8—861no—
500#117—21no—
501#117—21no—
502#117—21no—
503#117C22×D4312yes—
504C2×C4⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C42—21no—
507#104—28no—
508#103—868no—
509#101—868no—
510C24—21no—
511C24#1062190011yescharacteristic
512#41—22no—
513#41—22no—
514#41—22no—
515#41—22no—
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41(C2×D43)⋊C414yes—
525#41(C2×D43)⋊C414yes—
526#41C2×D17214yes—
527#41C2×C22⋊D4314yes—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—434no—
532C2×Q8—862no—
533C2×Q8—862no—
534C2×Q8—862no—
535C2×Q8—862no—
536C2×Q8—862no—
537C2×Q8—862no—
538C2×Q8—862no—
539C2×Q8—862no—
540C2×Q8—862no—
541C2×Q8—862no—
542C2×Q8—862no—
543C2×Q8—862no—
544C2×Q8—862no—
545C2×Q8—862no—
546C2×Q8—862no—
547C2×Q8—1721no—
548C2×Q8—1721no—
549C2×Q8—1721no—
550C2×Q8—1721no—
551C2×Q8—1721no—
552C2×Q8—1721no—
553C2×Q8—1721no—
554C2×Q8—1721no—
555C2×Q8—1721no—
556C2×Q8—1721no—
557C2×Q8—1721no—
558C2×Q8—1721no—
559C2×Q8(C2×D43)⋊C412yes—
560C2×Q8(C2×D43)⋊C412yes—
561C2×Q8C2×C4×D4312yes—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4(C2×D43)⋊C412yes—
572C2×D4(C2×D43)⋊C412yes—
573C2×D4C2×C4×D4312yes—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—41no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—1721no—
586C22×C4—1721no—
587C22×C4—1721no—
588C22×C4—1721no—
589C22×C4C2×C4×D4311yescharacteristic
590C22×C4C2×C4×D4311yescharacteristic
591C22×C4C2×D17211yescharacteristic
592C22×C4C2×D17211yescharacteristic
593C22×C4D4×D4311yescharacteristic
594C22×C4D4×D4311yescharacteristic
595C22×C4D4×D4311yescharacteristic
596C22×C4D4×D4311yescharacteristic
597C22×C4#1062190011yescharacteristic
598C22×C4#1062190011yescharacteristic
599C22×C4#1062190011yescharacteristic
600C22×C4C2×C22⋊D4311yescharacteristic
601C22×C4C2×C22⋊D4311yescharacteristic
602C22×C4C23×D4311yescharacteristic
603Q16—8616no—
604SD16—8616no—
605M16—22no—
606M16—22no—
607M16—41no—
608M16—41no—
609M16—434no—
610M16—8616no—
611M16—862no—
612M16—862no—
613M16—862no—
614M16—862no—
615M16—862no—
616M16—862no—
617M16—862no—
618M16—862no—
619M16—862no—
620M16—862no—
621M16—862no—
622C2×C8—22no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—434no—
626C2×C8—434no—
627C2×C8—8616no—
628C2×C8—862no—
629C2×C8—862no—
630C2×C8—862no—
631C2×C8—862no—
632C2×C8—862no—
633C2×C8—862no—
634C2×C8—862no—
635C4⋊C4—22no—
636C4⋊C4—41no—
637C22⋊C4—22no—
638C22⋊C4—41no—
639C42—22no—
640C42—41no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—82no—
646C23(C22⋊D43)⋊C411yescharacteristic
647C23(C22⋊D43)⋊C411yescharacteristic
648C23#1306329711yescharacteristic
649C23#1306329711yescharacteristic
650C23#1306330911yescharacteristic
651C23#1306330911yescharacteristic
652C23C2×#1062190011yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—864no—
657Q8—864no—
658Q8—1722no—
659Q8—1722no—
660Q8—1722no—
661Q8—1722no—
662Q8—1722no—
663Q8—1722no—
664Q8C2×(C2×D43)⋊C414yes—
665D4—24no—
666D4—24no—
667D4—24no—
668D4—24no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4C2×(C2×D43)⋊C414yes—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—42no—
681C2×C4—82no—
682C2×C4—864no—
683C2×C4—1722no—
684C2×C4—1722no—
685C2×C4—1722no—
686C2×C4—1722no—
687C2×C4—1722no—
688C2×C4—1722no—
689C2×C4C2×(C2×D43)⋊C411yescharacteristic
690C2×C4C2×(C2×D43)⋊C411yescharacteristic
691C2×C4C2×(C2×D43)⋊C411yescharacteristic
692C2×C4C2×(C2×D43)⋊C411yescharacteristic
693C2×C4(C22⋊D43)⋊C411yescharacteristic
694C2×C4(C22⋊D43)⋊C411yescharacteristic
695C2×C4(C22⋊D43)⋊C411yescharacteristic
696C2×C4(C22⋊D43)⋊C411yescharacteristic
697C2×C4(C22⋊D43)⋊C411yescharacteristic
698C2×C4(C22⋊D43)⋊C411yescharacteristic
699C2×C4#1306329511yescharacteristic
700C2×C4#1306329511yescharacteristic
701C2×C4#1306329511yescharacteristic
702C2×C4#1306329511yescharacteristic
703C2×C4#1306329711yescharacteristic
704C2×C4#1306329711yescharacteristic
705C2×C4#1306329711yescharacteristic
706C2×C4#1306329711yescharacteristic
707C2×C4#1306329711yescharacteristic
708C2×C4#1306329711yescharacteristic
709C2×C4#1306330911yescharacteristic
710C2×C4#1306330911yescharacteristic
711C2×C4C22×C4×D4311yescharacteristic
712C2×C4C2×D4×D4311yescharacteristic
713C2×C4C2×D4×D4311yescharacteristic
714C2×C4C22×C22⋊D4311yescharacteristic
715C2×C4C22×D17211yescharacteristic
716C2×C4C2×#1062190011yescharacteristic
717C8—42no—
718C8—864no—
719C8—864no—
720C8—864no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—24no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—44no—
730C22—82no—
731C22—82no—
732C22#1458277611yescharacteristic
733C22#1458277611yescharacteristic
734C22#1458277611yescharacteristic
735C22#1458277611yescharacteristic
736C22C2×(C22⋊D43)⋊C411yescharacteristic
737C22C2×#1306329711yescharacteristic
738C22C2×#1306330911yescharacteristic
739C4—24no—
740C4—82no—
741C4—1724no—
742C4#1458277611yescharacteristic
743C4#1458277611yescharacteristic
744C4#1458277611yescharacteristic
745C4#1458277611yescharacteristic
746C4C22×(C2×D43)⋊C411yescharacteristic
747C4C2×(C22⋊D43)⋊C411yescharacteristic
748C4C2×#1306329511yescharacteristic
749C4C2×#1306329711yescharacteristic
750C2—21no—
751C2—21no—
752C2—21no—
753C2—21no—
754C2—21no—
755C2—21no—
756C2—44no—
757C2#1913506612yesdirect product factor
758C2C2×#1458277611yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#421C2
socleC22×C43#386
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#421D43
hypocenterC43C2×#1902
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
3. C2×#14582907C2semidirect
4. C22×#13063243C2semidirect
5. #19135066C2direct (N × H)
6. C2×#14582669C2semidirect
7. C2×C43⋊#338C2semidirect
14. C2×#13063355C4semidirect
16. C22×#10621885C4semidirect
17. C22×#10621883C4semidirect
29. #14582907C22semidirect
33. C2×#13063243C22semidirect
34. #14582669C22semidirect
35. C43⋊#338C22semidirect
63. C2×#10621885C2×C4semidirect
66. C2×#10621883C2×C4semidirect
386. C2×C43#1902semidirect
421. C43C2×#1902semidirect
757. C2#19135066direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633552
C2×#145836662
C2×#145829072
C22×#130632432
#191350662
C2×#145826692
C2×C43⋊#3382
C2×C43×#4212
C2×#190243