Finite Group Databasebeta

← C2×#19135144 #25098623

Subgroups — C2×#19135144 #25098623

Order 11008.

1670 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic
2C2×#14583473C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic
4C22×#13063244C211yesmaximal, characteristic, complemented
5#19135144C218yesmaximal, direct product factor
6C2×#14582671C211yesmaximal, characteristic, complemented
7C2×#14582670C211yesmaximal, characteristic, complemented
8C22×#101×C43C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10#14583665—22no—
11#14583665—22no—
12#14583665—22no—
13#14583665C2214yes—
14C2×#13063333—22no—
15C2×#13063331—22no—
16C22×#10621877C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C2×M16×D43—22no—
19#14583473—22no—
20#14583473—22no—
21#14583473C414yes—
22#14583473C2214yes—
23C2×#13063323—21no—
24C2×#13063314—21no—
25C2×#13063308C414yes—
26C2×#13063301—22no—
27C2×#13063284C2211yescharacteristic
28#14582881—22no—
29#14582881C2214yes—
30C2×#13063244—22no—
31C2×#13063244—22no—
32C2×#13063244C2214yescomplemented
33C2×#13063243—21no—
34C2×#13063241—21no—
35#14582671C2214yescomplemented
36#14582670C2214yescomplemented
37C23×Q8×C43C2211yescharacteristic
38C22×M16×C43C2211yescharacteristic
39C22×M16×C43C2211yescharacteristic
40C2×#101×C43—22no—
41C2×#101×C43—22no—
42C2×#101×C43C2214yescomplemented
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898C2×C412yes—
52C2×#10621898D412yes—
53C2×#10621898D412yes—
54C2×#10621898C2312yes—
55C22×Dic86D411yescharacteristic
56C22×D172D411yescharacteristic
57C22×C22⋊D43C2×C412yes—
58C22×C4×D43D412yes—
59#13063333—28no—
60#13063333—28no—
61#13063331—28no—
62#13063331—28no—
63C2×#10621877—21no—
64C2×#10621877—21no—
65C2×#10621877—21no—
66C2×#10621877—21no—
67C2×#10621877—21no—
68C2×#10621877—21no—
69C2×#10621877—21no—
70C2×#10621877—21no—
71C2×#10621877D412yes—
72C2×#10621877D412yes—
73C2×#10621877C2312yes—
74C2×#10621877C2312yes—
75C2×#10621872—24no—
76M16×D43—28no—
77M16×D43—28no—
78C22×C43⋊C8—21no—
79C22×C43⋊C8—21no—
80C2×C8×D43—24no—
81#13063323—24no—
82#13063323—24no—
83#13063314—24no—
84#13063314—24no—
85#13063308—28no—
86#13063308C2×C4116yes—
87#13063301—28no—
88#13063301—28no—
89#13063284—21no—
90#13063284—21no—
91#13063284C2×C412yes—
92#13063284C2312yes—
93C2×C4⋊Dic43—21no—
94C2×Dic43⋊C4—24no—
95C2×C22⋊Dic43C2×C412yes—
96C2×(C2×D43)⋊C4—24no—
97C2×C4×Dic43—21no—
98#13063244—28no—
99#13063243—24no—
100#13063241—24no—
101C22×Q8×C43—21no—
102C22×Q8×C43—21no—
103C22×Q8×C43—21no—
104C22×Q8×C43—21no—
105C22×Q8×C43—21no—
106C22×Q8×C43—21no—
107C22×Q8×C43—21no—
108C22×Q8×C43—21no—
109C22×Q8×C43—21no—
110C22×Q8×C43—21no—
111C22×Q8×C43—21no—
112C22×Q8×C43—21no—
113C22×Q8×C43C2×C412yes—
114C22×Q8×C43C2312yes—
115C23×C4×C43C2×C412yes—
116C23×C4×C43C2311yescharacteristic
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43—21no—
120C2×M16×C43—21no—
121C2×M16×C43—21no—
122C2×M16×C43—21no—
123C2×M16×C43—21no—
124C2×M16×C43—21no—
125C2×M16×C43D412yes—
126C2×M16×C43D412yes—
127C2×M16×C43C2312yes—
128C2×M16×C43C2312yes—
129C22×C8×C43—21no—
130C22×C8×C43—21no—
131#101×C43—28no—
132C24×C43C22×C411yescharacteristic
133C23×D43C22⋊C412yes—
134C2×Q8×C43—22no—
135C2×Q8×C43—22no—
136C2×Q8×C43—22no—
137C2×Q8×C43—22no—
138C2×Q8×C43—22no—
139C2×Q8×C43—22no—
140C2×Q8×C43—22no—
141C2×Q8×C43—22no—
142C2×Q8×C43—22no—
143C2×Q8×C43—22no—
144C2×Q8×C43—22no—
145C2×Q8×C43—22no—
146C2×Q8×C43—41no—
147C2×Q8×C43—41no—
148C2×Q8×C43—41no—
149C2×Q8×C43—41no—
150C2×Q8×C43—41no—
151C2×Q8×C43—41no—
152C2×Q8×C43—41no—
153C2×Q8×C43—41no—
154C2×Q8×C43—41no—
155C2×Q8×C43—41no—
156C2×Q8×C43—41no—
157C2×Q8×C43—41no—
158C2×Q8×C43—41no—
159C2×Q8×C43—41no—
160C2×Q8×C43—41no—
161C2×Q8×C43—41no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43C22×C414yes—
169C22×C4×C43C22×C411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43#4111yescharacteristic
179C22×C4×C43#4111yescharacteristic
180C22×C4×C43#4111yescharacteristic
181C22×C4×C43#4111yescharacteristic
182C22×C4×C43C2411yescharacteristic
183C2×C22⋊D43—22no—
184C2×C22⋊D43—22no—
185C2×C22⋊D43—22no—
186C2×C22⋊D43—22no—
187C2×C22⋊D43C22⋊C414yes—
188C2×C22⋊D43C22×C414yes—
189C22×Dic43—22no—
190C22×Dic43C22⋊C412yes—
191#10621898—22no—
192#10621898—22no—
193#10621898—22no—
194#10621898—22no—
195#10621898—22no—
196#10621898—22no—
197#10621898—22no—
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—22no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172C22⋊C412yes—
212C2×D172C2×D412yes—
213C2×C4×D43—22no—
214C2×C4×D43—22no—
215C2×C4×D43—22no—
216C2×C4×D43—22no—
217C2×C4×D43C22⋊C414yes—
218C2×C4×D43C2×D414yes—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86C22⋊C412yes—
224C2×Dic86C2×D412yes—
225M16×C43—22no—
226M16×C43—22no—
227M16×C43—22no—
228M16×C43—22no—
229M16×C43—22no—
230M16×C43—41no—
231M16×C43—41no—
232M16×C43C2×D414yes—
233C2×C8×C43—22no—
234C2×C8×C43—22no—
235C2×C8×C43—22no—
236C2×C8×C43—22no—
237C2×C8×C43—41no—
238C2×C8×C43—41no—
239C22⋊Dic43—22no—
240C22⋊Dic43C22×C414yes—
241(C2×D43)⋊C4—216no—
242C4⋊Dic43—22no—
243C4⋊Dic43—22no—
244Dic43⋊C4—216no—
245C4×Dic43—22no—
246C4×Dic43—22no—
247#10621877—22no—
248#10621877—22no—
249#10621877—22no—
250#10621877—22no—
251#10621877—22no—
252#10621877—41no—
253#10621877—41no—
254#10621877C2×D414yes—
255C2×C43⋊C8—22no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8—22no—
259C2×C43⋊C8—41no—
260C2×C43⋊C8—41no—
261#10621872—216no—
262C8×D43—216no—
263C23×C43—42no—
264C23×C43C2×C22⋊C411yescharacteristic
265C23×C43C2×C22⋊C411yescharacteristic
266C23×C43C4×D411yescharacteristic
267C23×C43C4×D411yescharacteristic
268C23×C43C4×D411yescharacteristic
269C23×C43C4×D411yescharacteristic
270C23×C43C23×C411yescharacteristic
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—44no—
274C22×D43C2×C22⋊C414yes—
275Q8×C43—42no—
276Q8×C43—42no—
277Q8×C43—42no—
278Q8×C43—42no—
279Q8×C43—42no—
280Q8×C43—42no—
281Q8×C43—42no—
282Q8×C43—42no—
283C2×C4×C43—24no—
284C2×C4×C43—24no—
285C2×C4×C43—24no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43C2×C22⋊C411yescharacteristic
291C2×C4×C43C2×C22⋊C411yescharacteristic
292C2×C4×C43C4×D411yescharacteristic
293C2×C4×C43C4×D411yescharacteristic
294C2×C4×C43C4×D411yescharacteristic
295C2×C4×C43C4×D411yescharacteristic
296C2×C4×C43#12011yescharacteristic
297C2×C4×C43#12011yescharacteristic
298C2×C4×C43#12011yescharacteristic
299C2×C4×C43#12011yescharacteristic
300C2×C4×C43#12111yescharacteristic
301C2×C4×C43#12111yescharacteristic
302C2×C4×C43#12111yescharacteristic
303C2×C4×C43#12111yescharacteristic
304C2×C4×C43#12111yescharacteristic
305C2×C4×C43#12111yescharacteristic
306C2×C4×C43#12111yescharacteristic
307C2×C4×C43#12111yescharacteristic
308C2×C4×C43#12311yescharacteristic
309C2×C4×C43#12311yescharacteristic
310C2×C4×C43#12311yescharacteristic
311C2×C4×C43#12311yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C22⋊D43—24no—
319C22⋊D43—24no—
320C22⋊D43—24no—
321C22⋊D43—24no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—24no—
325C2×Dic43—44no—
326C2×Dic43C2×C22⋊C414yes—
327D172—22no—
328D172—22no—
329D172—22no—
330D172—22no—
331C4×D43—24no—
332C4×D43—24no—
333C4×D43—24no—
334C4×D43—24no—
335Dic86—22no—
336Dic86—22no—
337Dic86—22no—
338Dic86—22no—
339C8×C43—24no—
340C8×C43—42no—
341C43⋊C8—24no—
342C43⋊C8—42no—
343C2×#1915—431nomaximal, Sylow
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43#38611yescharacteristic
352C22×C43#38611yescharacteristic
353C22×C43#38611yescharacteristic
354C22×C43#38611yescharacteristic
355C22×C43C22×C22⋊C411yescharacteristic
356C22×C43C2×C4×D411yescharacteristic
357C22×C43C2×C4×D411yescharacteristic
358C2×D43—24no—
359C2×D43—44no—
360C2×D43—44no—
361C2×D43—82no—
362C4×C43—44no—
363C4×C43#38611yescharacteristic
364C4×C43#38611yescharacteristic
365C4×C43#38611yescharacteristic
366C4×C43#38611yescharacteristic
367C4×C43C2×#12011yescharacteristic
368C4×C43C2×#12111yescharacteristic
369C4×C43C2×#12111yescharacteristic
370C4×C43C2×#12311yescharacteristic
371Dic43—24no—
372Dic43—44no—
373C2×#568—431no—
374C2×#536—431no—
375C2×#413—431no—
376C22×#101—431no—
377C22×#101D4311yescharacteristic, complemented
378#1915—438no—
379C2×#344—431no—
380C2×#344—431no—
381C2×C43—21no—
382C2×C43—21no—
383C2×C43—21no—
384C2×C43—21no—
385C2×C43—21no—
386C2×C43—21no—
387C2×C43#191512yescomplemented
388C2×C43C2×#38611yescharacteristic
389D43—44no—
390C22×#41—431no—
391C23×Q8C2×D4311yescharacteristic
392#568—434no—
393#568—862no—
394#568—862no—
395#568—862no—
396C2×#131—862no—
397C2×#131—862no—
398C22×M16—431no—
399C22×M16—431no—
400C22×M16—862no—
401C22×M16C2×D4311yescharacteristic
402C22×M16C2×D4311yescharacteristic
403#536—434no—
404#536—434no—
405#536—862no—
406#536—862no—
407C2×C4⋊Q8—861no—
408C2×#124—861no—
409C2×#123—434no—
410C2×C22⋊Q8—862no—
411C2×#117—431no—
412#413—434no—
413#413—862no—
414C2×#101—22no—
415C2×#101—22no—
416C2×#101—434no—
417C2×#101—861no—
418C2×#101—862no—
419C2×#101—862no—
420C2×#101C2×D4314yescomplemented
421C2×#100—861no—
422#344—434no—
423#344—434no—
424C43C2×#191511yescharacteristic, complemented, Sylow
425C2×#41—432no—
426C2×#41—432no—
427C2×#41—432no—
428C2×#41—432no—
429C2×#41—861no—
430C2×#41—861no—
431C2×#41—861no—
432C2×#41—861no—
433C2×#41—861no—
434C2×#41—861no—
435C2×#41—861no—
436C2×#41—861no—
437C22×Q8—21no—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8—21no—
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8—21no—
449C22×Q8—431no—
450C22×Q8C4×D4312yes—
451C22×Q8C22×D4312yes—
452C22×D4—432no—
453C22×D4—431no—
454C23×C4—432no—
455C23×C4C4×D4312yes—
456C23×C4C22×D4311yescharacteristic
457#131—868no—
458#131—868no—
459#131—868no—
460#131—868no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—432no—
470C2×M16—432no—
471C2×M16—432no—
472C2×M16—432no—
473C2×M16—864no—
474C2×M16—868no—
475C2×M16—868no—
476C2×M16—861no—
477C2×M16—861no—
478C2×M16—861no—
479C2×M16—861no—
480C2×M16—861no—
481C2×M16—861no—
482C2×M16—861no—
483C2×M16—861no—
484C2×M16C22⋊D4312yes—
485C2×M16C22⋊D4312yes—
486C2×M16C22×D4312yes—
487C2×M16C22×D4312yes—
488C22×C8—21no—
489C22×C8—21no—
490C22×C8—864no—
491C22×C8—861no—
492C22×C8—861no—
493C4⋊Q8—864no—
494C4⋊Q8—864no—
495#124—864no—
496#124—864no—
497#123—4316no—
498#123—868no—
499C22⋊Q8—868no—
500C22⋊Q8—868no—
501#117—432no—
502#117—432no—
503#117—861no—
504#117—861no—
505C2×C4⋊C4—864no—
506C2×C4⋊C4—861no—
507C2×C22⋊C4—432no—
508C2×C22⋊C4—864no—
509C2×C42—861no—
510#101—28no—
511#101—864no—
512#101—868no—
513#100—864no—
514C24—432no—
515C24C2×C4×D4311yescharacteristic
516#41—862no—
517#41—862no—
518#41—862no—
519#41—862no—
520#41—862no—
521#41—862no—
522#41—862no—
523#41—862no—
524#41—862no—
525#41—862no—
526#41—862no—
527#41—862no—
528#41—862no—
529#41—862no—
530#41—862no—
531#41—862no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×Q8—432no—
561C2×Q8—432no—
562C2×Q8—861no—
563C2×Q8—861no—
564C2×Q8—861no—
565C2×Q8—861no—
566C2×D4—434no—
567C2×D4—434no—
568C2×D4—432no—
569C2×D4—432no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—861no—
575C2×D4—861no—
576C2×D4—861no—
577C2×D4—861no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—432no—
585C22×C4—434no—
586C22×C4—434no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4C2×C4×D4314yes—
593C22×C4C2×C4×D4311yescharacteristic
594C22×C4#1062189811yescharacteristic
595C22×C4#1062189811yescharacteristic
596C22×C4D4×D4311yescharacteristic
597C22×C4D4×D4311yescharacteristic
598C22×C4D4×D4311yescharacteristic
599C22×C4D4×D4311yescharacteristic
600C22×C4D4×D4311yescharacteristic
601C22×C4D4×D4311yescharacteristic
602C22×C4#1062190011yescharacteristic
603C22×C4#1062190011yescharacteristic
604C22×C4C2×C22⋊D4311yescharacteristic
605C22×C4C2×C22⋊D4311yescharacteristic
606C22×C4C23×D4311yescharacteristic
607M16—22no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—22no—
612M16—41no—
613M16—41no—
614M16—434no—
615M16—8616no—
616M16—862no—
617M16—862no—
618M16—862no—
619M16—862no—
620M16—862no—
621M16—1721no—
622M16—1721no—
623M16C2×C22⋊D4314yes—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—8616no—
631C2×C8—862no—
632C2×C8—862no—
633C2×C8—862no—
634C2×C8—862no—
635C2×C8—1721no—
636C2×C8—1721no—
637C4⋊C4—8616no—
638C4⋊C4—862no—
639C4⋊C4—862no—
640C22⋊C4—434no—
641C22⋊C4—8616no—
642C22⋊C4—862no—
643C42—862no—
644C42—862no—
645C23—42no—
646C23—434no—
647C23—862no—
648C23—862no—
649C23—1724no—
650C23C22⋊C4×D4311yescharacteristic
651C23C22⋊C4×D4311yescharacteristic
652C23(C22⋊D43)⋊C411yescharacteristic
653C23(C22⋊D43)⋊C411yescharacteristic
654C23C4×C22⋊D4311yescharacteristic
655C23C4×C22⋊D4311yescharacteristic
656C23C22×C4×D4311yescharacteristic
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—862no—
666Q8—862no—
667Q8—862no—
668Q8—862no—
669D4—864no—
670D4—864no—
671D4—864no—
672D4—864no—
673D4—862no—
674D4—862no—
675D4—862no—
676D4—862no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—434no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—864no—
688C2×C4—864no—
689C2×C4—864no—
690C2×C4—864no—
691C2×C4—864no—
692C2×C4—1724no—
693C2×C4C22⋊C4×D4311yescharacteristic
694C2×C4C22⋊C4×D4311yescharacteristic
695C2×C4(C22⋊D43)⋊C411yescharacteristic
696C2×C4(C22⋊D43)⋊C411yescharacteristic
697C2×C4C4×C22⋊D4311yescharacteristic
698C2×C4C4×C22⋊D4311yescharacteristic
699C2×C4#1306329311yescharacteristic
700C2×C4#1306329311yescharacteristic
701C2×C4#1306329311yescharacteristic
702C2×C4#1306329311yescharacteristic
703C2×C4#1306329611yescharacteristic
704C2×C4#1306329611yescharacteristic
705C2×C4#1306329611yescharacteristic
706C2×C4#1306329611yescharacteristic
707C2×C4#1306329811yescharacteristic
708C2×C4#1306329811yescharacteristic
709C2×C4#1306329811yescharacteristic
710C2×C4#1306329811yescharacteristic
711C2×C4#1306330711yescharacteristic
712C2×C4#1306330711yescharacteristic
713C2×C4#1306330711yescharacteristic
714C2×C4#1306330711yescharacteristic
715C2×C4C2×D4×D4311yescharacteristic
716C2×C4C2×D4×D4311yescharacteristic
717C2×C4C2×D4×D4311yescharacteristic
718C2×C4C22×C22⋊D4311yescharacteristic
719C2×C4C2×#1062190011yescharacteristic
720C2×C4C2×#1062189811yescharacteristic
721C8—24no—
722C8—42no—
723C8—864no—
724C8—1722no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—864no—
733C22—3442no—
734C22—1724no—
735C22—1724no—
736C22#1458277511yescharacteristic
737C22#1458277511yescharacteristic
738C22#1458277511yescharacteristic
739C22#1458277511yescharacteristic
740C22C2×C22⋊C4×D4311yescharacteristic
741C22C2×(C22⋊D43)⋊C411yescharacteristic
742C22C2×C4×C22⋊D4311yescharacteristic
743C4—44no—
744C4—864no—
745C4—1724no—
746C4#1458277511yescharacteristic
747C4#1458277511yescharacteristic
748C4#1458277511yescharacteristic
749C4#1458277511yescharacteristic
750C4C2×#1306329311yescharacteristic
751C4C2×#1306329611yescharacteristic
752C4C2×#1306329811yescharacteristic
753C4C2×#1306330711yescharacteristic
754C2—21no—
755C2—21no—
756C2—21no—
757C2—21no—
758C2—21no—
759C2—21no—
760C2—1724no—
761C2#1913514412yesdirect product factor
762C2C2×#1458277511yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#101×C43C2
socleC22×C43#386
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC22×#101D43
hypocenterC43C2×#1915
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
4. C22×#13063244C2semidirect
5. #19135144C2direct (N × H)
6. C2×#14582671C2semidirect
7. C2×#14582670C2semidirect
8. C22×#101×C43C2semidirect
32. C2×#13063244C22semidirect
35. #14582671C22semidirect
36. #14582670C22semidirect
42. C2×#101×C43C22semidirect
377. C22×#101D43semidirect
387. C2×C43#1915semidirect
420. C2×#101C2×D43semidirect
424. C43C2×#1915semidirect
761. C2#19135144direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836652
C2×#145834732
C2×#145828812
C22×#130632442
#191351442
C2×#145826712
C2×#145826702
C22×#101×C432
C2×#191543