Finite Group Databasebeta

← C2×#19144452 #25964185

Subgroups — C2×#19144452 #25964185

Order 11008.

2094 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583526C211yesmaximal, characteristic, complemented
2C2×#14583378C211yesmaximal, characteristic
3#19144452C2116yesmaximal, direct product factor
4C2×#14583209C211yesmaximal, characteristic, complemented
5C2×#14583207C211yesmaximal, characteristic, complemented
6C2×#14583183C211yesmaximal, characteristic, complemented
7C2×#14583181C211yesmaximal, characteristic, complemented
8C2×#14583199C211yesmaximal, characteristic, complemented
9C2×#14583197C211yesmaximal, characteristic, complemented
10C2×#14583187C211yesmaximal, characteristic, complemented
11C2×#14582938C211yesmaximal, characteristic, complemented
12C2×#106×D43C211yesmaximal, characteristic, complemented
13C2×#14582924C211yesmaximal, characteristic, complemented
14C2×#14582897C211yesmaximal, characteristic
15C2×#14582892C211yesmaximal, characteristic
16C2×C43×#476C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583526—24no—
21#14583526C2218yescomplemented
22C2×#13063324C2211yescharacteristic
23C2×#13063323—21no—
24C2×#13063317C2211yescharacteristic
25C2×#13063316C2211yescharacteristic
26C2×#13063315—21no—
27C2×#13063303—21no—
28C2×#13063301—21no—
29#14583378—24no—
30#14583378C2218yes—
31C2×C4×Dic86C2211yescharacteristic
32C2×#13063290C2211yescharacteristic
33C2×D4×Dic43C2211yescharacteristic
34C2×C4×C22⋊D43—21no—
35C2×(C22⋊D43)⋊C4—21no—
36C2×#13063283C2211yescharacteristic
37C2×#13063282C2211yescharacteristic
38C2×#13063281—21no—
39C22×Dic43⋊C4—21no—
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583209C2218yescomplemented
43#14583207C2218yescomplemented
44#14583199C2218yescomplemented
45#14583197C2218yescomplemented
46#14583187C2218yescomplemented
47#14583183C2218yescomplemented
48#14583181C2218yescomplemented
49#14582938C2218yescomplemented
50C2×#13063259C2211yescharacteristic
51C2×#13063258C2211yescharacteristic
52C2×#13063257C2211yescharacteristic
53C2×#13063256C2211yescharacteristic
54C2×#13063256C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56#106×D43C2218yescomplemented
57#14582924C2218yescomplemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61#14582897C2218yes—
62#14582892C2218yes—
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×#13063248C2211yescharacteristic
67C2×#13063246C2211yescharacteristic
68C2×#13063246C2211yescharacteristic
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C43×#476C2218yescomplemented
72C2×#106×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621900—22no—
78C2×#10621900—24no—
79C2×#10621900Q818yescomplemented
80C2×#10621900C2314yes—
81C22×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C22×C22⋊D43—21no—
84C23×Dic43—21no—
85C23×Dic43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43C2311yescharacteristic
89C2×#10621872—24no—
90C2×#10621872C2314yes—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C2×C8×D43—24no—
94C2×C8×D43C2314yes—
95#13063324—22no—
96#13063324C2314yes—
97#13063323—28no—
98#13063317—22no—
99#13063317C2314yes—
100#13063316—22no—
101#13063316C2314yes—
102#13063315—28no—
103#13063303—28no—
104#13063301—28no—
105C4×Dic86—22no—
106C4×Dic86C2314yes—
107#13063290—22no—
108#13063290C2314yes—
109D4×Dic43—22no—
110D4×Dic43C2314yes—
111C4×C22⋊D43—28no—
112(C22⋊D43)⋊C4—28no—
113#13063283—22no—
114#13063283C2314yes—
115#13063282D414yes—
116#13063282C2314yes—
117#13063281—28no—
118C2×C4⋊Dic43—21no—
119C2×C4⋊Dic43C2311yescharacteristic
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×Dic43⋊C4—21no—
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—28no—
131C2×Dic43⋊C4D411yescharacteristic
132C2×Dic43⋊C4D411yescharacteristic
133C4⋊C4×D43—22no—
134C4⋊C4×D43—22no—
135C4⋊C4×D43C2314yes—
136C4⋊C4×D43C2314yes—
137C2×C22⋊Dic43—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4D411yescharacteristic
140C2×(C2×D43)⋊C4D411yescharacteristic
141C2×C4×Dic43—21no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43C2311yescharacteristic
145#13063259C2314yes—
146#13063258C2314yes—
147#13063257C2314yes—
148#13063256C2314yes—
149#13063256C2314yes—
150#13063256C2314yes—
151C4⋊(C43⋊C8)C2314yes—
152Dic43⋊C8C2314yes—
153Dic43⋊C8C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063248C2314yes—
157#13063248C2314yes—
158#13063246C2314yes—
159#13063246C2314yes—
160C22×Q8×C43—21no—
161C22×D4×C43C2311yescharacteristic
162C23×C4×C43—21no—
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C4⋊Q8×C43—22no—
166C4⋊Q8×C43C2314yes—
167C4×D4×C43—22no—
168C4×D4×C43C2314yes—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C22⋊C4×C43—21no—
174C2×C42×C43C2311yescharacteristic
175#106×C43C2314yes—
176#106×C43C2314yes—
177C4⋊C8×C43C2314yes—
178#102×C43C2314yes—
179#102×C43C2314yes—
180C24×C43—21no—
181C23×D43C2×D411yescharacteristic
182C2×Q8×C43—24no—
183C2×Q8×C43—82no—
184C2×D4×C43—21no—
185C2×D4×C43—22no—
186C2×D4×C43C2×Q814yes—
187C2×D4×C43C2412yes—
188C22×C4×C43—24no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—82no—
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—28no—
197C2×C22⋊D43—24no—
198C22×Dic43—28no—
199C22×Dic43—24no—
200C22×Dic43—24no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—82no—
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209#10621900—216no—
210#10621900—28no—
211#10621900C2×Q8116yescomplemented
212C2×C4×D43—24no—
213C2×C4×D43—24no—
214C2×C4×D43—82no—
215C2×C4×D43—82no—
216C2×C4×D43C2×D412yes—
217C2×C4×D43C2×Q814yes—
218C2×C4×D43#4114yes—
219C2×C4×D43C2412yes—
220C2×Dic86—21no—
221C2×Dic86—22no—
222C2×Dic86—24no—
223C2×Dic86—82no—
224C2×Dic86C2×Q814yes—
225C2×Dic86C2412yes—
226C2×C8×C43—22no—
227C2×C8×C43—22no—
228C2×C8×C43C2412yes—
229C2×C8×C43C2412yes—
230C4⋊C4×C43—24no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43C2412yes—
235C4⋊C4×C43C2412yes—
236C4⋊C4×C43C2412yes—
237C22⋊C4×C43—24no—
238C42×C43C2×D412yes—
239C42×C43C2412yes—
240C22⋊Dic43—24no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4C2×D414yes—
243(C2×D43)⋊C4C2×D414yes—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—24no—
248C4⋊Dic43C2412yes—
249C4⋊Dic43C2412yes—
250C4⋊Dic43C2412yes—
251Dic43⋊C4—24no—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4C2×D414yes—
260Dic43⋊C4C2×D414yes—
261C4×Dic43—24no—
262C4×Dic43—24no—
263C4×Dic43—24no—
264C4×Dic43C2×D412yes—
265C4×Dic43C2412yes—
266C2×C43⋊C8—22no—
267C2×C43⋊C8—22no—
268C2×C43⋊C8C2412yes—
269C2×C43⋊C8C2412yes—
270#10621872—28no—
271C8×D43—28no—
272C23×C43—24no—
273C23×C43—22no—
274C23×C43—42no—
275C23×C43—42no—
276C23×C43C22×D411yescharacteristic
277C22×D43—22no—
278C22×D43—22no—
279C22×D43C22⋊Q814yes—
280C22×D43C22×D412yes—
281Q8×C43—84no—
282D4×C43—24no—
283D4×C43—22no—
284D4×C43C22×Q814yes—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—84no—
294C2×C4×C43C22×D412yes—
295C2×C4×C43C22×D412yes—
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C22×Q812yes—
298C2×C4×C43C2×#4112yes—
299C2×C4×C43C2511yescharacteristic
300C22⋊D43—216no—
301C2×Dic43—24no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—216no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—84no—
313C2×Dic43C22⋊Q814yes—
314C2×Dic43C22×D412yes—
315C2×Dic43C22×D412yes—
316C2×Dic43C22×D412yes—
317C4×D43—84no—
318C4×D43—84no—
319C4×D43C22⋊Q818yes—
320C4×D43C22×Q814yes—
321C4×D43C2×#4114yes—
322Dic86—24no—
323Dic86—22no—
324Dic86—84no—
325Dic86C22×Q814yes—
326C8×C43—22no—
327C8×C43—22no—
328C43⋊C8—22no—
329C43⋊C8—22no—
330C2×#3084—431nomaximal, Sylow
331C22×C43—24no—
332C22×C43—48no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43C2×C22⋊Q812yes—
336C22×C43#57712yes—
337C22×C43#57712yes—
338C22×C43C23×D411yescharacteristic
339C2×D43—28no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43C2×C22⋊Q814yes—
343C4×C43—22no—
344C4×C43—22no—
345C4×C43—42no—
346C4×C43—42no—
347C4×C43—42no—
348C4×C43C2×C22⋊Q812yes—
349C4×C43C23×Q811yescharacteristic
350C4×C43C22×#4111yescharacteristic
351Dic43—24no—
352Dic43—22no—
353Dic43—22no—
354Dic43—42no—
355Dic43—42no—
356Dic43—42no—
357Dic43C2×C22⋊Q814yes—
358C2×#544—431no—
359C2×#520—431no—
360#3084—4316no—
361C2×#479—431no—
362C2×#479—431no—
363C2×#475—431no—
364C2×#475—431no—
365C2×#478—431no—
366C2×#478—431no—
367C2×#476—431no—
368C2×#476D4311yescharacteristic, complemented
369C2×#428—431no—
370C22×#106—431no—
371C2×#424—431no—
372C2×#417—431no—
373C2×#416—431no—
374C2×C43—44no—
375C2×C43#308414yescomplemented
376C2×C43C22×C22⋊Q811yescharacteristic
377C2×C43C2×#57711yescharacteristic
378C2×C43C2×#57711yescharacteristic
379D43—24no—
380C22×#41—431no—
381C22×M16—431no—
382C23×C8—431no—
383#544—438no—
384#544—864no—
385C2×C4⋊Q8—431no—
386C2×C4⋊Q8—861no—
387C2×C4⋊Q8C2×D4311yescharacteristic
388C2×#125—431no—
389C2×#125—431no—
390C2×#125—861no—
391C2×C22⋊Q8—861no—
392C2×C22⋊Q8—861no—
393#520—438no—
394#520—864no—
395C2×C4×Q8—431no—
396C2×C4×Q8—431no—
397C2×C4×D4—431no—
398C2×C4×D4—861no—
399C2×C4×D4—861no—
400C2×C4×D4C2×D4311yescharacteristic
401C2×#117—431no—
402C2×#117—431no—
403C2×#117—861no—
404C22×C4⋊C4—431no—
405C22×C4⋊C4—431no—
406C22×C4⋊C4—861no—
407#479—438no—
408#479—438no—
409#478—438no—
410#478—438no—
411#476—438no—
412#476C2×D4318yescomplemented
413#475—438no—
414#475—438no—
415#428—438no—
416C2×#107—431no—
417C2×#107—431no—
418C2×#106—431no—
419C2×#106—431no—
420C2×#106—431no—
421C2×#106—431no—
422C2×#106—438no—
423C2×#106C2×D4311yescharacteristic
424C2×#106C2×D4311yescharacteristic
425#424—438no—
426C2×C4⋊C8—431no—
427C2×C4⋊C8—431no—
428C2×C4⋊C8—431no—
429C2×C4⋊C8C2×D4311yescharacteristic
430#417—438no—
431#416—438no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102C2×D4311yescharacteristic
439C2×#102C2×D4311yescharacteristic
440C43C2×#308411yescharacteristic, complemented, Sylow
441C2×#41—438no—
442C2×#41—434no—
443C2×#41—862no—
444C2×#41—864no—
445C22×Q8—21no—
446C22×Q8—431no—
447C22×Q8—861no—
448C22×D4—861no—
449C22×D4C22×D4311yescharacteristic
450C23×C4—21no—
451C23×C4—431no—
452C23×C4—861no—
453C23×C4—861no—
454C23×C4—861no—
455C23×C4—861no—
456C2×M16—434no—
457C2×M16—864no—
458C22×C8—431no—
459C22×C8—431no—
460C22×C8—434no—
461C22×C8—864no—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464C4⋊Q8—22no—
465C4⋊Q8—434no—
466C4⋊Q8—862no—
467C4⋊Q8—868no—
468C4⋊Q8C22×D4314yes—
469#125—434no—
470#125—434no—
471#125—862no—
472#125—868no—
473#125—862no—
474C22⋊Q8—868no—
475C22⋊Q8—868no—
476C4×Q8—434no—
477C4×Q8—434no—
478C4×Q8—862no—
479C4×Q8—862no—
480C4×D4—22no—
481C4×D4—434no—
482C4×D4—862no—
483C4×D4—868no—
484C4×D4—868no—
485C4×D4C22×D4314yes—
486#117—434no—
487#117—434no—
488#117—434no—
489#117—868no—
490#117—862no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—434no—
498C2×C4⋊C4—434no—
499C2×C4⋊C4—862no—
500C2×C4⋊C4—862no—
501C2×C4⋊C4—868no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—431no—
516C2×C22⋊C4—431no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C42—431no—
520C2×C42—861no—
521C2×C42—861no—
522C2×C42—861no—
523C2×C42C22×D4311yescharacteristic
524#107—434no—
525#107—434no—
526#106—434no—
527#106—434no—
528#106—434no—
529#106—434no—
530#106C22×D4314yes—
531#106C22×D4314yes—
532C4⋊C8—434no—
533C4⋊C8—434no—
534C4⋊C8—434no—
535C4⋊C8C22×D4314yes—
536#103—434no—
537#103—434no—
538#103—434no—
539#103—434no—
540#102—434no—
541#102—434no—
542#102C22×D4314yes—
543#102C22×D4314yes—
544C24—21no—
545C24—431no—
546#41—4316no—
547#41—8616no—
548#41—868no—
549C2×Q8—24no—
550C2×Q8—82no—
551C2×Q8—434no—
552C2×Q8—432no—
553C2×Q8—864no—
554C2×Q8—861no—
555C2×Q8—862no—
556C2×Q8—3442no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—864no—
560C2×D4—868no—
561C2×D4Q8×D4314yes—
562C2×D4C23×D4312yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—82no—
568C22×C4—431no—
569C22×C4—432no—
570C22×C4—434no—
571C22×C4—434no—
572C22×C4—432no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—864no—
576C22×C4—864no—
577C22×C4—864no—
578C22×C4—868no—
579C22×C4—864no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—3442no—
585C22×C4—3442no—
586C22×C4—3442no—
587C22×C4D4×D4311yescharacteristic
588C22×C4D4×D4311yescharacteristic
589C22×C4C23×D4311yescharacteristic
590M16—868no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—432no—
594C2×C8—432no—
595C2×C8—868no—
596C2×C8—862no—
597C2×C8—862no—
598C2×C8C23×D4312yes—
599C2×C8C23×D4312yes—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—434no—
605C4⋊C4—434no—
606C4⋊C4—432no—
607C4⋊C4—432no—
608C4⋊C4—432no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4C23×D4312yes—
622C4⋊C4C23×D4312yes—
623C4⋊C4C23×D4312yes—
624C22⋊C4—24no—
625C22⋊C4—434no—
626C22⋊C4—434no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C42—432no—
630C42—432no—
631C42—864no—
632C42—864no—
633C42—864no—
634C42D4×D4312yes—
635C42C23×D4312yes—
636C23—24no—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—434no—
641C23—432no—
642C23—862no—
643C23—862no—
644C23C2×D4×D4311yescharacteristic
645Q8—84no—
646Q8—434no—
647Q8—864no—
648Q8—862no—
649Q8—3444no—
650D4—24no—
651D4—22no—
652D4—8616no—
653D4C2×Q8×D4314yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—84no—
663C2×C4—434no—
664C2×C4—432no—
665C2×C4—438no—
666C2×C4—434no—
667C2×C4—434no—
668C2×C4—432no—
669C2×C4—432no—
670C2×C4—8616no—
671C2×C4—864no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—3444no—
679C2×C4—3444no—
680C2×C4—3444no—
681C2×C4—1722no—
682C2×C4—1722no—
683C2×C4—1722no—
684C2×C4C2×D4×D4312yes—
685C2×C4C2×D4×D4312yes—
686C2×C4C2×D4×D4311yescharacteristic
687C2×C4C2×Q8×D4312yes—
688C2×C4#41×D4312yes—
689C2×C4C24×D4311yescharacteristic
690C8—22no—
691C8—22no—
692C8—862no—
693C8—862no—
694C22—24no—
695C22—48no—
696C22—42no—
697C22—42no—
698C22—434no—
699C22—868no—
700C22—862no—
701C22—862no—
702C22C22⋊Q8×D4312yes—
703C22#1458370512yes—
704C22#1458370912yes—
705C22C22×D4×D4311yescharacteristic
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—434no—
712C4—862no—
713C4—862no—
714C4—864no—
715C4—1722no—
716C4—1722no—
717C4—1722no—
718C4C22⋊Q8×D4312yes—
719C4C22×Q8×D4311yescharacteristic
720C4C2×#41×D4311yescharacteristic
721C2—44no—
722C2—864no—
723C2#1914445214yesdirect product factor
724C2C2×C22⋊Q8×D4311yescharacteristic
725C2C2×#1458370511yescharacteristic
726C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#476C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
hypercenterC2×#476D43
hypocenterC43C2×#3084
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#14583526C2semidirect
3. #19144452C2direct (N × H)
4. C2×#14583209C2semidirect
5. C2×#14583207C2semidirect
6. C2×#14583183C2semidirect
7. C2×#14583181C2semidirect
8. C2×#14583199C2semidirect
9. C2×#14583197C2semidirect
10. C2×#14583187C2semidirect
11. C2×#14582938C2semidirect
12. C2×#106×D43C2semidirect
13. C2×#14582924C2semidirect
16. C2×C43×#476C2semidirect
21. #14583526C22semidirect
42. #14583209C22semidirect
43. #14583207C22semidirect
44. #14583199C22semidirect
45. #14583197C22semidirect
46. #14583187C22semidirect
47. #14583183C22semidirect
48. #14583181C22semidirect
49. #14582938C22semidirect
56. #106×D43C22semidirect
57. #14582924C22semidirect
71. C43×#476C22semidirect
79. C2×#10621900Q8semidirect
211. #10621900C2×Q8semidirect
368. C2×#476D43semidirect
375. C2×C43#3084semidirect
412. #476C2×D43semidirect
440. C43C2×#3084semidirect
723. C2#19144452direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835262
C2×#145833782
#191444522
C2×#145832092
C2×#145832072
C2×#145831832
C2×#145831812
C2×#145831992
C2×#145831972
C2×#145831872
C2×#145829382
C2×#106×D432
C2×#145829242
C2×#145828972
C2×#145828922
C2×C43×#4762
C2×#308443