Finite Group Databasebeta

← C2×#19144430 #25964161

Subgroups — C2×#19144430 #25964161

Order 11008.

2018 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583526C211yesmaximal, characteristic
2C2×#14583375C211yesmaximal, characteristic
3#19144430C2116yesmaximal, direct product factor
4C2×#14583209C211yesmaximal, characteristic, complemented
5C2×#14583207C211yesmaximal, characteristic, complemented
6C2×#14583206C211yesmaximal, characteristic, complemented
7C2×#14583204C211yesmaximal, characteristic, complemented
8C2×#14583192C211yesmaximal, characteristic, complemented
9C2×#14583191C211yesmaximal, characteristic, complemented
10C2×#14583183C211yesmaximal, characteristic, complemented
11C2×#14582938C211yesmaximal, characteristic
12C2×#14582934C211yesmaximal, characteristic
13C2×#14582924C211yesmaximal, characteristic
14C2×#14582906C211yesmaximal, characteristic
15C2×#103×D43C211yesmaximal, characteristic
16C2×C43×#475C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583526—24no—
21#14583526C2218yes—
22C2×#13063324C2211yescharacteristic
23C2×#13063323—21no—
24C2×#13063317C2211yescharacteristic
25C2×#13063316C2211yescharacteristic
26C2×#13063315—21no—
27C2×#13063303—21no—
28C2×#13063301—21no—
29#14583375—24no—
30#14583375C2218yes—
31C2×Q8×Dic43C2211yescharacteristic
32C2×C4×Dic86—21no—
33C2×C4×Dic86C2211yescharacteristic
34C2×#13063290—21no—
35C2×#13063290C2211yescharacteristic
36C2×#13063283—21no—
37C2×#13063283C2211yescharacteristic
38C2×#13063283C2211yescharacteristic
39C2×#13063282—21no—
40C2×#13063282C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583209C2218yescomplemented
43#14583207C2218yescomplemented
44#14583206C2218yescomplemented
45#14583204C2218yescomplemented
46#14583192C2218yescomplemented
47#14583191C2218yescomplemented
48#14583183C2218yescomplemented
49#14582938C2218yes—
50#14582934C2218yes—
51C2×#13063259C2211yescharacteristic
52C2×#13063258C2211yescharacteristic
53C2×#13063258C2211yescharacteristic
54C2×#13063258C2211yescharacteristic
55C2×#13063257C2211yescharacteristic
56C2×#13063256C2211yescharacteristic
57#14582924C2218yes—
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61#14582906C2218yes—
62C2×#13063250C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063249C2211yescharacteristic
65C2×#13063249C2211yescharacteristic
66C2×#13063248C2211yescharacteristic
67C2×#13063248C2211yescharacteristic
68#103×D43C2218yes—
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C43×#475C2218yescomplemented
72C2×#106×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86—21no—
79C22×Dic86C2311yescharacteristic
80C2×Q8×D43—22no—
81C2×Q8×D43—24no—
82C2×Q8×D43Q818yescomplemented
83C2×Q8×D43C2314yes—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43C2311yescharacteristic
87C2×#10621872—24no—
88C2×#10621872C2314yes—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C2×C8×D43—24no—
92C2×C8×D43C2314yes—
93#13063324—22no—
94#13063324C2314yes—
95#13063323—28no—
96#13063317—22no—
97#13063317C2314yes—
98#13063316—22no—
99#13063316C2314yes—
100#13063315—28no—
101#13063303—28no—
102#13063301—28no—
103Q8×Dic43—22no—
104Q8×Dic43C2314yes—
105C4×Dic86—22no—
106C4×Dic86—28no—
107C4×Dic86C2314yes—
108#13063290—28no—
109#13063290—22no—
110#13063290C2314yes—
111#13063283—22no—
112#13063283—22no—
113#13063283—28no—
114#13063283C2314yes—
115#13063283C2314yes—
116#13063282—28no—
117#13063282D414yes—
118#13063282C2314yes—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
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—21no—
131C2×Dic43⋊C4D411yescharacteristic
132C2×Dic43⋊C4D411yescharacteristic
133C4⋊C4×D43—22no—
134C4⋊C4×D43C2314yes—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4D411yescharacteristic
138C2×(C2×D43)⋊C4D411yescharacteristic
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43C2311yescharacteristic
145#13063259C2314yes—
146#13063258C2314yes—
147#13063258C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150#13063256C2314yes—
151C4⋊(C43⋊C8)C2314yes—
152Dic43⋊C8C2314yes—
153Dic43⋊C8C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063249C2314yes—
157#13063249C2314yes—
158#13063248C2314yes—
159#13063248C2314yes—
160C22×Q8×C43—21no—
161C22×Q8×C43C2311yescharacteristic
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C4⋊Q8×C43—22no—
165C4⋊Q8×C43C2314yes—
166C4×Q8×C43—22no—
167C4×Q8×C43C2314yes—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C42×C43—21no—
174C2×C42×C43C2311yescharacteristic
175#106×C43C2314yes—
176#106×C43C2314yes—
177C4⋊C8×C43C2314yes—
178#103×C43C2314yes—
179#103×C43C2314yes—
180C23×D43C2×D411yescharacteristic
181C2×Q8×C43—21no—
182C2×Q8×C43—24no—
183C2×Q8×C43—22no—
184C2×Q8×C43—82no—
185C2×Q8×C43C2×Q814yes—
186C2×Q8×C43C2412yes—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200C22×Dic43C2×D411yescharacteristic
201Q8×D43—216no—
202Q8×D43—28no—
203Q8×D43C2×Q8116yescomplemented
204C2×C4×D43—28no—
205C2×C4×D43—24no—
206C2×C4×D43—24no—
207C2×C4×D43—82no—
208C2×C4×D43C2×D412yes—
209C2×C4×D43C2×Q814yes—
210C2×C4×D43#4114yes—
211C2×C4×D43C2412yes—
212C2×Dic86—21no—
213C2×Dic86—22no—
214C2×Dic86—28no—
215C2×Dic86—24no—
216C2×Dic86—24no—
217C2×Dic86—82no—
218C2×Dic86C2×Q814yes—
219C2×Dic86C2412yes—
220C2×C8×C43—22no—
221C2×C8×C43—22no—
222C2×C8×C43C2412yes—
223C2×C8×C43C2412yes—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—24no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43C2412yes—
230C4⋊C4×C43C2412yes—
231C4⋊C4×C43C2412yes—
232C42×C43—24no—
233C42×C43C2×D412yes—
234C42×C43C2412yes—
235(C2×D43)⋊C4—24no—
236(C2×D43)⋊C4—24no—
237(C2×D43)⋊C4C2×D414yes—
238(C2×D43)⋊C4C2×D414yes—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—24no—
243C4⋊Dic43—24no—
244C4⋊Dic43C2412yes—
245C4⋊Dic43C2412yes—
246C4⋊Dic43C2412yes—
247Dic43⋊C4—24no—
248Dic43⋊C4—24no—
249Dic43⋊C4—24no—
250Dic43⋊C4—24no—
251Dic43⋊C4—24no—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4C2×D414yes—
255Dic43⋊C4C2×D414yes—
256C4×Dic43—24no—
257C4×Dic43—24no—
258C4×Dic43—24no—
259C4×Dic43—24no—
260C4×Dic43—24no—
261C4×Dic43C2×D412yes—
262C4×Dic43C2412yes—
263C2×C43⋊C8—22no—
264C2×C43⋊C8—22no—
265C2×C43⋊C8C2412yes—
266C2×C43⋊C8C2412yes—
267#10621872—28no—
268C8×D43—28no—
269C23×C43C22×D411yescharacteristic
270C22×D43—22no—
271C22×D43—22no—
272C22×D43C22⋊Q814yes—
273C22×D43C22×D412yes—
274Q8×C43—24no—
275Q8×C43—22no—
276Q8×C43—84no—
277Q8×C43C22×Q814yes—
278C2×C4×C43—24no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43C22×D412yes—
289C2×C4×C43C22×D412yes—
290C2×C4×C43C22×D411yescharacteristic
291C2×C4×C43C22×Q812yes—
292C2×C4×C43C2×#4112yes—
293C2×C4×C43C2511yescharacteristic
294C2×Dic43—24no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—42no—
302C2×Dic43—42no—
303C2×Dic43—42no—
304C2×Dic43C22⋊Q814yes—
305C2×Dic43C22×D412yes—
306C2×Dic43C22×D412yes—
307C2×Dic43C22×D412yes—
308C4×D43—216no—
309C4×D43—84no—
310C4×D43C22⋊Q818yes—
311C4×D43C22×Q814yes—
312C4×D43C2×#4114yes—
313Dic86—24no—
314Dic86—22no—
315Dic86—216no—
316Dic86—84no—
317Dic86C22×Q814yes—
318C8×C43—22no—
319C8×C43—22no—
320C43⋊C8—22no—
321C43⋊C8—22no—
322C2×#3082—431nomaximal, Sylow
323C22×C43C2×C22⋊Q812yes—
324C22×C43#57712yes—
325C22×C43#57812yes—
326C22×C43C23×D411yescharacteristic
327C2×D43—28no—
328C2×D43—22no—
329C2×D43—22no—
330C2×D43C2×C22⋊Q814yes—
331C4×C43—24no—
332C4×C43—22no—
333C4×C43—22no—
334C4×C43—42no—
335C4×C43—42no—
336C4×C43—42no—
337C4×C43C2×C22⋊Q812yes—
338C4×C43C23×Q811yescharacteristic
339C4×C43C22×#4111yescharacteristic
340Dic43—24no—
341Dic43—22no—
342Dic43—22no—
343Dic43—42no—
344Dic43—42no—
345Dic43—42no—
346Dic43C2×C22⋊Q814yes—
347C2×#544—431no—
348C2×#519—431no—
349#3082—4316no—
350C2×#479—431no—
351C2×#479—431no—
352C2×#479—431no—
353C2×#479—431no—
354C2×#477—431no—
355C2×#477—431no—
356C2×#475—431no—
357C2×#475D4311yescharacteristic, complemented
358C2×#428—431no—
359C2×#427—431no—
360C2×#424—431no—
361C2×#419—431no—
362C22×#103—431no—
363C2×C43#308214yescomplemented
364C2×C43C22×C22⋊Q811yescharacteristic
365C2×C43C2×#57711yescharacteristic
366C2×C43C2×#57811yescharacteristic
367D43—24no—
368C23×Q8—431no—
369C22×M16—431no—
370C23×C8—431no—
371#544—438no—
372#544—864no—
373C2×C4⋊Q8—431no—
374C2×C4⋊Q8—861no—
375C2×C4⋊Q8C2×D4311yescharacteristic
376C2×#125—431no—
377C2×#125—431no—
378C2×#125—861no—
379C2×C22⋊Q8—861no—
380C2×C22⋊Q8—861no—
381#519—438no—
382#519—864no—
383C2×C4×Q8—431no—
384C2×C4×Q8—431no—
385C2×C4×Q8—431no—
386C2×C4×Q8—861no—
387C2×C4×Q8—861no—
388C2×C4×Q8C2×D4311yescharacteristic
389C2×#117—431no—
390C2×#117—431no—
391C2×#117—431no—
392C2×#117—861no—
393C2×#117—861no—
394C22×C4⋊C4—431no—
395#479—438no—
396#479—438no—
397#479—438no—
398#479—438no—
399#477—438no—
400#477—438no—
401#475—438no—
402#475C2×D4318yescomplemented
403#428—438no—
404#427—438no—
405C2×#107—431no—
406C2×#107—431no—
407C2×#107—431no—
408C2×#107—431no—
409C2×#106—431no—
410C2×#106—431no—
411C2×#106C2×D4311yescharacteristic
412C2×#106C2×D4311yescharacteristic
413#424—438no—
414C2×C4⋊C8—431no—
415C2×C4⋊C8—431no—
416C2×C4⋊C8—431no—
417C2×C4⋊C8C2×D4311yescharacteristic
418#419—438no—
419C2×#103—431no—
420C2×#103—431no—
421C2×#103—431no—
422C2×#103—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—438no—
426C2×#103C2×D4311yescharacteristic
427C2×#103C2×D4311yescharacteristic
428C43C2×#308211yescharacteristic, complemented, Sylow
429C22×Q8—21no—
430C22×Q8—438no—
431C22×Q8—434no—
432C22×Q8—431no—
433C22×Q8—861no—
434C22×Q8—861no—
435C22×Q8—862no—
436C22×Q8—864no—
437C22×Q8C22×D4311yescharacteristic
438C23×C4—431no—
439C23×C4—861no—
440C23×C4—861no—
441C2×M16—434no—
442C2×M16—864no—
443C22×C8—431no—
444C22×C8—431no—
445C22×C8—434no—
446C22×C8—864no—
447C22×C8C22×D4311yescharacteristic
448C22×C8C22×D4311yescharacteristic
449C4⋊Q8—22no—
450C4⋊Q8—434no—
451C4⋊Q8—862no—
452C4⋊Q8—868no—
453C4⋊Q8C22×D4314yes—
454#125—434no—
455#125—434no—
456#125—862no—
457#125—868no—
458#125—862no—
459C22⋊Q8—868no—
460C22⋊Q8—868no—
461C4×Q8—22no—
462C4×Q8—434no—
463C4×Q8—434no—
464C4×Q8—434no—
465C4×Q8—868no—
466C4×Q8—862no—
467C4×Q8—862no—
468C4×Q8—868no—
469C4×Q8—862no—
470C4×Q8C22×D4314yes—
471#117—434no—
472#117—434no—
473#117—434no—
474#117—434no—
475#117—868no—
476#117—868no—
477#117—862no—
478#117—862no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—434no—
487C2×C4⋊C4—862no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C22⋊C4—431no—
501C2×C22⋊C4—431no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C42—21no—
505C2×C42—431no—
506C2×C42—861no—
507C2×C42—861no—
508C2×C42—861no—
509C2×C42—861no—
510C2×C42—861no—
511C2×C42C22×D4311yescharacteristic
512#107—434no—
513#107—434no—
514#107—434no—
515#107—434no—
516#106—434no—
517#106—434no—
518#106C22×D4314yes—
519#106C22×D4314yes—
520C4⋊C8—434no—
521C4⋊C8—434no—
522C4⋊C8—434no—
523C4⋊C8C22×D4314yes—
524#103—434no—
525#103—434no—
526#103—434no—
527#103—434no—
528#103—434no—
529#103—434no—
530#103C22×D4314yes—
531#103C22×D4314yes—
532C24—431no—
533C2×Q8—21no—
534C2×Q8—24no—
535C2×Q8—22no—
536C2×Q8—82no—
537C2×Q8—4316no—
538C2×Q8—434no—
539C2×Q8—432no—
540C2×Q8—864no—
541C2×Q8—868no—
542C2×Q8—864no—
543C2×Q8—8616no—
544C2×Q8—868no—
545C2×Q8—861no—
546C2×Q8—862no—
547C2×Q8—3442no—
548C2×Q8Q8×D4314yes—
549C2×Q8C23×D4312yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—431no—
555C22×C4—432no—
556C22×C4—434no—
557C22×C4—434no—
558C22×C4—432no—
559C22×C4—431no—
560C22×C4—431no—
561C22×C4—864no—
562C22×C4—868no—
563C22×C4—864no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—3442no—
569C22×C4D4×D4311yescharacteristic
570C22×C4D4×D4311yescharacteristic
571C22×C4C23×D4311yescharacteristic
572M16—868no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—432no—
576C2×C8—432no—
577C2×C8—868no—
578C2×C8—862no—
579C2×C8—862no—
580C2×C8C23×D4312yes—
581C2×C8C23×D4312yes—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—434no—
588C4⋊C4—434no—
589C4⋊C4—432no—
590C4⋊C4—432no—
591C4⋊C4—432no—
592C4⋊C4—864no—
593C4⋊C4—864no—
594C4⋊C4—864no—
595C4⋊C4—864no—
596C4⋊C4—864no—
597C4⋊C4—864no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—864no—
602C4⋊C4—864no—
603C4⋊C4—864no—
604C4⋊C4C23×D4312yes—
605C4⋊C4C23×D4312yes—
606C4⋊C4C23×D4312yes—
607C22⋊C4—434no—
608C22⋊C4—434no—
609C22⋊C4—864no—
610C22⋊C4—864no—
611C42—24no—
612C42—432no—
613C42—432no—
614C42—864no—
615C42—864no—
616C42—864no—
617C42—864no—
618C42—864no—
619C42D4×D4312yes—
620C42C23×D4312yes—
621C23—434no—
622C23—432no—
623C23—862no—
624C23—862no—
625C23C2×D4×D4311yescharacteristic
626Q8—24no—
627Q8—22no—
628Q8—84no—
629Q8—434no—
630Q8—8616no—
631Q8—864no—
632Q8—862no—
633Q8—3444no—
634Q8C2×Q8×D4314yes—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—434no—
646C2×C4—432no—
647C2×C4—438no—
648C2×C4—434no—
649C2×C4—434no—
650C2×C4—432no—
651C2×C4—432no—
652C2×C4—8616no—
653C2×C4—864no—
654C2×C4—862no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—3444no—
661C2×C4—1722no—
662C2×C4—1722no—
663C2×C4—1722no—
664C2×C4C2×D4×D4312yes—
665C2×C4C2×D4×D4312yes—
666C2×C4C2×D4×D4311yescharacteristic
667C2×C4C2×Q8×D4312yes—
668C2×C4#41×D4312yes—
669C2×C4C24×D4311yescharacteristic
670C8—22no—
671C8—22no—
672C8—862no—
673C8—862no—
674C22—434no—
675C22—862no—
676C22—862no—
677C22—868no—
678C22C22⋊Q8×D4312yes—
679C22#1458370512yes—
680C22#1458371512yes—
681C22C22×D4×D4311yescharacteristic
682C4—22no—
683C4—24no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—434no—
689C4—862no—
690C4—864no—
691C4—862no—
692C4—1722no—
693C4—1722no—
694C4—1722no—
695C4C22⋊Q8×D4312yes—
696C4C22×Q8×D4311yescharacteristic
697C4C2×#41×D4311yescharacteristic
698C2—864no—
699C2#1914443014yesdirect product factor
700C2C2×C22⋊Q8×D4311yescharacteristic
701C2C2×#1458370511yescharacteristic
702C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#475C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenterC2×#475D43
hypocenterC43C2×#3082
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #19144430C2direct (N × H)
4. C2×#14583209C2semidirect
5. C2×#14583207C2semidirect
6. C2×#14583206C2semidirect
7. C2×#14583204C2semidirect
8. C2×#14583192C2semidirect
9. C2×#14583191C2semidirect
10. C2×#14583183C2semidirect
16. C2×C43×#475C2semidirect
42. #14583209C22semidirect
43. #14583207C22semidirect
44. #14583206C22semidirect
45. #14583204C22semidirect
46. #14583192C22semidirect
47. #14583191C22semidirect
48. #14583183C22semidirect
71. C43×#475C22semidirect
82. C2×Q8×D43Q8semidirect
203. Q8×D43C2×Q8semidirect
357. C2×#475D43semidirect
363. C2×C43#3082semidirect
402. #475C2×D43semidirect
428. C43C2×#3082semidirect
699. C2#19144430direct (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×#145833752
#191444302
C2×#145832092
C2×#145832072
C2×#145832062
C2×#145832042
C2×#145831922
C2×#145831912
C2×#145831832
C2×#145829382
C2×#145829342
C2×#145829242
C2×#145829062
C2×#103×D432
C2×C43×#4752
C2×#308243