Finite Group Databasebeta

← C2×#19147429 #25976369

Subgroups — C2×#19147429 #25976369

Order 11008.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583621C211yesmaximal, characteristic, complemented
2C2×#14583610C211yesmaximal, characteristic, complemented
3#19147429C2116yesmaximal, direct product factor
4C2×#14583266C211yesmaximal, characteristic, complemented
5C2×#14583261C211yesmaximal, characteristic, complemented
6C2×#14583255C211yesmaximal, characteristic, complemented
7C2×#14583209C211yesmaximal, characteristic, complemented
8C2×#14583198C211yesmaximal, characteristic, complemented
9C2×#14583117C211yesmaximal, characteristic
10C2×#14583115C211yesmaximal, characteristic
11C2×#14583103C211yesmaximal, characteristic, complemented
12C2×#14583028C211yesmaximal, characteristic, complemented
13C2×#14583010C211yesmaximal, characteristic
14C2×#14582997C211yesmaximal, characteristic, complemented
15C2×#14582986C211yesmaximal, characteristic, complemented
16C2×C43×#475C211yesmaximal, characteristic, complemented
17C22×#10621873C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×D344C2211yescharacteristic
20#14583621—24no—
21#14583621C2218yescomplemented
22#14583610—24no—
23#14583610C2218yescomplemented
24C2×#13063323C2211yescharacteristic
25C2×#13063320—21no—
26C2×#13063319—21no—
27C2×#13063316C2211yescharacteristic
28C2×#13063316C2211yescharacteristic
29C2×#13063314C2211yescharacteristic
30C2×#13063313C2211yescharacteristic
31C2×#13063305—21no—
32C2×#13063303—21no—
33C2×#13063301—21no—
34C2×#13063301—21no—
35C2×C4×Dic86C2211yescharacteristic
36C2×#13063290C2211yescharacteristic
37C2×C4×D172C2211yescharacteristic
38C2×#13063287C2211yescharacteristic
39C2×#13063287C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×#13063282—21no—
42C2×C4⋊C4×D43—21no—
43#14583266C2218yescomplemented
44#14583261C2218yescomplemented
45#14583255C2218yescomplemented
46#14583209C2218yescomplemented
47#14583198C2218yescomplemented
48#14583117C2218yes—
49#14583115C2218yes—
50#14583103C2218yescomplemented
51#14583028C2218yescomplemented
52#14583010C2218yes—
53#14582997C2218yescomplemented
54#14582986C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57C2×Dic43⋊C8C2211yescharacteristic
58C2×#13063250C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063248C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063236C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
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×Dic86D411yescharacteristic
78C22×Dic86C2311yescharacteristic
79C22×D172C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×C4×D43—21no—
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C2×#10621873—24no—
86C2×#10621873C2314yes—
87C2×#10621884—24no—
88C2×#10621884C2314yes—
89C2×D344—24no—
90C2×D344C2314yes—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93#13063323—22no—
94#13063323C2314yes—
95#13063320—28no—
96#13063319—28no—
97#13063316—22no—
98#13063316—22no—
99#13063316C2314yes—
100#13063316C2314yes—
101#13063314—22no—
102#13063314C2314yes—
103#13063313—22no—
104#13063313C2314yes—
105#13063305—28no—
106#13063303—28no—
107#13063301—28no—
108#13063301—28no—
109C4×Dic86D414yes—
110C4×Dic86C2314yes—
111#13063290—22no—
112#13063290C2314yes—
113C4×D172—22no—
114C4×D172C2314yes—
115#13063287—22no—
116#13063287—22no—
117#13063287—22no—
118#13063287C2314yes—
119#13063287C2314yes—
120#13063287C2314yes—
121#13063282—28no—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43D411yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
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—28no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43C2311yescharacteristic
144C2×C4×Dic43C2311yescharacteristic
145#13063258C2314yes—
146Dic43⋊C8C2314yes—
147Dic43⋊C8C2314yes—
148#13063250C2314yes—
149#13063249C2314yes—
150#13063248C2314yes—
151#13063248C2314yes—
152#13063247C2314yes—
153#13063245C2314yes—
154#13063245C2314yes—
155#13063245C2314yes—
156#13063236C2314yes—
157#13063235C2314yes—
158C8×Dic43C2314yes—
159C22×Q8×C43—21no—
160C22×Q8×C43C2311yescharacteristic
161C22×C8×C43C2311yescharacteristic
162C22×C8×C43C2311yescharacteristic
163C4⋊Q8×C43—22no—
164C4⋊Q8×C43C2314yes—
165C4×Q8×C43—22no—
166C4×Q8×C43C2314yes—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C42×C43—21no—
173C2×C42×C43C2311yescharacteristic
174#106×C43C2314yes—
175#106×C43C2314yes—
176C4⋊C8×C43C2314yes—
177#103×C43C2314yes—
178#103×C43C2314yes—
179C23×D43—21no—
180C23×D43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—24no—
183C2×Q8×C43—22no—
184C2×Q8×C43—22no—
185C2×Q8×C43—82no—
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×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200C2×D172—21no—
201C2×D172—22no—
202C2×D172—21no—
203C2×D172—22no—
204C2×D172—22no—
205C2×D172#4114yes—
206C2×D172C2412yes—
207C2×D172C2412yes—
208C2×C4×D43—24no—
209C2×C4×D43—24no—
210C2×C4×D43—24no—
211C2×C4×D43—24no—
212C2×C4×D43—44no—
213C2×C4×D43—44no—
214C2×C4×D43—82no—
215C2×C4×D43—82no—
216C2×Dic86—22no—
217C2×Dic86—22no—
218C2×Dic86—21no—
219C2×Dic86—42no—
220C2×Dic86C2×D414yes—
221C2×Dic86C2412yes—
222C2×C8×C43—22no—
223C2×C8×C43—22no—
224C2×C8×C43C2412yes—
225C2×C8×C43C2412yes—
226C4⋊C4×C43—24no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43C2412yes—
232C4⋊C4×C43C2412yes—
233C4⋊C4×C43C2412yes—
234C42×C43—24no—
235C42×C43C2×D412yes—
236C42×C43C2412yes—
237#10621884—28no—
238(C2×D43)⋊C4—24no—
239(C2×D43)⋊C4—24no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246C4⋊Dic43—21no—
247C4⋊Dic43—24no—
248C4⋊Dic43—24no—
249C4⋊Dic43C2×D414yes—
250C4⋊Dic43C2412yes—
251Dic43⋊C4—24no—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4C2×D414yes—
257Dic43⋊C4C2×D414yes—
258C4×Dic43—24no—
259C4×Dic43C2×D412yes—
260C4×Dic43C2×D412yes—
261C4×Dic43C2412yes—
262C4×Dic43C2412yes—
263C2×C43⋊C8—22no—
264C2×C43⋊C8—22no—
265C2×C43⋊C8C2412yes—
266C2×C43⋊C8C2412yes—
267D344—28no—
268#10621873—28no—
269C23×C43C22×D411yescharacteristic
270C22×D43—24no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—42no—
274C22×D43—42no—
275C22×D43—42no—
276C22×D43—42no—
277C22×D43—42no—
278Q8×C43—22no—
279Q8×C43—22no—
280Q8×C43—42no—
281Q8×C43—84no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43C22×D412yes—
293C2×C4×C43C22×D412yes—
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C2×#4112yes—
296C2×C4×C432−1+412yes—
297C2×C4×C43C2511yescharacteristic
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—42no—
305C2×Dic43—42no—
306C2×Dic43C22×D412yes—
307C2×Dic43C22×D412yes—
308C2×Dic43C22×D412yes—
309C2×Dic43C22×D412yes—
310D172—24no—
311D172—22no—
312D172—22no—
313D172—22no—
314D172—42no—
315D172C2×#4114yes—
316C4×D43—48no—
317C4×D43—48no—
318C4×D43—84no—
319C4×D43—84no—
320Dic86—22no—
321Dic86—22no—
322Dic86—44no—
323Dic86—42no—
324C8×C43—22no—
325C8×C43—22no—
326C43⋊C8—22no—
327C43⋊C8—22no—
328C2×#3376—431nomaximal, Sylow
329C22×C43#54812yes—
330C22×C43#57512yes—
331C22×C43#57712yes—
332C22×C43C23×D411yescharacteristic
333C2×D43—24no—
334C2×D43—48no—
335C2×D43—42no—
336C2×D43—42no—
337C2×D43—42no—
338C2×D43—42no—
339C2×D43—42no—
340C2×D43—84no—
341C4×C43—22no—
342C4×C43—22no—
343C4×C43—42no—
344C4×C43—42no—
345C4×C43—42no—
346C4×C43—42no—
347C4×C43#54812yes—
348C4×C43C22×#4111yescharacteristic
349C4×C43C2×2−1+411yescharacteristic
350Dic43—22no—
351Dic43—22no—
352Dic43—22no—
353Dic43—22no—
354Dic43—42no—
355Dic43—42no—
356C2×#556—431no—
357C2×#554—431no—
358#3376—4316no—
359C2×#491—431no—
360C2×#489—431no—
361C2×#488—431no—
362C2×#479—431no—
363C2×#475D4311yescharacteristic, complemented
364C2×#478—431no—
365C2×#463—431no—
366C2×#463—431no—
367C2×#461—431no—
368C2×#446—431no—
369C2×#442—431no—
370C2×#440—431no—
371C2×C4×SD16—431no—
372C2×C43#337614yescomplemented
373C2×C43C2×#54811yescharacteristic
374C2×C43C2×#57511yescharacteristic
375C2×C43C2×#57711yescharacteristic
376D43—44no—
377D43—82no—
378C22×SD16—431no—
379C22×SD16—431no—
380C22×D8—431no—
381#556—438no—
382#556—864no—
383#554—438no—
384#554—864no—
385C2×C4⋊Q8—431no—
386C2×C4⋊Q8C2×D4311yescharacteristic
387C2×#126—861no—
388C2×#126—861no—
389C2×#125—431no—
390C2×#125—431no—
391C2×#124—431no—
392C2×#124—431no—
393C2×C22⋊Q8—861no—
394C2×C22⋊Q8—861no—
395C2×C22⋊Q8—861no—
396C2×C22⋊Q8—861no—
397C2×C4×Q8—431no—
398C2×C4×Q8—431no—
399C2×C4×Q8C2×D4311yescharacteristic
400C2×C4×D4—431no—
401C2×C4×D4—431no—
402C2×C4×D4—431no—
403C2×C4×D4—431no—
404C2×#117—861no—
405C22×C4⋊C4—861no—
406#491—438no—
407#489—438no—
408#488—438no—
409#479—438no—
410#478—438no—
411#475C2×D4318yescomplemented
412#463—438no—
413#463—438no—
414#461—438no—
415#446—438no—
416#442—438no—
417#440—438no—
418C4×SD16—438no—
419C2×#107—431no—
420C2×#106C2×D4311yescharacteristic
421C2×#106C2×D4311yescharacteristic
422C2×C4⋊C8—431no—
423C2×C4⋊C8—431no—
424C2×C4⋊C8C2×D4311yescharacteristic
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103C2×D4311yescharacteristic
430C2×#103C2×D4311yescharacteristic
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×#102—431no—
435C2×#97—431no—
436C2×#97—431no—
437C2×C4×C8—431no—
438C43C2×#337611yescharacteristic, complemented, Sylow
439C22×Q8—21no—
440C22×Q8—431no—
441C22×Q8—431no—
442C22×Q8C22×D4311yescharacteristic
443C22×D4—431no—
444C22×D4—431no—
445C23×C4—861no—
446C23×C4—861no—
447C23×C4—861no—
448C23×C4—861no—
449C2×SD16—434no—
450C2×SD16—434no—
451C2×SD16—864no—
452C2×SD16—864no—
453C2×D8—434no—
454C2×D8—864no—
455C22×C8—431no—
456C22×C8—431no—
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459C4⋊Q8—22no—
460C4⋊Q8—434no—
461C4⋊Q8—862no—
462C4⋊Q8C22×D4314yes—
463#126—868no—
464#126—868no—
465#125—434no—
466#125—434no—
467#125—862no—
468#125—862no—
469#124—434no—
470#124—434no—
471#124—862no—
472#124—862no—
473C22⋊Q8—868no—
474C22⋊Q8—868no—
475C22⋊Q8—868no—
476C22⋊Q8—868no—
477C4×Q8—22no—
478C4×Q8—434no—
479C4×Q8—434no—
480C4×Q8—434no—
481C4×Q8—862no—
482C4×Q8C22×D4314yes—
483C4×D4—434no—
484C4×D4—434no—
485C4×D4—434no—
486C4×D4—434no—
487C4×D4—862no—
488C4×D4—862no—
489C4×D4—862no—
490C4×D4—862no—
491#117—868no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—868no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C42—21no—
518C2×C42—431no—
519C2×C42—431no—
520C2×C42—861no—
521C2×C42C22×D4311yescharacteristic
522#107—434no—
523#106C22×D4314yes—
524#106C22×D4314yes—
525C4⋊C8—434no—
526C4⋊C8—434no—
527C4⋊C8C22×D4314yes—
528#103—434no—
529#103—434no—
530#103—434no—
531#103—434no—
532#103C22×D4314yes—
533#103C22×D4314yes—
534#102—434no—
535#102—434no—
536#102—434no—
537#102—434no—
538#97—434no—
539#97—434no—
540C4×C8—434no—
541C24—861no—
542C24—861no—
543C2×Q8—21no—
544C2×Q8—24no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—82no—
548C2×Q8—434no—
549C2×Q8—432no—
550C2×Q8—861no—
551C2×Q8—862no—
552C2×Q8—862no—
553C2×Q8—1722no—
554C2×Q8C23×D4312yes—
555C2×D4—434no—
556C2×D4—432no—
557C2×D4—432no—
558C2×D4—861no—
559C2×D4—861no—
560C2×D4—862no—
561C2×D4—862no—
562C2×D4—862no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—431no—
568C22×C4—431no—
569C22×C4—431no—
570C22×C4—431no—
571C22×C4—864no—
572C22×C4—864no—
573C22×C4—864no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—864no—
577C22×C4—3442no—
578C22×C4—3442no—
579C22×C4—1724no—
580C22×C4—1724no—
581C22×C4D4×D4311yescharacteristic
582C22×C4D4×D4311yescharacteristic
583C22×C4C23×D4311yescharacteristic
584SD16—868no—
585SD16—868no—
586D8—868no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—432no—
590C2×C8—432no—
591C2×C8—862no—
592C2×C8—862no—
593C2×C8C23×D4312yes—
594C2×C8C23×D4312yes—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—434no—
601C4⋊C4—434no—
602C4⋊C4—434no—
603C4⋊C4—432no—
604C4⋊C4—864no—
605C4⋊C4—864no—
606C4⋊C4—864no—
607C4⋊C4—864no—
608C4⋊C4—864no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—861no—
612C4⋊C4C23×D4312yes—
613C4⋊C4C23×D4312yes—
614C4⋊C4C23×D4312yes—
615C22⋊C4—864no—
616C22⋊C4—864no—
617C22⋊C4—864no—
618C22⋊C4—864no—
619C22⋊C4—864no—
620C22⋊C4—864no—
621C22⋊C4—864no—
622C22⋊C4—864no—
623C42—24no—
624C42—432no—
625C42—432no—
626C42—432no—
627C42—432no—
628C42—864no—
629C42D4×D4312yes—
630C42C23×D4312yes—
631C23—864no—
632C23—862no—
633C23—862no—
634C23—1722no—
635C23—1722no—
636C23—1722no—
637C23—1722no—
638C23—1722no—
639C23C2×D4×D4311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—42no—
643Q8—84no—
644Q8—862no—
645Q8—862no—
646Q8—1724no—
647Q8—1722no—
648D4—434no—
649D4—864no—
650D4—862no—
651D4—862no—
652D4—862no—
653D4—1722no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—432no—
665C2×C4—432no—
666C2×C4—432no—
667C2×C4—432no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—3444no—
675C2×C4—3444no—
676C2×C4—1728no—
677C2×C4—1728no—
678C2×C4—1722no—
679C2×C4—1722no—
680C2×C4C2×D4×D4312yes—
681C2×C4C2×D4×D4312yes—
682C2×C4C2×D4×D4311yescharacteristic
683C2×C4#41×D4312yes—
684C2×C4#1306337312yes—
685C2×C4C24×D4311yescharacteristic
686C8—22no—
687C8—22no—
688C8—862no—
689C8—862no—
690C22—864no—
691C22—3444no—
692C22—1722no—
693C22—1722no—
694C22—1722no—
695C22—1722no—
696C22—1722no—
697C22—1728no—
698C22#1458355912yes—
699C22#1458369812yes—
700C22#1458370512yes—
701C22C22×D4×D4311yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—862no—
709C4—862no—
710C4—862no—
711C4—862no—
712C4—1722no—
713C4—1722no—
714C4#1458355912yes—
715C4C2×#41×D4311yescharacteristic
716C4C2×#1306337311yescharacteristic
717C2—3442no—
718C2—1724no—
719C2#1914742914yesdirect product factor
720C2C2×#1458355911yescharacteristic
721C2C2×#1458369811yescharacteristic
722C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#475C2
socleC23×C43C22×D4
prime radicalC22×D344C22
hypercenterC2×#475D43
hypocenterC43C2×#3376
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
1. C2×#14583621C2semidirect
2. C2×#14583610C2semidirect
3. #19147429C2direct (N × H)
4. C2×#14583266C2semidirect
5. C2×#14583261C2semidirect
6. C2×#14583255C2semidirect
7. C2×#14583209C2semidirect
8. C2×#14583198C2semidirect
11. C2×#14583103C2semidirect
12. C2×#14583028C2semidirect
14. C2×#14582997C2semidirect
15. C2×#14582986C2semidirect
16. C2×C43×#475C2semidirect
21. #14583621C22semidirect
23. #14583610C22semidirect
43. #14583266C22semidirect
44. #14583261C22semidirect
45. #14583255C22semidirect
46. #14583209C22semidirect
47. #14583198C22semidirect
50. #14583103C22semidirect
51. #14583028C22semidirect
53. #14582997C22semidirect
54. #14582986C22semidirect
71. C43×#475C22semidirect
363. C2×#475D43semidirect
372. C2×C43#3376semidirect
411. #475C2×D43semidirect
438. C43C2×#3376semidirect
719. C2#19147429direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836212
C2×#145836102
#191474292
C2×#145832662
C2×#145832612
C2×#145832552
C2×#145832092
C2×#145831982
C2×#145831172
C2×#145831152
C2×#145831032
C2×#145830282
C2×#145830102
C2×#145829972
C2×#145829862
C2×C43×#4752
C2×#337643