Finite Group Databasebeta

← C2×#19147540 #25977124

Subgroups — C2×#19147540 #25977124

Order 11008.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583627C211yesmaximal, characteristic, complemented
2#19147540C2116yesmaximal, direct product factor
3C2×#14583309C211yesmaximal, characteristic, complemented
4C2×#14583305C211yesmaximal, characteristic, complemented
5C2×#14583298C211yesmaximal, characteristic, complemented
6C2×#14583203C211yesmaximal, characteristic, complemented
7C2×#14583203C211yesmaximal, characteristic, complemented
8C2×#14583181C211yesmaximal, characteristic, complemented
9C2×#14583199C211yesmaximal, characteristic
10C2×#14583199C211yesmaximal, characteristic
11C2×#14583189C211yesmaximal, characteristic
12C2×#14583030C211yesmaximal, characteristic, complemented
13C2×#14582999C211yesmaximal, characteristic
14C2×#14582999C211yesmaximal, characteristic
15C2×C4×#10621883C211yesmaximal, characteristic
16C2×C43×#554C211yesmaximal, characteristic
17C22×#10621883C2211yescharacteristic
18#14583627—24no—
19#14583627C2218yescomplemented
20C2×#13063325C2211yescharacteristic
21C2×#13063323—21no—
22C2×#13063317C2211yescharacteristic
23C2×#13063317C2211yescharacteristic
24C2×#13063315—21no—
25C2×#13063315—21no—
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×Dic86C2211yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×#13063290—21no—
30#14583309C2218yescomplemented
31#14583305C2218yescomplemented
32#14583298C2218yescomplemented
33#14583203C2218yescomplemented
34#14583203C2218yescomplemented
35#14583199C2218yes—
36#14583199C2218yes—
37#14583189C2218yes—
38#14583181C2218yescomplemented
39#14583030C2218yescomplemented
40#14582999C2218yes—
41#14582999C2218yes—
42C4×#10621883C2218yes—
43C2×#13063258C2211yescharacteristic
44C2×#13063258C2211yescharacteristic
45C2×#13063258C2211yescharacteristic
46C2×#13063258C2211yescharacteristic
47C2×#13063256C2211yescharacteristic
48C2×#13063256C2211yescharacteristic
49C2×#13063256C2211yescharacteristic
50C2×#13063256C2211yescharacteristic
51C2×#13063256C2211yescharacteristic
52C2×C4⋊(C43⋊C8)C2211yescharacteristic
53C2×C4⋊(C43⋊C8)C2211yescharacteristic
54C2×C4⋊(C43⋊C8)C2211yescharacteristic
55C2×#13063248C2211yescharacteristic
56C2×#13063248C2211yescharacteristic
57C2×#13063248C2211yescharacteristic
58C2×#13063246C2211yescharacteristic
59C2×#13063246C2211yescharacteristic
60C2×#13063246C2211yescharacteristic
61C2×#13063236C2211yescharacteristic
62C2×#13063236C2211yescharacteristic
63C2×C4×C43⋊C8C2211yescharacteristic
64C43×#554—24no—
65C43×#554C2218yes—
66C2×C4⋊Q8×C43C2211yescharacteristic
67C2×#125×C43C2211yescharacteristic
68C2×#125×C43C2211yescharacteristic
69C2×C22⋊Q8×C43—21no—
70C2×C22⋊Q8×C43—21no—
71C2×C22⋊Q8×C43—21no—
72C2×C4×Q8×C43C2211yescharacteristic
73C2×C4×D4×C43C2211yescharacteristic
74C2×C4×D4×C43C2211yescharacteristic
75C2×C4×D4×C43C2211yescharacteristic
76C22×C4⋊C4×C43—21no—
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C2×#10621883Q818yescomplemented
80C2×#10621883C2314yes—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85#13063325—22no—
86#13063325C2314yes—
87#13063323—28no—
88#13063317—22no—
89#13063317—22no—
90#13063317C2314yes—
91#13063317C2314yes—
92#13063315—28no—
93#13063315—28no—
94C4×Dic86—22no—
95C4×Dic86—22no—
96C4×Dic86—22no—
97C4×Dic86C2314yes—
98C4×Dic86C2314yes—
99C4×Dic86C2314yes—
100#13063290—28no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115#13063258C2314yes—
116#13063258C2314yes—
117#13063258C2314yes—
118#13063258C2314yes—
119#13063256C2314yes—
120#13063256C2314yes—
121#13063256C2314yes—
122#13063256C2314yes—
123#13063256C2314yes—
124C4⋊(C43⋊C8)C2314yes—
125C4⋊(C43⋊C8)C2314yes—
126C4⋊(C43⋊C8)C2314yes—
127#13063248C2314yes—
128#13063248C2314yes—
129#13063248C2314yes—
130#13063246C2314yes—
131#13063246C2314yes—
132#13063246C2314yes—
133#13063236C2314yes—
134#13063236C2314yes—
135C4×C43⋊C8C2314yes—
136C22×Q8×C43—21no—
137C22×Q8×C43D411yescharacteristic
138C22×D4×C43C2311yescharacteristic
139C23×C4×C43—21no—
140C23×C4×C43—21no—
141C23×C4×C43—21no—
142C4⋊Q8×C43—22no—
143C4⋊Q8×C43C2314yes—
144#125×C43—22no—
145#125×C43—22no—
146#125×C43C2314yes—
147#125×C43C2314yes—
148C22⋊Q8×C43—28no—
149C22⋊Q8×C43—28no—
150C22⋊Q8×C43—28no—
151C4×Q8×C43D414yes—
152C4×Q8×C43C2314yes—
153C4×D4×C43—22no—
154C4×D4×C43—22no—
155C4×D4×C43—22no—
156C4×D4×C43C2314yes—
157C4×D4×C43C2314yes—
158C4×D4×C43C2314yes—
159C2×C4⋊C4×C43—21no—
160C2×C4⋊C4×C43—21no—
161C2×C4⋊C4×C43—21no—
162C2×C4⋊C4×C43—21no—
163C2×C4⋊C4×C43—21no—
164C2×C4⋊C4×C43—28no—
165C2×C4⋊C4×C43D411yescharacteristic
166C2×C4⋊C4×C43D411yescharacteristic
167C2×C4⋊C4×C43D411yescharacteristic
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C22⋊C4×C43—21no—
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C42×C43C2311yescharacteristic
175C2×C42×C43C2311yescharacteristic
176C2×C42×C43C2311yescharacteristic
177C24×C43—21no—
178C2×Q8×C43—24no—
179C2×Q8×C43—42no—
180C2×Q8×C43—82no—
181C2×Q8×C43C2×D414yes—
182C2×D4×C43—21no—
183C2×D4×C43—22no—
184C2×D4×C43C2×Q814yes—
185C2×D4×C43C2412yes—
186C22×C4×C43—24no—
187C22×C4×C43—24no—
188C22×C4×C43—24no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—44no—
193C22×C4×C43—82no—
194C22×C4×C43—82no—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C2×Dic86—21no—
207C2×Dic86—22no—
208C2×Dic86—24no—
209C2×Dic86—44no—
210C2×Dic86C2×Q814yes—
211C2×Dic86C2412yes—
212C4⋊C4×C43—24no—
213C4⋊C4×C43—24no—
214C4⋊C4×C43—24no—
215C4⋊C4×C43—24no—
216C4⋊C4×C43—24no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43C2×D414yes—
221C4⋊C4×C43C2×D414yes—
222C4⋊C4×C43C2×D414yes—
223C4⋊C4×C43C2412yes—
224C4⋊C4×C43C2412yes—
225C4⋊C4×C43C2412yes—
226C22⋊C4×C43—24no—
227C22⋊C4×C43—24no—
228C22⋊C4×C43—24no—
229C42×C43C2×D412yes—
230C42×C43C2×D412yes—
231C42×C43C2×D412yes—
232C42×C43C2412yes—
233C42×C43C2412yes—
234C42×C43C2412yes—
235#10621883C2×Q8116yescomplemented
236C4⋊Dic43—24no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43C2412yes—
241C4⋊Dic43C2412yes—
242C4⋊Dic43C2412yes—
243Dic43⋊C4—24no—
244Dic43⋊C4—24no—
245Dic43⋊C4—24no—
246Dic43⋊C4—24no—
247Dic43⋊C4—24no—
248Dic43⋊C4—24no—
249Dic43⋊C4—24no—
250C4×Dic43—24no—
251C4×Dic43—24no—
252C4×Dic43—24no—
253C2×C43⋊C8—22no—
254C2×C43⋊C8—22no—
255C2×C43⋊C8—22no—
256C2×C43⋊C8C2×Q814yes—
257C2×C43⋊C8C2412yes—
258C2×C43⋊C8C2412yes—
259C2×C43⋊C8C2412yes—
260C2×C43⋊C8C2412yes—
261C23×C43—24no—
262C23×C43—22no—
263C23×C43—42no—
264C23×C43—42no—
265C23×C43C22×D411yescharacteristic
266Q8×C43—44no—
267Q8×C43—84no—
268D4×C43—24no—
269D4×C43—22no—
270D4×C43C22×Q814yes—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—48no—
281C2×C4×C43—42no—
282C2×C4×C43—42no—
283C2×C4×C43—42no—
284C2×C4×C43—84no—
285C2×C4×C43—84no—
286C2×C4×C43C22×D412yes—
287C2×C4×C43C22×D412yes—
288C2×C4×C43C22×D412yes—
289C2×C4×C43C22×D412yes—
290C2×C4×C43C22×D412yes—
291C2×C4×C43C22×D412yes—
292C2×C4×C43C22×D411yescharacteristic
293C2×C4×C43C22×Q812yes—
294C2×C4×C432−1+412yes—
295C2×C4×C43C2511yescharacteristic
296C2×Dic43—24no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—42no—
302C2×Dic43—42no—
303C2×Dic43—42no—
304Dic86—24no—
305Dic86—22no—
306Dic86—48no—
307Dic86C22×Q814yes—
308C43⋊C8—22no—
309C43⋊C8—22no—
310C43⋊C8—22no—
311C43⋊C8C22×Q814yes—
312C2×#3388—431nomaximal, Sylow
313C22×C43—24no—
314C22×C43—48no—
315C22×C43—42no—
316C22×C43—42no—
317C22×C43D4×Q812yes—
318C22×C43#57512yes—
319C22×C43#57712yes—
320C22×C43C23×D411yescharacteristic
321C4×C43—22no—
322C4×C43—22no—
323C4×C43—22no—
324C4×C43—22no—
325C4×C43—22no—
326C4×C43—22no—
327C4×C43—42no—
328C4×C43—42no—
329C4×C43—42no—
330C4×C43D4×Q812yes—
331C4×C43C23×Q811yescharacteristic
332C4×C43C2×2−1+411yescharacteristic
333Dic43—24no—
334Dic43—42no—
335Dic43—42no—
336Dic43—42no—
337C2×#557—431no—
338C2×#554D4311yescharacteristic
339#3388—4316no—
340C2×#501—431no—
341C2×#501—431no—
342C2×#499—431no—
343C2×#479—431no—
344C2×#479—431no—
345C2×#475—431no—
346C2×#478—431no—
347C2×#478—431no—
348C2×#476—431no—
349C2×#446—431no—
350C2×#440—431no—
351C2×#440—431no—
352C2×C4×SD16—431no—
353C2×C43—44no—
354C2×C43#338814yescomplemented
355C2×C43C2×D4×Q811yescharacteristic
356C2×C43C2×#57511yescharacteristic
357C2×C43C2×#57711yescharacteristic
358C22×SD16—431no—
359#557—438no—
360#557—864no—
361#554—24no—
362#554C2×D4318yes—
363C2×C4⋊Q8—431no—
364C2×C4⋊Q8—861no—
365C2×C4⋊Q8C2×D4311yescharacteristic
366C2×#125—431no—
367C2×#125—431no—
368C2×#125—861no—
369C2×#125—861no—
370C2×#125C2×D4311yescharacteristic
371C2×#125C2×D4311yescharacteristic
372C2×C22⋊Q8—21no—
373C2×C22⋊Q8—21no—
374C2×C22⋊Q8—21no—
375C2×C4×Q8—431no—
376C2×C4×Q8—431no—
377C2×C4×Q8—431no—
378C2×C4×Q8—861no—
379C2×C4×Q8C2×D4311yescharacteristic
380C2×C4×D4C2×D4311yescharacteristic
381C2×C4×D4C2×D4311yescharacteristic
382C2×C4×D4C2×D4311yescharacteristic
383C22×C4⋊C4—21no—
384#501—438no—
385#501—438no—
386#499—438no—
387#479—438no—
388#479—438no—
389#478—438no—
390#478—438no—
391#476—438no—
392#475—438no—
393#446—438no—
394#440—438no—
395#440—438no—
396C4×SD16—438no—
397C2×#107—431no—
398C2×#107—431no—
399C2×#107—431no—
400C2×#107—431no—
401C2×#106—431no—
402C2×#106—431no—
403C2×#106—431no—
404C2×#106—431no—
405C2×#106—431no—
406C2×C4⋊C8—431no—
407C2×C4⋊C8—431no—
408C2×C4⋊C8—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#97—431no—
416C2×#97—431no—
417C2×C4×C8—431no—
418C43C2×#338811yescharacteristic, complemented, Sylow
419C22×Q8—21no—
420C22×Q8—431no—
421C22×Q8—861no—
422C22×Q8C22⋊D4311yescharacteristic
423C22×D4C22×D4311yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C2×SD16—438no—
428C2×SD16—434no—
429C22×C8—431no—
430C22×C8—431no—
431C22×C8—431no—
432C22×C8—431no—
433C4⋊Q8—22no—
434C4⋊Q8—434no—
435C4⋊Q8—868no—
436C4⋊Q8—862no—
437C4⋊Q8C22×D4314yes—
438#125—22no—
439#125—22no—
440#125—434no—
441#125—434no—
442#125—868no—
443#125—868no—
444#125—862no—
445#125—862no—
446#125C22×D4314yes—
447#125C22×D4314yes—
448C22⋊Q8—28no—
449C22⋊Q8—28no—
450C22⋊Q8—28no—
451C4×Q8—434no—
452C4×Q8—434no—
453C4×Q8—434no—
454C4×Q8—868no—
455C4×Q8—862no—
456C4×Q8—862no—
457C4×Q8—862no—
458C4×Q8C22⋊D4314yes—
459C4×Q8C22×D4314yes—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4C22×D4314yes—
464C4×D4C22×D4314yes—
465C4×D4C22×D4314yes—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—28no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4C22⋊D4311yescharacteristic
484C2×C4⋊C4C22⋊D4311yescharacteristic
485C2×C4⋊C4C22⋊D4311yescharacteristic
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C42—861no—
493C2×C42—861no—
494C2×C42—861no—
495C2×C42C22×D4311yescharacteristic
496C2×C42C22×D4311yescharacteristic
497C2×C42C22×D4311yescharacteristic
498#107—434no—
499#107—434no—
500#107—434no—
501#107—434no—
502#106—434no—
503#106—434no—
504#106—434no—
505#106—434no—
506#106—434no—
507C4⋊C8—434no—
508C4⋊C8—434no—
509C4⋊C8—434no—
510#103—434no—
511#103—434no—
512#103—434no—
513#102—434no—
514#102—434no—
515#102—434no—
516#97—434no—
517#97—434no—
518C4×C8—434no—
519C24—21no—
520C2×Q8—24no—
521C2×Q8—42no—
522C2×Q8—82no—
523C2×Q8—434no—
524C2×Q8—432no—
525C2×Q8—861no—
526C2×Q8—864no—
527C2×Q8—862no—
528C2×Q8—1724no—
529C2×Q8C2×C22⋊D4314yes—
530C2×D4—21no—
531C2×D4—22no—
532C2×D4Q8×D4314yes—
533C2×D4C23×D4312yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—44no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4C2×C22⋊D4311yescharacteristic
548C22×C4C2×C22⋊D4311yescharacteristic
549C22×C4C2×C22⋊D4311yescharacteristic
550C22×C4C2×C22⋊D4311yescharacteristic
551C22×C4C2×C22⋊D4311yescharacteristic
552C22×C4C2×C22⋊D4311yescharacteristic
553C22×C4C23×D4311yescharacteristic
554SD16—4316no—
555C2×C8—434no—
556C2×C8—432no—
557C2×C8—432no—
558C2×C8—432no—
559C2×C8—432no—
560C2×C8—862no—
561C2×C8—862no—
562C2×C8—862no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—432no—
572C4⋊C4—432no—
573C4⋊C4—432no—
574C4⋊C4—861no—
575C4⋊C4—861no—
576C4⋊C4—861no—
577C4⋊C4—864no—
578C4⋊C4—864no—
579C4⋊C4—864no—
580C4⋊C4—864no—
581C4⋊C4—864no—
582C4⋊C4—864no—
583C4⋊C4—864no—
584C4⋊C4—864no—
585C4⋊C4C2×C22⋊D4314yes—
586C4⋊C4C2×C22⋊D4314yes—
587C4⋊C4C2×C22⋊D4314yes—
588C4⋊C4C23×D4312yes—
589C4⋊C4C23×D4312yes—
590C4⋊C4C23×D4312yes—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C42—864no—
595C42—864no—
596C42—864no—
597C42C2×C22⋊D4312yes—
598C42C2×C22⋊D4312yes—
599C42C2×C22⋊D4312yes—
600C42C23×D4312yes—
601C42C23×D4312yes—
602C42C23×D4312yes—
603C23—24no—
604C23—22no—
605C23—42no—
606C23—42no—
607C23C22×C22⋊D4311yescharacteristic
608Q8—44no—
609Q8—84no—
610Q8—434no—
611Q8—864no—
612Q8—862no—
613Q8—1728no—
614D4—24no—
615D4—22no—
616D4C2×Q8×D4314yes—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—48no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—84no—
631C2×C4—84no—
632C2×C4—864no—
633C2×C4—862no—
634C2×C4—862no—
635C2×C4—862no—
636C2×C4—862no—
637C2×C4—1722no—
638C2×C4—1722no—
639C2×C4—1722no—
640C2×C4C22×C22⋊D4312yes—
641C2×C4C22×C22⋊D4312yes—
642C2×C4C22×C22⋊D4312yes—
643C2×C4C22×C22⋊D4312yes—
644C2×C4C22×C22⋊D4312yes—
645C2×C4C22×C22⋊D4312yes—
646C2×C4C22×C22⋊D4311yescharacteristic
647C2×C4C2×Q8×D4312yes—
648C2×C4#1306337312yes—
649C2×C4C24×D4311yescharacteristic
650C8—434no—
651C8—862no—
652C8—862no—
653C8—862no—
654C22—24no—
655C22—48no—
656C22—42no—
657C22—42no—
658C22Q8×C22⋊D4312yes—
659C22#1458369712yes—
660C22#1458371012yes—
661C22C23×C22⋊D4311yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—22no—
667C4—22no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—864no—
672C4—1722no—
673C4—1722no—
674C4—1722no—
675C4Q8×C22⋊D4312yes—
676C4C22×Q8×D4311yescharacteristic
677C4C2×#1306337311yescharacteristic
678C2—44no—
679C2#1914754014yesdirect product factor
680C2C2×Q8×C22⋊D4311yescharacteristic
681C2C2×#1458369711yescharacteristic
682C2C2×#1458371011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#554C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC2×#554D43
hypocenterC43C2×#3388
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#14583627C2semidirect
2. #19147540C2direct (N × H)
3. C2×#14583309C2semidirect
4. C2×#14583305C2semidirect
5. C2×#14583298C2semidirect
6. C2×#14583203C2semidirect
7. C2×#14583203C2semidirect
8. C2×#14583181C2semidirect
12. C2×#14583030C2semidirect
19. #14583627C22semidirect
30. #14583309C22semidirect
31. #14583305C22semidirect
32. #14583298C22semidirect
33. #14583203C22semidirect
34. #14583203C22semidirect
38. #14583181C22semidirect
39. #14583030C22semidirect
79. C2×#10621883Q8semidirect
235. #10621883C2×Q8semidirect
354. C2×C43#3388semidirect
418. C43C2×#3388semidirect
679. C2#19147540direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836272
#191475402
C2×#145833092
C2×#145833052
C2×#145832982
C2×#145832032
C2×#145831812
C2×#145831992
C2×#145831892
C2×#145830302
C2×#145829992
C2×C4×#106218832
C2×C43×#5542
C2×#338843