Finite Group Databasebeta

← C2×#19146018 #25969520

Subgroups — C2×#19146018 #25969520

Order 11008.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583518C211yesmaximal, characteristic
2C2×#14583507C211yesmaximal, characteristic, complemented
3#19146018C2116yesmaximal, direct product factor
4C2×#14583204C211yesmaximal, characteristic, complemented
5C2×#14583194C211yesmaximal, characteristic, complemented
6C2×#14583185C211yesmaximal, characteristic, complemented
7C2×#14583201C211yesmaximal, characteristic, complemented
8C2×#14583154C211yesmaximal, characteristic, complemented
9C2×#14583144C211yesmaximal, characteristic
10C2×#14583139C211yesmaximal, characteristic, complemented
11C2×#14583125C211yesmaximal, characteristic
12C2×#14583118C211yesmaximal, characteristic, complemented
13C2×#14583107C211yesmaximal, characteristic, complemented
14C2×#14583102C211yesmaximal, characteristic, complemented
15C2×#14582924C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621885C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583518—24no—
22#14583518C2218yes—
23#14583507—24no—
24#14583507C2218yescomplemented
25C2×#13063325C2211yescharacteristic
26C2×#13063323C2211yescharacteristic
27C2×#13063320—21no—
28C2×#13063319—21no—
29C2×#13063318—21no—
30C2×#13063317—21no—
31C2×#13063316C2211yescharacteristic
32C2×#13063315—21no—
33C2×#13063311—21no—
34C2×#13063309—21no—
35C2×#13063305C2211yescharacteristic
36C2×#13063302—21no—
37C2×#13063301C2211yescharacteristic
38C2×#13063301C2211yescharacteristic
39C2×#13063296C2211yescharacteristic
40C2×Q8×Dic43C2211yescharacteristic
41C2×C4×Dic86C2211yescharacteristic
42C2×D4×Dic43C2211yescharacteristic
43C2×#13063282C2211yescharacteristic
44#14583204C2218yescomplemented
45#14583201C2218yescomplemented
46#14583194C2218yescomplemented
47#14583185C2218yescomplemented
48#14583154C2218yescomplemented
49#14583144C2218yes—
50#14583139C2218yescomplemented
51#14583125C2218yes—
52#14583118C2218yescomplemented
53#14583107C2218yescomplemented
54#14583102C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59#14582924C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063249C2211yescharacteristic
66C2×#13063249C2211yescharacteristic
67C2×#13063249C2211yescharacteristic
68C2×#13063246C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C43×#464C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×C22⋊D43—21no—
80C23×Dic43—21no—
81C22×C4×D43C2311yescharacteristic
82C2×#10621885—42no—
83C2×#10621885C2314yes—
84C2×#10621883—42no—
85C2×#10621883C2314yes—
86C2×#10621872—42no—
87C2×#10621872C2314yes—
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C2×C8×D43—42no—
91C2×C8×D43C2314yes—
92#13063325—22no—
93#13063325C2314yes—
94#13063323—22no—
95#13063323C2314yes—
96#13063320—28no—
97#13063319—28no—
98#13063318—28no—
99#13063317—28no—
100#13063316—22no—
101#13063316C2314yes—
102#13063315—28no—
103#13063311—28no—
104#13063309—28no—
105#13063305—22no—
106#13063305C2314yes—
107#13063302—28no—
108#13063301—22no—
109#13063301—22no—
110#13063301C2314yes—
111#13063301C2314yes—
112#13063296—22no—
113#13063296C2314yes—
114Q8×Dic43—22no—
115Q8×Dic43C2314yes—
116C4×Dic86—22no—
117C4×Dic86C2314yes—
118D4×Dic43—22no—
119D4×Dic43C2314yes—
120#13063282D414yes—
121#13063282C2314yes—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4D411yescharacteristic
136C2×Dic43⋊C4D411yescharacteristic
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4D411yescharacteristic
143C2×(C2×D43)⋊C4D411yescharacteristic
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063258C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150#13063257C2314yes—
151C4⋊(C43⋊C8)C2314yes—
152Dic43⋊C8C2314yes—
153Dic43⋊C8C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063249C2314yes—
157#13063249C2314yes—
158#13063249C2314yes—
159#13063246C2314yes—
160C22×Q8×C43C2311yescharacteristic
161C22×Q8×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C2×Q16×C43—42no—
164C2×Q16×C43C2314yes—
165C2×SD16×C43—42no—
166C2×SD16×C43C2314yes—
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169#124×C43—22no—
170#124×C43C2314yes—
171C4×Q8×C43—22no—
172C4×Q8×C43C2314yes—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C42×C43—21no—
178C2×C42×C43C2311yescharacteristic
179C4⋊C8×C43C2314yes—
180#103×C43C2314yes—
181#102×C43C2314yes—
182C24×C43—21no—
183C23×D43C2×D411yescharacteristic
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43—22no—
190C2×Q8×C43C2412yes—
191C2×Q8×C43C2412yes—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43C2412yes—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—24no—
203C2×C22⋊D43—82no—
204C22×Dic43—24no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—82no—
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C2×C4×D43—22no—
214C2×C4×D43—22no—
215C2×C4×D43C2×D412yes—
216C2×C4×D43C2412yes—
217C2×Dic86—22no—
218C2×Dic86—22no—
219C2×Dic86—21no—
220C2×Dic86—24no—
221C2×Dic86—82no—
222C2×Dic86C2412yes—
223Q16×C43—44no—
224SD16×C43—44no—
225C2×C8×C43—22no—
226C2×C8×C43—22no—
227C2×C8×C43C2412yes—
228C2×C8×C43C2412yes—
229C4⋊C4×C43—24no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43C2412yes—
232C22⋊C4×C43—24no—
233C22⋊C4×C43—24no—
234C42×C43—24no—
235C42×C43C2×D412yes—
236C42×C43C2412yes—
237C22⋊Dic43—24no—
238C22⋊Dic43—24no—
239#10621885—44no—
240#10621883—44no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4C2×D414yes—
245(C2×D43)⋊C4C2×D414yes—
246C4⋊Dic43—24no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—24no—
251C4⋊Dic43—24no—
252C4⋊Dic43—24no—
253C4⋊Dic43C2412yes—
254C4⋊Dic43C2412yes—
255C4⋊Dic43C2412yes—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4C2×D414yes—
263Dic43⋊C4C2×D414yes—
264C4×Dic43—24no—
265C4×Dic43—24no—
266C4×Dic43C2×D412yes—
267C4×Dic43C2412yes—
268C2×C43⋊C8—22no—
269C2×C43⋊C8—22no—
270C2×C43⋊C8C2412yes—
271C2×C43⋊C8C2412yes—
272#10621872—44no—
273C8×D43—44no—
274C23×C43—22no—
275C23×C43—42no—
276C23×C43—42no—
277C23×C43—42no—
278C23×C43C22×D411yescharacteristic
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43C22×D412yes—
283Q8×C43—22no—
284Q8×C43—22no—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—42no—
288Q8×C43—42no—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—42no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43C22×D412yes—
301C2×C4×C43C22×D412yes—
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43H(5,𝔽2)12yes—
304C2×C4×C432−1+412yes—
305C2×C4×C43C2511yescharacteristic
306C22⋊D43—84no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—84no—
319C2×Dic43C22×D412yes—
320C2×Dic43C22×D412yes—
321C2×Dic43C22×D412yes—
322C4×D43—24no—
323C4×D43—22no—
324C4×D43—22no—
325Dic86—22no—
326Dic86—22no—
327Dic86—42no—
328Dic86—84no—
329C8×C43—22no—
330C8×C43—22no—
331C43⋊C8—22no—
332C43⋊C8—22no—
333C2×#3258—431nomaximal, Sylow
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—84no—
338C22×C43#53712yes—
339C22×C43#57712yes—
340C22×C43#57812yes—
341C22×C43C23×D411yescharacteristic
342C2×D43—22no—
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—44no—
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—42no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43#53712yes—
352C4×C43C2×H(5,𝔽2)11yescharacteristic
353C4×C43C2×2−1+411yescharacteristic
354Dic43—22no—
355Dic43—22no—
356Dic43—22no—
357Dic43—42no—
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361C2×#542—431no—
362C2×#541—431no—
363#3258—4316no—
364C2×#479—431no—
365C2×#477—431no—
366C2×#475—431no—
367C2×#478—431no—
368C2×#470—431no—
369C2×#468—431no—
370C2×#467—431no—
371C2×#465—431no—
372C2×#464—431no—
373C2×#464D4311yescharacteristic, complemented
374C2×#462—431no—
375C2×#461—431no—
376C2×#424—431no—
377C2×C43—82no—
378C2×C43#325814yescomplemented
379C2×C43C2×#53711yescharacteristic
380C2×C43C2×#57711yescharacteristic
381C2×C43C2×#57811yescharacteristic
382D43—42no—
383C22×Q16—431no—
384C22×Q16C2×D4311yescharacteristic
385C22×SD16—431no—
386C22×SD16C2×D4311yescharacteristic
387C22×M16—431no—
388C23×C8—431no—
389#542—438no—
390#542—864no—
391#541—438no—
392#541—864no—
393C2×C4⋊Q8—431no—
394C2×C4⋊Q8—431no—
395C2×#126—861no—
396C2×#126—861no—
397C2×#126—861no—
398C2×#125—431no—
399C2×#125—861no—
400C2×#125—861no—
401C2×#124—861no—
402C2×#124C2×D4311yescharacteristic
403C2×#123—861no—
404C2×C22⋊Q8—431no—
405C2×C22⋊Q8—431no—
406C2×C22⋊Q8—431no—
407C2×C22⋊Q8—861no—
408C2×#121—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×Q8C2×D4311yescharacteristic
412C2×C4×D4—431no—
413C2×#117—431no—
414#479—438no—
415#478—438no—
416#477—438no—
417#475—438no—
418#470—438no—
419#468—438no—
420#467—438no—
421#465—438no—
422#464—438no—
423#464C2×D4318yescomplemented
424#462—438no—
425#461—438no—
426C2×#107—431no—
427C2×#107—431no—
428C2×#106—431no—
429C2×#106—431no—
430#424—438no—
431C2×C4⋊C8—431no—
432C2×C4⋊C8—431no—
433C2×C4⋊C8—431no—
434C2×C4⋊C8C2×D4311yescharacteristic
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103—431no—
440C2×#103C2×D4311yescharacteristic
441C2×#102—431no—
442C2×#102C2×D4311yescharacteristic
443C43C2×#325811yescharacteristic, complemented, Sylow
444C22×Q8—431no—
445C22×Q8—861no—
446C22×Q8C22×D4311yescharacteristic
447C22×Q8C22×D4311yescharacteristic
448C22×D4—861no—
449C22×D4C22×D4311yescharacteristic
450C23×C4—431no—
451C23×C4—861no—
452C2×Q16—42no—
453C2×Q16—434no—
454C2×Q16—1722no—
455C2×Q16C22×D4314yes—
456C2×SD16—42no—
457C2×SD16—434no—
458C2×SD16—1722no—
459C2×SD16C22×D4314yes—
460C2×M16—434no—
461C2×M16—1722no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—434no—
465C22×C8—1722no—
466C22×C8C22×D4311yescharacteristic
467C22×C8C22×D4311yescharacteristic
468C4⋊Q8—434no—
469C4⋊Q8—434no—
470C4⋊Q8—862no—
471C4⋊Q8—862no—
472#126—868no—
473#126—868no—
474#126—868no—
475#125—434no—
476#125—868no—
477#125—862no—
478#125—868no—
479#124—22no—
480#124—868no—
481#124C22×D4314yes—
482#123—868no—
483C22⋊Q8—434no—
484C22⋊Q8—434no—
485C22⋊Q8—434no—
486C22⋊Q8—868no—
487C22⋊Q8—862no—
488C22⋊Q8—862no—
489C22⋊Q8—862no—
490#121—434no—
491#121—862no—
492C4×Q8—22no—
493C4×Q8—434no—
494C4×Q8—434no—
495C4×Q8—862no—
496C4×Q8—862no—
497C4×Q8C22×D4314yes—
498C4×D4—434no—
499C4×D4—862no—
500#117—434no—
501#117—434no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C42—21no—
529C2×C42—431no—
530C2×C42—861no—
531C2×C42—861no—
532C2×C42C22×D4311yescharacteristic
533#107—434no—
534#107—434no—
535#106—434no—
536#106—434no—
537C4⋊C8—434no—
538C4⋊C8—434no—
539C4⋊C8—434no—
540C4⋊C8C22×D4314yes—
541#103—434no—
542#103—434no—
543#103—434no—
544#103—434no—
545#103—434no—
546#103C22×D4314yes—
547#102—434no—
548#102C22×D4314yes—
549C24—21no—
550C24—431no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—432no—
558C2×Q8—864no—
559C2×Q8—861no—
560C2×Q8—862no—
561C2×Q8—862no—
562C2×Q8—3442no—
563C2×Q8C23×D4312yes—
564C2×Q8C23×D4312yes—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—864no—
569C2×D4—3442no—
570C2×D4C23×D4312yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—431no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—432no—
578C22×C4—432no—
579C22×C4—864no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—3442no—
587C22×C4D4×D4311yescharacteristic
588C22×C4D4×D4311yescharacteristic
589C22×C4C23×D4311yescharacteristic
590Q16—44no—
591Q16—1724no—
592SD16—44no—
593SD16—1724no—
594M16—1724no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—432no—
598C2×C8—432no—
599C2×C8—862no—
600C2×C8—862no—
601C2×C8—1724no—
602C2×C8C23×D4312yes—
603C2×C8C23×D4312yes—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—434no—
607C4⋊C4—434no—
608C4⋊C4—432no—
609C4⋊C4—432no—
610C4⋊C4—432no—
611C4⋊C4—864no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4C23×D4312yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—434no—
628C22⋊C4—434no—
629C22⋊C4—864no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C42—24no—
635C42—432no—
636C42—432no—
637C42—864no—
638C42—864no—
639C42D4×D4312yes—
640C42C23×D4312yes—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—432no—
646C23—862no—
647C23—862no—
648C23—862no—
649C23C2×D4×D4311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—862no—
657Q8—862no—
658Q8—3444no—
659Q8—1722no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—3444no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—432no—
673C2×C4—432no—
674C2×C4—432no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—864no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—3444no—
686C2×C4—1722no—
687C2×C4—1722no—
688C2×C4—1722no—
689C2×C4—1722no—
690C2×C4C2×D4×D4312yes—
691C2×C4C2×D4×D4312yes—
692C2×C4C2×D4×D4311yescharacteristic
693C2×C4#1306337012yes—
694C2×C4#1306337212yes—
695C2×C4C24×D4311yescharacteristic
696C8—22no—
697C8—22no—
698C8—862no—
699C8—862no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—862no—
705C22—862no—
706C22—862no—
707C22—1724no—
708C22#1458347812yes—
709C22#1458370612yes—
710C22#1458371512yes—
711C22C22×D4×D4311yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—862no—
718C4—862no—
719C4—862no—
720C4—1722no—
721C4—1722no—
722C4—1722no—
723C4—1722no—
724C4#1458347812yes—
725C4C2×#1306337011yescharacteristic
726C4C2×#1306337211yescharacteristic
727C2—82no—
728C2—1722no—
729C2#1914601814yesdirect product factor
730C2C2×#1458347811yescharacteristic
731C2C2×#1458370611yescharacteristic
732C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenterC2×#464D43
hypocenterC43C2×#3258
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×#14583507C2semidirect
3. #19146018C2direct (N × H)
4. C2×#14583204C2semidirect
5. C2×#14583194C2semidirect
6. C2×#14583185C2semidirect
7. C2×#14583201C2semidirect
8. C2×#14583154C2semidirect
10. C2×#14583139C2semidirect
12. C2×#14583118C2semidirect
13. C2×#14583107C2semidirect
14. C2×#14583102C2semidirect
15. C2×#14582924C2semidirect
16. C2×C43×#464C2semidirect
24. #14583507C22semidirect
44. #14583204C22semidirect
45. #14583201C22semidirect
46. #14583194C22semidirect
47. #14583185C22semidirect
48. #14583154C22semidirect
50. #14583139C22semidirect
52. #14583118C22semidirect
53. #14583107C22semidirect
54. #14583102C22semidirect
59. #14582924C22semidirect
73. C43×#464C22semidirect
373. C2×#464D43semidirect
378. C2×C43#3258semidirect
423. #464C2×D43semidirect
443. C43C2×#3258semidirect
729. C2#19146018direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835182
C2×#145835072
#191460182
C2×#145832042
C2×#145831942
C2×#145831852
C2×#145832012
C2×#145831542
C2×#145831442
C2×#145831392
C2×#145831252
C2×#145831182
C2×#145831072
C2×#145831022
C2×#145829242
C2×C43×#4642
C2×#325843