Finite Group Databasebeta

← C2×#19145965 #25969450

Subgroups — C2×#19145965 #25969450

Order 11008.

1898 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic, complemented
2C2×#14583428C211yesmaximal, characteristic
3#19145965C2116yesmaximal, direct product factor
4C2×#14583207C211yesmaximal, characteristic, complemented
5C2×#14583206C211yesmaximal, characteristic, complemented
6C2×#14583192C211yesmaximal, characteristic, complemented
7C2×#14583187C211yesmaximal, characteristic, complemented
8C2×#14583156C211yesmaximal, characteristic, complemented
9C2×#14583154C211yesmaximal, characteristic, complemented
10C2×#14583144C211yesmaximal, characteristic
11C2×#14583142C211yesmaximal, characteristic
12C2×#14583118C211yesmaximal, characteristic, complemented
13C2×#14583107C211yesmaximal, characteristic, complemented
14C2×#14583102C211yesmaximal, characteristic, complemented
15C2×#14582921C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621885C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21#14583453—24no—
22#14583453C2218yescomplemented
23C2×#13063324C2211yescharacteristic
24C2×#13063323C2211yescharacteristic
25#14583428—24no—
26#14583428C2218yes—
27C2×#13063318—21no—
28C2×#13063317C2211yescharacteristic
29C2×#13063315—21no—
30C2×#13063307—21no—
31C2×#13063305C2211yescharacteristic
32C2×#13063303—21no—
33C2×#13063301C2211yescharacteristic
34C2×#13063301C2211yescharacteristic
35C2×#13063296C2211yescharacteristic
36C2×Q8×Dic43C2211yescharacteristic
37C2×C4×Dic86—21no—
38C2×C4×Dic86C2211yescharacteristic
39C2×D4×Dic43C2211yescharacteristic
40C2×(C22⋊D43)⋊C4—21no—
41C2×#13063282—21no—
42C2×#13063281—21no—
43C2×C42×D43C2211yescharacteristic
44#14583207C2218yescomplemented
45#14583206C2218yescomplemented
46#14583192C2218yescomplemented
47#14583187C2218yescomplemented
48#14583156C2218yescomplemented
49#14583154C2218yescomplemented
50#14583144C2218yes—
51#14583142C2218yes—
52#14583118C2218yescomplemented
53#14583107C2218yescomplemented
54#14583102C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59#14582921C2218yescomplemented
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×D43D411yescharacteristic
82C22×C4×D43D411yescharacteristic
83C22×C4×D43C2311yescharacteristic
84C2×#10621885—42no—
85C2×#10621885C2314yes—
86C2×#10621883—42no—
87C2×#10621883C2314yes—
88C2×#10621872—42no—
89C2×#10621872—42no—
90C2×#10621872C2314yes—
91C2×#10621872C2314yes—
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94#13063324—22no—
95#13063324C2314yes—
96#13063323—22no—
97#13063323C2314yes—
98#13063318—28no—
99#13063317—22no—
100#13063317C2314yes—
101#13063315—28no—
102#13063307—28no—
103#13063305—22no—
104#13063305C2314yes—
105#13063303—28no—
106#13063301—22no—
107#13063301—22no—
108#13063301C2314yes—
109#13063301C2314yes—
110#13063296—22no—
111#13063296C2314yes—
112Q8×Dic43—22no—
113Q8×Dic43C2314yes—
114C4×Dic86—22no—
115C4×Dic86—28no—
116C4×Dic86C2314yes—
117D4×Dic43—22no—
118D4×Dic43C2314yes—
119(C22⋊D43)⋊C4—28no—
120#13063282—28no—
121#13063281—28no—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
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×C22⋊Dic43—21no—
136C2×C22⋊Dic43—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43C2311yescharacteristic
145C42×D43D414yes—
146C42×D43C2314yes—
147#13063259C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150#13063256C2314yes—
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—44no—
204C22×Dic43—24no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—44no—
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C2×C4×D43—22no—
214C2×C4×D43—22no—
215C2×C4×D43—24no—
216C2×C4×D43—42no—
217C2×C4×D43C2×D412yes—
218C2×C4×D43C2×D414yes—
219C2×C4×D43C2×D414yes—
220C2×C4×D43C2412yes—
221C2×Dic86—22no—
222C2×Dic86—22no—
223C2×Dic86—21no—
224C2×Dic86—24no—
225C2×Dic86—44no—
226C2×Dic86C2412yes—
227Q16×C43—44no—
228SD16×C43—44no—
229C2×C8×C43—22no—
230C2×C8×C43—22no—
231C2×C8×C43C2412yes—
232C2×C8×C43C2412yes—
233C4⋊C4×C43—24no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C2412yes—
236C22⋊C4×C43—24no—
237C22⋊C4×C43—24no—
238C42×C43—24no—
239C42×C43C2×D412yes—
240C42×C43C2412yes—
241C22⋊Dic43—24no—
242C22⋊Dic43—24no—
243#10621885—44no—
244#10621883—44no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
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⋊C4—24no—
263Dic43⋊C4—24no—
264C4×Dic43—24no—
265C4×Dic43—24no—
266C4×Dic43C2×D412yes—
267C4×Dic43C2×D414yes—
268C4×Dic43C2×D414yes—
269C4×Dic43C2412yes—
270C2×C43⋊C8—22no—
271C2×C43⋊C8—22no—
272C2×C43⋊C8C2412yes—
273C2×C43⋊C8C2412yes—
274#10621872—44no—
275#10621872—44no—
276C23×C43—22no—
277C23×C43—42no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43C22×D411yescharacteristic
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43C22×D412yes—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—22no—
288Q8×C43—22no—
289Q8×C43—42no—
290Q8×C43—42no—
291D4×C43—22no—
292D4×C43—22no—
293D4×C43—42no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43C22×D412yes—
303C2×C4×C43C22×D412yes—
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43H(5,𝔽2)12yes—
306C2×C4×C432−1+412yes—
307C2×C4×C43C2511yescharacteristic
308C22⋊D43—48no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—48no—
320C2×Dic43#13714yes—
321C2×Dic43C22×D412yes—
322C2×Dic43C22×D412yes—
323C2×Dic43C22×D412yes—
324C4×D43—24no—
325C4×D43—22no—
326C4×D43—22no—
327C4×D43—28no—
328C4×D43—44no—
329Dic86—22no—
330Dic86—22no—
331Dic86—48no—
332Dic86—42no—
333C8×C43—22no—
334C8×C43—22no—
335C43⋊C8—22no—
336C43⋊C8—22no—
337C2×#3252—431nomaximal, Sylow
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—84no—
342C22×C43#53712yes—
343C22×C43C2×#13712yes—
344C22×C43#57512yes—
345C22×C43C23×D411yescharacteristic
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—44no—
350C4×C43—22no—
351C4×C43—22no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43#53712yes—
356C4×C43C2×H(5,𝔽2)11yescharacteristic
357C4×C43C2×2−1+411yescharacteristic
358Dic43—22no—
359Dic43—22no—
360Dic43—42no—
361Dic43—42no—
362Dic43—42no—
363Dic43—42no—
364Dic43C2×#13714yes—
365C2×#533—431no—
366C2×#529—431no—
367#3252—4316no—
368C2×#479—431no—
369C2×#479—431no—
370C2×#477—431no—
371C2×#476—431no—
372C2×#470—431no—
373C2×#470—431no—
374C2×#468—431no—
375C2×#468—431no—
376C2×#464—431no—
377C2×#464D4311yescharacteristic, complemented
378C2×#462—431no—
379C2×#461—431no—
380C2×#423—431no—
381C2×C43—82no—
382C2×C43#325214yescomplemented
383C2×C43C2×#53711yescharacteristic
384C2×C43C22×#13711yescharacteristic
385C2×C43C2×#57511yescharacteristic
386D43—42no—
387C22×Q16—431no—
388C22×Q16C2×D4311yescharacteristic
389C22×SD16—431no—
390C22×SD16C2×D4311yescharacteristic
391C22×M16—431no—
392C22×M16—431no—
393#533—438no—
394#533—864no—
395C2×C4⋊Q8—431no—
396C2×C4⋊Q8—431no—
397#529—438no—
398#529—864no—
399C2×#126—861no—
400C2×#125—431no—
401C2×#125—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×Q8—861no—
412C2×C4×Q8C2×D4311yescharacteristic
413C2×C4×D4—431no—
414C2×C4×D4—861no—
415C2×#117—861no—
416C2×#117—861no—
417C22×C42—431no—
418#479—438no—
419#479—438no—
420#477—438no—
421#476—438no—
422#470—438no—
423#470—438no—
424#468—438no—
425#468—438no—
426#464—438no—
427#464C2×D4318yescomplemented
428#462—438no—
429#461—438no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#106—431no—
433C2×#106—431no—
434#423—438no—
435C2×C4⋊C8—431no—
436C2×C4⋊C8—431no—
437C2×C4⋊C8—431no—
438C2×C4⋊C8C2×D4311yescharacteristic
439C2×#103—431no—
440C2×#103—431no—
441C2×#103—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#103C2×D4311yescharacteristic
445C2×#102—431no—
446C2×#102C2×D4311yescharacteristic
447C43C2×#325211yescharacteristic, complemented, Sylow
448C22×Q8—431no—
449C22×Q8—861no—
450C22×Q8C22×D4311yescharacteristic
451C22×Q8C22×D4311yescharacteristic
452C22×D4—861no—
453C22×D4C22×D4311yescharacteristic
454C23×C4—431no—
455C23×C4—431no—
456C23×C4—431no—
457C23×C4—861no—
458C2×Q16—42no—
459C2×Q16—434no—
460C2×Q16—1722no—
461C2×Q16C22×D4314yes—
462C2×SD16—42no—
463C2×SD16—434no—
464C2×SD16—1722no—
465C2×SD16C22×D4314yes—
466C2×M16—434no—
467C2×M16—434no—
468C2×M16—1722no—
469C2×M16—1722no—
470C22×C8—431no—
471C22×C8—431no—
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474C4⋊Q8—434no—
475C4⋊Q8—434no—
476C4⋊Q8—862no—
477C4⋊Q8—862no—
478#126—868no—
479#125—434no—
480#125—868no—
481#125—862no—
482#124—22no—
483#124C22×D4314yes—
484#123—868no—
485C22⋊Q8—434no—
486C22⋊Q8—434no—
487C22⋊Q8—434no—
488C22⋊Q8—862no—
489C22⋊Q8—868no—
490C22⋊Q8—862no—
491C22⋊Q8—862no—
492#121—434no—
493#121—862no—
494C4×Q8—22no—
495C4×Q8—434no—
496C4×Q8—434no—
497C4×Q8—868no—
498C4×Q8—862no—
499C4×Q8—862no—
500C4×Q8C22×D4314yes—
501C4×D4—434no—
502C4×D4—862no—
503C4×D4—868no—
504#117—868no—
505#117—868no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
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⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
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—431no—
531C2×C42—431no—
532C2×C42—434no—
533C2×C42—434no—
534C2×C42—861no—
535C2×C42—861no—
536C2×C42C22×D4311yescharacteristic
537#107—434no—
538#107—434no—
539#106—434no—
540#106—434no—
541C4⋊C8—434no—
542C4⋊C8—434no—
543C4⋊C8—434no—
544C4⋊C8C22×D4314yes—
545#103—434no—
546#103—434no—
547#103—434no—
548#103—434no—
549#103—434no—
550#103C22×D4314yes—
551#102—434no—
552#102C22×D4314yes—
553C24—21no—
554C24—431no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—432no—
562C2×Q8—864no—
563C2×Q8—861no—
564C2×Q8—862no—
565C2×Q8—862no—
566C2×Q8—1724no—
567C2×Q8C23×D4312yes—
568C2×Q8C23×D4312yes—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—864no—
573C2×D4—1724no—
574C2×D4C23×D4312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—434no—
582C22×C4—432no—
583C22×C4—432no—
584C22×C4—434no—
585C22×C4—864no—
586C22×C4—864no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—1722no—
594C22×C4—1724no—
595C22×C4D4×D4311yescharacteristic
596C22×C4D4×D4311yescharacteristic
597C22×C4C23×D4311yescharacteristic
598Q16—44no—
599Q16—1724no—
600SD16—44no—
601SD16—1724no—
602M16—1724no—
603M16—1724no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—432no—
607C2×C8—432no—
608C2×C8—862no—
609C2×C8—862no—
610C2×C8C23×D4312yes—
611C2×C8C23×D4312yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—432no—
615C4⋊C4—432no—
616C4⋊C4—432no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4C23×D4312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C42—24no—
639C42—434no—
640C42—432no—
641C42—434no—
642C42—432no—
643C42—864no—
644C42—864no—
645C42D4×D4312yes—
646C42C23×D4312yes—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—432no—
652C23—862no—
653C23—862no—
654C23—862no—
655C23C2×D4×D4311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—862no—
663Q8—862no—
664Q8—1728no—
665Q8—1722no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—1728no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—434no—
679C2×C4—432no—
680C2×C4—432no—
681C2×C4—432no—
682C2×C4—868no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—864no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—1724no—
693C2×C4—1728no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4—1722no—
698C2×C4C2×D4×D4312yes—
699C2×C4C2×D4×D4312yes—
700C2×C4C2×D4×D4311yescharacteristic
701C2×C4#1306337012yes—
702C2×C4#1306337212yes—
703C2×C4C24×D4311yescharacteristic
704C8—22no—
705C8—22no—
706C8—862no—
707C8—862no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—84no—
712C22—862no—
713C22—862no—
714C22—862no—
715C22—1724no—
716C22#1458347812yes—
717C22#137×D4312yes—
718C22#1458369612yes—
719C22C22×D4×D4311yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—434no—
726C4—862no—
727C4—862no—
728C4—1722no—
729C4—1722no—
730C4—1722no—
731C4—1722no—
732C4#1458347812yes—
733C4C2×#1306337011yescharacteristic
734C4C2×#1306337211yescharacteristic
735C2—82no—
736C2—1722no—
737C2#1914596514yesdirect product factor
738C2C2×#1458347811yescharacteristic
739C2C2×#137×D4311yescharacteristic
740C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenterC2×#464D43
hypocenterC43C2×#3252
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
1. C2×#14583453C2semidirect
3. #19145965C2direct (N × H)
4. C2×#14583207C2semidirect
5. C2×#14583206C2semidirect
6. C2×#14583192C2semidirect
7. C2×#14583187C2semidirect
8. C2×#14583156C2semidirect
9. C2×#14583154C2semidirect
12. C2×#14583118C2semidirect
13. C2×#14583107C2semidirect
14. C2×#14583102C2semidirect
15. C2×#14582921C2semidirect
16. C2×C43×#464C2semidirect
22. #14583453C22semidirect
44. #14583207C22semidirect
45. #14583206C22semidirect
46. #14583192C22semidirect
47. #14583187C22semidirect
48. #14583156C22semidirect
49. #14583154C22semidirect
52. #14583118C22semidirect
53. #14583107C22semidirect
54. #14583102C22semidirect
59. #14582921C22semidirect
73. C43×#464C22semidirect
377. C2×#464D43semidirect
382. C2×C43#3252semidirect
427. #464C2×D43semidirect
447. C43C2×#3252semidirect
737. C2#19145965direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834532
C2×#145834282
#191459652
C2×#145832072
C2×#145832062
C2×#145831922
C2×#145831872
C2×#145831562
C2×#145831542
C2×#145831442
C2×#145831422
C2×#145831182
C2×#145831072
C2×#145831022
C2×#145829212
C2×C43×#4642
C2×#325243