Finite Group Databasebeta

← C2×#19147074 #25975170

Subgroups — C2×#19147074 #25975170

Order 11008.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583595C211yesmaximal, characteristic
2#19147074C2116yesmaximal, direct product factor
3C2×#14583305C211yesmaximal, characteristic, complemented
4C2×#14583232C211yesmaximal, characteristic, complemented
5C2×#14583217C211yesmaximal, characteristic, complemented
6C2×#14583237C211yesmaximal, characteristic, complemented
7C2×#14583212C211yesmaximal, characteristic, complemented
8C2×#14583206C211yesmaximal, characteristic, complemented
9C2×#14583176C211yesmaximal, characteristic, complemented
10C2×#14583147C211yesmaximal, characteristic, complemented
11C2×#14583130C211yesmaximal, characteristic, complemented
12C2×#14582997C211yesmaximal, characteristic, complemented
13C2×#14582971C211yesmaximal, characteristic, complemented
14C2×#14582939C211yesmaximal, characteristic, complemented
15C22×#13063258C211yesmaximal, characteristic, complemented
16C2×C43×#554C211yesmaximal, characteristic, complemented
17C22×#10621884C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20#14583595—24no—
21#14583595C2218yes—
22C2×#13063320—21no—
23C2×#13063317C2211yescharacteristic
24C2×#13063307—21no—
25C2×#13063299C2211yescharacteristic
26C2×#13063299C2211yescharacteristic
27C2×#13063297—21no—
28C2×C4×D172C2211yescharacteristic
29C2×(C22⋊D43)⋊C4—21no—
30C2×#13063284C2211yescharacteristic
31C22×C4⋊Dic43C2211yescharacteristic
32#14583305C2218yescomplemented
33#14583237C2218yescomplemented
34#14583232C2218yescomplemented
35#14583217C2218yescomplemented
36#14583212C2218yescomplemented
37#14583206C2218yescomplemented
38#14583176C2218yescomplemented
39#14583147C2218yescomplemented
40#14583130C2218yescomplemented
41#14582997C2218yescomplemented
42#14582971C2218yescomplemented
43#14582939C2218yescomplemented
44C2×#13063258C2211yescharacteristic
45C2×#13063258C2211yescharacteristic
46C2×#13063258C2211yescharacteristic
47C2×#13063258C2211yescharacteristic
48C2×#13063258C2211yescharacteristic
49C2×#13063258C2211yescharacteristic
50C2×#13063258C2218yescomplemented
51C2×#13063256C2211yescharacteristic
52C2×#13063256C2211yescharacteristic
53C2×#13063256C2211yescharacteristic
54C2×C4⋊(C43⋊C8)C2211yescharacteristic
55C2×#13063249C2211yescharacteristic
56C2×#13063249C2211yescharacteristic
57C2×#13063249C2211yescharacteristic
58C2×#13063245C2211yescharacteristic
59C2×#13063245C2211yescharacteristic
60C2×#13063245C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×C22⋊(C43⋊C8)C2211yescharacteristic
63C2×#13063236C2211yescharacteristic
64C43×#554—24no—
65C43×#554C2218yescomplemented
66C2×C4⋊Q8×C43C2211yescharacteristic
67C2×#125×C43—21no—
68C2×C22⋊Q8×C43—21no—
69C2×C22⋊Q8×C43—21no—
70C2×C22⋊Q8×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C2×C4×D4×C43—21no—
74C2×C4×D4×C43C2211yescharacteristic
75C22×C4⋊C4×C43C2211yescharacteristic
76C22×C4⋊C4×C43C2211yescharacteristic
77C22×D172C2311yescharacteristic
78C22×C22⋊D43—21no—
79C22×C22⋊D43—21no—
80C23×Dic43—21no—
81C22×C4×D43—21no—
82C2×#10621884—24no—
83C2×#10621884C2314yes—
84C2×#10621877—24no—
85C2×#10621877C2314yes—
86C22×C43⋊C8—24no—
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2314yes—
91C22×C43⋊C8C2311yescharacteristic
92#13063320—28no—
93#13063317—22no—
94#13063317C2314yes—
95#13063307—28no—
96#13063299—22no—
97#13063299—22no—
98#13063299C2314yes—
99#13063299C2314yes—
100#13063297—28no—
101C4×D172—22no—
102C4×D172C2314yes—
103(C22⋊D43)⋊C4—28no—
104#13063284—22no—
105#13063284C2314yes—
106C2×C4⋊Dic43—22no—
107C2×C4⋊Dic43—21no—
108C2×C4⋊Dic43C2314yes—
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×C4⋊Dic43C2311yescharacteristic
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C2×C22⋊Dic43—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×C4×Dic43—21no—
119#13063258C2314yes—
120#13063258C2314yes—
121#13063258C2314yes—
122#13063258C2314yes—
123#13063258C2314yes—
124#13063258C2314yes—
125#13063256C2314yes—
126#13063256C2314yes—
127#13063256C2314yes—
128C4⋊(C43⋊C8)C2314yes—
129#13063249C2314yes—
130#13063249C2314yes—
131#13063249C2314yes—
132#13063245C2314yes—
133#13063245C2314yes—
134#13063245C2314yes—
135C22⋊(C43⋊C8)C2314yes—
136C22⋊(C43⋊C8)C2314yes—
137#13063236C2314yes—
138C22×Q8×C43—21no—
139C22×Q8×C43C2311yescharacteristic
140C22×D4×C43D411yescharacteristic
141C23×C4×C43—21no—
142C23×C4×C43—21no—
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C4⋊Q8×C43—22no—
146C4⋊Q8×C43C2314yes—
147#125×C43—28no—
148C22⋊Q8×C43—22no—
149C22⋊Q8×C43—22no—
150C22⋊Q8×C43—28no—
151C22⋊Q8×C43—28no—
152C22⋊Q8×C43C2314yes—
153C22⋊Q8×C43C2314yes—
154C4×Q8×C43—22no—
155C4×Q8×C43C2314yes—
156C4×D4×C43—28no—
157C4×D4×C43D414yes—
158C4×D4×C43C2314yes—
159C2×C4⋊C4×C43—21no—
160C2×C4⋊C4×C43—21no—
161C2×C4⋊C4×C43—22no—
162C2×C4⋊C4×C43—22no—
163C2×C4⋊C4×C43—21no—
164C2×C4⋊C4×C43—21no—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43D411yescharacteristic
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2314yes—
172C2×C4⋊C4×C43C2314yes—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43D411yescharacteristic
176C2×C22⋊C4×C43D411yescharacteristic
177C2×C42×C43—21no—
178C2×C42×C43C2311yescharacteristic
179C24×C43C2×D411yescharacteristic
180C24×C43C2×D411yescharacteristic
181C23×D43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—24no—
184C2×Q8×C43—22no—
185C2×Q8×C43—22no—
186C2×Q8×C43—82no—
187C2×Q8×C43C2412yes—
188C2×D4×C43—24no—
189C2×D4×C43C2×D414yes—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—24no—
199C22×C4×C43—24no—
200C22×C4×C43—82no—
201C22×C4×C43—82no—
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D412yes—
207C22×C4×C43C2×D412yes—
208C22×C4×C43C2412yes—
209C22×C4×C43C2412yes—
210C22×C4×C43C2411yescharacteristic
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—44no—
214C2×C22⋊D43—82no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—24no—
219C22×Dic43—82no—
220C2×D172—21no—
221C2×D172—22no—
222C2×D172—22no—
223C2×D172C2412yes—
224C2×C4×D43—24no—
225C2×C4×D43—82no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—24no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—24no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—24no—
234C4⋊C4×C43—24no—
235C4⋊C4×C43C2×D414yes—
236C4⋊C4×C43C2412yes—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C22⋊C4×C43—24no—
240C22⋊C4×C43—24no—
241C22⋊C4×C43C2×D414yes—
242C22⋊C4×C43C2×D414yes—
243C42×C43—24no—
244C42×C43C2×D412yes—
245C42×C43C2412yes—
246C22⋊Dic43—24no—
247#10621884—28no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—24no—
254C4⋊Dic43—21no—
255C4⋊Dic43C2412yes—
256C4⋊Dic43C2412yes—
257C4⋊Dic43C2412yes—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260C4×Dic43—24no—
261#10621877—28no—
262C2×C43⋊C8—22no—
263C2×C43⋊C8—22no—
264C2×C43⋊C8—22no—
265C2×C43⋊C8—28no—
266C2×C43⋊C8#4114yes—
267C2×C43⋊C8C2412yes—
268C2×C43⋊C8C2412yes—
269C2×C43⋊C8C2412yes—
270C2×C43⋊C8C2412yes—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43#13714yes—
277C23×C43C22×D412yes—
278C23×C43C22×D412yes—
279C23×C43C22×D411yescharacteristic
280C22×D43—22no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43—42no—
284Q8×C43—22no—
285Q8×C43—22no—
286Q8×C43—42no—
287Q8×C43—84no—
288D4×C43—28no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—24no—
294C2×C4×C43—24no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43—84no—
308C2×C4×C43—84no—
309C2×C4×C43C22×D412yes—
310C2×C4×C43C22×D412yes—
311C2×C4×C43C22×D412yes—
312C2×C4×C43C22×D412yes—
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C2×#4112yes—
315C2×C4×C432−1+412yes—
316C2×C4×C43C2511yescharacteristic
317C22⋊D43—48no—
318C22⋊D43—84no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—84no—
326D172—22no—
327D172—22no—
328D172—42no—
329C4×D43—84no—
330C43⋊C8—22no—
331C43⋊C8—22no—
332C43⋊C8—22no—
333C43⋊C8C2×#4114yes—
334C2×#3346—431nomaximal, Sylow
335C22×C43—28no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—44no—
342C22×C43#54712yes—
343C22×C43C2×#13714yes—
344C22×C43C2×#13712yes—
345C22×C43#57612yes—
346C22×C43C23×D411yescharacteristic
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—84no—
351C4×C43—22no—
352C4×C43—22no—
353C4×C43—22no—
354C4×C43—22no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43—42no—
358C4×C43—42no—
359C4×C43#54712yes—
360C4×C43C22×#4111yescharacteristic
361C4×C43C2×2−1+411yescharacteristic
362Dic43—42no—
363Dic43—42no—
364Dic43—42no—
365C2×#554D4311yescharacteristic, complemented
366C2×#553—431no—
367#3346—4316no—
368C2×#501—431no—
369C2×#484—431no—
370C2×#481—431no—
371C2×#485—431no—
372C2×#480—431no—
373C2×#479—431no—
374C2×#474—431no—
375C2×#468—431no—
376C2×#465—431no—
377C2×#440—431no—
378C2×#435—431no—
379C2×#428—431no—
380C22×#107—431no—
381C2×C43—24no—
382C2×C43—42no—
383C2×C43#334614yescomplemented
384C2×C43C2×#54711yescharacteristic
385C2×C43C22×#13711yescharacteristic
386C2×C43C2×#57611yescharacteristic
387D43—82no—
388C22×SD16—431no—
389C22×M16—431no—
390C23×C8—431no—
391#554—24no—
392#554C2×D4318yescomplemented
393#553—438no—
394#553—864no—
395C2×C4⋊Q8C2×D4311yescharacteristic
396C2×#126—861no—
397C2×#125—21no—
398C2×#125—431no—
399C2×#123—861no—
400C2×C22⋊Q8—21no—
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8C2×D4311yescharacteristic
403C2×C22⋊Q8C2×D4311yescharacteristic
404C2×#121—431no—
405C2×#121—431no—
406C2×#121—861no—
407C2×C4×Q8C2×D4311yescharacteristic
408C2×C4×D4—21no—
409C2×C4×D4—431no—
410C2×C4×D4—861no—
411C2×C4×D4C2×D4311yescharacteristic
412C2×#117—431no—
413C22×C4⋊C4—431no—
414C22×C4⋊C4C2×D4311yescharacteristic
415C22×C4⋊C4C2×D4311yescharacteristic
416#501—438no—
417#485—438no—
418#484—438no—
419#481—438no—
420#480—438no—
421#479—438no—
422#474—438no—
423#468—438no—
424#465—438no—
425#440—438no—
426#435—438no—
427#428—438no—
428C2×#107—431no—
429C2×#107—431no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#107—438no—
433C2×#107—431no—
434C2×#107—431no—
435C2×#106—431no—
436C2×#106—431no—
437C2×#106—431no—
438C2×C4⋊C8—431no—
439C2×#103—431no—
440C2×#103—431no—
441C2×#103—431no—
442C2×#102—431no—
443C2×#102—431no—
444C2×#102—431no—
445C2×C22⋊C8—431no—
446C2×C22⋊C8—431no—
447C2×#97—431no—
448C43C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—21no—
450C22×Q8C22×D4311yescharacteristic
451C22×D4—431no—
452C22×D4—861no—
453C22×D4—861no—
454C22×D4C22⋊D4311yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—861no—
458C23×C4—861no—
459C23×C4C22×D4311yescharacteristic
460C23×C4C22×D4311yescharacteristic
461C2×SD16—434no—
462C2×SD16—864no—
463C2×M16—434no—
464C2×M16—864no—
465C22×C8—431no—
466C22×C8—431no—
467C22×C8—434no—
468C22×C8—431no—
469C22×C8—431no—
470C22×C8—864no—
471C4⋊Q8—22no—
472C4⋊Q8C22×D4314yes—
473#126—868no—
474#125—28no—
475#125—434no—
476#125—862no—
477#123—868no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—28no—
481C22⋊Q8—28no—
482C22⋊Q8C22×D4314yes—
483C22⋊Q8C22×D4314yes—
484#121—434no—
485#121—434no—
486#121—868no—
487#121—862no—
488#121—862no—
489C4×Q8—22no—
490C4×Q8C22×D4314yes—
491C4×D4—28no—
492C4×D4—434no—
493C4×D4—868no—
494C4×D4—862no—
495C4×D4C22⋊D4314yes—
496C4×D4C22×D4314yes—
497#117—434no—
498#117—862no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—434no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—862no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4C22⋊D4311yescharacteristic
516C2×C4⋊C4C22×D4311yescharacteristic
517C2×C4⋊C4C22×D4311yescharacteristic
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C4⋊C4C22×D4314yes—
520C2×C4⋊C4C22×D4314yes—
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⋊C4C22⋊D4311yescharacteristic
528C2×C22⋊C4C22⋊D4311yescharacteristic
529C2×C42—21no—
530C2×C42—861no—
531C2×C42C22×D4311yescharacteristic
532#107—434no—
533#107—434no—
534#107—434no—
535#107—434no—
536#107—434no—
537#107—434no—
538#106—434no—
539#106—434no—
540#106—434no—
541C4⋊C8—434no—
542#103—434no—
543#103—434no—
544#103—434no—
545#102—434no—
546#102—434no—
547#102—434no—
548C22⋊C8—434no—
549C22⋊C8—434no—
550#97—434no—
551C24—861no—
552C24C2×C22⋊D4311yescharacteristic
553C24C2×C22⋊D4311yescharacteristic
554C2×Q8—21no—
555C2×Q8—24no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—82no—
559C2×Q8C23×D4312yes—
560C2×D4—24no—
561C2×D4—432no—
562C2×D4—864no—
563C2×D4—864no—
564C2×D4—861no—
565C2×D4—862no—
566C2×D4—862no—
567C2×D4—3442no—
568C2×D4—1724no—
569C2×D4C2×C22⋊D4314yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—864no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—864no—
587C22×C4—3442no—
588C22×C4—3442no—
589C22×C4C2×C22⋊D4312yes—
590C22×C4C2×C22⋊D4312yes—
591C22×C4C2×C22⋊D4311yescharacteristic
592C22×C4C2×C22⋊D4311yescharacteristic
593C22×C4C2×C22⋊D4311yescharacteristic
594C22×C4C2×C22⋊D4311yescharacteristic
595C22×C4C23×D4312yes—
596C22×C4C23×D4312yes—
597C22×C4C23×D4311yescharacteristic
598SD16—868no—
599M16—868no—
600C2×C8—434no—
601C2×C8—432no—
602C2×C8—432no—
603C2×C8—432no—
604C2×C8—432no—
605C2×C8—868no—
606C2×C8—862no—
607C2×C8—862no—
608C2×C8—862no—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—432no—
619C4⋊C4—432no—
620C4⋊C4—432no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—864no—
624C4⋊C4—861no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4C2×C22⋊D4314yes—
628C4⋊C4C23×D4312yes—
629C4⋊C4C23×D4312yes—
630C4⋊C4C23×D4312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4C2×C22⋊D4314yes—
638C22⋊C4C2×C22⋊D4314yes—
639C42—24no—
640C42—864no—
641C42C2×C22⋊D4312yes—
642C42C23×D4312yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—862no—
649C23—1722no—
650C23—1722no—
651C23—1722no—
652C23#1306335614yes—
653C23C22×C22⋊D4312yes—
654C23C22×C22⋊D4312yes—
655C23C22×C22⋊D4311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—84no—
660D4—28no—
661D4—862no—
662D4—862no—
663D4—3444no—
664D4—1728no—
665D4—1722no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—84no—
685C2×C4—84no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—3444no—
690C2×C4—3444no—
691C2×C4—1722no—
692C2×C4—1722no—
693C2×C4—1722no—
694C2×C4C22×C22⋊D4312yes—
695C2×C4C22×C22⋊D4312yes—
696C2×C4C22×C22⋊D4312yes—
697C2×C4C22×C22⋊D4312yes—
698C2×C4C22×C22⋊D4311yescharacteristic
699C2×C4#41×D4312yes—
700C2×C4#1306337212yes—
701C2×C4C24×D4311yescharacteristic
702C8—434no—
703C8—862no—
704C8—862no—
705C8—862no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—3444no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22#1458354812yes—
718C22C2×#1306335614yes—
719C22C2×#1306335612yes—
720C22#1458370212yes—
721C22C23×C22⋊D4311yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—1722no—
731C4—1722no—
732C4—1722no—
733C4#1458354812yes—
734C4C2×#41×D4311yescharacteristic
735C4C2×#1306337211yescharacteristic
736C2—24no—
737C2—42no—
738C2—3442no—
739C2#1914707414yesdirect product factor
740C2C2×#1458354811yescharacteristic
741C2C22×#1306335611yescharacteristic
742C2C2×#1458370211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#554C2
socleC23×C43C22×D4
prime radicalC2×#14583595C2
hypercenterC2×#554D43
hypocenterC43C2×#3346
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #19147074C2direct (N × H)
3. C2×#14583305C2semidirect
4. C2×#14583232C2semidirect
5. C2×#14583217C2semidirect
6. C2×#14583237C2semidirect
7. C2×#14583212C2semidirect
8. C2×#14583206C2semidirect
9. C2×#14583176C2semidirect
10. C2×#14583147C2semidirect
11. C2×#14583130C2semidirect
12. C2×#14582997C2semidirect
13. C2×#14582971C2semidirect
14. C2×#14582939C2semidirect
15. C22×#13063258C2semidirect
16. C2×C43×#554C2semidirect
32. #14583305C22semidirect
33. #14583237C22semidirect
34. #14583232C22semidirect
35. #14583217C22semidirect
36. #14583212C22semidirect
37. #14583206C22semidirect
38. #14583176C22semidirect
39. #14583147C22semidirect
40. #14583130C22semidirect
41. #14582997C22semidirect
42. #14582971C22semidirect
43. #14582939C22semidirect
50. C2×#13063258C22semidirect
65. C43×#554C22semidirect
365. C2×#554D43semidirect
383. C2×C43#3346semidirect
392. #554C2×D43semidirect
448. C43C2×#3346semidirect
739. C2#19147074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835952
#191470742
C2×#145833052
C2×#145832322
C2×#145832172
C2×#145832372
C2×#145832122
C2×#145832062
C2×#145831762
C2×#145831472
C2×#145831302
C2×#145829972
C2×#145829712
C2×#145829392
C22×#130632582
C2×C43×#5542
C2×#334643