Finite Group Databasebeta

← C2×#19147155 #25975275

Subgroups — C2×#19147155 #25975275

Order 11008.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583595C211yesmaximal, characteristic
2#19147155C2116yesmaximal, direct product factor
3C2×#14583298C211yesmaximal, characteristic, complemented
4C2×#14583217C211yesmaximal, characteristic, complemented
5C2×#14583237C211yesmaximal, characteristic, complemented
6C2×#14583223C211yesmaximal, characteristic, complemented
7C2×#14583227C211yesmaximal, characteristic, complemented
8C2×#14583206C211yesmaximal, characteristic, complemented
9C2×#14583196C211yesmaximal, characteristic, complemented
10C2×#14583147C211yesmaximal, characteristic, complemented
11C2×#14583147C211yesmaximal, characteristic, complemented
12C2×C4×#10621884C211yesmaximal, characteristic, complemented
13C2×#14582977C211yesmaximal, characteristic, complemented
14C2×#14582942C211yesmaximal, characteristic, complemented
15C2×#14582939C211yesmaximal, characteristic, complemented
16C2×C43×#552C211yesmaximal, characteristic, complemented
17C22×#10621884C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
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#14583298C2218yescomplemented
33#14583237C2218yescomplemented
34#14583227C2218yescomplemented
35#14583223C2218yescomplemented
36#14583217C2218yescomplemented
37#14583206C2218yescomplemented
38#14583196C2218yescomplemented
39#14583147C2218yescomplemented
40#14583147C2218yescomplemented
41C4×#10621884C2218yescomplemented
42#14582977C2218yescomplemented
43#14582942C2218yescomplemented
44#14582939C2218yescomplemented
45C2×#13063258C2211yescharacteristic
46C2×#13063258C2211yescharacteristic
47C2×#13063258C2211yescharacteristic
48C2×#13063258C2211yescharacteristic
49C2×#13063256C2211yescharacteristic
50C2×#13063256C2211yescharacteristic
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×C4×C43⋊C8C2211yescharacteristic
64C43×#552—24no—
65C43×#552C2218yescomplemented
66C2×#126×C43—21no—
67C2×#125×C43—21no—
68C2×#125×C43C2211yescharacteristic
69C2×#123×C43—21no—
70C2×C22⋊Q8×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C2×C4×D4×C43C2211yescharacteristic
74C2×#117×C43—21no—
75C2×#117×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×#10621877—24no—
86C2×#10621877C2314yes—
87C2×#10621877C2314yes—
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
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#13063256C2314yes—
124#13063256C2314yes—
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—
137C4×C43⋊C8C2314yes—
138C22×Q8×C43C2311yescharacteristic
139C22×D4×C43D411yescharacteristic
140C23×C4×C43—21no—
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143#126×C43—28no—
144#125×C43—28no—
145#125×C43—22no—
146#125×C43C2314yes—
147#123×C43—28no—
148C22⋊Q8×C43—22no—
149C22⋊Q8×C43—22no—
150C22⋊Q8×C43C2314yes—
151C22⋊Q8×C43C2314yes—
152C4×Q8×C43—22no—
153C4×Q8×C43C2314yes—
154C4×D4×C43D414yes—
155C4×D4×C43C2314yes—
156#117×C43—22no—
157#117×C43—28no—
158#117×C43C2314yes—
159C2×C4⋊C4×C43—21no—
160C2×C4⋊C4×C43—22no—
161C2×C4⋊C4×C43—21no—
162C2×C4⋊C4×C43—21no—
163C2×C4⋊C4×C43—21no—
164C2×C4⋊C4×C43—21no—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43D411yescharacteristic
167C2×C4⋊C4×C43C2311yescharacteristic
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2314yes—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C22⋊C4×C43—21no—
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43D411yescharacteristic
175C2×C22⋊C4×C43D411yescharacteristic
176C2×C42×C43—21no—
177C2×C42×C43—21no—
178C2×C42×C43C2311yescharacteristic
179C24×C43C2×D411yescharacteristic
180C24×C43C2×D411yescharacteristic
181C23×D43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—22no—
184C2×Q8×C43—22no—
185C2×Q8×C43C2412yes—
186C2×D4×C43—42no—
187C2×D4×C43C2×D414yes—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—24no—
197C22×C4×C43—44no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D412yes—
203C22×C4×C43C2×D412yes—
204C22×C4×C43C2412yes—
205C22×C4×C43C2412yes—
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—24no—
208C2×C22⋊D43—24no—
209C2×C22⋊D43—44no—
210C2×C22⋊D43—82no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—24no—
215C22×Dic43—82no—
216C2×D172—21no—
217C2×D172—22no—
218C2×D172—22no—
219C2×D172C2412yes—
220C2×C4×D43—24no—
221C2×C4×D43—82no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—24no—
226C4⋊C4×C43—24no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—24no—
229C4⋊C4×C43—24no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43C2×D414yes—
232C4⋊C4×C43C2412yes—
233C4⋊C4×C43C2412yes—
234C4⋊C4×C43C2412yes—
235C22⋊C4×C43—24no—
236C22⋊C4×C43—24no—
237C22⋊C4×C43—24no—
238C22⋊C4×C43C2×D414yes—
239C22⋊C4×C43C2×D414yes—
240C42×C43—24no—
241C42×C43—24no—
242C42×C43C2×D412yes—
243C42×C43C2412yes—
244C22⋊Dic43—24no—
245#10621884—28no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—24no—
252C4⋊Dic43—21no—
253C4⋊Dic43C2412yes—
254C4⋊Dic43C2412yes—
255C4⋊Dic43C2412yes—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258C4×Dic43—24no—
259#10621877—28no—
260#10621877—28no—
261C2×C43⋊C8—22no—
262C2×C43⋊C8—22no—
263C2×C43⋊C8—22no—
264C2×C43⋊C8#4114yes—
265C2×C43⋊C8C2412yes—
266C2×C43⋊C8C2412yes—
267C2×C43⋊C8C2412yes—
268C2×C43⋊C8C2412yes—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43C22×D412yes—
276C23×C43C22×D412yes—
277C23×C43C22×D411yescharacteristic
278C22×D43—22no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43—42no—
282Q8×C43—22no—
283Q8×C43—22no—
284Q8×C43—42no—
285D4×C43—44no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—24no—
291C2×C4×C43—24no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—48no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D412yes—
307C2×C4×C43C22×D412yes—
308C2×C4×C43C22×D412yes—
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C2×#4112yes—
311C2×C4×C432−1+412yes—
312C2×C4×C43C2511yescharacteristic
313C22⋊D43—48no—
314C22⋊D43—84no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—84no—
322D172—22no—
323D172—22no—
324D172—42no—
325C4×D43—84no—
326C43⋊C8—22no—
327C43⋊C8—22no—
328C43⋊C8—22no—
329C43⋊C8C2×#4114yes—
330C2×#3351—431nomaximal, Sylow
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—44no—
338C22×C43—44no—
339C22×C43#54712yes—
340C22×C43#57512yes—
341C22×C43#57712yes—
342C22×C43C23×D411yescharacteristic
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—84no—
347C4×C43—22no—
348C4×C43—22no—
349C4×C43—22no—
350C4×C43—22no—
351C4×C43—42no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43#54712yes—
356C4×C43C22×#4111yescharacteristic
357C4×C43C2×2−1+411yescharacteristic
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361C2×#553—431no—
362C2×#552D4311yescharacteristic, complemented
363#3351—4316no—
364C2×#499—431no—
365C2×#481—431no—
366C2×#485—431no—
367C2×#482—431no—
368C2×#483—431no—
369C2×#479—431no—
370C2×#478—431no—
371C2×#468—431no—
372C2×#468—431no—
373C2×C4×SD16—431no—
374C2×#436—431no—
375C2×#428—431no—
376C2×#428—431no—
377C2×C43—42no—
378C2×C43—42no—
379C2×C43#335114yescomplemented
380C2×C43C2×#54711yescharacteristic
381C2×C43C2×#57511yescharacteristic
382C2×C43C2×#57711yescharacteristic
383D43—82no—
384C22×SD16—431no—
385C22×M16—431no—
386C22×M16—431no—
387#553—438no—
388#553—864no—
389#552—24no—
390#552C2×D4318yescomplemented
391C2×#126—21no—
392C2×#126—861no—
393C2×#125—21no—
394C2×#125—431no—
395C2×#125C2×D4311yescharacteristic
396C2×#123—21no—
397C2×#123—861no—
398C2×C22⋊Q8C2×D4311yescharacteristic
399C2×C22⋊Q8C2×D4311yescharacteristic
400C2×#121—431no—
401C2×#121—431no—
402C2×#121—861no—
403C2×C4×Q8C2×D4311yescharacteristic
404C2×C4×D4—431no—
405C2×C4×D4—861no—
406C2×C4×D4C2×D4311yescharacteristic
407C2×#117—21no—
408C2×#117—431no—
409C2×#117C2×D4311yescharacteristic
410C22×C4⋊C4—431no—
411C22×C4⋊C4C2×D4311yescharacteristic
412#499—438no—
413#485—438no—
414#483—438no—
415#482—438no—
416#481—438no—
417#479—438no—
418#478—438no—
419#468—438no—
420#468—438no—
421C4×SD16—438no—
422#436—438no—
423#428—438no—
424#428—438no—
425C2×#107—431no—
426C2×#107—431no—
427C2×#107—431no—
428C2×#107—431no—
429C2×#106—431no—
430C2×#106—431no—
431C2×#106—431no—
432C2×#106—431no—
433C2×#106—431no—
434C2×C4⋊C8—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#102—431no—
439C2×#102—431no—
440C2×#102—431no—
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C4×C8—431no—
444C43C2×#335111yescharacteristic, complemented, Sylow
445C22×Q8C22×D4311yescharacteristic
446C22×D4—431no—
447C22×D4—861no—
448C22×D4—861no—
449C22×D4C22⋊D4311yescharacteristic
450C23×C4—21no—
451C23×C4—861no—
452C23×C4—861no—
453C23×C4C22×D4311yescharacteristic
454C23×C4C22×D4311yescharacteristic
455C2×SD16—434no—
456C2×SD16—864no—
457C2×M16—434no—
458C2×M16—434no—
459C2×M16—864no—
460C2×M16—864no—
461C22×C8—431no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—431no—
465#126—28no—
466#126—868no—
467#125—28no—
468#125—22no—
469#125—434no—
470#125—862no—
471#125C22×D4314yes—
472#123—28no—
473#123—868no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8C22×D4314yes—
477C22⋊Q8C22×D4314yes—
478#121—434no—
479#121—434no—
480#121—868no—
481#121—862no—
482#121—862no—
483C4×Q8—22no—
484C4×Q8C22×D4314yes—
485C4×D4—434no—
486C4×D4—868no—
487C4×D4—862no—
488C4×D4C22⋊D4314yes—
489C4×D4C22×D4314yes—
490#117—22no—
491#117—28no—
492#117—434no—
493#117—862no—
494#117C22×D4314yes—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—434no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—862no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4C22⋊D4311yescharacteristic
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C4⋊C4C22×D4314yes—
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4C22⋊D4311yescharacteristic
523C2×C22⋊C4C22⋊D4311yescharacteristic
524C2×C42—21no—
525C2×C42—21no—
526C2×C42—861no—
527C2×C42C22×D4311yescharacteristic
528#107—434no—
529#107—434no—
530#107—434no—
531#107—434no—
532#106—434no—
533#106—434no—
534#106—434no—
535#106—434no—
536#106—434no—
537C4⋊C8—434no—
538#103—434no—
539#103—434no—
540#103—434no—
541#102—434no—
542#102—434no—
543#102—434no—
544C22⋊C8—434no—
545C22⋊C8—434no—
546C4×C8—434no—
547C24—861no—
548C24C2×C22⋊D4311yescharacteristic
549C24C2×C22⋊D4311yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8C23×D4312yes—
554C2×D4—42no—
555C2×D4—432no—
556C2×D4—864no—
557C2×D4—864no—
558C2×D4—861no—
559C2×D4—862no—
560C2×D4—862no—
561C2×D4—3442no—
562C2×D4—1724no—
563C2×D4C2×C22⋊D4314yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—44no—
574C22×C4—864no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—864no—
579C22×C4—3442no—
580C22×C4—3442no—
581C22×C4C2×C22⋊D4312yes—
582C22×C4C2×C22⋊D4312yes—
583C22×C4C2×C22⋊D4311yescharacteristic
584C22×C4C2×C22⋊D4311yescharacteristic
585C22×C4C2×C22⋊D4311yescharacteristic
586C22×C4C2×C22⋊D4311yescharacteristic
587C22×C4C23×D4312yes—
588C22×C4C23×D4312yes—
589C22×C4C23×D4311yescharacteristic
590SD16—868no—
591M16—868no—
592M16—868no—
593C2×C8—434no—
594C2×C8—432no—
595C2×C8—432no—
596C2×C8—432no—
597C2×C8—432no—
598C2×C8—862no—
599C2×C8—862no—
600C2×C8—862no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—21no—
610C4⋊C4—432no—
611C4⋊C4—432no—
612C4⋊C4—432no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—864no—
616C4⋊C4—861no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4C2×C22⋊D4314yes—
620C4⋊C4C23×D4312yes—
621C4⋊C4C23×D4312yes—
622C4⋊C4C23×D4312yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—864no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C22⋊C4—864no—
630C22⋊C4C2×C22⋊D4314yes—
631C22⋊C4C2×C22⋊D4314yes—
632C42—24no—
633C42—24no—
634C42—864no—
635C42C2×C22⋊D4312yes—
636C42C23×D4312yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—862no—
644C23—1722no—
645C23—1722no—
646C23—1722no—
647C23C22×C22⋊D4312yes—
648C23C22×C22⋊D4312yes—
649C23C22×C22⋊D4311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—44no—
654D4—862no—
655D4—862no—
656D4—3444no—
657D4—1728no—
658D4—1722no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—48no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—3444no—
682C2×C4—3444no—
683C2×C4—1722no—
684C2×C4—1722no—
685C2×C4—1722no—
686C2×C4C22×C22⋊D4312yes—
687C2×C4C22×C22⋊D4312yes—
688C2×C4C22×C22⋊D4312yes—
689C2×C4C22×C22⋊D4312yes—
690C2×C4C22×C22⋊D4311yescharacteristic
691C2×C4#41×D4312yes—
692C2×C4#1306337212yes—
693C2×C4C24×D4311yescharacteristic
694C8—434no—
695C8—862no—
696C8—862no—
697C8—862no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—3444no—
707C22—1722no—
708C22—1722no—
709C22—1722no—
710C22#1458354812yes—
711C22#1458369712yes—
712C22#1458370712yes—
713C22C23×C22⋊D4311yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—1722no—
723C4—1722no—
724C4—1722no—
725C4#1458354812yes—
726C4C2×#41×D4311yescharacteristic
727C4C2×#1306337211yescharacteristic
728C2—42no—
729C2—42no—
730C2—3442no—
731C2#1914715514yesdirect product factor
732C2C2×#1458354811yescharacteristic
733C2C2×#1458369711yescharacteristic
734C2C2×#1458370711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#552C2
socleC23×C43C22×D4
prime radicalC2×#14583595C2
hypercenterC2×#552D43
hypocenterC43C2×#3351
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #19147155C2direct (N × H)
3. C2×#14583298C2semidirect
4. C2×#14583217C2semidirect
5. C2×#14583237C2semidirect
6. C2×#14583223C2semidirect
7. C2×#14583227C2semidirect
8. C2×#14583206C2semidirect
9. C2×#14583196C2semidirect
10. C2×#14583147C2semidirect
11. C2×#14583147C2semidirect
12. C2×C4×#10621884C2semidirect
13. C2×#14582977C2semidirect
14. C2×#14582942C2semidirect
15. C2×#14582939C2semidirect
16. C2×C43×#552C2semidirect
32. #14583298C22semidirect
33. #14583237C22semidirect
34. #14583227C22semidirect
35. #14583223C22semidirect
36. #14583217C22semidirect
37. #14583206C22semidirect
38. #14583196C22semidirect
39. #14583147C22semidirect
40. #14583147C22semidirect
41. C4×#10621884C22semidirect
42. #14582977C22semidirect
43. #14582942C22semidirect
44. #14582939C22semidirect
65. C43×#552C22semidirect
362. C2×#552D43semidirect
379. C2×C43#3351semidirect
390. #552C2×D43semidirect
444. C43C2×#3351semidirect
731. C2#19147155direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835952
#191471552
C2×#145832982
C2×#145832172
C2×#145832372
C2×#145832232
C2×#145832272
C2×#145832062
C2×#145831962
C2×#145831472
C2×C4×#106218842
C2×#145829772
C2×#145829422
C2×#145829392
C2×C43×#5522
C2×#335143