Finite Group Databasebeta

← C2×#19147044 #25975138

Subgroups — C2×#19147044 #25975138

Order 11008.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic
2#19147044C2116yesmaximal, direct product factor
3C2×#14583305C211yesmaximal, characteristic, complemented
4C2×#14583234C211yesmaximal, characteristic, complemented
5C2×#14583237C211yesmaximal, characteristic, complemented
6C2×#14583229C211yesmaximal, characteristic, complemented
7C2×#14583227C211yesmaximal, characteristic, complemented
8C2×#14583206C211yesmaximal, characteristic, complemented
9C2×#14583181C211yesmaximal, characteristic, complemented
10C2×#14583155C211yesmaximal, characteristic, complemented
11C2×#14583138C211yesmaximal, characteristic, complemented
12C2×#14583004C211yesmaximal, characteristic, complemented
13C2×#14582971C211yesmaximal, characteristic
14C2×#14582939C211yesmaximal, characteristic, complemented
15C22×#13063256C211yesmaximal, characteristic, complemented
16C2×C43×#554C211yesmaximal, characteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20#14583589—24no—
21#14583589C2218yes—
22C2×#13063318—21no—
23C2×#13063317C2211yescharacteristic
24C2×#13063315—21no—
25C2×#13063306—21no—
26C2×#13063304C2211yescharacteristic
27C2×#13063304C2211yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30C2×#13063281—21no—
31C22×C4⋊Dic43C2211yescharacteristic
32#14583305C2218yescomplemented
33#14583237C2218yescomplemented
34#14583234C2218yescomplemented
35#14583229C2218yescomplemented
36#14583227C2218yescomplemented
37#14583206C2218yescomplemented
38#14583181C2218yescomplemented
39#14583155C2218yescomplemented
40#14583138C2218yescomplemented
41#14583004C2218yescomplemented
42#14582971C2218yes—
43#14582939C2218yescomplemented
44C2×#13063258C2211yescharacteristic
45C2×#13063258C2211yescharacteristic
46C2×#13063258C2211yescharacteristic
47C2×#13063256C2211yescharacteristic
48C2×#13063256C2211yescharacteristic
49C2×#13063256C2211yescharacteristic
50C2×#13063256C2211yescharacteristic
51C2×#13063256C2211yescharacteristic
52C2×#13063256C2211yescharacteristic
53C2×#13063256C2218yescomplemented
54C2×C4⋊(C43⋊C8)C2211yescharacteristic
55C2×#13063249C2211yescharacteristic
56C2×#13063249C2211yescharacteristic
57C2×#13063249C2211yescharacteristic
58C2×#13063248C2211yescharacteristic
59C2×#13063248C2211yescharacteristic
60C2×#13063248C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×C22⋊(C43⋊C8)C2211yescharacteristic
63C2×#13063236C2211yescharacteristic
64C43×#554—24no—
65C43×#554C2218yes—
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×Dic86C2311yescharacteristic
78C23×Dic43—21no—
79C2×#10621885—24no—
80C2×#10621885C2314yes—
81C2×#10621877—24no—
82C2×#10621877C2314yes—
83C22×C43⋊C8—24no—
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2314yes—
88C22×C43⋊C8C2311yescharacteristic
89#13063318—28no—
90#13063317—22no—
91#13063317C2314yes—
92#13063315—28no—
93#13063306—28no—
94#13063304—22no—
95#13063304—22no—
96#13063304C2314yes—
97#13063304C2314yes—
98C4×Dic86—22no—
99C4×Dic86C2314yes—
100#13063284—22no—
101#13063284C2314yes—
102#13063281—28no—
103C2×C4⋊Dic43—22no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43C2314yes—
106C2×C4⋊Dic43C2311yescharacteristic
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C2×C22⋊Dic43—21no—
115C2×C22⋊Dic43—21no—
116C2×C22⋊Dic43—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119#13063258C2314yes—
120#13063258C2314yes—
121#13063258C2314yes—
122#13063256C2314yes—
123#13063256C2314yes—
124#13063256C2314yes—
125#13063256C2314yes—
126#13063256C2314yes—
127#13063256C2314yes—
128C4⋊(C43⋊C8)C2314yes—
129#13063249C2314yes—
130#13063249C2314yes—
131#13063249C2314yes—
132#13063248C2314yes—
133#13063248C2314yes—
134#13063248C2314yes—
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
181C2×Q8×C43—21no—
182C2×Q8×C43—24no—
183C2×Q8×C43—22no—
184C2×Q8×C43—22no—
185C2×Q8×C43—82no—
186C2×Q8×C43C2412yes—
187C2×D4×C43—24no—
188C2×D4×C43C2×D414yes—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—24no—
198C22×C4×C43—24no—
199C22×C4×C43—82no—
200C22×C4×C43—82no—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D412yes—
206C22×C4×C43C2×D412yes—
207C22×C4×C43C2412yes—
208C22×C4×C43C2412yes—
209C22×C4×C43C2411yescharacteristic
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—24no—
215C22×Dic43—44no—
216C2×Dic86—22no—
217C2×Dic86—22no—
218C2×Dic86—21no—
219C2×Dic86C2412yes—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—24no—
222C4⋊C4×C43—24no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—24no—
226C4⋊C4×C43—24no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—24no—
229C4⋊C4×C43C2×D414yes—
230C4⋊C4×C43C2412yes—
231C4⋊C4×C43C2412yes—
232C4⋊C4×C43C2412yes—
233C22⋊C4×C43—24no—
234C22⋊C4×C43—24no—
235C22⋊C4×C43C2×D414yes—
236C22⋊C4×C43C2×D414yes—
237C42×C43—24no—
238C42×C43C2×D412yes—
239C42×C43C2412yes—
240C22⋊Dic43—24no—
241C22⋊Dic43—24no—
242C22⋊Dic43—24no—
243#10621885—28no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—24no—
247C4⋊Dic43—21no—
248C4⋊Dic43C2412yes—
249C4⋊Dic43C2412yes—
250C4⋊Dic43C2412yes—
251Dic43⋊C4—24no—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256C4×Dic43—24no—
257C4×Dic43—24no—
258#10621877—28no—
259C2×C43⋊C8—22no—
260C2×C43⋊C8—22no—
261C2×C43⋊C8—22no—
262C2×C43⋊C8—28no—
263C2×C43⋊C8#4114yes—
264C2×C43⋊C8C2412yes—
265C2×C43⋊C8C2412yes—
266C2×C43⋊C8C2412yes—
267C2×C43⋊C8C2412yes—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43#13714yes—
274C23×C43C22×D412yes—
275C23×C43C22×D412yes—
276C23×C43C22×D411yescharacteristic
277Q8×C43—22no—
278Q8×C43—22no—
279Q8×C43—42no—
280Q8×C43—84no—
281D4×C43—28no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—24no—
287C2×C4×C43—24no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—84no—
301C2×C4×C43—84no—
302C2×C4×C43C22×D412yes—
303C2×C4×C43C22×D412yes—
304C2×C4×C43C22×D412yes—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C2×#4112yes—
308C2×C4×C432−1+412yes—
309C2×C4×C43C2511yescharacteristic
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—42no—
315C2×Dic43—48no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319Dic86—22no—
320Dic86—22no—
321Dic86—42no—
322C43⋊C8—22no—
323C43⋊C8—22no—
324C43⋊C8—22no—
325C43⋊C8C2×#4114yes—
326C2×#3344—431nomaximal, Sylow
327C22×C43—28no—
328C22×C43—22no—
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—44no—
334C22×C43#54712yes—
335C22×C43C2×#13714yes—
336C22×C43C2×#13712yes—
337C22×C43#57712yes—
338C22×C43C23×D411yescharacteristic
339C4×C43—22no—
340C4×C43—22no—
341C4×C43—22no—
342C4×C43—22no—
343C4×C43—42no—
344C4×C43—42no—
345C4×C43—42no—
346C4×C43—42no—
347C4×C43#54712yes—
348C4×C43C22×#4111yescharacteristic
349C4×C43C2×2−1+411yescharacteristic
350Dic43—42no—
351Dic43—42no—
352Dic43—42no—
353Dic43—42no—
354C2×#554D4311yescharacteristic
355C2×#552—431no—
356#3344—4316no—
357C2×#501—431no—
358C2×#484—431no—
359C2×#485—431no—
360C2×#483—431no—
361C2×#483—431no—
362C2×#479—431no—
363C2×#475—431no—
364C2×#470—431no—
365C2×#467—431no—
366C2×#441—431no—
367C2×#435—431no—
368C2×#428—431no—
369C22×#106—431no—
370C2×C43—24no—
371C2×C43—42no—
372C2×C43#334414yescomplemented
373C2×C43C2×#54711yescharacteristic
374C2×C43C22×#13711yescharacteristic
375C2×C43C2×#57711yescharacteristic
376C22×Q16—431no—
377C22×M16—431no—
378C23×C8—431no—
379#554—24no—
380#554C2×D4318yes—
381#552—438no—
382#552—864no—
383C2×C4⋊Q8C2×D4311yescharacteristic
384C2×#126—861no—
385C2×#125—21no—
386C2×#125—431no—
387C2×#125—861no—
388C2×#123—861no—
389C2×C22⋊Q8—21no—
390C2×C22⋊Q8—21no—
391C2×C22⋊Q8—431no—
392C2×C22⋊Q8—431no—
393C2×C22⋊Q8C2×D4311yescharacteristic
394C2×C22⋊Q8C2×D4311yescharacteristic
395C2×C4×Q8—431no—
396C2×C4×Q8C2×D4311yescharacteristic
397C2×C4×D4—21no—
398C2×C4×D4C2×D4311yescharacteristic
399C2×#117—431no—
400C2×#117—861no—
401C22×C4⋊C4—431no—
402C22×C4⋊C4C2×D4311yescharacteristic
403C22×C4⋊C4C2×D4311yescharacteristic
404#501—438no—
405#485—438no—
406#484—438no—
407#483—438no—
408#483—438no—
409#479—438no—
410#475—438no—
411#470—438no—
412#467—438no—
413#441—438no—
414#435—438no—
415#428—438no—
416C2×#107—431no—
417C2×#107—431no—
418C2×#107—431no—
419C2×#106—431no—
420C2×#106—431no—
421C2×#106—431no—
422C2×#106—431no—
423C2×#106—438no—
424C2×#106—431no—
425C2×#106—431no—
426C2×C4⋊C8—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×C22⋊C8—431no—
434C2×C22⋊C8—431no—
435C2×#97—431no—
436C43C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—21no—
438C22×Q8—431no—
439C22×Q8C22×D4311yescharacteristic
440C22×D4C22⋊D4311yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—861no—
444C23×C4C22×D4311yescharacteristic
445C23×C4C22×D4311yescharacteristic
446C2×Q16—434no—
447C2×Q16—864no—
448C2×M16—434no—
449C2×M16—864no—
450C22×C8—431no—
451C22×C8—431no—
452C22×C8—434no—
453C22×C8—431no—
454C22×C8—431no—
455C22×C8—864no—
456C4⋊Q8—22no—
457C4⋊Q8C22×D4314yes—
458#126—868no—
459#125—28no—
460#125—434no—
461#125—868no—
462#125—862no—
463#123—868no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—28no—
467C22⋊Q8—28no—
468C22⋊Q8—434no—
469C22⋊Q8—434no—
470C22⋊Q8—862no—
471C22⋊Q8—862no—
472C22⋊Q8C22×D4314yes—
473C22⋊Q8C22×D4314yes—
474C4×Q8—22no—
475C4×Q8—434no—
476C4×Q8—862no—
477C4×Q8C22×D4314yes—
478C4×D4—28no—
479C4×D4C22⋊D4314yes—
480C4×D4C22×D4314yes—
481#117—434no—
482#117—862no—
483#117—868no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—434no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—862no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4C22⋊D4311yescharacteristic
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4314yes—
508C2×C4⋊C4C22×D4314yes—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4C22⋊D4311yescharacteristic
515C2×C22⋊C4C22⋊D4311yescharacteristic
516C2×C42—21no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42C22×D4311yescharacteristic
520#107—434no—
521#107—434no—
522#107—434no—
523#106—434no—
524#106—434no—
525#106—434no—
526#106—434no—
527#106—434no—
528#106—434no—
529C4⋊C8—434no—
530#103—434no—
531#103—434no—
532#103—434no—
533#103—434no—
534#103—434no—
535#103—434no—
536C22⋊C8—434no—
537C22⋊C8—434no—
538#97—434no—
539C24C2×C22⋊D4311yescharacteristic
540C24C2×C22⋊D4311yescharacteristic
541C2×Q8—21no—
542C2×Q8—24no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—82no—
546C2×Q8—432no—
547C2×Q8—861no—
548C2×Q8—862no—
549C2×Q8—862no—
550C2×Q8C23×D4312yes—
551C2×D4—24no—
552C2×D4C2×C22⋊D4314yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—864no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—1724no—
571C22×C4C2×C22⋊D4312yes—
572C22×C4C2×C22⋊D4312yes—
573C22×C4C2×C22⋊D4311yescharacteristic
574C22×C4C2×C22⋊D4311yescharacteristic
575C22×C4C2×C22⋊D4311yescharacteristic
576C22×C4C2×C22⋊D4311yescharacteristic
577C22×C4C23×D4312yes—
578C22×C4C23×D4312yes—
579C22×C4C23×D4311yescharacteristic
580Q16—868no—
581M16—868no—
582C2×C8—434no—
583C2×C8—432no—
584C2×C8—432no—
585C2×C8—432no—
586C2×C8—432no—
587C2×C8—868no—
588C2×C8—862no—
589C2×C8—862no—
590C2×C8—862no—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—432no—
601C4⋊C4—432no—
602C4⋊C4—432no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—864no—
606C4⋊C4—861no—
607C4⋊C4—864no—
608C4⋊C4—864no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4C2×C22⋊D4314yes—
613C4⋊C4C23×D4312yes—
614C4⋊C4C23×D4312yes—
615C4⋊C4C23×D4312yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—864no—
619C22⋊C4—864no—
620C22⋊C4—864no—
621C22⋊C4C2×C22⋊D4314yes—
622C22⋊C4C2×C22⋊D4314yes—
623C42—24no—
624C42—864no—
625C42—864no—
626C42C2×C22⋊D4312yes—
627C42C23×D4312yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1306335614yes—
634C23C22×C22⋊D4312yes—
635C23C22×C22⋊D4312yes—
636C23C22×C22⋊D4311yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—42no—
640Q8—84no—
641Q8—862no—
642Q8—862no—
643Q8—1722no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—1728no—
670C2×C4—1722no—
671C2×C4—1722no—
672C2×C4—1722no—
673C2×C4—1722no—
674C2×C4C22×C22⋊D4312yes—
675C2×C4C22×C22⋊D4312yes—
676C2×C4C22×C22⋊D4312yes—
677C2×C4C22×C22⋊D4312yes—
678C2×C4C22×C22⋊D4311yescharacteristic
679C2×C4#41×D4312yes—
680C2×C4#1306337212yes—
681C2×C4C24×D4311yescharacteristic
682C8—434no—
683C8—862no—
684C8—862no—
685C8—862no—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1458354812yes—
694C22C2×#1306335614yes—
695C22C2×#1306335612yes—
696C22#1458371012yes—
697C22C23×C22⋊D4311yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—1722no—
707C4—1722no—
708C4—1722no—
709C4—1722no—
710C4#1458354812yes—
711C4C2×#41×D4311yescharacteristic
712C4C2×#1306337211yescharacteristic
713C2—24no—
714C2—42no—
715C2#1914704414yesdirect product factor
716C2C2×#1458354811yescharacteristic
717C2C22×#1306335611yescharacteristic
718C2C2×#1458371011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#554C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenterC2×#554D43
hypocenterC43C2×#3344
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. #19147044C2direct (N × H)
3. C2×#14583305C2semidirect
4. C2×#14583234C2semidirect
5. C2×#14583237C2semidirect
6. C2×#14583229C2semidirect
7. C2×#14583227C2semidirect
8. C2×#14583206C2semidirect
9. C2×#14583181C2semidirect
10. C2×#14583155C2semidirect
11. C2×#14583138C2semidirect
12. C2×#14583004C2semidirect
14. C2×#14582939C2semidirect
15. C22×#13063256C2semidirect
32. #14583305C22semidirect
33. #14583237C22semidirect
34. #14583234C22semidirect
35. #14583229C22semidirect
36. #14583227C22semidirect
37. #14583206C22semidirect
38. #14583181C22semidirect
39. #14583155C22semidirect
40. #14583138C22semidirect
41. #14583004C22semidirect
43. #14582939C22semidirect
53. C2×#13063256C22semidirect
372. C2×C43#3344semidirect
436. C43C2×#3344semidirect
715. C2#19147044direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835892
#191470442
C2×#145833052
C2×#145832342
C2×#145832372
C2×#145832292
C2×#145832272
C2×#145832062
C2×#145831812
C2×#145831552
C2×#145831382
C2×#145830042
C2×#145829712
C2×#145829392
C22×#130632562
C2×C43×#5542
C2×#334443