Finite Group Databasebeta

← C2×#19147052 #25975146

Subgroups — C2×#19147052 #25975146

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×#14583606C211yesmaximal, characteristic
2C2×#14583589C211yesmaximal, characteristic
3#19147052C2116yesmaximal, direct product factor
4C2×#14583308C211yesmaximal, characteristic, complemented
5C2×#14583235C211yesmaximal, characteristic, complemented
6C2×#14583241C211yesmaximal, characteristic, complemented
7C2×#14583230C211yesmaximal, characteristic, complemented
8C2×#14583230C211yesmaximal, characteristic, complemented
9C2×#14583207C211yesmaximal, characteristic, complemented
10C2×#14583185C211yesmaximal, characteristic, complemented
11C2×#14583157C211yesmaximal, characteristic, complemented
12C2×#14583140C211yesmaximal, characteristic, complemented
13C2×#14583007C211yesmaximal, characteristic, complemented
14C2×#14582941C211yesmaximal, characteristic, complemented
15C22×#13063257C211yesmaximal, characteristic, complemented
16C2×C43×#435C211yesmaximal, characteristic
17C22×Dic172C2211yescharacteristic
18#14583606—24no—
19#14583606C2218yes—
20#14583589—24no—
21#14583589C2218yes—
22C2×#13063325C2211yescharacteristic
23C2×#13063318—21no—
24C2×#13063317C2211yescharacteristic
25C2×#13063316—21no—
26C2×#13063315—21no—
27C2×#13063306—21no—
28C2×#13063304C2211yescharacteristic
29C2×#13063304C2211yescharacteristic
30C2×#13063304C2211yescharacteristic
31C2×#13063304C2211yescharacteristic
32C2×#13063302—21no—
33C2×#13063302—21no—
34C2×C4×Dic86C2211yescharacteristic
35C2×C4×Dic86C2211yescharacteristic
36C2×D4×Dic43—21no—
37C2×#13063284C2211yescharacteristic
38C2×#13063281—21no—
39C22×C4⋊Dic43C2211yescharacteristic
40C22×C4⋊Dic43C2211yescharacteristic
41C22×C4⋊Dic43C2211yescharacteristic
42#14583308C2218yescomplemented
43#14583241C2218yescomplemented
44#14583235C2218yescomplemented
45#14583230C2218yescomplemented
46#14583230C2218yescomplemented
47#14583207C2218yescomplemented
48#14583185C2218yescomplemented
49#14583157C2218yescomplemented
50#14583140C2218yescomplemented
51#14583007C2218yescomplemented
52#14582941C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063259C2211yescharacteristic
55C2×#13063259C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59C2×#13063257C2211yescharacteristic
60C2×#13063257C2211yescharacteristic
61C2×#13063257C2211yescharacteristic
62C2×#13063257C2218yescomplemented
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063250C2211yescharacteristic
67C2×#13063250C2211yescharacteristic
68C2×#13063250C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#435C2218yes—
73C2×C4⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×C22⋊C8×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C23×Dic43—21no—
81C23×Dic43—21no—
82C23×Dic43—21no—
83C2×Dic172—24no—
84C2×Dic172C2314yes—
85#13063325—22no—
86#13063325C2314yes—
87#13063318—28no—
88#13063317—22no—
89#13063317C2314yes—
90#13063316—28no—
91#13063315—28no—
92#13063306—28no—
93#13063304—22no—
94#13063304—22no—
95#13063304—22no—
96#13063304—22no—
97#13063304C2314yes—
98#13063304C2314yes—
99#13063304C2314yes—
100#13063304C2314yes—
101#13063302—28no—
102#13063302—28no—
103C4×Dic86—22no—
104C4×Dic86—22no—
105C4×Dic86C2314yes—
106C4×Dic86C2314yes—
107D4×Dic43—28no—
108#13063284—22no—
109#13063284C2314yes—
110#13063281—28no—
111C2×C4⋊Dic43—22no—
112C2×C4⋊Dic43—22no—
113C2×C4⋊Dic43—22no—
114C2×C4⋊Dic43—21no—
115C2×C4⋊Dic43—21no—
116C2×C4⋊Dic43—21no—
117C2×C4⋊Dic43—21no—
118C2×C4⋊Dic43C2314yes—
119C2×C4⋊Dic43C2311yescharacteristic
120C2×C4⋊Dic43C2314yes—
121C2×C4⋊Dic43C2314yes—
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
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×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43—21no—
143#13063259C2314yes—
144#13063259C2314yes—
145#13063259C2314yes—
146#13063257C2314yes—
147#13063257C2314yes—
148#13063257C2314yes—
149#13063257C2314yes—
150#13063257C2314yes—
151#13063257C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063250C2314yes—
158C22×D4×C43D411yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C23×C4×C43C2311yescharacteristic
161C2×M16×C43—24no—
162C2×M16×C43C2314yes—
163C22×C8×C43—24no—
164C22×C8×C43C2314yes—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C4×D4×C43D414yes—
170C4×D4×C43C2314yes—
171C2×C4⋊C4×C43D411yescharacteristic
172C2×C22⋊C4×C43D411yescharacteristic
173C2×C22⋊C4×C43D411yescharacteristic
174C2×C42×C43C2311yescharacteristic
175C4⋊C8×C43C2314yes—
176C22⋊C8×C43C2314yes—
177C22⋊C8×C43C2314yes—
178#97×C43C2314yes—
179C24×C43C2×D411yescharacteristic
180C24×C43C2×D411yescharacteristic
181C2×D4×C43—24no—
182C2×D4×C43C2×D414yes—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D412yes—
192C22×C4×C43C2×D412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2411yescharacteristic
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—24no—
205C22×Dic43—24no—
206C22×Dic43—24no—
207C22×Dic43—44no—
208C22×Dic43—82no—
209C22×Dic43—82no—
210C2×Dic86—22no—
211C2×Dic86—22no—
212C2×Dic86—22no—
213C2×Dic86—22no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—24no—
217C2×Dic86—82no—
218C2×Dic86C2412yes—
219C2×Dic86C2412yes—
220M16×C43—28no—
221C2×C8×C43—22no—
222C2×C8×C43—22no—
223C2×C8×C43—22no—
224C2×C8×C43—28no—
225C2×C8×C43#4114yes—
226C2×C8×C43C2412yes—
227C2×C8×C43C2412yes—
228C2×C8×C43C2412yes—
229C2×C8×C43C2412yes—
230C4⋊C4×C43C2×D414yes—
231C22⋊C4×C43C2×D414yes—
232C22⋊C4×C43C2×D414yes—
233C42×C43C2×D412yes—
234C42×C43C2412yes—
235C22⋊Dic43—24no—
236C22⋊Dic43—24no—
237C22⋊Dic43—24no—
238C22⋊Dic43—24no—
239C22⋊Dic43—24no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—24no—
243C4⋊Dic43—24no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—24no—
248C4⋊Dic43—24no—
249C4⋊Dic43—21no—
250C4⋊Dic43C2412yes—
251C4⋊Dic43C2412yes—
252C4⋊Dic43C2412yes—
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×Dic43—24no—
267Dic172—28no—
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
277D4×C43—28no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—24no—
283C2×C4×C43—24no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43C22×D412yes—
289C2×C4×C43C22×D412yes—
290C2×C4×C43C22×D412yes—
291C2×C4×C43C22×D412yes—
292C2×C4×C43C22×D411yescharacteristic
293C2×C4×C43C2×#4112yes—
294C2×C4×C432−1+412yes—
295C2×C4×C43C2511yescharacteristic
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—42no—
305C2×Dic43—42no—
306C2×Dic43—48no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—84no—
314C2×Dic43—84no—
315Dic86—22no—
316Dic86—22no—
317Dic86—22no—
318Dic86—22no—
319Dic86—42no—
320Dic86—42no—
321Dic86—84no—
322C8×C43—22no—
323C8×C43—22no—
324C8×C43—22no—
325C8×C43C2×#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#54712yes—
344C4×C43C22×#4111yescharacteristic
345C4×C43C2×2−1+411yescharacteristic
346Dic43—42no—
347Dic43—42no—
348Dic43—42no—
349Dic43—42no—
350Dic43—42no—
351Dic43—42no—
352Dic43—42no—
353Dic43—42no—
354C2×#554—431no—
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×#435D4311yescharacteristic
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×M16C2×D4311yescharacteristic
378C23×C8C2×D4311yescharacteristic
379#554—438no—
380#554—864no—
381#552—438no—
382#552—864no—
383C2×C4⋊Q8—431no—
384C2×#126—861no—
385C2×#125—431no—
386C2×#125—861no—
387C2×#125—861no—
388C2×#123—861no—
389C2×C22⋊Q8—431no—
390C2×C22⋊Q8—431no—
391C2×C22⋊Q8—431no—
392C2×C22⋊Q8—431no—
393C2×C22⋊Q8—861no—
394C2×C22⋊Q8—861no—
395C2×C4×Q8—431no—
396C2×C4×Q8—431no—
397C2×C4×D4—861no—
398C2×C4×D4C2×D4311yescharacteristic
399C2×#117—431no—
400C2×#117—861no—
401C22×C4⋊C4—431no—
402C22×C4⋊C4—431no—
403C22×C4⋊C4—431no—
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#435C2×D4318yes—
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⋊C8C2×D4311yescharacteristic
427C2×#103—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×C22⋊C8C2×D4311yescharacteristic
434C2×C22⋊C8C2×D4311yescharacteristic
435C2×#97C2×D4311yescharacteristic
436C43C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—431no—
438C22×Q8—431no—
439C22×Q8—861no—
440C22×D4D17211yescharacteristic
441C23×C4—861no—
442C23×C4—861no—
443C23×C4—861no—
444C23×C4C22×D4311yescharacteristic
445C23×C4C22×D4311yescharacteristic
446C2×Q16—434no—
447C2×Q16—864no—
448C2×M16—24no—
449C2×M16C22×D4314yes—
450C22×C8—24no—
451C22×C8C22×D4311yescharacteristic
452C22×C8C22×D4314yes—
453C22×C8C22×D4311yescharacteristic
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456C4⋊Q8—434no—
457C4⋊Q8—862no—
458#126—868no—
459#125—434no—
460#125—868no—
461#125—868no—
462#125—862no—
463#123—868no—
464C22⋊Q8—434no—
465C22⋊Q8—434no—
466C22⋊Q8—434no—
467C22⋊Q8—434no—
468C22⋊Q8—862no—
469C22⋊Q8—862no—
470C22⋊Q8—862no—
471C22⋊Q8—862no—
472C22⋊Q8—868no—
473C22⋊Q8—868no—
474C4×Q8—434no—
475C4×Q8—434no—
476C4×Q8—862no—
477C4×Q8—862no—
478C4×D4—868no—
479C4×D4D17214yes—
480C4×D4C22×D4314yes—
481#117—434no—
482#117—862no—
483#117—868no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—434no—
490C2×C4⋊C4—434no—
491C2×C4⋊C4—434no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—862no—
497C2×C4⋊C4—862no—
498C2×C4⋊C4—862no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4D17211yescharacteristic
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4D17211yescharacteristic
515C2×C22⋊C4D17211yescharacteristic
516C2×C42—861no—
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⋊C8C22×D4314yes—
530#103—434no—
531#103—434no—
532#103—434no—
533#103—434no—
534#103—434no—
535#103—434no—
536C22⋊C8C22×D4314yes—
537C22⋊C8C22×D4314yes—
538#97C22×D4314yes—
539C24C2×D17211yescharacteristic
540C24C2×D17211yescharacteristic
541C2×Q8—432no—
542C2×Q8—432no—
543C2×Q8—864no—
544C2×Q8—861no—
545C2×Q8—861no—
546C2×Q8—862no—
547C2×Q8—862no—
548C2×Q8—862no—
549C2×Q8—862no—
550C2×Q8—3442no—
551C2×D4—24no—
552C2×D4C2×D17214yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—864no—
558C22×C4—864no—
559C22×C4—864no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—3442no—
569C22×C4—3442no—
570C22×C4—1724no—
571C22×C4C2×D17212yes—
572C22×C4C2×D17212yes—
573C22×C4C2×D17211yescharacteristic
574C22×C4C2×D17211yescharacteristic
575C22×C4C2×D17211yescharacteristic
576C22×C4C2×D17211yescharacteristic
577C22×C4C23×D4312yes—
578C22×C4C23×D4312yes—
579C22×C4C23×D4311yescharacteristic
580Q16—868no—
581M16—28no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—28no—
586C2×C8#1062190014yes—
587C2×C8C23×D4312yes—
588C2×C8C23×D4312yes—
589C2×C8C23×D4312yes—
590C2×C8C23×D4312yes—
591C4⋊C4—432no—
592C4⋊C4—432no—
593C4⋊C4—432no—
594C4⋊C4—432no—
595C4⋊C4—432no—
596C4⋊C4—432no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—864no—
600C4⋊C4—864no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—864no—
605C4⋊C4—861no—
606C4⋊C4—864no—
607C4⋊C4—864no—
608C4⋊C4—864no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4C2×D17214yes—
616C22⋊C4—864no—
617C22⋊C4—864no—
618C22⋊C4—864no—
619C22⋊C4—864no—
620C22⋊C4—864no—
621C22⋊C4C2×D17214yes—
622C22⋊C4C2×D17214yes—
623C42—864no—
624C42—864no—
625C42—864no—
626C42C2×D17212yes—
627C42C23×D4312yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1306335814yes—
634C23C22×D17212yes—
635C23C22×D17212yes—
636C23C22×D17211yescharacteristic
637Q8—862no—
638Q8—862no—
639Q8—862no—
640Q8—862no—
641Q8—3444no—
642Q8—1722no—
643Q8—1722no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—3444no—
664C2×C4—3444no—
665C2×C4—1722no—
666C2×C4—1722no—
667C2×C4—1728no—
668C2×C4—1722no—
669C2×C4—1722no—
670C2×C4—1722no—
671C2×C4—1722no—
672C2×C4—1722no—
673C2×C4—1722no—
674C2×C4C22×D17212yes—
675C2×C4C22×D17212yes—
676C2×C4C22×D17212yes—
677C2×C4C22×D17212yes—
678C2×C4C22×D17211yescharacteristic
679C2×C4C2×#1062190012yes—
680C2×C4#1306337212yes—
681C2×C4C24×D4311yescharacteristic
682C8—22no—
683C8—22no—
684C8—22no—
685C8C2×#1062190014yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1458355312yes—
694C22C2×#1306335814yes—
695C22C2×#1306335812yes—
696C22#1458371112yes—
697C22C23×D17211yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—1722no—
703C4—1722no—
704C4—1722no—
705C4—1722no—
706C4—1722no—
707C4—1722no—
708C4—1722no—
709C4—1722no—
710C4#1458355312yes—
711C4C22×#1062190011yescharacteristic
712C4C2×#1306337211yescharacteristic
713C2—24no—
714C2—42no—
715C2#1914705214yesdirect product factor
716C2C2×#1458355311yescharacteristic
717C2C22×#1306335811yescharacteristic
718C2C2×#1458371111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenterC2×#435D43
hypocenterC43C2×#3344
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #19147052C2direct (N × H)
4. C2×#14583308C2semidirect
5. C2×#14583235C2semidirect
6. C2×#14583241C2semidirect
7. C2×#14583230C2semidirect
8. C2×#14583230C2semidirect
9. C2×#14583207C2semidirect
10. C2×#14583185C2semidirect
11. C2×#14583157C2semidirect
12. C2×#14583140C2semidirect
13. C2×#14583007C2semidirect
14. C2×#14582941C2semidirect
15. C22×#13063257C2semidirect
42. #14583308C22semidirect
43. #14583241C22semidirect
44. #14583235C22semidirect
45. #14583230C22semidirect
46. #14583230C22semidirect
47. #14583207C22semidirect
48. #14583185C22semidirect
49. #14583157C22semidirect
50. #14583140C22semidirect
51. #14583007C22semidirect
52. #14582941C22semidirect
62. C2×#13063257C22semidirect
372. C2×C43#3344semidirect
436. C43C2×#3344semidirect
715. C2#19147052direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836062
C2×#145835892
#191470522
C2×#145833082
C2×#145832352
C2×#145832412
C2×#145832302
C2×#145832072
C2×#145831852
C2×#145831572
C2×#145831402
C2×#145830072
C2×#145829412
C22×#130632572
C2×C43×#4352
C2×#334443