Finite Group Databasebeta

← C2×#20275698 #27388730

Subgroups — C2×#20275698 #27388730

Order 13568.

1698 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133194C211yesmaximal, characteristic
2C2×#16810481C211yesmaximal, characteristic
3C2×C22⋊C4×Dic53C211yesmaximal, characteristic
4#20275698C218yesmaximal, direct product factor
5C2×#16810390C211yesmaximal, characteristic
6C2×#16810389C211yesmaximal, characteristic
7C2×#16810389C211yesmaximal, characteristic
8C2×C53×#342C211yesmaximal, characteristic
9C23×Dic106C411yescharacteristic, complemented
10C24×Dic53C2211yescharacteristic
11C2×#13133194—21no—
12C2×#13133194—21no—
13C2×#13133194—21no—
14C2×#13133194—21no—
15C2×#13133194—22no—
16C2×#13133194—22no—
17C2×#13133194C414yescomplemented
18C2×#13133194C2214yes—
19C22×C4⋊Dic53C411yescharacteristic, complemented
20C22×#11719919—21no—
21C22×#11719919C411yescharacteristic, complemented
22C22×#11719919C411yescharacteristic, complemented
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C4×Dic53—21no—
27#16810481—22no—
28#16810481C2214yes—
29C22⋊C4×Dic53—22no—
30C22⋊C4×Dic53C2214yes—
31C2×#13133124—21no—
32C2×#13133124—21no—
33#16810390C2214yes—
34#16810389C2214yes—
35#16810389C2214yes—
36C22×C22⋊C4×C53C2211yescharacteristic
37C22×C22⋊C4×C53C2211yescharacteristic
38C22×C22⋊C4×C53C2211yescharacteristic
39C53×#342C2214yes—
40C22×Dic106—21no—
41C22×Dic106—22no—
42C22×Dic106—21no—
43C22×Dic106—44no—
44C22×Dic106C2×C414yescomplemented
45C23×Dic53—21no—
46C23×Dic53—21no—
47C23×Dic53—44no—
48C23×Dic53C2×C411yescharacteristic
49C23×Dic53C2×C411yescharacteristic
50C23×Dic53C2×C411yescharacteristic
51C23×Dic53C2×C411yescharacteristic
52C23×Dic53C2×C412yes—
53C23×Dic53D411yescharacteristic
54C23×Dic53D411yescharacteristic
55C23×Dic53D411yescharacteristic
56C23×Dic53D411yescharacteristic
57C23×Dic53D412yes—
58C23×Dic53D412yes—
59C23×Dic53C2312yes—
60#13133194—24no—
61#13133194—24no—
62#13133194—24no—
63#13133194—24no—
64#13133194—24no—
65#13133194—24no—
66#13133194—24no—
67#13133194—24no—
68C2×C4⋊Dic53—21no—
69C2×C4⋊Dic53—21no—
70C2×C4⋊Dic53—22no—
71C2×C4⋊Dic53C2×C414yescomplemented
72C2×#11719919—21no—
73C2×#11719919—21no—
74C2×#11719919—22no—
75C2×#11719919—21no—
76C2×#11719919—22no—
77C2×#11719919—21no—
78C2×#11719919—24no—
79C2×#11719919—44no—
80C2×#11719919C2×C414yescomplemented
81C2×#11719919C2×C414yescomplemented
82C2×C22⋊Dic53—21no—
83C2×C22⋊Dic53—21no—
84C2×C22⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C22⋊Dic53—21no—
88C2×C22⋊Dic53—22no—
89C2×C22⋊Dic53—22no—
90C2×C22⋊Dic53—22no—
91C2×C22⋊Dic53C2×C412yes—
92C2×C22⋊Dic53Q814yescomplemented
93C2×C22⋊Dic53C2312yes—
94C2×C22⋊Dic53C2312yes—
95C2×C22⋊Dic53C2312yes—
96C2×C4×Dic53—24no—
97C2×C4×Dic53—44no—
98#13133124—24no—
99#13133124—24no—
100C25×C53C2311yescharacteristic
101C23×C4×C53—21no—
102C23×C4×C53—21no—
103C23×C4×C53C2×C411yescharacteristic
104C23×C4×C53C2×C411yescharacteristic
105C2×C22⋊C4×C53—21no—
106C2×C22⋊C4×C53—21no—
107C2×C22⋊C4×C53—21no—
108C2×C22⋊C4×C53—21no—
109C2×C22⋊C4×C53—21no—
110C2×C22⋊C4×C53—21no—
111C2×C22⋊C4×C53—22no—
112C2×C22⋊C4×C53—22no—
113C2×C22⋊C4×C53—22no—
114C2×C22⋊C4×C53C2×C412yes—
115C2×C22⋊C4×C53Q814yescomplemented
116C2×C22⋊C4×C53C2312yes—
117C2×C22⋊C4×C53C2312yes—
118C2×C22⋊C4×C53C2312yes—
119C24×C53—42no—
120C24×C53—42no—
121C24×C53C22×C411yescharacteristic
122C24×C53C22×C411yescharacteristic
123C24×C53C2×D411yescharacteristic
124C24×C53C2×D411yescharacteristic
125C24×C53C2×D411yescharacteristic
126C24×C53C2×D411yescharacteristic
127C24×C53C2×Q812yes—
128C24×C53C2×Q812yes—
129C24×C53#4112yes—
130C24×C53#4112yes—
131C24×C53C2411yescharacteristic
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—24no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—42no—
140C22×C4×C53—42no—
141C22×C4×C53—42no—
142C22×C4×C53—42no—
143C22×C4×C53—42no—
144C22×C4×C53—42no—
145C22×C4×C53—42no—
146C22×C4×C53C22×C412yes—
147C22×C4×C53C22×C412yes—
148C22×Dic53—24no—
149C22×Dic53—24no—
150C22×Dic53—24no—
151C22×Dic53—21no—
152C22×Dic53—21no—
153C22×Dic53—21no—
154C22×Dic53—21no—
155C22×Dic53—24no—
156C22×Dic53—22no—
157C22×Dic53—22no—
158C22×Dic53—44no—
159C22×Dic53—44no—
160C22×Dic53—44no—
161C22×Dic53—44no—
162C22×Dic53—42no—
163C22×Dic53—42no—
164C22×Dic53—42no—
165C22×Dic53—42no—
166C22×Dic53—42no—
167C22×Dic53—42no—
168C22×Dic53—42no—
169C22×Dic53—42no—
170C22×Dic53—42no—
171C22×Dic53—42no—
172C22×Dic53C22⋊C411yescharacteristic
173C22×Dic53C22⋊C411yescharacteristic
174C22×Dic53C22⋊C411yescharacteristic
175C22×Dic53C22⋊C412yes—
176C22×Dic53C22⋊C412yes—
177C22×Dic53C22⋊C412yes—
178C22×Dic53C22⋊C412yes—
179C22×Dic53C22⋊C412yes—
180C22×Dic53C22⋊C412yes—
181C22×Dic53C22⋊C411yescharacteristic
182C22×Dic53C22×C412yes—
183C22×Dic53C22×C412yes—
184C22×Dic53C22×C412yes—
185C22×Dic53C22×C412yes—
186C22×Dic53C2×D412yes—
187C22×Dic53C2×D412yes—
188C22×Dic53C2×D412yes—
189C22×Dic53C2×D412yes—
190C2×Dic106—24no—
191C2×Dic106—24no—
192C2×Dic106—44no—
193C2×Dic106—48no—
194C2×Dic106—44no—
195C2×Dic106—48no—
196C22⋊C4×C53—22no—
197C22⋊C4×C53—22no—
198C22⋊C4×C53—24no—
199C22⋊C4×C53—22no—
200C22⋊C4×C53—22no—
201C22⋊C4×C53—22no—
202C22⋊C4×C53—22no—
203C22⋊C4×C53—22no—
204C22⋊C4×C53—42no—
205C22⋊C4×C53C2×Q814yescomplemented
206C22⋊Dic53—22no—
207C22⋊Dic53—22no—
208C22⋊Dic53—24no—
209C22⋊Dic53—22no—
210C22⋊Dic53—22no—
211C22⋊Dic53—22no—
212C22⋊Dic53—22no—
213C22⋊Dic53—22no—
214C22⋊Dic53—42no—
215C22⋊Dic53C2×Q814yescomplemented
216C4⋊Dic53—24no—
217C4⋊Dic53—24no—
218#11719919—24no—
219#11719919—24no—
220#11719919—24no—
221#11719919—24no—
222#11719919—48no—
223C4×Dic53—48no—
224C23×C53—22no—
225C23×C53—22no—
226C23×C53—22no—
227C23×C53—22no—
228C23×C53—22no—
229C23×C53—22no—
230C23×C53—41no—
231C23×C53—41no—
232C23×C53—41no—
233C23×C53—41no—
234C23×C53—41no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53—44no—
238C23×C53—44no—
239C23×C53—44no—
240C23×C53—44no—
241C23×C53—41no—
242C23×C53C2×C22⋊C411yescharacteristic
243C23×C53C2×C22⋊C411yescharacteristic
244C23×C53C2×C22⋊C411yescharacteristic
245C23×C53C2×C22⋊C411yescharacteristic
246C23×C53C4×Q812yes—
247C23×C53C4×Q812yes—
248C23×C53C4×Q812yes—
249C23×C53C4×Q812yes—
250C23×C53C22⋊Q812yes—
251C23×C53C22⋊Q812yes—
252C23×C53C22⋊Q812yes—
253C23×C53C22⋊Q812yes—
254C23×C53#12412yes—
255C23×C53#12412yes—
256C23×C53C4⋊Q812yes—
257C23×C53C4⋊Q812yes—
258C23×C53C23×C411yescharacteristic
259C23×C53C22×D411yescharacteristic
260C23×C53C22×D411yescharacteristic
261C23×C53C22×Q811yescharacteristic
262C23×C53C22×Q811yescharacteristic
263C23×C53C2×#4111yescharacteristic
264C23×C53C2×#4111yescharacteristic
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—24no—
268C2×C4×C53—42no—
269C2×C4×C53—42no—
270C2×C4×C53—48no—
271C2×C4×C53—42no—
272C2×C4×C53—42no—
273C2×C4×C53—42no—
274C2×C4×C53—42no—
275C2×C4×C53—42no—
276C2×C4×C53—42no—
277C2×C4×C53—42no—
278C2×C4×C53—42no—
279C2×C4×C53—42no—
280C2×C4×C53—84no—
281C2×Dic53—22no—
282C2×Dic53—22no—
283C2×Dic53—22no—
284C2×Dic53—24no—
285C2×Dic53—24no—
286C2×Dic53—24no—
287C2×Dic53—24no—
288C2×Dic53—24no—
289C2×Dic53—24no—
290C2×Dic53—22no—
291C2×Dic53—22no—
292C2×Dic53—24no—
293C2×Dic53—42no—
294C2×Dic53—42no—
295C2×Dic53—42no—
296C2×Dic53—42no—
297C2×Dic53—42no—
298C2×Dic53—42no—
299C2×Dic53—42no—
300C2×Dic53—42no—
301C2×Dic53—48no—
302C2×Dic53—42no—
303C2×Dic53—42no—
304C2×Dic53—42no—
305C2×Dic53—42no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—84no—
312C2×Dic53#9914yes—
313C2×Dic53C2×C22⋊C412yes—
314C2×Dic53C2×C22⋊C412yes—
315C2×Dic53C2×C22⋊C412yes—
316C2×Dic53C2×C22⋊C412yes—
317Dic106—48no—
318Dic106—48no—
319C2×#1996—531nomaximal, Sylow
320C22×C53—21no—
321C22×C53—21no—
322C22×C53—21no—
323C22×C53—21no—
324C22×C53—21no—
325C22×C53—21no—
326C22×C53—21no—
327C22×C53—21no—
328C22×C53—21no—
329C22×C53—21no—
330C22×C53—21no—
331C22×C53—21no—
332C22×C53—24no—
333C22×C53—24no—
334C22×C53—24no—
335C22×C53—24no—
336C22×C53—24no—
337C22×C53—24no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—41no—
345C22×C53—41no—
346C22×C53—41no—
347C22×C53—41no—
348C22×C53#39112yes—
349C22×C53#39112yes—
350C22×C53#39112yes—
351C22×C53#39112yes—
352C22×C53C2×#9912yes—
353C22×C53#41012yes—
354C22×C53C22×C22⋊C411yescharacteristic
355C22×C53C2×C4×Q811yescharacteristic
356C22×C53C2×C4×Q811yescharacteristic
357C22×C53C2×C22⋊Q811yescharacteristic
358C22×C53C2×C22⋊Q811yescharacteristic
359C22×C53C2×#12411yescharacteristic
360C22×C53C2×C4⋊Q811yescharacteristic
361C4×C53—44no—
362C4×C53—42no—
363C4×C53—42no—
364C4×C53—82no—
365Dic53—22no—
366Dic53—22no—
367Dic53—22no—
368Dic53—44no—
369Dic53—42no—
370Dic53—42no—
371Dic53—82no—
372Dic53C2×#9914yes—
373C22×C22⋊Q8—531no—
374C2×#380—531no—
375C2×C4×C22⋊C4—531no—
376#1996—538no—
377C2×#342—531no—
378C2×#342—531no—
379C2×#342—531no—
380C2×#342D5311yescharacteristic
381C2×C53—21no—
382C2×C53—21no—
383C2×C53—21no—
384C2×C53—21no—
385C2×C53—21no—
386C2×C53—21no—
387C2×C53—22no—
388C2×C53—22no—
389C2×C53—22no—
390C2×C53#199614yescomplemented
391C2×C53C2×#39111yescharacteristic
392C2×C53C22×#9911yescharacteristic
393C2×C53C2×#41011yescharacteristic
394C23×Q8—531no—
395C24×C4—531no—
396C2×C22⋊Q8—534no—
397C2×C22⋊Q8—534no—
398C2×C22⋊Q8—1061no—
399C2×C22⋊Q8—1061no—
400C2×C22⋊Q8—1061no—
401C2×C22⋊Q8—1061no—
402C2×C22⋊Q8—1062no—
403C2×C22⋊Q8—1062no—
404C22×C4⋊C4—531no—
405C22×C4⋊C4—531no—
406C22×C4⋊C4—531no—
407C22×C4⋊C4—1061no—
408C22×C22⋊C4—531no—
409C22×C22⋊C4—531no—
410C22×C22⋊C4—531no—
411C22×C22⋊C4C2×D5311yescharacteristic
412C22×C22⋊C4C2×D5311yescharacteristic
413C22×C22⋊C4C2×D5311yescharacteristic
414C22×C42—1061no—
415#380—534no—
416#380—1062no—
417C4×C22⋊C4—534no—
418C4×C22⋊C4—1062no—
419C2×#95—1061no—
420C2×#95—1061no—
421#342—534no—
422#342—534no—
423#342—534no—
424#342C2×D5314yes—
425C53C2×#199611yescharacteristic, complemented, Sylow
426C25C22×D5311yescharacteristic
427C22×Q8—534no—
428C22×Q8—1062no—
429C22×Q8—1061no—
430C22×Q8—1061no—
431C22×Q8—2124no—
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—531no—
435C23×C4—531no—
436C23×C4—531no—
437C23×C4—531no—
438C23×C4—532no—
439C23×C4—531no—
440C23×C4—531no—
441C23×C4—532no—
442C23×C4—532no—
443C23×C4—532no—
444C23×C4—531no—
445C23×C4—531no—
446C23×C4—1061no—
447C23×C4—1061no—
448C23×C4—2124no—
449C23×C4C4×D5311yescharacteristic
450C23×C4C4×D5311yescharacteristic
451C22⋊Q8—1064no—
452C22⋊Q8—1064no—
453C22⋊Q8—1064no—
454C22⋊Q8—1064no—
455C22⋊Q8—1064no—
456C22⋊Q8—1064no—
457C22⋊Q8—1064no—
458C22⋊Q8—1064no—
459C2×C4⋊C4—534no—
460C2×C4⋊C4—534no—
461C2×C4⋊C4—534no—
462C2×C4⋊C4—1062no—
463C2×C4⋊C4—1062no—
464C2×C4⋊C4—1061no—
465C2×C4⋊C4—1061no—
466C2×C4⋊C4—1061no—
467C2×C4⋊C4—1061no—
468C2×C4⋊C4—1062no—
469C2×C4⋊C4—1061no—
470C2×C4⋊C4—1061no—
471C2×C4⋊C4—1064no—
472C2×C4⋊C4—2124no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—534no—
483C2×C22⋊C4—532no—
484C2×C22⋊C4—532no—
485C2×C22⋊C4—532no—
486C2×C22⋊C4—532no—
487C2×C22⋊C4—1062no—
488C2×C22⋊C4—1061no—
489C2×C22⋊C4—1061no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4—1061no—
492C2×C22⋊C4—1061no—
493C2×C22⋊C4—1062no—
494C2×C22⋊C4—1062no—
495C2×C22⋊C4—1061no—
496C2×C22⋊C4Dic10614yescomplemented
497C2×C22⋊C4C4×D5312yes—
498C2×C22⋊C4C22×D5312yes—
499C2×C22⋊C4C22×D5312yes—
500C2×C22⋊C4C22×D5312yes—
501C2×C42—1064no—
502C2×C42—2124no—
503#95—1064no—
504#95—1064no—
505C24—42no—
506C24—42no—
507C24C2×Dic10612yes—
508C24C2×C4×D5311yescharacteristic
509C24C2×C4×D5311yescharacteristic
510C24#1171994512yes—
511C24D4×D5311yescharacteristic
512C24D4×D5311yescharacteristic
513C24D4×D5311yescharacteristic
514C24D4×D5311yescharacteristic
515C24#1171994712yes—
516C24Q8×D5312yes—
517C24C23×D5311yescharacteristic
518C2×Q8—1064no—
519C2×Q8—1064no—
520C2×Q8—2124no—
521C2×Q8—2128no—
522C2×Q8—2128no—
523C2×Q8—2124no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—531no—
539C22×C4—532no—
540C22×C4—532no—
541C22×C4—532no—
542C22×C4—531no—
543C22×C4—531no—
544C22×C4—531no—
545C22×C4—532no—
546C22×C4—532no—
547C22×C4—532no—
548C22×C4—532no—
549C22×C4—532no—
550C22×C4—532no—
551C22×C4—532no—
552C22×C4—532no—
553C22×C4—532no—
554C22×C4—532no—
555C22×C4—532no—
556C22×C4—1064no—
557C22×C4—1064no—
558C22×C4—1064no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1064no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—2124no—
567C22×C4—2124no—
568C22×C4—2124no—
569C22×C4—2124no—
570C22×C4—2122no—
571C22×C4—2122no—
572C22×C4—2122no—
573C22×C4—2122no—
574C22×C4—2122no—
575C22×C4—2122no—
576C22×C4—2122no—
577C22×C4—2122no—
578C22×C4—2122no—
579C22×C4—2122no—
580C22×C4C2×C4×D5312yes—
581C22×C4C2×C4×D5312yes—
582C4⋊C4—1064no—
583C4⋊C4—1064no—
584C4⋊C4—1064no—
585C4⋊C4—1064no—
586C4⋊C4—1064no—
587C4⋊C4—1064no—
588C4⋊C4—2128no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—24no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—42no—
598C22⋊C4—534no—
599C22⋊C4—1062no—
600C22⋊C4—1062no—
601C22⋊C4—1064no—
602C22⋊C4—1062no—
603C22⋊C4—1062no—
604C22⋊C4—1062no—
605C22⋊C4—1062no—
606C22⋊C4—1062no—
607C22⋊C4—2122no—
608C22⋊C4C2×Dic10614yescomplemented
609C42—2128no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—44no—
621C23—41no—
622C23—44no—
623C23—41no—
624C23—41no—
625C23—44no—
626C23—44no—
627C23—41no—
628C23C22⋊C4×D5311yescharacteristic
629C23C22⋊C4×D5311yescharacteristic
630C23C22⋊C4×D5311yescharacteristic
631C23C22⋊C4×D5311yescharacteristic
632C23#1313318212yes—
633C23#1313318212yes—
634C23C4×Dic10612yes—
635C23C4×Dic10612yes—
636C23#1313319412yes—
637C23#1313319412yes—
638C23#1313319512yes—
639C23#1313319512yes—
640C23#1313320312yes—
641C23#1313320312yes—
642C23#1313321612yes—
643C23#1313321612yes—
644C23C22×C4×D5311yescharacteristic
645C23C2×D4×D5311yescharacteristic
646C23C2×D4×D5311yescharacteristic
647C23C2×Q8×D5311yescharacteristic
648C23C22×Dic10611yescharacteristic
649C23C2×#1171994711yescharacteristic
650C23C2×#1171994511yescharacteristic
651Q8—2128no—
652Q8—2128no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—48no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—84no—
669C2×C4—532no—
670C2×C4—534no—
671C2×C4—532no—
672C2×C4—532no—
673C2×C4—532no—
674C2×C4—1064no—
675C2×C4—1064no—
676C2×C4—1064no—
677C2×C4—1064no—
678C2×C4—1064no—
679C2×C4—1064no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1064no—
686C2×C4—4244no—
687C2×C4—2122no—
688C2×C4—2122no—
689C2×C4—2122no—
690C2×C4—2122no—
691C2×C4—2122no—
692C2×C4—2122no—
693C2×C4—2122no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4—2122no—
697C2×C4—2122no—
698C2×C4—2128no—
699C2×C4—2122no—
700C2×C4—2122no—
701C2×C4—2122no—
702C2×C4—2122no—
703C2×C4—2122no—
704C2×C4—2122no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—24no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—24no—
722C22—24no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22#1681052712yes—
734C22#1681052712yes—
735C22#1681052712yes—
736C22#1681052712yes—
737C22#99×D5312yes—
738C22#1681059512yes—
739C22C2×C22⋊C4×D5311yescharacteristic
740C22C2×#1313318211yescharacteristic
741C22C2×C4×Dic10611yescharacteristic
742C22C2×#1313319411yescharacteristic
743C22C2×#1313319511yescharacteristic
744C22C2×#1313320311yescharacteristic
745C22C2×#1313321611yescharacteristic
746C4—44no—
747C4—42no—
748C4—42no—
749C4—82no—
750C4—534no—
751C4—1062no—
752C4—1062no—
753C4—1062no—
754C4—4242no—
755C4—2124no—
756C4—2122no—
757C4—2122no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—22no—
762C2—22no—
763C2—22no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2#2027569814yesdirect product factor
768C2C2×#1681052711yescharacteristic
769C2C2×#99×D5311yescharacteristic
770C2C2×#1681059511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D53
commutatorC23×C53C23×C4
FrattiniC24C23×D53
FittingC2×C53×#342C2
socleC23×C53C2×C22⋊C4
prime radicalC25×C53C23
cosocleC24×C53C24
hypercenterC2×#342D53
hypocenterC53C2×#1996
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. #20275698C2direct (N × H)
9. C23×Dic106C4semidirect
17. C2×#13133194C4semidirect
19. C22×C4⋊Dic53C4semidirect
21. C22×#11719919C4semidirect
22. C22×#11719919C4semidirect
44. C22×Dic106C2×C4semidirect
71. C2×C4⋊Dic53C2×C4semidirect
80. C2×#11719919C2×C4semidirect
81. C2×#11719919C2×C4semidirect
92. C2×C22⋊Dic53Q8semidirect
115. C2×C22⋊C4×C53Q8semidirect
205. C22⋊C4×C53C2×Q8semidirect
215. C22⋊Dic53C2×Q8semidirect
390. C2×C53#1996semidirect
425. C53C2×#1996semidirect
496. C2×C22⋊C4Dic106semidirect
608. C22⋊C4C2×Dic106semidirect
767. C2#20275698direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131331942
C2×#168104812
C2×C22⋊C4×Dic532
#202756982
C2×#168103902
C2×#168103892
C2×C53×#3422
C2×#199653