Finite Group Databasebeta

← C4×#11719082 #16791542

Subgroups — C4×#11719082 #16791542

Order 3328.

1742 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719082C212yesmaximal
2C2×C4×C4⋊#261C211yesmaximal, characteristic
3C2×C42×#261C211yesmaximal, characteristic
4#13130016C212yesmaximal
5#13130015C212yesmaximal
6#13130011C212yesmaximal
7C4×(C2×#261)⋊C4C211yesmaximal, characteristic
8C4×(C2×#261)⋊C4C211yesmaximal, characteristic
9C4×(C2×#261)⋊C4C211yesmaximal, characteristic
10C4×(C2×#261)⋊C4C211yesmaximal, characteristic
11C4×C4⋊C4×D13C211yesmaximal, characteristic
12C22×C4⋊#261C2212yes—
13C22×C4×#261C2211yescharacteristic
14C22×C4×#261C2211yescharacteristic
15C22×C4×#261C2212yes—
16C22×C4×#261C2212yes—
17C22×C4×#261C2211yescharacteristic
18C22×C4×#261C2211yescharacteristic
19C2×C4⋊C4×D13C2211yescharacteristic
20C2×C4⋊C4×D13C2211yescharacteristic
21C2×C42×D13C2211yescharacteristic
22C2×C42×D13C2211yescharacteristic
23C2×C42×D13C2211yescharacteristic
24C2×(C2×#261)⋊C4C2212yes—
25C2×(C2×#261)⋊C4C2212yes—
26C2×(C2×#261)⋊C4C2212yes—
27C2×(C2×#261)⋊C4C2212yes—
28C2×(C2×#261)⋊C4C2212yes—
29C2×(C2×#261)⋊C4C2212yes—
30C2×(C2×#261)⋊C4C2212yes—
31C2×(C2×#261)⋊C4C2212yes—
32C2×(C2×#261)⋊C4C2212yes—
33#11719082C4116yesdirect product factor
34C4×C4⋊#261—24no—
35C42×#261—24no—
36C4×C13×C4⋊C4C411yescharacteristic, complemented
37C4⋊C4×Dic13C411yescharacteristic, complemented
38C4⋊C4×Dic13C411yescharacteristic, complemented
39C4×C4⋊Dic13C411yescharacteristic, complemented
40C4×#6101C411yescharacteristic, complemented
41C4×#6101C411yescharacteristic, complemented
42D13×#95C2211yescharacteristic
43D13×#95C2211yescharacteristic
44#11718310C411yescharacteristic, complemented
45#11718310C411yescharacteristic, complemented
46C23×#261C2312yes—
47C23×#261C2312yes—
48C23×#261C2312yes—
49C23×#261C2312yes—
50C22×C4×D13C2311yescharacteristic
51C22×C4×D13C2311yescharacteristic
52C22×C4×D13C2311yescharacteristic
53C22×C4×D13C2311yescharacteristic
54C22×C4×D13C2311yescharacteristic
55C22×C4×D13C2311yescharacteristic
56C22×C4×D13C2311yescharacteristic
57C2×C4⋊#261—24no—
58C2×C4⋊#261—24no—
59C2×C4⋊#261C2×C418yes—
60C2×C4×#261—24no—
61C2×C4×#261—24no—
62C2×C4×#261—24no—
63C2×C4×#261—24no—
64C2×C4×#261—22no—
65C2×C4×#261—24no—
66C2×C4×#261—22no—
67C2×C4×#261—22no—
68C2×C4×#261—22no—
69C2×C4×#261—22no—
70C2×C4×#261—22no—
71C2×C4×#261—22no—
72C2×C4×#261—22no—
73C2×C4×#261—22no—
74C2×C4×#261—22no—
75C2×C4×#261C2×C418yes—
76C2×C4×#261D414yes—
77C2×C4×#261Q814yes—
78C2×C13×C4⋊C4C2×C411yescharacteristic
79C2×C13×C4⋊C4C2×C411yescharacteristic
80C2×C42×C13C2×C411yescharacteristic
81C2×C42×C13C2×C411yescharacteristic
82C2×C42×C13C2×C411yescharacteristic
83C2×C4⋊Dic13C2×C411yescharacteristic
84C2×C4⋊Dic13C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×#6101C2×C411yescharacteristic
89C2×C4×Dic13C2×C411yescharacteristic
90C2×C4×Dic13C2×C411yescharacteristic
91C2×C4×Dic13C2×C411yescharacteristic
92C2×C4×Dic13C2×C411yescharacteristic
93C2×C4×Dic13C2×C411yescharacteristic
94C2×C4×Dic13C2×C411yescharacteristic
95C2×C4×Dic13C2×C411yescharacteristic
96C2×C4×Dic13C2×C411yescharacteristic
97C2×C4×Dic13C2×C411yescharacteristic
98C4⋊C4×D13—24no—
99C4⋊C4×D13C2×C418yes—
100C42×D13—22no—
101C42×D13—22no—
102C42×D13—22no—
103C42×D13—22no—
104C42×D13—22no—
105C42×D13—22no—
106(C2×#261)⋊C4—24no—
107(C2×#261)⋊C4—24no—
108(C2×#261)⋊C4—24no—
109(C2×#261)⋊C4—24no—
110(C2×#261)⋊C4—24no—
111(C2×#261)⋊C4C2×C418yes—
112(C2×#261)⋊C4C2×C418yes—
113(C2×#261)⋊C4C2×C418yes—
114(C2×#261)⋊C4C2×C418yes—
115C13×#95C2×C411yescharacteristic
116C13×#95C2×C411yescharacteristic
117#88071C2×C411yescharacteristic
118#88071C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#88071C2×C411yescharacteristic
121#88071C2×C411yescharacteristic
122#88071C2×C411yescharacteristic
123C4×#387—131nomaximal, Sylow
124C23×D13C2411yescharacteristic
125C22×#261—22no—
126C22×#261—22no—
127C22×#261—22no—
128C22×#261—22no—
129C22×#261—22no—
130C22×#261—22no—
131C22×#261—22no—
132C22×#261—22no—
133C22×#261—22no—
134C22×#261—22no—
135C22×#261—22no—
136C22×#261—22no—
137C22×#261—22no—
138C22×#261—22no—
139C22×#261—22no—
140C22×#261—22no—
141C22×#261—22no—
142C22×#261—22no—
143C22×#261—22no—
144C22×#261—22no—
145C22×#261C22×C414yes—
146C22×#261C22×C414yes—
147C22×#261C22×C414yes—
148C22×#261C22×C414yes—
149C22×#261C2×D414yes—
150C22×#261C2×Q814yes—
151C22×#261#4114yes—
152C22×#261#4114yes—
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C22×C411yescharacteristic
155C22×C4×C13C22×C411yescharacteristic
156C22×C4×C13C22×C411yescharacteristic
157C22×C4×C13C22×C411yescharacteristic
158C22×C4×C13C22×C411yescharacteristic
159C22×C4×C13C22×C411yescharacteristic
160C22×Dic13C22×C411yescharacteristic
161C22×Dic13C22×C411yescharacteristic
162C22×Dic13C22×C411yescharacteristic
163C22×Dic13C22×C411yescharacteristic
164C22×Dic13C22×C411yescharacteristic
165C22×Dic13C22×C411yescharacteristic
166C22×Dic13C22×C411yescharacteristic
167C2×C4×D13—21no—
168C2×C4×D13—21no—
169C2×C4×D13—21no—
170C2×C4×D13—21no—
171C2×C4×D13—21no—
172C2×C4×D13—21no—
173C2×C4×D13—21no—
174C2×C4×D13—21no—
175C2×C4×D13—22no—
176C2×C4×D13—22no—
177C2×C4×D13—22no—
178C2×C4×D13—22no—
179C2×C4×D13—21no—
180C2×C4×D13—22no—
181C2×C4×D13—22no—
182C2×C4×D13—22no—
183C2×C4×D13—21no—
184C2×C4×D13—21no—
185C2×C4×D13—21no—
186C2×C4×D13—22no—
187C2×C4×D13C22×C414yes—
188C2×C4×D13C22×C414yes—
189C2×C4×D13C22×C414yes—
190C2×C4×D13C2×D412yes—
191C2×C4×D13C2×Q812yes—
192C2×C4×D13#4114yes—
193C2×C4×D13#4112yes—
194C2×C4×D13#4112yes—
195C2×C4×D13#4112yes—
196C2×C4×D13#4112yes—
197C4⋊#261—216no—
198C4×#261—216no—
199C4×#261—216no—
200C4×#261—28no—
201C4×#261—28no—
202C4×#261—44no—
203C4×#261—44no—
204C13×C4⋊C4—22no—
205C13×C4⋊C4C4214yescomplemented
206C42×C13—22no—
207C42×C13—22no—
208C42×C13—22no—
209C4⋊Dic13—22no—
210C4⋊Dic13C4214yescomplemented
211#6101—22no—
212#6101—22no—
213#6101C4214yescomplemented
214#6101C4214yescomplemented
215C4×Dic13—22no—
216C4×Dic13—22no—
217C4×Dic13—22no—
218C4×Dic13—22no—
219C4×Dic13—22no—
220C4×Dic13—22no—
221C4×Dic13—22no—
222C4×Dic13—22no—
223C4×Dic13—22no—
224C2×#387—132no—
225C2×C4×C4⋊C4—131no—
226C2×C4×C4⋊C4—131no—
227C2×C43—131no—
228#1436—132no—
229#1436—132no—
230#1434—132no—
231C4×#95—131no—
232C4×#95—131no—
233C4×#95—131no—
234C4×#95—131no—
235C23×C13C23×C411yescharacteristic
236C22×D13C23×C412yes—
237C22×D13C22×D411yescharacteristic
238C22×D13C22×Q811yescharacteristic
239C22×D13C2×#4112yes—
240C22×D13C2×#4112yes—
241C22×D13C2×#4111yescharacteristic
242C22×D13C2×#4111yescharacteristic
243C22×D13C2×#4111yescharacteristic
244C22×D13C2×#4112yes—
245C22×D13C2×#4111yescharacteristic
246C2×#261—24no—
247C2×#261—24no—
248C2×#261—24no—
249C2×#261—24no—
250C2×#261—24no—
251C2×#261—24no—
252C2×#261—24no—
253C2×#261—24no—
254C2×#261—24no—
255C2×#261—24no—
256C2×#261—24no—
257C2×#261—24no—
258C2×#261—24no—
259C2×#261—24no—
260C2×#261—24no—
261C2×#261—24no—
262C2×#261—24no—
263C2×#261—24no—
264C2×#261—42no—
265C2×#261—42no—
266C2×#261—42no—
267C2×#261—42no—
268C2×#261—42no—
269C2×#261—42no—
270C2×#261—42no—
271C2×#261—42no—
272C2×#261C4×D418yes—
273C2×#261C4×Q818yes—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13C2×C4212yes—
289C2×C4×C13C2×C4212yes—
290C2×C4×C13C2×C4212yes—
291C2×C4×C13#11712yes—
292C2×C4×C13#11712yes—
293C2×C4×C13C4×D412yes—
294C2×C4×C13C4×Q812yes—
295C2×Dic13—21no—
296C2×Dic13—21no—
297C2×Dic13—21no—
298C2×Dic13—21no—
299C2×Dic13—21no—
300C2×Dic13—21no—
301C2×Dic13—21no—
302C2×Dic13—21no—
303C2×Dic13—21no—
304C2×Dic13—21no—
305C2×Dic13—21no—
306C2×Dic13—21no—
307C2×Dic13—21no—
308C2×Dic13—21no—
309C2×Dic13C2×C4212yes—
310C2×Dic13C2×C4212yes—
311C2×Dic13C2×C4212yes—
312C2×Dic13#11712yes—
313C2×Dic13#11712yes—
314C2×Dic13C4×D412yes—
315C2×Dic13C4×Q812yes—
316C4×D13—24no—
317C4×D13—24no—
318C4×D13—24no—
319C4×D13—24no—
320C4×D13—24no—
321C4×D13—24no—
322C4×D13—24no—
323C4×D13—24no—
324C4×D13—42no—
325C4×D13—42no—
326C4×D13—42no—
327C4×D13—42no—
328C4×D13C22⋊Q814yes—
329C4×D13#12314yes—
330C4×D13#12514yes—
331C4×D13#12614yes—
332C22×C4⋊C4—131no—
333C22×C4⋊C4—132no—
334C22×C4⋊C4—131no—
335C22×C42—131no—
336C22×C42—131no—
337C22×C42—132no—
338C22×C42—131no—
339C22×C42—131no—
340C22×C42—131no—
341C22×C42—131no—
342C22×C42—131no—
343C22×C42—132no—
344#387—1316no—
345C4×C4⋊C4—131no—
346C4×C4⋊C4—131no—
347C4×C4⋊C4—131no—
348C4×C4⋊C4—131no—
349C4×C4⋊C4—131no—
350C4×C4⋊C4—131no—
351C4×C4⋊C4—131no—
352C4×C4⋊C4—264no—
353C4×C4⋊C4#26111yescharacteristic, complemented
354C2×#95—132no—
355C2×#95—132no—
356C2×#95—132no—
357C2×#95—132no—
358C2×#95—131no—
359C2×#95—131no—
360C2×#95—132no—
361C2×#95—132no—
362C2×#95—132no—
363C2×#95—132no—
364C2×#95—132no—
365C43—264no—
366C22×C13C22×C4211yescharacteristic
367C22×C13C2×#11711yescharacteristic
368C22×C13C2×#11711yescharacteristic
369C22×C13C2×C4×D411yescharacteristic
370C22×C13C2×C4×Q811yescharacteristic
371C22×C13C4×#4111yescharacteristic
372C22×C13C4×#4111yescharacteristic
373C2×D13C2×C4×D412yes—
374C2×D13C2×C4×Q812yes—
375C2×D13C4×#4112yes—
376C2×D13C4×#4112yes—
377C2×D13C4×#4112yes—
378C2×D13C4×#4112yes—
379C2×D13C2×C22⋊Q811yescharacteristic
380C2×D13C2×#12311yescharacteristic
381C2×D13#52512yes—
382C2×D13C2×#12511yescharacteristic
383C2×D13C2×#12611yescharacteristic
384C2×D13#52912yes—
385C2×D13#52912yes—
386C2×D13#52912yes—
387C2×D13#52912yes—
388C2×D13#53312yes—
389#261—28no—
390#261—28no—
391#261—44no—
392#261—44no—
393C4×C13—22no—
394C4×C13—22no—
395C4×C13—22no—
396C4×C13—22no—
397C4×C13—41no—
398C4×C13—41no—
399C4×C13#38714yescomplemented
400Dic13—22no—
401Dic13—22no—
402Dic13—22no—
403Dic13—22no—
404Dic13—41no—
405Dic13—41no—
406Dic13#38714yescomplemented
407C23×C4—131no—
408C23×C4—132no—
409C23×C4—132no—
410C23×C4—131no—
411C23×C4—131no—
412C23×C4—131no—
413C23×C4—131no—
414C23×C4—132no—
415C23×C4—132no—
416C23×C4—131no—
417C23×C4—131no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4—131no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4—138no—
422C2×C4⋊C4—138no—
423C2×C4⋊C4—131no—
424C2×C4⋊C4—131no—
425C2×C4⋊C4—131no—
426C2×C4⋊C4—264no—
427C2×C4⋊C4—264no—
428C2×C4⋊C4—264no—
429C2×C4⋊C4C2×#26111yescharacteristic
430C2×C4⋊C4C2×#26111yescharacteristic
431C2×C42—134no—
432C2×C42—138no—
433C2×C42—134no—
434C2×C42—131no—
435C2×C42—131no—
436C2×C42—131no—
437C2×C42—131no—
438C2×C42—131no—
439C2×C42—131no—
440C2×C42—131no—
441C2×C42—131no—
442C2×C42—131no—
443C2×C42—262no—
444C2×C42—262no—
445C2×C42—262no—
446C2×C42—262no—
447C2×C42—262no—
448C2×C42—262no—
449C2×C42—262no—
450C2×C42—264no—
451C2×C42—264no—
452C2×C42—262no—
453C2×C42—262no—
454C2×C42—262no—
455C2×C42—264no—
456C2×C42—264no—
457C2×C42—264no—
458C2×C42—262no—
459C2×C42—262no—
460C2×C42—262no—
461C2×C42—262no—
462C2×C42—262no—
463C2×C42—262no—
464C2×C42C2×#26111yescharacteristic
465C2×C42C2×#26111yescharacteristic
466C2×C42C2×#26111yescharacteristic
467#95—138no—
468#95—138no—
469#95—138no—
470#95—138no—
471#95—131no—
472#95—131no—
473#95—131no—
474#95—131no—
475#95—131no—
476#95—131no—
477#95—264no—
478#95—264no—
479#95—264no—
480#95—264no—
481#95—264no—
482#95C2×#26111yescharacteristic
483#95C2×#26111yescharacteristic
484C2×C13C4×#11711yescharacteristic
485C2×C13C42×D411yescharacteristic
486C2×C13C42×Q811yescharacteristic
487C2×C13C2×#38711yescharacteristic
488C2×C13#229011yescharacteristic
489C2×C13#229511yescharacteristic
490C2×C13#229811yescharacteristic
491D13C4×#12312yes—
492D13C4×C22⋊Q812yes—
493D13C4×#12612yes—
494D13C4×#12512yes—
495C24—131no—
496C22×C4—131no—
497C22×C4—132no—
498C22×C4—132no—
499C22×C4—132no—
500C22×C4—132no—
501C22×C4—132no—
502C22×C4—132no—
503C22×C4—134no—
504C22×C4—134no—
505C22×C4—134no—
506C22×C4—134no—
507C22×C4—134no—
508C22×C4—134no—
509C22×C4—131no—
510C22×C4—131no—
511C22×C4—131no—
512C22×C4—131no—
513C22×C4—134no—
514C22×C4—134no—
515C22×C4—134no—
516C22×C4—134no—
517C22×C4—134no—
518C22×C4—134no—
519C22×C4—131no—
520C22×C4—131no—
521C22×C4—261no—
522C22×C4—261no—
523C22×C4—261no—
524C22×C4—261no—
525C22×C4—261no—
526C22×C4—261no—
527C22×C4—261no—
528C22×C4—261no—
529C22×C4—262no—
530C22×C4—262no—
531C22×C4—262no—
532C22×C4—262no—
533C22×C4—261no—
534C22×C4—262no—
535C22×C4—262no—
536C22×C4—262no—
537C22×C4—261no—
538C22×C4—261no—
539C22×C4—261no—
540C22×C4—262no—
541C22×C4—262no—
542C22×C4—262no—
543C22×C4—262no—
544C22×C4—262no—
545C22×C4—262no—
546C22×C4—262no—
547C22×C4—262no—
548C22×C4—262no—
549C22×C4—262no—
550C22×C4—262no—
551C22×C4—262no—
552C22×C4—262no—
553C22×C4—262no—
554C22×C4—262no—
555C22×C4—262no—
556C22×C4—262no—
557C22×C4—262no—
558C22×C4—262no—
559C22×C4—262no—
560C22×C4—262no—
561C22×C4C22×#26111yescharacteristic
562C22×C4C22×#26111yescharacteristic
563C22×C4C22×#26111yescharacteristic
564C22×C4C22×#26111yescharacteristic
565C22×C4C22×#26111yescharacteristic
566C22×C4C22×#26111yescharacteristic
567C22×C4C22×#26111yescharacteristic
568C4⋊C4—22no—
569C4⋊C4—134no—
570C4⋊C4—134no—
571C4⋊C4—134no—
572C4⋊C4—262no—
573C4⋊C4—262no—
574C4⋊C4—2616no—
575C4⋊C4—262no—
576C4⋊C4C4×#26114yescomplemented
577C42—22no—
578C42—22no—
579C42—22no—
580C42—262no—
581C42—262no—
582C42—262no—
583C42—262no—
584C42—262no—
585C42—262no—
586C42—268no—
587C42—268no—
588C42—2616no—
589C42—2616no—
590C42—262no—
591C42—262no—
592C42—262no—
593C42—524no—
594C42—524no—
595C13C4×#38711yescharacteristic, complemented, Sylow
596C23—132no—
597C23—131no—
598C23—131no—
599C23—132no—
600C23—131no—
601C23—131no—
602C23—131no—
603C23—131no—
604C23—132no—
605C23—132no—
606C23C23×#26111yescharacteristic
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—132no—
622C2×C4—132no—
623C2×C4—132no—
624C2×C4—134no—
625C2×C4—134no—
626C2×C4—134no—
627C2×C4—134no—
628C2×C4—138no—
629C2×C4—138no—
630C2×C4—132no—
631C2×C4—132no—
632C2×C4—132no—
633C2×C4—132no—
634C2×C4—264no—
635C2×C4—264no—
636C2×C4—264no—
637C2×C4—264no—
638C2×C4—264no—
639C2×C4—264no—
640C2×C4—264no—
641C2×C4—264no—
642C2×C4—264no—
643C2×C4—264no—
644C2×C4—264no—
645C2×C4—264no—
646C2×C4—264no—
647C2×C4—264no—
648C2×C4—264no—
649C2×C4—264no—
650C2×C4—264no—
651C2×C4—264no—
652C2×C4—264no—
653C2×C4—264no—
654C2×C4—261no—
655C2×C4—261no—
656C2×C4—261no—
657C2×C4—261no—
658C2×C4—261no—
659C2×C4—261no—
660C2×C4—261no—
661C2×C4—261no—
662C2×C4—264no—
663C2×C4—264no—
664C2×C4—264no—
665C2×C4—264no—
666C2×C4—264no—
667C2×C4—264no—
668C2×C4—261no—
669C2×C4—261no—
670C2×C4—261no—
671C2×C4—261no—
672C2×C4—261no—
673C2×C4—261no—
674C2×C4—522no—
675C2×C4—522no—
676C2×C4—522no—
677C2×C4—522no—
678C2×C4—522no—
679C2×C4—522no—
680C2×C4—522no—
681C2×C4—522no—
682C2×C4—522no—
683C2×C4—522no—
684C2×C4—522no—
685C2×C4—522no—
686C2×C4C2×C4×#26112yes—
687C2×C4C2×C4×#26112yes—
688C2×C4C2×C4×#26112yes—
689C2×C4#8823712yes—
690C2×C4#8823712yes—
691C2×C4D4×#26112yes—
692C2×C4Q8×#26112yes—
693C22—132no—
694C22—132no—
695C22—132no—
696C22—132no—
697C22—132no—
698C22—132no—
699C22—131no—
700C22—131no—
701C22—131no—
702C22—131no—
703C22—132no—
704C22—132no—
705C22—132no—
706C22—132no—
707C22—132no—
708C22—132no—
709C22C22×C4×#26111yescharacteristic
710C22C2×#8823711yescharacteristic
711C22C2×#8823711yescharacteristic
712C22C2×D4×#26111yescharacteristic
713C22C2×Q8×#26111yescharacteristic
714C22#41×#26111yescharacteristic
715C22#41×#26111yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—134no—
723C4—268no—
724C4—268no—
725C4—262no—
726C4—262no—
727C4—262no—
728C4—262no—
729C4—524no—
730C4—524no—
731C4—521no—
732C4—521no—
733C4#1171908214yesdirect product factor
734C2—132no—
735C2—132no—
736C2—132no—
737C2—132no—
738C2C4×#8823711yescharacteristic
739C2C4×D4×#26111yescharacteristic
740C2C4×Q8×#26111yescharacteristic
741C2C2×#1171908211yescharacteristic
742C2#1313129011yescharacteristic
743C2#1313129511yescharacteristic
744C2#1313129811yescharacteristic
subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC4×C13×C4⋊C4C4
socleC23×C13C23×C4
prime radical, cosocleC23×D13C24
hypercenterC4×C4⋊C4#261
hypocenterC13C4×#387
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
33. #11719082C4direct (N × H)
36. C4×C13×C4⋊C4C4semidirect
37. C4⋊C4×Dic13C4semidirect
38. C4⋊C4×Dic13C4semidirect
39. C4×C4⋊Dic13C4semidirect
40. C4×#6101C4semidirect
41. C4×#6101C4semidirect
44. #11718310C4semidirect
45. #11718310C4semidirect
205. C13×C4⋊C4C42semidirect
210. C4⋊Dic13C42semidirect
213. #6101C42semidirect
214. #6101C42semidirect
353. C4×C4⋊C4#261semidirect
399. C4×C13#387semidirect
406. Dic13#387semidirect
576. C4⋊C4C4×#261semidirect
595. C13C4×#387semidirect
733. C4#11719082direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117190822
C2×C4×C4⋊#2612
C2×C42×#2612
#131300162
#131300152
#131300112
C4×(C2×#261)⋊C42
C4×C4⋊C4×D132
C4×#38713