Finite Group Databasebeta

← C4×#11719136 #16791555

Subgroups — C4×#11719136 #16791555

Order 3328.

2782 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719136C212yesmaximal
2C2×C4×C4⋊#261C212yesmaximal, complemented
3C2×C4×C22⋊#261C212yesmaximal
4#13130014C212yesmaximal, complemented
5#13130012C212yesmaximal, complemented
6#13130010C212yesmaximal
7C4×(C2×#261)⋊C4C212yesmaximal, complemented
8C22×C42×D13C211yesmaximal, characteristic
9C23×C4×D13C2211yescharacteristic
10C23×C4×D13C2211yescharacteristic
11C23×C4×D13C2211yescharacteristic
12C22×C22⋊#261C2214yes—
13C22×C4⋊#261C2214yes—
14C22×C4×#261C2214yes—
15C22×C42×C13C411yescharacteristic, complemented
16C22×C4×Dic13C411yescharacteristic, complemented
17C22×C4×Dic13C411yescharacteristic, complemented
18C22×C4×Dic13C411yescharacteristic, complemented
19C2×C42×D13—28no—
20C2×C42×D13C411yescharacteristic, complemented
21C2×C42×D13C411yescharacteristic, complemented
22C2×C42×D13C411yescharacteristic, complemented
23C2×C42×D13C411yescharacteristic, complemented
24C2×C42×D13C2211yescharacteristic
25C2×C42×D13C2211yescharacteristic
26C2×C42×D13C2211yescharacteristic
27C2×C42×D13C2211yescharacteristic
28#11719136C4116yesdirect product factor
29C4×C22⋊#261—28no—
30C2×(C2×#261)⋊C4C2214yes—
31C2×(C2×#261)⋊C4C2214yes—
32C2×(C2×#261)⋊C4C2214yes—
33C2×(C2×#261)⋊C4C2214yes—
34C4×C4⋊#261—28no—
35C24×D13C2311yescharacteristic
36C23×#261C2318yes—
37C23×C4×C13C2×C411yescharacteristic
38C23×C4×C13C2×C411yescharacteristic
39C23×C4×C13C2×C411yescharacteristic
40C23×Dic13C2×C411yescharacteristic
41C23×Dic13C2×C411yescharacteristic
42C23×Dic13C2×C411yescharacteristic
43C22×C4×D13—24no—
44C22×C4×D13—24no—
45C22×C4×D13—24no—
46C22×C4×D13—24no—
47C22×C4×D13—24no—
48C22×C4×D13—24no—
49C22×C4×D13—24no—
50C22×C4×D13C2×C411yescharacteristic
51C22×C4×D13C2×C411yescharacteristic
52C22×C4×D13C2×C411yescharacteristic
53C22×C4×D13C2×C411yescharacteristic
54C22×C4×D13C2×C418yes—
55C22×C4×D13C2×C411yescharacteristic
56C22×C4×D13C2×C411yescharacteristic
57C22×C4×D13D414yes—
58C22×C4×D13Q814yes—
59C22×C4×D13C2311yescharacteristic
60C22×C4×D13C2311yescharacteristic
61C22×C4×D13C2311yescharacteristic
62C22×C4×D13C2311yescharacteristic
63C22×C4×D13C2311yescharacteristic
64C22×C4×D13C2311yescharacteristic
65C2×C22⋊#261—28no—
66C2×C22⋊#261—28no—
67C2×C22⋊#261C2×C4116yes—
68C2×C4⋊#261—28no—
69C2×C4⋊#261—28no—
70C2×C4⋊#261C2×C4116yescomplemented
71C2×C4×#261—28no—
72C2×C4×#261—28no—
73C2×C4×#261—28no—
74C2×C42×C13—24no—
75C2×C42×C13C2×C411yescharacteristic
76C2×C42×C13C2×C411yescharacteristic
77C2×C42×C13C2×C411yescharacteristic
78C2×C42×C13C2×C411yescharacteristic
79C2×C4×Dic13—24no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13C2×C411yescharacteristic
83C2×C4×Dic13C2×C411yescharacteristic
84C2×C4×Dic13C2×C411yescharacteristic
85C2×C4×Dic13C2×C411yescharacteristic
86C2×C4×Dic13C2×C411yescharacteristic
87C2×C4×Dic13C2×C411yescharacteristic
88C2×C4×Dic13C2×C411yescharacteristic
89C2×C4×Dic13C2×C411yescharacteristic
90C2×C4×Dic13C2×C411yescharacteristic
91C2×C4×Dic13C2×C411yescharacteristic
92C2×C4×Dic13C2×C411yescharacteristic
93C2×C4×Dic13C2×C411yescharacteristic
94C42×D13—24no—
95C42×D13—24no—
96C42×D13—24no—
97C42×D13—24no—
98C42×D13—24no—
99C42×D13—24no—
100C42×D13—24no—
101C42×D13D418yes—
102(C2×#261)⋊C4—28no—
103(C2×#261)⋊C4—28no—
104(C2×#261)⋊C4—28no—
105(C2×#261)⋊C4C2×C4116yescomplemented
106C4×#380—131nomaximal, Sylow
107C24×C13C22×C411yescharacteristic
108C23×D13—22no—
109C23×D13—22no—
110C23×D13—22no—
111C23×D13—22no—
112C23×D13C22×C411yescharacteristic
113C23×D13C22×C414yes—
114C23×D13C2×D412yes—
115C23×D13C2×Q812yes—
116C23×D13#4114yes—
117C23×D13C2411yescharacteristic
118C22×#261—28no—
119C22×#261—28no—
120C22×#261—28no—
121C22×#261—28no—
122C22×#261—28no—
123C22×#261—28no—
124C22×#261C22×C4116yes—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13C4214yescomplemented
133C22×C4×C13C4⋊C414yescomplemented
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C411yescharacteristic
139C22×C4×C13C22×C411yescharacteristic
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13C4214yescomplemented
148C22×Dic13C4⋊C414yescomplemented
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C22×Dic13C22×C411yescharacteristic
153C22×Dic13C22×C411yescharacteristic
154C22×Dic13C22×C411yescharacteristic
155C2×C4×D13—232no—
156C2×C4×D13—22no—
157C2×C4×D13—22no—
158C2×C4×D13—22no—
159C2×C4×D13—22no—
160C2×C4×D13—22no—
161C2×C4×D13—22no—
162C2×C4×D13—22no—
163C2×C4×D13—22no—
164C2×C4×D13—22no—
165C2×C4×D13—22no—
166C2×C4×D13—22no—
167C2×C4×D13—22no—
168C2×C4×D13—22no—
169C2×C4×D13—22no—
170C2×C4×D13—22no—
171C2×C4×D13—22no—
172C2×C4×D13—22no—
173C2×C4×D13—22no—
174C2×C4×D13—22no—
175C2×C4×D13—22no—
176C2×C4×D13—22no—
177C2×C4×D13—22no—
178C2×C4×D13—232no—
179C2×C4×D13—216no—
180C2×C4×D13—216no—
181C2×C4×D13C4214yescomplemented
182C2×C4×D13C4214yescomplemented
183C2×C4×D13C4⋊C414yescomplemented
184C2×C4×D13C4⋊C414yescomplemented
185C2×C4×D13C22×C414yes—
186C2×C4×D13C22×C414yes—
187C2×C4×D13C2×D414yes—
188C2×C4×D13C2×D412yes—
189C2×C4×D13C2×D414yes—
190C2×C4×D13C2×D412yes—
191C2×C4×D13C2×D414yes—
192C2×C4×D13C2×Q812yes—
193C2×C4×D13C2×Q812yes—
194C2×C4×D13#4114yes—
195C2×C4×D13#4114yes—
196C2×C4×D13#4114yes—
197C22⋊#261—232no—
198C4⋊#261—232no—
199C4×#261—416no—
200C42×C13—22no—
201C42×C13—22no—
202C42×C13—22no—
203C42×C13C22⋊C414yescomplemented
204C4×Dic13—22no—
205C4×Dic13—22no—
206C4×Dic13—22no—
207C4×Dic13—22no—
208C4×Dic13—22no—
209C4×Dic13—22no—
210C4×Dic13—22no—
211C4×Dic13—22no—
212C4×Dic13—22no—
213C4×Dic13C22⋊C414yescomplemented
214C4×Dic13C22⋊C414yescomplemented
215C4×Dic13C22⋊C414yescomplemented
216C23×C42—131no—
217C2×#380—132no—
218C2×C4×C4⋊C4—132no—
219C2×C4×C22⋊C4—132no—
220C4⋊#95—132no—
221#1434—132no—
222C22⋊#95—132no—
223C4×#95—132no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13C2×C4212yes—
229C23×C13C2×C4⋊C412yes—
230C23×C13#11712yes—
231C23×C13C23×C411yescharacteristic
232C22×D13—21no—
233C22×D13—21no—
234C22×D13—21no—
235C22×D13—21no—
236C22×D13—28no—
237C22×D13—28no—
238C22×D13—24no—
239C22×D13—24no—
240C22×D13—28no—
241C22×D13—28no—
242C22×D13—24no—
243C22×D13—24no—
244C22×D13C2×C4212yes—
245C22×D13C2×C4⋊C412yes—
246C22×D13#11712yes—
247C22×D13C4×D418yes—
248C22×D13C4×Q818yes—
249C22×D13C23×C412yes—
250C22×D13C22×D411yescharacteristic
251C22×D13C22×D412yes—
252C22×D13C22×Q811yescharacteristic
253C22×D13C2×#4112yes—
254C22×D13C2×#4112yes—
255C22×D13C2×#4112yes—
256C22×D13C2×#4112yes—
257C2×#261—216no—
258C2×#261—216no—
259C2×#261—216no—
260C2×#261—48no—
261C2×#261—48no—
262C2×#261—48no—
263C2×#261—48no—
264C2×C4×C13—28no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—28no—
274C2×C4×C13—28no—
275C2×C4×C13C2×C4212yes—
276C2×C4×C13C2×C4212yes—
277C2×C4×C13C2×C22⋊C412yes—
278C2×C4×C13C2×C22⋊C412yes—
279C2×C4×C13C2×C22⋊C412yes—
280C2×C4×C13C2×C4⋊C412yes—
281C2×C4×C13C2×C4⋊C412yes—
282C2×C4×C13#11712yes—
283C2×C4×C13#11712yes—
284C2×C4×C13#11712yes—
285C2×Dic13—28no—
286C2×Dic13—21no—
287C2×Dic13—21no—
288C2×Dic13—21no—
289C2×Dic13—21no—
290C2×Dic13—21no—
291C2×Dic13—21no—
292C2×Dic13—21no—
293C2×Dic13—21no—
294C2×Dic13—28no—
295C2×Dic13—28no—
296C2×Dic13C2×C4212yes—
297C2×Dic13C2×C4212yes—
298C2×Dic13C2×C22⋊C412yes—
299C2×Dic13C2×C22⋊C412yes—
300C2×Dic13C2×C22⋊C412yes—
301C2×Dic13C2×C4⋊C412yes—
302C2×Dic13C2×C4⋊C412yes—
303C2×Dic13#11712yes—
304C2×Dic13#11712yes—
305C2×Dic13#11712yes—
306C4×D13—28no—
307C4×D13—28no—
308C4×D13—28no—
309C4×D13—24no—
310C4×D13—24no—
311C4×D13—28no—
312C4×D13—28no—
313C4×D13—28no—
314C4×D13—28no—
315C4×D13—28no—
316C4×D13—28no—
317C4×D13C4×D4116yes—
318C4×D13#12118yes—
319C4×D13C22⋊Q818yes—
320C24×C4—131no—
321C24×C4—131no—
322C24×C4—131no—
323C22×C4⋊C4—134no—
324C22×C22⋊C4—134no—
325C22×C42—131no—
326C22×C42—131no—
327C22×C42—131no—
328C22×C42—131no—
329C22×C42—131no—
330C22×C42—131no—
331C22×C42—131no—
332C22×C42—131no—
333C22×C42—131no—
334C22×C42—131no—
335C22×C42—131no—
336C22×C42—134no—
337C22×C42—268no—
338C22×C42#26111yescharacteristic, complemented
339#380—1316no—
340C4×C4⋊C4—268no—
341C4×C22⋊C4—268no—
342C2×#95—134no—
343C2×#95—134no—
344C2×#95—134no—
345C2×#95—134no—
346C22×C13—22no—
347C22×C13—22no—
348C22×C13—22no—
349C22×C13—22no—
350C22×C13—22no—
351C22×C13—22no—
352C22×C13C4×C4⋊C414yescomplemented
353C22×C13C22×C4211yescharacteristic
354C22×C13C22×C22⋊C411yescharacteristic
355C22×C13C22×C4⋊C411yescharacteristic
356C22×C13C2×#11711yescharacteristic
357C22×C13C2×#11711yescharacteristic
358C22×C13C2×#11711yescharacteristic
359C22×C13C2×#11711yescharacteristic
360C2×D13—22no—
361C2×D13—22no—
362C2×D13—22no—
363C2×D13—22no—
364C2×D13—22no—
365C2×D13—22no—
366C2×D13—216no—
367C2×D13—216no—
368C2×D13C4×C4⋊C414yescomplemented
369C2×D13C2×C4×D412yes—
370C2×D13C2×C4×D414yes—
371C2×D13C2×C4×Q812yes—
372C2×D13C4×#4114yes—
373C2×D13C2×#12112yes—
374C2×D13C2×C22⋊Q812yes—
375C2×D13#52514yes—
376C2×D13#52914yes—
377C2×D13#53212yes—
378C2×D13#53312yes—
379#261—416no—
380C4×C13—22no—
381C4×C13—22no—
382C4×C13—22no—
383C4×C13—22no—
384C4×C13C4×C22⋊C414yescomplemented
385C4×C13#38014yescomplemented
386Dic13—22no—
387Dic13—22no—
388Dic13—22no—
389Dic13—22no—
390Dic13C4×C22⋊C414yescomplemented
391Dic13#38014yescomplemented
392C25—131no—
393C23×C4—131no—
394C23×C4—131no—
395C23×C4—131no—
396C23×C4—131no—
397C23×C4—138no—
398C23×C4—134no—
399C23×C4—134no—
400C23×C4—131no—
401C23×C4—131no—
402C23×C4—131no—
403C23×C4—131no—
404C23×C4—131no—
405C23×C4—131no—
406C23×C4—131no—
407C23×C4—131no—
408C23×C4—138no—
409C23×C4—131no—
410C23×C4—131no—
411C23×C4—131no—
412C23×C4—264no—
413C23×C4—264no—
414C23×C4—264no—
415C23×C4—264no—
416C23×C4—264no—
417C23×C4—264no—
418C23×C4—264no—
419C23×C4C2×#26111yescharacteristic
420C23×C4C2×#26111yescharacteristic
421C23×C4C2×#26111yescharacteristic
422C2×C4⋊C4—1316no—
423C2×C4⋊C4—268no—
424C2×C4⋊C4—268no—
425C2×C22⋊C4—1316no—
426C2×C22⋊C4—268no—
427C2×C22⋊C4—268no—
428C2×C42—24no—
429C2×C42—131no—
430C2×C42—131no—
431C2×C42—131no—
432C2×C42—138no—
433C2×C42—131no—
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—264no—
443C2×C42—264no—
444C2×C42—264no—
445C2×C42—264no—
446C2×C42—264no—
447C2×C42—264no—
448C2×C42—264no—
449C2×C42—264no—
450C2×C42—264no—
451C2×C42—264no—
452C2×C42—268no—
453C2×C42—268no—
454C2×C42—268no—
455C2×C42C2×#26111yescharacteristic
456C2×C42C2×#26111yescharacteristic
457C2×C42C2×#26111yescharacteristic
458C2×C42C2×#26111yescharacteristic
459#95—1316no—
460#95—268no—
461#95—268no—
462#95—268no—
463C2×C13—24no—
464C2×C13C2×C4×C22⋊C411yescharacteristic
465C2×C13C2×C4×C4⋊C411yescharacteristic
466C2×C13C4×#11711yescharacteristic
467C2×C13C2×#38011yescharacteristic
468C2×C13#228011yescharacteristic
469C2×C13#228311yescharacteristic
470C2×C13#228511yescharacteristic
471D13—24no—
472D13C4×#12114yes—
473D13C4×C22⋊Q814yes—
474C24—131no—
475C24—134no—
476C24—132no—
477C24—132no—
478C24—134no—
479C24—131no—
480C24—262no—
481C24—262no—
482C24—262no—
483C24—262no—
484C24C22×#26111yescharacteristic
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—131no—
493C22×C4—131no—
494C22×C4—134no—
495C22×C4—132no—
496C22×C4—132no—
497C22×C4—134no—
498C22×C4—134no—
499C22×C4—134no—
500C22×C4—134no—
501C22×C4—134no—
502C22×C4—134no—
503C22×C4—131no—
504C22×C4—131no—
505C22×C4—131no—
506C22×C4—131no—
507C22×C4—134no—
508C22×C4—134no—
509C22×C4—134no—
510C22×C4—132no—
511C22×C4—134no—
512C22×C4—134no—
513C22×C4—132no—
514C22×C4—134no—
515C22×C4—134no—
516C22×C4—1316no—
517C22×C4—262no—
518C22×C4—262no—
519C22×C4—262no—
520C22×C4—262no—
521C22×C4—262no—
522C22×C4—262no—
523C22×C4—2632no—
524C22×C4—2616no—
525C22×C4—2616no—
526C22×C4—262no—
527C22×C4—262no—
528C22×C4—262no—
529C22×C4—262no—
530C22×C4—262no—
531C22×C4—262no—
532C22×C4—262no—
533C22×C4—262no—
534C22×C4—262no—
535C22×C4—262no—
536C22×C4—2632no—
537C22×C4—262no—
538C22×C4—262no—
539C22×C4—262no—
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—268no—
551C22×C4—268no—
552C22×C4—268no—
553C22×C4—268no—
554C22×C4—268no—
555C22×C4—268no—
556C22×C4C4×#26114yescomplemented
557C22×C4C4⋊#26114yescomplemented
558C22×C4C22×#26111yescharacteristic
559C22×C4C22×#26111yescharacteristic
560C22×C4C22×#26111yescharacteristic
561C22×C4C22×#26111yescharacteristic
562C22×C4C22×#26111yescharacteristic
563C22×C4C22×#26111yescharacteristic
564C4⋊C4—2632no—
565C22⋊C4—2632no—
566C42—22no—
567C42—22no—
568C42—22no—
569C42—134no—
570C42—134no—
571C42—134no—
572C42—262no—
573C42—262no—
574C42—262no—
575C42—262no—
576C42—262no—
577C42—262no—
578C42—262no—
579C42—262no—
580C42—262no—
581C42—5216no—
582C42C22⋊#26114yescomplemented
583C13C4×#38011yescharacteristic, complemented, Sylow
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—132no—
589C23—131no—
590C23—131no—
591C23—132no—
592C23—132no—
593C23—132no—
594C23—132no—
595C23—132no—
596C23—138no—
597C23—138no—
598C23—132no—
599C23—132no—
600C23—132no—
601C23—268no—
602C23—264no—
603C23—264no—
604C23—268no—
605C23—268no—
606C23—268no—
607C23—264no—
608C23—264no—
609C23—261no—
610C23—261no—
611C23—261no—
612C23—261no—
613C23C2×C4×#26112yes—
614C23C2×C4⋊#26112yes—
615C23#8823712yes—
616C23C23×#26111yescharacteristic
617C2×C4—28no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—28no—
627C2×C4—28no—
628C2×C4—132no—
629C2×C4—132no—
630C2×C4—132no—
631C2×C4—132no—
632C2×C4—132no—
633C2×C4—132no—
634C2×C4—1316no—
635C2×C4—138no—
636C2×C4—138no—
637C2×C4—132no—
638C2×C4—132no—
639C2×C4—132no—
640C2×C4—132no—
641C2×C4—268no—
642C2×C4—268no—
643C2×C4—268no—
644C2×C4—264no—
645C2×C4—264no—
646C2×C4—268no—
647C2×C4—268no—
648C2×C4—268no—
649C2×C4—268no—
650C2×C4—268no—
651C2×C4—268no—
652C2×C4—268no—
653C2×C4—261no—
654C2×C4—261no—
655C2×C4—261no—
656C2×C4—261no—
657C2×C4—261no—
658C2×C4—261no—
659C2×C4—261no—
660C2×C4—261no—
661C2×C4—268no—
662C2×C4—268no—
663C2×C4—2616no—
664C2×C4—2616no—
665C2×C4—2616no—
666C2×C4—528no—
667C2×C4—528no—
668C2×C4—528no—
669C2×C4—528no—
670C2×C4C2×C4×#26112yes—
671C2×C4C2×C4×#26112yes—
672C2×C4C2×C4⋊#26112yes—
673C2×C4C2×C4⋊#26112yes—
674C2×C4#8823712yes—
675C2×C4#8823712yes—
676C2×C4#8823712yes—
677C2×C4C2×C22⋊#26112yes—
678C2×C4C2×C22⋊#26112yes—
679C2×C4C2×C22⋊#26112yes—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—134no—
687C22—132no—
688C22—132no—
689C22—134no—
690C22—132no—
691C22—132no—
692C22—134no—
693C22—134no—
694C22—132no—
695C22—132no—
696C22—134no—
697C22—2616no—
698C22—2616no—
699C22—262no—
700C22—262no—
701C22—262no—
702C22—262no—
703C22—262no—
704C22—262no—
705C22C4×C4⋊#26114yescomplemented
706C22C22×C4×#26111yescharacteristic
707C22C22×C4⋊#26111yescharacteristic
708C22C2×#8823711yescharacteristic
709C22C2×#8823711yescharacteristic
710C22C2×#8823711yescharacteristic
711C22C2×#8823711yescharacteristic
712C22C22×C22⋊#26111yescharacteristic
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—134no—
718C4—134no—
719C4—262no—
720C4—262no—
721C4—262no—
722C4—262no—
723C4—5216no—
724C4C4×C22⋊#26114yescomplemented
725C4#1171913614yesdirect product factor
726C2—24no—
727C2—134no—
728C2—134no—
729C2—264no—
730C2C2×C4×C22⋊#26111yescharacteristic
731C2C2×C4×C4⋊#26111yescharacteristic
732C2C4×#8823711yescharacteristic
733C2C2×#1171913611yescharacteristic
734C2#1313128011yescharacteristic
735C2#1313128311yescharacteristic
736C2#1313128511yescharacteristic
subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC22×C42×C13C4
socleC23×C13C23×C4
prime radicalC24×D13C23
cosocleC23×D13C24
hypercenterC22×C42#261
hypocenterC13C4×#380
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊#261C2semidirect
4. #13130014C2semidirect
5. #13130012C2semidirect
7. C4×(C2×#261)⋊C4C2semidirect
15. C22×C42×C13C4semidirect
16. C22×C4×Dic13C4semidirect
17. C22×C4×Dic13C4semidirect
18. C22×C4×Dic13C4semidirect
20. C2×C42×D13C4semidirect
21. C2×C42×D13C4semidirect
22. C2×C42×D13C4semidirect
23. C2×C42×D13C4semidirect
28. #11719136C4direct (N × H)
70. C2×C4⋊#261C2×C4semidirect
105. (C2×#261)⋊C4C2×C4semidirect
132. C22×C4×C13C42semidirect
133. C22×C4×C13C4⋊C4semidirect
147. C22×Dic13C42semidirect
148. C22×Dic13C4⋊C4semidirect
181. C2×C4×D13C42semidirect
182. C2×C4×D13C42semidirect
183. C2×C4×D13C4⋊C4semidirect
184. C2×C4×D13C4⋊C4semidirect
203. C42×C13C22⋊C4semidirect
213. C4×Dic13C22⋊C4semidirect
214. C4×Dic13C22⋊C4semidirect
215. C4×Dic13C22⋊C4semidirect
338. C22×C42#261semidirect
352. C22×C13C4×C4⋊C4semidirect
368. C2×D13C4×C4⋊C4semidirect
384. C4×C13C4×C22⋊C4semidirect
385. C4×C13#380semidirect
390. Dic13C4×C22⋊C4semidirect
391. Dic13#380semidirect
556. C22×C4C4×#261semidirect
557. C22×C4C4⋊#261semidirect
582. C42C22⋊#261semidirect
583. C13C4×#380semidirect
705. C22C4×C4⋊#261semidirect
724. C4C4×C22⋊#261semidirect
725. C4#11719136direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191362
C2×C4×C4⋊#2612
C2×C4×C22⋊#2612
#131300142
#131300122
#131300102
C4×(C2×#261)⋊C42
C22×C42×D132
C4×#38013