Finite Group Databasebeta

← C4⋊C4×C22⋊#261 #16791616

Subgroups — C4⋊C4×C22⋊#261 #16791616

Order 3328.

2574 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719136C211yesmaximal, characteristic
2C2×C4⋊C4×#261C212yesmaximal, complemented
3C2×C4×C22⋊#261C212yesmaximal
4C2×C4×C22⋊#261C211yesmaximal, characteristic
5#13130015C214yesmaximal, complemented
6#13130013C212yesmaximal, complemented
7#13130010C212yesmaximal
8C22×C4⋊C4×D13C211yesmaximal, characteristic
9C23×C4×D13C2212yes—
10C23×C4×D13C2211yescharacteristic
11C22×C22⋊#261C2212yes—
12C22×C22⋊#261C2211yescharacteristic
13C22×C22⋊#261C2211yescharacteristic
14C22×C4⋊#261C2212yes—
15C22×C4×#261C2214yes—
16C22×C4×#261C2212yes—
17C22×C13×C4⋊C4C411yescharacteristic, complemented
18C22×C4⋊Dic13C411yescharacteristic, complemented
19C22×#6101C412yescomplemented
20C2×C4⋊C4×D13—28no—
21C2×C4⋊C4×D13C411yescharacteristic, complemented
22C2×C4⋊C4×D13C411yescharacteristic, complemented
23C2×C4⋊C4×D13C412yescomplemented
24C2×C4⋊C4×D13C2211yescharacteristic
25C2×C4⋊C4×D13C2212yes—
26C2×C4⋊C4×D13C2211yescharacteristic
27#11719136C418yescomplemented
28C4×C22⋊#261—28no—
29C4×C22⋊#261C418yescomplemented
30C2×(C2×#261)⋊C4C2214yes—
31C2×(C2×#261)⋊C4C2214yes—
32C2×(C2×#261)⋊C4C2214yes—
33C2×(C2×#261)⋊C4C2212yes—
34C2×(C2×#261)⋊C4C2212yes—
35C4⋊C4×#261—28no—
36C24×D13C2311yescharacteristic
37C23×#261C2314yes—
38C23×#261C2312yes—
39C23×#261C2312yes—
40C23×C4×C13C2×C412yes—
41C23×C4×C13C2×C411yescharacteristic
42C23×Dic13C2×C412yes—
43C23×Dic13C2×C411yescharacteristic
44C22×C4×D13—24no—
45C22×C4×D13—24no—
46C22×C4×D13—24no—
47C22×C4×D13—24no—
48C22×C4×D13—28no—
49C22×C4×D13—44no—
50C22×C4×D13C2×C412yes—
51C22×C4×D13C2×C412yes—
52C22×C4×D13C2×C411yescharacteristic
53C22×C4×D13C2×C411yescharacteristic
54C22×C4×D13C2×C414yes—
55C22×C4×D13C2×C414yes—
56C22×C4×D13C2312yes—
57C22×C4×D13C2311yescharacteristic
58C22×C4×D13C2312yes—
59C22×C4×D13C2311yescharacteristic
60C2×C22⋊#261—24no—
61C2×C22⋊#261—22no—
62C2×C22⋊#261—22no—
63C2×C22⋊#261—24no—
64C2×C22⋊#261C2×C414yes—
65C2×C22⋊#261C2×C418yes—
66C2×C22⋊#261C2×C414yes—
67C2×C22⋊#261D414yes—
68C2×C22⋊#261Q814yes—
69C2×C4⋊#261—24no—
70C2×C4⋊#261—24no—
71C2×C4⋊#261C2×C418yescomplemented
72C2×C4×#261—24no—
73C2×C4×#261—24no—
74C2×C4×#261—28no—
75C2×C4×#261—28no—
76C2×C4×#261—44no—
77C2×C4×#261C2×C418yescomplemented
78C2×C13×C4⋊C4—24no—
79C2×C13×C4⋊C4C2×C411yescharacteristic
80C2×C13×C4⋊C4C2×C412yes—
81C2×C13×C4⋊C4C2×C411yescharacteristic
82C2×C4⋊Dic13—24no—
83C2×C4⋊Dic13C2×C411yescharacteristic
84C2×C4⋊Dic13C2×C412yes—
85C2×C4⋊Dic13C2×C411yescharacteristic
86C2×#6101—28no—
87C2×#6101C2×C412yes—
88C2×#6101C2×C412yes—
89C2×#6101C2×C412yes—
90C2×#6101C2×C412yes—
91C4⋊C4×D13—28no—
92C4⋊C4×D13—24no—
93C4⋊C4×D13—24no—
94C4⋊C4×D13—24no—
95C4⋊C4×D13—28no—
96C4⋊C4×D13D418yes—
97(C2×#261)⋊C4—28no—
98(C2×#261)⋊C4—28no—
99(C2×#261)⋊C4—44no—
100(C2×#261)⋊C4C2×C418yescomplemented
101(C2×#261)⋊C4C2×C418yescomplemented
102C22⋊C4×C4⋊C4—131nomaximal, Sylow
103C24×C13C22×C411yescharacteristic
104C23×D13—22no—
105C23×D13—22no—
106C23×D13—22no—
107C23×D13—22no—
108C23×D13C22×C411yescharacteristic
109C23×D13C22×C412yes—
110C23×D13C22×C412yes—
111C23×D13C2×D412yes—
112C23×D13C2×Q812yes—
113C23×D13#4112yes—
114C23×D13#4112yes—
115C23×D13C2411yescharacteristic
116C22×#261—22no—
117C22×#261—22no—
118C22×#261—22no—
119C22×#261—22no—
120C22×#261—22no—
121C22×#261—24no—
122C22×#261—24no—
123C22×#261—22no—
124C22×#261—24no—
125C22×#261—22no—
126C22×#261—22no—
127C22×#261—24no—
128C22×#261—22no—
129C22×#261—24no—
130C22×#261—24no—
131C22×#261—22no—
132C22×#261C22×C414yes—
133C22×#261C22×C418yes—
134C22×#261C22×C414yes—
135C22×#261C2×D414yes—
136C22×#261C2×Q814yes—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—24no—
140C22×C4×C13—24no—
141C22×C4×C13—42no—
142C22×C4×C13C4214yescomplemented
143C22×C4×C13C22×C412yes—
144C22×C4×C13C22×C411yescharacteristic
145C22×C4×C13C22×C412yes—
146C22×C4×C13C22×C411yescharacteristic
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—24no—
150C22×Dic13—24no—
151C22×Dic13—42no—
152C22×Dic13C4214yescomplemented
153C22×Dic13C22×C412yes—
154C22×Dic13C22×C411yescharacteristic
155C22×Dic13C22×C412yes—
156C22×Dic13C22×C411yescharacteristic
157C2×C4×D13—22no—
158C2×C4×D13—22no—
159C2×C4×D13—22no—
160C2×C4×D13—22no—
161C2×C4×D13—24no—
162C2×C4×D13—22no—
163C2×C4×D13—22no—
164C2×C4×D13—22no—
165C2×C4×D13—22no—
166C2×C4×D13—216no—
167C2×C4×D13—216no—
168C2×C4×D13—24no—
169C2×C4×D13—24no—
170C2×C4×D13—22no—
171C2×C4×D13—24no—
172C2×C4×D13—22no—
173C2×C4×D13—24no—
174C2×C4×D13—24no—
175C2×C4×D13—24no—
176C2×C4×D13—416no—
177C2×C4×D13—416no—
178C2×C4×D13—42no—
179C2×C4×D13—42no—
180C2×C4×D13C4214yescomplemented
181C2×C4×D13C4214yescomplemented
182C2×C4×D13C22×C412yes—
183C2×C4×D13C22×C412yes—
184C2×C4×D13C22×C412yes—
185C2×C4×D13C22×C412yes—
186C2×C4×D13C2×D418yes—
187C2×C4×D13C2×D414yes—
188C2×C4×D13#4114yes—
189C22⋊#261—28no—
190C22⋊#261—216no—
191C22⋊#261C4⋊C4116yesdirect product factor
192C4⋊#261—216no—
193C4×#261—216no—
194C4×#261—416no—
195C13×C4⋊C4—24no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4C22⋊C414yescomplemented
198C4⋊Dic13—22no—
199C4⋊Dic13—24no—
200C4⋊Dic13C22⋊C414yescomplemented
201#6101—24no—
202#6101—24no—
203#6101—24no—
204#6101C22⋊C418yescomplemented
205C23×C4⋊C4—131no—
206C2×#380—131no—
207C2×C4×C4⋊C4—132no—
208C2×C4×C22⋊C4—131no—
209C2×C4×C22⋊C4—132no—
210#1436—134no—
211C4⋊#95—132no—
212C22⋊#95—132no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13C2×C4212yes—
218C23×C13C4×D412yes—
219C23×C13C4×Q812yes—
220C23×C13C23×C411yescharacteristic
221C22×D13—21no—
222C22×D13—21no—
223C22×D13—21no—
224C22×D13—21no—
225C22×D13—24no—
226C22×D13—24no—
227C22×D13—24no—
228C22×D13—24no—
229C22×D13—24no—
230C22×D13—24no—
231C22×D13—24no—
232C22×D13—24no—
233C22×D13—24no—
234C22×D13—24no—
235C22×D13—24no—
236C22×D13—24no—
237C22×D13C2×C4212yes—
238C22×D13C2×C4⋊C414yes—
239C22×D13#11714yes—
240C22×D13C4×D414yes—
241C22×D13C4×D412yes—
242C22×D13C4×Q814yes—
243C22×D13C4×Q812yes—
244C22×D13C23×C411yescharacteristic
245C22×D13C23×C411yescharacteristic
246C22×D13C22×D411yescharacteristic
247C22×D13C22×D412yes—
248C22×D13C22×Q811yescharacteristic
249C22×D13C2×#4111yescharacteristic
250C22×D13C2×#4111yescharacteristic
251C22×D13C2×#4112yes—
252C22×D13H(5,𝔽2)12yes—
253C22×D132−1+412yes—
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—28no—
263C2×#261—28no—
264C2×#261—24no—
265C2×#261—28no—
266C2×#261—44no—
267C2×#261—42no—
268C2×#261—44no—
269C2×#261—42no—
270C2×#261—44no—
271C2×#261—42no—
272C2×#261—42no—
273C2×#261—44no—
274C2×#261C2×C4⋊C418yescomplemented
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—28no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—48no—
284C2×C4×C13C2×C4212yes—
285C2×C4×C13C2×C4212yes—
286C2×C4×C13C2×C22⋊C414yes—
287C2×C4×C13C2×C22⋊C412yes—
288C2×C4×C13#11712yes—
289C2×Dic13—21no—
290C2×Dic13—21no—
291C2×Dic13—22no—
292C2×Dic13—22no—
293C2×Dic13—28no—
294C2×Dic13—22no—
295C2×Dic13—22no—
296C2×Dic13—22no—
297C2×Dic13—48no—
298C2×Dic13C2×C4212yes—
299C2×Dic13C2×C4212yes—
300C2×Dic13C2×C22⋊C414yes—
301C2×Dic13C2×C22⋊C412yes—
302C2×Dic13#11712yes—
303C4×D13—24no—
304C4×D13—24no—
305C4×D13—28no—
306C4×D13—28no—
307C4×D13—28no—
308C4×D13—28no—
309C4×D13—48no—
310C4×D13—48no—
311C4×D13—44no—
312C4×D13—44no—
313C4×D13C4×D418yes—
314C4×D13C4×D418yes—
315C24×C4—131no—
316C24×C4—132no—
317C22×C4⋊C4—131no—
318C22×C4⋊C4—132no—
319C22×C4⋊C4—132no—
320C22×C4⋊C4—131no—
321C22×C4⋊C4—132no—
322C22×C4⋊C4—131no—
323C22×C4⋊C4—131no—
324C22×C4⋊C4—131no—
325C22×C4⋊C4—132no—
326C22×C4⋊C4—268no—
327C22×C4⋊C4#26111yescharacteristic, complemented
328C22×C22⋊C4—131no—
329C22×C22⋊C4—131no—
330C22×C22⋊C4—132no—
331C22×C42—132no—
332C22×C42—134no—
333#380—138no—
334C4×C4⋊C4—268no—
335C4×C22⋊C4—138no—
336C4×C22⋊C4—268no—
337C2×#95—132no—
338C2×#95—132no—
339C2×#95—134no—
340C2×#95—134no—
341C2×#95—134no—
342C22×C13—22no—
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13—22no—
347C22×C13—22no—
348C22×C13C4×C4⋊C414yescomplemented
349C22×C13C22×C4211yescharacteristic
350C22×C13C22×C22⋊C411yescharacteristic
351C22×C13C2×#11711yescharacteristic
352C22×C13C2×C4×D411yescharacteristic
353C22×C13C2×C4×Q811yescharacteristic
354C22×C13#51811yescharacteristic
355C22×C13#51911yescharacteristic
356C2×D13—22no—
357C2×D13—22no—
358C2×D13—22no—
359C2×D13—22no—
360C2×D13—22no—
361C2×D13—22no—
362C2×D13—28no—
363C2×D13—28no—
364C2×D13—28no—
365C2×D13—28no—
366C2×D13C4×C4⋊C414yescomplemented
367C2×D13C22×C4⋊C411yescharacteristic
368C2×D13C2×#11711yescharacteristic
369C2×D13C2×C4×D412yes—
370C2×D13C2×C4×D412yes—
371C2×D13C2×C4×D411yescharacteristic
372C2×D13C2×C4×Q811yescharacteristic
373C2×D13#52012yes—
374C2×D13#52012yes—
375C2×D13D4212yes—
376C2×D13#54612yes—
377C2×D13#54712yes—
378C2×D13#54812yes—
379C2×D13D4×Q812yes—
380C2×D13#55212yes—
381C2×D13#55312yes—
382C2×D13#55412yes—
383#261—28no—
384#261—44no—
385#261—48no—
386C4×C13—24no—
387C4×C13—22no—
388C4×C13—42no—
389C4×C13C4×C22⋊C414yescomplemented
390Dic13—24no—
391Dic13—22no—
392Dic13—42no—
393Dic13C4×C22⋊C414yescomplemented
394C25—131no—
395C23×C4—131no—
396C23×C4—132no—
397C23×C4—131no—
398C23×C4—134no—
399C23×C4—134no—
400C23×C4—131no—
401C23×C4—132no—
402C23×C4—131no—
403C23×C4—131no—
404C23×C4—134no—
405C23×C4—132no—
406C23×C4—132no—
407C23×C4—132no—
408C23×C4—132no—
409C23×C4—132no—
410C23×C4—264no—
411C23×C4—264no—
412C23×C4—268no—
413C23×C4—264no—
414C23×C4—264no—
415C23×C4—524no—
416C23×C4C2×#26112yes—
417C23×C4C2×#26111yescharacteristic
418C2×C4⋊C4—24no—
419C2×C4⋊C4—132no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4—138no—
422C2×C4⋊C4—138no—
423C2×C4⋊C4—132no—
424C2×C4⋊C4—132no—
425C2×C4⋊C4—132no—
426C2×C4⋊C4—132no—
427C2×C4⋊C4—131no—
428C2×C4⋊C4—268no—
429C2×C4⋊C4—264no—
430C2×C4⋊C4—264no—
431C2×C4⋊C4—268no—
432C2×C4⋊C4—268no—
433C2×C4⋊C4—264no—
434C2×C4⋊C4—264no—
435C2×C4⋊C4—264no—
436C2×C4⋊C4—264no—
437C2×C4⋊C4C2×#26111yescharacteristic
438C2×C4⋊C4C2×#26112yes—
439C2×C4⋊C4C2×#26111yescharacteristic
440C2×C22⋊C4—134no—
441C2×C22⋊C4—134no—
442C2×C22⋊C4—134no—
443C2×C22⋊C4—134no—
444C2×C22⋊C4—138no—
445C2×C22⋊C4—264no—
446C2×C22⋊C4—262no—
447C2×C22⋊C4—262no—
448C2×C22⋊C4—264no—
449C2×C42—138no—
450C2×C42—264no—
451C2×C42—264no—
452C2×C42—268no—
453C2×C42—268no—
454C2×C42—524no—
455#95—138no—
456#95—138no—
457#95—268no—
458#95—268no—
459#95—524no—
460C2×C13—24no—
461C2×C13C2×C4×C22⋊C411yescharacteristic
462C2×C13C2×C4×C4⋊C411yescharacteristic
463C2×C13#227411yescharacteristic
464C2×C13D4×C22⋊C411yescharacteristic
465C2×C13Q8×C22⋊C411yescharacteristic
466C2×C13#234411yescharacteristic
467C2×C13#234511yescharacteristic
468D13—24no—
469D13D4×C4⋊C412yes—
470D13#235212yes—
471D13#236012yes—
472D13#236112yes—
473C24—131no—
474C24—132no—
475C24—132no—
476C24—132no—
477C24—132no—
478C24—132no—
479C24—132no—
480C24—131no—
481C24—262no—
482C24—262no—
483C24—262no—
484C24—262no—
485C24C22×#26111yescharacteristic
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—42no—
491C22×C4—131no—
492C22×C4—132no—
493C22×C4—132no—
494C22×C4—134no—
495C22×C4—134no—
496C22×C4—134no—
497C22×C4—134no—
498C22×C4—134no—
499C22×C4—134no—
500C22×C4—131no—
501C22×C4—132no—
502C22×C4—132no—
503C22×C4—132no—
504C22×C4—134no—
505C22×C4—134no—
506C22×C4—138no—
507C22×C4—134no—
508C22×C4—138no—
509C22×C4—132no—
510C22×C4—262no—
511C22×C4—262no—
512C22×C4—2616no—
513C22×C4—2616no—
514C22×C4—264no—
515C22×C4—262no—
516C22×C4—264no—
517C22×C4—262no—
518C22×C4—262no—
519C22×C4—262no—
520C22×C4—262no—
521C22×C4—264no—
522C22×C4—264no—
523C22×C4—264no—
524C22×C4—264no—
525C22×C4—262no—
526C22×C4—262no—
527C22×C4—262no—
528C22×C4—264no—
529C22×C4—262no—
530C22×C4—262no—
531C22×C4—262no—
532C22×C4—262no—
533C22×C4—262no—
534C22×C4—262no—
535C22×C4—262no—
536C22×C4—264no—
537C22×C4—264no—
538C22×C4—262no—
539C22×C4—264no—
540C22×C4—262no—
541C22×C4—262no—
542C22×C4—264no—
543C22×C4—262no—
544C22×C4—264no—
545C22×C4—264no—
546C22×C4—262no—
547C22×C4—264no—
548C22×C4—264no—
549C22×C4—522no—
550C22×C4—522no—
551C22×C4—5216no—
552C22×C4—5216no—
553C22×C4—522no—
554C22×C4C4×#26114yescomplemented
555C22×C4C22×#26112yes—
556C22×C4C22×#26111yescharacteristic
557C22×C4C22×#26112yes—
558C22×C4C22×#26111yescharacteristic
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—138no—
562C4⋊C4—134no—
563C4⋊C4—264no—
564C4⋊C4—264no—
565C4⋊C4—264no—
566C4⋊C4—2616no—
567C4⋊C4—264no—
568C4⋊C4—262no—
569C4⋊C4C22⋊#26114yesdirect product factor
570C22⋊C4—1316no—
571C22⋊C4—2616no—
572C22⋊C4—268no—
573C42—2616no—
574C42—5216no—
575C13C22⋊C4×C4⋊C411yescharacteristic, complemented, Sylow
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—131no—
581C23—131no—
582C23—132no—
583C23—131no—
584C23—131no—
585C23—132no—
586C23—131no—
587C23—131no—
588C23—132no—
589C23—132no—
590C23—134no—
591C23—134no—
592C23—134no—
593C23—134no—
594C23—132no—
595C23—132no—
596C23—132no—
597C23—264no—
598C23—264no—
599C23—264no—
600C23—264no—
601C23—264no—
602C23—264no—
603C23—264no—
604C23—264no—
605C23—264no—
606C23—264no—
607C23—264no—
608C23—264no—
609C23—261no—
610C23—261no—
611C23—261no—
612C23—261no—
613C23C2×C4×#26112yes—
614C23D4×#26112yes—
615C23Q8×#26112yes—
616C23C23×#26111yescharacteristic
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—28no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—48no—
626C2×C4—132no—
627C2×C4—132no—
628C2×C4—132no—
629C2×C4—138no—
630C2×C4—138no—
631C2×C4—138no—
632C2×C4—132no—
633C2×C4—134no—
634C2×C4—268no—
635C2×C4—268no—
636C2×C4—264no—
637C2×C4—264no—
638C2×C4—268no—
639C2×C4—268no—
640C2×C4—264no—
641C2×C4—264no—
642C2×C4—264no—
643C2×C4—264no—
644C2×C4—264no—
645C2×C4—264no—
646C2×C4—261no—
647C2×C4—262no—
648C2×C4—262no—
649C2×C4—261no—
650C2×C4—268no—
651C2×C4—264no—
652C2×C4—264no—
653C2×C4—268no—
654C2×C4—268no—
655C2×C4—264no—
656C2×C4—268no—
657C2×C4—262no—
658C2×C4—262no—
659C2×C4—262no—
660C2×C4—528no—
661C2×C4—528no—
662C2×C4—524no—
663C2×C4—524no—
664C2×C4—528no—
665C2×C4—524no—
666C2×C4—522no—
667C2×C4—522no—
668C2×C4—524no—
669C2×C4—524no—
670C2×C4—522no—
671C2×C4—522no—
672C2×C4—524no—
673C2×C4C2×C4×#26112yes—
674C2×C4C2×C4×#26112yes—
675C2×C4#8823712yes—
676C2×C4C2×C22⋊#26114yes—
677C2×C4C2×C22⋊#26112yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—132no—
685C22—132no—
686C22—131no—
687C22—131no—
688C22—131no—
689C22—131no—
690C22—132no—
691C22—132no—
692C22—132no—
693C22—132no—
694C22—132no—
695C22—132no—
696C22—132no—
697C22—132no—
698C22—132no—
699C22—132no—
700C22—134no—
701C22—268no—
702C22—268no—
703C22—268no—
704C22—268no—
705C22—262no—
706C22—262no—
707C22—262no—
708C22—262no—
709C22—262no—
710C22—262no—
711C22C4⋊C4×#26114yescomplemented
712C22C22×C4×#26111yescharacteristic
713C22C2×#8823711yescharacteristic
714C22C2×D4×#26111yescharacteristic
715C22#1171962311yescharacteristic
716C22C2×Q8×#26111yescharacteristic
717C22#1171962711yescharacteristic
718C22C22×C22⋊#26111yescharacteristic
719C4—22no—
720C4—24no—
721C4—42no—
722C4—134no—
723C4—268no—
724C4—262no—
725C4—264no—
726C4—528no—
727C4—524no—
728C4—522no—
729C4C4×C22⋊#26114yescomplemented
730C2—24no—
731C2—132no—
732C2—132no—
733C2—132no—
734C2—132no—
735C2—264no—
736C2C2×C4×C22⋊#26111yescharacteristic
737C2C2×C4⋊C4×#26111yescharacteristic
738C2#1313127411yescharacteristic
739C2D4×C22⋊#26111yescharacteristic
740C2Q8×C22⋊#26111yescharacteristic
741C2#1313134411yescharacteristic
742C2#1313134511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC22×C13×C4⋊C4C4
socleC23×C13C23×C4
prime radicalC24×D13C23
cosocleC23×D13C24
hypercenterC22×C4⋊C4#261
hypocenterC13C22⋊C4×C4⋊C4
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×#261C2semidirect
5. #13130015C2semidirect
6. #13130013C2semidirect
17. C22×C13×C4⋊C4C4semidirect
18. C22×C4⋊Dic13C4semidirect
19. C22×#6101C4semidirect
21. C2×C4⋊C4×D13C4semidirect
22. C2×C4⋊C4×D13C4semidirect
23. C2×C4⋊C4×D13C4semidirect
27. #11719136C4semidirect
29. C4×C22⋊#261C4semidirect
71. C2×C4⋊#261C2×C4semidirect
77. C2×C4×#261C2×C4semidirect
100. (C2×#261)⋊C4C2×C4semidirect
101. (C2×#261)⋊C4C2×C4semidirect
142. C22×C4×C13C42semidirect
152. C22×Dic13C42semidirect
180. C2×C4×D13C42semidirect
181. C2×C4×D13C42semidirect
191. C22⋊#261C4⋊C4direct (N × H)
197. C13×C4⋊C4C22⋊C4semidirect
200. C4⋊Dic13C22⋊C4semidirect
204. #6101C22⋊C4semidirect
274. C2×#261C2×C4⋊C4semidirect
327. C22×C4⋊C4#261semidirect
348. C22×C13C4×C4⋊C4semidirect
366. C2×D13C4×C4⋊C4semidirect
389. C4×C13C4×C22⋊C4semidirect
393. Dic13C4×C22⋊C4semidirect
554. C22×C4C4×#261semidirect
569. C4⋊C4C22⋊#261direct (N × H)
575. C13C22⋊C4×C4⋊C4semidirect
711. C22C4⋊C4×#261semidirect
729. C4C4×C22⋊#261semidirect

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
#131300152
#131300132
#131300102
C22×C4⋊C4×D132
C22⋊C4×C4⋊C413