Finite Group Databasebeta

← C2×#13123772 #16727287

Subgroups — C2×#13123772 #16727287

Order 3328.

1894 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719283C211yesmaximal, characteristic
2#13123772C2116yesmaximal, direct product factor
3C2×#11718685C211yesmaximal, characteristic, complemented
4C2×#11718340C211yesmaximal, characteristic, complemented
5C2×#11718489C211yesmaximal, characteristic, complemented
6C2×#11718489C211yesmaximal, characteristic, complemented
7C2×#11718362C211yesmaximal, characteristic, complemented
8C2×#11718362C211yesmaximal, characteristic, complemented
9C2×#11718492C211yesmaximal, characteristic, complemented
10C2×#11718500C211yesmaximal, characteristic
11C2×#11718500C211yesmaximal, characteristic
12C2×#11718498C211yesmaximal, characteristic
13C2×#11718369C211yesmaximal, characteristic
14C2×#11718350C211yesmaximal, characteristic
15C2×D13×#97C211yesmaximal, characteristic
16C2×C13×#446C211yesmaximal, characteristic, complemented
17C2×C4×Q8×C13C2211yescharacteristic
18C2×#88200C411yescharacteristic
19C2×#88198C411yescharacteristic
20C22×#6094C2211yescharacteristic
21C22×#6094C2211yescharacteristic
22C22×C8×D13C2211yescharacteristic
23C22×C8×D13C2211yescharacteristic
24#11719283C418yes—
25#11719283C2218yes—
26C2×#88151C411yescharacteristic
27C2×#88150C411yescharacteristic
28C2×#88150C411yescharacteristic
29C2×#88143C411yescharacteristic
30C2×#88143C411yescharacteristic
31C2×#88142C411yescharacteristic
32C2×#88126C2211yescharacteristic
33C2×#88126C2211yescharacteristic
34C2×C42×D13C2211yescharacteristic
35C2×C4×Dic26C2211yescharacteristic
36C2×C4×Dic26C2211yescharacteristic
37C2×C4×Dic26C2211yescharacteristic
38C13×#446C2218yescomplemented
39C2×C13×C4⋊C8C2211yescharacteristic
40C2×C13×C4⋊C8C2211yescharacteristic
41C2×C13×C4⋊C8C2211yescharacteristic
42C2×C13×#97C2211yescharacteristic
43C2×C13×#97C2211yescharacteristic
44C2×C4×C8×C13C2211yescharacteristic
45C2×#88055C2211yescharacteristic
46C2×#88055C2211yescharacteristic
47C2×#88055C2211yescharacteristic
48C2×#88055C2211yescharacteristic
49C2×#88054C2211yescharacteristic
50C2×#88054C2211yescharacteristic
51C2×#88054C2211yescharacteristic
52C2×#88054C2211yescharacteristic
53C2×#88054C2211yescharacteristic
54C2×#88054C2211yescharacteristic
55C2×C8×Dic13C2211yescharacteristic
56C2×C8×Dic13C2211yescharacteristic
57#11718685C2218yescomplemented
58C2×C4⋊#1055C2211yescharacteristic
59C2×C4⋊#1055C2211yescharacteristic
60C2×C4⋊#1055C2211yescharacteristic
61C2×#88043C2211yescharacteristic
62C2×#88043C2211yescharacteristic
63C2×C4×#1055C2211yescharacteristic
64#11718500C2218yes—
65#11718500C2218yes—
66#11718498C2218yes—
67#11718492C2218yescomplemented
68#11718489C2218yescomplemented
69#11718489C2218yescomplemented
70#11718369C2218yes—
71D13×#97C2218yes—
72#11718362C2218yescomplemented
73#11718362C2218yescomplemented
74#11718350C2218yes—
75#11718340C2218yescomplemented
76C22×Q8×C13C2×C411yescharacteristic
77C22×C4×D13C2×C411yescharacteristic
78C22×C4×D13C2×C411yescharacteristic
79C22×C4×D13C2311yescharacteristic
80C22×Dic26C2×C411yescharacteristic
81C22×Dic26C2×C411yescharacteristic
82C22×Dic26C2×C411yescharacteristic
83C22×C8×C13C2311yescharacteristic
84C22×C8×C13C2311yescharacteristic
85C22×C8×C13C2311yescharacteristic
86C22×C8×C13C2311yescharacteristic
87C4×Q8×C13C2×C414yes—
88C4×Q8×C13C2314yes—
89C2×C13×C4⋊C4C2×C411yescharacteristic
90C2×C13×C4⋊C4C2×C411yescharacteristic
91C2×C13×C4⋊C4C2×C411yescharacteristic
92C2×C42×C13C2311yescharacteristic
93C2×C42×C13C2311yescharacteristic
94C2×C42×C13C2311yescharacteristic
95#88200C2×C418yes—
96#88198C2×C418yes—
97C2×#6103C2×C411yescharacteristic
98C2×#6103C2×C411yescharacteristic
99C2×#6103C2×C411yescharacteristic
100C2×#6103C2×C411yescharacteristic
101C2×C4⋊Dic13C2×C411yescharacteristic
102C2×C4⋊Dic13C2×C411yescharacteristic
103C2×C4⋊Dic13C2×C411yescharacteristic
104C2×#6101C2×C411yescharacteristic
105C2×#6101C2×C411yescharacteristic
106C2×#6101C2×C411yescharacteristic
107C2×#6101C2×C411yescharacteristic
108C2×#6101C2×C411yescharacteristic
109C2×#6101C2×C411yescharacteristic
110C2×#6101C2×C411yescharacteristic
111C2×#6101C2×C411yescharacteristic
112C2×#6101C2×C411yescharacteristic
113C2×#6101C2×C411yescharacteristic
114C2×C4×Dic13C2×C411yescharacteristic
115C2×C4×Dic13C2×C411yescharacteristic
116C2×C4×Dic13C2311yescharacteristic
117C2×C4×Dic13C2311yescharacteristic
118C2×C4×Dic13C2311yescharacteristic
119C22×#1055C2311yescharacteristic
120C22×#1055C2311yescharacteristic
121C22×#1055C2311yescharacteristic
122C22×#1055C2311yescharacteristic
123C2×#6094—24no—
124C2×#6094—24no—
125C2×#6094C2314yes—
126C2×#6094C2314yes—
127C2×C8×D13—24no—
128C2×C8×D13Q818yescomplemented
129C2×C8×D13C2314yes—
130C2×C8×D13C2314yes—
131#88151C2×C418yes—
132#88150C2×C418yes—
133#88150C2×C418yes—
134#88143C2×C418yes—
135#88143C2×C418yes—
136#88142C2×C418yes—
137#88126C2×C414yes—
138#88126C2×C414yes—
139#88126C2314yes—
140#88126C2314yes—
141C42×D13C2×C414yes—
142C42×D13C2314yes—
143C4×Dic26C2×C414yes—
144C4×Dic26C2×C414yes—
145C4×Dic26C2×C414yes—
146C4×Dic26C2314yes—
147C4×Dic26C2314yes—
148C4×Dic26C2314yes—
149C13×C4⋊C8C2314yes—
150C13×C4⋊C8C2314yes—
151C13×C4⋊C8C2314yes—
152C13×#97C2314yes—
153C13×#97C2314yes—
154C4×C8×C13C2314yes—
155#88055C2314yes—
156#88055C2314yes—
157#88055C2314yes—
158#88055C2314yes—
159#88054C2314yes—
160#88054C2314yes—
161#88054C2314yes—
162#88054C2314yes—
163#88054C2314yes—
164#88054C2314yes—
165C8×Dic13C2314yes—
166C8×Dic13C2314yes—
167C4⋊#1055C2314yes—
168C4⋊#1055C2314yes—
169C4⋊#1055C2314yes—
170#88043C2314yes—
171#88043C2314yes—
172C4×#1055C2314yes—
173C2×#2961—131nomaximal, Sylow
174C23×D13C22×C411yescharacteristic
175C2×Q8×C13—42no—
176C2×Q8×C13C22×C414yes—
177C22×C4×C13C22×C411yescharacteristic
178C22×C4×C13C22×C411yescharacteristic
179C22×C4×C13C22×C411yescharacteristic
180C22×C4×C13C22×C411yescharacteristic
181C22×C4×C13C22×C411yescharacteristic
182C22×C4×C13C22×C411yescharacteristic
183C22×C4×C13C2411yescharacteristic
184C22×Dic13C22×C411yescharacteristic
185C22×Dic13C22×C411yescharacteristic
186C22×Dic13C22×C411yescharacteristic
187C22×Dic13C22×C411yescharacteristic
188C22×Dic13C22×C411yescharacteristic
189C22×Dic13C22×C411yescharacteristic
190C22×Dic13C22×C411yescharacteristic
191C2×C4×D13—42no—
192C2×C4×D13—42no—
193C2×C4×D13C22×C414yes—
194C2×C4×D13C22×C414yes—
195C2×C4×D13C22×C412yes—
196C2×C4×D13C2×Q814yes—
197C2×C4×D13#4114yes—
198C2×C4×D13C2412yes—
199C2×Dic26—42no—
200C2×Dic26—42no—
201C2×Dic26—42no—
202C2×Dic26C22×C414yes—
203C2×Dic26C22×C414yes—
204C2×Dic26C22×C414yes—
205C2×C8×C13—22no—
206C2×C8×C13—22no—
207C2×C8×C13—22no—
208C2×C8×C13C2×Q814yes—
209C2×C8×C13C2412yes—
210C2×C8×C13C2412yes—
211C2×C8×C13C2412yes—
212C2×C8×C13C2412yes—
213C13×C4⋊C4C22×C414yes—
214C13×C4⋊C4C22×C414yes—
215C13×C4⋊C4C22×C414yes—
216C42×C13C22×C412yes—
217C42×C13C22×C412yes—
218C42×C13C22×C412yes—
219C42×C13C2412yes—
220C42×C13C2412yes—
221C42×C13C2412yes—
222#6103C22×C414yes—
223#6103C22×C414yes—
224#6103C22×C414yes—
225#6103C22×C414yes—
226C4⋊Dic13C22×C414yes—
227C4⋊Dic13C22×C414yes—
228C4⋊Dic13C22×C414yes—
229#6101C22×C414yes—
230#6101C22×C414yes—
231#6101C22×C414yes—
232#6101C22×C414yes—
233#6101C22×C414yes—
234#6101C22×C414yes—
235#6101C22×C414yes—
236#6101C22×C414yes—
237#6101C22×C414yes—
238#6101C22×C414yes—
239C4×Dic13C22×C412yes—
240C4×Dic13C22×C412yes—
241C4×Dic13C22×C412yes—
242C4×Dic13C22×C414yes—
243C4×Dic13C22×C414yes—
244C4×Dic13C2412yes—
245C4×Dic13C2412yes—
246C4×Dic13C2412yes—
247C2×#1055—22no—
248C2×#1055—22no—
249C2×#1055—22no—
250C2×#1055C2×Q814yes—
251C2×#1055C2412yes—
252C2×#1055C2412yes—
253C2×#1055C2412yes—
254C2×#1055C2412yes—
255#6094—28no—
256#6094—28no—
257C8×D13—28no—
258C8×D13C2×Q8116yescomplemented
259C2×#533—131no—
260#2961—1316no—
261C2×#446—131no—
262C2×#446—131no—
263C2×#446—131no—
264C2×#446—131no—
265C2×#446—131no—
266C2×#446—131no—
267C2×#446—131no—
268C2×#446D1311yescharacteristic, complemented
269C2×#424—131no—
270C2×#424—131no—
271C2×#423—131no—
272C2×#405—131no—
273C2×#405—131no—
274C22×#97—131no—
275C23×C13C23×C411yescharacteristic
276C22×D13—22no—
277C22×D13—22no—
278C22×D13C4×Q814yes—
279C22×D13C23×C412yes—
280Q8×C13—44no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13C23×C412yes—
288C2×C4×C13C23×C412yes—
289C2×C4×C13C23×C412yes—
290C2×C4×C13C23×C412yes—
291C2×C4×C13C23×C412yes—
292C2×C4×C13C23×C412yes—
293C2×C4×C13C23×C411yescharacteristic
294C2×C4×C13C22×Q812yes—
295C2×C4×C13C2×#4112yes—
296C2×C4×C13C2511yescharacteristic
297C2×Dic13—22no—
298C2×Dic13—22no—
299C2×Dic13—22no—
300C2×Dic13—22no—
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13C4×Q814yes—
304C2×Dic13C23×C412yes—
305C2×Dic13C23×C412yes—
306C2×Dic13C23×C412yes—
307C2×Dic13C23×C412yes—
308C2×Dic13C23×C412yes—
309C2×Dic13C23×C412yes—
310C2×Dic13C23×C412yes—
311C4×D13—44no—
312C4×D13—44no—
313C4×D13C4×Q818yes—
314C4×D13C22×Q814yes—
315C4×D13C2×#4114yes—
316Dic26—44no—
317Dic26—44no—
318Dic26—44no—
319C8×C13—22no—
320C8×C13—22no—
321C8×C13—22no—
322C8×C13C22×Q814yes—
323#1055—22no—
324#1055—22no—
325#1055—22no—
326#1055C22×Q814yes—
327C22×M16—131no—
328C22×M16—131no—
329C23×C8—131no—
330C23×C8—131no—
331#533—138no—
332#533—138no—
333C2×C4⋊Q8—131no—
334C2×C4⋊Q8—131no—
335C2×#125—131no—
336C2×#125—131no—
337C2×C22⋊Q8—131no—
338C2×C22⋊Q8—131no—
339C2×C22⋊Q8—131no—
340C2×C22⋊Q8—131no—
341C2×C4×Q8—131no—
342C2×C4×Q8—131no—
343C2×C4×Q8—131no—
344C2×C4×Q8C2×D1311yescharacteristic
345C2×#117—131no—
346C2×#117—131no—
347C22×C42—131no—
348#446—138no—
349#446—138no—
350#446—138no—
351#446—138no—
352#446—138no—
353#446—138no—
354#446—138no—
355#446C2×D1318yescomplemented
356#424—138no—
357#424—138no—
358#423—138no—
359C2×C4⋊C8—131no—
360C2×C4⋊C8—131no—
361C2×C4⋊C8—131no—
362C2×C4⋊C8—131no—
363C2×C4⋊C8—131no—
364C2×C4⋊C8—131no—
365C2×C4⋊C8—131no—
366C2×C4⋊C8—131no—
367C2×C4⋊C8—131no—
368C2×C4⋊C8C2×D1311yescharacteristic
369C2×C4⋊C8C2×D1311yescharacteristic
370C2×C4⋊C8C2×D1311yescharacteristic
371#405—138no—
372#405—138no—
373C2×#97—131no—
374C2×#97—131no—
375C2×#97—131no—
376C2×#97—131no—
377C2×#97—131no—
378C2×#97—131no—
379C2×#97—138no—
380C2×#97C2×D1311yescharacteristic
381C2×#97C2×D1311yescharacteristic
382C2×C4×C8—131no—
383C2×C4×C8—131no—
384C2×C4×C8—131no—
385C2×C4×C8C2×D1311yescharacteristic
386C22×C13C2×C4×Q812yes—
387C22×C13#56812yes—
388C22×C13#56812yes—
389C22×C13C24×C411yescharacteristic
390C2×D13—28no—
391C2×D13—22no—
392C2×D13—22no—
393C2×D13C2×C4×Q814yes—
394C4×C13—22no—
395C4×C13—22no—
396C4×C13—22no—
397C4×C13—22no—
398C4×C13—22no—
399C4×C13—22no—
400C4×C13C2×C4×Q812yes—
401C4×C13C23×Q811yescharacteristic
402C4×C13C22×#4111yescharacteristic
403Dic13—22no—
404Dic13—22no—
405Dic13—22no—
406Dic13—22no—
407Dic13—22no—
408Dic13—22no—
409Dic13C2×C4×Q814yes—
410C22×Q8—131no—
411C22×Q8—131no—
412C22×Q8—131no—
413C22×Q8C4×D1311yescharacteristic
414C23×C4—131no—
415C23×C4—131no—
416C23×C4—131no—
417C2×M16—134no—
418C2×M16—134no—
419C2×M16—264no—
420C2×M16—264no—
421C22×C8—131no—
422C22×C8—138no—
423C22×C8—134no—
424C22×C8—131no—
425C22×C8—131no—
426C22×C8—131no—
427C22×C8—134no—
428C22×C8—264no—
429C22×C8C22×D1311yescharacteristic
430C22×C8C22×D1311yescharacteristic
431C22×C8C22×D1311yescharacteristic
432C22×C8C22×D1311yescharacteristic
433C4⋊Q8—138no—
434C4⋊Q8—138no—
435#125—138no—
436#125—138no—
437C22⋊Q8—138no—
438C22⋊Q8—138no—
439C22⋊Q8—138no—
440C22⋊Q8—138no—
441C4×Q8—134no—
442C4×Q8—134no—
443C4×Q8—134no—
444C4×Q8—134no—
445C4×Q8—134no—
446C4×Q8—134no—
447C4×Q8C4×D1314yes—
448C4×Q8C22×D1314yes—
449#117—134no—
450#117—134no—
451#117—134no—
452#117—134no—
453C2×C4⋊C4—131no—
454C2×C4⋊C4—131no—
455C2×C4⋊C4—131no—
456C2×C4⋊C4—131no—
457C2×C4⋊C4—131no—
458C2×C4⋊C4—131no—
459C2×C4⋊C4—131no—
460C2×C4⋊C4—131no—
461C2×C4⋊C4—131no—
462C2×C4⋊C4—131no—
463C2×C4⋊C4—131no—
464C2×C4⋊C4—131no—
465C2×C4⋊C4—131no—
466C2×C4⋊C4C4×D1311yescharacteristic
467C2×C4⋊C4C4×D1311yescharacteristic
468C2×C4⋊C4C4×D1311yescharacteristic
469C2×C22⋊C4—131no—
470C2×C22⋊C4—131no—
471C2×C22⋊C4—131no—
472C2×C22⋊C4—131no—
473C2×C42—131no—
474C2×C42—131no—
475C2×C42—131no—
476C2×C42—131no—
477C2×C42—131no—
478C2×C42—134no—
479C2×C42—134no—
480C2×C42C22×D1311yescharacteristic
481C2×C42C22×D1311yescharacteristic
482C2×C42C22×D1311yescharacteristic
483C4⋊C8—134no—
484C4⋊C8—134no—
485C4⋊C8—134no—
486C4⋊C8—134no—
487C4⋊C8—134no—
488C4⋊C8—134no—
489C4⋊C8—134no—
490C4⋊C8—134no—
491C4⋊C8—134no—
492C4⋊C8C22×D1314yes—
493C4⋊C8C22×D1314yes—
494C4⋊C8C22×D1314yes—
495#97—134no—
496#97—134no—
497#97—134no—
498#97—134no—
499#97—134no—
500#97—134no—
501#97C22×D1314yes—
502#97C22×D1314yes—
503C4×C8—134no—
504C4×C8—134no—
505C4×C8—134no—
506C4×C8C22×D1314yes—
507C2×C13#296114yescomplemented
508C2×C13C22×C4×Q811yescharacteristic
509C2×C13C2×#56811yescharacteristic
510C2×C13C2×#56811yescharacteristic
511D13—24no—
512C24—131no—
513C2×Q8—42no—
514C2×Q8—134no—
515C2×Q8—134no—
516C2×Q8—134no—
517C2×Q8—522no—
518C2×Q8—522no—
519C2×Q8—522no—
520C2×Q8C2×C4×D1314yes—
521C22×C4—131no—
522C22×C4—132no—
523C22×C4—134no—
524C22×C4—134no—
525C22×C4—132no—
526C22×C4—131no—
527C22×C4—131no—
528C22×C4—131no—
529C22×C4—131no—
530C22×C4—131no—
531C22×C4—131no—
532C22×C4—134no—
533C22×C4—134no—
534C22×C4—522no—
535C22×C4—522no—
536C22×C4C2×C4×D1311yescharacteristic
537C22×C4C2×C4×D1311yescharacteristic
538C22×C4C2×C4×D1311yescharacteristic
539C22×C4C2×C4×D1311yescharacteristic
540C22×C4C2×C4×D1311yescharacteristic
541C22×C4C2×C4×D1311yescharacteristic
542C22×C4C23×D1311yescharacteristic
543M16—268no—
544M16—268no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—134no—
549C2×C8—132no—
550C2×C8—1316no—
551C2×C8—132no—
552C2×C8—132no—
553C2×C8—132no—
554C2×C8—268no—
555C2×C8—262no—
556C2×C8—262no—
557C2×C8—262no—
558C2×C8Q8×D1314yes—
559C2×C8C23×D1312yes—
560C2×C8C23×D1312yes—
561C2×C8C23×D1312yes—
562C2×C8C23×D1312yes—
563C4⋊C4—134no—
564C4⋊C4—134no—
565C4⋊C4—134no—
566C4⋊C4—134no—
567C4⋊C4—134no—
568C4⋊C4—134no—
569C4⋊C4—134no—
570C4⋊C4—134no—
571C4⋊C4—134no—
572C4⋊C4—134no—
573C4⋊C4—134no—
574C4⋊C4—134no—
575C4⋊C4—134no—
576C4⋊C4C2×C4×D1314yes—
577C4⋊C4C2×C4×D1314yes—
578C4⋊C4C2×C4×D1314yes—
579C22⋊C4—134no—
580C22⋊C4—134no—
581C22⋊C4—134no—
582C22⋊C4—134no—
583C42—132no—
584C42—134no—
585C42—134no—
586C42—132no—
587C42—132no—
588C42—132no—
589C42—132no—
590C42—132no—
591C42C2×C4×D1312yes—
592C42C2×C4×D1312yes—
593C42C2×C4×D1312yes—
594C42C23×D1312yes—
595C42C23×D1312yes—
596C42C23×D1312yes—
597C13C2×#296111yescharacteristic, complemented, Sylow
598C23—134no—
599C23—132no—
600C23—262no—
601C23—262no—
602C23C22×C4×D1311yescharacteristic
603Q8—44no—
604Q8—524no—
605Q8—524no—
606Q8—524no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—134no—
614C2×C4—132no—
615C2×C4—138no—
616C2×C4—134no—
617C2×C4—134no—
618C2×C4—132no—
619C2×C4—132no—
620C2×C4—132no—
621C2×C4—132no—
622C2×C4—132no—
623C2×C4—132no—
624C2×C4—262no—
625C2×C4—262no—
626C2×C4—262no—
627C2×C4—262no—
628C2×C4—262no—
629C2×C4—262no—
630C2×C4—524no—
631C2×C4—524no—
632C2×C4C22×C4×D1312yes—
633C2×C4C22×C4×D1312yes—
634C2×C4C22×C4×D1312yes—
635C2×C4C22×C4×D1312yes—
636C2×C4C22×C4×D1312yes—
637C2×C4C22×C4×D1312yes—
638C2×C4C22×C4×D1311yescharacteristic
639C2×C4C2×Q8×D1312yes—
640C2×C4#41×D1312yes—
641C2×C4C24×D1311yescharacteristic
642C8—22no—
643C8—22no—
644C8—22no—
645C8—134no—
646C8—262no—
647C8—262no—
648C8—262no—
649C8C2×Q8×D1314yes—
650C22—134no—
651C22—262no—
652C22—262no—
653C22—268no—
654C22C4×Q8×D1312yes—
655C22#1171945012yes—
656C22#1171945512yes—
657C22C23×C4×D1311yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—134no—
665C4—262no—
666C4—262no—
667C4—262no—
668C4—262no—
669C4—262no—
670C4—262no—
671C4C4×Q8×D1312yes—
672C4C22×Q8×D1311yescharacteristic
673C4C2×#41×D1311yescharacteristic
674C2—264no—
675C2#1312377214yesdirect product factor
676C2C2×C4×Q8×D1311yescharacteristic
677C2C2×#1171945511yescharacteristic
678C2C2×#1171945011yescharacteristic
subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C13×#446C2
socleC23×C13C23×C4
prime radicalC23×D13C22×C4
cosocleC2×C4×C13C25
hypercenterC2×#446D13
hypocenterC13C2×#2961
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #13123772C2direct (N × H)
3. C2×#11718685C2semidirect
4. C2×#11718340C2semidirect
5. C2×#11718489C2semidirect
6. C2×#11718489C2semidirect
7. C2×#11718362C2semidirect
8. C2×#11718362C2semidirect
9. C2×#11718492C2semidirect
16. C2×C13×#446C2semidirect
38. C13×#446C22semidirect
57. #11718685C22semidirect
67. #11718492C22semidirect
68. #11718489C22semidirect
69. #11718489C22semidirect
72. #11718362C22semidirect
73. #11718362C22semidirect
75. #11718340C22semidirect
128. C2×C8×D13Q8semidirect
258. C8×D13C2×Q8semidirect
268. C2×#446D13semidirect
355. #446C2×D13semidirect
507. C2×C13#2961semidirect
597. C13C2×#2961semidirect
675. C2#13123772direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192832
#131237722
C2×#117186852
C2×#117183402
C2×#117184892
C2×#117183622
C2×#117184922
C2×#117185002
C2×#117184982
C2×#117183692
C2×#117183502
C2×D13×#972
C2×C13×#4462
C2×#296113