Finite Group Databasebeta

← #16731331

Subgroups — #16731331

Order 3328.

2138 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic26C211yesmaximal, characteristic, complemented
2#13125003C214yesmaximal, complemented
3#13124962C212yesmaximal, complemented
4#13124954C212yesmaximal, complemented
5#13124912C214yesmaximal, complemented
6#13124871C212yesmaximal, complemented
7#13124863C212yesmaximal, complemented
8#13124756C212yesmaximal, complemented
9#13124637C212yesmaximal, complemented
10#13124304C212yesmaximal, complemented
11#13124069C212yesmaximal, complemented
12C4×#88205C214yesmaximal, complemented
13#13123469C211yesmaximal, characteristic, complemented
14C13×#3444C211yesmaximal, characteristic
15C23×Dic26C2211yescharacteristic
16C13×#533C2211yescharacteristic
17C13×#533C2211yescharacteristic
18C13×#533C2211yescharacteristic
19C13×#532C2211yescharacteristic
20C13×#532C2211yescharacteristic
21C13×#532C2211yescharacteristic
22C13×#529—21no—
23C13×#529—21no—
24C13×#529—21no—
25C13×#529—21no—
26C13×#529C2212yes—
27C13×#529C2212yes—
28C13×#525—21no—
29C13×#525—21no—
30C13×#525C2212yes—
31C4×C13×#41—21no—
32C4×C13×#41—21no—
33C4×C13×#41C2212yes—
34C22×C42×C13C2211yescharacteristic
35C2×#88205C2214yes—
36C22×C4⋊Dic13C2211yescharacteristic
37C22×#6101—21no—
38C22×C4×Dic13—21no—
39C2×C4×Dic26—21no—
40C2×C4×Dic26—21no—
41C2×C4×Dic26—21no—
42C2×C4×Dic26—21no—
43C2×C4×Dic26—21no—
44C2×C4×Dic26—21no—
45C2×C4×Dic26C2212yes—
46C2×C4×Dic26C2212yes—
47C2×C4×Dic26C2212yes—
48C2×C4×Dic26C2212yes—
49C2×C4×Dic26C2212yes—
50C2×C4×Dic26C2212yes—
51#11718893C2214yes—
52#11718868C2212yes—
53#11718755C2214yescomplemented
54#11718752C2214yescomplemented
55#11718751C2214yescomplemented
56#11718736C2214yescomplemented
57#11718724C2218yescomplemented
58#11718715C2218yescomplemented
59#11718711C2214yes—
60#11718711C2214yes—
61#11718705C2214yes—
62#11718704C2214yes—
63#11718701C2214yes—
64#11718701C2214yes—
65#11718695C2214yes—
66#11718694C2214yes—
67#11718691C2218yescomplemented
68C4×#6107C2218yescomplemented
69#11718679C2218yescomplemented
70C4×#6105C2218yescomplemented
71#11718665C2214yes—
72#11718656C2214yes—
73#11718587C2212yes—
74#11718587C2212yes—
75#11718586C2212yes—
76#11718586C2212yes—
77#11718585C2212yes—
78C4×#6099C2212yes—
79C2×C13×#41—21no—
80C2×C13×#41—21no—
81C2×C13×#41C2312yes—
82C23×C4×C13D411yescharacteristic
83C23×C4×C13D411yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×Dic13—21no—
86C23×Dic13—21no—
87C22×Dic26—21no—
88C22×Dic26—21no—
89C22×Dic26—21no—
90C22×Dic26—28no—
91C22×Dic26C2312yes—
92C22×Dic26C2312yes—
93C22×Dic26C2312yes—
94C13×C4⋊Q8C2311yescharacteristic
95C13×C4⋊Q8C2311yescharacteristic
96C13×C4⋊Q8C2311yescharacteristic
97C13×#127C2311yescharacteristic
98C13×#126—22no—
99C13×#126—22no—
100C13×#125—21no—
101C13×#125—21no—
102C13×#125C2312yes—
103C13×#124—21no—
104C13×#124—21no—
105C13×#124C2312yes—
106C13×#123—22no—
107C13×#123—22no—
108C13×#123—22no—
109C13×C22⋊Q8—21no—
110C13×C22⋊Q8—21no—
111C13×C22⋊Q8—21no—
112C13×C22⋊Q8—21no—
113C13×C22⋊Q8C2312yes—
114C13×C22⋊Q8C2312yes—
115C13×#121—21no—
116C13×#121—21no—
117C13×#121—21no—
118C13×#121—21no—
119C13×#121C2312yes—
120C13×#121C2312yes—
121C13×#120—22no—
122C4×Q8×C13—21no—
123C4×Q8×C13—21no—
124C4×Q8×C13—21no—
125C4×Q8×C13—21no—
126C4×Q8×C13C2312yes—
127C4×Q8×C13C2312yes—
128C4×D4×C13—22no—
129C4×D4×C13—22no—
130C4×D4×C13—22no—
131C4×D4×C13—22no—
132C4×D4×C13—22no—
133C4×D4×C13—22no—
134C4×D4×C13—21no—
135C4×D4×C13—21no—
136C4×D4×C13—21no—
137C4×D4×C13—21no—
138C4×D4×C13C2312yes—
139C4×D4×C13C2312yes—
140C13×#117—21no—
141C13×#117—21no—
142C13×#117—22no—
143C13×#117—22no—
144C13×#117—22no—
145C13×#117C2312yes—
146C2×C42×C13—22no—
147C2×C42×C13D411yescharacteristic
148C2×C42×C13D411yescharacteristic
149C2×C42×C13D411yescharacteristic
150C2×C42×C13D411yescharacteristic
151C2×C42×C13D411yescharacteristic
152C2×C42×C13D411yescharacteristic
153C2×C42×C13C2311yescharacteristic
154C2×C42×C13C2311yescharacteristic
155C2×C42×C13C2311yescharacteristic
156C2×C42×C13C2311yescharacteristic
157C2×C42×C13C2311yescharacteristic
158C2×C42×C13C2311yescharacteristic
159#88205—216no—
160C2×#6107C2318yes—
161C2×#6105C2318yes—
162C2×C4⋊Dic13—21no—
163C2×C4⋊Dic13—21no—
164C2×C4⋊Dic13—21no—
165C2×C4⋊Dic13C2312yes—
166C2×C4⋊Dic13C2312yes—
167C2×C4⋊Dic13C2312yes—
168C2×#6101—22no—
169C2×#6101—22no—
170C2×#6101—22no—
171C2×#6101—22no—
172C2×#6101—22no—
173C2×#6101—22no—
174C2×C4×Dic13—22no—
175C2×C4×Dic13—22no—
176C2×C4×Dic13—22no—
177C2×C4×Dic13—22no—
178C2×C4×Dic13—22no—
179C2×C4×Dic13—22no—
180C2×#6099C2314yes—
181C4×Dic26—22no—
182C4×Dic26—22no—
183C4×Dic26—22no—
184C4×Dic26—22no—
185C4×Dic26—22no—
186C4×Dic26—22no—
187C4×Dic26—22no—
188C4×Dic26—22no—
189C4×Dic26—22no—
190C4×Dic26—22no—
191C4×Dic26—22no—
192C4×Dic26—22no—
193C4×Dic26C2314yes—
194C4×Dic26C2314yes—
195C4×Dic26C2314yes—
196C4×Dic26C2314yes—
197#88075C2318yes—
198#88072C2318yes—
199C22⋊#1055C2314yes—
200C22⋊#1055C2314yes—
201#88050C2318yes—
202#88050C2318yes—
203#88048C2318yes—
204#88047C2318yes—
205C4⋊#1055C2314yes—
206C4⋊#1055C2314yes—
207#88043C2314yes—
208C4×#1055C2314yes—
209#60560—131nomaximal, Sylow
210C24×C13C2×D411yescharacteristic
211C13×#41—28no—
212C13×#41—44no—
213C13×#41—44no—
214C2×Q8×C13—21no—
215C2×Q8×C13—21no—
216C2×Q8×C13C2412yes—
217C2×D4×C13—22no—
218C2×D4×C13—22no—
219C2×D4×C13—22no—
220C2×D4×C13—21no—
221C2×D4×C13—21no—
222C2×D4×C13C2412yes—
223C22×C4×C13—24no—
224C22×C4×C13—24no—
225C22×C4×C13—22no—
226C22×C4×C13—22no—
227C22×C4×C13—22no—
228C22×C4×C13—42no—
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2×D411yescharacteristic
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13C2×D411yescharacteristic
235C22×C4×C13C2×D411yescharacteristic
236C22×C4×C13C2×D411yescharacteristic
237C22×C4×C13C2×D411yescharacteristic
238C22×C4×C13C2×D411yescharacteristic
239C22×C4×C13C2×D411yescharacteristic
240C22×C4×C13C2×D411yescharacteristic
241C22×C4×C13C2×D411yescharacteristic
242C22×C4×C13C2×D411yescharacteristic
243C22×C4×C13C2×D411yescharacteristic
244C22×C4×C13C2411yescharacteristic
245C22×C4×C13C2411yescharacteristic
246C22×C4×C13C2411yescharacteristic
247C22×Dic13—28no—
248C22×Dic13—22no—
249C22×Dic13—22no—
250C22×Dic13—22no—
251C22×Dic13—22no—
252C22×Dic13—22no—
253C22×Dic13—22no—
254C22×Dic13—44no—
255C2×Dic26—28no—
256C2×Dic26—28no—
257C2×Dic26—28no—
258C2×Dic26—22no—
259C2×Dic26—22no—
260C2×Dic26—22no—
261C2×Dic26—24no—
262C2×Dic26—28no—
263C2×Dic26—28no—
264C2×Dic26#4118yescomplemented
265C2×Dic26C2414yes—
266C13×C4⋊C4—21no—
267C13×C4⋊C4—21no—
268C13×C4⋊C4—21no—
269C13×C4⋊C4—21no—
270C13×C4⋊C4—22no—
271C13×C4⋊C4—22no—
272C13×C4⋊C4—22no—
273C13×C4⋊C4—22no—
274C13×C4⋊C4—22no—
275C13×C4⋊C4—22no—
276C13×C4⋊C4C2412yes—
277C13×C4⋊C4C2412yes—
278C13×C22⋊C4—22no—
279C13×C22⋊C4—22no—
280C13×C22⋊C4—22no—
281C13×C22⋊C4—22no—
282C13×C22⋊C4—22no—
283C13×C22⋊C4—22no—
284C13×C22⋊C4—22no—
285C13×C22⋊C4—22no—
286C13×C22⋊C4—22no—
287C42×C13—22no—
288C42×C13—22no—
289C42×C13—22no—
290C42×C13C2×D411yescharacteristic
291C42×C13C2×D411yescharacteristic
292C42×C13C2×D411yescharacteristic
293C42×C13C2×D411yescharacteristic
294C42×C13C2×D411yescharacteristic
295C42×C13C2×D411yescharacteristic
296C42×C13C2×D411yescharacteristic
297C42×C13C2×D411yescharacteristic
298C42×C13C2×D411yescharacteristic
299C42×C13C2×D411yescharacteristic
300C42×C13C2×D411yescharacteristic
301C42×C13C2×D411yescharacteristic
302C42×C13C2411yescharacteristic
303C42×C13C2411yescharacteristic
304C42×C13C2411yescharacteristic
305C42×C13C2411yescharacteristic
306#6107—216no—
307#6105—216no—
308C4⋊Dic13—22no—
309C4⋊Dic13—22no—
310C4⋊Dic13—22no—
311C4⋊Dic13C2414yes—
312#6101—24no—
313#6101—24no—
314#6101—24no—
315#6101—24no—
316C4×Dic13—24no—
317C4×Dic13—24no—
318C4×Dic13—24no—
319C4×Dic13—24no—
320#6099—28no—
321C2×#1055C2418yes—
322#3444D1311yescharacteristic
323C22×C4×Q8—131no—
324#3117—134no—
325#3113—132no—
326#3112—132no—
327#3108—134no—
328#3104—132no—
329#3103—132no—
330#3092—132no—
331#3078—132no—
332#3037—132no—
333#3004—132no—
334C4×#137—134no—
335#2920—131no—
336C23×C13—22no—
337C23×C13—22no—
338C23×C13—22no—
339C23×C13—22no—
340C23×C13C22×D411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C23×C13C22×D411yescharacteristic
343Q8×C13—24no—
344Q8×C13—42no—
345Q8×C13—42no—
346D4×C13—24no—
347D4×C13—42no—
348D4×C13—44no—
349D4×C13—44no—
350D4×C13—44no—
351D4×C13—42no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—44no—
372C2×C4×C13—44no—
373C2×C4×C13—44no—
374C2×C4×C13#13714yescomplemented
375C2×C4×C13C22×D411yescharacteristic
376C2×C4×C13C22×D411yescharacteristic
377C2×C4×C13C22×D411yescharacteristic
378C2×C4×C13C22×D411yescharacteristic
379C2×C4×C13C22×D411yescharacteristic
380C2×C4×C13C22×D411yescharacteristic
381C2×C4×C13C22×D411yescharacteristic
382C2×C4×C13C22×D411yescharacteristic
383C2×C4×C13C22×D411yescharacteristic
384C2×C4×C13C22×D411yescharacteristic
385C2×C4×C13C22×D411yescharacteristic
386C2×C4×C13C2×#4114yes—
387C2×C4×C13C2511yescharacteristic
388C2×Dic13—28no—
389C2×Dic13—28no—
390C2×Dic13—28no—
391C2×Dic13—24no—
392C2×Dic13—24no—
393C2×Dic13—44no—
394C2×Dic13—44no—
395C2×Dic13—44no—
396Dic26—28no—
397Dic26—28no—
398Dic26—28no—
399Dic26—24no—
400Dic26C2×#4118yes—
401#1055—28no—
402C23×Q8—131no—
403C2×#137—134no—
404#533C2×D1311yescharacteristic
405#533C2×D1311yescharacteristic
406#533C2×D1311yescharacteristic
407#532C2×D1311yescharacteristic
408#532C2×D1311yescharacteristic
409#532C2×D1311yescharacteristic
410#529—21no—
411#529—21no—
412#529—21no—
413#529—21no—
414#529C2×D1312yes—
415#529C2×D1312yes—
416#525—21no—
417#525—21no—
418#525C2×D1312yes—
419C4×#41—21no—
420C4×#41—21no—
421C4×#41C2×D1312yes—
422C2×C4×Q8—132no—
423C2×C4×Q8—132no—
424C2×C4×Q8—132no—
425C2×C4×Q8—132no—
426C2×C4×Q8—132no—
427C2×C4×Q8—132no—
428C2×C4×Q8—261no—
429C2×C4×Q8—261no—
430C2×C4×Q8—261no—
431C2×C4×Q8—261no—
432C2×C4×Q8—261no—
433C2×C4×Q8—261no—
434C22×C4⋊C4—131no—
435C22×C4⋊C4—261no—
436C22×C42—261no—
437C22×C42C2×D1311yescharacteristic
438#484—134no—
439#483—134no—
440#481—134no—
441#480—134no—
442#479—138no—
443#477—134no—
444#475—134no—
445#464—138no—
446#462—134no—
447#460—134no—
448#451—134no—
449#451—134no—
450#448—134no—
451#448—134no—
452#441—138no—
453#440—138no—
454C4×Q16—138no—
455C4×SD16—138no—
456#432—132no—
457#432—132no—
458#431—132no—
459#431—132no—
460#428—134no—
461#423—132no—
462#419—134no—
463#417—134no—
464#407—132no—
465C4×M16—132no—
466C22×C13—28no—
467C22×C13—21no—
468C22×C13—21no—
469C22×C13—21no—
470C22×C13—21no—
471C22×C13—21no—
472C22×C13—21no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13#52512yes—
477C22×C13C2×#13712yes—
478C22×C13#57512yes—
479C22×C13C23×D411yescharacteristic
480C4×C13—21no—
481C4×C13—21no—
482C4×C13—21no—
483C4×C13—21no—
484C4×C13—21no—
485C4×C13—21no—
486C4×C13—21no—
487C4×C13—21no—
488C4×C13—42no—
489C4×C13—42no—
490C4×C13—42no—
491C4×C13#52512yes—
492C4×C13C2×#13712yes—
493C4×C13C2×#13712yes—
494C4×C13C22×#4112yes—
495Dic13—28no—
496Dic13—44no—
497C2×#41—21no—
498C2×#41—21no—
499C2×#41C22×D1312yes—
500C22×Q8—132no—
501C22×Q8—132no—
502C22×Q8—132no—
503C22×Q8—268no—
504C22×Q8—261no—
505C22×Q8—261no—
506C22×Q8—261no—
507C23×C4—261no—
508C23×C4—261no—
509C23×C4C22⋊D1311yescharacteristic
510C23×C4C22⋊D1311yescharacteristic
511C23×C4C22×D1311yescharacteristic
512#137—2616no—
513C2×Q16—138no—
514C2×SD16—138no—
515C2×M16—134no—
516C4⋊Q8C22×D1311yescharacteristic
517C4⋊Q8C22×D1311yescharacteristic
518C4⋊Q8C22×D1311yescharacteristic
519#127C22×D1311yescharacteristic
520#126—22no—
521#126—22no—
522#125—21no—
523#125—21no—
524#125C22×D1312yes—
525#124—21no—
526#124—21no—
527#124C22×D1312yes—
528#123—22no—
529#123—22no—
530#123—22no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8C22×D1312yes—
536C22⋊Q8C22×D1312yes—
537#121—21no—
538#121—21no—
539#121—21no—
540#121—21no—
541#121C22×D1312yes—
542#121C22×D1312yes—
543#120—22no—
544C4×Q8—21no—
545C4×Q8—21no—
546C4×Q8—21no—
547C4×Q8—21no—
548C4×Q8—134no—
549C4×Q8—134no—
550C4×Q8—134no—
551C4×Q8—134no—
552C4×Q8—262no—
553C4×Q8—262no—
554C4×Q8—262no—
555C4×Q8—262no—
556C4×Q8—262no—
557C4×Q8—262no—
558C4×Q8—262no—
559C4×Q8—262no—
560C4×Q8—262no—
561C4×Q8—262no—
562C4×Q8—262no—
563C4×Q8—262no—
564C4×Q8C22×D1312yes—
565C4×Q8C22×D1312yes—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—21no—
573C4×D4—21no—
574C4×D4—21no—
575C4×D4—21no—
576C4×D4C22×D1312yes—
577C4×D4C22×D1312yes—
578#117—21no—
579#117—21no—
580#117—22no—
581#117—22no—
582#117—22no—
583#117C22×D1312yes—
584C2×C4⋊C4—132no—
585C2×C4⋊C4—132no—
586C2×C4⋊C4—132no—
587C2×C4⋊C4—261no—
588C2×C4⋊C4—261no—
589C2×C4⋊C4—261no—
590C2×C4⋊C4—262no—
591C2×C4⋊C4—262no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—262no—
594C2×C4⋊C4—262no—
595C2×C4⋊C4—262no—
596C2×C42—22no—
597C2×C42—262no—
598C2×C42—262no—
599C2×C42—262no—
600C2×C42—262no—
601C2×C42—262no—
602C2×C42—262no—
603C2×C42C22⋊D1311yescharacteristic
604C2×C42C22⋊D1311yescharacteristic
605C2×C42C22⋊D1311yescharacteristic
606C2×C42C22⋊D1311yescharacteristic
607C2×C42C22⋊D1311yescharacteristic
608C2×C42C22⋊D1311yescharacteristic
609C2×C42C22×D1311yescharacteristic
610C2×C42C22×D1311yescharacteristic
611C2×C42C22×D1311yescharacteristic
612C2×C42C22×D1311yescharacteristic
613C2×C42C22×D1311yescharacteristic
614C2×C42C22×D1311yescharacteristic
615#107—138no—
616#106—138no—
617C4⋊C8—134no—
618C4⋊C8—134no—
619#103—138no—
620#103—138no—
621#103—138no—
622#102—138no—
623C22⋊C8—134no—
624C22⋊C8—134no—
625#97—134no—
626C4×C8—134no—
627C2×C13—22no—
628C2×C13—22no—
629C2×C13—22no—
630C2×C13—82no—
631C2×C13C2×#52511yescharacteristic
632C2×C13C22×#13711yescharacteristic
633C2×C13C2×#57511yescharacteristic
634C24C2×C22⋊D1311yescharacteristic
635#41—28no—
636#41—44no—
637#41—44no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—138no—
641C2×Q8—134no—
642C2×Q8—268no—
643C2×Q8—268no—
644C2×Q8—268no—
645C2×Q8—268no—
646C2×Q8—268no—
647C2×Q8—264no—
648C2×Q8—262no—
649C2×Q8—262no—
650C2×Q8—262no—
651C2×Q8C23×D1312yes—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4C23×D1312yes—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—42no—
664C22×C4—268no—
665C22×C4—262no—
666C22×C4—262no—
667C22×C4—262no—
668C22×C4—262no—
669C22×C4—262no—
670C22×C4—262no—
671C22×C4—524no—
672C22×C4C2×C22⋊D1311yescharacteristic
673C22×C4C2×C22⋊D1311yescharacteristic
674C22×C4C2×C22⋊D1311yescharacteristic
675C22×C4C2×C22⋊D1311yescharacteristic
676C22×C4C2×C22⋊D1311yescharacteristic
677C22×C4C2×C22⋊D1311yescharacteristic
678C22×C4C2×C22⋊D1311yescharacteristic
679C22×C4C2×C22⋊D1311yescharacteristic
680C22×C4C2×C22⋊D1311yescharacteristic
681C22×C4C2×C22⋊D1311yescharacteristic
682C22×C4C2×C22⋊D1311yescharacteristic
683C22×C4C2×C22⋊D1311yescharacteristic
684C22×C4C2×C22⋊D1311yescharacteristic
685C22×C4C2×C22⋊D1311yescharacteristic
686C22×C4C2×C22⋊D1311yescharacteristic
687C22×C4C23×D1311yescharacteristic
688C22×C4C23×D1311yescharacteristic
689C22×C4C23×D1311yescharacteristic
690Q16—2616no—
691SD16—2616no—
692M16—268no—
693C2×C8—138no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—134no—
705C4⋊C4—262no—
706C4⋊C4—262no—
707C4⋊C4—262no—
708C4⋊C4—264no—
709C4⋊C4—264no—
710C4⋊C4—264no—
711C4⋊C4—264no—
712C4⋊C4C23×D1312yes—
713C4⋊C4C23×D1312yes—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—264no—
727C42—264no—
728C42—264no—
729C42—264no—
730C42C2×C22⋊D1311yescharacteristic
731C42C2×C22⋊D1311yescharacteristic
732C42C2×C22⋊D1311yescharacteristic
733C42C2×C22⋊D1311yescharacteristic
734C42C2×C22⋊D1311yescharacteristic
735C42C2×C22⋊D1311yescharacteristic
736C42C2×C22⋊D1311yescharacteristic
737C42C2×C22⋊D1311yescharacteristic
738C42C2×C22⋊D1311yescharacteristic
739C42C2×C22⋊D1311yescharacteristic
740C42C2×C22⋊D1311yescharacteristic
741C42C2×C22⋊D1311yescharacteristic
742C42C23×D1311yescharacteristic
743C42C23×D1311yescharacteristic
744C42C23×D1311yescharacteristic
745C42C23×D1311yescharacteristic
746C13#6056011yescharacteristic, complemented, Sylow
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23C22×C22⋊D1311yescharacteristic
752C23C22×C22⋊D1311yescharacteristic
753C23C22×C22⋊D1311yescharacteristic
754Q8—24no—
755Q8—42no—
756Q8—42no—
757Q8—138no—
758Q8—268no—
759Q8—268no—
760Q8—268no—
761Q8—264no—
762D4—24no—
763D4—42no—
764D4—44no—
765D4—44no—
766D4—44no—
767D4—42no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—268no—
791C2×C4—268no—
792C2×C4—268no—
793C2×C4—264no—
794C2×C4—264no—
795C2×C4—524no—
796C2×C4—524no—
797C2×C4—524no—
798C2×C4#8820514yescomplemented
799C2×C4#41×D1314yes—
800C2×C4C22×C22⋊D1311yescharacteristic
801C2×C4C22×C22⋊D1311yescharacteristic
802C2×C4C22×C22⋊D1311yescharacteristic
803C2×C4C22×C22⋊D1311yescharacteristic
804C2×C4C22×C22⋊D1311yescharacteristic
805C2×C4C22×C22⋊D1311yescharacteristic
806C2×C4C22×C22⋊D1311yescharacteristic
807C2×C4C22×C22⋊D1311yescharacteristic
808C2×C4C22×C22⋊D1311yescharacteristic
809C2×C4C22×C22⋊D1311yescharacteristic
810C2×C4C22×C22⋊D1311yescharacteristic
811C2×C4C24×D1311yescharacteristic
812C8—268no—
813C22—28no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22#1171952712yes—
824C22C2×#8820512yes—
825C22#1171953312yes—
826C22C23×C22⋊D1311yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—268no—
839C4—524no—
840C4C2×#8820512yes—
841C4C2×#8820512yes—
842C4#1171953312yes—
843C4C2×#41×D1312yes—
844C2—22no—
845C2—22no—
846C2—22no—
847C2—82no—
848C2C2×#1171953311yescharacteristic
849C2C22×#8820511yescharacteristic
850C2C2×#1171952711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC13×#3444C2
socleC22×C13C23×D4
hypercenter#3444D13
hypocenterC13#60560
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic26C2semidirect
2. #13125003C2semidirect
3. #13124962C2semidirect
4. #13124954C2semidirect
5. #13124912C2semidirect
6. #13124871C2semidirect
7. #13124863C2semidirect
8. #13124756C2semidirect
9. #13124637C2semidirect
10. #13124304C2semidirect
11. #13124069C2semidirect
12. C4×#88205C2semidirect
13. #13123469C2semidirect
53. #11718755C22semidirect
54. #11718752C22semidirect
55. #11718751C22semidirect
56. #11718736C22semidirect
57. #11718724C22semidirect
58. #11718715C22semidirect
67. #11718691C22semidirect
68. C4×#6107C22semidirect
69. #11718679C22semidirect
70. C4×#6105C22semidirect
264. C2×Dic26#41semidirect
374. C2×C4×C13#137semidirect
746. C13#60560semidirect
798. C2×C4#88205semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic262
#131250032
#131249622
#131249542
#131249122
#131248712
#131248632
#131247562
#131246372
#131243042
#131240692
C4×#882052
#131234692
C13×#34442
#6056013