Finite Group Databasebeta

← #15879470

Subgroups — #15879470

Order 3328.

1114 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719216C211yesmaximal, characteristic
2#13117713C211yesmaximal, characteristic, complemented
3#13115821C211yesmaximal, characteristic, complemented
4#13115821C212yesmaximal, complemented
5#13115820C212yesmaximal, complemented
6#13115820C211yesmaximal, characteristic, complemented
7#13114821C212yesmaximal
8#13114821C211yesmaximal, characteristic
9C4×#88046C211yesmaximal, characteristic
10C4×#88046C212yesmaximal
11C13×#2345C211yesmaximal, characteristic, complemented
12C22×C13×C4⋊C4C2211yescharacteristic
13C2×C4×C22⋊D13C2211yescharacteristic
14C2×C4×C22⋊D13C2212yes—
15C2×#88178C2212yes—
16C2×#88178C2211yescharacteristic
17#11719216—21no—
18#11719216—22no—
19#11719216—21no—
20#11719216—21no—
21#11719216—22no—
22#11719216—21no—
23C2×#88151C411yescharacteristic, complemented
24C2×#88150C412yescomplemented
25C2×C4⋊C4×D13C411yescharacteristic, complemented
26C2×#88143C412yescomplemented
27C2×#88142C411yescharacteristic, complemented
28C2×#88141C411yescharacteristic, complemented
29C13×#389—21no—
30C13×#387—22no—
31C13×#380C2212yes—
32C13×#380C2211yescharacteristic
33C4×C13×C4⋊C4—21no—
34C4×C13×C22⋊C4C2211yescharacteristic
35C4×C13×C22⋊C4C2212yes—
36#11718873C2212yes—
37#11718873C2211yescharacteristic
38C4×C22⋊Dic13C2211yescharacteristic
39C4×C22⋊Dic13C2212yes—
40#11718646—21no—
41#11718642—22no—
42C4⋊C4×Dic13—21no—
43C2×#88046C2211yescharacteristic
44C2×#88046C2212yes—
45C2×#88046C2211yescharacteristic
46#11718119C2212yes—
47#11718119C2211yescharacteristic
48#11718119C2212yes—
49#11718119C2211yescharacteristic
50#11718119C2212yes—
51#11718119C2212yes—
52#11718119C2212yes—
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2312yes—
55C22×C22⋊D13C2311yescharacteristic
56C22×C4×D13C2×C411yescharacteristic
57C22×C4×D13C2×C412yes—
58C22×Dic26C2×C411yescharacteristic
59C22×Dic26C2×C412yes—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4C2×C411yescharacteristic
63C2×C13×C4⋊C4C2×C411yescharacteristic
64C2×C13×C4⋊C4C2×C412yes—
65C2×C13×C4⋊C4D411yescharacteristic
66C2×C13×C4⋊C4D412yes—
67C2×C13×C4⋊C4D411yescharacteristic
68C2×C13×C4⋊C4D411yescharacteristic
69C2×C13×C4⋊C4D412yes—
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C22⋊C4C2311yescharacteristic
72C2×C13×C22⋊C4C2312yes—
73C2×C13×C22⋊C4C2311yescharacteristic
74C2×C42×C13—21no—
75C2×C42×C13—22no—
76C2×C22⋊Dic13C2311yescharacteristic
77C2×C22⋊Dic13C2312yes—
78C2×C22⋊Dic13C2312yes—
79C2×C22⋊Dic13C2311yescharacteristic
80C2×C22⋊Dic13C2311yescharacteristic
81C4×C22⋊D13—21no—
82C4×C22⋊D13—21no—
83C4×C22⋊D13—22no—
84C4×C22⋊D13—22no—
85C4×C22⋊D13—21no—
86C4×C22⋊D13—21no—
87C4×C22⋊D13—22no—
88C4×C22⋊D13—22no—
89C2×#6103C2×C411yescharacteristic
90C2×#6103C2×C412yes—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13C2×C411yescharacteristic
94C2×C4⋊Dic13C2×C412yes—
95#88178—22no—
96#88178—22no—
97#88178—21no—
98#88178—21no—
99#88178—22no—
100#88178—22no—
101#88178—21no—
102#88178—21no—
103C2×#6101C2×C412yes—
104C2×#6101C2×C412yes—
105C2×#6101C2×C411yescharacteristic
106C2×#6101C2×C412yes—
107C2×#6101C2×C412yes—
108C2×C4×Dic13—21no—
109C2×C4×Dic13—22no—
110C2×C4×Dic13C2×C411yescharacteristic
111C2×C4×Dic13C2×C412yes—
112#88151—22no—
113#88151—21no—
114#88151—21no—
115#88150—22no—
116#88150—22no—
117#88150—22no—
118#88150—22no—
119C4⋊C4×D13—22no—
120C4⋊C4×D13—21no—
121C4⋊C4×D13—21no—
122#88143—22no—
123#88143—22no—
124#88143—22no—
125#88143—22no—
126#88142—22no—
127#88142—21no—
128#88142—21no—
129#88141—22no—
130#88141—21no—
131#88141—21no—
132C13×#95—21no—
133C13×#95—22no—
134C13×#95—22no—
135C13×#95—21no—
136#88071—21no—
137#88071—22no—
138#88071—22no—
139#88071—21no—
140#88046—22no—
141#88046—24no—
142#88046Q814yescomplemented
143#22513—131nomaximal, Sylow
144C24×C13C2411yescharacteristic
145C23×D13C22×C411yescharacteristic
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—22no—
149C22×C4×C13—42no—
150C22×C4×C13—82no—
151C22×C4×C13C22×C411yescharacteristic
152C22×C4×C13C22×C412yes—
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C22×C412yes—
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×D412yes—
163C2×C22⋊D13—21no—
164C2×C22⋊D13—21no—
165C2×C22⋊D13—21no—
166C2×C22⋊D13—21no—
167C2×C22⋊D13C2×Q812yes—
168C2×C22⋊D13#4112yes—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—22no—
172C22×Dic13C22×C411yescharacteristic
173C22×Dic13C22×C412yes—
174C22×Dic13C22×C411yescharacteristic
175C22×Dic13C22×C411yescharacteristic
176C22×Dic13C22×C412yes—
177C2×C4×D13—21no—
178C2×C4×D13—21no—
179C2×C4×D13—22no—
180C2×C4×D13—22no—
181C2×C4×D13—42no—
182C2×C4×D13—82no—
183C2×Dic26—21no—
184C2×Dic26—21no—
185C2×Dic26—22no—
186C2×Dic26—22no—
187C2×Dic26—42no—
188C2×Dic26—82no—
189C13×C4⋊C4—42no—
190C13×C4⋊C4—82no—
191C13×C4⋊C4C22⋊C412yes—
192C13×C4⋊C4C22⋊C411yescharacteristic
193C13×C4⋊C4C22⋊C411yescharacteristic
194C13×C4⋊C4C22⋊C412yes—
195C13×C4⋊C4C22⋊C411yescharacteristic
196C13×C4⋊C4C22⋊C411yescharacteristic
197C13×C4⋊C4C22⋊C412yes—
198C13×C4⋊C4C22⋊C412yes—
199C13×C4⋊C4C22⋊C412yes—
200C13×C4⋊C4C22⋊C412yes—
201C13×C22⋊C4—21no—
202C13×C22⋊C4—21no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—21no—
205C13×C22⋊C4—22no—
206C13×C22⋊C4C2×Q812yes—
207C42×C13—42no—
208C42×C13—82no—
209C22⋊Dic13—22no—
210C22⋊Dic13—21no—
211C22⋊Dic13—22no—
212C22⋊Dic13—21no—
213C22⋊Dic13—21no—
214C22⋊Dic13—21no—
215C22⋊Dic13—22no—
216C22⋊Dic13—21no—
217C22⋊Dic13—22no—
218C22⋊Dic13C2×Q812yes—
219#6103—21no—
220#6103—21no—
221#6103—22no—
222#6103—22no—
223C4⋊Dic13—21no—
224C4⋊Dic13—21no—
225C4⋊Dic13—22no—
226C4⋊Dic13—22no—
227C4⋊Dic13—42no—
228C4⋊Dic13—82no—
229#6101—22no—
230#6101—22no—
231#6101—22no—
232#6101—22no—
233#6101—21no—
234#6101—21no—
235#6101—22no—
236#6101—22no—
237#6101—22no—
238#6101—22no—
239C4×Dic13—21no—
240C4×Dic13—21no—
241C4×Dic13—22no—
242C4×Dic13—22no—
243C4×Dic13—42no—
244C4×Dic13—82no—
245C2×#554—131no—
246#2345—131no—
247#2345D1311yescharacteristic, complemented
248#1996—132no—
249#1996—131no—
250#1996—132no—
251#1996—131no—
252#1799—132no—
253#1799—131no—
254C4×#99—132no—
255C4×#99—131no—
256C23×C13—41no—
257C23×C13—41no—
258C23×C13C23×C411yescharacteristic
259C23×C13C22×D411yescharacteristic
260C23×C13C22×D411yescharacteristic
261C23×C13C22×Q811yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C132−1+411yescharacteristic
264C23×C132−1+411yescharacteristic
265C22×D13—21no—
266C22×D13—21no—
267C22×D13—41no—
268C22×D13—41no—
269C22×D13C4×Q812yes—
270C2×C4×C13—22no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—42no—
277C2×C4×C13—42no—
278C2×C4×C13—42no—
279C2×C4×C13—42no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—42no—
291C2×C4×C13C2×C22⋊C412yes—
292C2×C4×C13C2×C22⋊C412yes—
293C2×C4×C13C2×C22⋊C411yescharacteristic
294C2×C4×C13C2×C22⋊C411yescharacteristic
295C2×C4×C13C2×C22⋊C411yescharacteristic
296C2×C4×C13C2×C22⋊C412yes—
297C2×C4×C13C2×C22⋊C412yes—
298C2×C4×C13C2×C22⋊C411yescharacteristic
299C22⋊D13—22no—
300C22⋊D13—22no—
301C22⋊D13—22no—
302C22⋊D13—22no—
303C2×Dic13—21no—
304C2×Dic13—21no—
305C2×Dic13—22no—
306C2×Dic13—21no—
307C2×Dic13—21no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—41no—
311C2×Dic13—41no—
312C2×Dic13—42no—
313C2×Dic13—41no—
314C2×Dic13—42no—
315C2×Dic13—41no—
316C2×Dic13—41no—
317C2×Dic13—42no—
318C2×Dic13—42no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—42no—
322C2×Dic13C4×Q812yes—
323C4×D13—42no—
324C4×D13—42no—
325C4×D13—82no—
326C4×D13—82no—
327Dic26—42no—
328Dic26—42no—
329Dic26—82no—
330Dic26—82no—
331#554—261no—
332#554—262no—
333#554—261no—
334#554—261no—
335#554—262no—
336#554—261no—
337C2×C4⋊Q8—131no—
338C2×#125—132no—
339C2×C22⋊Q8—132no—
340C2×C22⋊Q8—131no—
341C2×C22⋊Q8—132no—
342C2×C22⋊Q8—131no—
343C2×C4×Q8—131no—
344C2×C4×D4—132no—
345C2×C4×D4—131no—
346C22×C4⋊C4—131no—
347C22×C4⋊C4C2×D1311yescharacteristic
348C2×#99—131no—
349C2×#99—131no—
350C2×#99—132no—
351#389—21no—
352#389—261no—
353#387—22no—
354#387—262no—
355#380—132no—
356#380—131no—
357#380C2×D1312yes—
358#380C2×D1311yescharacteristic
359C4×C4⋊C4—21no—
360C4×C4⋊C4—261no—
361C4×C22⋊C4—131no—
362C4×C22⋊C4—132no—
363C4×C22⋊C4C2×D1311yescharacteristic
364C4×C22⋊C4C2×D1312yes—
365#342—132no—
366#342—132no—
367#342—132no—
368#342—132no—
369#342—131no—
370#342—132no—
371#342—131no—
372C22×C13—21no—
373C22×C13—21no—
374C22×C13—21no—
375C22×C13—21no—
376C22×C13—21no—
377C22×C13—21no—
378C22×C13—41no—
379C22×C13—41no—
380C22×C13—41no—
381C22×C13—41no—
382C22×C13C22×C22⋊C411yescharacteristic
383C22×C13C2×C4×Q811yescharacteristic
384C22×C13#51911yescharacteristic
385C22×C13#54811yescharacteristic
386C22×C13#54811yescharacteristic
387C22×C13D4×Q811yescharacteristic
388C22×C13D4×Q811yescharacteristic
389C2×D13—22no—
390C2×D13—42no—
391C2×D13—41no—
392C2×D13—41no—
393C2×D13—42no—
394C4×C13—21no—
395C4×C13—21no—
396C4×C13—21no—
397C4×C13—22no—
398C4×C13—22no—
399C4×C13—22no—
400C4×C13—22no—
401C4×C13—42no—
402C4×C13—81no—
403C4×C13—82no—
404C4×C13#41012yes—
405Dic13—22no—
406Dic13—42no—
407Dic13—42no—
408Dic13—41no—
409Dic13—41no—
410Dic13—42no—
411Dic13—81no—
412Dic13—82no—
413C22×Q8—131no—
414C22×Q8—132no—
415C22×D4—131no—
416C23×C4—131no—
417C23×C4—132no—
418C23×C4C22×D1311yescharacteristic
419C23×C4C22×D1312yes—
420C4⋊Q8—262no—
421C4⋊Q8—261no—
422C4⋊Q8—261no—
423#125—262no—
424#125—262no—
425#125—262no—
426#125—262no—
427C22⋊Q8—262no—
428C22⋊Q8—262no—
429C22⋊Q8—261no—
430C22⋊Q8—261no—
431C22⋊Q8—262no—
432C22⋊Q8—262no—
433C22⋊Q8—261no—
434C22⋊Q8—261no—
435C22⋊Q8—262no—
436C22⋊Q8—262no—
437C22⋊Q8—262no—
438C22⋊Q8—262no—
439C22⋊Q8—262no—
440C22⋊Q8—261no—
441C22⋊Q8—261no—
442C4×Q8—262no—
443C4×Q8—261no—
444C4×Q8—261no—
445C4×D4—262no—
446C4×D4—262no—
447C4×D4—261no—
448C4×D4—261no—
449C4×D4—262no—
450C4×D4—262no—
451C4×D4—261no—
452C4×D4—261no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—132no—
456C2×C4⋊C4—131no—
457C2×C4⋊C4—131no—
458C2×C4⋊C4—132no—
459C2×C4⋊C4—132no—
460C2×C4⋊C4—132no—
461C2×C4⋊C4—132no—
462C2×C4⋊C4—262no—
463C2×C4⋊C4—261no—
464C2×C4⋊C4—261no—
465C2×C4⋊C4—261no—
466C2×C4⋊C4—262no—
467C2×C4⋊C4C4×D1311yescharacteristic
468C2×C4⋊C4C4×D1312yes—
469C2×C4⋊C4C4×D1311yescharacteristic
470C2×C4⋊C4D5211yescharacteristic
471C2×C4⋊C4D5212yes—
472C2×C4⋊C4D5211yescharacteristic
473C2×C4⋊C4C22⋊D1311yescharacteristic
474C2×C4⋊C4C22⋊D1312yes—
475C2×C4⋊C4C22⋊D1311yescharacteristic
476C2×C22⋊C4—131no—
477C2×C22⋊C4—132no—
478C2×C22⋊C4—131no—
479C2×C22⋊C4—132no—
480C2×C22⋊C4—131no—
481C2×C22⋊C4—131no—
482C2×C22⋊C4—132no—
483C2×C22⋊C4C22×D1311yescharacteristic
484C2×C22⋊C4C22×D1312yes—
485C2×C22⋊C4C22×D1311yescharacteristic
486C2×C42—21no—
487C2×C42—22no—
488C2×C42—132no—
489C2×C42—131no—
490C2×C42—261no—
491C2×C42—262no—
492#99—134no—
493#99—262no—
494#99—264no—
495#95—21no—
496#95—22no—
497#95—22no—
498#95—21no—
499#95—261no—
500#95—262no—
501#95—262no—
502#95—261no—
503C2×C13—21no—
504C2×C13—21no—
505C2×C13—21no—
506C2×C13—21no—
507C2×C13—21no—
508C2×C13—21no—
509C2×C13Q8×C22⋊C411yescharacteristic
510C2×C13C2×#41011yescharacteristic
511C2×C13#288311yescharacteristic
512D13—42no—
513C24—131no—
514C24C23×D1311yescharacteristic
515C2×Q8—261no—
516C2×Q8—261no—
517C2×Q8—262no—
518C2×Q8—262no—
519C2×Q8—522no—
520C2×Q8—1042no—
521C2×D4—132no—
522C2×D4—132no—
523C2×D4—261no—
524C2×D4—261no—
525C2×D4—261no—
526C2×D4—261no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—42no—
531C22×C4—82no—
532C22×C4—131no—
533C22×C4—132no—
534C22×C4—131no—
535C22×C4—131no—
536C22×C4—132no—
537C22×C4—261no—
538C22×C4—261no—
539C22×C4—261no—
540C22×C4—262no—
541C22×C4—262no—
542C22×C4—261no—
543C22×C4—262no—
544C22×C4—522no—
545C22×C4—1042no—
546C22×C4C2×C4×D1311yescharacteristic
547C22×C4C2×C4×D1312yes—
548C22×C4C2×C4×D1311yescharacteristic
549C22×C4C2×C4×D1312yes—
550C22×C4C2×D5211yescharacteristic
551C22×C4C2×D5211yescharacteristic
552C22×C4C2×D5212yes—
553C22×C4C2×D5212yes—
554C22×C4C2×C22⋊D1311yescharacteristic
555C22×C4C2×C22⋊D1311yescharacteristic
556C22×C4C2×C22⋊D1312yes—
557C22×C4C2×C22⋊D1312yes—
558C4⋊C4—42no—
559C4⋊C4—82no—
560C4⋊C4—262no—
561C4⋊C4—262no—
562C4⋊C4—261no—
563C4⋊C4—261no—
564C4⋊C4—261no—
565C4⋊C4—261no—
566C4⋊C4—262no—
567C4⋊C4—262no—
568C4⋊C4—262no—
569C4⋊C4—262no—
570C4⋊C4—262no—
571C4⋊C4—262no—
572C4⋊C4—262no—
573C4⋊C4—262no—
574C4⋊C4—522no—
575C4⋊C4—1042no—
576C4⋊C4#610312yes—
577C4⋊C4#610311yescharacteristic
578C4⋊C4#610311yescharacteristic
579C4⋊C4#610312yes—
580C4⋊C4#610312yes—
581C4⋊C4#610312yes—
582C4⋊C4#610312yes—
583C4⋊C4#610312yes—
584C4⋊C4#610311yescharacteristic
585C4⋊C4#610311yescharacteristic
586C22⋊C4—21no—
587C22⋊C4—21no—
588C22⋊C4—22no—
589C22⋊C4—21no—
590C22⋊C4—22no—
591C22⋊C4—132no—
592C22⋊C4—262no—
593C22⋊C4—261no—
594C22⋊C4—261no—
595C22⋊C4—262no—
596C22⋊C4—261no—
597C22⋊C4—262no—
598C22⋊C4—262no—
599C22⋊C4—261no—
600C22⋊C4—261no—
601C22⋊C4—261no—
602C22⋊C4—262no—
603C22⋊C4—261no—
604C22⋊C4—262no—
605C22⋊C4Q8×D1312yes—
606C42—42no—
607C42—82no—
608C42—262no—
609C42—262no—
610C42—261no—
611C42—261no—
612C42—522no—
613C42—1042no—
614C13#2251311yescharacteristic, complemented, Sylow
615C23—41no—
616C23—41no—
617C23—132no—
618C23—261no—
619C23—261no—
620C23—521no—
621C23—521no—
622C23C22×C4×D1311yescharacteristic
623C23C22×D5211yescharacteristic
624C23C2×Q8×D1311yescharacteristic
625C23#8825411yescharacteristic
626C23#41×D1311yescharacteristic
627C23#8825711yescharacteristic
628C23C22×C22⋊D1311yescharacteristic
629Q8—522no—
630Q8—522no—
631Q8—1042no—
632Q8—1042no—
633D4—262no—
634D4—262no—
635D4—262no—
636D4—262no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—132no—
659C2×C4—261no—
660C2×C4—261no—
661C2×C4—262no—
662C2×C4—261no—
663C2×C4—261no—
664C2×C4—262no—
665C2×C4—262no—
666C2×C4—522no—
667C2×C4—521no—
668C2×C4—521no—
669C2×C4—522no—
670C2×C4—521no—
671C2×C4—522no—
672C2×C4—522no—
673C2×C4—521no—
674C2×C4—521no—
675C2×C4—522no—
676C2×C4—522no—
677C2×C4—521no—
678C2×C4—521no—
679C2×C4—522no—
680C2×C4—1042no—
681C2×C4—1042no—
682C2×C4C2×#610312yes—
683C2×C4C2×#610312yes—
684C2×C4C2×#610311yescharacteristic
685C2×C4C2×#610311yescharacteristic
686C2×C4C2×#610311yescharacteristic
687C2×C4C2×#610312yes—
688C2×C4C2×#610312yes—
689C2×C4C2×#610311yescharacteristic
690C22—21no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—262no—
701C22—522no—
702C22—522no—
703C22—521no—
704C22—521no—
705C22C4×Q8×D1311yescharacteristic
706C22#1171927711yescharacteristic
707C22Q8×D5211yescharacteristic
708C22#1171928111yescharacteristic
709C22C22×#610311yescharacteristic
710C22Q8×C22⋊D1311yescharacteristic
711C22#1171953611yescharacteristic
712C4—21no—
713C4—21no—
714C4—21no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—22no—
719C4—42no—
720C4—81no—
721C4—82no—
722C4—262no—
723C4—522no—
724C4—521no—
725C4—522no—
726C4—522no—
727C4—521no—
728C4—1041no—
729C4—1042no—
730C4#1171866712yes—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—21no—
735C2—21no—
736C2—21no—
737C2—522no—
738C2Q8×#610311yescharacteristic
739C2C2×#1171866711yescharacteristic
740C2#1312329611yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC13×#2345C2
socleC22×C13C22×C22⋊C4
prime radicalC22×C22⋊D13C23
cosocleC24×C13C24
hypercenter#2345D13
hypocenterC13#22513
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #13117713C2semidirect
3. #13115821C2semidirect
4. #13115821C2semidirect
5. #13115820C2semidirect
6. #13115820C2semidirect
11. C13×#2345C2semidirect
23. C2×#88151C4semidirect
24. C2×#88150C4semidirect
25. C2×C4⋊C4×D13C4semidirect
26. C2×#88143C4semidirect
27. C2×#88142C4semidirect
28. C2×#88141C4semidirect
142. #88046Q8semidirect
247. #2345D13semidirect
614. C13#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#117192162
#131177132
#131158212
#131158202
#131148212
C4×#880462
C13×#23452
#2251313