Finite Group Databasebeta

← #15913824

Subgroups — #15913824

Order 3328.

984 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718713C211yesmaximal, characteristic, complemented
2C2×#11718712C211yesmaximal, characteristic, complemented
3C2×#11718751C211yesmaximal, characteristic, complemented
4C2×#11718672C211yesmaximal, characteristic
5#13119745C211yesmaximal, characteristic
6#13116036C211yesmaximal, characteristic, complemented
7#13116029C211yesmaximal, characteristic, complemented
8#13115844C211yesmaximal, characteristic, complemented
9#13115844C211yesmaximal, characteristic, complemented
10#13115657C211yesmaximal, characteristic, complemented
11#13115604C211yesmaximal, characteristic, complemented
12#13115270C211yesmaximal, characteristic, complemented
13#13115260C211yesmaximal, characteristic, complemented
14#13114669C211yesmaximal, characteristic, complemented
15C13×#2542C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8C2211yescharacteristic
18C2×C13×C22⋊Q8C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C4×D4×C13C2211yescharacteristic
22C22×#6107C2211yescharacteristic
23C22×#6107C2211yescharacteristic
24C2×#88178C2211yescharacteristic
25C2×#88178C2211yescharacteristic
26C22×#6099C2211yescharacteristic
27C23×#1055C2211yescharacteristic
28C2×C4×Dic26C2211yescharacteristic
29C13×#399—21no—
30C13×#399—21no—
31C13×#390—21no—
32C13×#384—21no—
33C4×C13×C4⋊C4C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39C2×#88075C2211yescharacteristic
40#11718883—21no—
41#11718873C2211yescharacteristic
42#11718873C2211yescharacteristic
43C2×C22⋊#1055C2211yescharacteristic
44C2×C22⋊#1055C2211yescharacteristic
45#11718751—24no—
46#11718713—24no—
47#11718712—24no—
48#11718672—24no—
49#11718641—21no—
50C2×#88050C2211yescharacteristic
51C2×#88050C2211yescharacteristic
52C2×#88048C2211yescharacteristic
53C2×#88047C2211yescharacteristic
54#11718605—21no—
55#11718605—21no—
56#11718597C2211yescharacteristic
57C2×C4⋊#1055C2211yescharacteristic
58C2×#88043C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718121C2211yescharacteristic
63C22×Q8×C13C2311yescharacteristic
64C22×Q8×C13C2311yescharacteristic
65C22×D4×C13D411yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C22×Dic26C2311yescharacteristic
69C13×C4⋊Q8—22no—
70C13×C4⋊Q8—22no—
71C13×C22⋊Q8—22no—
72C13×C22⋊Q8—22no—
73C13×C22⋊Q8—22no—
74C13×C22⋊Q8—22no—
75C13×C22⋊Q8—41no—
76C13×C22⋊Q8—41no—
77C13×C22⋊Q8—41no—
78C13×C22⋊Q8—41no—
79C4×D4×C13—22no—
80C4×D4×C13—22no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—21no—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4D411yescharacteristic
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C22⋊C4—21no—
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4—21no—
94C2×C13×C22⋊C4D411yescharacteristic
95C2×C13×C22⋊C4D411yescharacteristic
96C2×C42×C13—21no—
97C2×C42×C13C2311yescharacteristic
98C2×C22⋊Dic13—21no—
99C2×C22⋊Dic13—21no—
100C2×C22⋊Dic13—21no—
101C2×C22⋊Dic13—21no—
102C2×#6107—22no—
103C2×#6107—22no—
104C2×#6107—22no—
105C2×#6107—22no—
106C2×#6107—41no—
107C2×#6107—41no—
108C2×C4⋊Dic13C2311yescharacteristic
109C2×C4⋊Dic13C2311yescharacteristic
110C2×C4⋊Dic13C2311yescharacteristic
111#88178—22no—
112#88178—22no—
113#88178—41no—
114#88178—41no—
115C2×#6101—21no—
116C2×#6101—21no—
117C2×#6101—21no—
118C2×C4×Dic13—21no—
119C2×#6099—22no—
120C2×#6099—22no—
121C2×#6099—41no—
122C22×#1055—22no—
123C22×#1055—22no—
124C22×#1055—41no—
125C22×#1055C2311yescharacteristic
126C22×#1055C2311yescharacteristic
127C22×#1055C2311yescharacteristic
128C22×#1055C2311yescharacteristic
129C4×Dic26—22no—
130C4×Dic26—22no—
131C13×#95—21no—
132#88075—22no—
133#88075—22no—
134#88075—22no—
135#88075—22no—
136#88075—41no—
137#88075—41no—
138#88071—21no—
139#88071—21no—
140#88071—21no—
141#88071—21no—
142C22⋊#1055—22no—
143C22⋊#1055—22no—
144#88050—22no—
145#88050D414yescomplemented
146#88048—22no—
147#88047—22no—
148C4⋊#1055D414yes—
149#88043—22no—
150#25398—131nomaximal, Sylow
151C24×C13C2×D411yescharacteristic
152C24×C13C2×D411yescharacteristic
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C2×Q8×C13—21no—
158C2×Q8×C13—21no—
159C2×Q8×C13—21no—
160C2×Q8×C13—21no—
161C2×Q8×C13—21no—
162C2×Q8×C13—21no—
163C2×Q8×C13—21no—
164C2×Q8×C13—21no—
165C2×D4×C13—22no—
166C2×D4×C13—22no—
167C2×D4×C13—41no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2×D411yescharacteristic
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2411yescharacteristic
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C2×Dic26—21no—
194C2×Dic26—21no—
195C2×Dic26—21no—
196C2×Dic26—21no—
197C2×Dic26—21no—
198C2×Dic26C2×D412yes—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—42no—
203C13×C4⋊C4—42no—
204C13×C4⋊C4—42no—
205C13×C4⋊C4—42no—
206C13×C4⋊C4—42no—
207C13×C4⋊C4—42no—
208C13×C4⋊C4C2×D412yes—
209C13×C4⋊C4#4112yes—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—42no—
213C13×C22⋊C4—42no—
214C13×C22⋊C4—42no—
215C13×C22⋊C4—42no—
216C42×C13—42no—
217C42×C13C2×D412yes—
218C42×C13#4112yes—
219C22⋊Dic13—42no—
220C22⋊Dic13—42no—
221C22⋊Dic13—42no—
222C22⋊Dic13—42no—
223#6107—44no—
224#6107—44no—
225C4⋊Dic13—21no—
226C4⋊Dic13—21no—
227C4⋊Dic13—21no—
228C4⋊Dic13—21no—
229C4⋊Dic13—21no—
230C4⋊Dic13—21no—
231#6101—42no—
232#6101—42no—
233#6101—42no—
234C4×Dic13—42no—
235#6099—44no—
236C2×#1055—21no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055—21no—
244C2×#1055—21no—
245C2×#1055—44no—
246C2×#1055C2×D412yes—
247C2×#1055C2×D412yes—
248C2×#1055C2×D412yes—
249C2×#470—131no—
250C2×#467—131no—
251C2×#462—131no—
252C2×#435—131no—
253#2542D1311yescharacteristic
254#2536—131no—
255#2036—131no—
256#2035—131no—
257#2001—131no—
258#2001—131no—
259#1960—131no—
260#1949—131no—
261#1894—131no—
262#1892—131no—
263#1763—131no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13—21no—
272C23×C13—21no—
273C23×C13—21no—
274C23×C13—21no—
275C23×C13—21no—
276C23×C13—21no—
277C23×C13#13712yes—
278C23×C13C22×D411yescharacteristic
279Q8×C13—41no—
280Q8×C13—41no—
281Q8×C13—41no—
282Q8×C13—41no—
283Q8×C13—41no—
284Q8×C13—41no—
285Q8×C13—41no—
286Q8×C13—41no—
287D4×C13—44no—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—21no—
299C2×C4×C13—21no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13#12112yes—
319C2×C4×C13#12112yes—
320C2×C4×C13C22×D411yescharacteristic
321C2×C4×C13C22×D411yescharacteristic
322C2×C4×C13C2×#4111yescharacteristic
323C2×C4×C13C2×#4111yescharacteristic
324C2×C4×C13H(5,𝔽2)11yescharacteristic
325C2×C4×C13H(5,𝔽2)11yescharacteristic
326C2×Dic13—22no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338Dic26—22no—
339Dic26—22no—
340Dic26—41no—
341Dic26—41no—
342#1055—22no—
343#1055—22no—
344#1055—22no—
345#1055—41no—
346C22×Q16—131no—
347C22×Q16—131no—
348C22×M16—131no—
349C23×C8—131no—
350C2×C4⋊Q8C2×D1311yescharacteristic
351C2×C22⋊Q8—131no—
352C2×C22⋊Q8—131no—
353C2×C22⋊Q8C2×D1311yescharacteristic
354C2×C22⋊Q8C2×D1311yescharacteristic
355C2×C22⋊Q8C2×D1311yescharacteristic
356C2×C22⋊Q8C2×D1311yescharacteristic
357C2×C4×Q8—131no—
358C2×C4×D4C2×D1311yescharacteristic
359#470—264no—
360#467—264no—
361#462—264no—
362#435—264no—
363C2×#107—131no—
364C2×#106—131no—
365C2×C4⋊C8—131no—
366C2×#103—131no—
367C2×#103—131no—
368C2×#103—131no—
369C2×#103—131no—
370C2×#103—131no—
371C2×#103—131no—
372C2×#103—131no—
373C2×#103—131no—
374C2×C22⋊C8—131no—
375C2×C22⋊C8—131no—
376C2×#97—131no—
377#399—21no—
378#399—21no—
379#398—261no—
380#394—261no—
381#390—21no—
382#388—261no—
383#388—261no—
384#384—21no—
385#382—131no—
386#380—131no—
387#380—131no—
388C4×C4⋊C4C2×D1311yescharacteristic
389#340—131no—
390#340—131no—
391#340—131no—
392#340—131no—
393C22×C13—22no—
394C22×C13—22no—
395C22×C13—22no—
396C22×C13—41no—
397C22×C13—41no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—41no—
401C22×C13—41no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13—41no—
405C22×C13—41no—
406C22×C13—41no—
407C22×C13C2×#12111yescharacteristic
408C22×C13D4211yescharacteristic
409C22×C13#54611yescharacteristic
410C22×C13C2×#13711yescharacteristic
411C22×C13#57511yescharacteristic
412C22×C13#57811yescharacteristic
413C22×C13#57811yescharacteristic
414C4×C13—22no—
415C4×C13—22no—
416C4×C13—41no—
417C4×C13—41no—
418C4×C13—42no—
419C4×C13—42no—
420C4×C13—81no—
421C4×C13—81no—
422C4×C13#53211yescharacteristic
423C4×C13#54011yescharacteristic
424C4×C13D4211yescharacteristic
425C4×C13#55011yescharacteristic
426Dic13—42no—
427Dic13—81no—
428Dic13—81no—
429Dic13—81no—
430C22×Q8—131no—
431C22×Q8C22×D1311yescharacteristic
432C22×Q8C22×D1311yescharacteristic
433C22×D4C22⋊D1311yescharacteristic
434C23×C4C22×D1311yescharacteristic
435C23×C4C22×D1311yescharacteristic
436C2×Q16—262no—
437C2×Q16—262no—
438C2×Q16—262no—
439C2×Q16—262no—
440C2×Q16—521no—
441C2×Q16—521no—
442C2×M16—262no—
443C2×M16—262no—
444C2×M16—521no—
445C22×C8—131no—
446C22×C8—131no—
447C22×C8—131no—
448C22×C8—131no—
449C22×C8—262no—
450C22×C8—262no—
451C22×C8—521no—
452C4⋊Q8—22no—
453C4⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456C22⋊Q8—22no—
457C22⋊Q8—22no—
458C22⋊Q8—41no—
459C22⋊Q8—41no—
460C22⋊Q8—41no—
461C22⋊Q8—41no—
462C22⋊Q8—262no—
463C22⋊Q8—262no—
464C22⋊Q8—521no—
465C22⋊Q8—521no—
466C4×Q8—262no—
467C4×Q8—262no—
468C4×D4—22no—
469C4×D4—22no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—131no—
477C2×C4⋊C4—131no—
478C2×C4⋊C4—131no—
479C2×C4⋊C4—261no—
480C2×C4⋊C4—261no—
481C2×C4⋊C4—261no—
482C2×C4⋊C4C22⋊D1311yescharacteristic
483C2×C4⋊C4C22×D1311yescharacteristic
484C2×C4⋊C4C22×D1311yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—261no—
490C2×C22⋊C4—261no—
491C2×C22⋊C4—261no—
492C2×C22⋊C4—261no—
493C2×C22⋊C4C22⋊D1311yescharacteristic
494C2×C22⋊C4C22⋊D1311yescharacteristic
495C2×C42—21no—
496C2×C42—261no—
497C2×C42C22×D1311yescharacteristic
498#107—262no—
499#106—262no—
500C4⋊C8—134no—
501#103—134no—
502#103—262no—
503#103—262no—
504#103—262no—
505#103—262no—
506#103—262no—
507#103—521no—
508#103—521no—
509C22⋊C8—262no—
510C22⋊C8—262no—
511#97—262no—
512#95—21no—
513#95—261no—
514#95—261no—
515#95—261no—
516#95—261no—
517C2×C13—42no—
518C2×C13—81no—
519C2×C13#242811yescharacteristic
520C2×C13#305611yescharacteristic
521C2×C13#305911yescharacteristic
522C2×C13#326911yescharacteristic
523C2×C13#327011yescharacteristic
524C2×C13#331211yescharacteristic
525C2×C13#331511yescharacteristic
526C24C2×C22⋊D1311yescharacteristic
527C24C2×C22⋊D1311yescharacteristic
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—132no—
541C2×Q8—261no—
542C2×Q8—261no—
543C2×Q8—261no—
544C2×Q8—261no—
545C2×Q8—261no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—41no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4C2×C22⋊D1311yescharacteristic
570C22×C4C2×C22⋊D1311yescharacteristic
571C22×C4C2×C22⋊D1311yescharacteristic
572C22×C4C2×C22⋊D1311yescharacteristic
573C22×C4C23×D1311yescharacteristic
574Q16—524no—
575Q16—524no—
576M16—524no—
577C2×C8—132no—
578C2×C8—132no—
579C2×C8—132no—
580C2×C8—261no—
581C2×C8—261no—
582C2×C8—261no—
583C2×C8—261no—
584C2×C8—261no—
585C2×C8—261no—
586C2×C8—261no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8—524no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—261no—
600C4⋊C4—261no—
601C4⋊C4—261no—
602C4⋊C4—261no—
603C4⋊C4—261no—
604C4⋊C4—261no—
605C4⋊C4—522no—
606C4⋊C4—522no—
607C4⋊C4—522no—
608C4⋊C4D4×D1312yes—
609C4⋊C4#612912yes—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—522no—
617C22⋊C4—522no—
618C22⋊C4—522no—
619C22⋊C4—522no—
620C42—42no—
621C42—522no—
622C42D4×D1312yes—
623C42#612912yes—
624C13#2539811yescharacteristic, complemented, Sylow
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23#8819612yes—
639C23C22×C22⋊D1311yescharacteristic
640Q8—41no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—262no—
649Q8—262no—
650Q8—521no—
651Q8—521no—
652D4—44no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—262no—
684C2×C4—521no—
685C2×C4—521no—
686C2×C4—521no—
687C2×C4—521no—
688C2×C4—521no—
689C2×C4—521no—
690C2×C4—521no—
691C2×C4—521no—
692C2×C4—521no—
693C2×C4—521no—
694C2×C4—521no—
695C2×C4#8819312yes—
696C2×C4#8819312yes—
697C2×C4C2×D4×D1311yescharacteristic
698C2×C4C2×D4×D1311yescharacteristic
699C2×C4C2×#612911yescharacteristic
700C2×C4C2×#612911yescharacteristic
701C2×C4#8825111yescharacteristic
702C2×C4#8825111yescharacteristic
703C8—262no—
704C8—262no—
705C8—262no—
706C8—521no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22D4×C22⋊D1311yescharacteristic
722C22C2×#8819311yescharacteristic
723C22#1171951111yescharacteristic
724C22C2×#8819611yescharacteristic
725C22#1171952711yescharacteristic
726C22#1171954311yescharacteristic
727C22#1171954311yescharacteristic
728C4—22no—
729C4—22no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—42no—
734C4—81no—
735C4—81no—
736C4—522no—
737C4—1041no—
738C4—1041no—
739C4—1041no—
740C4#1171942111yescharacteristic
741C4#1171942211yescharacteristic
742C4#1171942311yescharacteristic
743C4#1171942411yescharacteristic
744C2—42no—
745C2—81no—
746C2#1311842711yescharacteristic
747C2#1312446211yescharacteristic
748C2#1312448811yescharacteristic
749C2#1312638711yescharacteristic
750C2#1312640711yescharacteristic
751C2#1312688711yescharacteristic
752C2#1312693211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2542C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenter#2542D13
hypocenterC13#25398
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. C2×#11718713C2semidirect
2. C2×#11718712C2semidirect
3. C2×#11718751C2semidirect
6. #13116036C2semidirect
7. #13116029C2semidirect
8. #13115844C2semidirect
9. #13115844C2semidirect
10. #13115657C2semidirect
11. #13115604C2semidirect
12. #13115270C2semidirect
13. #13115260C2semidirect
14. #13114669C2semidirect
145. #88050D4semidirect
624. C13#25398semidirect

Maximal subgroups

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

subgroupindex
C2×#117187132
C2×#117187122
C2×#117187512
C2×#117186722
#131197452
#131160362
#131160292
#131158442
#131156572
#131156042
#131152702
#131152602
#131146692
C13×#25422
#2539813