Finite Group Databasebeta

← #15770487

Subgroups — #15770487

Order 3328.

1206 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88060C211yesmaximal, characteristic
2C22×#88060C211yesmaximal, characteristic
3C2×C4×#6103C211yesmaximal, characteristic
4C2×#11718116C211yesmaximal, characteristic, complemented
5C2×#11718142C211yesmaximal, characteristic, complemented
6C2×#11718142C211yesmaximal, characteristic, complemented
7C2×C13×#336C211yesmaximal, characteristic, complemented
8C23×C4×D13C2211yescharacteristic
9C23×C8×C13C2211yescharacteristic
10C23×C8×C13C2211yescharacteristic
11C22×C42×C13C2211yescharacteristic
12C22×#6103C411yescharacteristic
13C22×#6103C411yescharacteristic
14C22×C4×Dic13C2211yescharacteristic
15C23×#1055C2211yescharacteristic
16C23×#1055C2211yescharacteristic
17C2×#88071C411yescharacteristic
18C2×#88071C411yescharacteristic
19C2×#88060—22no—
20C2×#88060—22no—
21C2×#88060—22no—
22C2×#88060—22no—
23C2×#88060—22no—
24C2×#88060—22no—
25C4×#6103—22no—
26C4×#6103—22no—
27C13×#336—22no—
28#11718142—22no—
29#11718142—22no—
30#11718116—22no—
31C24×D13C2×C411yescharacteristic
32C23×C4×C13C2×C411yescharacteristic
33C23×C4×C13C2×C411yescharacteristic
34C23×C4×C13C2311yescharacteristic
35C23×Dic13C2×C411yescharacteristic
36C23×Dic13C2×C411yescharacteristic
37C23×Dic13C2×C411yescharacteristic
38C22×C4×D13—21no—
39C22×C4×D13—21no—
40C22×C4×D13—21no—
41C22×C4×D13—21no—
42C22×C4×D13—21no—
43C22×C4×D13—21no—
44C22×C4×D13—21no—
45C22×C4×D13—21no—
46C22×C4×D13—21no—
47C22×C4×D13—21no—
48C22×C4×D13—21no—
49C22×C4×D13—21no—
50C22×C4×D13D412yes—
51C22×C4×D13D412yes—
52C22×C8×C13—21no—
53C22×C8×C13—21no—
54C22×C8×C13—21no—
55C22×C8×C13—21no—
56C22×C8×C13—21no—
57C22×C8×C13—21no—
58C22×C8×C13—21no—
59C22×C8×C13—21no—
60C22×C8×C13—21no—
61C22×C8×C13—21no—
62C22×C8×C13—21no—
63C22×C8×C13—21no—
64C22×C8×C13D412yes—
65C22×C8×C13D412yes—
66C2×C42×C13—21no—
67C2×C42×C13—21no—
68C2×C42×C13—21no—
69C2×C42×C13—21no—
70C2×C42×C13—21no—
71C2×C42×C13—21no—
72C2×#6103—22no—
73C2×#6103—22no—
74C2×#6103—22no—
75C2×#6103—22no—
76C2×#6103—22no—
77C2×#6103C814yescomplemented
78C2×C4×Dic13—21no—
79C2×C4×Dic13—21no—
80C2×C4×Dic13—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13—21no—
83C2×C4×Dic13—21no—
84C22×#1055—21no—
85C22×#1055—21no—
86C22×#1055—21no—
87C22×#1055—21no—
88C22×#1055—21no—
89C22×#1055—21no—
90C22×#1055—21no—
91C22×#1055—21no—
92C22×#1055—21no—
93C22×#1055—21no—
94C22×#1055—21no—
95C22×#1055—21no—
96C22×#1055D412yes—
97C22×#1055D412yes—
98#88071—22no—
99#88071—22no—
100#88060—28no—
101#88060—28no—
102#11147—131nomaximal, Sylow
103C24×C13C22×C411yescharacteristic
104C23×D13—21no—
105C23×D13—21no—
106C23×D13—21no—
107C23×D13—21no—
108C23×D13—21no—
109C23×D13—21no—
110C23×D13—21no—
111C23×D13—21no—
112C23×D13—21no—
113C23×D13—21no—
114C23×D13—21no—
115C23×D13—21no—
116C23×D13C22⋊C412yes—
117C23×D13C2×C812yes—
118C23×D13M1612yes—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13C2×C812yes—
132C22×C4×C13M1612yes—
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13#4111yescharacteristic
140C22×C4×C13#4111yescharacteristic
141C22×C4×C13#4111yescharacteristic
142C22×C4×C13#4111yescharacteristic
143C22×C4×C13#4111yescharacteristic
144C22×C4×C13#4111yescharacteristic
145C22×C4×C13#4111yescharacteristic
146C22×C4×C13#4111yescharacteristic
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13C22⋊C412yes—
166C22×Dic13C2×C812yes—
167C22×Dic13M1612yes—
168C2×C4×D13—22no—
169C2×C4×D13—22no—
170C2×C4×D13—22no—
171C2×C4×D13—22no—
172C2×C4×D13—22no—
173C2×C4×D13—22no—
174C2×C4×D13—22no—
175C2×C4×D13—22no—
176C2×C4×D13—22no—
177C2×C4×D13—22no—
178C2×C4×D13—22no—
179C2×C4×D13—22no—
180C2×C4×D13—41no—
181C2×C4×D13—41no—
182C2×C4×D13—41no—
183C2×C4×D13—41no—
184C2×C4×D13—41no—
185C2×C4×D13—41no—
186C2×C4×D13—41no—
187C2×C4×D13—41no—
188C2×C4×D13—41no—
189C2×C4×D13—41no—
190C2×C4×D13—41no—
191C2×C4×D13—41no—
192C2×C4×D13—41no—
193C2×C4×D13—41no—
194C2×C4×D13—41no—
195C2×C4×D13—41no—
196C2×C8×C13—22no—
197C2×C8×C13—22no—
198C2×C8×C13—22no—
199C2×C8×C13—22no—
200C2×C8×C13—22no—
201C2×C8×C13—22no—
202C2×C8×C13—41no—
203C2×C8×C13—41no—
204C2×C8×C13—41no—
205C2×C8×C13—41no—
206C2×C8×C13—41no—
207C2×C8×C13—41no—
208C2×C8×C13—41no—
209C2×C8×C13—41no—
210C42×C13—41no—
211C42×C13—41no—
212C42×C13—41no—
213C42×C13—41no—
214#6103—28no—
215#6103—28no—
216C4×Dic13—41no—
217C4×Dic13—41no—
218C4×Dic13—41no—
219C4×Dic13—41no—
220C2×#1055—22no—
221C2×#1055—22no—
222C2×#1055—22no—
223C2×#1055—22no—
224C2×#1055—22no—
225C2×#1055—22no—
226C2×#1055—41no—
227C2×#1055—41no—
228C2×#1055—41no—
229C2×#1055—41no—
230C2×#1055—41no—
231C2×#1055—41no—
232C2×#1055—41no—
233C2×#1055—41no—
234C22×C22⋊C8—131no—
235C22×C22⋊C8—131no—
236C2×C4×C22⋊C4—131no—
237C2×#336—131no—
238C2×#336—131no—
239C2×#336—131no—
240C2×#336D1311yescharacteristic, complemented
241C23×C13C2×C22⋊C411yescharacteristic
242C23×C13#11711yescharacteristic
243C23×C13#11711yescharacteristic
244C23×C13C4×D411yescharacteristic
245C23×C13C4×D411yescharacteristic
246C23×C13C4×D411yescharacteristic
247C23×C13C4×D411yescharacteristic
248C23×C13C22×C811yescharacteristic
249C23×C13C2×M1611yescharacteristic
250C23×C13C2×M1611yescharacteristic
251C23×C13C2×M1611yescharacteristic
252C23×C13#13111yescharacteristic
253C23×C13#13111yescharacteristic
254C23×C13#13111yescharacteristic
255C23×C13#13111yescharacteristic
256C22×D13—22no—
257C22×D13—22no—
258C22×D13—22no—
259C22×D13—22no—
260C22×D13—22no—
261C22×D13—22no—
262C22×D13—22no—
263C22×D13—22no—
264C22×D13—22no—
265C22×D13—22no—
266C22×D13—22no—
267C22×D13—22no—
268C22×D13—22no—
269C22×D13—22no—
270C22×D13—22no—
271C22×D13—22no—
272C22×D13—22no—
273C22×D13—22no—
274C22×D13—41no—
275C22×D13—41no—
276C22×D13—41no—
277C22×D13—41no—
278C22×D13—41no—
279C22×D13—41no—
280C22×D13—41no—
281C22×D13—41no—
282C22×D13—41no—
283C22×D13—41no—
284C22×D13—41no—
285C22×D13—41no—
286C22×D13—41no—
287C22×D13—41no—
288C22×D13—41no—
289C22×D13—41no—
290C22×D13C22⋊C814yes—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13#12011yescharacteristic
306C2×C4×C13#12011yescharacteristic
307C2×C4×C13#12111yescharacteristic
308C2×C4×C13#12111yescharacteristic
309C2×C4×C13#12111yescharacteristic
310C2×C4×C13#12111yescharacteristic
311C2×C4×C13#12111yescharacteristic
312C2×C4×C13#12111yescharacteristic
313C2×C4×C13#12111yescharacteristic
314C2×C4×C13#12111yescharacteristic
315C2×C4×C13#12311yescharacteristic
316C2×C4×C13#12311yescharacteristic
317C2×C4×C13#12311yescharacteristic
318C2×C4×C13#12311yescharacteristic
319C2×C4×C13#12311yescharacteristic
320C2×C4×C13#12311yescharacteristic
321C2×C4×C13#12311yescharacteristic
322C2×C4×C13#12311yescharacteristic
323C2×C4×C13#12311yescharacteristic
324C2×C4×C13#12311yescharacteristic
325C2×C4×C13#12411yescharacteristic
326C2×C4×C13#12411yescharacteristic
327C2×C4×C13#12411yescharacteristic
328C2×C4×C13#12411yescharacteristic
329C2×C4×C13#12611yescharacteristic
330C2×C4×C13#12611yescharacteristic
331C2×C4×C13#12611yescharacteristic
332C2×C4×C13#12611yescharacteristic
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345C2×Dic13—41no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—41no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C4×D13—42no—
355C4×D13—42no—
356C4×D13—42no—
357C4×D13—42no—
358C4×D13—42no—
359C4×D13—42no—
360C4×D13—42no—
361C4×D13—42no—
362C8×C13—42no—
363C8×C13—42no—
364#1055—42no—
365#1055—42no—
366C24×C4—131no—
367C23×C8—131no—
368C23×C8—131no—
369C23×C8C2×D1311yescharacteristic
370C23×C8C2×D1311yescharacteristic
371C22×C22⋊C4—131no—
372C22×C22⋊C4—131no—
373C22×C42—131no—
374C22×C42C2×D1311yescharacteristic
375C2×C22⋊C8—262no—
376C2×C22⋊C8—262no—
377C2×C22⋊C8—262no—
378C2×C22⋊C8—262no—
379C2×C22⋊C8—262no—
380C2×C22⋊C8—262no—
381C4×C22⋊C4—262no—
382C4×C22⋊C4—262no—
383C2×#95—131no—
384C2×#95—131no—
385#336—22no—
386#336—262no—
387#336—262no—
388#336—262no—
389C22×C13#38111yescharacteristic
390C22×C13#38611yescharacteristic
391C22×C13#38611yescharacteristic
392C22×C13#38811yescharacteristic
393C22×C13#38811yescharacteristic
394C22×C13#38811yescharacteristic
395C22×C13#38811yescharacteristic
396C22×C13C2×C22⋊C811yescharacteristic
397C22×C13#40711yescharacteristic
398C22×C13#40811yescharacteristic
399C22×C13#40811yescharacteristic
400C22×C13#43111yescharacteristic
401C22×C13#43111yescharacteristic
402C22×C13#43211yescharacteristic
403C22×C13#43211yescharacteristic
404C22×C13#43311yescharacteristic
405C22×C13#43311yescharacteristic
406C22×C13#43311yescharacteristic
407C22×C13#43311yescharacteristic
408C22×C13C8×D411yescharacteristic
409C22×C13C8×D411yescharacteristic
410C22×C13C8×D411yescharacteristic
411C22×C13C8×D411yescharacteristic
412C22×C13#43511yescharacteristic
413C22×C13#43511yescharacteristic
414C22×C13#43511yescharacteristic
415C22×C13#43511yescharacteristic
416C22×C13#43511yescharacteristic
417C22×C13#43511yescharacteristic
418C22×C13#43511yescharacteristic
419C22×C13#43511yescharacteristic
420C22×C13#43611yescharacteristic
421C22×C13#43611yescharacteristic
422C22×C13#43611yescharacteristic
423C22×C13#43611yescharacteristic
424C2×D13—24no—
425C2×D13—24no—
426C2×D13—24no—
427C2×D13—42no—
428C2×D13—42no—
429C2×D13—42no—
430C2×D13—42no—
431C2×D13—42no—
432C2×D13—42no—
433C2×D13—42no—
434C2×D13—42no—
435C2×D13—42no—
436C2×D13—42no—
437C2×D13—42no—
438C2×D13—42no—
439C4×C13—42no—
440C4×C13—42no—
441C4×C13#39411yescharacteristic
442C4×C13#39411yescharacteristic
443C4×C13#39411yescharacteristic
444C4×C13#39411yescharacteristic
445C4×C13#39711yescharacteristic
446C4×C13#39711yescharacteristic
447C4×C13#39711yescharacteristic
448C4×C13#39711yescharacteristic
449Dic13—42no—
450Dic13—42no—
451Dic13—42no—
452C25—131no—
453C23×C4—131no—
454C23×C4—131no—
455C23×C4—131no—
456C23×C4—132no—
457C23×C4—132no—
458C23×C4—261no—
459C23×C4—261no—
460C23×C4—261no—
461C23×C4—261no—
462C23×C4—261no—
463C23×C4—261no—
464C23×C4—261no—
465C23×C4—261no—
466C23×C4—261no—
467C23×C4—261no—
468C23×C4—261no—
469C23×C4—261no—
470C23×C4C4×D1311yescharacteristic
471C23×C4C4×D1311yescharacteristic
472C23×C4C22×D1311yescharacteristic
473C22×C8—21no—
474C22×C8—21no—
475C22×C8—21no—
476C22×C8—21no—
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—132no—
486C22×C8—132no—
487C22×C8—261no—
488C22×C8—261no—
489C22×C8—261no—
490C22×C8—261no—
491C22×C8—261no—
492C22×C8—261no—
493C22×C8—261no—
494C22×C8—261no—
495C22×C8—261no—
496C22×C8—261no—
497C22×C8—261no—
498C22×C8—261no—
499C22×C8D5212yes—
500C22×C8C22⋊D1312yes—
501C2×C22⋊C4—134no—
502C2×C22⋊C4—262no—
503C2×C22⋊C4—262no—
504C2×C22⋊C4—262no—
505C2×C22⋊C4—262no—
506C2×C22⋊C4—262no—
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42—21no—
511C2×C42—21no—
512C2×C42—21no—
513C2×C42—261no—
514C2×C42—261no—
515C2×C42—261no—
516C2×C42—261no—
517C2×C42—261no—
518C2×C42—261no—
519C22⋊C8—268no—
520C22⋊C8—268no—
521#95—262no—
522#95—262no—
523C2×C13#144011yescharacteristic
524C2×C13#181711yescharacteristic
525C2×C13#181811yescharacteristic
526C2×C13#186911yescharacteristic
527C2×C13#186911yescharacteristic
528C2×C13#187011yescharacteristic
529C2×C13#187011yescharacteristic
530C2×C13#192311yescharacteristic
531C2×C13#192311yescharacteristic
532C2×C13#192311yescharacteristic
533C2×C13#192311yescharacteristic
534C2×C13#192411yescharacteristic
535C2×C13#192411yescharacteristic
536C2×C13#192411yescharacteristic
537C2×C13#192411yescharacteristic
538D13—44no—
539C24—132no—
540C24—132no—
541C24—132no—
542C24—261no—
543C24—261no—
544C24—261no—
545C24—261no—
546C24—261no—
547C24—261no—
548C24—261no—
549C24—261no—
550C24—261no—
551C24—261no—
552C24—261no—
553C24—261no—
554C24C2×C4×D1311yescharacteristic
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—21no—
566C22×C4—21no—
567C22×C4—132no—
568C22×C4—132no—
569C22×C4—132no—
570C22×C4—261no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—521no—
601C22×C4—521no—
602C22×C4—521no—
603C22×C4—521no—
604C22×C4—521no—
605C22×C4—521no—
606C22×C4—521no—
607C22×C4—521no—
608C22×C4—521no—
609C22×C4—521no—
610C22×C4—521no—
611C22×C4—521no—
612C22×C4—521no—
613C22×C4—521no—
614C22×C4—521no—
615C22×C4—521no—
616C22×C4C8×D1312yes—
617C22×C4#609412yes—
618C22×C4C2×D5211yescharacteristic
619C22×C4#612711yescharacteristic
620C22×C4#612711yescharacteristic
621C22×C4#612711yescharacteristic
622C22×C4#612711yescharacteristic
623C22×C4D4×D1311yescharacteristic
624C22×C4D4×D1311yescharacteristic
625C22×C4D4×D1311yescharacteristic
626C22×C4D4×D1311yescharacteristic
627C22×C4#612911yescharacteristic
628C22×C4#612911yescharacteristic
629C22×C4#613111yescharacteristic
630C22×C4#613111yescharacteristic
631C22×C4C2×C22⋊D1311yescharacteristic
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—262no—
647C2×C8—262no—
648C2×C8—262no—
649C2×C8—262no—
650C2×C8—262no—
651C2×C8—262no—
652C2×C8—521no—
653C2×C8—521no—
654C2×C8—521no—
655C2×C8—521no—
656C2×C8—521no—
657C2×C8—521no—
658C2×C8—521no—
659C2×C8—521no—
660C22⋊C4—268no—
661C22⋊C4—268no—
662C42—41no—
663C42—41no—
664C42—41no—
665C42—41no—
666C42—521no—
667C42—521no—
668C42—521no—
669C42—521no—
670C13#1114711yescharacteristic, complemented, Sylow
671C23—134no—
672C23—262no—
673C23—262no—
674C23—262no—
675C23—262no—
676C23—262no—
677C23—262no—
678C23—262no—
679C23—262no—
680C23—262no—
681C23—262no—
682C23—262no—
683C23—262no—
684C23—262no—
685C23—262no—
686C23—262no—
687C23—262no—
688C23—262no—
689C23—262no—
690C23—521no—
691C23—521no—
692C23—521no—
693C23—521no—
694C23—521no—
695C23—521no—
696C23—521no—
697C23—521no—
698C23—521no—
699C23—521no—
700C23—521no—
701C23—521no—
702C23—521no—
703C23—521no—
704C23—521no—
705C23—521no—
706C23#8812611yescharacteristic
707C23C4×D5211yescharacteristic
708C23C22⋊C4×D1311yescharacteristic
709C23#8813511yescharacteristic
710C23#8814611yescharacteristic
711C23#8814711yescharacteristic
712C23C2×C8×D1311yescharacteristic
713C23C2×#609411yescharacteristic
714C23#8815511yescharacteristic
715C23#8815511yescharacteristic
716C23M16×D1311yescharacteristic
717C23M16×D1311yescharacteristic
718C23#8816111yescharacteristic
719C23#8816111yescharacteristic
720C23C4×C22⋊D1311yescharacteristic
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—521no—
745C2×C4—521no—
746C2×C4—521no—
747C2×C4—521no—
748C2×C4—521no—
749C2×C4—521no—
750C2×C4—521no—
751C2×C4—521no—
752C2×C4—521no—
753C2×C4—521no—
754C2×C4—521no—
755C2×C4—521no—
756C2×C4—522no—
757C2×C4—522no—
758C2×C4—522no—
759C2×C4—522no—
760C2×C4—522no—
761C2×C4—522no—
762C2×C4—522no—
763C2×C4—522no—
764C2×C4#8812911yescharacteristic
765C2×C4#8813011yescharacteristic
766C2×C4#8813611yescharacteristic
767C2×C4#8813711yescharacteristic
768C2×C4#8813711yescharacteristic
769C2×C4#8813711yescharacteristic
770C2×C4#8813811yescharacteristic
771C2×C4#8813811yescharacteristic
772C2×C4#8813811yescharacteristic
773C2×C4#8813911yescharacteristic
774C2×C4#8813911yescharacteristic
775C2×C4#8814011yescharacteristic
776C2×C4#8814811yescharacteristic
777C2×C4#8814811yescharacteristic
778C2×C4#8814811yescharacteristic
779C2×C4#8814811yescharacteristic
780C2×C4#8814811yescharacteristic
781C2×C4#8814911yescharacteristic
782C2×C4#8814911yescharacteristic
783C2×C4#8815211yescharacteristic
784C2×C4#8815211yescharacteristic
785C2×C4#8815211yescharacteristic
786C2×C4#8818311yescharacteristic
787C2×C4#8818411yescharacteristic
788C2×C4#8819111yescharacteristic
789C2×C4#8819211yescharacteristic
790C2×C4#8819311yescharacteristic
791C2×C4#8820111yescharacteristic
792C8—42no—
793C8—42no—
794C8—522no—
795C8—522no—
796C22—264no—
797C22—264no—
798C22—264no—
799C22—522no—
800C22—522no—
801C22—522no—
802C22—522no—
803C22—522no—
804C22—522no—
805C22—522no—
806C22—522no—
807C22—522no—
808C22—522no—
809C22—522no—
810C22—522no—
811C22#1171832511yescharacteristic
812C22#1171832611yescharacteristic
813C22#1171833011yescharacteristic
814C22#1171833111yescharacteristic
815C22#1171834611yescharacteristic
816C22C8×D5211yescharacteristic
817C22#1171834911yescharacteristic
818C22#1171835111yescharacteristic
819C22#1171836611yescharacteristic
820C22#1171836711yescharacteristic
821C22#1171836711yescharacteristic
822C22#1171837011yescharacteristic
823C22D13×C22⋊C811yescharacteristic
824C22#1171838611yescharacteristic
825C22#1171838711yescharacteristic
826C22#1171838811yescharacteristic
827C22#1171838811yescharacteristic
828C22#1171838911yescharacteristic
829C22#1171839011yescharacteristic
830C22#1171839111yescharacteristic
831C22#1171849411yescharacteristic
832C22#1171849511yescharacteristic
833C22#1171849611yescharacteristic
834C22#1171849711yescharacteristic
835C22#1171849711yescharacteristic
836C22#1171849911yescharacteristic
837C22#1171850111yescharacteristic
838C22#1171850111yescharacteristic
839C22#1171860111yescharacteristic
840C22#1171861711yescharacteristic
841C22#1171865111yescharacteristic
842C22C8×C22⋊D1311yescharacteristic
843C22#1171877211yescharacteristic
844C22#1171878811yescharacteristic
845C22#1171878911yescharacteristic
846C4—42no—
847C4—42no—
848C4—522no—
849C4—522no—
850C4—522no—
851C4#1171833311yescharacteristic
852C4#1171833511yescharacteristic
853C4#1171833611yescharacteristic
854C4#1171833611yescharacteristic
855C4#1171862011yescharacteristic
856C4#1171862211yescharacteristic
857C4#1171865211yescharacteristic
858C4#1171865411yescharacteristic
859C2—524no—
860C2#1311308411yescharacteristic
861C2#1311490311yescharacteristic
862C2#1311490611yescharacteristic
863C2#1311512511yescharacteristic
864C2#1311512711yescharacteristic
865C2#1311513011yescharacteristic
866C2#1311513211yescharacteristic
867C2#1311544011yescharacteristic
868C2#1311544111yescharacteristic
869C2#1311544211yescharacteristic
870C2#1311544311yescharacteristic
871C2#1311544711yescharacteristic
872C2#1311544811yescharacteristic
873C2#1311544911yescharacteristic
874C2#1311545011yescharacteristic
subgroupG/H
center, FrattiniC23×C4C22×D13
commutatorC23×C13C22×C8
FittingC2×C13×#336C2
socleC24×C13C22×C4
prime radicalC24×D13C2×C4
cosocleC23×C4×C13C23
hypercenterC2×#336D13
hypocenterC13#11147
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
4. C2×#11718116C2semidirect
5. C2×#11718142C2semidirect
6. C2×#11718142C2semidirect
7. C2×C13×#336C2semidirect
77. C2×#6103C8semidirect
240. C2×#336D13semidirect
670. C13#11147semidirect

Maximal subgroups

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

subgroupindex
C22×#880602
C2×C4×#61032
C2×#117181162
C2×#117181422
C2×C13×#3362
#1114713