Finite Group Databasebeta

← #15769837

Subgroups — #15769837

Order 3328.

1262 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88054C211yesmaximal, characteristic, complemented
2C22×#88060C211yesmaximal, characteristic
3C22×#88060C211yesmaximal, characteristic
4C2×C4×#6103C211yesmaximal, characteristic
5C2×#11718116C211yesmaximal, 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—
25C2×#88054—22no—
26C2×#88054—22no—
27C2×#88054—22no—
28C4×#6103—22no—
29C4×#6103—22no—
30C13×#336—22no—
31#11718142—22no—
32#11718116—22no—
33C24×D13C2×C411yescharacteristic
34C23×C4×C13C2×C411yescharacteristic
35C23×C4×C13C2×C411yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C23×Dic13C2×C411yescharacteristic
38C23×Dic13C2×C411yescharacteristic
39C23×Dic13C2×C411yescharacteristic
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×D13—21no—
51C22×C4×D13—21no—
52C22×C4×D13D412yes—
53C22×C4×D13Q812yes—
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×C13—21no—
65C22×C8×C13—21no—
66C22×C8×C13D412yes—
67C22×C8×C13D412yes—
68C2×C42×C13—21no—
69C2×C42×C13—21no—
70C2×C42×C13—21no—
71C2×C42×C13—21no—
72C2×C42×C13—21no—
73C2×C42×C13—21no—
74C2×#6103—22no—
75C2×#6103—22no—
76C2×#6103—22no—
77C2×#6103—22no—
78C2×#6103—22no—
79C2×#6103C814yescomplemented
80C2×C4×Dic13—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13—21no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13D412yes—
85C2×C4×Dic13D412yes—
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×#1055—21no—
97C22×#1055—21no—
98C22×#1055D412yes—
99C22×#1055D412yes—
100#88071—22no—
101#88071—22no—
102#88060—28no—
103#88060—28no—
104#88054—28no—
105#11042—131nomaximal, Sylow
106C24×C13C22×C411yescharacteristic
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×D13—21no—
117C23×D13—21no—
118C23×D13—21no—
119C23×D13C4⋊C412yes—
120C23×D13C2×C812yes—
121C23×D13M1612yes—
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×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13C2×C812yes—
135C22×C4×C13M1612yes—
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×Q811yescharacteristic
144C22×C4×C13#4111yescharacteristic
145C22×C4×C13#4111yescharacteristic
146C22×C4×C13#4111yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C22×C4×C13#4111yescharacteristic
149C22×C4×C13#4111yescharacteristic
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×Dic13—21no—
166C22×Dic13C22⋊C412yes—
167C22×Dic13C22⋊C412yes—
168C22×Dic13C4⋊C412yes—
169C22×Dic13C2×C812yes—
170C22×Dic13M1612yes—
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—22no—
181C2×C4×D13—22no—
182C2×C4×D13—22no—
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×C4×D13—41no—
197C2×C4×D13—41no—
198C2×C4×D13—41no—
199C2×C8×C13—22no—
200C2×C8×C13—22no—
201C2×C8×C13—22no—
202C2×C8×C13—22no—
203C2×C8×C13—22no—
204C2×C8×C13—22no—
205C2×C8×C13—41no—
206C2×C8×C13—41no—
207C2×C8×C13—41no—
208C2×C8×C13—41no—
209C2×C8×C13—41no—
210C2×C8×C13—41no—
211C2×C8×C13—41no—
212C2×C8×C13—41no—
213C42×C13—41no—
214C42×C13—41no—
215C42×C13—41no—
216C42×C13—41no—
217#6103—28no—
218#6103—28no—
219C4×Dic13—22no—
220C4×Dic13—22no—
221C4×Dic13—22no—
222C4×Dic13—22no—
223C2×#1055—22no—
224C2×#1055—22no—
225C2×#1055—22no—
226C2×#1055—22no—
227C2×#1055—22no—
228C2×#1055—22no—
229C2×#1055—41no—
230C2×#1055—41no—
231C2×#1055—41no—
232C2×#1055—41no—
233C2×#1055—41no—
234C2×#1055—41no—
235C2×#1055—41no—
236C2×#1055—41no—
237C22×C4⋊C8—131no—
238C22×C22⋊C8—131no—
239C22×C22⋊C8—131no—
240C2×C4×C22⋊C4—131no—
241C2×#336—131no—
242C2×#336—131no—
243C2×#336D1311yescharacteristic, complemented
244C23×C13C2×C22⋊C411yescharacteristic
245C23×C13C2×C4⋊C411yescharacteristic
246C23×C13#11711yescharacteristic
247C23×C13C4×D411yescharacteristic
248C23×C13C4×D411yescharacteristic
249C23×C13C4×D411yescharacteristic
250C23×C13C4×D411yescharacteristic
251C23×C13C22×C811yescharacteristic
252C23×C13C2×M1611yescharacteristic
253C23×C13C2×M1611yescharacteristic
254C23×C13C2×M1611yescharacteristic
255C23×C13#13111yescharacteristic
256C23×C13#13111yescharacteristic
257C23×C13#13111yescharacteristic
258C23×C13#13111yescharacteristic
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—22no—
275C22×D13—22no—
276C22×D13—22no—
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×D13—41no—
291C22×D13—41no—
292C22×D13—41no—
293C22×D13C4⋊C814yescomplemented
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
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#12011yescharacteristic
309C2×C4×C13#12011yescharacteristic
310C2×C4×C13#12011yescharacteristic
311C2×C4×C13#12111yescharacteristic
312C2×C4×C13#12111yescharacteristic
313C2×C4×C13#12111yescharacteristic
314C2×C4×C13#12111yescharacteristic
315C2×C4×C13#12111yescharacteristic
316C2×C4×C13#12111yescharacteristic
317C2×C4×C13#12111yescharacteristic
318C2×C4×C13#12111yescharacteristic
319C2×C4×C13C22⋊Q811yescharacteristic
320C2×C4×C13C22⋊Q811yescharacteristic
321C2×C4×C13C22⋊Q811yescharacteristic
322C2×C4×C13C22⋊Q811yescharacteristic
323C2×C4×C13C22⋊Q811yescharacteristic
324C2×C4×C13C22⋊Q811yescharacteristic
325C2×C4×C13#12311yescharacteristic
326C2×C4×C13#12311yescharacteristic
327C2×C4×C13#12311yescharacteristic
328C2×C4×C13#12311yescharacteristic
329C2×C4×C13#12311yescharacteristic
330C2×C4×C13#12411yescharacteristic
331C2×C4×C13#12411yescharacteristic
332C2×C4×C13#12411yescharacteristic
333C2×C4×C13#12611yescharacteristic
334C2×C4×C13#12611yescharacteristic
335C2×C4×C13#12711yescharacteristic
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—41no—
349C2×Dic13—41no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—41no—
355C2×Dic13—41no—
356C2×Dic13C22⋊C814yescomplemented
357C4×D13—42no—
358C4×D13—42no—
359C4×D13—42no—
360C4×D13—42no—
361C4×D13—42no—
362C4×D13—42no—
363C4×D13—42no—
364C4×D13—42no—
365C8×C13—42no—
366C8×C13—42no—
367#1055—42no—
368#1055—42no—
369C24×C4—131no—
370C23×C8—131no—
371C23×C8—131no—
372C23×C8C2×D1311yescharacteristic
373C23×C8C2×D1311yescharacteristic
374C22×C22⋊C4—131no—
375C22×C22⋊C4—131no—
376C22×C42—131no—
377C22×C42C2×D1311yescharacteristic
378C2×C4⋊C8—262no—
379C2×C4⋊C8—262no—
380C2×C4⋊C8—262no—
381C2×C22⋊C8—262no—
382C2×C22⋊C8—262no—
383C2×C22⋊C8—262no—
384C2×C22⋊C8—262no—
385C2×C22⋊C8—262no—
386C2×C22⋊C8—262no—
387C4×C22⋊C4—262no—
388C4×C22⋊C4—262no—
389C2×#95—131no—
390C2×#95—131no—
391#336—22no—
392#336—262no—
393#336—262no—
394C22×C13#38011yescharacteristic
395C22×C13#38511yescharacteristic
396C22×C13#38511yescharacteristic
397C22×C13#38611yescharacteristic
398C22×C13#38811yescharacteristic
399C22×C13#38811yescharacteristic
400C22×C13#39011yescharacteristic
401C22×C13C2×C22⋊C811yescharacteristic
402C22×C13#40711yescharacteristic
403C22×C13#40811yescharacteristic
404C22×C13#40811yescharacteristic
405C22×C13C2×C4⋊C811yescharacteristic
406C22×C13#42311yescharacteristic
407C22×C13#42411yescharacteristic
408C22×C13#42411yescharacteristic
409C22×C13#43111yescharacteristic
410C22×C13#43211yescharacteristic
411C22×C13#43311yescharacteristic
412C22×C13#43311yescharacteristic
413C22×C13C8×D411yescharacteristic
414C22×C13C8×D411yescharacteristic
415C22×C13C8×D411yescharacteristic
416C22×C13C8×D411yescharacteristic
417C22×C13#43511yescharacteristic
418C22×C13#43511yescharacteristic
419C22×C13#43511yescharacteristic
420C22×C13#43511yescharacteristic
421C22×C13#43511yescharacteristic
422C22×C13#43511yescharacteristic
423C22×C13#43511yescharacteristic
424C22×C13#43511yescharacteristic
425C22×C13#43611yescharacteristic
426C22×C13#43611yescharacteristic
427C22×C13#43611yescharacteristic
428C22×C13#43611yescharacteristic
429C2×D13—24no—
430C2×D13—24no—
431C2×D13—24no—
432C2×D13—42no—
433C2×D13—42no—
434C2×D13—42no—
435C2×D13—42no—
436C2×D13—42no—
437C2×D13—42no—
438C2×D13—42no—
439C2×D13—42no—
440C2×D13—42no—
441C2×D13—42no—
442C2×D13—42no—
443C2×D13—42no—
444C4×C13—42no—
445C4×C13—42no—
446C4×C13#39211yescharacteristic
447C4×C13#39311yescharacteristic
448C4×C13#39411yescharacteristic
449C4×C13#39411yescharacteristic
450C4×C13#39611yescharacteristic
451C4×C13#39611yescharacteristic
452C4×C13#39711yescharacteristic
453C4×C13#39911yescharacteristic
454Dic13—24no—
455Dic13—42no—
456Dic13—42no—
457C25—131no—
458C23×C4—131no—
459C23×C4—131no—
460C23×C4—131no—
461C23×C4—132no—
462C23×C4—132no—
463C23×C4—261no—
464C23×C4—261no—
465C23×C4—261no—
466C23×C4—261no—
467C23×C4—261no—
468C23×C4—261no—
469C23×C4—261no—
470C23×C4—261no—
471C23×C4—261no—
472C23×C4—261no—
473C23×C4—261no—
474C23×C4—261no—
475C23×C4C4×D1311yescharacteristic
476C23×C4C4×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8—21no—
487C22×C8—21no—
488C22×C8—21no—
489C22×C8—21no—
490C22×C8—132no—
491C22×C8—132no—
492C22×C8—261no—
493C22×C8—261no—
494C22×C8—261no—
495C22×C8—261no—
496C22×C8—261no—
497C22×C8—261no—
498C22×C8—261no—
499C22×C8—261no—
500C22×C8—261no—
501C22×C8—261no—
502C22×C8—261no—
503C22×C8—261no—
504C22×C8D5212yes—
505C22×C8C22⋊D1312yes—
506C2×C22⋊C4—134no—
507C2×C22⋊C4—262no—
508C2×C22⋊C4—262no—
509C2×C22⋊C4—262no—
510C2×C22⋊C4—262no—
511C2×C22⋊C4—262no—
512C2×C42—21no—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—132no—
519C2×C42—132no—
520C2×C42—261no—
521C2×C42—261no—
522C2×C42—261no—
523C2×C42—261no—
524C4⋊C8—268no—
525C22⋊C8—268no—
526C22⋊C8—268no—
527#95—262no—
528#95—262no—
529C2×C13#143911yescharacteristic
530C2×C13#179711yescharacteristic
531C2×C13#179811yescharacteristic
532C2×C13#185011yescharacteristic
533C2×C13#185011yescharacteristic
534C2×C13#185111yescharacteristic
535C2×C13#185111yescharacteristic
536C2×C13#186911yescharacteristic
537C2×C13#187011yescharacteristic
538C2×C13#192311yescharacteristic
539C2×C13#192311yescharacteristic
540C2×C13#192411yescharacteristic
541C2×C13#192411yescharacteristic
542C2×C13#195411yescharacteristic
543C2×C13#195511yescharacteristic
544D13—44no—
545C24—132no—
546C24—132no—
547C24—132no—
548C24—261no—
549C24—261no—
550C24—261no—
551C24—261no—
552C24—261no—
553C24—261no—
554C24—261no—
555C24—261no—
556C24—261no—
557C24—261no—
558C24—261no—
559C24—261no—
560C24C2×C4×D1311yescharacteristic
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—132no—
574C22×C4—132no—
575C22×C4—132no—
576C22×C4—132no—
577C22×C4—132no—
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—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—261no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
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×C4—521no—
617C22×C4—521no—
618C22×C4—521no—
619C22×C4—521no—
620C22×C4—521no—
621C22×C4—521no—
622C22×C4C8×D1312yes—
623C22×C4#609412yes—
624C22×C4C2×D5211yescharacteristic
625C22×C4#612711yescharacteristic
626C22×C4#612711yescharacteristic
627C22×C4#612711yescharacteristic
628C22×C4#612711yescharacteristic
629C22×C4D4×D1311yescharacteristic
630C22×C4D4×D1311yescharacteristic
631C22×C4D4×D1311yescharacteristic
632C22×C4D4×D1311yescharacteristic
633C22×C4D4×D1311yescharacteristic
634C22×C4#612911yescharacteristic
635C22×C4Q8×D1311yescharacteristic
636C22×C4#613111yescharacteristic
637C22×C4C2×C22⋊D1311yescharacteristic
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—262no—
653C2×C8—262no—
654C2×C8—262no—
655C2×C8—262no—
656C2×C8—262no—
657C2×C8—262no—
658C2×C8—521no—
659C2×C8—521no—
660C2×C8—521no—
661C2×C8—521no—
662C2×C8—521no—
663C2×C8—521no—
664C2×C8—521no—
665C2×C8—521no—
666C22⋊C4—268no—
667C22⋊C4—268no—
668C42—41no—
669C42—41no—
670C42—41no—
671C42—41no—
672C42—262no—
673C42—262no—
674C42—262no—
675C42—262no—
676C13#1104211yescharacteristic, complemented, Sylow
677C23—134no—
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—262no—
691C23—262no—
692C23—262no—
693C23—262no—
694C23—262no—
695C23—262no—
696C23—521no—
697C23—521no—
698C23—521no—
699C23—521no—
700C23—521no—
701C23—521no—
702C23—521no—
703C23—521no—
704C23—521no—
705C23—521no—
706C23—521no—
707C23—521no—
708C23—521no—
709C23—521no—
710C23—521no—
711C23—521no—
712C23#8812611yescharacteristic
713C23C4×D5211yescharacteristic
714C23C22⋊C4×D1311yescharacteristic
715C23#8813511yescharacteristic
716C23C4⋊C4×D1311yescharacteristic
717C23#8814711yescharacteristic
718C23C2×C8×D1311yescharacteristic
719C23C2×#609411yescharacteristic
720C23#8815511yescharacteristic
721C23#8815511yescharacteristic
722C23M16×D1311yescharacteristic
723C23M16×D1311yescharacteristic
724C23#8816111yescharacteristic
725C23#8816111yescharacteristic
726C23C4×C22⋊D1311yescharacteristic
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—134no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—262no—
748C2×C4—262no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—521no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—521no—
758C2×C4—521no—
759C2×C4—521no—
760C2×C4—521no—
761C2×C4—521no—
762C2×C4—522no—
763C2×C4—522no—
764C2×C4—522no—
765C2×C4—522no—
766C2×C4—522no—
767C2×C4—522no—
768C2×C4—522no—
769C2×C4—522no—
770C2×C4#8812911yescharacteristic
771C2×C4#8813011yescharacteristic
772C2×C4#8813611yescharacteristic
773C2×C4#8813611yescharacteristic
774C2×C4#8813711yescharacteristic
775C2×C4#8813811yescharacteristic
776C2×C4#8813811yescharacteristic
777C2×C4#8813811yescharacteristic
778C2×C4#8813811yescharacteristic
779C2×C4#8813811yescharacteristic
780C2×C4#8813911yescharacteristic
781C2×C4#8813911yescharacteristic
782C2×C4#8814811yescharacteristic
783C2×C4#8814811yescharacteristic
784C2×C4#8814811yescharacteristic
785C2×C4#8814911yescharacteristic
786C2×C4#8815011yescharacteristic
787C2×C4#8815011yescharacteristic
788C2×C4#8815011yescharacteristic
789C2×C4#8815011yescharacteristic
790C2×C4#8815111yescharacteristic
791C2×C4#8815211yescharacteristic
792C2×C4#8818311yescharacteristic
793C2×C4#8818411yescharacteristic
794C2×C4#8819111yescharacteristic
795C2×C4#8819311yescharacteristic
796C2×C4#8819411yescharacteristic
797C2×C4#8820011yescharacteristic
798C8—42no—
799C8—42no—
800C8—522no—
801C8—522no—
802C22—264no—
803C22—264no—
804C22—264no—
805C22—522no—
806C22—522no—
807C22—522no—
808C22—522no—
809C22—522no—
810C22—522no—
811C22—522no—
812C22—522no—
813C22—522no—
814C22—522no—
815C22—522no—
816C22—522no—
817C22#1171832611yescharacteristic
818C22#1171832811yescharacteristic
819C22#1171832911yescharacteristic
820C22#1171833011yescharacteristic
821C22#1171834611yescharacteristic
822C22C8×D5211yescharacteristic
823C22#1171834911yescharacteristic
824C22#1171835111yescharacteristic
825C22#1171836611yescharacteristic
826C22#1171836711yescharacteristic
827C22#1171836711yescharacteristic
828C22#1171837011yescharacteristic
829C22D13×C22⋊C811yescharacteristic
830C22#1171838611yescharacteristic
831C22#1171838711yescharacteristic
832C22#1171838811yescharacteristic
833C22#1171838811yescharacteristic
834C22#1171838911yescharacteristic
835C22#1171839011yescharacteristic
836C22#1171839111yescharacteristic
837C22D13×C4⋊C811yescharacteristic
838C22#1171849511yescharacteristic
839C22#1171849711yescharacteristic
840C22#1171849711yescharacteristic
841C22#1171849811yescharacteristic
842C22#1171849911yescharacteristic
843C22#1171850011yescharacteristic
844C22#1171850011yescharacteristic
845C22#1171860111yescharacteristic
846C22#1171861811yescharacteristic
847C22#1171865011yescharacteristic
848C22C8×C22⋊D1311yescharacteristic
849C22#1171877211yescharacteristic
850C22#1171878811yescharacteristic
851C22#1171878911yescharacteristic
852C4—42no—
853C4—42no—
854C4—264no—
855C4—522no—
856C4—522no—
857C4#1171833311yescharacteristic
858C4#1171833411yescharacteristic
859C4#1171833611yescharacteristic
860C4#1171833711yescharacteristic
861C4#1171862011yescharacteristic
862C4#1171862111yescharacteristic
863C4#1171865311yescharacteristic
864C4#1171865511yescharacteristic
865C2—524no—
866C2#1311308011yescharacteristic
867C2#1311481511yescharacteristic
868C2#1311481911yescharacteristic
869C2#1311501211yescharacteristic
870C2#1311501511yescharacteristic
871C2#1311501711yescharacteristic
872C2#1311502011yescharacteristic
873C2#1311512711yescharacteristic
874C2#1311513211yescharacteristic
875C2#1311544011yescharacteristic
876C2#1311544211yescharacteristic
877C2#1311544711yescharacteristic
878C2#1311544911yescharacteristic
879C2#1311562811yescharacteristic
880C2#1311563211yescharacteristic
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#11042
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
1. C22×#88054C2semidirect
5. C2×#11718116C2semidirect
6. C2×#11718142C2semidirect
7. C2×C13×#336C2semidirect
79. C2×#6103C8semidirect
243. C2×#336D13semidirect
293. C22×D13C4⋊C8semidirect
356. C2×Dic13C22⋊C8semidirect
676. C13#11042semidirect

Maximal subgroups

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

subgroupindex
C22×#880542
C22×#880602
C2×C4×#61032
C2×#117181162
C2×#117181422
C2×C13×#3362
#1104213