Finite Group Databasebeta

← #15869028

Subgroups — #15869028

Order 3328.

1058 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718788C211yesmaximal, characteristic, complemented
2C2×C8×C22⋊D13C211yesmaximal, characteristic, complemented
3C2×#11718783C211yesmaximal, characteristic, complemented
4#13118078C211yesmaximal, characteristic
5#13115632C211yesmaximal, characteristic, complemented
6#13115556C211yesmaximal, characteristic, complemented
7#13115445C211yesmaximal, characteristic, complemented
8#13115441C211yesmaximal, characteristic, complemented
9#13115129C211yesmaximal, characteristic, complemented
10#13115126C211yesmaximal, characteristic, complemented
11#13114818C211yesmaximal, characteristic, complemented
12#13114704C211yesmaximal, characteristic, complemented
13#13114613C211yesmaximal, characteristic, complemented
14#13114612C211yesmaximal, characteristic, complemented
15C2×C13×#435C211yesmaximal, characteristic, complemented
16C22×C13×M16C2211yescharacteristic
17C23×C8×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×C4×C22⋊D13C2211yescharacteristic
20C2×C4×C22⋊D13C2211yescharacteristic
21C2×#88180C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C22×C8×D13C2211yescharacteristic
24C13×#435—24no—
25C2×C13×C4⋊C8C2211yescharacteristic
26C2×C13×C22⋊C8C2211yescharacteristic
27C2×C13×C22⋊C8C2211yescharacteristic
28C2×C13×#97C2211yescharacteristic
29#11718884C411yescharacteristic
30#11718883C411yescharacteristic
31C4×C22⋊Dic13C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35#11718788—24no—
36#11718783—24no—
37C8×C22⋊D13—24no—
38C2×#88060C2211yescharacteristic
39C2×#88060C2211yescharacteristic
40C2×#88060C2211yescharacteristic
41C2×#88055C2211yescharacteristic
42C2×#88055C2211yescharacteristic
43C2×#88055C2211yescharacteristic
44C2×#88054C2211yescharacteristic
45C2×#88054C2211yescharacteristic
46C2×#88054C2211yescharacteristic
47C2×C8×Dic13C2211yescharacteristic
48C2×C8×Dic13C2211yescharacteristic
49#11718655C411yescharacteristic
50#11718645C411yescharacteristic
51#11718622C411yescharacteristic
52#11718620C411yescharacteristic
53#11718613C411yescharacteristic
54#11718609C411yescharacteristic
55C4×#6103C2211yescharacteristic
56C4×#6101C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63C22×D4×C13C2×C411yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C22×C22⋊D13C2×C411yescharacteristic
67C22×C22⋊D13C2×C411yescharacteristic
68C22×C4×D13C2311yescharacteristic
69C2×C13×M16—22no—
70C2×C13×M16—22no—
71C2×C13×M16D414yescomplemented
72C22×C8×C13—22no—
73C22×C8×C13—22no—
74C22×C8×C13—22no—
75C22×C8×C13C2311yescharacteristic
76C22×C8×C13C2311yescharacteristic
77C22×C8×C13C2311yescharacteristic
78C22×C8×C13C2311yescharacteristic
79C4×D4×C13—22no—
80C4×D4×C13—22no—
81C2×C13×C4⋊C4C2×C411yescharacteristic
82C2×C13×C22⋊C4C2×C411yescharacteristic
83C2×C13×C22⋊C4C2×C411yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C22⋊Dic13C2×C411yescharacteristic
86C2×C22⋊Dic13C2×C411yescharacteristic
87C2×C22⋊Dic13C2×C411yescharacteristic
88C2×C22⋊Dic13C2×C411yescharacteristic
89C2×C22⋊Dic13C2×C411yescharacteristic
90C2×C22⋊Dic13C2×C411yescharacteristic
91C4×C22⋊D13—22no—
92C4×C22⋊D13—22no—
93C4×C22⋊D13—22no—
94C4×C22⋊D13—22no—
95C2×#6103C2×C411yescharacteristic
96C2×#6103C2×C411yescharacteristic
97C2×#6103C2×C411yescharacteristic
98C2×#6103C2×C411yescharacteristic
99#88180—22no—
100#88180—22no—
101C2×C4⋊Dic13C2×C411yescharacteristic
102C2×C4⋊Dic13C2×C411yescharacteristic
103C2×#6101C2×C411yescharacteristic
104C2×#6101C2×C411yescharacteristic
105C2×#6101C2×C411yescharacteristic
106C2×#6101C2×C411yescharacteristic
107C2×C4×Dic13C2311yescharacteristic
108C2×C4×Dic13C2311yescharacteristic
109C2×C4×Dic13C2311yescharacteristic
110C22×#1055—22no—
111C22×#1055—22no—
112C22×#1055—22no—
113C22×#1055C2311yescharacteristic
114C22×#1055C2311yescharacteristic
115C22×#1055C2311yescharacteristic
116C22×#1055C2311yescharacteristic
117C2×C8×D13—22no—
118C2×C8×D13—22no—
119C2×C8×D13—22no—
120C13×C4⋊C8—22no—
121C13×C22⋊C8—22no—
122C13×C22⋊C8—22no—
123C13×#97—22no—
124#88071C2×C411yescharacteristic
125#88071C2×C411yescharacteristic
126#88071C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129#88071C2×C411yescharacteristic
130C22⋊#1055—22no—
131C22⋊#1055—22no—
132C22⋊#1055—22no—
133#88060—22no—
134#88060—22no—
135#88060—22no—
136#88055—22no—
137#88055—22no—
138#88055—22no—
139#88054—22no—
140#88054—22no—
141#88054—22no—
142C8×Dic13—22no—
143C8×Dic13D414yescomplemented
144#21492—131nomaximal, Sylow
145C24×C13C22×C411yescharacteristic
146C24×C13C22×C411yescharacteristic
147C23×D13C22×C411yescharacteristic
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—41no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13C22×C411yescharacteristic
162C22×C4×C13C22×C411yescharacteristic
163C22×C4×C13C22×C411yescharacteristic
164C22×C4×C13C22×C411yescharacteristic
165C22×C4×C13C2×D412yes—
166C22×C4×C13#4112yes—
167C22×C4×C13C2411yescharacteristic
168C2×C22⋊D13—22no—
169C2×C22⋊D13—22no—
170C2×C22⋊D13—22no—
171C2×C22⋊D13—22no—
172C2×C22⋊D13—22no—
173C2×C22⋊D13—41no—
174C22×Dic13C22×C411yescharacteristic
175C22×Dic13C22×C411yescharacteristic
176C22×Dic13C22×C411yescharacteristic
177C22×Dic13C22×C411yescharacteristic
178C22×Dic13C22×C411yescharacteristic
179C22×Dic13C22×C411yescharacteristic
180C22×Dic13C22×C411yescharacteristic
181C2×C4×D13—21no—
182C2×C4×D13—21no—
183C2×C4×D13—21no—
184C2×C4×D13—21no—
185C2×C4×D13—21no—
186C2×C4×D13—21no—
187C13×M16—28no—
188C2×C8×C13—21no—
189C2×C8×C13—21no—
190C2×C8×C13—21no—
191C2×C8×C13—21no—
192C2×C8×C13—21no—
193C2×C8×C13—21no—
194C2×C8×C13—21no—
195C2×C8×C13—21no—
196C2×C8×C13—44no—
197C2×C8×C13C2×D412yes—
198C2×C8×C13C2×D412yes—
199C2×C8×C13C2×D412yes—
200C2×C8×C13#4112yes—
201C13×C4⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—22no—
204C42×C13—21no—
205C42×C13—21no—
206C22⋊Dic13—22no—
207C22⋊Dic13—22no—
208C22⋊Dic13—22no—
209C22⋊Dic13—22no—
210C22⋊Dic13—22no—
211C22⋊Dic13—41no—
212#6103—22no—
213#6103—22no—
214#6103—22no—
215#6103—41no—
216C4⋊Dic13—22no—
217C4⋊Dic13—22no—
218#6101—22no—
219#6101—22no—
220#6101—41no—
221#6101—41no—
222C4×Dic13—21no—
223C4×Dic13—21no—
224C4×Dic13—21no—
225C4×Dic13—21no—
226C4×Dic13C2×D412yes—
227C4×Dic13#4112yes—
228C2×#1055—28no—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055C2×D412yes—
240C2×#1055#4112yes—
241C8×D13—44no—
242C2×#435—131no—
243C2×#435D1311yescharacteristic, complemented
244C2×C8×D4—131no—
245C2×#405—131no—
246#2392—131no—
247#1955—131no—
248#1940—131no—
249#1923—131no—
250#1923—131no—
251#1869—131no—
252#1869—131no—
253#1798—131no—
254#1770—131no—
255#1752—131no—
256#1752—131no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13C4×D412yes—
270C23×C13#13112yes—
271C23×C13C23×C411yescharacteristic
272C22×D13—21no—
273C22×D13—21no—
274C22×D13—21no—
275C22×D13—21no—
276C22×D13—21no—
277C22×D13—21no—
278C22×D13#13112yes—
279D4×C13—44no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
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—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13C4×D412yes—
300C2×C4×C13C22×D411yescharacteristic
301C2×C4×C13C22×D411yescharacteristic
302C2×C4×C13C2×#4111yescharacteristic
303C2×C4×C13C2×#4111yescharacteristic
304C2×C4×C13C2×#4111yescharacteristic
305C2×C4×C13C2×#4111yescharacteristic
306C22⋊D13—28no—
307C22⋊D13—44no—
308C2×Dic13—21no—
309C2×Dic13—21no—
310C2×Dic13—21no—
311C2×Dic13—21no—
312C2×Dic13—21no—
313C2×Dic13—21no—
314C2×Dic13—21no—
315C2×Dic13—21no—
316C2×Dic13—21no—
317C2×Dic13—21no—
318C2×Dic13—21no—
319C2×Dic13—21no—
320C2×Dic13—21no—
321C2×Dic13—21no—
322C2×Dic13—21no—
323C2×Dic13—21no—
324C2×Dic13—21no—
325C2×Dic13—21no—
326C2×Dic13—21no—
327C2×Dic13C4×D412yes—
328C2×Dic13C4×D412yes—
329C4×D13—41no—
330C4×D13—41no—
331C4×D13—41no—
332C4×D13—41no—
333C8×C13—22no—
334C8×C13—41no—
335C8×C13—41no—
336C8×C13#12114yes—
337#1055—22no—
338#1055—22no—
339#1055—41no—
340#1055—41no—
341C22×M16C2×D1311yescharacteristic
342C23×C8—131no—
343C23×C8—131no—
344C23×C8C2×D1311yescharacteristic
345C2×C4×D4—131no—
346C2×C4×D4—131no—
347C2×C4×D4C2×D1311yescharacteristic
348C2×#117—131no—
349#435—24no—
350#435—264no—
351C8×D4—264no—
352C2×C4⋊C8—131no—
353C2×C4⋊C8—131no—
354C2×C4⋊C8—131no—
355C2×C4⋊C8C2×D1311yescharacteristic
356C2×C22⋊C8—131no—
357C2×C22⋊C8—131no—
358C2×C22⋊C8—131no—
359C2×C22⋊C8—131no—
360C2×C22⋊C8—131no—
361C2×C22⋊C8—131no—
362C2×C22⋊C8C2×D1311yescharacteristic
363C2×C22⋊C8C2×D1311yescharacteristic
364#405—264no—
365C2×#97—131no—
366C2×#97—131no—
367C2×#97—131no—
368C2×#97C2×D1311yescharacteristic
369C2×C4×C8—131no—
370C2×C4×C8—131no—
371#398—131no—
372#397—131no—
373#396—131no—
374#396—131no—
375#394—131no—
376#394—131no—
377#394—131no—
378#392—131no—
379C4×C4⋊C4—131no—
380C4×C22⋊C4—131no—
381C4×C22⋊C4—131no—
382#336—131no—
383#336—131no—
384#336—131no—
385#336—131no—
386#336—131no—
387#336—131no—
388C22×C13—22no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—22no—
393C22×C13—22no—
394C22×C13—41no—
395C22×C13—41no—
396C22×C13—41no—
397C22×C13—41no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—41no—
401C22×C13—41no—
402C22×C13C2×C4×D411yescharacteristic
403C22×C13C2×C4×D411yescharacteristic
404C22×C13C4×#4111yescharacteristic
405C22×C13C2×#13111yescharacteristic
406C22×C13C2×#13111yescharacteristic
407C22×C13#56811yescharacteristic
408C22×C13#56811yescharacteristic
409C2×D13—22no—
410C2×D13—22no—
411C2×D13—22no—
412C2×D13—41no—
413C2×D13—41no—
414C2×D13—41no—
415C2×D13—41no—
416C4×C13—22no—
417C4×C13—41no—
418C4×C13—41no—
419C4×C13—41no—
420C4×C13C2×#12111yescharacteristic
421C4×C13#52511yescharacteristic
422C4×C13#52911yescharacteristic
423C4×C13#53211yescharacteristic
424Dic13—22no—
425Dic13—22no—
426Dic13—41no—
427Dic13—41no—
428Dic13—41no—
429Dic13—41no—
430Dic13—41no—
431C22×D4—131no—
432C22×D4—131no—
433C22×D4C4×D1311yescharacteristic
434C23×C4—131no—
435C23×C4C22×D1311yescharacteristic
436C23×C4C22×D1311yescharacteristic
437C2×M16—22no—
438C2×M16—22no—
439C2×M16C22⋊D1314yescomplemented
440C22×C8—22no—
441C22×C8—22no—
442C22×C8—22no—
443C22×C8—131no—
444C22×C8—131no—
445C22×C8—131no—
446C22×C8—131no—
447C22×C8—262no—
448C22×C8—262no—
449C22×C8—262no—
450C22×C8—262no—
451C22×C8—262no—
452C22×C8—262no—
453C22×C8C22×D1311yescharacteristic
454C22×C8C22×D1311yescharacteristic
455C22×C8C22×D1311yescharacteristic
456C22×C8C22×D1311yescharacteristic
457C4×D4—22no—
458C4×D4—22no—
459C4×D4—262no—
460C4×D4—262no—
461C4×D4—262no—
462C4×D4—262no—
463#117—262no—
464#117—262no—
465C2×C4⋊C4—131no—
466C2×C4⋊C4—131no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—131no—
470C2×C4⋊C4—131no—
471C2×C4⋊C4C4×D1311yescharacteristic
472C2×C22⋊C4—131no—
473C2×C22⋊C4—131no—
474C2×C22⋊C4—131no—
475C2×C22⋊C4—131no—
476C2×C22⋊C4—131no—
477C2×C22⋊C4—131no—
478C2×C22⋊C4—131no—
479C2×C22⋊C4—131no—
480C2×C22⋊C4—131no—
481C2×C22⋊C4—131no—
482C2×C22⋊C4C4×D1311yescharacteristic
483C2×C22⋊C4C4×D1311yescharacteristic
484C2×C42—131no—
485C2×C42—131no—
486C2×C42—131no—
487C2×C42C22×D1311yescharacteristic
488C4⋊C8—22no—
489C4⋊C8—262no—
490C4⋊C8—262no—
491C4⋊C8—262no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8—262no—
495C22⋊C8—262no—
496C22⋊C8—262no—
497C22⋊C8—262no—
498C22⋊C8—262no—
499C22⋊C8—262no—
500#97—22no—
501#97—262no—
502#97—262no—
503#97—262no—
504C4×C8—134no—
505C4×C8—262no—
506#95—131no—
507#95—131no—
508#95—131no—
509#95—131no—
510#95—131no—
511#95—131no—
512C2×C13—42no—
513C2×C13—42no—
514C2×C13C4×#12111yescharacteristic
515C2×C13#292911yescharacteristic
516C2×C13#293211yescharacteristic
517C2×C13#293311yescharacteristic
518C2×C13#293311yescharacteristic
519C2×C13#296811yescharacteristic
520C2×C13#296811yescharacteristic
521D13—42no—
522C24—131no—
523C24C2×C4×D1311yescharacteristic
524C24C2×C4×D1311yescharacteristic
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—41no—
528C2×D4—262no—
529C2×D4—262no—
530C2×D4—262no—
531C2×D4—262no—
532C2×D4—262no—
533C2×D4—521no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—131no—
545C22×C4—131no—
546C22×C4—131no—
547C22×C4—131no—
548C22×C4—131no—
549C22×C4—131no—
550C22×C4—131no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4C2×C4×D1311yescharacteristic
558C22×C4C2×C4×D1311yescharacteristic
559C22×C4C2×C4×D1311yescharacteristic
560C22×C4C2×C4×D1311yescharacteristic
561C22×C4#612712yes—
562C22×C4C2×C22⋊D1312yes—
563C22×C4C23×D1311yescharacteristic
564M16—28no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—44no—
574C2×C8—132no—
575C2×C8—132no—
576C2×C8—268no—
577C2×C8—261no—
578C2×C8—261no—
579C2×C8—261no—
580C2×C8—261no—
581C2×C8—261no—
582C2×C8—261no—
583C2×C8—261no—
584C2×C8—261no—
585C2×C8—261no—
586C2×C8—261no—
587C2×C8—524no—
588C2×C8D4×D1312yes—
589C2×C8#612912yes—
590C2×C8C2×C22⋊D1312yes—
591C2×C8C2×C22⋊D1312yes—
592C4⋊C4—22no—
593C4⋊C4—262no—
594C4⋊C4—262no—
595C4⋊C4—262no—
596C4⋊C4—262no—
597C4⋊C4—521no—
598C4⋊C4—521no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—262no—
602C22⋊C4—262no—
603C22⋊C4—262no—
604C22⋊C4—262no—
605C22⋊C4—262no—
606C22⋊C4—262no—
607C22⋊C4—262no—
608C22⋊C4—262no—
609C22⋊C4—521no—
610C22⋊C4—521no—
611C42—21no—
612C42—21no—
613C42—132no—
614C42—132no—
615C42—261no—
616C42—261no—
617C42—261no—
618C42—261no—
619C13#2149211yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—132no—
633C23—261no—
634C23—261no—
635C23—261no—
636C23—261no—
637C23—261no—
638C23—261no—
639C23#8816112yes—
640C23C4×C22⋊D1312yes—
641C23C22×C4×D1311yescharacteristic
642D4—44no—
643D4—268no—
644D4—524no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—132no—
665C2×C4—132no—
666C2×C4—261no—
667C2×C4—261no—
668C2×C4—261no—
669C2×C4—261no—
670C2×C4—261no—
671C2×C4—261no—
672C2×C4—261no—
673C2×C4—261no—
674C2×C4—261no—
675C2×C4—261no—
676C2×C4—261no—
677C2×C4—261no—
678C2×C4—261no—
679C2×C4—261no—
680C2×C4—261no—
681C2×C4—261no—
682C2×C4—261no—
683C2×C4—261no—
684C2×C4—261no—
685C2×C4—521no—
686C2×C4—521no—
687C2×C4—521no—
688C2×C4—521no—
689C2×C4C4×C22⋊D1312yes—
690C2×C4C2×#612711yescharacteristic
691C2×C4C2×D4×D1311yescharacteristic
692C2×C4C2×#612911yescharacteristic
693C2×C4#41×D1311yescharacteristic
694C2×C4#41×D1311yescharacteristic
695C2×C4C22×C22⋊D1311yescharacteristic
696C8—22no—
697C8—41no—
698C8—41no—
699C8—262no—
700C8—262no—
701C8—521no—
702C8—521no—
703C8#8819314yes—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—262no—
719C22—262no—
720C22—262no—
721C22—521no—
722C22—521no—
723C22—521no—
724C22—521no—
725C22C4×#612911yescharacteristic
726C22C4×D4×D1311yescharacteristic
727C22C2×#8816111yescharacteristic
728C22#1171945011yescharacteristic
729C22D13×#13111yescharacteristic
730C22#1171945511yescharacteristic
731C22C2×C4×C22⋊D1311yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—262no—
737C4—262no—
738C4—521no—
739C4—521no—
740C4—521no—
741C4—521no—
742C4—521no—
743C4#1171924311yescharacteristic
744C4#1171925211yescharacteristic
745C4C2×#8819311yescharacteristic
746C4#1171953711yescharacteristic
747C2—42no—
748C2—42no—
749C2—522no—
750C2C4×#8819311yescharacteristic
751C2#1312352711yescharacteristic
752C2#1312355011yescharacteristic
753C2#1312355811yescharacteristic
754C2#1312356111yescharacteristic
755C2#1312382711yescharacteristic
756C2#1312383111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#435C2
prime radical#11718884C4
cosocleC22×C4×C13C24
hypercenterC2×#435D13
hypocenterC13#21492
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#11718788C2semidirect
2. C2×C8×C22⋊D13C2semidirect
3. C2×#11718783C2semidirect
5. #13115632C2semidirect
6. #13115556C2semidirect
7. #13115445C2semidirect
8. #13115441C2semidirect
9. #13115129C2semidirect
10. #13115126C2semidirect
11. #13114818C2semidirect
12. #13114704C2semidirect
13. #13114613C2semidirect
14. #13114612C2semidirect
15. C2×C13×#435C2semidirect
71. C2×C13×M16D4semidirect
143. C8×Dic13D4semidirect
243. C2×#435D13semidirect
439. C2×M16C22⋊D13semidirect
619. C13#21492semidirect

Maximal subgroups

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

subgroupindex
C2×#117187882
C2×C8×C22⋊D132
C2×#117187832
#131180782
#131156322
#131155562
#131154452
#131154412
#131151292
#131151262
#131148182
#131147042
#131146132
#131146122
C2×C13×#4352
#2149213