Finite Group Databasebeta

← #15875262

Subgroups — #15875262

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×C22⋊D13C211yesmaximal, characteristic, complemented
2C2×#11718494C211yesmaximal, characteristic, complemented
3C4×#88138C211yesmaximal, characteristic
4#13115629C211yesmaximal, characteristic, complemented
5#13115628C211yesmaximal, characteristic, complemented
6#13115628C211yesmaximal, characteristic, complemented
7#13115551C211yesmaximal, characteristic, complemented
8#13115444C211yesmaximal, characteristic, complemented
9#13115443C211yesmaximal, characteristic, complemented
10#13115128C211yesmaximal, characteristic, complemented
11#13115127C211yesmaximal, characteristic, complemented
12#13115012C211yesmaximal, characteristic, complemented
13#13114815C211yesmaximal, characteristic, complemented
14#13114697C211yesmaximal, characteristic, complemented
15C13×#1850C211yesmaximal, characteristic, complemented
16C23×C8×C13C2211yescharacteristic
17C2×C4×C22⋊D13C2211yescharacteristic
18C2×C4×C22⋊D13C2211yescharacteristic
19C22×C8×D13C2211yescharacteristic
20C2×#88138C411yescharacteristic
21C2×C4×D52C2211yescharacteristic
22C2×C42×D13C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×C22⋊C8C2211yescharacteristic
26C4×C13×C22⋊C4C2211yescharacteristic
27C2×C22⋊#1055C2211yescharacteristic
28C2×C22⋊#1055C2211yescharacteristic
29C8×C22⋊D13—24no—
30C2×#88060C2211yescharacteristic
31C2×#88060C2211yescharacteristic
32C2×#88060C2211yescharacteristic
33C2×#88060C2211yescharacteristic
34C2×#88060C2211yescharacteristic
35C2×#88060C2211yescharacteristic
36C2×#88060C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38C2×#88054C2211yescharacteristic
39C2×#88054C2211yescharacteristic
40C2×C8×Dic13C2211yescharacteristic
41C2×C8×Dic13C2211yescharacteristic
42C2×C8×Dic13C2211yescharacteristic
43#11718618C411yescharacteristic
44#11718617C411yescharacteristic
45#11718612C411yescharacteristic
46C4×#6103C2211yescharacteristic
47C4×#6101C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718494—24no—
51#11718330C411yescharacteristic
52#11718328C411yescharacteristic
53#11718326C411yescharacteristic
54#11718308C411yescharacteristic
55C13×#336C2211yescharacteristic
56C13×#336C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13C2×C411yescharacteristic
63C22×C22⋊D13C2×C411yescharacteristic
64C22×D52C2×C411yescharacteristic
65C22×C4×D13C2×C411yescharacteristic
66C22×C4×D13C2×C411yescharacteristic
67C22×C4×D13C2311yescharacteristic
68C22×C4×D13C2311yescharacteristic
69C22×C8×C13—22no—
70C22×C8×C13—41no—
71C22×C8×C13—41no—
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C22×C8×C13C2311yescharacteristic
75C22×C8×C13C2311yescharacteristic
76C2×C13×C22⋊C4C2×C411yescharacteristic
77C2×C13×C22⋊C4C2×C411yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C22⋊Dic13C2×C411yescharacteristic
81C2×C22⋊Dic13C2×C411yescharacteristic
82C4×C22⋊D13—22no—
83C4×C22⋊D13—22no—
84C4×C22⋊D13—41no—
85C4×C22⋊D13—41no—
86C2×#6103C2×C411yescharacteristic
87C2×#6103C2×C411yescharacteristic
88C2×#6103C2×C411yescharacteristic
89C2×#6103C2×C411yescharacteristic
90C2×#6103C2×C411yescharacteristic
91C2×#6103C2×C411yescharacteristic
92C2×C4⋊Dic13C2×C411yescharacteristic
93C2×#6101C2×C411yescharacteristic
94C2×#6101C2×C411yescharacteristic
95C2×#6101C2×C411yescharacteristic
96C2×#6101C2×C411yescharacteristic
97C2×C4×Dic13C2×C411yescharacteristic
98C2×C4×Dic13C2×C411yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C2×C8×D13—22no—
106C2×C8×D13—41no—
107C2×C8×D13—41no—
108#88138C818yescomplemented
109C4×D52—41no—
110C4×D52—41no—
111C42×D13—22no—
112C42×D13—22no—
113C13×C4⋊C8—22no—
114C13×C4⋊C8—41no—
115C13×C22⋊C8—41no—
116C13×#95C2×C411yescharacteristic
117C13×#95C2×C411yescharacteristic
118#88071C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#88071C2×C411yescharacteristic
121#88071C2×C411yescharacteristic
122C22⋊#1055—22no—
123C22⋊#1055—41no—
124#88060—22no—
125#88060—22no—
126#88060—22no—
127#88060—41no—
128#88060—41no—
129#88060—41no—
130#88060—41no—
131#88054—22no—
132#88054—22no—
133#88054—41no—
134C8×Dic13—22no—
135C8×Dic13—41no—
136C8×Dic13D414yescomplemented
137C4⋊#1055—22no—
138C4×#1055—41no—
139#22133—131nomaximal, Sylow
140C24×C13C22×C411yescharacteristic
141C23×D13C22×C411yescharacteristic
142C23×D13C22×C411yescharacteristic
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C22×C411yescharacteristic
151C22×C4×C13C22×C411yescharacteristic
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C2411yescharacteristic
155C2×C22⋊D13—22no—
156C2×C22⋊D13—22no—
157C2×C22⋊D13—41no—
158C2×C22⋊D13—41no—
159C2×C22⋊D13C2×C814yes—
160C2×C22⋊D13C2×C814yescomplemented
161C22×Dic13C22×C411yescharacteristic
162C22×Dic13C22×C411yescharacteristic
163C22×Dic13C22×C411yescharacteristic
164C22×Dic13C22×C411yescharacteristic
165C22×Dic13C22×C411yescharacteristic
166C22×Dic13C22×C411yescharacteristic
167C2×D52—41no—
168C2×D52—41no—
169C2×D52C2×C814yescomplemented
170C2×C4×D13—22no—
171C2×C4×D13—22no—
172C2×C4×D13—21no—
173C2×C4×D13—21no—
174C2×C4×D13—21no—
175C2×C4×D13—21no—
176C2×C4×D13—21no—
177C2×C4×D13—21no—
178C2×C4×D13—21no—
179C2×C4×D13—21no—
180C2×C4×D13—21no—
181C2×C4×D13—21no—
182C2×C4×D13—21no—
183C2×C4×D13—21no—
184C2×C4×D13—22no—
185C2×C4×D13—41no—
186C2×C4×D13—41no—
187C2×C4×D13C2×C814yescomplemented
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—21no—
197C2×C8×C13—21no—
198C2×C8×C13—21no—
199C2×C8×C13—44no—
200C2×C8×C13C2×D412yes—
201C13×C22⋊C4—41no—
202C13×C22⋊C4C2×C814yescomplemented
203C42×C13—21no—
204C42×C13—21no—
205C42×C13—21no—
206C42×C13—21no—
207C22⋊Dic13—22no—
208C22⋊Dic13—41no—
209#6103—22no—
210#6103—41no—
211#6103—41no—
212#6103—41no—
213#6103—41no—
214#6103C2×C814yescomplemented
215C4⋊Dic13—41no—
216#6101—22no—
217#6101—22no—
218#6101—41no—
219#6101C2×C814yescomplemented
220C4×Dic13—21no—
221C4×Dic13—21no—
222C4×Dic13—22no—
223C4×Dic13—22no—
224C4×Dic13C2×D412yes—
225C4×Dic13#4112yes—
226C2×#1055—21no—
227C2×#1055—21no—
228C2×#1055—21no—
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×#1055C2×D412yes—
238C8×D13—44no—
239C2×C8×D4—131no—
240C2×#431—131no—
241C4×#121—131no—
242#1954—131no—
243#1954—131no—
244#1954—131no—
245#1939—131no—
246#1923—131no—
247#1923—131no—
248#1869—131no—
249#1869—131no—
250#1850—131no—
251#1850D1311yescharacteristic, complemented
252#1797—131no—
253C8×C4⋊C4—131no—
254C23×C13—21no—
255C23×C13—21no—
256C23×C13—21no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13C22×C812yes—
261C23×C13C23×C411yescharacteristic
262C22×D13—21no—
263C22×D13—21no—
264C22×D13—21no—
265C22×D13—21no—
266C22×D13—21no—
267C22×D13—21no—
268C22×D13—21no—
269C22×D13—21no—
270C22×D13—21no—
271C22×D13—21no—
272C22×D13—21no—
273C22×D13—21no—
274C22×D13C22×C812yes—
275C22×D13C22×C812yes—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13C22×C812yes—
294C2×C4×C13C22×C812yes—
295C2×C4×C13C22×D411yescharacteristic
296C2×C4×C13C2×#4111yescharacteristic
297C2×C4×C13H(5,𝔽2)11yescharacteristic
298C2×C4×C13H(5,𝔽2)11yescharacteristic
299C2×C4×C13H(5,𝔽2)11yescharacteristic
300C2×C4×C132−1+411yescharacteristic
301C22⋊D13—28no—
302C22⋊D13—44no—
303C2×Dic13—21no—
304C2×Dic13—21no—
305C2×Dic13—21no—
306C2×Dic13—21no—
307C2×Dic13—21no—
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×Dic13C4×D412yes—
317C2×Dic13C4×D412yes—
318C2×Dic13C22×C812yes—
319C2×Dic13C22×C812yes—
320C2×Dic13#13112yes—
321D52—44no—
322C4×D13—28no—
323C4×D13—44no—
324C4×D13—41no—
325C4×D13—41no—
326C4×D13—41no—
327C4×D13—41no—
328C4×D13—41no—
329C4×D13—41no—
330C4×D13—41no—
331C4×D13—41no—
332C8×C13—22no—
333C8×C13—41no—
334C8×C13—41no—
335C8×C13—41no—
336#1055—22no—
337#1055—41no—
338#1055—41no—
339#1055—41no—
340C23×C8—131no—
341C23×C8C2×D1311yescharacteristic
342C2×#121—131no—
343C2×C4×D4—131no—
344C2×C4×D4—131no—
345C2×C4×D4—131no—
346C22×C42—131no—
347C8×D4—264no—
348#431—264no—
349C2×C4⋊C8—131no—
350C2×C4⋊C8—131no—
351C2×C4⋊C8—131no—
352C2×C4⋊C8—131no—
353C2×C4⋊C8C2×D1311yescharacteristic
354C2×C4⋊C8C2×D1311yescharacteristic
355C2×C22⋊C8—131no—
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⋊C8—131no—
363C2×C22⋊C8—131no—
364C2×C22⋊C8C2×D1311yescharacteristic
365C2×C4×C8—131no—
366C2×C4×C8—131no—
367C2×C4×C8—131no—
368C2×C4×C8—131no—
369#390—131no—
370#389—131no—
371#388—131no—
372#388—131no—
373#386—131no—
374#386—131no—
375#380—131no—
376C4×C4⋊C4—131no—
377C4×C22⋊C4—131no—
378C4×C22⋊C4C2×D1311yescharacteristic
379#336—131no—
380#336—131no—
381#336—131no—
382#336—131no—
383#336C2×D1311yescharacteristic
384#336C2×D1311yescharacteristic
385C22×C13—22no—
386C22×C13—22no—
387C22×C13—22no—
388C22×C13—41no—
389C22×C13—41no—
390C22×C13—41no—
391C22×C13—41no—
392C22×C13C2×C4×D411yescharacteristic
393C22×C13#51811yescharacteristic
394C22×C13#52011yescharacteristic
395C22×C13C23×C811yescharacteristic
396C22×C13C2×#13111yescharacteristic
397C22×C13#56811yescharacteristic
398C22×C13#56811yescharacteristic
399C2×D13—22no—
400C2×D13—22no—
401C2×D13—22no—
402C2×D13—22no—
403C2×D13—22no—
404C2×D13—22no—
405C2×D13—41no—
406C2×D13—41no—
407C2×D13—41no—
408C2×D13—41no—
409C2×D13—41no—
410C2×D13—41no—
411C2×D13—41no—
412C2×D13—41no—
413C4×C13—22no—
414C4×C13—22no—
415C4×C13—41no—
416C4×C13—41no—
417C4×C13—41no—
418C4×C13#53511yescharacteristic
419C4×C13#53711yescharacteristic
420C4×C13#54011yescharacteristic
421C4×C13#54211yescharacteristic
422Dic13—22no—
423Dic13—22no—
424Dic13—41no—
425Dic13—41no—
426Dic13—41no—
427Dic13C8×D414yes—
428C22×D4—131no—
429C22×D4—131no—
430C22×D4—131no—
431C23×C4—131no—
432C23×C4—131no—
433C23×C4—131no—
434C23×C4—131no—
435C23×C4C22×D1311yescharacteristic
436C22×C8—22no—
437C22×C8—41no—
438C22×C8—41no—
439C22×C8—131no—
440C22×C8—131no—
441C22×C8—131no—
442C22×C8—131no—
443C22×C8—262no—
444C22×C8—521no—
445C22×C8—521no—
446C22×C8C22×D1311yescharacteristic
447C22×C8C22×D1311yescharacteristic
448C22×C8C22×D1311yescharacteristic
449C22×C8C22×D1311yescharacteristic
450#121—138no—
451C4×D4—262no—
452C4×D4—262no—
453C4×D4—521no—
454C4×D4—521no—
455C4×D4—521no—
456C4×D4—521no—
457C2×C4⋊C4—131no—
458C2×C4⋊C4—131no—
459C2×C4⋊C4—131no—
460C2×C4⋊C4—131no—
461C2×C4⋊C4—131no—
462C2×C22⋊C4—131no—
463C2×C22⋊C4—131no—
464C2×C22⋊C4—131no—
465C2×C22⋊C4—131no—
466C2×C22⋊C4—131no—
467C2×C22⋊C4—131no—
468C2×C22⋊C4—131no—
469C2×C22⋊C4—131no—
470C2×C22⋊C4C4×D1311yescharacteristic
471C2×C22⋊C4C4×D1311yescharacteristic
472C2×C42—131no—
473C2×C42—131no—
474C2×C42—131no—
475C2×C42—131no—
476C2×C42—262no—
477C2×C42—262no—
478C2×C42C22×D1311yescharacteristic
479C2×C42C22×D1311yescharacteristic
480C4⋊C8—22no—
481C4⋊C8—41no—
482C4⋊C8—262no—
483C4⋊C8—262no—
484C4⋊C8—262no—
485C4⋊C8—521no—
486C22⋊C8—41no—
487C22⋊C8—262no—
488C22⋊C8—262no—
489C22⋊C8—262no—
490C22⋊C8—262no—
491C22⋊C8—521no—
492C22⋊C8—521no—
493C22⋊C8—521no—
494C22⋊C8—521no—
495C22⋊C8—521no—
496C4×C8—134no—
497C4×C8—262no—
498C4×C8—521no—
499C4×C8—521no—
500#95—131no—
501#95—131no—
502#95—131no—
503#95—131no—
504#95C4×D1311yescharacteristic
505#95C4×D1311yescharacteristic
506C2×C13—42no—
507C2×C13#232411yescharacteristic
508C2×C13C2×C8×D411yescharacteristic
509C2×C13#293011yescharacteristic
510C2×C13#297211yescharacteristic
511C2×C13#298111yescharacteristic
512C2×C13#298811yescharacteristic
513C2×C13#299311yescharacteristic
514D13—42no—
515D13—42no—
516C24—131no—
517C24—131no—
518C24C2×C4×D1311yescharacteristic
519C2×D4—134no—
520C2×D4—134no—
521C2×D4—134no—
522C2×D4—262no—
523C2×D4—262no—
524C2×D4—521no—
525C2×D4—521no—
526C2×D4—521no—
527C2×D4—521no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—131no—
535C22×C4—131no—
536C22×C4—131no—
537C22×C4—134no—
538C22×C4—131no—
539C22×C4—131no—
540C22×C4—131no—
541C22×C4—262no—
542C22×C4—262no—
543C22×C4—262no—
544C22×C4—261no—
545C22×C4—261no—
546C22×C4—261no—
547C22×C4—261no—
548C22×C4—261no—
549C22×C4—261no—
550C22×C4—261no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—521no—
557C22×C4—521no—
558C22×C4C2×C4×D1311yescharacteristic
559C22×C4C2×C4×D1311yescharacteristic
560C22×C4C2×C4×D1311yescharacteristic
561C22×C4C2×C4×D1311yescharacteristic
562C22×C4C2×C4×D1311yescharacteristic
563C22×C4C23×D1311yescharacteristic
564C2×C8—21no—
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—21no—
574C2×C8—21no—
575C2×C8—44no—
576C2×C8—132no—
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—261no—
588C2×C8—524no—
589C2×C8D4×D1312yes—
590C4⋊C4—134no—
591C4⋊C4—262no—
592C4⋊C4—262no—
593C4⋊C4—521no—
594C4⋊C4—521no—
595C22⋊C4—41no—
596C22⋊C4—134no—
597C22⋊C4—262no—
598C22⋊C4—262no—
599C22⋊C4—521no—
600C22⋊C4—521no—
601C22⋊C4—521no—
602C22⋊C4—521no—
603C22⋊C4—521no—
604C22⋊C4C8×D1314yescomplemented
605C42—21no—
606C42—21no—
607C42—21no—
608C42—21no—
609C42—132no—
610C42—132no—
611C42—262no—
612C42—262no—
613C42—261no—
614C42—261no—
615C13#2213311yescharacteristic, complemented, Sylow
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—132no—
623C23—132no—
624C23—261no—
625C23—261no—
626C23—261no—
627C23—261no—
628C23—261no—
629C23—261no—
630C23—261no—
631C23—261no—
632C23—261no—
633C23—261no—
634C23—261no—
635C23—261no—
636C23C2×C8×D1312yes—
637C23C22×C4×D1311yescharacteristic
638D4—268no—
639D4—524no—
640D4—524no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—132no—
659C2×C4—132no—
660C2×C4—132no—
661C2×C4—132no—
662C2×C4—132no—
663C2×C4—268no—
664C2×C4—261no—
665C2×C4—261no—
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—524no—
678C2×C4—521no—
679C2×C4—521no—
680C2×C4—521no—
681C2×C4—521no—
682C2×C4—521no—
683C2×C4—521no—
684C2×C4—521no—
685C2×C4—521no—
686C2×C4C2×C8×D1312yes—
687C2×C4C2×C8×D1312yes—
688C2×C4C2×D4×D1311yescharacteristic
689C2×C4#8825111yescharacteristic
690C2×C4#8825111yescharacteristic
691C2×C4#8825411yescharacteristic
692C2×C4#41×D1311yescharacteristic
693C2×C4#8825611yescharacteristic
694C8—22no—
695C8—41no—
696C8—41no—
697C8—41no—
698C8—262no—
699C8—521no—
700C8—521no—
701C8—521no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—262no—
710C22—262no—
711C22—262no—
712C22—262no—
713C22—262no—
714C22—262no—
715C22—521no—
716C22—521no—
717C22—521no—
718C22—521no—
719C22—521no—
720C22—521no—
721C22—521no—
722C22—521no—
723C22#1171920911yescharacteristic
724C22C4×D4×D1311yescharacteristic
725C22#1171925011yescharacteristic
726C22C22×C8×D1311yescharacteristic
727C22#1171945011yescharacteristic
728C22D13×#13111yescharacteristic
729C22#1171945511yescharacteristic
730C4—22no—
731C4—22no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—134no—
736C4—262no—
737C4—262no—
738C4—521no—
739C4—521no—
740C4—521no—
741C4#1171929711yescharacteristic
742C4#1171933411yescharacteristic
743C4#1171934511yescharacteristic
744C4#1171936811yescharacteristic
745C2—42no—
746C2—522no—
747C2—522no—
748C2#1311752811yescharacteristic
749C2C8×D4×D1311yescharacteristic
750C2#1312353411yescharacteristic
751C2#1312385711yescharacteristic
752C2#1312390811yescharacteristic
753C2#1312394511yescharacteristic
754C2#1312398311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C23×C8
FittingC13×#1850C2
socleC23×C13C23×C4
prime radicalC2×#88138C4
cosocleC22×C4×C13C24
hypercenter#1850D13
hypocenterC13#22133
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×C8×C22⋊D13C2semidirect
2. C2×#11718494C2semidirect
4. #13115629C2semidirect
5. #13115628C2semidirect
6. #13115628C2semidirect
7. #13115551C2semidirect
8. #13115444C2semidirect
9. #13115443C2semidirect
10. #13115128C2semidirect
11. #13115127C2semidirect
12. #13115012C2semidirect
13. #13114815C2semidirect
14. #13114697C2semidirect
15. C13×#1850C2semidirect
108. #88138C8semidirect
136. C8×Dic13D4semidirect
160. C2×C22⋊D13C2×C8semidirect
169. C2×D52C2×C8semidirect
187. C2×C4×D13C2×C8semidirect
202. C13×C22⋊C4C2×C8semidirect
214. #6103C2×C8semidirect
219. #6101C2×C8semidirect
251. #1850D13semidirect
604. C22⋊C4C8×D13semidirect
615. C13#22133semidirect

Maximal subgroups

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

subgroupindex
C2×C8×C22⋊D132
C2×#117184942
C4×#881382
#131156292
#131156282
#131155512
#131154442
#131154432
#131151282
#131151272
#131150122
#131148152
#131146972
C13×#18502
#2213313