Finite Group Databasebeta

← #15873173

Subgroups — #15873173

Order 3328.

1030 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718771C211yesmaximal, characteristic
2C2×#11718388C211yesmaximal, characteristic
3#13117322C211yesmaximal, characteristic
4#13115021C211yesmaximal, characteristic, complemented
5#13115018C211yesmaximal, characteristic, complemented
6#13115017C211yesmaximal, characteristic, complemented
7#13115017C211yesmaximal, characteristic, complemented
8#13115015C211yesmaximal, characteristic, complemented
9#13115015C211yesmaximal, characteristic, complemented
10#13115014C211yesmaximal, characteristic, complemented
11#13114819C211yesmaximal, characteristic, complemented
12#13114817C211yesmaximal, characteristic, complemented
13#13114815C211yesmaximal, characteristic, complemented
14#13114813C211yesmaximal, characteristic, complemented
15C13×#1850C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C23×C8×C13C2211yescharacteristic
18C22×#6099C2211yescharacteristic
19C22×#6094C2211yescharacteristic
20C22×C8×D13C2211yescharacteristic
21C2×#88126C2211yescharacteristic
22C2×C42×D13C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×C22⋊C8C2211yescharacteristic
26C4×C13×C22⋊C4C2211yescharacteristic
27C4×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊#1055C2211yescharacteristic
29#11718771—24no—
30C2×#88060C2211yescharacteristic
31C2×#88060C2211yescharacteristic
32C2×#88060C2211yescharacteristic
33C2×#88060C2211yescharacteristic
34C2×#88060C2211yescharacteristic
35C2×#88060C2211yescharacteristic
36C2×#88054C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38C2×#88054C2211yescharacteristic
39C2×#88054C2211yescharacteristic
40#11718618C411yescharacteristic
41#11718618C411yescharacteristic
42#11718617C411yescharacteristic
43#11718617C411yescharacteristic
44C4×#6103C2211yescharacteristic
45C4×#6103C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48#11718388—24no—
49#11718326C411yescharacteristic
50#11718326C411yescharacteristic
51#11718307C411yescharacteristic
52#11718307C411yescharacteristic
53C13×#336C2211yescharacteristic
54C13×#336C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13C2×C411yescharacteristic
63C22×C22⋊D13C2×C411yescharacteristic
64C2×#6127—41no—
65C2×#6127—41no—
66C2×#6127—41no—
67C2×#6127—41no—
68C2×#6127D414yes—
69C2×#6127Q814yes—
70C22×D52C2×C411yescharacteristic
71C22×C4×D13C2×C411yescharacteristic
72C22×C4×D13C2×C411yescharacteristic
73C22×C4×D13C2311yescharacteristic
74C22×C4×D13C2311yescharacteristic
75C22×Dic26C2×C411yescharacteristic
76C22×C8×C13—22no—
77C22×C8×C13—41no—
78C22×C8×C13—41no—
79C22×C8×C13C2311yescharacteristic
80C22×C8×C13C2311yescharacteristic
81C22×C8×C13C2311yescharacteristic
82C22×C8×C13C2311yescharacteristic
83C2×C13×C22⋊C4C2×C411yescharacteristic
84C2×C13×C22⋊C4C2×C411yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13C2×C411yescharacteristic
88C2×C22⋊Dic13C2×C411yescharacteristic
89C2×#6103C2×C411yescharacteristic
90C2×#6103C2×C411yescharacteristic
91C2×#6103C2×C411yescharacteristic
92C2×#6103C2×C411yescharacteristic
93C2×#6103C2×C411yescharacteristic
94C2×#6103C2×C411yescharacteristic
95C2×#6101C2×C411yescharacteristic
96C2×#6101C2×C411yescharacteristic
97C2×C4×Dic13C2×C411yescharacteristic
98C2×C4×Dic13C2×C411yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C2×#6099—22no—
102C2×#6099—41no—
103C2×#6099—41no—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C2×#6094—22no—
109C2×#6094—41no—
110C2×#6094—41no—
111C2×C8×D13—22no—
112C2×C8×D13—41no—
113C2×C8×D13—41no—
114#88126—41no—
115#88126—41no—
116C42×D13—41no—
117C42×D13—41no—
118C13×C4⋊C8—41no—
119C13×C4⋊C8—41no—
120C13×C22⋊C8—22no—
121C13×#95C2×C411yescharacteristic
122C13×#95C2×C411yescharacteristic
123#88071C2×C411yescharacteristic
124#88071C2×C411yescharacteristic
125#88071C2×C411yescharacteristic
126#88071C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129C22⋊#1055—22no—
130#88060—22no—
131#88060—22no—
132#88060—22no—
133#88060—22no—
134#88060—22no—
135#88060—22no—
136#88054—41no—
137#88054—41no—
138#88054—41no—
139#88054—41no—
140C4⋊#1055—41no—
141C4⋊#1055—41no—
142#21937—131nomaximal, Sylow
143C24×C13C22×C411yescharacteristic
144C23×D13C22×C411yescharacteristic
145C23×D13C22×C411yescharacteristic
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13C22×C411yescharacteristic
151C22×C4×C13C22×C411yescharacteristic
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C22×C411yescharacteristic
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×Q812yes—
157C22×C4×C13C2411yescharacteristic
158C2×C22⋊D13—41no—
159C2×C22⋊D13—41no—
160C2×C22⋊D13—41no—
161C2×C22⋊D13—41no—
162C2×C22⋊D13C4⋊C414yes—
163C2×C22⋊D13C4⋊C414yes—
164C22×Dic13C22×C411yescharacteristic
165C22×Dic13C22×C411yescharacteristic
166C22×Dic13C22×C411yescharacteristic
167C22×Dic13C22×C411yescharacteristic
168C22×Dic13C22×C411yescharacteristic
169C22×Dic13C22×C411yescharacteristic
170#6127—44no—
171#6127—44no—
172#6127—44no—
173#6127—44no—
174C2×D52—41no—
175C2×D52—41no—
176C2×D52C4⋊C414yes—
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—21no—
185C2×C4×D13—22no—
186C2×C4×D13—22no—
187C2×C4×D13—41no—
188C2×C4×D13—41no—
189C2×C4×D13—41no—
190C2×C4×D13—41no—
191C2×C4×D13C2×D412yes—
192C2×C4×D13C2×D412yes—
193C2×C4×D13C2×Q812yes—
194C2×C4×D13C2×Q812yes—
195C2×Dic26—41no—
196C2×Dic26—41no—
197C2×Dic26C4⋊C414yes—
198C2×C8×C13—21no—
199C2×C8×C13—21no—
200C2×C8×C13—21no—
201C2×C8×C13—21no—
202C2×C8×C13—21no—
203C2×C8×C13—21no—
204C2×C8×C13—21no—
205C2×C8×C13—21no—
206C2×C8×C13—21no—
207C2×C8×C13—21no—
208C2×C8×C13—21no—
209C2×C8×C13—21no—
210C2×C8×C13—44no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—41no—
213C42×C13—21no—
214C42×C13—21no—
215C42×C13—21no—
216C42×C13—21no—
217C22⋊Dic13—22no—
218C22⋊Dic13—41no—
219#6103—22no—
220#6103—22no—
221#6103—41no—
222#6103—41no—
223#6103—41no—
224#6103—41no—
225#6101—41no—
226#6101—41no—
227C4×Dic13—21no—
228C4×Dic13—21no—
229C4×Dic13—21no—
230C4×Dic13—21no—
231C4×Dic13—41no—
232C4×Dic13—41no—
233#6099—44no—
234C2×#1055—21no—
235C2×#1055—21no—
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—21no—
246#6094—44no—
247C8×D13—44no—
248C2×#408—131no—
249C2×#408—131no—
250#2297—131no—
251#1851—131no—
252#1851—131no—
253#1851—131no—
254#1851—131no—
255#1850—131no—
256#1850—131no—
257#1850—131no—
258#1850D1311yescharacteristic, complemented
259#1798—131no—
260#1798—131no—
261#1797—131no—
262#1797—131no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13C2×C4⋊C412yes—
270C23×C13C23×C411yescharacteristic
271C22×D13—21no—
272C22×D13—21no—
273C22×D13—21no—
274C22×D13—21no—
275C22×D13—21no—
276C22×D13—21no—
277C22×D13—21no—
278C22×D13—21no—
279C22×D13—21no—
280C22×D13—21no—
281C22×D13—21no—
282C22×D13—21no—
283C22×D13C2×C4⋊C412yes—
284C22×D13C2×C4⋊C412yes—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—21no—
298C2×C4×C13—21no—
299C2×C4×C13—21no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13C2×C4⋊C412yes—
303C2×C4×C13#13112yes—
304C2×C4×C13C22×D411yescharacteristic
305C2×C4×C13C22×Q811yescharacteristic
306C2×C4×C13H(5,𝔽2)11yescharacteristic
307C2×C4×C13H(5,𝔽2)11yescharacteristic
308C2×C4×C13H(5,𝔽2)11yescharacteristic
309C2×C4×C13H(5,𝔽2)11yescharacteristic
310C22⋊D13—44no—
311C22⋊D13—44no—
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×Dic13C2×C4⋊C412yes—
328C2×Dic13C2×C4⋊C412yes—
329C2×Dic13#13112yes—
330D52—44no—
331C4×D13—22no—
332C4×D13—22no—
333C4×D13—22no—
334C4×D13—22no—
335C4×D13—22no—
336C4×D13—22no—
337C4×D13—22no—
338C4×D13—22no—
339C4×D13—44no—
340C4×D13—44no—
341Dic26—44no—
342C8×C13—41no—
343C8×C13—41no—
344C8×C13—41no—
345C8×C13—41no—
346#1055—41no—
347#1055—41no—
348#1055—41no—
349#1055—41no—
350C22×#41—131no—
351C22×M16—131no—
352C22×M16—131no—
353C23×C8—131no—
354C23×C8C2×D1311yescharacteristic
355C2×#117—131no—
356C22×C42—131no—
357C2×C4⋊C8—131no—
358C2×C4⋊C8—131no—
359C2×C4⋊C8—131no—
360C2×C4⋊C8—131no—
361C2×C4⋊C8—131no—
362C2×C4⋊C8—131no—
363C2×C4⋊C8C2×D1311yescharacteristic
364C2×C4⋊C8C2×D1311yescharacteristic
365#408—264no—
366#408—264no—
367C2×C22⋊C8—131no—
368C2×C22⋊C8—131no—
369C2×C22⋊C8—131no—
370C2×C22⋊C8—131no—
371C2×C22⋊C8—131no—
372C2×C22⋊C8—131no—
373C2×C22⋊C8—131no—
374C2×C22⋊C8C2×D1311yescharacteristic
375#391—131no—
376#391—131no—
377#390—131no—
378#390—131no—
379#386—131no—
380#386—131no—
381#386—131no—
382#386—131no—
383C4×C22⋊C4—131no—
384C4×C22⋊C4—131no—
385C4×C22⋊C4—131no—
386C4×C22⋊C4C2×D1311yescharacteristic
387#336—131no—
388#336—131no—
389#336—131no—
390#336—131no—
391#336—131no—
392#336—131no—
393#336C2×D1311yescharacteristic
394#336C2×D1311yescharacteristic
395C22×C13—22no—
396C22×C13—22no—
397C22×C13—22no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—41no—
401C22×C13—41no—
402C22×C13C22×C4⋊C411yescharacteristic
403C22×C13#51811yescharacteristic
404C22×C13#51811yescharacteristic
405C22×C13C2×#13111yescharacteristic
406C22×C13C2×#13111yescharacteristic
407C22×C13#56811yescharacteristic
408C22×C13#56811yescharacteristic
409C2×D13—22no—
410C2×D13—22no—
411C2×D13—22no—
412C2×D13—22no—
413C2×D13—22no—
414C2×D13—22no—
415C2×D13—41no—
416C2×D13—41no—
417C2×D13—41no—
418C2×D13—41no—
419C2×D13—41no—
420C2×D13—41no—
421C2×D13—41no—
422C2×D13—41no—
423C4×C13—22no—
424C4×C13—22no—
425C4×C13—41no—
426C4×C13—41no—
427C4×C13—41no—
428C4×C13#53411yescharacteristic
429C4×C13#53411yescharacteristic
430C4×C13#54311yescharacteristic
431C4×C13#54311yescharacteristic
432Dic13—22no—
433Dic13—22no—
434Dic13—22no—
435Dic13—41no—
436Dic13—41no—
437Dic13—41no—
438C2×#41—134no—
439C2×#41—134no—
440C2×#41—521no—
441C2×#41—521no—
442C2×#41—521no—
443C2×#41—521no—
444C22×Q8—131no—
445C22×D4—131no—
446C22×D4—131no—
447C22×D4—131no—
448C23×C4—131no—
449C23×C4—131no—
450C23×C4—131no—
451C23×C4—131no—
452C23×C4C22×D1311yescharacteristic
453C2×M16—262no—
454C2×M16—262no—
455C2×M16—521no—
456C2×M16—521no—
457C2×M16—521no—
458C2×M16—521no—
459C22×C8—22no—
460C22×C8—41no—
461C22×C8—41no—
462C22×C8—131no—
463C22×C8—131no—
464C22×C8—131no—
465C22×C8—131no—
466C22×C8—262no—
467C22×C8—521no—
468C22×C8—521no—
469C22×C8C22×D1311yescharacteristic
470C22×C8C22×D1311yescharacteristic
471C22×C8C22×D1311yescharacteristic
472C22×C8C22×D1311yescharacteristic
473#117—521no—
474#117—521no—
475C2×C4⋊C4—131no—
476C2×C4⋊C4—131no—
477C2×C22⋊C4—131no—
478C2×C22⋊C4—131no—
479C2×C22⋊C4—131no—
480C2×C22⋊C4—131no—
481C2×C22⋊C4—131no—
482C2×C22⋊C4—131no—
483C2×C22⋊C4—131no—
484C2×C22⋊C4—131no—
485C2×C22⋊C4C4×D1311yescharacteristic
486C2×C22⋊C4C4×D1311yescharacteristic
487C2×C42—131no—
488C2×C42—131no—
489C2×C42—131no—
490C2×C42—131no—
491C2×C42—521no—
492C2×C42—521no—
493C2×C42C22×D1311yescharacteristic
494C2×C42C22×D1311yescharacteristic
495C4⋊C8—41no—
496C4⋊C8—41no—
497C4⋊C8—521no—
498C4⋊C8—521no—
499C4⋊C8—521no—
500C4⋊C8—521no—
501C4⋊C8—521no—
502C4⋊C8—521no—
503C22⋊C8—22no—
504C22⋊C8—262no—
505C22⋊C8—262no—
506C22⋊C8—262no—
507C22⋊C8—262no—
508C22⋊C8—262no—
509C22⋊C8—262no—
510C22⋊C8—262no—
511#95—131no—
512#95—131no—
513#95—131no—
514#95—131no—
515#95—131no—
516#95—131no—
517#95C4×D1311yescharacteristic
518#95C4×D1311yescharacteristic
519C2×C13—42no—
520C2×C13#231511yescharacteristic
521C2×C13#290611yescharacteristic
522C2×C13#290611yescharacteristic
523C2×C13#297711yescharacteristic
524C2×C13#297811yescharacteristic
525C2×C13#298111yescharacteristic
526C2×C13#298111yescharacteristic
527D13—42no—
528D13—42no—
529C24—131no—
530C24—131no—
531C24C2×C4×D1311yescharacteristic
532#41—524no—
533#41—524no—
534#41—524no—
535#41—524no—
536C2×Q8—134no—
537C2×Q8—521no—
538C2×Q8—521no—
539C2×D4—134no—
540C2×D4—134no—
541C2×D4—134no—
542C2×D4—521no—
543C2×D4—521no—
544C2×D4—521no—
545C2×D4—521no—
546C2×D4—521no—
547C2×D4—521no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—131no—
553C22×C4—131no—
554C22×C4—131no—
555C22×C4—132no—
556C22×C4—132no—
557C22×C4—132no—
558C22×C4—132no—
559C22×C4—131no—
560C22×C4—131no—
561C22×C4—131no—
562C22×C4—262no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—262no—
572C22×C4—521no—
573C22×C4—521no—
574C22×C4—521no—
575C22×C4—521no—
576C22×C4C2×C4×D1311yescharacteristic
577C22×C4C2×C4×D1311yescharacteristic
578C22×C4C2×C4×D1311yescharacteristic
579C22×C4C2×C4×D1311yescharacteristic
580C22×C4C2×C4×D1311yescharacteristic
581C22×C4D4×D1312yes—
582C22×C4Q8×D1312yes—
583C22×C4C23×D1311yescharacteristic
584M16—524no—
585M16—524no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—44no—
599C2×C8—261no—
600C2×C8—261no—
601C2×C8—261no—
602C2×C8—261no—
603C2×C8—261no—
604C2×C8—261no—
605C2×C8—261no—
606C2×C8—261no—
607C2×C8—261no—
608C2×C8—261no—
609C2×C8—261no—
610C2×C8—261no—
611C2×C8—524no—
612C4⋊C4—521no—
613C4⋊C4—521no—
614C22⋊C4—22no—
615C22⋊C4—41no—
616C22⋊C4—262no—
617C22⋊C4—262no—
618C22⋊C4—262no—
619C22⋊C4—521no—
620C22⋊C4—521no—
621C22⋊C4—521no—
622C22⋊C4—521no—
623C22⋊C4—521no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—261no—
629C42—261no—
630C42—261no—
631C42—261no—
632C42—521no—
633C42—521no—
634C13#2193711yescharacteristic, complemented, Sylow
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—132no—
642C23—132no—
643C23—261no—
644C23—261no—
645C23—261no—
646C23—261no—
647C23—261no—
648C23—261no—
649C23—261no—
650C23—261no—
651C23—261no—
652C23—261no—
653C23—261no—
654C23—261no—
655C23C4⋊C4×D1312yes—
656C23C22×C4×D1311yescharacteristic
657Q8—524no—
658D4—524no—
659D4—524no—
660D4—524no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—132no—
679C2×C4—132no—
680C2×C4—132no—
681C2×C4—261no—
682C2×C4—261no—
683C2×C4—261no—
684C2×C4—261no—
685C2×C4—261no—
686C2×C4—261no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—262no—
695C2×C4—261no—
696C2×C4—261no—
697C2×C4—261no—
698C2×C4—261no—
699C2×C4—261no—
700C2×C4—261no—
701C2×C4—261no—
702C2×C4—261no—
703C2×C4—261no—
704C2×C4—524no—
705C2×C4—524no—
706C2×C4C4⋊C4×D1312yes—
707C2×C4#8815512yes—
708C2×C4C2×D4×D1311yescharacteristic
709C2×C4#8825111yescharacteristic
710C2×C4#8825111yescharacteristic
711C2×C4C2×Q8×D1311yescharacteristic
712C2×C4#8825611yescharacteristic
713C2×C4#8825611yescharacteristic
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C8—521no—
719C8—521no—
720C8—521no—
721C8—521no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—262no—
730C22—262no—
731C22—262no—
732C22—262no—
733C22—262no—
734C22—262no—
735C22—521no—
736C22—521no—
737C22—521no—
738C22—521no—
739C22—521no—
740C22—521no—
741C22—521no—
742C22—521no—
743C22C2×C4⋊C4×D1311yescharacteristic
744C22#1171925011yescharacteristic
745C22#1171925011yescharacteristic
746C22C2×#8815511yescharacteristic
747C22#1171945011yescharacteristic
748C22D13×#13111yescharacteristic
749C22#1171945511yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—262no—
756C4—262no—
757C4—262no—
758C4—521no—
759C4—521no—
760C4—521no—
761C4#1171929411yescharacteristic
762C4#1171933911yescharacteristic
763C4#1171933911yescharacteristic
764C4#1171935811yescharacteristic
765C2—42no—
766C2—522no—
767C2—522no—
768C2#1311744711yescharacteristic
769C2#1312340111yescharacteristic
770C2#1312340311yescharacteristic
771C2#1312388911yescharacteristic
772C2#1312389511yescharacteristic
773C2#1312390811yescharacteristic
774C2#1312391011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1850C2
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenter#1850D13
hypocenterC13#21937
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
4. #13115021C2semidirect
5. #13115018C2semidirect
6. #13115017C2semidirect
7. #13115017C2semidirect
8. #13115015C2semidirect
9. #13115015C2semidirect
10. #13115014C2semidirect
11. #13114819C2semidirect
12. #13114817C2semidirect
13. #13114815C2semidirect
14. #13114813C2semidirect
15. C13×#1850C2semidirect
258. #1850D13semidirect
634. C13#21937semidirect

Maximal subgroups

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

subgroupindex
C2×#117187712
C2×#117183882
#131173222
#131150212
#131150182
#131150172
#131150152
#131150142
#131148192
#131148172
#131148152
#131148132
C13×#18502
#2193713