Finite Group Databasebeta

← #15879261

Subgroups — #15879261

Order 3328.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719260C211yesmaximal, characteristic
2C2×#11718672C211yesmaximal, characteristic, complemented
3#13115808C211yesmaximal, characteristic, complemented
4#13115784C211yesmaximal, characteristic, complemented
5#13115272C211yesmaximal, characteristic, complemented
6#13115262C211yesmaximal, characteristic, complemented
7#13115158C211yesmaximal, characteristic, complemented
8#13115153C211yesmaximal, characteristic, complemented
9#13114924C211yesmaximal, characteristic, complemented
10#13114920C211yesmaximal, characteristic, complemented
11#13114843C211yesmaximal, characteristic, complemented
12#13114664C211yesmaximal, characteristic, complemented
13#13114557C211yesmaximal, characteristic, complemented
14C2×#11718121C211yesmaximal, characteristic, complemented
15C13×#2352C211yesmaximal, characteristic, complemented
16C22×#6129—21no—
17C2×C4×D4×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C2×#88184C2211yescharacteristic
21C2×#88184C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C23×#1055C2211yescharacteristic
26#11719260—24no—
27#11719260C418yescomplemented
28C2×#88151—21no—
29C2×#88140—21no—
30C2×#88140—21no—
31C2×C4×D52C2211yescharacteristic
32C2×#88123C2211yescharacteristic
33C13×#388—21no—
34C13×#387—21no—
35C13×#386—21no—
36C13×#382C2211yescharacteristic
37C13×#380C2211yescharacteristic
38C13×#380C2211yescharacteristic
39C4×C13×C4⋊C4C2211yescharacteristic
40C4×C13×C22⋊C4—21no—
41C2×C22⋊#1055C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43#11718672—24no—
44C2×#88049C2211yescharacteristic
45C2×#88049C2211yescharacteristic
46C2×#88049C2211yescharacteristic
47C2×#88049C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×#88043C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×D4×C13D411yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C22×C22⋊D13—21no—
67C22×C22⋊D13—21no—
68C23×Dic13—21no—
69C23×Dic13—21no—
70C2×#6129—28no—
71C2×#6129—44no—
72C2×#6129—44no—
73C22×D52C2311yescharacteristic
74C22×C4×D13—21no—
75C22×Dic26—21no—
76C4×D4×C13C2×C414yes—
77C4×D4×C13D414yes—
78C13×#117—22no—
79C13×#117—41no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—41no—
83C2×C13×C4⋊C4D411yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C4⋊C4C2311yescharacteristic
87C2×C13×C4⋊C4C2311yescharacteristic
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4—21no—
90C2×C13×C22⋊C4—21no—
91C2×C13×C22⋊C4D411yescharacteristic
92C2×C13×C22⋊C4D411yescharacteristic
93C2×C42×C13—21no—
94C2×C42×C13—21no—
95C2×C42×C13C2311yescharacteristic
96#88184—22no—
97#88184—22no—
98#88184C2×C414yes—
99#88184C2×C414yescomplemented
100C2×#6103—21no—
101C2×#6103—21no—
102C2×#6103—21no—
103C2×C4⋊Dic13—21no—
104C2×C4⋊Dic13—21no—
105C2×C4⋊Dic13—21no—
106C2×C4⋊Dic13—22no—
107C2×C4⋊Dic13—22no—
108C2×C4⋊Dic13C2×C414yes—
109C2×C4⋊Dic13C2×C414yescomplemented
110C2×C4⋊Dic13C2311yescharacteristic
111C2×C4⋊Dic13C2311yescharacteristic
112C2×C4⋊Dic13C2311yescharacteristic
113C2×#6099—22no—
114C2×#6099—22no—
115C2×#6099—41no—
116C22×#1055—22no—
117C22×#1055—22no—
118C22×#1055—41no—
119C22×#1055C2311yescharacteristic
120C22×#1055C2311yescharacteristic
121C22×#1055C2311yescharacteristic
122C22×#1055C2311yescharacteristic
123#88151—28no—
124#88140—28no—
125#88140—28no—
126C4×D52—22no—
127C4×D52C2×C414yescomplemented
128#88123—22no—
129#88123C2×C414yescomplemented
130C13×#95—21no—
131C13×#95—21no—
132C13×#95—21no—
133C13×#95—21no—
134C13×#95—21no—
135C22⋊#1055—22no—
136C22⋊#1055—22no—
137#88049—22no—
138#88049—22no—
139#88049—41no—
140#88049—41no—
141C4⋊#1055—22no—
142#88043—22no—
143#22495—131nomaximal, Sylow
144C24×C13C2×D411yescharacteristic
145C24×C13C2×D411yescharacteristic
146C23×D13—21no—
147C2×D4×C13—22no—
148C2×D4×C13—22no—
149C2×D4×C13C22⋊C414yes—
150C22×C4×C13—21no—
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×C13—21no—
162C22×C4×C13—42no—
163C22×C4×C13—42no—
164C22×C4×C13—81no—
165C22×C4×C13C22×C412yes—
166C22×C4×C13C22×C412yes—
167C22×C4×C13C2×D412yes—
168C22×C4×C13C2×D412yes—
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2411yescharacteristic
174C2×C22⋊D13—24no—
175C2×C22⋊D13—24no—
176C2×C22⋊D13—42no—
177C2×C22⋊D13—42no—
178C2×C22⋊D13—42no—
179C2×C22⋊D13—42no—
180C22×Dic13—24no—
181C22×Dic13—24no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C22×Dic13—42no—
186C22×Dic13—42no—
187C22×Dic13—42no—
188C22×Dic13—42no—
189#6129—432no—
190C2×D52—21no—
191C2×D52—21no—
192C2×D52—21no—
193C2×D52—21no—
194C2×D52—21no—
195C2×D52C22×C412yes—
196C2×C4×D13—24no—
197C2×C4×D13—42no—
198C2×C4×D13—42no—
199C2×Dic26—24no—
200C2×Dic26—42no—
201C2×Dic26—42no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—21no—
207C13×C4⋊C4—21no—
208C13×C4⋊C4—21no—
209C13×C4⋊C4—42no—
210C13×C4⋊C4C22⋊C414yes—
211C13×C4⋊C4#4112yescomplemented
212C13×C22⋊C4—42no—
213C13×C22⋊C4—42no—
214C13×C22⋊C4—81no—
215C13×C22⋊C4C22⋊C414yes—
216C13×C22⋊C4C22⋊C414yes—
217C42×C13—42no—
218C42×C13—81no—
219C42×C13C22×C412yes—
220C42×C13C2×D412yes—
221#6103—24no—
222#6103—24no—
223#6103—24no—
224C4⋊Dic13—24no—
225C4⋊Dic13—24no—
226C4⋊Dic13—24no—
227C4⋊Dic13—21no—
228C4⋊Dic13—21no—
229C4⋊Dic13—21no—
230C4⋊Dic13C22×C412yes—
231C4⋊Dic13C22×C412yes—
232C4⋊Dic13C22×C412yes—
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—44no—
246C2×#1055#4112yescomplemented
247C2×#547—131no—
248C2×#435—131no—
249#2352D1311yescharacteristic, complemented
250#1993—131no—
251#1987—131no—
252#1895—131no—
253#1893—131no—
254#1875—131no—
255#1874—131no—
256#1824—131no—
257#1823—131no—
258#1804—131no—
259#1762—131no—
260#1736—131no—
261C2×#340—131no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13—21no—
272C23×C13C2×C22⋊C412yes—
273C23×C13C2×C22⋊C412yes—
274C23×C13AGL(1,ℤ/8)12yes—
275C23×C13AGL(1,ℤ/8)12yes—
276C23×C13C22×D411yescharacteristic
277C22×D13—22no—
278C22×D13—41no—
279C22×D13—41no—
280C22×D13—41no—
281C22×D13—41no—
282C22×D13—41no—
283C22×D13—41no—
284D4×C13—28no—
285C2×C4×C13—21no—
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—22no—
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—22no—
301C2×C4×C13—22no—
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—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—84no—
314C2×C4×C13C2×C22⋊C412yes—
315C2×C4×C13C2×C22⋊C412yes—
316C2×C4×C13C2×C22⋊C412yes—
317C2×C4×C13C2×C22⋊C412yes—
318C2×C4×C13C23×C411yescharacteristic
319C2×C4×C13C22×D411yescharacteristic
320C2×C4×C13C2×#4111yescharacteristic
321C2×C4×C13C2×#4111yescharacteristic
322C2×C4×C13H(5,𝔽2)11yescharacteristic
323C2×C4×C132−1+411yescharacteristic
324C22⋊D13—48no—
325C22⋊D13—48no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—48no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—48no—
337D52—22no—
338D52—22no—
339D52—41no—
340D52—41no—
341C4×D13—48no—
342Dic26—48no—
343#1055—22no—
344#1055—41no—
345#1055—41no—
346#1055—41no—
347C22×#41—261no—
348C22×M16—131no—
349C23×C8—131no—
350#547—138no—
351#547—264no—
352C2×C4⋊Q8—131no—
353C2×#123—261no—
354C2×#123—261no—
355C2×C22⋊Q8—261no—
356C2×#121—131no—
357C2×#121—131no—
358C2×C4×D4—131no—
359C2×C4×D4C2×D1311yescharacteristic
360C2×#117C2×D1311yescharacteristic
361C22×C4⋊C4—131no—
362C22×C4⋊C4—131no—
363C22×C4⋊C4C2×D1311yescharacteristic
364#435—264no—
365C2×C4⋊C8—131no—
366C2×#102—131no—
367C2×#102—131no—
368C2×#102—131no—
369C2×#102—131no—
370C2×C22⋊C8—131no—
371C2×C22⋊C8—131no—
372C2×#97—131no—
373#388—21no—
374#387—21no—
375#386—21no—
376#382C2×D1311yescharacteristic
377#380C2×D1311yescharacteristic
378#380C2×D1311yescharacteristic
379C4×C4⋊C4C2×D1311yescharacteristic
380C4×C22⋊C4—21no—
381#340—131no—
382#340—131no—
383#340—131no—
384#340—131no—
385#340—131no—
386#340—131no—
387#340—131no—
388#340—131no—
389#340—131no—
390#340—131no—
391#340—131no—
392#340—131no—
393C22×C13—22no—
394C22×C13—22no—
395C22×C13—22no—
396C22×C13—22no—
397C22×C13—22no—
398C22×C13—22no—
399C22×C13—22no—
400C22×C13—22no—
401C22×C13—22no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13—41no—
405C22×C13—41no—
406C22×C13#41814yes—
407C22×C13C22×C22⋊C411yescharacteristic
408C22×C13#54611yescharacteristic
409C22×C13#54711yescharacteristic
410C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
411C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
412C22×C13#57711yescharacteristic
413C22×C13#57811yescharacteristic
414C2×D13—42no—
415C2×D13—42no—
416C2×D13—42no—
417C2×D13—81no—
418C2×D13—81no—
419C2×D13—81no—
420C2×D13—81no—
421C4×C13—22no—
422C4×C13—22no—
423C4×C13—22no—
424C4×C13—22no—
425C4×C13—42no—
426C4×C13—81no—
427C4×C13—81no—
428C4×C13—81no—
429C4×C13C4×#4111yescharacteristic
430C4×C13#52011yescharacteristic
431C4×C13#54611yescharacteristic
432C4×C13#54711yescharacteristic
433Dic13—42no—
434Dic13—42no—
435Dic13—42no—
436C2×#41—268no—
437C2×#41—524no—
438C2×#41—524no—
439C22×Q8—261no—
440C22×D4—131no—
441C22×D4—261no—
442C22×D4—261no—
443C22×D4C22⋊D1311yescharacteristic
444C23×C4—21no—
445C23×C4—261no—
446C23×C4—261no—
447C23×C4—261no—
448C23×C4C22×D1311yescharacteristic
449C23×C4C22×D1311yescharacteristic
450C2×M16—262no—
451C2×M16—262no—
452C2×M16—521no—
453C22×C8—131no—
454C22×C8—131no—
455C22×C8—131no—
456C22×C8—131no—
457C22×C8—262no—
458C22×C8—262no—
459C22×C8—521no—
460C4⋊Q8—134no—
461C4⋊Q8—262no—
462#123—268no—
463#123—268no—
464C22⋊Q8—268no—
465#121—134no—
466#121—134no—
467#121—262no—
468#121—262no—
469C4×D4—134no—
470C4×D4—262no—
471C4×D4C4×D1314yes—
472C4×D4D5214yes—
473#117—22no—
474#117—41no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4—134no—
479C2×C4⋊C4—134no—
480C2×C4⋊C4—131no—
481C2×C4⋊C4—131no—
482C2×C4⋊C4—131no—
483C2×C4⋊C4—262no—
484C2×C4⋊C4—262no—
485C2×C4⋊C4—261no—
486C2×C4⋊C4—261no—
487C2×C4⋊C4—261no—
488C2×C4⋊C4C22⋊D1311yescharacteristic
489C2×C4⋊C4C22×D1311yescharacteristic
490C2×C4⋊C4C22×D1311yescharacteristic
491C2×C4⋊C4C22×D1311yescharacteristic
492C2×C4⋊C4C22×D1311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—261no—
497C2×C22⋊C4—261no—
498C2×C22⋊C4—261no—
499C2×C22⋊C4C22⋊D1311yescharacteristic
500C2×C22⋊C4C22⋊D1311yescharacteristic
501C2×C42—21no—
502C2×C42—21no—
503C2×C42C22×D1311yescharacteristic
504C4⋊C8—262no—
505#102—262no—
506#102—262no—
507#102—521no—
508#102—521no—
509C22⋊C8—262no—
510C22⋊C8—262no—
511#97—262no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517C2×C13—24no—
518C2×C13—42no—
519C2×C13#233911yescharacteristic
520C2×C13C2×#41811yescharacteristic
521C2×C13#289811yescharacteristic
522C2×C13#330611yescharacteristic
523C2×C13#330811yescharacteristic
524C2×C13#334311yescharacteristic
525C2×C13#334511yescharacteristic
526D13—82no—
527C24—261no—
528C24C2×C22⋊D1311yescharacteristic
529C24C2×C22⋊D1311yescharacteristic
530#41—5232no—
531C2×Q8—264no—
532C2×Q8—522no—
533C2×Q8—522no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—132no—
537C2×D4—264no—
538C2×D4—264no—
539C2×D4—261no—
540C2×D4—261no—
541C2×D4—261no—
542C2×D4—261no—
543C2×D4—261no—
544C2×D4—522no—
545C2×D4—522no—
546C2×D4—522no—
547C2×D4—522no—
548C2×D4#610314yes—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—81no—
564C22×C4—264no—
565C22×C4—264no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—264no—
570C22×C4—522no—
571C22×C4—522no—
572C22×C4—522no—
573C22×C4—522no—
574C22×C4—522no—
575C22×C4—522no—
576C22×C4C2×C4×D1312yes—
577C22×C4C2×C4×D1312yes—
578C22×C4C2×D5212yes—
579C22×C4C2×D5212yes—
580C22×C4C2×C22⋊D1311yescharacteristic
581C22×C4C2×C22⋊D1311yescharacteristic
582C22×C4C2×C22⋊D1311yescharacteristic
583C22×C4C2×C22⋊D1311yescharacteristic
584C22×C4C23×D1311yescharacteristic
585M16—524no—
586C2×C8—132no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8—261no—
590C2×C8—261no—
591C2×C8—261no—
592C2×C8—261no—
593C2×C8—261no—
594C2×C8—261no—
595C2×C8—261no—
596C2×C8—261no—
597C2×C8—261no—
598C2×C8—524no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—42no—
607C4⋊C4—132no—
608C4⋊C4—132no—
609C4⋊C4—132no—
610C4⋊C4—264no—
611C4⋊C4—264no—
612C4⋊C4—264no—
613C4⋊C4—261no—
614C4⋊C4—261no—
615C4⋊C4—261no—
616C4⋊C4#610314yes—
617C4⋊C4#612912yescomplemented
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—264no—
622C22⋊C4—264no—
623C22⋊C4—264no—
624C22⋊C4#610314yes—
625C22⋊C4#610314yes—
626C42—42no—
627C42—81no—
628C42C2×C4×D1312yes—
629C42C2×D5212yes—
630C13#2249511yescharacteristic, complemented, Sylow
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—262no—
642C23—521no—
643C23—521no—
644C23—521no—
645C23—521no—
646C23—521no—
647C23—521no—
648C23C2×#610312yes—
649C23C2×#610312yes—
650C23#8820312yes—
651C23#8820312yes—
652C23C22×C22⋊D1311yescharacteristic
653Q8—528no—
654D4—28no—
655D4—262no—
656D4—262no—
657D4—528no—
658D4—528no—
659D4—521no—
660D4—521no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—528no—
694C2×C4—528no—
695C2×C4—528no—
696C2×C4—521no—
697C2×C4—521no—
698C2×C4—521no—
699C2×C4—521no—
700C2×C4—521no—
701C2×C4—521no—
702C2×C4C2×#610312yes—
703C2×C4C2×#610312yes—
704C2×C4C2×#610312yes—
705C2×C4C2×#610312yes—
706C2×C4C22×C4×D1311yescharacteristic
707C2×C4C22×D5211yescharacteristic
708C2×C4C2×#612911yescharacteristic
709C2×C4#8825111yescharacteristic
710C2×C4#41×D1311yescharacteristic
711C2×C4#8825711yescharacteristic
712C8—262no—
713C8—521no—
714C8—521no—
715C8—521no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—522no—
730C22—522no—
731C22—522no—
732C22—1041no—
733C22—1041no—
734C22—1041no—
735C22—1041no—
736C22#1171866214yes—
737C22C22×#610311yescharacteristic
738C22#1171951111yescharacteristic
739C22C2×#8820311yescharacteristic
740C22C2×#8820311yescharacteristic
741C22#1171952911yescharacteristic
742C22#1171954111yescharacteristic
743C22#1171954311yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—522no—
753C4—522no—
754C4—522no—
755C4C4×#612911yescharacteristic
756C4#1171925111yescharacteristic
757C4#1171925911yescharacteristic
758C4#1171926011yescharacteristic
759C2—24no—
760C2—42no—
761C2—1042no—
762C2#1311766111yescharacteristic
763C2C2×#1171866211yescharacteristic
764C2#1312336611yescharacteristic
765C2#1312679711yescharacteristic
766C2#1312682711yescharacteristic
767C2#1312727611yescharacteristic
768C2#1312730011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2352C2
socleC23×C13C22×D4
prime radicalC2×#11719260C2
cosocleC22×C4×C13C24
hypercenter#2352D13
hypocenterC13#22495
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#11718672C2semidirect
3. #13115808C2semidirect
4. #13115784C2semidirect
5. #13115272C2semidirect
6. #13115262C2semidirect
7. #13115158C2semidirect
8. #13115153C2semidirect
9. #13114924C2semidirect
10. #13114920C2semidirect
11. #13114843C2semidirect
12. #13114664C2semidirect
13. #13114557C2semidirect
14. C2×#11718121C2semidirect
15. C13×#2352C2semidirect
27. #11719260C4semidirect
99. #88184C2×C4semidirect
109. C2×C4⋊Dic13C2×C4semidirect
127. C4×D52C2×C4semidirect
129. #88123C2×C4semidirect
211. C13×C4⋊C4#41semidirect
246. C2×#1055#41semidirect
249. #2352D13semidirect
617. C4⋊C4#6129semidirect
630. C13#22495semidirect

Maximal subgroups

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

subgroupindex
C2×#117192602
C2×#117186722
#131158082
#131157842
#131152722
#131152622
#131151582
#131151532
#131149242
#131149202
#131148432
#131146642
#131145572
C2×#117181212
C13×#23522
#2249513