Finite Group Databasebeta

← #15868698

Subgroups — #15868698

Order 3328.

1400 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×#11718888C211yesmaximal, characteristic
2C2×#11718687C211yesmaximal, characteristic, complemented
3C2×C4×#6106C211yesmaximal, characteristic, complemented
4#13117529C211yesmaximal, characteristic
5#13115191C211yesmaximal, characteristic, complemented
6#13115191C211yesmaximal, characteristic, complemented
7#13115158C211yesmaximal, characteristic
8#13115104C211yesmaximal, characteristic, complemented
9#13115090C211yesmaximal, characteristic, complemented
10#13115035C211yesmaximal, characteristic, complemented
11#13114771C211yesmaximal, characteristic, complemented
12#13114666C211yesmaximal, characteristic, complemented
13C4×#88075C211yesmaximal, characteristic, complemented
14#13114602C211yesmaximal, characteristic, complemented
15C2×C13×#519C211yesmaximal, characteristic, complemented
16C23×Q8×C13C2211yescharacteristic
17C13×#519—24no—
18C13×#519—24no—
19C2×C4×Q8×C13—21no—
20C2×C4×Q8×C13—21no—
21C2×C4×Q8×C13C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×Q8×C13C2211yescharacteristic
24C2×C4×Q8×C13C2211yescharacteristic
25C2×C13×#117—21no—
26C2×C13×#117—21no—
27C2×C13×#117C2211yescharacteristic
28C2×C13×#117C2211yescharacteristic
29C22×#6106C2211yescharacteristic
30C22×#6106C2211yescharacteristic
31C2×#88184C2211yescharacteristic
32C2×C4×D52C2211yescharacteristic
33#11718888C418yescomplemented
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39C2×#88075C2211yescharacteristic
40#11718873C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43#11718687—24no—
44C4×#6106—24no—
45#11718651—21no—
46#11718650—21no—
47C2×#88049C2211yescharacteristic
48C2×#88049C2211yescharacteristic
49C2×#88048C2211yescharacteristic
50C2×#88047C2211yescharacteristic
51#11718618—21no—
52#11718617—21no—
53#11718600C2211yescharacteristic
54C4×C4⋊Dic13C2211yescharacteristic
55#11718589C2211yescharacteristic
56C2×#88043C2211yescharacteristic
57C2×C4×#1055C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718116C2211yescharacteristic
63#11718116C2211yescharacteristic
64C22×Q8×C13—22no—
65C22×Q8×C13—22no—
66C22×Q8×C13—22no—
67C22×Q8×C13—22no—
68C22×Q8×C13—21no—
69C22×Q8×C13—22no—
70C22×Q8×C13C2×C414yescomplemented
71C22×Q8×C13C2311yescharacteristic
72C22×Q8×C13C2311yescharacteristic
73C23×C4×C13—21no—
74C23×C4×C13C2311yescharacteristic
75C22×C22⋊D13—21no—
76C22×D52C2311yescharacteristic
77C22×C4×D13—21no—
78C4×Q8×C13—28no—
79C4×Q8×C13—28no—
80C4×Q8×C13—22no—
81C4×Q8×C13—22no—
82C4×Q8×C13—22no—
83C4×Q8×C13—22no—
84C4×Q8×C13—22no—
85C4×Q8×C13—22no—
86C4×Q8×C13D414yescomplemented
87C4×Q8×C13D414yescomplemented
88C13×#117—28no—
89C13×#117—28no—
90C13×#117—22no—
91C13×#117—22no—
92C13×#117—22no—
93C13×#117—22no—
94C2×C13×C4⋊C4—21no—
95C2×C13×C4⋊C4—21no—
96C2×C13×C4⋊C4—21no—
97C2×C13×C4⋊C4—21no—
98C2×C13×C4⋊C4D411yescharacteristic
99C2×C13×C4⋊C4D411yescharacteristic
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C22⋊C4—21no—
103C2×C13×C22⋊C4D411yescharacteristic
104C2×C13×C22⋊C4D411yescharacteristic
105C2×C42×C13—21no—
106C2×C42×C13—21no—
107C2×C42×C13—21no—
108C2×C42×C13—21no—
109C2×C42×C13—21no—
110C2×C42×C13C2311yescharacteristic
111C2×C42×C13C2311yescharacteristic
112C2×C22⋊Dic13—21no—
113C2×#6106—22no—
114C2×#6106—22no—
115C2×#6106—22no—
116C2×#6106—22no—
117C2×#6106C2×C414yes—
118C2×#6106C2×C414yes—
119#88184—22no—
120#88184C2×C414yes—
121C2×#6103—21no—
122C2×#6103—21no—
123C2×#6103—21no—
124C2×#6103—21no—
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4⋊Dic13C2311yescharacteristic
127C2×C4⋊Dic13C2311yescharacteristic
128C2×#6101—21no—
129C2×C4×Dic13—21no—
130C22×#1055C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132C22×#1055C2311yescharacteristic
133C22×#1055C2311yescharacteristic
134C4×D52—22no—
135C4×D52—22no—
136#88075—22no—
137#88075—22no—
138#88075—22no—
139#88075—22no—
140#88075C2×C414yescomplemented
141#88075C2×C414yescomplemented
142#88071—21no—
143#88071—21no—
144#88071—21no—
145C22⋊#1055—22no—
146C22⋊#1055C2×C414yescomplemented
147#88049—22no—
148#88049—22no—
149#88048—22no—
150#88047—22no—
151#88043—22no—
152C4×#1055—22no—
153#21462—131nomaximal, Sylow
154C24×C13C2×D411yescharacteristic
155C23×D13—21no—
156C2×Q8×C13—24no—
157C2×Q8×C13—28no—
158C2×Q8×C13—28no—
159C2×Q8×C13—24no—
160C2×Q8×C13—28no—
161C2×Q8×C13—28no—
162C2×Q8×C13—24no—
163C2×Q8×C13—21no—
164C2×Q8×C13—21no—
165C2×Q8×C13—21no—
166C2×Q8×C13—21no—
167C2×Q8×C13—21no—
168C2×Q8×C13—21no—
169C2×Q8×C13C22×C412yes—
170C2×Q8×C13C22×C412yes—
171C2×Q8×C13C2×D412yes—
172C2×Q8×C13C2×D412yes—
173C2×Q8×C13#4112yes—
174C2×Q8×C13#4112yes—
175C22×C4×C13—24no—
176C22×C4×C13—24no—
177C22×C4×C13—24no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13C22×C412yes—
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C22×C4×C13#4112yes—
193C22×C4×C13C2411yescharacteristic
194C2×C22⋊D13—24no—
195C2×C22⋊D13—81no—
196C2×C22⋊D13—81no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C2×D52—21no—
201C2×D52—21no—
202C2×D52—21no—
203C2×D52—21no—
204C2×D52—21no—
205C2×D52C22×C412yes—
206C2×C4×D13—42no—
207C2×C4×D13—81no—
208C2×C4×D13—81no—
209C13×C4⋊C4—24no—
210C13×C4⋊C4—24no—
211C13×C4⋊C4—24no—
212C13×C4⋊C4—24no—
213C13×C4⋊C4—22no—
214C13×C4⋊C4—22no—
215C13×C4⋊C4—21no—
216C13×C4⋊C4—21no—
217C13×C4⋊C4C2×D412yes—
218C13×C4⋊C4C2×D412yes—
219C13×C22⋊C4—24no—
220C13×C22⋊C4—22no—
221C13×C22⋊C4—22no—
222C42×C13—24no—
223C42×C13—24no—
224C42×C13—24no—
225C42×C13—24no—
226C42×C13—24no—
227C42×C13—21no—
228C42×C13—21no—
229C42×C13C2×D412yes—
230C42×C13C2×D412yes—
231C22⋊Dic13—81no—
232#6106—28no—
233#6106—28no—
234#6103—24no—
235#6103—42no—
236#6103—81no—
237#6103—81no—
238C4⋊Dic13—21no—
239C4⋊Dic13—21no—
240C4⋊Dic13—21no—
241C4⋊Dic13—21no—
242C4⋊Dic13—21no—
243C4⋊Dic13C22×C412yes—
244#6101—81no—
245C4×Dic13—81no—
246C2×#1055—21no—
247C2×#1055—21no—
248C2×#1055—21no—
249C2×#1055—21no—
250C2×#1055—21no—
251C2×#1055—21no—
252C2×#1055—21no—
253C2×#1055—21no—
254C2×#1055—21no—
255C2×#1055—21no—
256C2×#1055C22×C412yes—
257C2×#1055C22×C412yes—
258C2×#519D1311yescharacteristic, complemented
259C2×#448—131no—
260C2×#440—131no—
261C2×C4×SD16—131no—
262#2324—131no—
263#1880—131no—
264#1880—131no—
265#1875—131no—
266#1865—131no—
267#1863—131no—
268#1854—131no—
269#1787—131no—
270#1763—131no—
271C4×#103—131no—
272#1750—131no—
273C23×C13—21no—
274C23×C13—21no—
275C23×C13—21no—
276C23×C13—21no—
277C23×C13—21no—
278C23×C13—21no—
279C23×C13C4×D412yes—
280C23×C13C22×D411yescharacteristic
281C22×D13—22no—
282C22×D13—41no—
283C22×D13—41no—
284C22×D13—41no—
285C22×D13—41no—
286C22×D13—41no—
287C22×D13—41no—
288Q8×C13—216no—
289Q8×C13—22no—
290Q8×C13—22no—
291Q8×C13—22no—
292Q8×C13—22no—
293Q8×C13—22no—
294Q8×C13—22no—
295Q8×C13C4×D414yes—
296Q8×C13C4×D414yes—
297C2×C4×C13—216no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—21no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—21no—
306C2×C4×C13—21no—
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—21no—
315C2×C4×C13—21no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—21no—
319C2×C4×C13—21no—
320C2×C4×C13—21no—
321C2×C4×C13—21no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13C4×D412yes—
327C2×C4×C13#12012yes—
328C2×C4×C13#12012yes—
329C2×C4×C13C23×C411yescharacteristic
330C2×C4×C13C22×D411yescharacteristic
331C2×C4×C13C22×D411yescharacteristic
332C2×C4×C13C2×#4111yescharacteristic
333C2×C4×C13C2×#4111yescharacteristic
334C2×C4×C13C2×#4111yescharacteristic
335C22⋊D13—84no—
336C2×Dic13—22no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—41no—
341C2×Dic13—41no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345D52—22no—
346D52—22no—
347D52—41no—
348D52—41no—
349C4×D13—84no—
350#1055—22no—
351#1055—22no—
352#1055—41no—
353#1055—41no—
354C23×Q8C2×D1311yescharacteristic
355C22×SD16—131no—
356C22×SD16—131no—
357C2×#121—131no—
358#519—24no—
359#519—24no—
360C2×C4×Q8—21no—
361C2×C4×Q8—21no—
362C2×C4×Q8C2×D1311yescharacteristic
363C2×C4×Q8C2×D1311yescharacteristic
364C2×C4×Q8C2×D1311yescharacteristic
365C2×C4×Q8C2×D1311yescharacteristic
366C2×C4×D4—131no—
367C2×#117—21no—
368C2×#117—21no—
369C2×#117C2×D1311yescharacteristic
370C2×#117C2×D1311yescharacteristic
371#448—138no—
372#440—264no—
373C4×SD16—264no—
374C2×#107—131no—
375C2×#106—131no—
376C2×#103—131no—
377C2×#103—131no—
378C2×#103—131no—
379C2×#103—131no—
380C2×#103—131no—
381C2×#103—131no—
382C2×#102—131no—
383C2×#102—131no—
384C2×C22⋊C8—131no—
385C2×C22⋊C8—131no—
386C2×#97—131no—
387C2×C4×C8—131no—
388#390—131no—
389#390—261no—
390#389—131no—
391#388—261no—
392#386—261no—
393#385—261no—
394#380—131no—
395C4×C4⋊C4—131no—
396#340—131no—
397#340—131no—
398#340—131no—
399#340—131no—
400#336—131no—
401#336—131no—
402C22×C13—22no—
403C22×C13—22no—
404C22×C13—22no—
405C22×C13—41no—
406C22×C13—41no—
407C22×C13—41no—
408C22×C13—41no—
409C22×C13C2×C4×D411yescharacteristic
410C22×C13C2×#12011yescharacteristic
411C22×C13#52511yescharacteristic
412C22×C13#57711yescharacteristic
413C22×C13#57711yescharacteristic
414C22×C13#57711yescharacteristic
415C22×C13#57811yescharacteristic
416C2×D13—42no—
417C2×D13—42no—
418C2×D13—42no—
419C2×D13—81no—
420C2×D13—81no—
421C2×D13—81no—
422C2×D13—81no—
423C4×C13—22no—
424C4×C13—22no—
425C4×C13—24no—
426C4×C13—24no—
427C4×C13—22no—
428C4×C13—41no—
429C4×C13—42no—
430C4×C13—41no—
431C4×C13—42no—
432C4×C13C2×C4×D411yescharacteristic
433C4×C13C2×C4×D411yescharacteristic
434C4×C13#52511yescharacteristic
435C4×C13#52511yescharacteristic
436Dic13—42no—
437Dic13—81no—
438Dic13—81no—
439C22×Q8—22no—
440C22×Q8—22no—
441C22×Q8—22no—
442C22×Q8—22no—
443C22×Q8—22no—
444C22×Q8—21no—
445C22×Q8C4×D1314yescomplemented
446C22×Q8C22×D1311yescharacteristic
447C22×Q8C22×D1311yescharacteristic
448C22×D4—131no—
449C22×D4—261no—
450C23×C4—21no—
451C23×C4—261no—
452C23×C4C22×D1311yescharacteristic
453C2×SD16—134no—
454C2×SD16—134no—
455C2×SD16—262no—
456C2×SD16—262no—
457C2×SD16—262no—
458C2×SD16—262no—
459C22×C8—131no—
460C22×C8—131no—
461C22×C8—131no—
462C22×C8—131no—
463#121—134no—
464#121—262no—
465C4×Q8—28no—
466C4×Q8—28no—
467C4×Q8—22no—
468C4×Q8—22no—
469C4×Q8—22no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8C22⋊D1314yescomplemented
474C4×Q8C22⋊D1314yescomplemented
475C4×D4—262no—
476C4×D4—262no—
477#117—28no—
478#117—28no—
479#117—22no—
480#117—22no—
481#117—22no—
482#117—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—131no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—261no—
491C2×C4⋊C4C22⋊D1311yescharacteristic
492C2×C4⋊C4C22⋊D1311yescharacteristic
493C2×C4⋊C4C22×D1311yescharacteristic
494C2×C4⋊C4C22×D1311yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—261no—
497C2×C22⋊C4—261no—
498C2×C22⋊C4—261no—
499C2×C22⋊C4—261no—
500C2×C22⋊C4—261no—
501C2×C22⋊C4C22⋊D1311yescharacteristic
502C2×C22⋊C4C22⋊D1311yescharacteristic
503C2×C42—21no—
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42—21no—
508C2×C42—261no—
509C2×C42C22×D1311yescharacteristic
510C2×C42C22×D1311yescharacteristic
511#107—262no—
512#106—262no—
513#103—134no—
514#103—134no—
515#103—262no—
516#103—262no—
517#103—262no—
518#103—262no—
519#102—262no—
520#102—262no—
521C22⋊C8—134no—
522C22⋊C8—262no—
523#97—262no—
524C4×C8—262no—
525#95—261no—
526#95—261no—
527#95—261no—
528C2×C13—42no—
529C2×C13C4×#12011yescharacteristic
530C2×C13#294711yescharacteristic
531C2×C13#294911yescharacteristic
532C2×C13#301011yescharacteristic
533C2×C13#301311yescharacteristic
534C2×C13#312111yescharacteristic
535C2×C13#312611yescharacteristic
536D13—82no—
537C24—261no—
538C24C2×C22⋊D1311yescharacteristic
539C2×Q8—24no—
540C2×Q8—28no—
541C2×Q8—28no—
542C2×Q8—24no—
543C2×Q8—28no—
544C2×Q8—28no—
545C2×Q8—24no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8C2×C4×D1312yes—
553C2×Q8C2×C4×D1312yes—
554C2×Q8#612712yes—
555C2×Q8#612712yes—
556C2×Q8C2×C22⋊D1312yes—
557C2×Q8C2×C22⋊D1312yes—
558C2×D4—132no—
559C2×D4—264no—
560C2×D4—261no—
561C2×D4—261no—
562C2×D4—261no—
563C2×D4—261no—
564C2×D4—261no—
565C2×D4—1041no—
566C2×D4—1041no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—522no—
582C22×C4—1041no—
583C22×C4—1041no—
584C22×C4C2×C4×D1312yes—
585C22×C4#612712yes—
586C22×C4C2×C22⋊D1311yescharacteristic
587C22×C4C2×C22⋊D1311yescharacteristic
588C22×C4C2×C22⋊D1311yescharacteristic
589C22×C4C2×C22⋊D1311yescharacteristic
590C22×C4C2×C22⋊D1311yescharacteristic
591C22×C4C23×D1311yescharacteristic
592SD16—268no—
593SD16—268no—
594C2×C8—132no—
595C2×C8—132no—
596C2×C8—261no—
597C2×C8—261no—
598C2×C8—261no—
599C2×C8—261no—
600C2×C8—261no—
601C2×C8—261no—
602C2×C8—261no—
603C2×C8—261no—
604C2×C8—261no—
605C2×C8—261no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—132no—
615C4⋊C4—261no—
616C4⋊C4—261no—
617C4⋊C4—261no—
618C4⋊C4—261no—
619C4⋊C4—261no—
620C4⋊C4—1041no—
621C4⋊C4C2×C22⋊D1312yes—
622C4⋊C4C2×C22⋊D1312yes—
623C22⋊C4—24no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—264no—
627C22⋊C4—522no—
628C22⋊C4—1041no—
629C22⋊C4—1041no—
630C22⋊C4—1041no—
631C42—24no—
632C42—24no—
633C42—24no—
634C42—24no—
635C42—24no—
636C42—21no—
637C42—21no—
638C42—1041no—
639C42C2×C22⋊D1312yes—
640C42C2×C22⋊D1312yes—
641C13#2146211yescharacteristic, complemented, Sylow
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—262no—
649C23—521no—
650C23—521no—
651C23—521no—
652C23—521no—
653C23—521no—
654C23—521no—
655C23C4×C22⋊D1312yes—
656C23C22×C22⋊D1311yescharacteristic
657Q8—216no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—22no—
664Q8C4×C22⋊D1314yes—
665Q8C4×C22⋊D1314yes—
666D4—262no—
667D4—262no—
668D4—521no—
669D4—521no—
670D4—1044no—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—262no—
701C2×C4—521no—
702C2×C4—521no—
703C2×C4—521no—
704C2×C4—521no—
705C2×C4—521no—
706C2×C4—521no—
707C2×C4—521no—
708C2×C4—521no—
709C2×C4—1044no—
710C2×C4C4×C22⋊D1312yes—
711C2×C4#8820712yes—
712C2×C4#8820712yes—
713C2×C4C22×C4×D1311yescharacteristic
714C2×C4C2×#612711yescharacteristic
715C2×C4C2×#612711yescharacteristic
716C2×C4C2×#612711yescharacteristic
717C2×C4C22×C22⋊D1311yescharacteristic
718C2×C4C22×C22⋊D1311yescharacteristic
719C8—262no—
720C8—262no—
721C8—521no—
722C8—521no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—522no—
731C22—522no—
732C22—522no—
733C22—1041no—
734C22—1041no—
735C22—1041no—
736C22—1041no—
737C22C2×C4×C22⋊D1311yescharacteristic
738C22#1171949611yescharacteristic
739C22#1171954211yescharacteristic
740C22#1171954211yescharacteristic
741C22#1171954211yescharacteristic
742C22#1171954311yescharacteristic
743C22C2×#8820711yescharacteristic
744C4—22no—
745C4—22no—
746C4—24no—
747C4—24no—
748C4—22no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—42no—
753C4—522no—
754C4—1041no—
755C4—1041no—
756C4C2×C4×C22⋊D1311yescharacteristic
757C4C2×C4×C22⋊D1311yescharacteristic
758C4#1171949611yescharacteristic
759C4#1171949611yescharacteristic
760C2—42no—
761C2—1042no—
762C2C4×#8820711yescharacteristic
763C2#1312367911yescharacteristic
764C2#1312369511yescharacteristic
765C2#1312412211yescharacteristic
766C2#1312415111yescharacteristic
767C2#1312506511yescharacteristic
768C2#1312512711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#519C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
cosocleC22×C4×C13C24
hypercenterC2×#519D13
hypocenterC13#21462
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. C2×#11718687C2semidirect
3. C2×C4×#6106C2semidirect
5. #13115191C2semidirect
6. #13115191C2semidirect
8. #13115104C2semidirect
9. #13115090C2semidirect
10. #13115035C2semidirect
11. #13114771C2semidirect
12. #13114666C2semidirect
13. C4×#88075C2semidirect
14. #13114602C2semidirect
15. C2×C13×#519C2semidirect
33. #11718888C4semidirect
70. C22×Q8×C13C2×C4semidirect
86. C4×Q8×C13D4semidirect
87. C4×Q8×C13D4semidirect
140. #88075C2×C4semidirect
141. #88075C2×C4semidirect
146. C22⋊#1055C2×C4semidirect
258. C2×#519D13semidirect
445. C22×Q8C4×D13semidirect
473. C4×Q8C22⋊D13semidirect
474. C4×Q8C22⋊D13semidirect
641. C13#21462semidirect

Maximal subgroups

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

subgroupindex
C2×#117188882
C2×#117186872
C2×C4×#61062
#131175292
#131151912
#131151582
#131151042
#131150902
#131150352
#131147712
#131146662
C4×#880752
#131146022
C2×C13×#5192
#2146213