Finite Group Databasebeta

← #15919973

Subgroups — #15919973

Order 3328.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718748C211yesmaximal, characteristic, complemented
2C22×#88049C211yesmaximal, characteristic
3C22⋊C4×D52C211yesmaximal, characteristic
4#13116365C211yesmaximal, characteristic, complemented
5#13116221C211yesmaximal, characteristic, complemented
6#13116221C211yesmaximal, characteristic, complemented
7#13115969C211yesmaximal, characteristic, complemented
8#13115082C211yesmaximal, characteristic, complemented
9#13115082C211yesmaximal, characteristic, complemented
10#13115024C211yesmaximal, characteristic, complemented
11#13115016C211yesmaximal, characteristic, complemented
12#13114863C211yesmaximal, characteristic, complemented
13#13114833C211yesmaximal, characteristic, complemented
14#13114766C211yesmaximal, characteristic
15C13×#2440C211yesmaximal, characteristic, complemented
16C23×D52C2211yescharacteristic
17C2×C13×C4⋊Q8C2211yescharacteristic, complemented
18C2×C13×C22⋊Q8—21no—
19C22×C13×C4⋊C4C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×C22⋊C4×D13—21no—
22C2×C4×D52C2211yescharacteristic
23C2×C4×D52C2211yescharacteristic
24C13×#398—21no—
25C13×#395—21no—
26C13×#389C2211yescharacteristic, complemented
27C13×#389C2211yescharacteristic, complemented
28C13×#385—21no—
29C13×#384C2211yescharacteristic, complemented
30C13×#380C2211yescharacteristic
31C4×C13×C22⋊C4C2211yescharacteristic
32#11718873C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34#11718748—24no—
35C2×#88049—24no—
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88049C2211yescharacteristic
41C2×#88049C2211yescharacteristic
42C2×#88049C2211yescharacteristic
43C2×#88049C2211yescharacteristic
44C2×#88047C2211yescharacteristic, complemented
45C2×#88047C2211yescharacteristic, complemented
46C2×#88047C2211yescharacteristic, complemented
47C2×#88047C2211yescharacteristic, complemented
48#11718616—21no—
49#11718600C2211yescharacteristic
50#11718600C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic, complemented
52C2×C4⋊#1055C2211yescharacteristic, complemented
53#11718326—21no—
54#11718326—21no—
55#11718121C2211yescharacteristic, complemented
56#11718121C2211yescharacteristic, complemented
57#11718121C2211yescharacteristic, complemented
58#11718121C2211yescharacteristic, complemented
59#11718116C2211yescharacteristic, complemented
60#11718116C2211yescharacteristic, complemented
61C24×D13—21no—
62C22×Q8×C13—21no—
63C23×C4×C13—21no—
64C23×C4×C13C2311yescharacteristic
65C22×D52—22no—
66C22×D52—22no—
67C22×D52—21no—
68C22×D52—22no—
69C22×D52—41no—
70C22×D52—41no—
71C22×D52Q814yescomplemented
72C22×D52C2311yescharacteristic
73C22×D52C2311yescharacteristic
74C22×C4×D13—21no—
75C22×C4×D13—21no—
76C13×C4⋊Q8—22no—
77C13×C4⋊Q8—41no—
78C13×C22⋊Q8—44no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—21no—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—41no—
87C2×C13×C4⋊C4C2311yescharacteristic
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C4⋊C4C2311yescharacteristic
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4D411yescharacteristic
93C2×C13×C22⋊C4D411yescharacteristic
94C2×C42×C13C2311yescharacteristic
95C2×C42×C13C2311yescharacteristic
96C2×C22⋊Dic13—21no—
97C2×#6103—21no—
98C2×#6103—21no—
99C2×#6103—21no—
100C2×#6103—21no—
101C2×#6103—21no—
102C2×#6103—21no—
103C2×C4⋊Dic13C2311yescharacteristic
104C2×C4⋊Dic13C2311yescharacteristic
105C22×#1055—22no—
106C22×#1055—22no—
107C22×#1055—41no—
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C22⋊C4×D13—44no—
113C4×D52—22no—
114C4×D52—22no—
115C4×D52—41no—
116C4×D52—41no—
117C13×#95—21no—
118C13×#95—21no—
119C13×#95—21no—
120C13×#95D411yescharacteristic
121C13×#95D411yescharacteristic
122#88071—21no—
123C22⋊#1055—22no—
124#88049—22no—
125#88049—22no—
126#88049—22no—
127#88049—22no—
128#88049—22no—
129#88049—41no—
130#88049—41no—
131#88049D414yes—
132#88047—22no—
133#88047—22no—
134#88047—41no—
135#88047—41no—
136C4⋊#1055—22no—
137C4⋊#1055—41no—
138#25950—131nomaximal, Sylow
139C24×C13C2×D411yescharacteristic
140C23×D13—21no—
141C23×D13—21no—
142C23×D13—24no—
143C23×D13—42no—
144C23×D13—42no—
145C23×D13—42no—
146C23×D13—42no—
147C23×D13—81no—
148C23×D13—81no—
149C2×Q8×C13—42no—
150C2×Q8×C13—42no—
151C2×Q8×C13—81no—
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—42no—
161C22×C4×C13—42no—
162C22×C4×C13—81no—
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×Q812yes—
169C22×C4×C13#4112yes—
170C22×C4×C13C2411yescharacteristic
171C22×Dic13—21no—
172C22×Dic13—21no—
173C2×D52—21no—
174C2×D52—21no—
175C2×D52—21no—
176C2×D52—21no—
177C2×D52—21no—
178C2×D52—21no—
179C2×D52—21no—
180C2×D52—28no—
181C2×D52—24no—
182C2×D52—21no—
183C2×D52—44no—
184C2×D52—44no—
185C2×D52—44no—
186C2×D52—42no—
187C2×D52—42no—
188C2×D52C2×D412yes—
189C2×D52C2×Q812yes—
190C2×D52C2×Q812yes—
191C2×D52#4112yes—
192C2×C4×D13—42no—
193C2×C4×D13—42no—
194C2×C4×D13—42no—
195C2×C4×D13—42no—
196C2×C4×D13—81no—
197C2×C4×D13—81no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—42no—
206C13×C4⋊C4—42no—
207C13×C4⋊C4—42no—
208C13×C4⋊C4—42no—
209C13×C4⋊C4—42no—
210C13×C4⋊C4—81no—
211C13×C4⋊C4C2×D412yes—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—42no—
214C13×C22⋊C4D814yes—
215C42×C13—21no—
216C42×C13—21no—
217C42×C13—21no—
218C42×C13—21no—
219C22⋊Dic13—42no—
220#6103—42no—
221#6103—42no—
222#6103—42no—
223#6103—42no—
224#6103—81no—
225#6103—81no—
226C4⋊Dic13—21no—
227C4⋊Dic13—21no—
228C4⋊Dic13—21no—
229C4⋊Dic13—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×#1055—21no—
240C2×#1055—21no—
241C2×#1055—44no—
242C2×#1055C2×D412yes—
243C2×#474—131no—
244C22×#102—131no—
245#2440D1311yescharacteristic, complemented
246D4×C22⋊C4—131no—
247#2093—131no—
248#2067—131no—
249#2067—131no—
250#2023—131no—
251#1862—131no—
252#1862—131no—
253#1852—131no—
254#1850—131no—
255#1808—131no—
256#1802—131no—
257#1786—131no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13C22⋊Q812yes—
263C23×C13C2×D812yes—
264C23×C13#13712yes—
265C23×C13C22×D411yescharacteristic
266C22×D13—22no—
267C22×D13—22no—
268C22×D13—22no—
269C22×D13—22no—
270C22×D13—48no—
271C22×D13—41no—
272C22×D13—41no—
273C22×D13—41no—
274C22×D13—41no—
275C22×D13—41no—
276C22×D13—41no—
277C22×D13—41no—
278C22×D13—41no—
279C22×D13—41no—
280C22×D13—41no—
281C22×D13—48no—
282C22×D13—84no—
283C22×D13—84no—
284C22×D13—84no—
285C22×D13—84no—
286C22×D13—84no—
287Q8×C13—84no—
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—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—21no—
299C2×C4×C13—22no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—21no—
304C2×C4×C13—21no—
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—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—84no—
317C2×C4×C13C22⋊Q812yes—
318C2×C4×C13C2×D812yes—
319C2×C4×C13C2×D812yes—
320C2×C4×C13C22×D411yescharacteristic
321C2×C4×C13C22×Q811yescharacteristic
322C2×C4×C13C2×#4111yescharacteristic
323C2×C4×C13C2×#4111yescharacteristic
324C2×C4×C13H(5,𝔽2)11yescharacteristic
325C2×C4×C13H(5,𝔽2)11yescharacteristic
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332D52—22no—
333D52—22no—
334D52—22no—
335D52—22no—
336D52—22no—
337D52—48no—
338D52—41no—
339D52—41no—
340D52C22⋊Q814yescomplemented
341C4×D13—84no—
342C4×D13—84no—
343#1055—22no—
344#1055—41no—
345#1055—41no—
346#1055—41no—
347C23×D4—131no—
348C23×C8—131no—
349C2×C4⋊Q8C2×D1311yescharacteristic, complemented
350C2×C22⋊Q8—21no—
351C2×C4×D4—131no—
352C2×C4×D4—131no—
353C22×C4⋊C4C2×D1311yescharacteristic
354C22×C22⋊C4—261no—
355#474—264no—
356C2×#107—131no—
357C2×#107—131no—
358C2×#107—131no—
359C2×#107—131no—
360C2×C4⋊C8—131no—
361C2×C4⋊C8—131no—
362C2×#102—131no—
363C2×#102—131no—
364C2×#102—131no—
365C2×#102—131no—
366C2×#102—131no—
367C2×#102—131no—
368C2×#102—131no—
369C2×#102—131no—
370C2×#102—264no—
371C2×C22⋊C8—131no—
372#398—21no—
373#395—21no—
374#390—131no—
375#390—131no—
376#389C2×D1311yescharacteristic, complemented
377#389C2×D1311yescharacteristic, complemented
378#386—261no—
379#386—261no—
380#385—21no—
381#384C2×D1311yescharacteristic, complemented
382#380—131no—
383#380C2×D1311yescharacteristic
384#379—261no—
385C4×C22⋊C4C2×D1311yescharacteristic
386#340—131no—
387#340—131no—
388#340—131no—
389#340—131no—
390#336—131no—
391#336—131no—
392C22×C13—22no—
393C22×C13—22no—
394C22×C13—22no—
395C22×C13—22no—
396C22×C13—22no—
397C22×C13—22no—
398C22×C13#47414yescomplemented
399C22×C13C2×C22⋊Q811yescharacteristic
400C22×C13D4211yescharacteristic
401C22×C13#54611yescharacteristic
402C22×C13C22×D811yescharacteristic
403C22×C13C2×#13711yescharacteristic
404C22×C13#57611yescharacteristic
405C22×C13#57711yescharacteristic
406C2×D13—24no—
407C2×D13—42no—
408C2×D13—42no—
409C2×D13—42no—
410C2×D13—42no—
411C2×D13—42no—
412C2×D13—42no—
413C2×D13—42no—
414C2×D13—42no—
415C2×D13—42no—
416C2×D13—816no—
417C2×D13—81no—
418C2×D13—81no—
419C2×D13—81no—
420C2×D13—81no—
421C4×C13—22no—
422C4×C13—22no—
423C4×C13—22no—
424C4×C13—41no—
425C4×C13—42no—
426C4×C13—41no—
427C4×C13—81no—
428C4×C13—81no—
429C4×C13—81no—
430C4×C13C2×C22⋊Q811yescharacteristic
431C4×C13#54311yescharacteristic
432C4×C13#54611yescharacteristic
433C4×C13#55111yescharacteristic
434Dic13—81no—
435Dic13—81no—
436C25—261no—
437C22×Q8—21no—
438C22×D4—134no—
439C22×D4—131no—
440C22×D4—131no—
441C22×D4—262no—
442C22×D4—262no—
443C22×D4—262no—
444C22×D4—261no—
445C22×D4—521no—
446C22×D4—521no—
447C23×C4—21no—
448C23×C4—261no—
449C23×C4—261no—
450C23×C4C22×D1311yescharacteristic
451C22×C8—131no—
452C22×C8—131no—
453C22×C8—131no—
454C22×C8—131no—
455C22×C8—262no—
456C22×C8—262no—
457C22×C8—521no—
458C4⋊Q8—22no—
459C4⋊Q8—41no—
460C22⋊Q8—44no—
461C4×D4—262no—
462C4×D4—262no—
463C4×D4—521no—
464C4×D4—521no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4—131no—
474C2×C4⋊C4—131no—
475C2×C4⋊C4C22×D1311yescharacteristic
476C2×C4⋊C4C22×D1311yescharacteristic
477C2×C4⋊C4C22×D1311yescharacteristic
478C2×C4⋊C4C22×D1311yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—261no—
481C2×C22⋊C4—261no—
482C2×C22⋊C4—261no—
483C2×C22⋊C4—261no—
484C2×C22⋊C4—261no—
485C2×C22⋊C4—261no—
486C2×C22⋊C4—261no—
487C2×C22⋊C4—524no—
488C2×C22⋊C4C22⋊D1311yescharacteristic
489C2×C22⋊C4C22⋊D1311yescharacteristic
490C2×C42C22×D1311yescharacteristic
491C2×C42C22×D1311yescharacteristic
492#107—262no—
493#107—262no—
494#107—521no—
495#107—521no—
496C4⋊C8—262no—
497C4⋊C8—521no—
498#102—134no—
499#102—262no—
500#102—262no—
501#102—262no—
502#102—262no—
503#102—262no—
504#102—521no—
505#102—521no—
506C22⋊C8—262no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—261no—
511#95C22⋊D1311yescharacteristic
512#95C22⋊D1311yescharacteristic
513C2×C13—24no—
514C2×C13#243711yescharacteristic
515C2×C13C2×#47411yescharacteristic
516C2×C13#308111yescharacteristic
517C2×C13#326611yescharacteristic
518C2×C13D4×D811yescharacteristic
519C2×C13#329411yescharacteristic
520C2×C13#331411yescharacteristic
521D13—44no—
522D13—82no—
523C24—261no—
524C24—261no—
525C24—264no—
526C24—522no—
527C24—522no—
528C24—522no—
529C24—522no—
530C24—1041no—
531C24—1041no—
532C24C2×C22⋊D1311yescharacteristic
533C2×Q8—42no—
534C2×Q8—42no—
535C2×Q8—81no—
536C2×D4—132no—
537C2×D4—132no—
538C2×D4—132no—
539C2×D4—132no—
540C2×D4—268no—
541C2×D4—264no—
542C2×D4—261no—
543C2×D4—261no—
544C2×D4—261no—
545C2×D4—261no—
546C2×D4—261no—
547C2×D4—261no—
548C2×D4—261no—
549C2×D4—261no—
550C2×D4—524no—
551C2×D4—524no—
552C2×D4—524no—
553C2×D4—522no—
554C2×D4—522no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—81no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—522no—
569C22×C4—522no—
570C22×C4—522no—
571C22×C4—522no—
572C22×C4—1041no—
573C22×C4—1041no—
574C22×C4Q8×D1312yes—
575C22×C4#613112yes—
576C22×C4C2×C22⋊D1311yescharacteristic
577C22×C4C2×C22⋊D1311yescharacteristic
578C22×C4C2×C22⋊D1311yescharacteristic
579C22×C4C2×C22⋊D1311yescharacteristic
580C22×C4C2×C22⋊D1311yescharacteristic
581C22×C4C23×D1311yescharacteristic
582C2×C8—132no—
583C2×C8—261no—
584C2×C8—261no—
585C2×C8—261no—
586C2×C8—261no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8—261no—
590C2×C8—261no—
591C2×C8—261no—
592C2×C8—261no—
593C2×C8—261no—
594C2×C8—524no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—81no—
608C4⋊C4—261no—
609C4⋊C4—261no—
610C4⋊C4—261no—
611C4⋊C4—261no—
612C4⋊C4D4×D1312yes—
613C22⋊C4—22no—
614C22⋊C4—42no—
615C22⋊C4—522no—
616C22⋊C4—522no—
617C22⋊C4—522no—
618C22⋊C4—522no—
619C22⋊C4—522no—
620C22⋊C4—1041no—
621C22⋊C4—1041no—
622C22⋊C4#610414yes—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C13#2595011yescharacteristic, complemented, Sylow
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—262no—
633C23—262no—
634C23—262no—
635C23—262no—
636C23—528no—
637C23—521no—
638C23—521no—
639C23—521no—
640C23—521no—
641C23—521no—
642C23—521no—
643C23—521no—
644C23—528no—
645C23—521no—
646C23—521no—
647C23—521no—
648C23—1044no—
649C23—1044no—
650C23—1044no—
651C23—1044no—
652C23—1044no—
653C23C2×#610412yes—
654C23#8819612yes—
655C23#8820012yes—
656C23C22×C22⋊D1311yescharacteristic
657Q8—84no—
658D4—134no—
659D4—262no—
660D4—262no—
661D4—262no—
662D4—262no—
663D4—262no—
664D4—528no—
665D4—521no—
666D4—521no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—84no—
696C2×C4—521no—
697C2×C4—521no—
698C2×C4—521no—
699C2×C4—521no—
700C2×C4—521no—
701C2×C4—521no—
702C2×C4—1044no—
703C2×C4—1044no—
704C2×C4C2×#610412yes—
705C2×C4C2×#610412yes—
706C2×C4#8820012yes—
707C2×C4C2×D4×D1311yescharacteristic
708C2×C4#8825111yescharacteristic
709C2×C4C2×Q8×D1311yescharacteristic
710C2×C4C2×#613111yescharacteristic
711C2×C4#41×D1311yescharacteristic
712C2×C4#8825611yescharacteristic
713C8—262no—
714C8—521no—
715C8—521no—
716C8—521no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—264no—
724C22—522no—
725C22—522no—
726C22—522no—
727C22—522no—
728C22—522no—
729C22—522no—
730C22—522no—
731C22—522no—
732C22—522no—
733C22—10416no—
734C22—1041no—
735C22—1041no—
736C22—1041no—
737C22—1041no—
738C22#1171874814yescomplemented
739C22C22×#610411yescharacteristic
740C22D4×C22⋊D1311yescharacteristic
741C22C2×#8819611yescharacteristic
742C22C2×#8820011yescharacteristic
743C22#1171953411yescharacteristic
744C22#1171954011yescharacteristic
745C22#1171954211yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—42no—
750C4—41no—
751C4—41no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—1041no—
756C4—1041no—
757C4D13×C22⋊Q811yescharacteristic
758C4#1171933511yescharacteristic
759C4#1171933911yescharacteristic
760C4#1171934211yescharacteristic
761C2—24no—
762C2—524no—
763C2—1042no—
764C2#1311849911yescharacteristic
765C2C2×#1171874811yescharacteristic
766C2#1312466111yescharacteristic
767C2#1312634711yescharacteristic
768C2D4×#610411yescharacteristic
769C2#1312664311yescharacteristic
770C2#1312691111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2440C2
socleC23×C13C22×D4
prime radicalC23×D52C22
hypercenter#2440D13
hypocenterC13#25950
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#11718748C2semidirect
4. #13116365C2semidirect
5. #13116221C2semidirect
6. #13116221C2semidirect
7. #13115969C2semidirect
8. #13115082C2semidirect
9. #13115082C2semidirect
10. #13115024C2semidirect
11. #13115016C2semidirect
12. #13114863C2semidirect
13. #13114833C2semidirect
15. C13×#2440C2semidirect
17. C2×C13×C4⋊Q8C22semidirect
26. C13×#389C22semidirect
27. C13×#389C22semidirect
29. C13×#384C22semidirect
44. C2×#88047C22semidirect
45. C2×#88047C22semidirect
46. C2×#88047C22semidirect
47. C2×#88047C22semidirect
51. C2×C4⋊#1055C22semidirect
52. C2×C4⋊#1055C22semidirect
55. #11718121C22semidirect
56. #11718121C22semidirect
57. #11718121C22semidirect
58. #11718121C22semidirect
59. #11718116C22semidirect
60. #11718116C22semidirect
71. C22×D52Q8semidirect
245. #2440D13semidirect
340. D52C22⋊Q8semidirect
349. C2×C4⋊Q8C2×D13semidirect
376. #389C2×D13semidirect
377. #389C2×D13semidirect
381. #384C2×D13semidirect
398. C22×C13#474semidirect
627. C13#25950semidirect
738. C22#11718748semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
C22×#880492
C22⋊C4×D522
#131163652
#131162212
#131159692
#131150822
#131150242
#131150162
#131148632
#131148332
#131147662
C13×#24402
#2595013