Finite Group Databasebeta

← #15885144

Subgroups — #15885144

Order 3328.

992 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718499C211yesmaximal, characteristic, complemented
2C2×#11718789C211yesmaximal, characteristic, complemented
3C2×#11718772C211yesmaximal, characteristic, complemented
4#13118072C211yesmaximal, characteristic
5#13115633C211yesmaximal, characteristic, complemented
6#13115552C211yesmaximal, characteristic, complemented
7#13115448C211yesmaximal, characteristic, complemented
8#13115441C211yesmaximal, characteristic, complemented
9#13115133C211yesmaximal, characteristic, complemented
10#13115128C211yesmaximal, characteristic, complemented
11#13115017C211yesmaximal, characteristic, complemented
12#13115017C211yesmaximal, characteristic, complemented
13#13114713C211yesmaximal, characteristic, complemented
14#13114602C211yesmaximal, characteristic, complemented
15C2×C13×#424C211yesmaximal, characteristic, complemented
16C22×C13×M16C2211yescharacteristic
17C23×C8×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×C4×C22⋊D13C2211yescharacteristic
20C2×C4×C22⋊D13C2211yescharacteristic
21C22×#6094C2211yescharacteristic
22C22×#6094C2211yescharacteristic
23C2×C4×D52C2211yescharacteristic
24C13×#424—24no—
25C2×C13×C4⋊C8C2211yescharacteristic
26C2×C13×C4⋊C8C2211yescharacteristic
27C2×C13×C4⋊C8C2211yescharacteristic
28C2×C13×C4⋊C8C2211yescharacteristic
29C2×C22⋊#1055C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31#11718789—24no—
32#11718772—24no—
33C2×#88060C2211yescharacteristic
34C2×#88060C2211yescharacteristic
35C2×#88060C2211yescharacteristic
36C2×#88060C2211yescharacteristic
37C2×#88060C2211yescharacteristic
38C2×#88060C2211yescharacteristic
39C2×#88055C2211yescharacteristic
40C2×#88054C2211yescharacteristic
41C2×#88054C2211yescharacteristic
42C2×C8×Dic13C2211yescharacteristic
43#11718655C411yescharacteristic
44#11718655C411yescharacteristic
45#11718652C411yescharacteristic
46#11718644C411yescharacteristic
47#11718622C411yescharacteristic
48#11718622C411yescharacteristic
49#11718621C411yescharacteristic
50#11718614C411yescharacteristic
51C4×#6103C2211yescharacteristic
52C4×#6103C2211yescharacteristic
53C4×C4⋊Dic13C2211yescharacteristic
54C2×#88043C2211yescharacteristic
55C2×C4×#1055C2211yescharacteristic
56#11718499—24no—
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C22×C22⋊D13C2×C411yescharacteristic
65C22×C22⋊D13C2×C411yescharacteristic
66C22×D52C2×C411yescharacteristic
67C22×C4×D13C2311yescharacteristic
68C22×C4×D13C2311yescharacteristic
69C2×C13×M16—22no—
70C2×C13×M16—22no—
71C2×C13×M16—41no—
72C22×C8×C13—22no—
73C22×C8×C13—22no—
74C22×C8×C13—41no—
75C22×C8×C13C2311yescharacteristic
76C22×C8×C13C2311yescharacteristic
77C22×C8×C13C2311yescharacteristic
78C22×C8×C13C2311yescharacteristic
79C13×#117—22no—
80C13×#117—22no—
81C2×C13×C4⋊C4C2×C411yescharacteristic
82C2×C13×C4⋊C4C2×C411yescharacteristic
83C2×C13×C22⋊C4C2×C411yescharacteristic
84C2×C13×C22⋊C4C2×C411yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13C2×C411yescharacteristic
88C2×C22⋊Dic13C2×C411yescharacteristic
89C4×C22⋊D13—22no—
90C4×C22⋊D13—22no—
91C4×C22⋊D13—22no—
92C4×C22⋊D13—22no—
93C2×#6103C2×C411yescharacteristic
94C2×#6103C2×C411yescharacteristic
95C2×#6103C2×C411yescharacteristic
96C2×#6103C2×C411yescharacteristic
97C2×#6103C2×C411yescharacteristic
98C2×#6103C2×C411yescharacteristic
99C2×#6103C2×C411yescharacteristic
100C2×#6103C2×C411yescharacteristic
101C2×C4⋊Dic13C2×C411yescharacteristic
102C2×C4⋊Dic13C2×C411yescharacteristic
103C2×C4⋊Dic13C2×C411yescharacteristic
104C2×#6101C2×C411yescharacteristic
105C2×#6101C2×C411yescharacteristic
106C2×C4×Dic13C2311yescharacteristic
107C2×C4×Dic13C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C2×#6094—22no—
113C2×#6094—22no—
114C2×#6094—22no—
115C2×#6094—22no—
116C2×#6094—41no—
117C2×#6094—41no—
118C4×D52—22no—
119C4×D52—22no—
120C13×C4⋊C8—22no—
121C13×C4⋊C8—22no—
122C13×C4⋊C8—22no—
123C13×C4⋊C8D414yescomplemented
124#88071C2×C411yescharacteristic
125#88071C2×C411yescharacteristic
126#88071C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129#88071C2×C411yescharacteristic
130C22⋊#1055—22no—
131C22⋊#1055D414yescomplemented
132#88060—22no—
133#88060—22no—
134#88060—22no—
135#88060—22no—
136#88060—41no—
137#88060—41no—
138#88055—22no—
139#88054—22no—
140#88054—22no—
141C8×Dic13—22no—
142#88043—22no—
143C4×#1055—22no—
144#22994—131nomaximal, Sylow
145C24×C13C22×C411yescharacteristic
146C23×D13C22×C411yescharacteristic
147C23×D13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C22×C411yescharacteristic
155C22×C4×C13C22×C411yescharacteristic
156C22×C4×C13C22×C411yescharacteristic
157C22×C4×C13C2×D412yes—
158C22×C4×C13#4112yes—
159C22×C4×C13C2411yescharacteristic
160C2×C22⋊D13—22no—
161C2×C22⋊D13—22no—
162C2×C22⋊D13—22no—
163C2×C22⋊D13—41no—
164C2×C22⋊D13—41no—
165C2×C22⋊D13—41no—
166C22×Dic13C22×C411yescharacteristic
167C22×Dic13C22×C411yescharacteristic
168C22×Dic13C22×C411yescharacteristic
169C22×Dic13C22×C411yescharacteristic
170C22×Dic13C22×C411yescharacteristic
171C22×Dic13C22×C411yescharacteristic
172C2×D52—22no—
173C2×D52—41no—
174C2×D52—41no—
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—21no—
185C2×C4×D13—21no—
186C2×C4×D13—21no—
187C13×M16—44no—
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—44no—
199C2×C8×C13C2×D412yes—
200C2×C8×C13C2×D412yes—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—22no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—22no—
205C42×C13—21no—
206C42×C13—21no—
207C42×C13C2×D412yes—
208C42×C13#4112yes—
209C22⋊Dic13—22no—
210C22⋊Dic13—22no—
211#6103—22no—
212#6103—22no—
213#6103—22no—
214#6103—22no—
215#6103—22no—
216#6103—41no—
217#6103—41no—
218#6103—41no—
219C4⋊Dic13—22no—
220C4⋊Dic13—22no—
221C4⋊Dic13—41no—
222#6101—22no—
223#6101—22no—
224C4×Dic13—21no—
225C4×Dic13—21no—
226C4×Dic13—21no—
227C4×Dic13—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×#1055—21no—
238C2×#1055C2×D412yes—
239C2×#1055C2×D412yes—
240#6094—44no—
241#6094—44no—
242C2×#436—131no—
243C2×#436—131no—
244C2×#435—131no—
245C2×#424D1311yescharacteristic, complemented
246#2392—131no—
247#1955—131no—
248#1939—131no—
249#1924—131no—
250#1923—131no—
251#1870—131no—
252#1869—131no—
253#1851—131no—
254#1851—131no—
255#1771—131no—
256#1750—131no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13C4×D412yes—
264C23×C13C23×C411yescharacteristic
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×D13—21no—
275C22×D13—21no—
276C22×D13—21no—
277C22×D13—21no—
278C22×D13—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—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13C4×D412yes—
296C2×C4×C13C4×D412yes—
297C2×C4×C13C4×D412yes—
298C2×C4×C13C22×D411yescharacteristic
299C2×C4×C13C22×D411yescharacteristic
300C2×C4×C13C2×#4111yescharacteristic
301C2×C4×C13C2×#4111yescharacteristic
302C2×C4×C13H(5,𝔽2)11yescharacteristic
303C2×C4×C132−1+411yescharacteristic
304C22⋊D13—44no—
305C22⋊D13—44no—
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×Dic13—21no—
317C2×Dic13—21no—
318C2×Dic13—21no—
319C2×Dic13—21no—
320C2×Dic13—21no—
321C2×Dic13—21no—
322C2×Dic13—21no—
323C2×Dic13#13112yes—
324D52—44no—
325C4×D13—41no—
326C4×D13—41no—
327C4×D13—41no—
328C4×D13—41no—
329C4×D13—41no—
330C4×D13—41no—
331C4×D13—41no—
332C4×D13—41no—
333C8×C13—22no—
334C8×C13—22no—
335C8×C13—41no—
336C8×C13—41no—
337#1055—22no—
338#1055—22no—
339#1055—41no—
340#1055—41no—
341C22×M16—131no—
342C22×M16—131no—
343C22×M16C2×D1311yescharacteristic
344C23×C8C2×D1311yescharacteristic
345C2×C4×D4—131no—
346C2×C4×D4—131no—
347C2×C4×D4—131no—
348C2×#117C2×D1311yescharacteristic
349#436—264no—
350#436—264no—
351#435—264no—
352#424—24no—
353C2×C4⋊C8—131no—
354C2×C4⋊C8—131no—
355C2×C4⋊C8C2×D1311yescharacteristic
356C2×C4⋊C8C2×D1311yescharacteristic
357C2×C4⋊C8C2×D1311yescharacteristic
358C2×C4⋊C8C2×D1311yescharacteristic
359C2×C22⋊C8—131no—
360C2×C22⋊C8—131no—
361C2×C22⋊C8—131no—
362C2×C22⋊C8—131no—
363C2×C22⋊C8—131no—
364C2×C22⋊C8—131no—
365C2×C22⋊C8—131no—
366C2×C22⋊C8—131no—
367C2×#97—131no—
368C2×#97—131no—
369C2×C4×C8—131no—
370C2×C4×C8—131no—
371#398—131no—
372#397—131no—
373#396—131no—
374#396—131no—
375#394—131no—
376#394—131no—
377#394—131no—
378#392—131no—
379C4×C4⋊C4—131no—
380C4×C22⋊C4—131no—
381C4×C22⋊C4—131no—
382#336—131no—
383#336—131no—
384#336—131no—
385#336—131no—
386#336—131no—
387#336—131no—
388C22×C13—22no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—41no—
392C22×C13—41no—
393C22×C13—41no—
394C22×C13—41no—
395C22×C13C2×C4×D411yescharacteristic
396C22×C13C2×C4×D411yescharacteristic
397C22×C13#52011yescharacteristic
398C22×C13C2×#13111yescharacteristic
399C22×C13#56811yescharacteristic
400C22×C13#56811yescharacteristic
401C22×C13#56811yescharacteristic
402C2×D13—41no—
403C2×D13—41no—
404C2×D13—41no—
405C2×D13—41no—
406C2×D13—41no—
407C2×D13—41no—
408C2×D13—41no—
409C2×D13—41no—
410C2×D13—41no—
411C2×D13—41no—
412C2×D13—41no—
413C2×D13—41no—
414C2×D13—41no—
415C2×D13—41no—
416C4×C13—22no—
417C4×C13—22no—
418C4×C13—22no—
419C4×C13—41no—
420C4×C13—41no—
421C4×C13D4211yescharacteristic
422C4×C13#54711yescharacteristic
423C4×C13#54811yescharacteristic
424C4×C13#55311yescharacteristic
425Dic13—22no—
426Dic13—41no—
427Dic13—41no—
428Dic13—41no—
429Dic13—41no—
430Dic13—41no—
431C22×D4—131no—
432C22×D4—131no—
433C22×D4—131no—
434C23×C4—131no—
435C23×C4—131no—
436C23×C4C22×D1311yescharacteristic
437C2×M16—22no—
438C2×M16—22no—
439C2×M16—41no—
440C2×M16—262no—
441C2×M16—262no—
442C2×M16—262no—
443C2×M16—262no—
444C2×M16—521no—
445C2×M16—521no—
446C22×C8—22no—
447C22×C8—22no—
448C22×C8—41no—
449C22×C8—131no—
450C22×C8—131no—
451C22×C8—131no—
452C22×C8—131no—
453C22×C8C22×D1311yescharacteristic
454C22×C8C22×D1311yescharacteristic
455C22×C8C22×D1311yescharacteristic
456C22×C8C22×D1311yescharacteristic
457C4×D4—262no—
458C4×D4—262no—
459C4×D4—262no—
460C4×D4—262no—
461C4×D4—262no—
462C4×D4—262no—
463#117—22no—
464#117—22no—
465C2×C4⋊C4—131no—
466C2×C4⋊C4—131no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—131no—
470C2×C4⋊C4C4×D1311yescharacteristic
471C2×C4⋊C4C4×D1311yescharacteristic
472C2×C22⋊C4—131no—
473C2×C22⋊C4—131no—
474C2×C22⋊C4—131no—
475C2×C22⋊C4—131no—
476C2×C22⋊C4—131no—
477C2×C22⋊C4—131no—
478C2×C22⋊C4—131no—
479C2×C22⋊C4—131no—
480C2×C22⋊C4—131no—
481C2×C22⋊C4—131no—
482C2×C22⋊C4C4×D1311yescharacteristic
483C2×C22⋊C4C4×D1311yescharacteristic
484C2×C42—131no—
485C2×C42—131no—
486C2×C42C22×D1311yescharacteristic
487C2×C42C22×D1311yescharacteristic
488C4⋊C8—22no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—262no—
492C4⋊C8—262no—
493C4⋊C8C22⋊D1314yescomplemented
494C22⋊C8—134no—
495C22⋊C8—262no—
496C22⋊C8—262no—
497C22⋊C8—262no—
498C22⋊C8—262no—
499C22⋊C8—262no—
500C22⋊C8—521no—
501C22⋊C8—521no—
502#97—262no—
503#97—262no—
504C4×C8—262no—
505C4×C8—262no—
506#95—131no—
507#95—131no—
508#95—131no—
509#95—131no—
510#95—131no—
511#95—131no—
512C2×C13—42no—
513C2×C13#236111yescharacteristic
514C2×C13#293011yescharacteristic
515C2×C13#293011yescharacteristic
516C2×C13#293311yescharacteristic
517C2×C13#293511yescharacteristic
518C2×C13#299311yescharacteristic
519C2×C13#299511yescharacteristic
520D13—81no—
521D13—81no—
522C24—131no—
523C24—131no—
524C24C2×C4×D1311yescharacteristic
525C2×D4—262no—
526C2×D4—262no—
527C2×D4—262no—
528C2×D4—262no—
529C2×D4—521no—
530C2×D4—521no—
531C2×D4—521no—
532C2×D4—521no—
533C2×D4—521no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—131no—
539C22×C4—131no—
540C22×C4—131no—
541C22×C4—131no—
542C22×C4—131no—
543C22×C4—131no—
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×C4C2×C4×D1311yescharacteristic
557C22×C4C2×C4×D1311yescharacteristic
558C22×C4C2×C4×D1311yescharacteristic
559C22×C4C2×C4×D1311yescharacteristic
560C22×C4C2×C4×D1311yescharacteristic
561C22×C4D4×D1312yes—
562C22×C4#613112yes—
563C22×C4C23×D1311yescharacteristic
564M16—44no—
565M16—524no—
566M16—524no—
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—21no—
576C2×C8—21no—
577C2×C8—44no—
578C2×C8—132no—
579C2×C8—132no—
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—261no—
589C2×C8—261no—
590C2×C8C2×C22⋊D1312yes—
591C2×C8C2×C22⋊D1312yes—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—262no—
595C4⋊C4—262no—
596C4⋊C4—262no—
597C4⋊C4—262no—
598C4⋊C4—521no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—262no—
602C22⋊C4—262no—
603C22⋊C4—262no—
604C22⋊C4—262no—
605C22⋊C4—262no—
606C22⋊C4—262no—
607C22⋊C4—262no—
608C22⋊C4—521no—
609C22⋊C4—521no—
610C22⋊C4—521no—
611C42—21no—
612C42—21no—
613C42—261no—
614C42—261no—
615C42—261no—
616C42—261no—
617C42#612712yes—
618C42C2×C22⋊D1312yes—
619C13#2299411yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—261no—
627C23—261no—
628C23—261no—
629C23—261no—
630C23—261no—
631C23—261no—
632C23—261no—
633C23—261no—
634C23—261no—
635C23—261no—
636C23—261no—
637C23—261no—
638C23—261no—
639C23—261no—
640C23#8814712yes—
641C23C22×C4×D1311yescharacteristic
642D4—524no—
643D4—524no—
644D4—524no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—132no—
662C2×C4—261no—
663C2×C4—261no—
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—261no—
678C2×C4—261no—
679C2×C4—521no—
680C2×C4—521no—
681C2×C4—521no—
682C2×C4—521no—
683C2×C4—521no—
684C2×C4—521no—
685C2×C4—521no—
686C2×C4—521no—
687C2×C4#8814712yes—
688C2×C4C4×C22⋊D1312yes—
689C2×C4C4×C22⋊D1312yes—
690C2×C4C2×#612711yescharacteristic
691C2×C4C2×D4×D1311yescharacteristic
692C2×C4#8825111yescharacteristic
693C2×C4C2×#613111yescharacteristic
694C2×C4#8825411yescharacteristic
695C2×C4C22×C22⋊D1311yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—262no—
701C8—262no—
702C8—521no—
703C8—521no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—521no—
712C22—521no—
713C22—521no—
714C22—521no—
715C22—521no—
716C22—521no—
717C22—521no—
718C22—521no—
719C22—521no—
720C22—521no—
721C22—521no—
722C22—521no—
723C22—521no—
724C22—521no—
725C22C2×#8814711yescharacteristic
726C22#1171920911yescharacteristic
727C22D13×#13111yescharacteristic
728C22#1171945511yescharacteristic
729C22#1171945511yescharacteristic
730C22#1171945511yescharacteristic
731C22C2×C4×C22⋊D1311yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—262no—
738C4—521no—
739C4—521no—
740C4—521no—
741C4—521no—
742C4—521no—
743C4#1171921211yescharacteristic
744C4#1171921911yescharacteristic
745C4D4×C22⋊D1311yescharacteristic
746C4#1171952211yescharacteristic
747C2—42no—
748C2—1041no—
749C2—1041no—
750C2#1311785211yescharacteristic
751C2#1312353711yescharacteristic
752C2#1312353811yescharacteristic
753C2#1312356011yescharacteristic
754C2#1312357811yescharacteristic
755C2#1312398311yescharacteristic
756C2#1312400411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#424C2
prime radical#11718621C4
cosocleC22×C4×C13C24
hypercenterC2×#424D13
hypocenterC13#22994
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
1. C2×#11718499C2semidirect
2. C2×#11718789C2semidirect
3. C2×#11718772C2semidirect
5. #13115633C2semidirect
6. #13115552C2semidirect
7. #13115448C2semidirect
8. #13115441C2semidirect
9. #13115133C2semidirect
10. #13115128C2semidirect
11. #13115017C2semidirect
12. #13115017C2semidirect
13. #13114713C2semidirect
14. #13114602C2semidirect
15. C2×C13×#424C2semidirect
123. C13×C4⋊C8D4semidirect
131. C22⋊#1055D4semidirect
245. C2×#424D13semidirect
493. C4⋊C8C22⋊D13semidirect
619. C13#22994semidirect

Maximal subgroups

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

subgroupindex
C2×#117184992
C2×#117187892
C2×#117187722
#131180722
#131156332
#131155522
#131154482
#131154412
#131151332
#131151282
#131150172
#131147132
#131146022
C2×C13×#4242
#2299413