Finite Group Databasebeta

← #15885145

Subgroups — #15885145

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×#11718789C211yesmaximal, characteristic, complemented
2C2×#11718390C211yesmaximal, characteristic, complemented
3C2×#11718763C211yesmaximal, characteristic, complemented
4#13118078C211yesmaximal, characteristic
5#13115632C211yesmaximal, characteristic, complemented
6#13115551C211yesmaximal, characteristic, complemented
7#13115449C211yesmaximal, characteristic, complemented
8#13115439C211yesmaximal, characteristic, complemented
9#13115134C211yesmaximal, characteristic, complemented
10#13115128C211yesmaximal, characteristic, complemented
11#13115019C211yesmaximal, characteristic, complemented
12#13115017C211yesmaximal, characteristic, complemented
13#13114712C211yesmaximal, characteristic, complemented
14#13114604C211yesmaximal, characteristic, complemented
15C2×C13×#435C211yesmaximal, characteristic, complemented
16C22×C13×M16C2211yescharacteristic
17C23×C8×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×C4×C22⋊D13C2211yescharacteristic
20C2×C4×C22⋊D13C2211yescharacteristic
21C2×#88180C2211yescharacteristic
22C22×#6099C2211yescharacteristic
23C22×#6094C2211yescharacteristic
24C13×#435—24no—
25C2×C13×C4⋊C8C2211yescharacteristic
26C2×C13×C22⋊C8C2211yescharacteristic
27C2×C13×C22⋊C8C2211yescharacteristic
28C2×C13×#97C2211yescharacteristic
29#11718884C411yescharacteristic
30#11718883C411yescharacteristic
31C4×C22⋊Dic13C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35#11718789—24no—
36C2×#88060C2211yescharacteristic
37C2×#88060C2211yescharacteristic
38C2×#88060C2211yescharacteristic
39#11718763—24no—
40C2×#88055C2211yescharacteristic
41C2×#88054C2211yescharacteristic
42C2×#88054C2211yescharacteristic
43C2×#88054C2211yescharacteristic
44C2×#88054C2211yescharacteristic
45C2×#88054C2211yescharacteristic
46C2×C8×Dic13C2211yescharacteristic
47C2×C8×Dic13C2211yescharacteristic
48#11718655C411yescharacteristic
49#11718645C411yescharacteristic
50#11718622C411yescharacteristic
51#11718620C411yescharacteristic
52#11718613C411yescharacteristic
53#11718609C411yescharacteristic
54C4×#6103C2211yescharacteristic
55C4×#6101C2211yescharacteristic
56#11718390—24no—
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63C22×D4×C13C2×C411yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C22×C22⋊D13C2×C411yescharacteristic
67C22×C22⋊D13C2×C411yescharacteristic
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
79C4×D4×C13—22no—
80C4×D4×C13—22no—
81C2×C13×C4⋊C4C2×C411yescharacteristic
82C2×C13×C22⋊C4C2×C411yescharacteristic
83C2×C13×C22⋊C4C2×C411yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C22⋊Dic13C2×C411yescharacteristic
86C2×C22⋊Dic13C2×C411yescharacteristic
87C2×C22⋊Dic13C2×C411yescharacteristic
88C2×C22⋊Dic13C2×C411yescharacteristic
89C2×C22⋊Dic13C2×C411yescharacteristic
90C2×C22⋊Dic13C2×C411yescharacteristic
91C4×C22⋊D13—22no—
92C4×C22⋊D13—22no—
93C4×C22⋊D13—22no—
94C4×C22⋊D13—22no—
95C2×#6103C2×C411yescharacteristic
96C2×#6103C2×C411yescharacteristic
97C2×#6103C2×C411yescharacteristic
98C2×#6103C2×C411yescharacteristic
99#88180—22no—
100#88180—22no—
101C2×C4⋊Dic13C2×C411yescharacteristic
102C2×C4⋊Dic13C2×C411yescharacteristic
103C2×#6101C2×C411yescharacteristic
104C2×#6101C2×C411yescharacteristic
105C2×#6101C2×C411yescharacteristic
106C2×#6101C2×C411yescharacteristic
107C2×C4×Dic13C2311yescharacteristic
108C2×C4×Dic13C2311yescharacteristic
109C2×C4×Dic13C2311yescharacteristic
110C2×#6099—22no—
111C2×#6099—22no—
112C2×#6099—41no—
113C22×#1055C2311yescharacteristic
114C22×#1055C2311yescharacteristic
115C22×#1055C2311yescharacteristic
116C22×#1055C2311yescharacteristic
117C2×#6094—22no—
118C2×#6094—22no—
119C2×#6094—41no—
120C13×C4⋊C8—22no—
121C13×C22⋊C8—22no—
122C13×C22⋊C8D414yescomplemented
123C13×#97—22no—
124#88071C2×C411yescharacteristic
125#88071C2×C411yescharacteristic
126#88071C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129#88071C2×C411yescharacteristic
130C22⋊#1055—22no—
131C22⋊#1055—22no—
132C22⋊#1055—41no—
133#88060—22no—
134#88060—22no—
135#88060—41no—
136#88055—22no—
137#88054—22no—
138#88054—22no—
139#88054—22no—
140#88054—22no—
141#88054D414yescomplemented
142C8×Dic13—22no—
143C8×Dic13—22no—
144#22994—131nomaximal, Sylow
145C24×C13C22×C411yescharacteristic
146C24×C13C22×C411yescharacteristic
147C23×D13C22×C411yescharacteristic
148C2×D4×C13—22no—
149C2×D4×C13—41no—
150C2×D4×C13—41no—
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×C13C22×C411yescharacteristic
162C22×C4×C13C22×C411yescharacteristic
163C22×C4×C13C22×C411yescharacteristic
164C22×C4×C13C22×C411yescharacteristic
165C22×C4×C13C2×D412yes—
166C22×C4×C13#4112yes—
167C22×C4×C13C2411yescharacteristic
168C2×C22⋊D13—22no—
169C2×C22⋊D13—22no—
170C2×C22⋊D13—22no—
171C2×C22⋊D13—41no—
172C2×C22⋊D13—41no—
173C2×C22⋊D13—41no—
174C22×Dic13C22×C411yescharacteristic
175C22×Dic13C22×C411yescharacteristic
176C22×Dic13C22×C411yescharacteristic
177C22×Dic13C22×C411yescharacteristic
178C22×Dic13C22×C411yescharacteristic
179C22×Dic13C22×C411yescharacteristic
180C22×Dic13C22×C411yescharacteristic
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—44no—
198C2×C8×C13C2×D412yes—
199C2×C8×C13C2×D412yes—
200C2×C8×C13C2×D412yes—
201C13×C4⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—22no—
204C42×C13—21no—
205C42×C13—21no—
206C22⋊Dic13—22no—
207C22⋊Dic13—22no—
208C22⋊Dic13—22no—
209C22⋊Dic13—22no—
210C22⋊Dic13—22no—
211C22⋊Dic13—41no—
212#6103—22no—
213#6103—22no—
214#6103—41no—
215#6103—41no—
216C4⋊Dic13—22no—
217C4⋊Dic13—22no—
218#6101—22no—
219#6101—22no—
220#6101—22no—
221#6101—41no—
222C4×Dic13—21no—
223C4×Dic13—21no—
224C4×Dic13—21no—
225C4×Dic13—21no—
226C4×Dic13C2×D412yes—
227C4×Dic13#4112yes—
228#6099—44no—
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×#1055—21no—
239C2×#1055—21no—
240C2×#1055C2×D412yes—
241#6094—44no—
242C2×#436—131no—
243C2×#436—131no—
244C2×#435D1311yescharacteristic, complemented
245C2×#424—131no—
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×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13C4×D412yes—
271C23×C13C23×C411yescharacteristic
272C22×D13—21no—
273C22×D13—21no—
274C22×D13—21no—
275C22×D13—21no—
276C22×D13—21no—
277C22×D13—21no—
278C22×D13—21no—
279D4×C13—44no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
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—21no—
294C2×C4×C13—21no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13C4×D412yes—
300C2×C4×C13C22×D411yescharacteristic
301C2×C4×C13C22×D411yescharacteristic
302C2×C4×C13C2×#4111yescharacteristic
303C2×C4×C13C2×#4111yescharacteristic
304C2×C4×C13H(5,𝔽2)11yescharacteristic
305C2×C4×C132−1+411yescharacteristic
306C22⋊D13—44no—
307C22⋊D13—44no—
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—21no—
324C2×Dic13—21no—
325C2×Dic13—21no—
326C2×Dic13C4×D412yes—
327C2×Dic13C4×D412yes—
328C2×Dic13#13112yes—
329C4×D13—41no—
330C4×D13—41no—
331C4×D13—41no—
332C4×D13—41no—
333C8×C13—22no—
334C8×C13—22no—
335C8×C13—22no—
336C8×C13—41no—
337#1055—22no—
338#1055—41no—
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×D4C2×D1311yescharacteristic
348C2×#117—131no—
349#436—264no—
350#436—264no—
351#435—24no—
352#424—264no—
353C2×C4⋊C8—131no—
354C2×C4⋊C8—131no—
355C2×C4⋊C8—131no—
356C2×C4⋊C8—131no—
357C2×C4⋊C8—131no—
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⋊C8C2×D1311yescharacteristic
366C2×C22⋊C8C2×D1311yescharacteristic
367C2×#97—131no—
368C2×#97C2×D1311yescharacteristic
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×C13—41no—
396C22×C13—41no—
397C22×C13—41no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—41no—
401C22×C13—41no—
402C22×C13C2×C4×D411yescharacteristic
403C22×C13C2×C4×D411yescharacteristic
404C22×C13#52011yescharacteristic
405C22×C13C2×#13111yescharacteristic
406C22×C13#56811yescharacteristic
407C22×C13#56811yescharacteristic
408C22×C13#56811yescharacteristic
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—41no—
418C4×C13—41no—
419C4×C13—41no—
420C4×C13D4211yescharacteristic
421C4×C13#54711yescharacteristic
422C4×C13#54811yescharacteristic
423C4×C13#55311yescharacteristic
424Dic13—22no—
425Dic13—22no—
426Dic13—22no—
427Dic13—41no—
428Dic13—41no—
429Dic13—41no—
430Dic13—41no—
431C22×D4—131no—
432C22×D4—131no—
433C22×D4C4×D1311yescharacteristic
434C23×C4—131no—
435C23×C4C22×D1311yescharacteristic
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—22no—
458C4×D4—22no—
459C4×D4—262no—
460C4×D4—262no—
461C4×D4—262no—
462C4×D4—262no—
463#117—262no—
464#117—262no—
465C2×C4⋊C4—131no—
466C2×C4⋊C4—131no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—131no—
470C2×C4⋊C4—131no—
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×C42—131no—
487C2×C42C22×D1311yescharacteristic
488C4⋊C8—22no—
489C4⋊C8—134no—
490C4⋊C8—262no—
491C4⋊C8—262no—
492C4⋊C8—262no—
493C4⋊C8—262no—
494C22⋊C8—22no—
495C22⋊C8—262no—
496C22⋊C8—262no—
497C22⋊C8—262no—
498C22⋊C8—262no—
499C22⋊C8—521no—
500C22⋊C8—521no—
501C22⋊C8C22⋊D1314yescomplemented
502#97—22no—
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—81no—
514C2×C13#236111yescharacteristic
515C2×C13#293011yescharacteristic
516C2×C13#293011yescharacteristic
517C2×C13#293311yescharacteristic
518C2×C13#293511yescharacteristic
519C2×C13#299311yescharacteristic
520C2×C13#299511yescharacteristic
521D13—81no—
522C24—131no—
523C24C2×C4×D1311yescharacteristic
524C24C2×C4×D1311yescharacteristic
525C2×D4—22no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—262no—
529C2×D4—262no—
530C2×D4—262no—
531C2×D4—521no—
532C2×D4—521no—
533C2×D4—521no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—131no—
545C22×C4—131no—
546C22×C4—131no—
547C22×C4—131no—
548C22×C4—131no—
549C22×C4—131no—
550C22×C4—131no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4C2×C4×D1311yescharacteristic
558C22×C4C2×C4×D1311yescharacteristic
559C22×C4C2×C4×D1311yescharacteristic
560C22×C4C2×C4×D1311yescharacteristic
561C22×C4#612712yes—
562C22×C4C2×C22⋊D1312yes—
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—44no—
577C2×C8—132no—
578C2×C8—261no—
579C2×C8—261no—
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×C8D4×D1312yes—
590C2×C8C2×C22⋊D1312yes—
591C2×C8C2×C22⋊D1312yes—
592C4⋊C4—22no—
593C4⋊C4—262no—
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—132no—
614C42—132no—
615C42—261no—
616C42—261no—
617C42—261no—
618C42—261no—
619C13#2299411yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—261no—
634C23—261no—
635C23—261no—
636C23—261no—
637C23—261no—
638C23—261no—
639C23—261no—
640C23C4×C22⋊D1312yes—
641C23C22×C4×D1311yescharacteristic
642D4—44no—
643D4—524no—
644D4—524no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—132no—
665C2×C4—132no—
666C2×C4—132no—
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—261no—
680C2×C4—261no—
681C2×C4—261no—
682C2×C4—261no—
683C2×C4—261no—
684C2×C4—261no—
685C2×C4—521no—
686C2×C4—521no—
687C2×C4—521no—
688C2×C4—521no—
689C2×C4C4×C22⋊D1312yes—
690C2×C4C2×#612711yescharacteristic
691C2×C4C2×D4×D1311yescharacteristic
692C2×C4#8825111yescharacteristic
693C2×C4#41×D1311yescharacteristic
694C2×C4#8825711yescharacteristic
695C2×C4C22×C22⋊D1311yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—41no—
700C8—262no—
701C8—521no—
702C8—521no—
703C8—521no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—521no—
719C22—521no—
720C22—521no—
721C22—521no—
722C22—521no—
723C22—521no—
724C22—521no—
725C22C4×D4×D1311yescharacteristic
726C22#1171925111yescharacteristic
727C22#1171945011yescharacteristic
728C22#1171945011yescharacteristic
729C22D13×#13111yescharacteristic
730C22#1171945511yescharacteristic
731C22C2×C4×C22⋊D1311yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—262no—
737C4—262no—
738C4—262no—
739C4—521no—
740C4—521no—
741C4—521no—
742C4—521no—
743C4#1171924511yescharacteristic
744C4#1171925711yescharacteristic
745C4D4×C22⋊D1311yescharacteristic
746C4#1171952911yescharacteristic
747C2—42no—
748C2—81no—
749C2—1041no—
750C2#1311785311yescharacteristic
751C2#1312353411yescharacteristic
752C2#1312353911yescharacteristic
753C2#1312355811yescharacteristic
754C2#1312357711yescharacteristic
755C2#1312397811yescharacteristic
756C2#1312400211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#435C2
prime radical#11718884C4
cosocleC22×C4×C13C24
hypercenterC2×#435D13
hypocenterC13#22994
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#11718789C2semidirect
2. C2×#11718390C2semidirect
3. C2×#11718763C2semidirect
5. #13115632C2semidirect
6. #13115551C2semidirect
7. #13115449C2semidirect
8. #13115439C2semidirect
9. #13115134C2semidirect
10. #13115128C2semidirect
11. #13115019C2semidirect
12. #13115017C2semidirect
13. #13114712C2semidirect
14. #13114604C2semidirect
15. C2×C13×#435C2semidirect
122. C13×C22⋊C8D4semidirect
141. #88054D4semidirect
244. C2×#435D13semidirect
501. C22⋊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×#117187892
C2×#117183902
C2×#117187632
#131180782
#131156322
#131155512
#131154492
#131154392
#131151342
#131151282
#131150192
#131150172
#131147122
#131146042
C2×C13×#4352
#2299413