Finite Group Databasebeta

← #15869018

Subgroups — #15869018

Order 3328.

1094 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×D4×#1055C211yesmaximal, characteristic, complemented
2C2×#11718386C211yesmaximal, characteristic, complemented
3C2×#11718386C211yesmaximal, characteristic, complemented
4C2×#11718783C211yesmaximal, characteristic, complemented
5#13118078C211yesmaximal, characteristic
6#13115632C211yesmaximal, characteristic, complemented
7#13115558C211yesmaximal, characteristic, complemented
8#13115450C211yesmaximal, characteristic, complemented
9#13115446C211yesmaximal, characteristic, complemented
10#13115133C211yesmaximal, characteristic, complemented
11#13114818C211yesmaximal, characteristic, complemented
12#13114697C211yesmaximal, characteristic, complemented
13#13114610C211yesmaximal, characteristic, complemented
14#13114606C211yesmaximal, characteristic, complemented
15C13×#1870C211yesmaximal, characteristic, complemented
16C22×C13×M16C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×C22⋊D13C2211yescharacteristic
19C2×C4×C22⋊D13C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C22×C8×D13C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25C2×C13×C22⋊C8C2211yescharacteristic
26C2×C13×C22⋊C8C2211yescharacteristic
27#11718884C411yescharacteristic
28#11718883C411yescharacteristic
29C4×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32#11718783—24no—
33C2×#88060C2211yescharacteristic
34C2×#88060C2211yescharacteristic
35C2×#88060C2211yescharacteristic
36C2×#88055C2211yescharacteristic
37C2×#88055C2211yescharacteristic
38C2×#88054C2211yescharacteristic
39C2×#88054C2211yescharacteristic
40C2×#88054C2211yescharacteristic
41C2×C8×Dic13C2211yescharacteristic
42C2×C8×Dic13C2211yescharacteristic
43C2×C8×Dic13C2211yescharacteristic
44D4×#1055—24no—
45#11718655C411yescharacteristic
46#11718645C411yescharacteristic
47#11718622C411yescharacteristic
48#11718620C411yescharacteristic
49#11718613C411yescharacteristic
50#11718609C411yescharacteristic
51C4×#6103C2211yescharacteristic
52C4×#6101C2211yescharacteristic
53C2×C4⋊#1055C2211yescharacteristic
54C2×C4×#1055C2211yescharacteristic
55#11718386—24no—
56#11718386—24no—
57C13×#336C2211yescharacteristic
58C13×#336C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61#11718142C2211yescharacteristic
62#11718142C2211yescharacteristic
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—22no—
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C22×C8×C13C2311yescharacteristic
75C22×C8×C13C2311yescharacteristic
76C4×D4×C13—22no—
77C4×D4×C13—22no—
78C2×C13×C4⋊C4C2×C411yescharacteristic
79C2×C13×C22⋊C4C2×C411yescharacteristic
80C2×C13×C22⋊C4C2×C411yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C22⋊Dic13C2×C411yescharacteristic
83C2×C22⋊Dic13C2×C411yescharacteristic
84C2×C22⋊Dic13C2×C411yescharacteristic
85C2×C22⋊Dic13C2×C411yescharacteristic
86C2×C22⋊Dic13C2×C411yescharacteristic
87C2×C22⋊Dic13C2×C411yescharacteristic
88C4×C22⋊D13—22no—
89C4×C22⋊D13—22no—
90C4×C22⋊D13—22no—
91C4×C22⋊D13—22no—
92C2×#6103C2×C411yescharacteristic
93C2×#6103C2×C411yescharacteristic
94C2×#6103C2×C411yescharacteristic
95C2×#6103C2×C411yescharacteristic
96#88180—22no—
97#88180—22no—
98C2×C4⋊Dic13C2×C411yescharacteristic
99C2×C4⋊Dic13C2×C411yescharacteristic
100C2×#6101C2×C411yescharacteristic
101C2×#6101C2×C411yescharacteristic
102C2×#6101C2×C411yescharacteristic
103C2×#6101C2×C411yescharacteristic
104C2×C4×Dic13C2311yescharacteristic
105C2×C4×Dic13C2311yescharacteristic
106C2×C4×Dic13C2311yescharacteristic
107C22×#1055—22no—
108C22×#1055—22no—
109C22×#1055—22no—
110C22×#1055—22no—
111C22×#1055—22no—
112C22×#1055D414yescomplemented
113C22×#1055C2311yescharacteristic
114C22×#1055C2311yescharacteristic
115C22×#1055C2311yescharacteristic
116C22×#1055C2311yescharacteristic
117C2×C8×D13—22no—
118C2×C8×D13—22no—
119C2×C8×D13—22no—
120C13×C22⋊C8—22no—
121C13×C22⋊C8—22no—
122C13×C22⋊C8—22no—
123#88071C2×C411yescharacteristic
124#88071C2×C411yescharacteristic
125#88071C2×C411yescharacteristic
126#88071C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129C22⋊#1055—22no—
130C22⋊#1055—22no—
131#88060—22no—
132#88060—22no—
133#88060—22no—
134#88055—22no—
135#88055—22no—
136#88054—22no—
137#88054—22no—
138#88054—22no—
139C8×Dic13—22no—
140C8×Dic13—22no—
141C8×Dic13D414yescomplemented
142C4⋊#1055—22no—
143C4×#1055—22no—
144#21491—131nomaximal, Sylow
145C24×C13C22×C411yescharacteristic
146C24×C13C22×C411yescharacteristic
147C23×D13C22×C411yescharacteristic
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—22no—
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—22no—
172C2×C22⋊D13—22no—
173C2×C22⋊D13—22no—
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—28no—
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×C13C2×D412yes—
199C2×C8×C13#4112yes—
200C13×C4⋊C4—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C42×C13—21no—
204C42×C13—21no—
205C22⋊Dic13—22no—
206C22⋊Dic13—22no—
207C22⋊Dic13—22no—
208C22⋊Dic13—22no—
209C22⋊Dic13—22no—
210C22⋊Dic13—22no—
211#6103—22no—
212#6103—22no—
213#6103—22no—
214#6103—22no—
215C4⋊Dic13—22no—
216C4⋊Dic13—22no—
217#6101—22no—
218#6101—22no—
219#6101—22no—
220#6101—22no—
221C4×Dic13—21no—
222C4×Dic13—21no—
223C4×Dic13—21no—
224C4×Dic13—21no—
225C4×Dic13C2×D412yes—
226C4×Dic13#4112yes—
227C2×#1055—21no—
228C2×#1055—21no—
229C2×#1055—28no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—44no—
237C2×#1055C2×D412yes—
238C2×#1055C2×D412yes—
239C2×#1055C2×D412yes—
240C2×#1055#4112yes—
241C8×D13—44no—
242C2×C8×D4—131no—
243C2×C8×D4—131no—
244C2×C8×D4—131no—
245C2×#405—131no—
246#2392—131no—
247#1955—131no—
248#1940—131no—
249#1924—131no—
250#1924—131no—
251#1870—131no—
252#1870D1311yescharacteristic, complemented
253#1798—131no—
254C8×C4⋊C4—131no—
255C8×C22⋊C4—131no—
256C8×C22⋊C4—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×C13C4×D412yes—
270C23×C13#13112yes—
271C23×C13C23×C411yescharacteristic
272C22×D13—21no—
273C22×D13—21no—
274C22×D13—21no—
275C22×D13—21no—
276C22×D13—21no—
277C22×D13—21no—
278C22×D13#13112yes—
279D4×C13—28no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
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—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13C4×D412yes—
299C2×C4×C13#13112yes—
300C2×C4×C13C22×D411yescharacteristic
301C2×C4×C13C22×D411yescharacteristic
302C2×C4×C13C2×#4111yescharacteristic
303C2×C4×C13C2×#4111yescharacteristic
304C2×C4×C13C2×#4111yescharacteristic
305C2×C4×C13C2×#4111yescharacteristic
306C22⋊D13—28no—
307C22⋊D13—28no—
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—41no—
336C8×C13—41no—
337#1055—22no—
338#1055—41no—
339#1055—41no—
340#1055#12114yes—
341C22×M16C2×D1311yescharacteristic
342C23×C8—131no—
343C23×C8—131no—
344C23×C8—131no—
345C2×C4×D4—131no—
346C2×C4×D4—131no—
347C2×C4×D4C2×D1311yescharacteristic
348C2×#117—131no—
349C8×D4—264no—
350C8×D4—264no—
351C8×D4—264no—
352C2×C4⋊C8—131no—
353C2×C4⋊C8—131no—
354C2×C4⋊C8—131no—
355C2×C4⋊C8—131no—
356C2×C22⋊C8—131no—
357C2×C22⋊C8—131no—
358C2×C22⋊C8—131no—
359C2×C22⋊C8—131no—
360C2×C22⋊C8—131no—
361C2×C22⋊C8C2×D1311yescharacteristic
362C2×C22⋊C8C2×D1311yescharacteristic
363C2×C22⋊C8C2×D1311yescharacteristic
364#405—264no—
365C2×#97—131no—
366C2×#97—131no—
367C2×C4×C8—131no—
368C2×C4×C8—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#336C2×D1311yescharacteristic
387#336C2×D1311yescharacteristic
388C22×C13—22no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—22no—
393C22×C13—22no—
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×C13C4×#4111yescharacteristic
405C22×C13C2×#13111yescharacteristic
406C22×C13C2×#13111yescharacteristic
407C22×C13C2×#13111yescharacteristic
408C22×C13C2×#13111yescharacteristic
409C2×D13—22no—
410C2×D13—22no—
411C2×D13—22no—
412C2×D13—41no—
413C2×D13—41no—
414C2×D13—41no—
415C2×D13—41no—
416C4×C13—22no—
417C4×C13—22no—
418C4×C13—41no—
419C4×C13—41no—
420C4×C13C2×#12111yescharacteristic
421C4×C13#52511yescharacteristic
422C4×C13#52911yescharacteristic
423C4×C13#53211yescharacteristic
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—22no—
440C22×C8—131no—
441C22×C8—134no—
442C22×C8—131no—
443C22×C8—131no—
444C22×C8—131no—
445C22×C8—262no—
446C22×C8—262no—
447C22×C8—262no—
448C22×C8—262no—
449C22×C8—262no—
450C22×C8—262no—
451C22×C8—262no—
452C22×C8—262no—
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—262no—
489C4⋊C8—262no—
490C4⋊C8—262no—
491C4⋊C8—262no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495C22⋊C8—262no—
496C22⋊C8—262no—
497C22⋊C8—262no—
498C22⋊C8—262no—
499C22⋊C8—262no—
500#97—262no—
501#97—262no—
502C4×C8—134no—
503C4×C8—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—42no—
514C2×C13C4×#12111yescharacteristic
515C2×C13#292911yescharacteristic
516C2×C13#292911yescharacteristic
517C2×C13#292911yescharacteristic
518C2×C13#293111yescharacteristic
519C2×C13#296611yescharacteristic
520C2×C13#296611yescharacteristic
521D13—42no—
522C24—131no—
523C24C2×C4×D1311yescharacteristic
524C24C2×C4×D1311yescharacteristic
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—262no—
529C2×D4—262no—
530C2×D4—262no—
531C2×D4—262no—
532C2×D4—262no—
533C2×D4—262no—
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×C4D4×D1312yes—
562C22×C4#612912yes—
563C22×C4C23×D1311yescharacteristic
564M16—28no—
565C2×C8—21no—
566C2×C8—21no—
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—132no—
576C2×C8—132no—
577C2×C8—132no—
578C2×C8—132no—
579C2×C8—268no—
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—524no—
589C2×C8—524no—
590C2×C8D4×D1312yes—
591C2×C8#612912yes—
592C4⋊C4—22no—
593C4⋊C4—262no—
594C4⋊C4—262no—
595C4⋊C4—262no—
596C4⋊C4—262no—
597C4⋊C4—262no—
598C4⋊C4—262no—
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—262no—
609C22⋊C4—262no—
610C22⋊C4—262no—
611C42—21no—
612C42—21no—
613C42—132no—
614C42—132no—
615C42—261no—
616C42—261no—
617C42—261no—
618C42—261no—
619C13#2149111yescharacteristic, 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—132no—
633C23—261no—
634C23—261no—
635C23—261no—
636C23—261no—
637C23—261no—
638C23—261no—
639C23#8813512yes—
640C23#8816112yes—
641C23C22×C4×D1311yescharacteristic
642D4—28no—
643D4—268no—
644D4—268no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—132no—
664C2×C4—132no—
665C2×C4—132no—
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—261no—
680C2×C4—261no—
681C2×C4—261no—
682C2×C4—261no—
683C2×C4—261no—
684C2×C4—521no—
685C2×C4—521no—
686C2×C4—521no—
687C2×C4—521no—
688C2×C4#8813512yes—
689C2×C4#8816112yes—
690C2×C4C2×D4×D1311yescharacteristic
691C2×C4C2×D4×D1311yescharacteristic
692C2×C4C2×#612911yescharacteristic
693C2×C4C2×#612911yescharacteristic
694C2×C4#41×D1311yescharacteristic
695C2×C4#41×D1311yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—134no—
701C8—262no—
702C8—521no—
703C8—521no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—262no—
719C22—262no—
720C22—262no—
721C22—521no—
722C22—521no—
723C22—521no—
724C22—521no—
725C22C2×#8813511yescharacteristic
726C22C4×#612911yescharacteristic
727C22C4×D4×D1311yescharacteristic
728C22C2×#8816111yescharacteristic
729C22C2×#8816111yescharacteristic
730C22D13×#13111yescharacteristic
731C22D13×#13111yescharacteristic
732C4—22no—
733C4—22no—
734C4—41no—
735C4—41no—
736C4—262no—
737C4—262no—
738C4—262no—
739C4—521no—
740C4—521no—
741C4—521no—
742C4—521no—
743C4#1171929111yescharacteristic
744C4#1171930111yescharacteristic
745C4D13×#12111yescharacteristic
746C4#1171935411yescharacteristic
747C2—42no—
748C2—42no—
749C2—522no—
750C2#1311734611yescharacteristic
751C2#1312352611yescharacteristic
752C2#1312352711yescharacteristic
753C2#1312353311yescharacteristic
754C2#1312354511yescharacteristic
755C2#1312380611yescharacteristic
756C2#1312381411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1870C2
prime radical#11718884C4
cosocleC22×C4×C13C24
hypercenter#1870D13
hypocenterC13#21491
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×D4×#1055C2semidirect
2. C2×#11718386C2semidirect
3. C2×#11718386C2semidirect
4. C2×#11718783C2semidirect
6. #13115632C2semidirect
7. #13115558C2semidirect
8. #13115450C2semidirect
9. #13115446C2semidirect
10. #13115133C2semidirect
11. #13114818C2semidirect
12. #13114697C2semidirect
13. #13114610C2semidirect
14. #13114606C2semidirect
15. C13×#1870C2semidirect
112. C22×#1055D4semidirect
141. C8×Dic13D4semidirect
252. #1870D13semidirect
619. C13#21491semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#10552
C2×#117183862
C2×#117187832
#131180782
#131156322
#131155582
#131154502
#131154462
#131151332
#131148182
#131146972
#131146102
#131146062
C13×#18702
#2149113