Finite Group Databasebeta

← #15879003

Subgroups — #15879003

Order 3328.

1162 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719243C211yesmaximal, characteristic
2C2×#11718673C211yesmaximal, characteristic, complemented
3#13115776C211yesmaximal, characteristic, complemented
4#13115771C211yesmaximal, characteristic, complemented
5#13115133C211yesmaximal, characteristic, complemented
6#13115131C211yesmaximal, characteristic, complemented
7#13115131C211yesmaximal, characteristic, complemented
8#13115128C211yesmaximal, characteristic, complemented
9#13114905C211yesmaximal, characteristic, complemented
10#13114902C211yesmaximal, characteristic, complemented
11#13114817C211yesmaximal, characteristic, complemented
12#13114605C211yesmaximal, characteristic, complemented
13#13114532C211yesmaximal, characteristic, complemented
14#13114529C211yesmaximal, characteristic, complemented
15C2×C13×#435C211yesmaximal, characteristic, complemented
16C22×C13×M16C2211yescharacteristic
17C23×C8×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×#88193C411yescharacteristic
20C2×#88189C411yescharacteristic
21C2×C4×C22⋊D13C2211yescharacteristic
22C2×C4×C22⋊D13C2211yescharacteristic
23C2×#88180C2211yescharacteristic
24C22×C4×Dic13C2211yescharacteristic
25C22×#6099C2211yescharacteristic
26C22×#6099C2211yescharacteristic
27#11719243—24no—
28#11719243—24no—
29C2×#88152C411yescharacteristic
30C2×#88143C411yescharacteristic
31C2×#88140C411yescharacteristic
32C2×#88139C411yescharacteristic
33C2×#88133C411yescharacteristic
34C2×#88132C411yescharacteristic
35C2×#88126C2211yescharacteristic
36C2×C4×Dic26C2211yescharacteristic
37C13×#435—24no—
38C2×C13×C4⋊C8C2211yescharacteristic
39C2×C13×C22⋊C8C2211yescharacteristic
40C2×C13×C22⋊C8C2211yescharacteristic
41C2×C13×#97C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43C2×C22⋊#1055C2211yescharacteristic
44C2×#88060C2211yescharacteristic
45C2×#88060C2211yescharacteristic
46C2×#88060C2211yescharacteristic
47C2×#88060C2211yescharacteristic
48#11718673—24no—
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
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
68C23×Dic13C2×C411yescharacteristic
69C23×Dic13C2×C411yescharacteristic
70C22×C4×D13C2311yescharacteristic
71C22×Dic26C2×C411yescharacteristic
72C2×C13×M16—22no—
73C2×C13×M16—22no—
74C2×C13×M16—41no—
75C22×C8×C13—22no—
76C22×C8×C13—22no—
77C22×C8×C13—41no—
78C22×C8×C13C2311yescharacteristic
79C22×C8×C13C2311yescharacteristic
80C22×C8×C13C2311yescharacteristic
81C22×C8×C13C2311yescharacteristic
82C4×D4×C13D414yes—
83C4×D4×C13D414yes—
84C2×C13×C4⋊C4C2×C411yescharacteristic
85C2×C13×C22⋊C4C2×C411yescharacteristic
86C2×C13×C22⋊C4C2×C411yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C22⋊Dic13C2×C411yescharacteristic
89C2×C22⋊Dic13C2×C411yescharacteristic
90C2×C22⋊Dic13C2×C411yescharacteristic
91C2×C22⋊Dic13C2×C411yescharacteristic
92#88193—24no—
93#88189—24no—
94C4×C22⋊D13—22no—
95C4×C22⋊D13—22no—
96C4×C22⋊D13—22no—
97C4×C22⋊D13—22no—
98C2×#6103C2×C411yescharacteristic
99C2×#6103C2×C411yescharacteristic
100C2×#6103C2×C411yescharacteristic
101C2×#6103C2×C411yescharacteristic
102#88180—22no—
103#88180—22no—
104C2×C4⋊Dic13C2×C411yescharacteristic
105C2×C4⋊Dic13C2×C411yescharacteristic
106C2×C4⋊Dic13C2×C411yescharacteristic
107C2×#6101C2×C411yescharacteristic
108C2×#6101C2×C411yescharacteristic
109C2×#6101C2×C411yescharacteristic
110C2×#6101C2×C411yescharacteristic
111C2×#6101C2×C411yescharacteristic
112C2×#6101C2×C411yescharacteristic
113C2×C4×Dic13—22no—
114C2×C4×Dic13—22no—
115C2×C4×Dic13C2×C411yescharacteristic
116C2×C4×Dic13C2×C411yescharacteristic
117C2×C4×Dic13C2311yescharacteristic
118C2×C4×Dic13C2311yescharacteristic
119C2×C4×Dic13C2311yescharacteristic
120C2×#6099—22no—
121C2×#6099—22no—
122C2×#6099—22no—
123C2×#6099—22no—
124C2×#6099—41no—
125C2×#6099—41no—
126C22×#1055C2311yescharacteristic
127C22×#1055C2311yescharacteristic
128C22×#1055C2311yescharacteristic
129C22×#1055C2311yescharacteristic
130#88152—24no—
131#88143—24no—
132#88140—24no—
133#88139—24no—
134#88133—24no—
135#88132—24no—
136#88126—22no—
137#88126—22no—
138C4×Dic26—22no—
139C4×Dic26—22no—
140C13×C4⋊C8—22no—
141C13×C22⋊C8—22no—
142C13×C22⋊C8—22no—
143C13×#97—22no—
144C22⋊#1055—22no—
145C22⋊#1055—22no—
146#88060—22no—
147#88060—22no—
148#88060—41no—
149#88060—41no—
150C4⋊#1055—22no—
151C4×#1055—22no—
152#22472—131nomaximal, Sylow
153C24×C13C22×C411yescharacteristic
154C24×C13C22×C411yescharacteristic
155C23×D13C22×C411yescharacteristic
156C2×D4×C13—41no—
157C2×D4×C13—41no—
158C2×D4×C13C22⋊C414yes—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13C22×C411yescharacteristic
168C22×C4×C13C22×C411yescharacteristic
169C22×C4×C13C22×C411yescharacteristic
170C22×C4×C13C22×C411yescharacteristic
171C22×C4×C13C2×D412yes—
172C22×C4×C13C2×D412yes—
173C22×C4×C13C2×D412yes—
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2411yescharacteristic
176C2×C22⋊D13—22no—
177C2×C22⋊D13—22no—
178C2×C22⋊D13—22no—
179C2×C22⋊D13—41no—
180C2×C22⋊D13—41no—
181C2×C22⋊D13—41no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—41no—
186C22×Dic13—41no—
187C22×Dic13—41no—
188C22×Dic13C22×C411yescharacteristic
189C22×Dic13C22×C411yescharacteristic
190C22×Dic13C22×C411yescharacteristic
191C22×Dic13C22×C411yescharacteristic
192C22×Dic13C22×C411yescharacteristic
193C22×Dic13C22×C411yescharacteristic
194C22×Dic13C22×C411yescharacteristic
195C2×C4×D13—21no—
196C2×C4×D13—21no—
197C2×C4×D13—21no—
198C2×C4×D13—21no—
199C2×C4×D13—21no—
200C2×C4×D13—21no—
201C2×Dic26—22no—
202C2×Dic26—22no—
203C2×Dic26—41no—
204C13×M16—44no—
205C2×C8×C13—21no—
206C2×C8×C13—21no—
207C2×C8×C13—21no—
208C2×C8×C13—21no—
209C2×C8×C13—21no—
210C2×C8×C13—21no—
211C2×C8×C13—21no—
212C2×C8×C13—21no—
213C2×C8×C13—21no—
214C2×C8×C13—21no—
215C2×C8×C13—21no—
216C2×C8×C13—44no—
217C2×C8×C13#4112yes—
218C13×C4⋊C4C22⋊C414yes—
219C13×C22⋊C4C22⋊C414yes—
220C13×C22⋊C4C22⋊C414yes—
221C42×C13C2×D412yes—
222C42×C13C2×D412yes—
223C22⋊Dic13—22no—
224C22⋊Dic13—22no—
225C22⋊Dic13—22no—
226C22⋊Dic13—22no—
227#6103—22no—
228#6103—22no—
229#6103—22no—
230#6103—22no—
231C4⋊Dic13—22no—
232C4⋊Dic13—22no—
233C4⋊Dic13—22no—
234#6101—22no—
235#6101—22no—
236#6101—22no—
237#6101—22no—
238#6101—22no—
239#6101—22no—
240C4×Dic13—22no—
241C4×Dic13—22no—
242C4×Dic13—21no—
243C4×Dic13—21no—
244C4×Dic13—21no—
245C4×Dic13—21no—
246C4×Dic13—21no—
247C4×Dic13—21no—
248#6099—44no—
249#6099—44no—
250C2×#1055—21no—
251C2×#1055—21no—
252C2×#1055—21no—
253C2×#1055—21no—
254C2×#1055—21no—
255C2×#1055—21no—
256C2×#1055—21no—
257C2×#1055—21no—
258C2×#1055—21no—
259C2×#1055—21no—
260C2×#1055—21no—
261C2×#1055#4112yes—
262C2×#529—131no—
263C2×#436—131no—
264C2×#435D1311yescharacteristic, complemented
265#1985—131no—
266#1984—131no—
267#1870—131no—
268#1870—131no—
269#1870—131no—
270#1869—131no—
271#1818—131no—
272#1817—131no—
273#1798—131no—
274#1750—131no—
275#1729—131no—
276#1728—131no—
277C23×C13—21no—
278C23×C13—21no—
279C23×C13—21no—
280C23×C13—21no—
281C23×C13—21no—
282C23×C13—21no—
283C23×C13—21no—
284C23×C13—21no—
285C23×C13—21no—
286C23×C13—21no—
287C23×C13—21no—
288C23×C13—21no—
289C23×C13C2×C22⋊C412yes—
290C23×C13C2×C22⋊C412yes—
291C23×C13C23×C411yescharacteristic
292C22×D13—21no—
293C22×D13—21no—
294C22×D13—21no—
295C22×D13—21no—
296C22×D13—21no—
297C22×D13—21no—
298C22×D13—21no—
299D4×C13—44no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—21no—
304C2×C4×C13—21no—
305C2×C4×C13—21no—
306C2×C4×C13—21no—
307C2×C4×C13—21no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13C2×C22⋊C412yes—
317C2×C4×C13C2×C22⋊C412yes—
318C2×C4×C13C2×C22⋊C412yes—
319C2×C4×C13C2×C22⋊C412yes—
320C2×C4×C13C22×D411yescharacteristic
321C2×C4×C13C22×D411yescharacteristic
322C2×C4×C13C2×#4111yescharacteristic
323C2×C4×C13C2×#4111yescharacteristic
324C2×C4×C13H(5,𝔽2)11yescharacteristic
325C2×C4×C132−1+411yescharacteristic
326C22⋊D13—44no—
327C22⋊D13—44no—
328C2×Dic13—21no—
329C2×Dic13—21no—
330C2×Dic13—21no—
331C2×Dic13—21no—
332C2×Dic13—21no—
333C2×Dic13—21no—
334C2×Dic13—21no—
335C2×Dic13—21no—
336C2×Dic13—21no—
337C2×Dic13—21no—
338C2×Dic13—21no—
339C2×Dic13—21no—
340C2×Dic13—21no—
341C2×Dic13—21no—
342C2×Dic13—21no—
343C2×Dic13—21no—
344C2×Dic13—21no—
345C2×Dic13—21no—
346C2×Dic13—21no—
347C2×Dic13—21no—
348C2×Dic13—44no—
349C2×Dic13—44no—
350C2×Dic13#13112yes—
351C4×D13—41no—
352C4×D13—41no—
353C4×D13—41no—
354C4×D13—41no—
355Dic26—44no—
356C8×C13—22no—
357C8×C13—41no—
358C8×C13—41no—
359C8×C13—41no—
360#1055—22no—
361#1055—41no—
362#1055—41no—
363#1055—41no—
364C22×M16—131no—
365C22×M16—131no—
366C22×M16C2×D1311yescharacteristic
367C23×C8C2×D1311yescharacteristic
368#529—264no—
369#529—264no—
370C2×#126—131no—
371C2×#126—131no—
372C2×#125—131no—
373C2×#124—131no—
374C2×#123—131no—
375C2×#123—131no—
376C2×C22⋊Q8—131no—
377C2×#121—131no—
378C2×C4×Q8—131no—
379C2×C4×D4—131no—
380C2×C4×D4—131no—
381C2×C4×D4C2×D1311yescharacteristic
382C2×#117—131no—
383C2×#117—131no—
384C22×C42—131no—
385#436—264no—
386#435—24no—
387C2×C4⋊C8—131no—
388C2×C4⋊C8C2×D1311yescharacteristic
389C2×C22⋊C8—131no—
390C2×C22⋊C8—131no—
391C2×C22⋊C8—131no—
392C2×C22⋊C8—131no—
393C2×C22⋊C8—131no—
394C2×C22⋊C8—131no—
395C2×C22⋊C8C2×D1311yescharacteristic
396C2×C22⋊C8C2×D1311yescharacteristic
397C2×#97C2×D1311yescharacteristic
398C2×C4×C8—131no—
399#336—131no—
400#336—131no—
401#336—131no—
402#336—131no—
403#336—131no—
404#336—131no—
405#336—131no—
406#336—131no—
407#336—131no—
408#336—131no—
409#336—131no—
410#336—131no—
411C22×C13—22no—
412C22×C13—22no—
413C22×C13—22no—
414C22×C13—22no—
415C22×C13—22no—
416C22×C13—22no—
417C22×C13—41no—
418C22×C13—41no—
419C22×C13—41no—
420C22×C13—41no—
421C22×C13—41no—
422C22×C13—41no—
423C22×C13—41no—
424C22×C13—41no—
425C22×C13C22×C22⋊C411yescharacteristic
426C22×C13C4×#4111yescharacteristic
427C22×C13#52011yescharacteristic
428C22×C13C2×#13111yescharacteristic
429C22×C13#56811yescharacteristic
430C22×C13#56811yescharacteristic
431C22×C13#56811yescharacteristic
432C2×D13—41no—
433C2×D13—41no—
434C2×D13—41no—
435C2×D13—41no—
436C2×D13—41no—
437C2×D13—41no—
438C2×D13—41no—
439C4×C13—22no—
440C4×C13—22no—
441C4×C13—22no—
442C4×C13—22no—
443C4×C13#54611yescharacteristic
444C4×C13#54611yescharacteristic
445C4×C13#54711yescharacteristic
446C4×C13#54711yescharacteristic
447Dic13—22no—
448Dic13—41no—
449Dic13—41no—
450Dic13—41no—
451Dic13—41no—
452Dic13—41no—
453Dic13—41no—
454C22×Q8—131no—
455C22×D4—131no—
456C22×D4—131no—
457C22×D4C4×D1311yescharacteristic
458C23×C4—131no—
459C23×C4—131no—
460C23×C4—131no—
461C23×C4C22×D1311yescharacteristic
462C23×C4C22×D1311yescharacteristic
463C2×M16—22no—
464C2×M16—22no—
465C2×M16—41no—
466C2×M16—262no—
467C2×M16—262no—
468C2×M16—262no—
469C2×M16—262no—
470C2×M16—521no—
471C2×M16—521no—
472C22×C8—22no—
473C22×C8—22no—
474C22×C8—41no—
475C22×C8—131no—
476C22×C8—131no—
477C22×C8—131no—
478C22×C8—131no—
479C22×C8C22×D1311yescharacteristic
480C22×C8C22×D1311yescharacteristic
481C22×C8C22×D1311yescharacteristic
482C22×C8C22×D1311yescharacteristic
483#126—264no—
484#126—264no—
485#125—264no—
486#124—264no—
487#123—264no—
488#123—264no—
489C22⋊Q8—264no—
490#121—264no—
491C4×Q8—262no—
492C4×Q8—262no—
493C4×D4—262no—
494C4×D4—262no—
495C4×D4—262no—
496C4×D4—262no—
497C4×D4D5214yes—
498C4×D4C22⋊D1314yes—
499#117—262no—
500#117—262no—
501#117—262no—
502#117—262no—
503C2×C4⋊C4—131no—
504C2×C4⋊C4—131no—
505C2×C4⋊C4—131no—
506C2×C4⋊C4—131no—
507C2×C4⋊C4—131no—
508C2×C4⋊C4—131no—
509C2×C4⋊C4—131no—
510C2×C4⋊C4—131no—
511C2×C4⋊C4—131no—
512C2×C4⋊C4C4×D1311yescharacteristic
513C2×C22⋊C4—131no—
514C2×C22⋊C4—131no—
515C2×C22⋊C4—131no—
516C2×C22⋊C4—131no—
517C2×C22⋊C4—131no—
518C2×C22⋊C4—131no—
519C2×C22⋊C4—131no—
520C2×C22⋊C4—131no—
521C2×C22⋊C4C4×D1311yescharacteristic
522C2×C22⋊C4C4×D1311yescharacteristic
523C2×C42—131no—
524C2×C42—131no—
525C2×C42—131no—
526C2×C42—131no—
527C2×C42—131no—
528C2×C42—262no—
529C2×C42—262no—
530C2×C42C22×D1311yescharacteristic
531C4⋊C8—22no—
532C4⋊C8—262no—
533C22⋊C8—22no—
534C22⋊C8—22no—
535C22⋊C8—262no—
536C22⋊C8—262no—
537C22⋊C8—262no—
538C22⋊C8—262no—
539C22⋊C8—521no—
540C22⋊C8—521no—
541#97—22no—
542C4×C8—262no—
543C2×C13—42no—
544C2×C13—42no—
545C2×C13#233911yescharacteristic
546C2×C13#287911yescharacteristic
547C2×C13#288011yescharacteristic
548C2×C13#296711yescharacteristic
549C2×C13#296911yescharacteristic
550C2×C13#299311yescharacteristic
551C2×C13#299511yescharacteristic
552D13—81no—
553C24—131no—
554C24C2×C4×D1311yescharacteristic
555C24C2×C4×D1311yescharacteristic
556C2×Q8—262no—
557C2×Q8—262no—
558C2×Q8—521no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—262no—
562C2×D4—262no—
563C2×D4—262no—
564C2×D4—521no—
565C2×D4—521no—
566C2×D4—521no—
567C2×D4#610314yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—131no—
577C22×C4—131no—
578C22×C4—131no—
579C22×C4—131no—
580C22×C4—131no—
581C22×C4—131no—
582C22×C4—131no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—521no—
593C22×C4—521no—
594C22×C4—521no—
595C22×C4C2×C4×D1311yescharacteristic
596C22×C4C2×C4×D1311yescharacteristic
597C22×C4C2×C4×D1311yescharacteristic
598C22×C4C2×C4×D1311yescharacteristic
599C22×C4C2×D5212yes—
600C22×C4C2×D5212yes—
601C22×C4C2×C22⋊D1312yes—
602C22×C4C2×C22⋊D1312yes—
603C22×C4C23×D1311yescharacteristic
604M16—44no—
605M16—524no—
606M16—524no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—44no—
619C2×C8—132no—
620C2×C8—261no—
621C2×C8—261no—
622C2×C8—261no—
623C2×C8—261no—
624C2×C8—261no—
625C2×C8—261no—
626C2×C8—261no—
627C2×C8—261no—
628C2×C8—261no—
629C2×C8—261no—
630C2×C8—261no—
631C2×C8#612912yes—
632C4⋊C4—262no—
633C4⋊C4—262no—
634C4⋊C4—262no—
635C4⋊C4—262no—
636C4⋊C4—262no—
637C4⋊C4—262no—
638C4⋊C4—262no—
639C4⋊C4—262no—
640C4⋊C4—262no—
641C4⋊C4#610314yes—
642C22⋊C4—262no—
643C22⋊C4—262no—
644C22⋊C4—262no—
645C22⋊C4—262no—
646C22⋊C4—262no—
647C22⋊C4—262no—
648C22⋊C4—262no—
649C22⋊C4—262no—
650C22⋊C4#610314yes—
651C22⋊C4#610314yes—
652C42—262no—
653C42—262no—
654C42—261no—
655C42—261no—
656C42—261no—
657C42—261no—
658C42—261no—
659C42—261no—
660C42C2×D5212yes—
661C42C2×C22⋊D1312yes—
662C13#2247211yescharacteristic, complemented, Sylow
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—261no—
676C23—261no—
677C23—261no—
678C23—261no—
679C23—261no—
680C23—261no—
681C23—261no—
682C23C2×#610312yes—
683C23C2×#610312yes—
684C23C22×C4×D1311yescharacteristic
685Q8—524no—
686D4—44no—
687D4—524no—
688D4—524no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—132no—
706C2×C4—261no—
707C2×C4—261no—
708C2×C4—261no—
709C2×C4—261no—
710C2×C4—261no—
711C2×C4—261no—
712C2×C4—261no—
713C2×C4—261no—
714C2×C4—261no—
715C2×C4—261no—
716C2×C4—261no—
717C2×C4—261no—
718C2×C4—261no—
719C2×C4—261no—
720C2×C4—261no—
721C2×C4—261no—
722C2×C4—261no—
723C2×C4—261no—
724C2×C4—261no—
725C2×C4—261no—
726C2×C4—524no—
727C2×C4—524no—
728C2×C4—521no—
729C2×C4—521no—
730C2×C4—521no—
731C2×C4—521no—
732C2×C4C2×#610312yes—
733C2×C4C2×#610312yes—
734C2×C4C2×#610312yes—
735C2×C4C2×#610312yes—
736C2×C4C22×D5211yescharacteristic
737C2×C4C2×#612911yescharacteristic
738C2×C4#8825111yescharacteristic
739C2×C4#41×D1311yescharacteristic
740C2×C4#8825711yescharacteristic
741C2×C4C22×C22⋊D1311yescharacteristic
742C8—22no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—262no—
747C8—521no—
748C8—521no—
749C8—521no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—521no—
765C22—521no—
766C22—521no—
767C22—521no—
768C22—521no—
769C22—521no—
770C22—521no—
771C22C4×#612911yescharacteristic
772C22#1171925111yescharacteristic
773C22#1171945011yescharacteristic
774C22#1171945011yescharacteristic
775C22D13×#13111yescharacteristic
776C22#1171945511yescharacteristic
777C22C22×#610311yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—262no—
783C4—521no—
784C4—521no—
785C4—521no—
786C4—521no—
787C4—521no—
788C4—521no—
789C4#1171925911yescharacteristic
790C4#1171926011yescharacteristic
791C4#1171951111yescharacteristic
792C4#1171952911yescharacteristic
793C2—42no—
794C2—42no—
795C2—1041no—
796C2#1311766111yescharacteristic
797C2#1312328011yescharacteristic
798C2#1312328311yescharacteristic
799C2#1312381511yescharacteristic
800C2#1312383311yescharacteristic
801C2#1312397811yescharacteristic
802C2#1312400711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#435C2
prime radicalC2×#88193C4
cosocleC22×C4×C13C24
hypercenterC2×#435D13
hypocenterC13#22472
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#11718673C2semidirect
3. #13115776C2semidirect
4. #13115771C2semidirect
5. #13115133C2semidirect
6. #13115131C2semidirect
7. #13115131C2semidirect
8. #13115128C2semidirect
9. #13114905C2semidirect
10. #13114902C2semidirect
11. #13114817C2semidirect
12. #13114605C2semidirect
13. #13114532C2semidirect
14. #13114529C2semidirect
15. C2×C13×#435C2semidirect
264. C2×#435D13semidirect
662. C13#22472semidirect

Maximal subgroups

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

subgroupindex
C2×#117192432
C2×#117186732
#131157762
#131157712
#131151332
#131151312
#131151282
#131149052
#131149022
#131148172
#131146052
#131145322
#131145292
C2×C13×#4352
#2247213