Finite Group Databasebeta

← #15878985

Subgroups — #15878985

Order 3328.

1202 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×D4×#1055C211yesmaximal, characteristic, complemented
3#13115776C211yesmaximal, characteristic, complemented
4#13115771C211yesmaximal, characteristic, complemented
5#13115133C211yesmaximal, characteristic, complemented
6#13115128C211yesmaximal, characteristic, complemented
7#13115126C211yesmaximal, characteristic, complemented
8#13115126C211yesmaximal, characteristic, complemented
9#13114905C211yesmaximal, characteristic, complemented
10#13114902C211yesmaximal, characteristic, complemented
11#13114817C211yesmaximal, characteristic, complemented
12#13114605C211yesmaximal, characteristic, complemented
13#13114534C211yesmaximal, characteristic, complemented
14C2×#11718142C211yesmaximal, 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
25C23×#1055C2211yescharacteristic
26C23×#1055C2211yescharacteristic
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
48D4×#1055—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
120C22×#1055—22no—
121C22×#1055—22no—
122C22×#1055—22no—
123C22×#1055—22no—
124C22×#1055—41no—
125C22×#1055—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#22470—131nomaximal, Sylow
153C24×C13C22×C411yescharacteristic
154C24×C13C22×C411yescharacteristic
155C23×D13C22×C411yescharacteristic
156C2×D4×C13—22no—
157C2×D4×C13—22no—
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—22no—
180C2×C22⋊D13—22no—
181C2×C22⋊D13—41no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
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—
248C2×#1055—21no—
249C2×#1055—21no—
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—44no—
260C2×#1055—44no—
261C2×#1055#4112yes—
262C2×#529—131no—
263C2×#435D1311yescharacteristic, complemented
264C2×C8×D4—131no—
265#1985—131no—
266#1984—131no—
267#1870—131no—
268#1869—131no—
269#1869—131no—
270#1869—131no—
271#1818—131no—
272#1817—131no—
273#1798—131no—
274#1750—131no—
275#1729—131no—
276C2×#336—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×C13C2×C22⋊C412yes—
288C23×C13C2×C22⋊C412yes—
289C23×C13#13112yes—
290C23×C13#13112yes—
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—28no—
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×M16C2×D1311yescharacteristic
365C23×C8—131no—
366C23×C8—131no—
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#435—24no—
386C8×D4—264no—
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—22no—
418C22×C13—22no—
419C22×C13—22no—
420C22×C13—41no—
421C22×C13—41no—
422C22×C13—41no—
423C22×C13—41no—
424C22×C13#40814yes—
425C22×C13C22×C22⋊C411yescharacteristic
426C22×C13C4×#4111yescharacteristic
427C22×C13#52011yescharacteristic
428C22×C13C2×#13111yescharacteristic
429C22×C13C2×#13111yescharacteristic
430C22×C13C2×#13111yescharacteristic
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—
466C22×C8—22no—
467C22×C8—22no—
468C22×C8—41no—
469C22×C8—131no—
470C22×C8—131no—
471C22×C8—131no—
472C22×C8—131no—
473C22×C8—262no—
474C22×C8—262no—
475C22×C8—262no—
476C22×C8—262no—
477C22×C8—521no—
478C22×C8—521no—
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—24no—
544C2×C13—42no—
545C2×C13#233911yescharacteristic
546C2×C13C2×#40811yescharacteristic
547C2×C13#288011yescharacteristic
548C2×C13#296611yescharacteristic
549C2×C13#296811yescharacteristic
550C2×C13#299211yescharacteristic
551C2×C13#299411yescharacteristic
552D13—81no—
553C24—131no—
554C24C2×C4×D1311yescharacteristic
555C24C2×C4×D1311yescharacteristic
556C2×Q8—262no—
557C2×Q8—262no—
558C2×Q8—521no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—262no—
562C2×D4—262no—
563C2×D4—262no—
564C2×D4—262no—
565C2×D4—262no—
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—262no—
587C22×C4—262no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—261no—
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—
605C2×C8—21no—
606C2×C8—21no—
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—44no—
617C2×C8—132no—
618C2×C8—261no—
619C2×C8—261no—
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—524no—
630C2×C8—524no—
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#2247011yescharacteristic, complemented, Sylow
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—261no—
674C23—261no—
675C23—261no—
676C23—261no—
677C23—261no—
678C23—261no—
679C23—261no—
680C23#8816112yes—
681C23#8816112yes—
682C23C2×#610312yes—
683C23C2×#610312yes—
684C23C22×C4×D1311yescharacteristic
685Q8—524no—
686D4—28no—
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—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—521no—
764C22—521no—
765C22—521no—
766C22—521no—
767C22—521no—
768C22—521no—
769C22—521no—
770C22#1171879014yes—
771C22C4×#612911yescharacteristic
772C22#1171925111yescharacteristic
773C22C2×#8816111yescharacteristic
774C22C2×#8816111yescharacteristic
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—24no—
794C2—42no—
795C2—1041no—
796C2#1311766111yescharacteristic
797C2C2×#1171879011yescharacteristic
798C2#1312328311yescharacteristic
799C2#1312380611yescharacteristic
800C2#1312383111yescharacteristic
801C2#1312397611yescharacteristic
802C2#1312398911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#435C2
prime radicalC2×#88193C4
cosocleC22×C4×C13C24
hypercenterC2×#435D13
hypocenterC13#22470
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×D4×#1055C2semidirect
3. #13115776C2semidirect
4. #13115771C2semidirect
5. #13115133C2semidirect
6. #13115128C2semidirect
7. #13115126C2semidirect
8. #13115126C2semidirect
9. #13114905C2semidirect
10. #13114902C2semidirect
11. #13114817C2semidirect
12. #13114605C2semidirect
13. #13114534C2semidirect
14. C2×#11718142C2semidirect
15. C2×C13×#435C2semidirect
263. C2×#435D13semidirect
662. C13#22470semidirect

Maximal subgroups

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

subgroupindex
C2×#117192432
C2×D4×#10552
#131157762
#131157712
#131151332
#131151282
#131151262
#131149052
#131149022
#131148172
#131146052
#131145342
C2×#117181422
C2×C13×#4352
#2247013