Finite Group Databasebeta

← C2×#13131399 #16808008

Subgroups — C2×#13131399 #16808008

Order 3328.

3342 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D13⋊M16C211yesmaximal, characteristic
2C22×#88237C211yesmaximal, characteristic
3#13131399C2116yesmaximal, direct product factor
4C2×#11719099C214yesmaximal, complemented
5C2×#11719089C214yesmaximal, complemented
6C2×M16×#261C214yesmaximal, complemented
7C22×M16×D13C211yesmaximal, characteristic
8C23×C4×D13C2211yescharacteristic
9C22×C22⋊#261C412yes—
10C22×#6122C412yescomplemented
11C2×#88237C412yes—
12C2×#88237C412yes—
13C2×#88237C418yes—
14C2×#88237C2212yes—
15C2×#88237C2212yes—
16C2×#88237C2218yes—
17C22×C4⋊#261C412yes—
18C22×C4×#261C2212yes—
19C2×D13⋊M16C412yescomplemented
20C2×D13⋊M16C418yescomplemented
21C2×D13⋊M16C412yescomplemented
22C2×D13⋊M16C2212yes—
23C2×D13⋊M16C2212yes—
24C2×D13⋊M16C2218yes—
25C22×#6118C412yescomplemented
26C22×D13⋊C8C2212yes—
27C22×C13×M16C411yescharacteristic, complemented
28C22×#6099C411yescharacteristic, complemented
29C2×M16×D13C412yescomplemented
30C2×M16×D13C418yescomplemented
31C2×M16×D13C412yescomplemented
32C2×M16×D13C2212yes—
33C2×M16×D13C2212yes—
34C2×M16×D13C2218yes—
35C22×#6094C412yescomplemented
36C22×C8×D13C2212yes—
37#11719099C22132yescomplemented
38M16×#261C22132yescomplemented
39#11719089C22132yescomplemented
40C2×#88100C2218yescomplemented
41C2×C8×#261C2218yescomplemented
42C24×D13C2×C411yescharacteristic
43C23×#261C2×C414yes—
44C23×C4×C13C2×C411yescharacteristic
45C23×Dic13C2×C411yescharacteristic
46C22×C4×D13C2×C411yescharacteristic
47C22×C4×D13C2×C411yescharacteristic
48C22×C4×D13C2×C411yescharacteristic
49C22×C4×D13C2×C414yes—
50C22×C4×D13C2×C411yescharacteristic
51C22×C4×D13C2×C411yescharacteristic
52C22×C4×D13C2×C414yes—
53C22×C4×D13C2×C411yescharacteristic
54C22×C4×D13C2×C411yescharacteristic
55C22×C4×D13C2×C411yescharacteristic
56C22×C4×D13C2×C414yes—
57C22×C4×D13C2×C411yescharacteristic
58C22×C4×D13C2311yescharacteristic
59C22×C4×D13C2311yescharacteristic
60C22×C4×D13C2311yescharacteristic
61C22×C4×D13C2314yes—
62C2×C22⋊#261C2×C414yes—
63C2×C22⋊#261C2×C414yes—
64C2×C22⋊#261C2×C4116yes—
65C2×#6122C2×C414yes—
66C2×#6122C2×C414yescomplemented
67C2×#6122C2×C4116yescomplemented
68C22×#1057C2×C414yescomplemented
69#88237C2×C418yes—
70#88237C2×C418yes—
71#88237C2×C4116yes—
72#88237C2×C4116yes—
73#88237C2318yes—
74#88237C2318yes—
75C2×C4⋊#261C2×C414yes—
76C2×C4⋊#261C2×C414yes—
77C2×C4⋊#261C2×C4116yes—
78C2×C4×#261C2×C414yes—
79C2×C4×#261C2×C418yes—
80C2×C4×#261C2314yes—
81C2×C4×#261C2318yes—
82D13⋊M16C2×C418yes—
83D13⋊M16C2×C418yescomplemented
84D13⋊M16C2×C4116yescomplemented
85D13⋊M16C2×C4116yescomplemented
86D13⋊M16C2318yes—
87D13⋊M16C2318yes—
88C2×#6118C2×C414yes—
89C2×#6118C2×C4116yescomplemented
90C2×#6118C2×C414yescomplemented
91C2×D13⋊C8C2×C418yescomplemented
92C2×D13⋊C8C2×C414yescomplemented
93C2×D13⋊C8C2314yes—
94C2×D13⋊C8C2318yes—
95C2×C13×M16C2×C412yes—
96C2×C13×M16C2×C412yescomplemented
97C2×C13×M16C2×C418yescomplemented
98C22×C8×C13C2×C412yescomplemented
99C2×#6099C2×C412yes—
100C2×#6099C2×C412yescomplemented
101C2×#6099C2×C418yescomplemented
102C22×#1055C2×C412yescomplemented
103M16×D13C2×C418yes—
104M16×D13C2×C418yescomplemented
105M16×D13C2×C4116yescomplemented
106M16×D13C2×C4116yescomplemented
107M16×D13C2318yes—
108M16×D13C2318yes—
109C2×#6094C2×C414yes—
110C2×#6094C2×C4116yescomplemented
111C2×#6094C2×C414yescomplemented
112C2×C8×D13C2×C418yescomplemented
113C2×C8×D13C2×C414yescomplemented
114C2×C8×D13C2314yes—
115C2×C8×D13C2318yes—
116#88100C23132yescomplemented
117C8×#261C23132yescomplemented
118C2×#2873—131nomaximal, Sylow
119C24×C13C4211yescharacteristic
120C23×D13—44no—
121C23×D13C4214yes—
122C23×D13C4211yescharacteristic
123C23×D13C4211yescharacteristic
124C23×D13C4211yescharacteristic
125C23×D13C22×C411yescharacteristic
126C23×D13C22×C411yescharacteristic
127C23×D13C22×C411yescharacteristic
128C23×D13C22×C414yes—
129C22×#261—48no—
130C22×#261C22×C418yes—
131C22×#261C22×C4116yes—
132C22×C4×C13C4211yescharacteristic
133C22×C4×C13C4211yescharacteristic
134C22×C4×C13C4211yescharacteristic
135C22×C4×C13C4214yes—
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C414yes—
139C22×C4×C13C22×C411yescharacteristic
140C22×Dic13C4211yescharacteristic
141C22×Dic13C4211yescharacteristic
142C22×Dic13C4211yescharacteristic
143C22×Dic13C4214yes—
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C414yes—
148C2×C4×D13C4211yescharacteristic
149C2×C4×D13C4214yes—
150C2×C4×D13C4211yescharacteristic
151C2×C4×D13C4211yescharacteristic
152C2×C4×D13C4211yescharacteristic
153C2×C4×D13C4214yes—
154C2×C4×D13C4214yes—
155C2×C4×D13C4211yescharacteristic
156C2×C4×D13C4211yescharacteristic
157C2×C4×D13C4214yes—
158C2×C4×D13C4214yes—
159C2×C4×D13C4214yes—
160C2×C4×D13C4214yes—
161C2×C4×D13C4214yes—
162C2×C4×D13C4214yes—
163C2×C4×D13C22×C412yes—
164C2×C4×D13C22×C411yescharacteristic
165C2×C4×D13C22×C414yes—
166C2×C4×D13C22×C411yescharacteristic
167C2×C4×D13C22×C411yescharacteristic
168C2×C4×D13C22×C412yes—
169C2×C4×D13C22×C412yes—
170C2×C4×D13C22×C414yes—
171C2×C4×D13C22×C414yes—
172C2×C4×D13C22×C412yes—
173C2×C4×D13C22×C411yescharacteristic
174C2×C4×D13C22×C411yescharacteristic
175C2×C4×D13C22×C414yes—
176C2×C4×D13C22×C411yescharacteristic
177C2×C4×D13C22×C412yes—
178C2×C4×D13C22×C412yes—
179C2×C4×D13C22×C414yes—
180C2×C4×D13C22×C414yes—
181C2×C4×D13C22×C412yes—
182C2×C4×D13C22×C411yescharacteristic
183C2×C4×D13C22×C411yescharacteristic
184C2×C4×D13C22×C414yes—
185C2×C4×D13C22×C411yescharacteristic
186C2×C4×D13C22×C412yes—
187C2×C4×D13C22×C412yes—
188C2×C4×D13C22×C414yes—
189C2×C4×D13C22×C414yes—
190C2×C4×D13C2411yescharacteristic
191C2×C4×D13C2412yes—
192C2×C4×D13C2412yes—
193C2×C4×D13C2412yes—
194C22⋊#261C22×C4116yes—
195C22⋊#261C22×C4116yes—
196#6122C22×C4116yes—
197#6122C22×C4116yescomplemented
198C2×#1057C22×C418yes—
199C2×#1057C22×C4116yescomplemented
200C4⋊#261C22×C4116yes—
201C4⋊#261C22×C4116yes—
202C4×#261C22×C418yes—
203C4×#261C22×C4116yes—
204C4×#261C2418yes—
205#6118C22×C4116yes—
206#6118C22×C4116yescomplemented
207D13⋊C8C22×C418yes—
208D13⋊C8C22×C4116yescomplemented
209D13⋊C8C2418yes—
210C13×M16C22×C418yes—
211C13×M16C22×C418yescomplemented
212C2×C8×C13C22×C414yes—
213C2×C8×C13C22×C418yescomplemented
214#6099C22×C418yes—
215#6099C22×C418yescomplemented
216C2×#1055C22×C414yes—
217C2×#1055C22×C418yescomplemented
218#6094C22×C4116yes—
219#6094C22×C4116yescomplemented
220C8×D13C22×C418yes—
221C8×D13C22×C4116yescomplemented
222C8×D13C2418yes—
223C23×M16—131no—
224C23×M16—131no—
225C22×#117—131no—
226#2873—1316no—
227C2×#405—134no—
228C2×#405—134no—
229C2×C4×M16—134no—
230C23×C13—42no—
231C23×C13C2×C4211yescharacteristic
232C23×C13C2×C4211yescharacteristic
233C23×C13C2×C4211yescharacteristic
234C23×C13C2×C4214yes—
235C22×D13—24no—
236C22×D13—24no—
237C22×D13—24no—
238C22×D13—48no—
239C22×D13—48no—
240C22×D13—42no—
241C22×D13—42no—
242C22×D13—42no—
243C22×D13C2×C4211yescharacteristic
244C22×D13C2×C4211yescharacteristic
245C22×D13C2×C4211yescharacteristic
246C22×D13C2×C4212yes—
247C22×D13C2×C4212yes—
248C22×D13C2×C4212yes—
249C22×D13C2×C4214yes—
250C22×D13C2×C4214yes—
251C22×D13C2×C4214yes—
252C22×D13C23×C412yes—
253C22×D13C23×C412yes—
254C22×D13C23×C412yes—
255C22×D13C23×C411yescharacteristic
256C2×#261—216no—
257C2×#261—416no—
258C2×#261C23×C4116yes—
259C2×C4×C13C2×C4212yes—
260C2×C4×C13C2×C4214yes—
261C2×C4×C13C2×C4212yes—
262C2×C4×C13C2×C4214yes—
263C2×C4×C13C2×C4212yes—
264C2×C4×C13C2×C4214yes—
265C2×C4×C13C2×C4211yescharacteristic
266C2×C4×C13C2×C4211yescharacteristic
267C2×C4×C13C2×C4211yescharacteristic
268C2×C4×C13C23×C412yes—
269C2×C4×C13C23×C412yes—
270C2×C4×C13C23×C412yes—
271C2×C4×C13C23×C411yescharacteristic
272C2×Dic13C2×C4212yes—
273C2×Dic13C2×C4214yes—
274C2×Dic13C2×C4212yes—
275C2×Dic13C2×C4214yes—
276C2×Dic13C2×C4212yes—
277C2×Dic13C2×C4214yes—
278C2×Dic13C2×C4211yescharacteristic
279C2×Dic13C2×C4211yescharacteristic
280C2×Dic13C2×C4211yescharacteristic
281C2×Dic13C23×C411yescharacteristic
282C2×Dic13C23×C412yes—
283C2×Dic13C23×C412yes—
284C2×Dic13C23×C412yes—
285C4×D13C2×C4212yes—
286C4×D13C2×C4212yes—
287C4×D13C2×C4214yes—
288C4×D13C2×C4214yes—
289C4×D13C2×C4212yes—
290C4×D13C2×C4212yes—
291C4×D13C2×C4212yes—
292C4×D13C2×C4214yes—
293C4×D13C2×C4212yes—
294C4×D13C2×C4214yes—
295C4×D13C2×C4214yes—
296C4×D13C2×C4214yes—
297C4×D13C2×C4212yes—
298C4×D13C2×C4212yes—
299C4×D13C2×C4212yes—
300C4×D13C23×C411yescharacteristic
301C4×D13C23×C412yes—
302C4×D13C23×C412yes—
303C4×D13C23×C412yes—
304C4×D13C23×C411yescharacteristic
305C4×D13C23×C412yes—
306C4×D13C23×C412yes—
307C4×D13C23×C412yes—
308C4×D13C23×C411yescharacteristic
309C4×D13C23×C412yes—
310C4×D13C23×C412yes—
311C4×D13C23×C412yes—
312C4×D13C2511yescharacteristic
313#1057C23×C4116yes—
314C8×C13C23×C418yes—
315#1055C23×C418yes—
316C24×C4—131no—
317C22×M16—132no—
318C22×M16—132no—
319C22×M16—138no—
320C22×M16—132no—
321C22×M16—132no—
322C22×M16—138no—
323C22×M16—132no—
324C22×M16—132no—
325C22×M16—131no—
326C22×M16—132no—
327C22×M16—132no—
328C22×M16—132no—
329C22×M16—138no—
330C22×M16—132no—
331C22×M16—138no—
332C22×M16—132no—
333C22×M16#26111yescharacteristic, complemented
334C23×C8—132no—
335C23×C8—132no—
336C2×#117—132no—
337C2×#117—132no—
338C2×#117—138no—
339C2×#117—132no—
340C2×#117—132no—
341C2×#117—138no—
342C22×C4⋊C4—132no—
343C22×C22⋊C4—132no—
344C22×C42—132no—
345#405—1332no—
346#405—1332no—
347C4×M16—1332no—
348C2×#97—138no—
349C2×C4×C8—138no—
350C22×C13—22no—
351C22×C13—22no—
352C22×C13—22no—
353C22×C13—44no—
354C22×C13C22×C4212yes—
355C22×C13C22×C4212yes—
356C22×C13C22×C4212yes—
357C22×C13C22×C4211yescharacteristic
358C2×D13—22no—
359C2×D13—22no—
360C2×D13—22no—
361C2×D13—24no—
362C2×D13—24no—
363C2×D13—24no—
364C2×D13—24no—
365C2×D13—24no—
366C2×D13—24no—
367C2×D13—44no—
368C2×D13—44no—
369C2×D13—44no—
370C2×D13C22×C4212yes—
371C2×D13C22×C4212yes—
372C2×D13C22×C4212yes—
373C2×D13C22×C4211yescharacteristic
374C2×D13#56814yes—
375C2×D13C24×C411yescharacteristic
376#261—216no—
377C4×C13C22×C4212yes—
378C4×C13C22×C4212yes—
379C4×C13C22×C4212yes—
380C4×C13C22×C4211yescharacteristic
381C4×C13C24×C411yescharacteristic
382Dic13C22×C4211yescharacteristic
383Dic13C22×C4212yes—
384Dic13C22×C4212yes—
385Dic13C22×C4212yes—
386Dic13C24×C411yescharacteristic
387C25—131no—
388C23×C4—131no—
389C23×C4—131no—
390C23×C4—131no—
391C23×C4—131no—
392C23×C4—134no—
393C23×C4—131no—
394C23×C4—131no—
395C23×C4—131no—
396C23×C4—134no—
397C23×C4—131no—
398C23×C4—131no—
399C23×C4—134no—
400C23×C4—131no—
401C23×C4—134no—
402C23×C4—131no—
403C23×C4—131no—
404C23×C4—131no—
405C23×C4—134no—
406C23×C4C2×#26111yescharacteristic
407C2×M16—138no—
408C2×M16—138no—
409C2×M16—134no—
410C2×M16—134no—
411C2×M16—1316no—
412C2×M16—138no—
413C2×M16—138no—
414C2×M16—1316no—
415C2×M16—1316no—
416C2×M16—134no—
417C2×M16—134no—
418C2×M16—1316no—
419C2×M16—132no—
420C2×M16—138no—
421C2×M16—132no—
422C2×M16—138no—
423C2×M16—1316no—
424C2×M16—138no—
425C2×M16—138no—
426C2×M16—1316no—
427C2×M16—138no—
428C2×M16—134no—
429C2×M16—134no—
430C2×M16—1316no—
431C2×M16C2×#26112yes—
432C2×M16C2×#26112yescomplemented
433C2×M16C2×#26118yescomplemented
434C22×C8—134no—
435C22×C8—138no—
436C22×C8—138no—
437C22×C8—134no—
438C22×C8—134no—
439C22×C8—132no—
440C22×C8—134no—
441C22×C8—134no—
442C22×C8—138no—
443C22×C8—138no—
444C22×C8C2×#26112yescomplemented
445#117—138no—
446#117—138no—
447#117—138no—
448#117—138no—
449#117—1316no—
450#117—1316no—
451C2×C4⋊C4—134no—
452C2×C4⋊C4—134no—
453C2×C4⋊C4—1316no—
454C2×C22⋊C4—134no—
455C2×C22⋊C4—134no—
456C2×C22⋊C4—1316no—
457C2×C42—134no—
458C2×C42—138no—
459C2×C42—134no—
460C2×C42—138no—
461#97—1332no—
462C4×C8—1332no—
463C2×C13—22no—
464C2×C13—22no—
465C2×C13—22no—
466C2×C13#287312yescomplemented
467C2×C13C23×C4211yescharacteristic
468D13—22no—
469D13—22no—
470D13—22no—
471D13#287312yescomplemented
472D13C2×#56812yes—
473C24—131no—
474C24—131no—
475C24—131no—
476C24—134no—
477C24—134no—
478C24—131no—
479C24—131no—
480C24—131no—
481C24—524no—
482C24C4×#26111yescharacteristic
483C22×C4—131no—
484C22×C4—131no—
485C22×C4—131no—
486C22×C4—134no—
487C22×C4—131no—
488C22×C4—131no—
489C22×C4—131no—
490C22×C4—134no—
491C22×C4—131no—
492C22×C4—132no—
493C22×C4—131no—
494C22×C4—131no—
495C22×C4—134no—
496C22×C4—132no—
497C22×C4—132no—
498C22×C4—134no—
499C22×C4—134no—
500C22×C4—132no—
501C22×C4—131no—
502C22×C4—131no—
503C22×C4—131no—
504C22×C4—134no—
505C22×C4—132no—
506C22×C4—132no—
507C22×C4—134no—
508C22×C4—134no—
509C22×C4—134no—
510C22×C4—131no—
511C22×C4—131no—
512C22×C4—134no—
513C22×C4—134no—
514C22×C4—131no—
515C22×C4—131no—
516C22×C4—131no—
517C22×C4—131no—
518C22×C4—134no—
519C22×C4—134no—
520C22×C4—134no—
521C22×C4—134no—
522C22×C4—134no—
523C22×C4—134no—
524C22×C4—132no—
525C22×C4—132no—
526C22×C4—132no—
527C22×C4—132no—
528C22×C4—132no—
529C22×C4—134no—
530C22×C4—132no—
531C22×C4—134no—
532C22×C4—134no—
533C22×C4—131no—
534C22×C4—131no—
535C22×C4—131no—
536C22×C4—131no—
537C22×C4—138no—
538C22×C4—1316no—
539C22×C4—528no—
540C22×C4C4×#26111yescharacteristic
541C22×C4C4×#26111yescharacteristic
542C22×C4C4×#26111yescharacteristic
543C22×C4C4×#26114yes—
544C22×C4C22×#26114yes—
545C22×C4C22×#26111yescharacteristic
546C22×C4C22×#26111yescharacteristic
547C22×C4C22×#26111yescharacteristic
548M16—1316no—
549M16—1316no—
550M16—1316no—
551M16—1316no—
552M16—138no—
553M16—138no—
554M16—1316no—
555M16—1316no—
556M16C22×#26118yes—
557M16C22×#26118yescomplemented
558C2×C8—138no—
559C2×C8—138no—
560C2×C8—1316no—
561C2×C8—138no—
562C2×C8—1316no—
563C2×C8—138no—
564C2×C8—134no—
565C2×C8—138no—
566C2×C8—138no—
567C2×C8—1316no—
568C2×C8C22×#26114yes—
569C2×C8C22×#26118yescomplemented
570C4⋊C4—1316no—
571C4⋊C4—1316no—
572C22⋊C4—1316no—
573C22⋊C4—1316no—
574C42—138no—
575C42—138no—
576C42—1316no—
577C13C2×#287311yescharacteristic, complemented, Sylow
578C23—42no—
579C23—131no—
580C23—132no—
581C23—132no—
582C23—132no—
583C23—132no—
584C23—132no—
585C23—132no—
586C23—131no—
587C23—131no—
588C23—131no—
589C23—134no—
590C23—134no—
591C23—134no—
592C23—264no—
593C23—264no—
594C23—264no—
595C23—522no—
596C23—522no—
597C23—522no—
598C23—528no—
599C23—528no—
600C23C2×C4×#26111yescharacteristic
601C23C2×C4×#26111yescharacteristic
602C23C2×C4×#26111yescharacteristic
603C23C2×C4×#26114yes—
604C2×C4—132no—
605C2×C4—131no—
606C2×C4—132no—
607C2×C4—132no—
608C2×C4—132no—
609C2×C4—132no—
610C2×C4—134no—
611C2×C4—132no—
612C2×C4—134no—
613C2×C4—134no—
614C2×C4—131no—
615C2×C4—131no—
616C2×C4—131no—
617C2×C4—132no—
618C2×C4—131no—
619C2×C4—132no—
620C2×C4—132no—
621C2×C4—132no—
622C2×C4—131no—
623C2×C4—132no—
624C2×C4—132no—
625C2×C4—132no—
626C2×C4—132no—
627C2×C4—132no—
628C2×C4—132no—
629C2×C4—134no—
630C2×C4—134no—
631C2×C4—132no—
632C2×C4—132no—
633C2×C4—134no—
634C2×C4—134no—
635C2×C4—134no—
636C2×C4—134no—
637C2×C4—132no—
638C2×C4—132no—
639C2×C4—132no—
640C2×C4—131no—
641C2×C4—131no—
642C2×C4—132no—
643C2×C4—132no—
644C2×C4—132no—
645C2×C4—1316no—
646C2×C4—2616no—
647C2×C4—5216no—
648C2×C4C2×C4×#26114yes—
649C2×C4C2×C4×#26114yes—
650C2×C4C2×C4×#26114yes—
651C2×C4C2×C4×#26111yescharacteristic
652C2×C4C2×C4×#26111yescharacteristic
653C2×C4C2×C4×#26111yescharacteristic
654C2×C4C2×C4×#26112yes—
655C2×C4C2×C4×#26112yes—
656C2×C4C2×C4×#26112yes—
657C2×C4C23×#26112yes—
658C2×C4C23×#26112yes—
659C2×C4C23×#26112yes—
660C2×C4C23×#26111yescharacteristic
661C8—1316no—
662C8—138no—
663C8C23×#26118yes—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—44no—
668C22—131no—
669C22—131no—
670C22—134no—
671C22—132no—
672C22—132no—
673C22—132no—
674C22—264no—
675C22—264no—
676C22—264no—
677C22—264no—
678C22—264no—
679C22—264no—
680C22—262no—
681C22—262no—
682C22—262no—
683C22—524no—
684C22—524no—
685C22—524no—
686C22C22×C4×#26112yes—
687C22C22×C4×#26112yes—
688C22C22×C4×#26112yes—
689C22C22×C4×#26111yescharacteristic
690C4—131no—
691C4—131no—
692C4—132no—
693C4—132no—
694C4—132no—
695C4—2616no—
696C4C22×C4×#26112yes—
697C4C22×C4×#26112yes—
698C4C22×C4×#26112yes—
699C4C22×C4×#26111yescharacteristic
700C4C24×#26111yescharacteristic
701C2—22no—
702C2—22no—
703C2—22no—
704C2—132no—
705C2—132no—
706C2—262no—
707C2—262no—
708C2—262no—
709C2#1313139912yesdirect product factor
710C2C23×C4×#26111yescharacteristic
subgroupG/H
centerC2×C4C23×#261
commutatorC2×C13C23×C42
FrattiniC4C24×#261
FittingC22×C13×M16C4
socleC22×C13C22×C42
prime radicalC24×D13C2×C4
cosocleC4×D13C25
hypercenterC22×M16#261
hypocenterC13C2×#2873
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #13131399C2direct (N × H)
4. C2×#11719099C2semidirect
5. C2×#11719089C2semidirect
6. C2×M16×#261C2semidirect
10. C22×#6122C4semidirect
19. C2×D13⋊M16C4semidirect
20. C2×D13⋊M16C4semidirect
21. C2×D13⋊M16C4semidirect
25. C22×#6118C4semidirect
27. C22×C13×M16C4semidirect
28. C22×#6099C4semidirect
29. C2×M16×D13C4semidirect
30. C2×M16×D13C4semidirect
31. C2×M16×D13C4semidirect
35. C22×#6094C4semidirect
37. #11719099C22semidirect
38. M16×#261C22semidirect
39. #11719089C22semidirect
40. C2×#88100C22semidirect
41. C2×C8×#261C22semidirect
66. C2×#6122C2×C4semidirect
67. C2×#6122C2×C4semidirect
68. C22×#1057C2×C4semidirect
83. D13⋊M16C2×C4semidirect
84. D13⋊M16C2×C4semidirect
85. D13⋊M16C2×C4semidirect
89. C2×#6118C2×C4semidirect
90. C2×#6118C2×C4semidirect
91. C2×D13⋊C8C2×C4semidirect
92. C2×D13⋊C8C2×C4semidirect
96. C2×C13×M16C2×C4semidirect
97. C2×C13×M16C2×C4semidirect
98. C22×C8×C13C2×C4semidirect
100. C2×#6099C2×C4semidirect
101. C2×#6099C2×C4semidirect
102. C22×#1055C2×C4semidirect
104. M16×D13C2×C4semidirect
105. M16×D13C2×C4semidirect
106. M16×D13C2×C4semidirect
110. C2×#6094C2×C4semidirect
111. C2×#6094C2×C4semidirect
112. C2×C8×D13C2×C4semidirect
113. C2×C8×D13C2×C4semidirect
116. #88100C23semidirect
117. C8×#261C23semidirect
197. #6122C22×C4semidirect
199. C2×#1057C22×C4semidirect
206. #6118C22×C4semidirect
208. D13⋊C8C22×C4semidirect
211. C13×M16C22×C4semidirect
213. C2×C8×C13C22×C4semidirect
215. #6099C22×C4semidirect
217. C2×#1055C22×C4semidirect
219. #6094C22×C4semidirect
221. C8×D13C22×C4semidirect
333. C22×M16#261semidirect
432. C2×M16C2×#261semidirect
433. C2×M16C2×#261semidirect
444. C22×C8C2×#261semidirect
466. C2×C13#2873semidirect
471. D13#2873semidirect
557. M16C22×#261semidirect
569. C2×C8C22×#261semidirect
577. C13C2×#2873semidirect
709. C2#13131399direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D13⋊M162
C22×#882372
#131313992
C2×#117190992
C2×#117190892
C2×M16×#2612
C22×M16×D132
C2×#287313