Finite Group Databasebeta

← C2×#13131570 #16808283

Subgroups — C2×#13131570 #16808283

Order 3328.

2926 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88238C211yesmaximal, characteristic, complemented
2C22×D13⋊M16C211yesmaximal, characteristic, complemented
3#13131570C2116yesmaximal, direct product factor
4C2×#11719076C211yesmaximal, characteristic, complemented
5C2×#11719066C211yesmaximal, characteristic, complemented
6C2×#11719065C211yesmaximal, characteristic, complemented
7C2×#11719075C211yesmaximal, characteristic, complemented
8C2×#11719075C211yesmaximal, characteristic, complemented
9C2×#11719064C211yesmaximal, characteristic, complemented
10C2×#11719073C211yesmaximal, characteristic, complemented
11C2×#11719063C211yesmaximal, characteristic, complemented
12C2×#11719067C211yesmaximal, characteristic, complemented
13C2×#11719146C211yesmaximal, characteristic, complemented
14C22×#88111C211yesmaximal, characteristic, complemented
15C2×#11719062C211yesmaximal, characteristic, complemented
16C2×#11719361C211yesmaximal, characteristic
17C22×#6129C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C22×#6122C2211yescharacteristic
20C22×#6122C2211yescharacteristic
21C22×#6122C2211yescharacteristic, complemented
22C23×#1057C2211yescharacteristic
23C23×#1057C2211yescharacteristic
24C23×#1057C2211yescharacteristic, complemented
25C2×#88238—28no—
26C2×#88238C2218yescomplemented
27C2×D13⋊M16—28no—
28C2×D13⋊M16C2218yescomplemented
29C22×#6118C2211yescharacteristic
30C22×#6118C2211yescharacteristic
31C22×#6118C2211yescharacteristic, complemented
32C22×D13⋊C8C2211yescharacteristic
33C22×D13⋊C8C2211yescharacteristic
34C22×D13⋊C8C2211yescharacteristic, complemented
35C2×C13×#123C411yescharacteristic
36C2×#88191C411yescharacteristic
37C2×#88183C411yescharacteristic
38#11719361C418yes—
39#11719361C2218yes—
40C2×#88150C411yescharacteristic
41C2×#88150C411yescharacteristic
42C2×#88147C2211yescharacteristic
43C2×#88147C2211yescharacteristic
44C2×#88138C411yescharacteristic
45C2×#88138C411yescharacteristic
46C2×#88136C411yescharacteristic
47C2×#88135C2211yescharacteristic
48C2×#88135C2211yescharacteristic
49C2×#88131C2211yescharacteristic
50C2×C22⋊#1057C2211yescharacteristic, complemented
51C2×C22⋊#1057C2211yescharacteristic, complemented
52#11719146C2218yescomplemented
53C2×#88112C2211yescharacteristic, complemented
54C2×#88112C2211yescharacteristic, complemented
55C2×#88111C2211yescharacteristic
56C2×#88111C2211yescharacteristic
57C2×#88111C2211yescharacteristic
58C2×#88111C2211yescharacteristic
59C2×#88111C2218yescomplemented
60C2×#88111C2211yescharacteristic, complemented
61C2×#88111C2211yescharacteristic, complemented
62C2×#88110C2211yescharacteristic, complemented
63C2×#88110C2211yescharacteristic, complemented
64C2×C4⋊#1057C2211yescharacteristic, complemented
65C2×C4⋊#1057C2211yescharacteristic, complemented
66C2×C4×#1057C2211yescharacteristic, complemented
67C2×C4×#1057C2211yescharacteristic, complemented
68#11719076C2218yescomplemented
69#11719075C2218yescomplemented
70#11719075C2218yescomplemented
71#11719073C2218yescomplemented
72#11719067C2218yescomplemented
73#11719066C2218yescomplemented
74#11719065C2218yescomplemented
75#11719064C2218yescomplemented
76#11719063C2218yescomplemented
77#11719062C2218yescomplemented
78C24×D13C2×C411yescharacteristic
79C22×D4×C13C2×C411yescharacteristic
80C23×C4×C13C2×C411yescharacteristic
81C22×C22⋊D13C2×C411yescharacteristic
82C22×C22⋊D13C2×C411yescharacteristic
83C22×C22⋊D13C2×C411yescharacteristic
84C22×C22⋊D13C2×C411yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C2×#6129—24no—
88C2×#6129—24no—
89C2×#6129C2×C414yes—
90C2×#6129C2314yes—
91C22×D52C2×C411yescharacteristic
92C22×D52C2×C411yescharacteristic
93C22×C4×D13—24no—
94C22×C4×D13—24no—
95C22×C4×D13C2×C411yescharacteristic
96C22×C4×D13C2×C411yescharacteristic
97C22×C4×D13C2×C414yes—
98C22×C4×D13C2311yescharacteristic
99C22×C4×D13C2311yescharacteristic
100C22×C4×D13C2311yescharacteristic
101C22×C4×D13C2314yes—
102C22×Dic26C2×C411yescharacteristic
103C2×#6122—24no—
104C2×#6122—24no—
105C2×#6122D418yescomplemented
106C2×#6122C2314yes—
107C2×#6122C2314yes—
108C2×#6122C2314yescomplemented
109C22×#1057—24no—
110C22×#1057—24no—
111C22×#1057—24no—
112C22×#1057C2311yescharacteristic
113C22×#1057C2311yescharacteristic
114C22×#1057C2311yescharacteristic
115C22×#1057C2311yescharacteristic
116C22×#1057C2314yes—
117C22×#1057C2314yes—
118C22×#1057C2311yescharacteristic
119C22×#1057C2311yescharacteristic
120C22×#1057C2311yescharacteristic
121C22×#1057C2311yescharacteristic
122C22×#1057C2314yescomplemented
123#88238—232no—
124D13⋊M16—232no—
125C2×#6118—24no—
126C2×#6118—24no—
127C2×#6118—24no—
128C2×#6118C2314yes—
129C2×#6118C2314yes—
130C2×#6118C2314yescomplemented
131C2×D13⋊C8—24no—
132C2×D13⋊C8—24no—
133C2×D13⋊C8—24no—
134C2×D13⋊C8C2314yes—
135C2×D13⋊C8C2314yes—
136C2×D13⋊C8C2314yescomplemented
137C13×#123C2×C418yes—
138C2×C13×C4⋊C4C2×C411yescharacteristic
139C2×C13×C4⋊C4C2×C411yescharacteristic
140C2×C13×C22⋊C4C2×C411yescharacteristic
141C2×C13×C22⋊C4C2×C411yescharacteristic
142C2×C13×C22⋊C4C2×C411yescharacteristic
143C2×C22⋊Dic13C2×C411yescharacteristic
144#88191C2×C418yes—
145#88183C2×C418yes—
146C2×#6103C2×C411yescharacteristic
147C2×#6103C2×C411yescharacteristic
148C2×#6103C2×C411yescharacteristic
149C2×#6103C2×C411yescharacteristic
150C2×#6103C2×C411yescharacteristic
151C2×#6103C2×C411yescharacteristic
152C2×#6101C2×C411yescharacteristic
153C2×#6101C2×C411yescharacteristic
154C2×#6101C2×C411yescharacteristic
155C2×#6101C2×C411yescharacteristic
156C2×C4×Dic13C2311yescharacteristic
157C2×C4×Dic13C2311yescharacteristic
158#88150C2×C418yes—
159#88150C2×C418yes—
160#88147C2×C414yes—
161#88147C2×C414yes—
162#88147C2314yes—
163#88147C2314yes—
164#88138C2×C418yes—
165#88138C2×C418yes—
166#88136C2×C418yes—
167#88135C2×C414yes—
168#88135C2×C414yes—
169#88135C2314yes—
170#88135C2314yes—
171#88131C2×C414yes—
172#88131C2314yes—
173C22⋊#1057C2314yescomplemented
174C22⋊#1057C2314yescomplemented
175#88112C2314yescomplemented
176#88112C2314yescomplemented
177#88111C2314yes—
178#88111C2314yes—
179#88111C2314yes—
180#88111C2314yes—
181#88111C2314yescomplemented
182#88111C2314yescomplemented
183#88110C2314yescomplemented
184#88110C2314yescomplemented
185C4⋊#1057C2314yescomplemented
186C4⋊#1057C2314yescomplemented
187C4×#1057C2314yescomplemented
188C4×#1057C2314yescomplemented
189C2×#2933—131nomaximal, Sylow
190C24×C13C22×C411yescharacteristic
191C24×C13C22×C411yescharacteristic
192C23×D13—24no—
193C23×D13—24no—
194C23×D13—42no—
195C23×D13C22×C411yescharacteristic
196C23×D13C22×C411yescharacteristic
197C23×D13C22×C414yes—
198C23×D13C22×C411yescharacteristic
199C2×D4×C13—24no—
200C2×D4×C13C22×C414yes—
201C22×C4×C13—24no—
202C22×C4×C13C22×C411yescharacteristic
203C22×C4×C13C22×C411yescharacteristic
204C22×C4×C13C22×C411yescharacteristic
205C22×C4×C13C22×C411yescharacteristic
206C22×C4×C13C22×C411yescharacteristic
207C22×C4×C13C22×C414yes—
208C2×C22⋊D13—24no—
209C2×C22⋊D13—24no—
210C2×C22⋊D13—24no—
211C2×C22⋊D13—42no—
212C2×C22⋊D13C22×C414yes—
213C2×C22⋊D13C22×C414yes—
214C2×C22⋊D13C22×C414yes—
215C2×C22⋊D13C22×C414yes—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13C22×C412yes—
219C22×Dic13C22×C411yescharacteristic
220C22×Dic13C22×C411yescharacteristic
221C22×Dic13C22×C411yescharacteristic
222C22×Dic13C22×C412yes—
223C22×Dic13C22×C411yescharacteristic
224C22×Dic13C2×D414yes—
225C22×Dic13#4114yes—
226C22×Dic13C2412yes—
227C22×Dic13C2412yes—
228C22×Dic13C2411yescharacteristic
229#6129—216no—
230#6129—28no—
231#6129—28no—
232C2×D52—24no—
233C2×D52—42no—
234C2×D52C22×C414yes—
235C2×D52C22×C414yes—
236C2×C4×D13—24no—
237C2×C4×D13—24no—
238C2×C4×D13—216no—
239C2×C4×D13—22no—
240C2×C4×D13—22no—
241C2×C4×D13—22no—
242C2×C4×D13—28no—
243C2×C4×D13—22no—
244C2×C4×D13—22no—
245C2×C4×D13—28no—
246C2×C4×D13—22no—
247C2×C4×D13C22×C412yes—
248C2×C4×D13C22×C412yes—
249C2×C4×D13C22×C414yes—
250C2×C4×D13C22×C414yes—
251C2×C4×D13C22×C412yes—
252C2×C4×D13C2412yes—
253C2×C4×D13C2412yes—
254C2×C4×D13C2412yes—
255C2×Dic26—24no—
256C2×Dic26C22×C414yes—
257#6122—28no—
258#6122—28no—
259#6122C2×D4116yescomplemented
260C2×#1057—22no—
261C2×#1057—22no—
262C2×#1057—22no—
263C2×#1057—22no—
264C2×#1057—28no—
265C2×#1057—22no—
266C2×#1057—22no—
267C2×#1057—28no—
268C2×#1057—28no—
269C2×#1057C2×D414yes—
270C2×#1057C2×D414yes—
271C2×#1057C2412yes—
272C2×#1057C2412yes—
273C2×#1057C2412yes—
274C2×#1057C2412yes—
275C2×#1057C2412yes—
276C2×#1057C2412yes—
277C2×#1057C2412yes—
278C2×#1057C2412yes—
279#6118—28no—
280#6118—28no—
281#6118—28no—
282D13⋊C8—28no—
283D13⋊C8—28no—
284D13⋊C8—28no—
285C13×C4⋊C4C22×C414yes—
286C13×C4⋊C4C22×C414yes—
287C13×C22⋊C4C22×C414yes—
288C13×C22⋊C4C22×C414yes—
289C13×C22⋊C4C22×C414yes—
290C22⋊Dic13C22×C414yes—
291#6103C22×C414yes—
292#6103C22×C414yes—
293#6103C22×C414yes—
294#6103C22×C414yes—
295#6103C22×C414yes—
296#6103C22×C414yes—
297#6101C22×C414yes—
298#6101C22×C414yes—
299#6101C22×C414yes—
300#6101C22×C414yes—
301C4×Dic13C22×C412yes—
302C4×Dic13C22×C412yes—
303C4×Dic13C2412yes—
304C4×Dic13C2412yes—
305C22×#131—131no—
306C23×M16—131no—
307C2×#525—131no—
308#2933—1316no—
309C2×#436—131no—
310C2×#436—131no—
311C2×#435—131no—
312C2×#435—131no—
313C2×#435—131no—
314C2×#435—131no—
315C2×C8×D4—131no—
316C2×C8×D4—131no—
317C2×#424—131no—
318C2×#408—131no—
319C22×C22⋊C8—131no—
320C2×#405—131no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13C4×D414yes—
327C23×C13C23×C412yes—
328C23×C13C23×C412yes—
329C23×C13C23×C411yescharacteristic
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—28no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—22no—
336C22×D13—22no—
337C22×D13—22no—
338C22×D13—22no—
339C22×D13—28no—
340C22×D13—44no—
341C22×D13—416no—
342C22×D13#13114yescomplemented
343C22×D13C23×C412yes—
344C22×D13C23×C412yes—
345C22×D13C23×C412yes—
346D4×C13—28no—
347C2×C4×C13—22no—
348C2×C4×C13—28no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13C23×C412yes—
354C2×C4×C13C23×C412yes—
355C2×C4×C13C23×C412yes—
356C2×C4×C13C23×C412yes—
357C2×C4×C13C23×C412yes—
358C22⋊D13—28no—
359C22⋊D13—28no—
360C22⋊D13—28no—
361C22⋊D13—44no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—24no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13C4×D414yes—
369C2×Dic13C4×D418yes—
370C2×Dic13C23×C412yes—
371C2×Dic13C23×C412yes—
372C2×Dic13C23×C412yes—
373C2×Dic13C23×C411yescharacteristic
374C2×Dic13C23×C412yes—
375C2×Dic13C22×D412yes—
376C2×Dic13C22×D414yes—
377C2×Dic13C2×#4112yes—
378C2×Dic13C2×#4114yes—
379C2×Dic13C2511yescharacteristic
380D52—28no—
381D52—44no—
382C4×D13—28no—
383C4×D13—28no—
384C4×D13—24no—
385C4×D13—24no—
386C4×D13—24no—
387C4×D13—22no—
388C4×D13—22no—
389C4×D13—22no—
390C4×D13—22no—
391C4×D13—22no—
392C4×D13—22no—
393Dic26—28no—
394#1057—22no—
395#1057—22no—
396#1057—22no—
397#1057—22no—
398#1057—22no—
399#1057—22no—
400#1057C22×D414yes—
401#1057C22×D414yes—
402C22×#41—131no—
403C24×C4—131no—
404C2×#131—138no—
405C2×#131—268no—
406C22×M16—131no—
407C22×M16—131no—
408C22×M16—131no—
409C22×M16—131no—
410C22×M16—131no—
411C22×M16—131no—
412C22×M16—138no—
413C22×M16—268no—
414C23×C8—131no—
415C23×C8—131no—
416C23×C8—131no—
417C23×C8—131no—
418C23×C8—131no—
419C23×C8—131no—
420#525—138no—
421#525—138no—
422C2×#123—131no—
423C2×#123#26111yescharacteristic
424C2×C22⋊Q8—131no—
425C2×C22⋊Q8—131no—
426C2×#121—131no—
427C2×#121—131no—
428C2×#120—131no—
429C2×#120—131no—
430C2×C4×D4—131no—
431C2×C4×D4—131no—
432C2×C4×D4—131no—
433C2×C4×D4—131no—
434C2×#117—131no—
435#436—138no—
436#436—138no—
437#435—138no—
438#435—138no—
439#435—138no—
440#435—138no—
441C8×D4—138no—
442C8×D4—138no—
443#424—138no—
444C2×C4⋊C8—131no—
445C2×C4⋊C8—131no—
446C2×C4⋊C8—131no—
447C2×C4⋊C8—131no—
448#408—138no—
449C2×C22⋊C8—131no—
450C2×C22⋊C8—131no—
451C2×C22⋊C8—131no—
452C2×C22⋊C8—131no—
453C2×C22⋊C8—131no—
454C2×C22⋊C8—131no—
455C2×C22⋊C8—138no—
456C2×C22⋊C8—131no—
457C2×C22⋊C8—131no—
458#405—138no—
459C2×#97—131no—
460C2×#97—131no—
461C2×C4×C8—131no—
462C2×C4×C8—131no—
463C22×C13—28no—
464C22×C13—22no—
465C22×C13—22no—
466C22×C13—22no—
467C22×C13—22no—
468C22×C13—22no—
469C22×C13—44no—
470C22×C13C2×C4×D414yes—
471C22×C13C2×C4×D412yes—
472C22×C13C2×#13112yes—
473C22×C13#56812yes—
474C22×C13C24×C411yescharacteristic
475C2×D13—22no—
476C2×D13—28no—
477C2×D13—22no—
478C2×D13—22no—
479C2×D13—22no—
480C2×D13—22no—
481C2×D13—22no—
482C2×D13—22no—
483C2×D13—22no—
484C2×D13—416no—
485C2×D13—44no—
486C2×D13—44no—
487C2×D13C2×#13114yescomplemented
488C4×C13—22no—
489C4×C13—22no—
490C4×C13—22no—
491C4×C13—22no—
492C4×C13—22no—
493Dic13—22no—
494Dic13—22no—
495Dic13—22no—
496Dic13C2×C4×D414yes—
497Dic13C2×C4×D412yes—
498Dic13C23×D411yescharacteristic
499Dic13C22×#4111yescharacteristic
500C25—131no—
501C2×#41—134no—
502C2×#41—134no—
503C2×#41—264no—
504C2×#41—264no—
505C22×Q8—131no—
506C22×D4—131no—
507C22×D4—131no—
508C22×D4—131no—
509C22×D4—131no—
510C22×D4—131no—
511C22×D4—131no—
512C22×D4C2×#26111yescharacteristic
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—131no—
520C23×C4—134no—
521C23×C4—134no—
522C23×C4—264no—
523C23×C4—264no—
524C23×C4C2×#26111yescharacteristic
525#131—2632no—
526C2×M16—134no—
527C2×M16—138no—
528C2×M16—134no—
529C2×M16—134no—
530C2×M16—134no—
531C2×M16—134no—
532C2×M16—134no—
533C2×M16—264no—
534C2×M16—264no—
535C2×M16—264no—
536C2×M16—264no—
537C2×M16—2632no—
538C2×M16—264no—
539C22×C8—131no—
540C22×C8—131no—
541C22×C8—131no—
542C22×C8—131no—
543C22×C8—131no—
544C22×C8—131no—
545C22×C8—134no—
546C22×C8—134no—
547C22×C8—134no—
548C22×C8—134no—
549C22×C8—134no—
550C22×C8—131no—
551C22×C8—131no—
552C22×C8—134no—
553C22×C8—264no—
554C22×C8—264no—
555C22×C8—264no—
556C22×C8—264no—
557C22×C8—264no—
558C22×C8—264no—
559#123—138no—
560#123C2×#26118yes—
561C22⋊Q8—138no—
562C22⋊Q8—138no—
563#121—138no—
564#121—138no—
565#120—138no—
566#120—138no—
567C4×D4—134no—
568C4×D4—134no—
569C4×D4—134no—
570C4×D4—134no—
571C4×D4—134no—
572C4×D4—134no—
573C4×D4—134no—
574C4×D4—134no—
575#117—134no—
576#117—134no—
577C2×C4⋊C4—131no—
578C2×C4⋊C4—131no—
579C2×C4⋊C4—131no—
580C2×C4⋊C4—131no—
581C2×C4⋊C4C2×#26111yescharacteristic
582C2×C4⋊C4C2×#26111yescharacteristic
583C2×C22⋊C4—131no—
584C2×C22⋊C4—131no—
585C2×C22⋊C4—131no—
586C2×C22⋊C4—131no—
587C2×C22⋊C4—131no—
588C2×C22⋊C4—131no—
589C2×C22⋊C4—131no—
590C2×C22⋊C4C2×#26111yescharacteristic
591C2×C22⋊C4C2×#26111yescharacteristic
592C2×C22⋊C4C2×#26111yescharacteristic
593C2×C42—131no—
594C2×C42—131no—
595C4⋊C8—134no—
596C4⋊C8—134no—
597C4⋊C8—134no—
598C4⋊C8—134no—
599C22⋊C8—134no—
600C22⋊C8—134no—
601C22⋊C8—134no—
602C22⋊C8—134no—
603C22⋊C8—134no—
604C22⋊C8—134no—
605C22⋊C8—134no—
606C22⋊C8—134no—
607#97—134no—
608#97—134no—
609C4×C8—134no—
610C4×C8—134no—
611C2×C13—24no—
612C2×C13—42no—
613C2×C13#293314yescomplemented
614C2×C13C22×C4×D411yescharacteristic
615C2×C13C22×#13111yescharacteristic
616C2×C13C2×#56811yescharacteristic
617D13—24no—
618D13—42no—
619D13—42no—
620C24—131no—
621C24—131no—
622C24—131no—
623C24—134no—
624C24—264no—
625C24—264no—
626C24—522no—
627C24C22×#26111yescharacteristic
628C24C22×#26111yescharacteristic
629#41—268no—
630#41—268no—
631#41—2616no—
632C2×Q8—134no—
633C2×Q8—264no—
634C2×D4—24no—
635C2×D4—134no—
636C2×D4—134no—
637C2×D4—134no—
638C2×D4—134no—
639C2×D4—134no—
640C2×D4—134no—
641C2×D4—264no—
642C2×D4—264no—
643C2×D4—264no—
644C2×D4—264no—
645C2×D4—522no—
646C2×D4—522no—
647C2×D4C22×#26114yes—
648C22×C4—24no—
649C22×C4—134no—
650C22×C4—134no—
651C22×C4—132no—
652C22×C4—132no—
653C22×C4—131no—
654C22×C4—131no—
655C22×C4—132no—
656C22×C4—132no—
657C22×C4—131no—
658C22×C4—131no—
659C22×C4—131no—
660C22×C4—132no—
661C22×C4—132no—
662C22×C4—132no—
663C22×C4—132no—
664C22×C4—132no—
665C22×C4—132no—
666C22×C4—134no—
667C22×C4—134no—
668C22×C4—262no—
669C22×C4—262no—
670C22×C4—262no—
671C22×C4—268no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—268no—
675C22×C4—264no—
676C22×C4—264no—
677C22×C4—2616no—
678C22×C4—262no—
679C22×C4—262no—
680C22×C4—262no—
681C22×C4C22×#26114yes—
682C22×C4C22×#26111yescharacteristic
683C22×C4C22×#26111yescharacteristic
684C22×C4C22×#26111yescharacteristic
685C22×C4C22×#26111yescharacteristic
686C22×C4C22×#26111yescharacteristic
687M16—1316no—
688M16—268no—
689M16—268no—
690M16—268no—
691M16—268no—
692M16—268no—
693C2×C8—132no—
694C2×C8—132no—
695C2×C8—134no—
696C2×C8—134no—
697C2×C8—132no—
698C2×C8—132no—
699C2×C8—132no—
700C2×C8—132no—
701C2×C8—132no—
702C2×C8—132no—
703C2×C8—268no—
704C2×C8—268no—
705C2×C8—268no—
706C2×C8—268no—
707C2×C8—262no—
708C2×C8—262no—
709C2×C8—262no—
710C2×C8—262no—
711C2×C8—268no—
712C2×C8—262no—
713C2×C8—262no—
714C2×C8—268no—
715C4⋊C4—134no—
716C4⋊C4—134no—
717C4⋊C4—134no—
718C4⋊C4—134no—
719C4⋊C4C22×#26114yes—
720C4⋊C4C22×#26114yes—
721C22⋊C4—134no—
722C22⋊C4—134no—
723C22⋊C4—134no—
724C22⋊C4—134no—
725C22⋊C4—134no—
726C22⋊C4—134no—
727C22⋊C4—134no—
728C22⋊C4C22×#26114yes—
729C22⋊C4C22×#26114yes—
730C22⋊C4C22×#26114yes—
731C42—132no—
732C42—132no—
733C42—132no—
734C42—132no—
735C13C2×#293311yescharacteristic, complemented, Sylow
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—134no—
742C23—132no—
743C23—132no—
744C23—132no—
745C23—268no—
746C23—262no—
747C23—262no—
748C23—268no—
749C23—262no—
750C23—262no—
751C23—262no—
752C23—262no—
753C23—262no—
754C23—262no—
755C23—524no—
756C23—5216no—
757C23D4×#26114yes—
758C23C23×#26112yes—
759C23C23×#26112yes—
760C23C23×#26111yescharacteristic
761Q8—268no—
762D4—28no—
763D4—268no—
764D4—268no—
765D4—268no—
766D4—268no—
767D4—524no—
768D4—524no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—132no—
776C2×C4—134no—
777C2×C4—132no—
778C2×C4—134no—
779C2×C4—134no—
780C2×C4—138no—
781C2×C4—131no—
782C2×C4—131no—
783C2×C4—132no—
784C2×C4—132no—
785C2×C4—132no—
786C2×C4—132no—
787C2×C4—262no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—264no—
791C2×C4—264no—
792C2×C4—268no—
793C2×C4—268no—
794C2×C4—262no—
795C2×C4—262no—
796C2×C4—264no—
797C2×C4—262no—
798C2×C4—262no—
799C2×C4—264no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—262no—
803C2×C4—262no—
804C2×C4C23×#26112yes—
805C2×C4C23×#26112yes—
806C2×C4C23×#26112yes—
807C2×C4C23×#26112yes—
808C2×C4C23×#26112yes—
809C8—134no—
810C8—134no—
811C8—262no—
812C8—262no—
813C8—262no—
814C8—262no—
815C8—262no—
816C8—262no—
817C22—22no—
818C22—28no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—44no—
824C22—134no—
825C22—262no—
826C22—268no—
827C22—262no—
828C22—262no—
829C22—262no—
830C22—262no—
831C22—262no—
832C22—262no—
833C22—262no—
834C22—5216no—
835C22—524no—
836C22—524no—
837C22C2×D4×#26114yes—
838C22C2×D4×#26112yes—
839C22D13⋊#13112yes—
840C22#1171962912yes—
841C22C24×#26111yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—132no—
848C4—134no—
849C4—131no—
850C4—131no—
851C4—262no—
852C4—262no—
853C4—262no—
854C2—24no—
855C2—42no—
856C2—264no—
857C2—522no—
858C2—522no—
859C2#1313157014yesdirect product factor
860C2C22×D4×#26111yescharacteristic
861C2C2×D13⋊#13111yescharacteristic
862C2C2×#1171962911yescharacteristic
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×#123C4
socleC23×C13C23×C4
prime radicalC2×#11719361C2
cosocleC2×Dic13C25
hypercenterC2×#123#261
hypocenterC13C2×#2933
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×#88238C2semidirect
2. C22×D13⋊M16C2semidirect
3. #13131570C2direct (N × H)
4. C2×#11719076C2semidirect
5. C2×#11719066C2semidirect
6. C2×#11719065C2semidirect
7. C2×#11719075C2semidirect
8. C2×#11719075C2semidirect
9. C2×#11719064C2semidirect
10. C2×#11719073C2semidirect
11. C2×#11719063C2semidirect
12. C2×#11719067C2semidirect
13. C2×#11719146C2semidirect
14. C22×#88111C2semidirect
15. C2×#11719062C2semidirect
21. C22×#6122C22semidirect
24. C23×#1057C22semidirect
26. C2×#88238C22semidirect
28. C2×D13⋊M16C22semidirect
31. C22×#6118C22semidirect
34. C22×D13⋊C8C22semidirect
50. C2×C22⋊#1057C22semidirect
51. C2×C22⋊#1057C22semidirect
52. #11719146C22semidirect
53. C2×#88112C22semidirect
54. C2×#88112C22semidirect
59. C2×#88111C22semidirect
60. C2×#88111C22semidirect
61. C2×#88111C22semidirect
62. C2×#88110C22semidirect
63. C2×#88110C22semidirect
64. C2×C4⋊#1057C22semidirect
65. C2×C4⋊#1057C22semidirect
66. C2×C4×#1057C22semidirect
67. C2×C4×#1057C22semidirect
68. #11719076C22semidirect
69. #11719075C22semidirect
70. #11719075C22semidirect
71. #11719073C22semidirect
72. #11719067C22semidirect
73. #11719066C22semidirect
74. #11719065C22semidirect
75. #11719064C22semidirect
76. #11719063C22semidirect
77. #11719062C22semidirect
105. C2×#6122D4semidirect
108. C2×#6122C23semidirect
122. C22×#1057C23semidirect
130. C2×#6118C23semidirect
136. C2×D13⋊C8C23semidirect
173. C22⋊#1057C23semidirect
174. C22⋊#1057C23semidirect
175. #88112C23semidirect
176. #88112C23semidirect
181. #88111C23semidirect
182. #88111C23semidirect
183. #88110C23semidirect
184. #88110C23semidirect
185. C4⋊#1057C23semidirect
186. C4⋊#1057C23semidirect
187. C4×#1057C23semidirect
188. C4×#1057C23semidirect
259. #6122C2×D4semidirect
342. C22×D13#131semidirect
487. C2×D13C2×#131semidirect
613. C2×C13#2933semidirect
735. C13C2×#2933semidirect
859. C2#13131570direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882382
C22×D13⋊M162
#131315702
C2×#117190762
C2×#117190662
C2×#117190652
C2×#117190752
C2×#117190642
C2×#117190732
C2×#117190632
C2×#117190672
C2×#117191462
C22×#881112
C2×#117190622
C2×#117193612
C2×#293313