Finite Group Databasebeta

← C2×#13125044 #16731176

Subgroups — C2×#13125044 #16731176

Order 3328.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719228C211yesmaximal, characteristic
2#13125044C2116yesmaximal, direct product factor
3C2×#11718705C211yesmaximal, characteristic, complemented
4C2×#11718704C211yesmaximal, characteristic, complemented
5C2×#11718724C211yesmaximal, characteristic, complemented
6C2×#11718727C211yesmaximal, characteristic, complemented
7C2×#11718751C211yesmaximal, characteristic, complemented
8C2×#11718744C211yesmaximal, characteristic, complemented
9C2×#11718708C211yesmaximal, characteristic
10C2×#11718708C211yesmaximal, characteristic
11C2×#11718691C211yesmaximal, characteristic, complemented
12C2×#11718687C211yesmaximal, characteristic, complemented
13C2×C4×#6107C211yesmaximal, characteristic, complemented
14C2×C4×#6106C211yesmaximal, characteristic, complemented
15C2×#11718661C211yesmaximal, characteristic, complemented
16C2×C13×#541C211yesmaximal, characteristic, complemented
17C22×#6127C2211yescharacteristic
18C13×#541—24no—
19C13×#541C2218yescomplemented
20C2×C13×C4⋊Q8C2211yescharacteristic
21C2×C13×#126—21no—
22C2×C13×#126—21no—
23C2×C13×#125—21no—
24C2×C13×#125—21no—
25C2×C13×#125C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C13×C22⋊Q8C2211yescharacteristic
28C2×C4×Q8×C13C2211yescharacteristic
29C2×C4×Q8×C13C2211yescharacteristic
30C2×C13×#117C2211yescharacteristic
31C22×#6107C2211yescharacteristic
32C22×#6107C2211yescharacteristic
33C22×#6106C2211yescharacteristic
34C22×#6106C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36#11719228—24no—
37#11719228C2218yes—
38C2×#88146—21no—
39C2×C4⋊C4×D13—21no—
40C2×#88135—21no—
41C2×#88135—21no—
42C2×C4×D52C2211yescharacteristic
43C2×C4×D52C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C2×C4×Dic26C2211yescharacteristic
46C2×#88075C2211yescharacteristic
47C2×#88075C2211yescharacteristic
48C2×#88075C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×C22⋊#1055C2211yescharacteristic
51C2×C22⋊#1055C2211yescharacteristic
52#11718751C2218yescomplemented
53#11718744C2218yescomplemented
54#11718727C2218yescomplemented
55#11718724C2218yescomplemented
56#11718708C2218yes—
57#11718708C2218yes—
58#11718705C2218yescomplemented
59#11718704C2218yescomplemented
60#11718691C2218yescomplemented
61C4×#6107C2218yescomplemented
62#11718687C2218yescomplemented
63C4×#6106C2218yescomplemented
64#11718661C2218yescomplemented
65C2×#88050C2211yescharacteristic
66C2×#88050C2211yescharacteristic
67C2×#88049C2211yescharacteristic
68C2×#88049C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88048C2211yescharacteristic
71C2×#88047C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×C4⋊#1055C2211yescharacteristic
75C2×#88043C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×Q8×C13C2311yescharacteristic
78C22×Q8×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C22×C22⋊D13—21no—
81C23×Dic13—21no—
82C2×#6127—22no—
83C2×#6127—24no—
84C2×#6127—24no—
85C2×#6127C2314yes—
86C22×D52C2311yescharacteristic
87C22×C4×D13—21no—
88C22×C4×D13—21no—
89C22×C4×D13—21no—
90C22×Dic26C2311yescharacteristic
91C13×C4⋊Q8—22no—
92C13×C4⋊Q8C2314yes—
93C13×#126—28no—
94C13×#126—28no—
95C13×#125—28no—
96C13×#125—28no—
97C13×#125—22no—
98C13×#125C2314yes—
99C13×C22⋊Q8—22no—
100C13×C22⋊Q8—22no—
101C13×C22⋊Q8C2314yes—
102C13×C22⋊Q8C2314yes—
103C4×Q8×C13—22no—
104C4×Q8×C13—22no—
105C4×Q8×C13C2314yes—
106C4×Q8×C13C2314yes—
107C13×#117D414yes—
108C13×#117C2314yes—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4—21no—
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4D411yescharacteristic
118C2×C13×C4⋊C4D411yescharacteristic
119C2×C13×C4⋊C4C2311yescharacteristic
120C2×C13×C4⋊C4C2311yescharacteristic
121C2×C13×C22⋊C4—21no—
122C2×C13×C22⋊C4—21no—
123C2×C13×C22⋊C4D411yescharacteristic
124C2×C13×C22⋊C4D411yescharacteristic
125C2×C42×C13—21no—
126C2×C42×C13—21no—
127C2×C42×C13C2311yescharacteristic
128C2×C42×C13C2311yescharacteristic
129C2×#6107—24no—
130C2×#6107—24no—
131C2×#6107C2314yes—
132C2×#6107C2314yes—
133C2×#6106—24no—
134C2×#6106—24no—
135C2×#6106C2314yes—
136C2×#6106C2314yes—
137C2×#6103—21no—
138C2×#6103—21no—
139C2×C4⋊Dic13—21no—
140C2×C4⋊Dic13—22no—
141C2×C4⋊Dic13C2311yescharacteristic
142C2×C4⋊Dic13C2311yescharacteristic
143C2×C4⋊Dic13C2314yes—
144C2×#6101—21no—
145C2×#6101—21no—
146C2×C4×Dic13—21no—
147C2×C4×Dic13—21no—
148C22×#1055C2311yescharacteristic
149C22×#1055C2311yescharacteristic
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152#88146—28no—
153C4⋊C4×D13—28no—
154#88135—28no—
155#88135—28no—
156C4×D52—22no—
157C4×D52—22no—
158C4×D52C2314yes—
159C4×D52C2314yes—
160C4×Dic26—22no—
161C4×Dic26—22no—
162C4×Dic26C2314yes—
163C4×Dic26C2314yes—
164#88075C2314yes—
165#88075C2314yes—
166#88075C2314yes—
167#88075C2314yes—
168C22⋊#1055C2314yes—
169C22⋊#1055C2314yes—
170#88050C2314yes—
171#88050C2314yes—
172#88049C2314yes—
173#88049C2314yes—
174#88048C2314yes—
175#88048C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178C4⋊#1055C2314yes—
179C4⋊#1055C2314yes—
180#88043C2314yes—
181C4×#1055C2314yes—
182C2×#3120—131nomaximal, Sylow
183C24×C13C2×D411yescharacteristic
184C23×D13—21no—
185C2×Q8×C13—21no—
186C2×Q8×C13—21no—
187C2×Q8×C13—22no—
188C2×Q8×C13—22no—
189C2×Q8×C13—22no—
190C2×Q8×C13—22no—
191C2×Q8×C13C2412yes—
192C2×Q8×C13C2412yes—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2×D411yescharacteristic
204C22×C4×C13C2×D412yes—
205C22×C4×C13C2412yes—
206C22×C4×C13C2411yescharacteristic
207C2×C22⋊D13—28no—
208C2×C22⋊D13—24no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—24no—
213C22×Dic13—82no—
214#6127—216no—
215#6127—28no—
216#6127—28no—
217C2×D52—21no—
218C2×D52—22no—
219C2×D52#4114yes—
220C2×D52C2412yes—
221C2×C4×D13—28no—
222C2×C4×D13—24no—
223C2×C4×D13—24no—
224C2×C4×D13—24no—
225C2×C4×D13—82no—
226C2×C4×D13—82no—
227C2×Dic26—21no—
228C2×Dic26—22no—
229C2×Dic26#4114yes—
230C2×Dic26C2412yes—
231C13×C4⋊C4—24no—
232C13×C4⋊C4—24no—
233C13×C4⋊C4—24no—
234C13×C4⋊C4—24no—
235C13×C4⋊C4—24no—
236C13×C4⋊C4—24no—
237C13×C4⋊C4—24no—
238C13×C4⋊C4—24no—
239C13×C4⋊C4—21no—
240C13×C4⋊C4—21no—
241C13×C4⋊C4C2×D414yes—
242C13×C4⋊C4C2×D414yes—
243C13×C4⋊C4C2412yes—
244C13×C4⋊C4C2412yes—
245C13×C22⋊C4—24no—
246C13×C22⋊C4—24no—
247C13×C22⋊C4C2×D414yes—
248C13×C22⋊C4C2×D414yes—
249C42×C13—24no—
250C42×C13—24no—
251C42×C13C2×D412yes—
252C42×C13C2×D412yes—
253C42×C13C2412yes—
254C42×C13C2412yes—
255#6107—28no—
256#6107—28no—
257#6106—28no—
258#6106—28no—
259#6103—24no—
260#6103—24no—
261C4⋊Dic13—21no—
262C4⋊Dic13—21no—
263C4⋊Dic13—24no—
264C4⋊Dic13C2412yes—
265C4⋊Dic13C2412yes—
266#6101—24no—
267#6101—24no—
268C4×Dic13—24no—
269C4×Dic13—24no—
270C2×#1055—22no—
271C2×#1055—22no—
272C2×#1055—22no—
273C2×#1055—22no—
274C2×#1055C2412yes—
275C2×#1055C2412yes—
276C2×#1055C2412yes—
277C2×#1055C2412yes—
278C2×#541D1311yescharacteristic, complemented
279C2×#520—131no—
280#3120—1316no—
281C2×#484—131no—
282C2×#483—131no—
283C2×#479—131no—
284C2×#478—131no—
285C2×#462—131no—
286C2×#461—131no—
287C2×#452—131no—
288C2×#452—131no—
289C2×#441—131no—
290C2×#440—131no—
291C2×C4×Q16—131no—
292C2×C4×SD16—131no—
293C2×#433—131no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13C22×D412yes—
298C23×C13C22×D411yescharacteristic
299C22×D13—24no—
300C22×D13—22no—
301C22×D13—42no—
302C22×D13—42no—
303Q8×C13—22no—
304Q8×C13—22no—
305Q8×C13—22no—
306Q8×C13—22no—
307Q8×C13—42no—
308Q8×C13—42no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—24no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—42no—
322C2×C4×C13—42no—
323C2×C4×C13—42no—
324C2×C4×C13—42no—
325C2×C4×C13C22×D412yes—
326C2×C4×C13C22×D412yes—
327C2×C4×C13C22×D412yes—
328C2×C4×C13C22×D412yes—
329C2×C4×C13C22×D412yes—
330C2×C4×C13C22×D411yescharacteristic
331C2×C4×C13C2×#4112yes—
332C2×C4×C13C2×#4112yes—
333C2×C4×C13C2511yescharacteristic
334C22⋊D13—216no—
335C2×Dic13—24no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—84no—
342D52—24no—
343D52—22no—
344D52C2×#4114yes—
345C4×D13—216no—
346C4×D13—84no—
347C4×D13—84no—
348Dic26—24no—
349Dic26—22no—
350Dic26C2×#4114yes—
351#1055—22no—
352#1055—22no—
353#1055—22no—
354#1055—22no—
355C22×#41—131no—
356C22×Q16—131no—
357C22×Q16—131no—
358C22×SD16—131no—
359C22×SD16—131no—
360#541—24no—
361#541C2×D1318yescomplemented
362C2×C4⋊Q8C2×D1311yescharacteristic
363C2×#126—21no—
364C2×#126—21no—
365C2×#125—21no—
366C2×#125—21no—
367C2×#125C2×D1311yescharacteristic
368C2×C22⋊Q8C2×D1311yescharacteristic
369C2×C22⋊Q8C2×D1311yescharacteristic
370#520—138no—
371#520—264no—
372C2×C4×Q8—131no—
373C2×C4×Q8—131no—
374C2×C4×Q8C2×D1311yescharacteristic
375C2×C4×Q8C2×D1311yescharacteristic
376C2×C4×D4—131no—
377C2×C4×D4—131no—
378C2×C4×D4—261no—
379C2×C4×D4—261no—
380C2×#117—261no—
381C2×#117C2×D1311yescharacteristic
382C22×C4⋊C4—131no—
383C22×C4⋊C4—261no—
384#484—138no—
385#483—138no—
386#479—138no—
387#478—138no—
388#462—138no—
389#461—138no—
390#452—138no—
391#452—138no—
392#441—138no—
393#440—138no—
394C4×Q16—138no—
395C4×SD16—138no—
396#433—138no—
397C2×#107—131no—
398C2×#107—131no—
399C2×#106—131no—
400C2×#106—131no—
401C2×C4⋊C8—131no—
402C2×C4⋊C8—131no—
403C2×#103—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#103—131no—
408C2×#103—131no—
409C2×#102—131no—
410C2×#102—131no—
411C2×C22⋊C8—131no—
412C2×C22⋊C8—131no—
413C2×#97—131no—
414C2×C4×C8—131no—
415C22×C13—22no—
416C22×C13—22no—
417C22×C13—22no—
418C22×C13—44no—
419C22×C13#52512yes—
420C22×C13#57712yes—
421C22×C13#57812yes—
422C22×C13C23×D411yescharacteristic
423C2×D13—24no—
424C2×D13—48no—
425C2×D13—42no—
426C2×D13—42no—
427C4×C13—22no—
428C4×C13—22no—
429C4×C13—22no—
430C4×C13—22no—
431C4×C13—22no—
432C4×C13—42no—
433C4×C13—42no—
434C4×C13—42no—
435C4×C13—42no—
436C4×C13#52512yes—
437C4×C13C22×#4111yescharacteristic
438C4×C13C22×#4111yescharacteristic
439Dic13—24no—
440Dic13—42no—
441Dic13—42no—
442C2×#41—134no—
443C2×#41—264no—
444C2×#41—264no—
445C2×#41—262no—
446C22×Q8—131no—
447C22×Q8C22×D1311yescharacteristic
448C22×Q8C22×D1311yescharacteristic
449C22×D4—131no—
450C22×D4—261no—
451C23×C4—261no—
452C23×C4—261no—
453C23×C4—261no—
454C23×C4—261no—
455C23×C4C22×D1311yescharacteristic
456C2×Q16—134no—
457C2×Q16—134no—
458C2×Q16—264no—
459C2×Q16—264no—
460C2×SD16—134no—
461C2×SD16—134no—
462C2×SD16—264no—
463C2×SD16—264no—
464C22×C8—131no—
465C22×C8—131no—
466C22×C8—131no—
467C22×C8—131no—
468C4⋊Q8—22no—
469C4⋊Q8C22×D1314yes—
470#126—28no—
471#126—28no—
472#125—28no—
473#125—28no—
474#125—22no—
475#125C22×D1314yes—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8C22×D1314yes—
479C22⋊Q8C22×D1314yes—
480C4×Q8—22no—
481C4×Q8—22no—
482C4×Q8—134no—
483C4×Q8—134no—
484C4×Q8—262no—
485C4×Q8—262no—
486C4×Q8C22×D1314yes—
487C4×Q8C22×D1314yes—
488C4×D4—134no—
489C4×D4—134no—
490C4×D4—268no—
491C4×D4—268no—
492C4×D4—262no—
493C4×D4—262no—
494#117—268no—
495#117C22⋊D1314yes—
496#117C22×D1314yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—131no—
506C2×C4⋊C4—131no—
507C2×C4⋊C4—134no—
508C2×C4⋊C4—261no—
509C2×C4⋊C4—262no—
510C2×C4⋊C4—261no—
511C2×C4⋊C4—261no—
512C2×C4⋊C4—268no—
513C2×C4⋊C4C22⋊D1311yescharacteristic
514C2×C4⋊C4C22⋊D1311yescharacteristic
515C2×C4⋊C4C22×D1311yescharacteristic
516C2×C4⋊C4C22×D1311yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—261no—
520C2×C22⋊C4—261no—
521C2×C22⋊C4C22⋊D1311yescharacteristic
522C2×C22⋊C4C22⋊D1311yescharacteristic
523C2×C42—21no—
524C2×C42—21no—
525C2×C42—261no—
526C2×C42—261no—
527C2×C42C22×D1311yescharacteristic
528C2×C42C22×D1311yescharacteristic
529#107—134no—
530#107—134no—
531#106—134no—
532#106—134no—
533C4⋊C8—134no—
534C4⋊C8—134no—
535#103—134no—
536#103—134no—
537#103—134no—
538#103—134no—
539#103—134no—
540#103—134no—
541#102—134no—
542#102—134no—
543C22⋊C8—134no—
544C22⋊C8—134no—
545#97—134no—
546C4×C8—134no—
547C2×C13—42no—
548C2×C13#312014yescomplemented
549C2×C13C2×#52511yescharacteristic
550C2×C13C2×#57711yescharacteristic
551C2×C13C2×#57811yescharacteristic
552D13—44no—
553C24—261no—
554C24C2×C22⋊D1311yescharacteristic
555#41—268no—
556#41—268no—
557#41—2616no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—134no—
565C2×Q8—132no—
566C2×Q8—262no—
567C2×Q8—261no—
568C2×Q8C23×D1312yes—
569C2×Q8C23×D1312yes—
570C2×D4—134no—
571C2×D4—132no—
572C2×D4—268no—
573C2×D4—264no—
574C2×D4—262no—
575C2×D4—261no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—268no—
583C22×C4—261no—
584C22×C4—264no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—264no—
588C22×C4—264no—
589C22×C4—264no—
590C22×C4—1042no—
591C22×C4—1042no—
592C22×C4—1042no—
593C22×C4C2×C22⋊D1312yes—
594C22×C4C2×C22⋊D1311yescharacteristic
595C22×C4C2×C22⋊D1311yescharacteristic
596C22×C4C2×C22⋊D1311yescharacteristic
597C22×C4C2×C22⋊D1311yescharacteristic
598C22×C4C2×C22⋊D1311yescharacteristic
599C22×C4C23×D1312yes—
600C22×C4C23×D1311yescharacteristic
601Q16—268no—
602Q16—268no—
603SD16—268no—
604SD16—268no—
605C2×C8—132no—
606C2×C8—132no—
607C2×C8—132no—
608C2×C8—132no—
609C2×C8—262no—
610C2×C8—262no—
611C2×C8—262no—
612C2×C8—262no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—132no—
624C4⋊C4—132no—
625C4⋊C4—264no—
626C4⋊C4—261no—
627C4⋊C4—261no—
628C4⋊C4—264no—
629C4⋊C4—264no—
630C4⋊C4C2×C22⋊D1314yes—
631C4⋊C4C2×C22⋊D1314yes—
632C4⋊C4C23×D1312yes—
633C4⋊C4C23×D1312yes—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—264no—
637C22⋊C4—264no—
638C22⋊C4C2×C22⋊D1314yes—
639C22⋊C4C2×C22⋊D1314yes—
640C42—24no—
641C42—24no—
642C42—264no—
643C42—264no—
644C42C2×C22⋊D1312yes—
645C42C2×C22⋊D1312yes—
646C42C23×D1312yes—
647C42C23×D1312yes—
648C13C2×#312011yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—264no—
653C23—262no—
654C23—522no—
655C23—522no—
656C23C22×C22⋊D1312yes—
657C23C22×C22⋊D1311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—42no—
664Q8—134no—
665Q8—264no—
666Q8—262no—
667D4—134no—
668D4—2616no—
669D4—264no—
670D4—262no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—2616no—
688C2×C4—264no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—522no—
693C2×C4—522no—
694C2×C4—1044no—
695C2×C4—1044no—
696C2×C4—1044no—
697C2×C4#41×D1312yes—
698C2×C4#41×D1312yes—
699C2×C4C22×C22⋊D1312yes—
700C2×C4C22×C22⋊D1312yes—
701C2×C4C22×C22⋊D1312yes—
702C2×C4C22×C22⋊D1312yes—
703C2×C4C22×C22⋊D1312yes—
704C2×C4C22×C22⋊D1311yescharacteristic
705C2×C4C24×D1311yescharacteristic
706C8—262no—
707C8—262no—
708C8—262no—
709C8—262no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—264no—
715C22—522no—
716C22—522no—
717C22—528no—
718C22#1171953312yes—
719C22#1171954212yes—
720C22#1171954312yes—
721C22C23×C22⋊D1311yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—264no—
732C4—522no—
733C4—522no—
734C4#1171953312yes—
735C4C2×#41×D1311yescharacteristic
736C4C2×#41×D1311yescharacteristic
737C2—42no—
738C2—524no—
739C2#1312504414yesdirect product factor
740C2C2×#1171953311yescharacteristic
741C2C2×#1171954211yescharacteristic
742C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#541C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
hypercenterC2×#541D13
hypocenterC13C2×#3120
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #13125044C2direct (N × H)
3. C2×#11718705C2semidirect
4. C2×#11718704C2semidirect
5. C2×#11718724C2semidirect
6. C2×#11718727C2semidirect
7. C2×#11718751C2semidirect
8. C2×#11718744C2semidirect
11. C2×#11718691C2semidirect
12. C2×#11718687C2semidirect
13. C2×C4×#6107C2semidirect
14. C2×C4×#6106C2semidirect
15. C2×#11718661C2semidirect
16. C2×C13×#541C2semidirect
19. C13×#541C22semidirect
52. #11718751C22semidirect
53. #11718744C22semidirect
54. #11718727C22semidirect
55. #11718724C22semidirect
58. #11718705C22semidirect
59. #11718704C22semidirect
60. #11718691C22semidirect
61. C4×#6107C22semidirect
62. #11718687C22semidirect
63. C4×#6106C22semidirect
64. #11718661C22semidirect
278. C2×#541D13semidirect
361. #541C2×D13semidirect
548. C2×C13#3120semidirect
648. C13C2×#3120semidirect
739. C2#13125044direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192282
#131250442
C2×#117187052
C2×#117187042
C2×#117187242
C2×#117187272
C2×#117187512
C2×#117187442
C2×#117187082
C2×#117186912
C2×#117186872
C2×C4×#61072
C2×C4×#61062
C2×#117186612
C2×C13×#5412
C2×#312013