Finite Group Databasebeta

← #16807756

Subgroups — #16807756

Order 3328.

3112 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719631C211yesmaximal, characteristic, complemented
2C22×Q8×#261C211yesmaximal, characteristic, complemented
3#13131367C213yesmaximal, complemented
4#13131361C213yesmaximal, complemented
5#13131360C213yesmaximal, complemented
6Q8×C4⋊#261C211yesmaximal, characteristic, complemented
7D4×C4⋊#261C213yesmaximal, complemented
8#13131341C211yesmaximal, characteristic, complemented
9Q8×C22⋊#261C211yesmaximal, characteristic, complemented
10#13131326C213yesmaximal, complemented
11#13131323C213yesmaximal, complemented
12#121×#261C213yesmaximal, complemented
13#13131290C213yesmaximal, complemented
14#13131276C211yesmaximal, characteristic, complemented
15D13×#548C211yesmaximal, characteristic
16C2×#41×D13C2211yescharacteristic
17C22×Q8×D13C2211yescharacteristic
18#11719631—28no—
19C2×Q8×#261—28no—
20C2×Q8×#261C2211yescharacteristic
21C2×Q8×#261C2213yes—
22C2×Q8×#261C2211yescharacteristic
23C2×Q8×#261C2213yes—
24C2×Q8×#261C2211yescharacteristic
25C2×Q8×#261C2211yescharacteristic
26C2×D4×#261C2213yes—
27C2×D4×#261C2213yes—
28C2×D4×#261C2216yes—
29C2×#88237C2213yes—
30C22×C4⋊#261C2213yes—
31C22×C4⋊#261C2213yes—
32C22×C4×#261C2213yes—
33C13×#548C411yescharacteristic, complemented
34#11719536C411yescharacteristic, complemented
35#11719522C411yescharacteristic, complemented
36#11719382C413yescomplemented
37D13×#124C2213yes—
38#11719338C413yescomplemented
39D13×C22⋊Q8C2213yes—
40D13×#121C2213yes—
41#11719303C413yescomplemented
42#11719281C411yescharacteristic, complemented
43C4×Q8×D13C2211yescharacteristic
44#11719257C413yescomplemented
45C4×D4×D13C2213yes—
46(C2×#261)⋊Q8C2213yes—
47(C2×#261)⋊Q8C2213yes—
48#11719151C2213yes—
49#11719151C2213yes—
50#11719150C2213yes—
51#11719150C2213yes—
52#11719136C2213yes—
53#11719136C2213yes—
54C4×C22⋊#261C2213yes—
55C4×C22⋊#261C2213yes—
56#11719083C2213yes—
57#11719083C2216yes—
58#11719083C2213yes—
59#11719082C2213yes—
60#11719082C2213yes—
61C4⋊C4×#261C2213yes—
62C4⋊C4×#261C2213yes—
63#11719071C2213yes—
64#11719071C2213yes—
65#11719071C2216yes—
66#11719071C2216yes—
67#11719070C2211yescharacteristic
68#11719070C2213yes—
69#11719070C2216yes—
70#11719070C2216yes—
71C22⋊C4×#261C2216yes—
72#11719059C2213yes—
73C4×C4⋊#261C2213yes—
74C4×C4⋊#261C2213yes—
75#11719057C2213yes—
76C23×#261C2311yescharacteristic
77C23×#261C2313yes—
78C23×#261C2316yes—
79C2×C13×#41C2×C411yescharacteristic, complemented
80C22×Q8×C13C2×C411yescharacteristic, complemented
81#41×D13—24no—
82#41×D13—24no—
83C2×#6131C2×C411yescharacteristic, complemented
84C2×Q8×D13—24no—
85C2×Q8×D13—24no—
86C2×Q8×D13C2×C411yescharacteristic, complemented
87C2×Q8×D13C2×C413yescomplemented
88C2×Q8×D13C2313yes—
89C2×Q8×D13C2311yescharacteristic
90C2×#6129C2×C413yescomplemented
91C2×D4×D13C2313yes—
92C2×D4×D13C2313yes—
93C2×#6127C2×C413yescomplemented
94C22×C4×D13C2313yes—
95C22×C4×D13C2313yes—
96C22×Dic26C2×C413yescomplemented
97C2×C22⋊#261C2313yes—
98C2×C22⋊#261C2313yes—
99C2×C22⋊#261C2311yescharacteristic
100C2×C22⋊#261C2313yes—
101C2×C22⋊#261C2313yes—
102C2×C22⋊#261C2313yes—
103C2×C22⋊#261C2316yes—
104Q8×#261—24no—
105Q8×#261—24no—
106Q8×#261—24no—
107Q8×#261—212no—
108Q8×#261—212no—
109Q8×#261D418yescomplemented
110D4×#261—212no—
111D4×#261—212no—
112D4×#261—412no—
113#88237—212no—
114C2×C4⋊#261—212no—
115C2×C4⋊#261—212no—
116C2×C4⋊#261C2311yescharacteristic
117C2×C4⋊#261C2313yes—
118C2×C4⋊#261C2313yes—
119C2×C4⋊#261C2313yes—
120C2×C4⋊#261C2316yes—
121C2×C4⋊#261C2311yescharacteristic
122C2×C4⋊#261C2313yes—
123C2×C4⋊#261C2313yes—
124C2×C4⋊#261C2316yes—
125C2×C4⋊#261C2313yes—
126C2×C4×#261—212no—
127C2×C4×#261C2313yes—
128C2×C4×#261C2313yes—
129C2×C4×#261C2313yes—
130C2×C4×#261C2313yes—
131C2×C4×#261C2313yes—
132C2×C4×#261C2316yes—
133C2×C4×#261C2313yes—
134C13×#124C2×C413yescomplemented
135C13×C22⋊Q8C2×C413yescomplemented
136C13×#121C2×C413yescomplemented
137C4×Q8×C13C2×C411yescharacteristic, complemented
138C4×D4×C13C2×C413yescomplemented
139#88201C2×C413yescomplemented
140#88200C2×C413yescomplemented
141Q8×Dic13C2×C411yescharacteristic, complemented
142#88193C2×C416yescomplemented
143#88192C2×C413yescomplemented
144#88190C2×C413yescomplemented
145D4×Dic13C2×C413yescomplemented
146#88184C2×C413yescomplemented
147C4×C22⋊D13C2×C413yescomplemented
148C4×C22⋊D13C2×C413yescomplemented
149#88178C2×C413yescomplemented
150#88151C2×C413yescomplemented
151#88150C2×C416yescomplemented
152#88149C2×C413yescomplemented
153#88147C2×C413yescomplemented
154C4⋊C4×D13C2313yes—
155C4⋊C4×D13C2313yes—
156#88141C2×C413yescomplemented
157#88139C2×C416yescomplemented
158#88139C2×C416yescomplemented
159#88138C2×C416yescomplemented
160#88135C2×C413yescomplemented
161#88135C2×C413yescomplemented
162C22⋊C4×D13C2311yescharacteristic
163C22⋊C4×D13C2313yes—
164C22⋊C4×D13C2316yes—
165#88132C2×C416yescomplemented
166#88129C2×C413yescomplemented
167C4×D52C2×C413yescomplemented
168C42×D13C2313yes—
169C4×Dic26C2×C413yescomplemented
170(C2×#261)⋊C4C2311yescharacteristic
171(C2×#261)⋊C4C2313yes—
172(C2×#261)⋊C4C2313yes—
173(C2×#261)⋊C4C2313yes—
174(C2×#261)⋊C4C2313yes—
175(C2×#261)⋊C4C2313yes—
176(C2×#261)⋊C4C2316yes—
177(C2×#261)⋊C4C2313yes—
178(C2×#261)⋊C4C2311yescharacteristic
179(C2×#261)⋊C4C2313yes—
180(C2×#261)⋊C4C2313yes—
181#34294—131nomaximal, Sylow
182C23×D13C2413yes—
183C23×D13C2411yescharacteristic
184C22×#261—22no—
185C22×#261—22no—
186C22×#261—22no—
187C22×#261—26no—
188C22×#261—26no—
189C22×#261—212no—
190C22×#261—43no—
191C22×#261—46no—
192C22×#261—46no—
193C22×#261C2411yescharacteristic
194C22×#261C2411yescharacteristic
195C22×#261C2413yes—
196C22×#261C2413yes—
197C22×#261C2413yes—
198C22×#261C2411yescharacteristic
199C22×#261C2413yes—
200C22×#261C2411yescharacteristic
201C13×#41—24no—
202C2×Q8×C13—24no—
203C2×Q8×C13C22×C413yes—
204C2×Q8×C13C22×C411yescharacteristic
205C2×D4×C13C22×C413yes—
206C2×D4×C13C22×C413yes—
207C22×C4×C13C22×C413yes—
208C22×C4×C13C22×C413yes—
209C2×C22⋊D13C22×C413yes—
210C2×C22⋊D13C22×C413yes—
211C2×C22⋊D13C22×C416yes—
212C22×Dic13C22×C413yes—
213C22×Dic13C22×C413yes—
214#6131—24no—
215Q8×D13—24no—
216Q8×D13—26no—
217Q8×D13—26no—
218Q8×D13—212no—
219Q8×D13C2×D414yes—
220Q8×D13#4114yes—
221#6129—212no—
222D4×D13—26no—
223D4×D13—26no—
224D4×D13—26no—
225D4×D13—26no—
226#6127—212no—
227C2×D52C22×C413yes—
228C2×D52C22×C413yes—
229C2×C4×D13—26no—
230C2×C4×D13—26no—
231C2×C4×D13—26no—
232C2×C4×D13—26no—
233C2×C4×D13C22×C413yes—
234C2×C4×D13C22×C413yes—
235C2×C4×D13C22×C413yes—
236C2×C4×D13C22×C413yes—
237C2×C4×D13C2411yescharacteristic
238C2×C4×D13C2413yes—
239C2×C4×D13C2413yes—
240C2×C4×D13C2411yescharacteristic
241C2×C4×D13C2413yes—
242C2×Dic26—212no—
243C2×Dic26C22×C413yes—
244C2×Dic26C22×C416yes—
245C2×Dic26C22×C413yes—
246C22⋊#261—26no—
247C22⋊#261—22no—
248C22⋊#261—26no—
249C22⋊#261—26no—
250C22⋊#261—26no—
251C22⋊#261—46no—
252C22⋊#261—43no—
253C4⋊#261—26no—
254C4⋊#261—212no—
255C4⋊#261—22no—
256C4⋊#261—22no—
257C4⋊#261—26no—
258C4⋊#261—26no—
259C4⋊#261—26no—
260C4⋊#261—43no—
261C4⋊#261—46no—
262C4⋊#261C2×D4112yes—
263C4×#261—26no—
264C4×#261—26no—
265C4×#261—26no—
266C4×#261—26no—
267C4×#261—26no—
268C4×#261—46no—
269C4×#261C2×D4112yes—
270C13×C4⋊C4C22×C413yes—
271C13×C4⋊C4C22×C413yes—
272C13×C22⋊C4C22×C416yes—
273C13×C22⋊C4C22×C411yescharacteristic
274C13×C22⋊C4C22×C413yes—
275C42×C13C22×C413yes—
276C22⋊Dic13C22×C416yes—
277C22⋊Dic13C22×C413yes—
278C22⋊Dic13C22×C411yescharacteristic
279#6103C22×C411yescharacteristic
280#6103C22×C413yes—
281#6103C22×C416yes—
282#6103C22×C416yes—
283#6103C22×C413yes—
284#6103C22×C411yescharacteristic
285C4⋊Dic13C22×C413yes—
286C4⋊Dic13C22×C413yes—
287#6101C22×C416yes—
288#6101C22×C413yes—
289#6101C22×C413yes—
290C4×Dic13C22×C413yes—
291C4×Dic13C22×C413yes—
292C4×Dic13C22×C413yes—
293C2×#548—131no—
294C2×#520—131no—
295C22×C4×Q8—131no—
296#2367—133no—
297#2361—133no—
298#2360—133no—
299Q8×C4⋊C4—131no—
300D4×C4⋊C4—133no—
301#2341—131no—
302Q8×C22⋊C4—131no—
303#2326—133no—
304#2323—133no—
305C4×#121—133no—
306#2290—133no—
307#2276—131no—
308C23×C13C23×C413yes—
309C23×C13C23×C411yescharacteristic
310C22×D13—21no—
311C22×D13—21no—
312C22×D13—21no—
313C22×D13—21no—
314C22×D13—23no—
315C22×D13—23no—
316C22×D13—23no—
317C22×D13—23no—
318C22×D13—23no—
319C22×D13—23no—
320C22×D13C23×C413yes—
321C22×D13C23×C411yescharacteristic
322C22×D13H(5,𝔽2)12yes—
323C22×D132−1+412yes—
324C22×D13C2511yescharacteristic
325C2×#261—28no—
326C2×#261—21no—
327C2×#261—23no—
328C2×#261—21no—
329C2×#261—21no—
330C2×#261—21no—
331C2×#261—23no—
332C2×#261—21no—
333C2×#261—23no—
334C2×#261—23no—
335C2×#261—21no—
336C2×#261—23no—
337C2×#261—23no—
338C2×#261—23no—
339C2×#261—23no—
340C2×#261—21no—
341C2×#261—21no—
342C2×#261—21no—
343C2×#261—23no—
344C2×#261—23no—
345C2×#261—23no—
346C2×#261—21no—
347C2×#261—412no—
348C2×#261—812no—
349C2×#261C22×D412yes—
350C2×#261C22×D416yes—
351C2×#2612−1+412yes—
352Q8×C13—26no—
353Q8×C13C4×D414yescomplemented
354D4×C13—26no—
355D4×C13—26no—
356C2×C4×C13—26no—
357C2×C4×C13—26no—
358C2×C4×C13C23×C411yescharacteristic
359C2×C4×C13C23×C413yes—
360C2×C4×C13C23×C411yescharacteristic
361C2×C4×C13C23×C413yes—
362C2×C4×C13C23×C413yes—
363C22⋊D13—26no—
364C22⋊D13—26no—
365C22⋊D13—212no—
366C2×Dic13—26no—
367C2×Dic13—26no—
368C2×Dic13C23×C411yescharacteristic
369C2×Dic13C23×C413yes—
370C2×Dic13C23×C411yescharacteristic
371C2×Dic13C23×C413yes—
372C2×Dic13C23×C413yes—
373D52—26no—
374D52—26no—
375C4×D13—23no—
376C4×D13—21no—
377C4×D13—21no—
378C4×D13—23no—
379C4×D13—23no—
380C4×D13—21no—
381C4×D13—23no—
382C4×D13—21no—
383C4×D13—26no—
384C4×D13—26no—
385C4×D13—26no—
386C4×D13—26no—
387C4×D13C22×D416yes—
388C4×D13C2×#4116yes—
389Dic26—26no—
390Dic26—212no—
391Dic26C4×D4112yescomplemented
392C22×#41—131no—
393C23×Q8—131no—
394#548—131no—
395#548—131no—
396#548—133no—
397#548—133no—
398#548—133no—
399#548—131no—
400#548—133no—
401#548#26111yescharacteristic, complemented
402C2×#124—133no—
403C2×C22⋊Q8—133no—
404C2×#121—133no—
405#520—268no—
406C2×C4×Q8—131no—
407C2×C4×Q8—131no—
408C2×C4×Q8—133no—
409C2×C4×Q8—131no—
410C2×C4×Q8—131no—
411C2×C4×Q8—131no—
412C2×C4×Q8—133no—
413C2×C4×Q8—268no—
414C2×C4×D4—133no—
415C2×C4×D4—133no—
416C2×C4×D4—133no—
417C2×C4×D4—136no—
418C2×#117—133no—
419C22×C4⋊C4—133no—
420C22×C4⋊C4—133no—
421C22×C42—133no—
422#391—133no—
423#391—133no—
424#390—133no—
425#390—133no—
426#389—136no—
427#389—133no—
428#389—133no—
429#388—136no—
430#388—136no—
431#388—133no—
432#388—133no—
433#387—133no—
434#387—133no—
435#386—133no—
436#386—133no—
437#385—136no—
438#385—136no—
439#385—133no—
440#385—131no—
441#384—133no—
442#380—133no—
443#380—133no—
444C4×C4⋊C4—133no—
445C4×C4⋊C4—133no—
446C4×C4⋊C4—133no—
447C4×C4⋊C4—133no—
448C4×C22⋊C4—133no—
449C4×C22⋊C4—133no—
450C4×C22⋊C4—136no—
451#376—133no—
452C22×C13—21no—
453C22×C13—21no—
454C22×C13—23no—
455C22×C13—23no—
456C22×C13—23no—
457C22×C13#52012yescomplemented
458C22×C13C24×C411yescharacteristic
459C2×D13—21no—
460C2×D13—21no—
461C2×D13—22no—
462C2×D13—22no—
463C2×D13—22no—
464C2×D13—22no—
465C2×D13—23no—
466C2×D13—23no—
467C2×D13—23no—
468C2×D13—43no—
469C2×D13—43no—
470C2×D13—43no—
471C2×D13—43no—
472C2×D13#52012yescomplemented
473C2×D13C23×D411yescharacteristic
474C2×D13C22×#4111yescharacteristic
475C2×D13C2×H(5,𝔽2)11yescharacteristic
476C2×D13C2×2−1+411yescharacteristic
477C2×D13C2×2−1+411yescharacteristic
478C2×D13#58511yescharacteristic
479#261—22no—
480#261—22no—
481#261—26no—
482#261—41no—
483#261—43no—
484#261—43no—
485#261—41no—
486#261—43no—
487C4×C13—23no—
488C4×C13—21no—
489C4×C13—23no—
490C4×C13—21no—
491C4×C13C2×C4×D416yes—
492Dic13—23no—
493Dic13—21no—
494Dic13—23no—
495Dic13—21no—
496Dic13C2×C4×D416yes—
497C2×#41—131no—
498C2×#41—133no—
499C2×#41—133no—
500C2×#41—264no—
501C2×#41—264no—
502C2×#41C2×#26111yescharacteristic, complemented
503C22×Q8—131no—
504C22×Q8—133no—
505C22×Q8—133no—
506C22×Q8—131no—
507C22×Q8—133no—
508C22×Q8—264no—
509C22×Q8—264no—
510C22×Q8C2×#26111yescharacteristic, complemented
511C22×D4—133no—
512C22×D4—133no—
513C23×C4—133no—
514C23×C4—133no—
515C23×C4—131no—
516C23×C4—133no—
517C23×C4—136no—
518#124—133no—
519#124—133no—
520#124—136no—
521#124—136no—
522#124—133no—
523#124C2×#26113yescomplemented
524C22⋊Q8—133no—
525C22⋊Q8—133no—
526C22⋊Q8—136no—
527C22⋊Q8—133no—
528C22⋊Q8—136no—
529C22⋊Q8C2×#26113yescomplemented
530#121—133no—
531#121—136no—
532#121—133no—
533#121—133no—
534#121—136no—
535#121C2×#26113yescomplemented
536C4×Q8—138no—
537C4×Q8—131no—
538C4×Q8—133no—
539C4×Q8—133no—
540C4×Q8—2612no—
541C4×Q8—2612no—
542C4×Q8—264no—
543C4×Q8—264no—
544C4×Q8—264no—
545C4×Q8C2×#26111yescharacteristic, complemented
546C4×D4—133no—
547C4×D4—133no—
548C4×D4—133no—
549C4×D4—133no—
550C4×D4—133no—
551C4×D4—133no—
552C4×D4—133no—
553C4×D4—2612no—
554C4×D4—2612no—
555C4×D4—5212no—
556C4×D4C2×#26113yescomplemented
557#117—2612no—
558C2×C4⋊C4—133no—
559C2×C4⋊C4—133no—
560C2×C4⋊C4—133no—
561C2×C4⋊C4—133no—
562C2×C4⋊C4—133no—
563C2×C4⋊C4—133no—
564C2×C4⋊C4—136no—
565C2×C4⋊C4—131no—
566C2×C4⋊C4—133no—
567C2×C4⋊C4—131no—
568C2×C4⋊C4—136no—
569C2×C4⋊C4—133no—
570C2×C4⋊C4—2612no—
571C2×C4⋊C4—2612no—
572C2×C22⋊C4—131no—
573C2×C22⋊C4—133no—
574C2×C22⋊C4—136no—
575C2×C22⋊C4—133no—
576C2×C22⋊C4—133no—
577C2×C22⋊C4—133no—
578C2×C22⋊C4—131no—
579C2×C22⋊C4—133no—
580C2×C22⋊C4—136no—
581C2×C22⋊C4—133no—
582C2×C42—133no—
583C2×C42—133no—
584C2×C42—133no—
585C2×C42—133no—
586C2×C42—133no—
587C2×C42—133no—
588C2×C42—133no—
589C2×C42—136no—
590C2×C42—2612no—
591#95—131no—
592#95—133no—
593#95—133no—
594#95—133no—
595#95—131no—
596#95—133no—
597#95—133no—
598#95—136no—
599#95—133no—
600#95—133no—
601#95—133no—
602C2×C13—22no—
603C2×C13—43no—
604C2×C13C22×C4×D411yescharacteristic
605C2×C13C2×#52011yescharacteristic
606C2×C13C4×2−1+411yescharacteristic
607D13—22no—
608D13—43no—
609D13#348611yescharacteristic
610D13#348811yescharacteristic
611D13#351611yescharacteristic
612D13#352211yescharacteristic
613C24—131no—
614C24—133no—
615#41—24no—
616#41—2612no—
617#41—2612no—
618#41—264no—
619C2×Q8—24no—
620C2×Q8—134no—
621C2×Q8—134no—
622C2×Q8—133no—
623C2×Q8—136no—
624C2×Q8—133no—
625C2×Q8—2612no—
626C2×Q8—266no—
627C2×Q8—266no—
628C2×Q8—2612no—
629C2×Q8—264no—
630C2×Q8C22×#26113yes—
631C2×Q8C22×#26111yescharacteristic
632C2×D4—133no—
633C2×D4—133no—
634C2×D4—136no—
635C2×D4—133no—
636C2×D4—133no—
637C2×D4—266no—
638C2×D4—266no—
639C2×D4—266no—
640C2×D4—266no—
641C2×D4C22×#26113yes—
642C2×D4C22×#26113yes—
643C22×C4—133no—
644C22×C4—131no—
645C22×C4—131no—
646C22×C4—133no—
647C22×C4—133no—
648C22×C4—133no—
649C22×C4—131no—
650C22×C4—133no—
651C22×C4—133no—
652C22×C4—131no—
653C22×C4—133no—
654C22×C4—133no—
655C22×C4—133no—
656C22×C4—133no—
657C22×C4—131no—
658C22×C4—131no—
659C22×C4—133no—
660C22×C4—133no—
661C22×C4—133no—
662C22×C4—266no—
663C22×C4—266no—
664C22×C4—266no—
665C22×C4—266no—
666C22×C4—262no—
667C22×C4—262no—
668C22×C4—266no—
669C22×C4—2612no—
670C22×C4—262no—
671C22×C4—266no—
672C22×C4—523no—
673C22×C4—526no—
674C22×C4—526no—
675C22×C4C22×#26113yes—
676C22×C4C22×#26113yes—
677C4⋊C4—1312no—
678C4⋊C4—133no—
679C4⋊C4—133no—
680C4⋊C4—133no—
681C4⋊C4—136no—
682C4⋊C4—133no—
683C4⋊C4—266no—
684C4⋊C4—266no—
685C4⋊C4—266no—
686C4⋊C4—2612no—
687C4⋊C4—262no—
688C4⋊C4—266no—
689C4⋊C4—262no—
690C4⋊C4—526no—
691C4⋊C4—523no—
692C4⋊C4C22×#26113yes—
693C4⋊C4C22×#26113yes—
694C22⋊C4—131no—
695C22⋊C4—133no—
696C22⋊C4—136no—
697C22⋊C4—131no—
698C22⋊C4—131no—
699C22⋊C4—133no—
700C22⋊C4—133no—
701C22⋊C4—136no—
702C22⋊C4—136no—
703C22⋊C4—266no—
704C22⋊C4—266no—
705C22⋊C4—266no—
706C22⋊C4—266no—
707C22⋊C4—262no—
708C22⋊C4—526no—
709C22⋊C4—523no—
710C22⋊C4C22×#26111yescharacteristic
711C22⋊C4C22×#26113yes—
712C22⋊C4C22×#26116yes—
713C42—1312no—
714C42—133no—
715C42—133no—
716C42—133no—
717C42—266no—
718C42—266no—
719C42—266no—
720C42—266no—
721C42—266no—
722C42—526no—
723C42C22×#26113yes—
724C13#3429411yescharacteristic, complemented, Sylow
725C23—131no—
726C23—132no—
727C23—132no—
728C23—131no—
729C23—133no—
730C23—261no—
731C23—261no—
732C23—261no—
733C23—261no—
734C23—263no—
735C23—263no—
736C23—263no—
737C23—263no—
738C23—263no—
739C23—263no—
740C23C23×#26113yes—
741C23C23×#26111yescharacteristic
742Q8—26no—
743Q8—1312no—
744Q8—2612no—
745Q8—266no—
746Q8D4×#26114yescomplemented
747D4—26no—
748D4—26no—
749D4—266no—
750D4—2612no—
751D4—266no—
752D4—266no—
753D4—266no—
754C2×C4—26no—
755C2×C4—26no—
756C2×C4—133no—
757C2×C4—136no—
758C2×C4—136no—
759C2×C4—132no—
760C2×C4—136no—
761C2×C4—132no—
762C2×C4—131no—
763C2×C4—133no—
764C2×C4—133no—
765C2×C4—131no—
766C2×C4—266no—
767C2×C4—266no—
768C2×C4—263no—
769C2×C4—263no—
770C2×C4—261no—
771C2×C4—261no—
772C2×C4—261no—
773C2×C4—261no—
774C2×C4—263no—
775C2×C4—263no—
776C2×C4—266no—
777C2×C4—266no—
778C2×C4—261no—
779C2×C4—263no—
780C2×C4—261no—
781C2×C4—261no—
782C2×C4—261no—
783C2×C4—263no—
784C2×C4—268no—
785C2×C4—266no—
786C2×C4—266no—
787C2×C4—261no—
788C2×C4—261no—
789C2×C4—263no—
790C2×C4—263no—
791C2×C4—263no—
792C2×C4—263no—
793C2×C4—263no—
794C2×C4—261no—
795C2×C4—261no—
796C2×C4—263no—
797C2×C4—261no—
798C2×C4—263no—
799C2×C4—263no—
800C2×C4—261no—
801C2×C4—263no—
802C2×C4—5212no—
803C2×C4—10412no—
804C2×C4C23×#26111yescharacteristic
805C2×C4C23×#26113yes—
806C2×C4C23×#26113yes—
807C2×C4C23×#26111yescharacteristic
808C2×C4C23×#26113yes—
809C22—21no—
810C22—21no—
811C22—23no—
812C22—23no—
813C22—23no—
814C22—131no—
815C22—131no—
816C22—131no—
817C22—131no—
818C22—131no—
819C22—131no—
820C22—132no—
821C22—262no—
822C22—262no—
823C22—262no—
824C22—262no—
825C22—261no—
826C22—261no—
827C22—263no—
828C22—263no—
829C22—263no—
830C22—523no—
831C22—523no—
832C22—523no—
833C22—523no—
834C22#1171963112yescomplemented
835C22C24×#26111yescharacteristic
836C4—21no—
837C4—23no—
838C4—23no—
839C4—21no—
840C4—136no—
841C4—262no—
842C4—262no—
843C4—266no—
844C4—261no—
845C4—263no—
846C4—263no—
847C4—261no—
848C4—521no—
849C4—523no—
850C4—521no—
851C4—523no—
852C4—523no—
853C4C2×D4×#26116yes—
854C2—22no—
855C2—43no—
856C2—131no—
857C2—131no—
858C2—131no—
859C2—131no—
860C2—262no—
861C2—523no—
862C2C22×D4×#26111yescharacteristic
863C2C2×#1171963111yescharacteristic
864C22−1+4×#26111yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#548C4
prime radicalD13×#548C2
cosocleC22×D13C25
hypercenter#548#261
hypocenterC13#34294
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#11719631C2semidirect
2. C22×Q8×#261C2semidirect
3. #13131367C2semidirect
4. #13131361C2semidirect
5. #13131360C2semidirect
6. Q8×C4⋊#261C2semidirect
7. D4×C4⋊#261C2semidirect
8. #13131341C2semidirect
9. Q8×C22⋊#261C2semidirect
10. #13131326C2semidirect
11. #13131323C2semidirect
12. #121×#261C2semidirect
13. #13131290C2semidirect
14. #13131276C2semidirect
33. C13×#548C4semidirect
34. #11719536C4semidirect
35. #11719522C4semidirect
36. #11719382C4semidirect
38. #11719338C4semidirect
41. #11719303C4semidirect
42. #11719281C4semidirect
44. #11719257C4semidirect
79. C2×C13×#41C2×C4semidirect
80. C22×Q8×C13C2×C4semidirect
83. C2×#6131C2×C4semidirect
86. C2×Q8×D13C2×C4semidirect
87. C2×Q8×D13C2×C4semidirect
90. C2×#6129C2×C4semidirect
93. C2×#6127C2×C4semidirect
96. C22×Dic26C2×C4semidirect
109. Q8×#261D4semidirect
134. C13×#124C2×C4semidirect
135. C13×C22⋊Q8C2×C4semidirect
136. C13×#121C2×C4semidirect
137. C4×Q8×C13C2×C4semidirect
138. C4×D4×C13C2×C4semidirect
139. #88201C2×C4semidirect
140. #88200C2×C4semidirect
141. Q8×Dic13C2×C4semidirect
142. #88193C2×C4semidirect
143. #88192C2×C4semidirect
144. #88190C2×C4semidirect
145. D4×Dic13C2×C4semidirect
146. #88184C2×C4semidirect
147. C4×C22⋊D13C2×C4semidirect
148. C4×C22⋊D13C2×C4semidirect
149. #88178C2×C4semidirect
150. #88151C2×C4semidirect
151. #88150C2×C4semidirect
152. #88149C2×C4semidirect
153. #88147C2×C4semidirect
156. #88141C2×C4semidirect
157. #88139C2×C4semidirect
158. #88139C2×C4semidirect
159. #88138C2×C4semidirect
160. #88135C2×C4semidirect
161. #88135C2×C4semidirect
165. #88132C2×C4semidirect
166. #88129C2×C4semidirect
167. C4×D52C2×C4semidirect
169. C4×Dic26C2×C4semidirect
353. Q8×C13C4×D4semidirect
391. Dic26C4×D4semidirect
401. #548#261semidirect
457. C22×C13#520semidirect
472. C2×D13#520semidirect
502. C2×#41C2×#261semidirect
510. C22×Q8C2×#261semidirect
523. #124C2×#261semidirect
529. C22⋊Q8C2×#261semidirect
535. #121C2×#261semidirect
545. C4×Q8C2×#261semidirect
556. C4×D4C2×#261semidirect
724. C13#34294semidirect
746. Q8D4×#261semidirect
834. C22#11719631semidirect

Maximal subgroups

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

subgroupindex
C2×#117196312
C22×Q8×#2612
#131313672
#131313612
#131313602
Q8×C4⋊#2612
D4×C4⋊#2612
#131313412
Q8×C22⋊#2612
#131313262
#131313232
#121×#2612
#131312902
#131312762
D13×#5482
#3429413