Finite Group Databasebeta

← #16807757

Subgroups — #16807757

Order 3328.

3200 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719631C211yesmaximal, characteristic, complemented
2C2×#41×#261C211yesmaximal, characteristic, complemented
3#13131366C213yesmaximal, complemented
4#13131363C213yesmaximal, complemented
5#13131361C213yesmaximal, complemented
6#13131352C213yesmaximal, complemented
7#13131351C211yesmaximal, characteristic, complemented
8#13131341C211yesmaximal, characteristic, complemented
9#13131341C211yesmaximal, characteristic, complemented
10#13131328C213yesmaximal, complemented
11#13131324C213yesmaximal, complemented
12#121×#261C213yesmaximal, complemented
13#13131290C213yesmaximal, complemented
14#13131276C211yesmaximal, characteristic, complemented
15D13×#550C211yesmaximal, characteristic
16C2×#41×D13C2211yescharacteristic
17C2×#41×D13C2211yescharacteristic
18#11719631—28no—
19#41×#261—28no—
20C2×Q8×#261C2211yescharacteristic
21C2×Q8×#261C2211yescharacteristic
22C2×Q8×#261C2211yescharacteristic
23C2×Q8×#261C2211yescharacteristic
24C2×D4×#261C2213yes—
25C2×D4×#261C2213yes—
26C2×D4×#261C2213yes—
27C2×D4×#261C2213yes—
28C2×D4×#261C2216yes—
29C2×#88237C2213yes—
30C2×#88237C2213yes—
31C22×C4⋊#261C2213yes—
32C22×C4×#261C2213yes—
33C13×#550C411yescharacteristic, complemented
34#11719539C411yescharacteristic, complemented
35#11719539C411yescharacteristic, complemented
36#11719423C413yescomplemented
37D13×#127C2213yes—
38D13×#121C2213yes—
39D13×#121C2213yes—
40#11719304C413yescomplemented
41#11719304C413yescomplemented
42#11719282C411yescharacteristic, complemented
43C4×Q8×D13C2211yescharacteristic
44#11719258C413yescomplemented
45C4×D4×D13C2213yes—
46#11719151C2213yes—
47#11719151C2213yes—
48#11719151C2216yes—
49#11719151C2213yes—
50#11719151C2213yes—
51#11719150C2213yes—
52#11719150C2213yes—
53#11719150C2216yes—
54#11719150C2216yes—
55#11719150C2216yes—
56#11719136C2213yes—
57#11719136C2213yes—
58C4×C22⋊#261C2213yes—
59C4×C22⋊#261C2213yes—
60#11719083C2213yes—
61#11719083C2213yes—
62#11719082C2211yescharacteristic
63#11719082C2213yes—
64C4⋊C4×#261C2213yes—
65C4⋊C4×#261C2213yes—
66#11719071C2213yes—
67#11719071C2213yes—
68#11719071C2216yes—
69#11719070C2213yes—
70#11719070C2213yes—
71C22⋊C4×#261C2216yes—
72#11719060C2213yes—
73C4×C4⋊#261C2213yes—
74C4×C4⋊#261C2213yes—
75#11719057C2213yes—
76C23×#261C2313yes—
77C23×#261C2316yes—
78C23×#261C2313yes—
79C2×C13×#41C2×C411yescharacteristic, complemented
80C2×C13×#41C2×C411yescharacteristic, complemented
81#41×D13—24no—
82#41×D13—24no—
83#41×D13—24no—
84#41×D13—24no—
85C2×#6131C2×C411yescharacteristic, complemented
86C2×#6131C2×C411yescharacteristic, complemented
87C2×Q8×D13C2311yescharacteristic
88C2×#6129C2×C413yescomplemented
89C2×#6129C2×C413yescomplemented
90C2×D4×D13C2313yes—
91C2×D4×D13C2313yes—
92C2×D4×D13C2313yes—
93C2×D4×D13C2316yes—
94C2×#6127C2×C413yescomplemented
95C2×#6127C2×C413yescomplemented
96C22×C4×D13C2313yes—
97C22×C4×D13C2313yes—
98C2×C22⋊#261C2313yes—
99C2×C22⋊#261C2316yes—
100C2×C22⋊#261C2313yes—
101C2×C22⋊#261C2313yes—
102C2×C22⋊#261C2316yes—
103C2×C22⋊#261C2313yes—
104C2×C22⋊#261C2313yes—
105C2×C22⋊#261C2316yes—
106C2×C22⋊#261C2313yes—
107Q8×#261—24no—
108Q8×#261—24no—
109Q8×#261—24no—
110Q8×#261D418yescomplemented
111D4×#261—212no—
112D4×#261—212no—
113D4×#261—212no—
114D4×#261—212no—
115D4×#261—412no—
116#88237—212no—
117#88237—212no—
118C2×C4⋊#261—212no—
119C2×C4⋊#261C2313yes—
120C2×C4⋊#261C2313yes—
121C2×C4⋊#261C2313yes—
122C2×C4⋊#261C2313yes—
123C2×C4⋊#261C2311yescharacteristic
124C2×C4⋊#261C2313yes—
125C2×C4⋊#261C2313yes—
126C2×C4⋊#261C2313yes—
127C2×C4×#261—212no—
128C2×C4×#261C2313yes—
129C2×C4×#261C2313yes—
130C2×C4×#261C2313yes—
131C2×C4×#261C2313yes—
132C2×C4×#261C2311yescharacteristic
133C2×C4×#261C2316yes—
134C2×C4×#261C2313yes—
135C13×#127C2×C413yescomplemented
136C13×#121C2×C413yescomplemented
137C13×#121C2×C413yescomplemented
138C4×Q8×C13C2×C411yescharacteristic, complemented
139C4×D4×C13C2×C413yescomplemented
140Q8×Dic13C2×C411yescharacteristic, complemented
141#88194C2×C416yescomplemented
142#88194C2×C413yescomplemented
143#88194C2×C413yescomplemented
144#88194C2×C416yescomplemented
145#88193C2×C416yescomplemented
146#88193C2×C416yescomplemented
147#88192C2×C413yescomplemented
148#88192C2×C413yescomplemented
149D4×Dic13C2×C413yescomplemented
150#88184C2×C413yescomplemented
151#88184C2×C413yescomplemented
152C4×C22⋊D13C2×C413yescomplemented
153C4×C22⋊D13C2×C413yescomplemented
154#88149C2×C413yescomplemented
155#88149C2×C413yescomplemented
156#88147C2×C413yescomplemented
157C4⋊C4×D13C2311yescharacteristic
158C4⋊C4×D13C2313yes—
159#88141C2×C413yescomplemented
160#88138C2×C416yescomplemented
161#88138C2×C416yescomplemented
162#88135C2×C413yescomplemented
163#88135C2×C413yescomplemented
164C22⋊C4×D13C2313yes—
165C22⋊C4×D13C2313yes—
166#88128C2×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)⋊C4C2311yescharacteristic
175(C2×#261)⋊C4C2313yes—
176(C2×#261)⋊C4C2316yes—
177(C2×#261)⋊C4C2313yes—
178(C2×#261)⋊C4C2311yescharacteristic
179(C2×#261)⋊C4C2313yes—
180(C2×#261)⋊C4C2311yescharacteristic
181#34295—131nomaximal, Sylow
182C23×D13C2413yes—
183C23×D13C2413yes—
184C22×#261—26no—
185C22×#261—26no—
186C22×#261—26no—
187C22×#261—212no—
188C22×#261—43no—
189C22×#261—43no—
190C22×#261—43no—
191C22×#261—46no—
192C22×#261—46no—
193C22×#261C2411yescharacteristic
194C22×#261C2413yes—
195C22×#261C2413yes—
196C22×#261C2413yes—
197C22×#261C2411yescharacteristic
198C22×#261C2411yescharacteristic
199C22×#261C2413yes—
200C22×#261C2411yescharacteristic
201C13×#41—24no—
202C13×#41—24no—
203C2×Q8×C13C22×C411yescharacteristic
204C2×D4×C13C22×C413yes—
205C2×D4×C13C22×C413yes—
206C2×D4×C13C22×C413yes—
207C2×D4×C13C22×C416yes—
208C22×C4×C13C22×C413yes—
209C22×C4×C13C22×C413yes—
210C2×C22⋊D13C22×C416yes—
211C2×C22⋊D13C22×C416yes—
212C2×C22⋊D13C22×C413yes—
213C2×C22⋊D13C22×C413yes—
214C2×C22⋊D13C22×C416yes—
215C2×C22⋊D13C22×C416yes—
216C22×Dic13C22×C413yes—
217C22×Dic13C22×C413yes—
218#6131—24no—
219#6131—24no—
220Q8×D13C2×D414yes—
221Q8×D13#4114yes—
222#6129—212no—
223#6129—212no—
224D4×D13—26no—
225D4×D13—26no—
226D4×D13—26no—
227D4×D13—26no—
228D4×D13—46no—
229D4×D13—46no—
230D4×D13—43no—
231D4×D13—43no—
232#6127—212no—
233#6127—212no—
234C2×D52C22×C413yes—
235C2×D52C22×C413yes—
236C2×D52C22×C413yes—
237C2×D52C22×C416yes—
238C2×C4×D13—26no—
239C2×C4×D13—26no—
240C2×C4×D13—26no—
241C2×C4×D13—26no—
242C2×C4×D13C22×C413yes—
243C2×C4×D13C22×C413yes—
244C2×C4×D13C22×C413yes—
245C2×C4×D13C22×C413yes—
246C2×C4×D13C2411yescharacteristic
247C2×C4×D13C2413yes—
248C2×C4×D13C2411yescharacteristic
249C2×C4×D13C2411yescharacteristic
250C2×C4×D13C2413yes—
251C2×Dic26C22×C413yes—
252C22⋊#261—26no—
253C22⋊#261—212no—
254C22⋊#261—26no—
255C22⋊#261—26no—
256C22⋊#261—46no—
257C22⋊#261—43no—
258C22⋊#261—43no—
259C22⋊#261—46no—
260C22⋊#261—43no—
261C4⋊#261—26no—
262C4⋊#261—22no—
263C4⋊#261—26no—
264C4⋊#261—26no—
265C4⋊#261—26no—
266C4⋊#261—26no—
267C4⋊#261—43no—
268C4⋊#261C2×D4112yes—
269C4×#261—22no—
270C4×#261—26no—
271C4×#261—26no—
272C4×#261—26no—
273C4×#261—26no—
274C4×#261—46no—
275C4×#261C2×D4112yes—
276C13×C4⋊C4C22×C413yes—
277C13×C4⋊C4C22×C411yescharacteristic
278C13×C22⋊C4C22×C413yes—
279C13×C22⋊C4C22×C413yes—
280C42×C13C22×C413yes—
281C22⋊Dic13C22×C413yes—
282C22⋊Dic13C22×C413yes—
283#6103C22×C413yes—
284#6103C22×C413yes—
285#6103C22×C413yes—
286#6103C22×C413yes—
287C4⋊Dic13C22×C413yes—
288C4⋊Dic13C22×C411yescharacteristic
289#6101C22×C416yes—
290#6101C22×C411yescharacteristic
291#6101C22×C411yescharacteristic
292C4×Dic13C22×C413yes—
293C4×Dic13C22×C413yes—
294C4×Dic13C22×C413yes—
295C2×#550—131no—
296C2×#520—131no—
297C2×C4×#41—131no—
298#2366—133no—
299#2363—133no—
300#2361—133no—
301#2352—133no—
302#2351—131no—
303#2341—131no—
304#2341—131no—
305#2328—133no—
306#2324—133no—
307C4×#121—133no—
308#2290—133no—
309#2276—131no—
310C23×C13C23×C413yes—
311C23×C13C23×C413yes—
312C22×D13—23no—
313C22×D13—23no—
314C22×D13—23no—
315C22×D13—23no—
316C22×D13—23no—
317C22×D13—23no—
318C22×D13—23no—
319C22×D13—23no—
320C22×D13—23no—
321C22×D13—23no—
322C22×D13—23no—
323C22×D13—23no—
324C22×D13C23×C413yes—
325C22×D13C23×C413yes—
326C22×D13C2511yescharacteristic
327C2×#261—21no—
328C2×#261—23no—
329C2×#261—21no—
330C2×#261—21no—
331C2×#261—21no—
332C2×#261—23no—
333C2×#261—21no—
334C2×#261—23no—
335C2×#261—23no—
336C2×#261—21no—
337C2×#261—23no—
338C2×#261—23no—
339C2×#261—23no—
340C2×#261—21no—
341C2×#261—23no—
342C2×#261—21no—
343C2×#261—23no—
344C2×#261—21no—
345C2×#261—21no—
346C2×#261—23no—
347C2×#261—23no—
348C2×#261—412no—
349C2×#261—412no—
350C2×#261—812no—
351C2×#261C22×D412yes—
352C2×#261C22×D416yes—
353C2×#261H(5,𝔽2)12yes—
354Q8×C13C4×D414yescomplemented
355D4×C13—26no—
356D4×C13—26no—
357D4×C13—43no—
358D4×C13—46no—
359C2×C4×C13—26no—
360C2×C4×C13—26no—
361C2×C4×C13C23×C411yescharacteristic
362C2×C4×C13C23×C413yes—
363C2×C4×C13C23×C411yescharacteristic
364C2×C4×C13C23×C411yescharacteristic
365C2×C4×C13C23×C413yes—
366C22⋊D13—212no—
367C22⋊D13—212no—
368C22⋊D13—43no—
369C22⋊D13—43no—
370C22⋊D13—46no—
371C22⋊D13—46no—
372C2×Dic13—26no—
373C2×Dic13—26no—
374C2×Dic13C23×C411yescharacteristic
375C2×Dic13C23×C413yes—
376C2×Dic13C23×C411yescharacteristic
377C2×Dic13C23×C411yescharacteristic
378C2×Dic13C23×C413yes—
379D52—26no—
380D52—26no—
381D52—43no—
382D52—46no—
383C4×D13—21no—
384C4×D13—21no—
385C4×D13—21no—
386C4×D13—21no—
387C4×D13—23no—
388C4×D13—23no—
389C4×D13—21no—
390C4×D13—21no—
391C4×D13—26no—
392C4×D13—26no—
393C4×D13—26no—
394C4×D13—26no—
395C4×D13C22×D416yes—
396C4×D13C2×#4116yes—
397Dic26C4×D4112yescomplemented
398C22×#41—131no—
399C22×#41—131no—
400#550—131no—
401#550—131no—
402#550—133no—
403#550—133no—
404#550—133no—
405#550—131no—
406#550—133no—
407#550#26111yescharacteristic, complemented
408C2×#127—133no—
409C2×#121—133no—
410C2×#121—133no—
411#520—268no—
412C4×#41—268no—
413C2×C4×Q8—131no—
414C2×C4×Q8—131no—
415C2×C4×Q8—131no—
416C2×C4×Q8—131no—
417C2×C4×Q8—131no—
418C2×C4×D4—133no—
419C2×C4×D4—133no—
420C2×C4×D4—133no—
421C2×C4×D4—133no—
422C2×C4×D4—133no—
423C2×C4×D4—136no—
424C2×#117—133no—
425C2×#117—133no—
426C22×C4⋊C4—133no—
427C22×C42—133no—
428#390—133no—
429#390—136no—
430#390—133no—
431#390—133no—
432#390—133no—
433#389—133no—
434#389—133no—
435#388—136no—
436#388—133no—
437#388—133no—
438#387—133no—
439#387—131no—
440#386—136no—
441#386—133no—
442#386—136no—
443#386—136no—
444#386—133no—
445#385—133no—
446#385—133no—
447#382—133no—
448#380—133no—
449#380—133no—
450C4×C4⋊C4—133no—
451C4×C4⋊C4—133no—
452C4×C4⋊C4—133no—
453C4×C4⋊C4—133no—
454C4×C22⋊C4—133no—
455C4×C22⋊C4—133no—
456C4×C22⋊C4—136no—
457#376—133no—
458C22×C13—23no—
459C22×C13—23no—
460C22×C13—23no—
461C22×C13—23no—
462C22×C13—23no—
463C22×C13—23no—
464C22×C13C24×C411yescharacteristic
465C2×D13—23no—
466C2×D13—23no—
467C2×D13—23no—
468C2×D13—23no—
469C2×D13—23no—
470C2×D13—23no—
471C2×D13—43no—
472C2×D13—43no—
473C2×D13—43no—
474C2×D13—43no—
475C2×D13—43no—
476C2×D13—43no—
477C2×D13—43no—
478C2×D13—43no—
479C2×D13C23×D411yescharacteristic
480C2×D13C22×#4111yescharacteristic
481C2×D13C2×H(5,𝔽2)11yescharacteristic
482C2×D13#58511yescharacteristic
483C2×D13#58511yescharacteristic
484C2×D13#58511yescharacteristic
485#261—22no—
486#261—22no—
487#261—26no—
488#261—41no—
489#261—43no—
490#261—43no—
491#261—43no—
492#261—41no—
493C4×C13—21no—
494C4×C13—21no—
495C4×C13—21no—
496C4×C13—23no—
497C4×C13C2×C4×D416yes—
498Dic13—21no—
499Dic13—21no—
500Dic13—21no—
501Dic13—23no—
502Dic13C2×C4×D416yes—
503C2×#41—131no—
504C2×#41—131no—
505C2×#41—133no—
506C2×#41—133no—
507C2×#41—133no—
508C2×#41—133no—
509C2×#41—264no—
510C2×#41—264no—
511C2×#41—264no—
512C2×#41—264no—
513C2×#41C2×#26111yescharacteristic, complemented
514C2×#41C2×#26111yescharacteristic, complemented
515C22×Q8—131no—
516C22×D4—133no—
517C22×D4—133no—
518C22×D4—136no—
519C22×D4—133no—
520C23×C4—133no—
521C23×C4—133no—
522C23×C4—133no—
523C23×C4—136no—
524C23×C4—133no—
525#127—136no—
526#127—136no—
527#127—133no—
528#127—133no—
529#127—133no—
530#127C2×#26113yescomplemented
531#121—133no—
532#121—133no—
533#121—136no—
534#121—136no—
535#121—133no—
536#121—133no—
537#121—133no—
538#121—133no—
539#121—136no—
540#121—136no—
541#121C2×#26113yescomplemented
542#121C2×#26113yescomplemented
543C4×Q8—138no—
544C4×Q8—131no—
545C4×Q8—133no—
546C4×Q8—133no—
547C4×Q8—264no—
548C4×Q8—264no—
549C4×Q8—264no—
550C4×Q8C2×#26111yescharacteristic, complemented
551C4×D4—133no—
552C4×D4—133no—
553C4×D4—133no—
554C4×D4—133no—
555C4×D4—133no—
556C4×D4—133no—
557C4×D4—133no—
558C4×D4—2612no—
559C4×D4—2612no—
560C4×D4—2612no—
561C4×D4—2612no—
562C4×D4—5212no—
563C4×D4C2×#26113yescomplemented
564#117—2612no—
565#117—2612no—
566C2×C4⋊C4—133no—
567C2×C4⋊C4—131no—
568C2×C4⋊C4—133no—
569C2×C4⋊C4—133no—
570C2×C4⋊C4—133no—
571C2×C4⋊C4—131no—
572C2×C4⋊C4—133no—
573C2×C4⋊C4—133no—
574C2×C4⋊C4—133no—
575C2×C4⋊C4—133no—
576C2×C4⋊C4—2612no—
577C2×C22⋊C4—133no—
578C2×C22⋊C4—133no—
579C2×C22⋊C4—133no—
580C2×C22⋊C4—136no—
581C2×C22⋊C4—133no—
582C2×C22⋊C4—133no—
583C2×C22⋊C4—136no—
584C2×C22⋊C4—136no—
585C2×C22⋊C4—133no—
586C2×C22⋊C4—133no—
587C2×C22⋊C4—133no—
588C2×C42—133no—
589C2×C42—133no—
590C2×C42—133no—
591C2×C42—133no—
592C2×C42—133no—
593C2×C42—133no—
594C2×C42—131no—
595C2×C42—136no—
596C2×C42—2612no—
597#95—131no—
598#95—133no—
599#95—133no—
600#95—133no—
601#95—133no—
602#95—131no—
603#95—131no—
604#95—133no—
605#95—136no—
606#95—131no—
607#95—133no—
608C2×C13—43no—
609C2×C13—43no—
610C2×C13C22×C4×D411yescharacteristic
611C2×C13#342811yescharacteristic
612C2×C13C4×H(5,𝔽2)11yescharacteristic
613D13—43no—
614D13—43no—
615D13#348711yescharacteristic
616D13#348811yescharacteristic
617D13#351711yescharacteristic
618D13#352411yescharacteristic
619C24—133no—
620C24—133no—
621#41—24no—
622#41—24no—
623#41—2612no—
624#41—2612no—
625#41—2612no—
626#41—2612no—
627#41—264no—
628#41—264no—
629C2×Q8—134no—
630C2×Q8—134no—
631C2×Q8—133no—
632C2×Q8C22×#26111yescharacteristic
633C2×D4—136no—
634C2×D4—136no—
635C2×D4—133no—
636C2×D4—133no—
637C2×D4—136no—
638C2×D4—136no—
639C2×D4—133no—
640C2×D4—133no—
641C2×D4—133no—
642C2×D4—136no—
643C2×D4—266no—
644C2×D4—266no—
645C2×D4—266no—
646C2×D4—266no—
647C2×D4—526no—
648C2×D4—526no—
649C2×D4—523no—
650C2×D4—523no—
651C2×D4C22×#26113yes—
652C2×D4C22×#26113yes—
653C2×D4C22×#26113yes—
654C2×D4C22×#26116yes—
655C22×C4—133no—
656C22×C4—131no—
657C22×C4—133no—
658C22×C4—131no—
659C22×C4—133no—
660C22×C4—133no—
661C22×C4—131no—
662C22×C4—131no—
663C22×C4—133no—
664C22×C4—131no—
665C22×C4—133no—
666C22×C4—133no—
667C22×C4—133no—
668C22×C4—133no—
669C22×C4—131no—
670C22×C4—133no—
671C22×C4—133no—
672C22×C4—133no—
673C22×C4—131no—
674C22×C4—266no—
675C22×C4—266no—
676C22×C4—266no—
677C22×C4—266no—
678C22×C4—266no—
679C22×C4—266no—
680C22×C4—266no—
681C22×C4—2612no—
682C22×C4—523no—
683C22×C4—523no—
684C22×C4—523no—
685C22×C4—526no—
686C22×C4—526no—
687C22×C4C22×#26113yes—
688C22×C4C22×#26113yes—
689C4⋊C4—1312no—
690C4⋊C4—131no—
691C4⋊C4—131no—
692C4⋊C4—131no—
693C4⋊C4—136no—
694C4⋊C4—133no—
695C4⋊C4—266no—
696C4⋊C4—266no—
697C4⋊C4—262no—
698C4⋊C4—266no—
699C4⋊C4—266no—
700C4⋊C4—266no—
701C4⋊C4—523no—
702C4⋊C4C22×#26111yescharacteristic
703C4⋊C4C22×#26113yes—
704C22⋊C4—133no—
705C22⋊C4—133no—
706C22⋊C4—133no—
707C22⋊C4—133no—
708C22⋊C4—133no—
709C22⋊C4—133no—
710C22⋊C4—266no—
711C22⋊C4—266no—
712C22⋊C4—2612no—
713C22⋊C4—266no—
714C22⋊C4—526no—
715C22⋊C4—523no—
716C22⋊C4—526no—
717C22⋊C4—523no—
718C22⋊C4—523no—
719C22⋊C4C22×#26113yes—
720C22⋊C4C22×#26113yes—
721C42—1312no—
722C42—133no—
723C42—133no—
724C42—133no—
725C42—262no—
726C42—266no—
727C42—266no—
728C42—266no—
729C42—266no—
730C42—526no—
731C42C22×#26113yes—
732C13#3429511yescharacteristic, complemented, Sylow
733C23—131no—
734C23—133no—
735C23—133no—
736C23—263no—
737C23—263no—
738C23—263no—
739C23—263no—
740C23—263no—
741C23—263no—
742C23—263no—
743C23—263no—
744C23—263no—
745C23—263no—
746C23—263no—
747C23—263no—
748C23C23×#26113yes—
749C23C23×#26113yes—
750Q8—1312no—
751Q8D4×#26114yescomplemented
752D4—26no—
753D4—26no—
754D4—43no—
755D4—46no—
756D4—2612no—
757D4—2612no—
758D4—266no—
759D4—266no—
760D4—523no—
761D4—526no—
762D4—523no—
763D4—523no—
764D4—526no—
765D4—526no—
766C2×C4—26no—
767C2×C4—26no—
768C2×C4—133no—
769C2×C4—136no—
770C2×C4—136no—
771C2×C4—132no—
772C2×C4—136no—
773C2×C4—132no—
774C2×C4—131no—
775C2×C4—133no—
776C2×C4—131no—
777C2×C4—131no—
778C2×C4—266no—
779C2×C4—266no—
780C2×C4—261no—
781C2×C4—263no—
782C2×C4—261no—
783C2×C4—263no—
784C2×C4—261no—
785C2×C4—261no—
786C2×C4—261no—
787C2×C4—261no—
788C2×C4—266no—
789C2×C4—266no—
790C2×C4—261no—
791C2×C4—263no—
792C2×C4—261no—
793C2×C4—261no—
794C2×C4—261no—
795C2×C4—263no—
796C2×C4—266no—
797C2×C4—266no—
798C2×C4—261no—
799C2×C4—261no—
800C2×C4—263no—
801C2×C4—263no—
802C2×C4—263no—
803C2×C4—263no—
804C2×C4—261no—
805C2×C4—263no—
806C2×C4—261no—
807C2×C4—261no—
808C2×C4—263no—
809C2×C4—263no—
810C2×C4—263no—
811C2×C4—263no—
812C2×C4—261no—
813C2×C4—5212no—
814C2×C4—5212no—
815C2×C4—10412no—
816C2×C4C23×#26111yescharacteristic
817C2×C4C23×#26113yes—
818C2×C4C23×#26111yescharacteristic
819C2×C4C23×#26111yescharacteristic
820C2×C4C23×#26113yes—
821C22—23no—
822C22—23no—
823C22—23no—
824C22—23no—
825C22—23no—
826C22—23no—
827C22—131no—
828C22—131no—
829C22—131no—
830C22—131no—
831C22—131no—
832C22—131no—
833C22—263no—
834C22—263no—
835C22—263no—
836C22—263no—
837C22—263no—
838C22—263no—
839C22—523no—
840C22—523no—
841C22—523no—
842C22—523no—
843C22—523no—
844C22—523no—
845C22—523no—
846C22—523no—
847C22C24×#26111yescharacteristic
848C4—21no—
849C4—21no—
850C4—21no—
851C4—23no—
852C4—136no—
853C4—262no—
854C4—262no—
855C4—266no—
856C4—261no—
857C4—261no—
858C4—261no—
859C4—263no—
860C4—521no—
861C4—523no—
862C4—521no—
863C4—523no—
864C4—523no—
865C4C2×D4×#26116yes—
866C2—43no—
867C2—43no—
868C2—131no—
869C2—131no—
870C2—131no—
871C2—131no—
872C2—523no—
873C2—523no—
874C2C22×D4×#26111yescharacteristic
875C2#1313181611yescharacteristic
876C2H(5,𝔽2)×#26111yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#550C4
prime radicalD13×#550C2
cosocleC22×D13C25
hypercenter#550#261
hypocenterC13#34295
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#11719631C2semidirect
2. C2×#41×#261C2semidirect
3. #13131366C2semidirect
4. #13131363C2semidirect
5. #13131361C2semidirect
6. #13131352C2semidirect
7. #13131351C2semidirect
8. #13131341C2semidirect
9. #13131341C2semidirect
10. #13131328C2semidirect
11. #13131324C2semidirect
12. #121×#261C2semidirect
13. #13131290C2semidirect
14. #13131276C2semidirect
33. C13×#550C4semidirect
34. #11719539C4semidirect
35. #11719539C4semidirect
36. #11719423C4semidirect
40. #11719304C4semidirect
41. #11719304C4semidirect
42. #11719282C4semidirect
44. #11719258C4semidirect
79. C2×C13×#41C2×C4semidirect
80. C2×C13×#41C2×C4semidirect
85. C2×#6131C2×C4semidirect
86. C2×#6131C2×C4semidirect
88. C2×#6129C2×C4semidirect
89. C2×#6129C2×C4semidirect
94. C2×#6127C2×C4semidirect
95. C2×#6127C2×C4semidirect
110. Q8×#261D4semidirect
135. C13×#127C2×C4semidirect
136. C13×#121C2×C4semidirect
137. C13×#121C2×C4semidirect
138. C4×Q8×C13C2×C4semidirect
139. C4×D4×C13C2×C4semidirect
140. Q8×Dic13C2×C4semidirect
141. #88194C2×C4semidirect
142. #88194C2×C4semidirect
143. #88194C2×C4semidirect
144. #88194C2×C4semidirect
145. #88193C2×C4semidirect
146. #88193C2×C4semidirect
147. #88192C2×C4semidirect
148. #88192C2×C4semidirect
149. D4×Dic13C2×C4semidirect
150. #88184C2×C4semidirect
151. #88184C2×C4semidirect
152. C4×C22⋊D13C2×C4semidirect
153. C4×C22⋊D13C2×C4semidirect
154. #88149C2×C4semidirect
155. #88149C2×C4semidirect
156. #88147C2×C4semidirect
159. #88141C2×C4semidirect
160. #88138C2×C4semidirect
161. #88138C2×C4semidirect
162. #88135C2×C4semidirect
163. #88135C2×C4semidirect
166. #88128C2×C4semidirect
167. C4×D52C2×C4semidirect
169. C4×Dic26C2×C4semidirect
354. Q8×C13C4×D4semidirect
397. Dic26C4×D4semidirect
407. #550#261semidirect
513. C2×#41C2×#261semidirect
514. C2×#41C2×#261semidirect
530. #127C2×#261semidirect
541. #121C2×#261semidirect
542. #121C2×#261semidirect
550. C4×Q8C2×#261semidirect
563. C4×D4C2×#261semidirect
732. C13#34295semidirect
751. Q8D4×#261semidirect

Maximal subgroups

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

subgroupindex
C2×#117196312
C2×#41×#2612
#131313662
#131313632
#131313612
#131313522
#131313512
#131313412
#131313282
#131313242
#121×#2612
#131312902
#131312762
D13×#5502
#3429513