Finite Group Databasebeta

← #16740732

Subgroups — #16740732

Order 3328.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128542C211yesmaximal, characteristic, complemented
2#13127152C212yesmaximal, complemented
3#13127089C212yesmaximal, complemented
4#13126947C212yesmaximal, complemented
5#13126887C212yesmaximal, complemented
6#13126812C212yesmaximal, complemented
7#13126797C212yesmaximal, complemented
8#13126701C212yesmaximal, complemented
9#13126671C212yesmaximal, complemented
10#13125201C211yesmaximal, characteristic, complemented
11#13124821C211yesmaximal, characteristic, complemented
12C2×#11718704C211yesmaximal, characteristic, complemented
13#13124698C211yesmaximal, characteristic, complemented
14#13124495C211yesmaximal, characteristic, complemented
15#13124462C211yesmaximal, characteristic, complemented
16#13124382C211yesmaximal, characteristic, complemented
17#13124151C211yesmaximal, characteristic, complemented
18#13124054C211yesmaximal, characteristic, complemented
19#13123717C211yesmaximal, characteristic, complemented
20#13123563C211yesmaximal, characteristic, complemented
21#13123369C211yesmaximal, characteristic, complemented
22C2×#11718893C211yesmaximal, characteristic, complemented
23C13×#3489C211yesmaximal, characteristic, complemented
24C2×C13×2−1+4C2211yescharacteristic
25C22×C13×#41C2211yescharacteristic
26D4×Q8×C13C2212yes—
27C13×#548C2212yes—
28C13×#547—22no—
29C13×#547C2212yes—
30C13×#546—22no—
31C13×#546C2212yes—
32C13×#537—21no—
33C13×#537C2211yescharacteristic
34C13×#536—21no—
35C13×#536C2211yescharacteristic
36C13×#525—21no—
37C13×#525C2211yescharacteristic
38C2×C13×C22⋊Q8—21no—
39C2×C13×C22⋊Q8C2211yescharacteristic
40C13×#520C2211yescharacteristic
41#11719538C2211yescharacteristic, complemented
42#11719532C2211yescharacteristic, complemented
43C2×#88204C2211yescharacteristic
44C2×#88204C2211yescharacteristic
45C2×#88202C2211yescharacteristic, complemented
46C2×#88196C2211yescharacteristic, complemented
47#11719496C2211yescharacteristic
48C22×C4⋊Dic13C2211yescharacteristic
49C22×#6099C2211yescharacteristic
50#11719370—22no—
51#11719347—21no—
52#11719340—21no—
53#11719323—21no—
54#11719316—21no—
55#11719291—22no—
56#11719270C2212yescomplemented
57#11719260C2212yes—
58#11719248C2212yescomplemented
59#11719246C2212yes—
60#11719228C2211yescharacteristic, complemented
61#11719224C2211yescharacteristic, complemented
62#11718900C2211yescharacteristic
63#11718900C2211yescharacteristic
64#11718900C2212yescomplemented
65#11718899C2211yescharacteristic
66#11718899C2211yescharacteristic
67#11718899C2212yescomplemented
68#11718895C2211yescharacteristic, complemented
69#11718894C2211yescharacteristic
70#11718894C2211yescharacteristic
71#11718894C2212yescomplemented
72#11718893C2211yescharacteristic
73#11718893C2212yes—
74#11718893C2211yescharacteristic
75#11718893C2211yescharacteristic
76#11718893C2211yescharacteristic
77#11718893C2212yes—
78#11718893C2212yescomplemented
79#11718889C2211yescharacteristic
80#11718889C2212yescomplemented
81#11718888C2211yescharacteristic
82#11718888C2212yescomplemented
83#11718886C2211yescharacteristic, complemented
84#11718886C2212yescomplemented
85C2×#88075C2212yes—
86C2×#88075C2211yescharacteristic, complemented
87C2×#88075C2212yescomplemented
88C2×#88075C2211yescharacteristic, complemented
89#11718879C2211yescharacteristic
90#11718878C2211yescharacteristic
91C2×#88072C2212yes—
92C2×C22⋊#1055C2211yescharacteristic
93#11718751C2212yescomplemented
94#11718744C2212yescomplemented
95#11718743C2212yescomplemented
96#11718742C2212yescomplemented
97#11718718C2212yescomplemented
98#11718717C2212yescomplemented
99#11718716C2212yescomplemented
100#11718715C2212yescomplemented
101#11718713C2212yescomplemented
102#11718713C2212yescomplemented
103#11718712C2212yes—
104#11718710C2212yescomplemented
105#11718709C2212yes—
106#11718709C2212yescomplemented
107#11718706C2212yescomplemented
108#11718704C2212yes—
109#11718704C2212yes—
110#11718704C2212yescomplemented
111#11718704C2212yescomplemented
112#11718704C2212yescomplemented
113#11718702C2212yescomplemented
114#11718700C2212yescomplemented
115#11718696C2212yescomplemented
116#11718695C2212yescomplemented
117#11718691C2212yescomplemented
118C4×#6106C2212yescomplemented
119#11718683C2212yescomplemented
120#11718681C2212yescomplemented
121C4×#6105C2212yescomplemented
122#11718675C2212yescomplemented
123#11718673C2212yescomplemented
124#11718672C2212yes—
125#11718672C2212yescomplemented
126D4×#1055C2212yes—
127#11718670C2212yescomplemented
128#11718669C2212yescomplemented
129#11718660C2211yescharacteristic, complemented
130#11718658C2211yescharacteristic, complemented
131#11718627C2211yescharacteristic, complemented
132#11718625C2211yescharacteristic, complemented
133C2×#88048C2211yescharacteristic, complemented
134C2×#88048C2211yescharacteristic, complemented
135C13×2−1+4—24no—
136C13×2−1+4—42no—
137C2×C13×#41—21no—
138C2×C13×#41—22no—
139C2×C13×#41—21no—
140C2×C13×#41—21no—
141C2×C13×#41—24no—
142C2×C13×#41—42no—
143C2×C13×#41C2311yescharacteristic
144C2×C13×#41C2312yes—
145C2×C13×#41C2311yescharacteristic
146C2×C13×#41C2311yescharacteristic
147C2×C13×#41C2311yescharacteristic
148C2×C13×#41C2311yescharacteristic
149C22×Q8×C13—21no—
150C22×Q8×C13C2311yescharacteristic
151C22×Q8×C13C2312yes—
152C22×Q8×C13C2311yescharacteristic
153C22×D4×C13—21no—
154C22×D4×C13C2311yescharacteristic
155C23×C4×C13—21no—
156C23×C4×C13C2311yescharacteristic
157C23×Dic13—21no—
158C2×#6129—22no—
159C2×#6127C2311yescharacteristic
160C13×C4⋊Q8—22no—
161C13×C4⋊Q8C2312yes—
162C13×#124—22no—
163C13×#124C2312yes—
164C13×#123—22no—
165C13×#123—22no—
166C13×#123—22no—
167C13×#123—22no—
168C13×#123D412yes—
169C13×C22⋊Q8—21no—
170C13×C22⋊Q8—21no—
171C13×C22⋊Q8—21no—
172C13×C22⋊Q8—21no—
173C13×C22⋊Q8—22no—
174C13×C22⋊Q8—21no—
175C13×C22⋊Q8—22no—
176C13×C22⋊Q8—22no—
177C13×C22⋊Q8D411yescharacteristic
178C13×C22⋊Q8D411yescharacteristic
179C13×C22⋊Q8C2312yes—
180C13×C22⋊Q8C2312yes—
181C13×C22⋊Q8C2312yes—
182C13×#121—21no—
183C13×#121—22no—
184C13×#121—22no—
185C13×#121—22no—
186C13×#121—22no—
187C13×#121D411yescharacteristic
188C13×#121D411yescharacteristic
189C13×#121C2312yes—
190C13×#120—22no—
191C13×#120D412yes—
192C4×Q8×C13C2312yes—
193C4×D4×C13—22no—
194C4×D4×C13—22no—
195C4×D4×C13—22no—
196C4×D4×C13C2312yes—
197C4×D4×C13C2312yes—
198C4×D4×C13C2312yes—
199C13×#117—21no—
200C13×#117C2311yescharacteristic
201C2×C13×C4⋊C4—21no—
202C2×C13×C4⋊C4—21no—
203C2×C13×C4⋊C4—22no—
204C2×C13×C4⋊C4C2311yescharacteristic
205C2×C13×C22⋊C4—21no—
206C2×C13×C22⋊C4—22no—
207#88207—21no—
208#88204—24no—
209#88204—42no—
210#88202—42no—
211#88200—21no—
212Q8×Dic13—21no—
213C2×#6107C2311yescharacteristic
214C2×#6107C2312yes—
215C2×#6107C2311yescharacteristic
216#88196—42no—
217C2×#6106C2311yescharacteristic
218C2×#6106C2312yes—
219C2×#6106C2311yescharacteristic
220#88193—22no—
221#88193—22no—
222#88192—21no—
223#88189—22no—
224D4×Dic13—22no—
225D4×Dic13—22no—
226D4×Dic13—21no—
227C2×#6105C2311yescharacteristic
228C2×#6105C2311yescharacteristic
229C2×#6104C2311yescharacteristic
230C2×#6104C2311yescharacteristic
231#88184C2312yes—
232#88184C2311yescharacteristic
233#88184C2311yescharacteristic
234#88183—21no—
235C4×C22⋊D13—21no—
236C4×C22⋊D13—21no—
237#88180C2312yes—
238#88180C2311yescharacteristic
239C2×C4⋊Dic13—21no—
240C2×C4⋊Dic13—21no—
241C2×C4⋊Dic13—21no—
242C2×C4⋊Dic13C2312yes—
243C2×C4⋊Dic13C2312yes—
244C2×C4⋊Dic13C2312yes—
245C2×C4⋊Dic13C2311yescharacteristic
246C2×C4⋊Dic13C2311yescharacteristic
247#88178C2312yes—
248#88178C2311yescharacteristic
249#88178C2311yescharacteristic
250C2×#6099—42no—
251C2×#6099C2311yescharacteristic
252C2×#6099C2311yescharacteristic
253C2×#6099C2312yes—
254C2×#6099C2312yes—
255C22×#1055C2311yescharacteristic
256C22×#1055C2311yescharacteristic
257C22×#1055C2312yes—
258C22×#1055C2312yes—
259#88152—22no—
260#88151—22no—
261#88146—21no—
262C4⋊C4×D13—21no—
263#88144—21no—
264#88144—22no—
265#88143—22no—
266#88142—21no—
267#88140—22no—
268#88140—22no—
269#88137—22no—
270#88135—22no—
271#88135—22no—
272#88133—22no—
273#88132—22no—
274#88132—22no—
275#88132—22no—
276#88131—22no—
277C4×D52C2312yes—
278#88124C2312yes—
279#88123C2312yes—
280C4×Dic26C2312yes—
281#88075C2311yescharacteristic
282#88075C2312yes—
283#88075C2311yescharacteristic
284#88075C2312yes—
285#88075C2312yes—
286#88075C2312yes—
287#88075C2312yes—
288#88075C2312yes—
289#88075C2311yescharacteristic
290#88075C2312yes—
291#88075C2311yescharacteristic
292#88075C2312yes—
293#88075C2312yes—
294#88075C2312yes—
295#88072C2311yescharacteristic
296#88072C2312yes—
297#88072C2311yescharacteristic
298#88072C2312yes—
299#88072C2311yescharacteristic
300#88072C2312yes—
301#88072C2311yescharacteristic
302#88072C2312yes—
303C22⋊#1055C2311yescharacteristic
304C22⋊#1055C2312yes—
305C22⋊#1055C2311yescharacteristic
306C22⋊#1055C2312yes—
307C22⋊#1055C2311yescharacteristic
308C22⋊#1055C2311yescharacteristic
309#88050C2312yes—
310#88049C2312yes—
311#88048C2312yes—
312#88048C2312yes—
313#88048C2312yes—
314#88048C2312yes—
315#88048C2312yes—
316#88047C2312yes—
317C4⋊#1055C2312yes—
318C4⋊#1055C2312yes—
319#88043C2312yes—
320C4×#1055C2312yes—
321#61193—131nomaximal, Sylow
322C24×C13—21no—
323C24×C13C2×D411yescharacteristic
324C13×#41—22no—
325C13×#41—22no—
326C13×#41—22no—
327C13×#41—22no—
328C13×#41—22no—
329C13×#41—24no—
330C13×#41—22no—
331C13×#41—22no—
332C13×#41—44no—
333C13×#41—41no—
334C13×#41—41no—
335C13×#41—42no—
336C13×#41—44no—
337C13×#41—44no—
338C13×#41—48no—
339C13×#41#4114yescomplemented
340C2×Q8×C13—21no—
341C2×Q8×C13—22no—
342C2×Q8×C13—21no—
343C2×Q8×C13—22no—
344C2×Q8×C13—24no—
345C2×Q8×C13—22no—
346C2×Q8×C13—22no—
347C2×Q8×C13—41no—
348C2×Q8×C13—42no—
349C2×Q8×C13—44no—
350C2×Q8×C13C2×D411yescharacteristic
351C2×Q8×C13C2412yes—
352C2×Q8×C13C2411yescharacteristic
353C2×Q8×C13C2411yescharacteristic
354C2×D4×C13—21no—
355C2×D4×C13—22no—
356C2×D4×C13—22no—
357C2×D4×C13—21no—
358C2×D4×C13—21no—
359C2×D4×C13—21no—
360C2×D4×C13—22no—
361C2×D4×C13—21no—
362C2×D4×C13—41no—
363C2×D4×C13—44no—
364C2×D4×C13C2×D411yescharacteristic
365C2×D4×C13C2×D412yes—
366C2×D4×C13C2×D412yes—
367C2×D4×C13C2×D412yes—
368C2×D4×C13C2411yescharacteristic
369C2×D4×C13C2411yescharacteristic
370C22×C4×C13—21no—
371C22×C4×C13—22no—
372C22×C4×C13—22no—
373C22×C4×C13—21no—
374C22×C4×C13—22no—
375C22×C4×C13—21no—
376C22×C4×C13—21no—
377C22×C4×C13—22no—
378C22×C4×C13—21no—
379C22×C4×C13—21no—
380C22×C4×C13—21no—
381C22×C4×C13—22no—
382C22×C4×C13—44no—
383C22×C4×C13C2×D411yescharacteristic
384C22×C4×C13C2×D411yescharacteristic
385C22×C4×C13C2×D411yescharacteristic
386C22×C4×C13C2411yescharacteristic
387C22×C4×C13C2412yes—
388C22×C4×C13C2411yescharacteristic
389C22×C4×C13C2411yescharacteristic
390C2×C22⋊D13—21no—
391C2×C22⋊D13—21no—
392C2×C22⋊D13—21no—
393C2×C22⋊D13—22no—
394C22×Dic13—22no—
395C22×Dic13—21no—
396C22×Dic13—22no—
397C22×Dic13—22no—
398C22×Dic13—21no—
399C22×Dic13—82no—
400#6129—84no—
401#6127—22no—
402#6127—22no—
403C2×D52C2411yescharacteristic
404C2×C4×D13—21no—
405C2×C4×D13—22no—
406C2×Dic26—22no—
407C2×Dic26C2411yescharacteristic
408C13×C4⋊C4—22no—
409C13×C4⋊C4—21no—
410C13×C4⋊C4—22no—
411C13×C4⋊C4—22no—
412C13×C4⋊C4—22no—
413C13×C4⋊C4—22no—
414C13×C4⋊C4—22no—
415C13×C4⋊C4C2×D411yescharacteristic
416C13×C4⋊C4C2×D412yes—
417C13×C4⋊C4C2×D411yescharacteristic
418C13×C4⋊C4C2×D412yes—
419C13×C4⋊C4C2412yes—
420C13×C22⋊C4—22no—
421C13×C22⋊C4—22no—
422C13×C22⋊C4—22no—
423C13×C22⋊C4—22no—
424C13×C22⋊C4—22no—
425C13×C22⋊C4—22no—
426C13×C22⋊C4—22no—
427C13×C22⋊C4C2×D412yes—
428C13×C22⋊C4C2×D412yes—
429C13×C22⋊C4C2×D412yes—
430C13×C22⋊C4C2×D412yes—
431C13×C22⋊C4C2×D412yes—
432C42×C13—22no—
433C42×C13C2412yes—
434C22⋊Dic13—21no—
435C22⋊Dic13—21no—
436C22⋊Dic13—21no—
437C22⋊Dic13—22no—
438C22⋊Dic13—22no—
439#6107—22no—
440#6107—42no—
441#6107—41no—
442#6106—22no—
443#6106—42no—
444#6106—41no—
445#6105—22no—
446#6105—41no—
447#6104—22no—
448#6104—41no—
449#6103—22no—
450#6103—22no—
451#6103—21no—
452#6103—21no—
453C4⋊Dic13—22no—
454C4⋊Dic13—22no—
455C4⋊Dic13—22no—
456C4⋊Dic13—22no—
457C4⋊Dic13—21no—
458C4⋊Dic13—21no—
459C4⋊Dic13C2412yes—
460C4⋊Dic13C2411yescharacteristic
461C4⋊Dic13C2412yes—
462C4⋊Dic13C2411yescharacteristic
463#6101—22no—
464#6101—22no—
465#6101—22no—
466#6101—22no—
467#6101—21no—
468#6101—21no—
469C4×Dic13—22no—
470C4×Dic13—22no—
471C4×Dic13—21no—
472#6099—22no—
473#6099—22no—
474#6099—42no—
475#6099—42no—
476C2×#1055—22no—
477C2×#1055—22no—
478C2×#1055—42no—
479C2×#1055—42no—
480C2×#1055C2411yescharacteristic
481C2×#1055C2411yescharacteristic
482C2×#1055C2412yes—
483C2×#1055C2411yescharacteristic
484C2×#1055C2411yescharacteristic
485C2×#1055C2412yes—
486#3492—131no—
487#3489D1311yescharacteristic, complemented
488#3331—132no—
489#3326—132no—
490#3316—132no—
491#3312—132no—
492#3307—132no—
493#3306—132no—
494#3298—132no—
495#3296—132no—
496#3137—131no—
497#3099—131no—
498C2×#483—131no—
499#3084—131no—
500#3060—131no—
501#3056—131no—
502#3046—131no—
503#3013—131no—
504#3002—131no—
505#2952—131no—
506#2933—131no—
507#2898—131no—
508C2×#417—131no—
509C23×C13—22no—
510C23×C13—22no—
511C23×C13—21no—
512C23×C13—21no—
513C23×C13—41no—
514C23×C13—42no—
515C23×C13—42no—
516C23×C13—81no—
517C23×C13C22×D412yes—
518C23×C13C22×D411yescharacteristic
519C23×C13C22×D411yescharacteristic
520C23×C13C22×D411yescharacteristic
521C22×D13—21no—
522Q8×C13—22no—
523Q8×C13—21no—
524Q8×C13—22no—
525Q8×C13—21no—
526Q8×C13—22no—
527Q8×C13—21no—
528Q8×C13—44no—
529Q8×C13—42no—
530Q8×C13—42no—
531Q8×C13C2×#4112yes—
532D4×C13—24no—
533D4×C13—24no—
534D4×C13—24no—
535D4×C13—22no—
536D4×C13—21no—
537D4×C13—21no—
538D4×C13—21no—
539D4×C13—42no—
540D4×C13—42no—
541D4×C13—42no—
542D4×C13—42no—
543D4×C13—44no—
544D4×C13—42no—
545D4×C13—82no—
546D4×C13C2×#4112yes—
547C2×C4×C13—22no—
548C2×C4×C13—21no—
549C2×C4×C13—22no—
550C2×C4×C13—22no—
551C2×C4×C13—24no—
552C2×C4×C13—21no—
553C2×C4×C13—21no—
554C2×C4×C13—22no—
555C2×C4×C13—21no—
556C2×C4×C13—22no—
557C2×C4×C13—21no—
558C2×C4×C13—22no—
559C2×C4×C13—22no—
560C2×C4×C13—21no—
561C2×C4×C13—42no—
562C2×C4×C13—42no—
563C2×C4×C13—42no—
564C2×C4×C13—44no—
565C2×C4×C13—44no—
566C2×C4×C13—42no—
567C2×C4×C13—42no—
568C2×C4×C13—82no—
569C2×C4×C13—81no—
570C2×C4×C13C22×D412yes—
571C2×C4×C13C22×D412yes—
572C2×C4×C13C22×D412yes—
573C2×C4×C13C22×D411yescharacteristic
574C2×C4×C13C22×D411yescharacteristic
575C2×C4×C13C22×D411yescharacteristic
576C2×C4×C13C2×#4112yes—
577C2×C4×C13H(5,𝔽2)12yes—
578C2×C4×C13C2511yescharacteristic
579C22⋊D13—42no—
580C22⋊D13—42no—
581C22⋊D13—42no—
582C22⋊D13—82no—
583C2×Dic13—21no—
584C2×Dic13—21no—
585C2×Dic13—22no—
586C2×Dic13—21no—
587C2×Dic13—22no—
588C2×Dic13—44no—
589C2×Dic13—82no—
590C2×Dic13—81no—
591C2×Dic13—82no—
592C2×Dic13—81no—
593D52—21no—
594D52—21no—
595C4×D13—42no—
596C4×D13—82no—
597Dic26—21no—
598Dic26—21no—
599Dic26—82no—
600#1055—21no—
601#1055—21no—
602#1055—21no—
603#1055—21no—
604#1055—22no—
605#1055—22no—
606C2×2−1+4C2×D1311yescharacteristic
607C22×#41C2×D1311yescharacteristic
608C2×#137—131no—
609C2×#135—131no—
610C2×#135—131no—
611C2×#131—131no—
612C22×M16—131no—
613#554—132no—
614#554—261no—
615#553—132no—
616#553—261no—
617#552—132no—
618#552—261no—
619D4×Q8C2×D1312yes—
620#548C2×D1312yes—
621#547—22no—
622#547—132no—
623#547—261no—
624#547C2×D1312yes—
625#546—22no—
626#546C2×D1312yes—
627#544—131no—
628#539—262no—
629#537—21no—
630#537—131no—
631#537C2×D1311yescharacteristic
632#536—21no—
633#536C2×D1311yescharacteristic
634#525—21no—
635#525—131no—
636#525—262no—
637#525C2×D1311yescharacteristic
638C2×C22⋊Q8—21no—
639C2×C22⋊Q8C2×D1311yescharacteristic
640#520—131no—
641#520—131no—
642#520C2×D1311yescharacteristic
643C22×C4⋊C4—131no—
644#491—132no—
645#489—132no—
646#488—132no—
647#487—132no—
648#485—132no—
649#483—132no—
650#483—132no—
651#483—132no—
652#483—132no—
653#483—132no—
654#482—132no—
655#481—132no—
656#479—132no—
657#478—132no—
658#476—132no—
659#475—132no—
660#470—132no—
661#470—132no—
662#469—132no—
663#468—132no—
664#467—132no—
665#465—132no—
666#465—132no—
667#465—132no—
668#464—132no—
669#463—132no—
670#462—132no—
671#461—132no—
672#452—131no—
673#452—132no—
674#452—131no—
675#451—131no—
676#451—132no—
677#450—131no—
678#449—131no—
679#449—131no—
680#449—132no—
681#448—131no—
682#448—132no—
683#447—131no—
684#442—132no—
685#441—132no—
686C4×SD16—132no—
687C4×SD16—132no—
688#436—132no—
689#435—132no—
690#435—132no—
691C8×D4—132no—
692#428—131no—
693C2×#106—131no—
694C2×#106—131no—
695#424—131no—
696#419—131no—
697#419—132no—
698#417—132no—
699#417—132no—
700#417—131no—
701#417—131no—
702#417—131no—
703#417—131no—
704#417—132no—
705#417—131no—
706#416—131no—
707#416—131no—
708#416—132no—
709C2×#103—131no—
710C2×#103—131no—
711C2×#103—132no—
712C2×#103—132no—
713C2×#102—132no—
714#408—131no—
715C2×C22⋊C8—131no—
716#405—131no—
717C22×C13—21no—
718C22×C13—21no—
719C22×C13—21no—
720C22×C13—21no—
721C22×C13—21no—
722C22×C13—22no—
723C22×C13—21no—
724C22×C13—22no—
725C22×C13—22no—
726C22×C13—21no—
727C22×C13—22no—
728C22×C13—44no—
729C22×C13—41no—
730C22×C13—41no—
731C22×C13—41no—
732C22×C13—41no—
733C22×C13—41no—
734C22×C13—84no—
735C22×C13#54612yes—
736C22×C13#57712yes—
737C22×C13C23×D411yescharacteristic
738C2×D13—41no—
739C2×D13—41no—
740C2×D13—41no—
741C4×C13—22no—
742C4×C13—21no—
743C4×C13—21no—
744C4×C13—22no—
745C4×C13—22no—
746C4×C13—22no—
747C4×C13—42no—
748C4×C13—41no—
749C4×C13—42no—
750C4×C13#54612yes—
751C4×C13C22×#4111yescharacteristic
752C4×C13C2×H(5,𝔽2)11yescharacteristic
753Dic13—41no—
754Dic13—41no—
755Dic13—41no—
756Dic13—42no—
757Dic13—42no—
7582−1+4—24no—
7592−1+4—42no—
760C2×#41—21no—
761C2×#41—22no—
762C2×#41—21no—
763C2×#41—21no—
764C2×#41—24no—
765C2×#41—42no—
766C2×#41—131no—
767C2×#41—262no—
768C2×#41C22×D1311yescharacteristic
769C2×#41C22×D1312yes—
770C2×#41C22×D1311yescharacteristic
771C2×#41C22×D1311yescharacteristic
772C2×#41C22×D1311yescharacteristic
773C2×#41C22×D1311yescharacteristic
774C22×Q8—21no—
775C22×Q8C22×D1311yescharacteristic
776C22×Q8C22×D1312yes—
777C22×Q8C22×D1311yescharacteristic
778C22×D4—21no—
779C22×D4C22×D1311yescharacteristic
780C23×C4—21no—
781C23×C4—261no—
782C23×C4C22×D1311yescharacteristic
783#137—522no—
784#135—264no—
785#135—522no—
786C2×Q16—131no—
787C2×Q16—131no—
788C2×Q16—132no—
789C2×SD16—131no—
790C2×SD16—131no—
791C2×SD16—131no—
792C2×SD16—132no—
793C2×SD16—131no—
794C2×D8—131no—
795C2×D8—131no—
796#131—522no—
797C2×M16—131no—
798C2×M16—131no—
799C2×M16—132no—
800C2×M16—132no—
801C2×M16—522no—
802C22×C8—131no—
803C22×C8—131no—
804C22×C8—132no—
805C22×C8—132no—
806C4⋊Q8—22no—
807C4⋊Q8—132no—
808C4⋊Q8—261no—
809C4⋊Q8C22×D1312yes—
810#126—262no—
811#126—262no—
812#125—132no—
813#125—262no—
814#125—262no—
815#125—261no—
816#124—22no—
817#124C22×D1312yes—
818#123—22no—
819#123—22no—
820#123—22no—
821#123—22no—
822#123—262no—
823#123—261no—
824#123—262no—
825#123—262no—
826#123—262no—
827#123C22⋊D1312yes—
828C22⋊Q8—21no—
829C22⋊Q8—21no—
830C22⋊Q8—21no—
831C22⋊Q8—21no—
832C22⋊Q8—22no—
833C22⋊Q8—21no—
834C22⋊Q8—22no—
835C22⋊Q8—22no—
836C22⋊Q8—131no—
837C22⋊Q8—131no—
838C22⋊Q8—132no—
839C22⋊Q8—261no—
840C22⋊Q8—262no—
841C22⋊Q8—262no—
842C22⋊Q8—262no—
843C22⋊Q8—262no—
844C22⋊Q8C22⋊D1311yescharacteristic
845C22⋊Q8C22⋊D1311yescharacteristic
846C22⋊Q8C22×D1312yes—
847C22⋊Q8C22×D1312yes—
848C22⋊Q8C22×D1312yes—
849#121—21no—
850#121—22no—
851#121—22no—
852#121—22no—
853#121—22no—
854#121—131no—
855#121—131no—
856#121—132no—
857#121—262no—
858#121—262no—
859#121—261no—
860#121C22⋊D1311yescharacteristic
861#121C22⋊D1311yescharacteristic
862#121C22×D1312yes—
863#120—22no—
864#120—261no—
865#120C22⋊D1312yes—
866C4×Q8—132no—
867C4×Q8—261no—
868C4×Q8C22×D1312yes—
869C4×D4—22no—
870C4×D4—22no—
871C4×D4—22no—
872C4×D4—132no—
873C4×D4—262no—
874C4×D4—261no—
875C4×D4—262no—
876C4×D4—261no—
877C4×D4—261no—
878C4×D4—262no—
879C4×D4—262no—
880C4×D4C22×D1312yes—
881C4×D4C22×D1312yes—
882C4×D4C22×D1312yes—
883#117—21no—
884#117—131no—
885#117—132no—
886#117—261no—
887#117—262no—
888#117C22×D1311yescharacteristic
889C2×C4⋊C4—21no—
890C2×C4⋊C4—21no—
891C2×C4⋊C4—22no—
892C2×C4⋊C4—131no—
893C2×C4⋊C4—131no—
894C2×C4⋊C4—132no—
895C2×C4⋊C4—132no—
896C2×C4⋊C4—132no—
897C2×C4⋊C4—261no—
898C2×C4⋊C4—261no—
899C2×C4⋊C4—261no—
900C2×C4⋊C4—261no—
901C2×C4⋊C4C22×D1311yescharacteristic
902C2×C22⋊C4—21no—
903C2×C22⋊C4—22no—
904#107—132no—
905#106—132no—
906#106—132no—
907#106—132no—
908#106—132no—
909#106—132no—
910C4⋊C8—132no—
911C4⋊C8—132no—
912#103—131no—
913#103—132no—
914#103—132no—
915#103—132no—
916#103—132no—
917#103—132no—
918#103—132no—
919#103—132no—
920#103—132no—
921#103—132no—
922#103—131no—
923#103—132no—
924#103—131no—
925#103—131no—
926#103—132no—
927#102—132no—
928#102—132no—
929#102—132no—
930#102—132no—
931#102—131no—
932#102—131no—
933#102—131no—
934#102—131no—
935#102—132no—
936C22⋊C8—131no—
937C22⋊C8—131no—
938C22⋊C8—131no—
939C22⋊C8—131no—
940C22⋊C8—132no—
941C22⋊C8—132no—
942#97—132no—
943C4×C8—132no—
944C2×C13—22no—
945C2×C13—22no—
946C2×C13—42no—
947C2×C13—41no—
948C2×C13—42no—
949C2×C13—81no—
950C2×C13C2×#54611yescharacteristic
951C2×C13C2×#57711yescharacteristic
952C2×C13#358611yescharacteristic
953D13—81no—
954C24—21no—
955C24C2×C22⋊D1311yescharacteristic
956#41—22no—
957#41—22no—
958#41—22no—
959#41—22no—
960#41—22no—
961#41—24no—
962#41—22no—
963#41—22no—
964#41—44no—
965#41—41no—
966#41—41no—
967#41—42no—
968#41—44no—
969#41—44no—
970#41—48no—
971#41—262no—
972#41—262no—
973#41—1044no—
974#41#612914yescomplemented
975C2×Q8—21no—
976C2×Q8—22no—
977C2×Q8—21no—
978C2×Q8—22no—
979C2×Q8—24no—
980C2×Q8—22no—
981C2×Q8—22no—
982C2×Q8—41no—
983C2×Q8—42no—
984C2×Q8—44no—
985C2×Q8—131no—
986C2×Q8—262no—
987C2×Q8C2×C22⋊D1311yescharacteristic
988C2×Q8C23×D1312yes—
989C2×Q8C23×D1311yescharacteristic
990C2×Q8C23×D1311yescharacteristic
991C2×D4—21no—
992C2×D4—22no—
993C2×D4—22no—
994C2×D4—21no—
995C2×D4—21no—
996C2×D4—21no—
997C2×D4—22no—
998C2×D4—21no—
999C2×D4—41no—
1000C2×D4—44no—
1001C2×D4—131no—
1002C2×D4—261no—
1003C2×D4—261no—
1004C2×D4—261no—
1005C2×D4—262no—
1006C2×D4C2×C22⋊D1312yes—
1007C2×D4C2×C22⋊D1312yes—
1008C2×D4C2×C22⋊D1311yescharacteristic
1009C2×D4C2×C22⋊D1312yes—
1010C2×D4C23×D1311yescharacteristic
1011C2×D4C23×D1311yescharacteristic
1012C22×C4—22no—
1013C22×C4—22no—
1014C22×C4—21no—
1015C22×C4—21no—
1016C22×C4—22no—
1017C22×C4—21no—
1018C22×C4—21no—
1019C22×C4—22no—
1020C22×C4—21no—
1021C22×C4—21no—
1022C22×C4—21no—
1023C22×C4—22no—
1024C22×C4—44no—
1025C22×C4—262no—
1026C22×C4—261no—
1027C22×C4—262no—
1028C22×C4—261no—
1029C22×C4—262no—
1030C22×C4—261no—
1031C22×C4—262no—
1032C22×C4—1042no—
1033C22×C4C2×C22⋊D1311yescharacteristic
1034C22×C4C2×C22⋊D1311yescharacteristic
1035C22×C4C2×C22⋊D1311yescharacteristic
1036C22×C4C23×D1311yescharacteristic
1037C22×C4C23×D1311yescharacteristic
1038C22×C4C23×D1312yes—
1039C22×C4C23×D1311yescharacteristic
1040Q16—262no—
1041Q16—521no—
1042Q16—522no—
1043SD16—262no—
1044SD16—262no—
1045SD16—521no—
1046SD16—521no—
1047SD16—522no—
1048D8—262no—
1049D8—521no—
1050M16—262no—
1051M16—262no—
1052M16—522no—
1053M16—522no—
1054C2×C8—131no—
1055C2×C8—132no—
1056C2×C8—131no—
1057C2×C8—132no—
1058C2×C8—131no—
1059C2×C8—131no—
1060C2×C8—262no—
1061C2×C8—262no—
1062C2×C8—522no—
1063C2×C8—522no—
1064C4⋊C4—22no—
1065C4⋊C4—21no—
1066C4⋊C4—22no—
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—22no—
1070C4⋊C4—22no—
1071C4⋊C4—132no—
1072C4⋊C4—132no—
1073C4⋊C4—131no—
1074C4⋊C4—131no—
1075C4⋊C4—261no—
1076C4⋊C4—261no—
1077C4⋊C4—262no—
1078C4⋊C4—262no—
1079C4⋊C4—262no—
1080C4⋊C4—262no—
1081C4⋊C4—262no—
1082C4⋊C4—262no—
1083C4⋊C4—261no—
1084C4⋊C4—261no—
1085C4⋊C4—262no—
1086C4⋊C4—262no—
1087C4⋊C4C2×C22⋊D1311yescharacteristic
1088C4⋊C4C2×C22⋊D1312yes—
1089C4⋊C4C2×C22⋊D1311yescharacteristic
1090C4⋊C4C2×C22⋊D1312yes—
1091C4⋊C4C23×D1312yes—
1092C22⋊C4—22no—
1093C22⋊C4—22no—
1094C22⋊C4—22no—
1095C22⋊C4—22no—
1096C22⋊C4—22no—
1097C22⋊C4—22no—
1098C22⋊C4—22no—
1099C22⋊C4—261no—
1100C22⋊C4—262no—
1101C22⋊C4—261no—
1102C22⋊C4—261no—
1103C22⋊C4—262no—
1104C22⋊C4—262no—
1105C22⋊C4—262no—
1106C22⋊C4—261no—
1107C22⋊C4—261no—
1108C22⋊C4C2×C22⋊D1312yes—
1109C22⋊C4C2×C22⋊D1312yes—
1110C22⋊C4C2×C22⋊D1312yes—
1111C22⋊C4C2×C22⋊D1312yes—
1112C22⋊C4C2×C22⋊D1312yes—
1113C42—22no—
1114C42—262no—
1115C42—261no—
1116C42—262no—
1117C42C23×D1312yes—
1118C13#6119311yescharacteristic, complemented, Sylow
1119C23—22no—
1120C23—22no—
1121C23—21no—
1122C23—21no—
1123C23—41no—
1124C23—42no—
1125C23—42no—
1126C23—81no—
1127C23—261no—
1128C23C22×C22⋊D1311yescharacteristic
1129C23C22×C22⋊D1312yes—
1130C23C22×C22⋊D1311yescharacteristic
1131C23C22×C22⋊D1311yescharacteristic
1132Q8—22no—
1133Q8—21no—
1134Q8—22no—
1135Q8—21no—
1136Q8—22no—
1137Q8—21no—
1138Q8—44no—
1139Q8—42no—
1140Q8—42no—
1141Q8—261no—
1142Q8—261no—
1143Q8—1042no—
1144Q8C2×#612912yes—
1145D4—24no—
1146D4—24no—
1147D4—24no—
1148D4—22no—
1149D4—21no—
1150D4—21no—
1151D4—21no—
1152D4—42no—
1153D4—42no—
1154D4—42no—
1155D4—42no—
1156D4—44no—
1157D4—42no—
1158D4—82no—
1159D4—261no—
1160D4—261no—
1161D4—522no—
1162D4—522no—
1163D4—522no—
1164D4—1042no—
1165D4C2×#612912yes—
1166C2×C4—22no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—21no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—44no—
1184C2×C4—44no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—82no—
1188C2×C4—81no—
1189C2×C4—261no—
1190C2×C4—261no—
1191C2×C4—262no—
1192C2×C4—261no—
1193C2×C4—262no—
1194C2×C4—524no—
1195C2×C4—522no—
1196C2×C4—1042no—
1197C2×C4—1041no—
1198C2×C4—1042no—
1199C2×C4—1041no—
1200C2×C4—1042no—
1201C2×C4C2×#612912yes—
1202C2×C4#8825112yes—
1203C2×C4C22×C22⋊D1312yes—
1204C2×C4C22×C22⋊D1312yes—
1205C2×C4C22×C22⋊D1312yes—
1206C2×C4C22×C22⋊D1311yescharacteristic
1207C2×C4C22×C22⋊D1311yescharacteristic
1208C2×C4C22×C22⋊D1311yescharacteristic
1209C2×C4C24×D1311yescharacteristic
1210C8—261no—
1211C8—261no—
1212C8—261no—
1213C8—261no—
1214C8—262no—
1215C8—262no—
1216C22—21no—
1217C22—21no—
1218C22—21no—
1219C22—21no—
1220C22—21no—
1221C22—22no—
1222C22—22no—
1223C22—21no—
1224C22—22no—
1225C22—21no—
1226C22—22no—
1227C22—44no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—84no—
1234C22—521no—
1235C22—521no—
1236C22—521no—
1237C22#1171951112yes—
1238C22#1171954212yes—
1239C22C23×C22⋊D1311yescharacteristic
1240C4—21no—
1241C4—21no—
1242C4—22no—
1243C4—22no—
1244C4—22no—
1245C4—22no—
1246C4—41no—
1247C4—42no—
1248C4—42no—
1249C4—521no—
1250C4—522no—
1251C4—522no—
1252C4—521no—
1253C4—521no—
1254C4#1171951112yes—
1255C4C22×#612911yescharacteristic
1256C4C2×#8825111yescharacteristic
1257C2—22no—
1258C2—22no—
1259C2—41no—
1260C2—42no—
1261C2—42no—
1262C2—81no—
1263C2—1041no—
1264C2C2×#1171951111yescharacteristic
1265C2C2×#1171954211yescharacteristic
1266C2#1312962211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3489C2
socleC22×C13C23×D4
hypercenter#3489D13
hypocenterC13#61193
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #525 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #13128542C2semidirect
2. #13127152C2semidirect
3. #13127089C2semidirect
4. #13126947C2semidirect
5. #13126887C2semidirect
6. #13126812C2semidirect
7. #13126797C2semidirect
8. #13126701C2semidirect
9. #13126671C2semidirect
10. #13125201C2semidirect
11. #13124821C2semidirect
12. C2×#11718704C2semidirect
13. #13124698C2semidirect
14. #13124495C2semidirect
15. #13124462C2semidirect
16. #13124382C2semidirect
17. #13124151C2semidirect
18. #13124054C2semidirect
19. #13123717C2semidirect
20. #13123563C2semidirect
21. #13123369C2semidirect
22. C2×#11718893C2semidirect
23. C13×#3489C2semidirect
41. #11719538C22semidirect
42. #11719532C22semidirect
45. C2×#88202C22semidirect
46. C2×#88196C22semidirect
56. #11719270C22semidirect
58. #11719248C22semidirect
60. #11719228C22semidirect
61. #11719224C22semidirect
64. #11718900C22semidirect
67. #11718899C22semidirect
68. #11718895C22semidirect
71. #11718894C22semidirect
78. #11718893C22semidirect
80. #11718889C22semidirect
82. #11718888C22semidirect
83. #11718886C22semidirect
84. #11718886C22semidirect
86. C2×#88075C22semidirect
87. C2×#88075C22semidirect
88. C2×#88075C22semidirect
93. #11718751C22semidirect
94. #11718744C22semidirect
95. #11718743C22semidirect
96. #11718742C22semidirect
97. #11718718C22semidirect
98. #11718717C22semidirect
99. #11718716C22semidirect
100. #11718715C22semidirect
101. #11718713C22semidirect
102. #11718713C22semidirect
104. #11718710C22semidirect
106. #11718709C22semidirect
107. #11718706C22semidirect
110. #11718704C22semidirect
111. #11718704C22semidirect
112. #11718704C22semidirect
113. #11718702C22semidirect
114. #11718700C22semidirect
115. #11718696C22semidirect
116. #11718695C22semidirect
117. #11718691C22semidirect
118. C4×#6106C22semidirect
119. #11718683C22semidirect
120. #11718681C22semidirect
121. C4×#6105C22semidirect
122. #11718675C22semidirect
123. #11718673C22semidirect
125. #11718672C22semidirect
127. #11718670C22semidirect
128. #11718669C22semidirect
129. #11718660C22semidirect
130. #11718658C22semidirect
131. #11718627C22semidirect
132. #11718625C22semidirect
133. C2×#88048C22semidirect
134. C2×#88048C22semidirect
339. C13×#41#41semidirect
487. #3489D13semidirect
974. #41#6129semidirect
1118. C13#61193semidirect

Maximal subgroups

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

subgroupindex
#131285422
#131271522
#131270892
#131269472
#131268872
#131268122
#131267972
#131267012
#131266712
#131252012
#131248212
C2×#117187042
#131246982
#131244952
#131244622
#131243822
#131241512
#131240542
#131237172
#131235632
#131233692
C2×#117188932
C13×#34892
#6119313