Finite Group Databasebeta

← #33993810

Subgroups — #33993810

Order 18688.

7270 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624358C214yesmaximal, complemented
2#22624345C211yesmaximal, characteristic, complemented
3#22624336C211yesmaximal, characteristic, complemented
4#22624329C212yesmaximal, complemented
5#22624320C214yesmaximal, complemented
6#22624303C214yesmaximal, complemented
7#22624288C214yesmaximal, complemented
8#22624275C212yesmaximal, complemented
9#22624264C212yesmaximal, complemented
10#22624251C218yesmaximal, complemented
11#22624067C214yesmaximal, complemented
12#22623555C212yesmaximal, complemented
13#22623539C212yesmaximal, complemented
14#22623489C214yesmaximal, complemented
15D4×#11924028C214yesmaximal, complemented
16#22623345C218yesmaximal, complemented
17#22623260C214yesmaximal, complemented
18#22623227C212yesmaximal, complemented
19C2×#532×C73C211yesmaximal, characteristic, complemented
20C22×#11924028C2214yescomplemented
21#17989337C2214yescomplemented
22#17989336C2218yescomplemented
23#17989332C22116yescomplemented
24#17989331C2218yescomplemented
25#17989329C2214yescomplemented
26#17989325C22116yescomplemented
27#17989324C2218yescomplemented
28#17989323C2212yescomplemented
29#17989317C2212yescomplemented
30#17989307C2214yescomplemented
31#17989303C2212yescomplemented
32#17989302C2214yescomplemented
33#17989301C2218yescomplemented
34#17989299C2218yescomplemented
35#17989298C2214yescomplemented
36#17989294C2214yescomplemented
37#17989284C2218yescomplemented
38#17989283C2218yescomplemented
39#17989277C2218yescomplemented
40#17989272C2218yescomplemented
41#17989267C2218yescomplemented
42#17989263C22116yescomplemented
43#17989258C2214yescomplemented
44#17989257C2214yescomplemented
45#17989255C2218yescomplemented
46D4×Dic146C2214yescomplemented
47#17989246C2218yescomplemented
48#17989242C2214yescomplemented
49#17989241C2214yescomplemented
50#17989238C2218yescomplemented
51#17989234C2218yescomplemented
52#17989233C2218yescomplemented
53#17989231C2218yescomplemented
54#17989227C22116yescomplemented
55D4×D292C2214yescomplemented
56#17989222C2212yescomplemented
57D4×C22⋊D73C2218yescomplemented
58#17989214C2218yescomplemented
59#17989211C2218yescomplemented
60#17989204C2218yescomplemented
61#17989201C22116yescomplemented
62#17989191C2218yescomplemented
63#17989190C2218yescomplemented
64#17989187C22116yescomplemented
65#17989171C22116yescomplemented
66#17989169C22116yescomplemented
67#17989166C2218yescomplemented
68#17989165C2218yescomplemented
69#17989165C2218yescomplemented
70#17989161C2218yescomplemented
71#17989158C2214yescomplemented
72#17989158C2214yescomplemented
73#17989154C2218yescomplemented
74#17989153C2218yescomplemented
75#17989151C2214yescomplemented
76#17989151C2214yescomplemented
77#17989150C2218yescomplemented
78#17989146C2218yescomplemented
79#17989146C2218yescomplemented
80#17989144C2212yescomplemented
81#17989144C2212yescomplemented
82#17989144C2212yescomplemented
83#17989137C2212yes—
84#17989137C2212yescomplemented
85#17989137C2212yescomplemented
86#17989134C2218yescomplemented
87#17989133C2218yescomplemented
88#17989133C2218yescomplemented
89#17989121C2214yescomplemented
90#17989121C2214yescomplemented
91#17989121C2214yescomplemented
92#17989121C2214yescomplemented
93#17989121C2214yescomplemented
94#17989121C2214yescomplemented
95#17989119C2218yescomplemented
96#17989117C22116yescomplemented
97#17989098C2218yescomplemented
98#17989098C2214yescomplemented
99#17989098C2214yescomplemented
100#17989098C2214yescomplemented
101#17989096C22116yescomplemented
102#17989094C2218yescomplemented
103#17989094C2218yescomplemented
104C4×#11924028C2214yescomplemented
105C4×#11924028C2214yescomplemented
106C4×#11924028C2214yescomplemented
107C4×#11924027C2218yescomplemented
108C4×D4×D73C2218yescomplemented
109C2×#14556550C2214yescomplemented
110C22×#41×C73C2212yescomplemented
111#532×C73C2211yescharacteristic
112#532×C73C2211yescharacteristic
113#532×C73C2214yescomplemented
114#532×C73C2211yescharacteristic, complemented
115#532×C73C2212yescomplemented
116#532×C73C2211yescharacteristic, complemented
117#532×C73C2212yescomplemented
118#532×C73C2214yescomplemented
119C2×C4⋊Q8×C73C2211yescharacteristic, complemented
120C2×#127×C73C2211yescharacteristic
121C2×#124×C73C2212yescomplemented
122C2×#121×C73C2214yescomplemented
123C2×C4×D4×C73C2214yescomplemented
124C22×C42×C73C2211yescharacteristic, complemented
125C2×#11924028—416no—
126C2×#11924028C2314yes—
127C2×#11924028C2318yes—
128C2×#11924028C2314yes—
129C2×#11924028C2314yes—
130C2×#11924028C2318yes—
131C2×#11924028C2318yes—
132C2×#11924027C2318yes—
133C22×Dic146C2314yes—
134C22×D292C2314yes—
135C22×C22⋊D73C2318yes—
136C2×D4×D73C2318yes—
137C22×C4×D73C2318yes—
138#14556591C2312yes—
139#14556591C2312yes—
140#14556591C2312yes—
141#14556590C2318yes—
142#14556589C2318yes—
143#14556589C2318yes—
144#14556588C2312yes—
145#14556587C2318yes—
146#14556587C2318yes—
147#14556587C2318yes—
148#14556586C23116yes—
149#14556585C2318yes—
150#14556585C2318yes—
151#14556584C23116yes—
152#14556584C23116yes—
153#14556583C2314yes—
154#14556583C2314yes—
155#14556583C2314yes—
156#14556582C2318yes—
157#14556581C23116yes—
158#14556580C2318yes—
159#14556580C2318yes—
160#14556579C2314yes—
161#14556579C2314yes—
162#14556579C2314yes—
163#14556578C2318yes—
164#14556578C2318yes—
165#14556578C2318yes—
166#14556577C23116yes—
167#14556577C23116yes—
168#14556576C23116yes—
169#14556575C23116yes—
170#14556574C2318yes—
171#14556574C2318yes—
172#14556574C2318yes—
173#14556574C23116yes—
174#14556573C23116yes—
175#14556573C23116yes—
176#14556572C2318yes—
177#14556572C2318yes—
178#14556572C2318yes—
179#14556572C2318yes—
180#14556572C23116yes—
181#14556571C2318yes—
182#14556570C2314yes—
183#14556570C2314yes—
184#14556570C2314yes—
185#14556570C2314yes—
186#14556570C2314yes—
187#14556570C2314yes—
188#14556570C2318yes—
189#14556570C2318yes—
190#14556569C23116yes—
191#14556568C23116yes—
192#14556568C23116yes—
193#14556567C23116yes—
194#14556567C23116yes—
195#14556566C2318yes—
196#14556565C2314yes—
197#14556565C2314yes—
198#14556565C2314yes—
199#14556565C2314yes—
200#14556565C2314yes—
201#14556565C2314yes—
202#14556565C2318yes—
203#14556565C2318yes—
204#14556564C23116yes—
205#14556564C23116yes—
206#14556563C23116yes—
207#14556563C23116yes—
208#14556563C23116yes—
209#14556563C23116yes—
210#14556563C23116yes—
211#14556563C23116yes—
212#14556562C2318yes—
213#14556562C2318yes—
214#14556562C23116yes—
215#14556562C23116yes—
216#14556561C23116yes—
217#14556560C2318yes—
218#14556560C23116yes—
219#14556559C2318yes—
220#14556559C2318yes—
221#14556559C2318yes—
222#14556559C2318yes—
223#14556559C23116yes—
224C4×Dic146C2314yes—
225C4×Dic146C2314yes—
226C4×Dic146C2314yes—
227C4×Dic146C2314yes—
228C4×Dic146C2314yes—
229C4×Dic146C2314yes—
230#14556556C2318yes—
231C4×D292C2314yes—
232C4×D292C2314yes—
233C4×D292C2314yes—
234C4×D292C2314yes—
235C4×D292C2314yes—
236C4×D292C2314yes—
237D4×Dic73C2318yes—
238D4×Dic73C2318yes—
239#14556553C2318yes—
240C4×C22⋊D73C2318yes—
241C4×C22⋊D73C2318yes—
242C4×C22⋊D73C2318yes—
243C4×C22⋊D73C2318yes—
244C4×C22⋊D73C2318yes—
245C4×C22⋊D73C2318yes—
246C4×C22⋊D73C23116yes—
247C4×C22⋊D73C23116yes—
248#14556551C23116yes—
249#14556551C23116yes—
250#14556550C2314yes—
251#14556550C2314yes—
252#14556550C2314yes—
253#14556550C2314yes—
254#14556550C2314yes—
255#14556550C2318yes—
256#14556550C2318yes—
257#14556549C2318yes—
258#14556548C2318yes—
259#14556548C2318yes—
260#14556548C2318yes—
261#14556547C23116yes—
262C2×C4⋊Dic73C2318yes—
263C4⋊C4×D73C2318yes—
264C2×C22⋊Dic73C2318yes—
265C22⋊C4×D73C23116yes—
266C2×C4×Dic73C2318yes—
267C42×D73C2318yes—
268C2×#41×C73—48no—
269C2×#41×C73C2312yes—
270C2×#41×C73C2314yes—
271C2×#41×C73C2312yes—
272C2×#41×C73C2314yes—
273C2×#41×C73C2312yes—
274C2×#41×C73C2312yes—
275C22×Q8×C73C2312yes—
276C22×D4×C73C2312yes—
277C22×D4×C73C2314yes—
278C22×D4×C73C2314yes—
279C23×C4×C73C2314yes—
280C23×C4×C73C2311yescharacteristic
281C23×C4×C73C2312yes—
282C4⋊Q8×C73C2314yes—
283C4⋊Q8×C73C2311yescharacteristic
284C4⋊Q8×C73C2311yescharacteristic
285C4⋊Q8×C73C2312yes—
286#127×C73C2314yes—
287#127×C73C2311yescharacteristic
288#127×C73C2311yescharacteristic
289#127×C73C2312yes—
290#124×C73C2318yes—
291#124×C73C2312yes—
292#124×C73C2312yes—
293#124×C73C2312yes—
294#124×C73C2312yes—
295#121×C73C2314yes—
296#121×C73C2314yes—
297#121×C73C2318yes—
298#121×C73C2314yes—
299#121×C73C2314yes—
300#121×C73C2318yes—
301C4×D4×C73C2314yes—
302C4×D4×C73C2314yes—
303C4×D4×C73C2318yes—
304C4×D4×C73C2314yes—
305C4×D4×C73C2314yes—
306C4×D4×C73C2318yes—
307C2×C4⋊C4×C73C2314yes—
308C2×C22⋊C4×C73C2318yes—
309C2×C42×C73C2311yescharacteristic
310C2×C42×C73C2311yescharacteristic
311C2×C42×C73C2311yescharacteristic
312C2×C42×C73C2311yescharacteristic
313C2×C42×C73C2312yes—
314C2×C42×C73C2312yes—
315C2×C42×C73C2312yes—
316C2×C42×C73C2311yescharacteristic
317C2×C42×C73C2311yescharacteristic
318C23×D73C2418yes—
319#11924028—216no—
320#11924028—416no—
321#11924028—48no—
322#11924028—416no—
323#11924028—48no—
324#11924028—416no—
325#11924027—416no—
326C2×Dic146—48no—
327C2×Dic146C2414yes—
328C2×Dic146C2414yes—
329C2×Dic146C2414yes—
330C2×Dic146C2418yes—
331C2×D292—48no—
332C2×D292C2414yes—
333C2×D292C2414yes—
334C2×D292C2414yes—
335C2×D292C2418yes—
336C2×C22⋊D73—416no—
337C2×C22⋊D73C2418yes—
338C2×C22⋊D73C24116yes—
339C2×C22⋊D73C24116yes—
340C2×C22⋊D73C2418yes—
341C2×C22⋊D73C2418yes—
342C2×C22⋊D73C24116yes—
343D4×D73—416no—
344C22×Dic73C24116yes—
345C22×Dic73C2418yes—
346C2×C4×D73—416no—
347C2×C4×D73C2418yes—
348C2×C4×D73C2418yes—
349C2×C4×D73C2418yes—
350C2×C4×D73C24116yes—
351C4⋊Dic73C2414yes—
352C4⋊Dic73C2414yes—
353C4⋊Dic73C2414yes—
354C4⋊Dic73C24116yes—
355C4⋊Dic73C2414yes—
356C4⋊Dic73C2414yes—
357C4⋊Dic73C2414yes—
358#11924007C24116yes—
359#11924007C2418yes—
360#11924007C24116yes—
361#11924007C2418yes—
362#11924007C2418yes—
363#11924007C2418yes—
364#11924007C2418yes—
365#11924007C2418yes—
366C22⋊Dic73C24116yes—
367C22⋊Dic73C2418yes—
368C22⋊Dic73C2418yes—
369C22⋊Dic73C2418yes—
370C22⋊Dic73C24116yes—
371C22⋊Dic73C2418yes—
372C22⋊Dic73C2418yes—
373#11924005C2418yes—
374#11924005C24116yes—
375#11924005C2418yes—
376#11924005C2418yes—
377#11924005C2418yes—
378#11924005C2418yes—
379#11924005C2418yes—
380#11924005C24116yes—
381C4×Dic73C2418yes—
382C4×Dic73C2418yes—
383C4×Dic73C2418yes—
384C4×Dic73C2418yes—
385C4×Dic73C2418yes—
386C24×C73C2414yes—
387C24×C73C2411yescharacteristic
388#41×C73—44no—
389#41×C73—48no—
390#41×C73—44no—
391#41×C73—48no—
392#41×C73—44no—
393#41×C73—44no—
394C2×Q8×C73—44no—
395C2×Q8×C73C2412yes—
396C2×Q8×C73C2414yes—
397C2×Q8×C73C2412yes—
398C2×D4×C73—48no—
399C2×D4×C73—44no—
400C2×D4×C73—48no—
401C2×D4×C73C2414yes—
402C2×D4×C73C2414yes—
403C2×D4×C73C2418yes—
404C2×D4×C73C2414yes—
405C2×D4×C73C2414yes—
406C2×D4×C73C2414yes—
407C2×D4×C73C2414yes—
408C2×D4×C73C2412yes—
409C2×D4×C73C2414yes—
410C2×D4×C73C2412yes—
411C22×C4×C73—24no—
412C22×C4×C73—216no—
413C22×C4×C73—44no—
414C22×C4×C73C2412yes—
415C22×C4×C73C2412yes—
416C22×C4×C73C2412yes—
417C22×C4×C73C2411yescharacteristic
418C22×C4×C73C2411yescharacteristic
419C22×C4×C73C2411yescharacteristic
420C22×C4×C73C2411yescharacteristic
421C22×C4×C73C2411yescharacteristic
422C22×C4×C73C2414yes—
423C22×C4×C73C2414yes—
424C22×C4×C73C2414yes—
425C22×C4×C73C2414yes—
426C22×C4×C73C2414yes—
427C22×C4×C73C2412yes—
428C22×C4×C73C2412yes—
429C22×C4×C73C2412yes—
430C22×C4×C73C2411yescharacteristic
431C4⋊C4×C73C2414yes—
432C4⋊C4×C73C2414yes—
433C4⋊C4×C73C2418yes—
434C22⋊C4×C73C2418yes—
435C22⋊C4×C73C2418yes—
436C22⋊C4×C73C2418yes—
437C22⋊C4×C73C2418yes—
438C42×C73C2412yes—
439C42×C73C2412yes—
440C42×C73C2412yes—
441C42×C73C2412yes—
442C42×C73C2411yescharacteristic
443C42×C73C2412yes—
444C42×C73C2411yescharacteristic
445C42×C73C2412yes—
446C42×C73C2411yescharacteristic
447C42×C73C2411yescharacteristic
448C23×C73—22no—
449C23×C73—28no—
450C23×C73—42no—
451C23×C73—48no—
452C23×C73C2514yes—
453C23×C73C2514yes—
454C23×C73C2511yescharacteristic
455C23×C73C2511yescharacteristic
456C23×C73C2511yescharacteristic
457C22×D73—48no—
458C22×D73—416no—
459C22×D73C2518yes—
460Q8×C73—42no—
461Q8×C73—44no—
462Q8×C73—42no—
463D4×C73—28no—
464D4×C73—28no—
465D4×C73—48no—
466D4×C73—44no—
467D4×C73—44no—
468D4×C73—44no—
469D4×C73—44no—
470D4×C73—42no—
471D4×C73—44no—
472D4×C73—42no—
473C2×C4×C73—22no—
474C2×C4×C73—28no—
475C2×C4×C73—22no—
476C2×C4×C73—22no—
477C2×C4×C73—22no—
478C2×C4×C73—22no—
479C2×C4×C73—28no—
480C2×C4×C73—28no—
481C2×C4×C73—28no—
482C2×C4×C73—28no—
483C2×C4×C73—24no—
484C2×C4×C73—24no—
485C2×C4×C73—24no—
486C2×C4×C73—42no—
487C2×C4×C73—42no—
488C2×C4×C73—42no—
489C2×C4×C73H(5,𝔽2)14yes—
490C2×C4×C73C2512yes—
491C2×C4×C73C2512yes—
492C2×C4×C73C2512yes—
493C2×C4×C73C2511yescharacteristic
494C2×C4×C73C2511yescharacteristic
495C2×C4×C73C2514yes—
496C2×C4×C73C2514yes—
497C2×C4×C73C2511yescharacteristic
498C2×C4×C73C2512yes—
499C2×C4×C73C2511yescharacteristic
500C22⋊D73—216no—
501C22⋊D73—416no—
502C22⋊D73—416no—
503C22⋊D73—416no—
504C22⋊D73—48no—
505C22⋊D73—48no—
506C2×Dic73—48no—
507C2×Dic73—416no—
508C2×Dic73C2518yes—
509C2×Dic73C2518yes—
510C2×Dic73C2518yes—
511D292—28no—
512D292—28no—
513D292—48no—
514D292—44no—
515C4×D73—216no—
516C4×D73—216no—
517C4×D73—416no—
518C4×D73—48no—
519Dic146—28no—
520Dic146—28no—
521Dic146—48no—
522Dic146—44no—
523C22×C73—22no—
524C22×C73—24no—
525C22×C73—24no—
526C22×C73—21no—
527C22×C73—21no—
528C22×C73—28no—
529C22×C73—22no—
530C22×C73—22no—
531C22×C73—28no—
532C22×C73—44no—
533C22×C73—88no—
534C22×C73C2×H(5,𝔽2)12yes—
535C22×C73C2611yescharacteristic
536C2×D73—28no—
537C2×D73—28no—
538C2×D73—28no—
539C2×D73—816no—
540C4×C73—24no—
541C4×C73—24no—
542C4×C73—21no—
543C4×C73—21no—
544C4×C73—22no—
545C4×C73—22no—
546C4×C73—22no—
547C4×C73C2×H(5,𝔽2)12yes—
548C4×C73C2×H(5,𝔽2)12yes—
549C4×C73#58514yes—
550Dic73—28no—
551Dic73—28no—
552Dic73—28no—
553#62759—731nomaximal, Sylow
554C2×C73—22no—
555C2×C73—44no—
556C2×C73—41no—
557C2×C73—41no—
558C2×C73—44no—
559C2×C73C22×H(5,𝔽2)11yescharacteristic
560C2×C73C2×#58512yes—
561D73—48no—
562#3551—734no—
563#3550—731no—
564#3549—731no—
565#3548—732no—
566#3547—734no—
567#3546—734no—
568#3545—734no—
569#3544—732no—
570#3543—732no—
571#3542—738no—
572#3529—734no—
573#3483—732no—
574#3481—732no—
575#3475—734no—
576D4×#41—734no—
577#3460—738no—
578#3449—734no—
579#3444—732no—
580C2×#532D7311yescharacteristic, complemented
581C73#6275911yescharacteristic, complemented, Sylow
582C22×#41—734no—
583C22×#41C2×D7312yescomplemented
584#563—738no—
585#563—734no—
586#562—738no—
587#562—7316no—
588H(3,𝔽4)—734no—
589#560—738no—
590#560—7316no—
591#559—732no—
592Q82—732no—
593#556—734no—
594#555—732no—
595#555—738no—
596#555—738no—
597#555—734no—
598#554—734no—
599#554—734no—
600#553—738no—
601#553—738no—
602#552—738no—
603#552—738no—
604#551—738no—
605#551—7316no—
606#550—734no—
607#550—738no—
608#550—734no—
609D4×Q8—734no—
610#548—738no—
611#547—734no—
612#547—734no—
613#547—738no—
614#546—738no—
615#546—738no—
616#546—738no—
617#546—7316no—
618D42—738no—
619D42—732no—
620D42—734no—
621#544—738no—
622#542—738no—
623#542—7316no—
624#542—738no—
625#540—738no—
626#540—7316no—
627#540—738no—
628#538—7316no—
629#538—7316no—
630#537—738no—
631#537—738no—
632#537—738no—
633#536—734no—
634#536—734no—
635#536—738no—
636#535—734no—
637#535—734no—
638#535—738no—
639#535—738no—
640#535—738no—
641#534—738no—
642#534—738no—
643#533—732no—
644#533—732no—
645#533—732no—
646#532—738no—
647#532—738no—
648#532—738no—
649#532—732no—
650#532—732no—
651#532—732no—
652#532C2×D7311yescharacteristic
653#532C2×D7311yescharacteristic
654#532C2×D7314yescomplemented
655#532C2×D7311yescharacteristic, complemented
656#532C2×D7312yescomplemented
657#532C2×D7314yescomplemented
658#532C2×D7311yescharacteristic, complemented
659#532C2×D7312yescomplemented
660C2×C4⋊Q8C2×D7311yescharacteristic, complemented
661C2×#127C2×D7311yescharacteristic
662#529—738no—
663#529—7316no—
664#529—734no—
665#529—734no—
666#529—734no—
667#529—734no—
668#529—734no—
669#529—734no—
670C2×#124C2×D7312yescomplemented
671#525—738no—
672#525—738no—
673#525—734no—
674#525—734no—
675#525—734no—
676#525—738no—
677#525—7316no—
678C2×#121C2×D7314yescomplemented
679C4×#41—738no—
680C4×#41—734no—
681C4×#41—734no—
682C4×#41—734no—
683C2×C4×D4—738no—
684C2×C4×D4C2×D7314yescomplemented
685C2×#117—734no—
686C22×C42C2×D7311yescharacteristic, complemented
687C2×#41—48no—
688C2×#41—29216no—
689C2×#41—738no—
690C2×#41—734no—
691C2×#41—734no—
692C2×#41—738no—
693C2×#41—738no—
694C2×#41—738no—
695C2×#41—734no—
696C2×#41C22×D7312yes—
697C2×#41C22×D7314yes—
698C2×#41C22×D7312yes—
699C2×#41C22×D7312yes—
700C2×#41C22×D7314yes—
701C2×#41C22×D7312yes—
702C22×Q8—734no—
703C22×Q8C22×D7312yes—
704C22×D4—738no—
705C22×D4—738no—
706C22×D4—734no—
707C22×D4C22×D7314yes—
708C22×D4C22×D7314yes—
709C22×D4C22×D7312yes—
710C23×C4—738no—
711C23×C4C22×D7314yes—
712C23×C4C22×D7311yescharacteristic
713C23×C4C22×D7312yes—
714C4⋊Q8—738no—
715C4⋊Q8—738no—
716C4⋊Q8—738no—
717C4⋊Q8—732no—
718C4⋊Q8—732no—
719C4⋊Q8—732no—
720C4⋊Q8C22×D7311yescharacteristic
721C4⋊Q8C22×D7311yescharacteristic
722C4⋊Q8C22×D7314yes—
723C4⋊Q8C22×D7312yes—
724#127—738no—
725#127—738no—
726#127—738no—
727#127—732no—
728#127C22×D7311yescharacteristic
729#127C22×D7314yes—
730#127C22×D7311yescharacteristic
731#127C22×D7312yes—
732#126—7316no—
733#126—7316no—
734#126—7316no—
735#126—738no—
736#126—738no—
737#125—7316no—
738#125—738no—
739#125—734no—
740#125—734no—
741#125—734no—
742#124—738no—
743#124—738no—
744#124—738no—
745#124—738no—
746#124—738no—
747#124—7316no—
748#124—7316no—
749#124—734no—
750#124—734no—
751#124—734no—
752#124C22×D7312yes—
753#124C22×D7312yes—
754#124C22×D7318yes—
755#124C22×D7312yes—
756#124C22×D7312yes—
757#123—738no—
758#123—738no—
759#123—738no—
760#123—738no—
761#123—7316no—
762#123—738no—
763#123—738no—
764#123—738no—
765#123—7316no—
766#123—7316no—
767#123—7316no—
768#123—7316no—
769#123—7316no—
770C22⋊Q8—7316no—
771C22⋊Q8—7316no—
772C22⋊Q8—734no—
773C22⋊Q8—734no—
774C22⋊Q8—734no—
775C22⋊Q8—734no—
776C22⋊Q8—734no—
777C22⋊Q8—734no—
778C22⋊Q8—738no—
779C22⋊Q8—738no—
780C22⋊Q8—7316no—
781C22⋊Q8—738no—
782C22⋊Q8—7316no—
783C22⋊Q8—7316no—
784#121—7316no—
785#121—7316no—
786#121—7316no—
787#121—738no—
788#121—7316no—
789#121—7316no—
790#121—7316no—
791#121—7316no—
792#121—7316no—
793#121—738no—
794#121—734no—
795#121—734no—
796#121—734no—
797#121—734no—
798#121—734no—
799#121—734no—
800#121—738no—
801#121—738no—
802#121—738no—
803#121—7316no—
804#121—7316no—
805#121C22×D7314yes—
806#121C22×D7314yes—
807#121C22×D7314yes—
808#121C22×D7318yes—
809#121C22×D7314yes—
810#121C22×D7318yes—
811#120—738no—
812#120—7316no—
813#120—738no—
814#120—738no—
815#120—738no—
816#120—738no—
817#120—7316no—
818#120—7316no—
819C4×Q8—738no—
820C4×Q8—734no—
821C4×Q8—734no—
822C4×Q8—734no—
823C4×Q8—734no—
824C4×Q8—734no—
825C4×Q8—734no—
826C4×D4—738no—
827C4×D4—738no—
828C4×D4—7316no—
829C4×D4—7316no—
830C4×D4—738no—
831C4×D4—738no—
832C4×D4—738no—
833C4×D4—738no—
834C4×D4—738no—
835C4×D4—738no—
836C4×D4—738no—
837C4×D4—7316no—
838C4×D4—7316no—
839C4×D4—734no—
840C4×D4—734no—
841C4×D4—734no—
842C4×D4—734no—
843C4×D4—734no—
844C4×D4—734no—
845C4×D4C22×D7314yes—
846C4×D4C22×D7314yes—
847C4×D4C22×D7318yes—
848C4×D4C22×D7314yes—
849C4×D4C22×D7318yes—
850C4×D4C22×D7314yes—
851#117—734no—
852#117—738no—
853#117—738no—
854#117—734no—
855#117—734no—
856#117—734no—
857#117—734no—
858#117—738no—
859#117—7316no—
860#117—738no—
861#117—738no—
862#117—738no—
863C2×C4⋊C4—738no—
864C2×C4⋊C4—738no—
865C2×C4⋊C4C22×D7314yes—
866C2×C22⋊C4—738no—
867C2×C22⋊C4—7316no—
868C2×C22⋊C4C22×D7318yes—
869C2×C42—738no—
870C2×C42—738no—
871C2×C42C22×D7312yes—
872C2×C42C22×D7311yescharacteristic
873C2×C42C22×D7312yes—
874C2×C42C22×D7311yescharacteristic
875C2×C42C22×D7311yescharacteristic
876C2×C42C22×D7311yescharacteristic
877C2×C42C22×D7311yescharacteristic
878C2×C42C22×D7312yes—
879C2×C42C22×D7311yescharacteristic
880C24—738no—
881C24C23×D7314yes—
882C24C23×D7311yescharacteristic
883#41—44no—
884#41—48no—
885#41—44no—
886#41—48no—
887#41—44no—
888#41—44no—
889#41—29216no—
890#41—2928no—
891#41—29216no—
892#41—29216no—
893#41—2928no—
894#41—29216no—
895#41—14616no—
896C2×Q8—44no—
897C2×Q8—2928no—
898C2×Q8—734no—
899C2×Q8—738no—
900C2×Q8—734no—
901C2×Q8—734no—
902C2×Q8C23×D7312yes—
903C2×Q8C23×D7314yes—
904C2×Q8C23×D7312yes—
905C2×D4—48no—
906C2×D4—44no—
907C2×D4—48no—
908C2×D4—2928no—
909C2×D4—29216no—
910C2×D4—29216no—
911C2×D4—7316no—
912C2×D4—738no—
913C2×D4—738no—
914C2×D4—7316no—
915C2×D4—7316no—
916C2×D4—738no—
917C2×D4—734no—
918C2×D4—738no—
919C2×D4—734no—
920C2×D4—734no—
921C2×D4C23×D7314yes—
922C2×D4C23×D7314yes—
923C2×D4C23×D7318yes—
924C2×D4C23×D7312yes—
925C2×D4C23×D7314yes—
926C2×D4C23×D7314yes—
927C2×D4C23×D7314yes—
928C2×D4C23×D7314yes—
929C2×D4C23×D7312yes—
930C2×D4C23×D7314yes—
931C22×C4—24no—
932C22×C4—216no—
933C22×C4—44no—
934C22×C4—29216no—
935C22×C4—7316no—
936C22×C4—738no—
937C22×C4—738no—
938C22×C4—7316no—
939C22×C4—738no—
940C22×C4—738no—
941C22×C4C23×D7312yes—
942C22×C4C23×D7312yes—
943C22×C4C23×D7312yes—
944C22×C4C23×D7311yescharacteristic
945C22×C4C23×D7311yescharacteristic
946C22×C4C23×D7311yescharacteristic
947C22×C4C23×D7314yes—
948C22×C4C23×D7314yes—
949C22×C4C23×D7314yes—
950C22×C4C23×D7314yes—
951C22×C4C23×D7311yescharacteristic
952C22×C4C23×D7311yescharacteristic
953C22×C4C23×D7314yes—
954C22×C4C23×D7312yes—
955C22×C4C23×D7312yes—
956C22×C4C23×D7312yes—
957C22×C4C23×D7311yescharacteristic
958C4⋊C4—7316no—
959C4⋊C4—738no—
960C4⋊C4—738no—
961C4⋊C4—738no—
962C4⋊C4—7316no—
963C4⋊C4—738no—
964C4⋊C4—738no—
965C4⋊C4—738no—
966C4⋊C4—734no—
967C4⋊C4—734no—
968C4⋊C4—734no—
969C4⋊C4—7316no—
970C4⋊C4—734no—
971C4⋊C4—734no—
972C4⋊C4—734no—
973C4⋊C4C23×D7314yes—
974C4⋊C4C23×D7314yes—
975C4⋊C4C23×D7318yes—
976C22⋊C4—738no—
977C22⋊C4—738no—
978C22⋊C4—738no—
979C22⋊C4—7316no—
980C22⋊C4—738no—
981C22⋊C4—738no—
982C22⋊C4—7316no—
983C22⋊C4—738no—
984C22⋊C4—7316no—
985C22⋊C4—738no—
986C22⋊C4—7316no—
987C22⋊C4—738no—
988C22⋊C4—738no—
989C22⋊C4—738no—
990C22⋊C4—738no—
991C22⋊C4C23×D7318yes—
992C22⋊C4C23×D7318yes—
993C22⋊C4C23×D7318yes—
994C22⋊C4C23×D7318yes—
995C42—738no—
996C42—738no—
997C42—738no—
998C42—738no—
999C42—738no—
1000C42C23×D7311yescharacteristic
1001C42C23×D7312yes—
1002C42C23×D7311yescharacteristic
1003C42C23×D7312yes—
1004C42C23×D7312yes—
1005C42C23×D7312yes—
1006C42C23×D7311yescharacteristic
1007C42C23×D7311yescharacteristic
1008C42C23×D7312yes—
1009C42C23×D7312yes—
1010C23—22no—
1011C23—28no—
1012C23—42no—
1013C23—48no—
1014C23—2928no—
1015C23—29216no—
1016C23—738no—
1017C23C24×D7314yes—
1018C23C24×D7311yescharacteristic
1019C23C24×D7311yescharacteristic
1020C23C24×D7314yes—
1021C23C24×D7311yescharacteristic
1022Q8—42no—
1023Q8—44no—
1024Q8—42no—
1025Q8—2928no—
1026Q8—2924no—
1027Q8—1468no—
1028Q8—1468no—
1029D4—28no—
1030D4—28no—
1031D4—44no—
1032D4—44no—
1033D4—42no—
1034D4—44no—
1035D4—42no—
1036D4—44no—
1037D4—44no—
1038D4—48no—
1039D4—2928no—
1040D4—2924no—
1041D4—29216no—
1042D4—29216no—
1043D4—2928no—
1044D4—29216no—
1045D4—2928no—
1046D4—14616no—
1047D4—1468no—
1048D4—1468no—
1049C2×C4—22no—
1050C2×C4—28no—
1051C2×C4—28no—
1052C2×C4—28no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—28no—
1058C2×C4—28no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—42no—
1063C2×C4—42no—
1064C2×C4—42no—
1065C2×C4—29216no—
1066C2×C4—2928no—
1067C2×C4—2928no—
1068C2×C4—29216no—
1069C2×C4—738no—
1070C2×C4—738no—
1071C2×C4—738no—
1072C2×C4—14616no—
1073C2×C4—14616no—
1074C2×C4#1455663614yes—
1075C2×C4C24×D7312yes—
1076C2×C4C24×D7314yes—
1077C2×C4C24×D7312yes—
1078C2×C4C24×D7311yescharacteristic
1079C2×C4C24×D7311yescharacteristic
1080C2×C4C24×D7312yes—
1081C2×C4C24×D7314yes—
1082C2×C4C24×D7311yescharacteristic
1083C2×C4C24×D7312yes—
1084C2×C4C24×D7311yescharacteristic
1085C22—22no—
1086C22—24no—
1087C22—21no—
1088C22—21no—
1089C22—24no—
1090C22—22no—
1091C22—22no—
1092C22—28no—
1093C22—28no—
1094C22—44no—
1095C22—88no—
1096C22—58416no—
1097C22—1468no—
1098C22—1468no—
1099C22—1468no—
1100C22C2×#1455663612yes—
1101C22C25×D7311yescharacteristic
1102C4—24no—
1103C4—21no—
1104C4—21no—
1105C4—24no—
1106C4—22no—
1107C4—22no—
1108C4—22no—
1109C4—1468no—
1110C4—1468no—
1111C4—1468no—
1112C4C2×#1455663612yes—
1113C4C2×#1455663612yes—
1114C4#1798942314yes—
1115C2—22no—
1116C2—41no—
1117C2—41no—
1118C2—44no—
1119C2—44no—
1120C2—2928no—
1121C2C22×#1455663611yescharacteristic
1122C2C2×#1798942312yes—
subgroupG/H
centerC2×C4C24×D73
commutator, socle, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#532×C73C2
hypercenterC2×#532D73
hypocenterC73#62759
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #22624358C2semidirect
2. #22624345C2semidirect
3. #22624336C2semidirect
4. #22624329C2semidirect
5. #22624320C2semidirect
6. #22624303C2semidirect
7. #22624288C2semidirect
8. #22624275C2semidirect
9. #22624264C2semidirect
10. #22624251C2semidirect
11. #22624067C2semidirect
12. #22623555C2semidirect
13. #22623539C2semidirect
14. #22623489C2semidirect
15. D4×#11924028C2semidirect
16. #22623345C2semidirect
17. #22623260C2semidirect
18. #22623227C2semidirect
19. C2×#532×C73C2semidirect
20. C22×#11924028C22semidirect
21. #17989337C22semidirect
22. #17989336C22semidirect
23. #17989332C22semidirect
24. #17989331C22semidirect
25. #17989329C22semidirect
26. #17989325C22semidirect
27. #17989324C22semidirect
28. #17989323C22semidirect
29. #17989317C22semidirect
30. #17989307C22semidirect
31. #17989303C22semidirect
32. #17989302C22semidirect
33. #17989301C22semidirect
34. #17989299C22semidirect
35. #17989298C22semidirect
36. #17989294C22semidirect
37. #17989284C22semidirect
38. #17989283C22semidirect
39. #17989277C22semidirect
40. #17989272C22semidirect
41. #17989267C22semidirect
42. #17989263C22semidirect
43. #17989258C22semidirect
44. #17989257C22semidirect
45. #17989255C22semidirect
46. D4×Dic146C22semidirect
47. #17989246C22semidirect
48. #17989242C22semidirect
49. #17989241C22semidirect
50. #17989238C22semidirect
51. #17989234C22semidirect
52. #17989233C22semidirect
53. #17989231C22semidirect
54. #17989227C22semidirect
55. D4×D292C22semidirect
56. #17989222C22semidirect
57. D4×C22⋊D73C22semidirect
58. #17989214C22semidirect
59. #17989211C22semidirect
60. #17989204C22semidirect
61. #17989201C22semidirect
62. #17989191C22semidirect
63. #17989190C22semidirect
64. #17989187C22semidirect
65. #17989171C22semidirect
66. #17989169C22semidirect
67. #17989166C22semidirect
68. #17989165C22semidirect
69. #17989165C22semidirect
70. #17989161C22semidirect
71. #17989158C22semidirect
72. #17989158C22semidirect
73. #17989154C22semidirect
74. #17989153C22semidirect
75. #17989151C22semidirect
76. #17989151C22semidirect
77. #17989150C22semidirect
78. #17989146C22semidirect
79. #17989146C22semidirect
80. #17989144C22semidirect
81. #17989144C22semidirect
82. #17989144C22semidirect
84. #17989137C22semidirect
85. #17989137C22semidirect
86. #17989134C22semidirect
87. #17989133C22semidirect
88. #17989133C22semidirect
89. #17989121C22semidirect
90. #17989121C22semidirect
91. #17989121C22semidirect
92. #17989121C22semidirect
93. #17989121C22semidirect
94. #17989121C22semidirect
95. #17989119C22semidirect
96. #17989117C22semidirect
97. #17989098C22semidirect
98. #17989098C22semidirect
99. #17989098C22semidirect
100. #17989098C22semidirect
101. #17989096C22semidirect
102. #17989094C22semidirect
103. #17989094C22semidirect
104. C4×#11924028C22semidirect
105. C4×#11924028C22semidirect
106. C4×#11924028C22semidirect
107. C4×#11924027C22semidirect
108. C4×D4×D73C22semidirect
109. C2×#14556550C22semidirect
110. C22×#41×C73C22semidirect
113. #532×C73C22semidirect
114. #532×C73C22semidirect
115. #532×C73C22semidirect
116. #532×C73C22semidirect
117. #532×C73C22semidirect
118. #532×C73C22semidirect
119. C2×C4⋊Q8×C73C22semidirect
121. C2×#124×C73C22semidirect
122. C2×#121×C73C22semidirect
123. C2×C4×D4×C73C22semidirect
124. C22×C42×C73C22semidirect
580. C2×#532D73semidirect
581. C73#62759semidirect
583. C22×#41C2×D73semidirect
654. #532C2×D73semidirect
655. #532C2×D73semidirect
656. #532C2×D73semidirect
657. #532C2×D73semidirect
658. #532C2×D73semidirect
659. #532C2×D73semidirect
660. C2×C4⋊Q8C2×D73semidirect
670. C2×#124C2×D73semidirect
678. C2×#121C2×D73semidirect
684. C2×C4×D4C2×D73semidirect
686. C22×C42C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226243582
#226243452
#226243362
#226243292
#226243202
#226243032
#226242882
#226242752
#226242642
#226242512
#226240672
#226235552
#226235392
#226234892
D4×#119240282
#226233452
#226232602
#226232272
C2×#532×C732
#6275973