Finite Group Databasebeta

← #33993814

Subgroups — #33993814

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#22624355C214yesmaximal, complemented
2#22624345C211yesmaximal, characteristic, complemented
3#22624329C212yesmaximal, complemented
4#22624323C214yesmaximal, complemented
5#22624299C214yesmaximal, complemented
6#22624286C214yesmaximal, complemented
7#22624266C212yesmaximal, complemented
8#22624262C212yesmaximal, complemented
9#22624249C218yesmaximal, complemented
10#22624071C214yesmaximal, complemented
11#22623556C212yesmaximal, complemented
12#22623532C212yesmaximal, complemented
13#22623488C214yesmaximal, complemented
14D4×#11924027C214yesmaximal, complemented
15#22623344C218yesmaximal, complemented
16#22623262C214yesmaximal, complemented
17#22623226C212yesmaximal, complemented
18#532×D73C211yesmaximal, characteristic, complemented
19C73×#3549C211yesmaximal, characteristic, complemented
20C22×#11924027C2214yescomplemented
21C2×#41×D73C2212yescomplemented
22#17989337C2218yescomplemented
23#17989337C2214yescomplemented
24#17989331C2218yescomplemented
25#17989331C22116yescomplemented
26#17989326C2218yescomplemented
27#17989326C22116yescomplemented
28#17989323C2212yescomplemented
29#17989317C2212yescomplemented
30#17989307C2214yescomplemented
31#17989300C2218yescomplemented
32#17989299C2218yescomplemented
33#17989298C2214yescomplemented
34#17989294C2214yescomplemented
35#17989289C2218yescomplemented
36#17989284C2218yescomplemented
37#17989276C2218yescomplemented
38#17989276C2218yescomplemented
39#17989268C2218yescomplemented
40#17989267C22116yescomplemented
41#17989258C2214yescomplemented
42#17989257C2214yescomplemented
43#17989255C2218yescomplemented
44D4×Dic146C2214yescomplemented
45#17989243C2218yescomplemented
46#17989242C2214yescomplemented
47#17989241C2214yescomplemented
48#17989237C2218yescomplemented
49#17989234C2218yescomplemented
50#17989231C2218yescomplemented
51#17989231C2218yescomplemented
52#17989224C22116yescomplemented
53D4×C22⋊D73C2218yescomplemented
54#17989215C2218yescomplemented
55#17989206C22116yescomplemented
56#17989204C2218yescomplemented
57#17989204C2218yescomplemented
58#17989191C22116yescomplemented
59#17989190C2218yescomplemented
60#17989190C2218yescomplemented
61#17989172C22116yescomplemented
62#17989172C22116yescomplemented
63#17989166C2218yescomplemented
64#17989166C2218yescomplemented
65#17989165C2218yescomplemented
66#17989163C2214yescomplemented
67#17989158C2214yescomplemented
68#17989157C2218yescomplemented
69#17989154C2218yescomplemented
70#17989154C2214yescomplemented
71#17989150C2218yescomplemented
72#17989147C2218yescomplemented
73#17989147C2218yescomplemented
74#17989144C2212yescomplemented
75#17989142C2212yescomplemented
76#17989142C2212yescomplemented
77#17989138C2211yescharacteristic, complemented
78#17989137C2211yescharacteristic, complemented
79#17989136C2218yescomplemented
80#17989136C2212yescomplemented
81#17989135C2211yescharacteristic
82#17989135C2212yes—
83#17989135C2218yescomplemented
84#17989135C2212yescomplemented
85#17989134C2214yescomplemented
86#17989133C2212yescomplemented
87#17989132C2218yescomplemented
88#17989132C2214yescomplemented
89C4⋊Q8×D73C2211yescharacteristic, complemented
90#127×D73C2211yescharacteristic
91#17989119C2214yescomplemented
92#17989119C2214yescomplemented
93#17989118C2218yescomplemented
94#17989118C2214yescomplemented
95#17989118C2214yescomplemented
96#17989116C22116yescomplemented
97#17989116C2214yescomplemented
98#17989116C2214yescomplemented
99#124×D73C2212yescomplemented
100#17989097C2218yescomplemented
101#17989097C2214yescomplemented
102#17989097C2214yescomplemented
103#17989094C2214yescomplemented
104#17989093C2218yescomplemented
105#17989093C2218yescomplemented
106#17989093C22116yescomplemented
107#121×D73C2214yescomplemented
108#41×Dic73C2214yescomplemented
109#17989055C2218yescomplemented
110C4×#11924027C2214yescomplemented
111C4×#11924027C2214yescomplemented
112C2×D4×Dic73C2218yescomplemented
113C4×D4×D73C2214yescomplemented
114#117×D73C2214yescomplemented
115C2×C42×D73C2211yescharacteristic, complemented
116H(3,𝔽4)×C73C2214yescomplemented
117#555×C73C2214yescomplemented
118#555×C73C2212yescomplemented
119D42×C73C2212yescomplemented
120D42×C73C2214yescomplemented
121#535×C73C2214yescomplemented
122#535×C73C2218yescomplemented
123#532×C73C2211yescharacteristic
124#532×C73C2212yescomplemented
125C2×#11924029C2312yes—
126C2×#11924028C2312yes—
127C2×#11924028C2314yes—
128C2×#11924028C2318yes—
129C2×#11924027—416no—
130C2×#11924027C2314yes—
131C2×#11924027C2314yes—
132C2×#11924027C2318yes—
133C2×#11924027C2312yes—
134C2×#11924027C2314yes—
135C2×#11924027C2318yes—
136C2×#11924027C2318yes—
137#41×D73—48no—
138C22×Dic146C2314yes—
139C2×Q8×D73C2312yes—
140C22×C22⋊D73C2318yes—
141C2×D4×D73C2312yes—
142C2×D4×D73C2314yes—
143C2×D4×D73C2314yes—
144C23×Dic73C2318yes—
145C22×C4×D73C2311yescharacteristic
146C22×C4×D73C2314yes—
147C22×C4×D73C2312yes—
148#14556591C2311yescharacteristic
149#14556591C2312yes—
150#14556591C2312yes—
151#14556591C2318yes—
152#14556590C2314yes—
153#14556590C2318yes—
154#14556589C2312yes—
155#14556589C2318yes—
156#14556588C2311yescharacteristic
157#14556587C2314yes—
158#14556587C2312yes—
159#14556587C2318yes—
160#14556587C2318yes—
161#14556584C2318yes—
162#14556584C23116yes—
163#14556584C23116yes—
164#14556584C23116yes—
165#14556584C2318yes—
166#14556583C2314yes—
167#14556583C23116yes—
168#14556582C2314yes—
169#14556582C2314yes—
170#14556582C2318yes—
171#14556580C2312yes—
172#14556579C2312yes—
173#14556579C2318yes—
174#14556578C2312yes—
175#14556578C2314yes—
176#14556578C2318yes—
177#14556578C2314yes—
178#14556578C2318yes—
179#14556578C2318yes—
180#14556577C2318yes—
181#14556577C23116yes—
182#14556575C2318yes—
183#14556575C2318yes—
184#14556575C23116yes—
185#14556573C2318yes—
186#14556573C23116yes—
187#14556573C23116yes—
188#14556573C23116yes—
189#14556573C2318yes—
190#14556572C2318yes—
191#14556572C2318yes—
192#14556572C2318yes—
193#14556572C23116yes—
194#14556572C23116yes—
195#14556571C2314yes—
196#14556571C2314yes—
197#14556571C2318yes—
198#14556570C2314yes—
199#14556570C2314yes—
200#14556570C2318yes—
201#14556570C2318yes—
202#14556568C23116yes—
203#14556568C23116yes—
204#14556568C23116yes—
205#14556568C23116yes—
206#14556567C2314yes—
207#14556567C2314yes—
208#14556567C23116yes—
209#14556566C2314yes—
210#14556565C2314yes—
211#14556565C2318yes—
212#14556564C2318yes—
213#14556564C23116yes—
214#14556564C23116yes—
215#14556563C2318yes—
216#14556563C23116yes—
217#14556563C23116yes—
218#14556563C23116yes—
219#14556563C23116yes—
220#14556563C23116yes—
221#14556562C2314yes—
222#14556562C2314yes—
223#14556562C2314yes—
224#14556562C23116yes—
225#14556562C23116yes—
226#14556562C2314yes—
227#14556562C2314yes—
228#14556562C2318yes—
229#14556562C23116yes—
230#14556560C2318yes—
231#14556560C2318yes—
232#14556560C23116yes—
233#14556559C2318yes—
234#14556559C23116yes—
235Q8×Dic73C2314yes—
236Q8×Dic73C2314yes—
237C4×Dic146C2314yes—
238C4×Dic146C2314yes—
239#14556556C2314yes—
240#14556556C2314yes—
241#14556556C2318yes—
242C4×D292C2314yes—
243D4×Dic73C2314yes—
244D4×Dic73C2314yes—
245D4×Dic73C2314yes—
246D4×Dic73C2318yes—
247D4×Dic73C2314yes—
248D4×Dic73C2314yes—
249D4×Dic73C23116yes—
250D4×Dic73C2318yes—
251D4×Dic73C2318yes—
252D4×Dic73C2318yes—
253D4×Dic73C23116yes—
254#14556553C2314yes—
255#14556553C2318yes—
256C4×C22⋊D73C2318yes—
257C4×C22⋊D73C2318yes—
258C4×C22⋊D73C2318yes—
259#14556551C2318yes—
260#14556551C23116yes—
261#14556551C2318yes—
262#14556551C23116yes—
263#14556551C2318yes—
264#14556550C2314yes—
265#14556550C2314yes—
266#14556550C2318yes—
267#14556549C2314yes—
268#14556549C2314yes—
269#14556548C2318yes—
270#14556548C23116yes—
271#14556547C2318yes—
272#14556547C2318yes—
273#14556547C2318yes—
274C2×C4⋊Dic73C2318yes—
275C4⋊C4×D73C2314yes—
276C4⋊C4×D73C2318yes—
277C2×C22⋊Dic73C23116yes—
278C22⋊C4×D73C2318yes—
279C22⋊C4×D73C2318yes—
280C2×C4×Dic73C2312yes—
281C2×C4×Dic73C2318yes—
282C2×C4×Dic73C2311yescharacteristic
283C42×D73C2311yescharacteristic
284C42×D73C2312yes—
285C42×D73C2311yescharacteristic
286C42×D73C2312yes—
287C42×D73C2318yes—
288C42×D73C2311yescharacteristic
289C42×D73C2311yescharacteristic
290C2×#41×C73C2312yes—
291C2×#41×C73C2314yes—
292C22×D4×C73C2314yes—
293C22×D4×C73C2318yes—
294C4⋊Q8×C73C2311yescharacteristic
295C4⋊Q8×C73C2312yes—
296#127×C73C2311yescharacteristic
297#127×C73C2312yes—
298#127×C73C2318yes—
299#124×C73C2318yes—
300#124×C73C2312yes—
301#124×C73C23116yes—
302#124×C73C2314yes—
303#121×C73C2314yes—
304#121×C73C2318yes—
305#121×C73C2314yes—
306#121×C73C2318yes—
307#121×C73C2314yes—
308#121×C73C2318yes—
309#120×C73C2318yes—
310#120×C73C2318yes—
311#120×C73C23116yes—
312C4×D4×C73C2314yes—
313C4×D4×C73C2314yes—
314C4×D4×C73C2314yes—
315#117×C73C2314yes—
316#117×C73C2318yes—
317C2×C42×C73C2311yescharacteristic
318C23×D73C2414yes—
319C23×D73C2411yescharacteristic
320#11924029—44no—
321#11924028—416no—
322#11924028—44no—
323#11924028—48no—
324#11924027—216no—
325#11924027—416no—
326#11924027—48no—
327#11924027—48no—
328#11924027—44no—
329#11924027—416no—
330#11924027—416no—
331C2×Dic146—48no—
332C2×Dic146C2414yes—
333C2×Dic146C2414yes—
334C2×Dic146C2412yes—
335C2×Dic146C2414yes—
336C2×Dic146C2418yes—
337Q8×D73—44no—
338C2×D292C2414yes—
339C2×D292C2412yes—
340C2×D292C2414yes—
341C2×C22⋊D73—416no—
342C2×C22⋊D73C2418yes—
343C2×C22⋊D73C24116yes—
344C2×C22⋊D73C2418yes—
345C2×C22⋊D73C2418yes—
346C2×C22⋊D73C2414yes—
347C2×C22⋊D73C2414yes—
348C2×C22⋊D73C24116yes—
349C2×C22⋊D73C2414yes—
350D4×D73—48no—
351D4×D73—44no—
352D4×D73—48no—
353C22×Dic73—416no—
354C22×Dic73C2411yescharacteristic
355C22×Dic73C2418yes—
356C22×Dic73C2414yes—
357C22×Dic73C2412yes—
358C22×Dic73C2418yes—
359C22×Dic73C24116yes—
360C22×Dic73C2418yes—
361C2×C4×D73—24no—
362C2×C4×D73—216no—
363C2×C4×D73—44no—
364C2×C4×D73C2412yes—
365C2×C4×D73C2412yes—
366C2×C4×D73C2411yescharacteristic
367C2×C4×D73C2414yes—
368C2×C4×D73C2411yescharacteristic
369C2×C4×D73C2411yescharacteristic
370C2×C4×D73C2414yes—
371C2×C4×D73C2414yes—
372C2×C4×D73C2412yes—
373C2×C4×D73C2412yes—
374C2×C4×D73C24116yes—
375C2×C4×D73C2411yescharacteristic
376C4⋊Dic73C2414yes—
377C4⋊Dic73C2414yes—
378C4⋊Dic73C2414yes—
379C4⋊Dic73C24116yes—
380C4⋊Dic73C2418yes—
381C4⋊Dic73C2418yes—
382C4⋊Dic73C2414yes—
383C4⋊Dic73C2414yes—
384#11924007C24116yes—
385#11924007C2418yes—
386#11924007C2418yes—
387#11924007C2418yes—
388#11924007C2418yes—
389#11924007C2418yes—
390#11924007C24116yes—
391C22⋊Dic73C2418yes—
392C22⋊Dic73C2418yes—
393C22⋊Dic73C2418yes—
394C22⋊Dic73C24116yes—
395C22⋊Dic73C24116yes—
396C22⋊Dic73C2418yes—
397C22⋊Dic73C2418yes—
398C22⋊Dic73C2418yes—
399C22⋊Dic73C2418yes—
400#11924005C2418yes—
401#11924005C2418yes—
402#11924005C2418yes—
403#11924005C24116yes—
404#11924005C2418yes—
405C4×Dic73C2412yes—
406C4×Dic73C2411yescharacteristic
407C4×Dic73C2412yes—
408C4×Dic73C2418yes—
409C4×Dic73C2412yes—
410C4×Dic73C2412yes—
411C4×Dic73C2412yes—
412C4×Dic73C2411yescharacteristic
413C4×Dic73C2418yes—
414C4×Dic73C2418yes—
415C4×Dic73C2418yes—
416C24×C73C2418yes—
417#41×C73—48no—
418#41×C73—44no—
419C2×Q8×C73C2414yes—
420C2×Q8×C73C2412yes—
421C2×D4×C73—416no—
422C2×D4×C73—48no—
423C2×D4×C73C2414yes—
424C2×D4×C73C2414yes—
425C2×D4×C73C2414yes—
426C2×D4×C73C2414yes—
427C2×D4×C73C2412yes—
428C2×D4×C73C24116yes—
429C2×D4×C73C2418yes—
430C2×D4×C73C2418yes—
431C2×D4×C73C2414yes—
432C22×C4×C73C2412yes—
433C22×C4×C73C2411yescharacteristic
434C22×C4×C73C2418yes—
435C22×C4×C73C2414yes—
436C4⋊C4×C73C2414yes—
437C4⋊C4×C73C2414yes—
438C4⋊C4×C73C2414yes—
439C22⋊C4×C73C2418yes—
440C22⋊C4×C73C24116yes—
441C22⋊C4×C73C2418yes—
442C22⋊C4×C73C2418yes—
443C22⋊C4×C73C2418yes—
444C42×C73C2412yes—
445C42×C73C2411yescharacteristic
446C42×C73C2411yescharacteristic
447C42×C73C2418yes—
448C23×C73—416no—
449C23×C73—48no—
450C23×C73C2514yes—
451C23×C73C2518yes—
452C23×C73C2511yescharacteristic
453C22×D73—22no—
454C22×D73—28no—
455C22×D73—42no—
456C22×D73—48no—
457C22×D73C2511yescharacteristic
458C22×D73C2514yes—
459C22×D73C2511yescharacteristic
460Q8×C73—44no—
461Q8×C73—42no—
462D4×C73—28no—
463D4×C73—28no—
464D4×C73—28no—
465D4×C73—416no—
466D4×C73—48no—
467D4×C73—48no—
468D4×C73—44no—
469D4×C73—44no—
470D4×C73—42no—
471C2×C4×C73—28no—
472C2×C4×C73—22no—
473C2×C4×C73—216no—
474C2×C4×C73—24no—
475C2×C4×C73C2512yes—
476C2×C4×C73C2511yescharacteristic
477C2×C4×C73C2518yes—
478C2×C4×C73C2514yes—
479C2×C4×C73C2511yescharacteristic
480C2×C4×C73C2512yes—
481C22⋊D73—216no—
482C22⋊D73—48no—
483C22⋊D73—44no—
484C22⋊D73—44no—
485C22⋊D73—44no—
486C22⋊D73—416no—
487C22⋊D73—48no—
488C22⋊D73—416no—
489C2×Dic73—28no—
490C2×Dic73—22no—
491C2×Dic73—216no—
492C2×Dic73—42no—
493C2×Dic73—48no—
494C2×Dic73—416no—
495C2×Dic73—48no—
496C2×Dic73C2512yes—
497C2×Dic73C2518yes—
498C2×Dic73C2512yes—
499C2×Dic73C2511yescharacteristic
500C2×Dic73C2518yes—
501C2×Dic73C2514yes—
502C2×Dic73C2511yescharacteristic
503D292—28no—
504D292—44no—
505D292—42no—
506C4×D73—22no—
507C4×D73—28no—
508C4×D73—28no—
509C4×D73—22no—
510C4×D73—24no—
511C4×D73—24no—
512C4×D73—28no—
513C4×D73—22no—
514C4×D73—42no—
515C4×D73—42no—
516C4×D73—416no—
517C4×D73H(5,𝔽2)14yes—
518Dic146—28no—
519Dic146—28no—
520Dic146—44no—
521Dic146—42no—
522Dic146—48no—
523C22×C73—28no—
524C22×C73—24no—
525C22×C73—21no—
526C22×C73—28no—
527C22×C73—22no—
528C22×C73—28no—
529C22×C73—28no—
530C22×C73—816no—
531C22×C73C2611yescharacteristic
532C2×D73—22no—
533C2×D73—21no—
534C2×D73—24no—
535C2×D73—22no—
536C2×D73—28no—
537C2×D73—44no—
538C2×D73—88no—
539C2×D73C2×H(5,𝔽2)12yes—
540C4×C73—24no—
541C4×C73—21no—
542C4×C73—28no—
543C4×C73—22no—
544C4×C73C2×H(5,𝔽2)12yes—
545C4×C73#58514yes—
546Dic73—28no—
547Dic73—21no—
548Dic73—24no—
549Dic73—28no—
550Dic73—22no—
551Dic73—22no—
552Dic73C2×H(5,𝔽2)12yes—
553#62759—731nomaximal, Sylow
554C2×C73—41no—
555C2×C73—44no—
556C2×C73—48no—
557C2×C73C22×H(5,𝔽2)11yescharacteristic
558C2×C73C2×#58512yes—
559D73—22no—
560D73—41no—
561D73—44no—
562#3551—734no—
563#3550—731no—
564#3549D7311yescharacteristic, complemented
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×#532—731no—
581C73#6275911yescharacteristic, complemented, Sylow
582C22×#41—732no—
583C22×#41—734no—
584#563—738no—
585#563—734no—
586#562—7316no—
587#562—738no—
588H(3,𝔽4)C2×D7314yescomplemented
589#560—7316no—
590#560—738no—
591#559—732no—
592Q82—732no—
593#556—734no—
594#555—738no—
595#555—738no—
596#555C2×D7314yescomplemented
597#555C2×D7312yescomplemented
598#554—734no—
599#554—734no—
600#553—738no—
601#553—738no—
602#552—738no—
603#552—738no—
604#551—7316no—
605#551—738no—
606#550—734no—
607#550—738no—
608#550—734no—
609D4×Q8—734no—
610#548—738no—
611#547—738no—
612#547—734no—
613#547—734no—
614#546—738no—
615#546—738no—
616#546—738no—
617#546—7316no—
618D42—738no—
619D42C2×D7314yescomplemented
620D42C2×D7312yescomplemented
621#544—738no—
622#542—7316no—
623#542—738no—
624#542—738no—
625#540—7316no—
626#540—738no—
627#540—738no—
628#538—7316no—
629#538—7316no—
630#537—738no—
631#537—738no—
632#537—738no—
633#536—734no—
634#536—738no—
635#536—734no—
636#535—734no—
637#535—738no—
638#535—738no—
639#535C2×D7314yescomplemented
640#535C2×D7318yescomplemented
641#534—738no—
642#534—738no—
643#533—732no—
644#533—732no—
645#533—732no—
646#532—732no—
647#532—731no—
648#532—731no—
649#532—732no—
650#532—732no—
651#532—738no—
652#532—732no—
653#532—738no—
654#532—734no—
655#532—738no—
656#532—734no—
657#532—731no—
658#532C2×D7311yescharacteristic
659#532C2×D7312yescomplemented
660C2×C4⋊Q8—731no—
661C2×#127—731no—
662#529—734no—
663#529—734no—
664#529—7316no—
665#529—734no—
666#529—734no—
667#529—738no—
668#529—734no—
669#529—734no—
670C2×#124—732no—
671#525—734no—
672#525—734no—
673#525—734no—
674#525—738no—
675#525—738no—
676#525—738no—
677#525—7316no—
678C2×#121—734no—
679C4×#41—734no—
680C4×#41—734no—
681C4×#41—734no—
682C4×#41—738no—
683C2×C4×D4—738no—
684C2×C4×D4—734no—
685C2×#117—734no—
686C22×C42—731no—
687C2×#41—29216no—
688C2×#41—2928no—
689C2×#41—732no—
690C2×#41—734no—
691C2×#41—732no—
692C2×#41—734no—
693C2×#41—738no—
694C2×#41—738no—
695C2×#41—738no—
696C2×#41—734no—
697C2×#41—738no—
698C2×#41—734no—
699C2×#41—732no—
700C2×#41C22×D7314yes—
701C2×#41C22×D7312yes—
702C22×Q8—732no—
703C22×Q8—734no—
704C22×D4—738no—
705C22×D4—734no—
706C22×D4—734no—
707C22×D4—732no—
708C22×D4C22×D7318yes—
709C22×D4C22×D7314yes—
710C23×C4—738no—
711C23×C4—732no—
712C23×C4—734no—
713C23×C4—731no—
714C4⋊Q8—732no—
715C4⋊Q8—738no—
716C4⋊Q8—734no—
717C4⋊Q8—738no—
718C4⋊Q8—731no—
719C4⋊Q8—732no—
720C4⋊Q8—732no—
721C4⋊Q8—738no—
722C4⋊Q8C22×D7311yescharacteristic
723C4⋊Q8C22×D7312yes—
724#127—734no—
725#127—732no—
726#127—738no—
727#127—738no—
728#127—731no—
729#127C22×D7311yescharacteristic
730#127C22×D7312yes—
731#127C22×D7318yes—
732#126—738no—
733#126—738no—
734#126—7316no—
735#126—7316no—
736#126—7316no—
737#125—734no—
738#125—734no—
739#125—738no—
740#125—734no—
741#125—7316no—
742#124—732no—
743#124—732no—
744#124—734no—
745#124—734no—
746#124—738no—
747#124—738no—
748#124—738no—
749#124—738no—
750#124—7316no—
751#124—732no—
752#124—738no—
753#124C22×D7312yes—
754#124C22×D7314yes—
755#124C22×D73116yes—
756#124C22×D7318yes—
757#123—738no—
758#123—738no—
759#123—738no—
760#123—7316no—
761#123—7316no—
762#123—738no—
763#123—738no—
764#123—738no—
765#123—7316no—
766#123—738no—
767#123—7316no—
768#123—7316no—
769#123—7316no—
770C22⋊Q8—734no—
771C22⋊Q8—734no—
772C22⋊Q8—7316no—
773C22⋊Q8—734no—
774C22⋊Q8—734no—
775C22⋊Q8—738no—
776C22⋊Q8—738no—
777C22⋊Q8—734no—
778C22⋊Q8—734no—
779C22⋊Q8—738no—
780C22⋊Q8—7316no—
781C22⋊Q8—7316no—
782C22⋊Q8—7316no—
783C22⋊Q8—7316no—
784#121—738no—
785#121—734no—
786#121—734no—
787#121—734no—
788#121—734no—
789#121—734no—
790#121—7316no—
791#121—738no—
792#121—7316no—
793#121—7316no—
794#121—7316no—
795#121—7316no—
796#121—7316no—
797#121—7316no—
798#121—7316no—
799#121—734no—
800#121—738no—
801#121—734no—
802#121—738no—
803#121—7316no—
804#121—7316no—
805#121C22×D7314yes—
806#121C22×D7314yes—
807#121C22×D7314yes—
808#121C22×D7318yes—
809#121C22×D7318yes—
810#121C22×D7318yes—
811#120—738no—
812#120—738no—
813#120—7316no—
814#120—738no—
815#120—7316no—
816#120C22×D7318yes—
817#120C22×D7318yes—
818#120C22×D73116yes—
819C4×Q8—734no—
820C4×Q8—734no—
821C4×Q8—734no—
822C4×Q8—734no—
823C4×Q8—738no—
824C4×Q8—734no—
825C4×Q8—734no—
826C4×D4—734no—
827C4×D4—734no—
828C4×D4—7316no—
829C4×D4—738no—
830C4×D4—738no—
831C4×D4—7316no—
832C4×D4—734no—
833C4×D4—738no—
834C4×D4—738no—
835C4×D4—734no—
836C4×D4—734no—
837C4×D4—738no—
838C4×D4—738no—
839C4×D4—738no—
840C4×D4—734no—
841C4×D4—738no—
842C4×D4—738no—
843C4×D4—738no—
844C4×D4—7316no—
845C4×D4—738no—
846C4×D4—7316no—
847C4×D4—734no—
848C4×D4C22×D7314yes—
849C4×D4C22×D7314yes—
850C4×D4C22×D7314yes—
851#117—734no—
852#117—734no—
853#117—738no—
854#117—734no—
855#117—734no—
856#117—738no—
857#117—738no—
858#117—738no—
859#117—738no—
860#117—7316no—
861#117C22×D7314yes—
862#117C22×D7318yes—
863C2×C4⋊C4—738no—
864C2×C4⋊C4—738no—
865C2×C4⋊C4—734no—
866C2×C22⋊C4—7316no—
867C2×C22⋊C4—738no—
868C2×C22⋊C4—738no—
869C2×C42—738no—
870C2×C42—732no—
871C2×C42—731no—
872C2×C42—738no—
873C2×C42—732no—
874C2×C42—731no—
875C2×C42—731no—
876C2×C42—731no—
877C2×C42—731no—
878C2×C42—732no—
879C2×C42C22×D7311yescharacteristic
880C24—734no—
881C24—731no—
882C24C23×D7318yes—
883#41—44no—
884#41—48no—
885#41—29216no—
886#41—2928no—
887#41—2924no—
888#41—29216no—
889#41—2928no—
890#41—29216no—
891#41—2924no—
892#41—2928no—
893#41—29216no—
894#41—2924no—
895#41—14616no—
896C2×Q8—2928no—
897C2×Q8—2924no—
898C2×Q8—732no—
899C2×Q8—734no—
900C2×Q8—738no—
901C2×Q8—734no—
902C2×Q8—734no—
903C2×Q8C23×D7314yes—
904C2×Q8C23×D7312yes—
905C2×D4—416no—
906C2×D4—48no—
907C2×D4—29216no—
908C2×D4—2928no—
909C2×D4—2924no—
910C2×D4—2928no—
911C2×D4—7316no—
912C2×D4—738no—
913C2×D4—738no—
914C2×D4—734no—
915C2×D4—734no—
916C2×D4—7316no—
917C2×D4—734no—
918C2×D4—738no—
919C2×D4—734no—
920C2×D4—732no—
921C2×D4—734no—
922C2×D4C23×D7314yes—
923C2×D4C23×D7314yes—
924C2×D4C23×D7314yes—
925C2×D4C23×D73116yes—
926C2×D4C23×D7318yes—
927C2×D4C23×D7314yes—
928C2×D4C23×D7312yes—
929C2×D4C23×D7314yes—
930C2×D4C23×D7318yes—
931C22×C4—2924no—
932C22×C4—29216no—
933C22×C4—732no—
934C22×C4—738no—
935C22×C4—7316no—
936C22×C4—738no—
937C22×C4—732no—
938C22×C4—732no—
939C22×C4—7316no—
940C22×C4—731no—
941C22×C4—731no—
942C22×C4—738no—
943C22×C4—734no—
944C22×C4—732no—
945C22×C4—732no—
946C22×C4—734no—
947C22×C4—731no—
948C22×C4—731no—
949C22×C4—731no—
950C22×C4—734no—
951C22×C4—734no—
952C22×C4—14616no—
953C22×C4—1464no—
954C22×C4C23×D7312yes—
955C22×C4C23×D7311yescharacteristic
956C22×C4C23×D7318yes—
957C22×C4C23×D7314yes—
958C4⋊C4—7316no—
959C4⋊C4—738no—
960C4⋊C4—738no—
961C4⋊C4—738no—
962C4⋊C4—738no—
963C4⋊C4—7316no—
964C4⋊C4—738no—
965C4⋊C4—734no—
966C4⋊C4—734no—
967C4⋊C4—734no—
968C4⋊C4—7316no—
969C4⋊C4—738no—
970C4⋊C4—738no—
971C4⋊C4—734no—
972C4⋊C4—734no—
973C4⋊C4C23×D7314yes—
974C4⋊C4C23×D7314yes—
975C4⋊C4C23×D7314yes—
976C22⋊C4—738no—
977C22⋊C4—738no—
978C22⋊C4—738no—
979C22⋊C4—7316no—
980C22⋊C4—7316no—
981C22⋊C4—738no—
982C22⋊C4—738no—
983C22⋊C4—738no—
984C22⋊C4—738no—
985C22⋊C4—738no—
986C22⋊C4—738no—
987C22⋊C4—738no—
988C22⋊C4—7316no—
989C22⋊C4—738no—
990C22⋊C4C23×D7318yes—
991C22⋊C4C23×D7318yes—
992C22⋊C4C23×D7318yes—
993C22⋊C4C23×D7318yes—
994C22⋊C4C23×D73116yes—
995C42—732no—
996C42—731no—
997C42—738no—
998C42—732no—
999C42—732no—
1000C42—732no—
1001C42—732no—
1002C42—731no—
1003C42—738no—
1004C42—738no—
1005C42—738no—
1006C42C23×D7312yes—
1007C42C23×D7311yescharacteristic
1008C42C23×D7311yescharacteristic
1009C42C23×D7318yes—
1010C23—48no—
1011C23—416no—
1012C23—2922no—
1013C23—2928no—
1014C23—731no—
1015C23—734no—
1016C23—731no—
1017C23—1462no—
1018C23—1468no—
1019C23C24×D7314yes—
1020C23C24×D7311yescharacteristic
1021C23C24×D7318yes—
1022Q8—42no—
1023Q8—44no—
1024Q8—2924no—
1025Q8—2928no—
1026Q8—2922no—
1027Q8—1468no—
1028Q8—1468no—
1029D4—28no—
1030D4—28no—
1031D4—28no—
1032D4—48no—
1033D4—416no—
1034D4—44no—
1035D4—42no—
1036D4—48no—
1037D4—44no—
1038D4—2924no—
1039D4—2922no—
1040D4—2924no—
1041D4—2924no—
1042D4—29216no—
1043D4—2924no—
1044D4—2928no—
1045D4—29216no—
1046D4—2928no—
1047D4—14616no—
1048D4—1468no—
1049C2×C4—28no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—216no—
1053C2×C4—2922no—
1054C2×C4—2922no—
1055C2×C4—29216no—
1056C2×C4—2928no—
1057C2×C4—29216no—
1058C2×C4—2922no—
1059C2×C4—2928no—
1060C2×C4—731no—
1061C2×C4—734no—
1062C2×C4—732no—
1063C2×C4—738no—
1064C2×C4—732no—
1065C2×C4—731no—
1066C2×C4—738no—
1067C2×C4—734no—
1068C2×C4—1468no—
1069C2×C4—1462no—
1070C2×C4—1462no—
1071C2×C4—1468no—
1072C2×C4—1468no—
1073C2×C4—14616no—
1074C2×C4—1462no—
1075C2×C4—1468no—
1076C2×C4—1462no—
1077C2×C4—1464no—
1078C2×C4—1464no—
1079C2×C4C24×D7312yes—
1080C2×C4C24×D7318yes—
1081C2×C4C24×D7314yes—
1082C2×C4C24×D7311yescharacteristic
1083C2×C4C24×D7311yescharacteristic
1084C2×C4C24×D7312yes—
1085C22—24no—
1086C22—21no—
1087C22—28no—
1088C22—22no—
1089C22—28no—
1090C22—28no—
1091C22—28no—
1092C22—816no—
1093C22—2924no—
1094C22—5848no—
1095C22—732no—
1096C22—1461no—
1097C22—1464no—
1098C22—1468no—
1099C22—1462no—
1100C22—1462no—
1101C22C25×D7311yescharacteristic
1102C4—24no—
1103C4—21no—
1104C4—28no—
1105C4—22no—
1106C4—732no—
1107C4—1464no—
1108C4—1468no—
1109C4—1461no—
1110C4—1462no—
1111C4—1468no—
1112C4—1462no—
1113C4H(5,𝔽2)×D7312yes—
1114C4#1798942214yes—
1115C2—44no—
1116C2—48no—
1117C2—41no—
1118C2—2921no—
1119C2—2924no—
1120C2—1462no—
1121C2C2×H(5,𝔽2)×D7311yescharacteristic
1122C2C2×#1798942212yes—
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3549C2
hypercenter#3549D73
hypocenterC73#62759
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3549

Complements

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

NH ≅ G/Ntype
1. #22624355C2semidirect
2. #22624345C2semidirect
3. #22624329C2semidirect
4. #22624323C2semidirect
5. #22624299C2semidirect
6. #22624286C2semidirect
7. #22624266C2semidirect
8. #22624262C2semidirect
9. #22624249C2semidirect
10. #22624071C2semidirect
11. #22623556C2semidirect
12. #22623532C2semidirect
13. #22623488C2semidirect
14. D4×#11924027C2semidirect
15. #22623344C2semidirect
16. #22623262C2semidirect
17. #22623226C2semidirect
18. #532×D73C2semidirect
19. C73×#3549C2semidirect
20. C22×#11924027C22semidirect
21. C2×#41×D73C22semidirect
22. #17989337C22semidirect
23. #17989337C22semidirect
24. #17989331C22semidirect
25. #17989331C22semidirect
26. #17989326C22semidirect
27. #17989326C22semidirect
28. #17989323C22semidirect
29. #17989317C22semidirect
30. #17989307C22semidirect
31. #17989300C22semidirect
32. #17989299C22semidirect
33. #17989298C22semidirect
34. #17989294C22semidirect
35. #17989289C22semidirect
36. #17989284C22semidirect
37. #17989276C22semidirect
38. #17989276C22semidirect
39. #17989268C22semidirect
40. #17989267C22semidirect
41. #17989258C22semidirect
42. #17989257C22semidirect
43. #17989255C22semidirect
44. D4×Dic146C22semidirect
45. #17989243C22semidirect
46. #17989242C22semidirect
47. #17989241C22semidirect
48. #17989237C22semidirect
49. #17989234C22semidirect
50. #17989231C22semidirect
51. #17989231C22semidirect
52. #17989224C22semidirect
53. D4×C22⋊D73C22semidirect
54. #17989215C22semidirect
55. #17989206C22semidirect
56. #17989204C22semidirect
57. #17989204C22semidirect
58. #17989191C22semidirect
59. #17989190C22semidirect
60. #17989190C22semidirect
61. #17989172C22semidirect
62. #17989172C22semidirect
63. #17989166C22semidirect
64. #17989166C22semidirect
65. #17989165C22semidirect
66. #17989163C22semidirect
67. #17989158C22semidirect
68. #17989157C22semidirect
69. #17989154C22semidirect
70. #17989154C22semidirect
71. #17989150C22semidirect
72. #17989147C22semidirect
73. #17989147C22semidirect
74. #17989144C22semidirect
75. #17989142C22semidirect
76. #17989142C22semidirect
77. #17989138C22semidirect
78. #17989137C22semidirect
79. #17989136C22semidirect
80. #17989136C22semidirect
83. #17989135C22semidirect
84. #17989135C22semidirect
85. #17989134C22semidirect
86. #17989133C22semidirect
87. #17989132C22semidirect
88. #17989132C22semidirect
89. C4⋊Q8×D73C22semidirect
91. #17989119C22semidirect
92. #17989119C22semidirect
93. #17989118C22semidirect
94. #17989118C22semidirect
95. #17989118C22semidirect
96. #17989116C22semidirect
97. #17989116C22semidirect
98. #17989116C22semidirect
99. #124×D73C22semidirect
100. #17989097C22semidirect
101. #17989097C22semidirect
102. #17989097C22semidirect
103. #17989094C22semidirect
104. #17989093C22semidirect
105. #17989093C22semidirect
106. #17989093C22semidirect
107. #121×D73C22semidirect
108. #41×Dic73C22semidirect
109. #17989055C22semidirect
110. C4×#11924027C22semidirect
111. C4×#11924027C22semidirect
112. C2×D4×Dic73C22semidirect
113. C4×D4×D73C22semidirect
114. #117×D73C22semidirect
115. C2×C42×D73C22semidirect
116. H(3,𝔽4)×C73C22semidirect
117. #555×C73C22semidirect
118. #555×C73C22semidirect
119. D42×C73C22semidirect
120. D42×C73C22semidirect
121. #535×C73C22semidirect
122. #535×C73C22semidirect
124. #532×C73C22semidirect
564. #3549D73semidirect
581. C73#62759semidirect
588. H(3,𝔽4)C2×D73semidirect
596. #555C2×D73semidirect
597. #555C2×D73semidirect
619. D42C2×D73semidirect
620. D42C2×D73semidirect
639. #535C2×D73semidirect
640. #535C2×D73semidirect
659. #532C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226243552
#226243452
#226243292
#226243232
#226242992
#226242862
#226242662
#226242622
#226242492
#226240712
#226235562
#226235322
#226234882
D4×#119240272
#226233442
#226232622
#226232262
#532×D732
C73×#35492
#6275973