Finite Group Databasebeta

← #33993816

Subgroups — #33993816

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#22624360C214yesmaximal, complemented
2#22624336C211yesmaximal, characteristic, complemented
3#22624331C212yesmaximal, complemented
4#22624316C214yesmaximal, complemented
5#22624306C214yesmaximal, complemented
6#22624289C214yesmaximal, complemented
7#22624276C212yesmaximal, complemented
8#22624265C212yesmaximal, complemented
9#22624243C218yesmaximal, complemented
10#22624072C214yesmaximal, complemented
11#22623558C212yesmaximal, complemented
12#22623540C212yesmaximal, complemented
13#22623492C214yesmaximal, complemented
14D4×#11924029C214yesmaximal, complemented
15#22623351C218yesmaximal, complemented
16#22623263C214yesmaximal, complemented
17#22623228C212yesmaximal, complemented
18#532×D73C211yesmaximal, characteristic, complemented
19C73×#3550C211yesmaximal, characteristic, complemented
20C22×#11924029C2214yescomplemented
21C2×#41×D73C2212yescomplemented
22#17989336C2218yescomplemented
23#17989335C2218yescomplemented
24#17989333C22116yescomplemented
25#17989329C2214yescomplemented
26#17989328C22116yescomplemented
27#17989327C2218yescomplemented
28#17989303C2212yescomplemented
29#17989303C2218yescomplemented
30#17989303C2218yescomplemented
31#17989302C2214yescomplemented
32#17989297C2214yescomplemented
33#17989297C2214yescomplemented
34#17989287C2218yescomplemented
35#17989281C2218yescomplemented
36#17989278C2218yescomplemented
37#17989271C2218yescomplemented
38#17989265C2218yescomplemented
39#17989262C22116yescomplemented
40#17989259C2214yescomplemented
41#17989259C2218yescomplemented
42#17989259C2214yescomplemented
43#17989248C2218yescomplemented
44#17989240C2214yescomplemented
45#17989240C2218yescomplemented
46#17989240C2214yescomplemented
47#17989230C2218yescomplemented
48#17989230C2218yescomplemented
49#17989228C22116yescomplemented
50#17989228C2218yescomplemented
51D4×D292C2218yescomplemented
52D4×D292C2214yescomplemented
53#17989222C2212yescomplemented
54#17989214C2218yescomplemented
55#17989209C2218yescomplemented
56#17989207C22116yescomplemented
57#17989192C2218yescomplemented
58#17989189C22116yescomplemented
59#17989188C2218yescomplemented
60#17989176C22116yescomplemented
61#17989171C22116yescomplemented
62#17989167C2218yescomplemented
63#17989167C2218yescomplemented
64#17989167C2218yescomplemented
65#17989162C2218yescomplemented
66#17989161C2214yescomplemented
67#17989156C2214yescomplemented
68#17989155C2218yescomplemented
69#17989155C2218yescomplemented
70#17989153C2218yescomplemented
71#17989151C2214yescomplemented
72#17989148C2218yescomplemented
73#17989148C2218yescomplemented
74#17989142C2212yescomplemented
75#17989142C2212yescomplemented
76#17989138C2212yes—
77#17989138C2218yescomplemented
78#17989138C2212yescomplemented
79#17989138C2211yescharacteristic, complemented
80#17989138C2218yescomplemented
81#17989137C2211yescharacteristic, complemented
82#17989137C2212yescomplemented
83#17989136C2218yescomplemented
84#17989136C2212yescomplemented
85#17989135C2211yescharacteristic
86#17989134C2214yescomplemented
87#17989133C2212yescomplemented
88#17989132C2214yescomplemented
89C4⋊Q8×D73C2211yescharacteristic, complemented
90#127×D73C2211yescharacteristic
91#17989124C2214yescomplemented
92#17989124C2214yescomplemented
93#17989123C2214yescomplemented
94#17989123C2214yescomplemented
95#17989122C2214yescomplemented
96#17989122C2214yescomplemented
97#17989120C22116yescomplemented
98#17989116C2218yescomplemented
99#124×D73C2212yescomplemented
100#17989100C2218yescomplemented
101#17989100C2214yescomplemented
102#17989100C22116yescomplemented
103#17989100C2214yescomplemented
104#17989099C2214yescomplemented
105#17989095C2218yescomplemented
106#17989095C2218yescomplemented
107#121×D73C2214yescomplemented
108C4×#11924029C2218yescomplemented
109C4×#11924029C2214yescomplemented
110C4×#11924029C2214yescomplemented
111#17989055C2214yescomplemented
112C4×D4×D73C2214yescomplemented
113C4×D4×D73C2218yescomplemented
114#117×D73C2214yescomplemented
115C2×C42×D73C2211yescharacteristic, complemented
116#563×C73C2214yescomplemented
117#559×C73C2212yescomplemented
118Q82×C73C2212yescomplemented
119#556×C73C2214yescomplemented
120D4×Q8×C73C2214yescomplemented
121#542×C73C2218yescomplemented
122#536×C73C2214yescomplemented
123#533×C73C2212yescomplemented
124#532×C73C2211yescharacteristic
125C2×#11924029—416no—
126C2×#11924029C2314yes—
127C2×#11924029C2312yes—
128C2×#11924029C2318yes—
129C2×#11924029C2314yes—
130C2×#11924029C2318yes—
131C2×#11924029C2318yes—
132C2×#11924029C2318yes—
133C2×#11924028C2312yes—
134C2×#11924028C2314yes—
135C2×#11924028C2314yes—
136C2×#11924027C2314yes—
137C2×#11924027C2312yes—
138#41×D73—48no—
139C2×Q8×D73C2312yes—
140C22×D292C2318yes—
141C22×D292C2314yes—
142C2×D4×D73C2312yes—
143C2×D4×D73C2314yes—
144C2×D4×D73C2314yes—
145C2×D4×D73C2318yes—
146C22×C4×D73C2311yescharacteristic
147C22×C4×D73C2314yes—
148C22×C4×D73C2318yes—
149C22×C4×D73C2312yes—
150#14556591C2311yescharacteristic
151#14556591C2312yes—
152#14556590C2314yes—
153#14556589C2312yes—
154#14556589C2318yes—
155#14556588C2311yescharacteristic
156#14556588C2312yes—
157#14556588C2318yes—
158#14556588C2318yes—
159#14556587C2314yes—
160#14556587C2312yes—
161#14556587C2318yes—
162#14556586C2318yes—
163#14556586C2318yes—
164#14556585C23116yes—
165#14556584C23116yes—
166#14556583C2318yes—
167#14556582C2314yes—
168#14556582C2314yes—
169#14556581C23116yes—
170#14556580C2314yes—
171#14556580C2314yes—
172#14556580C2312yes—
173#14556580C2318yes—
174#14556580C2318yes—
175#14556580C23116yes—
176#14556579C2314yes—
177#14556579C2312yes—
178#14556579C2318yes—
179#14556578C2312yes—
180#14556577C23116yes—
181#14556577C2318yes—
182#14556576C23116yes—
183#14556576C2318yes—
184#14556576C2318yes—
185#14556576C23116yes—
186#14556576C23116yes—
187#14556576C23116yes—
188#14556575C2318yes—
189#14556574C2318yes—
190#14556574C2318yes—
191#14556573C23116yes—
192#14556573C23116yes—
193#14556571C2314yes—
194#14556571C2314yes—
195#14556569C23116yes—
196#14556569C23116yes—
197#14556569C23116yes—
198#14556567C2314yes—
199#14556567C2314yes—
200#14556567C2318yes—
201#14556567C2318yes—
202#14556567C23116yes—
203#14556566C2314yes—
204#14556566C2314yes—
205#14556566C2314yes—
206#14556566C2314yes—
207#14556566C2314yes—
208#14556566C23116yes—
209#14556566C23116yes—
210#14556566C2318yes—
211#14556566C2318yes—
212#14556566C23116yes—
213#14556566C2318yes—
214#14556566C23116yes—
215#14556565C2314yes—
216#14556565C2314yes—
217#14556565C2314yes—
218#14556565C2318yes—
219#14556565C23116yes—
220#14556564C23116yes—
221#14556564C2318yes—
222#14556564C23116yes—
223#14556564C23116yes—
224#14556564C23116yes—
225#14556564C23116yes—
226#14556563C2318yes—
227#14556562C2314yes—
228#14556562C2318yes—
229#14556561C2318yes—
230#14556561C2318yes—
231#14556561C23116yes—
232#14556561C2318yes—
233#14556561C23116yes—
234#14556561C23116yes—
235#14556559C2318yes—
236#14556559C2318yes—
237Q8×Dic73C2314yes—
238Q8×Dic73C2314yes—
239#14556556C2314yes—
240#14556556C2314yes—
241C4×D292C2314yes—
242C4×D292C2314yes—
243C4×D292C2318yes—
244C4×D292C2318yes—
245C4×D292C2314yes—
246C4×D292C23116yes—
247C4×D292C2318yes—
248C4×D292C2318yes—
249D4×Dic73C2314yes—
250#14556553C23116yes—
251#14556553C2314yes—
252#14556553C2318yes—
253#14556553C2314yes—
254#14556553C2318yes—
255#14556553C2314yes—
256#14556553C2314yes—
257#14556553C2314yes—
258C4×C22⋊D73C2318yes—
259C4×C22⋊D73C23116yes—
260#14556551C2318yes—
261#14556551C23116yes—
262#14556551C2318yes—
263#14556551C2318yes—
264#14556550C2314yes—
265#14556549C2318yes—
266#14556549C2318yes—
267#14556549C2314yes—
268#14556549C2314yes—
269#14556549C2318yes—
270#14556549C23116yes—
271#14556548C2318yes—
272#14556548C2318yes—
273#14556547C2318yes—
274C4⋊C4×D73C2314yes—
275C4⋊C4×D73C2318yes—
276C4⋊C4×D73C2318yes—
277C22⋊C4×D73C2318yes—
278C22⋊C4×D73C23116yes—
279C22⋊C4×D73C2318yes—
280C2×C4×Dic73C2311yescharacteristic
281C2×C4×Dic73C2312yes—
282C42×D73C2318yes—
283C42×D73C2311yescharacteristic
284C42×D73C2311yescharacteristic
285C42×D73C2311yescharacteristic
286C42×D73C2312yes—
287C42×D73C2311yescharacteristic
288C42×D73C2312yes—
289C42×D73C2318yes—
290C2×#41×C73C2312yes—
291C22×Q8×C73C2314yes—
292C4⋊Q8×C73C2311yescharacteristic
293C4⋊Q8×C73C2312yes—
294C4⋊Q8×C73C2312yes—
295C4⋊Q8×C73C2318yes—
296C4⋊Q8×C73C2318yes—
297#127×C73C2311yescharacteristic
298#126×C73C23116yes—
299#125×C73C2314yes—
300#124×C73C2318yes—
301#124×C73C2312yes—
302#124×C73C2318yes—
303#123×C73C2318yes—
304#123×C73C2318yes—
305C22⋊Q8×C73C2314yes—
306C22⋊Q8×C73C2314yes—
307C22⋊Q8×C73C2318yes—
308C22⋊Q8×C73C23116yes—
309#121×C73C2314yes—
310C4×Q8×C73C2314yes—
311C4×Q8×C73C2314yes—
312C4×Q8×C73C2318yes—
313C4×D4×C73C2314yes—
314C4×D4×C73C2318yes—
315#117×C73C2314yes—
316#117×C73C2314yes—
317C2×C42×C73C2311yescharacteristic
318C23×D73C2414yes—
319C23×D73C2411yescharacteristic
320C23×D73C2418yes—
321#11924029—216no—
322#11924029—44no—
323#11924029—416no—
324#11924029—416no—
325#11924029—416no—
326#11924029—48no—
327#11924029—416no—
328#11924028—48no—
329#11924028—44no—
330#11924028—48no—
331#11924027—44no—
332#11924027—48no—
333C2×Dic146C2414yes—
334C2×Dic146C2412yes—
335C2×Dic146C2414yes—
336Q8×D73—44no—
337C2×D292—48no—
338C2×D292—416no—
339C2×D292C2414yes—
340C2×D292C2414yes—
341C2×D292C2418yes—
342C2×D292C2414yes—
343C2×D292C2414yes—
344C2×D292C24116yes—
345C2×D292C2418yes—
346C2×D292C2418yes—
347C2×D292C24116yes—
348C2×D292C2414yes—
349C2×D292C2412yes—
350C2×C22⋊D73C2418yes—
351C2×C22⋊D73C24116yes—
352C2×C22⋊D73C2418yes—
353C2×C22⋊D73C2414yes—
354C2×C22⋊D73C2414yes—
355C2×C22⋊D73C2414yes—
356D4×D73—48no—
357D4×D73—416no—
358D4×D73—44no—
359D4×D73—48no—
360C22×Dic73C2411yescharacteristic
361C22×Dic73C2414yes—
362C22×Dic73C2412yes—
363C2×C4×D73—24no—
364C2×C4×D73—216no—
365C2×C4×D73—416no—
366C2×C4×D73—44no—
367C2×C4×D73C2412yes—
368C2×C4×D73C2412yes—
369C2×C4×D73C2414yes—
370C2×C4×D73C2411yescharacteristic
371C2×C4×D73C2411yescharacteristic
372C2×C4×D73C2411yescharacteristic
373C2×C4×D73C2418yes—
374C2×C4×D73C2418yes—
375C2×C4×D73C2414yes—
376C2×C4×D73C2414yes—
377C2×C4×D73C2412yes—
378C2×C4×D73C2412yes—
379C2×C4×D73C2418yes—
380C2×C4×D73C24116yes—
381C2×C4×D73C24116yes—
382C2×C4×D73C2411yescharacteristic
383C4⋊Dic73C2414yes—
384C4⋊Dic73C2414yes—
385C4⋊Dic73C2414yes—
386C4⋊Dic73C2418yes—
387C4⋊Dic73C2418yes—
388#11924007C24116yes—
389#11924007C2418yes—
390#11924007C24116yes—
391#11924007C2418yes—
392#11924007C2418yes—
393C22⋊Dic73C2418yes—
394C22⋊Dic73C2418yes—
395#11924005C2418yes—
396#11924005C2418yes—
397#11924005C2418yes—
398#11924005C24116yes—
399#11924005C2418yes—
400#11924005C2418yes—
401#11924005C2418yes—
402#11924005C2418yes—
403#11924005C24116yes—
404#11924005C2418yes—
405#11924005C2418yes—
406#11924005C2418yes—
407#11924005C24116yes—
408C4×Dic73C2412yes—
409C4×Dic73C2418yes—
410C4×Dic73C2412yes—
411C4×Dic73C2411yescharacteristic
412C4×Dic73C2412yes—
413C4×Dic73C2412yes—
414C4×Dic73C2412yes—
415C4×Dic73C2411yescharacteristic
416C4×Dic73C2418yes—
417C4×Dic73C2418yes—
418#41×C73—44no—
419C2×Q8×C73—48no—
420C2×Q8×C73C2414yes—
421C2×Q8×C73C2414yes—
422C2×Q8×C73C2418yes—
423C2×Q8×C73C2412yes—
424C2×D4×C73C2414yes—
425C2×D4×C73C2414yes—
426C2×D4×C73C2412yes—
427C22×C4×C73C2412yes—
428C22×C4×C73C2411yescharacteristic
429C22×C4×C73C2414yes—
430C22×C4×C73C2418yes—
431C4⋊C4×C73C2414yes—
432C4⋊C4×C73C2414yes—
433C4⋊C4×C73C2414yes—
434C4⋊C4×C73C2414yes—
435C4⋊C4×C73C2414yes—
436C4⋊C4×C73C2418yes—
437C4⋊C4×C73C24116yes—
438C4⋊C4×C73C2418yes—
439C22⋊C4×C73C2418yes—
440C22⋊C4×C73C2418yes—
441C22⋊C4×C73C2418yes—
442C22⋊C4×C73C24116yes—
443C42×C73C2412yes—
444C42×C73C2411yescharacteristic
445C42×C73C2411yescharacteristic
446C42×C73C2418yes—
447C42×C73C2418yes—
448C23×C73C2514yes—
449C23×C73C2511yescharacteristic
450C22×D73—22no—
451C22×D73—28no—
452C22×D73—42no—
453C22×D73—48no—
454C22×D73—48no—
455C22×D73—416no—
456C22×D73C2518yes—
457C22×D73C2514yes—
458C22×D73C2511yescharacteristic
459C22×D73C2511yescharacteristic
460Q8×C73—28no—
461Q8×C73—28no—
462Q8×C73—48no—
463Q8×C73—42no—
464D4×C73—28no—
465D4×C73—42no—
466D4×C73—44no—
467C2×C4×C73—28no—
468C2×C4×C73—22no—
469C2×C4×C73—24no—
470C2×C4×C73—48no—
471C2×C4×C73C2518yes—
472C2×C4×C73C2512yes—
473C2×C4×C73C2514yes—
474C2×C4×C73C2511yescharacteristic
475C2×C4×C73C2518yes—
476C2×C4×C73C2511yescharacteristic
477C2×C4×C73C2512yes—
478C22⋊D73—416no—
479C22⋊D73—48no—
480C22⋊D73—44no—
481C22⋊D73—44no—
482C22⋊D73—44no—
483C22⋊D73—48no—
484C2×Dic73—28no—
485C2×Dic73—22no—
486C2×Dic73—42no—
487C2×Dic73C2512yes—
488C2×Dic73C2518yes—
489C2×Dic73C2512yes—
490C2×Dic73C2511yescharacteristic
491C2×Dic73C2514yes—
492C2×Dic73C2511yescharacteristic
493D292—216no—
494D292—28no—
495D292—28no—
496D292—28no—
497D292—42no—
498D292—44no—
499D292—48no—
500D292—416no—
501D292—44no—
502D292—48no—
503D292—416no—
504C4×D73—22no—
505C4×D73—28no—
506C4×D73—22no—
507C4×D73—28no—
508C4×D73—24no—
509C4×D73—24no—
510C4×D73—216no—
511C4×D73—22no—
512C4×D73—28no—
513C4×D73—216no—
514C4×D73—42no—
515C4×D73—42no—
516C4×D73—416no—
517C4×D73—416no—
518C4×D73—48no—
519C4×D73H(5,𝔽2)14yes—
520Dic146—44no—
521Dic146—42no—
522Dic146—44no—
523C22×C73—21no—
524C22×C73—24no—
525C22×C73—22no—
526C22×C73—28no—
527C22×C73C2611yescharacteristic
528C2×D73—22no—
529C2×D73—24no—
530C2×D73—21no—
531C2×D73—28no—
532C2×D73—22no—
533C2×D73—28no—
534C2×D73—28no—
535C2×D73—28no—
536C2×D73—44no—
537C2×D73—88no—
538C2×D73—816no—
539C2×D73C2×H(5,𝔽2)12yes—
540C4×C73—21no—
541C4×C73—24no—
542C4×C73—28no—
543C4×C73—22no—
544C4×C73—28no—
545C4×C73C2×H(5,𝔽2)12yes—
546C4×C73#58514yes—
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×C73C22×H(5,𝔽2)11yescharacteristic
557C2×C73C2×#58512yes—
558D73—22no—
559D73—41no—
560D73—44no—
561D73—48no—
562#3551—734no—
563#3550D7311yescharacteristic, complemented
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×#532—731no—
581C73#6275911yescharacteristic, complemented, Sylow
582C22×#41—732no—
583C22×#41—734no—
584#563—738no—
585#563C2×D7314yescomplemented
586#562—738no—
587#562—7316no—
588H(3,𝔽4)—734no—
589#560—7316no—
590#560—738no—
591#559C2×D7312yescomplemented
592Q82C2×D7312yescomplemented
593#556C2×D7314yescomplemented
594#555—738no—
595#555—732no—
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—7316no—
605#551—738no—
606#550—734no—
607#550—738no—
608#550—734no—
609D4×Q8C2×D7314yescomplemented
610#548—738no—
611#547—738no—
612#547—734no—
613#547—734no—
614#546—738no—
615#546—738no—
616#546—7316no—
617#546—738no—
618D42—732no—
619D42—738no—
620D42—734no—
621#544—738no—
622#542—7316no—
623#542—738no—
624#542C2×D7318yescomplemented
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#536C2×D7314yescomplemented
636#535—734no—
637#535—738no—
638#535—738no—
639#535—738no—
640#535—734no—
641#534—738no—
642#534—738no—
643#533—732no—
644#533—732no—
645#533C2×D7312yescomplemented
646#532—732no—
647#532—732no—
648#532—731no—
649#532—732no—
650#532—738no—
651#532—738no—
652#532—731no—
653#532—732no—
654#532—738no—
655#532—734no—
656#532—734no—
657#532—731no—
658#532—732no—
659#532C2×D7311yescharacteristic
660C2×C4⋊Q8—731no—
661C2×#127—731no—
662#529—7316no—
663#529—734no—
664#529—734no—
665#529—738no—
666#529—734no—
667#529—734no—
668#529—734no—
669#529—734no—
670C2×#124—732no—
671#525—738no—
672#525—738no—
673#525—734no—
674#525—734no—
675#525—738no—
676#525—7316no—
677#525—734no—
678C2×#121—734no—
679C4×#41—734no—
680C4×#41—734no—
681C4×#41—738no—
682C4×#41—734no—
683C2×C4×D4—734no—
684C2×C4×D4—738no—
685C2×#117—734no—
686C22×C42—731no—
687C2×#41—29216no—
688C2×#41—2928no—
689C2×#41—734no—
690C2×#41—738no—
691C2×#41—738no—
692C2×#41—732no—
693C2×#41—738no—
694C2×#41—738no—
695C2×#41—734no—
696C2×#41—732no—
697C2×#41—734no—
698C2×#41—734no—
699C2×#41—734no—
700C2×#41—732no—
701C2×#41C22×D7312yes—
702C22×Q8—732no—
703C22×Q8C22×D7314yes—
704C22×D4—734no—
705C22×D4—738no—
706C22×D4—734no—
707C22×D4—732no—
708C22×D4—738no—
709C22×D4—734no—
710C23×C4—738no—
711C23×C4—732no—
712C23×C4—734no—
713C23×C4—731no—
714C4⋊Q8—732no—
715C4⋊Q8—738no—
716C4⋊Q8—734no—
717C4⋊Q8—731no—
718C4⋊Q8—732no—
719C4⋊Q8C22×D7311yescharacteristic
720C4⋊Q8C22×D7312yes—
721C4⋊Q8C22×D7312yes—
722C4⋊Q8C22×D7318yes—
723C4⋊Q8C22×D7318yes—
724#127—734no—
725#127—732no—
726#127—738no—
727#127—731no—
728#127—732no—
729#127—738no—
730#127—738no—
731#127C22×D7311yescharacteristic
732#126—738no—
733#126—738no—
734#126—7316no—
735#126—7316no—
736#126C22×D73116yes—
737#125—734no—
738#125—734no—
739#125—7316no—
740#125—738no—
741#125C22×D7314yes—
742#124—732no—
743#124—734no—
744#124—734no—
745#124—738no—
746#124—738no—
747#124—7316no—
748#124—732no—
749#124—738no—
750#124—7316no—
751#124—732no—
752#124—734no—
753#124—738no—
754#124C22×D7312yes—
755#124C22×D7318yes—
756#124C22×D7318yes—
757#123—738no—
758#123—738no—
759#123—738no—
760#123—738no—
761#123—7316no—
762#123—7316no—
763#123—7316no—
764#123—7316no—
765#123—738no—
766#123—7316no—
767#123—7316no—
768#123C22×D7318yes—
769#123C22×D7318yes—
770C22⋊Q8—734no—
771C22⋊Q8—734no—
772C22⋊Q8—738no—
773C22⋊Q8—7316no—
774C22⋊Q8—738no—
775C22⋊Q8—734no—
776C22⋊Q8—734no—
777C22⋊Q8—7316no—
778C22⋊Q8—7316no—
779C22⋊Q8—7316no—
780C22⋊Q8C22×D7314yes—
781C22⋊Q8C22×D7314yes—
782C22⋊Q8C22×D7318yes—
783C22⋊Q8C22×D73116yes—
784#121—738no—
785#121—734no—
786#121—738no—
787#121—734no—
788#121—734no—
789#121—734no—
790#121—738no—
791#121—7316no—
792#121—734no—
793#121—734no—
794#121—734no—
795#121—734no—
796#121—734no—
797#121—738no—
798#121—7316no—
799#121—7316no—
800#121—7316no—
801#121—738no—
802#121—738no—
803#121—7316no—
804#121—738no—
805#121—7316no—
806#121—7316no—
807#121—7316no—
808#121—7316no—
809#121—7316no—
810#121C22×D7314yes—
811#120—738no—
812#120—738no—
813#120—738no—
814#120—738no—
815#120—7316no—
816#120—738no—
817#120—7316no—
818#120—7316no—
819C4×Q8—734no—
820C4×Q8—734no—
821C4×Q8—734no—
822C4×Q8—734no—
823C4×Q8C22×D7314yes—
824C4×Q8C22×D7314yes—
825C4×Q8C22×D7318yes—
826C4×D4—734no—
827C4×D4—738no—
828C4×D4—7316no—
829C4×D4—734no—
830C4×D4—734no—
831C4×D4—734no—
832C4×D4—738no—
833C4×D4—7316no—
834C4×D4—738no—
835C4×D4—734no—
836C4×D4—734no—
837C4×D4—7316no—
838C4×D4—738no—
839C4×D4—738no—
840C4×D4—738no—
841C4×D4—734no—
842C4×D4—738no—
843C4×D4—738no—
844C4×D4—738no—
845C4×D4—734no—
846C4×D4—734no—
847C4×D4—7316no—
848C4×D4—738no—
849C4×D4C22×D7314yes—
850C4×D4C22×D7318yes—
851#117—734no—
852#117—734no—
853#117—738no—
854#117—734no—
855#117—738no—
856#117—738no—
857#117—7316no—
858#117—738no—
859#117—738no—
860#117—738no—
861#117C22×D7314yes—
862#117C22×D7314yes—
863C2×C4⋊C4—738no—
864C2×C4⋊C4—734no—
865C2×C4⋊C4—738no—
866C2×C22⋊C4—738no—
867C2×C22⋊C4—738no—
868C2×C22⋊C4—7316no—
869C2×C42—732no—
870C2×C42—731no—
871C2×C42—738no—
872C2×C42—732no—
873C2×C42—738no—
874C2×C42—731no—
875C2×C42—731no—
876C2×C42—731no—
877C2×C42—731no—
878C2×C42—732no—
879C2×C42C22×D7311yescharacteristic
880C24—738no—
881C24—734no—
882C24—731no—
883#41—44no—
884#41—2928no—
885#41—2924no—
886#41—2928no—
887#41—29216no—
888#41—2928no—
889#41—29216no—
890#41—29216no—
891#41—2924no—
892#41—2928no—
893#41—29216no—
894#41—2924no—
895#41—14616no—
896C2×Q8—48no—
897C2×Q8—2924no—
898C2×Q8—734no—
899C2×Q8—732no—
900C2×Q8—734no—
901C2×Q8C23×D7314yes—
902C2×Q8C23×D7314yes—
903C2×Q8C23×D7318yes—
904C2×Q8C23×D7312yes—
905C2×D4—2928no—
906C2×D4—29216no—
907C2×D4—2928no—
908C2×D4—29216no—
909C2×D4—2924no—
910C2×D4—2928no—
911C2×D4—7316no—
912C2×D4—738no—
913C2×D4—738no—
914C2×D4—734no—
915C2×D4—734no—
916C2×D4—734no—
917C2×D4—734no—
918C2×D4—738no—
919C2×D4—7316no—
920C2×D4—738no—
921C2×D4—7316no—
922C2×D4—732no—
923C2×D4—734no—
924C2×D4—734no—
925C2×D4—734no—
926C2×D4—738no—
927C2×D4—734no—
928C2×D4C23×D7314yes—
929C2×D4C23×D7312yes—
930C2×D4C23×D7314yes—
931C22×C4—2924no—
932C22×C4—29216no—
933C22×C4—732no—
934C22×C4—732no—
935C22×C4—732no—
936C22×C4—738no—
937C22×C4—7316no—
938C22×C4—7316no—
939C22×C4—731no—
940C22×C4—731no—
941C22×C4—734no—
942C22×C4—732no—
943C22×C4—732no—
944C22×C4—731no—
945C22×C4—734no—
946C22×C4—731no—
947C22×C4—731no—
948C22×C4—738no—
949C22×C4—738no—
950C22×C4—734no—
951C22×C4—734no—
952C22×C4—14616no—
953C22×C4—1464no—
954C22×C4C23×D7312yes—
955C22×C4C23×D7311yescharacteristic
956C22×C4C23×D7314yes—
957C22×C4C23×D7318yes—
958C4⋊C4—7316no—
959C4⋊C4—738no—
960C4⋊C4—7316no—
961C4⋊C4—738no—
962C4⋊C4—738no—
963C4⋊C4—734no—
964C4⋊C4—734no—
965C4⋊C4—734no—
966C4⋊C4—738no—
967C4⋊C4—738no—
968C4⋊C4C23×D7314yes—
969C4⋊C4C23×D7314yes—
970C4⋊C4C23×D7314yes—
971C4⋊C4C23×D7318yes—
972C4⋊C4C23×D7318yes—
973C4⋊C4C23×D73116yes—
974C4⋊C4C23×D7314yes—
975C4⋊C4C23×D7314yes—
976C22⋊C4—738no—
977C22⋊C4—738no—
978C22⋊C4—738no—
979C22⋊C4—738no—
980C22⋊C4—738no—
981C22⋊C4—7316no—
982C22⋊C4—738no—
983C22⋊C4—738no—
984C22⋊C4—738no—
985C22⋊C4—7316no—
986C22⋊C4—738no—
987C22⋊C4—738no—
988C22⋊C4—738no—
989C22⋊C4—738no—
990C22⋊C4—7316no—
991C22⋊C4C23×D7318yes—
992C22⋊C4C23×D73116yes—
993C22⋊C4C23×D7318yes—
994C22⋊C4C23×D7318yes—
995C42—732no—
996C42—731no—
997C42—738no—
998C42—732no—
999C42—732no—
1000C42—732no—
1001C42—732no—
1002C42—731no—
1003C42—738no—
1004C42—738no—
1005C42C23×D7312yes—
1006C42C23×D7311yescharacteristic
1007C42C23×D7311yescharacteristic
1008C42C23×D7318yes—
1009C42C23×D7318yes—
1010C23—2922no—
1011C23—2928no—
1012C23—29216no—
1013C23—2928no—
1014C23—731no—
1015C23—738no—
1016C23—734no—
1017C23—731no—
1018C23—1462no—
1019C23—1468no—
1020C23C24×D7314yes—
1021C23C24×D7311yescharacteristic
1022Q8—28no—
1023Q8—28no—
1024Q8—48no—
1025Q8—42no—
1026Q8—2922no—
1027Q8—2924no—
1028Q8—2924no—
1029D4—28no—
1030D4—42no—
1031D4—44no—
1032D4—2922no—
1033D4—2928no—
1034D4—2924no—
1035D4—29216no—
1036D4—2924no—
1037D4—29216no—
1038D4—2928no—
1039D4—2924no—
1040D4—2924no—
1041D4—2924no—
1042D4—2928no—
1043D4—29216no—
1044D4—2928no—
1045D4—14616no—
1046D4—1468no—
1047D4—1468no—
1048D4—1468no—
1049C2×C4—28no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—48no—
1053C2×C4—29216no—
1054C2×C4—2922no—
1055C2×C4—2922no—
1056C2×C4—2928no—
1057C2×C4—29216no—
1058C2×C4—2922no—
1059C2×C4—731no—
1060C2×C4—734no—
1061C2×C4—732no—
1062C2×C4—738no—
1063C2×C4—732no—
1064C2×C4—731no—
1065C2×C4—734no—
1066C2×C4—14616no—
1067C2×C4—1462no—
1068C2×C4—1468no—
1069C2×C4—1462no—
1070C2×C4—1468no—
1071C2×C4—1468no—
1072C2×C4—1462no—
1073C2×C4—1468no—
1074C2×C4—1462no—
1075C2×C4—1464no—
1076C2×C4—1464no—
1077C2×C4—14616no—
1078C2×C4C24×D7312yes—
1079C2×C4C24×D7311yescharacteristic
1080C2×C4C24×D7314yes—
1081C2×C4C24×D7318yes—
1082C2×C4C24×D7318yes—
1083C2×C4C24×D7311yescharacteristic
1084C2×C4C24×D7312yes—
1085C22—24no—
1086C22—21no—
1087C22—22no—
1088C22—28no—
1089C22—2924no—
1090C22—58416no—
1091C22—5848no—
1092C22—732no—
1093C22—1468no—
1094C22—1461no—
1095C22—1464no—
1096C22—1468no—
1097C22—1462no—
1098C22—1468no—
1099C22—1468no—
1100C22—1462no—
1101C22C25×D7311yescharacteristic
1102C4—21no—
1103C4—24no—
1104C4—28no—
1105C4—22no—
1106C4—28no—
1107C4—732no—
1108C4—1464no—
1109C4—1461no—
1110C4—1462no—
1111C4—1462no—
1112C4—1468no—
1113C4H(5,𝔽2)×D7312yes—
1114C4#1798942414yes—
1115C2—41no—
1116C2—44no—
1117C2—2921no—
1118C2—2928no—
1119C2—2924no—
1120C2—1462no—
1121C2C2×H(5,𝔽2)×D7311yescharacteristic
1122C2C2×#1798942412yes—
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3550C2
hypercenter#3550D73
hypocenterC73#62759
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #22624360C2semidirect
2. #22624336C2semidirect
3. #22624331C2semidirect
4. #22624316C2semidirect
5. #22624306C2semidirect
6. #22624289C2semidirect
7. #22624276C2semidirect
8. #22624265C2semidirect
9. #22624243C2semidirect
10. #22624072C2semidirect
11. #22623558C2semidirect
12. #22623540C2semidirect
13. #22623492C2semidirect
14. D4×#11924029C2semidirect
15. #22623351C2semidirect
16. #22623263C2semidirect
17. #22623228C2semidirect
18. #532×D73C2semidirect
19. C73×#3550C2semidirect
20. C22×#11924029C22semidirect
21. C2×#41×D73C22semidirect
22. #17989336C22semidirect
23. #17989335C22semidirect
24. #17989333C22semidirect
25. #17989329C22semidirect
26. #17989328C22semidirect
27. #17989327C22semidirect
28. #17989303C22semidirect
29. #17989303C22semidirect
30. #17989303C22semidirect
31. #17989302C22semidirect
32. #17989297C22semidirect
33. #17989297C22semidirect
34. #17989287C22semidirect
35. #17989281C22semidirect
36. #17989278C22semidirect
37. #17989271C22semidirect
38. #17989265C22semidirect
39. #17989262C22semidirect
40. #17989259C22semidirect
41. #17989259C22semidirect
42. #17989259C22semidirect
43. #17989248C22semidirect
44. #17989240C22semidirect
45. #17989240C22semidirect
46. #17989240C22semidirect
47. #17989230C22semidirect
48. #17989230C22semidirect
49. #17989228C22semidirect
50. #17989228C22semidirect
51. D4×D292C22semidirect
52. D4×D292C22semidirect
53. #17989222C22semidirect
54. #17989214C22semidirect
55. #17989209C22semidirect
56. #17989207C22semidirect
57. #17989192C22semidirect
58. #17989189C22semidirect
59. #17989188C22semidirect
60. #17989176C22semidirect
61. #17989171C22semidirect
62. #17989167C22semidirect
63. #17989167C22semidirect
64. #17989167C22semidirect
65. #17989162C22semidirect
66. #17989161C22semidirect
67. #17989156C22semidirect
68. #17989155C22semidirect
69. #17989155C22semidirect
70. #17989153C22semidirect
71. #17989151C22semidirect
72. #17989148C22semidirect
73. #17989148C22semidirect
74. #17989142C22semidirect
75. #17989142C22semidirect
77. #17989138C22semidirect
78. #17989138C22semidirect
79. #17989138C22semidirect
80. #17989138C22semidirect
81. #17989137C22semidirect
82. #17989137C22semidirect
83. #17989136C22semidirect
84. #17989136C22semidirect
86. #17989134C22semidirect
87. #17989133C22semidirect
88. #17989132C22semidirect
89. C4⋊Q8×D73C22semidirect
91. #17989124C22semidirect
92. #17989124C22semidirect
93. #17989123C22semidirect
94. #17989123C22semidirect
95. #17989122C22semidirect
96. #17989122C22semidirect
97. #17989120C22semidirect
98. #17989116C22semidirect
99. #124×D73C22semidirect
100. #17989100C22semidirect
101. #17989100C22semidirect
102. #17989100C22semidirect
103. #17989100C22semidirect
104. #17989099C22semidirect
105. #17989095C22semidirect
106. #17989095C22semidirect
107. #121×D73C22semidirect
108. C4×#11924029C22semidirect
109. C4×#11924029C22semidirect
110. C4×#11924029C22semidirect
111. #17989055C22semidirect
112. C4×D4×D73C22semidirect
113. C4×D4×D73C22semidirect
114. #117×D73C22semidirect
115. C2×C42×D73C22semidirect
116. #563×C73C22semidirect
117. #559×C73C22semidirect
118. Q82×C73C22semidirect
119. #556×C73C22semidirect
120. D4×Q8×C73C22semidirect
121. #542×C73C22semidirect
122. #536×C73C22semidirect
123. #533×C73C22semidirect
563. #3550D73semidirect
581. C73#62759semidirect
585. #563C2×D73semidirect
591. #559C2×D73semidirect
592. Q82C2×D73semidirect
593. #556C2×D73semidirect
609. D4×Q8C2×D73semidirect
624. #542C2×D73semidirect
635. #536C2×D73semidirect
645. #533C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226243602
#226243362
#226243312
#226243162
#226243062
#226242892
#226242762
#226242652
#226242432
#226240722
#226235582
#226235402
#226234922
D4×#119240292
#226233512
#226232632
#226232282
#532×D732
C73×#35502
#6275973