Finite Group Databasebeta

← #35196494

Subgroups — #35196494

Order 20224.

7094 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777487C214yesmaximal, complemented
2#23777476C214yesmaximal, complemented
3#23777394C214yesmaximal, complemented
4#23777382C214yesmaximal, complemented
5#23777264C216yesmaximal, complemented
6#23777206C211yesmaximal, characteristic, complemented
7#23777167C211yesmaximal, characteristic, complemented
8#23777106C216yesmaximal, complemented
9#23777051C211yesmaximal, characteristic, complemented
10#23777021C214yesmaximal, complemented
11#23777016C214yesmaximal, complemented
12#23776990C214yesmaximal, complemented
13Q8×#11929623C214yesmaximal, complemented
14#23776824C216yesmaximal, complemented
15#23776692C216yesmaximal, complemented
162−1+4×Dic79C211yesmaximal, characteristic, complemented
17#23776609C211yesmaximal, characteristic, complemented
18C22×Q8×Dic79C211yesmaximal, characteristic, complemented
19C79×#3486C211yesmaximal, characteristic, complemented
20C2×#14579209C2211yescharacteristic
21#19099295C22112yescomplemented
22Q8×Dic158C2214yescomplemented
23#19099292C2214yescomplemented
24#19099289C2214yescomplemented
25#19099289C2214yescomplemented
26#19099288C22112yescomplemented
27#19099287C22112yescomplemented
28#19099284C22112yescomplemented
29#19099282C22112yescomplemented
30#19099271C22112yes—
31#19099271C22112yescomplemented
32#19099270C22112yes—
33#19099265C22112yes—
34#19099259C22112yes—
35#19099255C22112yes—
36#19099255C22112yescomplemented
37#19099253C22112yes—
38#19099247C22112yescomplemented
39#19099232C2214yescomplemented
40Q8×C22⋊D79C2214yes—
41Q8×C22⋊D79C2214yes—
42Q8×C22⋊D79C2214yescomplemented
43#19099224C2214yes—
44#19099224C2214yes—
45#19099224C2214yescomplemented
46#19099220C2214yescomplemented
47#19099217C22112yes—
48#19099213C22112yes—
49#19099191C2216yes—
50#19099186C22112yescomplemented
51#19099182C22112yescomplemented
52#19099174C22112yescomplemented
53#19099173C22112yescomplemented
54#19099157C22124yes—
55#19099141C2216yes—
56#19099137C2216yes—
57#19099118C22112yescomplemented
58#19099116C2216yes—
59#19099115C2216yes—
60#19099115C2216yes—
61#19099115C22112yescomplemented
62#19099109C2216yes—
63#19099108C2216yes—
64#19099108C2216yes—
65#19099099C2216yes—
66#19099099C2216yes—
67#19099099C22112yescomplemented
68#19099094C2216yes—
69#19099094C2216yes—
70#19099093C22112yes—
71#19099093C22112yes—
72#19099092C22112yescomplemented
73#19099090C22112yes—
74#19099090C22112yes—
75#19099074C2216yes—
76#19099069C22112yes—
77#19099069C2214yes—
78#19099046C2216yes—
79#19099046C2214yescomplemented
80#19099045C2214yescomplemented
81#19099043C2216yes—
82#19099041C2211yescharacteristic
83#19099041C2214yescomplemented
84#19099039C2214yescomplemented
85#41×Dic79C2216yes—
86#41×Dic79C2214yescomplemented
87C4×#11929625C2214yescomplemented
88#19099031C2216yes—
89C4×#11929623C22112yes—
90C4×#11929623C22112yes—
91C2×Q8×Dic79C2213yes—
92C2×Q8×Dic79C2211yescharacteristic
93C2×Q8×Dic79C2214yes—
94C2×Q8×Dic79C2211yescharacteristic
95C2×Q8×Dic79C2214yes—
96C2×Q8×Dic79C2214yes—
97C2×Q8×Dic79C2213yes—
98C2×Q8×Dic79C2214yes—
99C2×Q8×Dic79C2214yescomplemented
100C4×Q8×D79C2214yescomplemented
101C22×C4⋊Dic79C2213yes—
102C22×C4×Dic79C2213yes—
103C2×2−1+4×C79C2211yescharacteristic
104C23×Q8×C79C2211yescharacteristic
105D4×Q8×C79C2214yes—
106D4×Q8×C79C2214yes—
107#548×C79C2214yes—
108#548×C79C2214yes—
109#536×C79C2216yes—
110#525×C79C2216yes—
111#519×C79C2211yescharacteristic
112#14579209—28no—
113C2×#11929625C2314yes—
114C2×#11929624C2316yes—
115C2×#11929623C2314yes—
116C2×#11929623C23112yes—
117C2×Q8×D79C2314yes—
118C23×Dic79C2311yescharacteristic
119C23×Dic79C2313yes—
120#14579161C23112yes—
121#14579160C23112yes—
122#14579160C2316yes—
123#14579160C2316yes—
124#14579159C23112yes—
125#14579159C2316yes—
126#14579157C2316yes—
127#14579156C23124yes—
128#14579156C23112yes—
129#14579156C23112yes—
130#14579154C23124yes—
131#14579154C23112yes—
132#14579154C23112yes—
133#14579153C23112yes—
134#14579152C23124yes—
135#14579152C23112yes—
136#14579152C2316yes—
137#14579152C2316yes—
138#14579151C23124yes—
139#14579151C23112yes—
140#14579151C23112yes—
141#14579150C23112yes—
142#14579150C2316yes—
143#14579148C2316yes—
144#14579147C23112yes—
145#14579147C23112yes—
146#14579145C23124yes—
147#14579145C23112yes—
148#14579145C2314yes—
149#14579144C23112yes—
150#14579143C23124yes—
151#14579142C23112yes—
152#14579142C2314yes—
153#14579141C23124yes—
154#14579140C23112yes—
155#14579140C2316yes—
156#14579140C2316yes—
157#14579138C23112yes—
158#14579138C23124yes—
159#14579138C23112yes—
160#14579138C2314yes—
161#14579138C2314yes—
162#14579137C23112yes—
163#14579137C23112yes—
164#14579137C23112yes—
165#14579135C23112yes—
166#14579135C2316yes—
167#14579135C2316yes—
168#14579133C23112yes—
169#14579133C23112yes—
170#14579133C2314yes—
171#14579133C2314yes—
172#14579132C23112yes—
173#14579130C2314yes—
174Q8×Dic79C23112yes—
175Q8×Dic79C2316yes—
176Q8×Dic79C2314yes—
177Q8×Dic79C2314yes—
178Q8×Dic79C2314yes—
179Q8×Dic79C2314yes—
180Q8×Dic79C23112yes—
181Q8×Dic79C23112yes—
182Q8×Dic79C23112yes—
183Q8×Dic79C2314yes—
184Q8×Dic79C2314yes—
185Q8×Dic79C23112yes—
186Q8×Dic79C2316yes—
187C4×Dic158C23112yes—
188C4×Dic158C23112yes—
189C4×Dic158C23112yes—
190#14579126C2316yes—
191#14579126C2316yes—
192#14579126C23112yes—
193#14579126C23112yes—
194C4×D316C23112yes—
195D4×Dic79C23112yes—
196D4×Dic79C2316yes—
197D4×Dic79C23112yes—
198D4×Dic79C23112yes—
199D4×Dic79C2314yes—
200D4×Dic79C2314yes—
201D4×Dic79C2316yes—
202#14579123C2316yes—
203#14579123C2316yes—
204C4×C22⋊D79C23112yes—
205C4×C22⋊D79C23112yes—
206C4×C22⋊D79C23112yes—
207C4×C22⋊D79C23112yes—
208(C22⋊D79)⋊C4C23112yes—
209(C22⋊D79)⋊C4C23112yes—
210(C22⋊D79)⋊C4C23112yes—
211(C22⋊D79)⋊C4C2314yes—
212(C22⋊D79)⋊C4C23112yes—
213(C22⋊D79)⋊C4C2314yes—
214#14579120C2316yes—
215#14579120C23112yes—
216#14579120C23112yes—
217#14579119C23112yes—
218#14579119C23112yes—
219#14579119C23112yes—
220#14579118C23112yes—
221#14579117C23112yes—
222#14579117C23112yes—
223#14579117C2314yes—
224#14579117C23112yes—
225C2×C4⋊Dic79C2313yes—
226C2×C4⋊Dic79C2316yes—
227C2×C4⋊Dic79C23112yes—
228C2×C4⋊Dic79C23112yes—
229C2×C4⋊Dic79C23112yes—
230C2×C4⋊Dic79C2313yes—
231C4⋊C4×D79C23112yes—
232C2×C4×Dic79C2316yes—
233C2×C4×Dic79C2316yes—
234C2×C4×Dic79C2313yes—
235C2×C4×Dic79C2313yes—
236C2×C4×Dic79C2313yes—
237C2×C4×Dic79C2316yes—
238C2×C4×Dic79C2316yes—
239C2×C4×Dic79C2313yes—
240C2×C4×Dic79C23112yes—
241C42×D79C23112yes—
2422−1+4×C79—28no—
243C2×#41×C79C2316yes—
244C2×#41×C79C2314yes—
245C22×Q8×C79—28no—
246C22×Q8×C79C2313yes—
247C22×Q8×C79C2314yes—
248C22×Q8×C79C2314yes—
249C22×Q8×C79C2314yes—
250C22×Q8×C79C2311yescharacteristic
251C23×C4×C79C2313yes—
252C4⋊Q8×C79C23112yes—
253#124×C79C23112yes—
254#123×C79C23112yes—
255C22⋊Q8×C79C23112yes—
256C22⋊Q8×C79C23112yes—
257C22⋊Q8×C79C2316yes—
258C22⋊Q8×C79C2316yes—
259#121×C79C2316yes—
260#121×C79C2316yes—
261#120×C79C2314yes—
262C4×Q8×C79C2314yes—
263C4×Q8×C79C2314yes—
264C4×D4×C79C23112yes—
265C4×D4×C79C23112yes—
266#117×C79C2316yes—
267#11929625—216no—
268#11929624—224no—
269#11929623—216no—
270#11929623—424no—
271C2×Dic158C2416yes—
272C2×Dic158C2414yes—
273C2×Dic158C24112yes—
274Q8×D79—216no—
275C2×D316C2416yes—
276C2×C22⋊D79C2414yes—
277C2×C22⋊D79C2414yes—
278C2×C22⋊D79C2414yes—
279C2×C22⋊D79C2414yes—
280C2×C22⋊D79C24112yes—
281C22×Dic79—24no—
282C22×Dic79—46no—
283C22×Dic79C2416yes—
284C22×Dic79C2414yes—
285C22×Dic79C2411yescharacteristic
286C22×Dic79C2411yescharacteristic
287C22×Dic79C2411yescharacteristic
288C22×Dic79C2411yescharacteristic
289C22×Dic79C2411yescharacteristic
290C22×Dic79C24112yes—
291C22×Dic79C2413yes—
292C22×Dic79C2416yes—
293C22×Dic79C2413yes—
294C22×Dic79C2411yescharacteristic
295C2×C4×D79C24112yes—
296C2×C4×D79C2414yes—
297C2×C4×D79C24112yes—
298C4⋊Dic79C24112yes—
299C4⋊Dic79C24112yes—
300C4⋊Dic79C24124yes—
301C4⋊Dic79C2416yes—
302C4⋊Dic79C24112yes—
303C4⋊Dic79C2414yes—
304C4⋊Dic79C24112yes—
305C4⋊Dic79C2416yes—
306C4⋊Dic79C2414yes—
307Dic79⋊C4C24112yes—
308Dic79⋊C4C2414yes—
309Dic79⋊C4C2414yes—
310Dic79⋊C4C24112yes—
311Dic79⋊C4C24112yes—
312Dic79⋊C4C2414yes—
313Dic79⋊C4C24112yes—
314Dic79⋊C4C24112yes—
315Dic79⋊C4C24112yes—
316Dic79⋊C4C2414yes—
317C22⋊Dic79C2414yes—
318C22⋊Dic79C2414yes—
319C22⋊Dic79C2414yes—
320C22⋊Dic79C24112yes—
321C22⋊Dic79C2414yes—
322C22⋊Dic79C24112yes—
323C22⋊Dic79C2414yes—
324(C2×D79)⋊C4C2414yes—
325(C2×D79)⋊C4C24112yes—
326(C2×D79)⋊C4C2414yes—
327(C2×D79)⋊C4C24112yes—
328(C2×D79)⋊C4C24112yes—
329(C2×D79)⋊C4C24112yes—
330C4×Dic79C2414yes—
331C4×Dic79C2416yes—
332C4×Dic79C24112yes—
333C4×Dic79C2416yes—
334C4×Dic79C2416yes—
335C4×Dic79C2414yes—
336C4×Dic79C2416yes—
337C4×Dic79C2416yes—
338C4×Dic79C2416yes—
339C4×Dic79C2416yes—
340C4×Dic79C2416yes—
341C4×Dic79C24112yes—
342C4×Dic79C24112yes—
343C24×C79C2411yescharacteristic
344#41×C79—216no—
345#41×C79—224no—
346C2×Q8×C79—216no—
347C2×Q8×C79—216no—
348C2×Q8×C79—216no—
349C2×Q8×C79—212no—
350C2×Q8×C79#4118yescomplemented
351C2×Q8×C79C24112yes—
352C2×Q8×C79C2416yes—
353C2×Q8×C79C2414yes—
354C2×D4×C79C2414yes—
355C2×D4×C79C2414yes—
356C2×D4×C79C2414yes—
357C2×D4×C79C2416yes—
358C22×C4×C79—212no—
359C22×C4×C79C2416yes—
360C22×C4×C79C2416yes—
361C22×C4×C79C24112yes—
362C22×C4×C79C2413yes—
363C22×C4×C79C2413yes—
364C4⋊C4×C79C2416yes—
365C4⋊C4×C79C2416yes—
366C4⋊C4×C79C24112yes—
367C4⋊C4×C79C24112yes—
368C22⋊C4×C79C2414yes—
369C22⋊C4×C79C2414yes—
370C22⋊C4×C79C2414yes—
371C22⋊C4×C79C24112yes—
372C22⋊C4×C79C24112yes—
373C42×C79C24112yes—
374C23×C79—22no—
375C23×C79—22no—
376C23×C79—22no—
377C23×C79C2514yes—
378C23×C79C2511yescharacteristic
379C23×C79C2511yescharacteristic
380C23×C79C2511yescharacteristic
381C22×D79C2514yes—
382Q8×C79—224no—
383Q8×C79—212no—
384Q8×C79C2×#41116yes—
385D4×C79—28no—
386D4×C79—28no—
387D4×C79—28no—
388D4×C79—212no—
389C2×C4×C79—26no—
390C2×C4×C79—212no—
391C2×C4×C79—212no—
392C2×C4×C79—224no—
393C2×C4×C79C2×#41112yes—
394C2×C4×C79C2516yes—
395C2×C4×C79C2514yes—
396C2×C4×C79C2514yes—
397C2×C4×C79C2514yes—
398C2×C4×C79C2516yes—
399C22⋊D79—28no—
400C22⋊D79—28no—
401C22⋊D79—28no—
402C22⋊D79—28no—
403C22⋊D79—412no—
404C2×Dic79—22no—
405C2×Dic79—212no—
406C2×Dic79—22no—
407C2×Dic79—22no—
408C2×Dic79—22no—
409C2×Dic79—22no—
410C2×Dic79—28no—
411C2×Dic79—43no—
412C2×Dic79—46no—
413C2×Dic79—43no—
414C2×Dic79—412no—
415C2×Dic792−1+414yescomplemented
416C2×Dic79C2511yescharacteristic
417C2×Dic79C2511yescharacteristic
418C2×Dic79C2516yes—
419C2×Dic79C2514yes—
420C2×Dic79C2514yes—
421C2×Dic79C2516yes—
422C2×Dic79C2514yes—
423C2×Dic79C2511yescharacteristic
424C2×Dic79C2511yescharacteristic
425D316—212no—
426C4×D79—224no—
427C4×D79—28no—
428C4×D79—412no—
429Dic158—212no—
430Dic158—28no—
431Dic158—412no—
432C22×C79—28no—
433C22×C79—21no—
434C22×C79—21no—
435C22×C79—21no—
436C22×C79—21no—
437C22×C79—21no—
438C22×C79—21no—
439C22×C79—24no—
440C22×C79—24no—
441C22×C79—24no—
442C22×C79C22×#4112yes—
443C22×C79C2×2−1+412yes—
444C22×C79#58512yes—
445C22×C79C2611yescharacteristic
446C2×D79—24no—
447C2×D79—24no—
448C2×D79—24no—
449C4×C79—24no—
450C4×C79—26no—
451C4×C79—24no—
452C4×C79—24no—
453C4×C79C22×#41112yes—
454Dic79—24no—
455Dic79—24no—
456Dic79—21no—
457Dic79—21no—
458Dic79—24no—
459Dic79—26no—
460Dic79—26no—
461Dic79C2×2−1+412yes—
462Dic79C2×2−1+412yes—
463#62788—791nomaximal, Sylow
464C2×C79—22no—
465C2×C79—22no—
466C2×C79—22no—
467C2×C79—44no—
468C2×C79C23×#4111yescharacteristic
469C2×C79C22×2−1+411yescharacteristic
470C2×C79C2×#58511yescharacteristic
471D79—44no—
472#3523—794no—
473#3522—794no—
474#3516—794no—
475#3516—794no—
476#3507—796no—
477#3502—791no—
478#3497—791no—
479#3492—796no—
480#3486—791no—
481#3486D7911yescharacteristic, complemented
482#3482—794no—
483#3482—794no—
484#3480—794no—
485Q8×#41—794no—
486#3461—796no—
487#3444—796no—
488C4×2−1+4—791no—
489C4×2−1+4—791no—
490C22×C4×Q8—791no—
491C79#6278811yescharacteristic, complemented, Sylow
492C2×2−1+4—791no—
493C2×2−1+4C2×D7911yescharacteristic
494C23×Q8C2×D7911yescharacteristic
495#559—7912no—
496Q82—794no—
497#557—7912no—
498#557—794no—
499#557—794no—
500#557—794no—
501#556—7912no—
502#556—7912no—
503#556—7912no—
504#554—7912no—
505#554—7912no—
506#554—7912no—
507#553—7912no—
508#553—7912no—
509#552—7912no—
510#552—7912no—
511#552—7912no—
512#552—7912no—
513#550—794no—
514D4×Q8—794no—
515D4×Q8—794no—
516D4×Q8—794no—
517D4×Q8C2×D7914yes—
518D4×Q8C2×D7914yes—
519#548—794no—
520#548—794no—
521#548—794no—
522#548—794no—
523#548C2×D7914yes—
524#548C2×D7914yes—
525#547—7912no—
526#547—7912no—
527#544—796no—
528#542—7912no—
529#542—7912no—
530#541—7912no—
531#541—7912no—
532#539—7924no—
533#537—796no—
534#536—796no—
535#536C2×D7916yes—
536#533—7912no—
537#533—796no—
538#533—796no—
539#533—7912no—
540#533—796no—
541#532—796no—
542#532—796no—
543#532—796no—
544#529—7912no—
545#529—7912no—
546#529—7912no—
547#529—796no—
548#529—796no—
549#529—7912no—
550#529—796no—
551#529—796no—
552#529—7912no—
553#529—7912no—
554#525—796no—
555#525—794no—
556#525—7912no—
557#525C2×D7916yes—
558#520—796no—
559#520—794no—
560#520—794no—
561#520—796no—
562#519—791no—
563#519—794no—
564#519—794no—
565#519C2×D7911yescharacteristic
566C4×#41—796no—
567C4×#41—794no—
568C4×#41—794no—
569C4×#41—7912no—
570C4×#41—7912no—
571C4×#41—796no—
572C2×C4×Q8—791no—
573C2×C4×Q8—793no—
574C2×C4×Q8—794no—
575C2×C4×Q8—794no—
576C2×C4×Q8—791no—
577C2×C4×Q8—793no—
578C2×C4×Q8—794no—
579C2×C4×Q8—794no—
580C2×C4×Q8—794no—
581C2×C4×Q8—794no—
582C22×C4⋊C4—793no—
583C22×C42—793no—
5842−1+4—28no—
5852−1+4—1588no—
586C2×#41—794no—
587C2×#41—7912no—
588C2×#41—794no—
589C2×#41—796no—
590C2×#41C22×D7916yes—
591C2×#41C22×D7914yes—
592C22×Q8—28no—
593C22×Q8—794no—
594C22×Q8C22×D7913yes—
595C22×Q8C22×D7914yes—
596C22×Q8C22×D7914yes—
597C22×Q8C22×D7914yes—
598C22×Q8C22×D7911yescharacteristic
599C23×C4—793no—
600C23×C4—791no—
601C23×C4C22×D7913yes—
602C4⋊Q8—796no—
603C4⋊Q8—7912no—
604C4⋊Q8—796no—
605C4⋊Q8—796no—
606C4⋊Q8—7912no—
607C4⋊Q8—7912no—
608C4⋊Q8C22×D79112yes—
609#127—796no—
610#126—7912no—
611#126—7912no—
612#126—7924no—
613#126—7912no—
614#126—7912no—
615#126—7924no—
616#125—7912no—
617#125—796no—
618#125—796no—
619#125—7912no—
620#125—7912no—
621#125—7924no—
622#125—7924no—
623#125—7912no—
624#124—796no—
625#124—7912no—
626#124—796no—
627#124—7912no—
628#124—7912no—
629#124C22×D79112yes—
630#123—794no—
631#123—7912no—
632#123—7912no—
633#123—794no—
634#123—7912no—
635#123—7924no—
636#123—7924no—
637#123C22×D79112yes—
638C22⋊Q8—7912no—
639C22⋊Q8—7912no—
640C22⋊Q8—7912no—
641C22⋊Q8—796no—
642C22⋊Q8—796no—
643C22⋊Q8—7912no—
644C22⋊Q8—7924no—
645C22⋊Q8—794no—
646C22⋊Q8—794no—
647C22⋊Q8—7912no—
648C22⋊Q8—7912no—
649C22⋊Q8—7924no—
650C22⋊Q8C22×D7916yes—
651C22⋊Q8C22×D7916yes—
652C22⋊Q8C22×D79112yes—
653C22⋊Q8C22×D79112yes—
654#121—794no—
655#121—794no—
656#121—7912no—
657#121—7912no—
658#121—7912no—
659#121—796no—
660#121—796no—
661#121—7912no—
662#121C22×D7916yes—
663#121C22×D7916yes—
664#120—794no—
665#120C22×D7914yes—
666C4×Q8—794no—
667C4×Q8—794no—
668C4×Q8—7912no—
669C4×Q8—7912no—
670C4×Q8—794no—
671C4×Q8—794no—
672C4×Q8—7912no—
673C4×Q8—7912no—
674C4×Q8—796no—
675C4×Q8—794no—
676C4×Q8—7912no—
677C4×Q8—796no—
678C4×Q8—794no—
679C4×Q8—796no—
680C4×Q8—796no—
681C4×Q8—7912no—
682C4×Q8—7912no—
683C4×Q8—7912no—
684C4×Q8—7912no—
685C4×Q8—7912no—
686C4×Q8C22×D7914yes—
687C4×Q8C22×D7914yes—
688C4×D4—794no—
689C4×D4—794no—
690C4×D4—796no—
691C4×D4—7912no—
692C4×D4—796no—
693C4×D4—7912no—
694C4×D4—7912no—
695C4×D4—7912no—
696C4×D4—7912no—
697C4×D4—7912no—
698C4×D4—7912no—
699C4×D4—796no—
700C4×D4—796no—
701C4×D4—794no—
702C4×D4—794no—
703C4×D4—7912no—
704C4×D4—7912no—
705C4×D4—7912no—
706C4×D4—7912no—
707C4×D4—7912no—
708C4×D4C22×D79112yes—
709C4×D4C22×D79112yes—
710#117—796no—
711#117—7912no—
712#117—7912no—
713#117—7912no—
714#117—7912no—
715#117—7912no—
716#117—794no—
717#117—7912no—
718#117—7912no—
719#117—7912no—
720#117—7912no—
721#117C22×D7916yes—
722C2×C4⋊C4—793no—
723C2×C4⋊C4—793no—
724C2×C4⋊C4—796no—
725C2×C4⋊C4—7912no—
726C2×C4⋊C4—7912no—
727C2×C4⋊C4—7912no—
728C2×C4⋊C4—7912no—
729C2×C42—793no—
730C2×C42—796no—
731C2×C42—796no—
732C2×C42—793no—
733C2×C42—796no—
734C2×C42—793no—
735C2×C42—796no—
736C2×C42—793no—
737C2×C42—7912no—
738C2×C42—7912no—
739C24C23×D7911yescharacteristic
740#41—216no—
741#41—224no—
742#41—31624no—
743#41—15816no—
744#41—15816no—
745#41—15824no—
746C2×Q8—216no—
747C2×Q8—216no—
748C2×Q8—216no—
749C2×Q8—212no—
750C2×Q8—7912no—
751C2×Q8—794no—
752C2×Q8—796no—
753C2×Q8—15816no—
754C2×Q8#1192962318yescomplemented
755C2×Q8C23×D79112yes—
756C2×Q8C23×D7916yes—
757C2×Q8C23×D7914yes—
758C2×D4—7912no—
759C2×D4—794no—
760C2×D4—794no—
761C2×D4—794no—
762C2×D4—794no—
763C2×D4—796no—
764C2×D4C23×D7914yes—
765C2×D4C23×D7916yes—
766C2×D4C23×D7914yes—
767C2×D4C23×D7914yes—
768C22×C4—212no—
769C22×C4—3166no—
770C22×C4—793no—
771C22×C4—796no—
772C22×C4—793no—
773C22×C4—7912no—
774C22×C4—7912no—
775C22×C4—791no—
776C22×C4—791no—
777C22×C4—791no—
778C22×C4—791no—
779C22×C4—791no—
780C22×C4—791no—
781C22×C4—794no—
782C22×C4—796no—
783C22×C4—794no—
784C22×C4—7912no—
785C22×C4—1584no—
786C22×C4C23×D7916yes—
787C22×C4C23×D7916yes—
788C22×C4C23×D7913yes—
789C22×C4C23×D79112yes—
790C22×C4C23×D7913yes—
791C4⋊C4—7912no—
792C4⋊C4—794no—
793C4⋊C4—794no—
794C4⋊C4—794no—
795C4⋊C4—794no—
796C4⋊C4—7912no—
797C4⋊C4—7912no—
798C4⋊C4—7912no—
799C4⋊C4—7912no—
800C4⋊C4—7912no—
801C4⋊C4—7912no—
802C4⋊C4—7912no—
803C4⋊C4—7924no—
804C4⋊C4—796no—
805C4⋊C4—7912no—
806C4⋊C4—796no—
807C4⋊C4—794no—
808C4⋊C4—794no—
809C4⋊C4—7912no—
810C4⋊C4C23×D7916yes—
811C4⋊C4C23×D7916yes—
812C4⋊C4C23×D79112yes—
813C4⋊C4C23×D79112yes—
814C22⋊C4—794no—
815C22⋊C4—794no—
816C22⋊C4—7912no—
817C22⋊C4—794no—
818C22⋊C4—794no—
819C22⋊C4—794no—
820C22⋊C4—7912no—
821C22⋊C4—7912no—
822C22⋊C4—794no—
823C22⋊C4—794no—
824C22⋊C4—7912no—
825C22⋊C4—7912no—
826C22⋊C4—7912no—
827C22⋊C4C23×D7914yes—
828C22⋊C4C23×D7914yes—
829C22⋊C4C23×D79112yes—
830C22⋊C4C23×D79112yes—
831C22⋊C4C23×D7914yes—
832C42—796no—
833C42—794no—
834C42—794no—
835C42—796no—
836C42—796no—
837C42—796no—
838C42—796no—
839C42—796no—
840C42—796no—
841C42—796no—
842C42—7912no—
843C42—7912no—
844C42—7912no—
845C42C23×D79112yes—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—794no—
850C23C24×D7914yes—
851C23C24×D7911yescharacteristic
852C23C24×D7911yescharacteristic
853C23C24×D7911yescharacteristic
854Q8—224no—
855Q8—212no—
856Q8—31612no—
857Q8—1588no—
858Q8—15812no—
859Q8C2×#11929623116yes—
860D4—28no—
861D4—28no—
862D4—28no—
863D4—212no—
864D4—31612no—
865D4—1588no—
866D4—1588no—
867D4—1588no—
868D4—1588no—
869D4—15812no—
870C2×C4—26no—
871C2×C4—212no—
872C2×C4—212no—
873C2×C4—224no—
874C2×C4—31612no—
875C2×C4—3163no—
876C2×C4—3166no—
877C2×C4—3163no—
878C2×C4—31612no—
879C2×C4—794no—
880C2×C4—791no—
881C2×C4—791no—
882C2×C4—791no—
883C2×C4—791no—
884C2×C4—796no—
885C2×C4—794no—
886C2×C4—794no—
887C2×C4—794no—
888C2×C4—796no—
889C2×C4—1588no—
890C2×C4—1582no—
891C2×C4—1582no—
892C2×C4—1582no—
893C2×C4—1582no—
894C2×C4—1588no—
895C2×C4—1582no—
896C2×C4—15812no—
897C2×C4—15824no—
898C2×C4C2×#11929623112yes—
899C2×C4C24×D7916yes—
900C2×C4C24×D7914yes—
901C2×C4C24×D7914yes—
902C2×C4C24×D7914yes—
903C2×C4C24×D7916yes—
904C22—28no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—1584no—
915C22—1584no—
916C22—1584no—
917C22C22×#1192962312yes—
918C222−1+4×D7912yes—
919C22#1909940012yes—
920C22C25×D7911yescharacteristic
921C4—24no—
922C4—26no—
923C4—24no—
924C4—24no—
925C4—792no—
926C4—792no—
927C4—1584no—
928C4—1581no—
929C4—1581no—
930C4—1584no—
931C4—1586no—
932C4—1584no—
933C4—1586no—
934C4C22×#11929623112yes—
935C2—22no—
936C2—22no—
937C2—22no—
938C2—44no—
939C2—3164no—
940C2C23×#1192962311yescharacteristic
941C2C2×2−1+4×D7911yescharacteristic
942C2C2×#1909940011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3486C2
hypercenter#3486D79
hypocenterC79#62788
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. #23777487C2semidirect
2. #23777476C2semidirect
3. #23777394C2semidirect
4. #23777382C2semidirect
5. #23777264C2semidirect
6. #23777206C2semidirect
7. #23777167C2semidirect
8. #23777106C2semidirect
9. #23777051C2semidirect
10. #23777021C2semidirect
11. #23777016C2semidirect
12. #23776990C2semidirect
13. Q8×#11929623C2semidirect
14. #23776824C2semidirect
15. #23776692C2semidirect
16. 2−1+4×Dic79C2semidirect
17. #23776609C2semidirect
18. C22×Q8×Dic79C2semidirect
19. C79×#3486C2semidirect
21. #19099295C22semidirect
22. Q8×Dic158C22semidirect
23. #19099292C22semidirect
24. #19099289C22semidirect
25. #19099289C22semidirect
26. #19099288C22semidirect
27. #19099287C22semidirect
28. #19099284C22semidirect
29. #19099282C22semidirect
31. #19099271C22semidirect
36. #19099255C22semidirect
38. #19099247C22semidirect
39. #19099232C22semidirect
42. Q8×C22⋊D79C22semidirect
45. #19099224C22semidirect
46. #19099220C22semidirect
50. #19099186C22semidirect
51. #19099182C22semidirect
52. #19099174C22semidirect
53. #19099173C22semidirect
57. #19099118C22semidirect
61. #19099115C22semidirect
67. #19099099C22semidirect
72. #19099092C22semidirect
79. #19099046C22semidirect
80. #19099045C22semidirect
83. #19099041C22semidirect
84. #19099039C22semidirect
86. #41×Dic79C22semidirect
87. C4×#11929625C22semidirect
99. C2×Q8×Dic79C22semidirect
100. C4×Q8×D79C22semidirect
350. C2×Q8×C79#41semidirect
415. C2×Dic792−1+4semidirect
481. #3486D79semidirect
491. C79#62788semidirect
754. C2×Q8#11929623semidirect

Maximal subgroups

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

subgroupindex
#237774872
#237774762
#237773942
#237773822
#237772642
#237772062
#237771672
#237771062
#237770512
#237770212
#237770162
#237769902
Q8×#119296232
#237768242
#237766922
2−1+4×Dic792
#237766092
C22×Q8×Dic792
C79×#34862
#6278879