Finite Group Databasebeta

← #35196557

Subgroups — #35196557

Order 20224.

7190 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777510C214yesmaximal, complemented
2#23777498C214yesmaximal, complemented
3#23777408C214yesmaximal, complemented
4#23777397C214yesmaximal, complemented
5#23777251C216yesmaximal, complemented
6#23777206C211yesmaximal, characteristic, complemented
7#23777167C211yesmaximal, characteristic, complemented
8#23777117C216yesmaximal, complemented
9#23777058C211yesmaximal, characteristic, complemented
10#23777023C214yesmaximal, complemented
11#23777016C214yesmaximal, complemented
12#23776999C214yesmaximal, complemented
13#23776990C214yesmaximal, complemented
14#23776813C216yesmaximal, complemented
15#23776692C216yesmaximal, complemented
162−1+4×Dic79C211yesmaximal, characteristic, complemented
17#23776609C211yesmaximal, characteristic, complemented
18C2×#41×Dic79C211yesmaximal, characteristic, complemented
19C79×#3487C211yesmaximal, characteristic, complemented
20C2×#14579209C2211yescharacteristic
21#19099299C22112yescomplemented
22#19099295C22112yescomplemented
23Q8×Dic158C2214yescomplemented
24#19099292C2214yescomplemented
25#19099289C2214yescomplemented
26#19099289C2214yescomplemented
27#19099284C22112yescomplemented
28#19099283C22112yescomplemented
29#19099282C22112yescomplemented
30#19099278C22112yescomplemented
31#19099277C22112yescomplemented
32#19099277C22112yescomplemented
33#19099265C22112yescomplemented
34#19099260C22112yescomplemented
35#19099260C22112yescomplemented
36#19099259C22112yescomplemented
37#19099253C22112yescomplemented
38#19099247C22112yescomplemented
39#19099233C22112yescomplemented
40#19099232C2214yes—
41#19099232C2214yes—
42#19099232C2214yescomplemented
43Q8×C22⋊D79C2214yescomplemented
44#19099224C2214yescomplemented
45#19099220C2214yes—
46#19099220C2214yes—
47#19099220C2214yescomplemented
48#19099213C22112yescomplemented
49#19099191C2216yes—
50#19099182C22112yescomplemented
51#19099180C22112yescomplemented
52#19099167C22112yescomplemented
53#19099166C22112yescomplemented
54#19099148C22124yes—
55#19099141C2216yes—
56#19099130C2216yes—
57#19099116C2216yes—
58#19099115C2216yescomplemented
59#19099115C2216yescomplemented
60#19099111C22112yescomplemented
61#19099109C2216yes—
62#19099108C22112yescomplemented
63#19099108C2216yescomplemented
64#19099108C2216yescomplemented
65#19099099C2216yescomplemented
66#19099099C2216yescomplemented
67#19099094C22112yescomplemented
68#19099094C2216yescomplemented
69#19099094C2216yescomplemented
70#19099093C22112yescomplemented
71#19099093C22112yescomplemented
72#19099092C22112yescomplemented
73#19099090C22112yes—
74#19099090C2214yes—
75#19099074C2216yes—
76#19099069C22112yes—
77#19099069C22112yes—
78#19099046C2216yes—
79#19099046C2214yescomplemented
80#19099045C2214yescomplemented
81#19099043C2216yes—
82#19099041C2211yescharacteristic
83#19099041C2214yescomplemented
84#19099039C2214yescomplemented
85#41×Dic79C2216yes—
86#41×Dic79C2214yes—
87#41×Dic79C2214yes—
88#41×Dic79C2214yes—
89#41×Dic79C2214yes—
90#41×Dic79C2214yescomplemented
91C4×#11929625C2214yescomplemented
92#19099031C2216yes—
93C4×#11929623C22112yescomplemented
94C4×#11929623C22112yescomplemented
95C2×Q8×Dic79C2211yescharacteristic
96C2×Q8×Dic79C2211yescharacteristic
97C2×Q8×Dic79C2214yescomplemented
98C4×Q8×D79C2214yescomplemented
99C2×D4×Dic79C2213yes—
100C2×D4×Dic79C2213yes—
101C2×#14579120C2213yes—
102C22×C4×Dic79C2213yes—
103C2×2−1+4×C79C2211yescharacteristic
104C22×#41×C79C2211yescharacteristic
105#550×C79C2214yes—
106#550×C79C2214yes—
107#548×C79C2214yes—
108#548×C79C2214yes—
109#535×C79C2216yes—
110#525×C79C2216yes—
111#519×C79C2211yescharacteristic
112#14579209—28no—
113C2×#11929625C2314yes—
114C2×#11929624C2316yes—
115C2×#11929623C23112yes—
116C2×#11929623C23112yes—
117C2×Q8×D79C2314yes—
118C23×Dic79C2313yes—
119C23×Dic79C2313yes—
120#14579161C23112yes—
121#14579160C23112yes—
122#14579160C2316yes—
123#14579160C2316yes—
124#14579159C2316yes—
125#14579157C23112yes—
126#14579157C2316yes—
127#14579156C23112yes—
128#14579156C2314yes—
129#14579154C23124yes—
130#14579154C23124yes—
131#14579154C23112yes—
132#14579154C2314yes—
133#14579153C23112yes—
134#14579152C23112yes—
135#14579152C2316yes—
136#14579152C2316yes—
137#14579151C23112yes—
138#14579151C2314yes—
139#14579150C2316yes—
140#14579148C23124yes—
141#14579148C23112yes—
142#14579148C2316yes—
143#14579147C23124yes—
144#14579147C23112yes—
145#14579147C2314yes—
146#14579145C23112yes—
147#14579145C23112yes—
148#14579144C2314yes—
149#14579143C23124yes—
150#14579142C23124yes—
151#14579142C23112yes—
152#14579142C23112yes—
153#14579140C23112yes—
154#14579140C2316yes—
155#14579140C2316yes—
156#14579138C23112yes—
157#14579138C23112yes—
158#14579138C23112yes—
159#14579138C2314yes—
160#14579137C23112yes—
161#14579135C23112yes—
162#14579135C2316yes—
163#14579135C2316yes—
164#14579133C23112yes—
165#14579133C23124yes—
166#14579133C23112yes—
167#14579133C23112yes—
168#14579133C2314yes—
169#14579132C23112yes—
170#14579132C23124yes—
171#14579132C23112yes—
172#14579132C23112yes—
173#14579130C23112yes—
174Q8×Dic79C2316yes—
175Q8×Dic79C2314yes—
176Q8×Dic79C2314yes—
177Q8×Dic79C2314yes—
178Q8×Dic79C2314yes—
179Q8×Dic79C23112yes—
180Q8×Dic79C2314yes—
181Q8×Dic79C2314yes—
182Q8×Dic79C2316yes—
183C4×Dic158C23112yes—
184C4×Dic158C23112yes—
185C4×Dic158C23112yes—
186#14579126C2316yes—
187#14579126C2316yes—
188#14579126C23112yes—
189#14579126C2314yes—
190C4×D316C23112yes—
191D4×Dic79C23112yes—
192D4×Dic79C23112yes—
193D4×Dic79C2316yes—
194D4×Dic79C23112yes—
195D4×Dic79C23112yes—
196D4×Dic79C23112yes—
197D4×Dic79C23112yes—
198D4×Dic79C23112yes—
199D4×Dic79C23112yes—
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#14579120C23112yes—
215#14579120C2316yes—
216#14579120C23112yes—
217#14579120C23112yes—
218#14579120C23112yes—
219#14579119C23112yes—
220#14579119C23112yes—
221#14579119C2314yes—
222#14579118C23112yes—
223#14579117C23112yes—
224#14579117C23112yes—
225#14579117C2314yes—
226#14579117C23112yes—
227C2×C4⋊Dic79C2313yes—
228C2×C4⋊Dic79C23112yes—
229C2×C4⋊Dic79C2313yes—
230C4⋊C4×D79C23112yes—
231C2×C22⋊Dic79C2316yes—
232C2×C4×Dic79C2311yescharacteristic
233C2×C4×Dic79C2313yes—
234C2×C4×Dic79C2313yes—
235C2×C4×Dic79C2313yes—
236C2×C4×Dic79C2316yes—
237C2×C4×Dic79C2316yes—
238C2×C4×Dic79C2316yes—
239C2×C4×Dic79C2316yes—
240C2×C4×Dic79C23112yes—
241C42×D79C23112yes—
2422−1+4×C79—28no—
243C2×#41×C79—28no—
244C2×#41×C79C2316yes—
245C2×#41×C79C2314yes—
246C2×#41×C79C2314yes—
247C2×#41×C79C2314yes—
248C22×Q8×C79C2314yes—
249C22×Q8×C79C2311yescharacteristic
250C22×D4×C79C2313yes—
251C23×C4×C79C2313yes—
252#127×C79C23112yes—
253#124×C79C23112yes—
254#123×C79C2314yes—
255C22⋊Q8×C79C2316yes—
256C22⋊Q8×C79C2316yes—
257#121×C79C23112yes—
258#121×C79C23112yes—
259#121×C79C2316yes—
260#121×C79C2316yes—
261#120×C79C23112yes—
262C4×Q8×C79C2314yes—
263C4×Q8×C79C2314yes—
264C4×D4×C79C23112yes—
265C4×D4×C79C23112yes—
266#117×C79C2316yes—
267#11929625—216no—
268#11929624—224no—
269#11929623—424no—
270#11929623—424no—
271C2×Dic158C2416yes—
272C2×Dic158C2414yes—
273C2×Dic158C24112yes—
274Q8×D79—216no—
275C2×D316C2416yes—
276C2×C22⋊D79C2414yes—
277C2×C22⋊D79C2414yes—
278C2×C22⋊D79C24112yes—
279C2×C22⋊D79C24112yes—
280C2×C22⋊D79C24112yes—
281C22×Dic79—46no—
282C22×Dic79—46no—
283C22×Dic79C2414yes—
284C22×Dic79C2416yes—
285C22×Dic79C2416yes—
286C22×Dic79C2411yescharacteristic
287C22×Dic79C2411yescharacteristic
288C22×Dic79C24112yes—
289C22×Dic79C2413yes—
290C22×Dic79C2413yes—
291C22×Dic79C2416yes—
292C22×Dic79C2416yes—
293C2×C4×D79C24112yes—
294C2×C4×D79C2414yes—
295C2×C4×D79C24112yes—
296C4⋊Dic79C24112yes—
297C4⋊Dic79C2416yes—
298C4⋊Dic79C24112yes—
299C4⋊Dic79C24112yes—
300C4⋊Dic79C2414yes—
301C4⋊Dic79C24112yes—
302C4⋊Dic79C2416yes—
303C4⋊Dic79C2414yes—
304Dic79⋊C4C24112yes—
305Dic79⋊C4C2414yes—
306Dic79⋊C4C2414yes—
307Dic79⋊C4C2414yes—
308Dic79⋊C4C2414yes—
309Dic79⋊C4C24112yes—
310Dic79⋊C4C24112yes—
311Dic79⋊C4C2414yes—
312Dic79⋊C4C24112yes—
313Dic79⋊C4C2414yes—
314C22⋊Dic79C24124yes—
315C22⋊Dic79C2414yes—
316C22⋊Dic79C24112yes—
317C22⋊Dic79C24112yes—
318C22⋊Dic79C24112yes—
319C22⋊Dic79C2414yes—
320C22⋊Dic79C24112yes—
321C22⋊Dic79C2414yes—
322(C2×D79)⋊C4C2414yes—
323(C2×D79)⋊C4C24112yes—
324(C2×D79)⋊C4C2414yes—
325(C2×D79)⋊C4C2414yes—
326(C2×D79)⋊C4C2414yes—
327(C2×D79)⋊C4C24112yes—
328C4×Dic79C2414yes—
329C4×Dic79C2416yes—
330C4×Dic79C24112yes—
331C4×Dic79C2411yescharacteristic
332C4×Dic79C2411yescharacteristic
333C4×Dic79C2411yescharacteristic
334C4×Dic79C2411yescharacteristic
335C4×Dic79C2414yes—
336C4×Dic79C2416yes—
337C4×Dic79C2416yes—
338C4×Dic79C2416yes—
339C4×Dic79C2416yes—
340C4×Dic79C2416yes—
341C4×Dic79C24112yes—
342C4×Dic79C24112yes—
343C24×C79C2413yes—
344#41×C79—216no—
345#41×C79—216no—
346#41×C79—216no—
347#41×C79—224no—
348C2×Q8×C79—216no—
349C2×Q8×C79#4118yescomplemented
350C2×Q8×C79C2416yes—
351C2×Q8×C79C2414yes—
352C2×D4×C79—212no—
353C2×D4×C79C2414yes—
354C2×D4×C79C24112yes—
355C2×D4×C79C2416yes—
356C2×D4×C79C24112yes—
357C2×D4×C79C24112yes—
358C22×C4×C79—212no—
359C22×C4×C79C24112yes—
360C22×C4×C79C2416yes—
361C22×C4×C79C2416yes—
362C22×C4×C79C2411yescharacteristic
363C22×C4×C79C2413yes—
364C4⋊C4×C79C2416yes—
365C4⋊C4×C79C2416yes—
366C4⋊C4×C79C2414yes—
367C4⋊C4×C79C2414yes—
368C22⋊C4×C79C2414yes—
369C22⋊C4×C79C2414yes—
370C22⋊C4×C79C2414yes—
371C22⋊C4×C79C24112yes—
372C22⋊C4×C79C24112yes—
373C42×C79C24112yes—
374C23×C79—26no—
375C23×C79—43no—
376C23×C79—43no—
377C23×C79C2516yes—
378C23×C79C2514yes—
379C23×C79C2511yescharacteristic
380C22×D79C2514yes—
381Q8×C79—212no—
382Q8×C79C2×#41116yes—
383D4×C79—28no—
384D4×C79—224no—
385D4×C79—212no—
386D4×C79—412no—
387D4×C79—412no—
388C2×C4×C79—22no—
389C2×C4×C79—212no—
390C2×C4×C79—212no—
391C2×C4×C79—224no—
392C2×C4×C79C2×#41112yes—
393C2×C4×C79C2511yescharacteristic
394C2×C4×C79C2511yescharacteristic
395C2×C4×C79C2514yes—
396C2×C4×C79C2514yes—
397C2×C4×C79C2514yes—
398C2×C4×C79C2516yes—
399C22⋊D79—28no—
400C22⋊D79—28no—
401C22⋊D79—412no—
402C22⋊D79—412no—
403C22⋊D79—412no—
404C2×Dic79—22no—
405C2×Dic79—22no—
406C2×Dic79—212no—
407C2×Dic79—212no—
408C2×Dic79—28no—
409C2×Dic79—43no—
410C2×Dic79—46no—
411C2×Dic79—43no—
412C2×Dic79—46no—
413C2×Dic79—412no—
414C2×Dic79C2511yescharacteristic
415C2×Dic79C2511yescharacteristic
416C2×Dic79C2516yes—
417C2×Dic79C2514yes—
418C2×Dic79C2516yes—
419C2×Dic79C2514yes—
420C2×Dic79C2514yes—
421C2×Dic79C2511yescharacteristic
422C2×Dic79C2511yescharacteristic
423D316—212no—
424C4×D79—224no—
425C4×D79—28no—
426C4×D79—412no—
427Dic158—212no—
428Dic158—28no—
429Dic158—412no—
430C22×C79—21no—
431C22×C79—21no—
432C22×C79—24no—
433C22×C79—26no—
434C22×C79—24no—
435C22×C79—24no—
436C22×C79—26no—
437C22×C79—26no—
438C22×C79—412no—
439C22×C79C22×#4112yes—
440C22×C79C2611yescharacteristic
441C2×D79—24no—
442C2×D79—24no—
443C2×D79—24no—
444C4×C79—21no—
445C4×C79—21no—
446C4×C79—24no—
447C4×C79—24no—
448C4×C79—24no—
449C4×C79C22×#41112yes—
450Dic79—24no—
451Dic79—24no—
452Dic79—24no—
453Dic79—26no—
454Dic79—26no—
455Dic79—21no—
456Dic79—21no—
457Dic79#58512yes—
458Dic79#58512yes—
459#62793—791nomaximal, Sylow
460C2×C79—22no—
461C2×C79—44no—
462C2×C79—46no—
463C2×C79C23×#4111yescharacteristic
464C2×C79C2×#58511yescharacteristic
465C2×C79C2×#58511yescharacteristic
466D79—44no—
467#3524—794no—
468#3524—794no—
469#3518—794no—
470#3517—794no—
471#3506—796no—
472#3502—791no—
473#3497—791no—
474#3493—796no—
475#3487—791no—
476#3487D7911yescharacteristic, complemented
477#3483—794no—
478#3482—794no—
479#3480—794no—
480#3480—794no—
481#3460—796no—
482#3444—796no—
483C4×2−1+4—791no—
484C4×2−1+4—791no—
485C2×C4×#41—791no—
486C79#6279311yescharacteristic, complemented, Sylow
487C2×2−1+4—791no—
488C2×2−1+4C2×D7911yescharacteristic
489C22×#41C2×D7911yescharacteristic
490#559—7912no—
491#559—7912no—
492Q82—794no—
493#557—794no—
494#557—794no—
495#557—794no—
496#556—7912no—
497#556—7912no—
498#556—7912no—
499#555—7912no—
500#555—7912no—
501#555—7912no—
502#553—7912no—
503#553—7912no—
504#553—7912no—
505#553—7912no—
506#552—7912no—
507#552—7912no—
508#550—794no—
509#550—794no—
510#550—794no—
511#550—7912no—
512#550C2×D7914yes—
513#550C2×D7914yes—
514D4×Q8—794no—
515#548—794no—
516#548—794no—
517#548—794no—
518#548—794no—
519#548C2×D7914yes—
520#548C2×D7914yes—
521#547—7912no—
522#544—796no—
523#542—7912no—
524#542—7912no—
525#540—7912no—
526#540—7912no—
527#538—7924no—
528#537—796no—
529#535—796no—
530#535C2×D7916yes—
531#533—796no—
532#533—796no—
533#533—796no—
534#532—796no—
535#532—7912no—
536#532—796no—
537#532—796no—
538#532—7912no—
539#529—7912no—
540#529—794no—
541#529—7912no—
542#529—796no—
543#529—796no—
544#529—796no—
545#529—796no—
546#529—7912no—
547#529—7912no—
548#529—7912no—
549#525—796no—
550#525—7912no—
551#525—7912no—
552#525C2×D7916yes—
553#520—796no—
554#520—794no—
555#520—794no—
556#520—796no—
557#519—791no—
558#519—794no—
559#519—794no—
560#519C2×D7911yescharacteristic
561C4×#41—794no—
562C4×#41—794no—
563C4×#41—794no—
564C4×#41—794no—
565C4×#41—796no—
566C4×#41—794no—
567C4×#41—794no—
568C4×#41—7912no—
569C4×#41—7912no—
570C4×#41—796no—
571C2×C4×Q8—791no—
572C2×C4×Q8—791no—
573C2×C4×Q8—794no—
574C2×C4×Q8—794no—
575C2×C4×D4—793no—
576C2×C4×D4—793no—
577C2×#117—793no—
578C22×C42—793no—
5792−1+4—28no—
5802−1+4—1588no—
581C2×#41—28no—
582C2×#41—794no—
583C2×#41—7912no—
584C2×#41—7912no—
585C2×#41—796no—
586C2×#41C22×D7914yes—
587C2×#41C22×D7914yes—
588C2×#41C22×D7916yes—
589C2×#41C22×D7914yes—
590C22×Q8—794no—
591C22×Q8C22×D7914yes—
592C22×Q8C22×D7911yescharacteristic
593C22×D4C22×D7913yes—
594C23×C4—793no—
595C23×C4—793no—
596C23×C4C22×D7913yes—
597C4⋊Q8—796no—
598C4⋊Q8—796no—
599C4⋊Q8—796no—
600C4⋊Q8—7912no—
601C4⋊Q8—7912no—
602#127—796no—
603#127—7912no—
604#127C22×D79112yes—
605#126—794no—
606#126—7912no—
607#126—794no—
608#126—7912no—
609#126—7924no—
610#126—7924no—
611#125—794no—
612#125—7912no—
613#125—796no—
614#125—796no—
615#125—7912no—
616#125—7912no—
617#124—796no—
618#124—796no—
619#124—7912no—
620#124—7924no—
621#124—794no—
622#124—7912no—
623#124—7924no—
624#124C22×D79112yes—
625#123—7912no—
626#123—7912no—
627#123—7924no—
628#123—794no—
629#123—7912no—
630#123—7912no—
631#123—7924no—
632#123C22×D7914yes—
633C22⋊Q8—7912no—
634C22⋊Q8—796no—
635C22⋊Q8—796no—
636C22⋊Q8—7912no—
637C22⋊Q8—794no—
638C22⋊Q8—7912no—
639C22⋊Q8—7912no—
640C22⋊Q8—7912no—
641C22⋊Q8C22×D7916yes—
642C22⋊Q8C22×D7916yes—
643#121—794no—
644#121—7912no—
645#121—7912no—
646#121—7912no—
647#121—7912no—
648#121—7912no—
649#121—7912no—
650#121—7924no—
651#121—7924no—
652#121—796no—
653#121—796no—
654#121—7912no—
655#121C22×D7916yes—
656#121C22×D7916yes—
657#121C22×D79112yes—
658#121C22×D79112yes—
659#120—7912no—
660#120C22×D79112yes—
661C4×Q8—794no—
662C4×Q8—796no—
663C4×Q8—794no—
664C4×Q8—794no—
665C4×Q8—794no—
666C4×Q8—794no—
667C4×Q8—7912no—
668C4×Q8—796no—
669C4×Q8—794no—
670C4×Q8—796no—
671C4×Q8—794no—
672C4×Q8—796no—
673C4×Q8—7912no—
674C4×Q8—7912no—
675C4×Q8—7912no—
676C4×Q8—7912no—
677C4×Q8C22×D7914yes—
678C4×Q8C22×D7914yes—
679C4×D4—7912no—
680C4×D4—7912no—
681C4×D4—7912no—
682C4×D4—7912no—
683C4×D4—794no—
684C4×D4—796no—
685C4×D4—7912no—
686C4×D4—796no—
687C4×D4—7912no—
688C4×D4—7912no—
689C4×D4—7912no—
690C4×D4—7912no—
691C4×D4—7912no—
692C4×D4—7912no—
693C4×D4—7912no—
694C4×D4—796no—
695C4×D4—796no—
696C4×D4—794no—
697C4×D4—794no—
698C4×D4—7912no—
699C4×D4—7912no—
700C4×D4—7912no—
701C4×D4—7912no—
702C4×D4—7912no—
703C4×D4C22×D79112yes—
704C4×D4C22×D79112yes—
705#117—7912no—
706#117—7912no—
707#117—796no—
708#117—7912no—
709#117—7912no—
710#117—794no—
711#117—7912no—
712#117—7912no—
713#117—794no—
714#117—7912no—
715#117—7912no—
716#117—7912no—
717#117—7912no—
718#117C22×D7916yes—
719C2×C4⋊C4—793no—
720C2×C4⋊C4—793no—
721C2×C4⋊C4—7912no—
722C2×C4⋊C4—7912no—
723C2×C22⋊C4—796no—
724C2×C42—793no—
725C2×C42—793no—
726C2×C42—793no—
727C2×C42—7912no—
728C2×C42—796no—
729C2×C42—796no—
730C2×C42—796no—
731C2×C42—796no—
732C2×C42—791no—
733C2×C42—7912no—
734C24C23×D7913yes—
735#41—216no—
736#41—216no—
737#41—216no—
738#41—224no—
739#41—31624no—
740#41—31624no—
741#41—15816no—
742#41—15824no—
743C2×Q8—216no—
744C2×Q8—7912no—
745C2×Q8—796no—
746C2×Q8—794no—
747C2×Q8—15816no—
748C2×Q8#1192962318yescomplemented
749C2×Q8C23×D7916yes—
750C2×Q8C23×D7914yes—
751C2×D4—212no—
752C2×D4—7912no—
753C2×D4—7912no—
754C2×D4—7912no—
755C2×D4—794no—
756C2×D4—794no—
757C2×D4—796no—
758C2×D4C23×D7914yes—
759C2×D4C23×D79112yes—
760C2×D4C23×D7916yes—
761C2×D4C23×D79112yes—
762C2×D4C23×D79112yes—
763C22×C4—212no—
764C22×C4—3166no—
765C22×C4—3166no—
766C22×C4—793no—
767C22×C4—793no—
768C22×C4—796no—
769C22×C4—796no—
770C22×C4—7912no—
771C22×C4—7912no—
772C22×C4—791no—
773C22×C4—791no—
774C22×C4—794no—
775C22×C4—796no—
776C22×C4—796no—
777C22×C4—794no—
778C22×C4—7912no—
779C22×C4C23×D7911yescharacteristic
780C22×C4C23×D7916yes—
781C22×C4C23×D7916yes—
782C22×C4C23×D79112yes—
783C22×C4C23×D7913yes—
784C4⋊C4—7912no—
785C4⋊C4—794no—
786C4⋊C4—794no—
787C4⋊C4—794no—
788C4⋊C4—794no—
789C4⋊C4—794no—
790C4⋊C4—794no—
791C4⋊C4—7912no—
792C4⋊C4—7912no—
793C4⋊C4—7912no—
794C4⋊C4—7912no—
795C4⋊C4—796no—
796C4⋊C4—7912no—
797C4⋊C4—7912no—
798C4⋊C4—796no—
799C4⋊C4—794no—
800C4⋊C4—794no—
801C4⋊C4—7912no—
802C4⋊C4C23×D7916yes—
803C4⋊C4C23×D7914yes—
804C4⋊C4C23×D7916yes—
805C4⋊C4C23×D7914yes—
806C22⋊C4—7924no—
807C22⋊C4—794no—
808C22⋊C4—794no—
809C22⋊C4—7912no—
810C22⋊C4—794no—
811C22⋊C4—7912no—
812C22⋊C4—7912no—
813C22⋊C4—7912no—
814C22⋊C4—794no—
815C22⋊C4—7912no—
816C22⋊C4—794no—
817C22⋊C4—794no—
818C22⋊C4—794no—
819C22⋊C4—7912no—
820C22⋊C4C23×D7914yes—
821C22⋊C4C23×D7914yes—
822C22⋊C4C23×D79112yes—
823C22⋊C4C23×D79112yes—
824C22⋊C4C23×D7914yes—
825C42—791no—
826C42—791no—
827C42—796no—
828C42—791no—
829C42—791no—
830C42—796no—
831C42—794no—
832C42—794no—
833C42—796no—
834C42—796no—
835C42—796no—
836C42—796no—
837C42—7912no—
838C42—7912no—
839C42—7912no—
840C42C23×D79112yes—
841C23—26no—
842C23—43no—
843C23—43no—
844C23—794no—
845C23C24×D7916yes—
846C23C24×D7914yes—
847C23C24×D7911yescharacteristic
848Q8—212no—
849Q8—31612no—
850Q8—1588no—
851Q8—15812no—
852Q8C2×#11929623116yes—
853D4—28no—
854D4—224no—
855D4—212no—
856D4—412no—
857D4—412no—
858D4—31612no—
859D4—31612no—
860D4—31612no—
861D4—1588no—
862D4—1588no—
863D4—15812no—
864C2×C4—22no—
865C2×C4—212no—
866C2×C4—212no—
867C2×C4—224no—
868C2×C4—31612no—
869C2×C4—3163no—
870C2×C4—3166no—
871C2×C4—3166no—
872C2×C4—3163no—
873C2×C4—31612no—
874C2×C4—791no—
875C2×C4—791no—
876C2×C4—791no—
877C2×C4—796no—
878C2×C4—791no—
879C2×C4—794no—
880C2×C4—794no—
881C2×C4—796no—
882C2×C4—794no—
883C2×C4—1588no—
884C2×C4—1582no—
885C2×C4—1582no—
886C2×C4—15812no—
887C2×C4—15812no—
888C2×C4—1588no—
889C2×C4—15824no—
890C2×C4C2×#11929623112yes—
891C2×C4C24×D7911yescharacteristic
892C2×C4C24×D7911yescharacteristic
893C2×C4C24×D7914yes—
894C2×C4C24×D7914yes—
895C2×C4C24×D7914yes—
896C2×C4C24×D7916yes—
897C22—21no—
898C22—21no—
899C22—24no—
900C22—26no—
901C22—24no—
902C22—26no—
903C22—26no—
904C22—24no—
905C22—412no—
906C22—1584no—
907C22—1584no—
908C22—1584no—
909C22C22×#1192962312yes—
910C22C25×D7911yescharacteristic
911C4—21no—
912C4—21no—
913C4—24no—
914C4—24no—
915C4—24no—
916C4—792no—
917C4—792no—
918C4—1584no—
919C4—1586no—
920C4—1581no—
921C4—1581no—
922C4—1584no—
923C4—1586no—
924C4—1584no—
925C4C22×#11929623112yes—
926C2—22no—
927C2—46no—
928C2—44no—
929C2—3164no—
930C2C23×#1192962311yescharacteristic
931C2#585×D7911yescharacteristic
932C2#585×D7911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3487C2
hypercenter#3487D79
hypocenterC79#62793
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. #23777510C2semidirect
2. #23777498C2semidirect
3. #23777408C2semidirect
4. #23777397C2semidirect
5. #23777251C2semidirect
6. #23777206C2semidirect
7. #23777167C2semidirect
8. #23777117C2semidirect
9. #23777058C2semidirect
10. #23777023C2semidirect
11. #23777016C2semidirect
12. #23776999C2semidirect
13. #23776990C2semidirect
14. #23776813C2semidirect
15. #23776692C2semidirect
16. 2−1+4×Dic79C2semidirect
17. #23776609C2semidirect
18. C2×#41×Dic79C2semidirect
19. C79×#3487C2semidirect
21. #19099299C22semidirect
22. #19099295C22semidirect
23. Q8×Dic158C22semidirect
24. #19099292C22semidirect
25. #19099289C22semidirect
26. #19099289C22semidirect
27. #19099284C22semidirect
28. #19099283C22semidirect
29. #19099282C22semidirect
30. #19099278C22semidirect
31. #19099277C22semidirect
32. #19099277C22semidirect
33. #19099265C22semidirect
34. #19099260C22semidirect
35. #19099260C22semidirect
36. #19099259C22semidirect
37. #19099253C22semidirect
38. #19099247C22semidirect
39. #19099233C22semidirect
42. #19099232C22semidirect
43. Q8×C22⋊D79C22semidirect
44. #19099224C22semidirect
47. #19099220C22semidirect
48. #19099213C22semidirect
50. #19099182C22semidirect
51. #19099180C22semidirect
52. #19099167C22semidirect
53. #19099166C22semidirect
58. #19099115C22semidirect
59. #19099115C22semidirect
60. #19099111C22semidirect
62. #19099108C22semidirect
63. #19099108C22semidirect
64. #19099108C22semidirect
65. #19099099C22semidirect
66. #19099099C22semidirect
67. #19099094C22semidirect
68. #19099094C22semidirect
69. #19099094C22semidirect
70. #19099093C22semidirect
71. #19099093C22semidirect
72. #19099092C22semidirect
79. #19099046C22semidirect
80. #19099045C22semidirect
83. #19099041C22semidirect
84. #19099039C22semidirect
90. #41×Dic79C22semidirect
91. C4×#11929625C22semidirect
93. C4×#11929623C22semidirect
94. C4×#11929623C22semidirect
97. C2×Q8×Dic79C22semidirect
98. C4×Q8×D79C22semidirect
349. C2×Q8×C79#41semidirect
476. #3487D79semidirect
486. C79#62793semidirect
748. C2×Q8#11929623semidirect

Maximal subgroups

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

subgroupindex
#237775102
#237774982
#237774082
#237773972
#237772512
#237772062
#237771672
#237771172
#237770582
#237770232
#237770162
#237769992
#237769902
#237768132
#237766922
2−1+4×Dic792
#237766092
C2×#41×Dic792
C79×#34872
#6279379