Finite Group Databasebeta

← #35410871

Subgroups — #35410871

Order 21248.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127823C211yesmaximal, characteristic, complemented
2C2×#19127818C211yesmaximal, characteristic, complemented
3#24916181C211yesmaximal, characteristic, complemented
4#24915891C211yesmaximal, characteristic, complemented
5#24908383C211yesmaximal, characteristic, complemented
6#24908239C211yesmaximal, characteristic, complemented
7#24908113C211yesmaximal, characteristic, complemented
8#24908113C211yesmaximal, characteristic, complemented
9#24907792C211yesmaximal, characteristic, complemented
10#24907792C211yesmaximal, characteristic, complemented
11#24907483C211yesmaximal, characteristic, complemented
12#24907340C211yesmaximal, characteristic, complemented
13#24907310C211yesmaximal, characteristic, complemented
14#24907303C211yesmaximal, characteristic, complemented
15C83×#3035C211yesmaximal, characteristic
16C2×#14581799C2211yescharacteristic
17C2×#14581799C2211yescharacteristic
18C2×#14581799C2211yescharacteristic
19C2×#14581799C2211yescharacteristic
20#19127823—24no—
21#19127818—24no—
22#19127773—21no—
23#19127773—21no—
24#19127773—21no—
25#19127773—21no—
26C2×#14581728C2211yescharacteristic
27C2×#14581728C2211yescharacteristic
28#19127725C2211yescharacteristic
29C2×#14581719C2211yescharacteristic
30C2×#14581719C2211yescharacteristic
31C2×#14581719C2211yescharacteristic
32C2×#14581719C2211yescharacteristic
33C2×#14581719C2211yescharacteristic
34C2×#14581719C2211yescharacteristic
35#19127668C2211yescharacteristic
36#19127668C2211yescharacteristic
37#19127657—21no—
38#19127657—21no—
39#19127657C2211yescharacteristic
40#19127657C2211yescharacteristic
41C4×#13050574—21no—
42C4×#13050574C2211yescharacteristic
43C2×#14581703—21no—
44C2×#14581703C2211yescharacteristic
45C2×#14581702C2211yescharacteristic
46C2×C8×Dic83C2211yescharacteristic
47C4×C4⋊Dic83C2211yescharacteristic
48#19127466C2211yescharacteristic
49#19127466C2211yescharacteristic
50#19127460C2211yescharacteristic
51#19127460C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54C2×#135×C83C2211yescharacteristic
55C2×#135×C83C2211yescharacteristic
56#532×C83C2211yescharacteristic
57C4×#41×C83C2211yescharacteristic
58#464×C83C411yescharacteristic, complemented
59#464×C83C411yescharacteristic, complemented
60#463×C83C411yescharacteristic, complemented
61#463×C83C411yescharacteristic, complemented
62#462×C83C411yescharacteristic, complemented
63#461×C83C411yescharacteristic, complemented
64#460×C83C411yescharacteristic, complemented
65#459×C83C411yescharacteristic, complemented
66C2×C4⋊C8×C83C2211yescharacteristic
67#416×C83C2211yescharacteristic
68#416×C83C2211yescharacteristic
69#14581799—22no—
70#14581799—22no—
71#14581799—22no—
72#14581799—22no—
73#14581799—22no—
74#14581799—22no—
75#14581799—22no—
76#14581799D414yescomplemented
77C2×#13050574—21no—
78C2×#13050574—21no—
79C2×#13050574—21no—
80C2×#13050574—21no—
81C2×#13050574C2311yescharacteristic
82C2×#13050574C2311yescharacteristic
83C2×#13050574C2311yescharacteristic
84C2×#13050574C2311yescharacteristic
85C22×C83⋊C8—21no—
86C22×C83⋊C8—21no—
87C22×C83⋊C8—21no—
88C22×C83⋊C8—21no—
89C22×C83⋊C8C2311yescharacteristic
90C22×C83⋊C8C2311yescharacteristic
91C2×C4⋊Dic83—21no—
92C2×C4×Dic83C2311yescharacteristic
93C2×C4×Dic83C2311yescharacteristic
94#14581728—22no—
95#14581728—22no—
96C4⋊(C83⋊C8)—21no—
97C4⋊(C83⋊C8)—21no—
98#14581719—22no—
99#14581719—22no—
100#14581719—22no—
101#14581719—22no—
102#14581719—22no—
103#14581719—22no—
104C22⋊(C83⋊C8)—21no—
105C22⋊(C83⋊C8)—21no—
106C22⋊(C83⋊C8)—21no—
107C22⋊(C83⋊C8)—21no—
108#14581703—21no—
109#14581703—21no—
110#14581703—21no—
111#14581703D411yescharacteristic
112#14581703D411yescharacteristic
113#14581703D411yescharacteristic
114#14581703D411yescharacteristic
115#14581702—22no—
116C4×C83⋊C8—21no—
117C4×C83⋊C8—21no—
118C4×C83⋊C8—21no—
119C8×Dic83—22no—
120C83⋊#95—21no—
121C2×#41×C83C2311yescharacteristic
122C2×#41×C83C2311yescharacteristic
123C2×#41×C83C2311yescharacteristic
124#135×C83—22no—
125#135×C83—22no—
126#135×C83—22no—
127#135×C83—22no—
128C2×Q16×C83C2×C411yescharacteristic
129C2×Q16×C83C2×C411yescharacteristic
130C2×SD16×C83C2×C411yescharacteristic
131C2×SD16×C83C2×C411yescharacteristic
132C2×SD16×C83C2×C411yescharacteristic
133C2×SD16×C83C2×C411yescharacteristic
134C2×D8×C83C2×C411yescharacteristic
135C2×D8×C83C2×C411yescharacteristic
136C22×C8×C83C2311yescharacteristic
137C22×C8×C83C2311yescharacteristic
138C4⋊Q8×C83C2×C411yescharacteristic
139#127×C83C2×C411yescharacteristic
140#124×C83C2×C411yescharacteristic
141#124×C83C2×C411yescharacteristic
142#121×C83—21no—
143#121×C83—21no—
144C4×Q8×C83C2×C411yescharacteristic
145C4×Q8×C83C2×C411yescharacteristic
146C4×D4×C83—21no—
147C4×D4×C83—21no—
148C4×D4×C83—21no—
149C4×D4×C83—21no—
150C4×D4×C83C2×C411yescharacteristic
151C4×D4×C83C2×C411yescharacteristic
152#117×C83—21no—
153#117×C83C2311yescharacteristic
154C2×C42×C83—21no—
155C2×C42×C83C2311yescharacteristic
156C4⋊C8×C83C2×C411yescharacteristic
157C4⋊C8×C83C2×C411yescharacteristic
158C4⋊C8×C83C2×C411yescharacteristic
159C4⋊C8×C83C2×C411yescharacteristic
160#103×C83C2×C411yescharacteristic
161#103×C83C2×C411yescharacteristic
162#103×C83C2×C411yescharacteristic
163#103×C83C2×C411yescharacteristic
164#102×C83C2×C411yescharacteristic
165#102×C83C2×C411yescharacteristic
166#102×C83C2×C411yescharacteristic
167#102×C83C2×C411yescharacteristic
168C22×Dic83—21no—
169C22×Dic83—21no—
170#13050574—24no—
171#13050574—21no—
172#13050574—21no—
173#13050574—24no—
174#13050574—21no—
175#13050574—21no—
176#13050574—21no—
177#13050574—21no—
178#13050574—42no—
179#13050574—42no—
180#13050574C2×D412yes—
181#13050574#4112yes—
182C2×C83⋊C8—24no—
183C2×C83⋊C8—21no—
184C2×C83⋊C8—21no—
185C2×C83⋊C8—21no—
186C2×C83⋊C8—21no—
187C2×C83⋊C8—24no—
188C2×C83⋊C8—21no—
189C2×C83⋊C8—21no—
190C2×C83⋊C8—42no—
191C2×C83⋊C8—42no—
192C2×C83⋊C8C2×D411yescharacteristic
193C2×C83⋊C8C2×D411yescharacteristic
194C2×C83⋊C8C2×D411yescharacteristic
195C2×C83⋊C8C2×D411yescharacteristic
196C2×C83⋊C8C2×D412yes—
197C2×C83⋊C8#4112yes—
198C4⋊Dic83—42no—
199C4×Dic83—21no—
200C4×Dic83—21no—
201C4×Dic83—21no—
202C4×Dic83—21no—
203#41×C83—21no—
204#41×C83—21no—
205#41×C83—21no—
206#41×C83—21no—
207#41×C83—21no—
208#41×C83—21no—
209#41×C83—21no—
210#41×C83—21no—
211#41×C83—21no—
212#41×C83—21no—
213#41×C83C2×D412yes—
214#41×C83#4112yes—
215C2×Q8×C83C22×C411yescharacteristic
216C2×Q8×C83C22×C411yescharacteristic
217C2×Q8×C83C22×C411yescharacteristic
218C2×D4×C83—21no—
219C2×D4×C83—21no—
220C2×D4×C83—21no—
221C2×D4×C83—21no—
222C2×D4×C83—21no—
223C2×D4×C83C22×C411yescharacteristic
224C2×D4×C83C22×C411yescharacteristic
225C2×D4×C83C22×C411yescharacteristic
226C22×C4×C83—21no—
227C22×C4×C83—21no—
228C22×C4×C83—21no—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83#4111yescharacteristic
232C22×C4×C83#4111yescharacteristic
233C22×C4×C83C2411yescharacteristic
234Q16×C83—22no—
235Q16×C83—22no—
236SD16×C83—22no—
237SD16×C83—22no—
238SD16×C83—22no—
239SD16×C83—22no—
240D8×C83—22no—
241D8×C83—22no—
242C2×C8×C83—21no—
243C2×C8×C83—21no—
244C2×C8×C83—21no—
245C2×C8×C83—21no—
246C2×C8×C83C22×C411yescharacteristic
247C2×C8×C83C22×C411yescharacteristic
248C2×C8×C83C22×C411yescharacteristic
249C2×C8×C83C22×C411yescharacteristic
250C4⋊C4×C83—21no—
251C4⋊C4×C83—21no—
252C4⋊C4×C83—21no—
253C4⋊C4×C83—21no—
254C4⋊C4×C83C22×C411yescharacteristic
255C4⋊C4×C83C22×C411yescharacteristic
256C22⋊C4×C83—21no—
257C22⋊C4×C83—21no—
258C22⋊C4×C83—21no—
259C22⋊C4×C83—21no—
260C22⋊C4×C83—21no—
261C22⋊C4×C83—21no—
262C22⋊C4×C83—21no—
263C42×C83—21no—
264C42×C83—21no—
265C42×C83—21no—
266C42×C83C22×C411yescharacteristic
267C42×C83C22×C411yescharacteristic
268C42×C83C2×D411yescharacteristic
269C42×C83C2×D411yescharacteristic
270C23×C83—21no—
271C23×C83—21no—
272C23×C83—21no—
273C23×C83C2×#4111yescharacteristic
274Q8×C83—21no—
275Q8×C83—21no—
276Q8×C83—21no—
277Q8×C83—21no—
278Q8×C83—21no—
279Q8×C83C4×D412yes—
280D4×C83—22no—
281D4×C83—22no—
282D4×C83—21no—
283D4×C83—21no—
284D4×C83—21no—
285D4×C83—21no—
286D4×C83—21no—
287D4×C83—41no—
288D4×C83—41no—
289D4×C83—41no—
290D4×C83—41no—
291D4×C83—81no—
292D4×C83—81no—
293D4×C83C4×D412yes—
294C2×C4×C83—21no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—21no—
298C2×C4×C83—21no—
299C2×C4×C83—21no—
300C2×C4×C83—21no—
301C2×C4×C83—41no—
302C2×C4×C83—41no—
303C2×C4×C83—41no—
304C2×C4×C83—41no—
305C2×C4×C83—41no—
306C2×C4×C83—41no—
307C2×C4×C83—81no—
308C2×C4×C83—81no—
309C2×C4×C83C4×D411yescharacteristic
310C2×C4×C83C4×D411yescharacteristic
311C2×C4×C83C4×D411yescharacteristic
312C2×C4×C83C4×D411yescharacteristic
313C2×C4×C83C23×C411yescharacteristic
314C2×C4×C83C22×D411yescharacteristic
315C2×C4×C83C22×D411yescharacteristic
316C2×C4×C83C2×#4111yescharacteristic
317C2×C4×C83C2×#4111yescharacteristic
318C2×C4×C83C2×#4111yescharacteristic
319C2×Dic83—22no—
320C2×Dic83—41no—
321C2×Dic83—41no—
322C2×Dic83—41no—
323C2×Dic83—41no—
324C2×Dic83—41no—
325C8×C83—21no—
326C8×C83—21no—
327C8×C83—21no—
328C8×C83—21no—
329C83⋊C8—22no—
330C83⋊C8—21no—
331C83⋊C8—22no—
332C83⋊C8—21no—
333C83⋊C8—41no—
334C83⋊C8—41no—
335C83⋊C8#12112yes—
336C83⋊C8#12112yes—
337C22×C83—21no—
338C22×C83—21no—
339C22×C83—22no—
340C22×C83—41no—
341C22×C83—41no—
342C22×C83—41no—
343C22×C83—41no—
344C22×C83—41no—
345C22×C83—41no—
346C22×C83—41no—
347C22×C83—41no—
348C22×C83C2×C4×D411yescharacteristic
349C22×C83#52911yescharacteristic
350C22×C83#53211yescharacteristic
351C4×C83—21no—
352C4×C83—21no—
353C4×C83—21no—
354C4×C83—21no—
355C4×C83—22no—
356C4×C83—41no—
357C4×C83—41no—
358C4×C83—41no—
359C4×C83—41no—
360C4×C83C2×C4×D411yescharacteristic
361C4×C83C4×#4111yescharacteristic
362C4×C83C2×#12111yescharacteristic
363C4×C83#52511yescharacteristic
364Dic83—42no—
365Dic83—81no—
366#21519—831nomaximal, Sylow
367C2×C83—21no—
368C2×C83—21no—
369C2×C83—42no—
370C2×C83—81no—
371C2×C83—81no—
372C2×C83C4×#12111yescharacteristic
373C2×C83#295611yescharacteristic
374C2×C83#295711yescharacteristic
375#3035D8311yescharacteristic
376C2×#444—831no—
377C2×#443—831no—
378#2932—831no—
379#2875—831no—
380#1980—831no—
381#1950—831no—
382#1929—831no—
383#1929—831no—
384#1876—831no—
385#1876—831no—
386#1806—831no—
387#1771—831no—
388#1765—831no—
389#1764—831no—
390C83#2151911yescharacteristic, complemented, Sylow
391C2×#135C2×D8311yescharacteristic
392C2×#135C2×D8311yescharacteristic
393C2×#131—831no—
394C2×#131—831no—
395C2×#131—831no—
396C2×#131—831no—
397#532C2×D8311yescharacteristic
398C4×#41C2×D8311yescharacteristic
399#464Dic8311yescharacteristic, complemented
400#464Dic8311yescharacteristic, complemented
401#463Dic8311yescharacteristic, complemented
402#463Dic8311yescharacteristic, complemented
403#462Dic8311yescharacteristic, complemented
404#461Dic8311yescharacteristic, complemented
405#460Dic8311yescharacteristic, complemented
406#459Dic8311yescharacteristic, complemented
407#444—1664no—
408#443—1664no—
409#435—1661no—
410#435—1661no—
411#435—1661no—
412#435—1661no—
413C2×#108—831no—
414C2×#108—831no—
415#423—831no—
416C2×C4⋊C8C2×D8311yescharacteristic
417C2×#104—831no—
418C2×#104—831no—
419C2×#104—831no—
420C2×#104—831no—
421C2×#104—831no—
422C2×#104—831no—
423#416C2×D8311yescharacteristic
424#416C2×D8311yescharacteristic
425#408—831no—
426#408—831no—
427#405—831no—
428#405—831no—
429#405—1661no—
430#405—1661no—
431C4×M16—831no—
432C4×M16—1661no—
433C2×#97—831no—
434C2×#97—831no—
435C2×#97—1661no—
436C2×C4×C8—831no—
437C4×C4⋊C4—831no—
438#341—831no—
439#341—831no—
440#339—831no—
441#339—831no—
442#336—831no—
443#336—831no—
444C2×#41C22×D8311yescharacteristic
445C2×#41C22×D8311yescharacteristic
446C2×#41C22×D8311yescharacteristic
447#135—22no—
448#135—22no—
449#135—22no—
450#135—22no—
451C2×Q16C2×Dic8311yescharacteristic
452C2×Q16C2×Dic8311yescharacteristic
453C2×SD16C2×Dic8311yescharacteristic
454C2×SD16C2×Dic8311yescharacteristic
455C2×SD16C2×Dic8311yescharacteristic
456C2×SD16C2×Dic8311yescharacteristic
457C2×D8C2×Dic8311yescharacteristic
458C2×D8C2×Dic8311yescharacteristic
459#131—834no—
460#131—1662no—
461#131—1662no—
462#131—1662no—
463#131—1662no—
464#131—1662no—
465#131—1662no—
466#131—1662no—
467C2×M16—831no—
468C2×M16—831no—
469C2×M16—831no—
470C2×M16—831no—
471C2×M16—1661no—
472C2×M16—1661no—
473C2×M16—1661no—
474C2×M16—1661no—
475C22×C8—831no—
476C22×C8—831no—
477C22×C8—1661no—
478C22×C8—1661no—
479C22×C8—1661no—
480C22×C8—1661no—
481C22×C8C22×D8311yescharacteristic
482C22×C8C22×D8311yescharacteristic
483C4⋊Q8C2×Dic8311yescharacteristic
484#127C2×Dic8311yescharacteristic
485#124C2×Dic8311yescharacteristic
486#124C2×Dic8311yescharacteristic
487#121—21no—
488#121—21no—
489C4×Q8C2×Dic8311yescharacteristic
490C4×Q8C2×Dic8311yescharacteristic
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4C2×Dic8311yescharacteristic
496C4×D4C2×Dic8311yescharacteristic
497#117—21no—
498#117C22×D8311yescharacteristic
499C2×C4⋊C4—1661no—
500C2×C42—21no—
501C2×C42—831no—
502C2×C42—831no—
503C2×C42C22×D8311yescharacteristic
504#108—1662no—
505#108—1662no—
506C4⋊C8—1661no—
507C4⋊C8—1661no—
508C4⋊C8C2×Dic8311yescharacteristic
509C4⋊C8C2×Dic8311yescharacteristic
510C4⋊C8C2×Dic8311yescharacteristic
511C4⋊C8C2×Dic8311yescharacteristic
512#104—1662no—
513#104—1662no—
514#104—1662no—
515#104—1662no—
516#104—1662no—
517#104—1662no—
518#103C2×Dic8311yescharacteristic
519#103C2×Dic8311yescharacteristic
520#103C2×Dic8311yescharacteristic
521#103C2×Dic8311yescharacteristic
522#102C2×Dic8311yescharacteristic
523#102C2×Dic8311yescharacteristic
524#102C2×Dic8311yescharacteristic
525#102C2×Dic8311yescharacteristic
526C22⋊C8—1661no—
527C22⋊C8—1661no—
528C22⋊C8—1661no—
529C22⋊C8—1661no—
530#97—831no—
531#97—831no—
532#97—831no—
533#97—831no—
534#97—1661no—
535#97—1661no—
536#97—1662no—
537#97—1661no—
538C4×C8—1661no—
539C4×C8—1661no—
540C4×C8—1662no—
541C4×C8—1661no—
542#95—1661no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41—21no—
553#41D4×D8312yes—
554#41#1305058912yes—
555C2×Q8C22×Dic8311yescharacteristic
556C2×Q8C22×Dic8311yescharacteristic
557C2×Q8C22×Dic8311yescharacteristic
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4C22×Dic8311yescharacteristic
564C2×D4C22×Dic8311yescharacteristic
565C2×D4C22×Dic8311yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—1661no—
572C22×C4—1661no—
573C22×C4#1305058911yescharacteristic
574C22×C4#1305058911yescharacteristic
575C22×C4C23×D8311yescharacteristic
576Q16—22no—
577Q16—22no—
578SD16—22no—
579SD16—22no—
580SD16—22no—
581SD16—22no—
582D8—22no—
583D8—22no—
584M16—3322no—
585M16—3322no—
586M16—832no—
587M16—832no—
588M16—1661no—
589M16—1661no—
590M16—1661no—
591M16—1661no—
592M16—1664no—
593M16—1664no—
594M16—1661no—
595M16—1661no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—3322no—
601C2×C8—3322no—
602C2×C8—832no—
603C2×C8—831no—
604C2×C8—831no—
605C2×C8—832no—
606C2×C8—831no—
607C2×C8—831no—
608C2×C8—1661no—
609C2×C8—1661no—
610C2×C8—1664no—
611C2×C8—1664no—
612C2×C8—1661no—
613C2×C8—1661no—
614C2×C8—1661no—
615C2×C8—1661no—
616C2×C8C22×Dic8311yescharacteristic
617C2×C8C22×Dic8311yescharacteristic
618C2×C8C22×Dic8311yescharacteristic
619C2×C8C22×Dic8311yescharacteristic
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—3322no—
625C4⋊C4C22×Dic8311yescharacteristic
626C4⋊C4C22×Dic8311yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—1661no—
638C42—1661no—
639C42—1661no—
640C42—1661no—
641C42C22×Dic8311yescharacteristic
642C42C22×Dic8311yescharacteristic
643C42D4×D8311yescharacteristic
644C42D4×D8311yescharacteristic
645C23—21no—
646C23—21no—
647C23—21no—
648C23C2×#1305058911yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8D4×Dic8312yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—81no—
667D4—81no—
668D4D4×Dic8312yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—3321no—
685C2×C4—3321no—
686C2×C4—3321no—
687C2×C4—3321no—
688C2×C4—3321no—
689C2×C4—1662no—
690C2×C4D4×Dic8311yescharacteristic
691C2×C4D4×Dic8311yescharacteristic
692C2×C4D4×Dic8311yescharacteristic
693C2×C4D4×Dic8311yescharacteristic
694C2×C4C23×Dic8311yescharacteristic
695C2×C4C2×D4×D8311yescharacteristic
696C2×C4C2×D4×D8311yescharacteristic
697C2×C4#41×D8311yescharacteristic
698C2×C4#41×D8311yescharacteristic
699C2×C4C2×#1305058911yescharacteristic
700C8—21no—
701C8—21no—
702C8—21no—
703C8—21no—
704C8—3321no—
705C8—3321no—
706C8—832no—
707C8—832no—
708C8—1662no—
709C8—1661no—
710C8—1661no—
711C8—1662no—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22C2×D4×Dic8311yescharacteristic
724C22#1912823211yescharacteristic
725C22#1912824611yescharacteristic
726C4—21no—
727C4—21no—
728C4—22no—
729C4—21no—
730C4—21no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—3322no—
736C4—6641no—
737C4C2×D4×Dic8311yescharacteristic
738C4#41×Dic8311yescharacteristic
739C4#121×D8311yescharacteristic
740C4#1912821111yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—81no—
745C2—81no—
746C2#121×Dic8311yescharacteristic
747C2#2491637311yescharacteristic
748C2#2491638011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
Fitting, prime radicalC83×#3035C2
socleC22×C83C2×C4×D4
cosocleC22×C4×C83C24
hypercenter#3035D83
hypocenterC83#21519
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. C2×#19127823C2semidirect
2. C2×#19127818C2semidirect
3. #24916181C2semidirect
4. #24915891C2semidirect
5. #24908383C2semidirect
6. #24908239C2semidirect
7. #24908113C2semidirect
8. #24908113C2semidirect
9. #24907792C2semidirect
10. #24907792C2semidirect
11. #24907483C2semidirect
12. #24907340C2semidirect
13. #24907310C2semidirect
14. #24907303C2semidirect
58. #464×C83C4semidirect
59. #464×C83C4semidirect
60. #463×C83C4semidirect
61. #463×C83C4semidirect
62. #462×C83C4semidirect
63. #461×C83C4semidirect
64. #460×C83C4semidirect
65. #459×C83C4semidirect
76. #14581799D4semidirect
390. C83#21519semidirect
399. #464Dic83semidirect
400. #464Dic83semidirect
401. #463Dic83semidirect
402. #463Dic83semidirect
403. #462Dic83semidirect
404. #461Dic83semidirect
405. #460Dic83semidirect
406. #459Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191278232
C2×#191278182
#249161812
#249158912
#249083832
#249082392
#249081132
#249077922
#249074832
#249073402
#249073102
#249073032
C83×#30352
#2151983