Finite Group Databasebeta

← #35312294

Subgroups — #35312294

Order 21248.

1194 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127561C211yesmaximal, characteristic
2C2×#19127468C212yesmaximal
3C2×#19127468C212yesmaximal
4#24905686C211yesmaximal, characteristic
5C2×#385×C83C211yesmaximal, characteristic
6C22×C4⋊Dic83—21no—
7C22×C22⋊Dic83C2212yes—
8C22×C22⋊Dic83C2212yes—
9#19127561—24no—
10C2×C83⋊#95—21no—
11C2×C83⋊#95—22no—
12#19127468—24no—
13#19127468—24no—
14C24×C4×C83C2211yescharacteristic
15C22×C4⋊C4×C83C412yescomplemented
16C22×C22⋊C4×C83C2211yescharacteristic
17C22×C22⋊C4×C83C2211yescharacteristic
18#385×C83—21no—
19#385×C83—22no—
20#385×C83—21no—
21C2×#95×C83C412yescomplemented
22C23×Dic83—22no—
23C23×Dic83—22no—
24C2×C4⋊Dic83—24no—
25C2×C4⋊Dic83—44no—
26C2×C22⋊Dic83—22no—
27C2×C22⋊Dic83—22no—
28C2×C22⋊Dic83—22no—
29C2×C22⋊Dic83—22no—
30C2×C22⋊Dic83—22no—
31C2×C22⋊Dic83—22no—
32C2×C22⋊Dic83—22no—
33C2×C22⋊Dic83—22no—
34C2×C22⋊Dic83—22no—
35C2×C22⋊Dic83—22no—
36C2×C22⋊Dic83D414yes—
37C2×C22⋊Dic83Q814yes—
38C83⋊#95—24no—
39C83⋊#95—44no—
40C25×C83C2311yescharacteristic
41C23×C4×C83—22no—
42C23×C4×C83—22no—
43C23×C4×C83—44no—
44C23×C4×C83C2×C412yes—
45C23×C4×C83C2×C411yescharacteristic
46C23×C4×C83C2×C411yescharacteristic
47C23×C4×C83C2×C412yes—
48C23×C4×C83D411yescharacteristic
49C23×C4×C83D412yes—
50C23×C4×C83D411yescharacteristic
51C2×C4⋊C4×C83—22no—
52C2×C4⋊C4×C83—22no—
53C2×C4⋊C4×C83—44no—
54C2×C22⋊C4×C83—21no—
55C2×C22⋊C4×C83—21no—
56C2×C22⋊C4×C83—21no—
57C2×C22⋊C4×C83—21no—
58C2×C22⋊C4×C83—22no—
59C2×C22⋊C4×C83—21no—
60C2×C22⋊C4×C83—21no—
61C2×C22⋊C4×C83—22no—
62C2×C22⋊C4×C83D412yes—
63C2×C22⋊C4×C83Q812yes—
64#95×C83—22no—
65#95×C83—22no—
66C22×Dic83—24no—
67C22×Dic83—24no—
68C22×Dic83—44no—
69C22×Dic83—44no—
70C22×Dic83—44no—
71C22×Dic83—44no—
72C22×Dic83—42no—
73C22×Dic83—42no—
74C22×Dic83—42no—
75C22×Dic83—42no—
76C4⋊Dic83—48no—
77C22⋊Dic83—24no—
78C22⋊Dic83—24no—
79C22⋊Dic83—24no—
80C22⋊Dic83—24no—
81C22⋊Dic83—42no—
82C22⋊Dic83—42no—
83C22⋊Dic83—42no—
84C22⋊Dic83—42no—
85C24×C83—42no—
86C24×C83—42no—
87C24×C83C22×C411yescharacteristic
88C24×C83C2×D412yes—
89C24×C83C2×D411yescharacteristic
90C24×C83C2×D411yescharacteristic
91C24×C83C2×D411yescharacteristic
92C24×C83C2×Q812yes—
93C24×C83C2×Q811yescharacteristic
94C24×C83#4112yes—
95C24×C83#4111yescharacteristic
96C24×C83#4111yescharacteristic
97C24×C83#4112yes—
98C22×C4×C83—21no—
99C22×C4×C83—21no—
100C22×C4×C83—24no—
101C22×C4×C83—22no—
102C22×C4×C83—22no—
103C22×C4×C83—24no—
104C22×C4×C83—21no—
105C22×C4×C83—24no—
106C22×C4×C83—21no—
107C22×C4×C83—24no—
108C22×C4×C83—24no—
109C22×C4×C83—21no—
110C22×C4×C83—21no—
111C22×C4×C83—22no—
112C22×C4×C83—22no—
113C22×C4×C83—42no—
114C22×C4×C83—42no—
115C22×C4×C83—42no—
116C22×C4×C83—48no—
117C22×C4×C83—48no—
118C22×C4×C83—42no—
119C22×C4×C83—42no—
120C22×C4×C83—42no—
121C22×C4×C83—42no—
122C22×C4×C83C22⋊C412yes—
123C22×C4×C83C22⋊C412yes—
124C22×C4×C83C4⋊C414yescomplemented
125C4⋊C4×C83—44no—
126C4⋊C4×C83—44no—
127C22⋊C4×C83—22no—
128C22⋊C4×C83—22no—
129C22⋊C4×C83—22no—
130C22⋊C4×C83—22no—
131C22⋊C4×C83—41no—
132C22⋊C4×C83—42no—
133C22⋊C4×C83—41no—
134C23×C83—22no—
135C23×C83—22no—
136C23×C83—22no—
137C23×C83—22no—
138C23×C83—22no—
139C23×C83—22no—
140C23×C83—42no—
141C23×C83—42no—
142C23×C83—42no—
143C23×C83—42no—
144C23×C83—44no—
145C23×C83—42no—
146C23×C83—42no—
147C23×C83—42no—
148C23×C83—42no—
149C23×C83—44no—
150C23×C83C2×C22⋊C411yescharacteristic
151C23×C83C2×C4⋊C411yescharacteristic
152C23×C83#11711yescharacteristic
153C23×C83C4×D412yes—
154C23×C83C4×Q812yes—
155C23×C83#12011yescharacteristic
156C23×C83#12112yes—
157C23×C83#12111yescharacteristic
158C23×C83#12111yescharacteristic
159C23×C83#12112yes—
160C23×C83C22⋊Q812yes—
161C23×C83C22⋊Q812yes—
162C23×C83C22⋊Q811yescharacteristic
163C23×C83C22⋊Q811yescharacteristic
164C23×C83C22⋊Q812yes—
165C23×C83#12311yescharacteristic
166C23×C83#12312yes—
167C23×C83#12411yescharacteristic
168C23×C83#12512yes—
169C23×C83#12512yes—
170C23×C83#12612yes—
171C23×C83C4⋊Q811yescharacteristic
172C23×C83C4⋊Q812yes—
173C2×C4×C83—24no—
174C2×C4×C83—24no—
175C2×C4×C83—22no—
176C2×C4×C83—22no—
177C2×C4×C83—24no—
178C2×C4×C83—22no—
179C2×C4×C83—22no—
180C2×C4×C83—22no—
181C2×C4×C83—48no—
182C2×C4×C83—48no—
183C2×C4×C83—44no—
184C2×C4×C83—42no—
185C2×C4×C83—42no—
186C2×C4×C83—42no—
187C2×C4×C83—42no—
188C2×C4×C83—44no—
189C2×C4×C83—41no—
190C2×C4×C83—41no—
191C2×C4×C83—42no—
192C2×C4×C83—42no—
193C2×C4×C83—82no—
194C2×C4×C83—82no—
195C2×C4×C83#9914yes—
196C2×Dic83—44no—
197C2×Dic83—44no—
198C2×Dic83—48no—
199C2×Dic83—44no—
200C2×Dic83—44no—
201C2×Dic83—84no—
202C2×Dic83—84no—
203C2×Dic83—82no—
204C2×Dic83—82no—
205C2×Dic83—84no—
206C22×C83—22no—
207C22×C83—22no—
208C22×C83—22no—
209C22×C83—22no—
210C22×C83—22no—
211C22×C83—22no—
212C22×C83—21no—
213C22×C83—22no—
214C22×C83—21no—
215C22×C83—22no—
216C22×C83—21no—
217C22×C83—22no—
218C22×C83—22no—
219C22×C83—21no—
220C22×C83—24no—
221C22×C83—22no—
222C22×C83—24no—
223C22×C83—22no—
224C22×C83—42no—
225C22×C83—42no—
226C22×C83—42no—
227C22×C83—42no—
228C22×C83—42no—
229C22×C83—42no—
230C22×C83—42no—
231C22×C83—42no—
232C22×C83#38011yescharacteristic
233C22×C83#38611yescharacteristic
234C22×C83#38712yes—
235C22×C83#38912yes—
236C22×C83#39111yescharacteristic
237C22×C83#39411yescharacteristic
238C22×C83#39511yescharacteristic
239C22×C83#39612yes—
240C22×C83#39811yescharacteristic
241C22×C83#39812yes—
242C22×C83#40011yescharacteristic
243C22×C83C2×#9912yes—
244C22×C83#41012yes—
245C4×C83—24no—
246C4×C83—44no—
247C4×C83—42no—
248C4×C83—81no—
249C4×C83—81no—
250Dic83—84no—
251Dic83—84no—
252#11203—831nomaximal, Sylow
253C2×C83—21no—
254C2×C83—22no—
255C2×C83—22no—
256C2×C83—22no—
257C2×C83—21no—
258C2×C83—21no—
259C2×C83—22no—
260C2×C83—21no—
261C2×C83#144111yescharacteristic
262C2×C83#179912yes—
263C2×C83#189811yescharacteristic
264C2×C83#189911yescharacteristic
265C2×C83#199612yes—
266C2×#385D8311yescharacteristic
267C2×#380—831no—
268C2×#342—832no—
269C2×#342—832no—
270C22⋊#95—831no—
271C83#1120311yescharacteristic, complemented, Sylow
272C24×C4C2×D8311yescharacteristic
273C22×C4⋊C4—1661no—
274C22×C4⋊C4Dic8312yescomplemented
275C22×C22⋊C4—832no—
276C22×C22⋊C4—832no—
277C22×C22⋊C4C2×D8311yescharacteristic
278C22×C22⋊C4C2×D8311yescharacteristic
279#385—21no—
280#385—22no—
281#385—21no—
282#380—1664no—
283C2×#95—1662no—
284C2×#95—1661no—
285C2×#95Dic8312yescomplemented
286#342—1664no—
287#342—1664no—
288C25C22×D8311yescharacteristic
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—44no—
292C23×C4—1662no—
293C23×C4—1662no—
294C23×C4C2×Dic8312yes—
295C23×C4C2×Dic8311yescharacteristic
296C23×C4C2×Dic8311yescharacteristic
297C23×C4C2×Dic8312yes—
298C23×C4C22⋊D8311yescharacteristic
299C23×C4C22⋊D8312yes—
300C23×C4C22⋊D8311yescharacteristic
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—3324no—
305C2×C4⋊C4—1664no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—834no—
315C2×C22⋊C4—834no—
316C2×C22⋊C4—1662no—
317C2×C22⋊C4—1662no—
318C2×C22⋊C4—1662no—
319C2×C22⋊C4—1662no—
320C2×C22⋊C4—1662no—
321C2×C22⋊C4—1662no—
322C2×C22⋊C4—1662no—
323C2×C22⋊C4—1662no—
324C2×C22⋊C4—1662no—
325C2×C22⋊C4—1662no—
326C2×C22⋊C4Dic16612yes—
327C2×C22⋊C4D33212yes—
328#95—22no—
329#95—22no—
330#95—3324no—
331#95—1664no—
332C24—42no—
333C24—42no—
334C24C22×Dic8311yescharacteristic
335C24D4×D8312yes—
336C24C2×C22⋊D8311yescharacteristic
337C24C2×C22⋊D8311yescharacteristic
338C24C2×D33211yescharacteristic
339C24Q8×D8312yes—
340C24C2×Dic16611yescharacteristic
341C24#1305058912yes—
342C24#1305059011yescharacteristic
343C24#1305059011yescharacteristic
344C24#1305059112yes—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—24no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—48no—
364C22×C4—48no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—3324no—
370C22×C4—3324no—
371C22×C4—3324no—
372C22×C4—3324no—
373C22×C4—3322no—
374C22×C4—3322no—
375C22×C4—3322no—
376C22×C4—3322no—
377C22×C4—1664no—
378C22×C4—1664no—
379C22×C4C22⋊Dic8312yes—
380C22×C4C22⋊Dic8312yes—
381C22×C4C4⋊Dic8314yescomplemented
382C4⋊C4—44no—
383C4⋊C4—44no—
384C4⋊C4—3328no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—41no—
390C22⋊C4—42no—
391C22⋊C4—41no—
392C22⋊C4—3322no—
393C22⋊C4—3322no—
394C22⋊C4—3322no—
395C22⋊C4—3322no—
396C22⋊C4—1664no—
397C22⋊C4—1664no—
398C22⋊C4—1664no—
399C22⋊C4—1664no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—44no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23—44no—
416C23C2×C22⋊Dic8311yescharacteristic
417C23C2×C4⋊Dic8311yescharacteristic
418C23#1458175111yescharacteristic
419C23D4×Dic8312yes—
420C23Q8×Dic8312yes—
421C23#1458176011yescharacteristic
422C23#1458176412yes—
423C23#1458176611yescharacteristic
424C23#1458176611yescharacteristic
425C23#1458176712yes—
426C23#1458176812yes—
427C23#1458177012yes—
428C23#1458177111yescharacteristic
429C23#1458177111yescharacteristic
430C23#1458177212yes—
431C23#1458177311yescharacteristic
432C23#1458177712yes—
433C23#1458178111yescharacteristic
434C23#1458178212yes—
435C23#1458178312yes—
436C23#1458178712yes—
437C23#1458179011yescharacteristic
438C23#1458179112yes—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—48no—
448C2×C4—48no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—3324no—
462C2×C4—3324no—
463C2×C4—3328no—
464C2×C4—3324no—
465C2×C4—3324no—
466C2×C4—6642no—
467C2×C4—6642no—
468C2×C4—6644no—
469C2×C4—6644no—
470C2×C4—6644no—
471C2×C4#1458170714yes—
472C22—21no—
473C22—21no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—21no—
478C22—22no—
479C22—21no—
480C22—24no—
481C22—22no—
482C22—22no—
483C22—24no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22#1912756111yescharacteristic
499C22#1912758111yescharacteristic
500C22#1912758712yes—
501C22#1912760012yes—
502C22#1912760811yescharacteristic
503C22#1912761811yescharacteristic
504C22#1912762111yescharacteristic
505C22#1912762312yes—
506C22#1912763111yescharacteristic
507C22#1912763412yes—
508C22#1912764011yescharacteristic
509C22C2×#1458170712yes—
510C22#1912767512yes—
511C4—24no—
512C4—42no—
513C4—44no—
514C4—81no—
515C4—81no—
516C4—6644no—
517C4—6644no—
518C2—21no—
519C2—22no—
520C2—22no—
521C2—22no—
522C2—21no—
523C2—21no—
524C2—22no—
525C2—21no—
526C2#2490571611yescharacteristic
527C2#2490745112yes—
528C2#2490791711yescharacteristic
529C2#2490792211yescharacteristic
530C2#2490844912yes—
subgroupG/H
centerC23C2×C22⋊Dic83
commutatorC24×C83C22×C4
FrattiniC25C22×D83
FittingC2×#385×C83C2
socleC23×C83C2×C22⋊C4
prime radical, cosocleC25×C83C23
hypercenterC2×#385D83
hypocenterC83#11203
LCSG ▷ C24×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
15. C22×C4⋊C4×C83C4semidirect
21. C2×#95×C83C4semidirect
124. C22×C4×C83C4⋊C4semidirect
271. C83#11203semidirect
274. C22×C4⋊C4Dic83semidirect
285. C2×#95Dic83semidirect
381. C22×C4C4⋊Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191275612
C2×#191274682
#249056862
C2×#385×C832
#1120383