Finite Group Databasebeta

← C83×#9927 #35237751

Subgroups — C83×#9927 #35237751

Order 21248.

654 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#483×C83C211yesmaximal, characteristic
2C83×#2627C211yesmaximal, characteristic
3C2×#398×C83C211yesmaximal, characteristic
4C83×#1823C211yesmaximal, characteristic
5C2×#328×C83C211yesmaximal, characteristic
6C2×#324×C83C211yesmaximal, characteristic
7C83×#1294C211yesmaximal, characteristic
8C2×C22⋊Q8×C83C2211yescharacteristic
9C22×C4⋊C4×C83—21no—
10C22×C4⋊C4×C83C2211yescharacteristic
11C22×C4⋊C4×C83C2211yescharacteristic
12#483×C83—22no—
13#483×C83—22no—
14C2×#106×C83—21no—
15C2×#103×C83—21no—
16C2×C22⋊C8×C83C2211yescharacteristic
17C2×C22⋊C8×C83C2211yescharacteristic
18#400×C83—21no—
19#398×C83—22no—
20#398×C83—22no—
21#398×C83—22no—
22#395×C83—21no—
23#385×C83—21no—
24#381×C83—21no—
25#380×C83C2211yescharacteristic
26C2×#95×C83—21no—
27C2×#95×C83C2211yescharacteristic
28#340×C83—22no—
29#328×C83—22no—
30#324×C83—22no—
31C22×Q8×C83D411yescharacteristic
32C23×C4×C83—21no—
33C23×C4×C83—21no—
34C23×C4×C83D411yescharacteristic
35C23×C4×C83D411yescharacteristic
36C23×C4×C83C2311yescharacteristic
37C22×C8×C83—21no—
38C22×C8×C83—21no—
39C22⋊Q8×C83—21no—
40C22⋊Q8×C83—21no—
41C22⋊Q8×C83—21no—
42C22⋊Q8×C83—21no—
43C2×C4⋊C4×C83—21no—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83—21no—
47C2×C4⋊C4×C83—24no—
48C2×C4⋊C4×C83—21no—
49C2×C4⋊C4×C83—21no—
50C2×C4⋊C4×C83—21no—
51C2×C4⋊C4×C83—21no—
52C2×C4⋊C4×C83—21no—
53C2×C4⋊C4×C83—21no—
54C2×C4⋊C4×C83—21no—
55C2×C4⋊C4×C83—21no—
56C2×C4⋊C4×C83—22no—
57C2×C4⋊C4×C83—42no—
58C2×C4⋊C4×C83—42no—
59C2×C4⋊C4×C83D412yes—
60C2×C4⋊C4×C83D411yescharacteristic
61C2×C4⋊C4×C83D412yes—
62C2×C22⋊C4×C83—21no—
63C2×C22⋊C4×C83—21no—
64#106×C83—24no—
65#103×C83—24no—
66C22⋊C8×C83—21no—
67C22⋊C8×C83—21no—
68C22⋊C8×C83—21no—
69C22⋊C8×C83D412yes—
70#95×C83—24no—
71#95×C83—22no—
72#95×C83—22no—
73#95×C83—22no—
74#95×C83—21no—
75#95×C83—21no—
76#95×C83D412yes—
77C24×C83C2×D411yescharacteristic
78C2×Q8×C83—21no—
79C2×Q8×C83—21no—
80C2×Q8×C83—42no—
81C22×C4×C83—24no—
82C22×C4×C83—22no—
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83—21no—
86C22×C4×C83—21no—
87C22×C4×C83—21no—
88C22×C4×C83—21no—
89C22×C4×C83—21no—
90C22×C4×C83—22no—
91C22×C4×C83—21no—
92C22×C4×C83—22no—
93C22×C4×C83—21no—
94C22×C4×C83—21no—
95C22×C4×C83—21no—
96C22×C4×C83—42no—
97C22×C4×C83—42no—
98C22×C4×C83—41no—
99C22×C4×C83—41no—
100C22×C4×C83—42no—
101C22×C4×C83—41no—
102C22×C4×C83—41no—
103C22×C4×C83—41no—
104C22×C4×C83—41no—
105C22×C4×C83—41no—
106C22×C4×C83—41no—
107C22×C4×C83SD1612yes—
108C22×C4×C83C2×D411yescharacteristic
109C22×C4×C83C2×D411yescharacteristic
110C22×C4×C83C2×D411yescharacteristic
111C22×C4×C83C2×D411yescharacteristic
112C22×C4×C83C2×D411yescharacteristic
113C22×C4×C83#4111yescharacteristic
114C2×C8×C83—22no—
115C2×C8×C83—42no—
116C2×C8×C83—42no—
117C2×C8×C83—41no—
118C4⋊C4×C83—22no—
119C4⋊C4×C83—21no—
120C4⋊C4×C83—22no—
121C4⋊C4×C83—21no—
122C4⋊C4×C83—42no—
123C4⋊C4×C83—48no—
124C4⋊C4×C83—41no—
125C4⋊C4×C83—41no—
126C4⋊C4×C83—41no—
127C4⋊C4×C83—41no—
128C4⋊C4×C83—41no—
129C4⋊C4×C83—41no—
130C4⋊C4×C83—41no—
131C4⋊C4×C83—41no—
132C4⋊C4×C83—82no—
133C22⋊C4×C83—41no—
134C22⋊C4×C83—41no—
135C22⋊C4×C83—41no—
136C22⋊C4×C83—41no—
137C23×C83—22no—
138C23×C83—22no—
139C23×C83#12011yescharacteristic
140C23×C83#12011yescharacteristic
141C23×C83#12111yescharacteristic
142C23×C83C2×SD1611yescharacteristic
143C23×C83#13511yescharacteristic
144C23×C83AGL(1,ℤ/8)11yescharacteristic
145C23×C83#13711yescharacteristic
146Q8×C83—42no—
147Q8×C83—81no—
148C2×C4×C83—22no—
149C2×C4×C83—22no—
150C2×C4×C83—24no—
151C2×C4×C83—22no—
152C2×C4×C83—22no—
153C2×C4×C83—22no—
154C2×C4×C83—41no—
155C2×C4×C83—41no—
156C2×C4×C83—41no—
157C2×C4×C83—41no—
158C2×C4×C83—44no—
159C2×C4×C83—44no—
160C2×C4×C83—42no—
161C2×C4×C83—41no—
162C2×C4×C83—41no—
163C2×C4×C83—42no—
164C2×C4×C83—41no—
165C2×C4×C83—41no—
166C2×C4×C83—42no—
167C2×C4×C83—41no—
168C2×C4×C83—41no—
169C2×C4×C83—42no—
170C2×C4×C83—41no—
171C2×C4×C83—42no—
172C2×C4×C83—42no—
173C2×C4×C83—42no—
174C2×C4×C83—42no—
175C2×C4×C83—42no—
176C2×C4×C83—42no—
177C2×C4×C83—42no—
178C2×C4×C83—42no—
179C2×C4×C83—81no—
180C2×C4×C83—81no—
181C2×C4×C83—81no—
182C2×C4×C83—81no—
183C2×C4×C83—81no—
184C2×C4×C83#12011yescharacteristic
185C2×C4×C83#12111yescharacteristic
186C2×C4×C83#12111yescharacteristic
187C2×C4×C83#12711yescharacteristic
188C8×C83—42no—
189C8×C83—81no—
190C22×C83—22no—
191C22×C83—22no—
192C22×C83—22no—
193C22×C83—22no—
194C22×C83—21no—
195C22×C83—21no—
196C22×C83—21no—
197C22×C83—21no—
198C22×C83#39211yescharacteristic
199C22×C83#44811yescharacteristic
200C22×C83#44911yescharacteristic
201C22×C83#45011yescharacteristic
202C22×C83#45211yescharacteristic
203C22×C83#45612yes—
204C22×C83#45812yes—
205C22×C83#46511yescharacteristic
206C22×C83#46811yescharacteristic
207C4×C83—21no—
208C4×C83—21no—
209C4×C83—21no—
210C4×C83—21no—
211C4×C83—44no—
212C4×C83—42no—
213C4×C83—82no—
214C4×C83—82no—
215C4×C83—81no—
216C4×C83—81no—
217C4×C83—81no—
218#9927C8311yesmaximal, characteristic, direct product factor, Sylow
219C2×C83—21no—
220C2×C83—21no—
221C2×C83—21no—
222C2×C83—21no—
223C2×C83#160912yes—
224C2×C83#161112yes—
225C2×C83#200011yescharacteristic
226C2×C83#200511yescharacteristic
227C2×C83#202211yescharacteristic
228C2×#483C2×C8311yescharacteristic
229#2627C2×C8311yescharacteristic
230C2×#398C2×C8311yescharacteristic
231#1823C2×C8311yescharacteristic
232C2×#328C2×C8311yescharacteristic
233C2×#324C2×C8311yescharacteristic
234#1294C2×C8311yescharacteristic
235C83#992711yescharacteristic, direct product factor, Sylow
236C2×C22⋊Q8C22×C8311yescharacteristic
237C22×C4⋊C4—21no—
238C22×C4⋊C4C22×C8311yescharacteristic
239C22×C4⋊C4C22×C8311yescharacteristic
240#483—22no—
241#483—22no—
242C2×#106—21no—
243C2×#103—21no—
244C2×C22⋊C8C22×C8311yescharacteristic
245C2×C22⋊C8C22×C8311yescharacteristic
246#400—21no—
247#398—22no—
248#398—22no—
249#398—22no—
250#395—21no—
251#385—21no—
252#381—21no—
253#380C22×C8311yescharacteristic
254C2×#95—21no—
255C2×#95C22×C8311yescharacteristic
256#340—22no—
257#328—22no—
258#324—22no—
259C22×Q8D4×C8311yescharacteristic
260C23×C4—21no—
261C23×C4—21no—
262C23×C4D4×C8311yescharacteristic
263C23×C4D4×C8311yescharacteristic
264C23×C4C23×C8311yescharacteristic
265C22×C8—21no—
266C22×C8—21no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4D4×C8312yes—
288C2×C4⋊C4D4×C8311yescharacteristic
289C2×C4⋊C4D4×C8312yes—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292#106—24no—
293#103—24no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8D4×C8312yes—
298#95—24no—
299#95—22no—
300#95—22no—
301#95—22no—
302#95—21no—
303#95—21no—
304#95D4×C8312yes—
305C24C2×D4×C8311yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—42no—
309C22×C4—24no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—42no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4SD16×C8312yes—
336C22×C4C2×D4×C8311yescharacteristic
337C22×C4C2×D4×C8311yescharacteristic
338C22×C4C2×D4×C8311yescharacteristic
339C22×C4C2×D4×C8311yescharacteristic
340C22×C4C2×D4×C8311yescharacteristic
341C22×C4#41×C8311yescharacteristic
342C2×C8—22no—
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—41no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—42no—
351C4⋊C4—48no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—82no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C23—22no—
366C23—22no—
367C23#120×C8311yescharacteristic
368C23#120×C8311yescharacteristic
369C23#121×C8311yescharacteristic
370C23C2×SD16×C8311yescharacteristic
371C23#135×C8311yescharacteristic
372C23AGL(1,ℤ/8)×C8311yescharacteristic
373C23#137×C8311yescharacteristic
374Q8—42no—
375Q8—81no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4#120×C8311yescharacteristic
413C2×C4#121×C8311yescharacteristic
414C2×C4#121×C8311yescharacteristic
415C2×C4#127×C8311yescharacteristic
416C8—42no—
417C8—81no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22#392×C8311yescharacteristic
427C22#448×C8311yescharacteristic
428C22#449×C8311yescharacteristic
429C22#450×C8311yescharacteristic
430C22#452×C8311yescharacteristic
431C22#456×C8312yes—
432C22#458×C8312yes—
433C22#465×C8311yescharacteristic
434C22#468×C8311yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—44no—
440C4—42no—
441C4—82no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4—82no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2C83×#160912yes—
451C2C83×#161112yes—
452C2C83×#200011yescharacteristic
453C2C83×#200511yescharacteristic
454C2C83×#202211yescharacteristic
subgroupG/H
center, socleC23×C83#120
commutator, Frattini, cosocleC23×C4C23×C83
prime radicalC24×C83C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C83 ◁ C23×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
218. #9927C83direct (N × H)
235. C83#9927direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#483×C832
C83×#26272
C2×#398×C832
C83×#18232
C2×#328×C832
C2×#324×C832
C83×#12942
#992783