Finite Group Databasebeta

← C83×#9933 #35237757

Subgroups — C83×#9933 #35237757

Order 21248.

568 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3193C211yesmaximal, characteristic
2C83×#3094C211yesmaximal, characteristic
3C83×#2625C211yesmaximal, characteristic, complemented
4C83×#1964C211yesmaximal, characteristic
5C83×#1826C211yesmaximal, characteristic, complemented
6C83×#1508C211yesmaximal, characteristic, complemented
7C83×#1305C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C83C2211yescharacteristic
9C2×#121×C83C2211yescharacteristic
10C2×#117×C83C2211yescharacteristic
11#484×C83—21no—
12#482×C83—22no—
13#481×C83—21no—
14#480×C83—21no—
15#480×C83—21no—
16#468×C83—22no—
17#450×C83—21no—
18#448×C83—21no—
19#428×C83—21no—
20#418×C83—21no—
21C2×#99×C83—22no—
22#407×C83C2211yescharacteristic
23#407×C83C2211yescharacteristic
24#400×C83—21no—
25#398×C83—21no—
26#397×C83—22no—
27#391×C83—21no—
28#389×C83—21no—
29#380×C83C2211yescharacteristic
30C4×C22⋊C4×C83C2211yescharacteristic
31#339×C83—22no—
32#328×C83—22no—
33C22×Q8×C83D411yescharacteristic
34C22×D4×C83—21no—
35C22×D4×C83D411yescharacteristic
36C23×C4×C83C2311yescharacteristic
37C2×SD16×C83—22no—
38C2×M16×C83—21no—
39C2×M16×C83D412yes—
40C22⋊Q8×C83—21no—
41C22⋊Q8×C83—21no—
42C22⋊Q8×C83—21no—
43C22⋊Q8×C83—21no—
44#121×C83—21no—
45#121×C83—21no—
46#121×C83—21no—
47#121×C83—21no—
48#117×C83—21no—
49#117×C83—21no—
50#117×C83—21no—
51#117×C83—21no—
52C2×C4⋊C4×C83—21no—
53C2×C4⋊C4×C83—21no—
54C2×C4⋊C4×C83—22no—
55C2×C4⋊C4×C83D411yescharacteristic
56C2×C4⋊C4×C83D411yescharacteristic
57C2×C4⋊C4×C83D411yescharacteristic
58C2×C4⋊C4×C83D411yescharacteristic
59C2×C22⋊C4×C83—21no—
60C2×C22⋊C4×C83—21no—
61C2×C22⋊C4×C83—21no—
62C2×C22⋊C4×C83—21no—
63C2×C22⋊C4×C83D412yes—
64C2×C42×C83—21no—
65C2×C42×C83—21no—
66#107×C83—22no—
67#107×C83—22no—
68#106×C83—22no—
69#103×C83—22no—
70#102×C83—22no—
71#102×C83—22no—
72#102×C83—22no—
73#99×C83—44no—
74C22⋊C8×C83—21no—
75C22⋊C8×C83—21no—
76C22⋊C8×C83—21no—
77C22⋊C8×C83D412yes—
78#95×C83—22no—
79#95×C83—22no—
80#95×C83—22no—
81#95×C83—21no—
82#95×C83—21no—
83C24×C83—21no—
84C24×C83C2×D411yescharacteristic
85C2×Q8×C83—21no—
86C2×Q8×C83—21no—
87C2×Q8×C83—42no—
88C2×D4×C83—21no—
89C2×D4×C83—21no—
90C2×D4×C83—42no—
91C2×D4×C83—42no—
92C2×D4×C83—42no—
93C2×D4×C83—41no—
94C2×D4×C83—41no—
95C22×C4×C83—21no—
96C22×C4×C83—21no—
97C22×C4×C83—22no—
98C22×C4×C83—21no—
99C22×C4×C83—21no—
100C22×C4×C83—21no—
101C22×C4×C83—42no—
102C22×C4×C83—41no—
103C22×C4×C83C2×D411yescharacteristic
104C22×C4×C83C2×D411yescharacteristic
105C22×C4×C83C2×D411yescharacteristic
106C22×C4×C83C2×D411yescharacteristic
107C22×C4×C83C2×D411yescharacteristic
108C22×C4×C83#4111yescharacteristic
109SD16×C83—82no—
110M16×C83—42no—
111M16×C83—42no—
112C2×C8×C83—22no—
113C2×C8×C83—22no—
114C4⋊C4×C83—21no—
115C4⋊C4×C83—21no—
116C4⋊C4×C83—21no—
117C4⋊C4×C83—21no—
118C4⋊C4×C83—21no—
119C4⋊C4×C83—21no—
120C4⋊C4×C83—21no—
121C4⋊C4×C83—21no—
122C4⋊C4×C83—42no—
123C4⋊C4×C83—41no—
124C4⋊C4×C83—41no—
125C4⋊C4×C83—82no—
126C22⋊C4×C83—22no—
127C22⋊C4×C83—41no—
128C22⋊C4×C83—41no—
129C22⋊C4×C83—41no—
130C22⋊C4×C83—41no—
131C22⋊C4×C83—41no—
132C22⋊C4×C83—41no—
133C22⋊C4×C83—41no—
134C22⋊C4×C83—42no—
135C42×C83—42no—
136C42×C83—41no—
137C42×C83—41no—
138C23×C83—21no—
139C23×C83—21no—
140C23×C83—41no—
141C23×C83—41no—
142C23×C83—42no—
143C23×C83—41no—
144C23×C83—81no—
145C23×C83—81no—
146C23×C83#12011yescharacteristic
147C23×C83#12111yescharacteristic
148C23×C83#12711yescharacteristic
149Q8×C83—42no—
150Q8×C83—81no—
151D4×C83—42no—
152D4×C83—42no—
153D4×C83—82no—
154D4×C83—81no—
155D4×C83—81no—
156C2×C4×C83—22no—
157C2×C4×C83—22no—
158C2×C4×C83—22no—
159C2×C4×C83—41no—
160C2×C4×C83—41no—
161C2×C4×C83—41no—
162C2×C4×C83—42no—
163C2×C4×C83—42no—
164C2×C4×C83—42no—
165C2×C4×C83—42no—
166C2×C4×C83—42no—
167C2×C4×C83—42no—
168C2×C4×C83—41no—
169C2×C4×C83—41no—
170C2×C4×C83—41no—
171C2×C4×C83—41no—
172C2×C4×C83—41no—
173C2×C4×C83—42no—
174C2×C4×C83—41no—
175C2×C4×C83—41no—
176C2×C4×C83—41no—
177C2×C4×C83—41no—
178C2×C4×C83—81no—
179C2×C4×C83—81no—
180C2×C4×C83#12011yescharacteristic
181C2×C4×C83#12011yescharacteristic
182C2×C4×C83#12111yescharacteristic
183C2×C4×C83#12111yescharacteristic
184C8×C83—42no—
185C8×C83—42no—
186C22×C83—21no—
187C22×C83—21no—
188C22×C83—21no—
189C22×C83—21no—
190C22×C83—21no—
191C22×C83—21no—
192C22×C83—21no—
193C22×C83—21no—
194C22×C83—81no—
195C22×C83—81no—
196C22×C83—81no—
197C22×C83—81no—
198C22×C83—81no—
199C22×C83—162no—
200C22×C83#39211yescharacteristic
201C22×C83#45311yescharacteristic
202C22×C83#45411yescharacteristic
203C4×C83—21no—
204C4×C83—21no—
205C4×C83—21no—
206C4×C83—82no—
207C4×C83—82no—
208C4×C83—81no—
209C4×C83—81no—
210C4×C83—81no—
211C4×C83—81no—
212C4×C83—81no—
213C4×C83#45812yes—
214#9933C8311yesmaximal, characteristic, direct product factor, Sylow
215C2×C83—21no—
216C2×C83—21no—
217C2×C83—41no—
218C2×C83—41no—
219C2×C83—161no—
220C2×C83#200611yescharacteristic
221C2×C83#200911yescharacteristic
222C2×C83#202211yescharacteristic
223#3193C2×C8311yescharacteristic
224#3094C2×C8311yescharacteristic
225#2625C2×C8311yescharacteristic, complemented
226#1964C2×C8311yescharacteristic
227#1826C2×C8311yescharacteristic, complemented
228#1508C2×C8311yescharacteristic, complemented
229#1305C2×C8311yescharacteristic, complemented
230C83#993311yescharacteristic, direct product factor, Sylow
231C2×C22⋊Q8C22×C8311yescharacteristic
232C2×#121C22×C8311yescharacteristic
233C2×#117C22×C8311yescharacteristic
234#484—21no—
235#482—22no—
236#481—21no—
237#480—21no—
238#480—21no—
239#468—22no—
240#450—21no—
241#448—21no—
242#428—21no—
243#418—21no—
244C2×#99—22no—
245#407C22×C8311yescharacteristic
246#407C22×C8311yescharacteristic
247#400—21no—
248#398—21no—
249#397—22no—
250#391—21no—
251#389—21no—
252#380C22×C8311yescharacteristic
253C4×C22⋊C4C22×C8311yescharacteristic
254#339—22no—
255#328—22no—
256C22×Q8D4×C8311yescharacteristic
257C22×D4—21no—
258C22×D4D4×C8311yescharacteristic
259C23×C4C23×C8311yescharacteristic
260C2×SD16—22no—
261C2×M16—21no—
262C2×M16D4×C8312yes—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267#121—21no—
268#121—21no—
269#121—21no—
270#121—21no—
271#117—21no—
272#117—21no—
273#117—21no—
274#117—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4D4×C8311yescharacteristic
279C2×C4⋊C4D4×C8311yescharacteristic
280C2×C4⋊C4D4×C8311yescharacteristic
281C2×C4⋊C4D4×C8311yescharacteristic
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4D4×C8312yes—
287C2×C42—21no—
288C2×C42—21no—
289#107—22no—
290#107—22no—
291#106—22no—
292#103—22no—
293#102—22no—
294#102—22no—
295#102—22no—
296#99—44no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8D4×C8312yes—
301#95—22no—
302#95—22no—
303#95—22no—
304#95—21no—
305#95—21no—
306C24—21no—
307C24C2×D4×C8311yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—42no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—42no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—42no—
325C22×C4—41no—
326C22×C4C2×D4×C8311yescharacteristic
327C22×C4C2×D4×C8311yescharacteristic
328C22×C4C2×D4×C8311yescharacteristic
329C22×C4C2×D4×C8311yescharacteristic
330C22×C4C2×D4×C8311yescharacteristic
331C22×C4#41×C8311yescharacteristic
332SD16—82no—
333M16—42no—
334M16—42no—
335C2×C8—22no—
336C2×C8—22no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—42no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—82no—
349C22⋊C4—22no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—42no—
358C42—42no—
359C42—41no—
360C42—41no—
361C23—21no—
362C23—21no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—41no—
367C23—81no—
368C23—81no—
369C23#120×C8311yescharacteristic
370C23#121×C8311yescharacteristic
371C23#127×C8311yescharacteristic
372Q8—42no—
373Q8—81no—
374D4—42no—
375D4—42no—
376D4—82no—
377D4—81no—
378D4—81no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4#120×C8311yescharacteristic
404C2×C4#120×C8311yescharacteristic
405C2×C4#121×C8311yescharacteristic
406C2×C4#121×C8311yescharacteristic
407C8—42no—
408C8—42no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—162no—
423C22#392×C8311yescharacteristic
424C22#453×C8311yescharacteristic
425C22#454×C8311yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—82no—
430C4—82no—
431C4—81no—
432C4—81no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4#458×C8312yes—
437C2—21no—
438C2—21no—
439C2—41no—
440C2—41no—
441C2—161no—
442C2C83×#200611yescharacteristic
443C2C83×#200911yescharacteristic
444C2C83×#202211yescharacteristic
subgroupG/H
center, socleC22×C83#392
commutator, Frattini, cosocleC23×C4C23×C83
prime radicalC2×#121×C83C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C23×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
3. C83×#2625C2semidirect
5. C83×#1826C2semidirect
6. C83×#1508C2semidirect
7. C83×#1305C2semidirect
214. #9933C83direct (N × H)
225. #2625C2×C83semidirect
227. #1826C2×C83semidirect
228. #1508C2×C83semidirect
229. #1305C2×C83semidirect
230. C83#9933direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#31932
C83×#30942
C83×#26252
C83×#19642
C83×#18262
C83×#15082
C83×#13052
#993383