Finite Group Databasebeta

← #25016190

Subgroups — #25016190

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063266C211yesmaximal, characteristic
2C2×Dic43⋊C16C211yesmaximal, characteristic, complemented
3C2×#14582701C211yesmaximal, characteristic, complemented
4#19135462C211yesmaximal, characteristic, complemented
5#19135459C211yesmaximal, characteristic, complemented
6#19132686C211yesmaximal, characteristic, complemented
7C2×C43×#357C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C2×#13063266—22no—
10C2×#13063266—22no—
11C2×#13063266—22no—
12C22×C43⋊C16C2211yescharacteristic
13C2×#13063259C2211yescharacteristic
14C2×#13063246—21no—
15C2×#13063245—21no—
16C2×C8×Dic43C2211yescharacteristic
17#14582802—21no—
18#14582800—21no—
19Dic43⋊C16—22no—
20#14582701—22no—
21C22×D8×C43C2211yescharacteristic
22C22×C16×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C43×#357—22no—
25C22×D172—21no—
26C2×D344—21no—
27C2×D344—21no—
28C2×D344—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344D412yes—
32C22×C43⋊C8D411yescharacteristic
33C2×C4⋊Dic43—21no—
34C2×C22⋊Dic43—41no—
35C2×C22⋊Dic43—41no—
36C2×(C2×D43)⋊C4—41no—
37C2×(C2×D43)⋊C4—41no—
38C2×C4×Dic43D411yescharacteristic
39#13063266—28no—
40C2×C43⋊C16—21no—
41C2×C43⋊C16—21no—
42C2×C43⋊C16D412yes—
43#13063259—21no—
44#13063259—21no—
45#13063246—42no—
46#13063245—42no—
47C8×Dic43—21no—
48C8×Dic43—21no—
49C22×D4×C43—21no—
50C2×D8×C43—21no—
51C2×D8×C43—21no—
52C2×D8×C43—21no—
53C2×D8×C43—21no—
54C2×D8×C43—21no—
55C2×D8×C43D412yes—
56C22×C8×C43C2311yescharacteristic
57C2×C4⋊C4×C43—21no—
58C2×C16×C43—21no—
59C2×C16×C43—21no—
60C2×C16×C43—21no—
61#107×C43—21no—
62#107×C43—21no—
63C24×C43—41no—
64C23×D43—41no—
65C2×D4×C43—22no—
66C2×D4×C43—41no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—41no—
74C22×Dic43D811yescharacteristic
75C22×Dic43D811yescharacteristic
76C2×D172—22no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172—41no—
82D8×C43—22no—
83D8×C43—22no—
84D8×C43—41no—
85D8×C43—41no—
86C2×C8×C43C2×D411yescharacteristic
87C2×C8×C43C2×D411yescharacteristic
88C2×C8×C43C2×D411yescharacteristic
89C2×C8×C43#4111yescharacteristic
90C2×C8×C43#4111yescharacteristic
91C2×C8×C43#4111yescharacteristic
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C22⋊Dic43—82no—
95C22⋊Dic43—82no—
96(C2×D43)⋊C4—82no—
97(C2×D43)⋊C4—82no—
98C4⋊Dic43—41no—
99C4⋊Dic43—41no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C2×C43⋊C8—21no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105D344—22no—
106D344—22no—
107D344—41no—
108D344—41no—
109C16×C43—41no—
110C43⋊C16—22no—
111C23×C43—42no—
112C23×C43—81no—
113C23×C43—81no—
114C23×C43—81no—
115C23×C43—81no—
116C23×C43—81no—
117C23×C43—81no—
118C23×C43C2×D811yescharacteristic
119C22×D43—42no—
120C22×D43—81no—
121C22×D43—81no—
122C22×D43—81no—
123C22×D43—81no—
124C22×D43—81no—
125C22×D43—81no—
126D4×C43—42no—
127D4×C43—42no—
128D4×C43—81no—
129D4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#13511yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—81no—
145C2×Dic43—81no—
146C2×Dic43—81no—
147C2×Dic43D1612yescomplemented
148D172—42no—
149D172—42no—
150D172—81no—
151D172—81no—
152C8×C43#12011yescharacteristic
153C8×C43#12311yescharacteristic
154C8×C43#12311yescharacteristic
155C8×C43#12411yescharacteristic
156C43⋊C8—41no—
157#13448—431nomaximal, Sylow
158C22×C43—82no—
159C22×C43—82no—
160C22×C43—82no—
161C22×C43—161no—
162C22×C43—161no—
163C22×C43—161no—
164C22×C43—161no—
165C22×C43#45911yescharacteristic
166C22×C43#45911yescharacteristic
167C22×C43#46611yescharacteristic
168C22×C43C2×D1611yescharacteristic
169C22×C43#50811yescharacteristic
170C22×C43#50911yescharacteristic
171C22×C43#50911yescharacteristic
172C2×D43—82no—
173C2×D43—82no—
174C2×D43—82no—
175C2×D43—161no—
176C2×D43—161no—
177C2×D43—161no—
178C2×D43—161no—
179C4×C43—161no—
180C4×C43#39411yescharacteristic
181C4×C43#46311yescharacteristic
182C4×C43#46311yescharacteristic
183C4×C43#46911yescharacteristic
184Dic43—22no—
185Dic43—41no—
186Dic43—161no—
187C22×D16—431no—
188C2×C4⋊C16—431no—
189C2×#357—431no—
190C2×#357D4311yescharacteristic, complemented
191#1970—431no—
192#1970—431no—
193#1380—431no—
194C2×C43—162no—
195C2×C43#205411yescharacteristic
196C2×C43#220611yescharacteristic
197C2×C43#220611yescharacteristic
198C2×C43#221011yescharacteristic
199C2×C43#221011yescharacteristic
200C2×C43#221511yescharacteristic
201C2×C43#221811yescharacteristic
202D43—162no—
203C22×D8—431no—
204C22×D8C2×D4311yescharacteristic
205C2×D16—862no—
206C2×D16—862no—
207C2×D16—862no—
208C22×C16—431no—
209C22×C16C2×D4311yescharacteristic
210C2×#107—431no—
211C2×#107C2×D4311yescharacteristic
212C2×#102—861no—
213C2×#102—861no—
214C2×C4×C8—431no—
215#390—861no—
216#390—861no—
217C4⋊C16—862no—
218#357—22no—
219#357—862no—
220C43#1344811yescharacteristic, complemented, Sylow
221C22×D4—21no—
222C22×D4—861no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—432no—
229C2×D8—861no—
230C2×D8—861no—
231C2×D8—861no—
232C2×D8—861no—
233C2×D8—861no—
234C2×D8C22⋊D4312yes—
235C22×C8—431no—
236C22×C8C22×D4311yescharacteristic
237C2×C4⋊C4—21no—
238C2×C4⋊C4—861no—
239C2×C22⋊C4—1721no—
240C2×C22⋊C4—1721no—
241C2×C22⋊C4—1721no—
242C2×C22⋊C4—1721no—
243C2×C42—431no—
244D16—868no—
245C2×C16—21no—
246C2×C16—21no—
247C2×C16—21no—
248C2×C16—432no—
249C2×C16—861no—
250C2×C16—861no—
251#107—21no—
252#107—21no—
253#107—861no—
254#107—861no—
255#102—1722no—
256#102—1722no—
257C4×C8—861no—
258C4×C8—861no—
259C24—41no—
260C24—1721no—
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—862no—
268C2×D4—1721no—
269C2×D4—1721no—
270C2×D4—1721no—
271C2×D4—1721no—
272C2×D4—1721no—
273C22×C4—41no—
274C22×C4—431no—
275C22×C4—431no—
276C22×C4—1721no—
277C22×C4D4×D4311yescharacteristic
278D8—22no—
279D8—22no—
280D8—41no—
281D8—41no—
282D8—862no—
283D8—862no—
284D8—1721no—
285D8—1721no—
286C2×C8—861no—
287C2×C8—861no—
288C2×C8—861no—
289C2×C8#1062189811yescharacteristic
290C2×C8#1062189811yescharacteristic
291C2×C8D4×D4311yescharacteristic
292C2×C8D4×D4311yescharacteristic
293C2×C8#1062190011yescharacteristic
294C2×C8C2×C22⋊D4311yescharacteristic
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C22⋊C4—3442no—
300C22⋊C4—3442no—
301C22⋊C4—3442no—
302C22⋊C4—3442no—
303C42—861no—
304C42—861no—
305C16—41no—
306C16—862no—
307C23—42no—
308C23—81no—
309C23—81no—
310C23—81no—
311C23—81no—
312C23—81no—
313C23—81no—
314C23—3441no—
315C23—3441no—
316C23—3441no—
317C23—3441no—
318C23—3441no—
319C23—3441no—
320C23—1722no—
321C23D8×D4311yescharacteristic
322D4—42no—
323D4—42no—
324D4—81no—
325D4—81no—
326D4—3441no—
327D4—3441no—
328D4—1722no—
329D4—1722no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—432no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—3441no—
340C2×C4—3441no—
341C2×C4—3441no—
342C2×C4#1306329711yescharacteristic
343C2×C4#1306329811yescharacteristic
344C2×C4#1306329811yescharacteristic
345C2×C4#1306334611yescharacteristic
346C2×C4#1306334911yescharacteristic
347C2×C4#1306335211yescharacteristic
348C8—1721no—
349C8#1306329311yescharacteristic
350C8#1306330711yescharacteristic
351C8#1306330811yescharacteristic
352C8#1306331111yescharacteristic
353C22—82no—
354C22—82no—
355C22—82no—
356C22—161no—
357C22—161no—
358C22—161no—
359C22—161no—
360C22—3442no—
361C22—3442no—
362C22—3442no—
363C22—6881no—
364C22—6881no—
365C22—6881no—
366C22—6881no—
367C22#1458309211yescharacteristic
368C22#1458309311yescharacteristic
369C22#1458313411yescharacteristic
370C22D16×D4311yescharacteristic
371C22#1458333011yescharacteristic
372C22#1458333311yescharacteristic
373C22#1458333611yescharacteristic
374C4—161no—
375C4—862no—
376C4—1721no—
377C4—6881no—
378C4#1458281411yescharacteristic
379C4#1458311311yescharacteristic
380C4#1458311611yescharacteristic
381C4#1458315111yescharacteristic
382C2—162no—
383C2—6882no—
384C2#1913590411yescharacteristic
385C2#1913662811yescharacteristic
386C2#1913662911yescharacteristic
387C2#1913664911yescharacteristic
388C2#1913665211yescharacteristic
389C2#1913668011yescharacteristic
390C2#1913669711yescharacteristic
subgroupG/H
centerC23D8×D43
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC2×C43×#357C2
socleC23×C43C2×D8
prime radicalC22×#13063266C2
hypercenterC2×#357D43
hypocenterC43#13448
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×Dic43⋊C16C2semidirect
3. C2×#14582701C2semidirect
4. #19135462C2semidirect
5. #19135459C2semidirect
6. #19132686C2semidirect
7. C2×C43×#357C2semidirect
147. C2×Dic43D16semidirect
190. C2×#357D43semidirect
220. C43#13448semidirect

Maximal subgroups

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

subgroupindex
C22×#130632662
C2×Dic43⋊C162
C2×#145827012
#191354622
#191354592
#191326862
C2×C43×#3572
#1344843