Finite Group Databasebeta

← #25113163

Subgroups — #25113163

Order 11008.

1014 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583606C211yesmaximal, characteristic
2M16×Dic86C212yesmaximal, complemented
3#19135586C214yesmaximal, complemented
4#19135584C212yesmaximal, complemented
5#19134587C211yesmaximal, characteristic
6#19134585C212yesmaximal
7#100×Dic43C212yesmaximal
8C4×#100×C43C211yesmaximal, characteristic
9#14583606—22no—
10#14583606—24no—
11#14583606—22no—
12C2×#13063325C2211yescharacteristic
13C2×#13063316C2212yes—
14C2×#13063304C412yes—
15C2×#13063302C414yes—
16C2×C4×Dic86C2211yescharacteristic
17C2×D4×Dic43C2212yes—
18C22×C4⋊Dic43C412yes—
19#14583029—22no—
20#14583027—24no—
21C8×Dic86—22no—
22#14582923C2212yes—
23#14582922C2214yes—
24C2×#13063242C2212yes—
25M16×Dic43C2214yes—
26#14582668C2212yes—
27#14582667C2214yes—
28#14582667C2214yes—
29C2×C4×D4×C43C2211yescharacteristic
30C2×#100×C43C2211yescharacteristic
31C2×#100×C43C2211yescharacteristic
32C4×M16×C43C2212yes—
33C43×#343C2212yes—
34C22×Dic86C2×C412yes—
35C22×Dic86C2×C411yescharacteristic
36C23×Dic43C2×C414yes—
37C2×#10621877C2314yes—
38#13063325—22no—
39#13063325—22no—
40#13063316—24no—
41#13063316—24no—
42#13063304—24no—
43#13063304—24no—
44#13063302—28no—
45#13063302—28no—
46C4×Dic86D412yes—
47C4×Dic86D414yes—
48C4×Dic86D412yes—
49D4×Dic43—24no—
50D4×Dic43—24no—
51C2×C4⋊Dic43—24no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43C2×C414yes—
55C2×C4⋊Dic43C2×C412yes—
56C2×C4⋊Dic43C2×C411yescharacteristic
57C2×C4⋊Dic43C2312yes—
58C2×Dic43⋊C4C2×C414yes—
59C2×Dic43⋊C4C2×C412yes—
60C2×C22⋊Dic43C2×C414yes—
61C2×C4×Dic43C2312yes—
62C4⋊(C43⋊C8)—22no—
63C4⋊(C43⋊C8)—22no—
64Dic43⋊C8—24no—
65Dic43⋊C8—24no—
66#13063242—24no—
67#13063235—24no—
68C8×Dic43—24no—
69C22×D4×C43C2311yescharacteristic
70C23×C4×C43C2×C412yes—
71C2×M16×C43C2312yes—
72C2×M16×C43C2312yes—
73C4×D4×C43—22no—
74C4×D4×C43—22no—
75C2×C4⋊C4×C43C2311yescharacteristic
76C2×C22⋊C4×C43C2×C412yes—
77C2×C42×C43C2311yescharacteristic
78#100×C43—22no—
79#100×C43Q814yescomplemented
80#97×C43—22no—
81C4×C8×C43—22no—
82C24×C43C22×C412yes—
83C2×D4×C43—22no—
84C2×D4×C43—22no—
85C2×D4×C43C2×Q812yes—
86C2×D4×C43#4112yes—
87C22×C4×C43—22no—
88C22×C4×C43—22no—
89C22×C4×C43—44no—
90C22×C4×C43C22×C411yescharacteristic
91C22×C4×C43C22×C412yes—
92C22×C4×C43C22×C411yescharacteristic
93C22×C4×C43C2411yescharacteristic
94C22×Dic43—24no—
95C22×Dic43—24no—
96C22×Dic43—84no—
97C22×Dic43C22×C414yes—
98C22×Dic43C22×C412yes—
99C22×Dic43C22×C412yes—
100C2×Dic86—24no—
101C2×Dic86—42no—
102C2×Dic86—82no—
103C2×Dic86C22⋊C412yes—
104C2×Dic86C22⋊C412yes—
105M16×C43—22no—
106M16×C43—22no—
107M16×C43—22no—
108M16×C43C2×Q814yes—
109C2×C8×C43—22no—
110C2×C8×C43—22no—
111C4⋊C4×C43—22no—
112C22⋊C4×C43—24no—
113C42×C43C2×D412yes—
114C42×C43C2×D412yes—
115C22⋊Dic43—28no—
116C4⋊Dic43—22no—
117C4⋊Dic43—22no—
118C4⋊Dic43—24no—
119C4⋊Dic43—24no—
120C4⋊Dic43—24no—
121C4⋊Dic43C22⋊C412yes—
122C4⋊Dic43C22⋊C411yescharacteristic
123C4⋊Dic43C22⋊C411yescharacteristic
124Dic43⋊C4—28no—
125Dic43⋊C4C22⋊C414yes—
126Dic43⋊C4C22⋊C414yes—
127C4×Dic43C2×D414yes—
128C4×Dic43C2×D414yes—
129#10621877—24no—
130#10621877—24no—
131C2×C43⋊C8—24no—
132C23×C43—22no—
133C23×C43—22no—
134C23×C43—42no—
135C23×C43—42no—
136C23×C43C4×Q814yes—
137C23×C43C23×C411yescharacteristic
138D4×C43—24no—
139D4×C43—24no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—41no—
143C2×C4×C43—44no—
144C2×C4×C43—44no—
145C2×C4×C43—42no—
146C2×C4×C43C2×C22⋊C412yes—
147C2×C4×C43C2×C22⋊C411yescharacteristic
148C2×C4×C43C2×C22⋊C411yescharacteristic
149C2×C4×C43C22×D412yes—
150C2×C4×C43C22×Q811yescharacteristic
151C2×C4×C43C2×#4111yescharacteristic
152C2×C4×C432−1+412yes—
153C2×Dic43—24no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—44no—
157C2×Dic43—84no—
158C2×Dic43—84no—
159C2×Dic43C2×C22⋊C414yes—
160C2×Dic43C2×C22⋊C412yes—
161C2×Dic43C2×C22⋊C412yes—
162Dic86—24no—
163Dic86—42no—
164Dic86—84no—
165C8×C43—24no—
166C8×C43—42no—
167C43⋊C8—44no—
168#22515—431nomaximal, Sylow
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—24no—
172C22×C43—44no—
173C22×C43—44no—
174C22×C43—42no—
175C22×C43—42no—
176C22×C43C22×C22⋊C411yescharacteristic
177C22×C43C2×C4×Q811yescharacteristic
178C22×C43#51911yescharacteristic
179C4×C43—21no—
180C4×C43—22no—
181C4×C43—42no—
182C4×C43#41312yes—
183C4×C43#54812yes—
184C4×C43D4×Q812yes—
185Dic43—24no—
186Dic43—22no—
187Dic43—22no—
188Dic43—44no—
189C2×#554—431no—
190Q8×M16—432no—
191#1998—434no—
192#1997—432no—
193#1800—432no—
194#1800—431no—
195C4×#100—432no—
196C4×#100D4311yescharacteristic
197C2×C43—21no—
198C2×C43—21no—
199C2×C43—44no—
200C2×C43Q8×C22⋊C411yescharacteristic
201C2×C43C2×#41311yescharacteristic
202C2×C43#288811yescharacteristic
203#554—862no—
204#554—862no—
205#554—864no—
206C2×C4⋊Q8—431no—
207C2×#125—432no—
208C2×C22⋊Q8—432no—
209C2×C22⋊Q8—434no—
210C2×C4×Q8—431no—
211C2×C4×D4—432no—
212C2×C4×D4C2×D4311yescharacteristic
213C22×C4⋊C4—432no—
214#446—862no—
215#446—864no—
216C8×Q8—862no—
217#423—434no—
218#423—432no—
219C2×#100—432no—
220C2×#100C2×D4311yescharacteristic
221C2×#100C2×D4311yescharacteristic
222C4×M16—434no—
223C4×M16C2×D4312yes—
224#343—434no—
225#343—434no—
226#343—432no—
227#343C2×D4312yes—
228C43#2251511yescharacteristic, complemented, Sylow
229C22×Q8—431no—
230C22×Q8—432no—
231C22×D4C22×D4311yescharacteristic
232C23×C4—434no—
233C23×C4C4×D4312yes—
234C2×M16—434no—
235C2×M16C22×D4312yes—
236C2×M16C22×D4312yes—
237C4⋊Q8—862no—
238C4⋊Q8—862no—
239#125—864no—
240#125—864no—
241C22⋊Q8—868no—
242C22⋊Q8—868no—
243C22⋊Q8—864no—
244C22⋊Q8—864no—
245C4×Q8—432no—
246C4×Q8—434no—
247C4×Q8—432no—
248C4×D4—22no—
249C4×D4—22no—
250C4×D4—864no—
251C4×D4—864no—
252C2×C4⋊C4—431no—
253C2×C4⋊C4—432no—
254C2×C4⋊C4—434no—
255C2×C4⋊C4—432no—
256C2×C4⋊C4—434no—
257C2×C4⋊C4—432no—
258C2×C4⋊C4—864no—
259C2×C4⋊C4—862no—
260C2×C4⋊C4—862no—
261C2×C4⋊C4C22×D4311yescharacteristic
262C2×C22⋊C4—434no—
263C2×C22⋊C4C4×D4312yes—
264C2×C42—432no—
265C2×C42C22×D4311yescharacteristic
266C4⋊C8—864no—
267C4⋊C8—864no—
268C4⋊C8—862no—
269C4⋊C8—862no—
270#100—22no—
271#100—864no—
272#100Dic8614yescomplemented
273#97—22no—
274#97—864no—
275C4×C8—22no—
276C4×C8—864no—
277C24C2×C4×D4312yes—
278C2×Q8—432no—
279C2×Q8—432no—
280C2×Q8—864no—
281C2×Q8—3442no—
282C2×Q8—1722no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4C2×Dic8612yes—
286C2×D4#1062189812yes—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—44no—
290C22×C4—432no—
291C22×C4—432no—
292C22×C4—434no—
293C22×C4—864no—
294C22×C4—864no—
295C22×C4—3444no—
296C22×C4C2×C4×D4311yescharacteristic
297C22×C4C2×C4×D4312yes—
298C22×C4C2×C4×D4311yescharacteristic
299C22×C4C23×D4311yescharacteristic
300M16—22no—
301M16—22no—
302M16—22no—
303M16—864no—
304M16—864no—
305M16C2×Dic8614yes—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—864no—
309C4⋊C4—22no—
310C4⋊C4—432no—
311C4⋊C4—431no—
312C4⋊C4—431no—
313C4⋊C4—434no—
314C4⋊C4—434no—
315C4⋊C4—864no—
316C4⋊C4—864no—
317C4⋊C4—868no—
318C4⋊C4—862no—
319C4⋊C4—862no—
320C4⋊C4—864no—
321C22⋊C4—24no—
322C22⋊C4—868no—
323C42—434no—
324C42—434no—
325C42D4×D4312yes—
326C42D4×D4312yes—
327C23—22no—
328C23—22no—
329C23—42no—
330C23—42no—
331C23C4×Dic8614yes—
332C23C22×C4×D4311yescharacteristic
333Q8—864no—
334Q8—3444no—
335Q8—1722no—
336D4—24no—
337D4—24no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—42no—
344C2×C4—434no—
345C2×C4—432no—
346C2×C4—432no—
347C2×C4—864no—
348C2×C4—3444no—
349C2×C4—3444no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4—1724no—
353C2×C4C22⋊C4×D4312yes—
354C2×C4C22⋊C4×D4311yescharacteristic
355C2×C4C22⋊C4×D4311yescharacteristic
356C2×C4C2×D4×D4312yes—
357C2×C4C22×Dic8611yescharacteristic
358C2×C4C2×#1062189811yescharacteristic
359C2×C4#1306337212yes—
360C8—24no—
361C8—42no—
362C8—1724no—
363C22—21no—
364C22—21no—
365C22—24no—
366C22—44no—
367C22—44no—
368C22—42no—
369C22—42no—
370C22C2×C22⋊C4×D4311yescharacteristic
371C22C2×C4×Dic8611yescharacteristic
372C22#1458337611yescharacteristic
373C4—21no—
374C4—22no—
375C4—42no—
376C4—864no—
377C4—862no—
378C4—862no—
379C4—1724no—
380C4#1458288012yes—
381C4#1458355812yes—
382C4D4×Dic8612yes—
383C2—21no—
384C2—21no—
385C2—44no—
386C2C22⋊C4×Dic8611yescharacteristic
387C2C2×#1458288011yescharacteristic
388C2#1914307211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#100×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenterC4×#100D43
hypocenterC43#22515
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. M16×Dic86C2semidirect
3. #19135586C2semidirect
4. #19135584C2semidirect
79. #100×C43Q8semidirect
228. C43#22515semidirect
272. #100Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145836062
M16×Dic862
#191355862
#191355842
#191345872
#191345852
#100×Dic432
C4×#100×C432
#2251543