Finite Group Databasebeta

← #25100888

Subgroups — #25100888

Order 11008.

862 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582981C211yesmaximal, characteristic
2#19137234C212yesmaximal, complemented
3#19135471C211yesmaximal, characteristic
4#19135469C211yesmaximal, characteristic
5#19135334C211yesmaximal, characteristic, complemented
6#19135279C212yesmaximal, complemented
7#19135277C212yesmaximal, complemented
8#106×Dic43C211yesmaximal, characteristic, complemented
9#19134419C212yesmaximal, complemented
10#19134283C211yesmaximal, characteristic, complemented
11C43×#1943C211yesmaximal, characteristic, complemented
12C22×D344C2211yescharacteristic
13C2×#13063287C2212yes—
14#14582981C418yescomplemented
15C2×#13063257C2211yescharacteristic
16C2×#13063247C2212yes—
17C2×#13063245C2212yes—
18C2×#13063245C2212yes—
19C2×#13063235C2211yescharacteristic
20C2×#13063235C2211yescharacteristic
21C2×C4×C43⋊C8C2211yescharacteristic
22C2×C8×Dic43C2211yescharacteristic
23C2×C8×Dic43C2211yescharacteristic
24#14582801C2212yes—
25#14582800C2212yes—
26#14582798C2212yes—
27#14582791—22no—
28#14582789—22no—
29#14582761—22no—
30#14582756—22no—
31C4⋊C4×Dic43C2212yes—
32#14582745C2211yescharacteristic
33#14582661C2212yes—
34#14582661C2212yes—
35C2×#107×C43C2211yescharacteristic
36C2×#106×C43C2211yescharacteristic
37C2×#97×C43C2211yescharacteristic
38C43×#389C2212yes—
39C43×#340C2212yes—
40C22×D172C2312yes—
41C22×C4×D43—22no—
42C2×D344—22no—
43C2×D344—22no—
44C2×D344C2×C414yes—
45C22×C43⋊C8C2311yescharacteristic
46C22×C43⋊C8C2311yescharacteristic
47#13063287—24no—
48#13063287C2×C418yes—
49C2×C4⋊Dic43—22no—
50C2×C4⋊Dic43C2312yes—
51C2×(C2×D43)⋊C4—22no—
52C2×(C2×D43)⋊C4—22no—
53C2×(C2×D43)⋊C4—22no—
54C2×(C2×D43)⋊C4—22no—
55C2×(C2×D43)⋊C4—22no—
56C2×C4×Dic43—22no—
57C2×C4×Dic43C2311yescharacteristic
58C2×C4×Dic43C2311yescharacteristic
59#13063257—22no—
60#13063247—24no—
61#13063245—24no—
62#13063245C2×C418yes—
63#13063235—22no—
64#13063235—22no—
65C4×C43⋊C8—22no—
66C8×Dic43—22no—
67C8×Dic43C2×C414yes—
68C43⋊#95—22no—
69C43⋊#95—22no—
70C43⋊#95D412yes—
71C43⋊#95D412yes—
72C22×C8×C43C2311yescharacteristic
73C22×C8×C43C2311yescharacteristic
74C2×C4⋊C4×C43—22no—
75C2×C4⋊C4×C43C2312yes—
76C2×C4⋊C4×C43C2312yes—
77C2×C42×C43C2311yescharacteristic
78#107×C43C2×C414yes—
79#106×C43—22no—
80#97×C43—22no—
81#95×C43—22no—
82C23×D43—22no—
83C22×C4×C43—22no—
84C22×C4×C43—22no—
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2411yescharacteristic
87C22×Dic43—22no—
88C22×Dic43C2×D412yes—
89C22×Dic43C2×D411yescharacteristic
90C22×Dic43C2×D411yescharacteristic
91C2×D172—22no—
92C2×D172—22no—
93C2×D172—22no—
94C2×D172—22no—
95C2×D172—22no—
96C2×D172C22×C414yes—
97C2×C4×D43—28no—
98C2×C4×D43—82no—
99C2×C4×D43—82no—
100C2×C8×C43—21no—
101C2×C8×C43—21no—
102C2×C8×C43C22×C412yes—
103C2×C8×C43#4112yes—
104C2×C8×C43#4112yes—
105C2×C8×C43#4112yes—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—82no—
110C4⋊C4×C43C22×C414yes—
111C42×C43—21no—
112C42×C43—21no—
113(C2×D43)⋊C4—28no—
114(C2×D43)⋊C4—82no—
115(C2×D43)⋊C4—82no—
116(C2×D43)⋊C4—82no—
117(C2×D43)⋊C4—82no—
118C4⋊Dic43—22no—
119C4⋊Dic43—22no—
120C4⋊Dic43—82no—
121C4×Dic43—21no—
122C4×Dic43—21no—
123C4×Dic43—82no—
124C4×Dic43C22×C412yes—
125C4×Dic43#4112yes—
126C2×C43⋊C8—21no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—21no—
130C2×C43⋊C8C22×C412yes—
131C2×C43⋊C8#4112yes—
132D344—28no—
133C23×C43C22×D411yescharacteristic
134C22×D43—24no—
135C22×D43—42no—
136C22×D43—42no—
137C22×D43—42no—
138C22×D43—42no—
139C22×D43—42no—
140C22×D43—42no—
141C2×C4×C43—24no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43C23×C411yescharacteristic
151C2×C4×C43C2×#4111yescharacteristic
152C2×C4×C43C2×#4111yescharacteristic
153C2×C4×C43C2×#4111yescharacteristic
154C2×C4×C43C2×#4111yescharacteristic
155C2×C4×C43C2×#4111yescharacteristic
156C2×Dic43—22no—
157C2×Dic43—22no—
158C2×Dic43—22no—
159C2×Dic43—22no—
160C2×Dic43—22no—
161C2×Dic43—42no—
162C2×Dic43—42no—
163C2×Dic43—42no—
164C2×Dic43C4×D412yes—
165C2×Dic43C4×D412yes—
166D172—24no—
167D172—24no—
168D172—42no—
169D172—42no—
170C4×D43—88no—
171C8×C43—22no—
172C8×C43#11714yes—
173C43⋊C8—22no—
174C43⋊C8—22no—
175#21284—431nomaximal, Sylow
176C22×C43C2×C4×D411yescharacteristic
177C22×C43#53211yescharacteristic
178C22×C43#53211yescharacteristic
179C22×C43#57612yes—
180C22×C43#57712yes—
181C2×D43—44no—
182C2×D43—44no—
183C2×D43—44no—
184C2×D43—82no—
185C2×D43—82no—
186C2×D43—82no—
187C2×D43—82no—
188C4×C43—42no—
189C4×C43—44no—
190C4×C43—82no—
191C4×C43C2×#11711yescharacteristic
192C4×C43C4×#4111yescharacteristic
193C4×C43#52911yescharacteristic
194C4×C43#52911yescharacteristic
195Dic43—22no—
196Dic43—22no—
197Dic43—42no—
198Dic43—82no—
199C2×C4×D8—431no—
200#2319—432no—
201#1972—431no—
202#1972—431no—
203#1943—431no—
204#1943D4311yescharacteristic, complemented
205#1934—432no—
206#1934—432no—
207C4×#106—431no—
208#1762—432no—
209#1726—431no—
210C2×C43#229311yescharacteristic
211C2×C43#294811yescharacteristic
212C2×C43#295211yescharacteristic
213C2×C43#317912yes—
214C2×C43#317912yes—
215D43—84no—
216C22×D8—431no—
217C2×C4×D4—432no—
218C4×D8—438no—
219C2×#107C2×D4311yescharacteristic
220C2×#106—431no—
221C2×#106C2×D4311yescharacteristic
222C2×#102—432no—
223C2×#102—432no—
224C2×#102—432no—
225C2×#97—431no—
226C2×#97—431no—
227C2×#97C2×D4311yescharacteristic
228C2×C4×C8—431no—
229C2×C4×C8—431no—
230C2×C4×C8—431no—
231#390—432no—
232#390—432no—
233#389—432no—
234#389C2×D4312yes—
235#388—862no—
236#388—862no—
237#381—862no—
238#380—862no—
239C4×C4⋊C4—432no—
240#376—431no—
241#340—432no—
242#340—432no—
243#340C2×D4312yes—
244C43#2128411yescharacteristic, complemented, Sylow
245C22×D4—432no—
246C23×C4—862no—
247C2×D8—434no—
248C2×D8—862no—
249C2×D8—862no—
250C22×C8—431no—
251C22×C8—431no—
252C22×C8C22×D4311yescharacteristic
253C22×C8C22×D4311yescharacteristic
254C4×D4—438no—
255C4×D4—864no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—432no—
258C2×C4⋊C4—862no—
259C2×C4⋊C4C22×D4312yes—
260C2×C4⋊C4C22×D4312yes—
261C2×C22⋊C4—862no—
262C2×C22⋊C4—862no—
263C2×C22⋊C4—862no—
264C2×C22⋊C4—862no—
265C2×C22⋊C4—862no—
266C2×C42—431no—
267C2×C42—431no—
268C2×C42—862no—
269C2×C42C22×D4311yescharacteristic
270#107C4×D4314yes—
271#106—22no—
272#106—862no—
273#102—438no—
274#102—864no—
275#102—864no—
276#97—22no—
277#97—862no—
278#97—862no—
279C4×C8—434no—
280C4×C8—862no—
281C4×C8—862no—
282#95—22no—
283#95—432no—
284#95—432no—
285#95—862no—
286#95—862no—
287C24—862no—
288C2×D4—434no—
289C2×D4—862no—
290C2×D4—862no—
291C2×D4—862no—
292C2×D4—862no—
293C2×D4—862no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—431no—
297C22×C4—431no—
298C22×C4—432no—
299C22×C4—868no—
300C22×C4—862no—
301C22×C4—3442no—
302C22×C4—3442no—
303C22×C4D4×D4312yes—
304C22×C4C23×D4311yescharacteristic
305D8—868no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—432no—
309C2×C8—432no—
310C2×C8—861no—
311C2×C8—861no—
312C2×C8—861no—
313C2×C8—861no—
314C2×C8C2×C4×D4312yes—
315C2×C8#1062190012yes—
316C2×C8#1062190212yes—
317C2×C8#1062190212yes—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—82no—
322C4⋊C4—862no—
323C4⋊C4—862no—
324C4⋊C4—3442no—
325C4⋊C4C2×C4×D4314yes—
326C22⋊C4—868no—
327C22⋊C4—3442no—
328C22⋊C4—3442no—
329C22⋊C4—3442no—
330C22⋊C4—3442no—
331C42—21no—
332C42—21no—
333C42—432no—
334C42—432no—
335C42—861no—
336C42—861no—
337C42—3442no—
338C23—864no—
339C23—1722no—
340C23—1722no—
341C23—1722no—
342C23—1722no—
343C23—1722no—
344C23—1722no—
345C23C2×D4×D4311yescharacteristic
346D4—864no—
347D4—864no—
348D4—1722no—
349D4—1722no—
350C2×C4—24no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—432no—
360C2×C4—432no—
361C2×C4—862no—
362C2×C4—862no—
363C2×C4—862no—
364C2×C4—862no—
365C2×C4—862no—
366C2×C4—3448no—
367C2×C4—1722no—
368C2×C4—1722no—
369C2×C4—1722no—
370C2×C4C22×C4×D4311yescharacteristic
371C2×C4#41×D4311yescharacteristic
372C2×C4#41×D4311yescharacteristic
373C2×C4C2×#1062190011yescharacteristic
374C2×C4C2×#1062190211yescharacteristic
375C2×C4C2×#1062190211yescharacteristic
376C8—22no—
377C8—862no—
378C8—862no—
379C8#1306328314yes—
380C22—3442no—
381C22—3442no—
382C22—3442no—
383C22—3442no—
384C22—1724no—
385C22—1724no—
386C22—1724no—
387C22C4×D4×D4311yescharacteristic
388C22#1458344411yescharacteristic
389C22#1458345011yescharacteristic
390C22#1458370312yes—
391C22#1458370812yes—
392C4—44no—
393C4—42no—
394C4—82no—
395C4—862no—
396C4—862no—
397C4—3442no—
398C4—1722no—
399C4C2×#1306328311yescharacteristic
400C4C4×#1062190211yescharacteristic
401C4#1458343411yescharacteristic
402C4#1458343511yescharacteristic
403C2—3444no—
404C2#1913705311yescharacteristic
405C2#1914344411yescharacteristic
406C2#1914347511yescharacteristic
407C2#1914527112yes—
408C2#1914528312yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1943C2
socleC23×C43C22×D4
prime radicalC22×D344C22
cosocleC22×C4×C43C24
hypercenter#1943D43
hypocenterC43#21284
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

Complements

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

NH ≅ G/Ntype
2. #19137234C2semidirect
5. #19135334C2semidirect
6. #19135279C2semidirect
7. #19135277C2semidirect
8. #106×Dic43C2semidirect
9. #19134419C2semidirect
10. #19134283C2semidirect
11. C43×#1943C2semidirect
14. #14582981C4semidirect
204. #1943D43semidirect
244. C43#21284semidirect

Maximal subgroups

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

subgroupindex
C2×#145829812
#191372342
#191354712
#191354692
#191353342
#191352792
#191352772
#106×Dic432
#191344192
#191342832
C43×#19432
#2128443