Finite Group Databasebeta

← #24992074

Subgroups — #24992074

Order 11008.

514 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#10621898C211yesmaximal, characteristic
2C4×#13063356C211yesmaximal, characteristic
3#19132980C211yesmaximal, characteristic
4#19132919C211yesmaximal, characteristic, complemented
5#19132445C211yesmaximal, characteristic, complemented
6#19132432C211yesmaximal, characteristic, complemented
7C2×C43×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#13063356C411yescharacteristic
9C4×#10621898C2211yescharacteristic
10C8×Dic86—21no—
11#14583004—21no—
12#14582997—21no—
13C4×#10621885—21no—
14C4×#10621884—21no—
15C8×D172—21no—
16C8×C22⋊D43—22no—
17#14582952C2211yescharacteristic
18#14582952C2211yescharacteristic
19#14582950—21no—
20#14582939C411yescharacteristic
21#14582908C411yescharacteristic
22#14582898C411yescharacteristic
23C4×#10621877C2211yescharacteristic
24C4×C8×D43—21no—
25#14582629—21no—
26#14582626—21no—
27#14582625—22no—
28C2×C4×Q8×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C43×Q8⋊C8—21no—
32C43×Q8⋊C8—21no—
33C2×#10621898C2×C411yescharacteristic
34#13063356—22no—
35#13063356C814yescomplemented
36C2×#10621885—21no—
37C2×#10621884—21no—
38C2×#10621877C2×C411yescharacteristic
39C2×#10621877C2×C411yescharacteristic
40C2×C8×D43—22no—
41C4×Dic86D411yescharacteristic
42C4×Dic86D411yescharacteristic
43C4×D172D411yescharacteristic
44C4×D172D411yescharacteristic
45C4×C22⋊D43—21no—
46C4×C22⋊D43—21no—
47#13063284C2×C411yescharacteristic
48#13063282—21no—
49C42×D43—21no—
50#13063258—21no—
51#13063256—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54Dic43⋊C8—22no—
55#13063249—21no—
56#13063249—21no—
57#13063248—21no—
58#13063245—21no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)D412yes—
61(C2×D43)⋊C8—22no—
62#13063236—21no—
63C4×C43⋊C8—21no—
64C4×C43⋊C8—21no—
65C4×C43⋊C8—21no—
66C8×Dic43—22no—
67C22×Q8×C43C2×C411yescharacteristic
68C22×C8×C43—21no—
69C22×C8×C43—21no—
70C4×Q8×C43—21no—
71C4×Q8×C43—21no—
72C4×Q8×C43—21no—
73C4×Q8×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43C2×C411yescharacteristic
76C2×C42×C43—21no—
77C2×C42×C43C2311yescharacteristic
78C4⋊C8×C43—21no—
79C4⋊C8×C43—21no—
80C4×C8×C43—21no—
81C4×C8×C43D411yescharacteristic
82C4×C8×C43D411yescharacteristic
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—21no—
87C2×Q8×C43—21no—
88C2×Q8×C43C2×C812yescomplemented
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C2×C22⋊D43—21no—
95#10621898—21no—
96#10621898—21no—
97#10621898C2×C812yes—
98#10621898M1612yes—
99C2×D172C22⋊C411yescharacteristic
100C2×C4×D43—21no—
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×Dic86C22⋊C411yescharacteristic
104C2×C8×C43—21no—
105C2×C8×C43—21no—
106C2×C8×C43—42no—
107C2×C8×C43—41no—
108C2×C8×C43—81no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C42×C43—41no—
114C42×C43—41no—
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43#4111yescharacteristic
119C22⋊Dic43—21no—
120#10621885—24no—
121#10621884—24no—
122(C2×D43)⋊C4—21no—
123(C2×D43)⋊C4—21no—
124C4⋊Dic43C22⋊C411yescharacteristic
125C4⋊Dic43C22⋊C411yescharacteristic
126Dic43⋊C4—21no—
127Dic43⋊C4—21no—
128C4×Dic43—21no—
129C4×Dic43—21no—
130C4×Dic43—21no—
131#10621877—21no—
132#10621877—21no—
133#10621877—21no—
134#10621877C2×C812yescomplemented
135C2×C43⋊C8—21no—
136C2×C43⋊C8—21no—
137C2×C43⋊C8—22no—
138C2×C43⋊C8—41no—
139C8×D43—44no—
140C23×C43C4×D411yescharacteristic
141C22×D43—21no—
142Q8×C43—22no—
143Q8×C43—22no—
144Q8×C43—41no—
145Q8×C43—41no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—22no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—81no—
154C2×C4×C43C2×C22⋊C411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43#12011yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12311yescharacteristic
160C2×C4×C43C22×C811yescharacteristic
161C2×C4×C43C2×M1611yescharacteristic
162C2×C4×C43#13111yescharacteristic
163C2×C4×C43#13111yescharacteristic
164C22⋊D43—22no—
165C22⋊D43—22no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169D172—21no—
170D172C22⋊C812yes—
171C4×D43—22no—
172C4×D43—22no—
173C4×D43—42no—
174C4×D43—41no—
175C4×D43—41no—
176Dic86—21no—
177Dic86C22⋊C812yes—
178C8×C43—22no—
179C8×C43—41no—
180C8×C43—81no—
181C43⋊C8—22no—
182C43⋊C8—42no—
183C43⋊C8—41no—
184C43⋊C8—81no—
185#9096—431nomaximal, Sylow
186C22×C43—21no—
187C22×C43—21no—
188C22×C43#38611yescharacteristic
189C22×C43C8×D411yescharacteristic
190C22×C43#43511yescharacteristic
191C2×D43—22no—
192C2×D43—41no—
193C2×D43—41no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—42no—
198C4×C43—81no—
199C4×C43C2×C22⋊C811yescharacteristic
200C4×C43#40811yescharacteristic
201C4×C43C8×D411yescharacteristic
202C4×C43#43511yescharacteristic
203C4×C43#47111yescharacteristic
204C4×C43#47311yescharacteristic
205Dic43—22no—
206Dic43—41no—
207Dic43—41no—
208C8×#41—431no—
209C4×#137—431no—
210#1477—431no—
211C2×Q8⋊C8D4311yescharacteristic, complemented
212#1461—431no—
213#1283—431no—
214#1278—431no—
215C2×C43—21no—
216C2×C43—21no—
217C2×C43#186911yescharacteristic
218C2×C43#190611yescharacteristic
219C2×C43#190811yescharacteristic
220D43—42no—
221C2×#137—431no—
222C4×#41—431no—
223C2×C4×Q8C2×D4311yescharacteristic
224C8×Q8—861no—
225#441—861no—
226#440—861no—
227C4×Q16—861no—
228C4×SD16—861no—
229C8×D4—861no—
230C8×D4—862no—
231#431—431no—
232#431—431no—
233#431—861no—
234#428—431no—
235C2×C4⋊C8C2×D4311yescharacteristic
236#419—431no—
237#417—431no—
238C4×M16—431no—
239C2×C4×C8—861no—
240C2×C4×C8C2×D4311yescharacteristic
241Q8⋊C8—21no—
242Q8⋊C8—21no—
243Q8⋊C8—861no—
244D4⋊C8—861no—
245#324—862no—
246C43#909611yescharacteristic, complemented, Sylow
247C2×#41—431no—
248C22×Q8C4×D4311yescharacteristic
249#137—434no—
250#137—862no—
251C2×Q16—861no—
252C2×SD16—861no—
253C2×M16—431no—
254C2×M16—431no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—862no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—431no—
263C4×Q8—431no—
264C4×D4—431no—
265C4×D4—431no—
266C4×D4—861no—
267C4×D4—861no—
268#117—431no—
269#117—861no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C4×D4311yescharacteristic
272C2×C42—21no—
273C2×C42—861no—
274C2×C42C22×D4311yescharacteristic
275#107—861no—
276#106—861no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—862no—
280C4⋊C8—861no—
281C4⋊C8—861no—
282#103—861no—
283#103—861no—
284#103—861no—
285#102—861no—
286C22⋊C8—432no—
287C22⋊C8—862no—
288C22⋊C8—861no—
289#97—861no—
290C4×C8—21no—
291C4×C8—862no—
292C4×C8—861no—
293C4×C8—861no—
294C4×C8—861no—
295C4×C8C22⋊D4311yescharacteristic
296C4×C8C22⋊D4311yescharacteristic
297#41—432no—
298#41—432no—
299#41—861no—
300#41—861no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—431no—
307C2×Q8C8×D4312yescomplemented
308C2×D4—431no—
309C2×D4—861no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4C2×C4×D4311yescharacteristic
316C22×C4D4×D4311yescharacteristic
317C22×C4#1062190011yescharacteristic
318Q16—864no—
319SD16—864no—
320M16—432no—
321M16—861no—
322M16—861no—
323M16—861no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—42no—
327C2×C8—41no—
328C2×C8—81no—
329C2×C8—861no—
330C2×C8—861no—
331C2×C8—862no—
332C2×C8—1724no—
333C2×C8—1721no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—431no—
339C4⋊C4—431no—
340C4⋊C4—861no—
341C4⋊C4—861no—
342C22⋊C4—861no—
343C22⋊C4—861no—
344C22⋊C4—861no—
345C42—41no—
346C42—41no—
347C42—861no—
348C42—861no—
349C42—861no—
350C42#1062189811yescharacteristic
351C42D4×D4311yescharacteristic
352C42D4×D4311yescharacteristic
353C42C2×C22⋊D4311yescharacteristic
354C23—861no—
355C23(C22⋊D43)⋊C411yescharacteristic
356Q8—22no—
357Q8—22no—
358Q8—41no—
359Q8—41no—
360Q8—432no—
361Q8—861no—
362D4—432no—
363D4—862no—
364D4—862no—
365D4—861no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—861no—
375C2×C4—862no—
376C2×C4—862no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—1722no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4C22⋊C4×D4311yescharacteristic
383C2×C4C4×C22⋊D4311yescharacteristic
384C2×C4#1306329311yescharacteristic
385C2×C4#1306329611yescharacteristic
386C2×C4#1306329811yescharacteristic
387C2×C4#1306330711yescharacteristic
388C2×C4C2×C8×D4311yescharacteristic
389C2×C4M16×D4311yescharacteristic
390C2×C4#1306333111yescharacteristic
391C2×C4#1306333311yescharacteristic
392C8—22no—
393C8—41no—
394C8—81no—
395C8—862no—
396C8—3441no—
397C8—1722no—
398C8—1721no—
399C22—21no—
400C22—21no—
401C22—862no—
402C22—1721no—
403C22—1721no—
404C22#1458277511yescharacteristic
405C22(C22⋊D43)⋊C811yescharacteristic
406C22#1458297311yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—42no—
411C4—81no—
412C4—862no—
413C4—1721no—
414C4—1721no—
415C4C22⋊C8×D4311yescharacteristic
416C4#1458286411yescharacteristic
417C4C8×C22⋊D4311yescharacteristic
418C4#1458296811yescharacteristic
419C4#1458315911yescharacteristic
420C4#1458317111yescharacteristic
421C2—21no—
422C2—21no—
423C2—1722no—
424C2#1913488411yescharacteristic
425C2#1913509911yescharacteristic
426C2#1913511311yescharacteristic
subgroupG/H
centerC2×C4#13063296
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC2×C43×Q8⋊C8C2
socleC22×C43#386
prime radicalC2×#10621898C2×C4
cosocleC2×C42×C43C23
hypercenterC2×Q8⋊C8D43
hypocenterC43#9096
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. #19132919C2semidirect
5. #19132445C2semidirect
6. #19132432C2semidirect
7. C2×C43×Q8⋊C8C2semidirect
35. #13063356C8semidirect
88. C2×Q8×C43C2×C8semidirect
134. #10621877C2×C8semidirect
211. C2×Q8⋊C8D43semidirect
246. C43#9096semidirect
307. C2×Q8C8×D43semidirect

Maximal subgroups

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

subgroupindex
C8×#106218982
C4×#130633562
#191329802
#191329192
#191324452
#191324322
C2×C43×Q8⋊C82
#909643