Finite Group Databasebeta

← #24991318

Subgroups — #24991318

Order 11008.

478 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143720C211yesmaximal, characteristic
2#19135573C211yesmaximal, characteristic, complemented
3C4×#13063252C211yesmaximal, characteristic
4#19133016C211yesmaximal, characteristic, complemented
5#19132486C211yesmaximal, characteristic, complemented
6#19132427C211yesmaximal, characteristic, complemented
7C43×#3107C211yesmaximal, characteristic
8#14583030—21no—
9#14582971—22no—
10D4×C43⋊C8—21no—
11#14582956—21no—
12#14582952C2211yescharacteristic
13#14582923C2211yescharacteristic
14C2×C4⋊(C43⋊C8)—21no—
15C2×#13063252—21no—
16C4×#10621877C2211yescharacteristic
17C42×Dic43C2211yescharacteristic
18#14582658—22no—
19#14582658—21no—
20Q8⋊(C43⋊C8)—21no—
21Q8⋊(C43⋊C8)—21no—
22C43×#533C2211yescharacteristic
23C4×#41×C43C2211yescharacteristic
24C43×#485—21no—
25C43×#475C411yescharacteristic, complemented
26C43×#474C411yescharacteristic, complemented
27C43×#462C411yescharacteristic, complemented
28C43×#461C411yescharacteristic, complemented
29C43×#452—21no—
30C4×Q16×C43—21no—
31C4×SD16×C43—21no—
32C43×#431C2211yescharacteristic
33C2×#10621877—21no—
34C2×#10621877D412yes—
35C22×C43⋊C8—22no—
36C2×C4×Dic43—21no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43—21no—
39C4⋊(C43⋊C8)—22no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)D411yescharacteristic
43C4⋊(C43⋊C8)D411yescharacteristic
44#13063252—24no—
45C22⋊(C43⋊C8)—22no—
46C22⋊(C43⋊C8)—21no—
47#13063236—22no—
48#13063236—21no—
49C4×C43⋊C8—21no—
50C4×C43⋊C8—21no—
51C2×#41×C43D411yescharacteristic
52C2×Q16×C43—21no—
53C2×SD16×C43—21no—
54C4⋊Q8×C43C2×C411yescharacteristic
55C4⋊Q8×C43C2×C411yescharacteristic
56#125×C43—21no—
57C22⋊Q8×C43—21no—
58C22⋊Q8×C43—21no—
59C4×Q8×C43—21no—
60C4×Q8×C43—21no—
61C4×Q8×C43C2×C411yescharacteristic
62C4×Q8×C43D411yescharacteristic
63C4×D4×C43—21no—
64C4×D4×C43—21no—
65C4×D4×C43C2×C411yescharacteristic
66C4×D4×C43D411yescharacteristic
67#117×C43—21no—
68#117×C43—21no—
69#117×C43D411yescharacteristic
70C2×C42×C43—21no—
71C2×C42×C43C2311yescharacteristic
72#107×C43—21no—
73#106×C43—21no—
74C4⋊C8×C43C2×C411yescharacteristic
75C4⋊C8×C43C2×C411yescharacteristic
76#103×C43—21no—
77#103×C43—21no—
78#103×C43—21no—
79#102×C43—21no—
80C22⋊C8×C43—21no—
81C4×C8×C43—21no—
82#41×C43—22no—
83#41×C43—41no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43C22⋊C411yescharacteristic
87C2×D4×C43—21no—
88C2×D4×C43C22⋊C411yescharacteristic
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43#4111yescharacteristic
95C22×Dic43—41no—
96Q16×C43—42no—
97SD16×C43—42no—
98C2×C8×C43—21no—
99C2×C8×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43C22⋊C411yescharacteristic
109C4⋊C4×C43C22⋊C411yescharacteristic
110C22⋊C4×C43—21no—
111C22⋊C4×C43—21no—
112C22⋊C4×C43—21no—
113C22⋊C4×C43—41no—
114C42×C43—21no—
115C42×C43—21no—
116C42×C43—21no—
117C42×C43—41no—
118C42×C43C22×C411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122C4×Dic43—22no—
123C4×Dic43—22no—
124C4×Dic43—22no—
125C4×Dic43—41no—
126C4×Dic43—41no—
127C4×Dic43—41no—
128#10621877—22no—
129#10621877—41no—
130#10621877—42no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—22no—
134C2×C43⋊C8—41no—
135C2×C43⋊C8—82no—
136C23×C43—21no—
137C23×C43#12111yescharacteristic
138Q8×C43—21no—
139Q8×C43—21no—
140Q8×C43—41no—
141Q8×C43—41no—
142Q8×C43—41no—
143Q8×C43—41no—
144D4×C43—21no—
145D4×C43—42no—
146D4×C43#10412yes—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—42no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43C2×C22⋊C411yescharacteristic
164C2×C4×C43C4×D411yescharacteristic
165C2×C4×C43C4×D411yescharacteristic
166C2×C4×C43#12011yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#12311yescharacteristic
169C2×Dic43—42no—
170C2×Dic43—42no—
171C2×Dic43—42no—
172C8×C43—41no—
173C8×C43—41no—
174C43⋊C8—42no—
175C43⋊C8—41no—
176C43⋊C8—42no—
177C43⋊C8—41no—
178#8971—431nomaximal, Sylow
179C22×C43—22no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43#38611yescharacteristic
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—41no—
190C4×C43—41no—
191C4×C43—41no—
192C4×C43—81no—
193C4×C43—81no—
194C4×C43C2×#10411yescharacteristic
195C4×C43#42111yescharacteristic
196C4×C43#44311yescharacteristic
197C4×C43#44411yescharacteristic
198C4×C43#45511yescharacteristic
199C4×C43#45611yescharacteristic
200Dic43—44no—
201#3107D4311yescharacteristic
202#2990—431no—
203#1994—431no—
204C4×#104—431no—
205#1485—431no—
206#1299—431no—
207#1276—431no—
208C2×C43—41no—
209C2×C43—42no—
210C2×C43#187111yescharacteristic
211C2×C43#187611yescharacteristic
212C2×C43#188211yescharacteristic
213#533C2×D4311yescharacteristic
214C4×#41C2×D4311yescharacteristic
215#485—21no—
216#475Dic4311yescharacteristic, complemented
217#474Dic4311yescharacteristic, complemented
218#462Dic4311yescharacteristic, complemented
219#461Dic4311yescharacteristic, complemented
220#452—21no—
221#446—861no—
222C4×Q16—21no—
223C4×SD16—21no—
224#435—862no—
225C8×D4—861no—
226#432—861no—
227#431—431no—
228#431C2×D4311yescharacteristic
229#423—431no—
230C2×C4⋊C8—861no—
231C2×#104—861no—
232C4×M16—431no—
233C43—431no—
234#339—862no—
235#339—861no—
236Q8⋊C8—861no—
237Q8⋊C8—861no—
238C43#897111yescharacteristic, complemented, Sylow
239C2×#41C22⋊D4311yescharacteristic
240C2×Q16—21no—
241C2×SD16—21no—
242C2×M16—432no—
243C2×M16—861no—
244C22×C8—862no—
245C4⋊Q8C2×Dic4311yescharacteristic
246C4⋊Q8C2×Dic4311yescharacteristic
247#125—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8C2×Dic4311yescharacteristic
253C4×Q8C22⋊D4311yescharacteristic
254C4×D4—21no—
255C4×D4—21no—
256C4×D4C2×Dic4311yescharacteristic
257C4×D4C22⋊D4311yescharacteristic
258#117—21no—
259#117—21no—
260#117C22⋊D4311yescharacteristic
261C2×C42—21no—
262C2×C42—861no—
263C2×C42—861no—
264C2×C42—861no—
265C2×C42C22×D4311yescharacteristic
266#107—21no—
267#106—21no—
268C4⋊C8—431no—
269C4⋊C8—431no—
270C4⋊C8—862no—
271C4⋊C8—861no—
272C4⋊C8—861no—
273C4⋊C8C2×Dic4311yescharacteristic
274C4⋊C8C2×Dic4311yescharacteristic
275#104—864no—
276#103—21no—
277#103—21no—
278#103—21no—
279#102—21no—
280C22⋊C8—21no—
281C22⋊C8—862no—
282C22⋊C8—861no—
283#97—862no—
284#97—861no—
285C4×C8—21no—
286C4×C8—861no—
287C4×C8—861no—
288#41—22no—
289#41—41no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8C22⋊Dic4311yescharacteristic
293C2×D4—21no—
294C2×D4C22⋊Dic4311yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—1721no—
299C22×C4D4×D4311yescharacteristic
300C22×C4#1062190011yescharacteristic
301C22×C4C2×C22⋊D4311yescharacteristic
302Q16—42no—
303SD16—42no—
304M16—862no—
305M16—1721no—
306M16—1722no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—861no—
310C2×C8—861no—
311C2×C8—862no—
312C2×C8—3442no—
313C2×C8—1721no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4C22⋊Dic4311yescharacteristic
323C4⋊C4C22⋊Dic4311yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—41no—
332C42—862no—
333C42—862no—
334C42—862no—
335C42—1721no—
336C42—1721no—
337C42—1721no—
338C42D4×D4311yescharacteristic
339C42#1062190011yescharacteristic
340C42C22×Dic4311yescharacteristic
341C42C2×C22⋊D4311yescharacteristic
342C23—21no—
343C23#1306329711yescharacteristic
344Q8—21no—
345Q8—21no—
346Q8—41no—
347Q8—41no—
348Q8—41no—
349Q8—41no—
350D4—21no—
351D4—42no—
352D4#1306325212yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—1722no—
370C2×C4—1722no—
371C2×C4—1722no—
372C2×C4C2×C22⋊Dic4311yescharacteristic
373C2×C4D4×Dic4311yescharacteristic
374C2×C4D4×Dic4311yescharacteristic
375C2×C4#1306329311yescharacteristic
376C2×C4#1306329711yescharacteristic
377C2×C4#1306330611yescharacteristic
378C8—41no—
379C8—41no—
380C8—1722no—
381C8—1721no—
382C8—1722no—
383C8—1721no—
384C22—21no—
385C22—22no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22#1458277911yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—81no—
398C4—81no—
399C4—1724no—
400C4C2×#1306325211yescharacteristic
401C4#1458291611yescharacteristic
402C4#1458301611yescharacteristic
403C4#1458302111yescharacteristic
404C4#1458307511yescharacteristic
405C4#1458308011yescharacteristic
406C2—41no—
407C2—42no—
408C2#1913489811yescharacteristic
409C2#1913492411yescharacteristic
410C2#1913496611yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3107C2
socleC22×C43#386
prime radicalC2×#41×C43D4
cosocleC2×C42×C43C23
hypercenter#3107D43
hypocenterC43#8971
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
2. #19135573C2semidirect
4. #19133016C2semidirect
5. #19132486C2semidirect
6. #19132427C2semidirect
25. C43×#475C4semidirect
26. C43×#474C4semidirect
27. C43×#462C4semidirect
28. C43×#461C4semidirect
216. #475Dic43semidirect
217. #474Dic43semidirect
218. #462Dic43semidirect
219. #461Dic43semidirect
238. C43#8971semidirect

Maximal subgroups

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

subgroupindex
#191437202
#191355732
C4×#130632522
#191330162
#191324862
#191324272
C43×#31072
#897143