Finite Group Databasebeta

← #25080027

Subgroups — #25080027

Order 11008.

562 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145774C212yesmaximal
2#19143570C211yesmaximal, characteristic
3#19134120C211yesmaximal, characteristic, complemented
4#19134115C211yesmaximal, characteristic, complemented
5#19134086C211yesmaximal, characteristic, complemented
6#19134081C211yesmaximal, characteristic, complemented
7#19134050C212yesmaximal, complemented
8#19134043C212yesmaximal, complemented
9#19133343C211yesmaximal, characteristic, complemented
10#19133305C212yesmaximal, complemented
11C43×#3170C211yesmaximal, characteristic, complemented
12#14583433C2211yescharacteristic
13#14583298—22no—
14#14583256—22no—
15#14583240—22no—
16#14583223—22no—
17#14583191C2212yes—
18#14583186C2212yes—
19#14583181C2212yes—
20#14583176C2212yes—
21#14583029C2211yescharacteristic
22C8×Dic86C2211yescharacteristic
23#14582978C2211yescharacteristic
24#14582970—21no—
25C8×D172C2211yescharacteristic
26C8×C22⋊D43—21no—
27#14582958—21no—
28#14582956C2211yescharacteristic
29#14582952C2212yes—
30#14582853—21no—
31#14582652C2212yes—
32#14582650C2211yescharacteristic
33#14582650C2211yescharacteristic
34#14582648C2212yes—
35#14582648C2212yes—
36#14582645C2212yes—
37#14582645C2212yes—
38C43×#533C2212yes—
39C43×#500C2211yescharacteristic
40C43×#494C2211yescharacteristic
41C43×#487C2212yes—
42C43×#467—21no—
43C43×#467—21no—
44C4×Q16×C43—21no—
45C4×Q16×C43—21no—
46C2×C4×C8×C43C2211yescharacteristic
47C2×#10621872—21no—
48C2×C8×D43—21no—
49#13063319—21no—
50#13063317D411yescharacteristic
51#13063313D411yescharacteristic
52#13063308—21no—
53#13063304D411yescharacteristic
54#13063299D411yescharacteristic
55C4×Dic86C2311yescharacteristic
56C4×D172C2311yescharacteristic
57C4×C22⋊D43—21no—
58#13063282—21no—
59#13063258—22no—
60#13063258—22no—
61#13063256—22no—
62#13063256—22no—
63C4⋊(C43⋊C8)C2311yescharacteristic
64C4⋊(C43⋊C8)C2311yescharacteristic
65C4⋊(C43⋊C8)C2312yes—
66C4⋊(C43⋊C8)C2312yes—
67Dic43⋊C8—21no—
68Dic43⋊C8—21no—
69#13063248—22no—
70#13063248—22no—
71#13063245—22no—
72#13063245—22no—
73C22⋊(C43⋊C8)—22no—
74C22⋊(C43⋊C8)—21no—
75(C2×D43)⋊C8—21no—
76(C2×D43)⋊C8—21no—
77#13063236—21no—
78#13063235—21no—
79C4×C43⋊C8—22no—
80C8×Dic43—21no—
81C2×Q16×C43—21no—
82C2×Q16×C43—21no—
83C22×C8×C43D411yescharacteristic
84C22×C8×C43D411yescharacteristic
85C4⋊Q8×C43C2312yes—
86C4⋊Q8×C43C2312yes—
87#125×C43—22no—
88C22⋊Q8×C43—22no—
89C22⋊Q8×C43—22no—
90C4×Q8×C43—22no—
91C4×Q8×C43—22no—
92#117×C43—22no—
93C2×C42×C43C2311yescharacteristic
94#107×C43—21no—
95#107×C43—21no—
96#103×C43—22no—
97#103×C43—22no—
98C4×C8×C43D411yescharacteristic
99C4×C8×C43D411yescharacteristic
100C4×C8×C43C2311yescharacteristic
101C4×C8×C43C2311yescharacteristic
102C2×Q8×C43—22no—
103C2×Q8×C43—22no—
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C2×C22⋊D43—21no—
108C2×D172C2×D411yescharacteristic
109C2×C4×D43—21no—
110C2×Dic86C2×D411yescharacteristic
111Q16×C43—42no—
112Q16×C43—42no—
113C2×C8×C43—22no—
114C2×C8×C43—41no—
115C2×C8×C43C2×D411yescharacteristic
116C2×C8×C43C2×D411yescharacteristic
117C2×C8×C43C2×D411yescharacteristic
118C2×C8×C43C2×D411yescharacteristic
119C4⋊C4×C43—22no—
120C4⋊C4×C43—22no—
121C4⋊C4×C43—22no—
122C4⋊C4×C43—22no—
123C4⋊C4×C43—42no—
124C4⋊C4×C43—42no—
125C22⋊C4×C43—42no—
126C42×C43—42no—
127C42×C43C2×D411yescharacteristic
128C42×C43C2×D411yescharacteristic
129C42×C43#4111yescharacteristic
130C42×C43C2411yescharacteristic
131C22⋊Dic43—21no—
132(C2×D43)⋊C4—21no—
133(C2×D43)⋊C4—21no—
134(C2×D43)⋊C4—21no—
135(C2×D43)⋊C4—21no—
136C4⋊Dic43C2×D411yescharacteristic
137C4⋊Dic43C2×D411yescharacteristic
138Dic43⋊C4—21no—
139Dic43⋊C4—21no—
140Dic43⋊C4—21no—
141Dic43⋊C4—21no—
142C4×Dic43—21no—
143C2×C43⋊C8—21no—
144C2×C43⋊C8—22no—
145C2×C43⋊C8—22no—
146C2×C43⋊C8—21no—
147#10621872—42no—
148C8×D43—42no—
149C23×C43#12111yescharacteristic
150C22×D43—21no—
151Q8×C43—42no—
152Q8×C43—42no—
153Q8×C43—82no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—22no—
157C2×C4×C43—41no—
158C2×C4×C43—42no—
159C2×C4×C43—42no—
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43C22×D411yescharacteristic
164C2×C4×C43C22×D411yescharacteristic
165C2×C4×C43C2×#4111yescharacteristic
166C22⋊D43—42no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170D172—22no—
171C4×D43—41no—
172C4×D43—41no—
173Dic86—22no—
174C8×C43—21no—
175C8×C43—21no—
176C8×C43—21no—
177C8×C43#13512yes—
178C43⋊C8—41no—
179C43⋊C8—41no—
180C43⋊C8—42no—
181C43⋊C8—42no—
182#19226—431nomaximal, Sylow
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43C2×#12111yescharacteristic
187C2×D43—41no—
188C2×D43—41no—
189C2×D43—41no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—82no—
195C4×C43—82no—
196C4×C43C2×#13511yescharacteristic
197C4×C43#57511yescharacteristic
198C4×C43#57812yes—
199Dic43—41no—
200Dic43—41no—
201Dic43—41no—
202#3233—432no—
203#3170D4311yescharacteristic, complemented
204#2966—431no—
205#1696—431no—
206#1695—431no—
207#1690—431no—
208#1689—431no—
209#1684—432no—
210#1683—432no—
211#1564—431no—
212#1554—432no—
213C2×C43—41no—
214C2×C43#303511yescharacteristic
215C2×C43#305911yescharacteristic
216C2×C43#306711yescharacteristic
217D43—81no—
218#533C2×D4312yes—
219#529—431no—
220#500C2×D4311yescharacteristic
221#499—862no—
222#494C2×D4311yescharacteristic
223#488—862no—
224#487C2×D4312yes—
225#485—862no—
226#482—862no—
227#477—432no—
228#476—432no—
229#475—432no—
230#474—432no—
231#467—21no—
232#467—21no—
233#446—431no—
234C8×Q8—431no—
235C4×Q16—21no—
236C4×Q16—21no—
237#436—431no—
238#435—861no—
239C8×D4—431no—
240C8×D4—861no—
241#433—861no—
242#432—431no—
243#431—432no—
244#405—861no—
245C2×C4×C8C2×D4311yescharacteristic
246#335—432no—
247#334—431no—
248#334—431no—
249#333—432no—
250#333—432no—
251#332—432no—
252#332—432no—
253C43#1922611yescharacteristic, complemented, Sylow
254C2×Q16—21no—
255C2×Q16—21no—
256C2×M16—861no—
257C22×C8—861no—
258C22×C8C22⋊D4311yescharacteristic
259C22×C8C22⋊D4311yescharacteristic
260C4⋊Q8C22×D4312yes—
261C4⋊Q8C22×D4312yes—
262#126—861no—
263#125—22no—
264#125—431no—
265#124—431no—
266#123—861no—
267C22⋊Q8—22no—
268C22⋊Q8—22no—
269C22⋊Q8—431no—
270#121—431no—
271C4×Q8—22no—
272C4×Q8—22no—
273C4×Q8—431no—
274C4×D4—431no—
275C4×D4—861no—
276#117—22no—
277#117—861no—
278C2×C42C22×D4311yescharacteristic
279#107—21no—
280#107—21no—
281#107—862no—
282#107—862no—
283#106—862no—
284#106—862no—
285C4⋊C8—431no—
286C4⋊C8—431no—
287C4⋊C8—432no—
288C4⋊C8—432no—
289C4⋊C8—861no—
290C4⋊C8—861no—
291#103—22no—
292#103—22no—
293#103—862no—
294#103—862no—
295#102—862no—
296#102—862no—
297C22⋊C8—862no—
298C22⋊C8—861no—
299C22⋊C8—861no—
300C22⋊C8—861no—
301#97—861no—
302#97—861no—
303C4×C8—861no—
304C4×C8—862no—
305C4×C8C22⋊D4311yescharacteristic
306C4×C8C22⋊D4311yescharacteristic
307C4×C8C22×D4311yescharacteristic
308C4×C8C22×D4311yescharacteristic
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8—431no—
312C2×D4—431no—
313C2×D4—861no—
314C22×C4—861no—
315C22×C4D4×D4311yescharacteristic
316C22×C4#1062190011yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318Q16—42no—
319Q16—42no—
320M16—1722no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—862no—
324C2×C8—862no—
325C2×C8—861no—
326C2×C8—861no—
327C2×C8—1722no—
328C2×C8C2×C22⋊D4311yescharacteristic
329C2×C8C2×C22⋊D4311yescharacteristic
330C2×C8C2×C22⋊D4311yescharacteristic
331C2×C8C2×C22⋊D4311yescharacteristic
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—431no—
339C4⋊C4—431no—
340C4⋊C4—861no—
341C4⋊C4—861no—
342C4⋊C4—861no—
343C4⋊C4—861no—
344C22⋊C4—42no—
345C22⋊C4—861no—
346C22⋊C4—861no—
347C22⋊C4—861no—
348C22⋊C4—861no—
349C22⋊C4—861no—
350C42—42no—
351C42—861no—
352C42D4×D4311yescharacteristic
353C42#1062190011yescharacteristic
354C42C2×C22⋊D4311yescharacteristic
355C42C23×D4311yescharacteristic
356C23—861no—
357C23#1306329611yescharacteristic
358Q8—42no—
359Q8—42no—
360Q8—82no—
361Q8—862no—
362D4—862no—
363D4—1722no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—22no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—861no—
371C2×C4—861no—
372C2×C4—861no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4#1306329611yescharacteristic
376C2×C4#1306329611yescharacteristic
377C2×C4#1306329611yescharacteristic
378C2×C4C2×D4×D4311yescharacteristic
379C2×C4C22×C22⋊D4311yescharacteristic
380C2×C4C2×#1062190011yescharacteristic
381C8—21no—
382C8—21no—
383C8—21no—
384C8—1721no—
385C8—1721no—
386C8—1722no—
387C8—1722no—
388C8#1306334512yes—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22C2×#1306329611yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—82no—
401C4—82no—
402C4—1721no—
403C4—1721no—
404C4—1721no—
405C4C2×#1306334511yescharacteristic
406C4#1458369711yescharacteristic
407C4#1458371212yes—
408C2—41no—
409C2—3441no—
410C2#1914404411yescharacteristic
411C2#1914424611yescharacteristic
412C2#1914431111yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3170C2
socleC22×C43C2×#121
prime radical#13063299D4
hypercenter#3170D43
hypocenterC43#19226
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #19134120C2semidirect
4. #19134115C2semidirect
5. #19134086C2semidirect
6. #19134081C2semidirect
7. #19134050C2semidirect
8. #19134043C2semidirect
9. #19133343C2semidirect
10. #19133305C2semidirect
11. C43×#3170C2semidirect
203. #3170D43semidirect
253. C43#19226semidirect

Maximal subgroups

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

subgroupindex
#191457742
#191435702
#191341202
#191341152
#191340862
#191340812
#191340502
#191340432
#191333432
#191333052
C43×#31702
#1922643