Finite Group Databasebeta

← #25125722

Subgroups — #25125722

Order 11008.

766 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143185C211yesmaximal, characteristic
2#19143184C211yesmaximal, characteristic
3C2×#14582935C211yesmaximal, characteristic
4C2×#14582927C211yesmaximal, characteristic
5#19136109C214yesmaximal, complemented
6#19136104C214yesmaximal, complemented
7#19134333C211yesmaximal, characteristic
8C2×#14582663C211yesmaximal, characteristic
9C43×#1742C211yesmaximal, characteristic
10C22×#10621877C2211yescharacteristic
11C23×C43⋊C8C2211yescharacteristic
12C2×#13063284C2211yescharacteristic
13C2×#13063284C2211yescharacteristic
14#14582942—22no—
15#14582941—22no—
16#14582941C2214yes—
17#14582939C2214yes—
18#14582937—22no—
19#14582935—22no—
20#14582935—22no—
21#14582935—22no—
22C2×#13063258C2212yes—
23C2×#13063256C2212yes—
24#14582927—22no—
25#14582927C2212yes—
26#14582927C2212yes—
27C2×Dic43⋊C8—22no—
28#14582667C2214yes—
29#14582663C2212yes—
30#14582663C2212yes—
31C22×M16×C43C2211yescharacteristic
32C22×M16×C43C2211yescharacteristic
33C2×#117×C43C2211yescharacteristic
34C43×#343C2214yes—
35C2×#10621877—21no—
36C2×#10621877—22no—
37C2×#10621877Q814yes—
38C2×#10621877C2312yes—
39C22×C43⋊C8—21no—
40C22×C43⋊C8—22no—
41C22×C43⋊C8—22no—
42C22×C43⋊C8D412yes—
43C22×C43⋊C8D412yes—
44C22×C43⋊C8C2311yescharacteristic
45C22×C43⋊C8C2311yescharacteristic
46#13063284—21no—
47#13063284—21no—
48#13063284—21no—
49#13063284—21no—
50#13063284—21no—
51#13063284—21no—
52#13063284D412yes—
53#13063284C2312yes—
54C2×C4⋊Dic43D412yes—
55C2×C4⋊Dic43C2312yes—
56C2×C22⋊Dic43—21no—
57C2×C22⋊Dic43—21no—
58C2×C4×Dic43—21no—
59C2×C4×Dic43—21no—
60#13063259—24no—
61#13063258—24no—
62#13063258—24no—
63#13063257—24no—
64#13063256—24no—
65#13063256—24no—
66Dic43⋊C8—24no—
67Dic43⋊C8—24no—
68C23×C4×C43C2311yescharacteristic
69C2×M16×C43—21no—
70C2×M16×C43—22no—
71C2×M16×C43—21no—
72C2×M16×C43—22no—
73C2×M16×C43—22no—
74C2×M16×C43Q814yes—
75C2×M16×C43C2312yes—
76C2×M16×C43C2312yes—
77C22×C8×C43—21no—
78C22×C8×C43—21no—
79#117×C43—21no—
80#117×C43—21no—
81#117×C43—21no—
82#117×C43—21no—
83C2×C4⋊C4×C43C2312yes—
84C2×C22⋊C4×C43—21no—
85C2×C42×C43—21no—
86C24×C43#4111yescharacteristic
87C22×C4×C43—22no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×Q812yes—
93C22×C4×C43C2×Q812yes—
94C22×C4×C43#4112yes—
95C22×C4×C43#4112yes—
96C22×C4×C43#4111yescharacteristic
97C22×C4×C43C2411yescharacteristic
98C22×Dic43—22no—
99C22×Dic43—22no—
100M16×C43—24no—
101M16×C43—22no—
102M16×C43—22no—
103M16×C43—22no—
104M16×C43—42no—
105M16×C43C2×Q814yes—
106C2×C8×C43—24no—
107C2×C8×C43—22no—
108C2×C8×C43—22no—
109C2×C8×C43—42no—
110C4⋊C4×C43—22no—
111C4⋊C4×C43—22no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C42×C43—41no—
115C42×C43—41no—
116C22⋊Dic43—22no—
117C22⋊Dic43—22no—
118C22⋊Dic43—41no—
119C22⋊Dic43—41no—
120C4⋊Dic43—22no—
121C4⋊Dic43—22no—
122C4⋊Dic43—22no—
123C4⋊Dic43C2×D414yes—
124C4×Dic43—22no—
125C4×Dic43—22no—
126C4×Dic43—41no—
127C4×Dic43—41no—
128#10621877—24no—
129#10621877—22no—
130#10621877C2×Q814yes—
131C2×C43⋊C8—24no—
132C2×C43⋊C8—24no—
133C2×C43⋊C8—24no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8—21no—
137C2×C43⋊C8—21no—
138C2×C43⋊C8—21no—
139C2×C43⋊C8C2×D412yes—
140C2×C43⋊C8C2×D412yes—
141C23×C43—42no—
142C23×C43#12111yescharacteristic
143C23×C43#12111yescharacteristic
144C23×C43#12512yes—
145C23×C43#12512yes—
146C23×C43C2×#4111yescharacteristic
147C2×C4×C43—42no—
148C2×C4×C43—82no—
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43C22⋊Q812yes—
152C2×C4×C43C22⋊Q812yes—
153C2×C4×C43C22⋊Q812yes—
154C2×C4×C43C22⋊Q812yes—
155C2×C4×C43#12312yes—
156C2×C4×C43#12312yes—
157C2×C4×C43#12512yes—
158C2×C4×C43#12512yes—
159C2×C4×C43C4⋊Q812yes—
160C2×C4×C43C4⋊Q812yes—
161C2×C4×C43C22×D411yescharacteristic
162C2×C4×C43C22×D411yescharacteristic
163C2×C4×C43C22×Q811yescharacteristic
164C2×C4×C43C22×Q811yescharacteristic
165C2×C4×C43C2×#4111yescharacteristic
166C2×C4×C43C2×#4111yescharacteristic
167C2×Dic43—24no—
168C2×Dic43—44no—
169C2×Dic43—42no—
170C2×Dic43—82no—
171C8×C43—24no—
172C8×C43—42no—
173C43⋊C8—24no—
174C43⋊C8—22no—
175C43⋊C8—22no—
176#23674—431nomaximal, Sylow
177C22×C43—22no—
178C22×C43—22no—
179C22×C43—22no—
180C22×C43—42no—
181C22×C43—42no—
182C22×C43#39812yes—
183C22×C43#39812yes—
184C22×C43C2×#12111yescharacteristic
185C22×C43C2×#12511yescharacteristic
186C22×C43C2×#12511yescharacteristic
187C4×C43—82no—
188C4×C43#39812yes—
189C4×C43#39812yes—
190C4×C43C2×C22⋊Q811yescharacteristic
191C4×C43C2×C22⋊Q811yescharacteristic
192C4×C43C2×#12311yescharacteristic
193C4×C43C2×C4⋊Q811yescharacteristic
194Dic43—44no—
195Dic43—82no—
196#2911—431no—
197#2911—431no—
198C2×#427—431no—
199C2×#424—431no—
200#2090—434no—
201#2089—434no—
202#1742—431no—
203#1742D4311yescharacteristic
204C2×#341—431no—
205C2×C43—21no—
206C2×C43—21no—
207C2×C43—22no—
208C2×C43—22no—
209C2×C43C2×#39811yescharacteristic
210C2×C43#306712yes—
211C22×M16—431no—
212C22×M16C2×D4311yescharacteristic
213C22×M16C2×D4311yescharacteristic
214C23×C8—431no—
215C2×#117—431no—
216C2×#117—431no—
217C2×#117C2×D4311yescharacteristic
218#428—434no—
219#428—434no—
220#428—862no—
221#428—862no—
222#427—862no—
223#427—862no—
224#427—862no—
225#427—862no—
226C2×#107—432no—
227C2×#106—432no—
228#424—432no—
229#424—432no—
230#424—862no—
231C2×C4⋊C8—862no—
232#343—434no—
233#343C2×D4314yes—
234#341—432no—
235#341—432no—
236C43#2367411yescharacteristic, complemented, Sylow
237C23×C4C22×D4311yescharacteristic
238C2×M16—21no—
239C2×M16—22no—
240C2×M16—21no—
241C2×M16—22no—
242C2×M16—22no—
243C2×M16—434no—
244C2×M16—432no—
245C2×M16—862no—
246C2×M16—861no—
247C2×M16Dic8614yes—
248C2×M16C22×D4312yes—
249C2×M16C22×D4312yes—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—432no—
253C22×C8—432no—
254C22×C8—431no—
255C22×C8—431no—
256C22×C8—862no—
257C22×C8—861no—
258C22×C8—862no—
259#117—21no—
260#117—21no—
261#117—21no—
262#117—21no—
263#117—432no—
264#117—432no—
265#117—861no—
266#117—861no—
267#117—861no—
268#117—861no—
269#117—861no—
270#117—861no—
271C2×C4⋊C4—432no—
272C2×C4⋊C4—432no—
273C2×C4⋊C4C22×D4312yes—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—861no—
276C2×C22⋊C4—861no—
277C2×C42—21no—
278C2×C42—861no—
279C2×C42—861no—
280#107—864no—
281#107—864no—
282#107—864no—
283#106—864no—
284#106—864no—
285#106—864no—
286C4⋊C8—864no—
287C4⋊C8—864no—
288C24#1062189811yescharacteristic
289C22×C4—22no—
290C22×C4—862no—
291C22×C4—862no—
292C22×C4C2×Dic8612yes—
293C22×C4#1062189811yescharacteristic
294C22×C4#1062189812yes—
295C22×C4D4×D4311yescharacteristic
296C22×C4D4×D4311yescharacteristic
297C22×C4D4×D4311yescharacteristic
298C22×C4D4×D4311yescharacteristic
299C22×C4#1062190012yes—
300C22×C4Q8×D4312yes—
301C22×C4C23×D4311yescharacteristic
302M16—24no—
303M16—22no—
304M16—22no—
305M16—22no—
306M16—42no—
307M16—434no—
308M16—864no—
309M16—862no—
310M16C2×Dic8614yes—
311C2×C8—24no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—42no—
315C2×C8—432no—
316C2×C8—432no—
317C2×C8—864no—
318C2×C8—864no—
319C2×C8—864no—
320C2×C8—862no—
321C2×C8—861no—
322C2×C8—861no—
323C2×C8—861no—
324C2×C8—861no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—434no—
328C4⋊C4—862no—
329C4⋊C4—862no—
330C4⋊C4—862no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—862no—
334C22⋊C4—862no—
335C22⋊C4—1721no—
336C22⋊C4—1721no—
337C42—41no—
338C42—41no—
339C42—862no—
340C42—862no—
341C42—1721no—
342C42—1721no—
343C23—42no—
344C23#1306329811yescharacteristic
345C23#1306329811yescharacteristic
346C23#1306331512yes—
347C23#1306331712yes—
348C23C2×#1062189811yescharacteristic
349C2×C4—42no—
350C2×C4—82no—
351C2×C4—864no—
352C2×C4—3442no—
353C2×C4—1722no—
354C2×C4—1724no—
355C2×C4#1306329811yescharacteristic
356C2×C4#1306329811yescharacteristic
357C2×C4#1306330212yes—
358C2×C4#1306330212yes—
359C2×C4#1306330312yes—
360C2×C4#1306330312yes—
361C2×C4#1306330712yes—
362C2×C4#1306330712yes—
363C2×C4#1306331512yes—
364C2×C4#1306331712yes—
365C2×C4#1306332412yes—
366C2×C4#1306332412yes—
367C2×C4C2×D4×D4311yescharacteristic
368C2×C4C2×D4×D4311yescharacteristic
369C2×C4C2×Q8×D4311yescharacteristic
370C2×C4C22×Dic8611yescharacteristic
371C2×C4C2×#1062190011yescharacteristic
372C2×C4C2×#1062189811yescharacteristic
373C8—24no—
374C8—42no—
375C8—864no—
376C8—862no—
377C8—862no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—42no—
382C22—42no—
383C22#1458283312yes—
384C22#1458283312yes—
385C22C2×#1306329811yescharacteristic
386C22C2×#1306331511yescharacteristic
387C22C2×#1306331711yescharacteristic
388C4—82no—
389C4—3442no—
390C4—1724no—
391C4#1458283312yes—
392C4#1458283312yes—
393C4C2×#1306330211yescharacteristic
394C4C2×#1306330311yescharacteristic
395C4C2×#1306330711yescharacteristic
396C4C2×#1306332411yescharacteristic
397C2—22no—
398C2—22no—
399C2—21no—
400C2—21no—
401C2C2×#1458283311yescharacteristic
402C2#1914431412yes—
subgroupG/H
centerC2×C4#13063298
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1742C2
socleC22×C43C2×#121
prime radicalC24×C43#41
hypercenter#1742D43
hypocenterC43#23674
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1742

Complements

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

NH ≅ G/Ntype
5. #19136109C2semidirect
6. #19136104C2semidirect
236. C43#23674semidirect

Maximal subgroups

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

subgroupindex
#191431852
#191431842
C2×#145829352
C2×#145829272
#191361092
#191361042
#191343332
C2×#145826632
C43×#17422
#2367443