Finite Group Databasebeta

← #25000977

Subgroups — #25000977

Order 11008.

438 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145416C211yesmaximal, characteristic
2#19135064C211yesmaximal, characteristic
3#19135026C211yesmaximal, characteristic
4#19134802C211yesmaximal, characteristic
5#19132958C211yesmaximal, characteristic
6#19132501C211yesmaximal, characteristic
7C43×#1520C211yesmaximal, characteristic
8C22×#10621877C2211yescharacteristic
9C2×#13063304C2211yescharacteristic
10#14583229—21no—
11#14583227—21no—
12#14583155—21no—
13#14583155—21no—
14#14583055—21no—
15#14583054—21no—
16C2×#13063261—21no—
17C2×#13063248—21no—
18C2×#13063244—21no—
19#14582863C2211yescharacteristic
20#14582863C2211yescharacteristic
21#14582668—21no—
22#14582664—21no—
23#14582661—21no—
24#14582624—22no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×C22⋊C8×C43C2211yescharacteristic
27C43×#380C2211yescharacteristic
28C43×#328—22no—
29C22×Dic86D411yescharacteristic
30C2×#10621885—21no—
31C2×#10621885—21no—
32C2×#10621877—21no—
33C2×#10621877—21no—
34C2×#10621877—21no—
35C2×#10621877—42no—
36C2×#10621877D411yescharacteristic
37C2×#10621877D411yescharacteristic
38C22×C43⋊C8—21no—
39#13063304—21no—
40#13063304—21no—
41#13063304—21no—
42#13063304—21no—
43C2×C4⋊Dic43D411yescharacteristic
44C2×Dic43⋊C4—21no—
45C2×C22⋊Dic43—21no—
46#13063261—42no—
47#13063256—21no—
48#13063256—21no—
49#13063249—21no—
50#13063249—21no—
51#13063248—21no—
52#13063248—21no—
53#13063248—42no—
54#13063244—42no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59C22×Q8×C43D411yescharacteristic
60C23×C4×C43C2311yescharacteristic
61C22×C8×C43—21no—
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43D412yes—
73#95×C43—21no—
74C24×C43#4111yescharacteristic
75C2×Q8×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43—41no—
78C2×Q8×C43—41no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C22×Dic43—21no—
91C22×Dic43—21no—
92C2×Dic86—21no—
93C2×Dic86—21no—
94C2×Dic86—41no—
95C2×Dic86—41no—
96C2×C8×C43—22no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C22⋊C4×C43—81no—
108C22⋊Dic43—41no—
109C22⋊Dic43—41no—
110#10621885—81no—
111#10621885—81no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114Dic43⋊C4—41no—
115Dic43⋊C4—41no—
116#10621877—22no—
117#10621877—22no—
118#10621877—41no—
119#10621877—41no—
120#10621877—41no—
121#10621877—41no—
122#10621877—41no—
123#10621877—41no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—21no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—41no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43#12111yescharacteristic
135C23×C43#12311yescharacteristic
136C23×C43#12411yescharacteristic
137Q8×C43—41no—
138Q8×C43—41no—
139Q8×C43—81no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—81no—
153C2×C4×C43—81no—
154C2×C4×C43—81no—
155C2×C4×C43—81no—
156C2×C4×C43#12011yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12311yescharacteristic
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—81no—
165Dic86—42no—
166Dic86—41no—
167Dic86—41no—
168C8×C43—42no—
169C43⋊C8—42no—
170C43⋊C8—41no—
171C43⋊C8—41no—
172C43⋊C8—81no—
173#10563—431nomaximal, Sylow
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—81no—
183C22×C43—81no—
184C22×C43#39411yescharacteristic
185C22×C43#47111yescharacteristic
186C22×C43#47311yescharacteristic
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—81no—
191C4×C43—81no—
192C4×C43—161no—
193C4×C43B(4,𝔽2)11yescharacteristic
194C4×C43#45811yescharacteristic
195Dic43—81no—
196Dic43—81no—
197#3195—431no—
198#1901—431no—
199#1894—431no—
200#1855—431no—
201#1520D4311yescharacteristic
202#1472—431no—
203#1305—431no—
204C2×C43—21no—
205C2×C43—21no—
206C2×C43—41no—
207C2×C43—41no—
208C2×C43#204411yescharacteristic
209C2×C43#204911yescharacteristic
210C2×C43#205211yescharacteristic
211C22×M16—431no—
212C2×C22⋊Q8—431no—
213C2×C22⋊Q8C2×D4311yescharacteristic
214#483—861no—
215#483—861no—
216#470—861no—
217#470—861no—
218#451—861no—
219#451—861no—
220C2×#108—861no—
221C2×#103—861no—
222C2×#101—861no—
223#407—431no—
224#407—431no—
225C2×C22⋊C8C2×D4311yescharacteristic
226#380C2×D4311yescharacteristic
227#343—861no—
228#341—861no—
229#340—861no—
230#328—22no—
231#324—862no—
232C43#1056311yescharacteristic, complemented, Sylow
233C22×Q8—431no—
234C22×Q8D17211yescharacteristic
235C23×C4C22×D4311yescharacteristic
236C2×Q16—861no—
237C2×Q16—861no—
238C2×M16—431no—
239C2×M16—431no—
240C2×M16—861no—
241C2×M16—861no—
242C2×M16—861no—
243C2×M16—1722no—
244C22×C8—21no—
245C22×C8—861no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C22⋊Q8—861no—
251C22⋊Q8—861no—
252C22⋊Q8—861no—
253C22⋊Q8—861no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4—861no—
258C2×C4⋊C4D17211yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—861no—
262#108—1722no—
263#106—861no—
264#106—861no—
265#103—861no—
266#103—861no—
267#103—861no—
268#103—861no—
269#103—1722no—
270#101—1722no—
271C22⋊C8—21no—
272C22⋊C8—861no—
273C22⋊C8—861no—
274C22⋊C8—861no—
275C22⋊C8—861no—
276C22⋊C8C22⋊D4312yes—
277#95—21no—
278C24#1062190011yescharacteristic
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—861no—
284C2×Q8—861no—
285C2×Q8—1721no—
286C2×Q8—1721no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4C2×D17211yescharacteristic
295C22×C4#1062189811yescharacteristic
296C22×C4D4×D4311yescharacteristic
297C22×C4D4×D4311yescharacteristic
298C22×C4#1062190011yescharacteristic
299C22×C4C2×C22⋊D4311yescharacteristic
300Q16—3441no—
301Q16—3441no—
302M16—862no—
303M16—862no—
304M16—1721no—
305M16—1721no—
306M16—1721no—
307M16—1721no—
308M16—1721no—
309M16—1721no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—862no—
314C2×C8—861no—
315C2×C8—861no—
316C2×C8—1721no—
317C2×C8—1721no—
318C2×C8—1721no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—861no—
326C4⋊C4—861no—
327C4⋊C4—1721no—
328C4⋊C4—1721no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—1721no—
333C22⋊C4—1721no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23#1306329611yescharacteristic
339C23#1306330911yescharacteristic
340C23#1306331111yescharacteristic
341Q8—41no—
342Q8—41no—
343Q8—81no—
344Q8—1722no—
345Q8—1721no—
346Q8—1721no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—3441no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4#1306329511yescharacteristic
369C2×C4#1306329711yescharacteristic
370C2×C4#1306329911yescharacteristic
371C2×C4#1306330711yescharacteristic
372C8—42no—
373C8—3441no—
374C8—1722no—
375C8—1721no—
376C8—1721no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22#1458281511yescharacteristic
388C22#1458315911yescharacteristic
389C22#1458317111yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—81no—
394C4—81no—
395C4—161no—
396C4—3441no—
397C4—3441no—
398C4#1458308711yescharacteristic
399C4#1458309011yescharacteristic
400C2—21no—
401C2—21no—
402C2—41no—
403C2—41no—
404C2#1913584511yescharacteristic
405C2#1913587611yescharacteristic
406C2#1913589511yescharacteristic
subgroupG/H
centerC22#14582815
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1520C2
socleC22×C43#394
prime radicalC24×C43#41
hypercenter#1520D43
hypocenterC43#10563
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
232. C43#10563semidirect

Maximal subgroups

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

subgroupindex
#191454162
#191350642
#191350262
#191348022
#191329582
#191325012
C43×#15202
#1056343