Finite Group Databasebeta

← #25013553

Subgroups — #25013553

Order 11008.

476 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144315C211yesmaximal, characteristic
2#19143206C211yesmaximal, characteristic, complemented
3#19136324C211yesmaximal, characteristic, complemented
4C2×#14582707C211yesmaximal, characteristic, complemented
5#19132707C211yesmaximal, characteristic, complemented
6#19132689C211yesmaximal, characteristic, complemented
7C2×C43×#350C211yesmaximal, characteristic, complemented
8#14583697—21no—
9C2×#13063347C2211yescharacteristic
10#14583666—21no—
11#14583174C412yes—
12#14583169C412yes—
13#14583162—22no—
14#14582948—22no—
15#14582948—21no—
16C2×#13063261—22no—
17C2×#13063261C2211yescharacteristic
18C2×#13063261C2211yescharacteristic
19C2×#13063261C2211yescharacteristic
20#14582881—21no—
21#14582707—22no—
22#14582707—22no—
23C2×#131×C43C2211yescharacteristic
24C2×M32×C43C2211yescharacteristic
25C22×C16×C43C2211yescharacteristic
26C43×#350—22no—
27C2×#10621898—21no—
28#13063356—41no—
29#13063355—22no—
30#13063351—41no—
31#13063350—22no—
32#13063347—21no—
33#13063347—21no—
34#13063347—21no—
35#13063347—21no—
36#13063345—42no—
37C2×Dic172C2×C411yescharacteristic
38C2×#10621873—21no—
39C2×D344C2×C411yescharacteristic
40#13063332—42no—
41#13063332—42no—
42C2×#10621877—24no—
43C2×#10621877—21no—
44C2×#10621877—21no—
45C2×#10621877—21no—
46#13063261—24no—
47#13063261—21no—
48#13063261—21no—
49#13063261—21no—
50#13063261C2×C412yes—
51#13063261D412yes—
52#13063261D412yes—
53#13063243—22no—
54#13063241—22no—
55C2×#41×C43D411yescharacteristic
56#131×C43—21no—
57#131×C43—21no—
58#131×C43C2×C412yes—
59#131×C43D412yes—
60C2×M16×C43—21no—
61C2×M16×C43D411yescharacteristic
62C22×C8×C43—21no—
63C22×C8×C43C2311yescharacteristic
64M32×C43—21no—
65M32×C43—21no—
66C2×C16×C43—21no—
67C2×C16×C43—21no—
68C2×C16×C43—21no—
69C2×C16×C43—21no—
70#41×C43—21no—
71#41×C43—21no—
72#41×C43C22⋊C412yes—
73#41×C43D812yes—
74C2×Q8×C43SD1611yescharacteristic
75C2×D4×C43—21no—
76C2×D4×C43SD1611yescharacteristic
77C22×C4×C43—21no—
78C22×C4×C43C2×D411yescharacteristic
79C2×C22⋊D43—41no—
80#10621898—41no—
81#10621898—41no—
82#10621898—41no—
83#10621898—41no—
84C2×D172—21no—
85C2×C4×D43—41no—
86C2×Dic86—21no—
87M16×C43—21no—
88M16×C43—22no—
89M16×C43—22no—
90M16×C43C22⋊C412yes—
91C2×C8×C43—21no—
92C2×C8×C43—22no—
93C2×C8×C43—22no—
94C2×C8×C43C22×C411yescharacteristic
95C2×C8×C43C2×D411yescharacteristic
96C2×C8×C43C2×D411yescharacteristic
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43#4111yescharacteristic
99C2×C8×C43#4111yescharacteristic
100#10621885—42no—
101#10621884—42no—
102#10621883—42no—
103#10621882—42no—
104#10621877—22no—
105#10621877—22no—
106#10621877—22no—
107#10621877—44no—
108#10621877—41no—
109#10621877—41no—
110#10621877—41no—
111C2×C43⋊C8—44no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115Dic172—21no—
116Dic172—21no—
117D344—21no—
118D344—21no—
119#10621873—41no—
120#10621873—41no—
121C16×C43—41no—
122C16×C43—41no—
123C23×C43—21no—
124C23×C43#13711yescharacteristic
125C22×D43—41no—
126Q8×C43—21no—
127Q8×C43#10212yes—
128D4×C43—22no—
129D4×C43—22no—
130D4×C43—21no—
131D4×C43#10212yes—
132C2×C4×C43—21no—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43C2×C22⋊C411yescharacteristic
136C2×C4×C43#12011yescharacteristic
137C2×C4×C43#12311yescharacteristic
138C2×C4×C43C2×D811yescharacteristic
139C2×C4×C43C2×SD1611yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C22⋊D43—81no—
142C22⋊D43—81no—
143C2×Dic43—41no—
144D172—41no—
145D172—41no—
146C4×D43—81no—
147C4×D43—81no—
148Dic86—41no—
149Dic86—41no—
150C8×C43—22no—
151C8×C43C4×D411yescharacteristic
152C8×C43C4×D411yescharacteristic
153C8×C43#12111yescharacteristic
154C8×C43#12111yescharacteristic
155C43⋊C8—42no—
156C43⋊C8—42no—
157C43⋊C8—42no—
158#12995—431nomaximal, Sylow
159C22×C43—22no—
160C22×C43—41no—
161C22×C43—81no—
162C22×C43#41711yescharacteristic
163C22×C43#44811yescharacteristic
164C22×C43#48011yescharacteristic
165C2×D43—81no—
166C2×D43—161no—
167C4×C43—22no—
168C4×C43#38611yescharacteristic
169C4×C43C2×#10211yescharacteristic
170C4×C43#44711yescharacteristic
171C4×C43#48111yescharacteristic
172Dic43—81no—
173#3067—431no—
174#2916—431no—
175#2143—431no—
176C2×#359—431no—
177C2×#350D4311yescharacteristic, complemented
178#1388—431no—
179#1381—431no—
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43—42no—
184C2×C43#187411yescharacteristic
185D43—161no—
186#575—861no—
187C2×#135—431no—
188#568—861no—
189C2×#131C2×D4311yescharacteristic
190C2×M32C2×D4311yescharacteristic
191C22×C16C2×D4311yescharacteristic
192#473—432no—
193#472—432no—
194#471—862no—
195#430—862no—
196#430—861no—
197C2×#108—431no—
198C2×#108—431no—
199C2×#108—431no—
200C2×#108—862no—
201#413—861no—
202#359—862no—
203#359—862no—
204#350—22no—
205C43#1299511yescharacteristic, complemented, Sylow
206C2×#41—861no—
207C2×#41D17211yescharacteristic
208#137—862no—
209#137—1721no—
210AGL(1,ℤ/8)—862no—
211AGL(1,ℤ/8)—1721no—
212#135—861no—
213#135—861no—
214#135—861no—
215#135—861no—
216#135—1722no—
217C2×Q16—431no—
218C2×SD16—861no—
219C2×D8—431no—
220#131—21no—
221#131—21no—
222#131—1722no—
223#131—1722no—
224#131C4×D4312yes—
225#131C22⋊D4312yes—
226C2×M16—21no—
227C2×M16—864no—
228C2×M16—861no—
229C2×M16—861no—
230C2×M16—861no—
231C2×M16D17211yescharacteristic
232C22×C8—21no—
233C22×C8C22×D4311yescharacteristic
234M32—21no—
235M32—21no—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—21no—
240#108—432no—
241#108—432no—
242#108—432no—
243#108—864no—
244#108—861no—
245#108—861no—
246#108—861no—
247#101—862no—
248#100—862no—
249#41—21no—
250#41—21no—
251#41—1721no—
252#41—1721no—
253#41—1721no—
254#41—1721no—
255#41D34412yes—
256#41(C2×D43)⋊C412yes—
257C2×Q8—861no—
258C2×Q8#1062187311yescharacteristic
259C2×D4—21no—
260C2×D4—861no—
261C2×D4—1721no—
262C2×D4#1062187311yescharacteristic
263C22×C4—21no—
264C22×C4—1721no—
265C22×C4C2×D17211yescharacteristic
266Q16—861no—
267Q16—861no—
268Q16—1722no—
269SD16—1722no—
270SD16—1722no—
271SD16—1721no—
272SD16—1721no—
273D8—861no—
274D8—861no—
275D8—1722no—
276M16—21no—
277M16—22no—
278M16—22no—
279M16—862no—
280M16—862no—
281M16—862no—
282M16—1724no—
283M16—1721no—
284M16—1721no—
285M16—1721no—
286M16(C2×D43)⋊C412yes—
287C2×C8—21no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—1724no—
291C2×C8—1721no—
292C2×C8—1721no—
293C2×C8—1721no—
294C2×C8C2×C4×D4311yescharacteristic
295C2×C8D4×D4311yescharacteristic
296C2×C8D4×D4311yescharacteristic
297C2×C8#1062190011yescharacteristic
298C2×C8#1062190011yescharacteristic
299C2×C8C2×C22⋊D4311yescharacteristic
300C16—41no—
301C16—41no—
302C23—21no—
303C23—1721no—
304C23#1306335811yescharacteristic
305Q8—21no—
306Q8—1721no—
307Q8—1721no—
308Q8#1306324712yes—
309D4—22no—
310D4—22no—
311D4—21no—
312D4—3441no—
313D4—3441no—
314D4—1721no—
315D4—1721no—
316D4#1306324712yes—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—1721no—
323C2×C4C2×(C2×D43)⋊C411yescharacteristic
324C2×C4#1306329511yescharacteristic
325C2×C4#1306330911yescharacteristic
326C2×C4C2×D34411yescharacteristic
327C2×C4C2×#1062187311yescharacteristic
328C2×C4#1306335311yescharacteristic
329C8—22no—
330C8—1722no—
331C8—1722no—
332C8—1722no—
333C8(C22⋊D43)⋊C411yescharacteristic
334C8(C22⋊D43)⋊C411yescharacteristic
335C8#1306329711yescharacteristic
336C8#1306329711yescharacteristic
337C22—22no—
338C22—41no—
339C22—81no—
340C22—3441no—
341C22—6881no—
342C22#1458290111yescharacteristic
343C22#1458304011yescharacteristic
344C22#1458321311yescharacteristic
345C4—22no—
346C4—3441no—
347C4#1458277611yescharacteristic
348C4C2×#1306324711yescharacteristic
349C4#1458303511yescharacteristic
350C4#1458321811yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—6881no—
356C2#1913491011yescharacteristic
subgroupG/H
centerC4#14583035
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#350C2
socleC2×C43#1874
prime radical#19144315C2
cosocleC22×C8×C43C23
hypercenterC2×#350D43
hypocenterC43#12995
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#131 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. #19143206C2semidirect
3. #19136324C2semidirect
4. C2×#14582707C2semidirect
5. #19132707C2semidirect
6. #19132689C2semidirect
7. C2×C43×#350C2semidirect
177. C2×#350D43semidirect
205. C43#12995semidirect

Maximal subgroups

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

subgroupindex
#191443152
#191432062
#191363242
C2×#145827072
#191327072
#191326892
C2×C43×#3502
#1299543