Finite Group Databasebeta

← #25096958

Subgroups — #25096958

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143017C211yesmaximal, characteristic
2#19134743C212yesmaximal, complemented
3#19134719C211yesmaximal, characteristic, complemented
4#19134697C212yesmaximal
5#19134642C211yesmaximal, characteristic
6#19134638C211yesmaximal, characteristic
7#19134477C211yesmaximal, characteristic, complemented
8#19134476C211yesmaximal, characteristic, complemented
9#19134394C212yesmaximal
10#19134349C212yesmaximal, complemented
11C43×#1833C211yesmaximal, characteristic, complemented
12C2×#13063333C2211yescharacteristic
13C2×#13063331C2211yescharacteristic
14#14583367C2211yescharacteristic
15C2×#13063261C2211yescharacteristic
16#14582937C2211yescharacteristic
17#14582881C2212yes—
18#14582872C2212yes—
19#14582857C2212yes—
20#14582856C412yescomplemented
21#14582855C2212yes—
22#14582855C2211yescharacteristic
23#14582853C412yescomplemented
24#14582851C412yescomplemented
25M16×Dic43C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27C4×C8×D43C412yescomplemented
28#14582670C2212yes—
29#14582660C2212yes—
30#14582658C2212yes—
31C43⋊#338C2212yes—
32#14582655C2212yes—
33#14582655C2212yes—
34C2×#108×C43C2211yescharacteristic
35C43×#427C2211yescharacteristic
36C43×#405C2211yescharacteristic
37C43×#344C2212yes—
38C43×H(3,ℤ/4)C2212yes—
39C2×#10621898C2311yescharacteristic
40#13063333—21no—
41#13063333—21no—
42#13063333—21no—
43#13063333—21no—
44#13063331—21no—
45#13063331—21no—
46#13063331—21no—
47#13063331—21no—
48C2×#10621877C2312yes—
49C2×#10621877C2311yescharacteristic
50C2×#10621872C2×C412yes—
51C2×#10621872C2×C412yes—
52C22×C43⋊C8C2311yescharacteristic
53C2×C8×D43C2×C412yes—
54C2×C8×D43C2×C412yes—
55#13063290—21no—
56#13063287—21no—
57(C22⋊D43)⋊C4—22no—
58#13063284C2312yes—
59#13063282C2×C412yes—
60C2×C4×Dic43C2311yescharacteristic
61C42×D43C2×C412yes—
62#13063261—21no—
63#13063261—21no—
64#13063259—21no—
65#13063257—21no—
66#13063243—22no—
67#13063241—22no—
68#13063239—24no—
69#13063236—22no—
70#13063236C2×C412yes—
71#13063235—22no—
72#13063235C2×C412yes—
73C4×C43⋊C8—22no—
74C4×C43⋊C8C2×C412yes—
75C8×Dic43—22no—
76C8×Dic43C2×C411yescharacteristic
77C8×Dic43C2×C412yes—
78C8×Dic43C2×C411yescharacteristic
79C8×Dic43C2×C411yescharacteristic
80C8×Dic43C2×C411yescharacteristic
81C2×M16×C43C2312yes—
82C2×M16×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84#117×C43C2312yes—
85#117×C43C2311yescharacteristic
86#108×C43—21no—
87#108×C43—21no—
88#107×C43—21no—
89#106×C43—21no—
90#97×C43C2×C412yes—
91C4×C8×C43C2×C412yes—
92C22×C4×C43C2411yescharacteristic
93C2×C22⋊D43#4112yes—
94C22×Dic43—21no—
95#10621898—21no—
96#10621898—21no—
97#10621898—21no—
98#10621898—21no—
99C2×D172#4111yescharacteristic
100C2×C4×D43—22no—
101C2×C4×D43C22×C412yes—
102C2×Dic86#4111yescharacteristic
103M16×C43—21no—
104M16×C43—21no—
105M16×C43—22no—
106M16×C43—22no—
107C2×C8×C43—22no—
108C2×C8×C43C22×C412yes—
109C2×C8×C43C22×C411yescharacteristic
110C2×C8×C43C22×C411yescharacteristic
111C2×C8×C43#4111yescharacteristic
112C2×C8×C43#4111yescharacteristic
113C2×C8×C43#4111yescharacteristic
114C2×C8×C43#4111yescharacteristic
115C4⋊C4×C43—21no—
116C4⋊C4×C43—22no—
117C22⋊C4×C43—21no—
118C22⋊C4×C43—22no—
119C42×C43—22no—
120C42×C43C22×C412yes—
121C22⋊Dic43—22no—
122(C2×D43)⋊C4—22no—
123C4⋊Dic43—22no—
124Dic43⋊C4—22no—
125C4×Dic43—21no—
126C4×Dic43—22no—
127C4×Dic43—22no—
128C4×Dic43C22×C411yescharacteristic
129C4×Dic43C22×C411yescharacteristic
130#10621877—21no—
131#10621877—21no—
132#10621877—22no—
133#10621877—22no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8C22×C412yes—
136C2×C43⋊C8C22×C411yescharacteristic
137C2×C43⋊C8C22×C411yescharacteristic
138C2×C43⋊C8#4111yescharacteristic
139C2×C43⋊C8#4111yescharacteristic
140C2×C43⋊C8#4111yescharacteristic
141C2×C43⋊C8#4111yescharacteristic
142#10621872—22no—
143#10621872—22no—
144#10621872—22no—
145#10621872—22no—
146C8×D43—22no—
147C8×D43—22no—
148C8×D43—22no—
149C8×D43—22no—
150C23×C43C2×#4111yescharacteristic
151C22×D43#11712yes—
152C2×C4×C43—22no—
153C2×C4×C43—42no—
154C2×C4×C43C23×C411yescharacteristic
155C2×C4×C43C2×#4111yescharacteristic
156C2×C4×C43C2×#4111yescharacteristic
157C2×C4×C43C2×#4111yescharacteristic
158C2×C4×C43C2×#4111yescharacteristic
159C2×C4×C43C2×#4111yescharacteristic
160C22⋊D43—22no—
161C22⋊D43—22no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—42no—
165C2×Dic43—42no—
166C2×Dic43#11712yes—
167D172—21no—
168D172—21no—
169C4×D43—22no—
170C4×D43—22no—
171C4×D43—44no—
172Dic86—21no—
173Dic86—21no—
174C8×C43—22no—
175C8×C43—42no—
176C8×C43#11711yescharacteristic
177C8×C43#11711yescharacteristic
178C8×C43#11711yescharacteristic
179C8×C43#11711yescharacteristic
180C43⋊C8—22no—
181C43⋊C8—42no—
182C43⋊C8#11711yescharacteristic
183C43⋊C8#11711yescharacteristic
184C43⋊C8#11711yescharacteristic
185C43⋊C8#11711yescharacteristic
186#20787—431nomaximal, Sylow
187C22×C43—41no—
188C22×C43C2×#11711yescharacteristic
189C22×C43#52911yescharacteristic
190C22×C43#52911yescharacteristic
191C2×D43—22no—
192C2×D43—42no—
193C4×C43—42no—
194C4×C43—82no—
195C4×C43C2×#11711yescharacteristic
196C4×C43C2×#11711yescharacteristic
197C4×C43#52911yescharacteristic
198C4×C43#52911yescharacteristic
199Dic43—22no—
200Dic43—22no—
201Dic43—41no—
202Dic43—82no—
203C4×#131—431no—
204#1841—432no—
205#1833—431no—
206#1833D4311yescharacteristic, complemented
207#1827—432no—
208#1813—431no—
209#1812—431no—
210#1772—431no—
211#1772—431no—
212#1757—432no—
213#1747—432no—
214C2×C43—21no—
215C2×C43—21no—
216C2×C43—21no—
217C2×C43#228311yescharacteristic
218D43—42no—
219C2×#131—431no—
220C2×#131—431no—
221C4×#41—431no—
222C2×#108—431no—
223C2×#108C2×D4311yescharacteristic
224#427—431no—
225#427C2×D4311yescharacteristic
226#413—432no—
227#410—432no—
228#405—431no—
229#405—432no—
230#405—432no—
231#405—432no—
232#405—432no—
233#405C2×D4311yescharacteristic
234C4×M16—431no—
235C4×M16—432no—
236C2×C4×C8—431no—
237C2×C4×C8—432no—
238#344—432no—
239#344C2×D4312yes—
240#339—432no—
241#339—432no—
242#338—432no—
243H(3,ℤ/4)—432no—
244H(3,ℤ/4)—432no—
245H(3,ℤ/4)C2×D4312yes—
246C43#2078711yescharacteristic, complemented, Sylow
247C2×#41—431no—
248#131—861no—
249#131—861no—
250#131—861no—
251#131—861no—
252#131—861no—
253#131—861no—
254#131—861no—
255#131—861no—
256C2×M16—431no—
257C2×M16—432no—
258C2×M16—432no—
259C2×M16—432no—
260C2×M16C22×D4312yes—
261C2×M16C22×D4311yescharacteristic
262C22×C8—431no—
263C22×C8—432no—
264C22×C8—432no—
265C22×C8C22×D4311yescharacteristic
266C4×Q8—861no—
267C4×D4—862no—
268C4×D4—861no—
269#117—432no—
270#117—432no—
271#117C22×D4312yes—
272#117C22×D4311yescharacteristic
273C2×C42—431no—
274C2×C42—432no—
275#108—21no—
276#108—21no—
277#108—861no—
278#108—861no—
279#107—21no—
280#107—861no—
281#106—21no—
282#106—861no—
283#101—862no—
284#100—862no—
285#99—864no—
286#97—432no—
287#97—432no—
288#97—862no—
289#97—862no—
290#97C4×D4312yes—
291C4×C8—431no—
292C4×C8—431no—
293C4×C8—432no—
294C4×C8—431no—
295C4×C8—431no—
296C4×C8—432no—
297C4×C8—862no—
298C4×C8—862no—
299C4×C8C4×D4312yes—
300#41—861no—
301#41—861no—
302#41—861no—
303#41—861no—
304C2×Q8—431no—
305C2×D4—432no—
306C2×D4—431no—
307C22×C4—432no—
308C22×C4—862no—
309C22×C4—861no—
310C22×C4C23×D4311yescharacteristic
311M16—21no—
312M16—21no—
313M16—22no—
314M16—22no—
315M16—862no—
316M16—862no—
317M16—861no—
318M16—861no—
319M16—862no—
320M16—862no—
321M16—862no—
322M16—862no—
323C2×C8—22no—
324C2×C8—431no—
325C2×C8—431no—
326C2×C8—431no—
327C2×C8—431no—
328C2×C8—431no—
329C2×C8—431no—
330C2×C8—432no—
331C2×C8—862no—
332C2×C8—862no—
333C2×C8—862no—
334C2×C8—862no—
335C2×C8—862no—
336C2×C8C2×C4×D4312yes—
337C2×C8C2×C4×D4311yescharacteristic
338C2×C8C2×C4×D4311yescharacteristic
339C2×C8#1062190011yescharacteristic
340C2×C8#1062190011yescharacteristic
341C2×C8#1062190211yescharacteristic
342C2×C8#1062190211yescharacteristic
343C4⋊C4—21no—
344C4⋊C4—22no—
345C4⋊C4—862no—
346C4⋊C4—862no—
347C22⋊C4—21no—
348C22⋊C4—22no—
349C22⋊C4—862no—
350C22⋊C4—862no—
351C42—22no—
352C42—431no—
353C42—431no—
354C42—862no—
355C42—861no—
356C42—862no—
357C42C2×C4×D4312yes—
358C23—432no—
359C23#41×D4311yescharacteristic
360Q8—861no—
361Q8—861no—
362D4—862no—
363D4—862no—
364D4—861no—
365D4—861no—
366C2×C4—22no—
367C2×C4—42no—
368C2×C4—432no—
369C2×C4—861no—
370C2×C4—862no—
371C2×C4—862no—
372C2×C4—861no—
373C2×C4—1724no—
374C2×C4—1722no—
375C2×C4—1722no—
376C2×C4C22×C4×D4311yescharacteristic
377C2×C4#41×D4311yescharacteristic
378C2×C4#41×D4311yescharacteristic
379C2×C4#41×D4311yescharacteristic
380C2×C4C2×#1062190011yescharacteristic
381C2×C4C2×#1062190211yescharacteristic
382C8—22no—
383C8—42no—
384C8—431no—
385C8—431no—
386C8—431no—
387C8—431no—
388C8—862no—
389C8—1722no—
390C8#1306328311yescharacteristic
391C8#1306328311yescharacteristic
392C8#1306328311yescharacteristic
393C8#1306328311yescharacteristic
394C22—41no—
395C22—862no—
396C22—1722no—
397C22#117×D4311yescharacteristic
398C22#1458342811yescharacteristic
399C22#1458343411yescharacteristic
400C4—42no—
401C4—82no—
402C4—862no—
403C4—862no—
404C4—3442no—
405C4—1721no—
406C4#117×D4311yescharacteristic
407C4C2×#1306328311yescharacteristic
408C4#1458342811yescharacteristic
409C4#1458343411yescharacteristic
410C2—21no—
411C2—21no—
412C2—21no—
413C2—1722no—
414C2#1913698811yescharacteristic
subgroupG/H
centerC4#117×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1833C2
socleC2×C43#2283
prime radicalC2×#10621898C23
cosocleC22×C4×C43C24
hypercenter#1833D43
hypocenterC43#20787
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ #117 ◁ #1833

Complements

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

NH ≅ G/Ntype
2. #19134743C2semidirect
3. #19134719C2semidirect
7. #19134477C2semidirect
8. #19134476C2semidirect
10. #19134349C2semidirect
11. C43×#1833C2semidirect
20. #14582856C4semidirect
23. #14582853C4semidirect
24. #14582851C4semidirect
27. C4×C8×D43C4semidirect
206. #1833D43semidirect
246. C43#20787semidirect

Maximal subgroups

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

subgroupindex
#191430172
#191347432
#191347192
#191346972
#191346422
#191346382
#191344772
#191344762
#191343942
#191343492
C43×#18332
#2078743