Finite Group Databasebeta

← #19134537

Subgroups — #19134537

Order 5504.

618 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C2×#41×D43C211yesmaximal, characteristic
2C2×#13063253C211yesmaximal, characteristic, complemented
3C2×#13063252C211yesmaximal, characteristic, complemented
4C2×#13063251C211yesmaximal, characteristic, complemented
5#14582862C211yesmaximal, characteristic, complemented
6C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
7C2×#104×C43C211yesmaximal, characteristic, complemented
8C2×#10621902C411yescharacteristic, complemented
9C2×#10621898—21no—
10C2×#10621898C2211yescharacteristic
11C2×#10621900—21no—
12C2×#10621900C411yescharacteristic, complemented
13#41×D43—22no—
14#41×D43—22no—
15#41×D43—22no—
16#41×D43—22no—
17C2×Q8×D43C411yescharacteristic, complemented
18C2×D4×D43—21no—
19C2×D4×D43C411yescharacteristic, complemented
20C22×C4×D43—21no—
21C22×C4×D43C2211yescharacteristic
22C2×#10621877C2211yescharacteristic, complemented
23C2×(C2×D43)⋊C4—21no—
24C2×C4×Dic43C2211yescharacteristic, complemented
25#13063253—22no—
26#13063252—22no—
27#13063251—22no—
28(C2×D43)⋊C8—21no—
29(C2×D43)⋊C8—21no—
30C43⋊#95—21no—
31C2×#41×C43C2211yescharacteristic
32C2×M16×C43C2211yescharacteristic, complemented
33C2×C42×C43C2211yescharacteristic, complemented
34#104×C43—22no—
35C23×D43—21no—
36C23×D43D411yescharacteristic
37#41×C43—21no—
38#41×C43—21no—
39#41×C43D412yes—
40#41×C43D412yes—
41C2×Q8×C43C2×C411yescharacteristic
42C2×D4×C43—21no—
43C2×D4×C43C2×C411yescharacteristic
44C22×C4×C43—21no—
45C22×C4×C43—21no—
46C22×C4×C43C2311yescharacteristic
47C2×C22⋊D43—21no—
48C2×C22⋊D43—21no—
49C2×C22⋊D43—21no—
50C22×Dic43—21no—
51C22×Dic43—21no—
52C22×Dic43D411yescharacteristic
53#10621902—22no—
54#10621902—22no—
55Q8×D43—22no—
56Q8×D43—22no—
57#10621900—24no—
58#10621900—24no—
59#10621900—22no—
60#10621900—22no—
61D4×D43—24no—
62D4×D43—24no—
63D4×D43—22no—
64D4×D43—22no—
65#10621898—24no—
66#10621898—24no—
67#10621898—21no—
68#10621898—21no—
69#10621898D412yes—
70#10621898D412yes—
71C2×D172—21no—
72C2×D172C2×C411yescharacteristic
73C2×C4×D43—24no—
74C2×C4×D43—24no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43C2×C411yescharacteristic
83C2×C4×D43C2×C411yescharacteristic
84C2×C4×D43D411yescharacteristic
85C2×C4×D43D411yescharacteristic
86C2×Dic86—21no—
87C2×Dic86C2×C411yescharacteristic
88M16×C43—21no—
89M16×C43—21no—
90C2×C8×C43—21no—
91C42×C43—21no—
92C42×C43—21no—
93(C2×D43)⋊C4—24no—
94C4×Dic43—21no—
95C4×Dic43—21no—
96#10621877—21no—
97#10621877—21no—
98C2×C43⋊C8—21no—
99C23×C43—21no—
100C23×C43C2×D411yescharacteristic
101C22×D43—24no—
102C22×D43—21no—
103C22×D43—21no—
104C22×D43—21no—
105C22×D43—22no—
106C22×D43—41no—
107C22×D43—42no—
108C22×D43—42no—
109C22×D43C22⋊C411yescharacteristic
110C22×D43C22⋊C411yescharacteristic
111Q8×C43—21no—
112Q8×C43C22⋊C412yescomplemented
113D4×C43—22no—
114D4×C43—22no—
115D4×C43—21no—
116D4×C43C22⋊C412yescomplemented
117C2×C4×C43—21no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43C22×C411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C22⋊D43—24no—
130C22⋊D43—24no—
131C22⋊D43—22no—
132C22⋊D43—22no—
133C2×Dic43—24no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—22no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43C22⋊C411yescharacteristic
141C2×Dic43C22⋊C411yescharacteristic
142D172—24no—
143D172—21no—
144D172C22⋊C412yescomplemented
145C4×D43—24no—
146C4×D43—24no—
147C4×D43—21no—
148C4×D43—21no—
149C4×D43—21no—
150C4×D43—21no—
151C4×D43—21no—
152C4×D43—21no—
153C4×D43—22no—
154C4×D43—22no—
155C4×D43—21no—
156C4×D43—21no—
157Dic86—24no—
158Dic86—21no—
159Dic86C22⋊C412yescomplemented
160C8×C43—41no—
161C43⋊C8—41no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—22no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43C2×C22⋊C411yescharacteristic
168C22×C43#12011yescharacteristic
169C22×C43#12011yescharacteristic
170C2×D43—21no—
171C2×D43—21no—
172C2×D43—22no—
173C2×D43—21no—
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—42no—
177C2×D43—42no—
178C2×D43—48no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43#10412yescomplemented
182C4×C43—22no—
183C4×C43—42no—
184C4×C43C2×C22⋊C411yescharacteristic
185C4×C43C2×C22⋊C411yescharacteristic
186C4×C43#12011yescharacteristic
187C4×C43#12011yescharacteristic
188Dic43—21no—
189Dic43—22no—
190Dic43—21no—
191Dic43—42no—
192#1789—431nomaximal, Sylow
193C2×C43—21no—
194C2×C43—21no—
195C2×C43—42no—
196C2×C43#37911yescharacteristic
197C2×C43C2×#10411yescharacteristic
198C2×C43#42111yescharacteristic
199D43—22no—
200D43—41no—
201D43—42no—
202C22×#41—431no—
203C2×#104—431no—
204C2×#104—431no—
205C2×#104—431no—
206C2×#104D4311yescharacteristic, complemented
207#407—431no—
208C4×C22⋊C4—431no—
209C43#178911yescharacteristic, complemented, Sylow
210C2×#41—431no—
211C2×#41—431no—
212C2×#41—431no—
213C2×#41—861no—
214C2×#41—861no—
215C2×#41—862no—
216C2×#41—862no—
217C2×#41—862no—
218C2×#41—862no—
219C2×#41C2×D4311yescharacteristic
220C22×Q8—431no—
221C22×D4—431no—
222C22×D4—861no—
223C23×C4—431no—
224C23×C4—861no—
225C2×M16—431no—
226C2×M16C2×D4311yescharacteristic, complemented
227C2×C22⋊C4—861no—
228C2×C42—431no—
229C2×C42C2×D4311yescharacteristic, complemented
230#104—22no—
231#104—862no—
232#104—862no—
233#104—862no—
234C22⋊C8—861no—
235C22⋊C8—861no—
236#95—861no—
237C24—431no—
238C24—861no—
239#41—21no—
240#41—21no—
241#41—432no—
242#41—432no—
243#41—864no—
244#41—864no—
245#41—862no—
246#41—864no—
247#41—864no—
248#41—862no—
249#41—862no—
250#41—862no—
251#41—861no—
252#41—861no—
253#41D17212yes—
254#41C22⋊D4312yes—
255C2×Q8—431no—
256C2×Q8—861no—
257C2×Q8—862no—
258C2×Q8—862no—
259C2×Q8C4×D4311yescharacteristic
260C2×D4—21no—
261C2×D4—431no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—862no—
265C2×D4—864no—
266C2×D4—864no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—862no—
270C2×D4C4×D4311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—431no—
274C22×C4—431no—
275C22×C4—431no—
276C22×C4—431no—
277C22×C4—431no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—864no—
281C22×C4—864no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4C22×D4311yescharacteristic
290M16—21no—
291M16—21no—
292M16—861no—
293M16—861no—
294C2×C8—21no—
295C2×C8—861no—
296C22⋊C4—864no—
297C42—21no—
298C42—21no—
299C42—861no—
300C42—861no—
301C23—21no—
302C23—431no—
303C23—431no—
304C23—862no—
305C23—864no—
306C23—861no—
307C23—861no—
308C23—861no—
309C23—1721no—
310C23—1722no—
311C23—1722no—
312C23D4×D4311yescharacteristic
313Q8—21no—
314Q8—432no—
315Q8—864no—
316Q8—861no—
317Q8(C2×D43)⋊C412yescomplemented
318D4—22no—
319D4—22no—
320D4—21no—
321D4—432no—
322D4—864no—
323D4—864no—
324D4—864no—
325D4—862no—
326D4—862no—
327D4—861no—
328D4(C2×D43)⋊C412yescomplemented
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—431no—
336C2×C4—431no—
337C2×C4—864no—
338C2×C4—864no—
339C2×C4—864no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—862no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—862no—
353C2×C4—862no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4C2×C4×D4311yescharacteristic
357C2×C4C2×D17211yescharacteristic
358C2×C4D4×D4311yescharacteristic
359C2×C4D4×D4311yescharacteristic
360C2×C4D4×D4311yescharacteristic
361C2×C4C2×C22⋊D4311yescharacteristic
362C8—41no—
363C8—1721no—
364C22—21no—
365C22—21no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—432no—
370C22—861no—
371C22—861no—
372C22—861no—
373C22—861no—
374C22—862no—
375C22—861no—
376C22—1722no—
377C22—1722no—
378C22—1728no—
379C22—1721no—
380C22—1721no—
381C22C22⋊C4×D4311yescharacteristic
382C22#1306329311yescharacteristic
383C22#1306329511yescharacteristic
384C4—22no—
385C4—42no—
386C4—861no—
387C4—861no—
388C4—862no—
389C4—1722no—
390C4C22⋊C4×D4311yescharacteristic
391C4C2×(C2×D43)⋊C411yescharacteristic
392C4#1306329311yescharacteristic
393C4#1306329511yescharacteristic
394C2—21no—
395C2—21no—
396C2—42no—
397C2—862no—
398C2—1721no—
399C2—1722no—
400C2#1458275411yescharacteristic
401C2#104×D4311yescharacteristic
402C2#1458291411yescharacteristic
subgroupG/H
centerC2×C4D4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC2×#104×C43C2
socleC22×C43C2×C22⋊C4
hypercenterC2×#104D43
hypocenterC43#1789
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#13063253C2semidirect
3. C2×#13063252C2semidirect
4. C2×#13063251C2semidirect
5. #14582862C2semidirect
6. C4×(C2×D43)⋊C4C2semidirect
7. C2×#104×C43C2semidirect
8. C2×#10621902C4semidirect
12. C2×#10621900C4semidirect
17. C2×Q8×D43C4semidirect
19. C2×D4×D43C4semidirect
22. C2×#10621877C22semidirect
24. C2×C4×Dic43C22semidirect
32. C2×M16×C43C22semidirect
33. C2×C42×C43C22semidirect
112. Q8×C43C22⋊C4semidirect
116. D4×C43C22⋊C4semidirect
144. D172C22⋊C4semidirect
159. Dic86C22⋊C4semidirect
181. C2×D43#104semidirect
206. C2×#104D43semidirect
209. C43#1789semidirect
226. C2×M16C2×D43semidirect
229. C2×C42C2×D43semidirect
317. Q8(C2×D43)⋊C4semidirect
328. D4(C2×D43)⋊C4semidirect