Finite Group Databasebeta

← #19146319

Subgroups — #19146319

Order 5504.

494 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
1C2×#13063346C211yesmaximal, characteristic, complemented
2#14583568C211yesmaximal, characteristic, complemented
3#14583548C211yesmaximal, characteristic, complemented
4#14583270C211yesmaximal, characteristic, complemented
5#14583128C211yesmaximal, characteristic, complemented
6#14583125C211yesmaximal, characteristic, complemented
7#14583107C211yesmaximal, characteristic, complemented
8#14583092C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583060C211yesmaximal, characteristic, complemented
11#14583044C211yesmaximal, characteristic, complemented
12#14583041C211yesmaximal, characteristic, complemented
13SD16×Dic43C211yesmaximal, characteristic, complemented
14C8×C22⋊D43C211yesmaximal, characteristic, complemented
15C2×#135×C43C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18#13063346—24no—
19C2×#10621885C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21C2×#10621883C2211yescharacteristic
22C2×#10621884C2211yescharacteristic
23C2×#10621882C2211yescharacteristic
24C2×C8×D43C2211yescharacteristic
25#13063323C2211yescharacteristic
26#13063321—21no—
27#13063321C2211yescharacteristic
28#13063308—21no—
29#13063306—21no—
30#13063304C2211yescharacteristic
31#13063301C2211yescharacteristic
32#13063299—21no—
33#13063299C2211yescharacteristic
34#13063297—21no—
35#13063296—21no—
36#13063296C2211yescharacteristic
37Q8×Dic43C2211yescharacteristic
38D4×Dic43C2211yescharacteristic
39C4×C22⋊D43—21no—
40C4×C22⋊D43C2211yescharacteristic
41C2×Dic43⋊C4—21no—
42#13063257C2211yescharacteristic
43Dic43⋊C8C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063249C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063246C2211yescharacteristic
50C22⋊(C43⋊C8)C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52C8×Dic43C2211yescharacteristic
53C2×#41×C43C2211yescharacteristic
54C2×#41×C43C2211yescharacteristic
55#135×C43—24no—
56C2×Q16×C43C2211yescharacteristic
57C2×SD16×C43C2211yescharacteristic
58C2×SD16×C43C2211yescharacteristic
59C2×D8×C43C2211yescharacteristic
60C22×C8×C43C2211yescharacteristic
61#41×C43—22no—
62#41×C43—22no—
63#41×C43—41no—
64#41×C43—41no—
65C2×Q8×C43C2311yescharacteristic
66C2×Q8×C43C2311yescharacteristic
67C2×D4×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43C2311yescharacteristic
70C2×D4×C43C2311yescharacteristic
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43C2311yescharacteristic
74C2×C22⋊D43—21no—
75C2×C22⋊D43—21no—
76C2×C22⋊D43—21no—
77C2×C22⋊D43—21no—
78C2×C22⋊D43—21no—
79C2×C22⋊D43D411yescharacteristic
80C22×Dic43—21no—
81C22×Dic43—21no—
82#10621902—22no—
83#10621902—41no—
84#10621900—22no—
85#10621900—41no—
86C2×D172—21no—
87C2×D172C2311yescharacteristic
88C2×C4×D43—21no—
89C2×C4×D43C2311yescharacteristic
90C2×Dic86C2311yescharacteristic
91Q16×C43—22no—
92SD16×C43—22no—
93SD16×C43D414yescomplemented
94D8×C43—22no—
95C2×C8×C43—22no—
96C2×C8×C43C2311yescharacteristic
97C2×C8×C43C2311yescharacteristic
98C22⋊Dic43—21no—
99C22⋊Dic43—21no—
100C22⋊Dic43—21no—
101C22⋊Dic43D411yescharacteristic
102#10621885—22no—
103#10621884—41no—
104#10621883—41no—
105#10621882—22no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4D411yescharacteristic
109C4⋊Dic43—21no—
110C4⋊Dic43C2311yescharacteristic
111C4⋊Dic43C2311yescharacteristic
112Dic43⋊C4—21no—
113Dic43⋊C4—21no—
114Dic43⋊C4—21no—
115Dic43⋊C4—21no—
116Dic43⋊C4D411yescharacteristic
117C4×Dic43—21no—
118C4×Dic43C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121#10621873—22no—
122C8×D43—22no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43C2×D411yescharacteristic
126C22×D43—21no—
127C22×D43C2×D411yescharacteristic
128Q8×C43—21no—
129Q8×C43—21no—
130Q8×C43—21no—
131Q8×C43C2×D412yes—
132D4×C43—21no—
133D4×C43—21no—
134D4×C43—21no—
135D4×C43—42no—
136D4×C43—42no—
137D4×C43C2×D412yes—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43C2×D411yescharacteristic
145C2×C4×C43C2411yescharacteristic
146C22⋊D43—22no—
147C22⋊D43—42no—
148C22⋊D43—42no—
149C22⋊D43—81no—
150C22⋊D43—81no—
151C22⋊D43—81no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43C2×D411yescharacteristic
158C2×Dic43C2×D411yescharacteristic
159C2×Dic43C2×D411yescharacteristic
160D172—21no—
161D172—21no—
162D172—42no—
163C4×D43—21no—
164C4×D43—21no—
165C4×D43—42no—
166Dic86—21no—
167Dic86—21no—
168C8×C43—21no—
169C8×C43C2×D412yes—
170C43⋊C8—21no—
171C43⋊C8—21no—
172C22×C43—22no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43C22×D411yescharacteristic
182C2×D43—21no—
183C2×D43—21no—
184C2×D43—21no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C4×C43—22no—
189C4×C43—21no—
190C4×C43—41no—
191C4×C43C22×D411yescharacteristic
192C4×C43H(5,𝔽2)11yescharacteristic
193Dic43—21no—
194Dic43—21no—
195Dic43—41no—
196Dic43—41no—
197Dic43—41no—
198Dic43#13512yescomplemented
199#3284—431nomaximal, Sylow
200C2×C43—41no—
201C2×C43—42no—
202C2×C43—81no—
203C2×C43D4211yescharacteristic
204C2×C43C2×#13511yescharacteristic
205C2×C43#57711yescharacteristic
206D43—41no—
207D43—81no—
208C2×#135—431no—
209C2×#135D4311yescharacteristic, complemented
210#550—431no—
211#547—431no—
212#492—431no—
213#465—431no—
214#465—431no—
215#462—431no—
216#459—431no—
217#452—431no—
218#452—431no—
219#449—431no—
220#449—431no—
221C4×SD16—431no—
222C8×D4—431no—
223C43#328411yescharacteristic, complemented, Sylow
224C2×#41—431no—
225C2×#41—431no—
226C2×#41C2×D4311yescharacteristic
227C2×#41C2×D4311yescharacteristic
228#135—24no—
229#135—864no—
230C2×Q16—431no—
231C2×Q16C2×D4311yescharacteristic
232C2×SD16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16C2×D4311yescharacteristic
236C2×SD16C2×D4311yescharacteristic
237C2×D8—431no—
238C2×D8C2×D4311yescharacteristic
239C22×C8—431no—
240C22×C8C2×D4311yescharacteristic
241C4⋊Q8—431no—
242#127—431no—
243#127—861no—
244#123—861no—
245#123—861no—
246C22⋊Q8—431no—
247C22⋊Q8—431no—
248#121—431no—
249#121—431no—
250#121—861no—
251#121—861no—
252#121—861no—
253C4×Q8—431no—
254C4×D4—431no—
255C4×D4—431no—
256C4×D4—861no—
257C2×C4⋊C4—861no—
258#106—431no—
259C4⋊C8—431no—
260#103—431no—
261#103—431no—
262#103—431no—
263#102—431no—
264#102—431no—
265#102—431no—
266C22⋊C8—431no—
267C22⋊C8—431no—
268C4×C8—431no—
269#41—22no—
270#41—22no—
271#41—41no—
272#41—41no—
273#41—862no—
274#41—862no—
275#41—1721no—
276#41—1721no—
277C2×Q8—431no—
278C2×Q8C22×D4311yescharacteristic
279C2×Q8C22×D4311yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—431no—
283C2×D4—431no—
284C2×D4—861no—
285C2×D4—861no—
286C2×D4—861no—
287C2×D4—861no—
288C2×D4—861no—
289C2×D4—861no—
290C2×D4C22×D4311yescharacteristic
291C2×D4C22×D4311yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—431no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—861no—
298C22×C4C22×D4311yescharacteristic
299Q16—22no—
300Q16—862no—
301SD16—22no—
302SD16—862no—
303SD16—1721no—
304SD16—1721no—
305SD16C22⋊D4314yescomplemented
306D8—22no—
307D8—862no—
308C2×C8—22no—
309C2×C8—431no—
310C2×C8—431no—
311C2×C8—862no—
312C2×C8C22×D4311yescharacteristic
313C2×C8C22×D4311yescharacteristic
314C4⋊C4—431no—
315C4⋊C4—431no—
316C4⋊C4—431no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C4⋊C4—861no—
320C4⋊C4—861no—
321C4⋊C4—861no—
322C22⋊C4—431no—
323C22⋊C4—431no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—861no—
328C22⋊C4—861no—
329C42—431no—
330C42—861no—
331C23—21no—
332C23—21no—
333C23—431no—
334C23—861no—
335C23D4×D4311yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—861no—
340Q8—861no—
341Q8C2×C22⋊D4312yes—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—42no—
347D4—862no—
348D4—861no—
349D4—861no—
350D4—3441no—
351D4—3441no—
352D4—3441no—
353D4—1722no—
354D4—1722no—
355D4—1722no—
356D4C2×C22⋊D4312yes—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—431no—
364C2×C4—431no—
365C2×C4—431no—
366C2×C4—861no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—861no—
370C2×C4—861no—
371C2×C4—1722no—
372C2×C4—1722no—
373C2×C4—1722no—
374C2×C4D4×D4311yescharacteristic
375C2×C4C23×D4311yescharacteristic
376C8—21no—
377C8—861no—
378C8—861no—
379C8C2×C22⋊D4312yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—861no—
390C22—861no—
391C22—861no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22C2×D4×D4311yescharacteristic
396C4—21no—
397C4—22no—
398C4—41no—
399C4—432no—
400C4—861no—
401C4—861no—
402C4—1721no—
403C4—1721no—
404C4—1721no—
405C4C22×C22⋊D4311yescharacteristic
406C4#1306337011yescharacteristic
407C2—41no—
408C2—42no—
409C2—81no—
410C2—3441no—
411C2—1721no—
412C2D4×C22⋊D4311yescharacteristic
413C2#135×D4311yescharacteristic
414C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#135×C43C2
socleC22×C43C22×D4
hypercenterC2×#135D43
hypocenterC43#3284
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#13063346C2semidirect
2. #14583568C2semidirect
3. #14583548C2semidirect
4. #14583270C2semidirect
5. #14583128C2semidirect
6. #14583125C2semidirect
7. #14583107C2semidirect
8. #14583092C2semidirect
9. #14583061C2semidirect
10. #14583060C2semidirect
11. #14583044C2semidirect
12. #14583041C2semidirect
13. SD16×Dic43C2semidirect
14. C8×C22⋊D43C2semidirect
15. C2×#135×C43C2semidirect
93. SD16×C43D4semidirect
198. Dic43#135semidirect
209. C2×#135D43semidirect
223. C43#3284semidirect
305. SD16C22⋊D43semidirect