Finite Group Databasebeta

← #14575190

Subgroups — #14575190

Order 2432.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597361C211yesmaximal, characteristic, complemented
2#11927201C211yesmaximal, characteristic, complemented
3#11927193C211yesmaximal, characteristic, complemented
4#11926935C211yesmaximal, characteristic, complemented
5#11926787C211yesmaximal, characteristic, complemented
6#11926785C211yesmaximal, characteristic, complemented
7#11926757C211yesmaximal, characteristic, complemented
8#11926752C211yesmaximal, characteristic, complemented
9#11926706C211yesmaximal, characteristic, complemented
10#11926706C211yesmaximal, characteristic, complemented
11#11926698C211yesmaximal, characteristic, complemented
12#11926686C211yesmaximal, characteristic, complemented
13#11926645C211yesmaximal, characteristic, complemented
14#11926615C211yesmaximal, characteristic, complemented
15C2×C19×#135C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×#41×C19C2211yescharacteristic
18C2×Q8×D19C2211yescharacteristic
19C2×#64543C2211yescharacteristic
20C19×#135—24no—
21C2×Q16×C19C2211yescharacteristic
22C2×SD16×C19C2211yescharacteristic
23C2×SD16×C19C2211yescharacteristic
24C2×D8×C19C2211yescharacteristic
25C22×C8×C19C2211yescharacteristic
26#10597392C2211yescharacteristic
27Q8×Dic19C2211yescharacteristic
28#10597390C2211yescharacteristic
29C2×#64528C2211yescharacteristic
30C2×#64528C2211yescharacteristic
31#10597385—21no—
32#10597384—21no—
33#10597384C2211yescharacteristic
34#10597382—21no—
35#10597382C2211yescharacteristic
36#10597381—21no—
37D4×Dic19C2211yescharacteristic
38C2×#64526C2211yescharacteristic
39C2×#64526C2211yescharacteristic
40#10597375—21no—
41C4×C22⋊D19—21no—
42C4×C22⋊D19C2211yescharacteristic
43#10597370—21no—
44#10597370C2211yescharacteristic
45#10597370C2211yescharacteristic
46C2×Dic19⋊C4—21no—
47#10597361—24no—
48C2×Dic76C2211yescharacteristic
49C2×#64515C2211yescharacteristic
50#10597292C2211yescharacteristic
51#10597292C2211yescharacteristic
52#10597289C2211yescharacteristic
53#10597289C2211yescharacteristic
54C22⋊(C19⋊C8)C2211yescharacteristic
55(C2×D19)⋊C8C2211yescharacteristic
56#10597275C2211yescharacteristic
57#10597273C2211yescharacteristic
58#10597273C2211yescharacteristic
59#10597272C2211yescharacteristic
60Dic19⋊C8C2211yescharacteristic
61#41×C19—22no—
62#41×C19—22no—
63#41×C19—41no—
64#41×C19—41no—
65C2×Q8×C19C2311yescharacteristic
66C2×Q8×C19C2311yescharacteristic
67C2×D4×C19—21no—
68C2×D4×C19—21no—
69C2×D4×C19C2311yescharacteristic
70C2×D4×C19C2311yescharacteristic
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19C2311yescharacteristic
74C2×C22⋊D19—21no—
75C2×C22⋊D19—21no—
76C2×C22⋊D19D411yescharacteristic
77C22×Dic19—21no—
78C22×Dic19—21no—
79Q8×D19—22no—
80Q8×D19—41no—
81#64543—22no—
82#64543—41no—
83C2×C4×D19—21no—
84C2×C4×D19C2311yescharacteristic
85C2×Dic38—21no—
86C2×Dic38C2311yescharacteristic
87C2×Dic38C2311yescharacteristic
88Q16×C19—22no—
89SD16×C19—22no—
90SD16×C19D414yescomplemented
91D8×C19—22no—
92C2×C8×C19—22no—
93C2×C8×C19C2311yescharacteristic
94C2×C8×C19C2311yescharacteristic
95C22⋊Dic19—21no—
96C22⋊Dic19—21no—
97C22⋊Dic19—21no—
98C22⋊Dic19—21no—
99C22⋊Dic19—21no—
100C22⋊Dic19—21no—
101C22⋊Dic19D411yescharacteristic
102#64528—22no—
103#64528—41no—
104#64526—22no—
105#64526—41no—
106(C2×D19)⋊C4—21no—
107(C2×D19)⋊C4D411yescharacteristic
108C4⋊Dic19—21no—
109C4⋊Dic19C2311yescharacteristic
110C4⋊Dic19C2311yescharacteristic
111Dic19⋊C4—21no—
112Dic19⋊C4—21no—
113Dic19⋊C4—21no—
114Dic19⋊C4—21no—
115Dic19⋊C4—21no—
116Dic19⋊C4D411yescharacteristic
117C4×Dic19—21no—
118C4×Dic19C2311yescharacteristic
119C2×C19⋊C8C2311yescharacteristic
120C2×C19⋊C8C2311yescharacteristic
121Dic76—22no—
122#64515—22no—
123C23×C19—21no—
124C23×C19—21no—
125C23×C19C2×D411yescharacteristic
126C22×D19C2×D411yescharacteristic
127Q8×C19—21no—
128Q8×C19—21no—
129Q8×C19—21no—
130Q8×C19C2×D412yes—
131D4×C19—21no—
132D4×C19—21no—
133D4×C19—21no—
134D4×C19—42no—
135D4×C19—42no—
136D4×C19C2×D412yes—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19C2×D411yescharacteristic
144C2×C4×C19C2411yescharacteristic
145C22⋊D19—41no—
146C22⋊D19—42no—
147C22⋊D19—42no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—21no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19C2×D411yescharacteristic
155C2×Dic19C2×D411yescharacteristic
156C2×Dic19C2×D411yescharacteristic
157C4×D19—21no—
158C4×D19—21no—
159C4×D19—42no—
160Dic38—21no—
161Dic38—21no—
162Dic38—21no—
163Dic38—21no—
164Dic38—42no—
165C8×C19—21no—
166C8×C19C2×D412yes—
167C19⋊C8—21no—
168C19⋊C8—21no—
169#3269—191nomaximal, Sylow
170C22×C19—22no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—41no—
175C22×C19—41no—
176C22×C19—41no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19C22×D411yescharacteristic
180C2×D19—21no—
181C2×D19—21no—
182C2×D19—21no—
183C4×C19—22no—
184C4×C19—21no—
185C4×C19—41no—
186C4×C19C22×D411yescharacteristic
187C4×C19H(5,𝔽2)11yescharacteristic
188Dic19—21no—
189Dic19—21no—
190Dic19—21no—
191Dic19—41no—
192Dic19—41no—
193Dic19—41no—
194Dic19—41no—
195C2×#137—191no—
196C2×#135D1911yescharacteristic, complemented
197#548—191no—
198#547—191no—
199#497—191no—
200#468—191no—
201#467—191no—
202#463—191no—
203#462—191no—
204#452—191no—
205#452—191no—
206#451—191no—
207#449—191no—
208#440—191no—
209#435—191no—
210C2×C19—41no—
211C2×C19—42no—
212C2×C19—81no—
213C2×C19D4211yescharacteristic
214C2×C19#57511yescharacteristic
215C2×C19#57811yescharacteristic
216D19—41no—
217C2×#41—191no—
218C2×#41C2×D1911yescharacteristic
219C2×#41C2×D1911yescharacteristic
220C22×Q8—191no—
221#137—384no—
222#135—24no—
223C2×Q16—191no—
224C2×Q16—191no—
225C2×Q16—191no—
226C2×Q16C2×D1911yescharacteristic
227C2×SD16—191no—
228C2×SD16—191no—
229C2×SD16C2×D1911yescharacteristic
230C2×SD16C2×D1911yescharacteristic
231C2×D8C2×D1911yescharacteristic
232C2×M16—191no—
233C22×C8C2×D1911yescharacteristic
234C4⋊Q8—191no—
235#124—191no—
236#124—381no—
237#123—381no—
238#123—381no—
239C22⋊Q8—191no—
240C22⋊Q8—191no—
241C22⋊Q8—191no—
242C22⋊Q8—381no—
243#121—191no—
244#121—381no—
245#121—381no—
246C4×Q8—191no—
247C4×D4—191no—
248C4×D4—191no—
249C4×D4—381no—
250C2×C4⋊C4—381no—
251#107—191no—
252C4⋊C8—191no—
253#103—191no—
254#103—191no—
255#103—191no—
256#103—191no—
257#102—191no—
258#102—191no—
259C22⋊C8—191no—
260C22⋊C8—191no—
261#97—191no—
262C19#326911yescharacteristic, complemented, Sylow
263#41—22no—
264#41—22no—
265#41—41no—
266#41—41no—
267#41—382no—
268#41—761no—
269C2×Q8—191no—
270C2×Q8—191no—
271C2×Q8—381no—
272C2×Q8—382no—
273C2×Q8—761no—
274C2×Q8C22×D1911yescharacteristic
275C2×Q8C22×D1911yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—191no—
279C2×D4—381no—
280C2×D4—381no—
281C2×D4C22×D1911yescharacteristic
282C2×D4C22×D1911yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—191no—
286C22×C4—381no—
287C22×C4—381no—
288C22×C4—381no—
289C22×C4C22×D1911yescharacteristic
290Q16—22no—
291Q16—382no—
292Q16—382no—
293Q16—761no—
294SD16—22no—
295SD16—382no—
296SD16—761no—
297SD16C22⋊D1914yescomplemented
298D8—22no—
299M16—382no—
300C2×C8—22no—
301C2×C8—191no—
302C2×C8—191no—
303C2×C8C22×D1911yescharacteristic
304C2×C8C22×D1911yescharacteristic
305C4⋊C4—191no—
306C4⋊C4—191no—
307C4⋊C4—191no—
308C4⋊C4—381no—
309C4⋊C4—381no—
310C4⋊C4—381no—
311C4⋊C4—381no—
312C4⋊C4—381no—
313C4⋊C4—381no—
314C22⋊C4—191no—
315C22⋊C4—191no—
316C22⋊C4—381no—
317C22⋊C4—381no—
318C22⋊C4—381no—
319C22⋊C4—381no—
320C22⋊C4—381no—
321C22⋊C4—381no—
322C22⋊C4—381no—
323C42—191no—
324C42—381no—
325C23—21no—
326C23—21no—
327C23—191no—
328C23D4×D1911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—381no—
333Q8—381no—
334Q8—381no—
335Q8—381no—
336Q8—762no—
337Q8C2×C22⋊D1912yes—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—761no—
344D4—762no—
345D4—762no—
346D4C2×C22⋊D1912yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—191no—
354C2×C4—191no—
355C2×C4—191no—
356C2×C4—381no—
357C2×C4—381no—
358C2×C4—381no—
359C2×C4—381no—
360C2×C4—381no—
361C2×C4—381no—
362C2×C4—762no—
363C2×C4—762no—
364C2×C4—762no—
365C2×C4D4×D1911yescharacteristic
366C2×C4C23×D1911yescharacteristic
367C8—21no—
368C8—381no—
369C8—381no—
370C8C2×C22⋊D1912yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—381no—
381C22—381no—
382C22—381no—
383C22C2×D4×D1911yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—381no—
388C4—381no—
389C4—381no—
390C4—761no—
391C4—761no—
392C4—761no—
393C4—761no—
394C4#1059743011yescharacteristic
395C4C22×C22⋊D1911yescharacteristic
396C2—41no—
397C2—42no—
398C2—81no—
399C2—761no—
400C2D4×C22⋊D1911yescharacteristic
401C2#1192734111yescharacteristic
402C2#1192735811yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×#135C2
socleC22×C19C22×D4
hypercenterC2×#135D19
hypocenterC19#3269
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#10597361C2semidirect
2. #11927201C2semidirect
3. #11927193C2semidirect
4. #11926935C2semidirect
5. #11926787C2semidirect
6. #11926785C2semidirect
7. #11926757C2semidirect
8. #11926752C2semidirect
9. #11926706C2semidirect
10. #11926706C2semidirect
11. #11926698C2semidirect
12. #11926686C2semidirect
13. #11926645C2semidirect
14. #11926615C2semidirect
15. C2×C19×#135C2semidirect
90. SD16×C19D4semidirect
196. C2×#135D19semidirect
262. C19#3269semidirect
297. SD16C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973612
#119272012
#119271932
#119269352
#119267872
#119267852
#119267572
#119267522
#119267062
#119266982
#119266862
#119266452
#119266152
C2×C19×#1352
#326919