Finite Group Databasebeta

← #18077256

Subgroups — #18077256

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573706C211yesmaximal, characteristic
2#14572760C211yesmaximal, characteristic
3#14564612C211yesmaximal, characteristic, complemented
4#14562057C211yesmaximal, characteristic, complemented
5#14561525C211yesmaximal, characteristic, complemented
6#14561468C211yesmaximal, characteristic, complemented
7C4×C19×#104C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926885—21no—
10#11926829C411yescharacteristic, complemented
11#11926824C411yescharacteristic, complemented
12#11926754C411yescharacteristic, complemented
13#11926749C411yescharacteristic, complemented
14#11926706—21no—
15#11926675—21no—
16C4×#64528—21no—
17C4×#64526—21no—
18#11926616—22no—
19D4×C19⋊C8—21no—
20#11926601—21no—
21#11926597C2211yescharacteristic
22#11926597C2211yescharacteristic
23#11926568C2211yescharacteristic
24C2×C4⋊(C19⋊C8)—21no—
25#11926304—22no—
26#11926276—21no—
27#11926276—21no—
28C4×#41×C19C2211yescharacteristic
29C2×C19×#104—21no—
30C4×M16×C19C2211yescharacteristic
31C43×C19C2211yescharacteristic
32C19×#339—21no—
33C2×#41×C19D411yescharacteristic
34C2×M16×C19—21no—
35C4×Q8×C19C2×C411yescharacteristic
36C4×Q8×C19D411yescharacteristic
37C4×D4×C19—21no—
38C4×D4×C19—21no—
39C4×D4×C19C2×C411yescharacteristic
40C4×D4×C19D411yescharacteristic
41C19×#117—21no—
42C19×#117D411yescharacteristic
43C2×C42×C19—21no—
44C2×C42×C19—21no—
45C2×C42×C19—21no—
46C2×C42×C19—21no—
47C2×C42×C19C2311yescharacteristic
48C2×#64528—21no—
49C2×#64526—21no—
50#10597372—21no—
51#10597370—21no—
52#10597370—21no—
53C2×#64520D412yes—
54C22×C19⋊C8—22no—
55#10597316—21no—
56#10597315C2×C411yescharacteristic
57#10597315C2×C411yescharacteristic
58C4×Dic38—21no—
59C4×Dic38—21no—
60C19×#104—24no—
61C19×#97—21no—
62C4×C8×C19—21no—
63#10597292—21no—
64#10597289—21no—
65C22⋊(C19⋊C8)—22no—
66C22⋊(C19⋊C8)—21no—
67C22⋊(C19⋊C8)—21no—
68#10597267—21no—
69#10597267—21no—
70#10597265—21no—
71#10597264—21no—
72C4⋊(C19⋊C8)—22no—
73C4⋊(C19⋊C8)—21no—
74C4⋊(C19⋊C8)—21no—
75C4⋊(C19⋊C8)C2×C411yescharacteristic
76C4⋊(C19⋊C8)C2×C411yescharacteristic
77C4⋊(C19⋊C8)D411yescharacteristic
78C4⋊(C19⋊C8)D411yescharacteristic
79#10597260—22no—
80C4×C19⋊C8—21no—
81C4×C19⋊C8—21no—
82#41×C19—22no—
83#41×C19—41no—
84C2×Q8×C19C22⋊C411yescharacteristic
85C2×D4×C19—21no—
86C2×D4×C19C22⋊C411yescharacteristic
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—41no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19#4111yescharacteristic
94C2×Dic38—21no—
95C2×Dic38—21no—
96M16×C19—22no—
97M16×C19—41no—
98C2×C8×C19—41no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19C22⋊C411yescharacteristic
102C4⋊C4×C19C22⋊C411yescharacteristic
103C22⋊C4×C19—21no—
104C22⋊C4×C19—21no—
105C22⋊C4×C19—21no—
106C42×C19—21no—
107C42×C19—21no—
108C42×C19—21no—
109C42×C19—22no—
110C42×C19—22no—
111C42×C19—22no—
112C42×C19—41no—
113C42×C19—41no—
114C42×C19—41no—
115C42×C19C22×C411yescharacteristic
116C42×C19C2×D411yescharacteristic
117C42×C19C2×D411yescharacteristic
118C42×C19#4111yescharacteristic
119C22⋊Dic19—41no—
120#64528—42no—
121#64526—42no—
122C4⋊Dic19—21no—
123C4⋊Dic19—21no—
124C4⋊Dic19—21no—
125C4⋊Dic19—21no—
126Dic19⋊C4—41no—
127Dic19⋊C4—41no—
128C4×Dic19—41no—
129#64520—42no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—21no—
133C2×C19⋊C8—21no—
134C2×C19⋊C8—22no—
135C2×C19⋊C8—82no—
136#8971—191nomaximal, Sylow
137C23×C19—21no—
138C23×C19#12111yescharacteristic
139Q8×C19—21no—
140Q8×C19—21no—
141D4×C19—21no—
142D4×C19—42no—
143D4×C19#10412yes—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19C2×C22⋊C411yescharacteristic
162C2×C4×C19C4×D411yescharacteristic
163C2×C4×C19C4×D411yescharacteristic
164C2×C4×C19#12011yescharacteristic
165C2×C4×C19#12111yescharacteristic
166C2×C4×C19#12311yescharacteristic
167C2×Dic19—41no—
168C2×Dic19—41no—
169Dic38—41no—
170Dic38—41no—
171Dic38—41no—
172Dic38—41no—
173C8×C19—42no—
174C19⋊C8—41no—
175C19⋊C8—41no—
176C19⋊C8—41no—
177C19⋊C8—42no—
178C19⋊C8—41no—
179#3107—191no—
180#2990—191no—
181#1994—191no—
182C4×#104D1911yescharacteristic
183#1485—191no—
184#1299—191no—
185#1276—191no—
186C22×C19—21no—
187C22×C19—22no—
188C22×C19—21no—
189C22×C19—21no—
190C22×C19—41no—
191C22×C19—41no—
192C22×C19#38611yescharacteristic
193C4×C19—21no—
194C4×C19—21no—
195C4×C19—21no—
196C4×C19—44no—
197C4×C19—41no—
198C4×C19—41no—
199C4×C19—41no—
200C4×C19C2×#10411yescharacteristic
201C4×C19#42111yescharacteristic
202C4×C19#44311yescharacteristic
203C4×C19#44411yescharacteristic
204C4×C19#45511yescharacteristic
205C4×C19#45611yescharacteristic
206Dic19—81no—
207Dic19—81no—
208#533—191no—
209C4×#41C2×D1911yescharacteristic
210#485—381no—
211#475—191no—
212#474—191no—
213#462—191no—
214#461—191no—
215#452—381no—
216#446—381no—
217C4×Q16—381no—
218C4×SD16—381no—
219#435—382no—
220C8×D4—381no—
221#432—381no—
222#431—191no—
223#431—191no—
224#423—191no—
225C2×C4⋊C8—381no—
226C2×#104—21no—
227C4×M16C2×D1911yescharacteristic
228C43C2×D1911yescharacteristic
229#339—21no—
230#339—382no—
231Q8⋊C8—381no—
232Q8⋊C8—381no—
233C2×C19—41no—
234C2×C19—42no—
235C2×C19#187111yescharacteristic
236C2×C19#187611yescharacteristic
237C2×C19#188211yescharacteristic
238C2×#41C22⋊D1911yescharacteristic
239C2×Q16—381no—
240C2×SD16—381no—
241C2×M16—21no—
242C2×M16—192no—
243C22×C8—382no—
244C4⋊Q8—191no—
245C4⋊Q8—191no—
246#125—381no—
247C22⋊Q8—381no—
248C22⋊Q8—381no—
249C4×Q8—381no—
250C4×Q8—381no—
251C4×Q8C4×D1911yescharacteristic
252C4×Q8D7611yescharacteristic
253C4×D4—21no—
254C4×D4—21no—
255C4×D4C4×D1911yescharacteristic
256C4×D4D7611yescharacteristic
257#117—21no—
258#117—381no—
259#117C22⋊D1911yescharacteristic
260C2×C42—21no—
261C2×C42—21no—
262C2×C42—21no—
263C2×C42—21no—
264C2×C42C22×D1911yescharacteristic
265#107—381no—
266#106—381no—
267C4⋊C8—191no—
268C4⋊C8—191no—
269C4⋊C8—191no—
270C4⋊C8—191no—
271C4⋊C8—382no—
272C4⋊C8—381no—
273C4⋊C8—381no—
274#104—24no—
275#103—381no—
276#103—381no—
277#103—381no—
278#102—381no—
279C22⋊C8—382no—
280C22⋊C8—381no—
281C22⋊C8—381no—
282#97—21no—
283#97—382no—
284C4×C8—21no—
285C4×C8—381no—
286C4×C8—381no—
287C19#897111yescharacteristic, complemented, Sylow
288#41—22no—
289#41—41no—
290C2×Q8—381no—
291C2×Q8—381no—
292C2×Q8(C2×D19)⋊C411yescharacteristic
293C2×D4—21no—
294C2×D4(C2×D19)⋊C411yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4D4×D1911yescharacteristic
300C22×C4#6454311yescharacteristic
301C22×C4C2×C22⋊D1911yescharacteristic
302Q16—762no—
303SD16—762no—
304M16—22no—
305M16—41no—
306M16—762no—
307C2×C8—41no—
308C2×C8—381no—
309C2×C8—381no—
310C2×C8—382no—
311C2×C8—381no—
312C2×C8—381no—
313C2×C8—1522no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—381no—
317C4⋊C4—381no—
318C4⋊C4—381no—
319C4⋊C4—381no—
320C4⋊C4—761no—
321C4⋊C4—761no—
322C4⋊C4(C2×D19)⋊C411yescharacteristic
323C4⋊C4(C2×D19)⋊C411yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—761no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—22no—
332C42—22no—
333C42—22no—
334C42—41no—
335C42—41no—
336C42—41no—
337C42—761no—
338C42C2×C4×D1911yescharacteristic
339C42C2×D7611yescharacteristic
340C42D4×D1911yescharacteristic
341C42#6454311yescharacteristic
342C23—21no—
343C23#1059738511yescharacteristic
344Q8—21no—
345Q8—21no—
346Q8—761no—
347Q8—761no—
348Q8—761no—
349Q8—761no—
350D4—21no—
351D4—42no—
352D4#1059726212yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—761no—
371C2×C4—761no—
372C2×C4(C22⋊D19)⋊C411yescharacteristic
373C2×C4(C22⋊D19)⋊C411yescharacteristic
374C2×C4#1059732811yescharacteristic
375C2×C4#1059733211yescharacteristic
376C2×C4C2×(C2×D19)⋊C411yescharacteristic
377C2×C4#1059738511yescharacteristic
378C8—42no—
379C8—761no—
380C8—761no—
381C8—761no—
382C8—762no—
383C8—761no—
384C22—21no—
385C22—22no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22#1192642111yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—44no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—1521no—
399C4—1521no—
400C4C2×#1059726211yescharacteristic
401C4#1192656211yescharacteristic
402C4#1192665811yescharacteristic
403C4#1192666311yescharacteristic
404C4#1192672311yescharacteristic
405C4#1192672811yescharacteristic
406C2—41no—
407C2—42no—
408C2#1456393511yescharacteristic
409C2#1456396011yescharacteristic
410C2#1456400211yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC4×C19×#104C2
socleC22×C19#386
prime radicalC2×#41×C19D4
cosocleC2×C42×C19C23
hypercenterC4×#104D19
hypocenterC19#8971
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
3. #14564612C2semidirect
4. #14562057C2semidirect
5. #14561525C2semidirect
6. #14561468C2semidirect
10. #11926829C4semidirect
11. #11926824C4semidirect
12. #11926754C4semidirect
13. #11926749C4semidirect
287. C19#8971semidirect

Maximal subgroups

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

subgroupindex
#145737062
#145727602
#145646122
#145620572
#145615252
#145614682
C4×C19×#1042
#897119