Finite Group Databasebeta

← #18078374

Subgroups — #18078374

Order 4864.

486 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573734C211yesmaximal, characteristic
2#14572670C211yesmaximal, characteristic
3#14562249C211yesmaximal, characteristic, complemented
4#14562133C211yesmaximal, characteristic, complemented
5#14561534C211yesmaximal, characteristic, complemented
6#14561491C211yesmaximal, characteristic, complemented
7C19×#1762C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926879—21no—
10#11926824C411yescharacteristic, complemented
11#11926824C411yescharacteristic, complemented
12#11926749C411yescharacteristic, complemented
13#11926749C411yescharacteristic, complemented
14#11926695—21no—
15#11926644—21no—
16#11926644—21no—
17#11926622—21no—
18#11926616—22no—
19D4×C19⋊C8—21no—
20#11926601C2211yescharacteristic
21#11926601C2211yescharacteristic
22#11926597C2211yescharacteristic
23#11926508—21no—
24C2×C22⋊(C19⋊C8)—21no—
25#11926285—22no—
26#11926280—21no—
27#11926280—21no—
28C2×C4×D4×C19C2211yescharacteristic
29C2×C19×#102—21no—
30C2×C19×#97C2211yescharacteristic
31C4×C4⋊C4×C19C2211yescharacteristic
32C19×#340—21no—
33C22×D4×C19D411yescharacteristic
34C23×C4×C19—21no—
35C22×C8×C19—21no—
36C4×D4×C19—21no—
37C4×D4×C19—21no—
38C4×D4×C19C2×C411yescharacteristic
39C4×D4×C19C2×C411yescharacteristic
40C4×D4×C19D411yescharacteristic
41C4×D4×C19D411yescharacteristic
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19D411yescharacteristic
44C2×C22⋊C4×C19—21no—
45C2×C42×C19—21no—
46C2×C42×C19C2311yescharacteristic
47C2×#64526—21no—
48C2×#64526—21no—
49#10597372—21no—
50#10597370—21no—
51#10597370—21no—
52C2×#64520—22no—
53C22×C19⋊C8—22no—
54#10597316—21no—
55#10597315C2×C411yescharacteristic
56#10597315C2×C411yescharacteristic
57C4×Dic38—21no—
58C4×Dic38—21no—
59C19×#102—24no—
60C19×#97—21no—
61C19×#97—21no—
62C19×#95—21no—
63#10597289—21no—
64#10597289—21no—
65C22⋊(C19⋊C8)—22no—
66C22⋊(C19⋊C8)—22no—
67C22⋊(C19⋊C8)—21no—
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)D411yescharacteristic
70C22⋊(C19⋊C8)D411yescharacteristic
71#10597267—21no—
72#10597267—21no—
73#10597264—21no—
74#10597264—21no—
75C4⋊(C19⋊C8)—21no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)C2×C411yescharacteristic
78C4⋊(C19⋊C8)C2×C411yescharacteristic
79#10597260—21no—
80#10597260D412yes—
81C4×C19⋊C8—21no—
82C24×C19—21no—
83C2×D4×C19—22no—
84C2×D4×C19—21no—
85C2×D4×C19—41no—
86C2×D4×C19C22⋊C411yescharacteristic
87C2×D4×C19C22⋊C411yescharacteristic
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—21no—
93C22×C4×C19—41no—
94C22×C4×C19—82no—
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19#4111yescharacteristic
98C2×Dic38—21no—
99C2×Dic38—21no—
100C2×C8×C19—22no—
101C2×C8×C19—41no—
102C2×C8×C19—41no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—22no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19C22⋊C411yescharacteristic
107C4⋊C4×C19C22⋊C411yescharacteristic
108C22⋊C4×C19—21no—
109C22⋊C4×C19—21no—
110C22⋊C4×C19—21no—
111C22⋊C4×C19—21no—
112C42×C19—81no—
113C42×C19C22×C411yescharacteristic
114C42×C19C2×D411yescharacteristic
115C42×C19C2×D411yescharacteristic
116C42×C19#4111yescharacteristic
117C22⋊Dic19—41no—
118#64526—42no—
119#64526—42no—
120C4⋊Dic19—21no—
121C4⋊Dic19—21no—
122C4⋊Dic19—21no—
123C4⋊Dic19—21no—
124Dic19⋊C4—41no—
125Dic19⋊C4—41no—
126C4×Dic19—41no—
127#64520—82no—
128C2×C19⋊C8—21no—
129C2×C19⋊C8—21no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—22no—
133C2×C19⋊C8—82no—
134#9165—191nomaximal, Sylow
135C23×C19—21no—
136C23×C19—21no—
137C23×C19—42no—
138C23×C19—41no—
139C23×C19—41no—
140C23×C19—81no—
141C23×C19#12111yescharacteristic
142D4×C19—21no—
143D4×C19—21no—
144D4×C19—21no—
145D4×C19—42no—
146D4×C19#10412yes—
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—41no—
154C2×C4×C19—42no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19—81no—
158C2×C4×C19—81no—
159C2×C4×C19—81no—
160C2×C4×C19—81no—
161C2×C4×C19—81no—
162C2×C4×C19C2×C22⋊C411yescharacteristic
163C2×C4×C19C4×D411yescharacteristic
164C2×C4×C19C4×D411yescharacteristic
165C2×C4×C19#12011yescharacteristic
166C2×C4×C19#12111yescharacteristic
167C2×C4×C19#12311yescharacteristic
168C2×Dic19—41no—
169C2×Dic19—41no—
170Dic38—41no—
171Dic38—41no—
172Dic38—81no—
173C8×C19—42no—
174C19⋊C8—41no—
175C19⋊C8—42no—
176C19⋊C8—41no—
177C19⋊C8—41no—
178C19⋊C8—41no—
179#3110—191no—
180#2974—191no—
181#1762D1911yescharacteristic
182#1531—191no—
183#1503—191no—
184#1302—191no—
185#1285—191no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—22no—
189C22×C19—41no—
190C22×C19—41no—
191C22×C19—41no—
192C22×C19—41no—
193C22×C19—41no—
194C22×C19—82no—
195C22×C19—82no—
196C22×C19#38611yescharacteristic
197C22×C19#47111yescharacteristic
198C22×C19#47311yescharacteristic
199C4×C19—21no—
200C4×C19—21no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—21no—
204C4×C19—41no—
205C4×C19—41no—
206C4×C19—82no—
207C4×C19C2×#10411yescharacteristic
208C4×C19#42111yescharacteristic
209Dic19—81no—
210Dic19—81no—
211#533—191no—
212C2×C4×D4C2×D1911yescharacteristic
213#484—381no—
214#474—191no—
215#474—191no—
216#461—191no—
217#461—191no—
218#450—381no—
219#440—381no—
220#440—381no—
221#436—381no—
222#435—382no—
223C8×D4—381no—
224#432—191no—
225#432—191no—
226#431—191no—
227C2×#102—21no—
228#407—381no—
229C2×C22⋊C8—381no—
230C2×#97C2×D1911yescharacteristic
231C4×C4⋊C4C2×D1911yescharacteristic
232#340—21no—
233#330—382no—
234#328—381no—
235#328—381no—
236C2×C19—21no—
237C2×C19—21no—
238C2×C19—42no—
239C2×C19—81no—
240C2×C19#187111yescharacteristic
241C2×C19#190411yescharacteristic
242C2×C19#190811yescharacteristic
243C22×D4C22⋊D1911yescharacteristic
244C23×C4—21no—
245C2×SD16—381no—
246C2×SD16—381no—
247C2×M16—382no—
248C22×C8—21no—
249C22×C8—382no—
250C4⋊Q8—191no—
251C4⋊Q8—191no—
252#125—381no—
253C22⋊Q8—381no—
254C22⋊Q8—381no—
255C4×Q8—381no—
256C4×Q8—381no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4C4×D1911yescharacteristic
260C4×D4C4×D1911yescharacteristic
261C4×D4D7611yescharacteristic
262C4×D4D7611yescharacteristic
263#117—381no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4C22⋊D1911yescharacteristic
266C2×C22⋊C4—21no—
267C2×C42—21no—
268C2×C42C22×D1911yescharacteristic
269#107—381no—
270#107—381no—
271C4⋊C8—191no—
272C4⋊C8—191no—
273C4⋊C8—381no—
274C4⋊C8—381no—
275#103—381no—
276#103—381no—
277#102—24no—
278#102—381no—
279#102—381no—
280C22⋊C8—191no—
281C22⋊C8—191no—
282C22⋊C8—382no—
283C22⋊C8—382no—
284C22⋊C8—381no—
285C22⋊C8—381no—
286#97—21no—
287#97—21no—
288#97—192no—
289#97—381no—
290C4×C8—381no—
291#95—21no—
292C19#916511yescharacteristic, complemented, Sylow
293C24—21no—
294C2×Q8—381no—
295C2×Q8—381no—
296C2×D4—22no—
297C2×D4—21no—
298C2×D4—41no—
299C2×D4(C2×D19)⋊C411yescharacteristic
300C2×D4(C2×D19)⋊C411yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—82no—
308C22×C4D4×D1911yescharacteristic
309C22×C4#6454311yescharacteristic
310C22×C4C2×C22⋊D1911yescharacteristic
311SD16—762no—
312SD16—762no—
313M16—1522no—
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—381no—
318C2×C8—381no—
319C2×C8—382no—
320C2×C8—381no—
321C2×C8—381no—
322C2×C8—1522no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—381no—
327C4⋊C4—381no—
328C4⋊C4—381no—
329C4⋊C4—381no—
330C4⋊C4—761no—
331C4⋊C4—761no—
332C4⋊C4(C2×D19)⋊C411yescharacteristic
333C4⋊C4(C2×D19)⋊C411yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—761no—
339C42—81no—
340C42—761no—
341C42C2×C4×D1911yescharacteristic
342C42C2×D7611yescharacteristic
343C42D4×D1911yescharacteristic
344C42#6454311yescharacteristic
345C23—21no—
346C23—21no—
347C23—42no—
348C23—41no—
349C23—41no—
350C23—81no—
351C23#1059738511yescharacteristic
352Q8—761no—
353Q8—761no—
354Q8—1521no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—42no—
359D4#1059726212yes—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—761no—
376C2×C4—761no—
377C2×C4(C22⋊D19)⋊C411yescharacteristic
378C2×C4(C22⋊D19)⋊C411yescharacteristic
379C2×C4#1059732811yescharacteristic
380C2×C4#1059733211yescharacteristic
381C2×C4C2×(C2×D19)⋊C411yescharacteristic
382C2×C4#1059738511yescharacteristic
383C8—42no—
384C8—761no—
385C8—762no—
386C8—761no—
387C8—761no—
388C8—761no—
389C22—21no—
390C22—21no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—82no—
398C22—82no—
399C22#1192642111yescharacteristic
400C22#1192680511yescharacteristic
401C22#1192681711yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—82no—
410C4—1521no—
411C4—1521no—
412C4C2×#1059726211yescharacteristic
413C4#1192656211yescharacteristic
414C2—21no—
415C2—21no—
416C2—42no—
417C2—81no—
418C2#1456393511yescharacteristic
419C2#1456412011yescharacteristic
420C2#1456414811yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1762C2
socleC22×C19#386
prime radicalC22×D4×C19D4
cosocleC2×C42×C19C23
hypercenter#1762D19
hypocenterC19#9165
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
3. #14562249C2semidirect
4. #14562133C2semidirect
5. #14561534C2semidirect
6. #14561491C2semidirect
10. #11926824C4semidirect
11. #11926824C4semidirect
12. #11926749C4semidirect
13. #11926749C4semidirect
292. C19#9165semidirect

Maximal subgroups

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

subgroupindex
#145737342
#145726702
#145622492
#145621332
#145615342
#145614912
C19×#17622
#916519