Finite Group Databasebeta

← #18078622

Subgroups — #18078622

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573423C211yesmaximal, characteristic
2#14563655C211yesmaximal, characteristic
3#14562135C211yesmaximal, characteristic, complemented
4#14562091C211yesmaximal, characteristic, complemented
5#14561531C211yesmaximal, characteristic, complemented
6#14561475C211yesmaximal, characteristic, complemented
7C8×#41×C19C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926851—21no—
10#11926844—21no—
11#11926839C411yescharacteristic, complemented
12#11926834C411yescharacteristic, complemented
13#11926829C411yescharacteristic, complemented
14#11926824C411yescharacteristic, complemented
15#11926580—21no—
16#11926568C2211yescharacteristic
17C2×C4⋊(C19⋊C8)C2211yescharacteristic
18C2×#10597294—21no—
19#11926540—21no—
20C4×C4⋊Dic19C2211yescharacteristic
21#11926303—21no—
22#11926282—22no—
23#11926276—21no—
24#11926276—21no—
25C4×#41×C19C2211yescharacteristic
26C8×Q8×C19—21no—
27C8×D4×C19—22no—
28C8×D4×C19—21no—
29C19×#431—21no—
30C19×#431C2211yescharacteristic
31C2×C4×C8×C19—21no—
32C2×C4×C8×C19C2211yescharacteristic
33C2×#41×C19D411yescharacteristic
34C22×C8×C19—22no—
35C22×C8×C19—21no—
36C4×Q8×C19C2×C411yescharacteristic
37C4×Q8×C19D411yescharacteristic
38C4×D4×C19—21no—
39C4×D4×C19—21no—
40C4×D4×C19C2×C411yescharacteristic
41C4×D4×C19D411yescharacteristic
42C19×#117—21no—
43C19×#117D411yescharacteristic
44C2×C42×C19—21no—
45C2×C42×C19C2311yescharacteristic
46#10597372—21no—
47C2×C4⋊Dic19—21no—
48#10597370—21no—
49#10597370—21no—
50C2×C4×Dic19—21no—
51C2×#64520—21no—
52C22×C19⋊C8—21no—
53#10597316—21no—
54#10597315C2×C411yescharacteristic
55#10597315C2×C411yescharacteristic
56C4×Dic38—21no—
57C4×Dic38—21no—
58C19×C4⋊C8—22no—
59C19×C4⋊C8—21no—
60C19×C22⋊C8—22no—
61C19×C22⋊C8D412yes—
62C4×C8×C19—22no—
63C4×C8×C19—21no—
64C4×C8×C19—21no—
65C4×C8×C19D411yescharacteristic
66C4×C8×C19D411yescharacteristic
67#10597294—42no—
68#10597292—21no—
69#10597292—21no—
70#10597289—21no—
71#10597289—21no—
72C19⋊#95—21no—
73#10597265—21no—
74#10597265—21no—
75#10597264—21no—
76#10597264—21no—
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)—21no—
79C4⋊(C19⋊C8)—21no—
80C4⋊(C19⋊C8)C2×C411yescharacteristic
81C4⋊(C19⋊C8)C2×C411yescharacteristic
82#41×C19—21no—
83#41×C19—21no—
84#41×C19SD1612yes—
85#41×C19Q1612yes—
86C2×Q8×C19C22⋊C411yescharacteristic
87C2×D4×C19—21no—
88C2×D4×C19C22⋊C411yescharacteristic
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19#4111yescharacteristic
95C22×Dic19—41no—
96C2×Dic38—21no—
97C2×Dic38—21no—
98C2×C8×C19—21no—
99C2×C8×C19—22no—
100C2×C8×C19—21no—
101C2×C8×C19—42no—
102C2×C8×C19—44no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19C22⋊C411yescharacteristic
106C4⋊C4×C19C22⋊C411yescharacteristic
107C22⋊C4×C19—21no—
108C22⋊C4×C19—21no—
109C22⋊C4×C19—21no—
110C42×C19—21no—
111C42×C19—21no—
112C42×C19—21no—
113C42×C19C22×C411yescharacteristic
114C42×C19C2×D411yescharacteristic
115C42×C19C2×D411yescharacteristic
116C42×C19#4111yescharacteristic
117C22⋊Dic19—41no—
118C4⋊Dic19—22no—
119C4⋊Dic19—21no—
120C4⋊Dic19—21no—
121C4⋊Dic19—21no—
122C4⋊Dic19—21no—
123C4⋊Dic19—41no—
124Dic19⋊C4—41no—
125Dic19⋊C4—41no—
126C4×Dic19—41no—
127C4×Dic19—41no—
128C4×Dic19—41no—
129#64520—41no—
130#64520—41no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—21no—
133C2×C19⋊C8—41no—
134C2×C19⋊C8—41no—
135C2×C19⋊C8—41no—
136#9207—191nomaximal, Sylow
137C23×C19—21no—
138C23×C19#12111yescharacteristic
139Q8×C19—21no—
140Q8×C19#10312yes—
141D4×C19—22no—
142D4×C19—22no—
143D4×C19—21no—
144D4×C19#10312yes—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—22no—
149C2×C4×C19—22no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—41no—
153C2×C4×C19—42no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19C2×C22⋊C411yescharacteristic
157C2×C4×C19C4×D411yescharacteristic
158C2×C4×C19C4×D411yescharacteristic
159C2×C4×C19#12011yescharacteristic
160C2×C4×C19#12111yescharacteristic
161C2×C4×C19#12311yescharacteristic
162C2×C4×C19C2×SD1611yescharacteristic
163C2×C4×C19C2×Q1611yescharacteristic
164C2×C4×C19#13511yescharacteristic
165C2×C4×C19#13511yescharacteristic
166C2×Dic19—42no—
167C2×Dic19—41no—
168C2×Dic19—41no—
169C2×Dic19—81no—
170C2×Dic19—81no—
171Dic38—41no—
172Dic38—41no—
173Dic38—81no—
174C8×C19—22no—
175C8×C19—42no—
176C8×C19—41no—
177C19⋊C8—41no—
178C19⋊C8—41no—
179C19⋊C8—81no—
180#3076—191no—
181C8×#41D1911yescharacteristic
182#1806—191no—
183#1503—191no—
184#1493—191no—
185#1301—191no—
186#1279—191no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—22no—
190C22×C19—41no—
191C22×C19—41no—
192C22×C19#38611yescharacteristic
193C22×C19#46511yescharacteristic
194C22×C19#46711yescharacteristic
195C4×C19—21no—
196C4×C19—22no—
197C4×C19—21no—
198C4×C19—21no—
199C4×C19—41no—
200C4×C19—41no—
201C4×C19C2×#10311yescharacteristic
202C4×C19#41611yescharacteristic
203C4×C19#44311yescharacteristic
204C4×C19#44411yescharacteristic
205C4×C19#46511yescharacteristic
206C4×C19#46711yescharacteristic
207Dic19—82no—
208Dic19—81no—
209Dic19—81no—
210#533—191no—
211C4×#41C2×D1911yescharacteristic
212#479—381no—
213#478—381no—
214#477—191no—
215#476—191no—
216#475—191no—
217#474—191no—
218C8×Q8—21no—
219C8×D4—21no—
220C8×D4—22no—
221#431—21no—
222#431C2×D1911yescharacteristic
223#427—381no—
224#423—191no—
225C2×C4⋊C8—191no—
226C2×#104—381no—
227#416—381no—
228C2×C4×C8—21no—
229C2×C4×C8C2×D1911yescharacteristic
230C4×C4⋊C4—191no—
231#339—381no—
232#328—382no—
233Q8⋊C8—381no—
234Q8⋊C8—381no—
235C2×C19—21no—
236C2×C19—21no—
237C2×C19—42no—
238C2×C19#187611yescharacteristic
239C2×C19#189211yescharacteristic
240C2×C19#190611yescharacteristic
241C2×#41D7611yescharacteristic
242C2×M16—381no—
243C22×C8—22no—
244C22×C8—21no—
245C22×C8—381no—
246C4⋊Q8—191no—
247C4⋊Q8—191no—
248#125—381no—
249C22⋊Q8—381no—
250C22⋊Q8—381no—
251C4×Q8—381no—
252C4×Q8—381no—
253C4×Q8C4×D1911yescharacteristic
254C4×Q8C22⋊D1911yescharacteristic
255C4×D4—21no—
256C4×D4—21no—
257C4×D4C4×D1911yescharacteristic
258C4×D4C22⋊D1911yescharacteristic
259#117—21no—
260#117—381no—
261#117D7611yescharacteristic
262C2×C4⋊C4—381no—
263C2×C42—21no—
264C2×C42—381no—
265C2×C42C22×D1911yescharacteristic
266#107—381no—
267#107—381no—
268#106—381no—
269#106—381no—
270C4⋊C8—22no—
271C4⋊C8—21no—
272C4⋊C8—191no—
273C4⋊C8—191no—
274C4⋊C8—381no—
275C4⋊C8—381no—
276C4⋊C8—381no—
277#104—762no—
278#103—381no—
279#103—381no—
280#102—381no—
281#102—381no—
282C22⋊C8—22no—
283C22⋊C8C22⋊D1912yes—
284C4×C8—22no—
285C4×C8—21no—
286C4×C8—21no—
287C4×C8C22⋊D1911yescharacteristic
288C4×C8C22⋊D1911yescharacteristic
289#95—381no—
290C19#920711yescharacteristic, complemented, Sylow
291#41—21no—
292#41—21no—
293#41#6451612yes—
294#41Dic7612yes—
295C2×Q8—381no—
296C2×Q8—381no—
297C2×Q8(C2×D19)⋊C411yescharacteristic
298C2×D4—21no—
299C2×D4(C2×D19)⋊C411yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—761no—
304C22×C4C2×D7611yescharacteristic
305C22×C4#6454111yescharacteristic
306C22×C4C2×C22⋊D1911yescharacteristic
307M16—761no—
308M16—761no—
309C2×C8—21no—
310C2×C8—22no—
311C2×C8—21no—
312C2×C8—42no—
313C2×C8—44no—
314C2×C8—381no—
315C2×C8—381no—
316C2×C8—761no—
317C2×C8—761no—
318C2×C8—761no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—382no—
322C4⋊C4—381no—
323C4⋊C4—381no—
324C4⋊C4—381no—
325C4⋊C4—381no—
326C4⋊C4—761no—
327C4⋊C4—761no—
328C4⋊C4—761no—
329C4⋊C4(C2×D19)⋊C411yescharacteristic
330C4⋊C4(C2×D19)⋊C411yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—761no—
335C42—21no—
336C42—21no—
337C42—21no—
338C42—761no—
339C42—761no—
340C42—761no—
341C42C2×C4×D1911yescharacteristic
342C42#6454111yescharacteristic
343C42C2×C22⋊D1911yescharacteristic
344C42C2×C22⋊D1911yescharacteristic
345C23—21no—
346C23#1059737611yescharacteristic
347Q8—21no—
348Q8—761no—
349Q8—761no—
350Q8—1521no—
351Q8#1059727312yes—
352D4—22no—
353D4—22no—
354D4—21no—
355D4#1059727312yes—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—762no—
368C2×C4—761no—
369C2×C4—761no—
370C2×C4—1521no—
371C2×C4—1521no—
372C2×C4C2×#6451611yescharacteristic
373C2×C4#1059735011yescharacteristic
374C2×C4#1059735011yescharacteristic
375C2×C4C2×Dic7611yescharacteristic
376C2×C4C2×(C2×D19)⋊C411yescharacteristic
377C2×C4C4×C22⋊D1911yescharacteristic
378C2×C4C4×C22⋊D1911yescharacteristic
379C2×C4#1059737511yescharacteristic
380C2×C4#1059737611yescharacteristic
381C2×C4#1059739911yescharacteristic
382C8—22no—
383C8—42no—
384C8—41no—
385C8—761no—
386C8—761no—
387C8—1521no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22#1192642311yescharacteristic
394C22#1192677311yescharacteristic
395C22#1192678511yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—1522no—
403C4—1521no—
404C4—1521no—
405C4C2×#1059727311yescharacteristic
406C4#1192654111yescharacteristic
407C4#1192665911yescharacteristic
408C4#1192666411yescharacteristic
409C4#1192677311yescharacteristic
410C4#1192678511yescharacteristic
411C2—21no—
412C2—21no—
413C2—42no—
414C2#1456396211yescharacteristic
415C2#1456405811yescharacteristic
416C2#1456413611yescharacteristic
subgroupG/H
centerC2×C4#10597376
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC8×#41×C19C2
socleC22×C19#386
prime radicalC2×#41×C19D4
cosocleC2×C42×C19C23
hypercenterC8×#41D19
hypocenterC19#9207
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
3. #14562135C2semidirect
4. #14562091C2semidirect
5. #14561531C2semidirect
6. #14561475C2semidirect
11. #11926839C4semidirect
12. #11926834C4semidirect
13. #11926829C4semidirect
14. #11926824C4semidirect
290. C19#9207semidirect

Maximal subgroups

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

subgroupindex
#145734232
#145636552
#145621352
#145620912
#145615312
#145614752
C8×#41×C192
#920719