Finite Group Databasebeta

← #18078650

Subgroups — #18078650

Order 4864.

536 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573695C211yesmaximal, characteristic
2#14562226C211yesmaximal, characteristic, complemented
3#14562087C211yesmaximal, characteristic, complemented
4#14562074C211yesmaximal, characteristic, complemented
5#14561525C211yesmaximal, characteristic, complemented
6#14561472C211yesmaximal, characteristic, complemented
7C4×C19×#131C211yesmaximal, characteristic, complemented
8#11927094C2211yescharacteristic
9#11926868—21no—
10#11926839C411yescharacteristic
11#11926834C411yescharacteristic
12#11926744C411yescharacteristic
13#11926739C411yescharacteristic
14#11926689—21no—
15C4×#64527—21no—
16C4×#64525—21no—
17#11926597C2211yescharacteristic
18#11926568C2211yescharacteristic
19C4×#64520C2211yescharacteristic
20#11926283—22no—
21Q8⋊(C19⋊C8)—21no—
22#11926273—21no—
23#11926273—21no—
24D4⋊(C19⋊C8)—21no—
25C2×C19×#131—21no—
26C4×#41×C19C2211yescharacteristic
27C19×#405—22no—
28C19×#405—21no—
29C4×M16×C19—21no—
30C4×M16×C19C2211yescharacteristic
31C2×C4×C8×C19—21no—
32C2×C4×C8×C19C2211yescharacteristic
33C2×#41×C19D411yescharacteristic
34C2×#64541—21no—
35C19×#131—24no—
36C19×#131—24no—
37C2×M16×C19—22no—
38C2×M16×C19—21no—
39C22×C8×C19—22no—
40C22×C8×C19—21no—
41C4×Q8×C19C2×C411yescharacteristic
42C4×Q8×C19D411yescharacteristic
43C4×D4×C19—21no—
44C4×D4×C19—21no—
45C4×D4×C19C2×C411yescharacteristic
46C4×D4×C19D411yescharacteristic
47C19×#117—21no—
48C19×#117D411yescharacteristic
49C2×C42×C19—21no—
50C2×C42×C19C2311yescharacteristic
51C2×#64527—21no—
52C2×#64525—21no—
53#10597376—21no—
54#10597376—21no—
55C2×#64520—21no—
56C2×#64520—21no—
57#10597321—21no—
58#10597320C2×C411yescharacteristic
59C4×D76—21no—
60C4×D76—21no—
61#10597315C2×C411yescharacteristic
62C19×#97—22no—
63C19×#97D412yes—
64C4×C8×C19—22no—
65C4×C8×C19—21no—
66C4×C8×C19—21no—
67C4×C8×C19D411yescharacteristic
68C4×C8×C19D411yescharacteristic
69#10597292—21no—
70#10597289—21no—
71C22⋊(C19⋊C8)—21no—
72#10597266—21no—
73#10597266—21no—
74#10597265—21no—
75#10597264—21no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)C2×C411yescharacteristic
79C4⋊(C19⋊C8)C2×C411yescharacteristic
80#10597260—21no—
81C4×C19⋊C8—21no—
82C4×C19⋊C8—21no—
83#41×C19—22no—
84#41×C19—22no—
85C2×Q8×C19C22⋊C411yescharacteristic
86C2×D4×C19—21no—
87C2×D4×C19C22⋊C411yescharacteristic
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19#4111yescharacteristic
93C22×C4×C19#4111yescharacteristic
94C2×C22⋊D19—41no—
95#64541—81no—
96#64541—81no—
97C2×D76—21no—
98C2×D76—21no—
99C2×D76—21no—
100C2×C4×D19—41no—
101C2×Dic38—21no—
102M16×C19—28no—
103M16×C19—22no—
104M16×C19—22no—
105C2×C8×C19—28no—
106C2×C8×C19—22no—
107C2×C8×C19—22no—
108C2×C8×C19—21no—
109C2×C8×C19—22no—
110C2×C8×C19—21no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—21no—
113C4⋊C4×C19C22⋊C411yescharacteristic
114C4⋊C4×C19C22⋊C411yescharacteristic
115C22⋊C4×C19—21no—
116C22⋊C4×C19—21no—
117C22⋊C4×C19—21no—
118C42×C19—21no—
119C42×C19—21no—
120C42×C19—21no—
121C42×C19C22×C411yescharacteristic
122C42×C19C2×D411yescharacteristic
123C42×C19C2×D411yescharacteristic
124C42×C19C2×D411yescharacteristic
125#64527—42no—
126#64525—42no—
127(C2×D19)⋊C4—41no—
128(C2×D19)⋊C4—41no—
129C4⋊Dic19—21no—
130C4⋊Dic19—21no—
131#64520—22no—
132#64520—41no—
133#64520—81no—
134C2×C19⋊C8—21no—
135C2×C19⋊C8—21no—
136C2×C19⋊C8—41no—
137C2×C19⋊C8—41no—
138#9211—191nomaximal, Sylow
139C23×C19—21no—
140C23×C19#12311yescharacteristic
141C22×D19—41no—
142Q8×C19—21no—
143Q8×C19#10412yes—
144D4×C19—24no—
145D4×C19—21no—
146D4×C19#10412yes—
147C2×C4×C19—24no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
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#12111yescharacteristic
167C22⋊D19—82no—
168C2×Dic19—41no—
169D76—41no—
170D76—41no—
171D76—41no—
172D76—41no—
173D76—81no—
174C4×D19—81no—
175C4×D19—81no—
176Dic38—81no—
177C8×C19—22no—
178C8×C19—24no—
179C8×C19—22no—
180C19⋊C8—42no—
181C19⋊C8—41no—
182C19⋊C8—41no—
183C19⋊C8—81no—
184#3106—191no—
185C4×#131D1911yescharacteristic, complemented
186#1525—191no—
187#1492—191no—
188#1489—191no—
189#1299—191no—
190#1278—191no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19—22no—
194C22×C19—21no—
195C22×C19—41no—
196C22×C19—41no—
197C22×C19#38611yescharacteristic
198C2×D19—81no—
199C2×D19—81no—
200C2×D19—81no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—22no—
204C4×C19—21no—
205C4×C19—41no—
206C4×C19—41no—
207C4×C19C2×#10411yescharacteristic
208C4×C19C2×#10411yescharacteristic
209C4×C19#44311yescharacteristic
210C4×C19#44411yescharacteristic
211C4×C19#47111yescharacteristic
212C4×C19#47211yescharacteristic
213Dic19—81no—
214C2×#131—21no—
215#532—191no—
216C4×#41C2×D1911yescharacteristic
217#482—381no—
218#477—191no—
219#476—191no—
220#460—191no—
221#459—191no—
222#449—381no—
223C4×SD16—381no—
224C4×D8—381no—
225#431—191no—
226#423—191no—
227#405—21no—
228#405—22no—
229C4×M16—21no—
230C4×M16—191no—
231C4×M16C2×D1911yescharacteristic
232C2×C4×C8—21no—
233C2×C4×C8C2×D1911yescharacteristic
234#329—382no—
235Q8⋊C8—381no—
236D4⋊C8—381no—
237D4⋊C8—381no—
238D4⋊C8—381no—
239C2×C19—41no—
240C2×C19—42no—
241C2×C19#187611yescharacteristic
242C2×C19#189611yescharacteristic
243C2×C19#190711yescharacteristic
244D19—161no—
245C2×#41—381no—
246C2×#41C22⋊D1911yescharacteristic
247C2×SD16—381no—
248C2×D8—381no—
249#131—24no—
250#131—24no—
251C2×M16—22no—
252C2×M16—21no—
253C2×M16—381no—
254C2×M16—381no—
255C22×C8—22no—
256C22×C8—21no—
257C4⋊Q8—191no—
258#127—191no—
259#124—381no—
260#121—381no—
261#121—381no—
262C4×Q8C4×D1911yescharacteristic
263C4×Q8D7611yescharacteristic
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—381no—
267C4×D4—381no—
268C4×D4C4×D1911yescharacteristic
269C4×D4D7611yescharacteristic
270#117—21no—
271#117C22⋊D1911yescharacteristic
272C2×C42—21no—
273C2×C42C22×D1911yescharacteristic
274#107—381no—
275#106—381no—
276C4⋊C8—191no—
277C4⋊C8—191no—
278C4⋊C8—381no—
279C4⋊C8—381no—
280#103—381no—
281#102—381no—
282#102—381no—
283#102—381no—
284C22⋊C8—381no—
285#97—22no—
286#97—381no—
287#97C22⋊D1912yes—
288C4×C8—22no—
289C4×C8—21no—
290C4×C8—21no—
291C4×C8—381no—
292C4×C8—381no—
293C4×C8C22⋊D1911yescharacteristic
294C4×C8C22⋊D1911yescharacteristic
295C19#921111yescharacteristic, complemented, Sylow
296#41—22no—
297#41—22no—
298#41—1521no—
299#41—1521no—
300C2×Q8—381no—
301C2×Q8(C2×D19)⋊C411yescharacteristic
302C2×D4—21no—
303C2×D4—381no—
304C2×D4—381no—
305C2×D4—381no—
306C2×D4—761no—
307C2×D4(C2×D19)⋊C411yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—761no—
312C22×C4#6454111yescharacteristic
313C22×C4#6454111yescharacteristic
314C22×C4C2×C22⋊D1911yescharacteristic
315SD16—762no—
316D8—762no—
317M16—28no—
318M16—22no—
319M16—22no—
320M16—382no—
321M16—761no—
322M16—1521no—
323C2×C8—28no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—381no—
330C2×C8—381no—
331C2×C8—761no—
332C2×C8—761no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—381no—
336C4⋊C4—381no—
337C4⋊C4(C2×D19)⋊C411yescharacteristic
338C4⋊C4(C2×D19)⋊C411yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—761no—
343C22⋊C4—761no—
344C42—21no—
345C42—21no—
346C42—21no—
347C42C2×C4×D1911yescharacteristic
348C42C2×D7611yescharacteristic
349C42C2×C22⋊D1911yescharacteristic
350C42C2×C22⋊D1911yescharacteristic
351C23—21no—
352C23—761no—
353C23#1059737511yescharacteristic
354Q8—21no—
355Q8—1521no—
356Q8#1059726212yes—
357D4—24no—
358D4—21no—
359D4—761no—
360D4—761no—
361D4—761no—
362D4—761no—
363D4—1521no—
364D4—1522no—
365D4#1059726212yes—
366C2×C4—24no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—761no—
381C2×C4—1521no—
382C2×C4—1521no—
383C2×C4C2×(C2×D19)⋊C411yescharacteristic
384C2×C4C4×C22⋊D1911yescharacteristic
385C2×C4C4×C22⋊D1911yescharacteristic
386C2×C4#1059737611yescharacteristic
387C2×C4#1059737611yescharacteristic
388C2×C4#1059739911yescharacteristic
389C8—22no—
390C8—24no—
391C8—22no—
392C8—762no—
393C8—761no—
394C8—761no—
395C8—1521no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—1521no—
403C22—1521no—
404C22—1521no—
405C22#1192642311yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—22no—
410C4—41no—
411C4—41no—
412C4—1521no—
413C4C2×#1059726211yescharacteristic
414C4C2×#1059726211yescharacteristic
415C4#1192665911yescharacteristic
416C4#1192666411yescharacteristic
417C4#1192680711yescharacteristic
418C4#1192681411yescharacteristic
419C2—41no—
420C2—42no—
421C2—3041no—
422C2#1456396211yescharacteristic
423C2#1456407811yescharacteristic
424C2#1456414311yescharacteristic
subgroupG/H
centerC2×C4#10597376
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC4×C19×#131C2
socleC22×C19#386
prime radical#14573695C2
cosocleC2×C42×C19C23
hypercenterC4×#131D19
hypocenterC19#9211
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
2. #14562226C2semidirect
3. #14562087C2semidirect
4. #14562074C2semidirect
5. #14561525C2semidirect
6. #14561472C2semidirect
7. C4×C19×#131C2semidirect
185. C4×#131D19semidirect
295. C19#9211semidirect

Maximal subgroups

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

subgroupindex
#145736952
#145622262
#145620872
#145620742
#145615252
#145614722
C4×C19×#1312
#921119