Finite Group Databasebeta

← #18077758

Subgroups — #18077758

Order 4864.

538 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574210C211yesmaximal, characteristic
2#14572379C211yesmaximal, characteristic, complemented
3#14564553C211yesmaximal, characteristic, complemented
4#14562035C211yesmaximal, characteristic, complemented
5#14561476C211yesmaximal, characteristic, complemented
6#14561471C211yesmaximal, characteristic, complemented
7C19×#1502C211yesmaximal, characteristic, complemented
8C2×#10597394—21no—
9#11927094C2211yescharacteristic
10#11926947C411yescharacteristic, complemented
11#11926920C411yescharacteristic, complemented
12#11926892C411yescharacteristic, complemented
13#11926890C411yescharacteristic, complemented
14#11926778—22no—
15C4×#64525—22no—
16#11926622—21no—
17#11926616—22no—
18D4×C19⋊C8—21no—
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20C2×#10597262—21no—
21C2×#10597262—21no—
22#11926511—21no—
23C4×#64520C2211yescharacteristic
24C2×C4×C19⋊C8C2211yescharacteristic
25#11926273—21no—
26#11926273—21no—
27C19×#532C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C4×C4⋊C4×C19C2211yescharacteristic
30C19×#327—22no—
31C2×#41×C19—21no—
32C2×#64541—21no—
33C19×C4⋊Q8C2×C411yescharacteristic
34C19×#127C2×C411yescharacteristic
35C19×#124—21no—
36C19×#121—21no—
37C19×#121D412yes—
38C4×D4×C19—21no—
39C4×D4×C19D412yes—
40C2×C4⋊C4×C19—21no—
41C2×C42×C19—21no—
42C2×C42×C19C2311yescharacteristic
43#10597394—42no—
44#10597394—42no—
45C2×#64525—22no—
46#10597376—21no—
47#10597376—21no—
48C2×#64520—22no—
49C2×#64520D411yescharacteristic
50C2×#64520D411yescharacteristic
51C22×C19⋊C8—22no—
52C22×C19⋊C8—21no—
53C22×C19⋊C8—21no—
54#10597321—21no—
55#10597320C2×C411yescharacteristic
56C4×D76—21no—
57C4×D76—21no—
58#10597315C2×C411yescharacteristic
59C19×C4⋊C8—21no—
60C19×C22⋊C8—21no—
61C4×C8×C19—21no—
62C19×#95—21no—
63#10597289—22no—
64C22⋊(C19⋊C8)—22no—
65C22⋊(C19⋊C8)—22no—
66#10597266—22no—
67#10597264—22no—
68#10597262—42no—
69#10597262—42no—
70C4⋊(C19⋊C8)—21no—
71C4⋊(C19⋊C8)D411yescharacteristic
72C4⋊(C19⋊C8)D411yescharacteristic
73#10597260—21no—
74C4×C19⋊C8—21no—
75C4×C19⋊C8—21no—
76C4×C19⋊C8C2×C411yescharacteristic
77C4×C19⋊C8C2×C411yescharacteristic
78#41×C19—41no—
79#41×C19—41no—
80#41×C19—41no—
81#41×C19—41no—
82C2×Q8×C19—21no—
83C2×D4×C19—22no—
84C2×D4×C19—21no—
85C2×D4×C19—21no—
86C2×D4×C19C22⋊C412yes—
87C22×C4×C19—22no—
88C22×C4×C19—41no—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19#4111yescharacteristic
92C2×C22⋊D19—41no—
93#64541—41no—
94#64541—41no—
95#64541—41no—
96#64541—41no—
97C2×D76—21no—
98C2×D76—21no—
99C2×D76—21no—
100C2×C4×D19—41no—
101C2×Dic38—21no—
102C2×C8×C19—41no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—22no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19C22⋊C412yes—
107C22⋊C4×C19—22no—
108C22⋊C4×C19—22no—
109C42×C19—41no—
110C42×C19—41no—
111C42×C19C22×C411yescharacteristic
112C42×C19C2×D411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C42×C19#4111yescharacteristic
115#64525—44no—
116(C2×D19)⋊C4—41no—
117(C2×D19)⋊C4—41no—
118C4⋊Dic19—21no—
119C4⋊Dic19—21no—
120#64520—21no—
121#64520—21no—
122#64520—21no—
123#64520—44no—
124#64520D812yescomplemented
125C2×C19⋊C8—21no—
126C2×C19⋊C8—21no—
127C2×C19⋊C8—21no—
128C2×C19⋊C8—21no—
129C2×C19⋊C8—21no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—44no—
132C2×C19⋊C8—42no—
133C2×C19⋊C8—41no—
134C2×C19⋊C8—41no—
135#9053—191nomaximal, Sylow
136C23×C19—22no—
137C23×C19#12111yescharacteristic
138C22×D19—41no—
139Q8×C19—41no—
140Q8×C19—41no—
141D4×C19—42no—
142D4×C19—42no—
143D4×C19—42no—
144D4×C19—41no—
145D4×C19—41no—
146D4×C19—41no—
147D4×C19—41no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—22no—
151C2×C4×C19—41no—
152C2×C4×C19—42no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19—81no—
156C2×C4×C19—81no—
157C2×C4×C19C2×C22⋊C411yescharacteristic
158C2×C4×C19C4×D411yescharacteristic
159C2×C4×C19C4×D411yescharacteristic
160C2×C4×C19#12011yescharacteristic
161C2×C4×C19#12111yescharacteristic
162C2×C4×C19#12311yescharacteristic
163C2×C4×C19C2×D811yescharacteristic
164C2×C4×C19#13511yescharacteristic
165C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
167C22⋊D19—81no—
168C22⋊D19—81no—
169C2×Dic19—41no—
170D76—42no—
171D76—41no—
172D76—41no—
173D76—41no—
174D76—41no—
175C4×D19—81no—
176C4×D19—81no—
177Dic38—41no—
178Dic38—41no—
179C8×C19—81no—
180C19⋊C8—22no—
181C19⋊C8—22no—
182C19⋊C8—41no—
183C19⋊C8—41no—
184C19⋊C8—41no—
185C19⋊C8—41no—
186#3169—191no—
187#2935—191no—
188#1980—191no—
189#1502D1911yescharacteristic, complemented
190#1480—191no—
191#1279—191no—
192#1278—191no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—42no—
196C22×C19—42no—
197C22×C19—42no—
198C22×C19#38611yescharacteristic
199C22×C19#45911yescharacteristic
200C22×C19#46311yescharacteristic
201C2×D19—81no—
202C2×D19—81no—
203C2×D19—81no—
204C4×C19—21no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—42no—
208C4×C19—82no—
209C4×C19C4×D811yescharacteristic
210C4×C19#44211yescharacteristic
211C4×C19#44311yescharacteristic
212C4×C19#44411yescharacteristic
213C4×C19#44711yescharacteristic
214C4×C19#44911yescharacteristic
215Dic19—81no—
216C2×#131—381no—
217#532—191no—
218#532C2×D1911yescharacteristic
219#500—191no—
220#493—191no—
221#486—191no—
222#486—191no—
223#466—382no—
224C4×D8—382no—
225#436—381no—
226#435—382no—
227C8×D4—381no—
228#431C2×D1911yescharacteristic
229C2×C4⋊C8—191no—
230C2×#104—381no—
231C2×#104—381no—
232#408—381no—
233C4×M16—191no—
234C2×C4×C8—191no—
235C4×C4⋊C4C2×D1911yescharacteristic
236#327—22no—
237D4⋊C8—381no—
238D4⋊C8—381no—
239C2×C19—21no—
240C2×C19—21no—
241C2×C19—82no—
242C2×C19#187611yescharacteristic
243C2×C19#187911yescharacteristic
244C2×C19#188411yescharacteristic
245D19—161no—
246C2×#41—21no—
247C2×#41—381no—
248C2×D8—382no—
249#131—762no—
250#131—762no—
251C2×M16—191no—
252C2×M16—191no—
253C2×M16—382no—
254C22×C8—382no—
255C22×C8—381no—
256C22×C8—381no—
257C4⋊Q8—191no—
258C4⋊Q8C4×D1911yescharacteristic
259#127—191no—
260#127C4×D1911yescharacteristic
261#124—21no—
262#124—381no—
263#121—21no—
264#121—381no—
265#121—381no—
266#121C22⋊D1912yes—
267C4×D4—21no—
268C4×D4—381no—
269C4×D4—381no—
270C4×D4D7612yes—
271C2×C4⋊C4—21no—
272C2×C42—21no—
273C2×C42C22×D1911yescharacteristic
274#107—382no—
275C4⋊C8—21no—
276C4⋊C8—191no—
277C4⋊C8—191no—
278C4⋊C8—381no—
279#104—762no—
280#104—762no—
281#102—382no—
282#102—382no—
283C22⋊C8—21no—
284C22⋊C8—382no—
285C22⋊C8—382no—
286#97—381no—
287C4×C8—21no—
288C4×C8—191no—
289C4×C8—191no—
290C4×C8—381no—
291C4×C8—381no—
292#95—21no—
293C19#905311yescharacteristic, complemented, Sylow
294#41—41no—
295#41—41no—
296#41—41no—
297#41—41no—
298#41—761no—
299#41—761no—
300#41—761no—
301#41—761no—
302C2×Q8—21no—
303C2×Q8—381no—
304C2×D4—22no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—381no—
308C2×D4—381no—
309C2×D4—381no—
310C2×D4—761no—
311C2×D4(C2×D19)⋊C412yes—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—761no—
315C22×C4D4×D1911yescharacteristic
316C22×C4#6454311yescharacteristic
317C22×C4C2×C22⋊D1911yescharacteristic
318D8—764no—
319M16—192no—
320M16—381no—
321M16—381no—
322M16—381no—
323M16—764no—
324C2×C8—41no—
325C2×C8—381no—
326C2×C8—381no—
327C2×C8—381no—
328C2×C8—381no—
329C2×C8—381no—
330C2×C8—381no—
331C2×C8—762no—
332C2×C8—764no—
333C2×C8—761no—
334C2×C8—761no—
335C4⋊C4—21no—
336C4⋊C4—22no—
337C4⋊C4—41no—
338C4⋊C4—381no—
339C4⋊C4—381no—
340C4⋊C4(C2×D19)⋊C412yes—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—761no—
344C22⋊C4—761no—
345C42—41no—
346C42—41no—
347C42C2×C4×D1911yescharacteristic
348C42C2×D7611yescharacteristic
349C42D4×D1911yescharacteristic
350C42#6454311yescharacteristic
351C23—22no—
352C23—761no—
353C23#1059738511yescharacteristic
354Q8—41no—
355Q8—41no—
356Q8—761no—
357Q8—761no—
358D4—42no—
359D4—42no—
360D4—42no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—41no—
365D4—762no—
366D4—761no—
367D4—761no—
368D4—761no—
369D4—761no—
370D4—1521no—
371D4—1521no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—761no—
382C2×C4—1521no—
383C2×C4—1521no—
384C2×C4(C22⋊D19)⋊C411yescharacteristic
385C2×C4(C22⋊D19)⋊C411yescharacteristic
386C2×C4#1059732811yescharacteristic
387C2×C4#1059733211yescharacteristic
388C2×C4D8×D1911yescharacteristic
389C2×C4#1059735711yescharacteristic
390C2×C4#1059736011yescharacteristic
391C2×C4#1059736211yescharacteristic
392C2×C4C2×(C2×D19)⋊C411yescharacteristic
393C2×C4#1059738511yescharacteristic
394C8—81no—
395C8—382no—
396C8—382no—
397C8—761no—
398C8—761no—
399C8—761no—
400C8—761no—
401C22—21no—
402C22—21no—
403C22—42no—
404C22—42no—
405C22—42no—
406C22—1521no—
407C22—1521no—
408C22—1521no—
409C22#1192642111yescharacteristic
410C22#1192673711yescharacteristic
411C22#1192676111yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—82no—
417C4—1521no—
418C4#1192662411yescharacteristic
419C4#1192665311yescharacteristic
420C4#1192665811yescharacteristic
421C4#1192666311yescharacteristic
422C4#1192667911yescharacteristic
423C4#1192669011yescharacteristic
424C2—21no—
425C2—21no—
426C2—82no—
427C2—3041no—
428C2#1456396011yescharacteristic
429C2#1456398111yescharacteristic
430C2#1456401611yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1502C2
socleC22×C19#386
prime radical#14574210C2
cosocleC2×C42×C19C23
hypercenter#1502D19
hypocenterC19#9053
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #14572379C2semidirect
3. #14564553C2semidirect
4. #14562035C2semidirect
5. #14561476C2semidirect
6. #14561471C2semidirect
7. C19×#1502C2semidirect
10. #11926947C4semidirect
11. #11926920C4semidirect
12. #11926892C4semidirect
13. #11926890C4semidirect
124. #64520D8semidirect
189. #1502D19semidirect
293. C19#9053semidirect

Maximal subgroups

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

subgroupindex
#145742102
#145723792
#145645532
#145620352
#145614762
#145614712
C19×#15022
#905319