Finite Group Databasebeta

← #18077757

Subgroups — #18077757

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#14572381C211yesmaximal, characteristic, complemented
3#14562129C211yesmaximal, characteristic, complemented
4#14562034C211yesmaximal, characteristic, complemented
5#14561476C211yesmaximal, characteristic, complemented
6#14561473C211yesmaximal, characteristic, complemented
7C19×#1980C211yesmaximal, characteristic, complemented
8C2×#10597353—21no—
9#11927094C2211yescharacteristic
10#11926947C411yescharacteristic, complemented
11#11926920C411yescharacteristic, complemented
12#11926892C411yescharacteristic, complemented
13#11926890C411yescharacteristic, complemented
14#11926778—22no—
15C4×#64525—22no—
16#11926623—21no—
17#11926617—22no—
18C8×D76—21no—
19#11926597C2211yescharacteristic
20C2×C4⋊(C19⋊C8)C2211yescharacteristic
21#11926512—21no—
22C2×C4×C19⋊C8C2211yescharacteristic
23#11926277—22no—
24D4⋊(C19⋊C8)—21no—
25D4⋊(C19⋊C8)—21no—
26C19×#532C2211yescharacteristic
27C2×C19×#104—21no—
28C2×C19×#104—21no—
29C4×M16×C19C2211yescharacteristic
30C4×C4⋊C4×C19C2211yescharacteristic
31C2×#41×C19—21no—
32C2×#64541—21no—
33C2×M16×C19D411yescharacteristic
34C2×M16×C19D411yescharacteristic
35C19×C4⋊Q8C2×C411yescharacteristic
36C19×#127C2×C411yescharacteristic
37C19×#124—21no—
38C19×#121—21no—
39C19×#121—21no—
40C4×D4×C19—21no—
41C4×D4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C42×C19—21no—
44C2×C42×C19C2311yescharacteristic
45C2×#64525—22no—
46#10597376—21no—
47#10597376D412yes—
48C22×C19⋊C8—21no—
49C22×C19⋊C8—21no—
50#10597353—42no—
51#10597353—42no—
52C2×#64515—22no—
53C2×C8×D19—22no—
54#10597321—21no—
55#10597320C2×C411yescharacteristic
56C4×D76—21no—
57C4×D76D412yes—
58#10597315C2×C411yescharacteristic
59C19×#104—42no—
60C19×#104—42no—
61C19×#97—21no—
62C4×C8×C19—21no—
63C19×#95—21no—
64#10597289—22no—
65C22⋊(C19⋊C8)—21no—
66(C2×D19)⋊C8—22no—
67(C2×D19)⋊C8—22no—
68#10597266—22no—
69#10597264—22no—
70C4⋊(C19⋊C8)—21no—
71C4⋊(C19⋊C8)—21no—
72C4⋊(C19⋊C8)D411yescharacteristic
73C4⋊(C19⋊C8)D411yescharacteristic
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—21no—
84C2×D4×C19—21no—
85C2×D4×C19—21no—
86C2×D4×C19—41no—
87C22×C4×C19—41no—
88C22×C4×C19—41no—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19#4111yescharacteristic
92C2×C22⋊D19—22no—
93#64541—41no—
94#64541—41no—
95#64541—41no—
96#64541—41no—
97C2×D76—21no—
98C2×D76—21no—
99C2×D76C22⋊C412yes—
100C2×C4×D19—22no—
101C2×Dic38—21no—
102M16×C19—21no—
103M16×C19—21no—
104M16×C19—21no—
105M16×C19D812yescomplemented
106C2×C8×C19—21no—
107C2×C8×C19—21no—
108C4⋊C4×C19—22no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—41no—
112C22⋊C4×C19—41no—
113C22⋊C4×C19—41no—
114C42×C19—41no—
115C42×C19—41no—
116C42×C19C22×C411yescharacteristic
117C42×C19C2×D411yescharacteristic
118C42×C19C2×D411yescharacteristic
119C42×C19#4111yescharacteristic
120#64525—44no—
121(C2×D19)⋊C4—22no—
122(C2×D19)⋊C4—22no—
123C4⋊Dic19—21no—
124C4⋊Dic19C22⋊C412yes—
125C2×C19⋊C8—21no—
126C2×C19⋊C8—21no—
127C2×C19⋊C8—21no—
128C2×C19⋊C8—21no—
129C2×C19⋊C8—42no—
130C2×C19⋊C8—41no—
131C2×C19⋊C8—41no—
132C2×C19⋊C8—41no—
133#64515—44no—
134C8×D19—44no—
135#9053—191nomaximal, Sylow
136C23×C19—41no—
137C23×C19#12111yescharacteristic
138C22×D19—22no—
139Q8×C19—41no—
140Q8×C19—41no—
141D4×C19—42no—
142D4×C19—41no—
143D4×C19—41no—
144D4×C19—41no—
145D4×C19—41no—
146D4×C19—81no—
147D4×C19—81no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—41no—
151C2×C4×C19—42no—
152C2×C4×C19—41no—
153C2×C4×C19—81no—
154C2×C4×C19—81no—
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—42no—
168C22⋊D19—42no—
169C2×Dic19—22no—
170D76—42no—
171D76—41no—
172D76—41no—
173D76—41no—
174D76—41no—
175C4×D19—42no—
176C4×D19—42no—
177Dic38—41no—
178Dic38—41no—
179C8×C19—22no—
180C8×C19—41no—
181C19⋊C8—22no—
182C19⋊C8—41no—
183C19⋊C8—41no—
184C19⋊C8—41no—
185C19⋊C8—81no—
186#3169—191no—
187#2935—191no—
188#1980D1911yescharacteristic, complemented
189#1502—191no—
190#1480—191no—
191#1279—191no—
192#1278—191no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—81no—
196C22×C19—81no—
197C22×C19—81no—
198C22×C19#38611yescharacteristic
199C22×C19#45911yescharacteristic
200C22×C19#46311yescharacteristic
201C2×D19—42no—
202C2×D19—42no—
203C2×D19—42no—
204C4×C19—21no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—82no—
208C4×C19—81no—
209C4×C19C4×D811yescharacteristic
210C4×C19#44211yescharacteristic
211C4×C19#44311yescharacteristic
212C4×C19#44411yescharacteristic
213C4×C19#44711yescharacteristic
214C4×C19#44911yescharacteristic
215Dic19—42no—
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#431—191no—
229C2×C4⋊C8—191no—
230C2×#104—21no—
231C2×#104—21no—
232#408—381no—
233C4×M16C2×D1911yescharacteristic
234C2×C4×C8—191no—
235C4×C4⋊C4C2×D1911yescharacteristic
236#327—382no—
237D4⋊C8—381no—
238D4⋊C8—381no—
239C2×C19—21no—
240C2×C19—21no—
241C2×C19—161no—
242C2×C19#187611yescharacteristic
243C2×C19#187911yescharacteristic
244C2×C19#188411yescharacteristic
245D19—82no—
246C2×#41—21no—
247C2×#41—381no—
248C2×D8—382no—
249#131—762no—
250#131—762no—
251C2×M16—382no—
252C2×M16C22⋊D1911yescharacteristic
253C2×M16C22⋊D1911yescharacteristic
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—21no—
265#121—192no—
266#121—381no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—192no—
270C4×D4—381no—
271C2×C4⋊C4—21no—
272C2×C42—21no—
273C2×C42C22×D1911yescharacteristic
274#107—382no—
275C4⋊C8—191no—
276C4⋊C8—191no—
277C4⋊C8—381no—
278C4⋊C8—381no—
279#104—42no—
280#104—42no—
281#102—382no—
282#102—382no—
283C22⋊C8—382no—
284C22⋊C8—382no—
285C22⋊C8—381no—
286#97—21no—
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—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—41no—
308C2×D4—192no—
309C2×D4—382no—
310C2×D4—381no—
311C2×D4—381no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—382no—
315C22×C4D4×D1911yescharacteristic
316C22×C4#6454311yescharacteristic
317C22×C4C2×C22⋊D1911yescharacteristic
318D8—764no—
319M16—21no—
320M16—21no—
321M16—21no—
322M16—764no—
323M16#6452512yescomplemented
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—381no—
327C2×C8—381no—
328C2×C8—381no—
329C2×C8—381no—
330C2×C8—764no—
331C2×C8—762no—
332C2×C8—761no—
333C2×C8—761no—
334C2×C8—761no—
335C4⋊C4—22no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—41no—
339C4⋊C4—192no—
340C4⋊C4—381no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—382no—
344C22⋊C4—382no—
345C42—41no—
346C42—41no—
347C42C2×C4×D1911yescharacteristic
348C42#6454111yescharacteristic
349C42D4×D1911yescharacteristic
350C42D4×D1911yescharacteristic
351C23—41no—
352C23—382no—
353C23#1059738411yescharacteristic
354Q8—41no—
355Q8—41no—
356Q8—761no—
357Q8—761no—
358D4—42no—
359D4—41no—
360D4—41no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—81no—
365D4—762no—
366D4—762no—
367D4—762no—
368D4—761no—
369D4—761no—
370D4—761no—
371D4—761no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—382no—
382C2×C4—762no—
383C2×C4—762no—
384C2×C4C22⋊C4×D1911yescharacteristic
385C2×C4(C22⋊D19)⋊C411yescharacteristic
386C2×C4#1059732911yescharacteristic
387C2×C4#1059733011yescharacteristic
388C2×C4C4×C22⋊D1911yescharacteristic
389C2×C4C2×#6452511yescharacteristic
390C2×C4#1059737811yescharacteristic
391C2×C4#1059738311yescharacteristic
392C2×C4#1059739511yescharacteristic
393C2×C4#1059739611yescharacteristic
394C8—22no—
395C8—41no—
396C8—382no—
397C8—761no—
398C8—761no—
399C8—761no—
400C8—1521no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—762no—
407C22—762no—
408C22—762no—
409C22#1192642011yescharacteristic
410C22#1192673611yescharacteristic
411C22#1192675611yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—82no—
416C4—81no—
417C4—762no—
418C4C4×#6452511yescharacteristic
419C4#1192665411yescharacteristic
420C4#1192665811yescharacteristic
421C4#1192666311yescharacteristic
422C4#1192667711yescharacteristic
423C4#1192668711yescharacteristic
424C2—21no—
425C2—21no—
426C2—161no—
427C2—1522no—
428C2#1456395911yescharacteristic
429C2#1456398611yescharacteristic
430C2#1456401511yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1980C2
socleC22×C19#386
prime radical#14574210C2
cosocleC2×C42×C19C23
hypercenter#1980D19
hypocenterC19#9053
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. #14572381C2semidirect
3. #14562129C2semidirect
4. #14562034C2semidirect
5. #14561476C2semidirect
6. #14561473C2semidirect
7. C19×#1980C2semidirect
10. #11926947C4semidirect
11. #11926920C4semidirect
12. #11926892C4semidirect
13. #11926890C4semidirect
105. M16×C19D8semidirect
188. #1980D19semidirect
293. C19#9053semidirect
323. M16#64525semidirect

Maximal subgroups

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

subgroupindex
#145742102
#145723812
#145621292
#145620342
#145614762
#145614732
C19×#19802
#905319