Finite Group Databasebeta

← #18077418

Subgroups — #18077418

Order 4864.

430 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573425C211yesmaximal, characteristic
2#14572300C211yesmaximal, characteristic
3#14562091C211yesmaximal, characteristic, complemented
4#14562037C211yesmaximal, characteristic, complemented
5#14562018C211yesmaximal, characteristic
6#14561532C211yesmaximal, characteristic, complemented
7C19×#1277C211yesmaximal, characteristic, complemented
8#11927101C2211yescharacteristic
9C4×#64541C2211yescharacteristic
10#11926852—21no—
11#11926845—21no—
12#11926840C411yescharacteristic
13#11926835C411yescharacteristic
14#11926830C411yescharacteristic
15#11926825C411yescharacteristic
16#11926604—22no—
17#11926600—21no—
18#11926597C2211yescharacteristic
19#11926596—21no—
20#11926582—21no—
21#11926568C2211yescharacteristic
22#11926541—21no—
23#11926510—21no—
24#11926499—21no—
25#11926276—21no—
26#11926276—22no—
27#11926274—21no—
28#11926274—21no—
29#11926273—21no—
30C2×C19×C4⋊C8C2211yescharacteristic
31C2×C19×C4⋊C8C2211yescharacteristic
32C2×C4×C8×C19C2211yescharacteristic
33C2×#64541D411yescharacteristic
34C22×C8×C19—21no—
35C22×C8×C19—21no—
36C22×C8×C19—21no—
37C2×C42×C19C2311yescharacteristic
38C4×C22⋊D19—21no—
39C4×C22⋊D19—21no—
40#10597372—21no—
41#10597372D411yescharacteristic
42#10597370—21no—
43#10597370—21no—
44C2×#64520—21no—
45C4×D76C2×C411yescharacteristic
46C4×D76D411yescharacteristic
47#10597318—21no—
48C42×D19—21no—
49#10597316—21no—
50#10597315C2×C411yescharacteristic
51#10597315C2×C411yescharacteristic
52C4×Dic38—21no—
53C4×Dic38—21no—
54C4×Dic38C2×C411yescharacteristic
55C4×Dic38D411yescharacteristic
56C19×C4⋊C8—21no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8C2×C411yescharacteristic
59C19×C4⋊C8C2×C411yescharacteristic
60C19×C4⋊C8D411yescharacteristic
61C19×C4⋊C8D411yescharacteristic
62C4×C8×C19—21no—
63C4×C8×C19—21no—
64C22⋊(C19⋊C8)—21no—
65#10597278—21no—
66#10597278—21no—
67(C2×D19)⋊C8—22no—
68(C2×D19)⋊C8—22no—
69#10597275—21no—
70#10597275—21no—
71#10597274—21no—
72#10597274—21no—
73#10597273—21no—
74#10597273—21no—
75#10597272—22no—
76C8×Dic19—22no—
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)—21no—
79C4⋊(C19⋊C8)D412yes—
80C4×C19⋊C8—21no—
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19#4111yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C2×C22⋊D19—21no—
85#64541—21no—
86#64541—21no—
87#64541—21no—
88#64541—21no—
89C2×D76C22⋊C411yescharacteristic
90C2×C4×D19—21no—
91C2×C4×D19—21no—
92C2×C4×D19—21no—
93C2×Dic38—21no—
94C2×Dic38—21no—
95C2×Dic38C22⋊C411yescharacteristic
96C2×C8×C19—22no—
97C2×C8×C19—21no—
98C2×C8×C19—21no—
99C2×C8×C19—21no—
100C2×C8×C19—21no—
101C2×C8×C19—41no—
102C2×C8×C19—41no—
103C2×C8×C19—41no—
104C2×C8×C19—41no—
105C2×C8×C19—41no—
106C2×C8×C19—41no—
107C42×C19C22×C411yescharacteristic
108C42×C19C2×D411yescharacteristic
109C42×C19C2×D411yescharacteristic
110C42×C19C2×D411yescharacteristic
111C22⋊Dic19—21no—
112C22⋊Dic19—41no—
113(C2×D19)⋊C4—21no—
114(C2×D19)⋊C4—21no—
115C4⋊Dic19—21no—
116C4⋊Dic19—21no—
117C4⋊Dic19—21no—
118C4⋊Dic19—21no—
119C4⋊Dic19C22⋊C411yescharacteristic
120C4⋊Dic19C22⋊C411yescharacteristic
121Dic19⋊C4—21no—
122Dic19⋊C4—21no—
123Dic19⋊C4—41no—
124Dic19⋊C4—41no—
125C4×Dic19—21no—
126C4×Dic19—21no—
127C4×Dic19—21no—
128C4×Dic19—41no—
129#64520—41no—
130#64520—41no—
131C2×C19⋊C8—22no—
132C2×C19⋊C8—41no—
133#8994—191nomaximal, Sylow
134C23×C19#12311yescharacteristic
135C22×D19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—41no—
139C2×C4×C19C2×C22⋊C411yescharacteristic
140C2×C4×C19C4×D411yescharacteristic
141C2×C4×C19C4×D411yescharacteristic
142C2×C4×C19#12011yescharacteristic
143C2×C4×C19#12111yescharacteristic
144C2×C4×C19#12111yescharacteristic
145C2×C4×C19#13511yescharacteristic
146C2×C4×C19#13511yescharacteristic
147C2×C4×C19#13711yescharacteristic
148C2×C4×C19#13711yescharacteristic
149C22⋊D19—41no—
150C22⋊D19—41no—
151C2×Dic19—21no—
152C2×Dic19—21no—
153C2×Dic19—21no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156D76—21no—
157D76—21no—
158C4×D19—41no—
159C4×D19—41no—
160C4×D19—41no—
161C4×D19—41no—
162C4×D19—81no—
163Dic38—21no—
164Dic38—21no—
165Dic38—42no—
166Dic38—41no—
167Dic38—41no—
168C8×C19—42no—
169C8×C19—41no—
170C8×C19—41no—
171C8×C19—41no—
172C8×C19—41no—
173C19⋊C8—42no—
174C19⋊C8—81no—
175#3076—191no—
176#2925—191no—
177#1493—191no—
178#1481—191no—
179#1476—191no—
180#1301—191no—
181#1277D1911yescharacteristic, complemented
182C22×C19—21no—
183C22×C19—21no—
184C22×C19#38611yescharacteristic
185C22×C19#48511yescharacteristic
186C22×C19#48511yescharacteristic
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—41no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19#41611yescharacteristic
194C4×C19#41911yescharacteristic
195C4×C19#44311yescharacteristic
196C4×C19#44411yescharacteristic
197C4×C19#45211yescharacteristic
198C4×C19#45211yescharacteristic
199Dic19—41no—
200Dic19—41no—
201Dic19—41no—
202Dic19—81no—
203Dic19—81no—
204#533—191no—
205C4×#41—191no—
206#479—381no—
207#478—381no—
208#477—191no—
209#476—191no—
210#475—191no—
211#474—191no—
212#433—382no—
213#432—381no—
214#431—191no—
215#431—381no—
216#427—381no—
217#423—191no—
218C2×C4⋊C8C2×D1911yescharacteristic
219C2×C4⋊C8C2×D1911yescharacteristic
220#416—381no—
221#408—381no—
222#405—381no—
223C2×C4×C8C2×D1911yescharacteristic
224Q8⋊C8—382no—
225Q8⋊C8—381no—
226Q8⋊C8—381no—
227Q8⋊C8—381no—
228D4⋊C8—381no—
229C2×C19—21no—
230C2×C19—21no—
231C2×C19#187311yescharacteristic
232C2×C19#187611yescharacteristic
233C2×C19#188111yescharacteristic
234D19—81no—
235C2×#41—191no—
236C2×M16—381no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C4⋊Q8—191no—
241C4⋊Q8—191no—
242#125—381no—
243C22⋊Q8—381no—
244C22⋊Q8—381no—
245C4×Q8—191no—
246C4×Q8—191no—
247C4×Q8—381no—
248C4×Q8—381no—
249C4×D4—191no—
250C4×D4—191no—
251C4×D4—381no—
252C4×D4—381no—
253#117—191no—
254#117—381no—
255#117—381no—
256C2×C42—381no—
257C2×C42C22×D1911yescharacteristic
258#107—381no—
259#107—381no—
260#106—381no—
261#106—381no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—192no—
265C4⋊C8—381no—
266C4⋊C8—381no—
267C4⋊C8C4×D1911yescharacteristic
268C4⋊C8C4×D1911yescharacteristic
269C4⋊C8D7611yescharacteristic
270C4⋊C8D7611yescharacteristic
271#103—381no—
272#103—381no—
273#102—381no—
274#102—381no—
275C22⋊C8—382no—
276C22⋊C8—382no—
277C22⋊C8—381no—
278#97—382no—
279C4×C8—21no—
280C4×C8—21no—
281C4×C8—382no—
282C4×C8—381no—
283C19#899411yescharacteristic, complemented, Sylow
284#41—381no—
285#41—381no—
286#41—381no—
287#41—381no—
288C2×Q8—191no—
289C2×Q8—381no—
290C2×Q8—381no—
291C2×D4—191no—
292C2×D4—381no—
293C22×C4—381no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4#6454111yescharacteristic
297C22×C4D4×D1911yescharacteristic
298C22×C4#6454511yescharacteristic
299M16—761no—
300M16—761no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—382no—
313C2×C8—761no—
314C4⋊C4—191no—
315C4⋊C4—191no—
316C4⋊C4—381no—
317C4⋊C4—381no—
318C4⋊C4—381no—
319C4⋊C4—381no—
320C4⋊C4—381no—
321C4⋊C4—381no—
322C4⋊C4—761no—
323C4⋊C4—761no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C22⋊C4—381no—
327C22⋊C4—761no—
328C42—381no—
329C42—381no—
330C42—381no—
331C42—761no—
332C42C2×C4×D1911yescharacteristic
333C42C2×D7611yescharacteristic
334C42D4×D1911yescharacteristic
335C42D4×D1911yescharacteristic
336C23—381no—
337C23#1059734011yescharacteristic
338Q8—381no—
339Q8—381no—
340Q8—762no—
341Q8—761no—
342Q8—761no—
343D4—381no—
344D4—381no—
345D4—761no—
346D4—761no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—381no—
351C2×C4—381no—
352C2×C4—381no—
353C2×C4—761no—
354C2×C4—761no—
355C2×C4—761no—
356C2×C4—761no—
357C2×C4—761no—
358C2×C4—761no—
359C2×C4—1521no—
360C2×C4C4×D7611yescharacteristic
361C2×C4C22⋊C4×D1911yescharacteristic
362C2×C4#1059732811yescharacteristic
363C2×C4#1059733011yescharacteristic
364C2×C4#1059733911yescharacteristic
365C2×C4#1059734111yescharacteristic
366C2×C4#1059735811yescharacteristic
367C2×C4#1059736111yescharacteristic
368C2×C4#1059736211yescharacteristic
369C2×C4#1059736411yescharacteristic
370C8—42no—
371C8—41no—
372C8—41no—
373C8—41no—
374C8—41no—
375C8—762no—
376C8—1521no—
377C22—21no—
378C22—21no—
379C22—761no—
380C22—761no—
381C22—761no—
382C22#1192642211yescharacteristic
383C22#1192688711yescharacteristic
384C22#1192688811yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—761no—
389C4—761no—
390C4—761no—
391C4—1521no—
392C4—1521no—
393C4#1192653711yescharacteristic
394C4#1192655111yescharacteristic
395C4#1192666211yescharacteristic
396C4#1192666711yescharacteristic
397C4#1192670711yescharacteristic
398C4#1192670911yescharacteristic
399C2—21no—
400C2—21no—
401C2—1521no—
402C2#1456394611yescharacteristic
403C2#1456396111yescharacteristic
404C2#1456399811yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1277C2
socleC22×C19#386
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1277D19
hypocenterC19#8994
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
3. #14562091C2semidirect
4. #14562037C2semidirect
6. #14561532C2semidirect
7. C19×#1277C2semidirect
181. #1277D19semidirect
283. C19#8994semidirect

Maximal subgroups

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

subgroupindex
#145734252
#145723002
#145620912
#145620372
#145620182
#145615322
C19×#12772
#899419