Finite Group Databasebeta

← #18078371

Subgroups — #18078371

Order 4864.

458 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572724C211yesmaximal, characteristic, complemented
2#14563465C211yesmaximal, characteristic, complemented
3#14562246C211yesmaximal, characteristic
4#14562130C211yesmaximal, characteristic
5#14561533C211yesmaximal, characteristic, complemented
6#14561492C211yesmaximal, characteristic, complemented
7C19×#3112C211yesmaximal, characteristic
8#11926675—22no—
9#11926675—21no—
10Q8×C19⋊C8—21no—
11#11926601—21no—
12#11926601C2211yescharacteristic
13#11926597—21no—
14#11926597C2211yescharacteristic
15C2×#10597292—21no—
16C2×#10597260C2211yescharacteristic
17C4×C4⋊Dic19C2211yescharacteristic
18#11926306—21no—
19#11926284—22no—
20#11926278—21no—
21#11926278—21no—
22C19×#532C2211yescharacteristic
23C2×C4×Q8×C19C2211yescharacteristic
24C19×#480—21no—
25C19×#477C411yescharacteristic, complemented
26C19×#477C411yescharacteristic, complemented
27C19×#460C411yescharacteristic, complemented
28C19×#460C411yescharacteristic, complemented
29C19×#448—21no—
30C19×#440—21no—
31C19×#440—21no—
32C19×#432C2211yescharacteristic
33C2×#41×C19—21no—
34C22×Q8×C19D411yescharacteristic
35C2×SD16×C19—21no—
36C2×SD16×C19—21no—
37C19×C4⋊Q8C2×C411yescharacteristic
38C19×#127C2×C411yescharacteristic
39C19×#124—21no—
40C19×#121—21no—
41C19×#121—21no—
42C4×Q8×C19—21no—
43C4×Q8×C19—21no—
44C4×Q8×C19C2×C411yescharacteristic
45C4×Q8×C19C2×C411yescharacteristic
46C4×Q8×C19D411yescharacteristic
47C4×Q8×C19D411yescharacteristic
48C4×D4×C19—21no—
49C4×D4×C19—21no—
50C2×C4⋊C4×C19—21no—
51C2×C4⋊C4×C19D411yescharacteristic
52C2×C42×C19—21no—
53C2×C42×C19C2311yescharacteristic
54C2×C4⋊Dic19—21no—
55C2×C4×Dic19—21no—
56C22×C19⋊C8—21no—
57C19×#107—21no—
58C19×#107—21no—
59C19×C4⋊C8C2×C411yescharacteristic
60C19×C4⋊C8C2×C411yescharacteristic
61C19×#103—21no—
62C19×#103—21no—
63C19×#102—21no—
64C19×#102—21no—
65C19×C22⋊C8—21no—
66C19×#97—21no—
67#10597292—24no—
68C19⋊#95—21no—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)D411yescharacteristic
71C22⋊(C19⋊C8)D411yescharacteristic
72C4⋊(C19⋊C8)—22no—
73C4⋊(C19⋊C8)—22no—
74C4⋊(C19⋊C8)—21no—
75C4⋊(C19⋊C8)—21no—
76#10597260—22no—
77#10597260—21no—
78#10597260—21no—
79#10597260D412yes—
80C4×C19⋊C8—22no—
81C4×C19⋊C8—21no—
82#41×C19—81no—
83#41×C19—81no—
84C2×Q8×C19—21no—
85C2×Q8×C19—22no—
86C2×Q8×C19—21no—
87C2×Q8×C19—41no—
88C2×Q8×C19C22⋊C411yescharacteristic
89C2×Q8×C19C22⋊C411yescharacteristic
90C2×D4×C19—21no—
91C2×D4×C19—21no—
92C2×D4×C19—21no—
93C2×D4×C19—41no—
94C22×C4×C19—21no—
95C22×C4×C19—21no—
96C22×C4×C19—41no—
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19#4111yescharacteristic
100C22×Dic19—41no—
101SD16×C19—42no—
102SD16×C19—42no—
103C2×C8×C19—21no—
104C2×C8×C19—21no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19C22⋊C411yescharacteristic
113C4⋊C4×C19C22⋊C411yescharacteristic
114C22⋊C4×C19—41no—
115C22⋊C4×C19—41no—
116C42×C19—21no—
117C42×C19—21no—
118C42×C19—21no—
119C42×C19—21no—
120C42×C19C22×C411yescharacteristic
121C42×C19C2×D411yescharacteristic
122C42×C19C2×D411yescharacteristic
123C42×C19#4111yescharacteristic
124C4⋊Dic19—22no—
125C4⋊Dic19—41no—
126C4×Dic19—81no—
127C2×C19⋊C8—22no—
128C2×C19⋊C8—21no—
129C2×C19⋊C8—21no—
130C2×C19⋊C8—22no—
131C2×C19⋊C8—41no—
132C2×C19⋊C8—41no—
133#9164—191nomaximal, Sylow
134C23×C19—41no—
135C23×C19#12111yescharacteristic
136Q8×C19—21no—
137Q8×C19—21no—
138Q8×C19—21no—
139Q8×C19—42no—
140Q8×C19—81no—
141Q8×C19#10412yes—
142D4×C19—41no—
143D4×C19—41no—
144D4×C19—81no—
145D4×C19—81no—
146D4×C19—81no—
147D4×C19—81no—
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—41no—
157C2×C4×C19—42no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—82no—
162C2×C4×C19C2×C22⋊C411yescharacteristic
163C2×C4×C19C4×D411yescharacteristic
164C2×C4×C19C4×D411yescharacteristic
165C2×C4×C19#12011yescharacteristic
166C2×C4×C19#12111yescharacteristic
167C2×C4×C19#12311yescharacteristic
168C2×Dic19—42no—
169C2×Dic19—81no—
170C2×Dic19—81no—
171C8×C19—41no—
172C8×C19—41no—
173C19⋊C8—41no—
174C19⋊C8—41no—
175C19⋊C8—42no—
176C19⋊C8—42no—
177#3112D1911yescharacteristic
178#2984—191no—
179#1763—191no—
180#1530—191no—
181#1502—191no—
182#1302—191no—
183#1285—191no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19—81no—
187C22×C19—81no—
188C22×C19—81no—
189C22×C19#38611yescharacteristic
190C22×C19#47111yescharacteristic
191C22×C19#47211yescharacteristic
192C4×C19—21no—
193C4×C19—22no—
194C4×C19—21no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—41no—
199C4×C19—41no—
200C4×C19—41no—
201C4×C19—81no—
202C4×C19C2×#10411yescharacteristic
203C4×C19#42111yescharacteristic
204Dic19—82no—
205#532C2×D1911yescharacteristic
206C2×C4×Q8C2×D1911yescharacteristic
207#480—21no—
208#477Dic1911yescharacteristic, complemented
209#477Dic1911yescharacteristic, complemented
210#460Dic1911yescharacteristic, complemented
211#460Dic1911yescharacteristic, complemented
212#448—21no—
213#446—382no—
214#446—381no—
215C8×Q8—381no—
216#440—21no—
217#440—21no—
218#432—191no—
219#432—381no—
220#432C2×D1911yescharacteristic
221#431—191no—
222#431—381no—
223C2×#103—381no—
224C2×#97—191no—
225C4×C4⋊C4—191no—
226#340—381no—
227#329—382no—
228#327—381no—
229#327—381no—
230C2×C19—21no—
231C2×C19—21no—
232C2×C19—161no—
233C2×C19#187111yescharacteristic
234C2×C19#190511yescharacteristic
235C2×C19#190711yescharacteristic
236C2×#41—21no—
237C22×Q8C22⋊D1911yescharacteristic
238C2×SD16—21no—
239C2×SD16—21no—
240C22×C8—381no—
241C4⋊Q8C2×Dic1911yescharacteristic
242#127C2×Dic1911yescharacteristic
243#124—21no—
244#121—21no—
245#121—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8C2×Dic1911yescharacteristic
249C4×Q8C2×Dic1911yescharacteristic
250C4×Q8C22⋊D1911yescharacteristic
251C4×Q8C22⋊D1911yescharacteristic
252C4×D4—21no—
253C4×D4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—381no—
256C2×C4⋊C4C22⋊D1911yescharacteristic
257C2×C42—21no—
258C2×C42—381no—
259C2×C42C22×D1911yescharacteristic
260#107—21no—
261#107—21no—
262C4⋊C8—382no—
263C4⋊C8—382no—
264C4⋊C8—381no—
265C4⋊C8—381no—
266C4⋊C8C2×Dic1911yescharacteristic
267C4⋊C8C2×Dic1911yescharacteristic
268#103—21no—
269#103—21no—
270#103—384no—
271#102—21no—
272#102—21no—
273C22⋊C8—21no—
274C22⋊C8—191no—
275C22⋊C8—191no—
276C22⋊C8—381no—
277#97—21no—
278#97—192no—
279#97—382no—
280#97—381no—
281#97—381no—
282C4×C8—382no—
283C4×C8—381no—
284#95—381no—
285C19#916411yescharacteristic, complemented, Sylow
286#41—81no—
287#41—81no—
288C2×Q8—21no—
289C2×Q8—22no—
290C2×Q8—21no—
291C2×Q8—41no—
292C2×Q8C22⋊Dic1911yescharacteristic
293C2×Q8C22⋊Dic1911yescharacteristic
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—761no—
302C22×C4D4×D1911yescharacteristic
303C22×C4#6454311yescharacteristic
304C22×C4C2×C22⋊D1911yescharacteristic
305SD16—42no—
306SD16—42no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—382no—
310C2×C8—381no—
311C2×C8—382no—
312C2×C8—381no—
313C2×C8—761no—
314C2×C8—761no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—382no—
323C4⋊C4—761no—
324C4⋊C4C22⋊Dic1911yescharacteristic
325C4⋊C4C22⋊Dic1911yescharacteristic
326C22⋊C4—41no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—21no—
332C42—1521no—
333C42D4×D1911yescharacteristic
334C42#6454311yescharacteristic
335C42C22×Dic1911yescharacteristic
336C42C2×C22⋊D1911yescharacteristic
337C23—41no—
338C23#1059738511yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—21no—
342Q8—42no—
343Q8—81no—
344Q8#1059729412yes—
345D4—41no—
346D4—41no—
347D4—81no—
348D4—81no—
349D4—81no—
350D4—81no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—82no—
365C2×C4—762no—
366C2×C4—1521no—
367C2×C4—1521no—
368C2×C4D4×Dic1911yescharacteristic
369C2×C4D4×Dic1911yescharacteristic
370C2×C4#1059738111yescharacteristic
371C2×C4#1059738311yescharacteristic
372C2×C4#1059738511yescharacteristic
373C2×C4C2×C22⋊Dic1911yescharacteristic
374C8—41no—
375C8—41no—
376C8—762no—
377C8—761no—
378C8—762no—
379C8—761no—
380C22—21no—
381C22—21no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22#1192642411yescharacteristic
386C22#1192680511yescharacteristic
387C22#1192681211yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—81no—
398C4—1522no—
399C4C2×#1059729411yescharacteristic
400C4#1192656111yescharacteristic
401C2—21no—
402C2—21no—
403C2—161no—
404C2#1456393811yescharacteristic
405C2#1456413111yescharacteristic
406C2#1456414511yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3112C2
socleC22×C19#386
prime radicalC19×#532C22
cosocleC2×C42×C19C23
hypercenter#3112D19
hypocenterC19#9164
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3112

Complements

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

NH ≅ G/Ntype
1. #14572724C2semidirect
2. #14563465C2semidirect
5. #14561533C2semidirect
6. #14561492C2semidirect
25. C19×#477C4semidirect
26. C19×#477C4semidirect
27. C19×#460C4semidirect
28. C19×#460C4semidirect
208. #477Dic19semidirect
209. #477Dic19semidirect
210. #460Dic19semidirect
211. #460Dic19semidirect
285. C19#9164semidirect

Maximal subgroups

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

subgroupindex
#145727242
#145634652
#145622462
#145621302
#145615332
#145614922
C19×#31122
#916419