Finite Group Databasebeta

← #18077409

Subgroups — #18077409

Order 4864.

476 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573417C211yesmaximal, characteristic
2#14572204C211yesmaximal, characteristic
3#14562038C211yesmaximal, characteristic, complemented
4#14562018C211yesmaximal, characteristic
5#14561530C211yesmaximal, characteristic, complemented
6#14561470C211yesmaximal, characteristic, complemented
7C19×#1493C211yesmaximal, characteristic, complemented
8C2×#10597353—21no—
9C4×#64541C2211yescharacteristic
10#11926848—21no—
11#11926841—21no—
12#11926836C411yescharacteristic
13#11926831C411yescharacteristic
14#11926826C411yescharacteristic
15#11926821C411yescharacteristic
16#11926597C2211yescharacteristic
17#11926580—21no—
18#11926572—21no—
19#11926569—22no—
20#11926566—21no—
21C2×C4⋊(C19⋊C8)C2211yescharacteristic
22C2×C4⋊(C19⋊C8)C2211yescharacteristic
23C4⋊C8×D19—21no—
24#11926538—21no—
25#11926276—21no—
26Q8⋊(C19⋊C8)—21no—
27Q8⋊(C19⋊C8)—21no—
28#11926273—21no—
29C19×#533C2211yescharacteristic
30C19×#423C2211yescharacteristic
31C2×C4×C8×C19C2211yescharacteristic
32C19×Q8⋊C8—22no—
33C2×#64541D411yescharacteristic
34C2×M16×C19—21no—
35C22×C8×C19—21no—
36C19×C4⋊Q8C2×C411yescharacteristic
37C19×C4⋊Q8C2×C411yescharacteristic
38C19×#125—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C4×Q8×C19—21no—
42C4×Q8×C19—21no—
43C19×#117—21no—
44C2×C42×C19C2311yescharacteristic
45C4×C22⋊D19—21no—
46C4×C22⋊D19—21no—
47#10597372D411yescharacteristic
48C22×C19⋊C8—21no—
49C22×C19⋊C8—21no—
50#10597353—42no—
51#10597353—42no—
52C2×#64515—22no—
53C2×C8×D19—22no—
54C4×D76C2×C411yescharacteristic
55C4×D76D411yescharacteristic
56#10597318—21no—
57C42×D19—21no—
58C4×Dic38C2×C411yescharacteristic
59C4×Dic38D411yescharacteristic
60C19×C4⋊C8—21no—
61C19×C4⋊C8D412yes—
62C4×C8×C19—21no—
63C4×C8×C19—21no—
64C22⋊(C19⋊C8)—21no—
65Dic19⋊C8—22no—
66Dic19⋊C8—22no—
67#10597267—21no—
68#10597267—21no—
69#10597266—21no—
70#10597266—21no—
71#10597265—21no—
72#10597265—21no—
73#10597264—21no—
74#10597264—21no—
75C4⋊(C19⋊C8)—21no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)C2×C411yescharacteristic
79C4⋊(C19⋊C8)C2×C411yescharacteristic
80C4⋊(C19⋊C8)D411yescharacteristic
81C4⋊(C19⋊C8)D411yescharacteristic
82C4×C19⋊C8—21no—
83C2×Q8×C19—21no—
84C2×Q8×C19—21no—
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19#4111yescharacteristic
87C22×C4×C19#4111yescharacteristic
88C2×C22⋊D19—21no—
89#64541—21no—
90#64541—21no—
91#64541SD1612yes—
92#64541Q1612yes—
93C2×D76C22⋊C411yescharacteristic
94C2×C4×D19—21no—
95C2×C4×D19—21no—
96C2×C4×D19—21no—
97C2×Dic38C22⋊C411yescharacteristic
98M16×C19—41no—
99M16×C19—41no—
100C2×C8×C19—22no—
101C2×C8×C19—22no—
102C2×C8×C19—41no—
103C2×C8×C19—41no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C22⋊C4×C19—41no—
111C42×C19—41no—
112C42×C19C22×C411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C42×C19C2×D411yescharacteristic
115C42×C19C2×D411yescharacteristic
116C22⋊Dic19—21no—
117(C2×D19)⋊C4—21no—
118(C2×D19)⋊C4—21no—
119C4⋊Dic19C22⋊C411yescharacteristic
120C4⋊Dic19C22⋊C411yescharacteristic
121Dic19⋊C4—21no—
122Dic19⋊C4—21no—
123C4×Dic19—21no—
124C4×Dic19—21no—
125C4×Dic19—21no—
126C2×C19⋊C8—21no—
127C2×C19⋊C8—21no—
128C2×C19⋊C8—21no—
129C2×C19⋊C8—21no—
130C2×C19⋊C8—41no—
131C2×C19⋊C8—41no—
132C2×C19⋊C8—41no—
133C2×C19⋊C8—41no—
134C2×C19⋊C8—41no—
135#64515—44no—
136C8×D19—44no—
137#8993—191nomaximal, Sylow
138C23×C19#12311yescharacteristic
139C22×D19—21no—
140Q8×C19—42no—
141Q8×C19—41no—
142Q8×C19—41no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19C2×C22⋊C411yescharacteristic
149C2×C4×C19C4×D411yescharacteristic
150C2×C4×C19C4×D411yescharacteristic
151C2×C4×C19#12011yescharacteristic
152C2×C4×C19#12111yescharacteristic
153C2×C4×C19#12111yescharacteristic
154C2×C4×C19C2×SD1611yescharacteristic
155C2×C4×C19C2×Q1611yescharacteristic
156C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C19#13711yescharacteristic
158C22⋊D19—22no—
159C22⋊D19—22no—
160C2×Dic19—21no—
161C2×Dic19—21no—
162C2×Dic19—21no—
163D76—21no—
164D76#10312yes—
165C4×D19—22no—
166C4×D19—22no—
167C4×D19—41no—
168C4×D19—41no—
169C4×D19—81no—
170Dic38—21no—
171Dic38#10312yes—
172C8×C19—42no—
173C8×C19—42no—
174C19⋊C8—41no—
175C19⋊C8—41no—
176C19⋊C8—41no—
177C19⋊C8—41no—
178C19⋊C8—81no—
179#3076—191no—
180#2906—191no—
181#1493D1911yescharacteristic, complemented
182#1481—191no—
183#1476—191no—
184#1301—191no—
185#1277—191no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19#38611yescharacteristic
189C22×C19#48311yescharacteristic
190C22×C19#48411yescharacteristic
191C2×D19—22no—
192C2×D19—41no—
193C2×D19—41no—
194C4×C19—21no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—81no—
198C4×C19—81no—
199C4×C19C2×#10311yescharacteristic
200C4×C19#41711yescharacteristic
201C4×C19#44311yescharacteristic
202C4×C19#44411yescharacteristic
203C4×C19#45011yescharacteristic
204C4×C19#45111yescharacteristic
205Dic19—22no—
206Dic19—41no—
207Dic19—41no—
208C2×#131—381no—
209#533C2×D1911yescharacteristic
210C4×#41—191no—
211#479—381no—
212#478—381no—
213#477—191no—
214#476—191no—
215#475—191no—
216#474—191no—
217#431—191no—
218#427—381no—
219#424—381no—
220#424—382no—
221#423—381no—
222#423C2×D1911yescharacteristic
223C2×C4⋊C8—191no—
224C2×C4⋊C8—191no—
225C2×C4⋊C8—381no—
226#416—381no—
227C2×C4×C8C2×D1911yescharacteristic
228Q8⋊C8—22no—
229Q8⋊C8—381no—
230Q8⋊C8—381no—
231Q8⋊C8—381no—
232D4⋊C8—381no—
233C2×C19—21no—
234C2×C19—21no—
235C2×C19#187211yescharacteristic
236C2×C19#187611yescharacteristic
237C2×C19#188111yescharacteristic
238D19—42no—
239C2×#41—191no—
240#131—762no—
241#131—762no—
242C2×M16—21no—
243C2×M16—382no—
244C22×C8—21no—
245C22×C8—382no—
246C22×C8—381no—
247C22×C8—381no—
248C4⋊Q8C4×D1911yescharacteristic
249C4⋊Q8C4×D1911yescharacteristic
250#125—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×Q8—191no—
256C4×Q8—191no—
257C4×D4—191no—
258C4×D4—191no—
259C4×D4—381no—
260C4×D4—381no—
261#117—21no—
262#117—191no—
263#117—381no—
264C2×C42—381no—
265C2×C42C22×D1911yescharacteristic
266#107—381no—
267#107—381no—
268#106—381no—
269#106—381no—
270C4⋊C8—21no—
271C4⋊C8—191no—
272C4⋊C8—191no—
273C4⋊C8—191no—
274C4⋊C8—191no—
275C4⋊C8—382no—
276C4⋊C8—382no—
277C4⋊C8—381no—
278C4⋊C8—381no—
279C4⋊C8—381no—
280C4⋊C8C22⋊D1912yes—
281#103—381no—
282#103—381no—
283#102—381no—
284#102—381no—
285C22⋊C8—381no—
286C4×C8—21no—
287C4×C8—21no—
288C4×C8—381no—
289C19#899311yescharacteristic, complemented, Sylow
290#41—192no—
291#41—192no—
292#41—381no—
293#41—381no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—191no—
297C2×D4—191no—
298C2×D4—381no—
299C22×C4—381no—
300C22×C4—381no—
301C22×C4—381no—
302C22×C4#6454111yescharacteristic
303C22×C4D4×D1911yescharacteristic
304C22×C4#6454311yescharacteristic
305M16—41no—
306M16—41no—
307M16—764no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—381no—
313C2×C8—381no—
314C2×C8—381no—
315C2×C8—381no—
316C2×C8—764no—
317C2×C8—761no—
318C2×C8—761no—
319C2×C8—761no—
320C2×C8—761no—
321C2×C8—761no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—191no—
329C4⋊C4—191no—
330C4⋊C4—381no—
331C4⋊C4—381no—
332C22⋊C4—41no—
333C22⋊C4—381no—
334C22⋊C4—381no—
335C22⋊C4—381no—
336C42—41no—
337C42—381no—
338C42—381no—
339C42—381no—
340C42C2×C4×D1911yescharacteristic
341C42D4×D1911yescharacteristic
342C42D4×D1911yescharacteristic
343C42C2×C22⋊D1911yescharacteristic
344C23—381no—
345C23#1059732911yescharacteristic
346Q8—42no—
347Q8—41no—
348Q8—41no—
349Q8—192no—
350Q8—381no—
351D4—192no—
352D4—382no—
353D4—382no—
354D4—381no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—381no—
361C2×C4—382no—
362C2×C4—382no—
363C2×C4—381no—
364C2×C4—381no—
365C2×C4—761no—
366C2×C4—761no—
367C2×C4—1521no—
368C2×C4C22⋊C4×D1911yescharacteristic
369C2×C4(C22⋊D19)⋊C411yescharacteristic
370C2×C4#1059733011yescharacteristic
371C2×C4SD16×D1911yescharacteristic
372C2×C4#1059736011yescharacteristic
373C2×C4Q16×D1911yescharacteristic
374C2×C4#1059736411yescharacteristic
375C2×C4C4×C22⋊D1911yescharacteristic
376C2×C4#1059738311yescharacteristic
377C2×C4#1059738411yescharacteristic
378C8—42no—
379C8—42no—
380C8—761no—
381C8—761no—
382C8—761no—
383C8—761no—
384C8—1521no—
385C22—21no—
386C22—21no—
387C22—382no—
388C22—761no—
389C22—761no—
390C22#1192642011yescharacteristic
391C22#1192687311yescharacteristic
392C22#1192687811yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—81no—
397C4—81no—
398C4—382no—
399C4—761no—
400C4—761no—
401C4#103×D1911yescharacteristic
402C4#1192654411yescharacteristic
403C4#1192665811yescharacteristic
404C4#1192666311yescharacteristic
405C4#1192669311yescharacteristic
406C4#1192669811yescharacteristic
407C2—21no—
408C2—21no—
409C2—762no—
410C2#1456393911yescharacteristic
411C2#1456395911yescharacteristic
412C2#1456400011yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1493C2
socleC22×C19#386
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1493D19
hypocenterC19#8993
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
3. #14562038C2semidirect
5. #14561530C2semidirect
6. #14561470C2semidirect
7. C19×#1493C2semidirect
181. #1493D19semidirect
289. C19#8993semidirect

Maximal subgroups

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

subgroupindex
#145734172
#145722042
#145620382
#145620182
#145615302
#145614702
C19×#14932
#899319