Finite Group Databasebeta

← #18078634

Subgroups — #18078634

Order 4864.

456 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573423C211yesmaximal, characteristic
2#14572602C211yesmaximal, characteristic
3#14562133C211yesmaximal, characteristic, complemented
4#14562089C211yesmaximal, characteristic, complemented
5#14561530C211yesmaximal, characteristic, complemented
6#14561476C211yesmaximal, characteristic, complemented
7C19×#1806C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926851—21no—
10#11926844—21no—
11#11926839C411yescharacteristic, complemented
12#11926834C411yescharacteristic, complemented
13#11926829C411yescharacteristic, complemented
14#11926824C411yescharacteristic, complemented
15#11926675—21no—
16#11926622—21no—
17#11926616—22no—
18#11926597—21no—
19#11926597C2211yescharacteristic
20#11926580—21no—
21C2×C4⋊(C19⋊C8)C2211yescharacteristic
22#11926540—21no—
23C4×#64520—21no—
24C2×C4×C19⋊C8C2211yescharacteristic
25#11926280—22no—
26#11926274—21no—
27#11926274—21no—
28C4×#41×C19C2211yescharacteristic
29C19×#423C2211yescharacteristic
30C2×C19×#104—21no—
31C4×C4⋊C4×C19C2211yescharacteristic
32C19×#339—21no—
33C2×#41×C19D411yescharacteristic
34C2×M16×C19—21no—
35C4×Q8×C19C2×C411yescharacteristic
36C4×Q8×C19D411yescharacteristic
37C4×D4×C19—21no—
38C4×D4×C19—21no—
39C4×D4×C19C2×C411yescharacteristic
40C4×D4×C19D411yescharacteristic
41C19×#117—21no—
42C19×#117D411yescharacteristic
43C2×C4⋊C4×C19—21no—
44C2×C42×C19—21no—
45C2×C42×C19—21no—
46C2×C42×C19C2311yescharacteristic
47#10597372—21no—
48#10597370—21no—
49#10597370—21no—
50C2×#64520—22no—
51C22×C19⋊C8—21no—
52C22×C19⋊C8—21no—
53#10597316—21no—
54#10597315C2×C411yescharacteristic
55#10597315C2×C411yescharacteristic
56C4×Dic38—21no—
57C4×Dic38—21no—
58C19×C4⋊C8—21no—
59C19×C4⋊C8—21no—
60C19×#104—42no—
61C19×#95—21no—
62#10597292—21no—
63#10597292—21no—
64#10597289—21no—
65#10597289—21no—
66C22⋊(C19⋊C8)—22no—
67C22⋊(C19⋊C8)D412yes—
68#10597265—21no—
69#10597265—21no—
70#10597264—21no—
71#10597264—21no—
72C4⋊(C19⋊C8)—22no—
73C4⋊(C19⋊C8)—21no—
74C4⋊(C19⋊C8)—21no—
75C4⋊(C19⋊C8)C2×C411yescharacteristic
76C4⋊(C19⋊C8)C2×C411yescharacteristic
77#10597260—22no—
78C4×C19⋊C8—21no—
79C4×C19⋊C8—21no—
80C4×C19⋊C8D411yescharacteristic
81C4×C19⋊C8D411yescharacteristic
82#41×C19—21no—
83#41×C19—21no—
84#41×C19—21no—
85#41×C19—21no—
86C2×Q8×C19C22⋊C411yescharacteristic
87C2×D4×C19—21no—
88C2×D4×C19C22⋊C411yescharacteristic
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—41no—
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19#4111yescharacteristic
96C2×Dic38—21no—
97C2×Dic38—21no—
98M16×C19—41no—
99M16×C19—41no—
100C2×C8×C19—41no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19—41no—
105C4⋊C4×C19C22⋊C411yescharacteristic
106C4⋊C4×C19C22⋊C411yescharacteristic
107C22⋊C4×C19—21no—
108C22⋊C4×C19—21no—
109C22⋊C4×C19—21no—
110C42×C19—21no—
111C42×C19—21no—
112C42×C19—21no—
113C42×C19—41no—
114C42×C19—41no—
115C42×C19C22×C411yescharacteristic
116C42×C19C2×D411yescharacteristic
117C42×C19C2×D411yescharacteristic
118C42×C19#4111yescharacteristic
119C22⋊Dic19—41no—
120C4⋊Dic19—21no—
121C4⋊Dic19—21no—
122C4⋊Dic19—21no—
123C4⋊Dic19—21no—
124Dic19⋊C4—41no—
125Dic19⋊C4—41no—
126C4×Dic19—41no—
127#64520—44no—
128C2×C19⋊C8—21no—
129C2×C19⋊C8—21no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—22no—
133C2×C19⋊C8—42no—
134C2×C19⋊C8—41no—
135C2×C19⋊C8—41no—
136#9209—191nomaximal, Sylow
137C23×C19—21no—
138C23×C19#12111yescharacteristic
139Q8×C19—21no—
140Q8×C19—21no—
141D4×C19—21no—
142D4×C19—21no—
143D4×C19—41no—
144D4×C19—41no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—41no—
151C2×C4×C19—42no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—42no—
157C2×C4×C19—81no—
158C2×C4×C19—81no—
159C2×C4×C19C2×C22⋊C411yescharacteristic
160C2×C4×C19C4×D411yescharacteristic
161C2×C4×C19C4×D411yescharacteristic
162C2×C4×C19#12011yescharacteristic
163C2×C4×C19#12111yescharacteristic
164C2×C4×C19#12311yescharacteristic
165C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C19#13711yescharacteristic
167C2×C4×C19#13711yescharacteristic
168C2×C4×C19#13711yescharacteristic
169C2×Dic19—41no—
170C2×Dic19—41no—
171Dic38—41no—
172Dic38—41no—
173Dic38—81no—
174C8×C19—81no—
175C19⋊C8—22no—
176C19⋊C8—41no—
177C19⋊C8—42no—
178C19⋊C8—41no—
179C19⋊C8—41no—
180#3076—191no—
181#2965—191no—
182#1806D1911yescharacteristic
183#1503—191no—
184#1493—191no—
185#1301—191no—
186#1279—191no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—41no—
190C22×C19—41no—
191C22×C19—41no—
192C22×C19#38611yescharacteristic
193C22×C19#46811yescharacteristic
194C22×C19#47011yescharacteristic
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—41no—
199C4×C19—41no—
200C4×C19—41no—
201C4×C19—82no—
202C4×C19#41711yescharacteristic
203C4×C19#41911yescharacteristic
204C4×C19#44311yescharacteristic
205C4×C19#44411yescharacteristic
206C4×C19#46811yescharacteristic
207C4×C19#47011yescharacteristic
208Dic19—81no—
209Dic19—81no—
210#533—191no—
211C4×#41C2×D1911yescharacteristic
212#479—381no—
213#478—381no—
214#477—191no—
215#476—191no—
216#475—191no—
217#474—191no—
218#446—381no—
219#436—381no—
220#435—382no—
221#431—191no—
222#431—381no—
223#427—381no—
224#423C2×D1911yescharacteristic
225C2×C4⋊C8—191no—
226C2×#104—21no—
227#416—381no—
228C4×M16—381no—
229C2×C4×C8—191no—
230C4×C4⋊C4C2×D1911yescharacteristic
231#339—21no—
232#328—382no—
233Q8⋊C8—381no—
234Q8⋊C8—381no—
235C2×C19—21no—
236C2×C19—21no—
237C2×C19—81no—
238C2×C19#187611yescharacteristic
239C2×C19#189411yescharacteristic
240C2×C19#190611yescharacteristic
241C2×#41C22⋊D1911yescharacteristic
242C2×M16—21no—
243C2×M16—382no—
244C22×C8—381no—
245C22×C8—381no—
246C4⋊Q8—191no—
247C4⋊Q8—191no—
248#125—381no—
249C22⋊Q8—381no—
250C22⋊Q8—381no—
251C4×Q8—381no—
252C4×Q8—381no—
253C4×Q8C4×D1911yescharacteristic
254C4×Q8D7611yescharacteristic
255C4×D4—21no—
256C4×D4—21no—
257C4×D4C4×D1911yescharacteristic
258C4×D4D7611yescharacteristic
259#117—21no—
260#117—381no—
261#117C22⋊D1911yescharacteristic
262C2×C4⋊C4—21no—
263C2×C42—21no—
264C2×C42—21no—
265C2×C42C22×D1911yescharacteristic
266#107—381no—
267#107—381no—
268#106—381no—
269#106—381no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—191no—
273C4⋊C8—191no—
274C4⋊C8—382no—
275C4⋊C8—381no—
276C4⋊C8—381no—
277#104—42no—
278#103—381no—
279#103—381no—
280#102—381no—
281#102—381no—
282C22⋊C8—192no—
283C22⋊C8—382no—
284#97—382no—
285C4×C8—191no—
286C4×C8—191no—
287C4×C8—381no—
288C4×C8—381no—
289#95—21no—
290C19#920911yescharacteristic, complemented, Sylow
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295C2×Q8—381no—
296C2×Q8—381no—
297C2×Q8(C2×D19)⋊C411yescharacteristic
298C2×D4—21no—
299C2×D4(C2×D19)⋊C411yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4D4×D1911yescharacteristic
305C22×C4#6454311yescharacteristic
306C22×C4C2×C22⋊D1911yescharacteristic
307M16—41no—
308M16—41no—
309M16—764no—
310C2×C8—41no—
311C2×C8—381no—
312C2×C8—381no—
313C2×C8—382no—
314C2×C8—381no—
315C2×C8—381no—
316C2×C8—762no—
317C2×C8—761no—
318C2×C8—761no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—381no—
324C4⋊C4—381no—
325C4⋊C4—381no—
326C4⋊C4—381no—
327C4⋊C4—761no—
328C4⋊C4—761no—
329C4⋊C4(C2×D19)⋊C411yescharacteristic
330C4⋊C4(C2×D19)⋊C411yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—761no—
335C42—21no—
336C42—21no—
337C42—21no—
338C42—41no—
339C42—41no—
340C42—761no—
341C42C2×C4×D1911yescharacteristic
342C42C2×D7611yescharacteristic
343C42D4×D1911yescharacteristic
344C42#6454311yescharacteristic
345C23—21no—
346C23#1059738511yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—761no—
350Q8—761no—
351Q8—1521no—
352D4—21no—
353D4—21no—
354D4—41no—
355D4—41no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—761no—
371C2×C4—761no—
372C2×C4(C22⋊D19)⋊C411yescharacteristic
373C2×C4(C22⋊D19)⋊C411yescharacteristic
374C2×C4#1059732811yescharacteristic
375C2×C4#1059733211yescharacteristic
376C2×C4C2×(C2×D19)⋊C411yescharacteristic
377C2×C4#1059737811yescharacteristic
378C2×C4#1059738511yescharacteristic
379C2×C4#1059738811yescharacteristic
380C2×C4#1059739711yescharacteristic
381C2×C4#1059739711yescharacteristic
382C8—81no—
383C8—382no—
384C8—761no—
385C8—762no—
386C8—761no—
387C8—761no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22#1192642111yescharacteristic
394C22#1192678811yescharacteristic
395C22#1192680011yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—82no—
403C4—1521no—
404C4—1521no—
405C4#1192654311yescharacteristic
406C4#1192655211yescharacteristic
407C4#1192665811yescharacteristic
408C4#1192666311yescharacteristic
409C4#1192678811yescharacteristic
410C4#1192680011yescharacteristic
411C2—21no—
412C2—21no—
413C2—81no—
414C2#1456396011yescharacteristic
415C2#1456406611yescharacteristic
416C2#1456413411yescharacteristic
subgroupG/H
centerC2×C4#10597385
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1806C2
socleC22×C19#386
prime radicalC2×#41×C19D4
cosocleC2×C42×C19C23
hypercenter#1806D19
hypocenterC19#9209
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
3. #14562133C2semidirect
4. #14562089C2semidirect
5. #14561530C2semidirect
6. #14561476C2semidirect
11. #11926839C4semidirect
12. #11926834C4semidirect
13. #11926829C4semidirect
14. #11926824C4semidirect
290. C19#9209semidirect

Maximal subgroups

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

subgroupindex
#145734232
#145726022
#145621332
#145620892
#145615302
#145614762
C19×#18062
#920919