Finite Group Databasebeta

← #18081556

Subgroups — #18081556

Order 4864.

482 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572008C211yesmaximal, characteristic
2#14563489C211yesmaximal, characteristic, complemented
3#14563383C211yesmaximal, characteristic, complemented
4C2×#11926286C211yesmaximal, characteristic, complemented
5C2×#11926283C211yesmaximal, characteristic
6C2×#11926283C211yesmaximal, characteristic
7C2×C19×#330C211yesmaximal, characteristic, complemented
8C2×#10597321C2211yescharacteristic
9C2×Dic19⋊C8—21no—
10C2×#10597260C2211yescharacteristic
11C2×#10597260C2211yescharacteristic
12#11926449C411yescharacteristic
13#11926449C411yescharacteristic
14#11926445C411yescharacteristic
15#11926445C411yescharacteristic
16#11926434—21no—
17#11926434—21no—
18#11926434—21no—
19#11926434—21no—
20C42×Dic19C2211yescharacteristic
21#11926298—21no—
22#11926298—21no—
23#11926298—21no—
24#11926286—22no—
25#11926283—22no—
26#11926283—22no—
27C2×C19×#125C2211yescharacteristic
28C2×C19×#97C2211yescharacteristic
29C2×C19×#97C2211yescharacteristic
30C19×#330—22no—
31C22×D76C2×C411yescharacteristic
32C22×Dic38C2×C411yescharacteristic
33C22×C8×C19—21no—
34C22×C8×C19—21no—
35C19×#125—21no—
36C19×#125—21no—
37C19×#125—21no—
38C19×#125—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19C2×C411yescharacteristic
42C2×C4⋊C4×C19C2×C411yescharacteristic
43C2×C42×C19C2311yescharacteristic
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×(C2×D19)⋊C4—21no—
50C2×C4×Dic19C2×C411yescharacteristic
51C2×C4×Dic19C2×C411yescharacteristic
52C2×C4×Dic19D411yescharacteristic
53C2×C4×Dic19D411yescharacteristic
54C2×C4×Dic19D411yescharacteristic
55C2×C4×Dic19D411yescharacteristic
56C22×C19⋊C8—21no—
57C22×C19⋊C8—21no—
58#10597321—21no—
59#10597321—21no—
60#10597321—21no—
61#10597321—21no—
62C19×#97—21no—
63C19×#97—21no—
64C19×#97—21no—
65C19×#97D412yes—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70Dic19⋊C8—24no—
71#10597260—21no—
72#10597260—21no—
73#10597260—21no—
74#10597260D412yes—
75C23×D19—21no—
76C22×C4×C19—21no—
77C22×C4×C19—21no—
78C22×C4×C19C22×C411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×Dic19—21no—
82C22×Dic19C22⋊C411yescharacteristic
83C22×Dic19C22⋊C411yescharacteristic
84C22×Dic19C22⋊C411yescharacteristic
85C22×Dic19C22⋊C411yescharacteristic
86C2×D76—21no—
87C2×D76—21no—
88C2×D76—41no—
89C2×D76—41no—
90C2×Dic38—21no—
91C2×Dic38—21no—
92C2×Dic38—41no—
93C2×Dic38—41no—
94C2×C8×C19—22no—
95C2×C8×C19—22no—
96C2×C8×C19—41no—
97C2×C8×C19—41no—
98C2×C8×C19—41no—
99C2×C8×C19—41no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—41no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C42×C19C2×D411yescharacteristic
109C42×C19C2×D411yescharacteristic
110C42×C19#4111yescharacteristic
111C42×C19#4111yescharacteristic
112(C2×D19)⋊C4—42no—
113(C2×D19)⋊C4—42no—
114(C2×D19)⋊C4—42no—
115(C2×D19)⋊C4—41no—
116(C2×D19)⋊C4—41no—
117(C2×D19)⋊C4—41no—
118(C2×D19)⋊C4—41no—
119(C2×D19)⋊C4—42no—
120C4×Dic19—22no—
121C4×Dic19—41no—
122C4×Dic19—41no—
123C4×Dic19—41no—
124C4×Dic19—41no—
125C4×Dic19—41no—
126C2×C19⋊C8—22no—
127C2×C19⋊C8—22no—
128C2×C19⋊C8—41no—
129C2×C19⋊C8—41no—
130C2×C19⋊C8—41no—
131C2×C19⋊C8—41no—
132#9688—191nomaximal, Sylow
133C23×C19C2×C22⋊C411yescharacteristic
134C22×D19—41no—
135C22×D19—41no—
136C22×D19—41no—
137C22×D19—41no—
138C22×D19—41no—
139C22×D19—41no—
140C22×D19—41no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19C4×D411yescharacteristic
154C2×C4×C19C4×D411yescharacteristic
155C2×C4×C19#12111yescharacteristic
156C2×C4×C19#12111yescharacteristic
157C2×C4×C19#12411yescharacteristic
158C2×C4×C19#12711yescharacteristic
159C2×Dic19—21no—
160C2×Dic19—21no—
161C2×Dic19—21no—
162C2×Dic19—21no—
163C2×Dic19—21no—
164C2×Dic19—21no—
165C2×Dic19—21no—
166C2×Dic19—21no—
167C2×Dic19—21no—
168C2×Dic19—21no—
169C2×Dic19—21no—
170C2×Dic19—41no—
171C2×Dic19—41no—
172C2×Dic19—41no—
173C2×Dic19#10412yes—
174D76—81no—
175D76—81no—
176Dic38—81no—
177Dic38—81no—
178C8×C19—42no—
179C8×C19—42no—
180C19⋊C8—42no—
181C19⋊C8—42no—
182#2861—191no—
183#1767—191no—
184#1745—191no—
185C2×#330—191no—
186C2×#330D1911yescharacteristic, complemented
187C2×#329—191no—
188C2×#329—191no—
189C22×C19#39011yescharacteristic
190C22×C19#41311yescharacteristic
191C22×C19#41311yescharacteristic
192C22×C19C2×#10411yescharacteristic
193C22×C19#42111yescharacteristic
194C22×C19#42111yescharacteristic
195C22×C19#42111yescharacteristic
196C2×D19—81no—
197C2×D19—81no—
198C2×D19—81no—
199C2×D19—81no—
200C2×D19—81no—
201C2×D19—81no—
202C2×D19—81no—
203C4×C19—21no—
204C4×C19—21no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—21no—
209C4×C19—81no—
210C4×C19—81no—
211Dic19—22no—
212Dic19—41no—
213Dic19—41no—
214Dic19—41no—
215Dic19—81no—
216C2×#125C2×D1911yescharacteristic
217C2×#124—191no—
218C2×C4⋊C8—381no—
219C2×#97—191no—
220C2×#97—191no—
221C2×#97C2×D1911yescharacteristic
222C2×#97C2×D1911yescharacteristic
223#391—191no—
224#391—191no—
225#390—191no—
226#390—191no—
227#388—381no—
228#388—381no—
229#388—381no—
230#388—381no—
231C43—191no—
232#336—381no—
233#336—381no—
234#336—381no—
235#330—22no—
236#330—382no—
237#329—382no—
238#329—382no—
239C2×C19#152911yescharacteristic
240C2×C19#153211yescharacteristic
241C2×C19#153511yescharacteristic
242C2×C19#153511yescharacteristic
243C2×C19#196311yescharacteristic
244C2×C19#196711yescharacteristic
245C2×C19#198011yescharacteristic
246D19—161no—
247C22×Q8—191no—
248C22×D4—191no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—381no—
252C22×C8—381no—
253#125—21no—
254#125—21no—
255#125—21no—
256#125—21no—
257#124—381no—
258#124—381no—
259#124—381no—
260#124—381no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4C4×D1911yescharacteristic
264C2×C4⋊C4C4×D1911yescharacteristic
265C2×C22⋊C4—381no—
266C2×C22⋊C4—381no—
267C2×C22⋊C4—381no—
268C2×C22⋊C4—381no—
269C2×C22⋊C4—381no—
270C2×C22⋊C4—381no—
271C2×C42—191no—
272C2×C42—191no—
273C2×C42—191no—
274C2×C42—191no—
275C2×C42—191no—
276C2×C42—191no—
277C2×C42C22×D1911yescharacteristic
278C4⋊C8—384no—
279#97—21no—
280#97—21no—
281#97—21no—
282#97—192no—
283#97—381no—
284#97—381no—
285#97—381no—
286#97C22⋊D1912yes—
287#95—381no—
288#95—381no—
289#95—381no—
290#95—381no—
291C19#968811yescharacteristic, complemented, Sylow
292C24—381no—
293C2×Q8—381no—
294C2×Q8—381no—
295C2×Q8—761no—
296C2×Q8—761no—
297C2×D4—381no—
298C2×D4—381no—
299C2×D4—761no—
300C2×D4—761no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—191no—
304C22×C4—191no—
305C22×C4—191no—
306C22×C4—191no—
307C22×C4—381no—
308C22×C4C2×C4×D1911yescharacteristic
309C22×C4D4×D1911yescharacteristic
310C22×C4D4×D1911yescharacteristic
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—382no—
318C2×C8—382no—
319C2×C8—761no—
320C2×C8—761no—
321C2×C8—761no—
322C2×C8—761no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C22⋊C4—762no—
332C22⋊C4—762no—
333C22⋊C4—762no—
334C22⋊C4—762no—
335C22⋊C4—761no—
336C22⋊C4—761no—
337C22⋊C4—761no—
338C22⋊C4—761no—
339C42—382no—
340C42—761no—
341C42—761no—
342C42—761no—
343C42—761no—
344C42—761no—
345C42#6454111yescharacteristic
346C42D4×D1911yescharacteristic
347C42#6454311yescharacteristic
348C42C2×C22⋊D1911yescharacteristic
349C23—761no—
350C23—761no—
351C23—761no—
352C23—761no—
353C23—761no—
354C23—761no—
355C23—761no—
356C23C22⋊C4×D1911yescharacteristic
357Q8—1521no—
358Q8—1521no—
359D4—1521no—
360D4—1521no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—192no—
374C2×C4—381no—
375C2×C4—381no—
376C2×C4—381no—
377C2×C4—381no—
378C2×C4—381no—
379C2×C4—381no—
380C2×C4—381no—
381C2×C4—381no—
382C2×C4—381no—
383C2×C4—381no—
384C2×C4—381no—
385C2×C4—761no—
386C2×C4—761no—
387C2×C4—761no—
388C2×C4(C22⋊D19)⋊C411yescharacteristic
389C2×C4#1059733011yescharacteristic
390C2×C4#1059733111yescharacteristic
391C2×C4C4×C22⋊D1911yescharacteristic
392C2×C4#1059738511yescharacteristic
393C2×C4#1059738611yescharacteristic
394C8—42no—
395C8—42no—
396C8—762no—
397C8—762no—
398C22—1521no—
399C22—1521no—
400C22—1521no—
401C22—1521no—
402C22—1521no—
403C22—1521no—
404C22—1521no—
405C22#1192644411yescharacteristic
406C22#1192652711yescharacteristic
407C22#1192652711yescharacteristic
408C22#104×D1911yescharacteristic
409C22#1192655911yescharacteristic
410C22#1192655911yescharacteristic
411C22#1192655911yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—382no—
421C4—761no—
422C4—761no—
423C4—761no—
424C4—1521no—
425C2—3041no—
426C2#1456224111yescharacteristic
427C2#1456225411yescharacteristic
428C2#1456226511yescharacteristic
429C2#1456226511yescharacteristic
430C2#1456446511yescharacteristic
431C2#1456448311yescharacteristic
432C2#1456455211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#330C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenterC2×#330D19
hypocenterC19#9688
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
2. #14563489C2semidirect
3. #14563383C2semidirect
4. C2×#11926286C2semidirect
7. C2×C19×#330C2semidirect
186. C2×#330D19semidirect
291. C19#9688semidirect

Maximal subgroups

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

subgroupindex
#145720082
#145634892
#145633832
C2×#119262862
C2×#119262832
C2×C19×#3302
#968819