Finite Group Databasebeta

← #18075309

Subgroups — #18075309

Order 4864.

540 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566174C211yesmaximal, characteristic
2#14563489C211yesmaximal, characteristic, complemented
3#14563489C211yesmaximal, characteristic, complemented
4C2×#11926283C211yesmaximal, characteristic
5C2×#11926283C211yesmaximal, characteristic
6#14561516C211yesmaximal, characteristic, complemented
7C19×#1295C211yesmaximal, characteristic, complemented
8C2×#10597321C2211yescharacteristic
9C2×#10597333C411yescharacteristic
10C2×#10597339C411yescharacteristic
11C2×Dic19⋊C8—21no—
12C2×Dic19⋊C8—21no—
13C2×#10597260C2211yescharacteristic
14C2×#10597260C2211yescharacteristic
15#11926449C411yescharacteristic
16#11926445C411yescharacteristic
17#11926433—21no—
18#11926433—21no—
19#11926391—21no—
20#11926391—21no—
21C42×Dic19C2211yescharacteristic
22#11926298—21no—
23#11926298—21no—
24#11926283—22no—
25#11926283—22no—
26C2×C19×#97C2211yescharacteristic
27C2×C19×#97C2211yescharacteristic
28C19×#382C2211yescharacteristic
29C22×D76C2×C411yescharacteristic
30C22×C4×D19—21no—
31C22×Dic38C2×C411yescharacteristic
32C22×C8×C19—21no—
33C22×C8×C19—21no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C42×C19C2311yescharacteristic
37C2×(C2×D19)⋊C4—21no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×Dic19⋊C4—21no—
43C2×C4×Dic19—21no—
44C2×C4×Dic19C2×C411yescharacteristic
45C2×C4×Dic19C2×C411yescharacteristic
46C2×C4×Dic19D411yescharacteristic
47C2×C4×Dic19D411yescharacteristic
48C2×C4×Dic19D411yescharacteristic
49C2×C4×Dic19D411yescharacteristic
50C22×C19⋊C8—21no—
51C22×C19⋊C8—21no—
52#10597339—42no—
53#10597333—42no—
54#10597321—21no—
55#10597321—21no—
56#10597321D412yes—
57#10597321Q812yes—
58C19×#97—21no—
59C19×#97—21no—
60C19×#97—21no—
61C19×#97—21no—
62C19×#95—21no—
63C19×#95—21no—
64C19⋊#95—21no—
65C19⋊#95—21no—
66Dic19⋊C8—24no—
67Dic19⋊C8—24no—
68#10597260—21no—
69#10597260—21no—
70#10597260—21no—
71#10597260—21no—
72C23×D19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19C22×C411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×Dic19—21no—
79C22×Dic19C22⋊C411yescharacteristic
80C22×Dic19C22⋊C411yescharacteristic
81C22×Dic19C22⋊C411yescharacteristic
82C22×Dic19C22⋊C411yescharacteristic
83C2×D76—21no—
84C2×D76—41no—
85C2×D76—41no—
86C2×D76C4⋊C412yes—
87C2×C4×D19—42no—
88C2×C4×D19—42no—
89C2×C4×D19—42no—
90C2×Dic38—21no—
91C2×Dic38—41no—
92C2×Dic38—41no—
93C2×Dic38C4⋊C412yes—
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—41no—
101C4⋊C4×C19—41no—
102C42×C19C2×D411yescharacteristic
103C42×C19C2×Q811yescharacteristic
104C42×C19#4111yescharacteristic
105C42×C19#4111yescharacteristic
106(C2×D19)⋊C4—22no—
107(C2×D19)⋊C4—22no—
108(C2×D19)⋊C4—22no—
109(C2×D19)⋊C4—22no—
110(C2×D19)⋊C4—42no—
111(C2×D19)⋊C4—42no—
112(C2×D19)⋊C4—42no—
113Dic19⋊C4—42no—
114C4×Dic19—22no—
115C4×Dic19—22no—
116C4×Dic19—22no—
117C4×Dic19—41no—
118C4×Dic19—41no—
119C4×Dic19—41no—
120C4×Dic19—42no—
121C2×C19⋊C8—22no—
122C2×C19⋊C8—22no—
123C2×C19⋊C8—41no—
124C2×C19⋊C8—41no—
125C2×C19⋊C8—41no—
126C2×C19⋊C8—41no—
127#8581—191nomaximal, Sylow
128C23×C19C2×C22⋊C411yescharacteristic
129C22×D19—22no—
130C22×D19—41no—
131C22×D19—41no—
132C22×D19—41no—
133C22×D19—41no—
134C22×D19—41no—
135C22×D19—41no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19C2×C4⋊C411yescharacteristic
149C2×C4×C19#11711yescharacteristic
150C2×C4×C19#12111yescharacteristic
151C2×C4×C19#12111yescharacteristic
152C2×C4×C19C22⋊Q811yescharacteristic
153C2×C4×C19C22⋊Q811yescharacteristic
154C2×Dic19—21no—
155C2×Dic19—21no—
156C2×Dic19—21no—
157C2×Dic19—21no—
158C2×Dic19—21no—
159C2×Dic19—21no—
160C2×Dic19—22no—
161C2×Dic19—21no—
162C2×Dic19—21no—
163C2×Dic19—21no—
164C2×Dic19—41no—
165C2×Dic19—41no—
166C2×Dic19#10012yes—
167C2×Dic19#10412yes—
168C2×Dic19#10412yes—
169D76—42no—
170D76—42no—
171C4×D19—84no—
172Dic38—42no—
173Dic38—42no—
174C8×C19—42no—
175C8×C19—42no—
176C19⋊C8—42no—
177C19⋊C8—42no—
178C4×#124—191no—
179#1767—191no—
180#1767—191no—
181C2×#329—191no—
182C2×#329—191no—
183#1295—191no—
184#1295D1911yescharacteristic, complemented
185C22×C19#38011yescharacteristic
186C22×C19C2×#10011yescharacteristic
187C22×C19#41311yescharacteristic
188C22×C19C2×#10411yescharacteristic
189C22×C19C2×#10411yescharacteristic
190C22×C19#42111yescharacteristic
191C22×C19#42111yescharacteristic
192C2×D19—42no—
193C2×D19—42no—
194C2×D19—42no—
195C2×D19—81no—
196C2×D19—81no—
197C2×D19—81no—
198C2×D19—81no—
199C4×C19—21no—
200C4×C19—21no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—21no—
204C4×C19—21no—
205C4×C19—81no—
206C4×C19—81no—
207Dic19—22no—
208Dic19—22no—
209Dic19—22no—
210Dic19—42no—
211Dic19—41no—
212C2×#124—191no—
213C2×C4×Q8—191no—
214C2×C4×D4—191no—
215C2×C4⋊C8—381no—
216C2×C4⋊C8—381no—
217C2×#97—191no—
218C2×#97—191no—
219C2×#97C2×D1911yescharacteristic
220C2×#97C2×D1911yescharacteristic
221#391—191no—
222#390—191no—
223#388—381no—
224#388—381no—
225#382C2×D1911yescharacteristic
226C4×C22⋊C4—381no—
227C4×C22⋊C4—381no—
228C43—191no—
229#336—381no—
230#336—381no—
231#329—382no—
232#329—382no—
233C2×C19#152411yescharacteristic
234C2×C19#152711yescharacteristic
235C2×C19#153011yescharacteristic
236C2×C19#153511yescharacteristic
237C2×C19#180011yescharacteristic
238C2×C19#180611yescharacteristic
239C2×C19#180611yescharacteristic
240D19—82no—
241C22×Q8—191no—
242C22×D4—191no—
243C23×C4—381no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—381no—
247C22×C8—381no—
248#124—192no—
249#124—192no—
250#124—381no—
251#124—381no—
252C4×Q8—762no—
253C4×D4—762no—
254C2×C4⋊C4—381no—
255C2×C4⋊C4C4×D1911yescharacteristic
256C2×C4⋊C4C4×D1911yescharacteristic
257C2×C22⋊C4—381no—
258C2×C22⋊C4—381no—
259C2×C22⋊C4—381no—
260C2×C22⋊C4—381no—
261C2×C22⋊C4—381no—
262C2×C42—191no—
263C2×C42—191no—
264C2×C42—191no—
265C2×C42—191no—
266C2×C42—191no—
267C2×C42—191no—
268C2×C42—381no—
269C2×C42C22×D1911yescharacteristic
270C4⋊C8—384no—
271C4⋊C8—384no—
272#97—21no—
273#97—21no—
274#97—21no—
275#97—21no—
276#97—381no—
277#97—381no—
278#97—381no—
279#97—381no—
280#95—21no—
281#95—21no—
282#95—381no—
283#95—381no—
284C19#858111yescharacteristic, complemented, Sylow
285C24—381no—
286C2×Q8—192no—
287C2×Q8—381no—
288C2×Q8—761no—
289C2×Q8—761no—
290C2×D4—192no—
291C2×D4—381no—
292C2×D4—761no—
293C2×D4—761no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—191no—
297C22×C4—191no—
298C22×C4—191no—
299C22×C4—191no—
300C22×C4—381no—
301C22×C4—762no—
302C22×C4—762no—
303C22×C4—762no—
304C22×C4C2×C4×D1911yescharacteristic
305C22×C4D4×D1911yescharacteristic
306C22×C4D4×D1911yescharacteristic
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—382no—
314C2×C8—382no—
315C2×C8—761no—
316C2×C8—761no—
317C2×C8—761no—
318C2×C8—761no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—762no—
322C22⋊C4—382no—
323C22⋊C4—382no—
324C22⋊C4—382no—
325C22⋊C4—382no—
326C22⋊C4—762no—
327C22⋊C4—762no—
328C22⋊C4—762no—
329C42—382no—
330C42—382no—
331C42—382no—
332C42—761no—
333C42—761no—
334C42—761no—
335C42—762no—
336C42#6454111yescharacteristic
337C42#6454111yescharacteristic
338C42D4×D1911yescharacteristic
339C42Q8×D1911yescharacteristic
340C23—382no—
341C23—761no—
342C23—761no—
343C23—761no—
344C23—761no—
345C23—761no—
346C23—761no—
347C23C22⋊C4×D1911yescharacteristic
348Q8—762no—
349Q8—762no—
350D4—762no—
351D4—762no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—192no—
365C2×C4—192no—
366C2×C4—192no—
367C2×C4—381no—
368C2×C4—381no—
369C2×C4—381no—
370C2×C4—381no—
371C2×C4—381no—
372C2×C4—381no—
373C2×C4—381no—
374C2×C4—381no—
375C2×C4—382no—
376C2×C4—381no—
377C2×C4—761no—
378C2×C4—761no—
379C2×C4—1524no—
380C2×C4#1059731811yescharacteristic
381C2×C4#1059733011yescharacteristic
382C2×C4#1059733011yescharacteristic
383C2×C4C4⋊C4×D1911yescharacteristic
384C2×C4#1059734211yescharacteristic
385C2×C4#1059734211yescharacteristic
386C8—42no—
387C8—42no—
388C8—762no—
389C8—762no—
390C22—762no—
391C22—762no—
392C22—762no—
393C22—1521no—
394C22—1521no—
395C22—1521no—
396C22—1521no—
397C22#1192640311yescharacteristic
398C22#100×D1911yescharacteristic
399C22#1192652711yescharacteristic
400C22#104×D1911yescharacteristic
401C22#104×D1911yescharacteristic
402C22#1192655911yescharacteristic
403C22#1192655911yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—81no—
411C4—81no—
412C4—382no—
413C4—382no—
414C4—382no—
415C4—762no—
416C4—761no—
417C2—1522no—
418C2#1456222211yescharacteristic
419C2#1456223111yescharacteristic
420C2#1456224411yescharacteristic
421C2#1456226511yescharacteristic
422C2#1456362611yescharacteristic
423C2#1456365411yescharacteristic
424C2#1456365411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1295C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1295D19
hypocenterC19#8581
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #14563489C2semidirect
3. #14563489C2semidirect
6. #14561516C2semidirect
7. C19×#1295C2semidirect
184. #1295D19semidirect
284. C19#8581semidirect

Maximal subgroups

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

subgroupindex
#145661742
#145634892
C2×#119262832
#145615162
C19×#12952
#858119