Finite Group Databasebeta

← #18077405

Subgroups — #18077405

Order 4864.

500 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573666C211yesmaximal, characteristic
2#14564554C211yesmaximal, characteristic
3C4×#10597292C211yesmaximal, characteristic, complemented
4#14562085C211yesmaximal, characteristic
5#14561536C211yesmaximal, characteristic, complemented
6#14561473C211yesmaximal, characteristic, complemented
7Q8×M16×C19C211yesmaximal, characteristic, complemented
8#11927094C2211yescharacteristic
9#11926862—21no—
10#11926829C411yescharacteristic, complemented
11#11926829C411yescharacteristic, complemented
12#11926744C411yescharacteristic, complemented
13#11926744C411yescharacteristic, complemented
14#11926683—21no—
15C4×#64527—21no—
16C4×#64527—21no—
17#11926597C2211yescharacteristic
18C2×#10597282—21no—
19C2×#10597282—21no—
20C2×#10597292—21no—
21C2×C4×C19⋊C8C2211yescharacteristic
22C4×C4⋊Dic19C2211yescharacteristic
23#11926306—21no—
24#11926271—22no—
25C2×C4×Q8×C19C2211yescharacteristic
26C19×#446—22no—
27C19×#446—21no—
28C8×Q8×C19—21no—
29C19×#423—21no—
30C19×#423C2211yescharacteristic
31C4×M16×C19—21no—
32C4×M16×C19C2211yescharacteristic
33C22×Q8×C19D411yescharacteristic
34C2×#64541—21no—
35C2×M16×C19—21no—
36C2×M16×C19D411yescharacteristic
37C2×M16×C19D411yescharacteristic
38C4×Q8×C19—21no—
39C4×Q8×C19—21no—
40C4×Q8×C19C2×C411yescharacteristic
41C4×Q8×C19C2×C411yescharacteristic
42C4×Q8×C19D411yescharacteristic
43C4×Q8×C19D411yescharacteristic
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19D411yescharacteristic
46C2×C42×C19—21no—
47C2×C42×C19C2311yescharacteristic
48C2×#64527—21no—
49C2×#64527—21no—
50#10597376—21no—
51#10597376—21no—
52C2×C4⋊Dic19—21no—
53C2×C4×Dic19—21no—
54C22×C19⋊C8—21no—
55#10597321—21no—
56#10597320C2×C411yescharacteristic
57C4×D76—21no—
58C4×D76—21no—
59#10597315C2×C411yescharacteristic
60C19×C4⋊C8—22no—
61C19×C4⋊C8—22no—
62C19×C4⋊C8—21no—
63C19×C4⋊C8D412yes—
64C19×#97—22no—
65C19×#97—21no—
66C4×C8×C19—22no—
67C4×C8×C19—21no—
68#10597292—24no—
69#10597292—21no—
70#10597292—21no—
71C19⋊#95—21no—
72C22⋊(C19⋊C8)—21no—
73#10597282—42no—
74#10597282—42no—
75#10597266—21no—
76#10597266—21no—
77#10597265—21no—
78#10597265—21no—
79C4⋊(C19⋊C8)C2×C411yescharacteristic
80C4⋊(C19⋊C8)C2×C411yescharacteristic
81C4×C19⋊C8—21no—
82C4×C19⋊C8—21no—
83C4×C19⋊C8—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—22no—
86C2×Q8×C19—41no—
87C2×Q8×C19C22⋊C411yescharacteristic
88C2×Q8×C19C22⋊C411yescharacteristic
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19#4111yescharacteristic
94C2×C22⋊D19—41no—
95C22×Dic19—41no—
96#64541—41no—
97#64541—41no—
98#64541—41no—
99#64541—41no—
100C2×D76—21no—
101C2×D76—21no—
102C2×D76—21no—
103C2×C4×D19—41no—
104C2×Dic38—21no—
105M16×C19—21no—
106M16×C19—21no—
107M16×C19—21no—
108M16×C19—41no—
109M16×C19—41no—
110M16×C19SD1612yescomplemented
111C2×C8×C19—21no—
112C2×C8×C19—22no—
113C2×C8×C19—21no—
114C4⋊C4×C19—21no—
115C4⋊C4×C19—21no—
116C4⋊C4×C19—21no—
117C4⋊C4×C19—21no—
118C4⋊C4×C19—21no—
119C4⋊C4×C19C22⋊C411yescharacteristic
120C4⋊C4×C19C22⋊C411yescharacteristic
121C42×C19—21no—
122C42×C19—21no—
123C42×C19—21no—
124C42×C19—21no—
125C42×C19C22×C411yescharacteristic
126C42×C19C2×D411yescharacteristic
127C42×C19C2×D411yescharacteristic
128C42×C19#4111yescharacteristic
129#64527—42no—
130#64527—42no—
131(C2×D19)⋊C4—41no—
132(C2×D19)⋊C4—41no—
133C4⋊Dic19—22no—
134C4⋊Dic19—21no—
135C4⋊Dic19—21no—
136C4⋊Dic19—41no—
137C4×Dic19—41no—
138C4×Dic19—41no—
139C2×C19⋊C8—22no—
140C2×C19⋊C8—21no—
141C2×C19⋊C8—21no—
142C2×C19⋊C8—41no—
143C2×C19⋊C8—41no—
144#8992—191nomaximal, Sylow
145C23×C19#12111yescharacteristic
146C22×D19—41no—
147Q8×C19—21no—
148Q8×C19—21no—
149Q8×C19—21no—
150Q8×C19—42no—
151Q8×C19#10412yescomplemented
152C2×C4×C19—21no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—41no—
159C2×C4×C19—42no—
160C2×C4×C19—81no—
161C2×C4×C19C2×C22⋊C411yescharacteristic
162C2×C4×C19C4×D411yescharacteristic
163C2×C4×C19C4×D411yescharacteristic
164C2×C4×C19#12011yescharacteristic
165C2×C4×C19#12111yescharacteristic
166C2×C4×C19#12311yescharacteristic
167C2×C4×C19C2×SD1611yescharacteristic
168C2×C4×C19#13511yescharacteristic
169C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C19#13711yescharacteristic
171C22⋊D19—81no—
172C22⋊D19—81no—
173C2×Dic19—42no—
174C2×Dic19—41no—
175C2×Dic19—81no—
176C2×Dic19—81no—
177D76—42no—
178D76—41no—
179D76—41no—
180D76—41no—
181D76—41no—
182C4×D19—81no—
183C4×D19—81no—
184Dic38—41no—
185Dic38—41no—
186C8×C19—22no—
187C8×C19—41no—
188C8×C19—42no—
189C19⋊C8—42no—
190C19⋊C8—41no—
191C19⋊C8—41no—
192#3103—191no—
193Q8×M16D1911yescharacteristic, complemented
194#1980—191no—
195C4×#103—191no—
196#1492—191no—
197#1303—191no—
198#1278—191no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19#38611yescharacteristic
202C22×C19#46011yescharacteristic
203C22×C19#46411yescharacteristic
204C2×D19—81no—
205C2×D19—81no—
206C2×D19—81no—
207C4×C19—21no—
208C4×C19—22no—
209C4×C19—21no—
210C4×C19—21no—
211C4×C19—41no—
212C4×C19—41no—
213C4×C19—41no—
214C4×C19C2×#10411yescharacteristic
215C4×C19#42111yescharacteristic
216C4×C19C4×SD1611yescharacteristic
217C4×C19#44011yescharacteristic
218C4×C19#44811yescharacteristic
219C4×C19#44911yescharacteristic
220Dic19—82no—
221Dic19—81no—
222#532—191no—
223C2×C4×Q8C2×D1911yescharacteristic
224#481—381no—
225#475—191no—
226#475—191no—
227#460—191no—
228#460—191no—
229#448—381no—
230#446—21no—
231#446—22no—
232C8×Q8—21no—
233C4×SD16—381no—
234C4×SD16—381no—
235#431—191no—
236#423—21no—
237#423C2×D1911yescharacteristic
238C2×#104—381no—
239C2×#104—381no—
240C2×#103—381no—
241C4×M16—21no—
242C4×M16C2×D1911yescharacteristic
243C2×C4×C8—191no—
244C4×C4⋊C4—191no—
245#340—381no—
246D4⋊C8—382no—
247C2×C19—21no—
248C2×C19—21no—
249C2×C19#187111yescharacteristic
250C2×C19#188011yescharacteristic
251C2×C19#188111yescharacteristic
252D19—161no—
253C2×#41—381no—
254C22×Q8D7611yescharacteristic
255C2×SD16—381no—
256C2×SD16—381no—
257C2×M16—21no—
258C2×M16C22⋊D1911yescharacteristic
259C2×M16C22⋊D1911yescharacteristic
260C22×C8—381no—
261C4⋊Q8—191no—
262#127—191no—
263#124—381no—
264#121—381no—
265#121—381no—
266C4×Q8—21no—
267C4×Q8—21no—
268C4×Q8C4×D1911yescharacteristic
269C4×Q8C4×D1911yescharacteristic
270C4×Q8C22⋊D1911yescharacteristic
271C4×Q8C22⋊D1911yescharacteristic
272C4×D4—381no—
273C4×D4—381no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—381no—
276C2×C4⋊C4D7611yescharacteristic
277C2×C42—21no—
278C2×C42—381no—
279C2×C42C22×D1911yescharacteristic
280#106—381no—
281#106—381no—
282C4⋊C8—22no—
283C4⋊C8—22no—
284C4⋊C8—21no—
285C4⋊C8—191no—
286C4⋊C8—191no—
287C4⋊C8C22⋊D1912yes—
288#104—762no—
289#104—762no—
290#103—384no—
291#103—381no—
292#103—381no—
293#102—381no—
294#102—381no—
295C22⋊C8—381no—
296#97—22no—
297#97—21no—
298C4×C8—22no—
299C4×C8—21no—
300C4×C8—381no—
301C4×C8—381no—
302C4×C8—381no—
303#95—381no—
304C19#899211yescharacteristic, complemented, Sylow
305#41—761no—
306#41—761no—
307#41—761no—
308#41—761no—
309C2×Q8—21no—
310C2×Q8—22no—
311C2×Q8—41no—
312C2×Q8—381no—
313C2×Q8(C2×D19)⋊C411yescharacteristic
314C2×Q8(C2×D19)⋊C411yescharacteristic
315C2×D4—381no—
316C2×D4—381no—
317C2×D4—381no—
318C2×D4—761no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—761no—
322C22×C4—761no—
323C22×C4C2×D7611yescharacteristic
324C22×C4#6454111yescharacteristic
325C22×C4C2×C22⋊D1911yescharacteristic
326SD16—762no—
327SD16—762no—
328M16—21no—
329M16—21no—
330M16—21no—
331M16—41no—
332M16—41no—
333M16#6452712yescomplemented
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—22no—
337C2×C8—382no—
338C2×C8—381no—
339C2×C8—381no—
340C2×C8—761no—
341C2×C8—761no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—382no—
348C4⋊C4—381no—
349C4⋊C4—381no—
350C4⋊C4—761no—
351C4⋊C4(C2×D19)⋊C411yescharacteristic
352C4⋊C4(C2×D19)⋊C411yescharacteristic
353C22⋊C4—761no—
354C22⋊C4—761no—
355C42—21no—
356C42—21no—
357C42—21no—
358C42—21no—
359C42—761no—
360C42—761no—
361C42C2×C4×D1911yescharacteristic
362C42#6454111yescharacteristic
363C42C2×C22⋊D1911yescharacteristic
364C42C2×C22⋊D1911yescharacteristic
365C23—761no—
366C23#1059737611yescharacteristic
367Q8—21no—
368Q8—21no—
369Q8—21no—
370Q8—42no—
371Q8—761no—
372Q8—761no—
373Q8#1059728212yescomplemented
374D4—762no—
375D4—761no—
376D4—761no—
377D4—761no—
378D4—761no—
379D4—1521no—
380D4—1521no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—81no—
390C2×C4—762no—
391C2×C4—761no—
392C2×C4—1521no—
393C2×C4—1521no—
394C2×C4—1521no—
395C2×C4—1521no—
396C2×C4C2×(C2×D19)⋊C411yescharacteristic
397C2×C4C4×C22⋊D1911yescharacteristic
398C2×C4C4×C22⋊D1911yescharacteristic
399C2×C4#1059737511yescharacteristic
400C2×C4#1059737611yescharacteristic
401C2×C4C2×#6452711yescharacteristic
402C2×C4#1059738811yescharacteristic
403C2×C4#1059739511yescharacteristic
404C2×C4#1059739611yescharacteristic
405C2×C4#1059739911yescharacteristic
406C8—22no—
407C8—41no—
408C8—42no—
409C8—762no—
410C8—761no—
411C8—761no—
412C22—21no—
413C22—21no—
414C22—1521no—
415C22—1521no—
416C22—1521no—
417C22#1192642311yescharacteristic
418C22#1192674411yescharacteristic
419C22#1192676611yescharacteristic
420C4—21no—
421C4—22no—
422C4—21no—
423C4—21no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—1522no—
428C4—1521no—
429C4C2×#1059728211yescharacteristic
430C4#1192656011yescharacteristic
431C4C4×#6452711yescharacteristic
432C4#1192664211yescharacteristic
433C4#1192668311yescharacteristic
434C4#1192668911yescharacteristic
435C2—21no—
436C2—21no—
437C2—3041no—
438C2#1456393711yescharacteristic
439C2#1456399011yescharacteristic
440C2#1456399711yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingQ8×M16×C19C2
socleC22×C19#386
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenterQ8×M16D19
hypocenterC19#8992
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
3. C4×#10597292C2semidirect
5. #14561536C2semidirect
6. #14561473C2semidirect
7. Q8×M16×C19C2semidirect
10. #11926829C4semidirect
11. #11926829C4semidirect
12. #11926744C4semidirect
13. #11926744C4semidirect
110. M16×C19SD16semidirect
151. Q8×C19#104semidirect
193. Q8×M16D19semidirect
304. C19#8992semidirect
333. M16#64527semidirect
373. Q8#10597282semidirect

Maximal subgroups

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

subgroupindex
#145736662
#145645542
C4×#105972922
#145620852
#145615362
#145614732
Q8×M16×C192
#899219