Finite Group Databasebeta

← #18078367

Subgroups — #18078367

Order 4864.

458 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573757C211yesmaximal, characteristic
2#14572724C211yesmaximal, characteristic, complemented
3#14562245C211yesmaximal, characteristic
4#14562129C211yesmaximal, characteristic
5#14561534C211yesmaximal, characteristic, complemented
6#14561491C211yesmaximal, characteristic, complemented
7C19×#1763C211yesmaximal, characteristic, complemented
8#11927094C2211yescharacteristic
9#11926857—21no—
10#11926839C411yescharacteristic, complemented
11#11926839C411yescharacteristic, complemented
12#11926744C411yescharacteristic, complemented
13#11926744C411yescharacteristic, complemented
14#11926683—21no—
15#11926675—22no—
16#11926675—21no—
17Q8×C19⋊C8—21no—
18#11926642—21no—
19#11926642—21no—
20#11926601—21no—
21#11926601C2211yescharacteristic
22#11926601C2211yescharacteristic
23#11926597—21no—
24#11926597C2211yescharacteristic
25#11926283—22no—
26#11926277—21no—
27#11926277—21no—
28C2×C4×Q8×C19C2211yescharacteristic
29C2×C19×#103—21no—
30C2×C19×#97C2211yescharacteristic
31C4×C4⋊C4×C19C2211yescharacteristic
32C19×#340—21no—
33C22×Q8×C19D411yescharacteristic
34C2×#64541—21no—
35C22×C8×C19—21no—
36C4×Q8×C19—21no—
37C4×Q8×C19—21no—
38C4×Q8×C19C2×C411yescharacteristic
39C4×Q8×C19C2×C411yescharacteristic
40C4×Q8×C19D411yescharacteristic
41C4×Q8×C19D411yescharacteristic
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19D411yescharacteristic
45C2×C42×C19—21no—
46C2×C42×C19—21no—
47C2×C42×C19C2311yescharacteristic
48C2×#64527—21no—
49C2×#64527—21no—
50#10597376—21no—
51#10597376—21no—
52#10597321—21no—
53#10597320C2×C411yescharacteristic
54C4×D76—21no—
55C4×D76—21no—
56#10597315C2×C411yescharacteristic
57C19×#103—24no—
58C19×#97—21no—
59C19×#97—21no—
60C19×#95—21no—
61#10597292—21no—
62#10597292—21no—
63C22⋊(C19⋊C8)—21no—
64C22⋊(C19⋊C8)—21no—
65C22⋊(C19⋊C8)D411yescharacteristic
66C22⋊(C19⋊C8)D411yescharacteristic
67#10597266—21no—
68#10597266—21no—
69#10597264—21no—
70#10597264—21no—
71C4⋊(C19⋊C8)—22no—
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—
78#10597260—21no—
79#10597260D412yes—
80C4×C19⋊C8—22no—
81C4×C19⋊C8—21no—
82C2×Q8×C19—21no—
83C2×Q8×C19—22no—
84C2×Q8×C19—41no—
85C2×Q8×C19C22⋊C411yescharacteristic
86C2×Q8×C19C22⋊C411yescharacteristic
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—41no—
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19#4111yescharacteristic
93C2×C22⋊D19—41no—
94#64541—81no—
95#64541—81no—
96C2×D76—21no—
97C2×D76—21no—
98C2×D76—21no—
99C2×C4×D19—41no—
100C2×Dic38—21no—
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—21no—
109C4⋊C4×C19—22no—
110C4⋊C4×C19—41no—
111C4⋊C4×C19C22⋊C411yescharacteristic
112C4⋊C4×C19C22⋊C411yescharacteristic
113C42×C19—21no—
114C42×C19—21no—
115C42×C19—21no—
116C42×C19—21no—
117C42×C19—81no—
118C42×C19C22×C411yescharacteristic
119C42×C19C2×D411yescharacteristic
120C42×C19C2×D411yescharacteristic
121C42×C19#4111yescharacteristic
122#64527—42no—
123#64527—42no—
124(C2×D19)⋊C4—41no—
125(C2×D19)⋊C4—41no—
126C4⋊Dic19—21no—
127C4⋊Dic19—21no—
128C2×C19⋊C8—21no—
129C2×C19⋊C8—21no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—22no—
133#9164—191nomaximal, Sylow
134C23×C19#12111yescharacteristic
135C22×D19—41no—
136Q8×C19—21no—
137Q8×C19—21no—
138Q8×C19—21no—
139Q8×C19—42no—
140Q8×C19#10412yes—
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—21no—
148C2×C4×C19—21no—
149C2×C4×C19—41no—
150C2×C4×C19—42no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—42no—
154C2×C4×C19—81no—
155C2×C4×C19—81no—
156C2×C4×C19C2×C22⋊C411yescharacteristic
157C2×C4×C19C4×D411yescharacteristic
158C2×C4×C19C4×D411yescharacteristic
159C2×C4×C19#12011yescharacteristic
160C2×C4×C19#12111yescharacteristic
161C2×C4×C19#12311yescharacteristic
162C22⋊D19—81no—
163C22⋊D19—81no—
164C2×Dic19—41no—
165D76—41no—
166D76—41no—
167D76—81no—
168D76—81no—
169C4×D19—82no—
170Dic38—81no—
171C8×C19—42no—
172C19⋊C8—41no—
173C19⋊C8—41no—
174C19⋊C8—42no—
175C19⋊C8—41no—
176C19⋊C8—41no—
177#3112—191no—
178#2984—191no—
179#1763D1911yescharacteristic, complemented
180#1530—191no—
181#1502—191no—
182#1302—191no—
183#1285—191no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19#38611yescharacteristic
187C22×C19#47111yescharacteristic
188C22×C19#47211yescharacteristic
189C2×D19—81no—
190C2×D19—81no—
191C2×D19—81no—
192C4×C19—21no—
193C4×C19—22no—
194C4×C19—21no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—41no—
199C4×C19—41no—
200C4×C19—41no—
201C4×C19—82no—
202C4×C19C2×#10411yescharacteristic
203C4×C19#42111yescharacteristic
204Dic19—81no—
205#532—191no—
206C2×C4×Q8C2×D1911yescharacteristic
207#480—381no—
208#477—191no—
209#477—191no—
210#460—191no—
211#460—191no—
212#448—381no—
213#446—382no—
214#446—381no—
215C8×Q8—381no—
216#440—381no—
217#440—381no—
218#432—191no—
219#432—191no—
220#432—381no—
221#431—191no—
222#431—381no—
223C2×#103—21no—
224C2×#97C2×D1911yescharacteristic
225C4×C4⋊C4C2×D1911yescharacteristic
226#340—21no—
227#329—382no—
228#327—381no—
229#327—381no—
230C2×C19—21no—
231C2×C19—21no—
232C2×C19#187111yescharacteristic
233C2×C19#190511yescharacteristic
234C2×C19#190711yescharacteristic
235D19—161no—
236C2×#41—381no—
237C22×Q8C22⋊D1911yescharacteristic
238C2×SD16—381no—
239C2×SD16—381no—
240C22×C8—21no—
241C4⋊Q8—191no—
242#127—191no—
243#124—381no—
244#121—381no—
245#121—381no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8C4×D1911yescharacteristic
249C4×Q8C4×D1911yescharacteristic
250C4×Q8D7611yescharacteristic
251C4×Q8D7611yescharacteristic
252C4×D4—381no—
253C4×D4—381no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4C22⋊D1911yescharacteristic
257C2×C42—21no—
258C2×C42—21no—
259C2×C42C22×D1911yescharacteristic
260#107—381no—
261#107—381no—
262C4⋊C8—191no—
263C4⋊C8—191no—
264C4⋊C8—382no—
265C4⋊C8—382no—
266C4⋊C8—381no—
267C4⋊C8—381no—
268#103—24no—
269#103—381no—
270#103—381no—
271#102—381no—
272#102—381no—
273C22⋊C8—191no—
274C22⋊C8—191no—
275C22⋊C8—381no—
276C22⋊C8—381no—
277#97—21no—
278#97—21no—
279#97—192no—
280#97—382no—
281#97—381no—
282C4×C8—382no—
283C4×C8—381no—
284#95—21no—
285C19#916411yescharacteristic, complemented, Sylow
286#41—1521no—
287#41—1521no—
288C2×Q8—21no—
289C2×Q8—22no—
290C2×Q8—41no—
291C2×Q8—381no—
292C2×Q8(C2×D19)⋊C411yescharacteristic
293C2×Q8(C2×D19)⋊C411yescharacteristic
294C2×D4—381no—
295C2×D4—381no—
296C2×D4—381no—
297C2×D4—761no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—761no—
302C22×C4D4×D1911yescharacteristic
303C22×C4#6454311yescharacteristic
304C22×C4C2×C22⋊D1911yescharacteristic
305SD16—762no—
306SD16—762no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—381no—
311C2×C8—382no—
312C2×C8—381no—
313C2×C8—381no—
314C2×C8—381no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—41no—
322C4⋊C4—381no—
323C4⋊C4—381no—
324C4⋊C4(C2×D19)⋊C411yescharacteristic
325C4⋊C4(C2×D19)⋊C411yescharacteristic
326C22⋊C4—761no—
327C22⋊C4—761no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—21no—
332C42—81no—
333C42C2×C4×D1911yescharacteristic
334C42C2×D7611yescharacteristic
335C42D4×D1911yescharacteristic
336C42#6454311yescharacteristic
337C23—761no—
338C23#1059738511yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—21no—
342Q8—42no—
343Q8—1521no—
344Q8#1059726212yes—
345D4—761no—
346D4—761no—
347D4—1521no—
348D4—1521no—
349D4—1521no—
350D4—1521no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—761no—
367C2×C4—1522no—
368C2×C4(C22⋊D19)⋊C411yescharacteristic
369C2×C4(C22⋊D19)⋊C411yescharacteristic
370C2×C4#1059732811yescharacteristic
371C2×C4#1059733211yescharacteristic
372C2×C4C2×(C2×D19)⋊C411yescharacteristic
373C2×C4#1059738511yescharacteristic
374C8—42no—
375C8—761no—
376C8—762no—
377C8—761no—
378C8—761no—
379C8—761no—
380C22—21no—
381C22—21no—
382C22—1521no—
383C22—1521no—
384C22—1521no—
385C22#1192642111yescharacteristic
386C22#1192680911yescharacteristic
387C22#1192681211yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—82no—
398C4—1521no—
399C4C2×#1059726211yescharacteristic
400C4#1192656211yescharacteristic
401C2—21no—
402C2—21no—
403C2—3041no—
404C2#1456393511yescharacteristic
405C2#1456412711yescharacteristic
406C2#1456414111yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1763C2
socleC22×C19#386
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#1763D19
hypocenterC19#9164
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. #14572724C2semidirect
5. #14561534C2semidirect
6. #14561491C2semidirect
7. C19×#1763C2semidirect
10. #11926839C4semidirect
11. #11926839C4semidirect
12. #11926744C4semidirect
13. #11926744C4semidirect
179. #1763D19semidirect
285. C19#9164semidirect

Maximal subgroups

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

subgroupindex
#145737572
#145727242
#145622452
#145621292
#145615342
#145614912
C19×#17632
#916419