Finite Group Databasebeta

← #18082784

Subgroups — #18082784

Order 4864.

672 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926862C211yesmaximal, characteristic
2#14569377C211yesmaximal, characteristic
3#14563725C211yesmaximal, characteristic, complemented
4C2×#11926277C211yesmaximal, characteristic
5C2×#11926270C211yesmaximal, characteristic, complemented
6#14561514C211yesmaximal, characteristic, complemented
7C2×C19×#400C211yesmaximal, characteristic, complemented
8C2×#10597375—21no—
9C2×#10597376C2211yescharacteristic
10#11926862—22no—
11#11926862—22no—
12C2×#10597265—21no—
13C2×#10597266—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926474—21no—
17#11926466—22no—
18#11926461—21no—
19#11926423—21no—
20#11926404C2211yescharacteristic
21#11926306—22no—
22#11926277—22no—
23#11926270—22no—
24C22×C4⋊C4×C19C2211yescharacteristic
25C22×C4⋊C4×C19C2211yescharacteristic
26C19×#400—22no—
27C19×#400—22no—
28C2×C19×#95—21no—
29C2×C19×#95—21no—
30C2×C19×#95C2211yescharacteristic
31C23×C4×C19—21no—
32C23×C4×C19—21no—
33C23×C4×C19D411yescharacteristic
34C23×C4×C19D411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C22×C22⋊D19—21no—
37C22×D76D411yescharacteristic
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19—21no—
49C2×C4⋊C4×C19D412yes—
50C2×C22⋊Dic19—21no—
51#10597376—21no—
52#10597376—21no—
53#10597376—21no—
54#10597376—21no—
55#10597375—42no—
56#10597375—42no—
57C2×(C2×D19)⋊C4—22no—
58C2×(C2×D19)⋊C4—21no—
59C2×(C2×D19)⋊C4—22no—
60C2×C4⋊Dic19D411yescharacteristic
61C2×C4⋊Dic19D412yes—
62C2×Dic19⋊C4—22no—
63C22×C19⋊C8—21no—
64C22×C19⋊C8—21no—
65C19×#95—24no—
66C19×#95—24no—
67C19×#95—21no—
68C19×#95D412yes—
69C19⋊#95—22no—
70C19⋊#95—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)D412yes—
75#10597266—24no—
76#10597265—24no—
77C24×C19C2×D411yescharacteristic
78C23×D19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19—22no—
88C22×C4×C19—22no—
89C22×C4×C19—21no—
90C22×C4×C19—42no—
91C22×C4×C19—42no—
92C22×C4×C19—42no—
93C22×C4×C19—42no—
94C22×C4×C19—44no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19—41no—
98C22×C4×C19—41no—
99C22×C4×C19SD1612yes—
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19#4111yescharacteristic
106C2×C22⋊D19—41no—
107C2×C22⋊D19—41no—
108C2×C22⋊D19—41no—
109C2×C22⋊D19—41no—
110C2×C22⋊D19—41no—
111C2×C22⋊D19—41no—
112C22×Dic19—22no—
113C22×Dic19—21no—
114C2×D76—21no—
115C2×D76—21no—
116C2×D76—42no—
117C4⋊C4×C19—22no—
118C4⋊C4×C19—22no—
119C4⋊C4×C19—41no—
120C4⋊C4×C19—41no—
121C4⋊C4×C19—41no—
122C4⋊C4×C19—41no—
123C4⋊C4×C19—41no—
124C4⋊C4×C19—41no—
125C22⋊Dic19—41no—
126C22⋊Dic19—41no—
127(C2×D19)⋊C4—44no—
128(C2×D19)⋊C4—41no—
129(C2×D19)⋊C4—41no—
130(C2×D19)⋊C4—82no—
131C4⋊Dic19—21no—
132C4⋊Dic19—21no—
133C4⋊Dic19—42no—
134Dic19⋊C4—44no—
135C2×C19⋊C8—22no—
136C2×C19⋊C8—42no—
137C2×C19⋊C8—42no—
138C2×C19⋊C8—41no—
139#9921—191nomaximal, Sylow
140C23×C19—22no—
141C23×C19—22no—
142C23×C19#12011yescharacteristic
143C23×C19#12011yescharacteristic
144C23×C19#12111yescharacteristic
145C23×C19C2×SD1611yescharacteristic
146C23×C19#13511yescharacteristic
147C23×C19AGL(1,ℤ/8)11yescharacteristic
148C23×C19#13711yescharacteristic
149C22×D19—41no—
150C22×D19—41no—
151C22×D19—41no—
152C22×D19—42no—
153C22×D19—42no—
154C2×C4×C19—22no—
155C2×C4×C19—22no—
156C2×C4×C19—22no—
157C2×C4×C19—22no—
158C2×C4×C19—22no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—42no—
168C2×C4×C19—42no—
169C2×C4×C19—44no—
170C2×C4×C19—42no—
171C2×C4×C19—42no—
172C2×C4×C19—41no—
173C2×C4×C19—42no—
174C2×C4×C19—42no—
175C2×C4×C19—82no—
176C2×C4×C19—82no—
177C2×C4×C19—82no—
178C2×C4×C19—82no—
179C2×C4×C19—81no—
180C2×C4×C19#12011yescharacteristic
181C2×C4×C19#12111yescharacteristic
182C2×C4×C19#12111yescharacteristic
183C2×C4×C19#12711yescharacteristic
184C22⋊D19—81no—
185C22⋊D19—81no—
186C22⋊D19—81no—
187C22⋊D19—81no—
188C2×Dic19—41no—
189C2×Dic19—41no—
190C2×Dic19—42no—
191C2×Dic19—41no—
192C2×Dic19—42no—
193C2×Dic19—42no—
194D76—42no—
195D76—81no—
196C19⋊C8—42no—
197C19⋊C8—81no—
198C2×#481—191no—
199#2618—191no—
200C2×#400D1911yescharacteristic, complemented
201#1824—191no—
202C2×#327—191no—
203C2×#324—191no—
204#1294—191no—
205C22×C19—22no—
206C22×C19—22no—
207C22×C19—22no—
208C22×C19—22no—
209C22×C19—21no—
210C22×C19—21no—
211C22×C19—21no—
212C22×C19—21no—
213C22×C19#39211yescharacteristic
214C22×C19#44811yescharacteristic
215C22×C19#44911yescharacteristic
216C22×C19#45011yescharacteristic
217C22×C19#45211yescharacteristic
218C22×C19#45412yes—
219C22×C19#45812yes—
220C22×C19#46511yescharacteristic
221C22×C19#46811yescharacteristic
222C2×D19—82no—
223C2×D19—82no—
224C2×D19—81no—
225C2×D19—81no—
226C2×D19—81no—
227C4×C19—21no—
228C4×C19—21no—
229C4×C19—21no—
230C4×C19—21no—
231C4×C19—42no—
232C4×C19—82no—
233C4×C19—82no—
234C4×C19—81no—
235Dic19—82no—
236Dic19—81no—
237C2×#123—381no—
238C2×#121—191no—
239C22×C4⋊C4C2×D1911yescharacteristic
240C22×C4⋊C4C2×D1911yescharacteristic
241#481—382no—
242#481—382no—
243C2×#106—381no—
244C2×#102—381no—
245C2×C22⋊C8—191no—
246C2×C22⋊C8—191no—
247#400—22no—
248#400—22no—
249#398—381no—
250#396—382no—
251#394—381no—
252#386—381no—
253#380—191no—
254C2×#95—21no—
255C2×#95—21no—
256C2×#95C2×D1911yescharacteristic
257#340—382no—
258#327—382no—
259#324—382no—
260C2×C19—21no—
261C2×C19—21no—
262C2×C19—21no—
263C2×C19—21no—
264C2×C19#161512yes—
265C2×C19#161612yes—
266C2×C19#200011yescharacteristic
267C2×C19#200311yescharacteristic
268C2×C19#202211yescharacteristic
269D19—161no—
270C22×D4—191no—
271C22×D4—381no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4C22⋊D1911yescharacteristic
275C23×C4C22⋊D1911yescharacteristic
276C23×C4C22×D1911yescharacteristic
277C22×C8—381no—
278C22×C8—381no—
279#123—762no—
280#123—762no—
281#121—381no—
282#121—381no—
283#121—381no—
284#121—381no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—191no—
297C2×C4⋊C4—192no—
298C2×C4⋊C4—382no—
299C2×C4⋊C4C22⋊D1912yes—
300C2×C22⋊C4—382no—
301C2×C22⋊C4—381no—
302C2×C22⋊C4—381no—
303C2×C22⋊C4—382no—
304#106—384no—
305#102—384no—
306C22⋊C8—192no—
307C22⋊C8—381no—
308C22⋊C8—381no—
309C22⋊C8—381no—
310#95—24no—
311#95—24no—
312#95—21no—
313#95—382no—
314#95—381no—
315#95C22⋊D1912yes—
316C19#992111yescharacteristic, complemented, Sylow
317C24—381no—
318C24C2×C22⋊D1911yescharacteristic
319C2×D4—381no—
320C2×D4—381no—
321C2×D4—762no—
322C2×D4—761no—
323C2×D4—761no—
324C2×D4—761no—
325C2×D4—761no—
326C2×D4—761no—
327C2×D4—761no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—44no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—382no—
349C22×C4—381no—
350C22×C4#6452712yes—
351C22×C4D4×D1911yescharacteristic
352C22×C4D4×D1911yescharacteristic
353C22×C4D4×D1911yescharacteristic
354C22×C4#6454311yescharacteristic
355C22×C4C2×C22⋊D1911yescharacteristic
356C22×C4C2×C22⋊D1911yescharacteristic
357C2×C8—382no—
358C2×C8—762no—
359C2×C8—762no—
360C2×C8—761no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—381no—
370C4⋊C4—381no—
371C4⋊C4—762no—
372C4⋊C4—764no—
373C22⋊C4—764no—
374C22⋊C4—761no—
375C22⋊C4—761no—
376C22⋊C4—761no—
377C22⋊C4—761no—
378C22⋊C4—1522no—
379C23—22no—
380C23—22no—
381C23—761no—
382C23—761no—
383C23—761no—
384C23—762no—
385C23—762no—
386C23#1059738311yescharacteristic
387C23#1059738511yescharacteristic
388C23C2×#6452711yescharacteristic
389C23#1059738811yescharacteristic
390C23#1059739511yescharacteristic
391C23#1059739611yescharacteristic
392C23#1059739911yescharacteristic
393D4—762no—
394D4—1521no—
395D4—1521no—
396D4—1521no—
397D4—1521no—
398D4—1521no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—81no—
425C2×C4—762no—
426C2×C4—761no—
427C2×C4—761no—
428C2×C4—761no—
429C2×C4—762no—
430C2×C4—762no—
431C2×C4#1059738311yescharacteristic
432C2×C4#1059738411yescharacteristic
433C2×C4#1059738511yescharacteristic
434C2×C4#1059738611yescharacteristic
435C8—762no—
436C8—1521no—
437C22—21no—
438C22—21no—
439C22—22no—
440C22—22no—
441C22—22no—
442C22—22no—
443C22—21no—
444C22—21no—
445C22—1521no—
446C22—1521no—
447C22—1522no—
448C22—1522no—
449C22—1521no—
450C22#1192645211yescharacteristic
451C22#1192668311yescharacteristic
452C22#1192668911yescharacteristic
453C22#1192669411yescharacteristic
454C22#1192670411yescharacteristic
455C22#1192671612yes—
456C22#1192673312yes—
457C22#1192677511yescharacteristic
458C22#1192679211yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—82no—
465C4—82no—
466C4—81no—
467C4—1521no—
468C4—1522no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—3041no—
474C2#1456266412yes—
475C2#1456267112yes—
476C2#1456463611yescharacteristic
477C2#1456465711yescharacteristic
478C2#1456476311yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#400C2
socleC23×C19#120
prime radicalC2×#10597376C22
hypercenterC2×#400D19
hypocenterC19#9921
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
3. #14563725C2semidirect
5. C2×#11926270C2semidirect
6. #14561514C2semidirect
7. C2×C19×#400C2semidirect
200. C2×#400D19semidirect
316. C19#9921semidirect

Maximal subgroups

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

subgroupindex
C2×#119268622
#145693772
#145637252
C2×#119262772
C2×#119262702
#145615142
C2×C19×#4002
#992119