Finite Group Databasebeta

← #18082785

Subgroups — #18082785

Order 4864.

672 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926862C211yesmaximal, characteristic
2#14569380C211yesmaximal, characteristic
3C2×#11926482C211yesmaximal, characteristic, complemented
4C2×#11926279C211yesmaximal, characteristic
5C2×#11926269C211yesmaximal, characteristic, complemented
6#14561513C211yesmaximal, characteristic, complemented
7C19×#1824C211yesmaximal, characteristic, complemented
8C2×#10597332—21no—
9C2×#10597376C2211yescharacteristic
10C22×Dic19⋊C4C2211yescharacteristic
11#11926862—22no—
12#11926862—22no—
13C2×#10597265—21no—
14C2×#10597266—21no—
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926482—22no—
17#11926482—22no—
18#11926476—21no—
19#11926466—22no—
20#11926462—21no—
21#11926421—21no—
22C2×C19⋊#95—21no—
23C2×C19⋊#95—21no—
24C2×C19⋊#95C2211yescharacteristic
25#11926279—22no—
26#11926269—22no—
27C22×C4⋊C4×C19C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C19×#380C2211yescharacteristic
30C19×#340—22no—
31C23×C4×C19—21no—
32C23×C4×C19C2311yescharacteristic
33C22×C22⋊D19—21no—
34C23×Dic19—21no—
35C23×Dic19D411yescharacteristic
36C23×Dic19D411yescharacteristic
37C22×D76D411yescharacteristic
38C22×C8×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×C19D412yes—
45C2×C4⋊C4×C19D412yes—
46C2×C22⋊C4×C19—21no—
47#10597376—21no—
48#10597376—21no—
49#10597376—21no—
50#10597376—21no—
51C2×(C2×D19)⋊C4—22no—
52C2×(C2×D19)⋊C4—21no—
53C2×(C2×D19)⋊C4—22no—
54C2×C4⋊Dic19—22no—
55C2×C4⋊Dic19D411yescharacteristic
56C2×Dic19⋊C4—21no—
57C2×Dic19⋊C4—21no—
58C2×Dic19⋊C4—21no—
59C2×Dic19⋊C4—21no—
60C2×Dic19⋊C4—21no—
61C2×Dic19⋊C4—21no—
62C22×C19⋊C8—21no—
63#10597332—42no—
64#10597332—42no—
65C19×C22⋊C8—21no—
66C19×C22⋊C8—21no—
67C19×#95—21no—
68C19⋊#95—24no—
69C19⋊#95—24no—
70C19⋊#95—22no—
71C19⋊#95—21no—
72C19⋊#95D412yes—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)D412yes—
75#10597266—24no—
76#10597265—24no—
77C24×C19C2×D411yescharacteristic
78C23×D19—21no—
79C22×C4×C19—22no—
80C22×C4×C19—22no—
81C22×C4×C19—42no—
82C22×C4×C19—44no—
83C22×C4×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19#4111yescharacteristic
91C2×C22⋊D19—41no—
92C2×C22⋊D19—41no—
93C2×C22⋊D19—41no—
94C2×C22⋊D19—41no—
95C2×C22⋊D19—41no—
96C2×C22⋊D19—41no—
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—21no—
100C22×Dic19—21no—
101C22×Dic19—21no—
102C22×Dic19—21no—
103C22×Dic19—22no—
104C22×Dic19—21no—
105C22×Dic19—21no—
106C22×Dic19—21no—
107C22×Dic19—21no—
108C22×Dic19—42no—
109C22×Dic19—42no—
110C22×Dic19—42no—
111C22×Dic19—41no—
112C22×Dic19—41no—
113C22×Dic19SD1612yes—
114C2×D76—21no—
115C2×D76—21no—
116C2×D76—42no—
117C2×C8×C19—42no—
118C2×C8×C19—41no—
119C4⋊C4×C19—22no—
120C4⋊C4×C19—22no—
121C4⋊C4×C19—42no—
122C4⋊C4×C19—41no—
123C4⋊C4×C19—41no—
124C22⋊C4×C19—41no—
125C22⋊C4×C19—41no—
126(C2×D19)⋊C4—44no—
127(C2×D19)⋊C4—41no—
128(C2×D19)⋊C4—41no—
129(C2×D19)⋊C4—82no—
130C4⋊Dic19—21no—
131C4⋊Dic19—21no—
132C4⋊Dic19—44no—
133Dic19⋊C4—41no—
134Dic19⋊C4—41no—
135Dic19⋊C4—41no—
136Dic19⋊C4—41no—
137C2×C19⋊C8—22no—
138C2×C19⋊C8—42no—
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—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—44no—
161C2×C4×C19—42no—
162C2×C4×C19—42no—
163C2×C4×C19—42no—
164C2×C4×C19—42no—
165C2×C4×C19—82no—
166C2×C4×C19—82no—
167C2×C4×C19#12011yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×C4×C19#12111yescharacteristic
170C2×C4×C19#12711yescharacteristic
171C22⋊D19—81no—
172C22⋊D19—81no—
173C22⋊D19—81no—
174C22⋊D19—81no—
175C2×Dic19—22no—
176C2×Dic19—22no—
177C2×Dic19—22no—
178C2×Dic19—41no—
179C2×Dic19—41no—
180C2×Dic19—41no—
181C2×Dic19—41no—
182C2×Dic19—42no—
183C2×Dic19—42no—
184C2×Dic19—42no—
185C2×Dic19—41no—
186C2×Dic19—41no—
187C2×Dic19—42no—
188C2×Dic19—41no—
189C2×Dic19—41no—
190C2×Dic19—42no—
191C2×Dic19—82no—
192C2×Dic19—82no—
193C2×Dic19—81no—
194D76—42no—
195D76—81no—
196C8×C19—81no—
197C19⋊C8—42no—
198C2×#481—191no—
199#2618—191no—
200C2×#400—191no—
201#1824D1911yescharacteristic, complemented
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—82no—
232C4×C19—82no—
233Dic19—42no—
234Dic19—82no—
235Dic19—81no—
236Dic19—81no—
237C2×#123—381no—
238C2×#121—191no—
239C22×C4⋊C4—191no—
240C22×C4⋊C4C2×D1911yescharacteristic
241#481—382no—
242#481—382no—
243C2×#106—381no—
244C2×#102—381no—
245C2×C22⋊C8—191no—
246C2×C22⋊C8C2×D1911yescharacteristic
247#400—382no—
248#400—382no—
249#398—381no—
250#396—382no—
251#394—381no—
252#386—381no—
253#380C2×D1911yescharacteristic
254C2×#95—191no—
255C2×#95—381no—
256C2×#95—381no—
257#340—22no—
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—191no—
274C23×C4—191no—
275C23×C4—381no—
276C23×C4C22×D1911yescharacteristic
277C22×C8—21no—
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—191no—
291C2×C4⋊C4—382no—
292C2×C4⋊C4—381no—
293C2×C4⋊C4—381no—
294C2×C4⋊C4—381no—
295C2×C4⋊C4—381no—
296C2×C4⋊C4—381no—
297C2×C4⋊C4—381no—
298C2×C4⋊C4D7612yes—
299C2×C4⋊C4C22⋊D1912yes—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—382no—
302C2×C22⋊C4—381no—
303C2×C22⋊C4—382no—
304#106—384no—
305#102—384no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—192no—
309C22⋊C8—381no—
310#95—21no—
311#95—192no—
312#95—384no—
313#95—384no—
314#95—382no—
315#95—381no—
316C19#992111yescharacteristic, complemented, Sylow
317C24—381no—
318C24D4×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—22no—
329C22×C4—22no—
330C22×C4—42no—
331C22×C4—44no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—192no—
335C22×C4—381no—
336C22×C4—381no—
337C22×C4—381no—
338C22×C4—381no—
339C22×C4—381no—
340C22×C4—381no—
341C22×C4—381no—
342C22×C4—381no—
343C22×C4—382no—
344C22×C4—381no—
345C22×C4—381no—
346C22×C4—762no—
347C22×C4—762no—
348C22×C4—762no—
349C22×C4—761no—
350C22×C4—761no—
351C22×C4C2×D7611yescharacteristic
352C22×C4#6454111yescharacteristic
353C22×C4D4×D1911yescharacteristic
354C22×C4D4×D1911yescharacteristic
355C22×C4D4×D1911yescharacteristic
356C22×C4C2×C22⋊D1911yescharacteristic
357C2×C8—42no—
358C2×C8—41no—
359C2×C8—382no—
360C2×C8—762no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—42no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—381no—
367C4⋊C4—381no—
368C4⋊C4—764no—
369C4⋊C4—761no—
370C4⋊C4—761no—
371C4⋊C4—761no—
372C4⋊C4—761no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—764no—
376C22⋊C4—761no—
377C22⋊C4—761no—
378C22⋊C4—1522no—
379C23—22no—
380C23—22no—
381C23—761no—
382C23—761no—
383C23—761no—
384C23—762no—
385C23—762no—
386C23#1059732811yescharacteristic
387C23#1059733011yescharacteristic
388C23SD16×D1911yescharacteristic
389C23#1059736011yescharacteristic
390C23#1059736411yescharacteristic
391C23#1059736511yescharacteristic
392C23#1059738311yescharacteristic
393D4—762no—
394D4—1521no—
395D4—1521no—
396D4—1521no—
397D4—1521no—
398D4—1521no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—382no—
413C2×C4—382no—
414C2×C4—382no—
415C2×C4—761no—
416C2×C4—761no—
417C2×C4—761no—
418C2×C4—761no—
419C2×C4—762no—
420C2×C4—762no—
421C2×C4—762no—
422C2×C4—762no—
423C2×C4—761no—
424C2×C4—761no—
425C2×C4—761no—
426C2×C4—761no—
427C2×C4—762no—
428C2×C4—1522no—
429C2×C4—1522no—
430C2×C4—1521no—
431C2×C4#1059732811yescharacteristic
432C2×C4#1059733011yescharacteristic
433C2×C4#1059737611yescharacteristic
434C2×C4#1059738611yescharacteristic
435C8—81no—
436C8—762no—
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#1192645311yescharacteristic
451C22#1192668411yescharacteristic
452C22#1192669211yescharacteristic
453C22#1192669311yescharacteristic
454C22#1192670511yescharacteristic
455C22#1192671512yes—
456C22#1192673312yes—
457C22#1192677611yescharacteristic
458C22#1192679311yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—82no—
464C4—82no—
465C4—762no—
466C4—1522no—
467C4—1521no—
468C4—1521no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—3041no—
474C2#1456266512yes—
475C2#1456267012yes—
476C2#1456463711yescharacteristic
477C2#1456465811yescharacteristic
478C2#1456476611yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1824C2
socleC23×C19#120
prime radicalC2×#10597376C22
hypercenter#1824D19
hypocenterC19#9921
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
3. C2×#11926482C2semidirect
5. C2×#11926269C2semidirect
6. #14561513C2semidirect
7. C19×#1824C2semidirect
201. #1824D19semidirect
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
#145693802
C2×#119264822
C2×#119262792
C2×#119262692
#145615132
C19×#18242
#992119