Finite Group Databasebeta

← #11791444

Subgroups — #11791444

Order 1152.

642 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63502C211yesmaximal, characteristic
2C2×C9×#102C211yesmaximal, characteristic, complemented
3C2×#63392C211yesmaximal, characteristic, complemented
4C2×#63380C211yesmaximal, characteristic, complemented
5C2×Dic9⋊C8C211yesmaximal, characteristic, complemented
6C4⋊C4×Dic9C211yesmaximal, characteristic, complemented
7C2×#63369C211yesmaximal, characteristic, complemented
8#70161—31nomaximal
9C22×D4×C9C2211yescharacteristic
10C22×#611—21no—
11C22×#611—21no—
12C22×D36C2211yescharacteristic
13C22×C8×C9C2211yescharacteristic
14C2×C9×C4⋊C4C2211yescharacteristic
15#63502—22no—
16#63502C414yescomplemented
17C2×C4⋊Dic9C2211yescharacteristic
18C2×C4×Dic9—21no—
19C2×C4×Dic9C2211yescharacteristic
20C22×C9⋊C8C2211yescharacteristic
21C9×#102—22no—
22#63392—22no—
23C9⋊#95—21no—
24#63380—22no—
25Dic9⋊C8—22no—
26#63369—22no—
27C2×#940—31no—
28C2×C3×#102D311yescharacteristic
29C2×#832—31no—
30C2×#821—31no—
31C2×Dic3⋊C8—31no—
32Dic3×C4⋊C4—31no—
33C2×#809—31no—
34C24×C9—21no—
35C23×D9—21no—
36C2×D4×C9—21no—
37C2×D4×C9—21no—
38C2×D4×C9—21no—
39C2×D4×C9—21no—
40C2×D4×C9—21no—
41C2×D4×C9C2×C412yes—
42C22×C4×C9—21no—
43C22×C4×C9C2311yescharacteristic
44C2×#611—24no—
45C2×#611—24no—
46C2×#611—42no—
47C2×#611—42no—
48C2×#611—42no—
49C2×#611—42no—
50C22×Dic9—21no—
51C22×Dic9D411yescharacteristic
52C22×Dic9D411yescharacteristic
53C2×D36—21no—
54C2×D36—21no—
55C2×D36—21no—
56C2×D36—21no—
57C2×D36—21no—
58C2×D36C2×C412yes—
59C2×C8×C9—21no—
60C2×C8×C9—21no—
61C2×C8×C9—21no—
62C9×C4⋊C4—21no—
63C9×C4⋊C4D412yescomplemented
64C4⋊Dic9—21no—
65C4⋊Dic9D412yescomplemented
66C4×Dic9—42no—
67C4×Dic9C2×C412yes—
68C4×Dic9D412yes—
69C2×C9⋊C8—21no—
70C2×C9⋊C8—21no—
71C2×C9⋊C8—21no—
72#1982—91noSylow
73C22×C3×D4C2×D311yescharacteristic
74C22×#67—61no—
75C22×#67—61no—
76C22×D12—31no—
77C22×C3×C8C2×D311yescharacteristic
78C2×C3×C4⋊C4C2×D311yescharacteristic
79#940—34no—
80#940—62no—
81C2×C4⋊Dic3—31no—
82C2×C4×Dic3—31no—
83C2×C4×Dic3—61no—
84C22×C3⋊C8—31no—
85C3×#102—22no—
86#832—62no—
87C3⋊#95—61no—
88#821—62no—
89Dic3⋊C8—62no—
90#809—62no—
91C23×C9—22no—
92C23×C9—41no—
93C23×C9—41no—
94C23×C9—41no—
95C23×C9—41no—
96C23×C9—41no—
97C23×C9—41no—
98C23×C9C2×D411yescharacteristic
99C22×D9—22no—
100C22×D9—41no—
101C22×D9—41no—
102C22×D9—41no—
103C22×D9—41no—
104C22×D9—41no—
105C22×D9—41no—
106D4×C9—22no—
107D4×C9—22no—
108D4×C9—41no—
109D4×C9—41no—
110C2×C4×C9—22no—
111C2×C4×C9—41no—
112C2×C4×C9—41no—
113C2×C4×C9C22×C411yescharacteristic
114C2×C4×C9C2×D411yescharacteristic
115C2×C4×C9C2×D411yescharacteristic
116C2×C4×C9C2×D411yescharacteristic
117C2×C4×C9#4111yescharacteristic
118C2×C4×C9#4111yescharacteristic
119#611—48no—
120#611—48no—
121C2×Dic9—21no—
122C2×Dic9—21no—
123C2×Dic9—22no—
124C2×Dic9—41no—
125C2×Dic9—41no—
126C2×Dic9C22⋊C412yes—
127C2×Dic9C22⋊C412yes—
128C2×Dic9D812yes—
129C2×Dic9SD1612yes—
130D36—22no—
131D36—22no—
132D36—41no—
133D36—41no—
134C8×C9—41no—
135C9⋊C8—41no—
136C2×#127—91no—
137C2×C4⋊C8—91no—
138C2×#102—91no—
139C2×#102—91no—
140C2×#102—91no—
141C2×#102D911yescharacteristic, complemented
142C4×C4⋊C4—91no—
143C24×C3—21no—
144C23×D3—61no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4C4×D312yes—
151C22×C3×C4—21no—
152C22×C3×C4C22×D311yescharacteristic
153C2×#67—64no—
154C2×#67—64no—
155C2×#67—122no—
156C2×#67—122no—
157C2×#67—122no—
158C2×#67—122no—
159C22×Dic3—31no—
160C22×Dic3—31no—
161C22×Dic3—61no—
162C2×D12—32no—
163C2×D12—61no—
164C2×D12—61no—
165C2×D12—61no—
166C2×D12—61no—
167C2×D12—61no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4#6712yes—
173C4⋊Dic3—32no—
174C4⋊Dic3—61no—
175C4×Dic3—32no—
176C4×Dic3—32no—
177C4×Dic3—122no—
178C2×C3⋊C8—61no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—61no—
181C22×C9—42no—
182C22×C9—42no—
183C22×C9—42no—
184C22×C9—81no—
185C22×C9—81no—
186C22×C9—81no—
187C22×C9—81no—
188C22×C9C2×C22⋊C411yescharacteristic
189C22×C9#12111yescharacteristic
190C22×C9#12111yescharacteristic
191C22×C9C2×D811yescharacteristic
192C22×C9C2×SD1611yescharacteristic
193C22×C9AGL(1,ℤ/8)11yescharacteristic
194C22×C9AGL(1,ℤ/8)11yescharacteristic
195C2×D9—42no—
196C2×D9—42no—
197C2×D9—42no—
198C2×D9—81no—
199C2×D9—81no—
200C2×D9—81no—
201C2×D9—81no—
202C4×C9—42no—
203C4×C9C4×D411yescharacteristic
204C4×C9C4×D411yescharacteristic
205C4×C9#12411yescharacteristic
206C4×C9#12711yescharacteristic
207Dic9—22no—
208Dic9—42no—
209Dic9#10214yescomplemented
210C22×D4—91no—
211C22×D4—181no—
212C22×D4—181no—
213C22×D4C2×D911yescharacteristic
214C22×C8—91no—
215C22×C8C2×D911yescharacteristic
216#127—94no—
217#127—182no—
218C2×C4⋊C4—91no—
219C2×C4⋊C4C2×D911yescharacteristic
220C2×C42—91no—
221C2×C42—181no—
222C4⋊C8—182no—
223#102—22no—
224#102—182no—
225#102—182no—
226#102—182no—
227#95—181no—
228C23×C3—22no—
229C23×C3—41no—
230C23×C3—41no—
231C23×C3—41no—
232C23×C3—41no—
233C23×C3—41no—
234C23×C3—41no—
235C23×C3D3×D411yescharacteristic
236C22×D3—62no—
237C22×D3—121no—
238C22×D3—121no—
239C22×D3—121no—
240C22×D3—121no—
241C22×D3—121no—
242C22×D3—121no—
243C3×D4—22no—
244C3×D4—22no—
245C3×D4—41no—
246C3×D4—41no—
247C2×C3×C4—22no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4C2×C4×D311yescharacteristic
251C2×C3×C4#23511yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4#23711yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256#67—128no—
257#67—128no—
258C2×Dic3—32no—
259C2×Dic3—32no—
260C2×Dic3—32no—
261C2×Dic3—32no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—62no—
265C2×Dic3—121no—
266C2×Dic3—121no—
267D12—62no—
268D12—62no—
269D12—121no—
270D12—121no—
271C3×C8—41no—
272C3⋊C8—121no—
273C2×C9—82no—
274C2×C9#39011yescharacteristic
275C2×C9C2×#10211yescharacteristic
276C2×C9#41811yescharacteristic
277C2×C9#45911yescharacteristic
278C2×C9#45911yescharacteristic
279C2×C9#46011yescharacteristic
280C2×C9#46011yescharacteristic
281D9—82no—
282C24—21no—
283C24—181no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—92no—
290C2×D4—184no—
291C2×D4—184no—
292C2×D4—181no—
293C2×D4—181no—
294C2×D4—181no—
295C2×D4—181no—
296C2×D4—181no—
297C2×D4—362no—
298C2×D4—362no—
299C2×D4—362no—
300C2×D4—362no—
301C2×D4C4×D912yes—
302C22×C4—21no—
303C22×C4—91no—
304C22×C4—91no—
305C22×C4—181no—
306C22×C4C22×D911yescharacteristic
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—181no—
311C2×C8—181no—
312C2×C8—181no—
313C4⋊C4—21no—
314C4⋊C4—92no—
315C4⋊C4—181no—
316C4⋊C4#61112yescomplemented
317C42—92no—
318C42—92no—
319C42—362no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3—42no—
323C22×C3—81no—
324C22×C3—81no—
325C22×C3—81no—
326C22×C3—81no—
327C22×C3D3×C22⋊C411yescharacteristic
328C22×C3#88411yescharacteristic
329C22×C3D3×D811yescharacteristic
330C22×C3#91111yescharacteristic
331C22×C3D3×SD1611yescharacteristic
332C22×C3#91411yescharacteristic
333C22×C3#93911yescharacteristic
334C2×D3—122no—
335C2×D3—122no—
336C2×D3—122no—
337C2×D3—241no—
338C2×D3—241no—
339C2×D3—241no—
340C2×D3—241no—
341C3×C4—42no—
342C3×C4#67⋊C411yescharacteristic
343C3×C4#88511yescharacteristic
344C3×C4C4×#6711yescharacteristic
345C3×C4#94011yescharacteristic
346Dic3—34no—
347Dic3—62no—
348Dic3—122no—
349C9#198211yescharacteristic, complemented, Sylow
350C23—22no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—182no—
358C23—361no—
359C23—361no—
360C23—361no—
361C23—361no—
362C23—361no—
363C23—361no—
364C23D4×D911yescharacteristic
365D4—22no—
366D4—22no—
367D4—41no—
368D4—41no—
369D4—182no—
370D4—182no—
371D4—368no—
372D4—368no—
373D4—361no—
374D4—361no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—92no—
379C2×C4—92no—
380C2×C4—92no—
381C2×C4—92no—
382C2×C4—181no—
383C2×C4—181no—
384C2×C4—182no—
385C2×C4—361no—
386C2×C4—361no—
387C2×C4C2×C4×D911yescharacteristic
388C2×C4#369711yescharacteristic
389C2×C4D4×D911yescharacteristic
390C2×C4D4×D911yescharacteristic
391C2×C4#369911yescharacteristic
392C2×C4C2×#61111yescharacteristic
393C8—41no—
394C8—361no—
395C2×C3—82no—
396C2×C3#476211yescharacteristic
397C2×C3D3×#10211yescharacteristic
398C2×C3#477011yescharacteristic
399C2×C3#478611yescharacteristic
400C2×C3#495711yescharacteristic
401C2×C3#515011yescharacteristic
402C2×C3#516311yescharacteristic
403D3—242no—
404C22—42no—
405C22—42no—
406C22—42no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—362no—
412C22—362no—
413C22—362no—
414C22—721no—
415C22—721no—
416C22—721no—
417C22—721no—
418C22C22⋊C4×D911yescharacteristic
419C22#6344611yescharacteristic
420C22D8×D911yescharacteristic
421C22#6347311yescharacteristic
422C22SD16×D911yescharacteristic
423C22#6347611yescharacteristic
424C22#6350111yescharacteristic
425C4—42no—
426C4—94no—
427C4—182no—
428C4—362no—
429C4#611⋊C411yescharacteristic
430C4#6344711yescharacteristic
431C4C4×#61111yescharacteristic
432C4#6350211yescharacteristic
433C3#7016111yescharacteristic
434C2—82no—
435C2—722no—
436C2#1058844211yescharacteristic
437C2D9×#10211yescharacteristic
438C2#1058845011yescharacteristic
439C2#1058846611yescharacteristic
440C2#1058863711yescharacteristic
441C2#1058883011yescharacteristic
442C2#1058884311yescharacteristic
subgroupG/H
centerC23D4×D9
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC2×C9×#102C2
socleC23×C3D3×D4
prime radicalC2×#63502C2
cosocleC22×C4×C9C23
hypercenterC2×#102D9
hypocenterC9#1982
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×C9×#102C2semidirect
3. C2×#63392C2semidirect
4. C2×#63380C2semidirect
5. C2×Dic9⋊C8C2semidirect
6. C4⋊C4×Dic9C2semidirect
7. C2×#63369C2semidirect
16. #63502C4semidirect
63. C9×C4⋊C4D4semidirect
65. C4⋊Dic9D4semidirect
141. C2×#102D9semidirect
209. Dic9#102semidirect
316. C4⋊C4#611semidirect
349. C9#1982semidirect

Maximal subgroups

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

subgroupindex
C2×#635022
C2×C9×#1022
C2×#633922
C2×#633802
C2×Dic9⋊C82
C4⋊C4×Dic92
C2×#633692
#701613