Finite Group Databasebeta

← #11793144

Subgroups — #11793144

Order 1152.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#121C211yesmaximal, characteristic
2C2×#63392C211yesmaximal, characteristic, complemented
3C2×#63392C211yesmaximal, characteristic, complemented
4#10588892C211yesmaximal, characteristic, complemented
5C2×#63389C211yesmaximal, characteristic, complemented
6C2×#63366C211yesmaximal, characteristic, complemented
7#10588206C211yesmaximal, characteristic, complemented
8#71679—31nomaximal
9C22×D4×C9—21no—
10C22×D4×C9C2211yescharacteristic
11C23×C4×C9C2211yescharacteristic
12C9×#121—22no—
13C9×#121—22no—
14C2×C9×C4⋊C4C2211yescharacteristic
15C2×C9×C22⋊C4—21no—
16C2×#3676—21no—
17C2×C4⋊Dic9C2211yescharacteristic
18C2×C4⋊Dic9C2211yescharacteristic
19C22×C9⋊C8C2211yescharacteristic
20C22×C9⋊C8C2211yescharacteristic
21#63392—22no—
22#63392—22no—
23C9⋊#95—21no—
24#63389—22no—
25#63366—22no—
26C2×C3×#121D311yescharacteristic
27C2×#832—31no—
28C2×#832—31no—
29#5212—31no—
30C2×#830—31no—
31C2×#807—31no—
32#4529—31no—
33C24×C9—21no—
34C24×C9D411yescharacteristic
35C2×D4×C9—24no—
36C2×D4×C9—21no—
37C2×D4×C9—21no—
38C2×D4×C9—21no—
39C2×D4×C9—21no—
40C2×D4×C9—21no—
41C2×D4×C9—42no—
42C2×D4×C9—42no—
43C2×D4×C9D412yes—
44C22×C4×C9—21no—
45C22×C4×C9—21no—
46C22×C4×C9—21no—
47C22×C4×C9—21no—
48C22×C4×C9—21no—
49C22×C4×C9—21no—
50C22×C4×C9—21no—
51C22×C4×C9D411yescharacteristic
52C22×C4×C9C2311yescharacteristic
53C22×Dic9—21no—
54C22×Dic9—21no—
55C9×C4⋊C4—21no—
56C9×C4⋊C4D412yes—
57C9×C22⋊C4—24no—
58#3676—42no—
59C4⋊Dic9—21no—
60C4⋊Dic9—21no—
61C4⋊Dic9—21no—
62C4⋊Dic9—21no—
63C2×C9⋊C8—21no—
64C2×C9⋊C8—21no—
65C2×C9⋊C8—21no—
66C2×C9⋊C8—21no—
67C2×C9⋊C8—21no—
68C2×C9⋊C8D412yescomplemented
69#2033—91noSylow
70C22×C3×D4—21no—
71C22×C3×D4C2×D311yescharacteristic
72C23×C3×C4C2×D311yescharacteristic
73C3×#121—22no—
74C3×#121—22no—
75C2×C3×C4⋊C4C2×D311yescharacteristic
76C2×C3×C22⋊C4—21no—
77C2×#217—61no—
78C2×C4⋊Dic3—31no—
79C2×C4⋊Dic3—31no—
80C22×C3⋊C8—31no—
81C22×C3⋊C8—31no—
82#832—62no—
83#832—62no—
84C3⋊#95—61no—
85#830—62no—
86#807—62no—
87C23×C9—21no—
88C23×C9—21no—
89C23×C9—21no—
90C23×C9—21no—
91C23×C9—21no—
92C23×C9—21no—
93C23×C9—22no—
94C23×C9—41no—
95C23×C9—41no—
96C23×C9—41no—
97C23×C9—41no—
98C23×C9—41no—
99C23×C9—41no—
100C23×C9D812yes—
101C23×C9C2×D411yescharacteristic
102D4×C9—22no—
103D4×C9—22no—
104D4×C9—48no—
105D4×C9—41no—
106D4×C9—41no—
107C2×C4×C9—21no—
108C2×C4×C9—22no—
109C2×C4×C9—21no—
110C2×C4×C9—21no—
111C2×C4×C9—41no—
112C2×C4×C9—41no—
113C2×C4×C9—41no—
114C2×C4×C9—41no—
115C2×C4×C9—41no—
116C2×C4×C9—41no—
117C2×C4×C9C2×D411yescharacteristic
118C2×C4×C9C2×D411yescharacteristic
119C2×C4×C9C2×D411yescharacteristic
120C2×C4×C9#4111yescharacteristic
121C2×C4×C9#4111yescharacteristic
122C2×C4×C9#4111yescharacteristic
123C2×Dic9—41no—
124C2×Dic9—41no—
125C2×Dic9—41no—
126C2×Dic9—41no—
127C2×Dic9—41no—
128C2×Dic9—41no—
129C9⋊C8—22no—
130C9⋊C8—41no—
131C2×#121D911yescharacteristic
132C2×#107—91no—
133C2×#102—91no—
134C2×#102—91no—
135C2×C22⋊C8—91no—
136#380—91no—
137#340—91no—
138C24×C3—21no—
139C24×C3#6711yescharacteristic
140C2×C3×D4—24no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—42no—
147C2×C3×D4—42no—
148C2×C3×D4#6712yes—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4#6711yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×Dic3—61no—
159C22×Dic3—61no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4#6712yes—
162C3×C22⋊C4—24no—
163#217—122no—
164C4⋊Dic3—61no—
165C4⋊Dic3—61no—
166C4⋊Dic3—61no—
167C4⋊Dic3—61no—
168C2×C3⋊C8—32no—
169C2×C3⋊C8—61no—
170C2×C3⋊C8—61no—
171C2×C3⋊C8—61no—
172C2×C3⋊C8—61no—
173C2×C3⋊C8—61no—
174C22×C9—22no—
175C22×C9—22no—
176C22×C9—22no—
177C22×C9—41no—
178C22×C9—41no—
179C22×C9—41no—
180C22×C9—41no—
181C22×C9—42no—
182C22×C9—42no—
183C22×C9—42no—
184C22×C9—81no—
185C22×C9—81no—
186C22×C9—81no—
187C22×C9—81no—
188C22×C9#12011yescharacteristic
189C22×C9#12111yescharacteristic
190C22×C9#12311yescharacteristic
191C22×C9C2×D811yescharacteristic
192C22×C9#13511yescharacteristic
193C22×C9AGL(1,ℤ/8)11yescharacteristic
194C22×C9#13711yescharacteristic
195C4×C9—41no—
196C4×C9—42no—
197C4×C9#12111yescharacteristic
198C4×C9#12111yescharacteristic
199C4×C9#12311yescharacteristic
200C4×C9#12411yescharacteristic
201Dic9—81no—
202Dic9—81no—
203C22×D4—21no—
204C22×D4C2×D911yescharacteristic
205C23×C4C2×D911yescharacteristic
206C22×C8—91no—
207C22×C8—91no—
208#121—22no—
209#121—22no—
210C2×C4⋊C4—91no—
211C2×C4⋊C4—91no—
212C2×C4⋊C4C2×D911yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—181no—
215#107—182no—
216#102—182no—
217#102—182no—
218C22⋊C8—182no—
219#95—181no—
220C23×C3—21no—
221C23×C3—21no—
222C23×C3—21no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—22no—
227C23×C3—41no—
228C23×C3—41no—
229C23×C3—41no—
230C23×C3—41no—
231C23×C3—41no—
232C23×C3—41no—
233C23×C3#21312yes—
234C23×C3C2×#6711yescharacteristic
235C3×D4—22no—
236C3×D4—22no—
237C3×D4—48no—
238C3×D4—41no—
239C3×D4—41no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—22no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4#23711yescharacteristic
252C2×C3×C4#23711yescharacteristic
253C2×C3×C4#23711yescharacteristic
254C2×C3×C4C2×#6711yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256C2×Dic3—121no—
257C2×Dic3—121no—
258C2×Dic3—121no—
259C2×Dic3—121no—
260C2×Dic3—121no—
261C2×Dic3—121no—
262C3⋊C8—62no—
263C3⋊C8—121no—
264C2×C9—42no—
265C2×C9—82no—
266C2×C9#39411yescharacteristic
267C2×C9#44711yescharacteristic
268C2×C9#45211yescharacteristic
269C2×C9#46611yescharacteristic
270C2×C9#46811yescharacteristic
271C2×C9#48011yescharacteristic
272C2×C9#48211yescharacteristic
273C24—21no—
274C24#61111yescharacteristic
275C2×D4—24no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4#61112yes—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—181no—
292C22×C4—181no—
293C22×C4#61111yescharacteristic
294C22×C4C22×D911yescharacteristic
295C2×C8—92no—
296C2×C8—181no—
297C2×C8—181no—
298C2×C8—181no—
299C2×C8—181no—
300C2×C8—181no—
301C4⋊C4—21no—
302C4⋊C4—181no—
303C4⋊C4—181no—
304C4⋊C4—181no—
305C4⋊C4—181no—
306C4⋊C4#61112yes—
307C22⋊C4—24no—
308C22⋊C4—362no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—42no—
317C22×C3—42no—
318C22×C3—42no—
319C22×C3—81no—
320C22×C3—81no—
321C22×C3—81no—
322C22×C3—81no—
323C22×C3C2×#21311yescharacteristic
324C22×C3#93211yescharacteristic
325C22×C3#93511yescharacteristic
326C22×C3#93911yescharacteristic
327C22×C3#95011yescharacteristic
328C22×C3#95111yescharacteristic
329C22×C3#95311yescharacteristic
330C3×C4—42no—
331C3×C4—41no—
332C3×C4#93511yescharacteristic
333C3×C4#93611yescharacteristic
334C3×C4#93811yescharacteristic
335C3×C4#93911yescharacteristic
336Dic3—241no—
337Dic3—241no—
338C9#203311yescharacteristic, complemented, Sylow
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—22no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23#367312yes—
353C23C2×#61111yescharacteristic
354D4—22no—
355D4—22no—
356D4—48no—
357D4—41no—
358D4—41no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—361no—
370C2×C4—361no—
371C2×C4—361no—
372C2×C4—361no—
373C2×C4—361no—
374C2×C4—361no—
375C2×C4D4×D911yescharacteristic
376C2×C4#369911yescharacteristic
377C2×C4#369911yescharacteristic
378C2×C4#369911yescharacteristic
379C2×C4C2×#61111yescharacteristic
380C2×C4C2×#61111yescharacteristic
381C8—182no—
382C8—361no—
383C2×C3—42no—
384C2×C3—82no—
385C2×C3#503311yescharacteristic
386C2×C3#503511yescharacteristic
387C2×C3#503811yescharacteristic
388C2×C3#504211yescharacteristic
389C2×C3#521711yescharacteristic
390C2×C3#522211yescharacteristic
391C2×C3#523911yescharacteristic
392C22—22no—
393C22—22no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22C2×#367311yescharacteristic
407C22#6349511yescharacteristic
408C22#6349711yescharacteristic
409C22#6350111yescharacteristic
410C22#6351111yescharacteristic
411C22#6351311yescharacteristic
412C22#6351511yescharacteristic
413C4—42no—
414C4—41no—
415C4—721no—
416C4—721no—
417C4#6349711yescharacteristic
418C4#6349811yescharacteristic
419C4#6350011yescharacteristic
420C4#6350111yescharacteristic
421C3#7167911yescharacteristic
422C2—42no—
423C2—82no—
424C2#1058871311yescharacteristic
425C2#1058871511yescharacteristic
426C2#1058871811yescharacteristic
427C2#1058872111yescharacteristic
428C2#1058889811yescharacteristic
429C2#1058890211yescharacteristic
430C2#1058891811yescharacteristic
subgroupG/H
centerC23C2×#611
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC2×C9×#121C2
socleC23×C3C2×#67
prime radicalC2×C3×#121D3
hypercenterC2×#121D9
hypocenterC9#2033
LCSG ▷ C22×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#63392C2semidirect
3. C2×#63392C2semidirect
4. #10588892C2semidirect
5. C2×#63389C2semidirect
6. C2×#63366C2semidirect
7. #10588206C2semidirect
68. C2×C9⋊C8D4semidirect
338. C9#2033semidirect

Maximal subgroups

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

subgroupindex
C2×C9×#1212
C2×#633922
#105888922
C2×#633892
C2×#633662
#105882062
#716793