Finite Group Databasebeta

← #11793153

Subgroups — #11793153

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×#63492C211yesmaximal, characteristic
2C9×#380C211yesmaximal, characteristic, complemented
3C2×#63389C211yesmaximal, characteristic, complemented
4C2×#63369C211yesmaximal, characteristic, complemented
5C2×#63369C211yesmaximal, characteristic, complemented
6C2×#63366C211yesmaximal, characteristic, complemented
7#10588206C211yesmaximal, characteristic, complemented
8#69523—31nomaximal
9C23×C4×C9C2211yescharacteristic
10C22×#611—21no—
11C22×D36C2211yescharacteristic
12C2×C9×C4⋊C4C2211yescharacteristic
13C2×C9×C4⋊C4C2211yescharacteristic
14C2×C9×C22⋊C4—21no—
15#63492—22no—
16#63492—22no—
17C2×(C2×D9)⋊C4—21no—
18C2×C4⋊Dic9C2211yescharacteristic
19C22×C9⋊C8C2211yescharacteristic
20C22×C9⋊C8C2211yescharacteristic
21C9×#95—21no—
22#63389—22no—
23#63369—22no—
24#63369—22no—
25#63366—22no—
26C2×#930—31no—
27C3×#380D311yescharacteristic
28C2×#830—31no—
29C2×#809—31no—
30C2×#809—31no—
31C2×#807—31no—
32#4529—31no—
33C24×C9D411yescharacteristic
34C23×D9—21no—
35C22×C4×C9—21no—
36C22×C4×C9—21no—
37C22×C4×C9—21no—
38C22×C4×C9—21no—
39C22×C4×C9—21no—
40C22×C4×C9—21no—
41C22×C4×C9—21no—
42C22×C4×C9—21no—
43C22×C4×C9D411yescharacteristic
44C22×C4×C9C2311yescharacteristic
45C2×#611—24no—
46C2×#611—42no—
47C2×#611—42no—
48C22×Dic9—21no—
49C2×D36—21no—
50C2×D36—21no—
51C2×D36—21no—
52C2×D36—21no—
53C2×D36—21no—
54C2×D36D412yes—
55C9×C4⋊C4—21no—
56C9×C4⋊C4—21no—
57C9×C4⋊C4—21no—
58C9×C4⋊C4—21no—
59C9×C22⋊C4—42no—
60(C2×D9)⋊C4—24no—
61C4⋊Dic9—21no—
62C4⋊Dic9D412yes—
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
70C23×C3×C4C2×D311yescharacteristic
71C22×#67—61no—
72C22×D12—31no—
73C2×C3×C4⋊C4C2×D311yescharacteristic
74C2×C3×C4⋊C4C2×D311yescharacteristic
75C2×C3×C22⋊C4—21no—
76#930—62no—
77#930—62no—
78C2×(C2×D3)⋊C4—61no—
79C2×C4⋊Dic3—31no—
80C22×C3⋊C8—31no—
81C22×C3⋊C8—31no—
82C3×#95—21no—
83#830—62no—
84#809—62no—
85#809—62no—
86#807—62no—
87C23×C9—21no—
88C23×C9—21no—
89C23×C9—21no—
90C23×C9—21no—
91C23×C9—21no—
92C23×C9—21no—
93C23×C9D812yes—
94C23×C9C2×D411yescharacteristic
95C22×D9—22no—
96C22×D9—41no—
97C22×D9—41no—
98C22×D9—41no—
99C22×D9—41no—
100C22×D9—41no—
101C22×D9—41no—
102C2×C4×C9—21no—
103C2×C4×C9—21no—
104C2×C4×C9—21no—
105C2×C4×C9—41no—
106C2×C4×C9—41no—
107C2×C4×C9—41no—
108C2×C4×C9—41no—
109C2×C4×C9—41no—
110C2×C4×C9—41no—
111C2×C4×C9—41no—
112C2×C4×C9—41no—
113C2×C4×C9—41no—
114C2×C4×C9—41no—
115C2×C4×C9C2×D411yescharacteristic
116C2×C4×C9C2×D411yescharacteristic
117C2×C4×C9C2×D411yescharacteristic
118C2×C4×C9#4111yescharacteristic
119C2×C4×C9#4111yescharacteristic
120C2×C4×C9#4111yescharacteristic
121#611—48no—
122C2×Dic9—22no—
123C2×Dic9—41no—
124C2×Dic9—41no—
125D36—22no—
126D36—22no—
127D36—41no—
128D36—41no—
129C9⋊C8—22no—
130C9⋊C8—41no—
131C2×#121—91no—
132C2×#107—91no—
133C2×#102—91no—
134C2×#102—91no—
135C2×C22⋊C8—91no—
136#380D911yescharacteristic, complemented
137#340—91no—
138C24×C3#6711yescharacteristic
139C23×D3—61no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4#6711yescharacteristic
149C22×C3×C4C22×D311yescharacteristic
150C2×#67—64no—
151C2×#67—122no—
152C2×#67—122no—
153C22×Dic3—61no—
154C2×D12—32no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—61no—
158C2×D12—61no—
159C2×D12—61no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C22⋊C4—42no—
165(C2×D3)⋊C4—64no—
166C4⋊Dic3—32no—
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#12011yescharacteristic
182C22×C9#12111yescharacteristic
183C22×C9#12311yescharacteristic
184C22×C9C2×D811yescharacteristic
185C22×C9#13511yescharacteristic
186C22×C9AGL(1,ℤ/8)11yescharacteristic
187C22×C9#13711yescharacteristic
188C2×D9—42no—
189C2×D9—42no—
190C2×D9—42no—
191C2×D9—81no—
192C2×D9—81no—
193C2×D9—81no—
194C2×D9—81no—
195C4×C9—41no—
196C4×C9—81no—
197C4×C9—81no—
198C4×C9#12111yescharacteristic
199C4×C9#12111yescharacteristic
200C4×C9#12311yescharacteristic
201C4×C9#12411yescharacteristic
202Dic9—42no—
203C22×D4—91no—
204C22×D4—181no—
205C23×C4C2×D911yescharacteristic
206C22×C8—91no—
207C22×C8—91no—
208#121—182no—
209#121—182no—
210C2×C4⋊C4—91no—
211C2×C4⋊C4C2×D911yescharacteristic
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—21no—
220C23×C3—21no—
221C23×C3—21no—
222C23×C3—21no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3#21312yes—
227C23×C3C2×#6711yescharacteristic
228C22×D3—62no—
229C22×D3—121no—
230C22×D3—121no—
231C22×D3—121no—
232C22×D3—121no—
233C22×D3—121no—
234C22×D3—121no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4#23511yescharacteristic
249C2×C3×C4#23511yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4#23711yescharacteristic
254#67—128no—
255C2×Dic3—62no—
256C2×Dic3—121no—
257C2×Dic3—121no—
258D12—62no—
259D12—62no—
260D12—121no—
261D12—121no—
262C3⋊C8—62no—
263C3⋊C8—121no—
264C2×C9—42no—
265C2×C9#39411yescharacteristic
266C2×C9#44711yescharacteristic
267C2×C9#45211yescharacteristic
268C2×C9#46611yescharacteristic
269C2×C9#46811yescharacteristic
270C2×C9#48011yescharacteristic
271C2×C9#48211yescharacteristic
272D9—82no—
273C24—181no—
274C24#61111yescharacteristic
275C2×D4—92no—
276C2×D4—184no—
277C2×D4—181no—
278C2×D4—181no—
279C2×D4—181no—
280C2×D4—181no—
281C2×D4—181no—
282C2×D4—362no—
283C2×D4—362no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
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—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—92no—
306C4⋊C4—181no—
307C22⋊C4—42no—
308C22⋊C4—184no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3#92911yescharacteristic
317C22×C3C2×#21311yescharacteristic
318C22×C3#93711yescharacteristic
319C22×C3#93911yescharacteristic
320C22×C3#94211yescharacteristic
321C22×C3#94911yescharacteristic
322C22×C3#95011yescharacteristic
323C2×D3—122no—
324C2×D3—122no—
325C2×D3—122no—
326C2×D3—241no—
327C2×D3—241no—
328C2×D3—241no—
329C2×D3—241no—
330C3×C4—41no—
331C3×C4—81no—
332C3×C4—81no—
333C3×C4#88311yescharacteristic
334C3×C4#88411yescharacteristic
335C3×C4#88411yescharacteristic
336C3×C4#88511yescharacteristic
337Dic3—122no—
338C9#203311yescharacteristic, complemented, Sylow
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—182no—
346C23—361no—
347C23—361no—
348C23—361no—
349C23—361no—
350C23—361no—
351C23—361no—
352C23#367312yes—
353C23C2×#61111yescharacteristic
354D4—182no—
355D4—182no—
356D4—368no—
357D4—361no—
358D4—361no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—182no—
373C2×C4—361no—
374C2×C4—361no—
375C2×C4#369711yescharacteristic
376C2×C4#369711yescharacteristic
377C2×C4D4×D911yescharacteristic
378C2×C4D4×D911yescharacteristic
379C2×C4D4×D911yescharacteristic
380C2×C4#369911yescharacteristic
381C8—182no—
382C8—361no—
383C2×C3—42no—
384C2×C3#495911yescharacteristic
385C2×C3#496711yescharacteristic
386C2×C3#500311yescharacteristic
387C2×C3#503611yescharacteristic
388C2×C3#503811yescharacteristic
389C2×C3#504711yescharacteristic
390C2×C3#504911yescharacteristic
391D3—242no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—362no—
400C22—362no—
401C22—362no—
402C22—721no—
403C22—721no—
404C22—721no—
405C22—721no—
406C22#6349111yescharacteristic
407C22C2×#367311yescharacteristic
408C22#6349911yescharacteristic
409C22#6350111yescharacteristic
410C22#6350511yescharacteristic
411C22#6351211yescharacteristic
412C22#6351311yescharacteristic
413C4—41no—
414C4—81no—
415C4—81no—
416C4—362no—
417C4#6344511yescharacteristic
418C4#6344611yescharacteristic
419C4#6344611yescharacteristic
420C4#6344711yescharacteristic
421C3#6952311yescharacteristic
422C2—42no—
423C2—722no—
424C2#1058863911yescharacteristic
425C2#1058865011yescharacteristic
426C2#1058868411yescharacteristic
427C2#1058871911yescharacteristic
428C2#1058872111yescharacteristic
429C2#1058873011yescharacteristic
430C2#1058873211yescharacteristic
subgroupG/H
centerC23C2×#611
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#380C2
socleC23×C3C2×#67
prime radicalC2×#63492C2
hypercenter#380D9
hypocenterC9#2033
LCSG ▷ C22×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C9×#380C2semidirect
3. C2×#63389C2semidirect
4. C2×#63369C2semidirect
5. C2×#63369C2semidirect
6. C2×#63366C2semidirect
7. #10588206C2semidirect
68. C2×C9⋊C8D4semidirect
136. #380D9semidirect
338. C9#2033semidirect

Maximal subgroups

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

subgroupindex
C2×#634922
C9×#3802
C2×#633892
C2×#633692
C2×#633662
#105882062
#695233