Finite Group Databasebeta

← #11793154

Subgroups — #11793154

Order 1152.

1104 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×#64139C211yesmaximal, characteristic
2C32×#380C211yesmaximal, characteristic, complemented
3C2×#63657C211yesmaximal, characteristic, complemented
4C2×#63636C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic, complemented
6C2×#63634C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#69523—34nomaximal
9C23×C32×C4C2211yescharacteristic
10C22×#638—21no—
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C22⋊C4—21no—
15#64139—22no—
16#64139—22no—
17C2×#3752—21no—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C32×#95—21no—
22#63657—22no—
23#63636—22no—
24#63636—22no—
25#63634—22no—
26C2×#930—34no—
27C3×#380D314yescomplemented
28C2×#830—34no—
29C2×#809—34no—
30C2×#809—34no—
31C2×#807—34no—
32#4529—34no—
33C24×C32D411yescharacteristic
34C23×C3⋊D3—21no—
35C22×C32×C4—21no—
36C22×C32×C4—21no—
37C22×C32×C4—21no—
38C22×C32×C4—21no—
39C22×C32×C4—21no—
40C22×C32×C4—21no—
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C2×#638—24no—
46C2×#638—42no—
47C2×#638—42no—
48C22×C3⋊Dic3—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)D412yes—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4—21no—
59C32×C22⋊C4—42no—
60#3752—24no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)D412yes—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)D412yescomplemented
69#2033—91noSylow
70C23×C3×C4C2×D314yes—
71C22×#67—64no—
72C22×D12—34no—
73C2×C3×C4⋊C4C2×D314yes—
74C2×C3×C4⋊C4C2×D314yes—
75C2×C3×C22⋊C4—24no—
76#930—68no—
77#930—68no—
78C2×(C2×D3)⋊C4—64no—
79C2×C4⋊Dic3—34no—
80C22×C3⋊C8—34no—
81C22×C3⋊C8—34no—
82C3×#95—24no—
83#830—68no—
84#809—68no—
85#809—68no—
86#807—68no—
87C23×C32—21no—
88C23×C32—21no—
89C23×C32—21no—
90C23×C32—21no—
91C23×C32—21no—
92C23×C32—21no—
93C23×C32D812yes—
94C23×C32C2×D411yescharacteristic
95C22×C3⋊D3—22no—
96C22×C3⋊D3—41no—
97C22×C3⋊D3—41no—
98C22×C3⋊D3—41no—
99C22×C3⋊D3—41no—
100C22×C3⋊D3—41no—
101C22×C3⋊D3—41no—
102C2×C32×C4—21no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121#638—48no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C4⋊(C3⋊D3)—22no—
126C4⋊(C3⋊D3)—22no—
127C4⋊(C3⋊D3)—41no—
128C4⋊(C3⋊D3)—41no—
129C3⋊(C3⋊C8)—22no—
130C3⋊(C3⋊C8)—41no—
131C2×#121—91no—
132C2×#107—91no—
133C2×#102—91no—
134C2×#102—91no—
135C2×C22⋊C8—91no—
136#380C3⋊D311yescharacteristic, complemented
137#340—91no—
138C24×C3#6714yes—
139C23×D3—64no—
140C22×C3×C4—24no—
141C22×C3×C4—24no—
142C22×C3×C4—24no—
143C22×C3×C4—24no—
144C22×C3×C4—24no—
145C22×C3×C4—24no—
146C22×C3×C4—24no—
147C22×C3×C4—24no—
148C22×C3×C4#6714yes—
149C22×C3×C4C22×D314yes—
150C2×#67—616no—
151C2×#67—128no—
152C2×#67—128no—
153C22×Dic3—64no—
154C2×D12—38no—
155C2×D12—64no—
156C2×D12—64no—
157C2×D12—64no—
158C2×D12—64no—
159C2×D12—64no—
160C3×C4⋊C4—24no—
161C3×C4⋊C4—24no—
162C3×C4⋊C4—24no—
163C3×C4⋊C4—24no—
164C3×C22⋊C4—48no—
165(C2×D3)⋊C4—616no—
166C4⋊Dic3—38no—
167C4⋊Dic3—64no—
168C2×C3⋊C8—38no—
169C2×C3⋊C8—64no—
170C2×C3⋊C8—64no—
171C2×C3⋊C8—64no—
172C2×C3⋊C8—64no—
173C2×C3⋊C8—64no—
174C22×C32—22no—
175C22×C32—22no—
176C22×C32—22no—
177C22×C32—41no—
178C22×C32—41no—
179C22×C32—41no—
180C22×C32—41no—
181C22×C32#12011yescharacteristic
182C22×C32#12111yescharacteristic
183C22×C32#12311yescharacteristic
184C22×C32C2×D811yescharacteristic
185C22×C32#13511yescharacteristic
186C22×C32AGL(1,ℤ/8)11yescharacteristic
187C22×C32#13711yescharacteristic
188C2×C3⋊D3—42no—
189C2×C3⋊D3—42no—
190C2×C3⋊D3—42no—
191C2×C3⋊D3—81no—
192C2×C3⋊D3—81no—
193C2×C3⋊D3—81no—
194C2×C3⋊D3—81no—
195C32×C4—41no—
196C32×C4—81no—
197C32×C4—81no—
198C32×C4#12111yescharacteristic
199C32×C4#12111yescharacteristic
200C32×C4#12311yescharacteristic
201C32×C4#12411yescharacteristic
202C3⋊Dic3—42no—
203C22×D4—91no—
204C22×D4—181no—
205C23×C4C2×C3⋊D311yescharacteristic
206C22×C8—91no—
207C22×C8—91no—
208#121—182no—
209#121—182no—
210C2×C4⋊C4—91no—
211C2×C4⋊C4C2×C3⋊D311yescharacteristic
212C2×C4⋊C4C2×C3⋊D311yescharacteristic
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—24no—
221C23×C3—24no—
222C23×C3—24no—
223C23×C3—24no—
224C23×C3—24no—
225C23×C3—24no—
226C23×C3#21318yes—
227C23×C3C2×#6714yes—
228C22×D3—68no—
229C22×D3—124no—
230C22×D3—124no—
231C22×D3—124no—
232C22×D3—124no—
233C22×D3—124no—
234C22×D3—124no—
235C2×C3×C4—24no—
236C2×C3×C4—24no—
237C2×C3×C4—24no—
238C2×C3×C4—44no—
239C2×C3×C4—44no—
240C2×C3×C4—44no—
241C2×C3×C4—44no—
242C2×C3×C4—44no—
243C2×C3×C4—44no—
244C2×C3×C4—44no—
245C2×C3×C4—44no—
246C2×C3×C4—44no—
247C2×C3×C4—44no—
248C2×C3×C4#23514yes—
249C2×C3×C4#23514yes—
250C2×C3×C4D3×D414yes—
251C2×C3×C4D3×D414yes—
252C2×C3×C4D3×D414yes—
253C2×C3×C4#23714yes—
254#67—1232no—
255C2×Dic3—68no—
256C2×Dic3—124no—
257C2×Dic3—124no—
258D12—68no—
259D12—68no—
260D12—124no—
261D12—124no—
262C3⋊C8—68no—
263C3⋊C8—124no—
264C2×C32—42no—
265C2×C32#39411yescharacteristic
266C2×C32#44711yescharacteristic
267C2×C32#45211yescharacteristic
268C2×C32#46611yescharacteristic
269C2×C32#46811yescharacteristic
270C2×C32#48011yescharacteristic
271C2×C32#48211yescharacteristic
272C3⋊D3—82no—
273C24—181no—
274C24#63811yescharacteristic
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#63811yescharacteristic
294C22×C4C22×C3⋊D311yescharacteristic
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—28no—
310C22×C3—28no—
311C22×C3—28no—
312C22×C3—44no—
313C22×C3—44no—
314C22×C3—44no—
315C22×C3—44no—
316C22×C3#92914yes—
317C22×C3C2×#21314yes—
318C22×C3#93714yes—
319C22×C3#93914yes—
320C22×C3#94214yes—
321C22×C3#94914yes—
322C22×C3#95014yes—
323C2×D3—128no—
324C2×D3—128no—
325C2×D3—128no—
326C2×D3—244no—
327C2×D3—244no—
328C2×D3—244no—
329C2×D3—244no—
330C3×C4—44no—
331C3×C4—84no—
332C3×C4—84no—
333C3×C4#88314yes—
334C3×C4#88414yes—
335C3×C4#88414yes—
336C3×C4#88514yes—
337Dic3—128no—
338C32#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#375312yes—
353C23C2×#63811yescharacteristic
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#382811yescharacteristic
376C2×C4#382811yescharacteristic
377C2×C4D4×C3⋊D311yescharacteristic
378C2×C4D4×C3⋊D311yescharacteristic
379C2×C4D4×C3⋊D311yescharacteristic
380C2×C4#383011yescharacteristic
381C8—182no—
382C8—361no—
383C2×C3—48no—
384C2×C3#495914yes—
385C2×C3#496714yes—
386C2×C3#500314yes—
387C2×C3#503614yes—
388C2×C3#503814yes—
389C2×C3#504714yes—
390C2×C3#504914yes—
391D3—248no—
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#6413811yescharacteristic
407C22C2×#375311yescharacteristic
408C22#6414611yescharacteristic
409C22#6414811yescharacteristic
410C22#6415111yescharacteristic
411C22#6415811yescharacteristic
412C22#6415911yescharacteristic
413C4—41no—
414C4—81no—
415C4—81no—
416C4—362no—
417C4#6409211yescharacteristic
418C4#6409311yescharacteristic
419C4#6409311yescharacteristic
420C4#6409411yescharacteristic
421C3#6952314yescomplemented
422C2—42no—
423C2—722no—
424C2#1059265811yescharacteristic
425C2#1059266611yescharacteristic
426C2#1059270211yescharacteristic
427C2#1059273511yescharacteristic
428C2#1059273711yescharacteristic
429C2#1059274611yescharacteristic
430C2#1059274811yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#380C2
socleC23×C32C2×D4
prime radicalC2×#64139C2
hypercenter#380C3⋊D3
hypocenterC32#2033
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C32×#380C2semidirect
3. C2×#63657C2semidirect
4. C2×#63636C2semidirect
5. C2×#63636C2semidirect
6. C2×#63634C2semidirect
7. #10589395C2semidirect
27. C3×#380D3semidirect
68. C2×C3⋊(C3⋊C8)D4semidirect
136. #380C3⋊D3semidirect
338. C32#2033semidirect
421. C3#69523semidirect

Maximal subgroups

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

subgroupindex
C2×#641392
C32×#3802
C2×#636572
C2×#636362
C2×#636342
#105893952
#695233