Finite Group Databasebeta

← #11793145

Subgroups — #11793145

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×C32×#121C211yesmaximal, characteristic
2C2×#63659C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4#10592911C211yesmaximal, characteristic, complemented
5C2×#63657C211yesmaximal, characteristic, complemented
6C2×#63634C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#71679—34nomaximal
9C22×C32×D4—21no—
10C22×C32×D4C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C32×#121—22no—
13C32×#121—22no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C22⋊C4—21no—
16C2×#3757—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21#63659—22no—
22#63659—22no—
23#63658—21no—
24#63657—22no—
25#63634—22no—
26C2×C3×#121D314yes—
27C2×#832—34no—
28C2×#832—34no—
29#5212—34no—
30C2×#830—34no—
31C2×#807—34no—
32#4529—34no—
33C24×C32—21no—
34C24×C32D411yescharacteristic
35C2×C32×D4—24no—
36C2×C32×D4—21no—
37C2×C32×D4—21no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4—42no—
42C2×C32×D4—42no—
43C2×C32×D4D412yes—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4D411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4D412yes—
57C32×C22⋊C4—24no—
58#3757—42no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
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
70C22×C3×D4—24no—
71C22×C3×D4C2×D314yes—
72C23×C3×C4C2×D314yes—
73C3×#121—28no—
74C3×#121—28no—
75C2×C3×C4⋊C4C2×D314yes—
76C2×C3×C22⋊C4—24no—
77C2×#217—64no—
78C2×C4⋊Dic3—34no—
79C2×C4⋊Dic3—34no—
80C22×C3⋊C8—34no—
81C22×C3⋊C8—34no—
82#832—68no—
83#832—68no—
84C3⋊#95—64no—
85#830—68no—
86#807—68no—
87C23×C32—21no—
88C23×C32—21no—
89C23×C32—21no—
90C23×C32—21no—
91C23×C32—21no—
92C23×C32—21no—
93C23×C32—22no—
94C23×C32—41no—
95C23×C32—41no—
96C23×C32—41no—
97C23×C32—41no—
98C23×C32—41no—
99C23×C32—41no—
100C23×C32D812yes—
101C23×C32C2×D411yescharacteristic
102C32×D4—22no—
103C32×D4—22no—
104C32×D4—48no—
105C32×D4—41no—
106C32×D4—41no—
107C2×C32×C4—21no—
108C2×C32×C4—22no—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C3⋊(C3⋊C8)—22no—
130C3⋊(C3⋊C8)—41no—
131C2×#121C3⋊D311yescharacteristic
132C2×#107—91no—
133C2×#102—91no—
134C2×#102—91no—
135C2×C22⋊C8—91no—
136#380—91no—
137#340—91no—
138C24×C3—24no—
139C24×C3#6714yes—
140C2×C3×D4—216no—
141C2×C3×D4—24no—
142C2×C3×D4—24no—
143C2×C3×D4—24no—
144C2×C3×D4—24no—
145C2×C3×D4—24no—
146C2×C3×D4—48no—
147C2×C3×D4—48no—
148C2×C3×D4#6718yes—
149C22×C3×C4—24no—
150C22×C3×C4—24no—
151C22×C3×C4—24no—
152C22×C3×C4—24no—
153C22×C3×C4—24no—
154C22×C3×C4—24no—
155C22×C3×C4—24no—
156C22×C3×C4#6714yes—
157C22×C3×C4C22×D314yes—
158C22×Dic3—64no—
159C22×Dic3—64no—
160C3×C4⋊C4—24no—
161C3×C4⋊C4#6718yes—
162C3×C22⋊C4—216no—
163#217—128no—
164C4⋊Dic3—64no—
165C4⋊Dic3—64no—
166C4⋊Dic3—64no—
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—42no—
182C22×C32—42no—
183C22×C32—42no—
184C22×C32—81no—
185C22×C32—81no—
186C22×C32—81no—
187C22×C32—81no—
188C22×C32#12011yescharacteristic
189C22×C32#12111yescharacteristic
190C22×C32#12311yescharacteristic
191C22×C32C2×D811yescharacteristic
192C22×C32#13511yescharacteristic
193C22×C32AGL(1,ℤ/8)11yescharacteristic
194C22×C32#13711yescharacteristic
195C32×C4—41no—
196C32×C4—42no—
197C32×C4#12111yescharacteristic
198C32×C4#12111yescharacteristic
199C32×C4#12311yescharacteristic
200C32×C4#12411yescharacteristic
201C3⋊Dic3—81no—
202C3⋊Dic3—81no—
203C22×D4—21no—
204C22×D4C2×C3⋊D311yescharacteristic
205C23×C4C2×C3⋊D311yescharacteristic
206C22×C8—91no—
207C22×C8—91no—
208#121—22no—
209#121—22no—
210C2×C4⋊C4—91no—
211C2×C4⋊C4—91no—
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—181no—
220C23×C3—24no—
221C23×C3—24no—
222C23×C3—24no—
223C23×C3—24no—
224C23×C3—24no—
225C23×C3—24no—
226C23×C3—28no—
227C23×C3—44no—
228C23×C3—44no—
229C23×C3—44no—
230C23×C3—44no—
231C23×C3—44no—
232C23×C3—44no—
233C23×C3#21318yes—
234C23×C3C2×#6714yes—
235C3×D4—28no—
236C3×D4—28no—
237C3×D4—432no—
238C3×D4—44no—
239C3×D4—44no—
240C2×C3×C4—24no—
241C2×C3×C4—24no—
242C2×C3×C4—24no—
243C2×C3×C4—28no—
244C2×C3×C4—44no—
245C2×C3×C4—44no—
246C2×C3×C4—44no—
247C2×C3×C4—44no—
248C2×C3×C4—44no—
249C2×C3×C4—44no—
250C2×C3×C4D3×D414yes—
251C2×C3×C4#23714yes—
252C2×C3×C4#23714yes—
253C2×C3×C4#23714yes—
254C2×C3×C4C2×#6714yes—
255C2×C3×C4C2×#6714yes—
256C2×Dic3—124no—
257C2×Dic3—124no—
258C2×Dic3—124no—
259C2×Dic3—124no—
260C2×Dic3—124no—
261C2×Dic3—124no—
262C3⋊C8—68no—
263C3⋊C8—124no—
264C2×C32—42no—
265C2×C32—82no—
266C2×C32#39411yescharacteristic
267C2×C32#44711yescharacteristic
268C2×C32#45211yescharacteristic
269C2×C32#46611yescharacteristic
270C2×C32#46811yescharacteristic
271C2×C32#48011yescharacteristic
272C2×C32#48211yescharacteristic
273C24—21no—
274C24#63811yescharacteristic
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#63812yes—
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#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—181no—
303C4⋊C4—181no—
304C4⋊C4—181no—
305C4⋊C4—181no—
306C4⋊C4#63812yes—
307C22⋊C4—24no—
308C22⋊C4—362no—
309C22×C3—28no—
310C22×C3—28no—
311C22×C3—28no—
312C22×C3—44no—
313C22×C3—44no—
314C22×C3—44no—
315C22×C3—44no—
316C22×C3—48no—
317C22×C3—48no—
318C22×C3—48no—
319C22×C3—84no—
320C22×C3—84no—
321C22×C3—84no—
322C22×C3—84no—
323C22×C3C2×#21314yes—
324C22×C3#93214yes—
325C22×C3#93514yes—
326C22×C3#93914yes—
327C22×C3#95014yes—
328C22×C3#95114yes—
329C22×C3#95314yes—
330C3×C4—48no—
331C3×C4—44no—
332C3×C4#93514yes—
333C3×C4#93614yes—
334C3×C4#93814yes—
335C3×C4#93914yes—
336Dic3—244no—
337Dic3—244no—
338C32#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#375312yes—
353C23C2×#63811yescharacteristic
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×C3⋊D311yescharacteristic
376C2×C4#383011yescharacteristic
377C2×C4#383011yescharacteristic
378C2×C4#383011yescharacteristic
379C2×C4C2×#63811yescharacteristic
380C2×C4C2×#63811yescharacteristic
381C8—182no—
382C8—361no—
383C2×C3—48no—
384C2×C3—88no—
385C2×C3#503314yes—
386C2×C3#503514yes—
387C2×C3#503814yes—
388C2×C3#504214yes—
389C2×C3#521714yes—
390C2×C3#522214yes—
391C2×C3#523914yes—
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×#375311yescharacteristic
407C22#6414111yescharacteristic
408C22#6414411yescharacteristic
409C22#6414811yescharacteristic
410C22#6415911yescharacteristic
411C22#6416011yescharacteristic
412C22#6416211yescharacteristic
413C4—42no—
414C4—41no—
415C4—721no—
416C4—721no—
417C4#6414411yescharacteristic
418C4#6414511yescharacteristic
419C4#6414711yescharacteristic
420C4#6414811yescharacteristic
421C3#7167914yescomplemented
422C2—42no—
423C2—82no—
424C2#1059273211yescharacteristic
425C2#1059273411yescharacteristic
426C2#1059273711yescharacteristic
427C2#1059274111yescharacteristic
428C2#1059291611yescharacteristic
429C2#1059292111yescharacteristic
430C2#1059293811yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
Fitting, prime radicalC2×C32×#121C2
socleC23×C32C2×D4
hypercenterC2×#121C3⋊D3
hypocenterC32#2033
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#63659C2semidirect
3. C2×#63659C2semidirect
4. #10592911C2semidirect
5. C2×#63657C2semidirect
6. C2×#63634C2semidirect
7. #10589395C2semidirect
68. C2×C3⋊(C3⋊C8)D4semidirect
338. C32#2033semidirect
421. C3#71679semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×#636592
#105929112
C2×#636572
C2×#636342
#105893952
#716793