Finite Group Databasebeta

← #11793160

Subgroups — #11793160

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×#64104C211yesmaximal, characteristic
2C2×C32×#107C211yesmaximal, characteristic, complemented
3C2×#63648C211yesmaximal, characteristic, complemented
4C2×#63647C211yesmaximal, characteristic, complemented
5#10592686C211yesmaximal, characteristic, complemented
6C2×#63636C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#70634—34nomaximal
9C22×C4⋊(C3⋊D3)—21no—
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3752—21no—
16C2×#3752—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19#64104—22no—
20#64104—22no—
21C32×#107—22no—
22#63658—21no—
23#63648—22no—
24#63647—22no—
25#63636—22no—
26C2×#895—34no—
27C2×C3×#107D314yescomplemented
28C2×#821—34no—
29C2×(C2×D3)⋊C8—34no—
30#4987—34no—
31C2×#809—34no—
32#4529—34no—
33C23×C3⋊D3—21no—
34C23×C3⋊D3D411yescharacteristic
35C22×C32×C4—21no—
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—24no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—42no—
47C2×C4⋊(C3⋊D3)—42no—
48C2×C4⋊(C3⋊D3)D412yes—
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—21no—
55C2×C32×C8—21no—
56C2×C32×C8—21no—
57C2×C32×C8D412yescomplemented
58C32×C4⋊C4—21no—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4D412yes—
62#3752—24no—
63#3752—42no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69#2033—91noSylow
70C22×D12—34no—
71C22×D12—64no—
72C22×C4×D3—34no—
73C22×C3×C8C2×D314yes—
74C2×C3×C4⋊C4C2×D314yes—
75C2×C3×C4⋊C4C2×D314yes—
76C2×(C2×D3)⋊C4—64no—
77C2×(C2×D3)⋊C4—64no—
78C2×C4⋊Dic3—34no—
79C22×C3⋊C8—34no—
80#895—68no—
81#895—68no—
82C3×#107—28no—
83C3⋊#95—64no—
84#821—68no—
85(C2×D3)⋊C8—68no—
86#809—68no—
87C23×C32C2×D411yescharacteristic
88C22×C3⋊D3—21no—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—21no—
91C22×C3⋊D3—21no—
92C22×C3⋊D3—21no—
93C22×C3⋊D3—21no—
94C22×C3⋊D3—22no—
95C22×C3⋊D3—41no—
96C22×C3⋊D3—41no—
97C22×C3⋊D3—41no—
98C22×C3⋊D3—41no—
99C22×C3⋊D3—41no—
100C22×C3⋊D3—41no—
101C22×C3⋊D3D812yes—
102C2×C32×C4—22no—
103C2×C32×C4—41no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—41no—
118C2×C3⋊Dic3—41no—
119C2×C3⋊Dic3—41no—
120C4⋊(C3⋊D3)—22no—
121C4⋊(C3⋊D3)—22no—
122C4⋊(C3⋊D3)—48no—
123C4⋊(C3⋊D3)—41no—
124C4⋊(C3⋊D3)—41no—
125C4×C3⋊D3—41no—
126C4×C3⋊D3—41no—
127C4×C3⋊D3—41no—
128C4×C3⋊D3—41no—
129C32×C8—22no—
130C3⋊(C3⋊C8)—41no—
131C2×#121—91no—
132C2×#107C3⋊D311yescharacteristic, complemented
133C2×#102—91no—
134C2×#102—91no—
135C2×C22⋊C8—91no—
136#380—91no—
137#340—91no—
138C23×D3—34no—
139C23×D3—64no—
140C22×C3×C4—24no—
141C22×C3×C4—24no—
142C22×C3×C4C22×D314yes—
143C22×Dic3—34no—
144C22×Dic3—64no—
145C2×D12—38no—
146C2×D12—64no—
147C2×D12—64no—
148C2×D12—64no—
149C2×D12—64no—
150C2×D12—616no—
151C2×D12—64no—
152C2×D12—128no—
153C2×D12—128no—
154C2×C4×D3—64no—
155C2×C4×D3—64no—
156C2×C4×D3—64no—
157C2×C4×D3—64no—
158C2×C4×D3—64no—
159C2×C4×D3—64no—
160C2×C3×C8—24no—
161C2×C3×C8—24no—
162C2×C3×C8D1218yescomplemented
163C3×C4⋊C4—24no—
164C3×C4⋊C4—24no—
165C3×C4⋊C4—24no—
166C3×C4⋊C4#6718yes—
167(C2×D3)⋊C4—616no—
168(C2×D3)⋊C4—128no—
169C4⋊Dic3—64no—
170C4⋊Dic3—64no—
171C2×C3⋊C8—64no—
172C2×C3⋊C8—64no—
173C2×C3⋊C8—64no—
174C22×C32#12011yescharacteristic
175C22×C32#12111yescharacteristic
176C22×C32#12311yescharacteristic
177C22×C32C2×D811yescharacteristic
178C22×C32#13511yescharacteristic
179C22×C32AGL(1,ℤ/8)11yescharacteristic
180C22×C32#13711yescharacteristic
181C2×C3⋊D3—22no—
182C2×C3⋊D3—22no—
183C2×C3⋊D3—22no—
184C2×C3⋊D3—41no—
185C2×C3⋊D3—41no—
186C2×C3⋊D3—41no—
187C2×C3⋊D3—41no—
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—42no—
196C32×C4—81no—
197C32×C4#12111yescharacteristic
198C32×C4#12111yescharacteristic
199C32×C4#12311yescharacteristic
200C32×C4#12411yescharacteristic
201C3⋊Dic3—41no—
202C3⋊Dic3—81no—
203C22×D4—91no—
204C22×D4—181no—
205C23×C4—91no—
206C22×C8—91no—
207C22×C8C2×C3⋊D311yescharacteristic
208#121—182no—
209#121—182no—
210C2×C4⋊C4—91no—
211C2×C4⋊C4C2×C3⋊D311yescharacteristic
212C2×C4⋊C4C2×C3⋊D311yescharacteristic
213C2×C22⋊C4—181no—
214C2×C22⋊C4—181no—
215#107—22no—
216#102—182no—
217#102—182no—
218C22⋊C8—182no—
219#95—181no—
220C23×C3D3×D414yes—
221C22×D3—38no—
222C22×D3—64no—
223C22×D3—64no—
224C22×D3—64no—
225C22×D3—64no—
226C22×D3—64no—
227C22×D3—64no—
228C22×D3—68no—
229C22×D3—124no—
230C22×D3—124no—
231C22×D3—124no—
232C22×D3—124no—
233C22×D3—124no—
234C22×D3—124no—
235C2×C3×C4—28no—
236C2×C3×C4—44no—
237C2×C3×C4—44no—
238C2×C3×C4—44no—
239C2×C3×C4—44no—
240C2×C3×C4—44no—
241C2×C3×C4C2×D1214yes—
242C2×C3×C4#23514yes—
243C2×C3×C4D3×D414yes—
244C2×C3×C4#23914yes—
245C2×C3×C4#23914yes—
246C2×C3×C4C2×#6714yes—
247C2×Dic3—64no—
248C2×Dic3—64no—
249C2×Dic3—64no—
250C2×Dic3—124no—
251C2×Dic3—124no—
252C2×Dic3—124no—
253D12—68no—
254D12—68no—
255D12—1232no—
256D12—124no—
257D12—124no—
258C4×D3—124no—
259C4×D3—124no—
260C4×D3—124no—
261C4×D3—124no—
262C3×C8—28no—
263C3⋊C8—124no—
264C2×C32#39411yescharacteristic
265C2×C32#44711yescharacteristic
266C2×C32#45211yescharacteristic
267C2×C32#46611yescharacteristic
268C2×C32#46811yescharacteristic
269C2×C32#48011yescharacteristic
270C2×C32#48211yescharacteristic
271C3⋊D3—42no—
272C3⋊D3—82no—
273C24—91no—
274C24—181no—
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—91no—
287C22×C4—181no—
288C22×C4—181no—
289C22×C4—181no—
290C22×C4—181no—
291C22×C4—181no—
292C22×C4—181no—
293C22×C4—181no—
294C22×C4C22×C3⋊D311yescharacteristic
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—181no—
298C2×C8—181no—
299C2×C8—181no—
300C2×C8C4⋊(C3⋊D3)12yescomplemented
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—181no—
305C4⋊C4—181no—
306C4⋊C4#63812yes—
307C22⋊C4—184no—
308C22⋊C4—362no—
309C22×C3#89414yes—
310C22×C3#89514yes—
311C22×C3D3×D814yes—
312C22×C3#91114yes—
313C22×C3#91814yes—
314C22×C3#91914yes—
315C22×C3#93714yes—
316C2×D3—68no—
317C2×D3—68no—
318C2×D3—68no—
319C2×D3—124no—
320C2×D3—124no—
321C2×D3—124no—
322C2×D3—124no—
323C2×D3—128no—
324C2×D3—128no—
325C2×D3—128no—
326C2×D3—244no—
327C2×D3—244no—
328C2×D3—244no—
329C2×D3—244no—
330C3×C4—48no—
331C3×C4—84no—
332C3×C4#89414yes—
333C3×C4#89514yes—
334C3×C4#93014yes—
335C3×C4#94714yes—
336Dic3—124no—
337Dic3—244no—
338C32#203311yescharacteristic, complemented, Sylow
339C23—92no—
340C23—181no—
341C23—181no—
342C23—181no—
343C23—181no—
344C23—181no—
345C23—181no—
346C23—182no—
347C23—361no—
348C23—361no—
349C23—361no—
350C23—361no—
351C23—361no—
352C23—361no—
353C23D4×C3⋊D311yescharacteristic
354D4—182no—
355D4—182no—
356D4—368no—
357D4—361no—
358D4—361no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—181no—
366C2×C4—181no—
367C2×C4—181no—
368C2×C4—361no—
369C2×C4—361no—
370C2×C4—361no—
371C2×C4—361no—
372C2×C4—361no—
373C2×C4—361no—
374C2×C4—361no—
375C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
376C2×C4#382811yescharacteristic
377C2×C4D4×C3⋊D311yescharacteristic
378C2×C4#383211yescharacteristic
379C2×C4#383211yescharacteristic
380C2×C4C2×#63811yescharacteristic
381C8—22no—
382C8—361no—
383C2×C3#488214yes—
384C2×C3#488314yes—
385C2×C3#488514yes—
386C2×C3#488614yes—
387C2×C3#499114yes—
388C2×C3#515614yes—
389C2×C3#518714yes—
390D3—128no—
391D3—248no—
392C22—182no—
393C22—182no—
394C22—182no—
395C22—361no—
396C22—361no—
397C22—361no—
398C22—361no—
399C22—362no—
400C22—362no—
401C22—362no—
402C22—721no—
403C22—721no—
404C22—721no—
405C22—721no—
406C22#6410311yescharacteristic
407C22#6410411yescharacteristic
408C22D8×C3⋊D311yescharacteristic
409C22#6412011yescharacteristic
410C22#6412711yescharacteristic
411C22#6412811yescharacteristic
412C22#6414611yescharacteristic
413C4—42no—
414C4—81no—
415C4—361no—
416C4—721no—
417C4#6410311yescharacteristic
418C4#6410411yescharacteristic
419C4#6413911yescharacteristic
420C4#6415611yescharacteristic
421C3#7063414yescomplemented
422C2—362no—
423C2—722no—
424C2#1059258111yescharacteristic
425C2#1059258211yescharacteristic
426C2#1059258411yescharacteristic
427C2#1059258511yescharacteristic
428C2#1059269011yescharacteristic
429C2#1059285511yescharacteristic
430C2#1059288611yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#107C2
socleC23×C32C2×D4
prime radicalC2×#64104C2
hypercenterC2×#107C3⋊D3
hypocenterC32#2033
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×C32×#107C2semidirect
3. C2×#63648C2semidirect
4. C2×#63647C2semidirect
5. #10592686C2semidirect
6. C2×#63636C2semidirect
7. #10589395C2semidirect
27. C2×C3×#107D3semidirect
57. C2×C32×C8D4semidirect
132. C2×#107C3⋊D3semidirect
162. C2×C3×C8D12semidirect
300. C2×C8C4⋊(C3⋊D3)semidirect
338. C32#2033semidirect
421. C3#70634semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
C2×C32×#1072
C2×#636482
C2×#636472
#105926862
C2×#636362
#105893952
#706343