Finite Group Databasebeta

← #11793148

Subgroups — #11793148

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×#64147C211yesmaximal, characteristic
2C2×C32×#102C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C2×#63647C211yesmaximal, characteristic, complemented
5#10592686C211yesmaximal, characteristic, complemented
6C2×#63634C211yesmaximal, characteristic, complemented
7#10589417C211yesmaximal, characteristic, complemented
8#70206—34nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×#638—21no—
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3757—21no—
15#64147—22no—
16#64147—22no—
17C2×#3752—21no—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C32×#102—22no—
22#63659—22no—
23#63658—21no—
24#63647—22no—
25#63634—22no—
26C2×#938—34no—
27C2×C3×#102D314yescomplemented
28C2×#832—34no—
29C2×(C2×D3)⋊C8—34no—
30#4987—34no—
31C2×#807—34no—
32#4551—34no—
33C24×C32—21no—
34C23×C3⋊D3D411yescharacteristic
35C2×C32×D4—21no—
36C2×C32×D4—21no—
37C2×C32×D4—21no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4D412yes—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C2×#638—24no—
44C2×#638—42no—
45C2×#638—42no—
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
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×C8—21no—
58C32×C4⋊C4—21no—
59C32×C4⋊C4—21no—
60#3757—24no—
61#3752—42no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)D412yes—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)D412yescomplemented
69#2033—91noSylow
70C22×C3×D4C2×D314yes—
71C22×#67—64no—
72C22×C4×D3—34no—
73C22×C3×C8C2×D314yes—
74C2×C3×C4⋊C4C2×D314yes—
75C2×#217—64no—
76#938—68no—
77#938—68no—
78C2×(C2×D3)⋊C4—64no—
79C2×C4⋊Dic3—34no—
80C2×C4⋊Dic3—34no—
81C22×C3⋊C8—34no—
82C3×#102—28no—
83#832—68no—
84C3⋊#95—64no—
85(C2×D3)⋊C8—68no—
86#807—68no—
87C23×C32—22no—
88C23×C32—41no—
89C23×C32—41no—
90C23×C32—41no—
91C23×C32—41no—
92C23×C32—41no—
93C23×C32—41no—
94C23×C32C2×D411yescharacteristic
95C22×C3⋊D3—21no—
96C22×C3⋊D3—21no—
97C22×C3⋊D3—21no—
98C22×C3⋊D3—21no—
99C22×C3⋊D3—21no—
100C22×C3⋊D3—21no—
101C22×C3⋊D3D812yes—
102C32×D4—22no—
103C32×D4—22no—
104C32×D4—41no—
105C32×D4—41no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115#638—48no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C4×C3⋊D3—41no—
126C4×C3⋊D3—41no—
127C4×C3⋊D3—41no—
128C4×C3⋊D3—41no—
129C32×C8—41no—
130C3⋊(C3⋊C8)—22no—
131C2×#121—91no—
132C2×#107—91no—
133C2×#102—91no—
134C2×#102C3⋊D311yescharacteristic, complemented
135C2×C22⋊C8—91no—
136#380—91no—
137#340—91no—
138C24×C3—24no—
139C23×D3—34no—
140C2×C3×D4—24no—
141C2×C3×D4—24no—
142C2×C3×D4—24no—
143C2×C3×D4—24no—
144C2×C3×D4—24no—
145C2×C3×D4#6718yes—
146C22×C3×C4—24no—
147C22×C3×C4C22×D314yes—
148C2×#67—616no—
149C2×#67—128no—
150C2×#67—128no—
151C22×Dic3—34no—
152C22×Dic3—64no—
153C22×Dic3—64no—
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×C8—24no—
163C3×C4⋊C4—24no—
164C3×C4⋊C4—24no—
165#217—616no—
166(C2×D3)⋊C4—128no—
167C4⋊Dic3—38no—
168C4⋊Dic3—64no—
169C4⋊Dic3—64no—
170C4⋊Dic3—64no—
171C2×C3⋊C8—38no—
172C2×C3⋊C8—64no—
173C2×C3⋊C8—64no—
174C22×C32—42no—
175C22×C32—42no—
176C22×C32—42no—
177C22×C32—81no—
178C22×C32—81no—
179C22×C32—81no—
180C22×C32—81no—
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—22no—
189C2×C3⋊D3—22no—
190C2×C3⋊D3—22no—
191C2×C3⋊D3—41no—
192C2×C3⋊D3—41no—
193C2×C3⋊D3—41no—
194C2×C3⋊D3—41no—
195C32×C4—81no—
196C32×C4#12111yescharacteristic
197C32×C4#12111yescharacteristic
198C32×C4#12311yescharacteristic
199C32×C4#12411yescharacteristic
200C3⋊Dic3—41no—
201C3⋊Dic3—42no—
202C3⋊Dic3—81no—
203C22×D4—181no—
204C22×D4C2×C3⋊D311yescharacteristic
205C23×C4—91no—
206C22×C8—91no—
207C22×C8C2×C3⋊D311yescharacteristic
208#121—182no—
209#121—182no—
210C2×C4⋊C4—91no—
211C2×C4⋊C4—91no—
212C2×C4⋊C4C2×C3⋊D311yescharacteristic
213C2×C22⋊C4—181no—
214C2×C22⋊C4—181no—
215#107—182no—
216#102—22no—
217#102—182no—
218C22⋊C8—182no—
219#95—181no—
220C23×C3—28no—
221C23×C3—44no—
222C23×C3—44no—
223C23×C3—44no—
224C23×C3—44no—
225C23×C3—44no—
226C23×C3—44no—
227C23×C3D3×D414yes—
228C22×D3—38no—
229C22×D3—64no—
230C22×D3—64no—
231C22×D3—64no—
232C22×D3—64no—
233C22×D3—64no—
234C22×D3—64no—
235C3×D4—28no—
236C3×D4—28no—
237C3×D4—44no—
238C3×D4—44no—
239C2×C3×C4—44no—
240C2×C3×C4—44no—
241C2×C3×C4—44no—
242C2×C3×C4#23514yes—
243C2×C3×C4#23514yes—
244C2×C3×C4D3×D414yes—
245C2×C3×C4D3×D414yes—
246C2×C3×C4#23714yes—
247C2×C3×C4C2×#6714yes—
248#67—1232no—
249C2×Dic3—64no—
250C2×Dic3—64no—
251C2×Dic3—68no—
252C2×Dic3—64no—
253C2×Dic3—124no—
254C2×Dic3—124no—
255C2×Dic3—124no—
256C2×Dic3—124no—
257C2×Dic3—124no—
258C4×D3—124no—
259C4×D3—124no—
260C4×D3—124no—
261C4×D3—124no—
262C3×C8—44no—
263C3⋊C8—68no—
264C2×C32—82no—
265C2×C32#39411yescharacteristic
266C2×C32#44711yescharacteristic
267C2×C32#45211yescharacteristic
268C2×C32#46611yescharacteristic
269C2×C32#46811yescharacteristic
270C2×C32#48011yescharacteristic
271C2×C32#48211yescharacteristic
272C3⋊D3—42no—
273C24—21no—
274C24—91no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—184no—
281C2×D4—362no—
282C2×D4—362no—
283C2×D4#63812yes—
284C22×C4—21no—
285C22×C4—91no—
286C22×C4—181no—
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—21no—
298C2×C8—92no—
299C2×C8—181no—
300C2×C8—181no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—92no—
304C4⋊C4—181no—
305C4⋊C4—181no—
306C4⋊C4—181no—
307C22⋊C4—184no—
308C22⋊C4—362no—
309C22×C3—48no—
310C22×C3—48no—
311C22×C3—48no—
312C22×C3—84no—
313C22×C3—84no—
314C22×C3—84no—
315C22×C3—84no—
316C22×C3#88314yes—
317C22×C3#88414yes—
318C22×C3D3×D814yes—
319C22×C3#91114yes—
320C22×C3#91514yes—
321C22×C3#91614yes—
322C22×C3#93714yes—
323C2×D3—68no—
324C2×D3—68no—
325C2×D3—68no—
326C2×D3—124no—
327C2×D3—124no—
328C2×D3—124no—
329C2×D3—124no—
330C3×C4—84no—
331C3×C4#88414yes—
332C3×C4#88514yes—
333C3×C4#92914yes—
334C3×C4#93914yes—
335Dic3—128no—
336Dic3—124no—
337Dic3—244no—
338C32#203311yescharacteristic, complemented, Sylow
339C23—22no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—92no—
347C23—181no—
348C23—181no—
349C23—181no—
350C23—181no—
351C23—181no—
352C23—181no—
353C23D4×C3⋊D311yescharacteristic
354D4—22no—
355D4—22no—
356D4—41no—
357D4—41no—
358D4—368no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—181no—
363C2×C4—181no—
364C2×C4—181no—
365C2×C4—182no—
366C2×C4—361no—
367C2×C4—361no—
368C2×C4—361no—
369C2×C4—361no—
370C2×C4—361no—
371C2×C4—361no—
372C2×C4—361no—
373C2×C4—361no—
374C2×C4—361no—
375C2×C4#382811yescharacteristic
376C2×C4#382811yescharacteristic
377C2×C4D4×C3⋊D311yescharacteristic
378C2×C4D4×C3⋊D311yescharacteristic
379C2×C4#383011yescharacteristic
380C2×C4C2×#63811yescharacteristic
381C8—41no—
382C8—182no—
383C2×C3—88no—
384C2×C3#477414yes—
385C2×C3#477514yes—
386C2×C3#477914yes—
387C2×C3#478014yes—
388C2×C3#495914yes—
389C2×C3#515614yes—
390C2×C3#517314yes—
391D3—128no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—182no—
400C22—182no—
401C22—182no—
402C22—361no—
403C22—361no—
404C22—361no—
405C22—361no—
406C22#6409211yescharacteristic
407C22#6409311yescharacteristic
408C22D8×C3⋊D311yescharacteristic
409C22#6412011yescharacteristic
410C22#6412411yescharacteristic
411C22#6412511yescharacteristic
412C22#6414611yescharacteristic
413C4—81no—
414C4—362no—
415C4—361no—
416C4—721no—
417C4#6409311yescharacteristic
418C4#6409411yescharacteristic
419C4#6413811yescharacteristic
420C4#6414811yescharacteristic
421C3#7020614yescomplemented
422C2—82no—
423C2—362no—
424C2#1059247311yescharacteristic
425C2#1059247411yescharacteristic
426C2#1059247811yescharacteristic
427C2#1059247911yescharacteristic
428C2#1059265811yescharacteristic
429C2#1059285511yescharacteristic
430C2#1059287211yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC2×#64147C2
hypercenterC2×#102C3⋊D3
hypocenterC32#2033
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×C32×#102C2semidirect
3. C2×#63659C2semidirect
4. C2×#63647C2semidirect
5. #10592686C2semidirect
6. C2×#63634C2semidirect
7. #10589417C2semidirect
27. C2×C3×#102D3semidirect
68. C2×C3⋊(C3⋊C8)D4semidirect
134. C2×#102C3⋊D3semidirect
338. C32#2033semidirect
421. C3#70206semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
C2×C32×#1022
C2×#636592
C2×#636472
#105926862
C2×#636342
#105894172
#702063