Finite Group Databasebeta

← #11788122

Subgroups — #11788122

Order 1152.

1236 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64147C211yesmaximal, characteristic
2C22×#3743C211yesmaximal, characteristic, complemented
3C2×C32×#102C211yesmaximal, characteristic, complemented
4C2×#63659C211yesmaximal, characteristic, complemented
5#10592686C211yesmaximal, characteristic, complemented
6#10589417C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#70203—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#64147C414yescomplemented
17C2×#3752—21no—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C2×#3743—22no—
22C2×#3743—22no—
23C2×#3743—22no—
24C32×#102—22no—
25#63659—22no—
26#63658—21no—
27C2×#938—34no—
28C22×ΓL(1,𝔽25)—34no—
29C2×C3×#102D314yescomplemented
30C2×#832—34no—
31#4987—34no—
32#4551—34no—
33#4529—34no—
34C24×C32—21no—
35C23×C3⋊D3D411yescharacteristic
36C2×C32×D4—21no—
37C2×C32×D4—21no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4C2×C412yes—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C2×#638—24no—
45C2×#638—42no—
46C2×#638—42no—
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3D411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3—21no—
54C2×C4×C3⋊D3C2×C412yes—
55C2×C4×C3⋊D3D412yes—
56C2×C32×C8—21no—
57C2×C32×C8—21no—
58C2×C32×C8D412yescomplemented
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61#3757—24no—
62#3752—42no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2×C412yes—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)D412yescomplemented
70#3743—28no—
71#1895—91noSylow
72C22×C3×D4C2×D314yes—
73C22×#67—64no—
74C22×C4×D3—34no—
75C22×C3×C8C2×D314yes—
76C2×C3×C4⋊C4C2×D314yes—
77C2×#217—64no—
78#938—316no—
79#938—68no—
80C2×(C2×D3)⋊C4—64no—
81C2×C4⋊Dic3—34no—
82C2×C4⋊Dic3—34no—
83C22×C3⋊C8—34no—
84C2×ΓL(1,𝔽25)—68no—
85C2×ΓL(1,𝔽25)—68no—
86C2×ΓL(1,𝔽25)—68no—
87C3×#102—28no—
88#832—68no—
89C3⋊#95—64no—
90C23×C32—22no—
91C23×C32—41no—
92C23×C32—41no—
93C23×C32—41no—
94C23×C32—41no—
95C23×C32—41no—
96C23×C32—41no—
97C23×C32C2×D411yescharacteristic
98C22×C3⋊D3—21no—
99C22×C3⋊D3—21no—
100C22×C3⋊D3—21no—
101C22×C3⋊D3—21no—
102C22×C3⋊D3—21no—
103C22×C3⋊D3—21no—
104C22×C3⋊D3C22⋊C412yes—
105C32×D4—22no—
106C32×D4—22no—
107C32×D4—41no—
108C32×D4—41no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118#638—48no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3C22⋊C412yes—
128C4×C3⋊D3—22no—
129C4×C3⋊D3—22no—
130C4×C3⋊D3—22no—
131C4×C3⋊D3—22no—
132C32×C8—22no—
133C3⋊(C3⋊C8)—22no—
134C22×M16—91no—
135C2×#121—91no—
136C2×#102—91no—
137C2×#102C3⋊D311yescharacteristic, complemented
138#380—91no—
139#340—91no—
140#340—91no—
141C24×C3—24no—
142C23×D3—34no—
143C2×C3×D4—24no—
144C2×C3×D4—24no—
145C2×C3×D4—24no—
146C2×C3×D4—24no—
147C2×C3×D4—24no—
148C2×C3×D4C4×D318yes—
149C22×C3×C4—24no—
150C22×C3×C4C22×D314yes—
151C2×#67—616no—
152C2×#67—128no—
153C2×#67—128no—
154C22×Dic3—34no—
155C22×Dic3—64no—
156C22×Dic3—64no—
157C2×C4×D3—38no—
158C2×C4×D3—38no—
159C2×C4×D3—64no—
160C2×C4×D3—64no—
161C2×C4×D3—64no—
162C2×C4×D3—64no—
163C2×C3×C8—24no—
164C2×C3×C8—24no—
165C2×C3×C8#6718yescomplemented
166C3×C4⋊C4—24no—
167C3×C4⋊C4—24no—
168#217—616no—
169(C2×D3)⋊C4—128no—
170C4⋊Dic3—38no—
171C4⋊Dic3—64no—
172C4⋊Dic3—64no—
173C4⋊Dic3—64no—
174C2×C3⋊C8—38no—
175C2×C3⋊C8—64no—
176C2×C3⋊C8—64no—
177ΓL(1,𝔽25)—632no—
178C22×C32—42no—
179C22×C32—42no—
180C22×C32—42no—
181C22×C32—81no—
182C22×C32—81no—
183C22×C32—81no—
184C22×C32—81no—
185C22×C32C2×C22⋊C411yescharacteristic
186C22×C32#12111yescharacteristic
187C22×C32#12111yescharacteristic
188C22×C32AGL(1,ℤ/8)11yescharacteristic
189C22×C32AGL(1,ℤ/8)11yescharacteristic
190C22×C32AGL(1,ℤ/8)11yescharacteristic
191C22×C32#13711yescharacteristic
192C2×C3⋊D3—22no—
193C2×C3⋊D3—22no—
194C2×C3⋊D3—22no—
195C2×C3⋊D3—41no—
196C2×C3⋊D3—41no—
197C2×C3⋊D3—41no—
198C2×C3⋊D3—41no—
199C32×C4—81no—
200C32×C4C4×D411yescharacteristic
201C32×C4C4×D411yescharacteristic
202C32×C4#12011yescharacteristic
203C32×C4#12311yescharacteristic
204C3⋊Dic3—22no—
205C3⋊Dic3—42no—
206C3⋊Dic3—81no—
207C22×D4—181no—
208C22×D4C2×C3⋊D311yescharacteristic
209C23×C4—91no—
210C2×M16—182no—
211C2×M16—182no—
212C2×M16—182no—
213C22×C8—91no—
214C22×C8C2×C3⋊D311yescharacteristic
215#121—94no—
216#121—182no—
217C2×C4⋊C4—91no—
218C2×C4⋊C4—91no—
219C2×C4⋊C4C2×C3⋊D311yescharacteristic
220C2×C22⋊C4—181no—
221C2×C22⋊C4—181no—
222#102—22no—
223#102—182no—
224#95—181no—
225C23×C3—28no—
226C23×C3—44no—
227C23×C3—44no—
228C23×C3—44no—
229C23×C3—44no—
230C23×C3—44no—
231C23×C3—44no—
232C23×C3D3×D414yes—
233C22×D3—38no—
234C22×D3—64no—
235C22×D3—64no—
236C22×D3—64no—
237C22×D3—64no—
238C22×D3—64no—
239C22×D3—64no—
240C3×D4—28no—
241C3×D4—28no—
242C3×D4—44no—
243C3×D4—44no—
244C2×C3×C4—44no—
245C2×C3×C4—44no—
246C2×C3×C4—44no—
247C2×C3×C4C2×C4×D314yes—
248C2×C3×C4#23514yes—
249C2×C3×C4D3×D414yes—
250C2×C3×C4D3×D414yes—
251C2×C3×C4#23714yes—
252C2×C3×C4C2×#6714yes—
253#67—1232no—
254C2×Dic3—38no—
255C2×Dic3—64no—
256C2×Dic3—64no—
257C2×Dic3—68no—
258C2×Dic3—124no—
259C2×Dic3—124no—
260C2×Dic3—124no—
261C2×Dic3—124no—
262C2×Dic3—124no—
263C4×D3—68no—
264C4×D3—68no—
265C4×D3—68no—
266C4×D3—68no—
267C3×C8—28no—
268C3⋊C8—68no—
269C2×C32—82no—
270C2×C32#38611yescharacteristic
271C2×C32#41711yescharacteristic
272C2×C32#41811yescharacteristic
273C2×C32#46811yescharacteristic
274C2×C32#46811yescharacteristic
275C2×C32#46911yescharacteristic
276C2×C32#46911yescharacteristic
277C3⋊D3—42no—
278C24—21no—
279C24—91no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—184no—
286C2×D4—362no—
287C2×D4—362no—
288C2×D4C4×C3⋊D312yes—
289C22×C4—21no—
290C22×C4—91no—
291C22×C4—92no—
292C22×C4—92no—
293C22×C4—181no—
294C22×C4—181no—
295C22×C4—181no—
296C22×C4—181no—
297C22×C4—181no—
298C22×C4—181no—
299C22×C4C22×C3⋊D311yescharacteristic
300M16—188no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—92no—
304C2×C8—181no—
305C2×C8—181no—
306C2×C8#63812yescomplemented
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—92no—
310C4⋊C4—181no—
311C4⋊C4—181no—
312C4⋊C4—181no—
313C22⋊C4—184no—
314C22⋊C4—362no—
315C22×C3—48no—
316C22×C3—48no—
317C22×C3—48no—
318C22×C3—84no—
319C22×C3—84no—
320C22×C3—84no—
321C22×C3—84no—
322C22×C3D3×C22⋊C414yes—
323C22×C3#88414yes—
324C22×C3#91114yes—
325C22×C3#91114yes—
326C22×C3#91414yes—
327C22×C3#91514yes—
328C22×C3#93814yes—
329C2×D3—68no—
330C2×D3—68no—
331C2×D3—68no—
332C2×D3—124no—
333C2×D3—124no—
334C2×D3—124no—
335C2×D3—124no—
336C3×C4—84no—
337C3×C4#67⋊C414yes—
338C3×C4#88314yes—
339C3×C4C4×#6714yes—
340C3×C4#93714yes—
341Dic3—68no—
342Dic3—128no—
343Dic3—244no—
344C32#189511yescharacteristic, complemented, Sylow
345C23—22no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—92no—
353C23—181no—
354C23—181no—
355C23—181no—
356C23—181no—
357C23—181no—
358C23—181no—
359C23D4×C3⋊D311yescharacteristic
360D4—22no—
361D4—22no—
362D4—41no—
363D4—41no—
364D4—368no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—92no—
369C2×C4—181no—
370C2×C4—181no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4—182no—
374C2×C4—182no—
375C2×C4—182no—
376C2×C4—361no—
377C2×C4—361no—
378C2×C4—361no—
379C2×C4—361no—
380C2×C4—361no—
381C2×C4C2×C4×C3⋊D311yescharacteristic
382C2×C4#382811yescharacteristic
383C2×C4D4×C3⋊D311yescharacteristic
384C2×C4D4×C3⋊D311yescharacteristic
385C2×C4#383011yescharacteristic
386C2×C4C2×#63811yescharacteristic
387C8—22no—
388C8—182no—
389C2×C3—88no—
390C2×C3#477014yes—
391C2×C3#477114yes—
392C2×C3#478014yes—
393C2×C3#478214yes—
394C2×C3#495614yes—
395C2×C3#515914yes—
396C2×C3#517414yes—
397D3—128no—
398C22—42no—
399C22—42no—
400C22—42no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—182no—
406C22—182no—
407C22—182no—
408C22—361no—
409C22—361no—
410C22—361no—
411C22—361no—
412C22C22⋊C4×C3⋊D311yescharacteristic
413C22#6409311yescharacteristic
414C22#6412011yescharacteristic
415C22#6412011yescharacteristic
416C22#6412311yescharacteristic
417C22#6412411yescharacteristic
418C22#6414711yescharacteristic
419C4—81no—
420C4—182no—
421C4—362no—
422C4—721no—
423C4#6409011yescharacteristic
424C4#6409211yescharacteristic
425C4C4×#63811yescharacteristic
426C4#6414611yescharacteristic
427C3#7020314yescomplemented
428C2—82no—
429C2—362no—
430C2#1059246911yescharacteristic
431C2#1059247011yescharacteristic
432C2#1059247911yescharacteristic
433C2#1059248111yescharacteristic
434C2#1059265511yescharacteristic
435C2#1059285811yescharacteristic
436C2#1059287311yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC2×#64147C2
cosocleC22×C32×C4C23
hypercenterC2×#102C3⋊D3
hypocenterC32#1895
LCSG ▷ C2×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. C22×#3743C2semidirect
3. C2×C32×#102C2semidirect
4. C2×#63659C2semidirect
5. #10592686C2semidirect
6. #10589417C2semidirect
7. #10589395C2semidirect
16. #64147C4semidirect
29. C2×C3×#102D3semidirect
58. C2×C32×C8D4semidirect
69. C2×C3⋊(C3⋊C8)D4semidirect
137. C2×#102C3⋊D3semidirect
165. C2×C3×C8#67semidirect
306. C2×C8#638semidirect
344. C32#1895semidirect
427. C3#70203semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
C22×#37432
C2×C32×#1022
C2×#636592
#105926862
#105894172
#105893952
#702033