Finite Group Databasebeta

← #11794307

Subgroups — #11794307

Order 1152.

749 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 749 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595954C211yesmaximal, characteristic
2C3×#4946C211yesmaximal, characteristic
3#10591718C212yesmaximal
4C3×#4526C211yesmaximal, characteristic
5#10589187C212yesmaximal
6#69594—31nomaximal
7#68958—31nomaximal
8C23×C3×Dic3C2211yescharacteristic
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3757C2212yes—
11#64133—21no—
12#64133—21no—
13#64087—22no—
14#64087—22no—
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2212yes—
17C2×C3×Dic3⋊C4—21no—
18C2×Dic3⋊Dic3—22no—
19C3×C3⋊#95—21no—
20#63579—22no—
21#5483—31no—
22#5483—31no—
23#5483—61no—
24C3×#385—31no—
25#5210—32no—
26#4950—32no—
27#4946D311yescharacteristic
28C3×#342—31no—
29#4527—32no—
30#4527—32no—
31#4526D311yescharacteristic
32C24×C32C2311yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C3⋊Dic3D412yes—
36C22×C3⋊Dic3D412yes—
37C2×#634—21no—
38C2×#634—21no—
39C22×C3×Dic3—21no—
40C22×C3×Dic3—21no—
41C22×C3×Dic3—22no—
42C22×C3×Dic3—22no—
43C22×C3×Dic3—42no—
44C32×C22⋊C4—22no—
45#3757—22no—
46#3757—22no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49#3750—22no—
50#3750—22no—
51C3×#217—21no—
52C3×#217—22no—
53C3×#217Q812yescomplemented
54C3×#217Q814yescomplemented
55C3×Dic3⋊C4—42no—
56Dic3⋊Dic3—44no—
57#2062—91noSylow
58C23×C3×C4—31no—
59C23×Dic3C2×D311yescharacteristic
60C2×C3×C4⋊C4—61no—
61C2×C3×C22⋊C4—21no—
62C2×C3×C22⋊C4—32no—
63C2×C3×C22⋊C4—31no—
64C2×C3×C22⋊C4C2×D311yescharacteristic
65C2×C3×C22⋊C4C2×D311yescharacteristic
66C2×#217—32no—
67C2×#217—32no—
68C2×#217—62no—
69C2×#217C2×D311yescharacteristic
70C2×#217C2×D312yes—
71C2×C4⋊Dic3—62no—
72#924—62no—
73#924—62no—
74#924—61no—
75#924—61no—
76#924—61no—
77#924—61no—
78C2×Dic3⋊C4—21no—
79C2×Dic3⋊C4—62no—
80#878—62no—
81#878—62no—
82#878—62no—
83#878—62no—
84#878—64no—
85#878—64no—
86C3×#95—61no—
87C3⋊#95—21no—
88C3⋊#95—62no—
89C3⋊#95—62no—
90C23×C32—41no—
91C23×C32—41no—
92C23×C32C2×D411yescharacteristic
93C23×C32C2×D412yes—
94C23×C32C2×Q812yes—
95C23×C32C2×Q811yescharacteristic
96C23×C32#4111yescharacteristic
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—42no—
104C2×C3⋊Dic3—42no—
105#634—81no—
106#634—81no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—42no—
112C2×C3×Dic3—41no—
113C2×C3×Dic3—42no—
114C2×C3×Dic3—41no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—41no—
117C2×C3×Dic3—41no—
118#543—91no—
119#385—31no—
120#385—92no—
121#342—31no—
122#342—92no—
123C24×C3—21no—
124C24×C3C22×D311yescharacteristic
125C24×C3C22×D311yescharacteristic
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—61no—
129C22×C3×C4—61no—
130C22×C3×C4—62no—
131C22×C3×C4—62no—
132C22×C3×C4—122no—
133C22×C3×C4D1211yescharacteristic
134C22×C3×C4D1211yescharacteristic
135C22×C3×C4#6711yescharacteristic
136C22×C3×C4#6711yescharacteristic
137C22×Dic3—22no—
138C22×Dic3—22no—
139C22×Dic3—21no—
140C22×Dic3—21no—
141C22×Dic3—32no—
142C22×Dic3—32no—
143C22×Dic3—32no—
144C22×Dic3—32no—
145C22×Dic3—42no—
146C22×Dic3—62no—
147C22×Dic3—62no—
148C2×Dic6—62no—
149C2×Dic6—62no—
150C2×Dic6—61no—
151C2×Dic6—61no—
152C2×Dic6—61no—
153C2×Dic6—61no—
154C3×C4⋊C4—122no—
155C3×C22⋊C4—24no—
156C3×C22⋊C4—22no—
157C3×C22⋊C4—22no—
158C3×C22⋊C4—34no—
159C3×C22⋊C4—32no—
160C3×C22⋊C4—62no—
161C3×C22⋊C4—61no—
162#217—21no—
163#217—22no—
164#217—64no—
165#217—64no—
166#217—62no—
167#217—62no—
168#217—62no—
169#217—62no—
170#217Dic614yescomplemented
171#217Dic612yescomplemented
172C4⋊Dic3—62no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—124no—
179Dic3⋊C4—42no—
180Dic3⋊C4—64no—
181Dic3⋊C4—64no—
182Dic3⋊C4—62no—
183Dic3⋊C4—62no—
184Dic3⋊C4—62no—
185Dic3⋊C4—62no—
186Dic3⋊C4—124no—
187C22×C32—22no—
188C22×C32—21no—
189C22×C32—22no—
190C22×C32—21no—
191C22×C32—42no—
192C22×C32—41no—
193C22×C32—41no—
194C22×C32#12011yescharacteristic
195C22×C32C22⋊Q812yes—
196C22×C32C22⋊Q811yescharacteristic
197C22×C32C4⋊Q811yescharacteristic
198C22×C32C4⋊Q812yes—
199C32×C4—41no—
200C32×C4—41no—
201C3⋊Dic3—42no—
202C3⋊Dic3—42no—
203C3×Dic3—44no—
204C3×Dic3—42no—
205C3×Dic3—42no—
206C23×C4—31no—
207C22⋊Q8—182no—
208C22⋊Q8—182no—
209C22⋊Q8—181no—
210C22⋊Q8—181no—
211C2×C4⋊C4—61no—
212C2×C4⋊C4—182no—
213C2×C22⋊C4—32no—
214C2×C22⋊C4—31no—
215C2×C22⋊C4—92no—
216C2×C22⋊C4D3211yescharacteristic
217#95—61no—
218#95—182no—
219C23×C3—21no—
220C23×C3—22no—
221C23×C3—21no—
222C23×C3—21no—
223C23×C3—22no—
224C23×C3—41no—
225C23×C3—41no—
226C23×C3—41no—
227C23×C3—41no—
228C23×C3—81no—
229C23×C3—81no—
230C23×C3C2×Dic612yes—
231C23×C3C2×Dic611yescharacteristic
232C23×C3C2×D1211yescharacteristic
233C23×C3#23511yescharacteristic
234C23×C3D3×D412yes—
235C23×C3D3×D412yes—
236C23×C3#23711yescharacteristic
237C23×C3D3×Q811yescharacteristic
238C23×C3D3×Q812yes—
239C23×C3C2×#6711yescharacteristic
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—64no—
251C2×C3×C4—62no—
252C2×C3×C4—64no—
253C2×C3×C4—62no—
254C2×C3×C4—81no—
255C2×C3×C4—81no—
256C2×C3×C4—122no—
257C2×C3×C4—121no—
258C2×C3×C4—121no—
259C2×C3×C4—122no—
260C2×C3×C4—122no—
261C2×C3×C4—121no—
262C2×C3×C4—121no—
263C2×Dic3—22no—
264C2×Dic3—24no—
265C2×Dic3—24no—
266C2×Dic3—22no—
267C2×Dic3—41no—
268C2×Dic3—42no—
269C2×Dic3—42no—
270C2×Dic3—41no—
271C2×Dic3—41no—
272C2×Dic3—42no—
273C2×Dic3—41no—
274C2×Dic3—64no—
275C2×Dic3—64no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—122no—
281C2×Dic3—122no—
282C2×Dic3—122no—
283C2×Dic3—122no—
284C2×Dic3—242no—
285C2×Dic3—242no—
286Dic6—242no—
287Dic6—242no—
288Dic6—241no—
289Dic6—241no—
290Dic6—241no—
291Dic6—241no—
292C2×C32—22no—
293C2×C32—21no—
294C2×C32—21no—
295C2×C32—22no—
296C2×C32#39511yescharacteristic
297C2×C32B(4,𝔽2)11yescharacteristic
298C2×C32#45811yescharacteristic
299C24C2×D3211yescharacteristic
300C2×Q8—181no—
301C2×Q8—181no—
302C22×C4—61no—
303C22×C4—61no—
304C22×C4—62no—
305C22×C4—62no—
306C22×C4—92no—
307C22×C4—92no—
308C22×C4—122no—
309C22×C4#62611yescharacteristic
310C22×C4#62611yescharacteristic
311C4⋊C4—122no—
312C4⋊C4—182no—
313C4⋊C4—182no—
314C4⋊C4—181no—
315C4⋊C4—181no—
316C4⋊C4—364no—
317C22⋊C4—22no—
318C22⋊C4—32no—
319C22⋊C4—34no—
320C22⋊C4—61no—
321C22⋊C4—62no—
322C22⋊C4—182no—
323C22⋊C4—182no—
324C22×C3—22no—
325C22×C3—21no—
326C22×C3—22no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—22no—
330C22×C3—21no—
331C22×C3—22no—
332C22×C3—22no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—22no—
336C22×C3—21no—
337C22×C3—42no—
338C22×C3—42no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—42no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—42no—
347C22×C3—81no—
348C22×C3—82no—
349C22×C3—81no—
350C22×C3#86911yescharacteristic
351C22×C3#87812yes—
352C22×C3#88211yescharacteristic
353C22×C3#88812yes—
354C22×C3#88812yes—
355C22×C3#89612yes—
356C22×C3#89711yescharacteristic
357C22×C3#92411yescharacteristic
358C22×C3#93711yescharacteristic
359C22×C3#94411yescharacteristic
360C3×C4—42no—
361C3×C4—42no—
362C3×C4—41no—
363C3×C4—41no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—122no—
367C3×C4—124no—
368C3×C4—122no—
369Dic3—44no—
370Dic3—42no—
371Dic3—42no—
372Dic3—124no—
373Dic3—124no—
374Dic3—122no—
375Dic3—122no—
376Dic3—122no—
377Dic3—122no—
378C32#206211yescharacteristic, complemented, Sylow
379C23—41no—
380C23—41no—
381C23D3×Dic611yescharacteristic
382C23D3×Dic612yes—
383C23#379511yescharacteristic
384C23C2×#62611yescharacteristic
385C23#381112yes—
386Q8—721no—
387Q8—721no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—62no—
393C2×C4—64no—
394C2×C4—62no—
395C2×C4—64no—
396C2×C4—121no—
397C2×C4—122no—
398C2×C4—121no—
399C2×C4—122no—
400C2×C4—121no—
401C2×C4—122no—
402C2×C4—121no—
403C2×C4—182no—
404C2×C4—182no—
405C2×C4—362no—
406C2×C4—362no—
407C2×C3—22no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—22no—
411C2×C3—21no—
412C2×C3—22no—
413C2×C3—22no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—41no—
419C2×C3—42no—
420C2×C3—42no—
421C2×C3—41no—
422C2×C3#465611yescharacteristic
423C2×C3#474111yescharacteristic
424C2×C3#474211yescharacteristic
425C2×C3#497911yescharacteristic
426C2×C3#503211yescharacteristic
427C2×C3#505311yescharacteristic
428C22—21no—
429C22—22no—
430C22—21no—
431C22—22no—
432C22—41no—
433C22—42no—
434C22—41no—
435C22#6384012yes—
436C22#6385711yescharacteristic
437C22#6386611yescharacteristic
438C22#6389612yes—
439C22#6398111yescharacteristic
440C4—41no—
441C4—41no—
442C4—122no—
443C4—124no—
444C4—122no—
445C4—362no—
446C4—362no—
447C3—21no—
448C3#6895811yescharacteristic, complemented
449C3#6959411yescharacteristic, complemented
450C2—21no—
451C2—22no—
452C2—22no—
453C2—21no—
454C2#1059135411yescharacteristic
455C2#1059153211yescharacteristic
456C2#1059153511yescharacteristic
subgroupG/H
centerC22#63981
commutator, prime radical, cosocleC24×C32C23
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
hypercenterC2×C22⋊C4D32
hypocenterC32#2062
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
53. C3×#217Q8semidirect
54. C3×#217Q8semidirect
170. #217Dic6semidirect
171. #217Dic6semidirect
378. C32#2062semidirect
448. C3#68958semidirect
449. C3#69594semidirect

Maximal subgroups

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

subgroupindex
#105959542
C3×#49462
#105917182
C3×#45262
#105891872
#695943
#689583