Finite Group Databasebeta

← #11787358

Subgroups — #11787358

Order 1152.

1037 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 1037 conjugacy classes of subgroups — too many to draw. Only its 164 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
1C2×#64147C211yesmaximal, characteristic
2C2×#63849C211yesmaximal, characteristic, complemented
3C2×C3×#832C212yesmaximal, complemented
4C2×#63557C211yesmaximal, characteristic, complemented
5#10589164C212yesmaximal, complemented
6#70201—32nomaximal
7C22×C32×D4C2211yescharacteristic
8C22×#638—21no—
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×#3757—21no—
11#64147—22no—
12#64147C414yescomplemented
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×#3722—21no—
17C2×Dic32—21no—
18#63849—24no—
19C3×#832—24no—
20#63557—22no—
21C2×#938—32no—
22C2×#938—61no—
23C2×#892—32no—
24C2×C3×#102—32no—
25C2×#832D312yescomplemented
26C2×(C2×D3)⋊C8—32no—
27#4551—32no—
28#4529—32no—
29C24×C32—21no—
30C23×C3⋊D3D411yescharacteristic
31C2×C32×D4—22no—
32C2×C32×D4—21no—
33C2×C32×D4—22no—
34C2×C32×D4C2×C412yes—
35C22×C32×C4C2311yescharacteristic
36C2×#638—24no—
37C2×#638—44no—
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40C2×C4×C3⋊D3—22no—
41C2×C4×C3⋊D3—22no—
42C2×C4×C3⋊D3C2×C412yes—
43C2×C4×C3⋊D3D412yes—
44C22×C3×Dic3—22no—
45#3757—24no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)C2×C412yes—
48C3×C4⋊Dic3—22no—
49C3×C4⋊Dic3D414yescomplemented
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8—22no—
53#3722—24no—
54Dic32—24no—
55#1875—91noSylow
56C22×C3×D4—21no—
57C22×C3×D4C2×D312yes—
58C22×#67—62no—
59C22×#67—62no—
60C22×C4×D3—32no—
61C22×C4×D3—61no—
62C22×C3×C8—32no—
63C2×C3×C4⋊C4—32no—
64C2×#217—62no—
65C2×#217—62no—
66#938—38no—
67#938—64no—
68#938—64no—
69#938—64no—
70C2×(C2×D3)⋊C4—62no—
71C2×C4⋊Dic3—32no—
72C2×C4⋊Dic3—61no—
73C2×C4⋊Dic3C2×D312yes—
74C2×C4×Dic3—62no—
75C22×C3⋊C8C2×D312yes—
76#892—64no—
77#892—64no—
78C3×#102—64no—
79#832—24no—
80(C2×D3)⋊C8—64no—
81C23×C32—22no—
82C23×C32—41no—
83C23×C32—41no—
84C23×C32—42no—
85C23×C32—42no—
86C23×C32C2×D411yescharacteristic
87C22×C3⋊D3—22no—
88C22×C3⋊D3—21no—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—22no—
91C22×C3⋊D3C22⋊C412yes—
92C32×D4—24no—
93C32×D4—42no—
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D412yes—
97C2×C32×C4#4112yes—
98#638—48no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—42no—
103C2×C3⋊Dic3C22⋊C412yes—
104C4×C3⋊D3—24no—
105C4×C3⋊D3—24no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—42no—
108C2×C3×Dic3—42no—
109C3×C3⋊C8—42no—
110C2×#121—91no—
111C2×#117—91no—
112C2×#102—32no—
113C2×C22⋊C8—91no—
114#340—92no—
115C24×C3—22no—
116C24×C3—22no—
117C23×D3—32no—
118C23×D3—61no—
119C2×C3×D4—22no—
120C2×C3×D4—22no—
121C2×C3×D4—22no—
122C2×C3×D4—22no—
123C2×C3×D4—22no—
124C2×C3×D4—22no—
125C2×C3×D4—22no—
126C2×C3×D4—42no—
127C2×C3×D4—42no—
128C2×C3×D4C4×D314yes—
129C22×C3×C4—21no—
130C22×C3×C4—62no—
131C22×C3×C4C22×D312yes—
132C2×#67—68no—
133C2×#67—68no—
134C2×#67—128no—
135C2×#67—124no—
136C2×#67—124no—
137C22×Dic3—22no—
138C22×Dic3—32no—
139C22×Dic3—61no—
140C22×Dic3—62no—
141C22×Dic3—62no—
142C2×C4×D3—34no—
143C2×C4×D3—34no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—122no—
151C2×C4×D3—122no—
152C2×C3×C8—62no—
153C2×C3×C8—62no—
154C2×C3×C8—62no—
155C3×C4⋊C4—34no—
156C3×C4⋊C4—62no—
157#217—68no—
158#217—68no—
159(C2×D3)⋊C4—68no—
160C4⋊Dic3—22no—
161C4⋊Dic3—34no—
162C4⋊Dic3—62no—
163C4⋊Dic3—62no—
164C4⋊Dic3—62no—
165C4⋊Dic3#6714yescomplemented
166C4×Dic3—68no—
167C2×C3⋊C8—22no—
168C2×C3⋊C8—22no—
169C2×C3⋊C8—22no—
170C22×C32—42no—
171C22×C32—42no—
172C22×C32—42no—
173C22×C32—82no—
174C22×C32—82no—
175C22×C32C2×C22⋊C411yescharacteristic
176C22×C32#12011yescharacteristic
177C22×C32#12311yescharacteristic
178C22×C32#13512yes—
179C22×C32AGL(1,ℤ/8)12yes—
180C2×C3⋊D3—22no—
181C2×C3⋊D3—22no—
182C2×C3⋊D3—22no—
183C2×C3⋊D3—42no—
184C2×C3⋊D3—42no—
185C32×C4C4×D412yes—
186C32×C4#12112yes—
187C3⋊Dic3—22no—
188C3⋊Dic3—42no—
189C3×Dic3—44no—
190C22×D4—181no—
191C22×D4D3211yescharacteristic
192C23×C4—91no—
193C22×C8—32no—
194#121—94no—
195#121—182no—
196#117—184no—
197C2×C4⋊C4—32no—
198C2×C4⋊C4—91no—
199C2×C22⋊C4—181no—
200C2×C22⋊C4—181no—
201C2×C42—181no—
202#102—64no—
203C22⋊C8—182no—
204C23×C3—24no—
205C23×C3—24no—
206C23×C3—21no—
207C23×C3—44no—
208C23×C3—42no—
209C23×C3—42no—
210C23×C3—44no—
211C23×C3—42no—
212C23×C3—42no—
213C23×C3—42no—
214C23×C3—42no—
215C23×C3—42no—
216C23×C3—42no—
217C23×C3D3×D412yes—
218C22×D3—34no—
219C22×D3—62no—
220C22×D3—64no—
221C22×D3—62no—
222C22×D3—62no—
223C22×D3—62no—
224C22×D3—62no—
225C22×D3—62no—
226C22×D3—62no—
227C22×D3—121no—
228C22×D3—121no—
229C22×D3—122no—
230C3×D4—24no—
231C3×D4—24no—
232C3×D4—44no—
233C3×D4—44no—
234C3×D4—42no—
235C3×D4—42no—
236C2×C3×C4—22no—
237C2×C3×C4—21no—
238C2×C3×C4—22no—
239C2×C3×C4—21no—
240C2×C3×C4—64no—
241C2×C3×C4—122no—
242C2×C3×C4—122no—
243C2×C3×C4C2×C4×D312yes—
244C2×C3×C4#23512yes—
245C2×C3×C4D3×D412yes—
246C2×C3×C4D3×D412yes—
247C2×C3×C4#23712yes—
248C2×C3×C4C2×#6712yes—
249#67—1216no—
250#67—1216no—
251C2×Dic3—24no—
252C2×Dic3—34no—
253C2×Dic3—42no—
254C2×Dic3—42no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—62no—
258C2×Dic3—64no—
259C2×Dic3—64no—
260C2×Dic3—121no—
261C2×Dic3—121no—
262C2×Dic3—124no—
263C2×Dic3—122no—
264C2×Dic3—122no—
265C4×D3—64no—
266C4×D3—64no—
267C4×D3—64no—
268C4×D3—64no—
269C4×D3—124no—
270C4×D3—124no—
271C3×C8—122no—
272C3⋊C8—42no—
273C2×C32—82no—
274C2×C32#38611yescharacteristic
275C2×C32#41611yescharacteristic
276C2×C32#41811yescharacteristic
277C2×C32#44912yes—
278C2×C32#48212yes—
279C3⋊D3—42no—
280C24—21no—
281C24—91no—
282C2×D4—22no—
283C2×D4—22no—
284C2×D4—21no—
285C2×D4—184no—
286C2×D4—364no—
287C2×D4#62412yes—
288C22×C4—62no—
289C22×C4—91no—
290C22×C4—92no—
291C22×C4—92no—
292C22×C4—182no—
293C22×C4—182no—
294C22×C4—181no—
295C22×C4C2×D3211yescharacteristic
296C2×C8—62no—
297C2×C8—62no—
298C2×C8—62no—
299C4⋊C4—34no—
300C4⋊C4—62no—
301C4⋊C4—92no—
302C4⋊C4—181no—
303C22⋊C4—184no—
304C22⋊C4—184no—
305C42—184no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—44no—
312C22×C3—44no—
313C22×C3—44no—
314C22×C3—44no—
315C22×C3—44no—
316C22×C3—44no—
317C22×C3—84no—
318C22×C3—84no—
319C22×C3—82no—
320C22×C3—82no—
321C22×C3—82no—
322C22×C3—82no—
323C22×C3D3×C22⋊C412yes—
324C22×C3#88312yes—
325C22×C3#91112yes—
326C22×C3#91212yes—
327C22×C3#91412yes—
328C22×C3#91612yes—
329C22×C3#93712yes—
330C2×D3—64no—
331C2×D3—64no—
332C2×D3—64no—
333C2×D3—64no—
334C2×D3—122no—
335C2×D3—122no—
336C2×D3—124no—
337C2×D3—124no—
338C2×D3—122no—
339C2×D3—122no—
340C2×D3—122no—
341C2×D3—122no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—124no—
345C3×C4#67⋊C412yes—
346C3×C4#88412yes—
347C3×C4C4×#6712yes—
348C3×C4#93812yes—
349Dic3—44no—
350Dic3—64no—
351Dic3—122no—
352Dic3—124no—
353Dic3—124no—
354C32#187511yescharacteristic, complemented, Sylow
355C23—22no—
356C23—42no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23—92no—
361C23—182no—
362C23—182no—
363C23—181no—
364C23—181no—
365C23#381111yescharacteristic
366D4—24no—
367D4—42no—
368D4—368no—
369C2×C4—64no—
370C2×C4—92no—
371C2×C4—122no—
372C2×C4—122no—
373C2×C4—181no—
374C2×C4—181no—
375C2×C4—184no—
376C2×C4—184no—
377C2×C4—182no—
378C2×C4—362no—
379C2×C4#380412yes—
380C2×C4C2×#62411yescharacteristic
381C2×C4D3×#6712yes—
382C2×C4#381111yescharacteristic
383C8—122no—
384C2×C3—22no—
385C2×C3—21no—
386C2×C3—22no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—84no—
390C2×C3—84no—
391C2×C3#477012yes—
392C2×C3#477212yes—
393C2×C3#477912yes—
394C2×C3#478412yes—
395C2×C3#495612yes—
396C2×C3#515812yes—
397C2×C3#517212yes—
398D3—124no—
399D3—124no—
400C22—42no—
401C22—42no—
402C22—42no—
403C22—82no—
404C22—82no—
405C22—182no—
406C22—182no—
407C22—182no—
408C22—362no—
409C22—362no—
410C22#6393612yes—
411C22#6393712yes—
412C22#6397411yescharacteristic
413C22#6397511yescharacteristic
414C22#6398311yescharacteristic
415C4—124no—
416C4—182no—
417C4—362no—
418C4#6395212yes—
419C4#6395812yes—
420C3—21no—
421C3#7020112yescomplemented
422C2—82no—
423C2—362no—
424C2#1059142411yescharacteristic
425C2#1059142512yes—
426C2#1059142611yescharacteristic
427C2#1059152012yes—
428C2#1059172211yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×#64147C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1875
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63849C2semidirect
3. C2×C3×#832C2semidirect
4. C2×#63557C2semidirect
5. #10589164C2semidirect
12. #64147C4semidirect
25. C2×#832D3semidirect
49. C3×C4⋊Dic3D4semidirect
165. C4⋊Dic3#67semidirect
354. C32#1875semidirect
421. C3#70201semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
C2×#638492
C2×C3×#8322
C2×#635572
#105891642
#702013