Finite Group Databasebeta

← #11787463

Subgroups — #11787463

Order 1152.

708 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C22×#3775C211yesmaximal, characteristic
2C2×#63902C211yesmaximal, characteristic
3C2×#63740C211yesmaximal, characteristic, complemented
4C2×#63739C211yesmaximal, characteristic
5#10591396C211yesmaximal, characteristic, complemented
6#10590207C211yesmaximal, characteristic, complemented
7#10590075C211yesmaximal, characteristic, complemented
8C22×#627C2211yescharacteristic
9C22×#625C2211yescharacteristic
10C22×D3×Dic3—21no—
11C22×#622C2211yescharacteristic
12C22×#622C2211yescharacteristic
13C2×#3775—22no—
14C2×#3775—22no—
15C2×#3775C414yescomplemented
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×#3724C2211yescharacteristic
19C2×#3724C2211yescharacteristic
20#63902—22no—
21#63902—22no—
22#63740—22no—
23#63739—22no—
24C3×C3⋊#95—21no—
25#63579—21no—
26C2×#67⋊C4—61no—
27#4646—61no—
28C23×C3×D3—21no—
29C22×C32×C4D411yescharacteristic
30C22×C3⋊Dic3D411yescharacteristic
31C22×C3⋊Dic3C2311yescharacteristic
32C22×C3×Dic3—21no—
33C22×C3×Dic3—21no—
34C22×C3×Dic3—21no—
35C2×#627—21no—
36C2×#627—21no—
37C2×#627—21no—
38C2×#627—21no—
39C2×#627—21no—
40C2×#627C2×C412yescomplemented
41C2×#625—21no—
42C2×#625—21no—
43C2×#625—21no—
44C2×#625C2×C412yes—
45C2×#625D412yes—
46C2×#625D412yes—
47C2×D3×Dic3—24no—
48C2×D3×Dic3—42no—
49C2×D3×Dic3—42no—
50C2×#622—21no—
51C2×#622—21no—
52C2×#622—21no—
53C2×#622—21no—
54C2×#622—21no—
55C2×#622C2×C412yescomplemented
56#3775—28no—
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3—21no—
59C3×(C2×D3)⋊C4—24no—
60#3724—21no—
61#3724—21no—
62#3724—21no—
63#3724D412yes—
64#1877—91nomaximal, Sylow
65C22×#67—61no—
66C23×Dic3—61no—
67C22×C4×D3—61no—
68C22×Dic6—61no—
69C2×C3×C22⋊C4—61no—
70C2×(C2×D3)⋊C4—21no—
71C2×Dic3⋊C4—61no—
72C2×Dic3⋊C4—61no—
73C2×C4×Dic3—61no—
74C2×C4×Dic3—61no—
75#67⋊C4—64no—
76#67⋊C4—64no—
77C3×#95—61no—
78C3⋊#95—21no—
79C3⋊#95—61no—
80C3⋊#95—61no—
81C23×C32C2×D411yescharacteristic
82C22×C3×D3—22no—
83C22×C3×D3—22no—
84C22×C3×D3—22no—
85C22×C3×D3—41no—
86C22×C3×D3—41no—
87C22×C3×D3—41no—
88C22×C3×D3—41no—
89C2×C32×C4—21no—
90C2×C32×C4—21no—
91C2×C32×C4—21no—
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—21no—
94C2×C3⋊Dic3SD1612yescomplemented
95C2×C3⋊Dic3C22×C411yescharacteristic
96C2×C3⋊Dic3C2×D411yescharacteristic
97C2×C3⋊Dic3C2×D411yescharacteristic
98C2×C3⋊Dic3C2×D411yescharacteristic
99C2×C3⋊Dic3#4111yescharacteristic
100C2×C3⋊Dic3#4111yescharacteristic
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3—41no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3—41no—
107C2×C3×Dic3—41no—
108C2×C3×Dic3—41no—
109C2×C3×Dic3—41no—
110#627—22no—
111#627—22no—
112#627—41no—
113#627—41no—
114#625—22no—
115#625—22no—
116#625—22no—
117#625C22⋊C414yes—
118D3×Dic3—48no—
119#622—22no—
120#622—41no—
121C22×SD16—91no—
122C2×C4×D4—91no—
123C2×#103—91no—
124C2×#102—91no—
125#391—91no—
126#340—91no—
127#336—91no—
128C24×C3—61no—
129C23×D3—21no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—61no—
133C22×C3×C4—61no—
134C22×C3×C4—61no—
135C2×#67—62no—
136C2×#67—62no—
137C2×#67—62no—
138C2×#67—62no—
139C2×#67—62no—
140C2×#67—62no—
141C22×Dic3—21no—
142C22×Dic3—21no—
143C22×Dic3—21no—
144C22×Dic3—61no—
145C22×Dic3—61no—
146C22×Dic3—61no—
147C22×Dic3—61no—
148C22×Dic3—64no—
149C22×Dic3—122no—
150C22×Dic3—122no—
151C2×C4×D3—64no—
152C2×C4×D3—122no—
153C2×C4×D3—122no—
154C2×Dic6—62no—
155C2×Dic6—62no—
156C2×Dic6—121no—
157C2×Dic6—121no—
158C2×Dic6—121no—
159C2×Dic6—121no—
160C3×C22⋊C4—64no—
161(C2×D3)⋊C4—24no—
162Dic3⋊C4—62no—
163Dic3⋊C4—62no—
164Dic3⋊C4—121no—
165Dic3⋊C4—121no—
166C4×Dic3—62no—
167C4×Dic3—62no—
168C4×Dic3—121no—
169C4×Dic3—121no—
170C22×C32C4×D411yescharacteristic
171C22×C32#12011yescharacteristic
172C22×C32#12111yescharacteristic
173C22×C32C2×SD1611yescharacteristic
174C22×C32#13511yescharacteristic
175C22×C32AGL(1,ℤ/8)11yescharacteristic
176C22×C32#13711yescharacteristic
177C2×C3×D3—24no—
178C2×C3×D3—42no—
179C2×C3×D3—42no—
180C2×C3×D3—42no—
181C2×C3×D3—42no—
182C2×C3×D3—42no—
183C2×C3×D3—42no—
184C32×C4—41no—
185C3⋊Dic3—22no—
186C3⋊Dic3C2×C22⋊C411yescharacteristic
187C3⋊Dic3C4×D411yescharacteristic
188C3⋊Dic3#12111yescharacteristic
189C3⋊Dic3#12311yescharacteristic
190C3×Dic3—42no—
191C3×Dic3—42no—
192C3×Dic3—81no—
193C22×Q8—91no—
194C22×D4—91no—
195C23×C4—181no—
196C2×SD16—94no—
197C2×SD16—182no—
198C2×SD16—182no—
199C22×C8—91no—
200C22×C8—91no—
201C4×D4—182no—
202C4×D4—182no—
203C2×C4⋊C4—91no—
204C2×C4⋊C4—91no—
205C2×C22⋊C4—61no—
206C2×C42—91no—
207#103—182no—
208#102—182no—
209#95—61no—
210#95—181no—
211C23×C3—21no—
212C23×C3—21no—
213C23×C3—62no—
214C23×C3—62no—
215C23×C3—62no—
216C23×C3—121no—
217C23×C3—121no—
218C23×C3—121no—
219C23×C3—121no—
220C22×D3—22no—
221C22×D3—22no—
222C22×D3—22no—
223C22×D3—41no—
224C22×D3—41no—
225C22×D3—41no—
226C22×D3—41no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—62no—
234C2×C3×C4—62no—
235C2×C3×C4—121no—
236C2×C3×C4—121no—
237C2×C3×C4—121no—
238C2×C3×C4—121no—
239C2×C3×C4—121no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242#67—64no—
243#67—64no—
244#67—64no—
245#67—64no—
246C2×Dic3—22no—
247C2×Dic3—22no—
248C2×Dic3—41no—
249C2×Dic3—41no—
250C2×Dic3—41no—
251C2×Dic3—41no—
252C2×Dic3—41no—
253C2×Dic3—41no—
254C2×Dic3—41no—
255C2×Dic3—62no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—121no—
272C2×Dic3—121no—
273C2×Dic3—128no—
274C4×D3—128no—
275Dic6—122no—
276Dic6—122no—
277Dic6—122no—
278Dic6—122no—
279C2×C32#38611yescharacteristic
280C2×C32C4×SD1611yescharacteristic
281C2×C32#44011yescharacteristic
282C2×C32#45011yescharacteristic
283C2×C32#45211yescharacteristic
284C2×C32#46111yescharacteristic
285C2×C32#46311yescharacteristic
286C3×D3—44no—
287C24—61no—
288C2×Q8—92no—
289C2×Q8—181no—
290C2×Q8—181no—
291C2×Q8—181no—
292C2×Q8—181no—
293C2×Q8—181no—
294C2×D4—92no—
295C2×D4—92no—
296C2×D4—92no—
297C2×D4—181no—
298C2×D4—181no—
299C2×D4—181no—
300C22×C4—61no—
301C22×C4—61no—
302C22×C4—61no—
303C22×C4—91no—
304C22×C4—91no—
305C22×C4—184no—
306C22×C4—362no—
307C22×C4—362no—
308C22×C4GO+(4,𝔽2)11yescharacteristic
309SD16—188no—
310C2×C8—92no—
311C2×C8—181no—
312C2×C8—181no—
313C2×C8—181no—
314C2×C8—181no—
315C2×C8—181no—
316C4⋊C4—92no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C22⋊C4—64no—
321C42—181no—
322C42—181no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—64no—
338C22×C3—122no—
339C22×C3—122no—
340C22×C3—122no—
341C22×C3—122no—
342C22×C3—122no—
343C22×C3—122no—
344C2×D3—24no—
345C2×D3—42no—
346C2×D3—42no—
347C2×D3—42no—
348C2×D3—42no—
349C2×D3—42no—
350C2×D3—42no—
351C3×C4—42no—
352C3×C4—42no—
353C3×C4—122no—
354C3×C4—122no—
355C3×C4—241no—
356Dic3—42no—
357Dic3—42no—
358Dic3—61no—
359Dic3—61no—
360Dic3—61no—
361Dic3—61no—
362Dic3—61no—
363Dic3—61no—
364Dic3—61no—
365Dic3—61no—
366Dic3—64no—
367Dic3—81no—
368Dic3—122no—
369C32#187711yescharacteristic, complemented, Sylow
370C23—62no—
371C23—62no—
372C23—62no—
373C23—121no—
374C23—121no—
375C23—121no—
376C23—121no—
377C23C2×GO+(4,𝔽2)11yescharacteristic
378Q8—182no—
379Q8—182no—
380Q8—361no—
381Q8—361no—
382D4—94no—
383D4—182no—
384D4—182no—
385D4—182no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4—91no—
392C2×C4—91no—
393C2×C4—91no—
394C2×C4—91no—
395C2×C4—91no—
396C2×C4—91no—
397C2×C4—92no—
398C2×C4—121no—
399C2×C4—121no—
400C2×C4—121no—
401C2×C4—121no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—181no—
406C2×C4—181no—
407C2×C4—368no—
408C8—182no—
409C8—361no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—124no—
425D3—44no—
426C22—64no—
427C22—122no—
428C22—122no—
429C22—122no—
430C22—122no—
431C22—122no—
432C22—122no—
433C22#6422411yescharacteristic
434C22#6422711yescharacteristic
435C22C4×GO+(4,𝔽2)11yescharacteristic
436C22#6423011yescharacteristic
437C22#6423711yescharacteristic
438C22#6423911yescharacteristic
439C22#6424111yescharacteristic
440C4—41no—
441C4—91no—
442C4—91no—
443C4—91no—
444C4—91no—
445C4—122no—
446C4—122no—
447C4—182no—
448C4—241no—
449C3—21no—
450C3—21no—
451C2—124no—
452C2#1059335411yescharacteristic
453C2#1059342811yescharacteristic
454C2#1059343211yescharacteristic
455C2#1059343311yescharacteristic
456C2#1059343811yescharacteristic
457C2#1059345311yescharacteristic
458C2#1059352411yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#625C22
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1877
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63740C2semidirect
5. #10591396C2semidirect
6. #10590207C2semidirect
7. #10590075C2semidirect
15. C2×#3775C4semidirect
40. C2×#627C2×C4semidirect
55. C2×#622C2×C4semidirect
94. C2×C3⋊Dic3SD16semidirect
369. C32#1877semidirect

Maximal subgroups

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

subgroupindex
C22×#37752
C2×#639022
C2×#637402
C2×#637392
#105913962
#105902072
#105900752
#18779