Finite Group Databasebeta

← #11778029

Subgroups — #11778029

Order 1152.

753 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 753 conjugacy classes of subgroups — too many to draw. Only its 88 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, complemented
2C3×#4960C211yesmaximal, characteristic
3#10591172C212yesmaximal, complemented
4C3×#4525C211yesmaximal, characteristic, complemented
5#10589154C212yesmaximal, complemented
6#69698—31nomaximal
7#68114—31nomaximal
8C22×C3×#67—21no—
9C22×C3×D12C2211yescharacteristic
10C2×C32×C22⋊C4C2211yescharacteristic
11C2×#3757—21no—
12#64133—21no—
13#64133C2212yes—
14#64087—22no—
15#64087—22no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×#3716—22no—
18C3×C3⋊#95C2211yescharacteristic
19C3×#830C2212yes—
20#63563—22no—
21#5483—31no—
22#5483—31no—
23#5483—61no—
24C3×#392—31no—
25#5218—32no—
26#4960D311yescharacteristic
27#4731—32no—
28C3×#323—31no—
29#4525D311yescharacteristic, complemented
30#4467—32no—
31#4452—32no—
32C24×C32D411yescharacteristic
33C23×C3×D3—21no—
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—21no—
38C2×#634—21no—
39C2×#634D412yescomplemented
40C2×C3×#67—42no—
41C2×C3×#67—42no—
42C2×C3×#67—42no—
43C22×C3×Dic3—21no—
44C2×C3×D12—22no—
45C2×C3×D12—42no—
46C32×C22⋊C4—22no—
47#3757—22no—
48#3757—22no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)D412yescomplemented
51#3750—22no—
52#3750—22no—
53C3×(C2×D3)⋊C4—42no—
54C2×C3×C3⋊C8—22no—
55#3716—44no—
56#1596—91noSylow
57C22×C3×D4—31no—
58C22×C3×D4—61no—
59C22×#67—21no—
60C22×D12C2×D311yescharacteristic
61C2×C3×C22⋊C4—21no—
62C2×C3×C22⋊C4—61no—
63C2×C3×C22⋊C4C2×D311yescharacteristic
64C2×C3×C22⋊C4C2×D311yescharacteristic
65C2×#217—62no—
66C2×#217—61no—
67C2×#217—61no—
68C2×#214—62no—
69C2×(C2×D3)⋊C4—21no—
70#924—32no—
71#924—32no—
72#924—62no—
73#924—62no—
74#924—61no—
75#924—61no—
76C2×#204—62no—
77#878—62no—
78#878—62no—
79#878—62no—
80#878—62no—
81#878—64no—
82#878—64no—
83C3×C22⋊C8—32no—
84C3×#95—31no—
85#832—62no—
86C3⋊#95C2×D311yescharacteristic
87#830C2×D312yes—
88#821—62no—
89C23×C32—21no—
90C23×C32—21no—
91C23×C32—41no—
92C23×C32—41no—
93C23×C32SD1612yescomplemented
94C23×C32C2×D411yescharacteristic
95C22×C3×D3—22no—
96C22×C3×D3—41no—
97C22×C3×D3—41no—
98C22×C3×D3—41no—
99C22×C3×D3—41no—
100C22×C3×D3—41no—
101C22×C3×D3—41no—
102C2×C32×C4—21no—
103C2×C32×C4—41no—
104C2×C32×C4—41no—
105C2×C32×C4C2×D412yes—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—81no—
109C2×C3⋊Dic3—81no—
110#634—42no—
111#634—81no—
112C3×#67—48no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—41no—
115C2×C3×Dic3—41no—
116C3×D12—24no—
117C3×D12—42no—
118C3×C3⋊C8—42no—
119#543—91no—
120#450—92no—
121#392—31no—
122#328—92no—
123#323—31no—
124C24×C3—21no—
125C24×C3—61no—
126C24×C3D1211yescharacteristic
127C24×C3#6711yescharacteristic
128C23×D3—21no—
129C2×C3×D4—62no—
130C2×C3×D4—122no—
131C2×C3×D4—122no—
132C2×C3×D4—122no—
133C2×C3×D4—122no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—61no—
137C22×C3×C4D1211yescharacteristic
138C22×C3×C4#6711yescharacteristic
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C22×D311yescharacteristic
141C2×#67—42no—
142C2×#67—42no—
143C2×#67—42no—
144C22×Dic3—21no—
145C22×Dic3—62no—
146C22×Dic3—62no—
147C22×Dic3—61no—
148C22×Dic3—61no—
149C22×Dic3—61no—
150C22×Dic3—61no—
151C2×D12—22no—
152C2×D12—42no—
153C2×Dic6—32no—
154C2×Dic6—32no—
155C2×Dic6—62no—
156C2×Dic6—62no—
157C2×Dic6—61no—
158C2×Dic6—61no—
159C2×C3×C8—62no—
160C3×C22⋊C4—24no—
161C3×C22⋊C4—22no—
162C3×C22⋊C4—22no—
163C3×C22⋊C4—122no—
164#217—64no—
165#217—62no—
166#217—62no—
167#217—64no—
168#217—62no—
169#217—62no—
170#214—124no—
171(C2×D3)⋊C4—42no—
172C4⋊Dic3—32no—
173C4⋊Dic3—32no—
174C4⋊Dic3—62no—
175C4⋊Dic3—62no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178Dic3⋊C4—64no—
179Dic3⋊C4—62no—
180Dic3⋊C4—62no—
181Dic3⋊C4—64no—
182Dic3⋊C4—62no—
183Dic3⋊C4—62no—
184C2×C3⋊C8—22no—
185#204—124no—
186C22×C32—22no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32—41no—
190C22×C32—41no—
191C22×C32—42no—
192C22×C32—81no—
193C22×C32#12011yescharacteristic
194C22×C32C2×SD1611yescharacteristic
195C22×C32#13711yescharacteristic
196C2×C3×D3—42no—
197C2×C3×D3—42no—
198C2×C3×D3—42no—
199C2×C3×D3—81no—
200C2×C3×D3—81no—
201C2×C3×D3—81no—
202C2×C3×D3—81no—
203C32×C4—22no—
204C32×C4—41no—
205C3⋊Dic3—42no—
206C3⋊Dic3—42no—
207C3×Dic3—42no—
208C22×D4—31no—
209C22×D4—61no—
210C2×SD16—182no—
211C22⋊Q8—92no—
212C22⋊Q8—182no—
213C22⋊Q8—182no—
214C22⋊Q8—181no—
215C2×C22⋊C4—61no—
216C2×C22⋊C4—181no—
217C2×C22⋊C4D3211yescharacteristic
218#102—182no—
219C22⋊C8—32no—
220#95—31no—
221C23×C3—22no—
222C23×C3—22no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—21no—
227C23×C3—22no—
228C23×C3—21no—
229C23×C3—41no—
230C23×C3—41no—
231C23×C3—41no—
232C23×C3—41no—
233C23×C3—62no—
234C23×C3—81no—
235C23×C3—81no—
236C23×C3—121no—
237C23×C3—121no—
238C23×C3—121no—
239C23×C3—121no—
240C23×C3—121no—
241C23×C3—121no—
242C23×C3#20412yescomplemented
243C23×C3#21412yescomplemented
244C23×C3C2×D1211yescharacteristic
245C23×C3C2×#6711yescharacteristic
246C22×D3—22no—
247C22×D3—41no—
248C22×D3—41no—
249C22×D3—41no—
250C22×D3—41no—
251C22×D3—41no—
252C22×D3—41no—
253C3×D4—64no—
254C3×D4—122no—
255C3×D4—128no—
256C2×C3×C4—22no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—22no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—62no—
265C2×C3×C4—81no—
266C2×C3×C4—81no—
267C2×C3×C4—121no—
268C2×C3×C4—121no—
269C2×C3×C4D3×D412yes—
270C2×C3×C4D3×D412yes—
271#67—48no—
272C2×Dic3—22no—
273C2×Dic3—41no—
274C2×Dic3—41no—
275C2×Dic3—64no—
276C2×Dic3—64no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—62no—
281C2×Dic3—242no—
282C2×Dic3—242no—
283C2×Dic3—241no—
284C2×Dic3—241no—
285C2×Dic3—241no—
286C2×Dic3—241no—
287D12—24no—
288D12—42no—
289Dic6—122no—
290Dic6—122no—
291Dic6—242no—
292Dic6—242no—
293Dic6—241no—
294Dic6—241no—
295C3×C8—122no—
296C3⋊C8—42no—
297C2×C32—21no—
298C2×C32—21no—
299C2×C32—42no—
300C2×C32#44811yescharacteristic
301C2×C32#45311yescharacteristic
302C2×C32B(4,𝔽2)11yescharacteristic
303C3×D3—82no—
304C24—61no—
305C24#62611yescharacteristic
306C2×Q8—92no—
307C2×Q8—181no—
308C2×D4—62no—
309C2×D4—122no—
310C2×D4—122no—
311C2×D4—122no—
312C2×D4—122no—
313C22×C4—61no—
314C22×C4—181no—
315C22×C4—181no—
316C22×C4#62611yescharacteristic
317C22×C4C2×D3211yescharacteristic
318SD16—364no—
319C2×C8—62no—
320C4⋊C4—92no—
321C4⋊C4—182no—
322C4⋊C4—181no—
323C4⋊C4—182no—
324C22⋊C4—22no—
325C22⋊C4—122no—
326C22⋊C4—182no—
327C22⋊C4—182no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—24no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—42no—
341C22×C3—42no—
342C22×C3—42no—
343C22×C3—42no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—82no—
349C22×C3—81no—
350C22×C3—81no—
351C22×C3—82no—
352C22×C3—122no—
353C22×C3—122no—
354C22×C3—122no—
355C22×C3—241no—
356C22×C3—241no—
357C22×C3—241no—
358C22×C3—241no—
359C22×C3#88211yescharacteristic
360C22×C3C2×#20411yescharacteristic
361C22×C3#90911yescharacteristic
362C22×C3C2×#21411yescharacteristic
363C22×C3#93711yescharacteristic
364C22×C3#95111yescharacteristic
365C2×D3—42no—
366C2×D3—42no—
367C2×D3—42no—
368C2×D3—81no—
369C2×D3—81no—
370C2×D3—81no—
371C2×D3—81no—
372C3×C4—22no—
373C3×C4—22no—
374C3×C4—42no—
375C3×C4—42no—
376C3×C4—41no—
377C3×C4—41no—
378C3×C4—122no—
379Dic3—42no—
380Dic3—124no—
381Dic3—124no—
382Dic3—122no—
383Dic3—122no—
384Dic3—122no—
385Dic3—122no—
386C32#159611yescharacteristic, complemented, Sylow
387C23—21no—
388C23—21no—
389C23—41no—
390C23—41no—
391C23—62no—
392C23—121no—
393C23—121no—
394C23—121no—
395C23—121no—
396C23—121no—
397C23—121no—
398C23#371612yescomplemented
399C23C2×#62611yescharacteristic
400Q8—362no—
401Q8—721no—
402D4—64no—
403D4—122no—
404D4—128no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—62no—
409C2×C4—121no—
410C2×C4—121no—
411C2×C4—182no—
412C2×C4—182no—
413C2×C4—721no—
414C2×C4—721no—
415C2×C4#381112yes—
416C8—122no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—41no—
425C2×C3—41no—
426C2×C3—44no—
427C2×C3—42no—
428C2×C3—42no—
429C2×C3—242no—
430C2×C3#473811yescharacteristic
431C2×C3#474111yescharacteristic
432C2×C3#474711yescharacteristic
433C2×C3#503211yescharacteristic
434C2×C3#504011yescharacteristic
435C2×C3#507711yescharacteristic
436D3—82no—
437C22—21no—
438C22—21no—
439C22—22no—
440C22—42no—
441C22—41no—
442C22—41no—
443C22—81no—
444C22—122no—
445C22—122no—
446C22—122no—
447C22—241no—
448C22—241no—
449C22—241no—
450C22—241no—
451C22C2×#371611yescharacteristic
452C22#6383111yescharacteristic
453C22#6398111yescharacteristic
454C4—22no—
455C4—41no—
456C4—122no—
457C4—362no—
458C4—362no—
459C3—21no—
460C3#6811411yescharacteristic, complemented
461C3#6969811yescharacteristic, complemented
462C2—21no—
463C2—21no—
464C2—42no—
465C2—242no—
466C2#1059118111yescharacteristic
467C2#1059151111yescharacteristic
468C2#1059153211yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC3×#4960C2
hypercenterC2×C22⋊C4D32
hypocenterC32#1596
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595954C2semidirect
3. #10591172C2semidirect
4. C3×#4525C2semidirect
5. #10589154C2semidirect
29. #4525D3semidirect
39. C2×#634D4semidirect
50. C4⋊(C3⋊Dic3)D4semidirect
93. C23×C32SD16semidirect
242. C23×C3#204semidirect
243. C23×C3#214semidirect
386. C32#1596semidirect
398. C23#3716semidirect
460. C3#68114semidirect
461. C3#69698semidirect

Maximal subgroups

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

subgroupindex
#105959542
C3×#49602
#105911722
C3×#45252
#105891542
#696983
#681143