Finite Group Databasebeta

← #11794308

Subgroups — #11794308

Order 1152.

745 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 745 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C3×#5483C211yesmaximal, characteristic
2#10592645C211yesmaximal, characteristic
3#10591719C212yesmaximal
4C3×#4526C211yesmaximal, characteristic
5#10589186C212yesmaximal
6#71895—31nomaximal
7#68958—31nomaximal
8C23×C3⋊Dic3C2211yescharacteristic
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3757C2211yescharacteristic
11C2×#3750—21no—
12C2×C3×#217C2212yes—
13C2×C3×#217C2212yes—
14C3×#924—21no—
15C3×#924—21no—
16C3×#878—22no—
17C3×#878—22no—
18C2×Dic3⋊Dic3—22no—
19#63658—21no—
20#63579—22no—
21C3×#543—31no—
22#5483D311yescharacteristic
23#4950—32no—
24#4946—31no—
25#4946—31no—
26#4946—32no—
27#4946—61no—
28C3×#342—31no—
29#4527—32no—
30#4526—32no—
31#4526D311yescharacteristic
32C24×C32C2311yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—22no—
38C22×C3⋊Dic3—42no—
39C22×C3×Dic3—22no—
40C22×C3×Dic3D412yes—
41C22×C3×Dic3D412yes—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C32×C22⋊C4—22no—
45#3757—21no—
46#3757Q812yescomplemented
47#3750—42no—
48C3×#217—22no—
49C3×#217—22no—
50C3×#217—22no—
51C3×#217Q814yescomplemented
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×Dic3⋊C4—22no—
55C3×Dic3⋊C4—22no—
56Dic3⋊Dic3—44no—
57#2062—91noSylow
58C23×Dic3—31no—
59C23×Dic3—31no—
60C23×Dic3—61no—
61C3×C22⋊Q8—62no—
62C3×C22⋊Q8—62no—
63C3×C22⋊Q8—61no—
64C3×C22⋊Q8—61no—
65C2×C3×C22⋊C4—21no—
66C2×C3×C22⋊C4—32no—
67C2×C3×C22⋊C4—32no—
68C2×C3×C22⋊C4C2×D311yescharacteristic
69C2×C3×C22⋊C4C2×D311yescharacteristic
70C2×#217—31no—
71C2×#217—31no—
72C2×#217—61no—
73C2×#217C2×D312yes—
74C2×#217C2×D312yes—
75C2×C4⋊Dic3—62no—
76#924—21no—
77#924—21no—
78C2×Dic3⋊C4—62no—
79C2×Dic3⋊C4—62no—
80C2×Dic3⋊C4—61no—
81C2×Dic3⋊C4—61no—
82#878—22no—
83#878—22no—
84C3⋊#95—62no—
85C3⋊#95—62no—
86C3⋊#95—61no—
87C3⋊#95—61no—
88C3⋊#95—62no—
89C23×C32—41no—
90C23×C32—41no—
91C23×C32C2×D411yescharacteristic
92C23×C32C2×D412yes—
93C23×C32C2×Q812yes—
94C23×C32C2×Q811yescharacteristic
95C23×C32#4111yescharacteristic
96C2×C32×C4—21no—
97C2×C32×C4—21no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—24no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3—42no—
107C2×C3⋊Dic3—41no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—42no—
112C2×C3×Dic3—42no—
113C2×C3×Dic3—42no—
114C2×C3×Dic3—42no—
115C3×Dic6—81no—
116C3×Dic6—81no—
117#543—31no—
118#385—92no—
119#385—91no—
120#342—31no—
121#342—92no—
122C24×C3—21no—
123C24×C3C22×D311yescharacteristic
124C24×C3C22×D311yescharacteristic
125C2×C3×Q8—61no—
126C2×C3×Q8—61no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—32no—
130C22×C3×C4—32no—
131C22×C3×C4—62no—
132C22×C3×C4D1211yescharacteristic
133C22×C3×C4D1211yescharacteristic
134C22×C3×C4#6711yescharacteristic
135C22×C3×C4#6711yescharacteristic
136C22×Dic3—22no—
137C22×Dic3—62no—
138C22×Dic3—62no—
139C22×Dic3—61no—
140C22×Dic3—61no—
141C22×Dic3—62no—
142C22×Dic3—61no—
143C22×Dic3—61no—
144C22×Dic3—62no—
145C22×Dic3—122no—
146C22×Dic3—122no—
147C22×Dic3—122no—
148C22×Dic3—124no—
149C22×Dic3#6712yes—
150C22×Dic3#6712yes—
151C2×Dic6—21no—
152C2×Dic6—21no—
153C3×C4⋊C4—62no—
154C3×C4⋊C4—62no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C22⋊C4—22no—
158C3×C22⋊C4—22no—
159C3×C22⋊C4—34no—
160C3×C22⋊C4—42no—
161C3×C22⋊C4—62no—
162C3×C22⋊C4—62no—
163C3×C22⋊C4—62no—
164#217—22no—
165#217—22no—
166#217—22no—
167#217—32no—
168#217—32no—
169#217—62no—
170#217—62no—
171#217—61no—
172#217—61no—
173#217Dic614yescomplemented
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—124no—
177Dic3⋊C4—22no—
178Dic3⋊C4—22no—
179Dic3⋊C4—124no—
180Dic3⋊C4—122no—
181Dic3⋊C4—122no—
182Dic3⋊C4—124no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32—22no—
186C22×C32—22no—
187C22×C32—42no—
188C22×C32—41no—
189C22×C32—41no—
190C22×C32#12011yescharacteristic
191C22×C32C22⋊Q812yes—
192C22×C32C22⋊Q811yescharacteristic
193C22×C32C4⋊Q811yescharacteristic
194C22×C32C4⋊Q812yes—
195C32×C4—41no—
196C32×C4—41no—
197C3⋊Dic3—42no—
198C3⋊Dic3—42no—
199C3×Dic3—44no—
200C3×Dic3—42no—
201C3×Dic3—42no—
202C23×C4—91no—
203C22⋊Q8—62no—
204C22⋊Q8—62no—
205C22⋊Q8—61no—
206C22⋊Q8—61no—
207C2×C4⋊C4—182no—
208C2×C4⋊C4—181no—
209C2×C22⋊C4—32no—
210C2×C22⋊C4—32no—
211C2×C22⋊C4—91no—
212C2×C22⋊C4D3211yescharacteristic
213#95—182no—
214#95—181no—
215C23×C3—22no—
216C23×C3—21no—
217C23×C3—21no—
218C23×C3—21no—
219C23×C3—22no—
220C23×C3—41no—
221C23×C3—41no—
222C23×C3—41no—
223C23×C3—41no—
224C23×C3—42no—
225C23×C3—42no—
226C23×C3C2×Dic612yes—
227C23×C3C2×D1211yescharacteristic
228C23×C3D3×D412yes—
229C23×C3#23711yescharacteristic
230C23×C3D3×Q812yes—
231C23×C3D3×Q811yescharacteristic
232C23×C3D3×Q811yescharacteristic
233C23×C3#23911yescharacteristic
234C23×C3C2×#6711yescharacteristic
235C23×C3C2×#6712yes—
236C3×Q8—241no—
237C3×Q8—241no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—42no—
249C2×C3×C4—42no—
250C2×C3×C4—62no—
251C2×C3×C4—62no—
252C2×C3×C4—64no—
253C2×C3×C4—122no—
254C2×C3×C4—122no—
255C2×C3×C4—122no—
256C2×C3×C4—122no—
257C2×Dic3—24no—
258C2×Dic3—22no—
259C2×Dic3—22no—
260C2×Dic3—42no—
261C2×Dic3—42no—
262C2×Dic3—42no—
263C2×Dic3—42no—
264C2×Dic3—64no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—64no—
268C2×Dic3—64no—
269C2×Dic3—64no—
270C2×Dic3—62no—
271C2×Dic3—62no—
272C2×Dic3—124no—
273C2×Dic3—122no—
274C2×Dic3—121no—
275C2×Dic3—121no—
276C2×Dic3—122no—
277C2×Dic3—121no—
278C2×Dic3—121no—
279C2×Dic3—122no—
280C2×Dic3—122no—
281C2×Dic3—121no—
282C2×Dic3—122no—
283C2×Dic3—121no—
284C2×Dic3—122no—
285C2×Dic3—124no—
286C2×Dic3—121no—
287C2×Dic3—121no—
288Dic6—81no—
289Dic6—81no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32—22no—
293C2×C32—22no—
294C2×C32#39511yescharacteristic
295C2×C32B(4,𝔽2)11yescharacteristic
296C2×C32#45811yescharacteristic
297C24C2×D3211yescharacteristic
298C2×Q8—61no—
299C2×Q8—61no—
300C22×C4—32no—
301C22×C4—32no—
302C22×C4—62no—
303C22×C4—181no—
304C22×C4—181no—
305C22×C4—182no—
306C22×C4—362no—
307C22×C4#62611yescharacteristic
308C22×C4#62611yescharacteristic
309C4⋊C4—62no—
310C4⋊C4—62no—
311C4⋊C4—61no—
312C4⋊C4—61no—
313C4⋊C4—362no—
314C4⋊C4—364no—
315C22⋊C4—22no—
316C22⋊C4—34no—
317C22⋊C4—62no—
318C22⋊C4—62no—
319C22⋊C4—62no—
320C22⋊C4—92no—
321C22⋊C4—181no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—22no—
325C22×C3—21no—
326C22×C3—22no—
327C22×C3—21no—
328C22×C3—22no—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—21no—
332C22×C3—22no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—22no—
336C22×C3—21no—
337C22×C3—42no—
338C22×C3—42no—
339C22×C3—42no—
340C22×C3—41no—
341C22×C3—42no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—44no—
346C22×C3—42no—
347C22×C3—42no—
348C22×C3#86911yescharacteristic
349C22×C3#87812yes—
350C22×C3#88211yescharacteristic
351C22×C3#88812yes—
352C22×C3#89711yescharacteristic
353C22×C3#94412yes—
354C22×C3#94411yescharacteristic
355C22×C3#94611yescharacteristic
356C22×C3#94612yes—
357C22×C3#95311yescharacteristic
358C3×C4—41no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—41no—
362C3×C4—81no—
363C3×C4—81no—
364C3×C4—124no—
365C3×C4—122no—
366C3×C4—122no—
367Dic3—44no—
368Dic3—42no—
369Dic3—42no—
370Dic3—124no—
371Dic3—124no—
372Dic3—122no—
373Dic3—122no—
374Dic3—122no—
375Dic3—122no—
376C32#206211yescharacteristic, complemented, Sylow
377C23—41no—
378C23—41no—
379C23D3×Dic612yes—
380C23#379611yescharacteristic
381C23#379711yescharacteristic
382C23C2×#62611yescharacteristic
383C23D3×#6712yes—
384Q8—241no—
385Q8—241no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—64no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—122no—
394C2×C4—122no—
395C2×C4—122no—
396C2×C4—122no—
397C2×C4—182no—
398C2×C4—184no—
399C2×C4—182no—
400C2×C4—361no—
401C2×C4—361no—
402C2×C4—362no—
403C2×C4—361no—
404C2×C4—361no—
405C2×C3—22no—
406C2×C3—22no—
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—42no—
419C2×C3—42no—
420C2×C3#465611yescharacteristic
421C2×C3#474111yescharacteristic
422C2×C3#474211yescharacteristic
423C2×C3#523011yescharacteristic
424C2×C3#524311yescharacteristic
425C2×C3#524411yescharacteristic
426C22—21no—
427C22—22no—
428C22—21no—
429C22—22no—
430C22—42no—
431C22—41no—
432C22—41no—
433C22#6383912yes—
434C22#6386611yescharacteristic
435C22#6387111yescharacteristic
436C22#6388712yes—
437C22#6397711yescharacteristic
438C4—41no—
439C4—41no—
440C4—124no—
441C4—122no—
442C4—122no—
443C4—362no—
444C4—362no—
445C3—21no—
446C3#6895811yescharacteristic, complemented
447C3#7189511yescharacteristic, complemented
448C2—22no—
449C2—21no—
450C2—22no—
451C2—21no—
452C2#1059134611yescharacteristic
453C2#1059153111yescharacteristic
454C2#1059153411yescharacteristic
subgroupG/H
centerC22#63977
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
46. #3757Q8semidirect
51. C3×#217Q8semidirect
173. #217Dic6semidirect
376. C32#2062semidirect
446. C3#68958semidirect
447. C3#71895semidirect

Maximal subgroups

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

subgroupindex
C3×#54832
#105926452
#105917192
C3×#45262
#105891862
#718953
#689583