Finite Group Databasebeta

← #11778706

Subgroups — #11778706

Order 1152.

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

normal subgroups only

This group has 512 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
1C3×#5634C211yesmaximal, characteristic
2C3×#5044C211yesmaximal, characteristic, complemented
3#10591324C211yesmaximal, characteristic
4#10591132C211yesmaximal, characteristic, complemented
5#10589404C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic
8#71891—31nomaximal
9#71176—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C3×#946—21no—
12C2×C3×(C2×D3)⋊C4C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C3×#924C2211yescharacteristic
15C3×#897—21no—
16C3×#896—21no—
17C3×#896—21no—
18C3×D3×C22⋊C4—21no—
19C3×#878—21no—
20C2×#3724—21no—
21C2×(C2×D3)⋊Dic3—21no—
22#63658C2211yescharacteristic
23#63657C2211yescharacteristic
24C3×#835—21no—
25C3×#830C2211yescharacteristic
26C3×#807—21no—
27#63576—21no—
28#63565—21no—
29C3×#543—31no—
30#5634D311yescharacteristic
31C3×#484—31no—
32#5044—31no—
33#5044D311yescharacteristic, complemented
34#4993—31no—
35#4970—31no—
36#4949—31no—
37#4538—31no—
38#4538—31no—
39#4538—31no—
40#4538—61no—
41#4525—31no—
42#4468—31no—
43#4467—31no—
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6D411yescharacteristic
54C32×C4⋊C4—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C22⋊C4—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C2×C3×C3⋊C8—21no—
71#3724—42no—
72(C2×D3)⋊Dic3—42no—
73#1614—91noSylow
74C3×C22⋊Q8—21no—
75C3×C22⋊Q8—31no—
76C3×C22⋊Q8—61no—
77C3×C22⋊Q8—61no—
78C3×C22⋊Q8—61no—
79C3×C22⋊Q8—61no—
80C3×C22⋊Q8—61no—
81C3×C22⋊Q8C2×D311yescharacteristic
82C3×C22⋊Q8C2×D311yescharacteristic
83C2×C3×C4⋊C4—31no—
84C2×C3×C22⋊C4—31no—
85C2×C3×C22⋊C4—61no—
86C2×#217—61no—
87#946—21no—
88C2×(C2×D3)⋊C4—61no—
89C2×(C2×D3)⋊C4C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91#924C2×D311yescharacteristic
92C2×Dic3⋊C4—61no—
93C2×Dic3⋊C4—61no—
94#897—21no—
95#896—21no—
96#896—21no—
97D3×C22⋊C4—21no—
98#878—21no—
99C3×#107—61no—
100C3×#103—61no—
101C3×C22⋊C8—31no—
102#835—21no—
103#835—61no—
104C3⋊#95—31no—
105C3⋊#95—31no—
106C3⋊#95—61no—
107#830—31no—
108#830—31no—
109#830—61no—
110#830C2×D311yescharacteristic
111#810—61no—
112#807—21no—
113#807—61no—
114#807—61no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C22×C3×D3—21no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3Q1612yes—
121C32×Q8—41no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C3×C4×D3—81no—
138C3×C4×D3—81no—
139C3×Dic6—41no—
140C3×Dic6—81no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—41no—
143#543—31no—
144#484—31no—
145#484—91no—
146#399—91no—
147#328—91no—
148#328—91no—
149#323—91no—
150C24×C3—31no—
151C23×D3#6711yescharacteristic
152C2×C3×Q8—21no—
153C2×C3×Q8—31no—
154C2×C3×Q8—61no—
155C2×C3×Q8#6711yescharacteristic
156C2×C3×Q8#6711yescharacteristic
157C22×C3×C4—21no—
158C22×C3×C4—31no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C22×Dic3—21no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—121no—
168C22×Dic3#6711yescharacteristic
169C2×C4×D3—21no—
170C2×C4×D3—21no—
171C2×Dic6—21no—
172C2×Dic6#6711yescharacteristic
173C2×C3×C8—61no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—31no—
178C3×C4⋊C4—41no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4#6711yescharacteristic
186C3×C4⋊C4#6711yescharacteristic
187C3×C22⋊C4—21no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—41no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195#217—21no—
196#217—122no—
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—122no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3—21no—
205C4⋊Dic3#6711yescharacteristic
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208Dic3⋊C4—21no—
209Dic3⋊C4—122no—
210Dic3⋊C4—122no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—121no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32#12011yescharacteristic
218C22×C32C2×Q1611yescharacteristic
219C22×C32#13711yescharacteristic
220C2×C3×D3—22no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C2×C3×D3—42no—
224C2×C3×D3—81no—
225C32×C4—21no—
226C32×C4—21no—
227C32×C4—41no—
228C32×C4—41no—
229C3⋊Dic3—42no—
230C3×Dic3—41no—
231C3×Dic3—41no—
232C3×Dic3—41no—
233C3×Dic3—81no—
234C22⋊Q8—31no—
235C22⋊Q8—61no—
236C22⋊Q8—61no—
237C22⋊Q8—61no—
238C22⋊Q8—61no—
239C22⋊Q8—61no—
240C22⋊Q8D3211yescharacteristic
241C2×C4⋊C4—31no—
242C2×C4⋊C4—181no—
243C2×C22⋊C4—31no—
244C2×C22⋊C4—61no—
245C2×C22⋊C4—181no—
246#107—61no—
247#107—181no—
248#103—61no—
249#103—181no—
250C22⋊C8—31no—
251C22⋊C8—91no—
252#95—91no—
253C23×C3—21no—
254C23×C3—32no—
255C23×C3—61no—
256C23×C3—61no—
257C23×C3—121no—
258C23×C3—121no—
259C23×C3D3×D411yescharacteristic
260C23×C3C2×#6711yescharacteristic
261C22×D3—21no—
262C22×D3—21no—
263C22×D3—41no—
264C22×D3—41no—
265C22×D3#21612yes—
266C3×Q8—41no—
267C3×Q8—41no—
268C3×Q8—81no—
269C3×Q8—121no—
270C3×Q8—241no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—81no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4—241no—
290C2×C3×C4—241no—
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4C2×#6711yescharacteristic
293C2×C3×C4C2×#6711yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—41no—
301C2×Dic3—41no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—122no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309C2×Dic3—241no—
310C2×Dic3—241no—
311C4×D3—81no—
312C4×D3—81no—
313Dic6—41no—
314Dic6—81no—
315C3×C8—121no—
316C3⋊C8—41no—
317C3⋊C8—121no—
318C3⋊C8—121no—
319C3⋊C8—241no—
320C2×C32—21no—
321C2×C32—21no—
322C2×C32#45111yescharacteristic
323C2×C32#45311yescharacteristic
324C2×C32#45811yescharacteristic
325C3×D3—42no—
326C24—31no—
327C2×Q8—31no—
328C2×Q8—61no—
329C2×Q8#62511yescharacteristic
330C22×C4—31no—
331C22×C4—61no—
332C22×C4—61no—
333C22×C4—61no—
334C22×C4—181no—
335C22×C4C2×D3211yescharacteristic
336C2×C8—61no—
337C2×C8—181no—
338C4⋊C4—21no—
339C4⋊C4—31no—
340C4⋊C4—61no—
341C4⋊C4—61no—
342C4⋊C4—61no—
343C4⋊C4—61no—
344C4⋊C4—61no—
345C4⋊C4—61no—
346C4⋊C4—362no—
347C4⋊C4#62511yescharacteristic
348C22⋊C4—21no—
349C22⋊C4—61no—
350C22⋊C4—61no—
351C22⋊C4—61no—
352C22⋊C4—61no—
353C22⋊C4—61no—
354C22⋊C4—362no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—62no—
365C22×C3—122no—
366C22×C3—121no—
367C22×C3—121no—
368C22×C3—241no—
369C22×C3D3×Q1611yescharacteristic
370C22×C3#91811yescharacteristic
371C22×C3#93711yescharacteristic
372C22×C3#94211yescharacteristic
373C22×C3C2×#21611yescharacteristic
374C22×C3#95311yescharacteristic
375C2×D3—22no—
376C2×D3—41no—
377C2×D3—41no—
378C2×D3—42no—
379C2×D3—81no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—41no—
385C3×C4—41no—
386C3×C4—41no—
387C3×C4—41no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—81no—
391C3×C4—81no—
392C3×C4—121no—
393C3×C4—121no—
394C3×C4—121no—
395C3×C4—241no—
396Dic3—41no—
397Dic3—41no—
398Dic3—41no—
399Dic3—81no—
400Dic3—122no—
401Dic3—122no—
402Dic3—242no—
403C32#161411yescharacteristic, complemented, Sylow
404C23—32no—
405C23—61no—
406C23—61no—
407C23—121no—
408C23—121no—
409C23D3×#6711yescharacteristic
410Q8—41no—
411Q8—121no—
412Q8—241no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—182no—
424C2×C4—241no—
425C2×C4—241no—
426C2×C4—361no—
427C2×C4—361no—
428C2×C4C2×#62511yescharacteristic
429C2×C4D3×#6711yescharacteristic
430C8—121no—
431C8—361no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—122no—
442C2×C3#505311yescharacteristic
443C2×C3#518611yescharacteristic
444C2×C3#519811yescharacteristic
445C2×C3#522811yescharacteristic
446C2×C3#524111yescharacteristic
447C2×C3#524311yescharacteristic
448D3—42no—
449C22—21no—
450C22—21no—
451C22—62no—
452C22—122no—
453C22—121no—
454C22—121no—
455C22—241no—
456C22D3×#21611yescharacteristic
457C22#6394811yescharacteristic
458C22#6397611yescharacteristic
459C4—21no—
460C4—21no—
461C4—41no—
462C4—41no—
463C4—121no—
464C4—121no—
465C4—121no—
466C4—241no—
467C4—362no—
468C3—21no—
469C3#7117611yescharacteristic, complemented
470C3#7189111yescharacteristic, complemented
471C2—21no—
472C2—21no—
473C2—122no—
474C2#1059153311yescharacteristic
475C2#1059159411yescharacteristic
476C2#1059166511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC23×C3×D3D4
hypercenterC22⋊Q8D32
hypocenterC32#1614
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5044C2semidirect
4. #10591132C2semidirect
5. #10589404C2semidirect
6. #10589152C2semidirect
33. #5044D3semidirect
403. C32#1614semidirect
469. C3#71176semidirect
470. C3#71891semidirect

Maximal subgroups

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

subgroupindex
C3×#56342
C3×#50442
#105913242
#105911322
#105894042
#105891522
#105891452
#718913
#711763