Finite Group Databasebeta

← #11794537

Subgroups — #11794537

Order 1152.

697 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592920C211yesmaximal, characteristic
2C2×C3×#832C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591357C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63572C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70194—31nomaximal
9#70180—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3757—21no—
12C2×#3757—21no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×Dic3⋊Dic3—21no—
20C3×#832—22no—
21C3×#832—22no—
22#63579—21no—
23#63575—22no—
24#63572—22no—
25C2×C3×#102—31no—
26C2×C3×#102—31no—
27#5221—31no—
28#5221—31no—
29#5221—61no—
30C2×#832D311yescharacteristic
31C2×#832D311yescharacteristic
32C2×#818—31no—
33C2×Dic3⋊C8—31no—
34C2×Dic3⋊C8—31no—
35#4984—31no—
36#4972—31no—
37C2×#807—31no—
38#4551—31no—
39#4529—31no—
40C24×C32—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4Q812yes—
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3D411yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53#3757—42no—
54#3757—42no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3D412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8D412yes—
69Dic3⋊Dic3—42no—
70#2067—91noSylow
71C22×C3×D4—21no—
72C22×C3×D4C2×D311yescharacteristic
73C22×C3×D4C2×D311yescharacteristic
74C22×C3×C8—31no—
75C22×C3×C8—31no—
76C2×C3×C4⋊C4—31no—
77C2×C3×C4⋊C4—31no—
78C2×#217—61no—
79C2×#217—61no—
80C2×#217—61no—
81C2×#217—61no—
82C2×#217—62no—
83C2×#217—62no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—61no—
87C2×C4⋊Dic3—61no—
88C2×C4⋊Dic3C2×D311yescharacteristic
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×Dic3⋊C4—61no—
91C2×C4×Dic3—31no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—61no—
94C22×C3⋊C8C2×D311yescharacteristic
95C22×C3⋊C8C2×D311yescharacteristic
96C3×#102—62no—
97C3×#102—62no—
98#832—22no—
99#832—22no—
100C3⋊#95—61no—
101C3⋊#95—61no—
102#818—62no—
103Dic3⋊C8—62no—
104Dic3⋊C8—62no—
105#807—62no—
106C23×C32—22no—
107C23×C32—41no—
108C23×C32—41no—
109C23×C32—41no—
110C23×C32—41no—
111C23×C32—41no—
112C23×C32—41no—
113C23×C32C2×D411yescharacteristic
114C32×D4—22no—
115C32×D4—22no—
116C32×D4—41no—
117C32×D4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×Q811yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3D812yes—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C3×C3⋊C8—22no—
140C3×C3⋊C8—41no—
141C2×#107—91no—
142C2×C4⋊C8—91no—
143C2×#102—31no—
144C2×#102—31no—
145#390—91no—
146#389—91no—
147#340—91no—
148C24×C3—22no—
149C24×C3—21no—
150C24×C3—21no—
151C2×C3×D4—22no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—22no—
163C2×C3×D4—41no—
164C2×C3×D4—41no—
165C2×C3×D4—41no—
166C2×C3×D4—41no—
167C2×C3×D4Dic612yes—
168C2×C3×D4Dic612yes—
169C22×C3×C4—21no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—31no—
177C22×Dic3—31no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—62no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C2×C3×C8—32no—
186C2×C3×C8—61no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C2×C3×C8—61no—
190C2×C3×C8—61no—
191C3×C4⋊C4—32no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195#217—122no—
196#217—122no—
197#217—124no—
198#217—124no—
199#217—122no—
200#217—122no—
201C4⋊Dic3—21no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—121no—
209C4⋊Dic3—121no—
210C4⋊Dic3—122no—
211C4⋊Dic3#6712yes—
212Dic3⋊C4—122no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217C4×Dic3—121no—
218C4×Dic3—121no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8#6712yes—
225C22×C32—42no—
226C22×C32—42no—
227C22×C32—42no—
228C22×C32—81no—
229C22×C32—81no—
230C22×C32—81no—
231C22×C32—81no—
232C22×C32#12111yescharacteristic
233C22×C32#12111yescharacteristic
234C22×C32C22⋊Q811yescharacteristic
235C22×C32C2×D811yescharacteristic
236C22×C32#13511yescharacteristic
237C22×C32AGL(1,ℤ/8)11yescharacteristic
238C22×C32#13711yescharacteristic
239C32×C4#12111yescharacteristic
240C32×C4C22⋊Q811yescharacteristic
241C32×C4C22⋊Q811yescharacteristic
242C32×C4#12611yescharacteristic
243C3⋊Dic3—22no—
244C3⋊Dic3—41no—
245C3⋊Dic3—81no—
246C3×Dic3—42no—
247C3×Dic3—81no—
248C22×D4D3211yescharacteristic
249C22×C8—31no—
250C22×C8—31no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—31no—
253C2×C4⋊C4—91no—
254C2×C4⋊C4—181no—
255C2×C22⋊C4—181no—
256C2×C22⋊C4—181no—
257C2×C42—91no—
258#107—182no—
259C4⋊C8—182no—
260#102—62no—
261#102—62no—
262#95—181no—
263C23×C3—24no—
264C23×C3—22no—
265C23×C3—22no—
266C23×C3—21no—
267C23×C3—42no—
268C23×C3—42no—
269C23×C3—42no—
270C23×C3—42no—
271C23×C3—42no—
272C23×C3—42no—
273C23×C3—41no—
274C23×C3—41no—
275C23×C3—41no—
276C23×C3—41no—
277C23×C3—41no—
278C23×C3—41no—
279C23×C3—41no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3D3×D411yescharacteristic
286C23×C3D3×D411yescharacteristic
287C3×D4—22no—
288C3×D4—22no—
289C3×D4—22no—
290C3×D4—22no—
291C3×D4—42no—
292C3×D4—42no—
293C3×D4—42no—
294C3×D4—42no—
295C3×D4—41no—
296C3×D4—41no—
297C3×D4—41no—
298C3×D4—41no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—62no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4C2×Dic611yescharacteristic
312C2×C3×C4C2×Dic611yescharacteristic
313C2×C3×C4#23511yescharacteristic
314C2×C3×C4#23511yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4#23711yescharacteristic
318C2×C3×C4#23711yescharacteristic
319C2×C3×C4#23711yescharacteristic
320C2×C3×C4#23711yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323C2×Dic3—22no—
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—62no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—62no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×Dic3—122no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C3×C8—62no—
357C3×C8—121no—
358C3⋊C8—22no—
359C3⋊C8—41no—
360C2×C32—82no—
361C2×C32#39611yescharacteristic
362C2×C32#45911yescharacteristic
363C2×C32#46411yescharacteristic
364C2×C32#46611yescharacteristic
365C2×C32#46811yescharacteristic
366C2×C32#47411yescharacteristic
367C2×C32#47811yescharacteristic
368C24—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4#62712yes—
375C22×C4—61no—
376C22×C4—61no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—181no—
380C22×C4C2×D3211yescharacteristic
381C2×C8—32no—
382C2×C8—61no—
383C2×C8—61no—
384C2×C8—61no—
385C2×C8—61no—
386C2×C8—61no—
387C4⋊C4—32no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C4⋊C4—362no—
394C22⋊C4—362no—
395C22⋊C4—362no—
396C42—181no—
397C42—181no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—44no—
406C22×C3—44no—
407C22×C3—44no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—82no—
415C22×C3—82no—
416C22×C3—82no—
417C22×C3—82no—
418C22×C3—81no—
419C22×C3—81no—
420C22×C3—81no—
421C22×C3—81no—
422C22×C3—81no—
423C22×C3—81no—
424C22×C3—81no—
425C22×C3—81no—
426C22×C3#87811yescharacteristic
427C22×C3#87811yescharacteristic
428C22×C3#88411yescharacteristic
429C22×C3#88411yescharacteristic
430C22×C3D3×D811yescharacteristic
431C22×C3D3×D811yescharacteristic
432C22×C3#91111yescharacteristic
433C22×C3#91211yescharacteristic
434C22×C3#91411yescharacteristic
435C22×C3#91511yescharacteristic
436C22×C3#91511yescharacteristic
437C22×C3#91611yescharacteristic
438C22×C3#93811yescharacteristic
439C22×C3#93911yescharacteristic
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—122no—
445C3×C4—241no—
446C3×C4#87811yescharacteristic
447C3×C4#87811yescharacteristic
448C3×C4#87911yescharacteristic
449C3×C4#87911yescharacteristic
450C3×C4#92411yescharacteristic
451C3×C4#92411yescharacteristic
452C3×C4#93811yescharacteristic
453C3×C4#93911yescharacteristic
454Dic3—42no—
455Dic3—62no—
456Dic3—62no—
457Dic3—81no—
458Dic3—122no—
459Dic3—122no—
460Dic3—121no—
461Dic3—121no—
462Dic3—242no—
463Dic3—241no—
464Dic3—241no—
465C32#206711yescharacteristic, complemented, Sylow
466C23—22no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23#381111yescharacteristic
474D4—22no—
475D4—22no—
476D4—41no—
477D4—41no—
478C2×C4—62no—
479C2×C4—92no—
480C2×C4—121no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—361no—
491C2×C4—361no—
492C2×C4—361no—
493C2×C4#380411yescharacteristic
494C2×C4#380411yescharacteristic
495C2×C4#380511yescharacteristic
496C2×C4C2×#62711yescharacteristic
497C2×C4D3×#6711yescharacteristic
498C2×C4D3×#6711yescharacteristic
499C8—62no—
500C8—121no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—84no—
509C2×C3—82no—
510C2×C3—82no—
511C2×C3#475911yescharacteristic
512C2×C3#475911yescharacteristic
513C2×C3#476311yescharacteristic
514C2×C3#476611yescharacteristic
515C2×C3#476711yescharacteristic
516C2×C3#477511yescharacteristic
517C2×C3#478011yescharacteristic
518C2×C3#478611yescharacteristic
519C2×C3#494811yescharacteristic
520C2×C3#494811yescharacteristic
521C2×C3#515011yescharacteristic
522C2×C3#515711yescharacteristic
523C2×C3#516611yescharacteristic
524C2×C3#517411yescharacteristic
525C22—42no—
526C22—42no—
527C22—42no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22#6392611yescharacteristic
533C22#6393111yescharacteristic
534C22#6393611yescharacteristic
535C22#6393711yescharacteristic
536C22#6395811yescharacteristic
537C22#6397111yescharacteristic
538C22#6398211yescharacteristic
539C4—122no—
540C4—182no—
541C4—241no—
542C4—361no—
543C4—721no—
544C4#6395611yescharacteristic
545C4#6396411yescharacteristic
546C4#6396411yescharacteristic
547C4#6397011yescharacteristic
548C3—21no—
549C3#7018011yescharacteristic, complemented
550C3#7019411yescharacteristic, complemented
551C2—82no—
552C2#1059143311yescharacteristic
553C2#1059144311yescharacteristic
554C2#1059145511yescharacteristic
555C2#1059146411yescharacteristic
556C2#1059147911yescharacteristic
557C2#1059149411yescharacteristic
558C2#1059169111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32#2067
LCSG ▷ C22×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
4. #10591357C2semidirect
5. C2×#63575C2semidirect
6. C2×#63572C2semidirect
7. #10589164C2semidirect
465. C32#2067semidirect
549. C3#70180semidirect
550. C3#70194semidirect

Maximal subgroups

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

subgroupindex
#105929202
C2×C3×#8322
#105913572
C2×#635752
C2×#635722
#105891642
#701943
#701803