Finite Group Databasebeta

← #11794535

Subgroups — #11794535

Order 1152.

669 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63659C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591212C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70180—31nomaximal
9#69653—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×#217—21no—
14C2×C3×#217—21no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×#3724—21no—
20#63659—22no—
21C3×#832—22no—
22#63579—21no—
23#63575—22no—
24Dic3⋊(C3⋊C8)—22no—
25C2×C3×#102—31no—
26C3×#390—31no—
27#5221D311yescharacteristic
28C2×#832—31no—
29C2×#832—31no—
30C2×#832—61no—
31C2×#832D311yescharacteristic
32C2×#818—31no—
33C2×Dic3⋊C8—31no—
34#4972—31no—
35C2×#807—31no—
36#4928—31no—
37C2×C4⋊(C3⋊C8)—31no—
38#4529—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×Dic3—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3D411yescharacteristic
52C22×C3×Dic3D411yescharacteristic
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)D412yes—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—42no—
59C3×#217—42no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8D412yes—
69#3724—42no—
70#2067—91noSylow
71C22×C3×D4—21no—
72C22×C3×D4C2×D311yescharacteristic
73C22×C3×D4C2×D311yescharacteristic
74C22×C3×C8—31no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—31no—
77C2×C3×C22⋊C4—61no—
78C2×C3×C22⋊C4—61no—
79C2×C3×C42—31no—
80C2×#217—21no—
81C2×#217—21no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—61no—
85C2×C4⋊Dic3C2×D311yescharacteristic
86C2×C4⋊Dic3C2×D311yescharacteristic
87C2×Dic3⋊C4—61no—
88C2×Dic3⋊C4—61no—
89C2×C4×Dic3C2×D311yescharacteristic
90C22×C3⋊C8—31no—
91C22×C3⋊C8—31no—
92C22×C3⋊C8—61no—
93C22×C3⋊C8C2×D311yescharacteristic
94C3×#102—62no—
95#832—22no—
96#832—62no—
97#832—62no—
98#832—64no—
99C3⋊#95—61no—
100C3⋊#95—61no—
101#818—62no—
102Dic3⋊C8—62no—
103#807—62no—
104C4⋊(C3⋊C8)—62no—
105C23×C32—22no—
106C23×C32—41no—
107C23×C32—41no—
108C23×C32—41no—
109C23×C32—41no—
110C23×C32—41no—
111C23×C32—41no—
112C23×C32C2×D411yescharacteristic
113C32×D4—22no—
114C32×D4—22no—
115C32×D4—41no—
116C32×D4—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×Q811yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3D812yes—
138C3⋊(C3⋊C8)—41no—
139C3×C3⋊C8—22no—
140C2×#107—91no—
141C2×C4⋊C8—91no—
142C2×#102—31no—
143C2×#102—91no—
144#390—31no—
145#389—91no—
146#340—91no—
147C24×C3—21no—
148C24×C3—21no—
149C24×C3—41no—
150C2×C3×D4—22no—
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×D4Dic612yes—
167C2×C3×D4Dic612yes—
168C22×C3×C4—21no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—61no—
172C22×C3×C4—61no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×Dic3—21no—
176C22×Dic3—21no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—121no—
180C22×Dic3#6711yescharacteristic
181C22×Dic3#6711yescharacteristic
182C2×C3×C8—32no—
183C2×C3×C8—61no—
184C2×C3×C8—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C22⋊C4—122no—
190C3×C22⋊C4—122no—
191C3×C42—61no—
192C3×C42—61no—
193#217—42no—
194#217—42no—
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—32no—
200C4⋊Dic3—32no—
201C4⋊Dic3—62no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—121no—
205Dic3⋊C4—122no—
206Dic3⋊C4—122no—
207C4×Dic3—21no—
208C4×Dic3—21no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—62no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—121no—
219C2×C3⋊C8—121no—
220C2×C3⋊C8#6712yes—
221C22×C32—42no—
222C22×C32—42no—
223C22×C32—42no—
224C22×C32—81no—
225C22×C32—81no—
226C22×C32—81no—
227C22×C32—81no—
228C22×C32#12111yescharacteristic
229C22×C32#12111yescharacteristic
230C22×C32C22⋊Q811yescharacteristic
231C22×C32C2×D811yescharacteristic
232C22×C32#13511yescharacteristic
233C22×C32AGL(1,ℤ/8)11yescharacteristic
234C22×C32#13711yescharacteristic
235C32×C4#12111yescharacteristic
236C32×C4C22⋊Q811yescharacteristic
237C32×C4C22⋊Q811yescharacteristic
238C32×C4#12611yescharacteristic
239C3⋊Dic3—42no—
240C3×Dic3—22no—
241C3×Dic3—41no—
242C3×Dic3—81no—
243C3×Dic3—81no—
244C22×D4D3211yescharacteristic
245C22×C8—31no—
246C22×C8—91no—
247C2×C4⋊C4—31no—
248C2×C4⋊C4—31no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—181no—
251C2×C22⋊C4—61no—
252C2×C22⋊C4—61no—
253C2×C42—31no—
254#107—182no—
255C4⋊C8—182no—
256#102—62no—
257#102—182no—
258#95—181no—
259C23×C3—22no—
260C23×C3—22no—
261C23×C3—21no—
262C23×C3—42no—
263C23×C3—42no—
264C23×C3—42no—
265C23×C3—41no—
266C23×C3—41no—
267C23×C3—41no—
268C23×C3—41no—
269C23×C3—41no—
270C23×C3—41no—
271C23×C3—41no—
272C23×C3—41no—
273C23×C3—41no—
274C23×C3—41no—
275C23×C3—41no—
276C23×C3—41no—
277C23×C3—81no—
278C23×C3—81no—
279C23×C3—81no—
280C23×C3—81no—
281C23×C3D3×D411yescharacteristic
282C23×C3C2×#6711yescharacteristic
283C3×D4—24no—
284C3×D4—22no—
285C3×D4—22no—
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—42no—
289C3×D4—42no—
290C3×D4—42no—
291C3×D4—41no—
292C3×D4—41no—
293C3×D4—41no—
294C3×D4—41no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—32no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—61no—
306C2×C3×C4—61no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4C2×Dic611yescharacteristic
314C2×C3×C4C2×Dic611yescharacteristic
315C2×C3×C4#23511yescharacteristic
316C2×C3×C4#23511yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4#23711yescharacteristic
321C2×C3×C4#23711yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4#23711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—21no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—41no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—122no—
339C2×Dic3—121no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—121no—
343C2×Dic3—241no—
344C2×Dic3—241no—
345C2×Dic3#21312yes—
346C3×C8—62no—
347C3⋊C8—22no—
348C3⋊C8—122no—
349C3⋊C8—121no—
350C3⋊C8—121no—
351C2×C32—82no—
352C2×C32#39611yescharacteristic
353C2×C32#45911yescharacteristic
354C2×C32#46411yescharacteristic
355C2×C32#46611yescharacteristic
356C2×C32#46811yescharacteristic
357C2×C32#47411yescharacteristic
358C2×C32#47811yescharacteristic
359C24—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4#62712yes—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—181no—
371C22×C4C2×D3211yescharacteristic
372C2×C8—32no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—181no—
376C2×C8—181no—
377C2×C8—181no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C4⋊C4—92no—
383C4⋊C4—181no—
384C4⋊C4—362no—
385C22⋊C4—122no—
386C22⋊C4—122no—
387C42—61no—
388C42—61no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—44no—
397C22×C3—42no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—82no—
404C22×C3—82no—
405C22×C3—82no—
406C22×C3—82no—
407C22×C3—82no—
408C22×C3—82no—
409C22×C3—81no—
410C22×C3—81no—
411C22×C3—81no—
412C22×C3—81no—
413C22×C3—81no—
414C22×C3—81no—
415C22×C3—81no—
416C22×C3—81no—
417C22×C3#87811yescharacteristic
418C22×C3#88411yescharacteristic
419C22×C3D3×D811yescharacteristic
420C22×C3#91211yescharacteristic
421C22×C3#91411yescharacteristic
422C22×C3#91511yescharacteristic
423C22×C3#92411yescharacteristic
424C22×C3C2×#21311yescharacteristic
425C22×C3#93211yescharacteristic
426C22×C3#93811yescharacteristic
427C22×C3#93811yescharacteristic
428C22×C3#93911yescharacteristic
429C22×C3#95011yescharacteristic
430C22×C3#95111yescharacteristic
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—62no—
436C3×C4—121no—
437C3×C4—241no—
438C3×C4—241no—
439C3×C4#87811yescharacteristic
440C3×C4#87811yescharacteristic
441C3×C4#87811yescharacteristic
442C3×C4#87911yescharacteristic
443C3×C4#87911yescharacteristic
444C3×C4#88411yescharacteristic
445C3×C4#92411yescharacteristic
446C3×C4#93911yescharacteristic
447Dic3—22no—
448Dic3—41no—
449Dic3—81no—
450Dic3—81no—
451Dic3—122no—
452Dic3—122no—
453Dic3—242no—
454C32#206711yescharacteristic, complemented, Sylow
455C23—22no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23D3×#6711yescharacteristic
463D4—22no—
464D4—22no—
465D4—41no—
466D4—41no—
467C2×C4—32no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—182no—
480C2×C4—361no—
481C2×C4—361no—
482C2×C4#380411yescharacteristic
483C2×C4#380411yescharacteristic
484C2×C4#380511yescharacteristic
485C2×C4C2×#62711yescharacteristic
486C2×C4D3×#6711yescharacteristic
487C2×C4#381111yescharacteristic
488C8—62no—
489C8—361no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—84no—
498C2×C3—82no—
499C2×C3—82no—
500C2×C3#475911yescharacteristic
501C2×C3#476611yescharacteristic
502C2×C3#476711yescharacteristic
503C2×C3#478611yescharacteristic
504C2×C3#494811yescharacteristic
505C2×C3#494811yescharacteristic
506C2×C3#500711yescharacteristic
507C2×C3#500911yescharacteristic
508C2×C3#503811yescharacteristic
509C2×C3#504211yescharacteristic
510C2×C3#505411yescharacteristic
511C2×C3#507211yescharacteristic
512C2×C3#515711yescharacteristic
513C2×C3#517411yescharacteristic
514C22—42no—
515C22—42no—
516C22—42no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22D3×#21311yescharacteristic
522C22#6392911yescharacteristic
523C22#6393311yescharacteristic
524C22#6393411yescharacteristic
525C22#6395811yescharacteristic
526C22#6396411yescharacteristic
527C22#6397011yescharacteristic
528C4—62no—
529C4—121no—
530C4—241no—
531C4—241no—
532C4—362no—
533C4#6395611yescharacteristic
534C4#6396411yescharacteristic
535C4#6397111yescharacteristic
536C4#6398211yescharacteristic
537C3—21no—
538C3#6965311yescharacteristic, complemented
539C3#7018011yescharacteristic, complemented
540C2—82no—
541C2#1059141011yescharacteristic
542C2#1059141111yescharacteristic
543C2#1059142911yescharacteristic
544C2#1059144111yescharacteristic
545C2#1059149811yescharacteristic
546C2#1059150211yescharacteristic
547C2#1059169111yescharacteristic
subgroupG/H
centerC23D3×#67
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. #10591212C2semidirect
5. C2×#63575C2semidirect
6. C2×Dic3⋊(C3⋊C8)C2semidirect
7. #10589163C2semidirect
454. C32#2067semidirect
538. C3#69653semidirect
539. C3#70180semidirect

Maximal subgroups

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

subgroupindex
C2×#636592
C3×#52212
C2×C3×#8322
#105912122
C2×#635752
C2×Dic3⋊(C3⋊C8)2
#105891632
#701803
#696533