Finite Group Databasebeta

← #11792212

Subgroups — #11792212

Order 1152.

779 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5526C211yesmaximal, characteristic
2C2×#63873C211yesmaximal, characteristic, complemented
3C2×#63827C211yesmaximal, characteristic
4C3×#5004C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic
6C2×#63560C211yesmaximal, characteristic, complemented
7#10589398C211yesmaximal, characteristic, complemented
8#71868—31nomaximal
9#70346—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#897—22no—
18C3×#886—22no—
19C3×#875—21no—
20C3×#869—21no—
21C2×#3724—22no—
22#63873—22no—
23#63873—22no—
24C2×#3718—21no—
25#63827—22no—
26#63827—22no—
27C2×#3715—21no—
28C3×#810—22no—
29#63568—22no—
30#63560—22no—
31C3×#536—31no—
32C2×#951—31no—
33C2×#944—31no—
34C2×#944—31no—
35C2×#942—31no—
36#5526D311yescharacteristic
37C3×#419—31no—
38C2×#837—31no—
39C2×#836—31no—
40C2×#825—31no—
41C2×#824—31no—
42#5004D311yescharacteristic, complemented
43#4532—31no—
44#4532—31no—
45#4532—61no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D412yes—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C2×C3×D12D411yescharacteristic
56C2×C3×C4×D3—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6D412yes—
69C2×C3×Dic6D411yescharacteristic
70C32×C4⋊C4D412yes—
71C32×C22⋊C4—21no—
72C32×C42—21no—
73C4×C3⋊Dic3—21no—
74C4×C3⋊Dic3D412yes—
75#3748—21no—
76#3748D412yes—
77C2×C3⋊(C3⋊C8)—21no—
78C3×(C2×D3)⋊C4—24no—
79C3×C4⋊Dic3—24no—
80C3×#208—21no—
81C3×#208—21no—
82C2×C3×C3⋊C8—21no—
83#3724—28no—
84#3718—24no—
85#3715—24no—
86#2005—91noSylow
87C2×C3×#41—31no—
88C22×C3×Q8—31no—
89C22×C3×Q8—31no—
90C2×#235C2×D311yescharacteristic
91C22×Dic6C2×D311yescharacteristic
92C22×Dic6C2×D311yescharacteristic
93C2×C3×M16—31no—
94C3×C4⋊Q8—61no—
95C3×#124—61no—
96C3×#123—62no—
97C3×C22⋊Q8—62no—
98C3×#117—21no—
99C3×#117C2×D311yescharacteristic
100C3×#117C2×D311yescharacteristic
101#951—62no—
102#951—62no—
103#944—62no—
104#944—62no—
105#944—62no—
106#944—62no—
107C2×#216—61no—
108C2×#216—61no—
109#942—62no—
110#942—62no—
111C2×#215—61no—
112C2×#214—61no—
113C2×Dic3⋊C4—62no—
114C2×Dic3⋊C4—62no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—61no—
118C2×#208—31no—
119C2×#208—31no—
120C2×#208—61no—
121C2×#208C2×D311yescharacteristic
122#897—22no—
123#886—22no—
124#875—21no—
125#869—21no—
126C3×#103—62no—
127#837—62no—
128#836—62no—
129#825—62no—
130#824—62no—
131#810—22no—
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—21no—
134C2×C32×C4—22no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C3⋊Dic3—24no—
142C2×C3⋊Dic3—22no—
143C3×#67—41no—
144C3×#67—41no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C3×D12—21no—
153C3×D12—21no—
154C3×C4×D3—41no—
155C3×C4×D3—41no—
156C3×Dic6—22no—
157C3×Dic6—21no—
158C3×Dic6—22no—
159C3×Dic6—21no—
160C3×Dic6—41no—
161C3×Dic6—41no—
162C3×Dic6—41no—
163C3×Dic6—41no—
164C3×Dic6—41no—
165C3×Dic6—41no—
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—41no—
168C2×#137—91no—
169#536—31no—
170C2×C4⋊Q8—91no—
171C2×#104—91no—
172#419—31no—
173C2×#101—91no—
174#339—91no—
175C3×#41—61no—
176C3×#41—61no—
177C3×#41—61no—
178C3×#41—61no—
179C2×C3×Q8—32no—
180C2×C3×Q8—31no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×Q8—61no—
185C2×C3×Q8—61no—
186C2×C3×Q8—61no—
187C2×C3×Q8—61no—
188C2×C3×Q8—61no—
189C2×C3×Q8—61no—
190C2×C3×Q8—61no—
191C2×C3×Q8—61no—
192C2×C3×D4—31no—
193C2×C3×D4—61no—
194C22×C3×C4—21no—
195C22×C3×C4—32no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C2×#67—21no—
201C22×Dic3—21no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C22×Dic3—121no—
205C22×Dic3#6712yes—
206#235—21no—
207#235—21no—
208#235—21no—
209#235—21no—
210C2×D12#6711yescharacteristic
211C2×C4×D3—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6—21no—
216C2×Dic6—21no—
217C2×Dic6—21no—
218C2×Dic6—21no—
219C2×Dic6—21no—
220C2×Dic6—21no—
221C2×Dic6—21no—
222C2×Dic6—21no—
223C2×Dic6D1212yes—
224C2×Dic6#6711yescharacteristic
225C3×M16—61no—
226C3×M16—61no—
227C2×C3×C8—61no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—64no—
230C3×C4⋊C4#6712yes—
231C3×C4⋊C4#6712yes—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—21no—
234C3×C22⋊C4—41no—
235C3×C22⋊C4—64no—
236C3×C42—21no—
237C3×C42—21no—
238C3×C42—41no—
239#216—64no—
240#216—64no—
241#215—64no—
242#214—64no—
243(C2×D3)⋊C4—24no—
244C4⋊Dic3—24no—
245Dic3⋊C4—68no—
246Dic3⋊C4—68no—
247C4×Dic3—32no—
248C4×Dic3—32no—
249C4×Dic3—62no—
250C4×Dic3—61no—
251C4×Dic3—61no—
252C4×Dic3—121no—
253#208—21no—
254#208—21no—
255#208—32no—
256#208—32no—
257#208—62no—
258#208—61no—
259#208—61no—
260#208—121no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—121no—
265C22×C32—22no—
266C22×C32#12011yescharacteristic
267C22×C32#12011yescharacteristic
268C22×C32#12111yescharacteristic
269C2×C3×D3—41no—
270C2×C3×D3—42no—
271C32×C4—42no—
272C32×C4#12011yescharacteristic
273C32×C4#12111yescharacteristic
274C32×C4#12111yescharacteristic
275C32×C4#12711yescharacteristic
276C3⋊Dic3—24no—
277C3×Dic3—42no—
278C3×Dic3—41no—
279C3×Dic3—42no—
280C2×#41—31no—
281C22×Q8—31no—
282C22×Q8—31no—
283#137—182no—
284#137—182no—
285C2×Q16—181no—
286C2×SD16—181no—
287C2×M16—31no—
288C2×M16—91no—
289C4⋊Q8—61no—
290C4⋊Q8—182no—
291C4⋊Q8—182no—
292#124—61no—
293#123—62no—
294C22⋊Q8—62no—
295#117D3211yescharacteristic
296C2×C4⋊C4—182no—
297C2×C42—91no—
298#104—182no—
299#103—62no—
300#101—182no—
301C23×C3—21no—
302C23×C3—61no—
303C23×C3D3×D411yescharacteristic
304C23×C3C2×#6711yescharacteristic
305C22×D3—21no—
306C3×Q8—61no—
307C3×Q8—61no—
308C3×Q8—62no—
309C3×Q8—62no—
310C3×Q8—121no—
311C3×Q8—121no—
312C3×Q8—121no—
313C3×Q8—121no—
314C3×Q8—121no—
315C3×Q8—121no—
316C3×D4—61no—
317C3×D4—61no—
318C3×D4—121no—
319C3×D4—121no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—42no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—61no—
334C2×C3×C4—121no—
335C2×C3×C4—121no—
336C2×C3×C4—121no—
337C2×C3×C4—121no—
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4#23511yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4#23711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350#67—41no—
351#67—41no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—21no—
356C2×Dic3—22no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—122no—
364C2×Dic3—124no—
365D12—21no—
366D12—21no—
367C4×D3—41no—
368C4×D3—41no—
369Dic6—22no—
370Dic6—22no—
371Dic6—21no—
372Dic6—21no—
373Dic6—41no—
374Dic6—41no—
375Dic6—41no—
376Dic6—41no—
377Dic6—41no—
378Dic6—41no—
379C3×C8—121no—
380C3⋊C8—41no—
381C3⋊C8—62no—
382C3⋊C8—62no—
383C3⋊C8—122no—
384C2×C32—21no—
385C2×C32—21no—
386C2×C32#39211yescharacteristic
387C2×C32#45612yes—
388C3×D3—81no—
389#41—61no—
390#41—61no—
391#41—61no—
392#41—61no—
393C2×Q8—32no—
394C2×Q8—31no—
395C2×Q8—61no—
396C2×Q8—61no—
397C2×Q8—61no—
398C2×Q8—61no—
399C2×Q8—61no—
400C2×Q8—61no—
401C2×Q8—61no—
402C2×Q8—61no—
403C2×Q8—61no—
404C2×Q8—61no—
405C2×Q8—61no—
406C2×D4—31no—
407C2×D4—61no—
408C22×C4—32no—
409C22×C4—61no—
410C22×C4—61no—
411C22×C4—181no—
412C22×C4C2×D3211yescharacteristic
413Q16—184no—
414SD16—184no—
415M16—61no—
416M16—61no—
417M16—92no—
418M16—181no—
419C2×C8—61no—
420C2×C8—181no—
421C4⋊C4—64no—
422C4⋊C4—188no—
423C4⋊C4#62512yes—
424C22⋊C4—21no—
425C22⋊C4—64no—
426C42—21no—
427C42—92no—
428C42—181no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—42no—
435C22×C3—122no—
436C22×C3—121no—
437C22×C3#88211yescharacteristic
438C22×C3#88411yescharacteristic
439C22×C3#93711yescharacteristic
440C22×C3#93711yescharacteristic
441C22×C3#93911yescharacteristic
442C22×C3#95311yescharacteristic
443C2×D3—41no—
444C2×D3—42no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—42no—
450C3×C4—42no—
451C3×C4—82no—
452C3×C4—122no—
453C3×C4—121no—
454C3×C4—122no—
455C3×C4#88211yescharacteristic
456C3×C4#88411yescharacteristic
457C3×C4#93011yescharacteristic
458C3×C4#93711yescharacteristic
459C3×C4#93811yescharacteristic
460C3×C4#93911yescharacteristic
461C3×C4#94011yescharacteristic
462C3×C4#94011yescharacteristic
463Dic3—42no—
464Dic3—41no—
465Dic3—42no—
466Dic3—64no—
467Dic3—64no—
468Dic3—124no—
469C32#200511yescharacteristic, complemented, Sylow
470C23—61no—
471C23D3×#6711yescharacteristic
472Q8—61no—
473Q8—62no—
474Q8—62no—
475Q8—61no—
476Q8—121no—
477Q8—121no—
478Q8—121no—
479Q8—121no—
480Q8—121no—
481Q8—121no—
482D4—61no—
483D4—61no—
484D4—121no—
485D4—121no—
486C2×C4—22no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—61no—
492C2×C4—121no—
493C2×C4—121no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4—184no—
497C2×C4—182no—
498C2×C4#379511yescharacteristic
499C2×C4D3×D1211yescharacteristic
500C2×C4#380211yescharacteristic
501C2×C4#380211yescharacteristic
502C2×C4C2×#62511yescharacteristic
503C2×C4D3×#6711yescharacteristic
504C8—121no—
505C8—182no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—22no—
512C2×C3—41no—
513C2×C3—41no—
514C2×C3—241no—
515C2×C3#496011yescharacteristic
516C2×C3#520512yes—
517C2×C3#522311yescharacteristic
518C2×C3#524612yes—
519D3—81no—
520C22—22no—
521C22—121no—
522C22—122no—
523C22#6388511yescharacteristic
524C22#6392211yescharacteristic
525C22#6397611yescharacteristic
526C4—42no—
527C4—122no—
528C4—121no—
529C4—122no—
530C4—184no—
531C4#6388511yescharacteristic
532C4#6390811yescharacteristic
533C4#6391411yescharacteristic
534C4#6392211yescharacteristic
535C3—21no—
536C3#7034611yescharacteristic, complemented
537C3#7186811yescharacteristic, complemented
538C2—21no—
539C2—21no—
540C2—241no—
541C2#1059138911yescharacteristic
542C2#1059168712yes—
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC2×C3×#235C22
hypercenter#117D32
hypocenterC32#2005
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#63873C2semidirect
4. C3×#5004C2semidirect
6. C2×#63560C2semidirect
7. #10589398C2semidirect
42. #5004D3semidirect
469. C32#2005semidirect
536. C3#70346semidirect
537. C3#71868semidirect

Maximal subgroups

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

subgroupindex
C3×#55262
C2×#638732
C2×#638272
C3×#50042
C2×#635682
C2×#635602
#105893982
#718683
#703463