Finite Group Databasebeta

← #11778178

Subgroups — #11778178

Order 1152.

739 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 739 conjugacy classes of subgroups — too many to draw. Only its 84 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×#5617C211yesmaximal, characteristic, complemented
2#10592735C211yesmaximal, characteristic, complemented
3#10591395C211yesmaximal, characteristic, complemented
4#10591183C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#71884—31nomaximal
9#68285—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#626—21no—
12C32×#121C2211yescharacteristic
13C2×#3753—21no—
14C3×#939—21no—
15C3×#937—21no—
16C3×D4×Dic3—21no—
17C2×C3×(C2×D3)⋊C4C2211yescharacteristic
18C3×#924C2211yescharacteristic
19C3×#898—21no—
20C3×#886—21no—
21C3×#885—21no—
22C2×#3722—21no—
23C2×#3717—21no—
24#63657C2211yescharacteristic
25#63636—21no—
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28#63564—21no—
29C3×#538—31no—
30#5617D311yescharacteristic, complemented
31#5046—31no—
32#5036—31no—
33#5036—31no—
34#5036—61no—
35#4960—31no—
36#4731—31no—
37#4671—31no—
38C3×#327—31no—
39#4538—31no—
40#4537D311yescharacteristic, complemented
41#4525—31no—
42#4468—31no—
43#4452—31no—
44C23×C3⋊D3—21no—
45C23×C3×D3D411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4D411yescharacteristic, complemented
48C22×C32×C4C2311yescharacteristic
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—42no—
52C2×C3×#67—21no—
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C2×C3×Dic6D411yescharacteristic, complemented
58C2×#626—42no—
59C2×#626—42no—
60C2×#626—42no—
61C32×C4⋊C4D411yescharacteristic, complemented
62C32×C22⋊C4—21no—
63#3753—42no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×#217—21no—
66C3×#217—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×(C2×D3)⋊C4—21no—
70C3×(C2×D3)⋊C4—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3D411yescharacteristic, complemented
73C3×Dic3⋊C4—21no—
74C3×C4×Dic3—21no—
75C2×C3×C3⋊C8—21no—
76#3722—42no—
77#3717—42no—
78#1600—91noSylow
79C22×#67—61no—
80C22×D12—31no—
81C22×D12—31no—
82C22×D12—61no—
83C22×D12—61no—
84C3×#126—61no—
85C3×#124—61no—
86C3×#123—61no—
87C3×C22⋊Q8—31no—
88C3×#121—21no—
89C3×#121—61no—
90C3×#121C2×D311yescharacteristic
91C3×#121C2×D311yescharacteristic
92C3×#120—61no—
93C3×C4×D4—61no—
94C2×C3×C22⋊C4—31no—
95C2×#215—61no—
96#939—21no—
97#937—21no—
98D4×Dic3—21no—
99C2×#213—62no—
100C2×#213—61no—
101C2×#213—61no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104C2×(C2×D3)⋊C4C2×D311yescharacteristic
105#924C2×D311yescharacteristic
106C2×#204—61no—
107#898—21no—
108#886—21no—
109#885—21no—
110C3×C22⋊C8—31no—
111C3×#95—31no—
112C3⋊#95C2×D311yescharacteristic
113#830—31no—
114#830—31no—
115#830—61no—
116#830C2×D311yescharacteristic
117#821—61no—
118#809—61no—
119#809—62no—
120#809—61no—
121#809—61no—
122C23×C32—21no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—22no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—41no—
131C22×C3×D3—21no—
132C22×C3×D3—21no—
133C22×C3×D3—21no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C32×D4—41no—
137C32×D4—41no—
138C32×D4—41no—
139C2×C32×C4—21no—
140C2×C32×C4—41no—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)—41no—
146C4⋊(C3⋊D3)—41no—
147C3×#67—81no—
148C3×#67—81no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—81no—
157C3×Dic6—41no—
158#626—48no—
159C3⋊(C3⋊C8)—41no—
160C3×C3⋊C8—41no—
161#538—31no—
162#450—91no—
163#447—91no—
164#392—91no—
165#328—91no—
166#327—31no—
167#323—91no—
168C24×C3—31no—
169C23×D3—61no—
170C23×D3—61no—
171C23×D3—121no—
172C23×D3#6711yescharacteristic
173C2×C3×Q8—31no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—41no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4D1211yescharacteristic, complemented
181C2×C3×D4#6711yescharacteristic, complemented
182C22×C3×C4—21no—
183C22×C3×C4—31no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C2×#67—21no—
189C2×#67—21no—
190C2×#67—122no—
191C2×#67—122no—
192C2×#67—122no—
193C22×Dic3—21no—
194C22×Dic3—21no—
195C22×Dic3#6711yescharacteristic
196C2×D12—62no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—121no—
202C2×D12—122no—
203C2×D12—122no—
204C2×D12—124no—
205C2×D12—122no—
206C2×D12—122no—
207C2×D12—122no—
208C2×Dic6#6711yescharacteristic, complemented
209C2×C3×C8—61no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—31no—
212C3×C4⋊C4—61no—
213C3×C4⋊C4—61no—
214C3×C4⋊C4D1211yescharacteristic, complemented
215C3×C4⋊C4#6711yescharacteristic, complemented
216C3×C22⋊C4—21no—
217C3×C22⋊C4—21no—
218C3×C22⋊C4—41no—
219C3×C22⋊C4—61no—
220C3×C22⋊C4—61no—
221C3×C22⋊C4—61no—
222C3×C22⋊C4—61no—
223C3×C22⋊C4—61no—
224C3×C22⋊C4—61no—
225C3×C42—61no—
226#217—21no—
227#217—21no—
228#215—122no—
229#213—122no—
230#213—122no—
231#213—124no—
232(C2×D3)⋊C4—21no—
233(C2×D3)⋊C4—21no—
234(C2×D3)⋊C4—21no—
235(C2×D3)⋊C4—21no—
236(C2×D3)⋊C4—122no—
237(C2×D3)⋊C4—122no—
238C4⋊Dic3—21no—
239C4⋊Dic3#6711yescharacteristic, complemented
240Dic3⋊C4—21no—
241C4×Dic3—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246#204—122no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32—41no—
250C22×C32—41no—
251C22×C32—41no—
252C22×C32#12011yescharacteristic
253C22×C32#13511yescharacteristic
254C22×C32AGL(1,ℤ/8)11yescharacteristic
255C2×C3⋊D3—42no—
256C2×C3⋊D3—42no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—81no—
259C2×C3⋊D3—81no—
260C2×C3⋊D3—81no—
261C2×C3⋊D3—81no—
262C2×C3×D3—42no—
263C2×C3×D3—41no—
264C2×C3×D3—41no—
265C2×C3×D3—41no—
266C2×C3×D3—81no—
267C32×C4—21no—
268C32×C4—21no—
269C32×C4—41no—
270C3×Dic3—42no—
271C3×Dic3—41no—
272C3×Dic3—41no—
273C3×Dic3—41no—
274C22×D4—91no—
275C22×D4—181no—
276C2×SD16—181no—
277C2×D8—181no—
278#126—61no—
279#124—61no—
280#123—61no—
281C22⋊Q8—31no—
282#121—61no—
283#121D3211yescharacteristic
284#120—61no—
285C4×D4—61no—
286C2×C22⋊C4—31no—
287C2×C22⋊C4—181no—
288#102—181no—
289#102—181no—
290C22⋊C8—31no—
291C22⋊C8—91no—
292#95—31no—
293C23×C3—21no—
294C23×C3—21no—
295C23×C3—21no—
296C23×C3—41no—
297C23×C3—61no—
298C23×C3—61no—
299C23×C3—61no—
300C23×C3—121no—
301C23×C3—121no—
302C23×C3D3×D411yescharacteristic
303C23×C3C2×#6711yescharacteristic
304C22×D3—21no—
305C22×D3—21no—
306C22×D3—21no—
307C22×D3—41no—
308C22×D3—41no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—122no—
312C22×D3—121no—
313C22×D3—121no—
314C22×D3—122no—
315C22×D3—121no—
316C22×D3—121no—
317C22×D3—121no—
318C22×D3—121no—
319C22×D3—122no—
320C22×D3—121no—
321C22×D3—121no—
322C22×D3—121no—
323C22×D3—121no—
324C22×D3—121no—
325C22×D3—121no—
326C22×D3—241no—
327C22×D3—241no—
328C22×D3—241no—
329C22×D3—241no—
330C3×Q8—121no—
331C3×D4—41no—
332C3×D4—41no—
333C3×D4—42no—
334C3×D4—41no—
335C3×D4—41no—
336C3×D4—41no—
337C3×D4—41no—
338C3×D4—81no—
339C3×D4—81no—
340C3×D4—241no—
341C3×D4—241no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—42no—
350C2×C3×C4—62no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4—121no—
357C2×C3×C4—241no—
358C2×C3×C4C2×D1211yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362#67—81no—
363#67—81no—
364#67—128no—
365C2×Dic3—22no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—41no—
370C2×Dic3—41no—
371C2×Dic3—41no—
372C2×Dic3—81no—
373D12—62no—
374D12—64no—
375D12—62no—
376D12—62no—
377D12—62no—
378D12—122no—
379D12—122no—
380D12—121no—
381D12—121no—
382D12—121no—
383D12—121no—
384D12—122no—
385D12—128no—
386Dic6—41no—
387C3×C8—121no—
388C3⋊C8—41no—
389C3⋊C8—122no—
390C3⋊C8—121no—
391C3⋊C8—121no—
392C2×C32—21no—
393C2×C32—21no—
394C2×C32—81no—
395C2×C32#44911yescharacteristic
396C2×C32#45311yescharacteristic
397C2×C32B(4,𝔽2)11yescharacteristic
398C3⋊D3—82no—
399C3×D3—81no—
400C24—31no—
401C24—181no—
402C2×Q8—31no—
403C2×D4—21no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—181no—
407C2×D4—181no—
408C2×D4—362no—
409C2×D4—362no—
410C2×D4—362no—
411C2×D4—362no—
412C2×D4#62611yescharacteristic, complemented
413C22×C4—31no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4C2×D3211yescharacteristic
417SD16—362no—
418D8—362no—
419C2×C8—61no—
420C2×C8—181no—
421C4⋊C4—31no—
422C4⋊C4—61no—
423C4⋊C4—61no—
424C4⋊C4#62611yescharacteristic, complemented
425C22⋊C4—21no—
426C22⋊C4—61no—
427C22⋊C4—61no—
428C22⋊C4—61no—
429C22⋊C4—61no—
430C22⋊C4—61no—
431C22⋊C4—61no—
432C22⋊C4—362no—
433C42—61no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—81no—
450C22×C3—81no—
451C22×C3—81no—
452C22×C3—122no—
453C22×C3—121no—
454C22×C3—121no—
455C22×C3—121no—
456C22×C3—241no—
457C22×C3#88211yescharacteristic
458C22×C3#91111yescharacteristic
459C22×C3#91611yescharacteristic
460C22×C3#94911yescharacteristic
461C22×C3#95011yescharacteristic
462C22×C3#95311yescharacteristic
463C2×D3—42no—
464C2×D3—41no—
465C2×D3—41no—
466C2×D3—41no—
467C2×D3—81no—
468C2×D3—124no—
469C2×D3—122no—
470C2×D3—122no—
471C2×D3—122no—
472C2×D3—122no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—242no—
476C2×D3—242no—
477C2×D3—241no—
478C2×D3—241no—
479C2×D3—241no—
480C2×D3—241no—
481C2×D3—242no—
482C2×D3—242no—
483C2×D3—242no—
484C2×D3—242no—
485C2×D3—241no—
486C2×D3—241no—
487C2×D3—241no—
488C2×D3—241no—
489C3×C4—22no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—41no—
495C3×C4—41no—
496C3×C4—41no—
497C3×C4—81no—
498C3×C4—122no—
499C3×C4—121no—
500C3×C4—121no—
501C3×C4—121no—
502Dic3—42no—
503Dic3—41no—
504Dic3—41no—
505Dic3—41no—
506C32#160011yescharacteristic, complemented, Sylow
507C23—21no—
508C23—61no—
509C23—61no—
510C23—61no—
511C23—121no—
512C23—121no—
513C23—182no—
514C23—361no—
515C23—361no—
516C23—361no—
517C23—361no—
518C23—361no—
519C23—361no—
520C23D3×#6711yescharacteristic
521Q8—121no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—182no—
526D4—182no—
527D4—241no—
528D4—241no—
529D4—361no—
530D4—361no—
531D4—368no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—62no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—121no—
539C2×C4—121no—
540C2×C4—121no—
541C2×C4—241no—
542C2×C4C2×#62611yescharacteristic
543C2×C4D3×#6711yescharacteristic
544C8—121no—
545C8—361no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—41no—
554C2×C3—41no—
555C2×C3—81no—
556C2×C3—81no—
557C2×C3—161no—
558C2×C3—241no—
559C2×C3#474111yescharacteristic
560C2×C3#478111yescharacteristic
561C2×C3#482211yescharacteristic
562C2×C3#523811yescharacteristic
563C2×C3#524111yescharacteristic
564C2×C3#524411yescharacteristic
565D3—81no—
566D3—244no—
567D3—242no—
568D3—242no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—122no—
575C22—121no—
576C22—121no—
577C22—121no—
578C22—241no—
579C22—362no—
580C22—362no—
581C22—362no—
582C22—721no—
583C22—721no—
584C22—721no—
585C22—721no—
586C22#6392511yescharacteristic
587C22#6393511yescharacteristic
588C22#6397711yescharacteristic
589C4—21no—
590C4—21no—
591C4—41no—
592C4—122no—
593C4—121no—
594C4—121no—
595C4—121no—
596C3—21no—
597C3#6828511yescharacteristic, complemented
598C3#7188411yescharacteristic, complemented
599C2—21no—
600C2—21no—
601C2—81no—
602C2—241no—
603C2—722no—
604C2#1059145211yescharacteristic
605C2#1059153111yescharacteristic
606C2#1059166611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32#120
hypercenter#121D32
hypocenterC32#1600
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5617C2semidirect
2. #10592735C2semidirect
3. #10591395C2semidirect
4. #10591183C2semidirect
5. C3×#4537C2semidirect
6. #10589153C2semidirect
7. #10589145C2semidirect
30. #5617D3semidirect
40. #4537D3semidirect
47. C2×C32×D4D4semidirect
57. C2×C3×Dic6D4semidirect
61. C32×C4⋊C4D4semidirect
72. C3×C4⋊Dic3D4semidirect
180. C2×C3×D4D12semidirect
181. C2×C3×D4#67semidirect
208. C2×Dic6#67semidirect
214. C3×C4⋊C4D12semidirect
215. C3×C4⋊C4#67semidirect
239. C4⋊Dic3#67semidirect
412. C2×D4#626semidirect
424. C4⋊C4#626semidirect
506. C32#1600semidirect
597. C3#68285semidirect
598. C3#71884semidirect

Maximal subgroups

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

subgroupindex
C3×#56172
#105927352
#105913952
#105911832
C3×#45372
#105891532
#105891452
#718843
#682853