Finite Group Databasebeta

← #11778113

Subgroups — #11778113

Order 1152.

659 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 659 conjugacy classes of subgroups — too many to draw. Only its 80 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
1#10594930C211yesmaximal, characteristic, complemented
2C3×#4732C211yesmaximal, characteristic, complemented
3#10591302C211yesmaximal, characteristic, complemented
4#10591160C211yesmaximal, characteristic, complemented
5#10589335C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#70971—31nomaximal
9#68293—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×#3805—21no—
12C2×#3750C2211yescharacteristic
13C3×#930C2211yescharacteristic
14C3×#930C2211yescharacteristic
15C2×C3×D24—21no—
16#63980—21no—
17C2×(C2×D3)⋊Dic3—21no—
18C2×(C2×D3)⋊Dic3—21no—
19#63899—21no—
20#63899—21no—
21#63885—21no—
22#63885—21no—
23C2×#3713—21no—
24C32×C22⋊C8C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×C3⋊#95C2211yescharacteristic
27C3×#821—21no—
28#63562—21no—
29#5597—31no—
30#5597—31no—
31C3×#447—31no—
32#5222—31no—
33#5217—31no—
34#5036—31no—
35#4732D311yescharacteristic, complemented
36#4672—31no—
37C3×#327—31no—
38#4537—31no—
39#4470D311yescharacteristic, complemented
40#4469—31no—
41#4469—31no—
42#4469—61no—
43#4451—31no—
44C23×C3×D3—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C22×C3×Dic3—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—42no—
54C2×C3×D12D411yescharacteristic
55C2×C3×D12D411yescharacteristic
56C2×#627—21no—
57C2×#625—21no—
58C2×#625—21no—
59#3805—42no—
60#3805—42no—
61C2×D3×Dic3—21no—
62C2×D3×Dic3—21no—
63C2×C32×C8—21no—
64#3750—21no—
65#3750—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×C4⋊Dic3D411yescharacteristic
70C3×C4⋊Dic3D411yescharacteristic
71C3×D24—42no—
72#3724—21no—
73(C2×D3)⋊Dic3—21no—
74(C2×D3)⋊Dic3—21no—
75(C2×D3)⋊Dic3—42no—
76(C2×D3)⋊Dic3—42no—
77#3713—42no—
78#1598—91noSylow
79C22×C3×D4—31no—
80C2×#237—61no—
81C2×#237—61no—
82C22×D12C2×D311yescharacteristic
83C2×C3×D8—61no—
84C3×#121—31no—
85C3×#121—31no—
86C2×#217—61no—
87C2×#217—61no—
88#939—61no—
89#939—61no—
90#939—61no—
91#939—61no—
92C2×#213—61no—
93C2×#213—61no—
94#930C2×D311yescharacteristic
95#930C2×D311yescharacteristic
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×Dic3⋊C4—31no—
99C2×Dic3⋊C4—31no—
100C2×Dic3⋊C4—61no—
101C2×D24—21no—
102#896—61no—
103#896—61no—
104#884—61no—
105#884—61no—
106#878—61no—
107#878—61no—
108C3×#102—61no—
109C3×C22⋊C8—21no—
110C3×C22⋊C8C2×D311yescharacteristic
111C3×C22⋊C8C2×D311yescharacteristic
112C3×#95—31no—
113#832—61no—
114C3⋊#95C2×D311yescharacteristic
115#830—31no—
116#830—31no—
117#830—61no—
118#821—21no—
119#809—61no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—22no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C2×C32×C4—41no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3D812yescomplemented
138C3×#67—41no—
139C3×#67—41no—
140C3×#67—41no—
141C3×#67—41no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C3×D12—22no—
148C3×D12—22no—
149C3×D12—41no—
150C3×D12—41no—
151C3×D12—41no—
152C3×D12—41no—
153#627—42no—
154#625—42no—
155#625—81no—
156D3×Dic3—42no—
157D3×Dic3—42no—
158C32×C8—41no—
159C3⋊(C3⋊C8)—41no—
160#537—91no—
161#447—31no—
162#447—91no—
163#394—91no—
164#327—31no—
165#327—91no—
166#324—91no—
167C24×C3—61no—
168C23×D3—21no—
169C2×C3×D4—31no—
170C2×C3×D4—31no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C2×C3×D4—122no—
176C22×C3×C4—21no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C2×#67—21no—
181C2×#67—21no—
182C2×#67—61no—
183C2×#67—61no—
184C2×#67—61no—
185C2×#67—61no—
186C22×Dic3—21no—
187C22×Dic3—31no—
188C22×Dic3—31no—
189C22×Dic3—31no—
190C22×Dic3—31no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195#237—122no—
196#237—122no—
197#237—122no—
198#237—122no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—42no—
202C2×D12D1211yescharacteristic
203C2×D12#6711yescharacteristic
204C2×C4×D3—61no—
205C2×C4×D3—61no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C3×D8—122no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—41no—
212C3×C4⋊C4—31no—
213C3×C4⋊C4—31no—
214C3×C22⋊C4—61no—
215C3×C22⋊C4—61no—
216#217—61no—
217#217—61no—
218#217—122no—
219#217—122no—
220#213—122no—
221#213—122no—
222(C2×D3)⋊C4—21no—
223(C2×D3)⋊C4—21no—
224(C2×D3)⋊C4—61no—
225(C2×D3)⋊C4—61no—
226(C2×D3)⋊C4—122no—
227(C2×D3)⋊C4—122no—
228C4⋊Dic3D1211yescharacteristic
229C4⋊Dic3#6711yescharacteristic
230Dic3⋊C4—61no—
231Dic3⋊C4—61no—
232Dic3⋊C4—61no—
233Dic3⋊C4—61no—
234Dic3⋊C4—61no—
235Dic3⋊C4—61no—
236Dic3⋊C4—121no—
237Dic3⋊C4—121no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—121no—
241D24—42no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32#12011yescharacteristic
245C22×C32C2×D811yescharacteristic
246C22×C32AGL(1,ℤ/8)11yescharacteristic
247C2×C3×D3—42no—
248C2×C3×D3—42no—
249C2×C3×D3—41no—
250C2×C3×D3—41no—
251C2×C3×D3—41no—
252C2×C3×D3—41no—
253C2×C3×D3—41no—
254C2×C3×D3—41no—
255C2×C3×D3—42no—
256C2×C3×D3—81no—
257C2×C3×D3—81no—
258C2×C3×D3—81no—
259C2×C3×D3—81no—
260C32×C4—21no—
261C32×C4—21no—
262C3⋊Dic3—22no—
263C3⋊Dic3—41no—
264C3×Dic3—41no—
265C3×Dic3—41no—
266C3×Dic3—81no—
267C2×#41—181no—
268C22×D4—31no—
269C2×D8—61no—
270C2×D8—181no—
271C22⋊Q8—181no—
272C22⋊Q8—181no—
273#121—31no—
274#121—31no—
275#121—181no—
276#121—181no—
277#121—181no—
278C2×C4⋊C4—91no—
279C2×C22⋊C4—181no—
280C2×C22⋊C4—181no—
281#102—61no—
282#102—181no—
283C22⋊C8—91no—
284C22⋊C8D3211yescharacteristic
285#95—31no—
286C23×C3—21no—
287C23×C3—62no—
288C23×C3—61no—
289C23×C3—61no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3—121no—
293C23×C3—121no—
294C23×C3—121no—
295C23×C3—121no—
296C23×C3D3×D411yescharacteristic
297C23×C3D3×D411yescharacteristic
298C22×D3—22no—
299C22×D3—21no—
300C22×D3—21no—
301C22×D3—41no—
302C22×D3—41no—
303C22×D3—41no—
304C22×D3—41no—
305C22×D3—41no—
306C22×D3—41no—
307C3×D4—62no—
308C3×D4—62no—
309C3×D4—121no—
310C3×D4—121no—
311C3×D4—121no—
312C3×D4—121no—
313C3×D4—121no—
314C3×D4—121no—
315C3×D4—121no—
316C3×D4—121no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—61no—
322C2×C3×C4—61no—
323C2×C3×C4—81no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4C2×D1211yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331#67—41no—
332#67—41no—
333#67—41no—
334#67—41no—
335#67—122no—
336#67—122no—
337#67—241no—
338#67—241no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—32no—
342C2×Dic3—32no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—62no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—122no—
357C2×Dic3—122no—
358C2×Dic3—121no—
359C2×Dic3—121no—
360C2×Dic3—241no—
361D12—22no—
362D12—22no—
363D12—41no—
364D12—41no—
365D12—41no—
366D12—41no—
367C4×D3—122no—
368C4×D3—122no—
369Dic6—122no—
370Dic6—122no—
371C3×C8—41no—
372C3×C8—41no—
373C3×C8—81no—
374C3⋊C8—121no—
375C3⋊C8—121no—
376C3⋊C8—241no—
377C2×C32—21no—
378C2×C32—21no—
379C2×C32#44711yescharacteristic
380C2×C32#45411yescharacteristic
381C2×C32B(4,𝔽2)11yescharacteristic
382C3×D3—81no—
383C3×D3—81no—
384C3×D3—82no—
385C24—61no—
386#41—362no—
387#41—362no—
388C2×Q8—181no—
389C2×D4—31no—
390C2×D4—31no—
391C2×D4—61no—
392C2×D4—61no—
393C2×D4—61no—
394C2×D4—61no—
395C2×D4—122no—
396C2×D4—181no—
397C2×D4—181no—
398C22×C4—61no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4C2×D3211yescharacteristic
404D8—122no—
405D8—362no—
406C2×C8—21no—
407C2×C8—181no—
408C4⋊C4—31no—
409C4⋊C4—31no—
410C4⋊C4—181no—
411C4⋊C4—181no—
412C4⋊C4—181no—
413C22⋊C4—61no—
414C22⋊C4—61no—
415C22⋊C4—181no—
416C22⋊C4—181no—
417C22⋊C4—362no—
418C22⋊C4—362no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—122no—
429C22×C3—122no—
430C22×C3—121no—
431C22×C3—121no—
432C22×C3—121no—
433C22×C3—122no—
434C22×C3—121no—
435C22×C3—121no—
436C22×C3—121no—
437C22×C3—241no—
438C22×C3—241no—
439C22×C3—241no—
440C22×C3—241no—
441C22×C3#88211yescharacteristic
442C22×C3D3×D811yescharacteristic
443C22×C3D3×D811yescharacteristic
444C22×C3#91111yescharacteristic
445C22×C3#91411yescharacteristic
446C22×C3#93711yescharacteristic
447C2×D3—42no—
448C2×D3—42no—
449C2×D3—41no—
450C2×D3—41no—
451C2×D3—41no—
452C2×D3—41no—
453C2×D3—42no—
454C2×D3—41no—
455C2×D3—41no—
456C2×D3—81no—
457C2×D3—81no—
458C2×D3—81no—
459C2×D3—81no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—121no—
467C3×C4—121no—
468C3×C4—241no—
469Dic3—41no—
470Dic3—41no—
471Dic3—62no—
472Dic3—62no—
473Dic3—81no—
474Dic3—122no—
475Dic3—121no—
476Dic3—121no—
477Dic3—241no—
478C32#159811yescharacteristic, complemented, Sylow
479C23—62no—
480C23—61no—
481C23—61no—
482C23—121no—
483C23—121no—
484C23—121no—
485C23—121no—
486C23—121no—
487C23—121no—
488C23#380211yescharacteristic
489Q8—362no—
490D4—62no—
491D4—62no—
492D4—121no—
493D4—121no—
494D4—121no—
495D4—121no—
496D4—121no—
497D4—121no—
498D4—121no—
499D4—121no—
500D4—362no—
501D4—721no—
502C2×C4—41no—
503C2×C4—61no—
504C2×C4—61no—
505C2×C4—92no—
506C2×C4—121no—
507C2×C4—121no—
508C2×C4—121no—
509C2×C4—181no—
510C2×C4—181no—
511C2×C4—181no—
512C2×C4—362no—
513C2×C4—362no—
514C2×C4—361no—
515C2×C4D3×D1211yescharacteristic
516C2×C4D3×#6711yescharacteristic
517C8—41no—
518C8—361no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—41no—
527C2×C3—41no—
528C2×C3—241no—
529C2×C3—242no—
530C2×C3—241no—
531C2×C3#474111yescharacteristic
532C2×C3#477311yescharacteristic
533C2×C3#482711yescharacteristic
534C2×C3#503211yescharacteristic
535C2×C3#515611yescharacteristic
536C2×C3#520111yescharacteristic
537D3—82no—
538D3—81no—
539D3—81no—
540C22—21no—
541C22—21no—
542C22—122no—
543C22—122no—
544C22—121no—
545C22—121no—
546C22—122no—
547C22—121no—
548C22—121no—
549C22—121no—
550C22—121no—
551C22—241no—
552C22—241no—
553C22—241no—
554C22—241no—
555C22#6379711yescharacteristic
556C22#6379811yescharacteristic
557C22#6392211yescharacteristic
558C4—21no—
559C4—21no—
560C4—121no—
561C4—121no—
562C4—182no—
563C4—241no—
564C4—361no—
565C3—21no—
566C3#6829311yescharacteristic, complemented
567C3#7097111yescharacteristic, complemented
568C2—21no—
569C2—21no—
570C2—242no—
571C2—241no—
572C2—241no—
573C2#1059040711yescharacteristic
574C2#1059094511yescharacteristic
575C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
hypercenterC22⋊C8D32
hypocenterC32#1598
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594930C2semidirect
2. C3×#4732C2semidirect
3. #10591302C2semidirect
4. #10591160C2semidirect
5. #10589335C2semidirect
6. C3×#4470C2semidirect
7. #10589149C2semidirect
35. #4732D3semidirect
39. #4470D3semidirect
137. C2×C3⋊Dic3D8semidirect
478. C32#1598semidirect
566. C3#68293semidirect
567. C3#70971semidirect

Maximal subgroups

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

subgroupindex
#105949302
C3×#47322
#105913022
#105911602
#105893352
C3×#44702
#105891492
#709713
#682933