Finite Group Databasebeta

← #11778177

Subgroups — #11778177

Order 1152.

734 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 78 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#10594977C211yesmaximal, characteristic, complemented
2#10592917C211yesmaximal, characteristic, complemented
3C3×#5223C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic, complemented
5#10589154C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#70969—31nomaximal
9#69697—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67—21no—
12C2×#3754—21no—
13#64133C2211yescharacteristic
14C2×C3×#217—21no—
15C2×C3×#213—21no—
16C3×#930C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4C2211yescharacteristic
18#63976—21no—
19Dic3×#67—21no—
20#63913—21no—
21#63891—21no—
22#63885—21no—
23#63858—21no—
24#63659—21no—
25#63657C2211yescharacteristic
26C3×#832—21no—
27C3×C3⋊#95C2211yescharacteristic
28C3×#830C2211yescharacteristic
29#5617—31no—
30#5494—31no—
31C3×#447—31no—
32C3×#392—31no—
33#5223D311yescharacteristic, complemented
34#5218—31no—
35#5218—31no—
36#5218—61no—
37#5217D311yescharacteristic, complemented
38#4537—31no—
39#4525—31no—
40#4468—31no—
41#4467—31no—
42#4452—31no—
43#4451—31no—
44C24×C32—21no—
45C23×C3×D3D411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—42no—
49C22×C32×C4C2311yescharacteristic
50C2×#634D411yescharacteristic, complemented
51C2×C3×#67—21no—
52C2×C3×#67—42no—
53C2×C3×#67—42no—
54C2×C3×#67—42no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C2×C3×D12D411yescharacteristic, complemented
58C2×#625—21no—
59C2×#625—21no—
60C2×D3×Dic3—21no—
61#3757—21no—
62#3754—42no—
63C4⋊(C3⋊Dic3)D411yescharacteristic, complemented
64#3750—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×#217—42no—
67C3×#213—42no—
68C3×(C2×D3)⋊C4—21no—
69C3×(C2×D3)⋊C4—21no—
70C3×(C2×D3)⋊C4—21no—
71C3×C4⋊Dic3D411yescharacteristic, complemented
72C2×C3×C3⋊C8—21no—
73Dic3⋊Dic3—21no—
74(C2×D3)⋊Dic3—21no—
75(C2×D3)⋊Dic3—21no—
76(C2×D3)⋊Dic3—21no—
77Dic32—21no—
78#1600—91noSylow
79C22×C3×D4—21no—
80C22×C3×D4—61no—
81C22×C3×D4C2×D311yescharacteristic
82C22×C3×D4C2×D311yescharacteristic
83C22×#67—21no—
84C2×C3×D8—61no—
85C3×#121—31no—
86C2×C3×C22⋊C4—31no—
87C2×C3×C22⋊C4—61no—
88#953—61no—
89C2×#217—21no—
90#939—61no—
91#937—61no—
92D4×Dic3—61no—
93C2×#214—61no—
94C2×#214—61no—
95C2×#214—62no—
96C2×#213—21no—
97#930C2×D311yescharacteristic
98C4×#67—61no—
99C2×(C2×D3)⋊C4C2×D311yescharacteristic
100#924—31no—
101#924—31no—
102#924—61no—
103#898—61no—
104#886—61no—
105#885—61no—
106#885—61no—
107#884—61no—
108#883—61no—
109#879—61no—
110C3×#102—61no—
111C3×C22⋊C8—31no—
112C3×#95—31no—
113#832—21no—
114#832—61no—
115#832—61no—
116#832—62no—
117C3⋊#95C2×D311yescharacteristic
118#830—31no—
119#830—31no—
120#830—61no—
121#830C2×D311yescharacteristic
122C23×C32—22no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32—41no—
128C23×C32—41no—
129C23×C32C2×D411yescharacteristic
130C22×C3×D3—21no—
131C22×C3×D3—21no—
132C22×C3×D3—21no—
133C22×C3×D3—21no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C32×D4—22no—
137C32×D4—22no—
138C32×D4—41no—
139C32×D4—41no—
140C2×C32×C4—41no—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145#634—41no—
146C3×#67—48no—
147C3×#67—41no—
148C3×#67—41no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C3×D12—41no—
156#625—81no—
157#625—81no—
158D3×Dic3—81no—
159C3⋊(C3⋊C8)—41no—
160C3×C3⋊C8—41no—
161#538—91no—
162#450—91no—
163#447—31no—
164#392—31no—
165#328—91no—
166#327—91no—
167#323—91no—
168C24×C3—21no—
169C24×C3—21no—
170C24×C3—31no—
171C24×C3—41no—
172C23×D3#6711yescharacteristic
173C2×C3×D4—22no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—31no—
179C2×C3×D4—41no—
180C2×C3×D4—42no—
181C2×C3×D4—42no—
182C2×C3×D4—44no—
183C2×C3×D4—61no—
184C2×C3×D4—122no—
185C2×C3×D4—122no—
186C2×C3×D4—122no—
187C22×C3×C4—21no—
188C22×C3×C4—31no—
189C22×C3×C4—61no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C2×#67—21no—
193C2×#67—42no—
194C2×#67—42no—
195C2×#67—42no—
196C2×#67—61no—
197C2×#67—61no—
198C2×#67—61no—
199C2×#67—61no—
200C22×Dic3—21no—
201C22×Dic3—61no—
202C22×Dic3#6711yescharacteristic
203C2×D12#6711yescharacteristic, complemented
204C2×C4×D3—61no—
205C2×Dic6—31no—
206C2×Dic6—31no—
207C2×Dic6—61no—
208C3×D8—122no—
209C2×C3×C8—61no—
210C3×C4⋊C4—31no—
211C3×C22⋊C4—61no—
212C3×C22⋊C4—61no—
213C3×C22⋊C4—61no—
214C3×C22⋊C4—122no—
215#217—42no—
216#217—61no—
217#217—61no—
218#217—61no—
219#217—61no—
220#217—61no—
221#217—121no—
222#214—122no—
223#214—122no—
224#214—124no—
225#213—42no—
226(C2×D3)⋊C4—21no—
227(C2×D3)⋊C4—21no—
228(C2×D3)⋊C4—21no—
229(C2×D3)⋊C4—61no—
230(C2×D3)⋊C4—61no—
231(C2×D3)⋊C4—61no—
232C4⋊Dic3—31no—
233C4⋊Dic3—31no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3#6711yescharacteristic, complemented
237Dic3⋊C4—61no—
238Dic3⋊C4—61no—
239Dic3⋊C4—61no—
240Dic3⋊C4—121no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32—42no—
250C22×C32—42no—
251C22×C32—42no—
252C22×C32—81no—
253C22×C32—81no—
254C22×C32—81no—
255C22×C32—81no—
256C22×C32#12011yescharacteristic
257C22×C32#13511yescharacteristic
258C22×C32AGL(1,ℤ/8)11yescharacteristic
259C2×C3×D3—42no—
260C2×C3×D3—41no—
261C2×C3×D3—41no—
262C2×C3×D3—41no—
263C2×C3×D3—41no—
264C2×C3×D3—41no—
265C2×C3×D3—41no—
266C2×C3×D3—81no—
267C32×C4—21no—
268C32×C4—21no—
269C3⋊Dic3—41no—
270C3⋊Dic3—41no—
271C3×Dic3—42no—
272C3×Dic3—41no—
273C3×Dic3—41no—
274C22×D4—61no—
275C22×D4D3211yescharacteristic
276C2×SD16—181no—
277C2×D8—61no—
278#126—181no—
279#124—181no—
280#123—181no—
281C22⋊Q8—91no—
282#121—31no—
283#121—181no—
284#120—181no—
285C4×D4—181no—
286C2×C22⋊C4—31no—
287C2×C22⋊C4—61no—
288#102—61no—
289#102—181no—
290C22⋊C8—31no—
291C22⋊C8—91no—
292#95—31no—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3—21no—
296C23×C3—42no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—42no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3—41no—
304C23×C3—42no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—41no—
310C23×C3—41no—
311C23×C3—61no—
312C23×C3—61no—
313C23×C3—61no—
314C23×C3—61no—
315C23×C3—81no—
316C23×C3—81no—
317C23×C3—81no—
318C23×C3—81no—
319C23×C3—121no—
320C23×C3—121no—
321C23×C3D3×D411yescharacteristic
322C23×C3C2×#6711yescharacteristic
323C22×D3—21no—
324C22×D3—21no—
325C22×D3—21no—
326C22×D3—21no—
327C22×D3—41no—
328C22×D3—41no—
329C3×D4—22no—
330C3×D4—24no—
331C3×D4—22no—
332C3×D4—22no—
333C3×D4—22no—
334C3×D4—42no—
335C3×D4—42no—
336C3×D4—41no—
337C3×D4—41no—
338C3×D4—41no—
339C3×D4—41no—
340C3×D4—42no—
341C3×D4—121no—
342C3×D4—128no—
343C3×D4—121no—
344C3×D4—121no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
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—121no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360#67—48no—
361#67—41no—
362#67—41no—
363#67—241no—
364#67—241no—
365#67—241no—
366#67—241no—
367C2×Dic3—22no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—41no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3—241no—
380D12—41no—
381C4×D3—241no—
382Dic6—121no—
383Dic6—121no—
384Dic6—122no—
385C3×C8—121no—
386C3⋊C8—41no—
387C3⋊C8—122no—
388C3⋊C8—121no—
389C3⋊C8—121no—
390C2×C32—21no—
391C2×C32—21no—
392C2×C32—82no—
393C2×C32#44911yescharacteristic
394C2×C32#45311yescharacteristic
395C2×C32B(4,𝔽2)11yescharacteristic
396C3×D3—81no—
397C3×D3—81no—
398C24—21no—
399C24—31no—
400C2×Q8—91no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—31no—
404C2×D4—42no—
405C2×D4—61no—
406C2×D4—122no—
407C2×D4—122no—
408C2×D4—122no—
409C2×D4—181no—
410C2×D4—181no—
411C22×C4—31no—
412C22×C4—61no—
413C22×C4—181no—
414C22×C4C2×D3211yescharacteristic
415SD16—362no—
416D8—122no—
417C2×C8—61no—
418C2×C8—181no—
419C4⋊C4—31no—
420C4⋊C4—91no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C22⋊C4—61no—
424C22⋊C4—61no—
425C22⋊C4—61no—
426C22⋊C4—122no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C42—181no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—42no—
442C22×C3—44no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—82no—
449C22×C3—82no—
450C22×C3—81no—
451C22×C3—81no—
452C22×C3—81no—
453C22×C3—81no—
454C22×C3—82no—
455C22×C3—82no—
456C22×C3—82no—
457C22×C3—82no—
458C22×C3—81no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—81no—
462C22×C3—122no—
463C22×C3—121no—
464C22×C3—121no—
465C22×C3—121no—
466C22×C3—121no—
467C22×C3—121no—
468C22×C3—121no—
469C22×C3—241no—
470C22×C3#91111yescharacteristic
471C22×C3#91211yescharacteristic
472C22×C3#93211yescharacteristic
473C22×C3#93711yescharacteristic
474C22×C3#93711yescharacteristic
475C22×C3#95011yescharacteristic
476C2×D3—42no—
477C2×D3—41no—
478C2×D3—41no—
479C2×D3—41no—
480C2×D3—41no—
481C2×D3—41no—
482C2×D3—41no—
483C2×D3—81no—
484C3×C4—22no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—41no—
490C3×C4—122no—
491C3×C4—121no—
492C3×C4—121no—
493Dic3—42no—
494Dic3—41no—
495Dic3—41no—
496Dic3—121no—
497Dic3—121no—
498Dic3—121no—
499Dic3—121no—
500Dic3—241no—
501Dic3—241no—
502C32#160011yescharacteristic, complemented, Sylow
503C23—22no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—61no—
511C23—61no—
512C23—61no—
513C23—61no—
514C23—121no—
515C23—121no—
516C23D3×#6711yescharacteristic
517Q8—361no—
518D4—22no—
519D4—22no—
520D4—41no—
521D4—41no—
522D4—121no—
523D4—128no—
524D4—121no—
525D4—121no—
526D4—721no—
527D4—721no—
528C2×C4—41no—
529C2×C4—62no—
530C2×C4—61no—
531C2×C4—61no—
532C2×C4—121no—
533C2×C4—121no—
534C2×C4—121no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—721no—
538C2×C4D3×#6711yescharacteristic
539C2×C4#381111yescharacteristic
540C8—121no—
541C8—361no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—41no—
550C2×C3—41no—
551C2×C3—84no—
552C2×C3—82no—
553C2×C3—82no—
554C2×C3—241no—
555C2×C3—241no—
556C2×C3#503211yescharacteristic
557C2×C3#503211yescharacteristic
558C2×C3#503711yescharacteristic
559C2×C3#507711yescharacteristic
560C2×C3#515811yescharacteristic
561C2×C3#519811yescharacteristic
562D3—81no—
563D3—81no—
564C22—21no—
565C22—21no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—122no—
574C22—121no—
575C22—121no—
576C22—121no—
577C22—121no—
578C22—121no—
579C22—121no—
580C22—241no—
581C22#6393211yescharacteristic
582C22#6393311yescharacteristic
583C22#6398311yescharacteristic
584C4—21no—
585C4—21no—
586C4—122no—
587C4—121no—
588C4—121no—
589C4—361no—
590C4—361no—
591C3—21no—
592C3#6969711yescharacteristic, complemented
593C3#7096911yescharacteristic, complemented
594C2—21no—
595C2—21no—
596C2—82no—
597C2—241no—
598C2—241no—
599C2#1059151911yescharacteristic
600C2#1059152311yescharacteristic
601C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#120
hypercenterC22×D4D32
hypocenterC32#1600
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #10594977C2semidirect
2. #10592917C2semidirect
3. C3×#5223C2semidirect
4. C3×#5217C2semidirect
5. #10589154C2semidirect
6. #10589149C2semidirect
7. #10589145C2semidirect
33. #5223D3semidirect
37. #5217D3semidirect
50. C2×#634D4semidirect
57. C2×C3×D12D4semidirect
63. C4⋊(C3⋊Dic3)D4semidirect
71. C3×C4⋊Dic3D4semidirect
203. C2×D12#67semidirect
236. C4⋊Dic3#67semidirect
502. C32#1600semidirect
592. C3#69697semidirect
593. C3#70969semidirect

Maximal subgroups

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

subgroupindex
#105949772
#105929172
C3×#52232
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