Finite Group Databasebeta

← #13049542

Subgroups — #13049542

Order 1296.

591 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 591 conjugacy classes of subgroups — too many to draw. Only its 70 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#10620157C211yesmaximal, characteristic, complemented
2#10620155C211yesmaximal, characteristic, complemented
3#10620154C211yesmaximal, characteristic, complemented
4C3×#6295C211yesmaximal, characteristic, complemented
5C3×#6293C211yesmaximal, characteristic, complemented
6C3×#6292C211yesmaximal, characteristic, complemented
7C3×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
8#89041—31nomaximal
9#88964—31nomaximal
10#88962—31nomaximal
11#88961—31nomaximal
12C2×C3×C3⋊(C3⋊D3)C2211yescharacteristic
13C2×C32×C3⋊D3C2211yescharacteristic
14C2×C32×C3⋊D3C2211yescharacteristic
15C3×C3⋊(C3⋊Dic3)C2211yescharacteristic
16C3×C3⋊(C3⋊Dic3)C2211yescharacteristic
17C32×C3⋊Dic3C2211yescharacteristic
18C33×Dic3C2211yescharacteristic
19C3×C4⋊(C3⋊D3)—31no—
20C3×C4×C3⋊D3—31no—
21C3×#634—31no—
22#6295—31no—
23#6295—31no—
24#6295—61no—
25#6295D311yescharacteristic, complemented
26#6294—31no—
27#6294—31no—
28#6294—31no—
29#6294—31no—
30#6294—61no—
31#6294—61no—
32#6293D311yescharacteristic, complemented
33#6292D311yescharacteristic, complemented
34#6291—31no—
35#6290—31no—
36#6289—31no—
37Dic3×C3⋊D3—31no—
38Dic3×C3⋊D3D311yescharacteristic, complemented
39D3×C3⋊Dic3—31no—
40D3×C3⋊Dic3—31no—
41C3×#627—31no—
42C3×#627—31no—
43C3×#627—61no—
44C3×#626—31no—
45C3×#626—31no—
46C3×#626—31no—
47C3×#626—31no—
48C3×#626—61no—
49C3×#625—31no—
50C3×D3×Dic3—31no—
51C3×D3×Dic3—31no—
52C3×D3×Dic3—61no—
53C2×C34C2311yescharacteristic
54C3×C3⋊(C3⋊D3)—21no—
55C32×C3⋊D3—21no—
56C32×C3⋊D3—21no—
57#3805—91no—
58#3804—91no—
59#3799—91no—
60#3796—91no—
61#3796—91no—
62#3795—91no—
63C2×C3⋊(C3⋊D3)C2×D311yescharacteristic
64C2×C3×C3⋊D3—21no—
65C2×C3×C3⋊D3—21no—
66C2×C3×C3⋊D3—31no—
67C2×C3×C3⋊D3—31no—
68C2×C3×C3⋊D3—31no—
69C2×C3×C3⋊D3—61no—
70C2×C3×C3⋊D3—61no—
71C2×C3×C3⋊D3—61no—
72C2×C3×C3⋊D3—121no—
73C2×C3×C3⋊D3C2×D311yescharacteristic
74C2×C3×C3⋊D3C2×D311yescharacteristic
75C2×C3×C3⋊D3C2×D311yescharacteristic
76C2×C3×C3⋊D3C2×D311yescharacteristic
77C2×C32×D3—31no—
78C2×C32×D3—31no—
79C2×C32×D3—31no—
80C2×C32×D3—31no—
81C2×C32×D3—61no—
82C2×C32×D3—61no—
83C33×C4—31no—
84C3⋊(C3⋊Dic3)C2×D311yescharacteristic
85C3⋊(C3⋊Dic3)C2×D311yescharacteristic
86C3×C3⋊Dic3—21no—
87C3×C3⋊Dic3—31no—
88C3×C3⋊Dic3—31no—
89C3×C3⋊Dic3—31no—
90C3×C3⋊Dic3—31no—
91C3×C3⋊Dic3—31no—
92C3×C3⋊Dic3—31no—
93C3×C3⋊Dic3—61no—
94C3×C3⋊Dic3—61no—
95C3×C3⋊Dic3—61no—
96C3×C3⋊Dic3—61no—
97C3×C3⋊Dic3—61no—
98C3×C3⋊Dic3—61no—
99C3×C3⋊Dic3—121no—
100C3×C3⋊Dic3—121no—
101C3×C3⋊Dic3C2×D311yescharacteristic
102C3×C3⋊Dic3C2×D311yescharacteristic
103C32×Dic3—21no—
104C32×Dic3—21no—
105C32×Dic3—21no—
106C32×Dic3—31no—
107C32×Dic3—31no—
108C32×Dic3—41no—
109C32×Dic3—61no—
110C32×Dic3C2×D311yescharacteristic
111C32×Dic3C2×D311yescharacteristic
112C32×Dic3C2×D311yescharacteristic
113C34#4111yescharacteristic, complemented, Sylow
114#638—91no—
115C2×C3⋊Dic3—91no—
116C4⋊(C3⋊D3)—31no—
117C4×C3⋊D3—31no—
118C4×C3⋊D3—91no—
119#634—31no—
120C3×#67—91no—
121C3×#67—91no—
122C3×#67—91no—
123C2×C3×Dic3—91no—
124C3×D12—91no—
125C3×D12—91no—
126C3×D12—91no—
127C3×D12—181no—
128C3×C4×D3—91no—
129C3×C4×D3—91no—
130C3×C4×D3—181no—
131C3×Dic6—91no—
132C3×Dic6—91no—
133C3×Dic6—91no—
134C3×Dic6—181no—
135#627—31no—
136#627—31no—
137#627—61no—
138#626—31no—
139#626—31no—
140#626—31no—
141#626—31no—
142#626—61no—
143#626—91no—
144#626—91no—
145#626—91no—
146#626—181no—
147#625—31no—
148#625—91no—
149#625—91no—
150#625—181no—
151#624—91no—
152#624—91no—
153#624—91no—
154#624—181no—
155D3×Dic3—31no—
156D3×Dic3—31no—
157D3×Dic3—61no—
158D3×Dic3—91no—
159D3×Dic3—91no—
160D3×Dic3—91no—
161D3×Dic3—91no—
162D3×Dic3—91no—
163D3×Dic3—91no—
164D3×Dic3—91no—
165D3×Dic3—181no—
166D3×Dic3—181no—
167D3×Dic3—181no—
168C2×C33—21no—
169C2×C33—21no—
170C2×C33—21no—
171C2×C33—21no—
172C2×C33—21no—
173C2×C33—21no—
174C2×C33—41no—
175C2×C33—41no—
176C2×C33—41no—
177C2×C33—41no—
178C2×C33—81no—
179C2×C33C22×D311yescharacteristic
180C2×C33C22×D311yescharacteristic
181C2×C33C22×D311yescharacteristic
182C2×C33C22×D311yescharacteristic
183C3⋊(C3⋊D3)—21no—
184C3×C3⋊D3—21no—
185C3×C3⋊D3—21no—
186C3×C3⋊D3—22no—
187C3×C3⋊D3—21no—
188C3×C3⋊D3—21no—
189C3×C3⋊D3—41no—
190C3×C3⋊D3—61no—
191C3×C3⋊D3—62no—
192C3×C3⋊D3—61no—
193C3×C3⋊D3—61no—
194C3×C3⋊D3—121no—
195C3×C3⋊D3—121no—
196C3×C3⋊D3—122no—
197C32×D3—61no—
198C32×D3—61no—
199C32×D3—62no—
200C32×D3—61no—
201C32×D3—61no—
202C32×D3—121no—
203#239—271no—
204#237—271no—
205#237—271no—
206#235—271no—
207C22×C32—91no—
208C22×C32—91no—
209C2×C3⋊D3—31no—
210C2×C3⋊D3—31no—
211C2×C3⋊D3—31no—
212C2×C3⋊D3—61no—
213C2×C3⋊D3—61no—
214C2×C3⋊D3—61no—
215C2×C3⋊D3—121no—
216C2×C3⋊D3D3211yescharacteristic
217C2×C3⋊D3D3211yescharacteristic
218C2×C3×D3—31no—
219C2×C3×D3—31no—
220C2×C3×D3—31no—
221C2×C3×D3—31no—
222C2×C3×D3—31no—
223C2×C3×D3—31no—
224C2×C3×D3—31no—
225C2×C3×D3—31no—
226C2×C3×D3—61no—
227C2×C3×D3—61no—
228C2×C3×D3—61no—
229C2×C3×D3—61no—
230C2×C3×D3—61no—
231C2×C3×D3—61no—
232C2×C3×D3—61no—
233C2×C3×D3—61no—
234C2×C3×D3—91no—
235C2×C3×D3—91no—
236C2×C3×D3—91no—
237C2×C3×D3—121no—
238C2×C3×D3—121no—
239C2×C3×D3—181no—
240C2×C3×D3—181no—
241C2×C3×D3—181no—
242C2×C3×D3—361no—
243C32×C4—31no—
244C32×C4—31no—
245C32×C4—31no—
246C32×C4—61no—
247C32×C4—61no—
248C32×C4—61no—
249C32×C4—91no—
250C32×C4—121no—
251C3⋊Dic3—31no—
252C3⋊Dic3—31no—
253C3⋊Dic3—31no—
254C3⋊Dic3—31no—
255C3⋊Dic3—31no—
256C3⋊Dic3—31no—
257C3⋊Dic3—61no—
258C3⋊Dic3—61no—
259C3⋊Dic3—61no—
260C3⋊Dic3—61no—
261C3⋊Dic3—61no—
262C3⋊Dic3—61no—
263C3⋊Dic3—121no—
264C3⋊Dic3—121no—
265C3⋊Dic3D3211yescharacteristic
266C3×Dic3—21no—
267C3×Dic3—21no—
268C3×Dic3—21no—
269C3×Dic3—31no—
270C3×Dic3—31no—
271C3×Dic3—31no—
272C3×Dic3—31no—
273C3×Dic3—41no—
274C3×Dic3—61no—
275C3×Dic3—61no—
276C3×Dic3—61no—
277C3×Dic3—61no—
278C3×Dic3—91no—
279C3×Dic3—91no—
280C3×Dic3—91no—
281C3×Dic3—91no—
282C3×Dic3—91no—
283C3×Dic3—91no—
284C3×Dic3—121no—
285C3×Dic3—181no—
286C3×Dic3—181no—
287C3×Dic3—181no—
288C3×Dic3—181no—
289C3×Dic3—181no—
290C3×Dic3—181no—
291C3×Dic3—361no—
292C3×Dic3—361no—
293C3×Dic3D3211yescharacteristic
294C3×Dic3D3211yescharacteristic
295C3×Dic3D3211yescharacteristic
296C33—21no—
297C33—21no—
298C33—21no—
299C33—21no—
300C33—21no—
301C33—21no—
302C33—41no—
303C33—41no—
304C33—41no—
305C33—41no—
306C33—81no—
307C33#23511yescharacteristic, complemented
308C33#23711yescharacteristic, complemented
309C33#23711yescharacteristic, complemented
310C33#23911yescharacteristic, complemented
311C3×Q8—271no—
312C3×D4—271no—
313C3×D4—271no—
314C2×C3×C4—271no—
315#67—91no—
316#67—91no—
317#67—91no—
318#67—271no—
319#67—271no—
320#67—271no—
321#67—541no—
322C2×Dic3—91no—
323C2×Dic3—271no—
324C2×Dic3—271no—
325C2×Dic3—271no—
326C2×Dic3—541no—
327D12—91no—
328D12—91no—
329D12—91no—
330D12—181no—
331D12—271no—
332C4×D3—91no—
333C4×D3—91no—
334C4×D3—181no—
335C4×D3—271no—
336C4×D3—271no—
337C4×D3—271no—
338C4×D3—271no—
339C4×D3—271no—
340C4×D3—541no—
341Dic6—91no—
342Dic6—91no—
343Dic6—91no—
344Dic6—181no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32—21no—
349C2×C32—21no—
350C2×C32—21no—
351C2×C32—21no—
352C2×C32—21no—
353C2×C32—21no—
354C2×C32—21no—
355C2×C32—21no—
356C2×C32—21no—
357C2×C32—41no—
358C2×C32—41no—
359C2×C32—41no—
360C2×C32—41no—
361C2×C32—41no—
362C2×C32—41no—
363C2×C32—41no—
364C2×C32—41no—
365C2×C32—41no—
366C2×C32—41no—
367C2×C32—41no—
368C2×C32—81no—
369C2×C32—81no—
370C2×C32—81no—
371C2×C32—81no—
372C2×C32—81no—
373C2×C32—81no—
374C2×C32—81no—
375C2×C32—181no—
376C2×C32—181no—
377C2×C32C2×D3211yescharacteristic
378C2×C32C2×D3211yescharacteristic
379C2×C32C2×D3211yescharacteristic
380C2×C32C2×D3211yescharacteristic
381C2×C32C2×D3211yescharacteristic
382C2×C32C2×D3211yescharacteristic
383C3⋊D3—21no—
384C3⋊D3—21no—
385C3⋊D3—61no—
386C3⋊D3—62no—
387C3⋊D3—61no—
388C3⋊D3—61no—
389C3⋊D3—121no—
390C3⋊D3—121no—
391C3⋊D3—122no—
392C3×D3—62no—
393C3×D3—62no—
394C3×D3—62no—
395C3×D3—62no—
396C3×D3—61no—
397C3×D3—61no—
398C3×D3—61no—
399C3×D3—61no—
400C3×D3—61no—
401C3×D3—61no—
402C3×D3—61no—
403C3×D3—61no—
404C3×D3—121no—
405C3×D3—121no—
406C3×D3—122no—
407C3×D3—121no—
408C3×D3—121no—
409C3×D3—122no—
410C3×D3—182no—
411C3×D3—181no—
412C3×D3—181no—
413C3×D3—181no—
414C3×D3—361no—
415C3×D3—361no—
416C3×D3—362no—
417#41—811noSylow
418C22×C3—91no—
419C22×C3—91no—
420C22×C3—91no—
421C22×C3—91no—
422C22×C3—181no—
423C22×C3—181no—
424C22×C3—271no—
425C2×D3—31no—
426C2×D3—31no—
427C2×D3—31no—
428C2×D3—31no—
429C2×D3—61no—
430C2×D3—61no—
431C2×D3—91no—
432C2×D3—91no—
433C2×D3—91no—
434C2×D3—181no—
435C2×D3—181no—
436C2×D3—181no—
437C2×D3—361no—
438C3×C4—31no—
439C3×C4—31no—
440C3×C4—31no—
441C3×C4—61no—
442C3×C4—61no—
443C3×C4—61no—
444C3×C4—91no—
445C3×C4—91no—
446C3×C4—121no—
447C3×C4—181no—
448C3×C4—271no—
449C3×C4—271no—
450Dic3—31no—
451Dic3—31no—
452Dic3—61no—
453Dic3—91no—
454Dic3—91no—
455Dic3—91no—
456Dic3—91no—
457Dic3—91no—
458Dic3—91no—
459Dic3—181no—
460Dic3—181no—
461Dic3—181no—
462Dic3—181no—
463Dic3—181no—
464Dic3—181no—
465Dic3—361no—
466Dic3—361no—
467Dic3#111311yescharacteristic
468C32—21no—
469C32—21no—
470C32—21no—
471C32—21no—
472C32—21no—
473C32—21no—
474C32—21no—
475C32—21no—
476C32—21no—
477C32—21no—
478C32—21no—
479C32—21no—
480C32—41no—
481C32—41no—
482C32—41no—
483C32—41no—
484C32—41no—
485C32—41no—
486C32—41no—
487C32—41no—
488C32—41no—
489C32—41no—
490C32—41no—
491C32—81no—
492C32—81no—
493C32—81no—
494C32—81no—
495C32—81no—
496C32—81no—
497C32—81no—
498C32#379511yescharacteristic, complemented
499C32#379611yescharacteristic, complemented
500C32#379611yescharacteristic, complemented
501C32#379911yescharacteristic, complemented
502C32#380411yescharacteristic, complemented
503C32#380511yescharacteristic, complemented
504Q8—271no—
505D4—271no—
506D4—271no—
507D4—811no—
508C2×C4—271no—
509C2×C4—811no—
510C2×C4—811no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—41no—
518C2×C3—41no—
519C2×C3—41no—
520C2×C3—41no—
521C2×C3—81no—
522C2×C3—182no—
523C2×C3—181no—
524C2×C3—181no—
525C2×C3—181no—
526C2×C3—181no—
527C2×C3—361no—
528C2×C3—541no—
529C2×C3D3311yescharacteristic
530C2×C3D3311yescharacteristic
531C2×C3D3311yescharacteristic
532C2×C3C2×#111311yescharacteristic
533D3—62no—
534D3—61no—
535D3—61no—
536D3—61no—
537D3—61no—
538D3—121no—
539D3—182no—
540D3—181no—
541D3—181no—
542D3—181no—
543D3—361no—
544D3—361no—
545D3—362no—
546C22—91no—
547C22—91no—
548C22—271no—
549C4—31no—
550C4—91no—
551C4—271no—
552C4—271no—
553C3—21no—
554C3—21no—
555C3—21no—
556C3—21no—
557C3—21no—
558C3—21no—
559C3—41no—
560C3—41no—
561C3—41no—
562C3—41no—
563C3—81no—
564C3#8896111yescharacteristic, complemented
565C3#8896211yescharacteristic, complemented
566C3#8896411yescharacteristic, complemented
567C3#8904111yescharacteristic, complemented
568C2—181no—
569C2—181no—
570C2—541no—
571C2D3×#111311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D3×#1113
commutator, Fitting, socle, cosocleC2×C34C23
hypocenterC34#41
LCSG ▷ C2×C34 ▷ C34
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #10620157C2semidirect
2. #10620155C2semidirect
3. #10620154C2semidirect
4. C3×#6295C2semidirect
5. C3×#6293C2semidirect
6. C3×#6292C2semidirect
7. C3×Dic3×C3⋊D3C2semidirect
25. #6295D3semidirect
32. #6293D3semidirect
33. #6292D3semidirect
38. Dic3×C3⋊D3D3semidirect
113. C34#41semidirect
307. C33#235semidirect
308. C33#237semidirect
309. C33#237semidirect
310. C33#239semidirect
498. C32#3795semidirect
499. C32#3796semidirect
500. C32#3796semidirect
501. C32#3799semidirect
502. C32#3804semidirect
503. C32#3805semidirect
564. C3#88961semidirect
565. C3#88962semidirect
566. C3#88964semidirect
567. C3#89041semidirect

Maximal subgroups

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

subgroupindex
#106201572
#106201552
#106201542
C3×#62952
C3×#62932
C3×#62922
C3×Dic3×C3⋊D32
#890413
#889643
#889623
#889613