Finite Group Databasebeta

← #13155539

Subgroups — #13155539

Order 1728.

614 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723452C211yesmaximal, characteristic
2#11722078C211yesmaximal, characteristic, complemented
3#11722024C211yesmaximal, characteristic
4#11722024C211yesmaximal, characteristic
5C3×#63572C211yesmaximal, characteristic, complemented
6C3×#63554C211yesmaximal, characteristic, complemented
7C3×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#10590648—31nomaximal
9#10590647—31nomaximal
10#10590298—31nomaximal
11C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
12C3×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
15C32×C4×Dic3C2211yescharacteristic
16C2×C32×C3⋊C8C2211yescharacteristic
17C2×C32×C3⋊C8C2211yescharacteristic
18#88806C411yescharacteristic
19#88806C411yescharacteristic
20#88804C411yescharacteristic
21#88804C411yescharacteristic
22#64081—31no—
23#63874—31no—
24#63874—31no—
25#63874—61no—
26#63647—31no—
27#63647—31no—
28C3×#815—31no—
29C3×Dic3⋊C8—31no—
30C3×Dic3⋊C8—31no—
31C3×C8×Dic3—31no—
32C3×#803—31no—
33C3×C4×C3⋊C8—31no—
34#63572—31no—
35#63572D311yescharacteristic, complemented
36Dic3⋊(C3⋊C8)—31no—
37Dic3⋊(C3⋊C8)—31no—
38#63557—31no—
39#63557—31no—
40#63557—31no—
41#63557—31no—
42#63557—61no—
43#63557—61no—
44#63554D311yescharacteristic, complemented
45Dic3×C3⋊C8D311yescharacteristic, complemented
46C22×C3⋊(C3⋊D3)C2×C411yescharacteristic
47C2×C33×C4C2311yescharacteristic
48C2×C3⋊(C3⋊Dic3)C2×C411yescharacteristic
49C4×C3⋊(C3⋊D3)—21no—
50C4×C3⋊(C3⋊D3)—21no—
51C2×C3×C3⋊Dic3C2×C411yescharacteristic
52C2×C3×C3⋊Dic3C2×C411yescharacteristic
53C2×C32×Dic3C2×C411yescharacteristic
54C2×C32×Dic3C2×C411yescharacteristic
55C3×C3⋊(C3⋊C8)—21no—
56C3×C3⋊(C3⋊C8)—21no—
57C32×C3⋊C8—21no—
58C32×C3⋊C8—21no—
59#4840—91no—
60#4709—91no—
61#4690—91no—
62C2×C4×C3⋊D3—31no—
63C2×C4×C3⋊D3—31no—
64C2×C4×C3⋊D3—31no—
65C2×C4×C3⋊D3—61no—
66C2×C4×C3⋊D3—61no—
67C2×C4×C3⋊D3—61no—
68C2×C4×C3⋊D3—121no—
69C2×C32×C8—31no—
70C2×C32×C8—31no—
71C32×C42—31no—
72#3752—31no—
73#3752—31no—
74#3750—31no—
75#3750—31no—
76C4×C3⋊Dic3C2×D311yescharacteristic
77C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
78C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
79C3×C4×Dic3—21no—
80C3×C4×Dic3—31no—
81C3×C4×Dic3—31no—
82C3×C4×Dic3—61no—
83C3×C4×Dic3C2×D311yescharacteristic
84C3×C4×Dic3C2×D311yescharacteristic
85C2×C3×C3⋊C8—21no—
86C2×C3×C3⋊C8—21no—
87C2×C3×C3⋊C8—31no—
88C2×C3×C3⋊C8—31no—
89C2×C3×C3⋊C8—31no—
90C2×C3×C3⋊C8—31no—
91C2×C3×C3⋊C8—61no—
92C2×C3×C3⋊C8—61no—
93C2×C3×C3⋊C8C2×D311yescharacteristic
94C2×C3×C3⋊C8C2×D311yescharacteristic
95C2×C3×C3⋊C8C2×D311yescharacteristic
96C2×C3×C3⋊C8C2×D311yescharacteristic
97#3724—31no—
98#3724—31no—
99#3724—31no—
100#3724—31no—
101#3724—61no—
102#3724—61no—
103#3722—31no—
104#3722—31no—
105#3722—31no—
106#3722—31no—
107#3722—61no—
108#3722—61no—
109C22×C33C22×C411yescharacteristic
110C2×C3⋊(C3⋊D3)—21no—
111C2×C3⋊(C3⋊D3)—21no—
112C2×C3⋊(C3⋊D3)—21no—
113C33×C4#4111yescharacteristic
114C33×C4#4111yescharacteristic
115C3⋊(C3⋊Dic3)—21no—
116C3×C3⋊Dic3—21no—
117C3×C3⋊Dic3—21no—
118C32×Dic3—21no—
119C32×Dic3—21no—
120#872—91no—
121#872—91no—
122#872—91no—
123#872—181no—
124C3×C4⋊C8—91no—
125C3×#97—91no—
126C3×C4×C8—91no—
127(C2×D3)⋊C8—91no—
128(C2×D3)⋊C8—91no—
129(C2×D3)⋊C8—91no—
130(C2×D3)⋊C8—91no—
131(C2×D3)⋊C8—91no—
132(C2×D3)⋊C8—91no—
133(C2×D3)⋊C8—181no—
134(C2×D3)⋊C8—181no—
135#815—31no—
136Dic3⋊C8—31no—
137Dic3⋊C8—31no—
138Dic3⋊C8—91no—
139Dic3⋊C8—91no—
140C8×Dic3—31no—
141C4⋊(C3⋊C8)—91no—
142#803—31no—
143C4×C3⋊C8—31no—
144C22×C3⋊D3—31no—
145C22×C3⋊D3—31no—
146C22×C3⋊D3—31no—
147C22×C3⋊D3—61no—
148C22×C3⋊D3—61no—
149C22×C3⋊D3—61no—
150C22×C3⋊D3—121no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—31no—
155C2×C32×C4—31no—
156C2×C32×C4—41no—
157C2×C32×C4C22×D311yescharacteristic
158C2×C32×C4C22×D311yescharacteristic
159C2×C32×C4C22×D311yescharacteristic
160C2×C3⋊Dic3—31no—
161C2×C3⋊Dic3—31no—
162C2×C3⋊Dic3—31no—
163C2×C3⋊Dic3—61no—
164C2×C3⋊Dic3—61no—
165C2×C3⋊Dic3—61no—
166C2×C3⋊Dic3—121no—
167C2×C3⋊Dic3C4×D311yescharacteristic
168C2×C3⋊Dic3C4×D311yescharacteristic
169C4×C3⋊D3—61no—
170C4×C3⋊D3—61no—
171C4×C3⋊D3—62no—
172C4×C3⋊D3—62no—
173C4×C3⋊D3—61no—
174C4×C3⋊D3—61no—
175C4×C3⋊D3—61no—
176C4×C3⋊D3—61no—
177C4×C3⋊D3—121no—
178C4×C3⋊D3—121no—
179C4×C3⋊D3—121no—
180C4×C3⋊D3—121no—
181C4×C3⋊D3—122no—
182C4×C3⋊D3—122no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—31no—
186C2×C3×Dic3—31no—
187C2×C3×Dic3—31no—
188C2×C3×Dic3—31no—
189C2×C3×Dic3—61no—
190C2×C3×Dic3—61no—
191C2×C3×Dic3C4×D311yescharacteristic
192C2×C3×Dic3C4×D311yescharacteristic
193C2×C3×Dic3C4×D311yescharacteristic
194C2×C3×Dic3C4×D311yescharacteristic
195C32×C8—61no—
196C32×C8—61no—
197C3⋊(C3⋊C8)—21no—
198C3⋊(C3⋊C8)—21no—
199C3×C3⋊C8—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8—21no—
202C3×C3⋊C8—21no—
203C3×C3⋊C8—41no—
204C3×C3⋊C8—41no—
205C3×C3⋊C8—61no—
206C3×C3⋊C8—61no—
207C3×C3⋊C8—61no—
208C3×C3⋊C8—61no—
209C3×C3⋊C8—121no—
210C3×C3⋊C8—121no—
211#433—271noSylow
212C2×C33#11711yescharacteristic
213C2×C33#13111yescharacteristic
214C2×C33#13111yescharacteristic
215C3⋊(C3⋊D3)—41no—
216C2×C4×D3—91no—
217C2×C4×D3—91no—
218C2×C4×D3—91no—
219C2×C4×D3—181no—
220C2×C4×D3—181no—
221C2×C4×D3—181no—
222C2×C4×D3—361no—
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225C2×C3×C8—31no—
226C2×C3×C8—31no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C2×C3×C8—91no—
230C2×C3×C8—91no—
231C3×C42—31no—
232C3×C42—31no—
233C3×C42—61no—
234C3×C42—91no—
235(C2×D3)⋊C4—91no—
236(C2×D3)⋊C4—91no—
237(C2×D3)⋊C4—91no—
238(C2×D3)⋊C4—91no—
239(C2×D3)⋊C4—91no—
240(C2×D3)⋊C4—91no—
241(C2×D3)⋊C4—181no—
242(C2×D3)⋊C4—181no—
243Dic3⋊C4—91no—
244Dic3⋊C4—91no—
245Dic3⋊C4—91no—
246Dic3⋊C4—91no—
247Dic3⋊C4—91no—
248Dic3⋊C4—91no—
249Dic3⋊C4—181no—
250Dic3⋊C4—181no—
251C4×Dic3—31no—
252C4×Dic3—31no—
253C4×Dic3—61no—
254C4×Dic3D3211yescharacteristic
255C2×C3⋊C8—31no—
256C2×C3⋊C8—31no—
257C2×C3⋊C8—31no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8D3211yescharacteristic
262C2×C3⋊C8D3211yescharacteristic
263C22×C32—21no—
264C22×C32—21no—
265C22×C32—21no—
266C22×C32—41no—
267C22×C32C2×C4×D311yescharacteristic
268C22×C32C2×C4×D311yescharacteristic
269C22×C32C2×C4×D311yescharacteristic
270C2×C3⋊D3—61no—
271C2×C3⋊D3—61no—
272C2×C3⋊D3—61no—
273C2×C3⋊D3—62no—
274C2×C3⋊D3—62no—
275C2×C3⋊D3—62no—
276C2×C3⋊D3—61no—
277C2×C3⋊D3—61no—
278C2×C3⋊D3—61no—
279C2×C3⋊D3—61no—
280C2×C3⋊D3—61no—
281C2×C3⋊D3—61no—
282C2×C3⋊D3—121no—
283C2×C3⋊D3—121no—
284C2×C3⋊D3—121no—
285C2×C3⋊D3—121no—
286C2×C3⋊D3—121no—
287C2×C3⋊D3—121no—
288C2×C3⋊D3—122no—
289C2×C3⋊D3—122no—
290C2×C3⋊D3—122no—
291C32×C4—21no—
292C32×C4—21no—
293C32×C4—21no—
294C32×C4—21no—
295C32×C4—21no—
296C32×C4—21no—
297C32×C4—41no—
298C32×C4—41no—
299C32×C4—61no—
300C32×C4—61no—
301C32×C4#23511yescharacteristic
302C32×C4#23511yescharacteristic
303C32×C4#23511yescharacteristic
304C32×C4#23511yescharacteristic
305C32×C4#23711yescharacteristic
306C32×C4#23911yescharacteristic
307C3⋊Dic3—21no—
308C3⋊Dic3—21no—
309C3⋊Dic3—61no—
310C3⋊Dic3—62no—
311C3⋊Dic3—61no—
312C3⋊Dic3—61no—
313C3⋊Dic3—121no—
314C3⋊Dic3—121no—
315C3⋊Dic3—122no—
316C3×Dic3—21no—
317C3×Dic3—21no—
318C3×Dic3—21no—
319C3×Dic3—21no—
320C3×Dic3—41no—
321C3×Dic3—41no—
322C3×Dic3—61no—
323C3×Dic3—61no—
324C3×Dic3—61no—
325C3×Dic3—61no—
326C3×Dic3—121no—
327C3×Dic3—121no—
328#117—271no—
329C4⋊C8—91no—
330C4⋊C8—271no—
331C22⋊C8—271no—
332C22⋊C8—271no—
333#97—91no—
334C4×C8—91no—
335C33#43311yescharacteristic, complemented, Sylow
336C22×D3—91no—
337C22×D3—91no—
338C22×D3—91no—
339C22×D3—181no—
340C22×D3—181no—
341C22×D3—181no—
342C22×D3—361no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—31no—
347C2×C3×C4—31no—
348C2×C3×C4—31no—
349C2×C3×C4—31no—
350C2×C3×C4—41no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—91no—
354C2×C3×C4—91no—
355C2×C3×C4C2×D3211yescharacteristic
356C2×C3×C4C2×D3211yescharacteristic
357C2×C3×C4C2×D3211yescharacteristic
358C2×Dic3—31no—
359C2×Dic3—31no—
360C2×Dic3—31no—
361C2×Dic3—31no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—91no—
365C2×Dic3—91no—
366C2×Dic3—91no—
367C2×Dic3—181no—
368C2×Dic3—181no—
369C2×Dic3—181no—
370C2×Dic3—361no—
371C2×Dic3#62411yescharacteristic
372C2×Dic3#62411yescharacteristic
373C4×D3—182no—
374C4×D3—182no—
375C4×D3—181no—
376C4×D3—181no—
377C4×D3—181no—
378C4×D3—181no—
379C4×D3—181no—
380C4×D3—181no—
381C4×D3—361no—
382C4×D3—361no—
383C4×D3—361no—
384C4×D3—361no—
385C4×D3—362no—
386C4×D3—362no—
387C3×C8—61no—
388C3×C8—61no—
389C3×C8—61no—
390C3×C8—61no—
391C3×C8—121no—
392C3×C8—121no—
393C3×C8—181no—
394C3×C8—181no—
395C3⋊C8—21no—
396C3⋊C8—21no—
397C3⋊C8—61no—
398C3⋊C8—61no—
399C3⋊C8—61no—
400C3⋊C8—61no—
401C3⋊C8—121no—
402C3⋊C8—121no—
403C2×C32—21no—
404C2×C32—21no—
405C2×C32—21no—
406C2×C32—21no—
407C2×C32—21no—
408C2×C32—21no—
409C2×C32—21no—
410C2×C32—21no—
411C2×C32—21no—
412C2×C32—41no—
413C2×C32—41no—
414C2×C32—41no—
415C2×C32#87211yescharacteristic
416C2×C32#87211yescharacteristic
417C2×C32#89211yescharacteristic
418C2×C32#90111yescharacteristic
419C2×C32#90111yescharacteristic
420C2×C32#90111yescharacteristic
421C2×C32#90711yescharacteristic
422C2×C32#90711yescharacteristic
423C2×C32#90711yescharacteristic
424C3⋊D3—122no—
425C3⋊D3—122no—
426C3⋊D3—122no—
427C3⋊D3—124no—
428C3⋊D3—121no—
429C3⋊D3—121no—
430C3⋊D3—121no—
431C22×C4—271no—
432C2×C8—31no—
433C2×C8—31no—
434C2×C8—91no—
435C2×C8—91no—
436C4⋊C4—271no—
437C4⋊C4—271no—
438C22⋊C4—271no—
439C22⋊C4—271no—
440C42—31no—
441C42—91no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—41no—
446C22×C3C4×D3211yescharacteristic
447C22×C3C4×D3211yescharacteristic
448C22×C3C2×#62411yescharacteristic
449C2×D3—182no—
450C2×D3—182no—
451C2×D3—182no—
452C2×D3—181no—
453C2×D3—181no—
454C2×D3—181no—
455C2×D3—181no—
456C2×D3—181no—
457C2×D3—181no—
458C2×D3—181no—
459C2×D3—181no—
460C2×D3—181no—
461C2×D3—361no—
462C2×D3—361no—
463C2×D3—361no—
464C2×D3—361no—
465C2×D3—361no—
466C2×D3—361no—
467C2×D3—362no—
468C2×D3—362no—
469C2×D3—362no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—41no—
477C3×C4—41no—
478C3×C4—61no—
479C3×C4—61no—
480C3×C4—61no—
481C3×C4—61no—
482C3×C4—121no—
483C3×C4—121no—
484C3×C4—181no—
485C3×C4—181no—
486C3×C4#379811yescharacteristic
487C3×C4#379811yescharacteristic
488C3×C4#379911yescharacteristic
489C3×C4#379911yescharacteristic
490C3×C4#380411yescharacteristic
491C3×C4#380411yescharacteristic
492Dic3—21no—
493Dic3—21no—
494Dic3—61no—
495Dic3—61no—
496Dic3—61no—
497Dic3—61no—
498Dic3—121no—
499Dic3—121no—
500Dic3—182no—
501Dic3—181no—
502Dic3—181no—
503Dic3—181no—
504Dic3—361no—
505Dic3—361no—
506Dic3—362no—
507C32—21no—
508C32—21no—
509C32—21no—
510C32—41no—
511C32#469011yescharacteristic, complemented
512C32#470911yescharacteristic, complemented
513C32#484011yescharacteristic, complemented
514C23—271no—
515C2×C4—31no—
516C2×C4—31no—
517C2×C4—91no—
518C2×C4—91no—
519C2×C4—271no—
520C2×C4—541no—
521C2×C4—541no—
522C2×C4D3311yescharacteristic
523C8—61no—
524C8—61no—
525C8—181no—
526C8—181no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—41no—
537C2×C3—41no—
538C2×C3—41no—
539C2×C3#6380311yescharacteristic
540C2×C3#6380411yescharacteristic
541C2×C3#6380411yescharacteristic
542C2×C3#6380511yescharacteristic
543C2×C3#6381711yescharacteristic
544C2×C3#6381711yescharacteristic
545C2×C3#6383611yescharacteristic
546C2×C3#6383611yescharacteristic
547C2×C3#6387411yescharacteristic
548D3—362no—
549D3—362no—
550D3—362no—
551D3—364no—
552D3—361no—
553D3—361no—
554D3—361no—
555C22—541no—
556C22—541no—
557C22—541no—
558C22D3×#62411yescharacteristic
559C4—61no—
560C4—61no—
561C4—181no—
562C4—181no—
563C4—541no—
564C4#8895911yescharacteristic
565C4#8896511yescharacteristic
566C3—21no—
567C3—21no—
568C3—21no—
569C3—41no—
570C3#1059029811yescharacteristic, complemented
571C3#1059064711yescharacteristic, complemented
572C3#1059064811yescharacteristic, complemented
573C2—1081no—
574C2#1172282411yescharacteristic
575C2#1172282511yescharacteristic
576C2#1172291811yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2×C4D33
commutator, socleC22×C33C22×C4
Fitting, cosocleC2×C33×C4C23
prime radicalC22×C3⋊(C3⋊D3)C2×C4
hypocenterC33#433
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11722078C2semidirect
5. C3×#63572C2semidirect
6. C3×#63554C2semidirect
7. C3×Dic3×C3⋊C8C2semidirect
35. #63572D3semidirect
44. #63554D3semidirect
45. Dic3×C3⋊C8D3semidirect
335. C33#433semidirect
511. C32#4690semidirect
512. C32#4709semidirect
513. C32#4840semidirect
570. C3#10590298semidirect
571. C3#10590647semidirect
572. C3#10590648semidirect

Maximal subgroups

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

subgroupindex
#117234522
#117220782
#117220242
C3×#635722
C3×#635542
C3×Dic3×C3⋊C82
#105906483
#105906473
#105902983