Finite Group Databasebeta

← #13177313

Subgroups — #13177313

Order 1728.

2380 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic, complemented
2C2×#89031C211yesmaximal, characteristic, complemented
3#11723971C211yesmaximal, characteristic, complemented
4C3×C4×#638C211yesmaximal, characteristic, complemented
5C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6#11723630C211yesmaximal, characteristic, complemented
7#11723612C211yesmaximal, characteristic, complemented
8#11723542C211yesmaximal, characteristic, complemented
9C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11723525C211yesmaximal, characteristic, complemented
11#11723523C211yesmaximal, characteristic, complemented
12#11723520C211yesmaximal, characteristic, complemented
13#11723491C211yesmaximal, characteristic, complemented
14#11723461C211yesmaximal, characteristic, complemented
15#11723419C211yesmaximal, characteristic, complemented
16#10595961—31nomaximal
17#10595073—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×#6312C2211yescharacteristic, complemented
23C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic
25C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
26C22×C32×Dic3C2211yescharacteristic, complemented
27D3×#638—24no—
28C2×#6293C2211yescharacteristic, complemented
29C2×#6292C2211yescharacteristic, complemented
30C2×#6291C2211yescharacteristic
31C2×#6291C2211yescharacteristic
32C2×#6291C2211yescharacteristic, complemented
33C2×#6290C2211yescharacteristic
34C2×#6289C2211yescharacteristic, complemented
35#89031—24no—
36C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
37C2×D3×C3⋊Dic3C2211yescharacteristic
38#88859C2211yescharacteristic, complemented
39#88859C2211yescharacteristic, complemented
40C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
41C3×#3757C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic, complemented
43C3×#3750C2211yescharacteristic, complemented
44C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×(C2×D3)⋊C4C2211yescharacteristic
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
49#88807C2211yescharacteristic, complemented
50#88807C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C22×#638—31no—
56C2×#3828—31no—
57C2×D3×#67—34no—
58C2×#3804—34no—
59C2×C32×C22⋊C4—31no—
60#64162—31no—
61#64139—31no—
62#64139—34no—
63#64139—64no—
64#64138—31no—
65C4×#638D311yescharacteristic, complemented
66#64094—31no—
67#64093—31no—
68#64093—31no—
69#64092—31no—
70#64091—31no—
71#64090—31no—
72C22⋊C4×C3⋊D3—31no—
73#64087—31no—
74C3×C4×#67—34no—
75C2×C3×(C2×D3)⋊C4D314yescomplemented
76#63977—34no—
77#63966—34no—
78#63923—34no—
79D3×(C2×D3)⋊C4—34no—
80#63910—34no—
81#63906—34no—
82#63893—34no—
83#63891—34no—
84#63880—34no—
85#63852—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C32×D3—22no—
91C22×C32×D3—22no—
92C22×C32×D3—41no—
93C22×C32×D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×C33×C4—41no—
99C2×C33×C4C2311yescharacteristic
100C2×C33×C4C2311yescharacteristic
101#6312—22no—
102#6312—22no—
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C4⋊(C3⋊(C3⋊D3))—41no—
106C3×#638D414yescomplemented
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C3×C4×C3⋊D3—41no—
111C2×C32×Dic3—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114#6293—22no—
115#6292—22no—
116#6291—22no—
117#6291—22no—
118#6291—41no—
119#6290—22no—
120#6289—22no—
121Dic3×C3⋊D3—22no—
122D3×C3⋊Dic3—22no—
123#5554—91no—
124#5490—94no—
125C24×C32—31no—
126C23×C3⋊D3—31no—
127C23×C3×D3C2×D314yes—
128C22×D32—34no—
129C22×C32×C4—24no—
130C22×C32×C4—31no—
131C22×C32×C4C2×D314yescomplemented
132C22×C32×C4C2×D311yescharacteristic, complemented
133C2×#638—31no—
134C2×#638—31no—
135C2×#638—34no—
136C2×#638—34no—
137C2×#638—31no—
138C2×#638—31no—
139C2×#638—31no—
140C2×#638—31no—
141C2×#638—64no—
142C2×#638—64no—
143C2×#638—64no—
144C2×#638C2×D311yescharacteristic
145C22×C3⋊Dic3—31no—
146#3828—64no—
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)—34no—
150C2×C4⋊(C3⋊D3)—64no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
154C2×#634—31no—
155C2×C3×#67—34no—
156C22×C3×Dic3C2×D314yescomplemented
157C2×C3×C4×D3—34no—
158D3×#67—616no—
159C2×#627—34no—
160C2×#626—34no—
161C2×#626—34no—
162C2×#626—34no—
163C2×#626—34no—
164C2×#625—34no—
165C2×#624—34no—
166#3804—616no—
167C2×D3×Dic3—34no—
168C2×D3×Dic3—34no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171C32×C22⋊C4—31no—
172C32×C22⋊C4—31no—
173#3757—31no—
174#3757—31no—
175#3757C2×D311yescharacteristic, complemented
176#3752—31no—
177#3752—31no—
178#3752—34no—
179#3752—34no—
180#3752—31no—
181#3752—31no—
182#3752—64no—
183#3752—64no—
184#3752C2×D311yescharacteristic, complemented
185C4⋊(C3⋊Dic3)—31no—
186C4⋊(C3⋊Dic3)—34no—
187C4⋊(C3⋊Dic3)—64no—
188#3750—31no—
189#3750—31no—
190#3750C2×D311yescharacteristic, complemented
191C4×C3⋊Dic3C2×D311yescharacteristic, complemented
192C3×#217—34no—
193C3×(C2×D3)⋊C4—34no—
194C3×(C2×D3)⋊C4C2×D314yes—
195C3×(C2×D3)⋊C4C2×D314yes—
196C3×(C2×D3)⋊C4C2×D314yescomplemented
197C3×(C2×D3)⋊C4C2×D314yescomplemented
198C3×Dic3⋊C4—34no—
199C3×C4×Dic3—34no—
200Dic3⋊Dic3—34no—
201Dic3⋊Dic3—34no—
202#3722—34no—
203#3722—34no—
204(C2×D3)⋊Dic3—34no—
205(C2×D3)⋊Dic3—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33C2×D412yes—
209C22×C33C2411yescharacteristic
210C2×C3⋊(C3⋊D3)—21no—
211C2×C3⋊(C3⋊D3)—21no—
212C2×C3⋊(C3⋊D3)—21no—
213C2×C3⋊(C3⋊D3)—21no—
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)—21no—
216C2×C3×C3⋊D3—21no—
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3C2×D412yes—
219C2×C32×D3—21no—
220C2×C32×D3—21no—
221C2×C32×D3—21no—
222C2×C32×D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—44no—
225C2×C32×D3#4112yescomplemented
226D3×C3⋊D3—44no—
227C33×C4—21no—
228C33×C4—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3×C3⋊Dic3—21no—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3C2×D412yes—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C22×#67—94no—
237C2×#237—91no—
238C2×D3×D4—91no—
239C2×#235—94no—
240C3×C4×D4—91no—
241C2×C3×C22⋊C4—34no—
242#953—94no—
243#930—94no—
244#930—91no—
245#930—91no—
246#930—184no—
247#929—94no—
248C4×#67—34no—
249C2×(C2×D3)⋊C4—91no—
250C2×(C2×D3)⋊C4C3⋊D311yescharacteristic, complemented
251#897—91no—
252#895—91no—
253#886—91no—
254#886—91no—
255#885—94no—
256#884—94no—
257#884—94no—
258#883—94no—
259#882—94no—
260#882—91no—
261#882—91no—
262#67⋊C4—94no—
263D3×C22⋊C4—94no—
264#878—94no—
265#875—91no—
266C4×D12—91no—
267C23×C32—24no—
268C23×C32—31no—
269C23×C32—31no—
270C23×C32—62no—
271C23×C32—62no—
272C23×C32—121no—
273C23×C32C22×D314yes—
274C23×C32C22×D311yescharacteristic
275C22×C3⋊D3—31no—
276C22×C3⋊D3—31no—
277C22×C3⋊D3—34no—
278C22×C3⋊D3—34no—
279C22×C3⋊D3—64no—
280C22×C3⋊D3—64no—
281C22×C3⋊D3—62no—
282C22×C3⋊D3—62no—
283C22×C3⋊D3—121no—
284C22×C3⋊D3C22×D311yescharacteristic
285C22×C3×D3—28no—
286C22×C3×D3—28no—
287C22×C3×D3—34no—
288C22×C3×D3—44no—
289C22×C3×D3C22×D314yes—
290C22×C3×D3C22×D314yes—
291C2×D32—68no—
292C2×D32—68no—
293C2×D32—124no—
294C2×C32×C4—24no—
295C2×C32×C4—24no—
296C2×C32×C4—31no—
297C2×C32×C4—31no—
298C2×C32×C4—41no—
299C2×C32×C4—44no—
300C2×C32×C4—48no—
301C2×C32×C4—62no—
302C2×C32×C4C22×D314yes—
303C2×C32×C4C22×D314yes—
304C2×C32×C4C22×D311yescharacteristic
305C2×C32×C4C22×D311yescharacteristic
306#638—62no—
307#638—62no—
308#638—62no—
309#638—62no—
310#638—62no—
311#638—68no—
312#638—68no—
313#638—128no—
314#638—128no—
315#638—121no—
316#638D1214yescomplemented
317C2×C3⋊Dic3—31no—
318C2×C3⋊Dic3—31no—
319C2×C3⋊Dic3—34no—
320C2×C3⋊Dic3—34no—
321C2×C3⋊Dic3—64no—
322C2×C3⋊Dic3—64no—
323C2×C3⋊Dic3—62no—
324C2×C3⋊Dic3C22×D311yescharacteristic
325C2×C3⋊Dic3C22×D311yescharacteristic
326C2×C3⋊Dic3C22×D311yescharacteristic
327C4⋊(C3⋊D3)—62no—
328C4⋊(C3⋊D3)—121no—
329C4⋊(C3⋊D3)—124no—
330C4⋊(C3⋊D3)—128no—
331C4×C3⋊D3—41no—
332C4×C3⋊D3—62no—
333C4×C3⋊D3—62no—
334#634—62no—
335C3×#67—316no—
336C2×C3×Dic3—28no—
337C2×C3×Dic3—34no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3—34no—
340C2×C3×Dic3C22×D314yes—
341C2×C3×Dic3C22×D314yes—
342C3×C4×D3—124no—
343#627—68no—
344#626—68no—
345#626—68no—
346#626—68no—
347#626—124no—
348#625—68no—
349#624—68no—
350D3×Dic3—68no—
351D3×Dic3—68no—
352#546—271noSylow
353C2×C33—22no—
354C2×C33C22×D411yescharacteristic
355C2×C33C2×#4111yescharacteristic
356C2×C33H(5,𝔽2)11yescharacteristic
357C3⋊(C3⋊D3)—41no—
358C3⋊(C3⋊D3)—41no—
359C3×C3⋊D3—22no—
360C32×D3—22no—
361C32×D3—41no—
362C24×C3—34no—
363C23×D3—94no—
364C23×D3—91no—
365C23×D3C2×C3⋊D311yescharacteristic
366C2×C3×D4—91no—
367C22×C3×C4—24no—
368C22×C3×C4—34no—
369C22×C3×C4—91no—
370C22×C3×C4D3214yescomplemented
371C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
372C2×#67—34no—
373C2×#67—94no—
374C2×#67—94no—
375C2×#67—94no—
376C2×#67—94no—
377C2×#67—94no—
378C2×#67—94no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—184no—
384C2×#67—184no—
385C2×#67—1816no—
386C22×Dic3—94no—
387C22×Dic3—91no—
388C22×Dic3C2×C3⋊D311yescharacteristic, complemented
389#237—184no—
390D3×D4—184no—
391#235—1816no—
392C2×D12—94no—
393C2×D12—91no—
394C2×D12—91no—
395C2×D12—91no—
396C2×D12—94no—
397C2×D12—91no—
398C2×D12—184no—
399C2×C4×D3—34no—
400C2×C4×D3—94no—
401C2×C4×D3—94no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×Dic6—94no—
405C2×Dic6—91no—
406C3×C4⋊C4—91no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—91no—
412C3×C22⋊C4—91no—
413C3×C42—91no—
414#217—34no—
415#217—94no—
416#217—94no—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—94no—
419(C2×D3)⋊C4—94no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4—94no—
423(C2×D3)⋊C4—94no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—184no—
429(C2×D3)⋊C4—184no—
430(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
431(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
432(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
433(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
434C4⋊Dic3—94no—
435C4⋊Dic3—91no—
436C4⋊Dic3—91no—
437C4⋊Dic3—91no—
438C4⋊Dic3—184no—
439Dic3⋊C4—34no—
440Dic3⋊C4—94no—
441Dic3⋊C4—94no—
442C4×Dic3—34no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—24no—
446C22×C32—28no—
447C22×C32—24no—
448C22×C32—24no—
449C22×C32—32no—
450C22×C32—44no—
451C22×C32—44no—
452C22×C32—61no—
453C22×C32—61no—
454C22×C32—61no—
455C22×C32—61no—
456C22×C32—61no—
457C22×C32—124no—
458C22×C32C2×D1212yes—
459C22×C32D3×D418yes—
460C22×C32C23×D314yes—
461C22×C32C23×D311yescharacteristic
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—61no—
465C2×C3⋊D3—61no—
466C2×C3⋊D3—61no—
467C2×C3⋊D3—61no—
468C2×C3⋊D3—61no—
469C2×C3⋊D3—61no—
470C2×C3⋊D3—64no—
471C2×C3⋊D3—64no—
472C2×C3⋊D3—64no—
473C2×C3⋊D3—64no—
474C2×C3⋊D3—64no—
475C2×C3⋊D3—64no—
476C2×C3⋊D3—124no—
477C2×C3⋊D3—124no—
478C2×C3⋊D3—124no—
479C2×C3⋊D3—124no—
480C2×C3⋊D3—124no—
481C2×C3⋊D3—124no—
482C2×C3⋊D3—124no—
483C2×C3⋊D3C2×D1212yes—
484C2×C3×D3—24no—
485C2×C3×D3—24no—
486C2×C3×D3—24no—
487C2×C3×D3—24no—
488C2×C3×D3—24no—
489C2×C3×D3—38no—
490C2×C3×D3—416no—
491C2×C3×D3—64no—
492C2×C3×D3—64no—
493C2×C3×D3#23518yescomplemented
494D32—1216no—
495C32×C4—28no—
496C32×C4—21no—
497C32×C4—24no—
498C32×C4—21no—
499C32×C4—24no—
500C32×C4—44no—
501C32×C4—61no—
502C32×C4—61no—
503C3⋊Dic3—21no—
504C3⋊Dic3—21no—
505C3⋊Dic3—61no—
506C3⋊Dic3—61no—
507C3⋊Dic3—64no—
508C3⋊Dic3—64no—
509C3⋊Dic3—124no—
510C3⋊Dic3—124no—
511C3⋊Dic3C2×D1212yes—
512C3×Dic3—24no—
513C3×Dic3—24no—
514C3×Dic3—38no—
515C3×Dic3—64no—
516C3×Dic3—64no—
517C2×#41—271no—
518C22×D4—271no—
519#124—271no—
520#123—271no—
521#123—271no—
522C22⋊Q8—271no—
523#121—271no—
524#121—271no—
525#121—271no—
526#120—271no—
527#120—271no—
528C4×D4—91no—
529C4×D4—271no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—271no—
532C33#54611yescharacteristic, complemented, Sylow
533C23×C3—24no—
534C23×C3—34no—
535C23×C3—34no—
536C23×C3—68no—
537C23×C3—68no—
538C23×C3—91no—
539C23×C3—124no—
540C23×C3C2×D3214yes—
541C23×C3C22×C3⋊D311yescharacteristic
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—34no—
545C22×D3—41no—
546C22×D3—94no—
547C22×D3—94no—
548C22×D3—91no—
549C22×D3—91no—
550C22×D3—184no—
551C22×D3—184no—
552C22×D3—182no—
553C22×D3—188no—
554C22×D3—188no—
555C22×D3—182no—
556C22×D3—361no—
557C22×D3—364no—
558C22×D3C22×C3⋊D311yescharacteristic
559C22×D3C22×C3⋊D311yescharacteristic
560C3×D4—94no—
561C2×C3×C4—24no—
562C2×C3×C4—24no—
563C2×C3×C4—34no—
564C2×C3×C4—34no—
565C2×C3×C4—44no—
566C2×C3×C4—41no—
567C2×C3×C4—48no—
568C2×C3×C4—68no—
569C2×C3×C4—91no—
570C2×C3×C4—91no—
571C2×C3×C4—91no—
572C2×C3×C4—361no—
573C2×C3×C4C2×D3214yes—
574C2×C3×C4C2×D3214yes—
575C2×C3×C4C22×C3⋊D311yescharacteristic
576C2×C3×C4C22×C3⋊D311yescharacteristic
577#67—316no—
578#67—182no—
579#67—188no—
580#67—188no—
581#67—182no—
582#67—188no—
583#67—188no—
584#67—188no—
585#67—182no—
586#67—182no—
587#67—368no—
588#67—368no—
589#67—364no—
590C2×Dic3—22no—
591C2×Dic3—34no—
592C2×Dic3—34no—
593C2×Dic3—34no—
594C2×Dic3—94no—
595C2×Dic3—94no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—184no—
599C2×Dic3—184no—
600C2×Dic3—182no—
601C2×Dic3—188no—
602C2×Dic3C22×C3⋊D311yescharacteristic
603C2×Dic3C22×C3⋊D311yescharacteristic
604D12—188no—
605D12—182no—
606D12—182no—
607D12—364no—
608D12—361no—
609D12—368no—
610D12—361no—
611C4×D3—124no—
612C4×D3—182no—
613C4×D3—188no—
614C4×D3—188no—
615C4×D3—182no—
616Dic6—182no—
617Dic6—188no—
618C2×C32—22no—
619C2×C32—24no—
620C2×C32—24no—
621C2×C32—24no—
622C2×C32—28no—
623C2×C32—48no—
624C2×C32—62no—
625C2×C32—121no—
626C2×C32C22×D1211yescharacteristic
627C2×C32C2×#23514yes—
628C2×C32C2×D3×D414yes—
629C2×C32#100414yes—
630C2×C32#100411yescharacteristic
631C2×C32D3×#4111yescharacteristic
632C3⋊D3—22no—
633C3⋊D3—121no—
634C3⋊D3—121no—
635C3⋊D3—124no—
636C3⋊D3—124no—
637C3⋊D3—244no—
638C3⋊D3—244no—
639C3×D3—28no—
640C3×D3—44no—
641C3×D3—68no—
642C24—31no—
643C24—271no—
644#41—544no—
645C2×Q8—271no—
646C2×D4—91no—
647C2×D4—271no—
648C2×D4—271no—
649C2×D4—271no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—271no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4—544no—
656C22×C4—31no—
657C22×C4—91no—
658C22×C4—271no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4D3×C3⋊D311yescharacteristic, complemented
662C4⋊C4—91no—
663C4⋊C4—271no—
664C4⋊C4—271no—
665C4⋊C4—271no—
666C22⋊C4—31no—
667C22⋊C4—31no—
668C22⋊C4—31no—
669C22⋊C4—31no—
670C22⋊C4—91no—
671C22⋊C4—91no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C42—91no—
679C22×C3—24no—
680C22×C3—24no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—24no—
684C22×C3—28no—
685C22×C3—38no—
686C22×C3—44no—
687C22×C3—44no—
688C22×C3—64no—
689C22×C3—64no—
690C22×C3—64no—
691C22×C3—64no—
692C22×C3—64no—
693C22×C3—92no—
694C22×C3—1216no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3D3×D1218yes—
698C22×C3D4×C3⋊D312yes—
699C22×C3C22×D3214yes—
700C22×C3C23×C3⋊D311yescharacteristic
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—38no—
707C2×D3—44no—
708C2×D3—64no—
709C2×D3—64no—
710C2×D3—184no—
711C2×D3—184no—
712C2×D3—184no—
713C2×D3—184no—
714C2×D3—184no—
715C2×D3—184no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—181no—
720C2×D3—181no—
721C2×D3—181no—
722C2×D3—364no—
723C2×D3—364no—
724C2×D3—364no—
725C2×D3—364no—
726C2×D3—364no—
727C2×D3—364no—
728C2×D3—364no—
729C2×D3—3616no—
730C2×D3#382812yescomplemented
731C3×C4—28no—
732C3×C4—24no—
733C3×C4—24no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—44no—
737C3×C4—64no—
738C3×C4—64no—
739C3×C4—92no—
740C3×C4—181no—
741C3×C4—181no—
742Dic3—21no—
743Dic3—21no—
744Dic3—38no—
745Dic3—64no—
746Dic3—64no—
747Dic3—184no—
748Dic3—184no—
749Dic3—181no—
750Dic3—181no—
751Dic3—364no—
752Dic3—364no—
753C32—24no—
754C32#549014yescomplemented
755C32#555411yescharacteristic, complemented
756C23—31no—
757C23—31no—
758C23—62no—
759C23—62no—
760C23—91no—
761C23—121no—
762C23—271no—
763C23—271no—
764C23—542no—
765C23—542no—
766C23—1081no—
767C23C2×D3×C3⋊D311yescharacteristic
768Q8—542no—
769D4—94no—
770D4—542no—
771D4—542no—
772D4—542no—
773D4—542no—
774D4—542no—
775D4—542no—
776D4—1081no—
777D4—1081no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—41no—
781C2×C4—62no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—91no—
785C2×C4—271no—
786C2×C4—271no—
787C2×C4—361no—
788C2×C4—542no—
789C2×C4—542no—
790C2×C4—542no—
791C2×C4C2×D3×C3⋊D311yescharacteristic
792C2×C4C2×D3×C3⋊D311yescharacteristic
793C2×C3—28no—
794C2×C3—22no—
795C2×C3—24no—
796C2×C3—24no—
797C2×C3—24no—
798C2×C3—48no—
799C2×C3—68no—
800C2×C3—124no—
801C2×C3—182no—
802C2×C3C2×D3×D1214yes—
803C2×C3D3×#23514yes—
804C2×C3#6433014yes—
805C2×C3C2×#382811yescharacteristic
806C2×C3C2×D4×C3⋊D311yescharacteristic
807C2×C3#6436111yescharacteristic
808D3—22no—
809D3—41no—
810D3—68no—
811D3—364no—
812D3—364no—
813D3—361no—
814D3—361no—
815D3—724no—
816D3—724no—
817C22—21no—
818C22—21no—
819C22—32no—
820C22—61no—
821C22—61no—
822C22—61no—
823C22—61no—
824C22—61no—
825C22—92no—
826C22—124no—
827C22—181no—
828C22—181no—
829C22—541no—
830C22—541no—
831C22—541no—
832C22—541no—
833C22—541no—
834C22—541no—
835C22—1084no—
836C22C3⋊D3×D1212yes—
837C22C22×D3×C3⋊D311yescharacteristic
838C4—21no—
839C4—21no—
840C4—61no—
841C4—61no—
842C4—92no—
843C4—181no—
844C4—181no—
845C4—541no—
846C4—541no—
847C3—24no—
848C3#1059507314yescomplemented
849C3#1059596111yescharacteristic, complemented
850C2—22no—
851C2—62no—
852C2—121no—
853C2—182no—
854C2—1081no—
855C2—1081no—
856C2C2×C3⋊D3×D1211yescharacteristic
857C2D3×#382811yescharacteristic
858C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×#638C2semidirect
2. C2×#89031C2semidirect
3. #11723971C2semidirect
4. C3×C4×#638C2semidirect
5. C2×C32×(C2×D3)⋊C4C2semidirect
6. #11723630C2semidirect
7. #11723612C2semidirect
8. #11723542C2semidirect
9. C3⋊D3×(C2×D3)⋊C4C2semidirect
10. #11723525C2semidirect
11. #11723523C2semidirect
12. #11723520C2semidirect
13. #11723491C2semidirect
14. #11723461C2semidirect
15. #11723419C2semidirect
20. C22×C33×C4C22semidirect
22. C2×#6312C22semidirect
23. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
25. C2×C3×C4×C3⋊D3C22semidirect
26. C22×C32×Dic3C22semidirect
28. C2×#6293C22semidirect
29. C2×#6292C22semidirect
32. C2×#6291C22semidirect
34. C2×#6289C22semidirect
36. C2×Dic3×C3⋊D3C22semidirect
38. #88859C22semidirect
39. #88859C22semidirect
40. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
41. C3×#3757C22semidirect
42. C3×#3752C22semidirect
43. C3×#3750C22semidirect
44. C3×C4×C3⋊Dic3C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. C32×(C2×D3)⋊C4C22semidirect
49. #88807C22semidirect
50. #88807C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
65. C4×#638D3semidirect
75. C2×C3×(C2×D3)⋊C4D3semidirect
106. C3×#638D4semidirect
131. C22×C32×C4C2×D3semidirect
132. C22×C32×C4C2×D3semidirect
153. C2×C4×C3⋊D3C2×D3semidirect
156. C22×C3×Dic3C2×D3semidirect
175. #3757C2×D3semidirect
184. #3752C2×D3semidirect
190. #3750C2×D3semidirect
191. C4×C3⋊Dic3C2×D3semidirect
196. C3×(C2×D3)⋊C4C2×D3semidirect
197. C3×(C2×D3)⋊C4C2×D3semidirect
225. C2×C32×D3#41semidirect
250. C2×(C2×D3)⋊C4C3⋊D3semidirect
316. #638D12semidirect
370. C22×C3×C4D32semidirect
371. C22×C3×C4C2×C3⋊D3semidirect
388. C22×Dic3C2×C3⋊D3semidirect
432. (C2×D3)⋊C4C2×C3⋊D3semidirect
433. (C2×D3)⋊C4C2×C3⋊D3semidirect
493. C2×C3×D3#235semidirect
532. C33#546semidirect
661. C22×C4D3×C3⋊D3semidirect
730. C2×D3#3828semidirect
754. C32#5490semidirect
755. C32#5554semidirect
848. C3#10595073semidirect
849. C3#10595961semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
C2×#890312
#117239712
C3×C4×#6382
C2×C32×(C2×D3)⋊C42
#117236302
#117236122
#117235422
C3⋊D3×(C2×D3)⋊C42
#117235252
#117235232
#117235202
#117234912
#117234612
#117234192
#105959613
#105950733