Finite Group Databasebeta

← #13177423

Subgroups — #13177423

Order 1728.

2948 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×#89031C211yesmaximal, characteristic, complemented
3C3×#64148C211yesmaximal, characteristic, complemented
4C32×#935C211yesmaximal, characteristic, complemented
5#11723639C211yesmaximal, characteristic, complemented
6#11723639C211yesmaximal, characteristic, complemented
7#11723627C211yesmaximal, characteristic, complemented
8#11723624C211yesmaximal, characteristic, complemented
9#11723622C211yesmaximal, characteristic, complemented
10C2×#88804C211yesmaximal, characteristic, complemented
11#11723592C211yesmaximal, characteristic, complemented
12#11723498C211yesmaximal, characteristic, complemented
13#11723486C211yesmaximal, characteristic, complemented
14#11723472C211yesmaximal, characteristic, complemented
15#11723442C211yesmaximal, characteristic, complemented
16#10596125—31nomaximal
17#10595163—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C23×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×#6312C2211yescharacteristic
23D4×C3⋊(C3⋊D3)—24no—
24C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
25C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
26C2×C3×#638C2211yescharacteristic, complemented
27C2×C3×#638C2211yescharacteristic, complemented
28C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
29C22×C32×Dic3C2211yescharacteristic, complemented
30C2×#6293C2211yescharacteristic, complemented
31C2×#6292C2211yescharacteristic
32C2×#6292C2211yescharacteristic, complemented
33C2×#6292C2211yescharacteristic, complemented
34C2×#6289C2211yescharacteristic, complemented
35C2×#6289C2211yescharacteristic, complemented
36#89031—24no—
37C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
38C3×#3757C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic, complemented
40C3×#3750C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42C32×#217C2211yescharacteristic, complemented
43C32×#217C2211yescharacteristic, complemented
44C32×Dic3⋊C4C2211yescharacteristic, complemented
45C32×Dic3⋊C4C2211yescharacteristic, complemented
46#88806C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53#88804C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C2×D4×C3⋊D3—34no—
57C2×D4×C3⋊D3—64no—
58C2×#3828—31no—
59C2×#3804—34no—
60C32×#123—31no—
61#64148D311yescharacteristic, complemented
62C2×#3752—31no—
63#64105—31no—
64#64104—31no—
65#64103—31no—
66#64102—31no—
67#64094—31no—
68#64093—31no—
69#64091—31no—
70#64091—31no—
71#64090—31no—
72C22⋊C4×C3⋊D3—31no—
73C3×#939—34no—
74C3×#935D314yescomplemented
75#63981—34no—
76#63981—34no—
77#63974—34no—
78#63971—34no—
79C2×#3722—34no—
80#63953—34no—
81#63952—34no—
82#63910—34no—
83#63897—34no—
84#63881—34no—
85#63865—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—22no—
90C22×C3⋊(C3⋊D3)—22no—
91C22×C3⋊(C3⋊D3)—22no—
92C22×C3⋊(C3⋊D3)—41no—
93C22×C3⋊(C3⋊D3)—41no—
94C22×C3⋊(C3⋊D3)C2311yescharacteristic
95C22×C3⋊(C3⋊D3)C2311yescharacteristic
96C22×C3⋊(C3⋊D3)C2311yescharacteristic
97C22×C3×C3⋊D3C2311yescharacteristic
98C33×D4—22no—
99C2×C33×C4C2311yescharacteristic
100#6312—22no—
101#6312D414yescomplemented
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C4⋊(C3⋊(C3⋊D3))—22no—
104C4×C3⋊(C3⋊D3)—22no—
105C3×#638—22no—
106C3×#638—41no—
107C2×C3×C3⋊Dic3—41no—
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C32×Dic3—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116#6293—22no—
117#6292—22no—
118#6292—22no—
119#6292—41no—
120#6289—22no—
121#6289—41no—
122Dic3×C3⋊D3—22no—
123#5654—94no—
124#5610—91no—
125C23×C3⋊D3—31no—
126C23×C3⋊D3—31no—
127C23×C3⋊D3—34no—
128C23×C3⋊D3—34no—
129C23×C3⋊D3—64no—
130C23×C3⋊D3—64no—
131C2×C32×D4—24no—
132C2×C32×D4C2×D314yes—
133C2×C32×D4C2×D311yescharacteristic
134C22×C32×C4—31no—
135C2×#638—31no—
136C2×#638—34no—
137C2×#638—31no—
138C2×#638—34no—
139C2×#638—64no—
140C2×#638—64no—
141C2×#638C2×D311yescharacteristic, complemented
142C2×#638C2×D311yescharacteristic, complemented
143C22×C3⋊Dic3C2×D311yescharacteristic, complemented
144D4×C3⋊D3—64no—
145D4×C3⋊D3—616no—
146D4×C3⋊D3—632no—
147#3828—64no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4⋊(C3⋊D3)—34no—
152C2×C4⋊(C3⋊D3)—31no—
153C2×C4⋊(C3⋊D3)—64no—
154C2×C4×C3⋊D3—31no—
155C2×C4×C3⋊D3—31no—
156C2×C4×C3⋊D3—34no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—31no—
159C2×C4×C3⋊D3—64no—
160C2×#634—31no—
161C2×C3×#67—34no—
162C2×C3×#67—34no—
163C22×C3×Dic3—34no—
164C22×C3×Dic3C2×D314yescomplemented
165C2×#627—34no—
166C2×#626—34no—
167C2×#626—34no—
168C2×#626—34no—
169C2×#624—34no—
170C2×#624—34no—
171#3804—616no—
172C2×D3×Dic3—34no—
173C32×C4⋊C4—31no—
174C32×C4⋊C4—31no—
175C32×C22⋊C4—31no—
176C32×C22⋊C4—31no—
177C32×C22⋊C4—31no—
178#3757C2×D311yescharacteristic, complemented
179#3752—31no—
180#3752—31no—
181#3752—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—31no—
186#3752C2×D311yescharacteristic, complemented
187#3750—31no—
188#3750C2×D311yescharacteristic, complemented
189C4×C3⋊Dic3—31no—
190C3×#217—34no—
191C3×#217C2×D314yescomplemented
192C3×#217C2×D314yescomplemented
193C3×#217C2×D314yescomplemented
194C3×(C2×D3)⋊C4—34no—
195C3×Dic3⋊C4—34no—
196C3×Dic3⋊C4C2×D314yescomplemented
197C3×Dic3⋊C4C2×D314yescomplemented
198#3724—34no—
199#3722—34no—
200#3722—34no—
201#3722—34no—
202#3722—34no—
203#3722—34no—
204#3722—34no—
205#3722—34no—
206Dic32—34no—
207C22×C33—21no—
208C22×C33—21no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33C2×D412yes—
213C22×C33C2411yescharacteristic
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)—21no—
216C2×C3⋊(C3⋊D3)—21no—
217C2×C3⋊(C3⋊D3)—21no—
218C2×C3⋊(C3⋊D3)—21no—
219C2×C3⋊(C3⋊D3)—21no—
220C2×C3⋊(C3⋊D3)—21no—
221C2×C3⋊(C3⋊D3)—44no—
222C2×C3⋊(C3⋊D3)—44no—
223C2×C3⋊(C3⋊D3)C2×D412yes—
224C2×C3⋊(C3⋊D3)#4112yescomplemented
225C2×C3×C3⋊D3—21no—
226C2×C3×C3⋊D3—21no—
227C2×C3×C3⋊D3—21no—
228C33×C4—21no—
229C3⋊(C3⋊Dic3)C2×D412yes—
230C3×C3⋊Dic3—21no—
231C3×C3⋊Dic3—21no—
232C3×C3⋊Dic3—21no—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C32×Dic3—21no—
237C2×#237—91no—
238C2×D3×D4—94no—
239C2×D3×D4—91no—
240C2×D3×D4—184no—
241C2×#235—94no—
242C3×#123—34no—
243C3×#121—91no—
244#939—34no—
245#939—91no—
246#937—91no—
247#937—91no—
248#935C3⋊D311yescharacteristic, complemented
249C4×#67—91no—
250C2×(C2×D3)⋊C4—94no—
251C2×(C2×D3)⋊C4—91no—
252#896—94no—
253#896—91no—
254#895—94no—
255#894—94no—
256#894—91no—
257#893—94no—
258#885—94no—
259#885—91no—
260#884—94no—
261#884—91no—
262#882—94no—
263#882—94no—
264#67⋊C4—94no—
265#67⋊C4—91no—
266D3×C22⋊C4—94no—
267D3×C22⋊C4—91no—
268C23×C32—24no—
269C23×C32—24no—
270C23×C32C22×D314yes—
271C23×C32C22×D314yes—
272C23×C32C22×D311yescharacteristic
273C23×C32C22×D311yescharacteristic
274C22×C3⋊D3—31no—
275C22×C3⋊D3—31no—
276C22×C3⋊D3—31no—
277C22×C3⋊D3—34no—
278C22×C3⋊D3—34no—
279C22×C3⋊D3—34no—
280C22×C3⋊D3—64no—
281C22×C3⋊D3—64no—
282C22×C3⋊D3—64no—
283C22×C3⋊D3—62no—
284C22×C3⋊D3—62no—
285C22×C3⋊D3—62no—
286C22×C3⋊D3—68no—
287C22×C3⋊D3—616no—
288C22×C3⋊D3—616no—
289C22×C3⋊D3—68no—
290C22×C3⋊D3—62no—
291C22×C3⋊D3—68no—
292C22×C3⋊D3—68no—
293C22×C3⋊D3—128no—
294C22×C3⋊D3—128no—
295C22×C3⋊D3—121no—
296C22×C3⋊D3—121no—
297C22×C3⋊D3—124no—
298C22×C3⋊D3—124no—
299C22×C3⋊D3—128no—
300C22×C3⋊D3—128no—
301C22×C3⋊D3C22×D311yescharacteristic
302C22×C3×D3—34no—
303C32×D4—216no—
304C32×D4—28no—
305C32×D4—22no—
306C2×C32×C4—24no—
307C2×C32×C4—31no—
308C2×C32×C4—31no—
309C2×C32×C4—31no—
310C2×C32×C4—31no—
311C2×C32×C4—62no—
312C2×C32×C4C22×D314yes—
313C2×C32×C4C22×D311yescharacteristic
314#638—22no—
315#638—34no—
316#638—316no—
317#638—41no—
318#638—616no—
319#638—62no—
320#638—68no—
321#638—616no—
322C2×C3⋊Dic3—31no—
323C2×C3⋊Dic3—34no—
324C2×C3⋊Dic3—41no—
325C2×C3⋊Dic3—64no—
326C2×C3⋊Dic3C22×D311yescharacteristic
327C2×C3⋊Dic3C22×D311yescharacteristic
328C2×C3⋊Dic3C22×D311yescharacteristic
329C4⋊(C3⋊D3)—62no—
330C4⋊(C3⋊D3)—68no—
331C4⋊(C3⋊D3)—616no—
332C4⋊(C3⋊D3)—62no—
333C4⋊(C3⋊D3)—62no—
334C4⋊(C3⋊D3)—121no—
335C4×C3⋊D3—62no—
336C4×C3⋊D3—62no—
337C4×C3⋊D3—68no—
338C4×C3⋊D3—62no—
339C4×C3⋊D3—616no—
340C4×C3⋊D3—121no—
341#634—62no—
342C3×#67—68no—
343C3×#67—124no—
344C2×C3×Dic3—28no—
345C2×C3×Dic3—34no—
346C2×C3×Dic3—34no—
347C2×C3×Dic3—34no—
348C2×C3×Dic3—124no—
349C2×C3×Dic3C22×D314yes—
350C2×C3×Dic3C22×D314yes—
351C2×C3×Dic3C22×D314yes—
352C2×C3×Dic3C22×D314yes—
353#627—68no—
354#626—68no—
355#626—68no—
356#626—124no—
357#624—68no—
358#624—124no—
359D3×Dic3—68no—
360#546—271noSylow
361C2×C33—22no—
362C2×C33—41no—
363C2×C33C22×D411yescharacteristic
364C2×C33C2×#4111yescharacteristic
365C2×C33H(5,𝔽2)11yescharacteristic
366C3⋊(C3⋊D3)—22no—
367C3⋊(C3⋊D3)—22no—
368C3⋊(C3⋊D3)—41no—
369C3×C3⋊D3—41no—
370C23×D3—94no—
371C23×D3—94no—
372C23×D3—91no—
373C23×D3—91no—
374C23×D3—184no—
375C23×D3—184no—
376C2×C3×D4—24no—
377C2×C3×D4—91no—
378C2×C3×D4—91no—
379C2×C3×D4D3214yes—
380C2×C3×D4C2×C3⋊D311yescharacteristic
381C22×C3×C4—34no—
382C22×C3×C4—91no—
383C2×#67—34no—
384C2×#67—34no—
385C2×#67—94no—
386C2×#67—91no—
387C2×#67—94no—
388C2×#67—91no—
389C2×#67—91no—
390C2×#67—91no—
391C2×#67—91no—
392C2×#67—184no—
393C2×#67—184no—
394C22×Dic3—34no—
395C22×Dic3—91no—
396C22×Dic3C2×C3⋊D311yescharacteristic, complemented
397#237—184no—
398D3×D4—1816no—
399D3×D4—184no—
400D3×D4—1832no—
401#235—1816no—
402C2×D12—94no—
403C2×D12—94no—
404C2×D12—94no—
405C2×D12—91no—
406C2×D12—94no—
407C2×D12—184no—
408C2×C4×D3—94no—
409C2×C4×D3—94no—
410C2×C4×D3—94no—
411C2×C4×D3—91no—
412C2×C4×D3—91no—
413C2×C4×D3—94no—
414C2×C4×D3—91no—
415C2×C4×D3—184no—
416C2×Dic6—94no—
417C2×Dic6—91no—
418C3×C4⋊C4—34no—
419C3×C4⋊C4—34no—
420C3×C4⋊C4—91no—
421C3×C22⋊C4—34no—
422C3×C22⋊C4—34no—
423C3×C22⋊C4—34no—
424C3×C22⋊C4—91no—
425C3×C22⋊C4—91no—
426#217—34no—
427#217C2×C3⋊D311yescharacteristic, complemented
428#217C2×C3⋊D311yescharacteristic, complemented
429#217C2×C3⋊D311yescharacteristic, complemented
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—94no—
432(C2×D3)⋊C4—94no—
433(C2×D3)⋊C4—94no—
434(C2×D3)⋊C4—94no—
435(C2×D3)⋊C4—94no—
436(C2×D3)⋊C4—94no—
437(C2×D3)⋊C4—94no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—91no—
445Dic3⋊C4—34no—
446Dic3⋊C4—94no—
447Dic3⋊C4—91no—
448Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
449Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
450C4×Dic3—94no—
451C4×Dic3—91no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—28no—
455C22×C32—24no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—24no—
460C22×C32—28no—
461C22×C32—24no—
462C22×C32—24no—
463C22×C32—24no—
464C22×C32—24no—
465C22×C32—44no—
466C22×C32—44no—
467C22×C32—44no—
468C22×C32—44no—
469C22×C32D3×D418yes—
470C22×C32D3×D412yes—
471C22×C32C23×D314yes—
472C22×C32C23×D311yescharacteristic
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3—21no—
476C2×C3⋊D3—32no—
477C2×C3⋊D3—32no—
478C2×C3⋊D3—38no—
479C2×C3⋊D3—38no—
480C2×C3⋊D3—68no—
481C2×C3⋊D3—68no—
482C2×C3⋊D3—68no—
483C2×C3⋊D3—68no—
484C2×C3⋊D3—64no—
485C2×C3⋊D3—61no—
486C2×C3⋊D3—61no—
487C2×C3⋊D3—61no—
488C2×C3⋊D3—61no—
489C2×C3⋊D3—64no—
490C2×C3⋊D3—68no—
491C2×C3⋊D3—64no—
492C2×C3⋊D3—61no—
493C2×C3⋊D3—61no—
494C2×C3⋊D3—61no—
495C2×C3⋊D3—64no—
496C2×C3⋊D3—64no—
497C2×C3⋊D3—64no—
498C2×C3⋊D3—64no—
499C2×C3⋊D3—124no—
500C2×C3⋊D3—124no—
501C2×C3⋊D3—124no—
502C2×C3⋊D3—124no—
503C2×C3⋊D3—124no—
504C2×C3⋊D3—1216no—
505C2×C3⋊D3—124no—
506C2×C3⋊D3—1216no—
507C2×C3⋊D3—1232no—
508C2×C3⋊D3—1232no—
509C2×C3×D3—64no—
510C2×C3×D3—64no—
511C2×C3×D3—64no—
512C32×C4—28no—
513C32×C4—24no—
514C32×C4—21no—
515C32×C4—61no—
516C32×C4—61no—
517C32×C4—61no—
518C32×C4—61no—
519C3⋊Dic3—21no—
520C3⋊Dic3—21no—
521C3⋊Dic3—21no—
522C3⋊Dic3—32no—
523C3⋊Dic3—38no—
524C3⋊Dic3—68no—
525C3×Dic3—24no—
526C3×Dic3—24no—
527C3×Dic3—24no—
528C3×Dic3—24no—
529C3×Dic3—64no—
530C3×Dic3—64no—
531C3×Dic3—64no—
532C2×#41—271no—
533C22×D4—271no—
534#124—271no—
535#123—31no—
536#123—271no—
537C22⋊Q8—271no—
538#121—91no—
539#121—271no—
540#121—271no—
541#120—271no—
542#120—271no—
543C4×D4—271no—
544C4×D4—271no—
545C2×C22⋊C4—271no—
546C2×C22⋊C4—271no—
547C33#54611yescharacteristic, complemented, Sylow
548C23×C3—24no—
549C23×C3—24no—
550C23×C3—91no—
551C23×C3C2×D3214yes—
552C23×C3C2×D3214yes—
553C23×C3C22×C3⋊D311yescharacteristic
554C23×C3C22×C3⋊D311yescharacteristic
555C22×D3—34no—
556C22×D3—94no—
557C22×D3—94no—
558C22×D3—91no—
559C22×D3—91no—
560C22×D3—94no—
561C22×D3—91no—
562C22×D3—184no—
563C22×D3—184no—
564C22×D3—184no—
565C22×D3—188no—
566C22×D3—182no—
567C22×D3—182no—
568C22×D3—182no—
569C22×D3—188no—
570C22×D3—188no—
571C22×D3—1816no—
572C22×D3—1816no—
573C22×D3—188no—
574C22×D3—182no—
575C22×D3—368no—
576C22×D3—368no—
577C22×D3—364no—
578C22×D3—364no—
579C22×D3—361no—
580C22×D3—361no—
581C22×D3—368no—
582C22×D3—368no—
583C3×D4—216no—
584C3×D4—28no—
585C3×D4—22no—
586C3×D4—182no—
587C3×D4—361no—
588C2×C3×C4—24no—
589C2×C3×C4—34no—
590C2×C3×C4—34no—
591C2×C3×C4—34no—
592C2×C3×C4—34no—
593C2×C3×C4—68no—
594C2×C3×C4—91no—
595C2×C3×C4—91no—
596C2×C3×C4—91no—
597C2×C3×C4—361no—
598C2×C3×C4C2×D3214yes—
599C2×C3×C4C22×C3⋊D311yescharacteristic
600#67—68no—
601#67—916no—
602#67—94no—
603#67—124no—
604#67—1816no—
605#67—182no—
606#67—182no—
607#67—188no—
608#67—182no—
609#67—1816no—
610#67—361no—
611C2×Dic3—22no—
612C2×Dic3—34no—
613C2×Dic3—34no—
614C2×Dic3—34no—
615C2×Dic3—94no—
616C2×Dic3—91no—
617C2×Dic3—124no—
618C2×Dic3—184no—
619C2×Dic3—182no—
620C2×Dic3C22×C3⋊D311yescharacteristic
621C2×Dic3C22×C3⋊D311yescharacteristic
622C2×Dic3C22×C3⋊D311yescharacteristic
623C2×Dic3C22×C3⋊D311yescharacteristic
624D12—188no—
625D12—182no—
626D12—1816no—
627D12—188no—
628D12—188no—
629D12—364no—
630C4×D3—182no—
631C4×D3—188no—
632C4×D3—188no—
633C4×D3—182no—
634C4×D3—188no—
635C4×D3—1816no—
636C4×D3—361no—
637C4×D3—364no—
638Dic6—182no—
639Dic6—188no—
640C2×C32—22no—
641C2×C32—24no—
642C2×C32—24no—
643C2×C32—24no—
644C2×C32—28no—
645C2×C32—48no—
646C2×C32—48no—
647C2×C32—44no—
648C2×C32—41no—
649C2×C32C2×D3×D414yes—
650C2×C32C2×D3×D411yescharacteristic
651C2×C32#100411yescharacteristic
652C2×C32D3×#4114yes—
653C2×C32D3×#4111yescharacteristic
654C2×C32#100914yes—
655C3⋊D3—41no—
656C3⋊D3—616no—
657C3⋊D3—68no—
658C3⋊D3—62no—
659C3⋊D3—62no—
660C3⋊D3—68no—
661C3⋊D3—128no—
662C3⋊D3—128no—
663C3⋊D3—124no—
664C3⋊D3—121no—
665C3×D3—124no—
666C24—271no—
667C24—271no—
668#41—544no—
669C2×Q8—271no—
670C2×D4—91no—
671C2×D4—91no—
672C2×D4—271no—
673C2×D4—271no—
674C2×D4—271no—
675C2×D4—271no—
676C2×D4—271no—
677C2×D4—271no—
678C2×D4—544no—
679C2×D4D3×C3⋊D311yescharacteristic
680C22×C4—31no—
681C22×C4—91no—
682C22×C4—271no—
683C22×C4—271no—
684C22×C4—271no—
685C22×C4—271no—
686C4⋊C4—31no—
687C4⋊C4—31no—
688C4⋊C4—91no—
689C4⋊C4—271no—
690C22⋊C4—31no—
691C22⋊C4—31no—
692C22⋊C4—31no—
693C22⋊C4—91no—
694C22⋊C4—91no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C22⋊C4—271no—
702C42—271no—
703C22×C3—24no—
704C22×C3—24no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—28no—
708C22×C3—24no—
709C22×C3—24no—
710C22×C3—24no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—24no—
715C22×C3—28no—
716C22×C3—44no—
717C22×C3—44no—
718C22×C3—44no—
719C22×C3—44no—
720C22×C3—181no—
721C22×C3—181no—
722C22×C3—181no—
723C22×C3#381118yes—
724C22×C3D4×C3⋊D312yes—
725C22×C3C22×D3214yes—
726C22×C3C23×C3⋊D311yescharacteristic
727C2×D3—64no—
728C2×D3—64no—
729C2×D3—64no—
730C2×D3—98no—
731C2×D3—98no—
732C2×D3—92no—
733C2×D3—92no—
734C2×D3—188no—
735C2×D3—188no—
736C2×D3—188no—
737C2×D3—188no—
738C2×D3—184no—
739C2×D3—184no—
740C2×D3—184no—
741C2×D3—184no—
742C2×D3—181no—
743C2×D3—181no—
744C2×D3—181no—
745C2×D3—181no—
746C2×D3—188no—
747C2×D3—184no—
748C2×D3—184no—
749C2×D3—184no—
750C2×D3—181no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—364no—
754C2×D3—364no—
755C2×D3—364no—
756C2×D3—364no—
757C2×D3—364no—
758C2×D3—3616no—
759C2×D3—364no—
760C2×D3—3616no—
761C2×D3—3632no—
762C2×D3—3632no—
763C3×C4—28no—
764C3×C4—24no—
765C3×C4—21no—
766C3×C4—64no—
767C3×C4—64no—
768C3×C4—64no—
769C3×C4—64no—
770C3×C4—181no—
771C3×C4—181no—
772C3×C4—181no—
773Dic3—21no—
774Dic3—21no—
775Dic3—21no—
776Dic3—21no—
777Dic3—64no—
778Dic3—64no—
779Dic3—64no—
780Dic3—98no—
781Dic3—92no—
782Dic3—188no—
783C32—24no—
784C32#561011yescharacteristic, complemented
785C32#565414yescomplemented
786C23—91no—
787C23—271no—
788C23—271no—
789C23—271no—
790C23—542no—
791C23—542no—
792C23—542no—
793C23—542no—
794C23—1081no—
795C23—1081no—
796C23C2×D3×C3⋊D311yescharacteristic
797C23C2×D3×C3⋊D311yescharacteristic
798Q8—542no—
799D4—22no—
800D4—182no—
801D4—274no—
802D4—361no—
803D4—542no—
804D4—542no—
805D4—542no—
806D4—542no—
807D4—1081no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—62no—
813C2×C4—91no—
814C2×C4—91no—
815C2×C4—91no—
816C2×C4—271no—
817C2×C4—361no—
818C2×C4—542no—
819C2×C4—542no—
820C2×C4—542no—
821C2×C4—1081no—
822C2×C4C2×D3×C3⋊D311yescharacteristic
823C2×C3—22no—
824C2×C3—28no—
825C2×C3—24no—
826C2×C3—24no—
827C2×C3—24no—
828C2×C3—48no—
829C2×C3—48no—
830C2×C3—41no—
831C2×C3—44no—
832C2×C3—361no—
833C2×C3#6431214yes—
834C2×C3#6431414yes—
835C2×C3C2×#381114yes—
836C2×C3C2×D4×C3⋊D311yescharacteristic
837C2×C3#41×C3⋊D311yescharacteristic
838C2×C3#6436611yescharacteristic
839D3—124no—
840D3—1816no—
841D3—182no—
842D3—182no—
843D3—188no—
844D3—188no—
845D3—368no—
846D3—368no—
847D3—361no—
848D3—364no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—181no—
855C22—181no—
856C22—181no—
857C22—272no—
858C22—272no—
859C22—541no—
860C22—541no—
861C22—541no—
862C22—541no—
863C22—541no—
864C22—541no—
865C22—541no—
866C22—1084no—
867C22—1084no—
868C22#8903912yes—
869C22C22×D3×C3⋊D311yescharacteristic
870C4—21no—
871C4—61no—
872C4—61no—
873C4—61no—
874C4—61no—
875C4—181no—
876C4—181no—
877C4—181no—
878C4—272no—
879C3—24no—
880C3#1059516314yescomplemented
881C3#1059612511yescharacteristic, complemented
882C2—22no—
883C2—41no—
884C2—361no—
885C2—542no—
886C2—542no—
887C2—1081no—
888C2#1172458611yescharacteristic
889C2#1172458911yescharacteristic
890C2C2×#8903911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊(C3⋊D3)C2semidirect
2. C2×#89031C2semidirect
3. C3×#64148C2semidirect
4. C32×#935C2semidirect
5. #11723639C2semidirect
6. #11723639C2semidirect
7. #11723627C2semidirect
8. #11723624C2semidirect
9. #11723622C2semidirect
10. C2×#88804C2semidirect
11. #11723592C2semidirect
12. #11723498C2semidirect
13. #11723486C2semidirect
14. #11723472C2semidirect
15. #11723442C2semidirect
26. C2×C3×#638C22semidirect
27. C2×C3×#638C22semidirect
28. C22×C3×C3⋊Dic3C22semidirect
29. C22×C32×Dic3C22semidirect
30. C2×#6293C22semidirect
32. C2×#6292C22semidirect
33. C2×#6292C22semidirect
34. C2×#6289C22semidirect
35. C2×#6289C22semidirect
37. C2×Dic3×C3⋊D3C22semidirect
38. C3×#3757C22semidirect
39. C3×#3752C22semidirect
40. C3×#3750C22semidirect
41. C32×#217C22semidirect
42. C32×#217C22semidirect
43. C32×#217C22semidirect
44. C32×Dic3⋊C4C22semidirect
45. C32×Dic3⋊C4C22semidirect
46. #88806C22semidirect
50. #88804C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
53. #88804C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
61. #64148D3semidirect
74. C3×#935D3semidirect
101. #6312D4semidirect
141. C2×#638C2×D3semidirect
142. C2×#638C2×D3semidirect
143. C22×C3⋊Dic3C2×D3semidirect
164. C22×C3×Dic3C2×D3semidirect
178. #3757C2×D3semidirect
186. #3752C2×D3semidirect
188. #3750C2×D3semidirect
191. C3×#217C2×D3semidirect
192. C3×#217C2×D3semidirect
193. C3×#217C2×D3semidirect
196. C3×Dic3⋊C4C2×D3semidirect
197. C3×Dic3⋊C4C2×D3semidirect
224. C2×C3⋊(C3⋊D3)#41semidirect
248. #935C3⋊D3semidirect
396. C22×Dic3C2×C3⋊D3semidirect
427. #217C2×C3⋊D3semidirect
428. #217C2×C3⋊D3semidirect
429. #217C2×C3⋊D3semidirect
448. Dic3⋊C4C2×C3⋊D3semidirect
449. Dic3⋊C4C2×C3⋊D3semidirect
547. C33#546semidirect
784. C32#5610semidirect
785. C32#5654semidirect
880. C3#10595163semidirect
881. C3#10596125semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊(C3⋊D3)2
C2×#890312
C3×#641482
C32×#9352
#117236392
#117236272
#117236242
#117236222
C2×#888042
#117235922
#117234982
#117234862
#117234722
#117234422
#105961253
#105951633