Finite Group Databasebeta

← #13177342

Subgroups — #13177342

Order 1728.

1876 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723971C211yesmaximal, characteristic, complemented
2C3×C4×#638C211yesmaximal, characteristic, complemented
3C32×#929C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723624C211yesmaximal, characteristic, complemented
6#11723599C211yesmaximal, characteristic, complemented
7#11723592C211yesmaximal, characteristic, complemented
8#11723542C211yesmaximal, characteristic, complemented
9C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11723512C211yesmaximal, characteristic, complemented
11#11723498C211yesmaximal, characteristic, complemented
12#11723483C211yesmaximal, characteristic, complemented
13#11723446C211yesmaximal, characteristic, complemented
14#11723430C211yesmaximal, characteristic, complemented
15#11723419C211yesmaximal, characteristic, complemented
16#10596128—31nomaximal
17#10595085—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic, complemented
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×#6293C2211yescharacteristic, complemented
27C2×#6292C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6289C2211yescharacteristic, complemented
30C2×Dic3×C3⋊D3C2211yescharacteristic
31#88859C2211yescharacteristic
32#88859C2211yescharacteristic, complemented
33C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
34C3×#3757C2211yescharacteristic, complemented
35C3×#3752C2211yescharacteristic
36C3×#3750C2211yescharacteristic, complemented
37C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
38C32×#217C2211yescharacteristic, complemented
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic, complemented
49#88803C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#123—31no—
54#64147—31no—
55#64146—31no—
56#64139—31no—
57#64139—34no—
58#64139—64no—
59C4×#638D311yescharacteristic, complemented
60#64107—31no—
61#64106—31no—
62#64103—31no—
63#64102—31no—
64#64094—31no—
65#64094—31no—
66#64093—31no—
67#64091—31no—
68C22⋊C4×C3⋊D3—31no—
69#64088—31no—
70C3×#929D314yescomplemented
71C3×C4×#67—34no—
72#63983—34no—
73#63971—34no—
74#63958—34no—
75#63953—34no—
76#63923—34no—
77D3×(C2×D3)⋊C4—34no—
78#63904—34no—
79#63897—34no—
80#63893—34no—
81#63868—34no—
82#63861—34no—
83#63852—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C32×D3C2311yescharacteristic
89C2×D3×C3⋊D3—22no—
90C2×D3×C3⋊D3—41no—
91C2×D3×C3⋊D3—41no—
92C2×C33×C4—41no—
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95#6312—41no—
96#6312—41no—
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C4⋊(C3⋊(C3⋊D3))—41no—
100C3×#638—22no—
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C3×C4×C3⋊D3—41no—
105C32×#67—41no—
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109#6293—41no—
110#6292—22no—
111#6291—41no—
112#6289—41no—
113Dic3×C3⋊D3—41no—
114#5657—94no—
115#5560—91no—
116C23×C3⋊D3—31no—
117C22×D32—34no—
118C2×C32×D4—31no—
119C22×C32×C4—24no—
120C22×C32×C4C2×D314yescomplemented
121C22×C32×C4C2×D311yescharacteristic, complemented
122C2×#638—31no—
123C2×#638—31no—
124C2×#638—34no—
125C2×#638—34no—
126C2×#638—31no—
127C2×#638—64no—
128C2×#638—64no—
129C2×#638C2×D311yescharacteristic
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4⋊(C3⋊D3)—34no—
133C2×C4⋊(C3⋊D3)—64no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3—31no—
136C2×C4×C3⋊D3C2×D311yescharacteristic
137C2×#634—31no—
138C2×C3×#67—34no—
139C2×C3×#67C2×D314yes—
140C2×C3×C4×D3—34no—
141C2×#627—34no—
142C2×#626—34no—
143C2×#626—34no—
144C2×#624—34no—
145C2×D3×Dic3—34no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C22⋊C4—31no—
149C32×C22⋊C4—31no—
150C32×C22⋊C4—31no—
151#3757—31no—
152#3757—31no—
153#3757C2×D311yescharacteristic, complemented
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—34no—
158#3752—34no—
159#3752—31no—
160#3752—31no—
161#3752—31no—
162#3752—31no—
163#3752—64no—
164#3752—64no—
165#3752C2×D311yescharacteristic
166C4⋊(C3⋊Dic3)—31no—
167C4⋊(C3⋊Dic3)—34no—
168C4⋊(C3⋊Dic3)—31no—
169C4⋊(C3⋊Dic3)—64no—
170#3750—31no—
171#3750C2×D311yescharacteristic, complemented
172C4×C3⋊Dic3—31no—
173C4×C3⋊Dic3C2×D311yescharacteristic, complemented
174C3×#217—34no—
175C3×#217C2×D314yescomplemented
176C3×(C2×D3)⋊C4—34no—
177C3×(C2×D3)⋊C4C2×D314yes—
178C3×(C2×D3)⋊C4C2×D314yes—
179C3×Dic3⋊C4—34no—
180C3×Dic3⋊C4C2×D314yescomplemented
181C3×Dic3⋊C4C2×D314yescomplemented
182C3×C4×Dic3—34no—
183#3724—34no—
184Dic3⋊Dic3—34no—
185#3722—34no—
186#3722—34no—
187#3722—34no—
188#3722—34no—
189(C2×D3)⋊Dic3—34no—
190(C2×D3)⋊Dic3—34no—
191(C2×D3)⋊Dic3—34no—
192Dic32—34no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33C2411yescharacteristic
197C2×C3⋊(C3⋊D3)—21no—
198C2×C3⋊(C3⋊D3)—21no—
199C2×C3⋊(C3⋊D3)—21no—
200C2×C3⋊(C3⋊D3)—21no—
201C2×C3⋊(C3⋊D3)—21no—
202C2×C3⋊(C3⋊D3)—21no—
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3—21no—
205C2×C3×C3⋊D3#4112yes—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209D3×C3⋊D3—44no—
210C33×C4—21no—
211C33×C4—21no—
212C3⋊(C3⋊Dic3)—21no—
213C3⋊(C3⋊Dic3)—21no—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#123—34no—
221C3×C4×D4—91no—
222#939—91no—
223#938—94no—
224#937—94no—
225#937—91no—
226#930—94no—
227#930—91no—
228#930—184no—
229#929C3⋊D311yescharacteristic, complemented
230C4×#67—34no—
231C4×#67—91no—
232C2×(C2×D3)⋊C4—91no—
233#898—94no—
234#898—91no—
235#897—94no—
236#894—94no—
237#894—91no—
238#893—94no—
239#885—94no—
240#885—94no—
241#885—91no—
242#884—94no—
243#884—91no—
244#882—94no—
245#882—91no—
246D3×C22⋊C4—94no—
247#879—94no—
248#878—91no—
249#876—91no—
250#875—91no—
251C23×C32—24no—
252C23×C32—31no—
253C23×C32C22×D314yes—
254C23×C32C22×D311yescharacteristic
255C22×C3⋊D3—31no—
256C22×C3⋊D3—31no—
257C22×C3⋊D3—34no—
258C22×C3⋊D3—34no—
259C22×C3⋊D3—64no—
260C22×C3⋊D3—64no—
261C22×C3⋊D3—62no—
262C22×C3⋊D3—121no—
263C22×C3⋊D3—121no—
264C22×C3⋊D3C22×D311yescharacteristic
265C22×C3×D3—34no—
266C22×C3×D3C22×D314yes—
267C2×D32—68no—
268C2×D32—124no—
269C2×D32—124no—
270C32×D4—121no—
271C2×C32×C4—24no—
272C2×C32×C4—24no—
273C2×C32×C4—31no—
274C2×C32×C4—31no—
275C2×C32×C4—31no—
276C2×C32×C4—41no—
277C2×C32×C4—44no—
278C2×C32×C4—48no—
279C2×C32×C4C22×D314yes—
280C2×C32×C4C22×D314yes—
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283#638—22no—
284#638—121no—
285#638—121no—
286#638—121no—
287#638—124no—
288#638—124no—
289#638—128no—
290#638—128no—
291C2×C3⋊Dic3—31no—
292C2×C3⋊Dic3—31no—
293C2×C3⋊Dic3—34no—
294C2×C3⋊Dic3—34no—
295C2×C3⋊Dic3—64no—
296C2×C3⋊Dic3—64no—
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C4⋊(C3⋊D3)—62no—
301C4⋊(C3⋊D3)—121no—
302C4⋊(C3⋊D3)—124no—
303C4⋊(C3⋊D3)—128no—
304C4×C3⋊D3—41no—
305C4×C3⋊D3—121no—
306C4×C3⋊D3—121no—
307#634—121no—
308C3×#67—44no—
309C3×#67—68no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3—34no—
313C2×C3×Dic3C22×D314yes—
314C2×C3×Dic3C22×D314yes—
315C2×C3×Dic3C22×D314yes—
316C3×C4×D3—124no—
317#627—124no—
318#626—68no—
319#626—124no—
320#624—124no—
321D3×Dic3—124no—
322#538—271noSylow
323C2×C33—41no—
324C2×C33C2×#4111yescharacteristic
325C2×C33H(5,𝔽2)11yescharacteristic
326C2×C33H(5,𝔽2)11yescharacteristic
327C3⋊(C3⋊D3)—41no—
328C3⋊(C3⋊D3)—41no—
329C3×C3⋊D3—22no—
330C32×D3—41no—
331C23×D3—94no—
332C23×D3—91no—
333C2×C3×D4—34no—
334C2×C3×D4—91no—
335C22×C3×C4—24no—
336C22×C3×C4—91no—
337C22×C3×C4D3214yescomplemented
338C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
339C2×#67—34no—
340C2×#67—94no—
341C2×#67—94no—
342C2×#67—94no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—184no—
347C2×#67—184no—
348C2×#67C2×C3⋊D311yescharacteristic
349C22×Dic3—91no—
350C2×D12—94no—
351C2×D12—91no—
352C2×D12—94no—
353C2×D12—91no—
354C2×D12—184no—
355C2×C4×D3—34no—
356C2×C4×D3—94no—
357C2×C4×D3—94no—
358C2×C4×D3—91no—
359C2×Dic6—94no—
360C2×Dic6—91no—
361C3×C4⋊C4—34no—
362C3×C4⋊C4—34no—
363C3×C4⋊C4—91no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—34no—
366C3×C22⋊C4—34no—
367C3×C22⋊C4—91no—
368C3×C22⋊C4—91no—
369C3×C42—91no—
370#217—34no—
371#217—94no—
372#217—94no—
373#217—91no—
374#217C2×C3⋊D311yescharacteristic, complemented
375(C2×D3)⋊C4—34no—
376(C2×D3)⋊C4—94no—
377(C2×D3)⋊C4—94no—
378(C2×D3)⋊C4—94no—
379(C2×D3)⋊C4—94no—
380(C2×D3)⋊C4—94no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—94no—
384(C2×D3)⋊C4—94no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—184no—
392(C2×D3)⋊C4—184no—
393(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
394(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
395C4⋊Dic3—94no—
396C4⋊Dic3—94no—
397C4⋊Dic3—91no—
398C4⋊Dic3—184no—
399Dic3⋊C4—34no—
400Dic3⋊C4—94no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
404Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
405C4×Dic3—34no—
406C4×Dic3—94no—
407C4×Dic3—91no—
408C22×C32—28no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—24no—
412C22×C32—21no—
413C22×C32—24no—
414C22×C32—24no—
415C22×C32—24no—
416C22×C32—44no—
417C22×C32—44no—
418C22×C32—61no—
419C22×C32—61no—
420C22×C32—61no—
421C22×C32C23×D314yes—
422C22×C32C23×D311yescharacteristic
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—61no—
426C2×C3⋊D3—61no—
427C2×C3⋊D3—61no—
428C2×C3⋊D3—61no—
429C2×C3⋊D3—61no—
430C2×C3⋊D3—61no—
431C2×C3⋊D3—64no—
432C2×C3⋊D3—64no—
433C2×C3⋊D3—64no—
434C2×C3⋊D3—64no—
435C2×C3⋊D3—64no—
436C2×C3⋊D3—64no—
437C2×C3⋊D3—124no—
438C2×C3⋊D3—124no—
439C2×C3⋊D3—124no—
440C2×C3⋊D3—124no—
441C2×C3⋊D3—124no—
442C2×C3⋊D3—124no—
443C2×C3⋊D3—124no—
444C2×C3⋊D3#23512yes—
445C2×C3×D3—24no—
446C2×C3×D3—24no—
447C2×C3×D3—24no—
448C2×C3×D3—38no—
449C2×C3×D3—64no—
450C2×C3×D3—64no—
451D32—1216no—
452C32×C4—28no—
453C32×C4—21no—
454C32×C4—24no—
455C32×C4—21no—
456C32×C4—24no—
457C32×C4—44no—
458C32×C4—61no—
459C32×C4—61no—
460C32×C4—61no—
461C3⋊Dic3—21no—
462C3⋊Dic3—21no—
463C3⋊Dic3—21no—
464C3⋊Dic3—61no—
465C3⋊Dic3—61no—
466C3⋊Dic3—64no—
467C3⋊Dic3—64no—
468C3⋊Dic3—124no—
469C3⋊Dic3—124no—
470C3×Dic3—24no—
471C3×Dic3—24no—
472C3×Dic3—24no—
473C3×Dic3—64no—
474C3×Dic3—64no—
475C3×Dic3—64no—
476#126—271no—
477#126—271no—
478#124—271no—
479#124—271no—
480#123—31no—
481#123—271no—
482C22⋊Q8—271no—
483#121—271no—
484#121—271no—
485#121—271no—
486#120—271no—
487#120—271no—
488C4×D4—91no—
489C4×D4—271no—
490C2×C22⋊C4—271no—
491C33#53811yescharacteristic, complemented, Sylow
492C23×C3—24no—
493C23×C3—34no—
494C23×C3—91no—
495C23×C3C2×D3214yes—
496C23×C3C22×C3⋊D311yescharacteristic
497C22×D3—34no—
498C22×D3—94no—
499C22×D3—94no—
500C22×D3—91no—
501C22×D3—91no—
502C22×D3—184no—
503C22×D3—184no—
504C22×D3—182no—
505C22×D3—188no—
506C22×D3—361no—
507C22×D3—361no—
508C22×D3—364no—
509C22×D3—364no—
510C22×D3C22×C3⋊D311yescharacteristic
511C3×D4—124no—
512C3×D4—182no—
513C2×C3×C4—24no—
514C2×C3×C4—24no—
515C2×C3×C4—34no—
516C2×C3×C4—34no—
517C2×C3×C4—34no—
518C2×C3×C4—44no—
519C2×C3×C4—41no—
520C2×C3×C4—48no—
521C2×C3×C4—91no—
522C2×C3×C4—91no—
523C2×C3×C4—91no—
524C2×C3×C4—361no—
525C2×C3×C4C2×D3214yes—
526C2×C3×C4C2×D3214yes—
527C2×C3×C4C22×C3⋊D311yescharacteristic
528C2×C3×C4C22×C3⋊D311yescharacteristic
529#67—41no—
530#67—68no—
531#67—182no—
532#67—364no—
533#67—364no—
534#67—364no—
535#67—361no—
536#67—361no—
537#67—368no—
538#67—368no—
539C2×Dic3—34no—
540C2×Dic3—34no—
541C2×Dic3—34no—
542C2×Dic3—94no—
543C2×Dic3—94no—
544C2×Dic3—91no—
545C2×Dic3—91no—
546C2×Dic3—184no—
547C2×Dic3—184no—
548C2×Dic3—361no—
549C2×Dic3C22×C3⋊D311yescharacteristic
550C2×Dic3C22×C3⋊D311yescharacteristic
551C2×Dic3C22×C3⋊D311yescharacteristic
552D12—188no—
553D12—364no—
554D12—361no—
555D12—368no—
556D12—361no—
557C4×D3—124no—
558C4×D3—361no—
559C4×D3—364no—
560C4×D3—364no—
561Dic6—361no—
562Dic6—364no—
563C2×C32—24no—
564C2×C32—24no—
565C2×C32—24no—
566C2×C32—48no—
567C2×C32—44no—
568C2×C32—41no—
569C2×C32—121no—
570C2×C32C2×#23511yescharacteristic
571C2×C32#100414yes—
572C2×C32#100411yescharacteristic
573C2×C32D3×#4114yes—
574C2×C32#100914yes—
575C2×C32#100911yescharacteristic
576C3⋊D3—22no—
577C3⋊D3—121no—
578C3⋊D3—121no—
579C3⋊D3—124no—
580C3⋊D3—124no—
581C3⋊D3—244no—
582C3⋊D3—244no—
583C3×D3—44no—
584C3×D3—68no—
585C24—271no—
586C2×Q8—271no—
587C2×D4—31no—
588C2×D4—91no—
589C2×D4—271no—
590C2×D4—271no—
591C2×D4—271no—
592C2×D4—271no—
593C2×D4—271no—
594C22×C4—91no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4D3×C3⋊D311yescharacteristic, complemented
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—91no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—31no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C22⋊C4—271no—
618C42—91no—
619C42—271no—
620C22×C3—28no—
621C22×C3—24no—
622C22×C3—24no—
623C22×C3—24no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—24no—
628C22×C3—44no—
629C22×C3—44no—
630C22×C3—64no—
631C22×C3—64no—
632C22×C3—64no—
633C22×C3—92no—
634C22×C3—181no—
635C22×C3—181no—
636C22×C3C22×D3214yes—
637C22×C3C23×C3⋊D311yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—38no—
642C2×D3—64no—
643C2×D3—64no—
644C2×D3—184no—
645C2×D3—184no—
646C2×D3—184no—
647C2×D3—184no—
648C2×D3—184no—
649C2×D3—184no—
650C2×D3—181no—
651C2×D3—181no—
652C2×D3—181no—
653C2×D3—181no—
654C2×D3—181no—
655C2×D3—181no—
656C2×D3—364no—
657C2×D3—364no—
658C2×D3—364no—
659C2×D3—364no—
660C2×D3—364no—
661C2×D3—364no—
662C2×D3—364no—
663C2×D3—3616no—
664C3×C4—28no—
665C3×C4—24no—
666C3×C4—24no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—44no—
670C3×C4—64no—
671C3×C4—64no—
672C3×C4—64no—
673C3×C4—181no—
674C3×C4—181no—
675C3×C4—181no—
676Dic3—21no—
677Dic3—21no—
678Dic3—21no—
679Dic3—64no—
680Dic3—64no—
681Dic3—64no—
682Dic3—184no—
683Dic3—184no—
684Dic3—181no—
685Dic3—181no—
686Dic3—364no—
687Dic3—364no—
688C32—24no—
689C32#556011yescharacteristic, complemented
690C32#565714yescomplemented
691C23—31no—
692C23—91no—
693C23—271no—
694C23—271no—
695C23—542no—
696C23—1081no—
697C23—1081no—
698C23C2×D3×C3⋊D311yescharacteristic
699Q8—1081no—
700D4—121no—
701D4—182no—
702D4—542no—
703D4—1081no—
704D4—1081no—
705D4—1081no—
706D4—1081no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—41no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—91no—
714C2×C4—271no—
715C2×C4—271no—
716C2×C4—361no—
717C2×C4—1081no—
718C2×C4—1081no—
719C2×C4C2×D3×C3⋊D311yescharacteristic
720C2×C4C2×D3×C3⋊D311yescharacteristic
721C2×C3—24no—
722C2×C3—24no—
723C2×C3—24no—
724C2×C3—48no—
725C2×C3—44no—
726C2×C3—41no—
727C2×C3—124no—
728C2×C3—182no—
729C2×C3D3×#23514yes—
730C2×C3#6430814yes—
731C2×C3#6433014yes—
732C2×C3#6436111yescharacteristic
733C2×C3#41×C3⋊D311yescharacteristic
734C2×C3#6436611yescharacteristic
735D3—41no—
736D3—68no—
737D3—364no—
738D3—364no—
739D3—361no—
740D3—361no—
741D3—724no—
742D3—724no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—61no—
747C22—61no—
748C22—61no—
749C22—92no—
750C22—181no—
751C22—181no—
752C22—541no—
753C22—541no—
754C22—541no—
755C22—541no—
756C22—541no—
757C22—541no—
758C22—1084no—
759C22C22×D3×C3⋊D311yescharacteristic
760C4—21no—
761C4—21no—
762C4—61no—
763C4—61no—
764C4—61no—
765C4—181no—
766C4—181no—
767C4—181no—
768C4—541no—
769C4—541no—
770C3—24no—
771C3#1059508514yescomplemented
772C3#1059612811yescharacteristic, complemented
773C2—41no—
774C2—121no—
775C2—182no—
776C2—1081no—
777C2—1081no—
778C2C3⋊D3×#23511yescharacteristic
779C2#1172458111yescharacteristic
780C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #11723971C2semidirect
2. C3×C4×#638C2semidirect
3. C32×#929C2semidirect
4. #11723643C2semidirect
5. #11723624C2semidirect
6. #11723599C2semidirect
7. #11723592C2semidirect
8. #11723542C2semidirect
9. C3⋊D3×(C2×D3)⋊C4C2semidirect
10. #11723512C2semidirect
11. #11723498C2semidirect
12. #11723483C2semidirect
13. #11723446C2semidirect
14. #11723430C2semidirect
15. #11723419C2semidirect
19. C22×C33×C4C22semidirect
21. C2×#6312C22semidirect
26. C2×#6293C22semidirect
29. C2×#6289C22semidirect
32. #88859C22semidirect
33. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
34. C3×#3757C22semidirect
36. C3×#3750C22semidirect
37. C3×C4×C3⋊Dic3C22semidirect
38. C32×#217C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
48. #88804C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
59. C4×#638D3semidirect
70. C3×#929D3semidirect
120. C22×C32×C4C2×D3semidirect
121. C22×C32×C4C2×D3semidirect
153. #3757C2×D3semidirect
171. #3750C2×D3semidirect
173. C4×C3⋊Dic3C2×D3semidirect
175. C3×#217C2×D3semidirect
180. C3×Dic3⋊C4C2×D3semidirect
181. C3×Dic3⋊C4C2×D3semidirect
229. #929C3⋊D3semidirect
337. C22×C3×C4D32semidirect
338. C22×C3×C4C2×C3⋊D3semidirect
374. #217C2×C3⋊D3semidirect
403. Dic3⋊C4C2×C3⋊D3semidirect
404. Dic3⋊C4C2×C3⋊D3semidirect
491. C33#538semidirect
597. C22×C4D3×C3⋊D3semidirect
689. C32#5560semidirect
690. C32#5657semidirect
771. C3#10595085semidirect
772. C3#10596128semidirect

Maximal subgroups

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

subgroupindex
#117239712
C3×C4×#6382
C32×#9292
#117236432
#117236242
#117235992
#117235922
#117235422
C3⋊D3×(C2×D3)⋊C42
#117235122
#117234982
#117234832
#117234462
#117234302
#117234192
#105961283
#105950853