Finite Group Databasebeta

← #13175424

Subgroups — #13175424

Order 1728.

1792 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723916C211yesmaximal, characteristic, complemented
2C3×#64081C211yesmaximal, characteristic, complemented
3C32×#872C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic
5C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6D3×#3752C211yesmaximal, characteristic, complemented
7#11723498C211yesmaximal, characteristic, complemented
8#11723497C211yesmaximal, characteristic, complemented
9#11723496C211yesmaximal, characteristic, complemented
10#11723471C211yesmaximal, characteristic, complemented
11#11723461C211yesmaximal, characteristic, complemented
12#11723453C211yesmaximal, characteristic, complemented
13#11723446C211yesmaximal, characteristic, complemented
14#11723417C211yesmaximal, characteristic, complemented
15#11723414C211yesmaximal, characteristic, complemented
16#10595998—31nomaximal
17#10594014—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
20C2×#6308C2211yescharacteristic, complemented
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6289C2211yescharacteristic, complemented
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×D3×C3⋊Dic3C2211yescharacteristic
28C33×C42C2211yescharacteristic, complemented
29#88859C2211yescharacteristic
30#88859C2211yescharacteristic
31#88859C2211yescharacteristic, complemented
32#88859C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×#3750C2211yescharacteristic, complemented
36C3×#3750C2211yescharacteristic, complemented
37C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic, complemented
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42C32×C4×Dic3C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic, complemented
51#88803C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53C32×#117—31no—
54#64138—31no—
55C2×#3752—31no—
56#64107—31no—
57#64105—31no—
58#64103—31no—
59#64103—31no—
60#64091—31no—
61#64090—31no—
62C22⋊C4×C3⋊D3—31no—
63#64087—31no—
64#64085—31no—
65#64084—31no—
66#64084—34no—
67#64084—64no—
68C4×C4⋊(C3⋊D3)—31no—
69#64081D311yescharacteristic, complemented
70C3×#872—34no—
71C3×#872D314yescomplemented
72#63923—34no—
73D3×(C2×D3)⋊C4—34no—
74D3×(C2×D3)⋊C4—34no—
75#63897—34no—
76#63896—34no—
77#63896—34no—
78#63880—34no—
79#63880—34no—
80#63868—34no—
81#63868—34no—
82#63850—34no—
83#63850—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C2×D3×C3⋊D3—22no—
89C2×D3×C3⋊D3—22no—
90C2×D3×C3⋊D3—41no—
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C4⋊(C3⋊(C3⋊D3))—41no—
97#6308—41no—
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C3×C4×C3⋊D3—22no—
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C32×C4×D3—22no—
106#6292—22no—
107#6291—22no—
108#6289—41no—
109Dic3×C3⋊D3—41no—
110D3×C3⋊Dic3—41no—
111#5527—94no—
112#5527—91no—
113C23×C3⋊D3—31no—
114C22×D32—34no—
115C22×C32×C4—31no—
116C2×#638—31no—
117C22×C3⋊Dic3—31no—
118C2×C4⋊(C3⋊D3)—31no—
119C2×C4⋊(C3⋊D3)—31no—
120C2×C4⋊(C3⋊D3)—34no—
121C2×C4⋊(C3⋊D3)—64no—
122C2×C4×C3⋊D3—31no—
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3C2×D311yescharacteristic
125C2×#634—31no—
126C2×#634—34no—
127C2×#634—64no—
128C2×C3×C4×D3—34no—
129C2×C3×C4×D3C2×D314yes—
130C2×#626—34no—
131C2×#626—34no—
132C2×#624—34no—
133C2×D3×Dic3—34no—
134C2×D3×Dic3—34no—
135C32×C4⋊C4—31no—
136C32×C4⋊C4—31no—
137C32×C22⋊C4—31no—
138C32×C22⋊C4—31no—
139C32×C42—24no—
140C32×C42—31no—
141C32×C42C2×D314yescomplemented
142C32×C42C2×D311yescharacteristic, complemented
143#3757—31no—
144#3752—31no—
145#3752—31no—
146#3752—31no—
147#3752—31no—
148#3752—31no—
149#3752—34no—
150#3752—34no—
151#3752—34no—
152#3752—34no—
153#3752—31no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—64no—
158#3752—64no—
159#3752—64no—
160#3752—64no—
161#3752C2×D311yescharacteristic
162#3752C2×D311yescharacteristic
163C4⋊(C3⋊Dic3)—31no—
164#3750—31no—
165#3750—31no—
166#3750—31no—
167#3750C2×D311yescharacteristic, complemented
168#3750C2×D311yescharacteristic, complemented
169C4×C3⋊Dic3C2×D311yescharacteristic, complemented
170C3×(C2×D3)⋊C4—34no—
171C3×(C2×D3)⋊C4—34no—
172C3×(C2×D3)⋊C4C2×D314yes—
173C3×(C2×D3)⋊C4C2×D314yes—
174C3×Dic3⋊C4—34no—
175C3×Dic3⋊C4—34no—
176C3×Dic3⋊C4C2×D314yescomplemented
177C3×Dic3⋊C4C2×D314yescomplemented
178C3×C4×Dic3—34no—
179C3×C4×Dic3C2×D314yescomplemented
180#3724—34no—
181#3724—34no—
182Dic3⋊Dic3—34no—
183Dic3⋊Dic3—34no—
184#3722—34no—
185#3722—34no—
186#3722—34no—
187#3722—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190C22×C33C2411yescharacteristic
191C2×C3⋊(C3⋊D3)—21no—
192C2×C3⋊(C3⋊D3)—21no—
193C2×C3⋊(C3⋊D3)—21no—
194C2×C3⋊(C3⋊D3)—21no—
195C2×C3⋊(C3⋊D3)—21no—
196C2×C3⋊(C3⋊D3)—21no—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3#4112yes—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3#4112yes—
203D3×C3⋊D3—44no—
204C33×C4—21no—
205C33×C4—21no—
206C33×C4—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3⋊(C3⋊Dic3)—21no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C32×Dic3—21no—
215C3×#117—34no—
216C3×#117—91no—
217#929—94no—
218#929—91no—
219C2×(C2×D3)⋊C4—94no—
220C2×(C2×D3)⋊C4—91no—
221#898—94no—
222#898—91no—
223#896—94no—
224#896—91no—
225#894—94no—
226#894—94no—
227#894—91no—
228#894—91no—
229#882—94no—
230#882—91no—
231#67⋊C4—94no—
232#67⋊C4—91no—
233D3×C22⋊C4—94no—
234D3×C22⋊C4—91no—
235#878—94no—
236#878—91no—
237#876—94no—
238#876—91no—
239#875—94no—
240#875—91no—
241#875—184no—
242C4×D12—94no—
243C4×D12—91no—
244#872—34no—
245#872C3⋊D311yescharacteristic, complemented
246C23×C32—31no—
247C22×C3⋊D3—31no—
248C22×C3⋊D3—31no—
249C22×C3⋊D3—34no—
250C22×C3⋊D3—34no—
251C22×C3⋊D3—64no—
252C22×C3⋊D3—64no—
253C22×C3⋊D3—62no—
254C22×C3⋊D3—62no—
255C22×C3⋊D3—121no—
256C22×C3⋊D3C22×D311yescharacteristic
257C22×C3×D3—34no—
258C22×C3×D3C22×D314yes—
259C2×D32—68no—
260C2×D32—68no—
261C2×D32—124no—
262C2×C32×C4—24no—
263C2×C32×C4—24no—
264C2×C32×C4—24no—
265C2×C32×C4—31no—
266C2×C32×C4—31no—
267C2×C32×C4—31no—
268C2×C32×C4—62no—
269C2×C32×C4C22×D314yes—
270C2×C32×C4C22×D314yes—
271C2×C32×C4C22×D314yes—
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275#638—62no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—31no—
278C2×C3⋊Dic3—34no—
279C2×C3⋊Dic3—34no—
280C2×C3⋊Dic3—64no—
281C2×C3⋊Dic3—64no—
282C2×C3⋊Dic3—121no—
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C4⋊(C3⋊D3)—62no—
287C4⋊(C3⋊D3)—121no—
288C4⋊(C3⋊D3)—124no—
289C4⋊(C3⋊D3)—128no—
290C4×C3⋊D3—22no—
291C4×C3⋊D3—121no—
292C4×C3⋊D3—121no—
293#634—121no—
294#634—124no—
295#634—128no—
296C2×C3×Dic3—34no—
297C2×C3×Dic3—34no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3C22×D314yes—
300C2×C3×Dic3C22×D314yes—
301C2×C3×Dic3C22×D314yes—
302C3×C4×D3—28no—
303C3×C4×D3—68no—
304#626—68no—
305#626—68no—
306#624—124no—
307D3×Dic3—124no—
308D3×Dic3—124no—
309#551—271noSylow
310C2×C33C2×#4111yescharacteristic
311C2×C33C2×#4111yescharacteristic
312C2×C33H(5,𝔽2)11yescharacteristic
313C3⋊(C3⋊D3)—41no—
314C3⋊(C3⋊D3)—41no—
315C3×C3⋊D3—22no—
316C32×D3—22no—
317C23×D3—94no—
318C23×D3—91no—
319C22×C3×C4—34no—
320C22×C3×C4—91no—
321C2×#67—94no—
322C2×#67—91no—
323C22×Dic3—94no—
324C22×Dic3—91no—
325C2×D12—94no—
326C2×D12—91no—
327C2×D12—94no—
328C2×D12—91no—
329C2×D12—184no—
330C2×C4×D3—34no—
331C2×C4×D3—94no—
332C2×C4×D3—94no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3C2×C3⋊D311yescharacteristic
336C2×Dic6—94no—
337C2×Dic6—91no—
338C2×Dic6—184no—
339C3×C4⋊C4—34no—
340C3×C4⋊C4—34no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C22⋊C4—34no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—91no—
346C3×C22⋊C4—91no—
347C3×C42—24no—
348C3×C42—34no—
349C3×C42—91no—
350C3×C42D3214yescomplemented
351C3×C42C2×C3⋊D311yescharacteristic, complemented
352#217—94no—
353#217—91no—
354(C2×D3)⋊C4—34no—
355(C2×D3)⋊C4—34no—
356(C2×D3)⋊C4—94no—
357(C2×D3)⋊C4—94no—
358(C2×D3)⋊C4—94no—
359(C2×D3)⋊C4—94no—
360(C2×D3)⋊C4—94no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—94no—
363(C2×D3)⋊C4—94no—
364(C2×D3)⋊C4—94no—
365(C2×D3)⋊C4—94no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—184no—
375(C2×D3)⋊C4—184no—
376(C2×D3)⋊C4—184no—
377(C2×D3)⋊C4—184no—
378(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
379(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
380C4⋊Dic3—94no—
381C4⋊Dic3—91no—
382Dic3⋊C4—34no—
383Dic3⋊C4—34no—
384Dic3⋊C4—94no—
385Dic3⋊C4—94no—
386Dic3⋊C4—94no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
391Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
392C4×Dic3—34no—
393C4×Dic3C2×C3⋊D311yescharacteristic, complemented
394C22×C32—24no—
395C22×C32—32no—
396C22×C32—61no—
397C22×C32—61no—
398C22×C32C23×D314yes—
399C22×C32C23×D311yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—61no—
403C2×C3⋊D3—61no—
404C2×C3⋊D3—61no—
405C2×C3⋊D3—61no—
406C2×C3⋊D3—61no—
407C2×C3⋊D3—61no—
408C2×C3⋊D3—64no—
409C2×C3⋊D3—64no—
410C2×C3⋊D3—64no—
411C2×C3⋊D3—64no—
412C2×C3⋊D3—64no—
413C2×C3⋊D3—64no—
414C2×C3⋊D3—124no—
415C2×C3⋊D3—124no—
416C2×C3⋊D3—124no—
417C2×C3⋊D3—124no—
418C2×C3⋊D3—124no—
419C2×C3⋊D3—124no—
420C2×C3⋊D3—124no—
421C2×C3⋊D3#23512yes—
422C2×C3×D3—24no—
423C2×C3×D3—24no—
424C2×C3×D3—38no—
425C2×C3×D3—64no—
426C2×C3×D3—64no—
427C2×C3×D3#23518yes—
428D32—1216no—
429C32×C4—28no—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4—24no—
433C32×C4—21no—
434C32×C4—24no—
435C32×C4—24no—
436C32×C4—44no—
437C32×C4—44no—
438C32×C4—61no—
439C32×C4—61no—
440C32×C4—61no—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3⋊Dic3—21no—
444C3⋊Dic3—61no—
445C3⋊Dic3—61no—
446C3⋊Dic3—64no—
447C3⋊Dic3—64no—
448C3⋊Dic3—124no—
449C3⋊Dic3—124no—
450C3×Dic3—24no—
451C3×Dic3—24no—
452C3×Dic3—24no—
453C3×Dic3—64no—
454C3×Dic3—64no—
455C3×Dic3—64no—
456#126—271no—
457#126—271no—
458#124—271no—
459#123—271no—
460#123—271no—
461#123—271no—
462C22⋊Q8—271no—
463C22⋊Q8—271no—
464#120—271no—
465C4×D4—271no—
466C4×D4—271no—
467#117—31no—
468#117—91no—
469C2×C22⋊C4—271no—
470C2×C22⋊C4—271no—
471C33#55111yescharacteristic, complemented, Sylow
472C23×C3—34no—
473C23×C3—91no—
474C22×D3—34no—
475C22×D3—94no—
476C22×D3—94no—
477C22×D3—91no—
478C22×D3—91no—
479C22×D3—184no—
480C22×D3—184no—
481C22×D3—182no—
482C22×D3—188no—
483C22×D3—188no—
484C22×D3—182no—
485C22×D3—361no—
486C22×D3—364no—
487C22×D3C22×C3⋊D311yescharacteristic
488C2×C3×C4—24no—
489C2×C3×C4—24no—
490C2×C3×C4—24no—
491C2×C3×C4—34no—
492C2×C3×C4—34no—
493C2×C3×C4—34no—
494C2×C3×C4—68no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—91no—
498C2×C3×C4—182no—
499C2×C3×C4C2×D3214yes—
500C2×C3×C4C2×D3214yes—
501C2×C3×C4C2×D3214yes—
502C2×C3×C4C22×C3⋊D311yescharacteristic
503C2×C3×C4C22×C3⋊D311yescharacteristic
504C2×C3×C4C22×C3⋊D311yescharacteristic
505#67—182no—
506#67—188no—
507C2×Dic3—34no—
508C2×Dic3—34no—
509C2×Dic3—34no—
510C2×Dic3—94no—
511C2×Dic3—94no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—184no—
515C2×Dic3—184no—
516C2×Dic3—361no—
517C2×Dic3—364no—
518C2×Dic3C22×C3⋊D311yescharacteristic
519C2×Dic3C22×C3⋊D311yescharacteristic
520C2×Dic3C22×C3⋊D311yescharacteristic
521D12—188no—
522D12—182no—
523D12—364no—
524D12—361no—
525D12—368no—
526C4×D3—22no—
527C4×D3—68no—
528C4×D3—361no—
529C4×D3—364no—
530C4×D3—364no—
531C4×D3—361no—
532Dic6—364no—
533Dic6—361no—
534Dic6—368no—
535C2×C32—24no—
536C2×C32—24no—
537C2×C32—24no—
538C2×C32—62no—
539C2×C32C2×#23514yes—
540C2×C32C2×#23511yescharacteristic
541C2×C32D3×#4114yes—
542C2×C32D3×#4111yescharacteristic
543C2×C32#100914yes—
544C2×C32#100911yescharacteristic
545C3⋊D3—22no—
546C3⋊D3—121no—
547C3⋊D3—121no—
548C3⋊D3—124no—
549C3⋊D3—124no—
550C3⋊D3—244no—
551C3⋊D3—244no—
552C3×D3—28no—
553C3×D3—68no—
554C24—271no—
555C2×Q8—271no—
556C2×D4—271no—
557C2×D4—271no—
558C2×D4—271no—
559C22×C4—31no—
560C22×C4—91no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—271no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C22⋊C4—31no—
573C22⋊C4—31no—
574C22⋊C4—91no—
575C22⋊C4—91no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4—271no—
586C42—31no—
587C42—91no—
588C42D3×C3⋊D311yescharacteristic, complemented
589C22×C3—24no—
590C22×C3—38no—
591C22×C3—64no—
592C22×C3—64no—
593C22×C3—92no—
594C22×C3—181no—
595C22×C3—181no—
596C22×C3C22×D3214yes—
597C22×C3C23×C3⋊D311yescharacteristic
598C2×D3—21no—
599C2×D3—21no—
600C2×D3—38no—
601C2×D3—64no—
602C2×D3—64no—
603C2×D3—184no—
604C2×D3—184no—
605C2×D3—184no—
606C2×D3—184no—
607C2×D3—184no—
608C2×D3—184no—
609C2×D3—181no—
610C2×D3—181no—
611C2×D3—181no—
612C2×D3—181no—
613C2×D3—181no—
614C2×D3—181no—
615C2×D3—364no—
616C2×D3—364no—
617C2×D3—364no—
618C2×D3—364no—
619C2×D3—364no—
620C2×D3—364no—
621C2×D3—364no—
622C2×D3—3616no—
623C2×D3#382812yes—
624C3×C4—28no—
625C3×C4—24no—
626C3×C4—24no—
627C3×C4—24no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—44no—
632C3×C4—44no—
633C3×C4—64no—
634C3×C4—64no—
635C3×C4—64no—
636C3×C4—181no—
637C3×C4—181no—
638C3×C4—181no—
639Dic3—21no—
640Dic3—21no—
641Dic3—21no—
642Dic3—64no—
643Dic3—64no—
644Dic3—64no—
645Dic3—184no—
646Dic3—184no—
647Dic3—181no—
648Dic3—181no—
649Dic3—364no—
650Dic3—364no—
651C32—24no—
652C32#552714yescomplemented
653C32#552711yescharacteristic, complemented
654C23—31no—
655C23—91no—
656C23—271no—
657C23—271no—
658C23—542no—
659C23—542no—
660C23—1081no—
661Q8—1081no—
662D4—542no—
663D4—542no—
664D4—1081no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—62no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—182no—
673C2×C4—271no—
674C2×C4—271no—
675C2×C4—1081no—
676C2×C4—1081no—
677C2×C4—1081no—
678C2×C4C2×D3×C3⋊D311yescharacteristic
679C2×C4C2×D3×C3⋊D311yescharacteristic
680C2×C4C2×D3×C3⋊D311yescharacteristic
681C2×C3—24no—
682C2×C3—24no—
683C2×C3—24no—
684C2×C3—68no—
685C2×C3—182no—
686C2×C3D3×#23514yes—
687C2×C3D3×#23514yes—
688C2×C3#6430814yes—
689C2×C3C2×#382811yescharacteristic
690C2×C3#41×C3⋊D311yescharacteristic
691C2×C3#6436611yescharacteristic
692D3—22no—
693D3—68no—
694D3—361no—
695D3—361no—
696D3—364no—
697D3—364no—
698D3—724no—
699D3—724no—
700C22—32no—
701C22—61no—
702C22—61no—
703C22—92no—
704C22—181no—
705C22—181no—
706C22—541no—
707C22—541no—
708C22—541no—
709C22—541no—
710C22—541no—
711C22—541no—
712C22—1084no—
713C22C22×D3×C3⋊D311yescharacteristic
714C4—21no—
715C4—21no—
716C4—21no—
717C4—61no—
718C4—61no—
719C4—61no—
720C4—181no—
721C4—181no—
722C4—181no—
723C4—541no—
724C4—541no—
725C3—24no—
726C3#1059401414yescomplemented
727C3#1059599811yescharacteristic, complemented
728C2—62no—
729C2—182no—
730C2—1081no—
731C2—1081no—
732C2D3×#382811yescharacteristic
733C2C3⋊D3×#23511yescharacteristic
734C2#1172458111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C42C22
prime radical#11723542C2
hypercenterC42D3×C3⋊D3
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #11723916C2semidirect
2. C3×#64081C2semidirect
3. C32×#872C2semidirect
5. C3⋊D3×(C2×D3)⋊C4C2semidirect
6. D3×#3752C2semidirect
7. #11723498C2semidirect
8. #11723497C2semidirect
9. #11723496C2semidirect
10. #11723471C2semidirect
11. #11723461C2semidirect
12. #11723453C2semidirect
13. #11723446C2semidirect
14. #11723417C2semidirect
15. #11723414C2semidirect
20. C2×#6308C22semidirect
25. C2×#6289C22semidirect
28. C33×C42C22semidirect
31. #88859C22semidirect
32. #88859C22semidirect
35. C3×#3750C22semidirect
36. C3×#3750C22semidirect
37. C3×C4×C3⋊Dic3C22semidirect
40. C32×Dic3⋊C4C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. C32×C4×Dic3C22semidirect
43. #88807C22semidirect
44. #88806C22semidirect
45. #88806C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
50. #88804C22semidirect
69. #64081D3semidirect
71. C3×#872D3semidirect
141. C32×C42C2×D3semidirect
142. C32×C42C2×D3semidirect
167. #3750C2×D3semidirect
168. #3750C2×D3semidirect
169. C4×C3⋊Dic3C2×D3semidirect
176. C3×Dic3⋊C4C2×D3semidirect
177. C3×Dic3⋊C4C2×D3semidirect
179. C3×C4×Dic3C2×D3semidirect
245. #872C3⋊D3semidirect
350. C3×C42D32semidirect
351. C3×C42C2×C3⋊D3semidirect
390. Dic3⋊C4C2×C3⋊D3semidirect
391. Dic3⋊C4C2×C3⋊D3semidirect
393. C4×Dic3C2×C3⋊D3semidirect
471. C33#551semidirect
588. C42D3×C3⋊D3semidirect
652. C32#5527semidirect
653. C32#5527semidirect
726. C3#10594014semidirect
727. C3#10595998semidirect

Maximal subgroups

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

subgroupindex
#117239162
C3×#640812
C32×#8722
#117235422
C3⋊D3×(C2×D3)⋊C42
D3×#37522
#117234982
#117234972
#117234962
#117234712
#117234612
#117234532
#117234462
#117234172
#117234142
#105959983
#105940143