Finite Group Databasebeta

← #13175839

Subgroups — #13175839

Order 1728.

2032 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723923C211yesmaximal, characteristic, complemented
2C3×#64093C211yesmaximal, characteristic, complemented
3C32×#879C211yesmaximal, characteristic, complemented
4#11723639C211yesmaximal, characteristic, complemented
5#11723639C211yesmaximal, characteristic, complemented
6#11723624C211yesmaximal, characteristic, complemented
7#11723623C211yesmaximal, characteristic, complemented
8#11723526C211yesmaximal, characteristic, complemented
9#11723517C211yesmaximal, characteristic, complemented
10#11723498C211yesmaximal, characteristic, complemented
11#11723493C211yesmaximal, characteristic, complemented
12#11723486C211yesmaximal, characteristic, complemented
13#11723482C211yesmaximal, characteristic, complemented
14#11723453C211yesmaximal, characteristic, complemented
15#11723417C211yesmaximal, characteristic, complemented
16#10596182—31nomaximal
17#10594242—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×#6312C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×#6292C2211yescharacteristic, complemented
31C2×#6292C2211yescharacteristic, complemented
32C2×#6289C2211yescharacteristic, complemented
33C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
34C33×C22⋊C4C2211yescharacteristic
35#88859C2211yescharacteristic
36#88859C2211yescharacteristic
37C3×#3752C2211yescharacteristic, complemented
38C3×#3750C2211yescharacteristic, complemented
39C32×#217C2211yescharacteristic
40C32×#217C2211yescharacteristic
41C32×C4⋊Dic3C2211yescharacteristic, complemented
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43C32×Dic3⋊C4C2211yescharacteristic, complemented
44C32×C4×Dic3C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46#88806C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51#88804C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53C32×#126—31no—
54#64104—31no—
55#64104—31no—
56#64104—31no—
57#64103—31no—
58#64103—31no—
59#64103—31no—
60#64093—31no—
61#64093—31no—
62#64093D311yescharacteristic, complemented
63#64091—31no—
64#64091—31no—
65#64091—31no—
66#64091—34no—
67#64091—64no—
68#64085—31no—
69#64083—31no—
70C3×#884—34no—
71C3×#879D314yescomplemented
72#63981—34no—
73#63981—34no—
74#63971—34no—
75#63958—34no—
76#63911—34no—
77#63910—34no—
78#63909—34no—
79#63897—34no—
80#63890—34no—
81#63886—34no—
82#63868—34no—
83#63850—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)—41no—
86C22×C3⋊(C3⋊D3)—41no—
87C22×C3⋊(C3⋊D3)—41no—
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3⋊(C3⋊D3)C2311yescharacteristic
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3×C3⋊D3C2311yescharacteristic
92C22×C3×C3⋊D3C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95#6312—41no—
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C4⋊(C3⋊(C3⋊D3))—41no—
98C4⋊(C3⋊(C3⋊D3))—41no—
99C3×#638—41no—
100C3×#638—41no—
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C3×C4⋊(C3⋊D3)—41no—
104C3×C4×C3⋊D3—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109#6292—41no—
110#6292—41no—
111#6292—41no—
112#6292—41no—
113#6292—41no—
114#6292—41no—
115#6289—41no—
116Dic3×C3⋊D3—41no—
117#5711—94no—
118#5620—91no—
119C23×C3⋊D3—31no—
120C23×C3⋊D3—34no—
121C23×C3⋊D3—64no—
122C2×#638—31no—
123C2×#638—34no—
124C2×#638—64no—
125C2×#638C2×D311yescharacteristic
126C2×#638C2×D311yescharacteristic
127C2×C4⋊(C3⋊D3)—31no—
128C2×C4⋊(C3⋊D3)—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4⋊(C3⋊D3)—31no—
133C2×C4⋊(C3⋊D3)—31no—
134C2×C4⋊(C3⋊D3)—31no—
135C2×C4⋊(C3⋊D3)—34no—
136C2×C4⋊(C3⋊D3)—34no—
137C2×C4⋊(C3⋊D3)—64no—
138C2×C4⋊(C3⋊D3)—64no—
139C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
140C2×C4×C3⋊D3—31no—
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
143C2×C3×#67—34no—
144C2×C3×#67—34no—
145C2×C3×D12—34no—
146C2×C3×C4×D3—34no—
147C2×#626—34no—
148C2×#626—34no—
149C2×#626—34no—
150C2×#626—34no—
151C2×#626—34no—
152C2×#626—34no—
153C2×#624—34no—
154C2×D3×Dic3—34no—
155C32×C4⋊C4—31no—
156C32×C4⋊C4—31no—
157C32×C4⋊C4—31no—
158C32×C22⋊C4—24no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4—31no—
161C32×C22⋊C4C2×D314yes—
162C32×C22⋊C4C2×D311yescharacteristic
163C32×C42—31no—
164#3752—31no—
165#3752—31no—
166#3752—31no—
167#3752—34no—
168#3752—34no—
169#3752—31no—
170#3752—31no—
171#3752—31no—
172#3752—31no—
173#3752—31no—
174#3752—64no—
175#3752—64no—
176#3752C2×D311yescharacteristic, complemented
177#3750—31no—
178#3750—31no—
179#3750C2×D311yescharacteristic, complemented
180C3×#217C2×D314yes—
181C3×#217C2×D314yes—
182C3×(C2×D3)⋊C4—34no—
183C3×C4⋊Dic3C2×D314yescomplemented
184C3×Dic3⋊C4—34no—
185C3×Dic3⋊C4C2×D314yescomplemented
186C3×Dic3⋊C4C2×D314yescomplemented
187C3×C4×Dic3C2×D314yescomplemented
188#3724—34no—
189Dic3⋊Dic3—34no—
190#3722—34no—
191#3722—34no—
192#3722—34no—
193#3722—34no—
194#3722—34no—
195(C2×D3)⋊Dic3—34no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33—21no—
199C22×C33C2411yescharacteristic
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)—21no—
206C2×C3⋊(C3⋊D3)—21no—
207C2×C3⋊(C3⋊D3)—21no—
208C2×C3⋊(C3⋊D3)—21no—
209C2×C3⋊(C3⋊D3)—44no—
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—
216C33×C4—21no—
217C33×C4—21no—
218C3⋊(C3⋊Dic3)—21no—
219C3×C3⋊Dic3—21no—
220C3×C3⋊Dic3—21no—
221C32×Dic3—21no—
222C32×Dic3—21no—
223C32×Dic3—21no—
224C32×Dic3—21no—
225C3×#126—34no—
226C3×#121—91no—
227#940—91no—
228#939—91no—
229#939—91no—
230#938—91no—
231#937—91no—
232#937—91no—
233#930—91no—
234#929—91no—
235#898—91no—
236#895—94no—
237#895—94no—
238#895—94no—
239#894—94no—
240#894—94no—
241#894—94no—
242#894—91no—
243#886—91no—
244#884—34no—
245#884—94no—
246#884—94no—
247#884—91no—
248#882—94no—
249#882—94no—
250#882—94no—
251#882—91no—
252#882—184no—
253#879C3⋊D311yescharacteristic, complemented
254#876—94no—
255#874—94no—
256C23×C32—24no—
257C23×C32C22×D314yes—
258C23×C32C22×D311yescharacteristic
259C22×C3⋊D3—31no—
260C22×C3⋊D3—31no—
261C22×C3⋊D3—31no—
262C22×C3⋊D3—34no—
263C22×C3⋊D3—34no—
264C22×C3⋊D3—34no—
265C22×C3⋊D3—64no—
266C22×C3⋊D3—64no—
267C22×C3⋊D3—64no—
268C22×C3⋊D3—121no—
269C22×C3⋊D3—121no—
270C22×C3⋊D3—121no—
271C22×C3⋊D3—124no—
272C22×C3⋊D3—124no—
273C22×C3⋊D3—124no—
274C22×C3⋊D3—128no—
275C22×C3⋊D3—128no—
276C22×C3⋊D3—128no—
277C22×C3⋊D3C22×D311yescharacteristic
278C22×C3⋊D3C22×D311yescharacteristic
279C22×C3×D3—34no—
280C22×C3×D3—34no—
281C2×C32×C4—24no—
282C2×C32×C4—24no—
283C2×C32×C4—31no—
284C2×C32×C4—31no—
285C2×C32×C4—31no—
286C2×C32×C4—31no—
287C2×C32×C4C22×D314yes—
288C2×C32×C4C22×D314yes—
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291#638—41no—
292#638—41no—
293#638—121no—
294#638—124no—
295#638—128no—
296C2×C3⋊Dic3—31no—
297C2×C3⋊Dic3—34no—
298C2×C3⋊Dic3—64no—
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301C4⋊(C3⋊D3)—41no—
302C4⋊(C3⋊D3)—121no—
303C4⋊(C3⋊D3)—121no—
304C4⋊(C3⋊D3)—124no—
305C4⋊(C3⋊D3)—124no—
306C4⋊(C3⋊D3)—128no—
307C4⋊(C3⋊D3)—128no—
308C4⋊(C3⋊D3)—121no—
309C4⋊(C3⋊D3)—121no—
310C4⋊(C3⋊D3)—121no—
311C4⋊(C3⋊D3)—121no—
312C4⋊(C3⋊D3)—121no—
313C4⋊(C3⋊D3)—121no—
314C4×C3⋊D3—41no—
315C4×C3⋊D3—121no—
316C4×C3⋊D3—121no—
317C3×#67—124no—
318C3×#67—124no—
319C2×C3×Dic3—34no—
320C2×C3×Dic3—34no—
321C2×C3×Dic3C22×D314yes—
322C2×C3×Dic3C22×D314yes—
323C2×C3×Dic3C22×D314yes—
324C2×C3×Dic3C22×D314yes—
325C3×D12—124no—
326C3×C4×D3—124no—
327#626—124no—
328#626—124no—
329#626—124no—
330#626—124no—
331#626—124no—
332#626—124no—
333#624—124no—
334D3×Dic3—124no—
335#560—271noSylow
336C2×C33—41no—
337C2×C33H(5,𝔽2)11yescharacteristic
338C2×C33H(5,𝔽2)11yescharacteristic
339C2×C33H(5,𝔽2)11yescharacteristic
340C3⋊(C3⋊D3)—41no—
341C3⋊(C3⋊D3)—41no—
342C3⋊(C3⋊D3)—41no—
343C3×C3⋊D3—41no—
344C3×C3⋊D3—41no—
345C23×D3—94no—
346C23×D3—91no—
347C23×D3—184no—
348C2×C3×D4—91no—
349C2×C3×D4—91no—
350C2×C3×D4—91no—
351C22×C3×C4—91no—
352C2×#67—34no—
353C2×#67—34no—
354C2×#67—94no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—184no—
363C22×Dic3—91no—
364C2×D12—34no—
365C2×D12—94no—
366C2×D12—94no—
367C2×D12—94no—
368C2×D12—94no—
369C2×D12—94no—
370C2×D12—94no—
371C2×D12—94no—
372C2×D12—94no—
373C2×D12—91no—
374C2×D12—91no—
375C2×D12—184no—
376C2×D12—184no—
377C2×C4×D3—34no—
378C2×C4×D3—94no—
379C2×C4×D3—94no—
380C2×C4×D3—91no—
381C3×C4⋊C4—34no—
382C3×C4⋊C4—34no—
383C3×C4⋊C4—34no—
384C3×C4⋊C4—91no—
385C3×C22⋊C4—24no—
386C3×C22⋊C4—34no—
387C3×C22⋊C4—34no—
388C3×C22⋊C4—91no—
389C3×C22⋊C4D3214yes—
390C3×C22⋊C4C2×C3⋊D311yescharacteristic
391C3×C42—34no—
392#217—91no—
393#217C2×C3⋊D311yescharacteristic
394#217C2×C3⋊D311yescharacteristic
395(C2×D3)⋊C4—34no—
396(C2×D3)⋊C4—94no—
397(C2×D3)⋊C4—94no—
398(C2×D3)⋊C4—94no—
399(C2×D3)⋊C4—94no—
400(C2×D3)⋊C4—94no—
401(C2×D3)⋊C4—94no—
402(C2×D3)⋊C4—94no—
403(C2×D3)⋊C4—94no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—184no—
412(C2×D3)⋊C4—184no—
413C4⋊Dic3—91no—
414C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
415Dic3⋊C4—34no—
416Dic3⋊C4—94no—
417Dic3⋊C4—94no—
418Dic3⋊C4—91no—
419Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
420Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
421C4×Dic3C2×C3⋊D311yescharacteristic, complemented
422C22×C32—28no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—24no—
426C22×C32—21no—
427C22×C32—24no—
428C22×C32—24no—
429C22×C32—24no—
430C22×C32—44no—
431C22×C32—44no—
432C22×C32C23×D314yes—
433C22×C32C23×D311yescharacteristic
434C2×C3⋊D3—21no—
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—68no—
441C2×C3⋊D3—68no—
442C2×C3⋊D3—61no—
443C2×C3⋊D3—61no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—61no—
447C2×C3⋊D3—61no—
448C2×C3⋊D3—61no—
449C2×C3⋊D3—64no—
450C2×C3⋊D3—64no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—61no—
453C2×C3⋊D3—64no—
454C2×C3⋊D3—64no—
455C2×C3⋊D3—64no—
456C2×C3⋊D3—64no—
457C2×C3⋊D3—64no—
458C2×C3⋊D3—64no—
459C2×C3⋊D3—64no—
460C2×C3⋊D3—124no—
461C2×C3⋊D3—124no—
462C2×C3⋊D3—124no—
463C2×C3⋊D3—124no—
464C2×C3⋊D3—124no—
465C2×C3⋊D3—124no—
466C2×C3⋊D3—124no—
467C2×C3⋊D3—1232no—
468C2×C3⋊D3—1216no—
469C2×C3⋊D3—124no—
470C2×C3×D3—64no—
471C2×C3×D3—64no—
472C2×C3×D3—64no—
473C2×C3×D3—64no—
474C2×C3×D3—64no—
475C2×C3×D3—64no—
476C32×C4—21no—
477C32×C4—21no—
478C32×C4—24no—
479C32×C4—24no—
480C32×C4—44no—
481C32×C4—44no—
482C32×C4—61no—
483C32×C4—61no—
484C32×C4—61no—
485C32×C4—61no—
486C3⋊Dic3—21no—
487C3⋊Dic3—21no—
488C3⋊Dic3—61no—
489C3⋊Dic3—64no—
490C3⋊Dic3—124no—
491C3×Dic3—24no—
492C3×Dic3—24no—
493C3×Dic3—24no—
494C3×Dic3—24no—
495C3×Dic3—64no—
496C3×Dic3—64no—
497#127—271no—
498#126—31no—
499#126—271no—
500#123—271no—
501#123—271no—
502#123—271no—
503#121—91no—
504#121—271no—
505#121—271no—
506#121—271no—
507#121—271no—
508#121—271no—
509#120—271no—
510#120—271no—
511#120—271no—
512C33#56011yescharacteristic, complemented, Sylow
513C23×C3—24no—
514C23×C3—91no—
515C23×C3—91no—
516C23×C3C2×D3214yes—
517C23×C3C22×C3⋊D311yescharacteristic
518C22×D3—34no—
519C22×D3—34no—
520C22×D3—94no—
521C22×D3—94no—
522C22×D3—94no—
523C22×D3—91no—
524C22×D3—91no—
525C22×D3—91no—
526C22×D3—184no—
527C22×D3—184no—
528C22×D3—184no—
529C22×D3—364no—
530C22×D3—364no—
531C22×D3—364no—
532C22×D3—361no—
533C22×D3—361no—
534C22×D3—361no—
535C22×D3—368no—
536C22×D3—368no—
537C22×D3—368no—
538C3×D4—361no—
539C3×D4—361no—
540C3×D4—361no—
541C2×C3×C4—24no—
542C2×C3×C4—24no—
543C2×C3×C4—34no—
544C2×C3×C4—34no—
545C2×C3×C4—34no—
546C2×C3×C4—34no—
547C2×C3×C4—91no—
548C2×C3×C4—91no—
549C2×C3×C4—361no—
550C2×C3×C4C2×D3214yes—
551C2×C3×C4C2×D3214yes—
552C2×C3×C4C22×C3⋊D311yescharacteristic
553C2×C3×C4C22×C3⋊D311yescharacteristic
554#67—124no—
555#67—124no—
556#67—361no—
557#67—361no—
558#67—361no—
559#67—361no—
560#67—361no—
561#67—361no—
562#67—364no—
563#67—361no—
564#67—368no—
565C2×Dic3—34no—
566C2×Dic3—34no—
567C2×Dic3—94no—
568C2×Dic3—91no—
569C2×Dic3—184no—
570C2×Dic3—361no—
571C2×Dic3C22×C3⋊D311yescharacteristic
572C2×Dic3C22×C3⋊D311yescharacteristic
573C2×Dic3C22×C3⋊D311yescharacteristic
574C2×Dic3C22×C3⋊D311yescharacteristic
575D12—124no—
576D12—364no—
577D12—364no—
578D12—361no—
579D12—361no—
580D12—368no—
581D12—368no—
582D12—364no—
583D12—364no—
584D12—364no—
585D12—364no—
586D12—364no—
587D12—364no—
588C4×D3—124no—
589C4×D3—361no—
590C4×D3—364no—
591C4×D3—364no—
592C2×C32—24no—
593C2×C32—24no—
594C2×C32—24no—
595C2×C32—48no—
596C2×C32—44no—
597C2×C32—41no—
598C2×C32#100411yescharacteristic
599C2×C32#100411yescharacteristic
600C2×C32#100914yes—
601C2×C32#100914yes—
602C2×C32#100914yes—
603C2×C32#100911yescharacteristic
604C3⋊D3—41no—
605C3⋊D3—41no—
606C3⋊D3—128no—
607C3⋊D3—128no—
608C3⋊D3—124no—
609C3⋊D3—124no—
610C3⋊D3—121no—
611C3⋊D3—121no—
612C3⋊D3—121no—
613C3⋊D3—124no—
614C3⋊D3—244no—
615C3×D3—124no—
616C3×D3—124no—
617C24—271no—
618C2×D4—91no—
619C2×D4—91no—
620C2×D4—91no—
621C2×D4—271no—
622C2×D4—271no—
623C2×D4—271no—
624C2×D4—271no—
625C2×D4—271no—
626C2×D4—271no—
627C2×D4—271no—
628C2×D4—271no—
629C2×D4—271no—
630C22×C4—91no—
631C22×C4—271no—
632C22×C4—271no—
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—91no—
637C4⋊C4—271no—
638C4⋊C4—271no—
639C22⋊C4—31no—
640C22⋊C4—31no—
641C22⋊C4—91no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4—271no—
648C22⋊C4—271no—
649C22⋊C4—271no—
650C22⋊C4D3×C3⋊D311yescharacteristic
651C42—31no—
652C22×C3—28no—
653C22×C3—24no—
654C22×C3—24no—
655C22×C3—24no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—24no—
660C22×C3—44no—
661C22×C3—44no—
662C22×C3—181no—
663C22×C3—181no—
664C22×C3—181no—
665C22×C3—181no—
666C22×C3—181no—
667C22×C3—181no—
668C22×C3C22×D3214yes—
669C22×C3C23×C3⋊D311yescharacteristic
670C2×D3—64no—
671C2×D3—64no—
672C2×D3—64no—
673C2×D3—64no—
674C2×D3—64no—
675C2×D3—64no—
676C2×D3—188no—
677C2×D3—188no—
678C2×D3—184no—
679C2×D3—184no—
680C2×D3—184no—
681C2×D3—184no—
682C2×D3—184no—
683C2×D3—184no—
684C2×D3—184no—
685C2×D3—184no—
686C2×D3—184no—
687C2×D3—181no—
688C2×D3—181no—
689C2×D3—181no—
690C2×D3—181no—
691C2×D3—181no—
692C2×D3—181no—
693C2×D3—181no—
694C2×D3—181no—
695C2×D3—181no—
696C2×D3—364no—
697C2×D3—364no—
698C2×D3—364no—
699C2×D3—364no—
700C2×D3—364no—
701C2×D3—364no—
702C2×D3—364no—
703C2×D3—3632no—
704C2×D3—364no—
705C2×D3—3616no—
706C3×C4—24no—
707C3×C4—24no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—44no—
711C3×C4—44no—
712C3×C4—64no—
713C3×C4—64no—
714C3×C4—64no—
715C3×C4—64no—
716C3×C4—181no—
717C3×C4—181no—
718Dic3—21no—
719Dic3—21no—
720Dic3—21no—
721Dic3—21no—
722Dic3—64no—
723Dic3—64no—
724Dic3—184no—
725Dic3—181no—
726Dic3—364no—
727C32—24no—
728C32#562011yescharacteristic, complemented
729C32#571114yescomplemented
730C23—91no—
731C23—91no—
732C23—271no—
733C23—271no—
734C23—271no—
735C23—1081no—
736C23—1081no—
737C23—1081no—
738C23C2×D3×C3⋊D311yescharacteristic
739D4—361no—
740D4—361no—
741D4—361no—
742D4—1081no—
743D4—1081no—
744D4—1081no—
745D4—1081no—
746D4—1081no—
747D4—1081no—
748D4—1081no—
749D4—1081no—
750D4—1081no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—31no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—271no—
758C2×C4—361no—
759C2×C4—1081no—
760C2×C4—1081no—
761C2×C4C2×D3×C3⋊D311yescharacteristic
762C2×C4C2×D3×C3⋊D311yescharacteristic
763C2×C3—24no—
764C2×C3—24no—
765C2×C3—24no—
766C2×C3—48no—
767C2×C3—41no—
768C2×C3—44no—
769C2×C3—361no—
770C2×C3—361no—
771C2×C3#6430814yes—
772C2×C3#6431414yes—
773C2×C3#6431414yes—
774C2×C3#6436611yescharacteristic
775C2×C3#6436611yescharacteristic
776C2×C3#6436611yescharacteristic
777D3—124no—
778D3—124no—
779D3—368no—
780D3—368no—
781D3—361no—
782D3—361no—
783D3—361no—
784D3—364no—
785D3—364no—
786D3—364no—
787D3—724no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—181no—
792C22—181no—
793C22—181no—
794C22—181no—
795C22—181no—
796C22—181no—
797C22—541no—
798C22—541no—
799C22—541no—
800C22—541no—
801C22—541no—
802C22—541no—
803C22—541no—
804C22—541no—
805C22—541no—
806C22—1084no—
807C22C22×D3×C3⋊D311yescharacteristic
808C4—21no—
809C4—21no—
810C4—61no—
811C4—61no—
812C4—61no—
813C4—61no—
814C4—181no—
815C4—181no—
816C4—541no—
817C3—24no—
818C3#1059424214yescomplemented
819C3#1059618211yescharacteristic, complemented
820C2—41no—
821C2—361no—
822C2—361no—
823C2—1081no—
824C2—1081no—
825C2—1081no—
826C2#1172458111yescharacteristic
827C2#1172458911yescharacteristic
828C2#1172458911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#560
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723923C2semidirect
2. C3×#64093C2semidirect
3. C32×#879C2semidirect
4. #11723639C2semidirect
5. #11723639C2semidirect
6. #11723624C2semidirect
7. #11723623C2semidirect
8. #11723526C2semidirect
9. #11723517C2semidirect
10. #11723498C2semidirect
11. #11723493C2semidirect
12. #11723486C2semidirect
13. #11723482C2semidirect
14. #11723453C2semidirect
15. #11723417C2semidirect
24. C2×C3×C4⋊(C3⋊D3)C22semidirect
25. C2×C3×C4×C3⋊D3C22semidirect
30. C2×#6292C22semidirect
31. C2×#6292C22semidirect
32. C2×#6289C22semidirect
33. C2×Dic3×C3⋊D3C22semidirect
37. C3×#3752C22semidirect
38. C3×#3750C22semidirect
41. C32×C4⋊Dic3C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. C32×Dic3⋊C4C22semidirect
44. C32×C4×Dic3C22semidirect
45. #88807C22semidirect
46. #88806C22semidirect
51. #88804C22semidirect
52. #88803C22semidirect
62. #64093D3semidirect
71. C3×#879D3semidirect
139. C2×C4⋊(C3⋊D3)C2×D3semidirect
142. C2×C4×C3⋊D3C2×D3semidirect
176. #3752C2×D3semidirect
179. #3750C2×D3semidirect
183. C3×C4⋊Dic3C2×D3semidirect
185. C3×Dic3⋊C4C2×D3semidirect
186. C3×Dic3⋊C4C2×D3semidirect
187. C3×C4×Dic3C2×D3semidirect
253. #879C3⋊D3semidirect
414. C4⋊Dic3C2×C3⋊D3semidirect
419. Dic3⋊C4C2×C3⋊D3semidirect
420. Dic3⋊C4C2×C3⋊D3semidirect
421. C4×Dic3C2×C3⋊D3semidirect
512. C33#560semidirect
728. C32#5620semidirect
729. C32#5711semidirect
818. C3#10594242semidirect
819. C3#10596182semidirect

Maximal subgroups

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

subgroupindex
#117239232
C3×#640932
C32×#8792
#117236392
#117236242
#117236232
#117235262
#117235172
#117234982
#117234932
#117234862
#117234822
#117234532
#117234172
#105961823
#105942423