Finite Group Databasebeta

← #13175843

Subgroups — #13175843

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×#64092C211yesmaximal, characteristic, complemented
3C32×#883C211yesmaximal, characteristic, complemented
4#11723639C211yesmaximal, characteristic, complemented
5#11723638C211yesmaximal, characteristic, complemented
6#11723633C211yesmaximal, characteristic, complemented
7#11723628C211yesmaximal, characteristic, complemented
8#11723526C211yesmaximal, characteristic, complemented
9#11723525C211yesmaximal, characteristic, complemented
10#11723520C211yesmaximal, characteristic, complemented
11#11723516C211yesmaximal, characteristic, complemented
12#11723514C211yesmaximal, characteristic, complemented
13#11723486C211yesmaximal, characteristic, complemented
14#11723411C211yesmaximal, characteristic, complemented
15#11723403C211yesmaximal, characteristic, complemented
16#10596137—31nomaximal
17#10594244—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×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic, complemented
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6292C2211yescharacteristic, complemented
29C2×#6291C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×#6291C2211yescharacteristic, complemented
32C2×#6290C2211yescharacteristic, complemented
33C2×#6289C2211yescharacteristic, complemented
34C33×C22⋊C4C2211yescharacteristic
35#88859C2211yescharacteristic
36#88859C2211yescharacteristic
37C3×#3757C2211yescharacteristic
38C3×#3752C2211yescharacteristic, complemented
39C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40C3×#3750C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C32×C4⋊Dic3C2211yescharacteristic, complemented
44C32×Dic3⋊C4C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51#88804C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#123—31no—
54#64149—31no—
55#64146—31no—
56#64139—31no—
57#64139—31no—
58#64107—31no—
59#64107—31no—
60#64104—31no—
61#64104—31no—
62#64093—31no—
63#64093—31no—
64#64092—31no—
65#64092D311yescharacteristic, complemented
66#64091—31no—
67#64091—31no—
68#64091—34no—
69#64091—64no—
70C3×#883—34no—
71C3×#883D314yescomplemented
72#63981—34no—
73#63981—34no—
74#63979—34no—
75#63975—34no—
76#63910—34no—
77#63910—34no—
78#63909—34no—
79#63909—34no—
80#63906—34no—
81#63906—34no—
82#63848—34no—
83#63848—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×C32×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—
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C3×C4×C3⋊D3—41no—
104C32×#67—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C32×C4×D3—41no—
109#6292—41no—
110#6292—41no—
111#6292—41no—
112#6291—41no—
113#6291—41no—
114#6291—41no—
115#6290—41no—
116#6289—41no—
117#5666—94no—
118#5666—91no—
119C23×C3⋊D3—31no—
120C23×C3⋊D3—34no—
121C23×C3⋊D3—64no—
122C2×C32×D4—31no—
123C22×C32×C4—31no—
124C2×#638—31no—
125C2×#638—34no—
126C2×#638—31no—
127C2×#638—31no—
128C2×#638—31no—
129C2×#638—31no—
130C2×#638—64no—
131C2×#638C2×D311yescharacteristic
132C2×C4⋊(C3⋊D3)—31no—
133C2×C4⋊(C3⋊D3)—31no—
134C2×C4⋊(C3⋊D3)—31no—
135C2×C4⋊(C3⋊D3)—31no—
136C2×C4⋊(C3⋊D3)—31no—
137C2×C4⋊(C3⋊D3)—34no—
138C2×C4⋊(C3⋊D3)—34no—
139C2×C4⋊(C3⋊D3)—64no—
140C2×C4⋊(C3⋊D3)—64no—
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
143C2×C3×#67—34no—
144C2×C3×#67C2×D314yes—
145C2×C3×C4×D3—34no—
146C2×C3×C4×D3C2×D314yescomplemented
147C2×#626—34no—
148C2×#626—34no—
149C2×#626—34no—
150C2×#626—34no—
151C2×#626—34no—
152C2×#626—34no—
153C2×#625—34no—
154C2×#624—34no—
155C32×C4⋊C4—31no—
156C32×C4⋊C4—31no—
157C32×C22⋊C4—24no—
158C32×C22⋊C4—31no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4C2×D314yes—
161C32×C22⋊C4C2×D311yescharacteristic
162#3757C2×D311yescharacteristic
163#3752—31no—
164#3752—31no—
165#3752—34no—
166#3752—34no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752—31no—
171#3752—31no—
172#3752—64no—
173#3752—64no—
174#3752C2×D311yescharacteristic, complemented
175C4⋊(C3⋊Dic3)—31no—
176C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
177#3750—31no—
178#3750C2×D311yescharacteristic, complemented
179C4×C3⋊Dic3—31no—
180C3×#217—34no—
181C3×#217C2×D314yes—
182C3×(C2×D3)⋊C4—34no—
183C3×(C2×D3)⋊C4C2×D314yescomplemented
184C3×C4⋊Dic3—34no—
185C3×C4⋊Dic3C2×D314yescomplemented
186C3×Dic3⋊C4—34no—
187C3×Dic3⋊C4C2×D314yescomplemented
188Dic3⋊Dic3—34no—
189Dic3⋊Dic3—34no—
190#3722—34no—
191#3722—34no—
192#3722—34no—
193#3722—34no—
194#3722—34no—
195Dic32—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×C32×D3—21no—
214C2×C32×D3—21no—
215C2×C32×D3—21no—
216C33×C4—21no—
217C33×C4—21no—
218C3⋊(C3⋊Dic3)—21no—
219C3×C3⋊Dic3—21no—
220C3×C3⋊Dic3—21no—
221C3×C3⋊Dic3—21no—
222C32×Dic3—21no—
223C32×Dic3—21no—
224C32×Dic3—21no—
225C3×#123—34no—
226C3×#123—91no—
227#940—94no—
228#940—91no—
229#937—94no—
230#937—91no—
231#930—94no—
232#930—94no—
233#930—91no—
234#930—91no—
235#898—94no—
236#898—94no—
237#898—91no—
238#898—91no—
239#895—94no—
240#895—94no—
241#895—91no—
242#895—91no—
243#884—94no—
244#884—94no—
245#884—91no—
246#884—91no—
247#883—34no—
248#883—94no—
249#883—91no—
250#883C3⋊D311yescharacteristic, complemented
251#882—94no—
252#882—91no—
253#882—94no—
254#882—91no—
255#882—184no—
256C23×C32—24no—
257C23×C32—31no—
258C23×C32C22×D314yes—
259C23×C32C22×D311yescharacteristic
260C22×C3⋊D3—31no—
261C22×C3⋊D3—31no—
262C22×C3⋊D3—31no—
263C22×C3⋊D3—34no—
264C22×C3⋊D3—34no—
265C22×C3⋊D3—34no—
266C22×C3⋊D3—64no—
267C22×C3⋊D3—64no—
268C22×C3⋊D3—64no—
269C22×C3⋊D3—121no—
270C22×C3⋊D3—121no—
271C22×C3⋊D3—121no—
272C22×C3⋊D3—124no—
273C22×C3⋊D3—124no—
274C22×C3⋊D3—124no—
275C22×C3⋊D3—128no—
276C22×C3⋊D3—128no—
277C22×C3⋊D3—128no—
278C22×C3⋊D3C22×D311yescharacteristic
279C22×C3×D3—34no—
280C22×C3×D3C22×D314yes—
281C32×D4—121no—
282C2×C32×C4—24no—
283C2×C32×C4—24no—
284C2×C32×C4—31no—
285C2×C32×C4—31no—
286C2×C32×C4—31no—
287C2×C32×C4—121no—
288C2×C32×C4C22×D314yes—
289C2×C32×C4C22×D314yes—
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292#638—41no—
293#638—121no—
294#638—121no—
295#638—121no—
296#638—121no—
297#638—121no—
298#638—124no—
299#638—128no—
300C2×C3⋊Dic3—31no—
301C2×C3⋊Dic3—34no—
302C2×C3⋊Dic3—64no—
303C2×C3⋊Dic3C22×D311yescharacteristic
304C2×C3⋊Dic3C22×D311yescharacteristic
305C2×C3⋊Dic3C22×D311yescharacteristic
306C4⋊(C3⋊D3)—121no—
307C4⋊(C3⋊D3)—121no—
308C4⋊(C3⋊D3)—124no—
309C4⋊(C3⋊D3)—124no—
310C4⋊(C3⋊D3)—128no—
311C4⋊(C3⋊D3)—128no—
312C4⋊(C3⋊D3)—121no—
313C4⋊(C3⋊D3)—121no—
314C4⋊(C3⋊D3)—121no—
315C4×C3⋊D3—41no—
316C4×C3⋊D3—121no—
317C3×#67—44no—
318C3×#67—124no—
319C2×C3×Dic3—34no—
320C2×C3×Dic3—34no—
321C2×C3×Dic3—34no—
322C2×C3×Dic3C22×D314yes—
323C2×C3×Dic3C22×D314yes—
324C2×C3×Dic3C22×D314yes—
325C3×C4×D3—44no—
326C3×C4×D3—124no—
327#626—124no—
328#626—124no—
329#626—124no—
330#626—124no—
331#626—124no—
332#626—124no—
333#625—124no—
334#624—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—
344C32×D3—41no—
345C23×D3—94no—
346C23×D3—91no—
347C23×D3—184no—
348C2×C3×D4—34no—
349C2×C3×D4—91no—
350C22×C3×C4—34no—
351C22×C3×C4—91no—
352C2×#67—34no—
353C2×#67—94no—
354C2×#67—94no—
355C2×#67—94no—
356C2×#67—94no—
357C2×#67—94no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—184no—
364C2×#67C2×C3⋊D311yescharacteristic
365C2×D12—94no—
366C2×D12—94no—
367C2×D12—94no—
368C2×D12—91no—
369C2×D12—91no—
370C2×D12—91no—
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—91no—
380C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
381C3×C4⋊C4—34no—
382C3×C4⋊C4—34no—
383C3×C4⋊C4—91no—
384C3×C4⋊C4—91no—
385C3×C22⋊C4—24no—
386C3×C22⋊C4—34no—
387C3×C22⋊C4—34no—
388C3×C22⋊C4—91no—
389C3×C22⋊C4—91no—
390C3×C22⋊C4D3214yes—
391C3×C22⋊C4C2×C3⋊D311yescharacteristic
392#217—34no—
393#217C2×C3⋊D311yescharacteristic
394(C2×D3)⋊C4—34no—
395(C2×D3)⋊C4—94no—
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—91no—
403(C2×D3)⋊C4—91no—
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—184no—
410(C2×D3)⋊C4—184no—
411(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
412C4⋊Dic3—34no—
413C4⋊Dic3—94no—
414C4⋊Dic3—91no—
415C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
416Dic3⋊C4—34no—
417Dic3⋊C4—94no—
418Dic3⋊C4—91no—
419Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
420C4×Dic3—94no—
421C4×Dic3—91no—
422C22×C32—28no—
423C22×C32—21no—
424C22×C32—24no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—24no—
428C22×C32—24no—
429C22×C32—24no—
430C22×C32—44no—
431C22×C32—44no—
432C22×C32—61no—
433C22×C32—61no—
434C22×C32—61no—
435C22×C32C23×D314yes—
436C22×C32C23×D311yescharacteristic
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—64no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—61no—
447C2×C3⋊D3—61no—
448C2×C3⋊D3—64no—
449C2×C3⋊D3—61no—
450C2×C3⋊D3—61no—
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—24no—
471C2×C3×D3—24no—
472C2×C3×D3—24no—
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—
485C3⋊Dic3—21no—
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—64no—
495C3×Dic3—64no—
496C3×Dic3—64no—
497#127—271no—
498#126—271no—
499#126—271no—
500#123—31no—
501#123—91no—
502#123—271no—
503#121—271no—
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—34no—
515C23×C3—91no—
516C23×C3C2×D3214yes—
517C23×C3C22×C3⋊D311yescharacteristic
518C22×D3—34no—
519C22×D3—94no—
520C22×D3—94no—
521C22×D3—94no—
522C22×D3—91no—
523C22×D3—91no—
524C22×D3—91no—
525C22×D3—184no—
526C22×D3—184no—
527C22×D3—184no—
528C22×D3—364no—
529C22×D3—364no—
530C22×D3—364no—
531C22×D3—361no—
532C22×D3—361no—
533C22×D3—361no—
534C22×D3—368no—
535C22×D3—368no—
536C22×D3—368no—
537C22×D3C22×C3⋊D311yescharacteristic
538C3×D4—124no—
539C3×D4—361no—
540C2×C3×C4—24no—
541C2×C3×C4—24no—
542C2×C3×C4—34no—
543C2×C3×C4—34no—
544C2×C3×C4—34no—
545C2×C3×C4—91no—
546C2×C3×C4—91no—
547C2×C3×C4—91no—
548C2×C3×C4—124no—
549C2×C3×C4—361no—
550C2×C3×C4C2×D3214yes—
551C2×C3×C4C2×D3214yes—
552C2×C3×C4C22×C3⋊D311yescharacteristic
553C2×C3×C4C22×C3⋊D311yescharacteristic
554#67—41no—
555#67—124no—
556#67—361no—
557#67—361no—
558#67—361no—
559#67—364no—
560#67—364no—
561#67—364no—
562#67—361no—
563#67—364no—
564#67—364no—
565#67—361no—
566#67—368no—
567C2×Dic3—34no—
568C2×Dic3—34no—
569C2×Dic3—34no—
570C2×Dic3—94no—
571C2×Dic3—91no—
572C2×Dic3—184no—
573C2×Dic3C22×C3⋊D311yescharacteristic
574C2×Dic3C22×C3⋊D311yescharacteristic
575C2×Dic3C22×C3⋊D311yescharacteristic
576D12—364no—
577D12—364no—
578D12—361no—
579D12—361no—
580D12—368no—
581D12—368no—
582D12—364no—
583D12—364no—
584D12—364no—
585D12—361no—
586D12—361no—
587D12—361no—
588C4×D3—41no—
589C4×D3—124no—
590C4×D3—361no—
591C4×D3—364no—
592C2×C32—24no—
593C2×C32—24no—
594C2×C32—24no—
595C2×C32—48no—
596C2×C32—44no—
597C2×C32—41no—
598C2×C32—121no—
599C2×C32#100414yes—
600C2×C32#100411yescharacteristic
601C2×C32#100914yes—
602C2×C32#100914yes—
603C2×C32#100911yescharacteristic
604C2×C32#100911yescharacteristic
605C3⋊D3—41no—
606C3⋊D3—128no—
607C3⋊D3—128no—
608C3⋊D3—121no—
609C3⋊D3—124no—
610C3⋊D3—124no—
611C3⋊D3—121no—
612C3⋊D3—121no—
613C3⋊D3—124no—
614C3⋊D3—244no—
615C3×D3—44no—
616C3×D3—124no—
617C24—271no—
618C2×D4—31no—
619C2×D4—91no—
620C2×D4—271no—
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—31no—
631C22×C4—91no—
632C22×C4—271no—
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—91no—
636C4⋊C4—91no—
637C4⋊C4—271no—
638C4⋊C4—271no—
639C22⋊C4—31no—
640C22⋊C4—31no—
641C22⋊C4—91no—
642C22⋊C4—91no—
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—271no—
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—64no—
663C22×C3—64no—
664C22×C3—64no—
665C22×C3—181no—
666C22×C3—181no—
667C22×C3—181no—
668C22×C3C22×D3214yes—
669C22×C3C23×C3⋊D311yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
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—181no—
716C3×C4—181no—
717C3×C4—181no—
718Dic3—21no—
719Dic3—21no—
720Dic3—21no—
721Dic3—64no—
722Dic3—64no—
723Dic3—64no—
724Dic3—184no—
725Dic3—181no—
726Dic3—364no—
727C32—24no—
728C32#566614yescomplemented
729C32#566611yescharacteristic, complemented
730C23—31no—
731C23—91no—
732C23—271no—
733C23—271no—
734C23—271no—
735C23—1081no—
736C23—1081no—
737C23—1081no—
738C23C2×D3×C3⋊D311yescharacteristic
739D4—121no—
740D4—361no—
741D4—1081no—
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—91no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—121no—
758C2×C4—271no—
759C2×C4—361no—
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—124no—
770C2×C3—361no—
771C2×C3#6430814yes—
772C2×C3#6431414yes—
773C2×C3#6431414yes—
774C2×C3#6436111yescharacteristic
775C2×C3#6436611yescharacteristic
776C2×C3#6436611yescharacteristic
777D3—41no—
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—61no—
792C22—61no—
793C22—61no—
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—181no—
814C4—181no—
815C4—181no—
816C4—541no—
817C3—24no—
818C3#1059424414yescomplemented
819C3#1059613711yescharacteristic, complemented
820C2—41no—
821C2—121no—
822C2—361no—
823C2—1081no—
824C2—1081no—
825C2—1081no—
826C2#1172458111yescharacteristic
827C2#1172458811yescharacteristic
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×#64092C2semidirect
3. C32×#883C2semidirect
4. #11723639C2semidirect
5. #11723638C2semidirect
6. #11723633C2semidirect
7. #11723628C2semidirect
8. #11723526C2semidirect
9. #11723525C2semidirect
10. #11723520C2semidirect
11. #11723516C2semidirect
12. #11723514C2semidirect
13. #11723486C2semidirect
14. #11723411C2semidirect
15. #11723403C2semidirect
23. C2×C3×C4×C3⋊D3C22semidirect
25. C2×C32×C4×D3C22semidirect
28. C2×#6292C22semidirect
31. C2×#6291C22semidirect
32. C2×#6290C22semidirect
33. C2×#6289C22semidirect
38. C3×#3752C22semidirect
39. C3×C4⋊(C3⋊Dic3)C22semidirect
40. C3×#3750C22semidirect
42. C32×(C2×D3)⋊C4C22semidirect
43. C32×C4⋊Dic3C22semidirect
44. C32×Dic3⋊C4C22semidirect
45. #88807C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88804C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
65. #64092D3semidirect
71. C3×#883D3semidirect
142. C2×C4×C3⋊D3C2×D3semidirect
146. C2×C3×C4×D3C2×D3semidirect
174. #3752C2×D3semidirect
176. C4⋊(C3⋊Dic3)C2×D3semidirect
178. #3750C2×D3semidirect
183. C3×(C2×D3)⋊C4C2×D3semidirect
185. C3×C4⋊Dic3C2×D3semidirect
187. C3×Dic3⋊C4C2×D3semidirect
250. #883C3⋊D3semidirect
380. C2×C4×D3C2×C3⋊D3semidirect
411. (C2×D3)⋊C4C2×C3⋊D3semidirect
415. C4⋊Dic3C2×C3⋊D3semidirect
419. Dic3⋊C4C2×C3⋊D3semidirect
512. C33#560semidirect
728. C32#5666semidirect
729. C32#5666semidirect
818. C3#10594244semidirect
819. C3#10596137semidirect

Maximal subgroups

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

subgroupindex
#117239232
C3×#640922
C32×#8832
#117236392
#117236382
#117236332
#117236282
#117235262
#117235252
#117235202
#117235162
#117235142
#117234862
#117234112
#117234032
#105961373
#105942443