Finite Group Databasebeta

← #13149377

Subgroups — #13149377

Order 1728.

816 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721754C211yesmaximal, characteristic, complemented
2C9×#895C211yesmaximal, characteristic, complemented
3C3×#63456C211yesmaximal, characteristic, complemented
4#11721050C211yesmaximal, characteristic, complemented
5#11721050C211yesmaximal, characteristic, complemented
6#11721049C211yesmaximal, characteristic, complemented
7#11721043C211yesmaximal, characteristic, complemented
8#11721036C211yesmaximal, characteristic, complemented
9#11721034C211yesmaximal, characteristic, complemented
10#11721033C211yesmaximal, characteristic, complemented
11#11721032C211yesmaximal, characteristic, complemented
12#11721021C211yesmaximal, characteristic, complemented
13#11721017C211yesmaximal, characteristic, complemented
14#11721016C211yesmaximal, characteristic, complemented
15#11720966C211yesmaximal, characteristic, complemented
16#10594662—31nomaximal
17#10589722—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C9×D12C2211yescharacteristic
20C2×C9×D12C2211yescharacteristic
21C2×C9×D12C2211yescharacteristic, complemented
22C2×C4×D3×C9C2211yescharacteristic, complemented
23C2×C3×D36C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic, complemented
25C2×#6195C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×#6194C2211yescharacteristic, complemented
31C2×#6194C2211yescharacteristic, complemented
32C2×D3×Dic9C2211yescharacteristic, complemented
33C2×#6192C2211yescharacteristic
34C3×C9×C4⋊C4C2211yescharacteristic, complemented
35#88536C2211yescharacteristic
36#88536C2211yescharacteristic
37#88536C2211yescharacteristic
38C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
39#88534C2211yescharacteristic, complemented
40C4×C3⋊Dic9C2211yescharacteristic, complemented
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×(C2×D9)⋊C4C2211yescharacteristic
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic
51Dic3⋊Dic9C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53#64107—31no—
54C3×#895D311yescharacteristic
55C3×#894—31no—
56#63922—31no—
57#63922—31no—
58#63922—31no—
59#63914—31no—
60#63908—31no—
61#63906—31no—
62#63906—31no—
63#63905—31no—
64#63891—31no—
65#63886—31no—
66#63885—31no—
67#63862—31no—
68C9×#121—31no—
69#63502—31no—
70#63501—31no—
71#63501—31no—
72#63500—31no—
73#63499—31no—
74#63499—31no—
75#63492—31no—
76#63491—31no—
77#63460—31no—
78#63460—61no—
79#63456D311yescharacteristic, complemented
80#63448—31no—
81#63446—31no—
82#63444—31no—
83#63441—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×D3×D9—41no—
91C2×D3×D9—41no—
92C2×D3×D9—41no—
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C9×D12—41no—
103C9×D12—41no—
104C9×D12—41no—
105C4×D3×C9—41no—
106C3×D36—41no—
107C3×C4×D9—41no—
108#6195—41no—
109#6195—41no—
110#6194—41no—
111#6194—41no—
112#6194—41no—
113#6194—41no—
114#6194—41no—
115D3×Dic9—41no—
116#6192—41no—
117#5666—91no—
118#5620—91no—
119C22×D32—31no—
120C2×C3×D12—31no—
121C2×C3×D12C2×D311yescharacteristic
122C2×C3×D12C2×D311yescharacteristic
123C2×C3×D12C2×D311yescharacteristic
124C2×C3×C4×D3—31no—
125C2×C3×C4×D3C2×D311yescharacteristic
126C2×#626—31no—
127C2×#626—31no—
128C2×#626—31no—
129C2×#625—31no—
130C2×#625—31no—
131C2×#625—31no—
132C2×#625—31no—
133C2×#625—31no—
134C2×D3×Dic3—31no—
135C23×D9—31no—
136C32×C4⋊C4C2×D311yescharacteristic
137#3752—31no—
138#3752—31no—
139#3752—31no—
140C4⋊(C3⋊Dic3)—31no—
141#3750—31no—
142C4×C3⋊Dic3—31no—
143C3×(C2×D3)⋊C4—31no—
144C3×(C2×D3)⋊C4—31no—
145C3×(C2×D3)⋊C4—31no—
146C3×(C2×D3)⋊C4C2×D311yescharacteristic
147C3×(C2×D3)⋊C4C2×D311yescharacteristic
148C3×Dic3⋊C4—31no—
149Dic3⋊Dic3—31no—
150Dic3⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155C2×D4×C9—31no—
156C2×D4×C9—31no—
157C2×D4×C9—31no—
158C22×C4×C9—31no—
159C2×#611—31no—
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—31no—
166C22×Dic9—31no—
167C2×D36—31no—
168C2×D36C2×D311yescharacteristic
169C2×C4×D9C2×D311yescharacteristic, complemented
170C9×C4⋊C4—21no—
171C9×C4⋊C4C2×D311yescharacteristic, complemented
172C9×C22⋊C4—31no—
173C9×C22⋊C4—31no—
174#3676—31no—
175#3676—31no—
176#3676—31no—
177(C2×D9)⋊C4—31no—
178(C2×D9)⋊C4—31no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—61no—
182(C2×D9)⋊C4—61no—
183(C2×D9)⋊C4—61no—
184(C2×D9)⋊C4C2×D311yescharacteristic
185(C2×D9)⋊C4C2×D311yescharacteristic
186(C2×D9)⋊C4C2×D311yescharacteristic, complemented
187C4⋊Dic9—31no—
188C4⋊Dic9—31no—
189C4⋊Dic9—61no—
190Dic9⋊C4—31no—
191Dic9⋊C4—31no—
192Dic9⋊C4—61no—
193Dic9⋊C4C2×D311yescharacteristic, complemented
194C4×Dic9—31no—
195C4×Dic9—61no—
196C22×C3×C9C2411yescharacteristic
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9—21no—
200C2×D3×C9—21no—
201C2×D3×C9—21no—
202C2×D3×C9—21no—
203C2×D3×C9—21no—
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×D3×C9—21no—
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×C3×D9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215D3×D9—44no—
216C3×C4×C9—21no—
217C3×C4×C9—21no—
218C3×C4×C9—21no—
219C3⋊Dic9—21no—
220C3⋊Dic9—21no—
221C3⋊Dic9—21no—
222C9×Dic3—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#123—91no—
226C3×#121—31no—
227#940—91no—
228#940—91no—
229#939—91no—
230#939—91no—
231#938—91no—
232#937—91no—
233#937—91no—
234#937—91no—
235#930—91no—
236#930—91no—
237#930—91no—
238#929—91no—
239#898—91no—
240#898—91no—
241#898—91no—
242#898—181no—
243#895—91no—
244#895D911yescharacteristic, complemented
245#894—31no—
246#886—91no—
247#884—91no—
248#884—91no—
249#884—91no—
250#883—91no—
251#883—91no—
252#882—91no—
253#882—91no—
254#882—91no—
255#879—91no—
256C22×C3⋊D3—31no—
257C22×C3×D3—31no—
258C22×C3×D3—31no—
259C22×C3×D3C22×D311yescharacteristic
260C22×C3×D3C22×D311yescharacteristic
261C22×C3×D3C22×D311yescharacteristic
262C2×D32—121no—
263C2×D32—121no—
264C2×D32—121no—
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268C2×C3⋊Dic3—31no—
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3C22×D311yescharacteristic
274C3×D12—41no—
275C3×D12—41no—
276C3×D12—41no—
277C3×D12—121no—
278C3×C4×D3—41no—
279C3×C4×D3—121no—
280#626—121no—
281#626—121no—
282#626—121no—
283#625—121no—
284#625—121no—
285#625—121no—
286#625—121no—
287#625—121no—
288D3×Dic3—121no—
289C23×C9—31no—
290C23×C9—31no—
291C23×C9—31no—
292C22×D9—31no—
293C22×D9—61no—
294C22×D9—121no—
295C22×D9—121no—
296C22×D9—121no—
297C22×D9C22×D311yescharacteristic
298C22×D9C22×D311yescharacteristic
299D4×C9—121no—
300D4×C9—121no—
301D4×C9—121no—
302C2×C4×C9—21no—
303C2×C4×C9—21no—
304C2×C4×C9—21no—
305C2×C4×C9—31no—
306C2×C4×C9—121no—
307C2×C4×C9C22×D311yescharacteristic
308C2×C4×C9C22×D311yescharacteristic
309C2×C4×C9C22×D311yescharacteristic
310#611—121no—
311#611—121no—
312#611—121no—
313#611—121no—
314#611—121no—
315#611—121no—
316#611—121no—
317C2×Dic9—31no—
318C2×Dic9—31no—
319C2×Dic9—31no—
320C2×Dic9—61no—
321C2×Dic9—61no—
322C2×Dic9—61no—
323C2×Dic9—121no—
324C2×Dic9C22×D311yescharacteristic
325C2×Dic9C22×D311yescharacteristic
326D36—41no—
327D36—121no—
328C4×D9—41no—
329#560—271noSylow
330C2×C3×C9H(5,𝔽2)11yescharacteristic
331C2×C3×C9H(5,𝔽2)11yescharacteristic
332C2×C3×C9H(5,𝔽2)11yescharacteristic
333C3⋊D9—41no—
334D3×C9—41no—
335D3×C9—41no—
336D3×C9—41no—
337C3×D9—41no—
338C3×D9—41no—
339C23×D3—91no—
340C23×D3—91no—
341C2×C3×D4—31no—
342C2×C3×D4—31no—
343C2×C3×D4—31no—
344C2×C3×D4—91no—
345C22×C3×C4—31no—
346C22×C3×C4—91no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67—91no—
352C2×#67—91no—
353C2×#67—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C22×Dic3—91no—
361C2×D12—31no—
362C2×D12—91no—
363C2×D12—91no—
364C2×D12—91no—
365C2×D12C2×D911yescharacteristic
366C2×D12C2×D911yescharacteristic
367C2×D12C2×D911yescharacteristic, complemented
368C2×C4×D3—31no—
369C2×C4×D3—91no—
370C2×C4×D3C2×D911yescharacteristic, complemented
371C3×C4⋊C4—21no—
372C3×C4⋊C4—91no—
373C3×C4⋊C4C2×D911yescharacteristic, complemented
374C3×C4⋊C4D3211yescharacteristic
375C3×C22⋊C4—31no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380#217—91no—
381#217—91no—
382#217—91no—
383#217—91no—
384(C2×D3)⋊C4—31no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—31no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4—181no—
398(C2×D3)⋊C4—181no—
399(C2×D3)⋊C4—181no—
400(C2×D3)⋊C4C2×D911yescharacteristic
401(C2×D3)⋊C4C2×D911yescharacteristic, complemented
402C4⋊Dic3—91no—
403C4⋊Dic3—91no—
404C4⋊Dic3—91no—
405C4⋊Dic3—91no—
406C4⋊Dic3—181no—
407Dic3⋊C4—31no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—181no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C4×Dic3—181no—
416C22×C32C23×D311yescharacteristic
417C2×C3⋊D3—61no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—61no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—61no—
430C2×C3×D3—61no—
431C2×C3×D3—61no—
432C2×C3×D3—61no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435D32—124no—
436C32×C4—21no—
437C32×C4—21no—
438C32×C4—21no—
439C3⋊Dic3—61no—
440C3⋊Dic3—61no—
441C3⋊Dic3—61no—
442C3×Dic3—21no—
443C3×Dic3—61no—
444C3×Dic3—61no—
445C22×C9—21no—
446C22×C9—61no—
447C22×C9—61no—
448C22×C9—61no—
449C22×C9—61no—
450C22×C9—61no—
451C22×C9—61no—
452C22×C9—61no—
453C22×C9—61no—
454C22×C9—61no—
455C22×C9C23×D311yescharacteristic
456C2×D9—21no—
457C2×D9—21no—
458C2×D9—21no—
459C2×D9—21no—
460C2×D9—21no—
461C2×D9—21no—
462C2×D9—61no—
463C2×D9—61no—
464C2×D9—61no—
465C2×D9—121no—
466C2×D9—121no—
467C2×D9—121no—
468C2×D9—124no—
469C4×C9—21no—
470C4×C9—21no—
471C4×C9—21no—
472C4×C9—41no—
473C4×C9—41no—
474C4×C9—41no—
475C4×C9—61no—
476Dic9—21no—
477Dic9—21no—
478Dic9—61no—
479Dic9—61no—
480Dic9—61no—
481Dic9—121no—
482Dic9—121no—
483Dic9—121no—
484#127—271no—
485#126—271no—
486#126—271no—
487#123—91no—
488#123—271no—
489#123—271no—
490#121—31no—
491#121—271no—
492#121—271no—
493#121—271no—
494#121—271no—
495#121—271no—
496#120—271no—
497#120—271no—
498#120—271no—
499C3×C9#56011yescharacteristic, complemented, Sylow
500C23×C3—31no—
501C23×C3—31no—
502C23×C3—31no—
503C23×C3—91no—
504C23×C3—91no—
505C22×D3—31no—
506C22×D3—31no—
507C22×D3—91no—
508C22×D3—91no—
509C22×D3—181no—
510C22×D3—361no—
511C22×D3—361no—
512C22×D3—361no—
513C22×D3—361no—
514C22×D3—361no—
515C22×D3—361no—
516C22×D3C22×D911yescharacteristic
517C22×D3C22×D911yescharacteristic
518C22×D3C22×D911yescharacteristic
519C3×D4—121no—
520C3×D4—121no—
521C3×D4—121no—
522C3×D4—361no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—31no—
527C2×C3×C4—91no—
528C2×C3×C4—91no—
529C2×C3×C4—121no—
530C2×C3×C4—361no—
531C2×C3×C4C22×D911yescharacteristic
532C2×C3×C4C22×D911yescharacteristic
533C2×C3×C4C22×D911yescharacteristic
534C2×C3×C4C2×D3211yescharacteristic
535C2×C3×C4C2×D3211yescharacteristic
536C2×C3×C4C2×D3211yescharacteristic
537#67—361no—
538#67—361no—
539#67—361no—
540#67—361no—
541#67—361no—
542#67—361no—
543#67—361no—
544#67—361no—
545#67—361no—
546#67—361no—
547#67—361no—
548#67—361no—
549#67—361no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—91no—
553C2×Dic3—91no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—91no—
557C2×Dic3—91no—
558C2×Dic3—181no—
559C2×Dic3—181no—
560C2×Dic3—181no—
561C2×Dic3—361no—
562C2×Dic3C22×D911yescharacteristic
563D12—41no—
564D12—41no—
565D12—41no—
566D12—121no—
567D12—361no—
568D12—361no—
569D12—361no—
570C4×D3—41no—
571C4×D3—121no—
572C4×D3—361no—
573C2×C32#100411yescharacteristic
574C2×C32#100411yescharacteristic
575C2×C32#100911yescharacteristic
576C3⋊D3—121no—
577C3×D3—41no—
578C3×D3—41no—
579C3×D3—41no—
580C3×D3—121no—
581C3×D3—121no—
582C2×C9—21no—
583C2×C9—21no—
584C2×C9—21no—
585C2×C9—121no—
586C2×C9—121no—
587C2×C9—121no—
588C2×C9#100411yescharacteristic
589C2×C9#100911yescharacteristic
590C2×C9#100911yescharacteristic
591D9—41no—
592D9—41no—
593D9—121no—
594D9—241no—
595C24—271no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—91no—
600C2×D4—271no—
601C2×D4—271no—
602C2×D4—271no—
603C2×D4—271no—
604C2×D4—271no—
605C2×D4—271no—
606C2×D4—271no—
607C2×D4—271no—
608C22×C4—31no—
609C22×C4—91no—
610C22×C4—271no—
611C4⋊C4—91no—
612C4⋊C4—271no—
613C4⋊C4—271no—
614C4⋊C4—271no—
615C4⋊C4—271no—
616C4⋊C4D3×D911yescharacteristic, complemented
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—91no—
622C22⋊C4—271no—
623C22⋊C4—271no—
624C22⋊C4—271no—
625C22⋊C4—271no—
626C22⋊C4—271no—
627C22⋊C4—271no—
628C22⋊C4—271no—
629C42—271no—
630C22×C3—21no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—181no—
641C22×C3—181no—
642C22×C3—181no—
643C22×C3—181no—
644C22×C3—181no—
645C22×C3—181no—
646C22×C3C23×D911yescharacteristic
647C22×C3C22×D3211yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—181no—
664C2×D3—181no—
665C2×D3—181no—
666C2×D3—181no—
667C2×D3—181no—
668C2×D3—181no—
669C2×D3—361no—
670C2×D3—361no—
671C2×D3—361no—
672C2×D3—364no—
673C2×D3—364no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—61no—
684C3×C4—181no—
685C3×C4—181no—
686Dic3—21no—
687Dic3—61no—
688Dic3—61no—
689Dic3—181no—
690Dic3—181no—
691Dic3—181no—
692Dic3—181no—
693Dic3—181no—
694Dic3—181no—
695Dic3—361no—
696Dic3—361no—
697Dic3—361no—
698C32#562011yescharacteristic
699C9—21no—
700C9#566611yescharacteristic, complemented
701C23—31no—
702C23—31no—
703C23—31no—
704C23—91no—
705C23—91no—
706C23—271no—
707C23—1081no—
708C23—1081no—
709C23—1081no—
710D4—121no—
711D4—121no—
712D4—121no—
713D4—361no—
714D4—1081no—
715D4—1081no—
716D4—1081no—
717D4—1081no—
718D4—1081no—
719D4—1081no—
720D4—1081no—
721D4—1081no—
722C2×C4—31no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—121no—
726C2×C4—271no—
727C2×C4—271no—
728C2×C4—271no—
729C2×C4—361no—
730C2×C4—1081no—
731C2×C4C2×D3×D911yescharacteristic
732C2×C4C2×D3×D911yescharacteristic
733C2×C4C2×D3×D911yescharacteristic
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—121no—
738C2×C3—121no—
739C2×C3—121no—
740C2×C3—361no—
741C2×C3—361no—
742C2×C3#6371011yescharacteristic
743C2×C3#6371011yescharacteristic
744C2×C3#6371511yescharacteristic
745C2×C3#6430711yescharacteristic
746C2×C3#6431311yescharacteristic
747C2×C3#6432011yescharacteristic
748D3—41no—
749D3—41no—
750D3—41no—
751D3—121no—
752D3—121no—
753D3—361no—
754D3—361no—
755D3—721no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—181no—
766C22—181no—
767C22—181no—
768C22—181no—
769C22—181no—
770C22—181no—
771C22—541no—
772C22—541no—
773C22—541no—
774C22—1084no—
775C22C22×D3×D911yescharacteristic
776C4—21no—
777C4—21no—
778C4—21no—
779C4—61no—
780C4—181no—
781C4—181no—
782C4—541no—
783C4—541no—
784C4—541no—
785C3—21no—
786C3#1058972211yescharacteristic, complemented
787C3#1059466211yescharacteristic
788C2—121no—
789C2—121no—
790C2—121no—
791C2—361no—
792C2—361no—
793C2—1081no—
794C2#1172247611yescharacteristic
795C2#1172249911yescharacteristic
796C2#1172251511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#560
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721754C2semidirect
2. C9×#895C2semidirect
3. C3×#63456C2semidirect
4. #11721050C2semidirect
5. #11721050C2semidirect
6. #11721049C2semidirect
7. #11721043C2semidirect
8. #11721036C2semidirect
9. #11721034C2semidirect
10. #11721033C2semidirect
11. #11721032C2semidirect
12. #11721021C2semidirect
13. #11721017C2semidirect
14. #11721016C2semidirect
15. #11720966C2semidirect
21. C2×C9×D12C22semidirect
22. C2×C4×D3×C9C22semidirect
24. C2×C3×C4×D9C22semidirect
30. C2×#6194C22semidirect
31. C2×#6194C22semidirect
32. C2×D3×Dic9C22semidirect
34. C3×C9×C4⋊C4C22semidirect
38. C4⋊(C3⋊Dic9)C22semidirect
39. #88534C22semidirect
40. C4×C3⋊Dic9C22semidirect
42. C9×(C2×D3)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×Dic9⋊C4C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
51. Dic3⋊Dic9C22semidirect
52. Dic9⋊Dic3C22semidirect
79. #63456D3semidirect
169. C2×C4×D9C2×D3semidirect
171. C9×C4⋊C4C2×D3semidirect
186. (C2×D9)⋊C4C2×D3semidirect
193. Dic9⋊C4C2×D3semidirect
244. #895D9semidirect
367. C2×D12C2×D9semidirect
370. C2×C4×D3C2×D9semidirect
373. C3×C4⋊C4C2×D9semidirect
401. (C2×D3)⋊C4C2×D9semidirect
499. C3×C9#560semidirect
616. C4⋊C4D3×D9semidirect
700. C9#5666semidirect
786. C3#10589722semidirect

Maximal subgroups

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

subgroupindex
#117217542
C9×#8952
C3×#634562
#117210502
#117210492
#117210432
#117210362
#117210342
#117210332
#117210322
#117210212
#117210172
#117210162
#117209662
#105946623
#105897223