Finite Group Databasebeta

← #13148370

Subgroups — #13148370

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#11721725C211yesmaximal, characteristic, complemented
2C9×#882C211yesmaximal, characteristic, complemented
3C3×#63446C211yesmaximal, characteristic, complemented
4#11721286C211yesmaximal, characteristic, complemented
5#11721286C211yesmaximal, characteristic, complemented
6#11721281C211yesmaximal, characteristic, complemented
7#11721270C211yesmaximal, characteristic, complemented
8#11721043C211yesmaximal, characteristic, complemented
9#11721036C211yesmaximal, characteristic, complemented
10#11721031C211yesmaximal, characteristic, complemented
11#11721016C211yesmaximal, characteristic, complemented
12#11721015C211yesmaximal, characteristic, complemented
13#11720989C211yesmaximal, characteristic, complemented
14#11720982C211yesmaximal, characteristic, complemented
15#11720966C211yesmaximal, characteristic, complemented
16#10594234—31nomaximal
17#10589697—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C2×C9×#67C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C2×C9×D12C2211yescharacteristic
23C2×C9×D12C2211yescharacteristic
24C2×C3×D36C2211yescharacteristic, complemented
25C2×C3×C4×D9C2211yescharacteristic, complemented
26C2×#6194C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×#6194C2211yescharacteristic, complemented
31C2×#6194C2211yescharacteristic, complemented
32C2×D3×Dic9C2211yescharacteristic, complemented
33C2×Dic3×D9C2211yescharacteristic, complemented
34C3×C9×C22⋊C4C2211yescharacteristic
35#88551C2211yescharacteristic
36#88551C2211yescharacteristic
37C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
38#88534C2211yescharacteristic, complemented
39#88534C2211yescharacteristic, complemented
40C4×C3⋊Dic9C2211yescharacteristic, complemented
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C3×Dic9⋊C4C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53#64088—31no—
54C3×#884—31no—
55C3×#882D311yescharacteristic
56#63976—31no—
57#63976—31no—
58#63970—31no—
59#63970—31no—
60#63914—31no—
61#63908—31no—
62#63905—31no—
63#63891—31no—
64#63885—31no—
65#63885—31no—
66#63884—31no—
67#63862—31no—
68C9×#120—31no—
69#63515—31no—
70#63515—31no—
71#63502—31no—
72#63501—31no—
73#63501—31no—
74#63500—31no—
75#63500—31no—
76#63497—31no—
77#63446—31no—
78#63446D311yescharacteristic, complemented
79#63445—31no—
80#63445—31no—
81#63441—31no—
82#63441—31no—
83#63441—61no—
84C23×C3×C9C2311yescharacteristic
85C22×D3×C9—41no—
86C22×D3×C9—41no—
87C22×D3×C9—41no—
88C22×D3×C9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×D3×C9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C22×C3×D9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C9×#67—41no—
100C3×#611—41no—
101C3×#611—41no—
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C9×D12—41no—
106C9×D12—41no—
107C3×D36—41no—
108C3×C4×D9—41no—
109#6194—41no—
110#6194—41no—
111#6194—41no—
112#6194—41no—
113#6194—41no—
114#6194—41no—
115D3×Dic9—41no—
116Dic3×D9—41no—
117#5620—91no—
118#5595—91no—
119C23×C3×D3C2×D311yescharacteristic
120C2×C3×#67—31no—
121C2×C3×#67—31no—
122C2×C3×#67C2×D311yescharacteristic
123C2×C3×D12—31no—
124C2×C3×D12C2×D311yescharacteristic
125C2×C3×D12C2×D311yescharacteristic
126C2×C3×C4×D3—31no—
127C2×#625—31no—
128C2×#625—31no—
129C2×#625—31no—
130C2×#625—31no—
131C2×#625—31no—
132C2×#625—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C24×C9—31no—
136C32×C22⋊C4C2×D311yescharacteristic
137#3757—31no—
138#3757—31no—
139C4⋊(C3⋊Dic3)—31no—
140#3750—31no—
141#3750—31no—
142C4×C3⋊Dic3—31no—
143C3×(C2×D3)⋊C4—31no—
144C3×(C2×D3)⋊C4C2×D311yescharacteristic
145C3×(C2×D3)⋊C4C2×D311yescharacteristic
146C3×Dic3⋊C4—31no—
147Dic3⋊Dic3—31no—
148Dic3⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊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—
158C2×#611—31no—
159C2×#611—31no—
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×#611—31no—
164C2×#611C2×D311yescharacteristic
165C2×#611C2×D311yescharacteristic
166C22×Dic9—31no—
167C2×D36C2×D311yescharacteristic, complemented
168C2×C4×D9—31no—
169C2×C4×D9C2×D311yescharacteristic, complemented
170C9×C22⋊C4—21no—
171C9×C22⋊C4—31no—
172C9×C22⋊C4—31no—
173C9×C22⋊C4C2×D311yescharacteristic
174#3676—31no—
175#3676—31no—
176#3676—31no—
177#3676—31no—
178#3676—31no—
179#3676—31no—
180#3676—31no—
181#3676—61no—
182#3676—61no—
183(C2×D9)⋊C4—31no—
184(C2×D9)⋊C4C2×D311yescharacteristic, complemented
185C4⋊Dic9—31no—
186C4⋊Dic9—31no—
187C4⋊Dic9—61no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—31no—
191Dic9⋊C4—61no—
192Dic9⋊C4—61no—
193Dic9⋊C4C2×D311yescharacteristic, complemented
194C4×Dic9—31no—
195C4×Dic9—61no—
196C22×C3×C9—21no—
197C22×C3×C9—21no—
198C22×C3×C9—21no—
199C22×C3×C9C2411yescharacteristic
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×D3×C9—44no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
216C3×C4×C9—21no—
217C3×C4×C9—21no—
218C3⋊Dic9—21no—
219C3⋊Dic9—21no—
220C3⋊Dic9—21no—
221C3⋊Dic9—21no—
222C9×Dic3—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#121—91no—
226C3×#120—31no—
227#953—91no—
228#953—91no—
229#940—91no—
230#940—91no—
231#939—91no—
232#939—91no—
233#939—91no—
234#939—91no—
235#938—91no—
236#938—91no—
237#938—91no—
238#937—91no—
239#937—91no—
240#935—91no—
241#930—91no—
242#929—91no—
243#898—91no—
244#894—91no—
245#886—91no—
246#884—31no—
247#884—91no—
248#884—91no—
249#883—91no—
250#883—91no—
251#882D911yescharacteristic, complemented
252#879—91no—
253#879—91no—
254#879—91no—
255#879—181no—
256C23×C32C22×D311yescharacteristic
257C22×C3×D3—31no—
258C22×C3×D3—31no—
259C22×C3×D3—41no—
260C22×C3×D3—41no—
261C22×C3×D3—41no—
262C22×C3×D3C22×D311yescharacteristic
263C22×C3×D3C22×D311yescharacteristic
264C22×C3×D3C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C3⋊Dic3—31no—
268C2×C3⋊Dic3—31no—
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C3×#67—41no—
272C3×#67—121no—
273C3×#67—121no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3C22×D311yescharacteristic
277C3×D12—41no—
278C3×D12—41no—
279C3×D12—121no—
280C3×C4×D3—121no—
281#625—121no—
282#625—121no—
283#625—121no—
284#625—121no—
285#625—121no—
286#625—121no—
287D3×Dic3—121no—
288D3×Dic3—121no—
289C23×C9—21no—
290C23×C9—31no—
291C23×C9—31no—
292C23×C9—31no—
293C23×C9—121no—
294C23×C9—121no—
295C23×C9—121no—
296C23×C9C22×D311yescharacteristic
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—31no—
305C2×C4×C9C22×D311yescharacteristic
306C2×C4×C9C22×D311yescharacteristic
307#611—41no—
308#611—41no—
309#611—121no—
310#611—121no—
311#611—121no—
312#611—121no—
313#611—121no—
314#611—121no—
315C2×Dic9—31no—
316C2×Dic9—31no—
317C2×Dic9—31no—
318C2×Dic9—31no—
319C2×Dic9—61no—
320C2×Dic9—61no—
321C2×Dic9—61no—
322C2×Dic9—61no—
323C2×Dic9—121no—
324C2×Dic9C22×D311yescharacteristic
325C2×Dic9C22×D311yescharacteristic
326D36—41no—
327C4×D9—41no—
328C4×D9—121no—
329#560—271noSylow
330C2×C3×C9—41no—
331C2×C3×C9H(5,𝔽2)11yescharacteristic
332C2×C3×C9H(5,𝔽2)11yescharacteristic
333C2×C3×C9H(5,𝔽2)11yescharacteristic
334D3×C9—41no—
335D3×C9—41no—
336D3×C9—41no—
337C3×D9—41no—
338C3×D9—41no—
339C24×C3—31no—
340C23×D3C2×D911yescharacteristic
341C2×C3×D4—31no—
342C2×C3×D4—31no—
343C2×C3×D4—31no—
344C2×C3×D4—91no—
345C2×C3×D4—91no—
346C2×C3×D4—91no—
347C22×C3×C4—91no—
348C2×#67—31no—
349C2×#67—31no—
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—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67C2×D911yescharacteristic
363C22×Dic3—91no—
364C22×Dic3—91no—
365C2×D12—31no—
366C2×D12C2×D911yescharacteristic
367C2×D12C2×D911yescharacteristic
368C2×C4×D3—31no—
369C2×C4×D3—91no—
370C2×C4×D3—91no—
371C3×C4⋊C4—91no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4C2×D911yescharacteristic
377C3×C22⋊C4D3211yescharacteristic
378#217—91no—
379#217—91no—
380#217—91no—
381#217—91no—
382#217—91no—
383#217—91no—
384#217—91no—
385#217—91no—
386#217—91no—
387#217—91no—
388#217—181no—
389#217—181no—
390(C2×D3)⋊C4—31no—
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)⋊C4C2×D911yescharacteristic
398(C2×D3)⋊C4C2×D911yescharacteristic
399C4⋊Dic3—91no—
400C4⋊Dic3—91no—
401C4⋊Dic3—91no—
402C4⋊Dic3—91no—
403C4⋊Dic3—181no—
404Dic3⋊C4—31no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—181no—
412Dic3⋊C4—181no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C4×Dic3—181no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32C23×D311yescharacteristic
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—44no—
430C2×C3×D3—61no—
431C2×C3×D3—61no—
432C2×C3×D3—61no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C32×C4—21no—
437C32×C4—21no—
438C3⋊Dic3—61no—
439C3⋊Dic3—61no—
440C3⋊Dic3—61no—
441C3⋊Dic3—61no—
442C3×Dic3—21no—
443C3×Dic3—61no—
444C3×Dic3—61no—
445C22×C9—21no—
446C22×C9—21no—
447C22×C9—21no—
448C22×C9—21no—
449C22×C9—41no—
450C22×C9—41no—
451C22×C9—41no—
452C22×C9—61no—
453C22×C9—61no—
454C22×C9—61no—
455C22×C9—61no—
456C22×C9—61no—
457C22×C9—61no—
458C22×C9—61no—
459C22×C9—61no—
460C22×C9—61no—
461C22×C9—124no—
462C22×C9C23×D311yescharacteristic
463C2×D9—21no—
464C2×D9—21no—
465C2×D9—21no—
466C2×D9—21no—
467C2×D9—21no—
468C2×D9—21no—
469C4×C9—21no—
470C4×C9—21no—
471C4×C9—41no—
472C4×C9—41no—
473C4×C9—61no—
474Dic9—21no—
475Dic9—21no—
476Dic9—61no—
477Dic9—61no—
478Dic9—61no—
479Dic9—61no—
480Dic9—121no—
481Dic9—121no—
482Dic9—121no—
483Dic9—121no—
484#127—271no—
485#126—271no—
486#126—271no—
487#123—271no—
488#123—271no—
489#123—271no—
490#121—91no—
491#121—271no—
492#121—271no—
493#121—271no—
494#121—271no—
495#121—271no—
496#120—31no—
497#120—271no—
498#120—271no—
499C3×C9#56011yescharacteristic, complemented, Sylow
500C23×C3—21no—
501C23×C3—31no—
502C23×C3—31no—
503C23×C3—31no—
504C23×C3—91no—
505C23×C3—91no—
506C23×C3—121no—
507C23×C3—121no—
508C23×C3—121no—
509C23×C3C22×D911yescharacteristic
510C23×C3C2×D3211yescharacteristic
511C22×D3—31no—
512C22×D3—31no—
513C22×D3—41no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3C22×D911yescharacteristic
517C22×D3C22×D911yescharacteristic
518C22×D3C22×D911yescharacteristic
519C3×D4—121no—
520C3×D4—121no—
521C3×D4—121no—
522C3×D4—361no—
523C3×D4—361no—
524C3×D4—361no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—91no—
529C2×C3×C4—91no—
530C2×C3×C4—361no—
531C2×C3×C4C22×D911yescharacteristic
532C2×C3×C4C22×D911yescharacteristic
533C2×C3×C4C2×D3211yescharacteristic
534C2×C3×C4C2×D3211yescharacteristic
535#67—41no—
536#67—121no—
537#67—121no—
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—91no—
559C2×Dic3—91no—
560C2×Dic3—181no—
561C2×Dic3—181no—
562C2×Dic3—181no—
563C2×Dic3—181no—
564C2×Dic3—361no—
565C2×Dic3—361no—
566C2×Dic3C22×D911yescharacteristic
567D12—41no—
568D12—41no—
569D12—121no—
570C4×D3—121no—
571C4×D3—361no—
572C4×D3—361no—
573C2×C32—41no—
574C2×C32#100411yescharacteristic
575C2×C32#100411yescharacteristic
576C2×C32#100411yescharacteristic
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—41no—
586C2×C9—81no—
587C2×C9—121no—
588C2×C9—121no—
589C2×C9—121no—
590C2×C9#100411yescharacteristic
591C2×C9#100411yescharacteristic
592C2×C9#100911yescharacteristic
593D9—41no—
594D9—41no—
595C24—31no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—91no—
600C2×D4—91no—
601C2×D4—91no—
602C2×D4—271no—
603C2×D4—271no—
604C2×D4—271no—
605C2×D4—271no—
606C2×D4—271no—
607C2×D4—271no—
608C22×C4—91no—
609C22×C4—271no—
610C22×C4—271no—
611C4⋊C4—91no—
612C4⋊C4—271no—
613C4⋊C4—271no—
614C4⋊C4—271no—
615C4⋊C4—271no—
616C4⋊C4—271no—
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—91no—
620C22⋊C4—271no—
621C22⋊C4—271no—
622C22⋊C4—271no—
623C22⋊C4—271no—
624C22⋊C4—271no—
625C22⋊C4—271no—
626C22⋊C4—271no—
627C22⋊C4—271no—
628C22⋊C4D3×D911yescharacteristic
629C42—271no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—124no—
650C22×C3—181no—
651C22×C3—181no—
652C22×C3—181no—
653C22×C3—181no—
654C22×C3—181no—
655C22×C3—181no—
656C22×C3C23×D911yescharacteristic
657C22×C3C22×D3211yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—44no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—61no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—181no—
682C3×C4—181no—
683Dic3—21no—
684Dic3—61no—
685Dic3—61no—
686Dic3—181no—
687Dic3—181no—
688Dic3—181no—
689Dic3—181no—
690Dic3—181no—
691Dic3—181no—
692Dic3—181no—
693Dic3—181no—
694Dic3—361no—
695Dic3—361no—
696Dic3—361no—
697Dic3—361no—
698C32#559511yescharacteristic
699C9—21no—
700C9#562011yescharacteristic, complemented
701C23—31no—
702C23—31no—
703C23—31no—
704C23—91no—
705C23—91no—
706C23—121no—
707C23—121no—
708C23—121no—
709C23C2×D3×D911yescharacteristic
710D4—121no—
711D4—121no—
712D4—121no—
713D4—361no—
714D4—361no—
715D4—361no—
716D4—1081no—
717D4—1081no—
718D4—1081no—
719D4—1081no—
720D4—1081no—
721D4—1081no—
722C2×C4—31no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—271no—
726C2×C4—271no—
727C2×C4—271no—
728C2×C4—271no—
729C2×C4—361no—
730C2×C4—1081no—
731C2×C4—1081no—
732C2×C4C2×D3×D911yescharacteristic
733C2×C4C2×D3×D911yescharacteristic
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—41no—
738C2×C3—41no—
739C2×C3—81no—
740C2×C3—121no—
741C2×C3—121no—
742C2×C3—121no—
743C2×C3—361no—
744C2×C3—361no—
745C2×C3#6371011yescharacteristic
746C2×C3#6371011yescharacteristic
747C2×C3#6371011yescharacteristic
748C2×C3#6430711yescharacteristic
749C2×C3#6431311yescharacteristic
750C2×C3#6431311yescharacteristic
751D3—41no—
752D3—41no—
753D3—41no—
754D3—121no—
755D3—121no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—124no—
769C22—181no—
770C22—181no—
771C22—181no—
772C22—181no—
773C22—181no—
774C22—181no—
775C22C22×D3×D911yescharacteristic
776C4—21no—
777C4—21no—
778C4—61no—
779C4—181no—
780C4—181no—
781C4—541no—
782C4—541no—
783C4—541no—
784C4—541no—
785C3—21no—
786C3#1058969711yescharacteristic, complemented
787C3#1059423411yescharacteristic
788C2—41no—
789C2—121no—
790C2—121no—
791C2—121no—
792C2—361no—
793C2—361no—
794C2#1172247611yescharacteristic
795C2#1172249911yescharacteristic
796C2#1172249911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#560
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721725C2semidirect
2. C9×#882C2semidirect
3. C3×#63446C2semidirect
4. #11721286C2semidirect
5. #11721286C2semidirect
6. #11721281C2semidirect
7. #11721270C2semidirect
8. #11721043C2semidirect
9. #11721036C2semidirect
10. #11721031C2semidirect
11. #11721016C2semidirect
12. #11721015C2semidirect
13. #11720989C2semidirect
14. #11720982C2semidirect
15. #11720966C2semidirect
24. C2×C3×D36C22semidirect
25. C2×C3×C4×D9C22semidirect
30. C2×#6194C22semidirect
31. C2×#6194C22semidirect
32. C2×D3×Dic9C22semidirect
33. C2×Dic3×D9C22semidirect
37. C4⋊(C3⋊Dic9)C22semidirect
38. #88534C22semidirect
39. #88534C22semidirect
40. C4×C3⋊Dic9C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C3×Dic9⋊C4C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. Dic3⋊Dic9C22semidirect
52. Dic9⋊Dic3C22semidirect
78. #63446D3semidirect
167. C2×D36C2×D3semidirect
169. C2×C4×D9C2×D3semidirect
184. (C2×D9)⋊C4C2×D3semidirect
193. Dic9⋊C4C2×D3semidirect
251. #882D9semidirect
499. C3×C9#560semidirect
700. C9#5620semidirect
786. C3#10589697semidirect

Maximal subgroups

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

subgroupindex
#117217252
C9×#8822
C3×#634462
#117212862
#117212812
#117212702
#117210432
#117210362
#117210312
#117210162
#117210152
#117209892
#117209822
#117209662
#105942343
#105896973