Finite Group Databasebeta

← #13150584

Subgroups — #13150584

Order 1728.

834 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721818C211yesmaximal, characteristic, complemented
2C9×#930C211yesmaximal, characteristic, complemented
3C3×#63492C211yesmaximal, characteristic, complemented
4#11721292C211yesmaximal, characteristic, complemented
5#11721289C211yesmaximal, characteristic, complemented
6#11721281C211yesmaximal, characteristic, complemented
7#11721270C211yesmaximal, characteristic, complemented
8#11721050C211yesmaximal, characteristic, complemented
9#11721049C211yesmaximal, characteristic, complemented
10#11721020C211yesmaximal, characteristic, complemented
11#11721016C211yesmaximal, characteristic, complemented
12#11720988C211yesmaximal, characteristic, complemented
13#11720982C211yesmaximal, characteristic, complemented
14#11720962C211yesmaximal, characteristic, complemented
15#11720946C211yesmaximal, characteristic, complemented
16#10595091—31nomaximal
17#10589722—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic, complemented
20C2×#6233C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic, complemented
23C2×C3×#611C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic, complemented
25C2×C9×D12C2211yescharacteristic
26C2×C3×D36C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×#6194C2211yescharacteristic, complemented
31C2×D3×Dic9C2211yescharacteristic, complemented
32C2×#6192C2211yescharacteristic
33C2×Dic3×D9C2211yescharacteristic, complemented
34#88551C2211yescharacteristic, complemented
35#88536C2211yescharacteristic
36#88536C2211yescharacteristic
37#88534C2211yescharacteristic, complemented
38#88534C2211yescharacteristic, complemented
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C9×C4⋊Dic3C2211yescharacteristic, complemented
44C3×C4⋊Dic9C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic
47#88445C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64138—31no—
54C3×#930—31no—
55C3×#930D311yescharacteristic
56#63983—31no—
57#63979—31no—
58#63970—31no—
59#63970—31no—
60#63922—31no—
61#63922—31no—
62#63890—31no—
63#63890—31no—
64#63885—31no—
65#63885—31no—
66#63858—31no—
67#63858—31no—
68C9×#121—31no—
69#63502—31no—
70#63501—31no—
71#63501—31no—
72#63500—31no—
73#63499—31no—
74#63499—31no—
75#63492D311yescharacteristic, complemented
76#63491—31no—
77#63491—61no—
78#63460—31no—
79#63456—31no—
80#63448—31no—
81#63446—31no—
82#63444—31no—
83#63441—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
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×C9—41no—
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96#6233—41no—
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C9×#67—41no—
101C9×#67—41no—
102C3×#611—41no—
103C3×#611—41no—
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C9×D12—41no—
109C3×D36—41no—
110#6195—41no—
111#6194—41no—
112#6194—41no—
113#6194—41no—
114D3×Dic9—41no—
115#6192—41no—
116Dic3×D9—41no—
117#5620—91no—
118#5620—91no—
119C22×D32—31no—
120C22×C32×C4C2×D311yescharacteristic
121C2×#638—31no—
122C2×C3×#67—31no—
123C2×C3×#67—31no—
124C2×C3×#67C2×D311yescharacteristic
125C2×C3×#67C2×D311yescharacteristic
126C2×C3×D12—31no—
127C2×C3×D12C2×D311yescharacteristic
128C2×#626—31no—
129C2×#626—31no—
130C2×#625—31no—
131C2×#625—31no—
132C2×#625—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C23×D9—31no—
136#3757—31no—
137#3752—31no—
138#3752—31no—
139#3750—31no—
140#3750—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4C2×D311yescharacteristic
144C3×(C2×D3)⋊C4C2×D311yescharacteristic
145C3×C4⋊Dic3—31no—
146C3×C4⋊Dic3C2×D311yescharacteristic
147Dic3⋊Dic3—31no—
148Dic3⋊Dic3—31no—
149#3722—31no—
150(C2×D3)⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154Dic32—31no—
155C2×D4×C9—31no—
156C2×D4×C9—31no—
157C2×D4×C9—31no—
158C22×C4×C9—21no—
159C22×C4×C9C2×D311yescharacteristic, complemented
160C2×#611—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—61no—
166C2×#611C2×D311yescharacteristic
167C2×#611C2×D311yescharacteristic, complemented
168C22×Dic9—31no—
169C2×D36—31no—
170C2×D36C2×D311yescharacteristic
171C2×C4×D9—31no—
172C9×C4⋊C4—31no—
173C9×C22⋊C4—31no—
174C9×C22⋊C4—31no—
175#3676—31no—
176#3676—31no—
177#3676—31no—
178#3676—61no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4—31no—
184(C2×D9)⋊C4—61no—
185(C2×D9)⋊C4—61no—
186(C2×D9)⋊C4C2×D311yescharacteristic
187(C2×D9)⋊C4C2×D311yescharacteristic, complemented
188C4⋊Dic9—31no—
189C4⋊Dic9C2×D311yescharacteristic, complemented
190Dic9⋊C4—31no—
191Dic9⋊C4—31no—
192Dic9⋊C4—31no—
193Dic9⋊C4—61no—
194Dic9⋊C4—61no—
195C4×Dic9—31no—
196C22×C3×C9—21no—
197C22×C3×C9—21no—
198C22×C3×C9—21no—
199C22×C3×C9C2411yescharacteristic
200C2×C3⋊D9—21no—
201C2×C3⋊D9—21no—
202C2×C3⋊D9—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⋊Dic9—21no—
219C3⋊Dic9—21no—
220C3⋊Dic9—21no—
221C9×Dic3—21no—
222C9×Dic3—21no—
223C3×Dic9—21no—
224C3×Dic9—21no—
225C3×#121—31no—
226C3×#121—91no—
227#940—91no—
228#940—91no—
229#939—91no—
230#939—91no—
231#939—91no—
232#939—91no—
233#938—91no—
234#938—91no—
235#937—91no—
236#937—91no—
237#937—91no—
238#937—91no—
239#930—31no—
240#930D911yescharacteristic, complemented
241#929—91no—
242#929—91no—
243#929—181no—
244#898—91no—
245#898—91no—
246#894—91no—
247#894—91no—
248#886—91no—
249#886—91no—
250#884—91no—
251#884—91no—
252#882—91no—
253#882—91no—
254#879—91no—
255#879—91no—
256C23×C32C22×D311yescharacteristic
257C22×C3⋊D3—31no—
258C22×C3×D3—31no—
259C22×C3×D3—31no—
260C22×C3×D3C22×D311yescharacteristic
261C22×C3×D3C22×D311yescharacteristic
262C2×D32—121no—
263C2×D32—121no—
264C2×D32—121no—
265C2×C32×C4—41no—
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268#638—121no—
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—31no—
272C3×#67—41no—
273C3×#67—41no—
274C3×#67—121no—
275C3×#67—121no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3C22×D311yescharacteristic
279C2×C3×Dic3C22×D311yescharacteristic
280C3×D12—41no—
281C3×D12—121no—
282#626—121no—
283#626—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×C9C22×D311yescharacteristic
293C22×D9—31no—
294C22×D9—61no—
295C22×D9—121no—
296C22×D9—121no—
297C22×D9—121no—
298C22×D9C22×D311yescharacteristic
299C22×D9C22×D311yescharacteristic
300D4×C9—121no—
301D4×C9—121no—
302D4×C9—121no—
303C2×C4×C9—21no—
304C2×C4×C9—21no—
305C2×C4×C9—31no—
306C2×C4×C9—31no—
307C2×C4×C9—41no—
308C2×C4×C9—42no—
309C2×C4×C9C22×D311yescharacteristic
310C2×C4×C9C22×D311yescharacteristic
311#611—41no—
312#611—41no—
313#611—121no—
314#611—121no—
315#611—121no—
316#611—121no—
317#611—121no—
318#611—122no—
319C2×Dic9—31no—
320C2×Dic9—31no—
321C2×Dic9—31no—
322C2×Dic9—61no—
323C2×Dic9—61no—
324C2×Dic9—61no—
325C2×Dic9—121no—
326C2×Dic9C22×D311yescharacteristic
327C2×Dic9C22×D311yescharacteristic
328D36—41no—
329D36—121no—
330C4×D9—121no—
331#560—271noSylow
332C2×C3×C9—41no—
333C2×C3×C9H(5,𝔽2)11yescharacteristic
334C2×C3×C9H(5,𝔽2)11yescharacteristic
335C2×C3×C9H(5,𝔽2)11yescharacteristic
336C3⋊D9—41no—
337D3×C9—41no—
338D3×C9—41no—
339C3×D9—41no—
340C3×D9—41no—
341C23×D3—91no—
342C23×D3—91no—
343C2×C3×D4—31no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C2×C3×D4—91no—
347C2×C3×D4—91no—
348C2×C3×D4—91no—
349C22×C3×C4—21no—
350C22×C3×C4C2×D911yescharacteristic, complemented
351C22×C3×C4D3211yescharacteristic
352C2×#67—31no—
353C2×#67—31no—
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×#67—91no—
363C2×#67—91no—
364C2×#67—181no—
365C2×#67C2×D911yescharacteristic
366C2×#67C2×D911yescharacteristic, complemented
367C22×Dic3—91no—
368C22×Dic3—91no—
369C2×D12—31no—
370C2×D12—91no—
371C2×D12—91no—
372C2×D12C2×D911yescharacteristic
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—91no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381#217—91no—
382#217—91no—
383#217—91no—
384#217—91no—
385#217—91no—
386#217—91no—
387#217—181no—
388(C2×D3)⋊C4—31no—
389(C2×D3)⋊C4—31no—
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—91no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—181no—
401(C2×D3)⋊C4—181no—
402(C2×D3)⋊C4C2×D911yescharacteristic
403(C2×D3)⋊C4C2×D911yescharacteristic, complemented
404C4⋊Dic3—31no—
405C4⋊Dic3—91no—
406C4⋊Dic3—91no—
407C4⋊Dic3C2×D911yescharacteristic, complemented
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—181no—
415Dic3⋊C4—181no—
416C4×Dic3—91no—
417C4×Dic3—91no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32C23×D311yescharacteristic
422C2×C3⋊D3—61no—
423C2×C3⋊D3—61no—
424C2×C3⋊D3—61no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—61no—
432C2×C3×D3—61no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C2×C3×D3—61no—
437D32—124no—
438C32×C4—21no—
439C32×C4—21no—
440C3⋊Dic3—61no—
441C3⋊Dic3—61no—
442C3⋊Dic3—61no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—61no—
446C3×Dic3—61no—
447C22×C9—22no—
448C22×C9—21no—
449C22×C9—21no—
450C22×C9—21no—
451C22×C9—21no—
452C22×C9—41no—
453C22×C9—41no—
454C22×C9—61no—
455C22×C9—61no—
456C22×C9—61no—
457C22×C9—61no—
458C22×C9—61no—
459C22×C9—61no—
460C22×C9C23×D311yescharacteristic
461C2×D9—21no—
462C2×D9—21no—
463C2×D9—21no—
464C2×D9—21no—
465C2×D9—21no—
466C2×D9—21no—
467C2×D9—61no—
468C2×D9—61no—
469C2×D9—61no—
470C2×D9—121no—
471C2×D9—121no—
472C2×D9—121no—
473C2×D9—124no—
474C4×C9—21no—
475C4×C9—21no—
476C4×C9—41no—
477C4×C9—41no—
478C4×C9—61no—
479C4×C9—61no—
480Dic9—21no—
481Dic9—21no—
482Dic9—61no—
483Dic9—61no—
484Dic9—61no—
485Dic9—121no—
486Dic9—121no—
487Dic9—121no—
488#127—271no—
489#126—271no—
490#126—271no—
491#123—271no—
492#123—271no—
493#123—271no—
494#121—31no—
495#121—91no—
496#121—271no—
497#121—271no—
498#121—271no—
499#121—271no—
500#120—271no—
501#120—271no—
502#120—271no—
503C3×C9#56011yescharacteristic, complemented, Sylow
504C23×C3—21no—
505C23×C3—31no—
506C23×C3—31no—
507C23×C3—91no—
508C23×C3—91no—
509C23×C3C22×D911yescharacteristic
510C23×C3C2×D3211yescharacteristic
511C22×D3—31no—
512C22×D3—31no—
513C22×D3—91no—
514C22×D3—91no—
515C22×D3—181no—
516C22×D3—361no—
517C22×D3—361no—
518C22×D3—361no—
519C22×D3—361no—
520C22×D3—361no—
521C22×D3—361no—
522C22×D3C22×D911yescharacteristic
523C22×D3C22×D911yescharacteristic
524C3×D4—121no—
525C3×D4—121no—
526C3×D4—121no—
527C3×D4—361no—
528C3×D4—361no—
529C3×D4—361no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—31no—
533C2×C3×C4—31no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—42no—
537C2×C3×C4—91no—
538C2×C3×C4—91no—
539C2×C3×C4C22×D911yescharacteristic
540C2×C3×C4C22×D911yescharacteristic
541C2×C3×C4C2×D3211yescharacteristic
542C2×C3×C4C2×D3211yescharacteristic
543#67—41no—
544#67—41no—
545#67—121no—
546#67—121no—
547#67—361no—
548#67—361no—
549#67—361no—
550#67—361no—
551#67—361no—
552#67—361no—
553#67—361no—
554#67—361no—
555#67—361no—
556#67—361no—
557#67—362no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—91no—
561C2×Dic3—91no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—181no—
567C2×Dic3—181no—
568C2×Dic3—181no—
569C2×Dic3—361no—
570C2×Dic3—361no—
571C2×Dic3C22×D911yescharacteristic
572C2×Dic3C22×D911yescharacteristic
573D12—41no—
574D12—121no—
575D12—361no—
576D12—361no—
577C4×D3—361no—
578C4×D3—361no—
579C2×C32—41no—
580C2×C32#100411yescharacteristic
581C2×C32#100411yescharacteristic
582C2×C32#100911yescharacteristic
583C3⋊D3—121no—
584C3×D3—41no—
585C3×D3—41no—
586C3×D3—121no—
587C3×D3—121no—
588C2×C9—21no—
589C2×C9—21no—
590C2×C9—21no—
591C2×C9—42no—
592C2×C9—41no—
593C2×C9—121no—
594C2×C9—121no—
595C2×C9#100411yescharacteristic
596C2×C9#100411yescharacteristic
597C2×C9#100911yescharacteristic
598D9—41no—
599D9—41no—
600D9—121no—
601D9—241no—
602C24—271no—
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—91no—
607C2×D4—91no—
608C2×D4—91no—
609C2×D4—271no—
610C2×D4—271no—
611C2×D4—271no—
612C2×D4—271no—
613C2×D4—271no—
614C2×D4—271no—
615C22×C4—271no—
616C22×C4—271no—
617C22×C4D3×D911yescharacteristic, complemented
618C4⋊C4—31no—
619C4⋊C4—91no—
620C4⋊C4—271no—
621C4⋊C4—271no—
622C4⋊C4—271no—
623C4⋊C4—271no—
624C22⋊C4—31no—
625C22⋊C4—31no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—271no—
629C22⋊C4—271no—
630C22⋊C4—271no—
631C22⋊C4—271no—
632C22⋊C4—271no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C42—271no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—181no—
654C22×C3—181no—
655C22×C3—181no—
656C22×C3—181no—
657C22×C3—181no—
658C22×C3—181no—
659C22×C3C23×D911yescharacteristic
660C22×C3C22×D3211yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—181no—
674C2×D3—181no—
675C2×D3—181no—
676C2×D3—181no—
677C2×D3—181no—
678C2×D3—181no—
679C2×D3—361no—
680C2×D3—361no—
681C2×D3—361no—
682C2×D3—364no—
683C2×D3—364no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—61no—
691C3×C4—61no—
692C3×C4—181no—
693C3×C4—181no—
694Dic3—21no—
695Dic3—21no—
696Dic3—61no—
697Dic3—61no—
698Dic3—181no—
699Dic3—181no—
700Dic3—181no—
701Dic3—181no—
702Dic3—181no—
703Dic3—181no—
704Dic3—361no—
705Dic3—361no—
706Dic3—361no—
707C32#562011yescharacteristic
708C9—21no—
709C9#562011yescharacteristic, complemented
710C23—31no—
711C23—31no—
712C23—91no—
713C23—91no—
714C23—271no—
715C23—1081no—
716C23—1081no—
717C23—1081no—
718C23C2×D3×D911yescharacteristic
719D4—121no—
720D4—121no—
721D4—121no—
722D4—361no—
723D4—361no—
724D4—361no—
725D4—1081no—
726D4—1081no—
727D4—1081no—
728D4—1081no—
729D4—1081no—
730D4—1081no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—41no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—271no—
737C2×C4—271no—
738C2×C4—271no—
739C2×C4—1081no—
740C2×C4—1081no—
741C2×C4C2×D3×D911yescharacteristic
742C2×C4C2×D3×D911yescharacteristic
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—42no—
747C2×C3—41no—
748C2×C3—41no—
749C2×C3—121no—
750C2×C3—121no—
751C2×C3—361no—
752C2×C3—361no—
753C2×C3#6371011yescharacteristic
754C2×C3#6371011yescharacteristic
755C2×C3#6371511yescharacteristic
756C2×C3#6430711yescharacteristic
757C2×C3#6430711yescharacteristic
758C2×C3#6433011yescharacteristic
759D3—41no—
760D3—41no—
761D3—121no—
762D3—121no—
763D3—361no—
764D3—361no—
765D3—721no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—181no—
776C22—181no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—181no—
781C22—541no—
782C22—541no—
783C22—541no—
784C22—1084no—
785C22C22×D3×D911yescharacteristic
786C4—21no—
787C4—21no—
788C4—61no—
789C4—61no—
790C4—181no—
791C4—181no—
792C4—541no—
793C4—541no—
794C4—541no—
795C3—21no—
796C3#1058972211yescharacteristic, complemented
797C3#1059509111yescharacteristic
798C2—41no—
799C2—121no—
800C2—121no—
801C2—361no—
802C2—361no—
803C2—1081no—
804C2#1172247611yescharacteristic
805C2#1172247711yescharacteristic
806C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
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. #11721818C2semidirect
2. C9×#930C2semidirect
3. C3×#63492C2semidirect
4. #11721292C2semidirect
5. #11721289C2semidirect
6. #11721281C2semidirect
7. #11721270C2semidirect
8. #11721050C2semidirect
9. #11721049C2semidirect
10. #11721020C2semidirect
11. #11721016C2semidirect
12. #11720988C2semidirect
13. #11720982C2semidirect
14. #11720962C2semidirect
15. #11720946C2semidirect
19. C22×C3×C4×C9C22semidirect
22. C2×C9×#67C22semidirect
24. C2×C3×#611C22semidirect
30. C2×#6194C22semidirect
31. C2×D3×Dic9C22semidirect
33. C2×Dic3×D9C22semidirect
34. #88551C22semidirect
37. #88534C22semidirect
38. #88534C22semidirect
40. C9×(C2×D3)⋊C4C22semidirect
42. C3×(C2×D9)⋊C4C22semidirect
43. C9×C4⋊Dic3C22semidirect
44. C3×C4⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
75. #63492D3semidirect
159. C22×C4×C9C2×D3semidirect
167. C2×#611C2×D3semidirect
187. (C2×D9)⋊C4C2×D3semidirect
189. C4⋊Dic9C2×D3semidirect
240. #930D9semidirect
350. C22×C3×C4C2×D9semidirect
366. C2×#67C2×D9semidirect
403. (C2×D3)⋊C4C2×D9semidirect
407. C4⋊Dic3C2×D9semidirect
503. C3×C9#560semidirect
617. C22×C4D3×D9semidirect
709. C9#5620semidirect
796. C3#10589722semidirect

Maximal subgroups

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

subgroupindex
#117218182
C9×#9302
C3×#634922
#117212922
#117212892
#117212812
#117212702
#117210502
#117210492
#117210202
#117210162
#117209882
#117209822
#117209622
#117209462
#105950913
#105897223