Finite Group Databasebeta

← #13148111

Subgroups — #13148111

Order 1728.

824 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721724C211yesmaximal, characteristic, complemented
2C9×#67⋊C4C211yesmaximal, characteristic, complemented
3C3×#63444C211yesmaximal, characteristic, complemented
4#11721290C211yesmaximal, characteristic, complemented
5#11721285C211yesmaximal, characteristic, complemented
6Dic3×#611C211yesmaximal, characteristic, complemented
7C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic, complemented
8#11721042C211yesmaximal, characteristic, complemented
9#11721037C211yesmaximal, characteristic, complemented
10#11721032C211yesmaximal, characteristic, complemented
11#11720982C211yesmaximal, characteristic, complemented
12#11720981C211yesmaximal, characteristic, complemented
13#11720949C211yesmaximal, characteristic, complemented
14#11720948C211yesmaximal, characteristic, complemented
15#11720947C211yesmaximal, characteristic, complemented
16#10594238—31nomaximal
17#10589662—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×#6226C2211yescharacteristic, complemented
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic, complemented
25C2×C3×D36C2211yescharacteristic
26C2×C3×D36C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic, complemented
30C2×Dic3×D9C2211yescharacteristic, complemented
31C3×C9×C22⋊C4C2211yescharacteristic
32#88551C2211yescharacteristic
33C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
34#88534C2211yescharacteristic, complemented
35#88534C2211yescharacteristic, complemented
36C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C9×Dic3⋊C4C2211yescharacteristic, complemented
40C4×C9×Dic3C2211yescharacteristic, complemented
41(C2×D3)⋊Dic9C2211yescharacteristic, complemented
42(C2×D9)⋊Dic3C2211yescharacteristic
43(C2×D9)⋊Dic3C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50#88442C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64087—31no—
54C3×#882—31no—
55C3×#67⋊C4D311yescharacteristic
56#63980—31no—
57#63976—31no—
58Dic3×#67—31no—
59C2×(C2×D3)⋊Dic3—31no—
60#63913—31no—
61#63908—31no—
62#63905—31no—
63#63885—31no—
64#63884—31no—
65#63861—31no—
66#63860—31no—
67#63859—31no—
68C4×D4×C9—31no—
69#63501—31no—
70#63499—31no—
71#63492—31no—
72#63491—31no—
73C4×#611—31no—
74C2×(C2×D9)⋊C4—31no—
75#63460—31no—
76#63456—31no—
77#63447—31no—
78#63446—31no—
79#63444D311yescharacteristic, complemented
80#63440—31no—
81#63440—61no—
82#63438—31no—
83#63437—31no—
84C23×C3×C9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×C3×D9—22no—
87C22×C3×D9—41no—
88C22×C3×D9—41no—
89C22×C3×D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3⋊Dic9—41no—
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99#6226—41no—
100C9×#67—22no—
101C3×#611—22no—
102C2×C9×Dic3—41no—
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C4×D3×C9—41no—
108C3×D36—41no—
109C3×D36—41no—
110#6194—41no—
111#6194—41no—
112#6194—41no—
113Dic3×D9—41no—
114#5593—91no—
115#5560—91no—
116C23×C3×D3—31no—
117C22×C3⋊Dic3—31no—
118C2×#634—31no—
119C2×C3×#67—31no—
120C2×C3×#67C2×D311yescharacteristic
121C22×C3×Dic3C2×D311yescharacteristic
122C2×C3×D12—31no—
123C2×C3×D12—31no—
124C2×C3×C4×D3C2×D311yescharacteristic
125C2×#625—31no—
126C2×#625—31no—
127C2×#625—31no—
128C2×D3×Dic3—31no—
129C23×D9C2×D311yescharacteristic
130C32×C22⋊C4C2×D311yescharacteristic
131#3757—31no—
132C4⋊(C3⋊Dic3)—31no—
133#3750—31no—
134#3750—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4—31no—
137C3×(C2×D3)⋊C4C2×D311yescharacteristic
138C3×Dic3⋊C4C2×D311yescharacteristic
139C3×C4×Dic3C2×D311yescharacteristic
140#3724—31no—
141Dic3⋊Dic3—31no—
142(C2×D3)⋊Dic3—31no—
143(C2×D3)⋊Dic3—31no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151Dic32—31no—
152C2×D4×C9—31no—
153C22×C4×C9—31no—
154C22×C4×C9—31no—
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—31no—
158C2×#611C2×D311yescharacteristic
159C22×Dic9—31no—
160C22×Dic9—61no—
161C2×D36C2×D311yescharacteristic
162C2×D36C2×D311yescharacteristic
163C2×C4×D9—31no—
164C2×Dic18—31no—
165C2×Dic18—61no—
166C9×C4⋊C4—31no—
167C9×C22⋊C4—21no—
168C9×C22⋊C4—31no—
169C9×C22⋊C4C2×D311yescharacteristic
170C42×C9—31no—
171#3676—31no—
172#3676—31no—
173#3676—61no—
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4—31no—
176(C2×D9)⋊C4—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—31no—
182(C2×D9)⋊C4C2×D311yescharacteristic
183(C2×D9)⋊C4C2×D311yescharacteristic
184C4⋊Dic9—31no—
185C4⋊Dic9—61no—
186Dic9⋊C4—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—61no—
191Dic9⋊C4—61no—
192C4×Dic9—31no—
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9#4112yes—
196C22×C3×C9C2411yescharacteristic
197C2×D3×C9—21no—
198C2×D3×C9—21no—
199C2×D3×C9—21no—
200C2×C3×D9—21no—
201C2×C3×D9—21no—
202C2×C3×D9—21no—
203C2×C3×D9—21no—
204C2×C3×D9—21no—
205C2×C3×D9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—44no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9—21no—
214C3⋊Dic9—21no—
215C3⋊Dic9—21no—
216C9×Dic3—21no—
217C9×Dic3—21no—
218C9×Dic3—21no—
219C3×Dic9—21no—
220C3×#120—91no—
221C3×C4×D4—31no—
222#953—91no—
223C2×#217—91no—
224#939—91no—
225#939—91no—
226#939—91no—
227#938—91no—
228#937—91no—
229#936—91no—
230#935—91no—
231D4×Dic3—91no—
232#930—91no—
233#929—91no—
234C4×#67—91no—
235C2×(C2×D3)⋊C4—91no—
236#898—91no—
237#894—91no—
238#885—91no—
239#885—91no—
240#884—91no—
241#883—91no—
242#882—31no—
243#67⋊C4D911yescharacteristic, complemented
244#879—91no—
245#879—91no—
246#878—91no—
247#878—91no—
248#878—181no—
249#876—91no—
250#875—91no—
251C23×C32C22×D311yescharacteristic
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3—62no—
256C22×C3×D3—121no—
257C22×C3×D3—121no—
258C22×C3×D3C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C3⋊Dic3—31no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—121no—
266#634—121no—
267C3×#67—22no—
268C3×#67—62no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—41no—
271C2×C3×Dic3C22×D311yescharacteristic
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C3×D12—121no—
275C3×D12—121no—
276C3×C4×D3—41no—
277#625—121no—
278#625—121no—
279#625—121no—
280D3×Dic3—121no—
281C23×C9—21no—
282C23×C9—31no—
283C23×C9C22×D311yescharacteristic
284C22×D9—22no—
285C22×D9—41no—
286C22×D9—41no—
287C22×D9C22×D311yescharacteristic
288C22×D9C22×D311yescharacteristic
289C22×D9C22×D311yescharacteristic
290D4×C9—62no—
291C2×C4×C9—21no—
292C2×C4×C9—21no—
293C2×C4×C9—31no—
294C2×C4×C9—31no—
295C2×C4×C9—31no—
296C2×C4×C9—121no—
297C2×C4×C9—121no—
298C2×C4×C9C22×D311yescharacteristic
299C2×C4×C9C22×D311yescharacteristic
300#611—22no—
301#611—121no—
302#611—121no—
303#611—121no—
304C2×Dic9—31no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—31no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9—61no—
311C2×Dic9—61no—
312C2×Dic9—121no—
313C2×Dic9—122no—
314C2×Dic9C22×D311yescharacteristic
315D36—41no—
316D36—41no—
317C4×D9—121no—
318Dic18—121no—
319Dic18—122no—
320#538—271noSylow
321C2×C3×C9—22no—
322C2×C3×C9C2×#4111yescharacteristic
323C2×C3×C9H(5,𝔽2)11yescharacteristic
324C2×C3×C9H(5,𝔽2)11yescharacteristic
325D3×C9—41no—
326C3×D9—41no—
327C3×D9—41no—
328C3×D9—41no—
329C24×C3—91no—
330C23×D3—31no—
331C2×C3×D4—31no—
332C2×C3×D4—91no—
333C2×C3×D4—91no—
334C2×C3×D4—91no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C2×#67—31no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67C2×D911yescharacteristic
345C22×Dic3—91no—
346C22×Dic3—91no—
347C22×Dic3—91no—
348C22×Dic3—181no—
349C22×Dic3C2×D911yescharacteristic
350C2×D12—31no—
351C2×D12—31no—
352C2×C4×D3—91no—
353C2×C4×D3C2×D911yescharacteristic, complemented
354C2×Dic6—91no—
355C2×Dic6—91no—
356C2×Dic6—181no—
357C3×C4⋊C4—31no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—91no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4C2×D911yescharacteristic
363C3×C22⋊C4D3211yescharacteristic
364C3×C42—31no—
365#217—91no—
366#217—91no—
367#217—91no—
368#217—91no—
369#217—91no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—91no—
374#217—91no—
375#217—91no—
376#217—181no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4C2×D911yescharacteristic, complemented
389C4⋊Dic3—91no—
390C4⋊Dic3—91no—
391C4⋊Dic3—91no—
392C4⋊Dic3—181no—
393Dic3⋊C4—91no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—181no—
401Dic3⋊C4—181no—
402Dic3⋊C4C2×D911yescharacteristic, complemented
403C4×Dic3—91no—
404C4×Dic3—91no—
405C4×Dic3C2×D911yescharacteristic, complemented
406C22×C32—21no—
407C22×C32—21no—
408C22×C32#23512yes—
409C22×C32C23×D311yescharacteristic
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—61no—
414C2×C3×D3—61no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C2×C3×D3—61no—
422C2×C3×D3—124no—
423C32×C4—21no—
424C32×C4—21no—
425C3⋊Dic3—61no—
426C3⋊Dic3—61no—
427C3⋊Dic3—61no—
428C3⋊Dic3—61no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—61no—
433C22×C9—21no—
434C22×C9—21no—
435C22×C9—21no—
436C22×C9—22no—
437C22×C9—41no—
438C22×C9—41no—
439C22×C9—61no—
440C22×C9—61no—
441C22×C9—61no—
442C22×C9#23712yes—
443C22×C9C23×D311yescharacteristic
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—21no—
450C2×D9—21no—
451C2×D9—21no—
452C2×D9—21no—
453C2×D9—44no—
454C4×C9—21no—
455C4×C9—21no—
456C4×C9—41no—
457C4×C9—41no—
458C4×C9—61no—
459C4×C9—61no—
460C4×C9—61no—
461Dic9—21no—
462Dic9—62no—
463Dic9—61no—
464Dic9—61no—
465Dic9—61no—
466Dic9—61no—
467Dic9—121no—
468Dic9—121no—
469Dic9—121no—
470#126—271no—
471#126—271no—
472#124—271no—
473#124—271no—
474#123—271no—
475#123—271no—
476C22⋊Q8—271no—
477#121—271no—
478#121—271no—
479#121—271no—
480#120—91no—
481#120—271no—
482C4×D4—31no—
483C4×D4—271no—
484C2×C22⋊C4—271no—
485C3×C9#53811yescharacteristic, complemented, Sylow
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—91no—
489C23×C3—91no—
490C23×C3—91no—
491C23×C3—182no—
492C23×C3—361no—
493C23×C3—361no—
494C23×C3C22×D911yescharacteristic
495C23×C3C2×D3211yescharacteristic
496C22×D3—31no—
497C22×D3—31no—
498C22×D3—31no—
499C22×D3—62no—
500C22×D3—121no—
501C22×D3—121no—
502C22×D3C22×D911yescharacteristic
503C3×D4—62no—
504C3×D4—182no—
505C3×D4—361no—
506C3×D4—361no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—91no—
513C2×C3×C4—121no—
514C2×C3×C4—121no—
515C2×C3×C4C22×D911yescharacteristic
516C2×C3×C4C22×D911yescharacteristic
517C2×C3×C4C2×D3211yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519#67—22no—
520#67—62no—
521#67—361no—
522#67—361no—
523#67—361no—
524#67—361no—
525#67—361no—
526#67—361no—
527C2×Dic3—31no—
528C2×Dic3—41no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—181no—
538C2×Dic3—181no—
539C2×Dic3—181no—
540C2×Dic3—181no—
541C2×Dic3—361no—
542C2×Dic3—361no—
543C2×Dic3—361no—
544C2×Dic3—362no—
545C2×Dic3C22×D911yescharacteristic
546C2×Dic3C22×D911yescharacteristic
547C2×Dic3C22×D911yescharacteristic
548D12—121no—
549D12—121no—
550C4×D3—41no—
551C4×D3—361no—
552Dic6—361no—
553Dic6—361no—
554Dic6—362no—
555C2×C32—22no—
556C2×C32C2×#23511yescharacteristic
557C2×C32#100411yescharacteristic
558C2×C32#100911yescharacteristic
559C3×D3—41no—
560C3×D3—121no—
561C3×D3—121no—
562C3×D3—121no—
563C2×C9—22no—
564C2×C9—21no—
565C2×C9—21no—
566C2×C9—21no—
567C2×C9—42no—
568C2×C9—121no—
569C2×C9C2×#23711yescharacteristic
570C2×C9#100411yescharacteristic
571C2×C9#100411yescharacteristic
572D9—41no—
573D9—41no—
574D9—41no—
575C24—91no—
576C2×Q8—271no—
577C2×D4—31no—
578C2×D4—91no—
579C2×D4—91no—
580C2×D4—91no—
581C2×D4—271no—
582C2×D4—271no—
583C2×D4—271no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—271no—
587C22×C4—271no—
588C4⋊C4—31no—
589C4⋊C4—271no—
590C4⋊C4—271no—
591C4⋊C4—271no—
592C4⋊C4—271no—
593C4⋊C4—271no—
594C22⋊C4—31no—
595C22⋊C4—91no—
596C22⋊C4—91no—
597C22⋊C4—271no—
598C22⋊C4—271no—
599C22⋊C4—271no—
600C22⋊C4—271no—
601C22⋊C4—271no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4D3×D911yescharacteristic
608C42—31no—
609C42—271no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—22no—
615C22×C3—21no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—181no—
622C22×C3—181no—
623C22×C3—181no—
624C22×C3—181no—
625C22×C3—181no—
626C22×C3—181no—
627C22×C3—181no—
628C22×C3—181no—
629C22×C3—181no—
630C22×C3—364no—
631C22×C3#369712yes—
632C22×C3C23×D911yescharacteristic
633C22×C3#379512yes—
634C22×C3C22×D3211yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—124no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—181no—
658Dic3—21no—
659Dic3—21no—
660Dic3—21no—
661Dic3—61no—
662Dic3—182no—
663Dic3—181no—
664Dic3—181no—
665Dic3—181no—
666Dic3—181no—
667Dic3—181no—
668Dic3—181no—
669Dic3—181no—
670Dic3—181no—
671Dic3—361no—
672Dic3—361no—
673Dic3—361no—
674C32#556011yescharacteristic
675C9—21no—
676C9#559311yescharacteristic, complemented
677C23—31no—
678C23—91no—
679C23—91no—
680C23—91no—
681C23—182no—
682C23—361no—
683C23—361no—
684C23C2×D3×D911yescharacteristic
685Q8—1081no—
686D4—62no—
687D4—182no—
688D4—361no—
689D4—361no—
690D4—1081no—
691D4—1081no—
692D4—1081no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—91no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—271no—
700C2×C4—271no—
701C2×C4—271no—
702C2×C4—271no—
703C2×C4—1081no—
704C2×C4—1081no—
705C2×C4C2×D3×D911yescharacteristic
706C2×C4C2×D3×D911yescharacteristic
707C2×C3—22no—
708C2×C3—22no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—42no—
713C2×C3—121no—
714C2×C3—361no—
715C2×C3—361no—
716C2×C3—361no—
717C2×C3C2×#369711yescharacteristic
718C2×C3#6371011yescharacteristic
719C2×C3#6371511yescharacteristic
720C2×C3C2×#379511yescharacteristic
721C2×C3#6431311yescharacteristic
722C2×C3#6431411yescharacteristic
723D3—41no—
724D3—121no—
725D3—121no—
726D3—121no—
727C22—21no—
728C22—21no—
729C22—61no—
730C22—61no—
731C22—61no—
732C22—181no—
733C22—181no—
734C22—181no—
735C22—181no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22—181no—
740C22—181no—
741C22—364no—
742C22#8864112yes—
743C22C22×D3×D911yescharacteristic
744C4—21no—
745C4—21no—
746C4—61no—
747C4—61no—
748C4—61no—
749C4—181no—
750C4—541no—
751C4—541no—
752C4—541no—
753C4—541no—
754C3—21no—
755C3#1058966211yescharacteristic, complemented
756C3#1059423811yescharacteristic
757C2—22no—
758C2—121no—
759C2—361no—
760C2—361no—
761C2—361no—
762C2C2×#8864111yescharacteristic
763C2#1172249911yescharacteristic
764C2#1172250111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#538
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. #11721724C2semidirect
2. C9×#67⋊C4C2semidirect
3. C3×#63444C2semidirect
4. #11721290C2semidirect
5. #11721285C2semidirect
6. Dic3×#611C2semidirect
7. C2×(C2×D9)⋊Dic3C2semidirect
8. #11721042C2semidirect
9. #11721037C2semidirect
10. #11721032C2semidirect
11. #11720982C2semidirect
12. #11720981C2semidirect
13. #11720949C2semidirect
14. #11720948C2semidirect
15. #11720947C2semidirect
20. C2×#6226C22semidirect
24. C2×C4×D3×C9C22semidirect
29. C2×#6194C22semidirect
30. C2×Dic3×D9C22semidirect
33. C4⋊(C3⋊Dic9)C22semidirect
34. #88534C22semidirect
35. #88534C22semidirect
36. C9×(C2×D3)⋊C4C22semidirect
39. C9×Dic3⋊C4C22semidirect
40. C4×C9×Dic3C22semidirect
41. (C2×D3)⋊Dic9C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. #88442C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
79. #63444D3semidirect
243. #67⋊C4D9semidirect
353. C2×C4×D3C2×D9semidirect
388. (C2×D3)⋊C4C2×D9semidirect
402. Dic3⋊C4C2×D9semidirect
405. C4×Dic3C2×D9semidirect
485. C3×C9#538semidirect
676. C9#5593semidirect
755. C3#10589662semidirect

Maximal subgroups

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

subgroupindex
#117217242
C9×#67⋊C42
C3×#634442
#117212902
#117212852
Dic3×#6112
C2×(C2×D9)⋊Dic32
#117210422
#117210372
#117210322
#117209822
#117209812
#117209492
#117209482
#117209472
#105942383
#105896623