Finite Group Databasebeta

← #13151170

Subgroups — #13151170

Order 1728.

798 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#11721835C211yesmaximal, characteristic, complemented
2C9×#939C211yesmaximal, characteristic, complemented
3C3×#63502C211yesmaximal, characteristic, complemented
4#11721290C211yesmaximal, characteristic, complemented
5#11721281C211yesmaximal, characteristic, complemented
6#11721281C211yesmaximal, characteristic, complemented
7#611⋊Dic3C211yesmaximal, characteristic, complemented
8Dic3×#611C211yesmaximal, characteristic, complemented
9#11721270C211yesmaximal, characteristic, complemented
10#11721269C211yesmaximal, characteristic, complemented
11#11721259C211yesmaximal, characteristic, complemented
12#11721010C211yesmaximal, characteristic, complemented
13#11720982C211yesmaximal, characteristic, complemented
14#11720981C211yesmaximal, characteristic, complemented
15#11720933C211yesmaximal, characteristic, complemented
16#10595188—31nomaximal
17#10589717—31nomaximal
18C2×C3×D4×C9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×C9×#67C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic
26C22×C9×Dic3C2211yescharacteristic
27C2×C3×D36C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×D3×Dic9C2211yescharacteristic
31C2×Dic3×D9C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33#88551C2211yescharacteristic
34#88551C2211yescharacteristic
35#88551C2211yescharacteristic
36#88534C2211yescharacteristic
37#88534C2211yescharacteristic
38C9×#217C2211yescharacteristic
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C9×Dic3⋊C4C2211yescharacteristic
41C3×C4×Dic9C2211yescharacteristic
42(C2×D3)⋊Dic9C2211yescharacteristic
43(C2×D9)⋊Dic3C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic
48#88442C2211yescharacteristic
49#88442C2211yescharacteristic
50Dic9⋊Dic3C2211yescharacteristic
51Dic9⋊Dic3C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64144—31no—
54C3×#940—31no—
55C3×#939D311yescharacteristic
56#63980—31no—
57#67⋊Dic3—31no—
58Dic3×#67—31no—
59#63970—31no—
60#63970—31no—
61#63970—31no—
62#63969—31no—
63#63961—31no—
64#63885—31no—
65#63884—31no—
66#63877—31no—
67#63867—31no—
68C9×#121—31no—
69#63502D311yescharacteristic, complemented
70#63501—31no—
71#63501—31no—
72#63501—31no—
73#63500—31no—
74#63497—31no—
75#63497—61no—
76#63491—31no—
77C4×#611—31no—
78#63456—31no—
79#63451—31no—
80#63446—31no—
81#63445—31no—
82#611⋊C4—31no—
83#63439—31no—
84C23×C3×C9C2311yescharacteristic
85C23×C3×C9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C3×D4×C9—41no—
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3⋊Dic9—41no—
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C9×#67—41no—
97C9×#67—41no—
98C3×#611—22no—
99C3×#611—22no—
100C3×#611—41no—
101C3×#611—41no—
102C2×C9×Dic3—41no—
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C3×D36—41no—
109#6194—41no—
110#6194—41no—
111D3×Dic9—22no—
112Dic3×D9—41no—
113Dic3×D9—41no—
114#5719—91no—
115#5615—91no—
116C2×C32×D4C2×D311yescharacteristic
117C22×C3⋊Dic3—31no—
118C2×C3×#67—31no—
119C2×C3×#67—31no—
120C2×C3×#67—31no—
121C2×C3×#67—31no—
122C2×C3×#67C2×D311yescharacteristic
123C2×C3×#67C2×D311yescharacteristic
124C22×C3×Dic3C2×D311yescharacteristic
125C2×C3×D12—31no—
126C2×#625—31no—
127C2×#625—31no—
128C2×D3×Dic3—31no—
129C2×D3×Dic3—31no—
130C2×D3×Dic3—31no—
131#3757—31no—
132#3757—31no—
133#3757—31no—
134#3750—31no—
135#3750—31no—
136C3×#217C2×D311yescharacteristic
137C3×(C2×D3)⋊C4C2×D311yescharacteristic
138C3×Dic3⋊C4C2×D311yescharacteristic
139C3×C4×Dic3—31no—
140#3724—31no—
141#3724—31no—
142Dic3⋊Dic3—31no—
143Dic3⋊Dic3—31no—
144Dic3⋊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—
150Dic32—31no—
151C2×D4×C9—21no—
152C2×D4×C9—31no—
153C2×D4×C9—31no—
154C2×D4×C9C2×D311yescharacteristic
155C22×C4×C9—31no—
156C2×#611—31no—
157C2×#611—31no—
158C2×#611C2×D311yescharacteristic
159C2×#611C2×D311yescharacteristic
160C2×#611C2×D311yescharacteristic
161C2×#611C2×D311yescharacteristic
162C22×Dic9—31no—
163C22×Dic9—31no—
164C22×Dic9—61no—
165C2×D36C2×D311yescharacteristic
166C2×C4×D9—31no—
167C2×C4×D9—31no—
168C9×C4⋊C4—31no—
169C9×C22⋊C4—31no—
170C9×C22⋊C4—31no—
171#3676—31no—
172#3676—31no—
173#3676—31no—
174#3676—31no—
175#3676—61no—
176#3676—61no—
177#3676—61no—
178(C2×D9)⋊C4—31no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—31no—
182C4⋊Dic9—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—61no—
190Dic9⋊C4—61no—
191C4×Dic9—31no—
192C4×Dic9C2×D311yescharacteristic
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
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×C3×D9—21no—
204C2×C3×D9—21no—
205C2×C3×D9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C3×C4×C9—21no—
210C3⋊Dic9—21no—
211C3⋊Dic9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9—21no—
214C9×Dic3—21no—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C3×Dic9—21no—
218C3×Dic9#4112yes—
219C3×#127—91no—
220C3×#121—31no—
221#940—31no—
222#939—91no—
223#939—91no—
224#939—91no—
225#939—91no—
226#939—91no—
227#939—91no—
228#939D911yescharacteristic, complemented
229#938—91no—
230#938—91no—
231#938—91no—
232#935—91no—
233#935—91no—
234#935—91no—
235#935—91no—
236#935—91no—
237#935—181no—
238D4×Dic3—91no—
239D4×Dic3—91no—
240#929—91no—
241C4×#67—91no—
242#894—91no—
243#889—91no—
244#884—91no—
245#883—91no—
246#67⋊C4—91no—
247#877—91no—
248#872—91no—
249#870—91no—
250C23×C32C22×D311yescharacteristic
251C23×C32C22×D311yescharacteristic
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3C22×D311yescharacteristic
255C32×D4—41no—
256C2×C32×C4C22×D311yescharacteristic
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—31no—
261C2×C3⋊Dic3—121no—
262C3×#67—41no—
263C3×#67—41no—
264C3×#67—62no—
265C3×#67—62no—
266C3×#67—121no—
267C3×#67—121no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—41no—
271C2×C3×Dic3C22×D311yescharacteristic
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C3×D12—121no—
275#625—121no—
276#625—121no—
277D3×Dic3—62no—
278D3×Dic3—121no—
279D3×Dic3—121no—
280C23×C9—21no—
281C23×C9—21no—
282C23×C9—31no—
283C23×C9C22×D311yescharacteristic
284C23×C9C22×D311yescharacteristic
285C22×D9C22×D311yescharacteristic
286C22×D9C22×D311yescharacteristic
287D4×C9—41no—
288D4×C9—42no—
289D4×C9—121no—
290D4×C9—121no—
291C2×C4×C9—21no—
292C2×C4×C9—31no—
293C2×C4×C9—31no—
294C2×C4×C9—31no—
295C2×C4×C9—121no—
296C2×C4×C9C22×D311yescharacteristic
297#611—22no—
298#611—22no—
299#611—41no—
300#611—41no—
301#611—121no—
302#611—121no—
303C2×Dic9—31no—
304C2×Dic9—31no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—61no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9—61no—
311C2×Dic9—62no—
312C2×Dic9—121no—
313C2×Dic9—122no—
314C2×Dic9C22×D311yescharacteristic
315C2×Dic9C22×D311yescharacteristic
316D36—41no—
317C4×D9—121no—
318C4×D9—121no—
319#540—271noSylow
320C2×C3×C9—41no—
321C2×C3×C9—41no—
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—
328C2×C3×D4—21no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—91no—
332C2×C3×D4—91no—
333C2×C3×D4—91no—
334C2×C3×D4—91no—
335C2×C3×D4—91no—
336C2×C3×D4C2×D911yescharacteristic
337C2×C3×D4D3211yescharacteristic
338C22×C3×C4—31no—
339C2×#67—31no—
340C2×#67—31no—
341C2×#67—31no—
342C2×#67—31no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—91no—
347C2×#67C2×D911yescharacteristic
348C2×#67C2×D911yescharacteristic
349C22×Dic3—91no—
350C22×Dic3—91no—
351C22×Dic3—91no—
352C22×Dic3—91no—
353C22×Dic3—91no—
354C22×Dic3—181no—
355C22×Dic3C2×D911yescharacteristic
356C2×D12—31no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C3×C4⋊C4—31no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—31no—
363C3×C42—91no—
364#217—91no—
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—181no—
376#217—181no—
377#217—181no—
378#217C2×D911yescharacteristic
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)⋊C4C2×D911yescharacteristic
385C4⋊Dic3—91no—
386C4⋊Dic3—91no—
387C4⋊Dic3—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—181no—
400Dic3⋊C4—181no—
401Dic3⋊C4C2×D911yescharacteristic
402C4×Dic3—31no—
403C4×Dic3—91no—
404C4×Dic3—91no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32C23×D311yescharacteristic
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C32×C4—21no—
422C3⋊Dic3—61no—
423C3⋊Dic3—61no—
424C3⋊Dic3—61no—
425C3⋊Dic3—61no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—32no—
430C3×Dic3—61no—
431C22×C9—22no—
432C22×C9—21no—
433C22×C9—21no—
434C22×C9—21no—
435C22×C9—21no—
436C22×C9—21no—
437C22×C9—21no—
438C22×C9—21no—
439C22×C9—41no—
440C22×C9—41no—
441C22×C9—41no—
442C22×C9—41no—
443C22×C9—41no—
444C22×C9—61no—
445C22×C9—61no—
446C22×C9—61no—
447C22×C9C23×D311yescharacteristic
448C2×D9—21no—
449C2×D9—21no—
450C2×D9—21no—
451C2×D9—21no—
452C2×D9—21no—
453C2×D9—21no—
454C4×C9—21no—
455C4×C9—41no—
456C4×C9—61no—
457C4×C9—61no—
458C4×C9—61no—
459Dic9—21no—
460Dic9—61no—
461Dic9—61no—
462Dic9—61no—
463Dic9—61no—
464Dic9—121no—
465Dic9—121no—
466Dic9—121no—
467Dic9—121no—
468Dic9#23712yes—
469#127—91no—
470#125—271no—
471#123—271no—
472#123—271no—
473#123—271no—
474#123—271no—
475#121—31no—
476#121—271no—
477#121—271no—
478#121—271no—
479#121—271no—
480#121—271no—
481C4×D4—271no—
482C4×D4—271no—
483#117—271no—
484C3×C9#54011yescharacteristic, complemented, Sylow
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—91no—
489C23×C3—91no—
490C23×C3C22×D911yescharacteristic
491C23×C3C22×D911yescharacteristic
492C23×C3C2×D3211yescharacteristic
493C23×C3C2×D3211yescharacteristic
494C22×D3—31no—
495C22×D3—31no—
496C22×D3C22×D911yescharacteristic
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—42no—
500C3×D4—121no—
501C3×D4—121no—
502C3×D4—182no—
503C3×D4—182no—
504C3×D4—361no—
505C3×D4—361no—
506C3×D4—361no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—91no—
512C2×C3×C4—91no—
513C2×C3×C4—121no—
514C2×C3×C4C22×D911yescharacteristic
515C2×C3×C4C2×D3211yescharacteristic
516#67—41no—
517#67—41no—
518#67—62no—
519#67—62no—
520#67—121no—
521#67—121no—
522#67—361no—
523#67—361no—
524#67—361no—
525#67—361no—
526C2×Dic3—31no—
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—182no—
542C2×Dic3—361no—
543C2×Dic3—361no—
544C2×Dic3—361no—
545C2×Dic3—361no—
546C2×Dic3—362no—
547C2×Dic3C22×D911yescharacteristic
548C2×Dic3C22×D911yescharacteristic
549C2×Dic3C22×D911yescharacteristic
550D12—121no—
551C4×D3—182no—
552C4×D3—361no—
553C4×D3—361no—
554C2×C32—41no—
555C2×C32—41no—
556C2×C32#100411yescharacteristic
557C2×C32#100411yescharacteristic
558C2×C32D3×#4111yescharacteristic
559C3×D3—41no—
560C3×D3—121no—
561C3×D3—121no—
562C2×C9—21no—
563C2×C9—21no—
564C2×C9—21no—
565C2×C9—42no—
566C2×C9—41no—
567C2×C9—41no—
568C2×C9—81no—
569C2×C9—121no—
570C2×C9C2×#23711yescharacteristic
571C2×C9#100411yescharacteristic
572C2×C9#100411yescharacteristic
573D9—41no—
574D9—41no—
575C2×D4—31no—
576C2×D4—31no—
577C2×D4—91no—
578C2×D4—91no—
579C2×D4—91no—
580C2×D4—91no—
581C2×D4—91no—
582C2×D4—271no—
583C2×D4—271no—
584C2×D4D3×D911yescharacteristic
585C22×C4—31no—
586C22×C4—271no—
587C22×C4—271no—
588C22×C4—271no—
589C22×C4—271no—
590C4⋊C4—31no—
591C4⋊C4—271no—
592C4⋊C4—271no—
593C4⋊C4—271no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C4⋊C4—271no—
598C22⋊C4—31no—
599C22⋊C4—31no—
600C22⋊C4—271no—
601C22⋊C4—271no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C42—91no—
609C42—271no—
610C22×C3—22no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—181no—
633C22×C3—181no—
634C22×C3—181no—
635C22×C3—181no—
636C22×C3—181no—
637C22×C3—181no—
638C22×C3C23×D911yescharacteristic
639C22×C3C22×D3211yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—61no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—41no—
652C3×C4—61no—
653C3×C4—61no—
654C3×C4—61no—
655C3×C4—92no—
656C3×C4—181no—
657Dic3—21no—
658Dic3—21no—
659Dic3—21no—
660Dic3—32no—
661Dic3—61no—
662Dic3—181no—
663Dic3—181no—
664Dic3—181no—
665Dic3—181no—
666Dic3—181no—
667Dic3—181no—
668Dic3—181no—
669Dic3—181no—
670Dic3—361no—
671Dic3—361no—
672Dic3—361no—
673Dic3—361no—
674C32#561511yescharacteristic
675C9—21no—
676C9#571911yescharacteristic, complemented
677C23—31no—
678C23—91no—
679C23—91no—
680C23C2×D3×D911yescharacteristic
681C23C2×D3×D911yescharacteristic
682D4—41no—
683D4—121no—
684D4—121no—
685D4—182no—
686D4—182no—
687D4—361no—
688D4—361no—
689D4—361no—
690D4—1081no—
691D4—1081no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—91no—
696C2×C4—91no—
697C2×C4—121no—
698C2×C4—271no—
699C2×C4—271no—
700C2×C4—271no—
701C2×C4—271no—
702C2×C4—542no—
703C2×C4—1081no—
704C2×C4—1081no—
705C2×C4—1081no—
706C2×C4C2×D3×D911yescharacteristic
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—42no—
711C2×C3—41no—
712C2×C3—41no—
713C2×C3—41no—
714C2×C3—41no—
715C2×C3—81no—
716C2×C3—121no—
717C2×C3—361no—
718C2×C3—361no—
719C2×C3#6371011yescharacteristic
720C2×C3#6371011yescharacteristic
721C2×C3#41×D911yescharacteristic
722C2×C3D3×#23711yescharacteristic
723C2×C3#6431311yescharacteristic
724C2×C3#6433011yescharacteristic
725D3—41no—
726D3—121no—
727D3—121no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—61no—
735C22—61no—
736C22—61no—
737C22—181no—
738C22—181no—
739C22—181no—
740C22—181no—
741C22—181no—
742C22—181no—
743C22C22×D3×D911yescharacteristic
744C4—21no—
745C4—61no—
746C4—61no—
747C4—61no—
748C4—92no—
749C4—181no—
750C4—541no—
751C4—541no—
752C4—541no—
753C4—541no—
754C3—21no—
755C3#1058971711yescharacteristic, complemented
756C3#1059518811yescharacteristic
757C2—41no—
758C2—41no—
759C2—121no—
760C2—361no—
761C2—361no—
762C2D9×#23711yescharacteristic
763C2#1172249911yescharacteristic
764C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#540
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #11721835C2semidirect
2. C9×#939C2semidirect
3. C3×#63502C2semidirect
4. #11721290C2semidirect
5. #11721281C2semidirect
6. #11721281C2semidirect
7. #611⋊Dic3C2semidirect
8. Dic3×#611C2semidirect
9. #11721270C2semidirect
10. #11721269C2semidirect
11. #11721259C2semidirect
12. #11721010C2semidirect
13. #11720982C2semidirect
14. #11720981C2semidirect
15. #11720933C2semidirect
69. #63502D3semidirect
228. #939D9semidirect
484. C3×C9#540semidirect
676. C9#5719semidirect
755. C3#10589717semidirect

Maximal subgroups

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

subgroupindex
#117218352
C9×#9392
C3×#635022
#117212902
#117212812
#611⋊Dic32
Dic3×#6112
#117212702
#117212692
#117212592
#117210102
#117209822
#117209812
#117209332
#105951883
#105897173