Finite Group Databasebeta

← #13151133

Subgroups — #13151133

Order 1728.

1084 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88663C211yesmaximal, characteristic, complemented
2C22×D3×Dic9C211yesmaximal, characteristic, complemented
3D4×C3⋊Dic9C211yesmaximal, characteristic, complemented
4C9×#937C211yesmaximal, characteristic, complemented
5C3×#63501C211yesmaximal, characteristic, complemented
6#11721286C211yesmaximal, characteristic, complemented
7#67⋊Dic9C211yesmaximal, characteristic, complemented
8#11721281C211yesmaximal, characteristic, complemented
9#11721280C211yesmaximal, characteristic, complemented
10#611⋊Dic3C211yesmaximal, characteristic, complemented
11#11721253C211yesmaximal, characteristic, complemented
12#11721028C211yesmaximal, characteristic, complemented
13#11721023C211yesmaximal, characteristic, complemented
14#11721021C211yesmaximal, characteristic, complemented
15#11721011C211yesmaximal, characteristic, complemented
16#10595130—31nomaximal
17#10589688—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C22×C3⋊Dic9C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic, complemented
26C22×C3×Dic9C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29#88663—24no—
30C2×D3×Dic9—24no—
31C2×D3×Dic9C2211yescharacteristic
32C2×D3×Dic9C2211yescharacteristic
33C2×D3×Dic9C2211yescharacteristic
34C2×D3×Dic9C2211yescharacteristic
35C2×Dic3×D9C2211yescharacteristic, complemented
36C2×#6189C2211yescharacteristic, complemented
37#88551C2211yescharacteristic
38#88551C2211yescharacteristic, complemented
39C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
40C4×C3⋊Dic9C2211yescharacteristic, complemented
41C9×#217C2211yescharacteristic
42C3×#3676C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic
44C9×(C2×D3)⋊C4C2211yescharacteristic
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×#3805—31no—
56C22×D3×Dic3—31no—
57D4×C3⋊Dic3—31no—
58C3×#939—31no—
59C3×#937D311yescharacteristic
60#63976—31no—
61#67⋊Dic3—31no—
62#67⋊Dic3—31no—
63#63970—31no—
64#63969—31no—
65#63964—31no—
66#63902—31no—
67#63893—31no—
68#63891—31no—
69#63878—31no—
70C23×Dic9—31no—
71C2×#3699—31no—
72C9×#120—31no—
73#63515—31no—
74#63501—31no—
75#63501D311yescharacteristic, complemented
76#63497—31no—
77D4×Dic9—31no—
78D4×Dic9—31no—
79D4×Dic9—61no—
80#63448—31no—
81#611⋊C4—31no—
82#611⋊C4—31no—
83#63440—31no—
84#63440—31no—
85#63439—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×D3×C9—22no—
89C22×D3×C9—22no—
90C22×D3×C9—22no—
91C22×D3×C9C2311yescharacteristic
92C22×D3×C9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
94C3×D4×C9—22no—
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3⋊Dic9—22no—
97C2×C3⋊Dic9—22no—
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C9×#67—22no—
103C9×#67—22no—
104C3×#611—22no—
105C3×#611—22no—
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9—22no—
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112#6194—22no—
113#6194—22no—
114D3×Dic9—22no—
115D3×Dic9—22no—
116D3×Dic9—22no—
117D3×Dic9D414yescomplemented
118Dic3×D9—22no—
119#6189—22no—
120#5606—91no—
121#5586—91no—
122C23×C3×D3C2×D311yescharacteristic
123C2×C32×D4C2×D311yescharacteristic
124C22×C3⋊Dic3—31no—
125C22×C3⋊Dic3—31no—
126C2×C3×#67—31no—
127C2×C3×#67—31no—
128C2×C3×#67C2×D311yescharacteristic
129C2×C3×#67C2×D311yescharacteristic
130C22×C3×Dic3—31no—
131C2×#627—31no—
132C2×#625—31no—
133C2×#625—31no—
134#3805—64no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137C2×D3×Dic3—31no—
138C2×D3×Dic3—31no—
139C2×D3×Dic3—31no—
140C2×D3×Dic3—64no—
141C24×C9—31no—
142#3757—31no—
143#3757—31no—
144C4⋊(C3⋊Dic3)—31no—
145C4×C3⋊Dic3—31no—
146C3×#217—31no—
147C3×#217C2×D311yescharacteristic
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4C2×D311yescharacteristic
150C3×(C2×D3)⋊C4C2×D311yescharacteristic
151C3×Dic3⋊C4—31no—
152#3724—31no—
153Dic3⋊Dic3—31no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159Dic32—31no—
160C2×D4×C9—21no—
161C2×D4×C9—31no—
162C2×D4×C9—31no—
163C2×D4×C9C2×D311yescharacteristic
164C2×#611—31no—
165C2×#611—31no—
166C2×#611C2×D311yescharacteristic
167C2×#611C2×D311yescharacteristic, complemented
168C22×Dic9—31no—
169C22×Dic9—31no—
170C22×Dic9—31no—
171C22×Dic9—31no—
172C22×Dic9—31no—
173C22×Dic9—31no—
174C22×Dic9—64no—
175C22×Dic9—61no—
176C22×Dic9—61no—
177C22×Dic9C2×D311yescharacteristic
178#3699—64no—
179C2×C4×D9—31no—
180C2×Dic18—31no—
181C9×C22⋊C4—31no—
182C9×C22⋊C4—31no—
183C9×C22⋊C4—31no—
184#3676—31no—
185#3676—31no—
186#3676—31no—
187#3676—31no—
188#3676—61no—
189#3676—61no—
190#3676C2×D311yescharacteristic, complemented
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4C2×D311yescharacteristic, complemented
193C4⋊Dic9—31no—
194C4⋊Dic9—31no—
195C4⋊Dic9—61no—
196Dic9⋊C4—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4—31no—
199Dic9⋊C4C2×D311yescharacteristic, complemented
200C4×Dic9—31no—
201C4×Dic9—31no—
202C4×Dic9—61no—
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9#4112yescomplemented
209C22×C3×C9C2411yescharacteristic
210C2×D3×C9—28no—
211C2×D3×C9—21no—
212C2×D3×C9—21no—
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9C2×D412yes—
216C2×D3×C9#4112yescomplemented
217C2×C3×D9—21no—
218C2×C3×D9—21no—
219C2×C3×D9—21no—
220C3×C4×C9—21no—
221C3⋊Dic9—21no—
222C3⋊Dic9—21no—
223C3⋊Dic9—21no—
224C3⋊Dic9C2×D412yes—
225C9×Dic3—21no—
226C9×Dic3—21no—
227C3×Dic9—21no—
228C3×Dic9—21no—
229C3×Dic9C2×D412yes—
230C23×Dic3—91no—
231C2×#237—91no—
232C2×#237—91no—
233C22×C4×D3—91no—
234C3×#121—91no—
235C3×#120—31no—
236#953—91no—
237#939—31no—
238#939—91no—
239#938—91no—
240#937—91no—
241#937D911yescharacteristic, complemented
242#935—91no—
243D4×Dic3—91no—
244D4×Dic3—91no—
245D4×Dic3—91no—
246D4×Dic3—91no—
247D4×Dic3—181no—
248#924—91no—
249#897—91no—
250#892—91no—
251#886—91no—
252#883—91no—
253#883—91no—
254#67⋊C4—91no—
255#67⋊C4—91no—
256#67⋊C4—91no—
257#67⋊C4—91no—
258#878—91no—
259#878—91no—
260#877—91no—
261C23×C32C22×D311yescharacteristic
262C23×C32C22×D311yescharacteristic
263C22×C3×D3—22no—
264C22×C3×D3—22no—
265C22×C3×D3—22no—
266C22×C3×D3—31no—
267C22×C3×D3C22×D311yescharacteristic
268C22×C3×D3C22×D311yescharacteristic
269C32×D4—22no—
270C2×C32×C4C22×D311yescharacteristic
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—62no—
276C2×C3⋊Dic3—62no—
277C3×#67—22no—
278C3×#67—22no—
279C3×#67—62no—
280C3×#67—62no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287#627—62no—
288#625—62no—
289#625—62no—
290D3×Dic3—34no—
291D3×Dic3—62no—
292D3×Dic3—62no—
293D3×Dic3—62no—
294D3×Dic3—62no—
295C23×C9—21no—
296C23×C9—21no—
297C23×C9—31no—
298C23×C9—31no—
299C23×C9—62no—
300C23×C9—62no—
301C23×C9—62no—
302C23×C9C22×D311yescharacteristic
303C23×C9C22×D311yescharacteristic
304C22×D9C22×D311yescharacteristic
305D4×C9—24no—
306D4×C9—22no—
307D4×C9—62no—
308D4×C9—62no—
309C2×C4×C9—21no—
310C2×C4×C9—31no—
311C2×C4×C9—31no—
312C2×C4×C9C22×D311yescharacteristic
313#611—22no—
314#611—22no—
315#611—62no—
316#611—62no—
317C2×Dic9—22no—
318C2×Dic9—31no—
319C2×Dic9—34no—
320C2×Dic9—31no—
321C2×Dic9—31no—
322C2×Dic9—31no—
323C2×Dic9—61no—
324C2×Dic9—61no—
325C2×Dic9—61no—
326C2×Dic9—61no—
327C2×Dic9—62no—
328C2×Dic9—62no—
329C2×Dic9—62no—
330C2×Dic9—62no—
331C2×Dic9—62no—
332C2×Dic9—122no—
333C2×Dic9—122no—
334C2×Dic9C22×D311yescharacteristic
335C2×Dic9C22×D311yescharacteristic
336C2×Dic9C22×D311yescharacteristic
337C4×D9—62no—
338Dic18—62no—
339#525—271noSylow
340C2×C3×C9—22no—
341C2×C3×C9—41no—
342C2×C3×C9C22×D411yescharacteristic
343C2×C3×C9C2×#4111yescharacteristic
344C2×C3×C9C2×#4111yescharacteristic
345D3×C9—22no—
346D3×C9—22no—
347C3×D9—41no—
348C24×C3—31no—
349C23×D3C2×D911yescharacteristic
350C2×C3×D4—21no—
351C2×C3×D4—31no—
352C2×C3×D4—31no—
353C2×C3×D4—91no—
354C2×C3×D4—91no—
355C2×C3×D4C2×D911yescharacteristic
356C2×C3×D4D3211yescharacteristic
357C22×C3×C4—91no—
358C2×#67—31no—
359C2×#67—31no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67C2×D911yescharacteristic
365C2×#67C2×D911yescharacteristic
366C22×Dic3—31no—
367C22×Dic3—91no—
368C22×Dic3—91no—
369C22×Dic3—91no—
370C22×Dic3—91no—
371C22×Dic3—91no—
372C22×Dic3—91no—
373C22×Dic3—91no—
374C22×Dic3—91no—
375C22×Dic3—91no—
376C22×Dic3—181no—
377C22×Dic3—181no—
378C22×Dic3—184no—
379#237—184no—
380#237—184no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×C4×D3—184no—
387C2×Dic6—91no—
388C2×Dic6—91no—
389C3×C4⋊C4—91no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—31no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—91no—
394C3×C22⋊C4—91no—
395#217—31no—
396#217—91no—
397#217—91no—
398#217—91no—
399#217—91no—
400#217—91no—
401#217—91no—
402#217—91no—
403#217—181no—
404#217—181no—
405#217C2×D911yescharacteristic
406(C2×D3)⋊C4—31no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4C2×D911yescharacteristic
411(C2×D3)⋊C4C2×D911yescharacteristic
412C4⋊Dic3—91no—
413C4⋊Dic3—91no—
414C4⋊Dic3—91no—
415C4⋊Dic3—91no—
416C4⋊Dic3—91no—
417C4⋊Dic3—181no—
418Dic3⋊C4—31no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424C4×Dic3—91no—
425C4×Dic3—91no—
426C4×Dic3—91no—
427C4×Dic3—91no—
428C4×Dic3—181no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32#23712yes—
435C22×C32C23×D311yescharacteristic
436C2×C3×D3—28no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3—61no—
444C2×C3×D3D3×D412yes—
445C2×C3×D3#23712yes—
446C32×C4—21no—
447C3⋊Dic3—32no—
448C3⋊Dic3—61no—
449C3⋊Dic3—61no—
450C3⋊Dic3—61no—
451C3×Dic3—21no—
452C3×Dic3—21no—
453C3×Dic3—32no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C22×C9—21no—
457C22×C9—21no—
458C22×C9—22no—
459C22×C9—21no—
460C22×C9—21no—
461C22×C9—21no—
462C22×C9—21no—
463C22×C9—22no—
464C22×C9—32no—
465C22×C9—32no—
466C22×C9—41no—
467C22×C9—41no—
468C22×C9—41no—
469C22×C9—41no—
470C22×C9—68no—
471C22×C9—61no—
472C22×C9—61no—
473C22×C9—61no—
474C22×C9—61no—
475C22×C9#23712yescomplemented
476C22×C9C23×D311yescharacteristic
477C2×D9—21no—
478C2×D9—21no—
479C2×D9—21no—
480C4×C9—22no—
481C4×C9—21no—
482C4×C9—61no—
483C4×C9—61no—
484Dic9—21no—
485Dic9—21no—
486Dic9—32no—
487Dic9—62no—
488Dic9—61no—
489Dic9—61no—
490Dic9—61no—
491Dic9—121no—
492Dic9—121no—
493Dic9—121no—
494Dic9D3×D412yes—
495C2×#41—271no—
496C23×C4—271no—
497#123—271no—
498#123—271no—
499C22⋊Q8—271no—
500C22⋊Q8—271no—
501#121—91no—
502#121—271no—
503#120—31no—
504#120—271no—
505C4×D4—271no—
506C4×D4—271no—
507C4×D4—271no—
508C4×D4—271no—
509#117—271no—
510C3×C9#52511yescharacteristic, complemented, Sylow
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—31no—
514C23×C3—31no—
515C23×C3—62no—
516C23×C3—62no—
517C23×C3—62no—
518C23×C3—91no—
519C23×C3C22×D911yescharacteristic
520C23×C3C22×D911yescharacteristic
521C23×C3C2×D3211yescharacteristic
522C23×C3C2×D3211yescharacteristic
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—31no—
527C22×D3C22×D911yescharacteristic
528C22×D3C22×D911yescharacteristic
529C3×D4—24no—
530C3×D4—22no—
531C3×D4—22no—
532C3×D4—62no—
533C3×D4—62no—
534C3×D4—182no—
535C3×D4—182no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—91no—
540C2×C3×C4—91no—
541C2×C3×C4—91no—
542C2×C3×C4—182no—
543C2×C3×C4C22×D911yescharacteristic
544C2×C3×C4C2×D3211yescharacteristic
545#67—22no—
546#67—22no—
547#67—62no—
548#67—62no—
549#67—182no—
550#67—182no—
551#67—182no—
552#67—182no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—62no—
557C2×Dic3—94no—
558C2×Dic3—91no—
559C2×Dic3—91no—
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—181no—
570C2×Dic3—182no—
571C2×Dic3—182no—
572C2×Dic3—182no—
573C2×Dic3—182no—
574C2×Dic3—182no—
575C2×Dic3—182no—
576C2×Dic3—182no—
577C2×Dic3—182no—
578C2×Dic3—362no—
579C2×Dic3—362no—
580C2×Dic3C22×D911yescharacteristic
581C2×Dic3C22×D911yescharacteristic
582C4×D3—94no—
583C4×D3—182no—
584C4×D3—182no—
585C4×D3—182no—
586C4×D3—182no—
587Dic6—182no—
588Dic6—182no—
589C2×C32—22no—
590C2×C32—41no—
591C2×C32C2×D3×D411yescharacteristic
592C2×C32C2×#23711yescharacteristic
593C2×C32C2×#23711yescharacteristic
594C3×D3—22no—
595C3×D3—22no—
596C3×D3—121no—
597C2×C9—22no—
598C2×C9—21no—
599C2×C9—21no—
600C2×C9—21no—
601C2×C9—42no—
602C2×C9—42no—
603C2×C9—41no—
604C2×C9—62no—
605C2×C9—62no—
606C2×C9C2×D3×D411yescharacteristic
607C2×C9C2×#23711yescharacteristic
608C2×C9D3×#4111yescharacteristic
609D9—41no—
610C24—31no—
611#41—544no—
612C2×Q8—271no—
613C2×D4—31no—
614C2×D4—31no—
615C2×D4—91no—
616C2×D4—91no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4D3×D911yescharacteristic
620C22×C4—91no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—271no—
628C22×C4—544no—
629C4⋊C4—91no—
630C4⋊C4—271no—
631C4⋊C4—271no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4—271no—
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—31no—
638C22⋊C4—91no—
639C22⋊C4—91no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C42—271no—
646C42—271no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—22no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—22no—
660C22×C3—32no—
661C22×C3—32no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—68no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—181no—
672C22×C3—181no—
673C22×C3—181no—
674C22×C3#369912yescomplemented
675C22×C3C23×D911yescharacteristic
676C22×C3#380512yes—
677C22×C3C22×D3211yescharacteristic
678C2×D3—28no—
679C2×D3—21no—
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3D4×D912yes—
687C2×D3#369912yescomplemented
688C3×C4—22no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—61no—
692C3×C4—61no—
693C3×C4—92no—
694C3×C4—181no—
695C3×C4—181no—
696Dic3—21no—
697Dic3—21no—
698Dic3—32no—
699Dic3—61no—
700Dic3—61no—
701Dic3—92no—
702Dic3—92no—
703Dic3—182no—
704Dic3—181no—
705Dic3—181no—
706Dic3—181no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710Dic3—361no—
711Dic3—361no—
712Dic3—361no—
713C32#558611yescharacteristic
714C9—21no—
715C9#560611yescharacteristic, complemented
716C23—31no—
717C23—31no—
718C23—62no—
719C23—62no—
720C23—62no—
721C23—91no—
722C23C2×D3×D911yescharacteristic
723C23C2×D3×D911yescharacteristic
724Q8—542no—
725D4—22no—
726D4—62no—
727D4—62no—
728D4—182no—
729D4—182no—
730D4—542no—
731D4—542no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—91no—
737C2×C4—182no—
738C2×C4—274no—
739C2×C4—271no—
740C2×C4—271no—
741C2×C4—271no—
742C2×C4—271no—
743C2×C4—542no—
744C2×C4—542no—
745C2×C4—542no—
746C2×C4—542no—
747C2×C4—542no—
748C2×C4—542no—
749C2×C4C2×D3×D911yescharacteristic
750C2×C3—22no—
751C2×C3—22no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—42no—
756C2×C3—42no—
757C2×C3—41no—
758C2×C3—41no—
759C2×C3—62no—
760C2×C3—62no—
761C2×C3—361no—
762C2×C3C2×D4×D911yescharacteristic
763C2×C3C2×#369911yescharacteristic
764C2×C3C2×#369911yescharacteristic
765C2×C3D32×D411yescharacteristic
766C2×C3D3×#23711yescharacteristic
767C2×C3C2×#380511yescharacteristic
768D3—22no—
769D3—22no—
770D3—121no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—32no—
777C22—32no—
778C22—68no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—181no—
784C22—181no—
785C22—181no—
786C22#8866312yescomplemented
787C22C22×D3×D911yescharacteristic
788C4—21no—
789C4—61no—
790C4—61no—
791C4—92no—
792C4—181no—
793C4—181no—
794C4—272no—
795C4—541no—
796C4—541no—
797C4—541no—
798C3—21no—
799C3#1058968811yescharacteristic, complemented
800C3#1059513011yescharacteristic
801C2—22no—
802C2—41no—
803C2—62no—
804C2—62no—
805C2—361no—
806C2D3×D4×D911yescharacteristic
807C2D3×#369911yescharacteristic
808C2C2×#8866311yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#525
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. C2×#88663C2semidirect
2. C22×D3×Dic9C2semidirect
3. D4×C3⋊Dic9C2semidirect
4. C9×#937C2semidirect
5. C3×#63501C2semidirect
6. #11721286C2semidirect
7. #67⋊Dic9C2semidirect
8. #11721281C2semidirect
9. #11721280C2semidirect
10. #611⋊Dic3C2semidirect
11. #11721253C2semidirect
12. #11721028C2semidirect
13. #11721023C2semidirect
14. #11721021C2semidirect
15. #11721011C2semidirect
21. C22×C3⋊Dic9C22semidirect
25. C2×C3×#611C22semidirect
35. C2×Dic3×D9C22semidirect
36. C2×#6189C22semidirect
38. #88551C22semidirect
39. C4⋊(C3⋊Dic9)C22semidirect
40. C4×C3⋊Dic9C22semidirect
42. C3×#3676C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×Dic9⋊C4C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. Dic9⋊Dic3C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
75. #63501D3semidirect
117. D3×Dic9D4semidirect
167. C2×#611C2×D3semidirect
190. #3676C2×D3semidirect
192. (C2×D9)⋊C4C2×D3semidirect
199. Dic9⋊C4C2×D3semidirect
208. C22×C3×C9#41semidirect
216. C2×D3×C9#41semidirect
241. #937D9semidirect
475. C22×C9#237semidirect
510. C3×C9#525semidirect
674. C22×C3#3699semidirect
687. C2×D3#3699semidirect
715. C9#5606semidirect
786. C22#88663semidirect
799. C3#10589688semidirect

Maximal subgroups

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

subgroupindex
C2×#886632
C22×D3×Dic92
D4×C3⋊Dic92
C9×#9372
C3×#635012
#117212862
#67⋊Dic92
#117212812
#117212802
#611⋊Dic32
#117212532
#117210282
#117210232
#117210212
#117210112
#105951303
#105896883