Finite Group Databasebeta

← #13148757

Subgroups — #13148757

Order 1728.

908 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic18C211yesmaximal, characteristic, complemented
2C2×D9×Dic6C211yesmaximal, characteristic, complemented
3#11721744C211yesmaximal, characteristic, complemented
4C9×#896C211yesmaximal, characteristic, complemented
5C3×#63458C211yesmaximal, characteristic, complemented
6#11721028C211yesmaximal, characteristic
7#11721024C211yesmaximal, characteristic, complemented
8#11721023C211yesmaximal, characteristic, complemented
9#11721012C211yesmaximal, characteristic
10#11720996C211yesmaximal, characteristic, complemented
11#11720991C211yesmaximal, characteristic, complemented
12#11720976C211yesmaximal, characteristic
13#11720904C211yesmaximal, characteristic, complemented
14#11720903C211yesmaximal, characteristic, complemented
15#11720902C211yesmaximal, characteristic, complemented
16#10594377—31nomaximal
17#10589734—31nomaximal
18C2×#6226C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×C4×D3×C9C2211yescharacteristic
21C2×C3×C4×D9C2211yescharacteristic
22C2×C9×Dic6C2211yescharacteristic
23C2×C3×Dic18C2211yescharacteristic
24C2×#6194C2211yescharacteristic
25C2×D3×Dic9C2211yescharacteristic
26C2×D3×Dic9C2211yescharacteristic
27C2×Dic3×D9C2211yescharacteristic
28C2×Dic3×D9C2211yescharacteristic
29C2×#6189C2211yescharacteristic
30C2×#6189C2211yescharacteristic
31C2×#6189C2211yescharacteristic
32D3×Dic18—24no—
33D9×Dic6—24no—
34C3×C9×C4⋊C4C2211yescharacteristic
35C4⋊(C3⋊Dic9)C2211yescharacteristic
36#88534C2211yescharacteristic
37#88534C2211yescharacteristic
38C4×C3⋊Dic9C2211yescharacteristic
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C9×(C2×D3)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C9×Dic3⋊C4C2211yescharacteristic
44C9×Dic3⋊C4C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic
50#88442C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×D3×Dic6—31no—
56C2×D3×Dic6—31no—
57#64097—31no—
58C3×#896—31no—
59C3×#896D311yescharacteristic
60#63902—31no—
61#63896—31no—
62#63896—31no—
63#63893—31no—
64#63893—31no—
65#63879—31no—
66#63879—31no—
67#63839—31no—
68#63839—31no—
69#63838—31no—
70C2×Q8×D9—31no—
71C22×Dic18—31no—
72C9×C22⋊Q8—31no—
73#63506—31no—
74C4×#611—31no—
75#63459—31no—
76#63458—31no—
77#63458D311yescharacteristic, complemented
78#63450—31no—
79#63450—31no—
80#63450—61no—
81#63449—31no—
82#611⋊C4—31no—
83#611⋊C4—31no—
84#63440—31no—
85#63440—31no—
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3⋊Dic9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95#6226—22no—
96#6226—22no—
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C4×D3×C9—22no—
104C3×C4×D9—22no—
105C9×Dic6—22no—
106C3×Dic18—22no—
107#6194Q814yescomplemented
108D3×Dic9—22no—
109D3×Dic9—22no—
110Dic3×D9—22no—
111Dic3×D9—22no—
112#6189—22no—
113#6189—22no—
114#6189D414yescomplemented
115#5632—91no—
116#5632—91no—
117C2×#634—31no—
118C2×#634—31no—
119C2×C3×C4×D3—31no—
120C2×C3×C4×D3C2×D311yescharacteristic
121C2×C3×Dic6—31no—
122C2×C3×Dic6C2×D311yescharacteristic
123C2×#627—31no—
124C2×#627—31no—
125C2×#627—31no—
126C2×#625—31no—
127C2×D3×Dic3—31no—
128C2×D3×Dic3—31no—
129C2×D3×Dic3—31no—
130C2×D3×Dic3—31no—
131D3×Dic6—64no—
132D3×Dic6—64no—
133C32×C4⋊C4C2×D311yescharacteristic
134C4⋊(C3⋊Dic3)—31no—
135#3750—31no—
136#3750—31no—
137C4×C3⋊Dic3—31no—
138C3×(C2×D3)⋊C4—31no—
139C3×(C2×D3)⋊C4—31no—
140C3×(C2×D3)⋊C4C2×D311yescharacteristic
141C3×(C2×D3)⋊C4C2×D311yescharacteristic
142C3×Dic3⋊C4—31no—
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4C2×D311yescharacteristic
145C3×Dic3⋊C4C2×D311yescharacteristic
146#3724—31no—
147#3724—31no—
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152Dic32—31no—
153Dic32—31no—
154C2×Q8×C9—31no—
155C22×C4×C9—31no—
156C2×#611—31no—
157C22×Dic9—31no—
158C22×Dic9—31no—
159Q8×D9—64no—
160C2×C4×D9—31no—
161C2×C4×D9—31no—
162C2×C4×D9C2×D311yescharacteristic
163C2×Dic18—31no—
164C2×Dic18—31no—
165C2×Dic18—31no—
166C2×Dic18—31no—
167C2×Dic18—31no—
168C2×Dic18—64no—
169C2×Dic18—61no—
170C2×Dic18—61no—
171C2×Dic18C2×D311yescharacteristic
172C9×C4⋊C4—21no—
173C9×C4⋊C4—31no—
174C9×C4⋊C4—31no—
175C9×C4⋊C4C2×D311yescharacteristic
176C9×C22⋊C4—31no—
177C9×C22⋊C4—31no—
178#3676—31no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4C2×D311yescharacteristic
181(C2×D9)⋊C4C2×D311yescharacteristic
182C4⋊Dic9—31no—
183C4⋊Dic9—31no—
184C4⋊Dic9—61no—
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—61no—
191Dic9⋊C4—61no—
192Dic9⋊C4C2×D311yescharacteristic
193Dic9⋊C4C2×D311yescharacteristic
194C4×Dic9—31no—
195C4×Dic9—31no—
196C4×Dic9—31no—
197C4×Dic9—61no—
198C22×C3×C9C2411yescharacteristic
199C2×D3×C9—21no—
200C2×D3×C9—21no—
201C2×D3×C9C2×Q812yescomplemented
202C2×C3×D9—21no—
203C2×C3×D9—21no—
204C2×C3×D9C2×Q812yescomplemented
205C3×C4×C9—21no—
206C3×C4×C9—21no—
207C3×C4×C9—21no—
208C3⋊Dic9—21no—
209C3⋊Dic9—21no—
210C3⋊Dic9C2×D412yes—
211C3⋊Dic9C2×Q812yescomplemented
212C9×Dic3—21no—
213C9×Dic3—21no—
214C9×Dic3C2×D412yes—
215C3×Dic9—21no—
216C3×Dic9—21no—
217C3×Dic9C2×D412yes—
218C2×D3×Q8—91no—
219C2×D3×Q8—91no—
220C22×Dic6—91no—
221C22×Dic6—91no—
222C3×C22⋊Q8—31no—
223C3×C22⋊Q8—91no—
224#944—91no—
225#944—91no—
226C4×#67—91no—
227C4×#67—91no—
228#897—91no—
229#897—91no—
230#896—31no—
231#896—91no—
232#896—91no—
233#896D911yescharacteristic, complemented
234#888—91no—
235#888—91no—
236#888—91no—
237#888—91no—
238#888—181no—
239#887—91no—
240#887—91no—
241#67⋊C4—91no—
242#67⋊C4—91no—
243#67⋊C4—91no—
244#67⋊C4—91no—
245#878—91no—
246#878—91no—
247#878—91no—
248#878—91no—
249C22×C3×D3—31no—
250C22×C3×D3C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258#634—62no—
259#634—62no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3C22×D311yescharacteristic
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C3×C4×D3—22no—
267C3×C4×D3—62no—
268C3×Dic6—22no—
269C3×Dic6—62no—
270#627—34no—
271#627—62no—
272#627—62no—
273#625—34no—
274D3×Dic3—62no—
275D3×Dic3—62no—
276D3×Dic3—62no—
277D3×Dic3—62no—
278C23×C9—31no—
279C22×D9C22×D311yescharacteristic
280Q8×C9—62no—
281C2×C4×C9—21no—
282C2×C4×C9—21no—
283C2×C4×C9—21no—
284C2×C4×C9—31no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—62no—
288C2×C4×C9C22×D311yescharacteristic
289C2×C4×C9C22×D311yescharacteristic
290C2×C4×C9C22×D311yescharacteristic
291#611—34no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—31no—
295C2×Dic9—31no—
296C2×Dic9—61no—
297C2×Dic9—61no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—62no—
301C2×Dic9—62no—
302C2×Dic9C22×D311yescharacteristic
303C2×Dic9C22×D311yescharacteristic
304C2×Dic9C22×D311yescharacteristic
305C4×D9—22no—
306C4×D9—62no—
307C4×D9—62no—
308Dic18—22no—
309Dic18—34no—
310Dic18—62no—
311Dic18—62no—
312Dic18—62no—
313Dic18—62no—
314Dic18—122no—
315Dic18—122no—
316D4×Q8—271noSylow
317C2×C3×C9C22×D411yescharacteristic
318C2×C3×C9C22×Q811yescharacteristic
319C2×C3×C92−1+411yescharacteristic
320D3×C9—22no—
321C3×D9—22no—
322C2×C3×Q8—31no—
323C2×C3×Q8—91no—
324C22×C3×C4—31no—
325C22×C3×C4—91no—
326C2×#67—91no—
327C2×#67—91no—
328C22×Dic3—91no—
329C22×Dic3—91no—
330C22×Dic3—91no—
331C22×Dic3—91no—
332D3×Q8—184no—
333D3×Q8—184no—
334C2×C4×D3—31no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×C4×D3C2×D911yescharacteristic
340C2×Dic6—31no—
341C2×Dic6—91no—
342C2×Dic6—91no—
343C2×Dic6—91no—
344C2×Dic6—91no—
345C2×Dic6—91no—
346C2×Dic6—91no—
347C2×Dic6—91no—
348C2×Dic6—91no—
349C2×Dic6—91no—
350C2×Dic6—91no—
351C2×Dic6—181no—
352C2×Dic6—181no—
353C2×Dic6—184no—
354C2×Dic6—184no—
355C2×Dic6C2×D911yescharacteristic
356C3×C4⋊C4—21no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—91no—
360C3×C4⋊C4—91no—
361C3×C4⋊C4C2×D911yescharacteristic
362C3×C4⋊C4D3211yescharacteristic
363C3×C22⋊C4—31no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367#217—91no—
368#217—91no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4C2×D911yescharacteristic
374(C2×D3)⋊C4C2×D911yescharacteristic
375C4⋊Dic3—91no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—181no—
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—181no—
393Dic3⋊C4—181no—
394Dic3⋊C4C2×D911yescharacteristic
395Dic3⋊C4C2×D911yescharacteristic
396C4×Dic3—91no—
397C4×Dic3—91no—
398C4×Dic3—91no—
399C4×Dic3—91no—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C4×Dic3—181no—
403C22×C32C23×D311yescharacteristic
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—32no—
407C2×C3×D3—61no—
408C2×C3×D3—61no—
409C2×C3×D3D3×Q812yes—
410C32×C4—21no—
411C32×C4—21no—
412C32×C4—21no—
413C3⋊Dic3—32no—
414C3⋊Dic3—32no—
415C3⋊Dic3—61no—
416C3⋊Dic3—61no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—32no—
420C3×Dic3—61no—
421C3×Dic3—61no—
422C3×Dic3D3×D412yes—
423C22×C9—21no—
424C22×C9—32no—
425C22×C9—61no—
426C22×C9—61no—
427C22×C9C23×D311yescharacteristic
428C2×D9—21no—
429C2×D9—21no—
430C2×D9D3×Q812yescomplemented
431C4×C9—22no—
432C4×C9—21no—
433C4×C9—21no—
434C4×C9—21no—
435C4×C9—32no—
436C4×C9—41no—
437C4×C9—41no—
438C4×C9—61no—
439C4×C9—61no—
440Dic9—21no—
441Dic9—21no—
442Dic9—32no—
443Dic9—32no—
444Dic9—62no—
445Dic9—62no—
446Dic9—61no—
447Dic9—61no—
448Dic9—121no—
449Dic9—121no—
450Dic9D3×D412yes—
451C22×Q8—271no—
452C22×Q8—271no—
453C4⋊Q8—271no—
454C4⋊Q8—271no—
455C4⋊Q8—271no—
456C22⋊Q8—31no—
457C22⋊Q8—91no—
458C22⋊Q8—271no—
459C22⋊Q8—271no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462C4×Q8—271no—
463C4×D4—271no—
464C4×D4—271no—
465C4×D4—271no—
466C3×C9D4×Q811yescharacteristic, complemented, Sylow
467C23×C3—31no—
468C23×C3—91no—
469C22×D3—31no—
470C22×D3C22×D911yescharacteristic
471C3×Q8—62no—
472C3×Q8—182no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—62no—
480C2×C3×C4—91no—
481C2×C3×C4—91no—
482C2×C3×C4—91no—
483C2×C3×C4—182no—
484C2×C3×C4C22×D911yescharacteristic
485C2×C3×C4C22×D911yescharacteristic
486C2×C3×C4C22×D911yescharacteristic
487C2×C3×C4C2×D3211yescharacteristic
488C2×C3×C4C2×D3211yescharacteristic
489C2×C3×C4C2×D3211yescharacteristic
490#67—94no—
491#67—94no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—91no—
496C2×Dic3—91no—
497C2×Dic3—91no—
498C2×Dic3—91no—
499C2×Dic3—91no—
500C2×Dic3—91no—
501C2×Dic3—91no—
502C2×Dic3—91no—
503C2×Dic3—181no—
504C2×Dic3—181no—
505C2×Dic3—181no—
506C2×Dic3—181no—
507C2×Dic3—182no—
508C2×Dic3—182no—
509C2×Dic3—182no—
510C2×Dic3—182no—
511C2×Dic3C22×D911yescharacteristic
512C2×Dic3C22×D911yescharacteristic
513C2×Dic3C22×D911yescharacteristic
514C4×D3—22no—
515C4×D3—62no—
516C4×D3—182no—
517C4×D3—182no—
518C4×D3—182no—
519C4×D3—182no—
520Dic6—22no—
521Dic6—62no—
522Dic6—94no—
523Dic6—94no—
524Dic6—182no—
525Dic6—182no—
526Dic6—182no—
527Dic6—182no—
528Dic6—182no—
529Dic6—182no—
530Dic6—182no—
531Dic6—182no—
532Dic6—362no—
533Dic6—362no—
534C2×C32C2×D3×D411yescharacteristic
535C2×C32C2×D3×Q811yescharacteristic
536C2×C32#101011yescharacteristic
537C3×D3—22no—
538C3×D3—62no—
539C2×C9—21no—
540C2×C9—21no—
541C2×C9—21no—
542C2×C9—62no—
543C2×C9C2×D3×D411yescharacteristic
544C2×C9C2×D3×Q811yescharacteristic
545C2×C9#101011yescharacteristic
546D9—22no—
547C2×Q8—31no—
548C2×Q8—91no—
549C2×Q8—271no—
550C2×Q8—271no—
551C2×Q8—271no—
552C2×Q8—271no—
553C2×Q8—271no—
554C2×Q8—544no—
555C2×Q8—544no—
556C2×D4—271no—
557C22×C4—31no—
558C22×C4—91no—
559C22×C4—271no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—271no—
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C4⋊C4D3×D911yescharacteristic
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C42—271no—
582C42—271no—
583C42—271no—
584C22×C3—21no—
585C22×C3—32no—
586C22×C3—61no—
587C22×C3—61no—
588C22×C3—92no—
589C22×C3—181no—
590C22×C3—181no—
591C22×C3C23×D911yescharacteristic
592C22×C3C22×D3211yescharacteristic
593C2×D3—21no—
594C2×D3—21no—
595C2×D3—32no—
596C2×D3—61no—
597C2×D3—61no—
598C2×D3Q8×D912yescomplemented
599C3×C4—22no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—32no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—61no—
610C3×C4—61no—
611C3×C4—92no—
612C3×C4—181no—
613C3×C4—181no—
614Dic3—21no—
615Dic3—21no—
616Dic3—32no—
617Dic3—61no—
618Dic3—61no—
619Dic3—92no—
620Dic3—92no—
621Dic3—92no—
622Dic3—92no—
623Dic3—182no—
624Dic3—182no—
625Dic3—181no—
626Dic3—181no—
627Dic3—181no—
628Dic3—181no—
629Dic3—361no—
630Dic3—361no—
631Dic3D4×D912yes—
632C32#563211yescharacteristic
633C9—21no—
634C9#563211yescharacteristic, complemented
635C23—31no—
636C23—91no—
637Q8—62no—
638Q8—182no—
639Q8—274no—
640Q8—542no—
641Q8—542no—
642Q8—542no—
643Q8—542no—
644D4—274no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—62no—
649C2×C4—91no—
650C2×C4—91no—
651C2×C4—91no—
652C2×C4—182no—
653C2×C4—271no—
654C2×C4—271no—
655C2×C4—271no—
656C2×C4—271no—
657C2×C4—542no—
658C2×C4—542no—
659C2×C4—542no—
660C2×C4—542no—
661C2×C4C2×D3×D911yescharacteristic
662C2×C4C2×D3×D911yescharacteristic
663C2×C4C2×D3×D911yescharacteristic
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—62no—
668C2×C3—182no—
669C2×C3C2×D4×D911yescharacteristic
670C2×C3C2×Q8×D911yescharacteristic
671C2×C3#6371611yescharacteristic
672C2×C3#6429811yescharacteristic
673C2×C3D32×D411yescharacteristic
674C2×C3D32×Q811yescharacteristic
675D3—22no—
676D3—62no—
677C22—32no—
678C22—61no—
679C22—61no—
680C22—92no—
681C22—181no—
682C22—181no—
683C22C22×D3×D911yescharacteristic
684C4—21no—
685C4—21no—
686C4—21no—
687C4—32no—
688C4—61no—
689C4—61no—
690C4—92no—
691C4—181no—
692C4—181no—
693C4—272no—
694C4—272no—
695C4—541no—
696C4—541no—
697C3—21no—
698C3#1058973411yescharacteristic, complemented
699C3#1059437711yescharacteristic
700C2—62no—
701C2—182no—
702C2#1172246511yescharacteristic
703C2D3×D4×D911yescharacteristic
704C2D3×Q8×D911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radicalC2×#6194C22
hypercenterC4⋊C4D3×D9
hypocenterC3×C9D4×Q8
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×Dic18C2semidirect
2. C2×D9×Dic6C2semidirect
3. #11721744C2semidirect
4. C9×#896C2semidirect
5. C3×#63458C2semidirect
7. #11721024C2semidirect
8. #11721023C2semidirect
10. #11720996C2semidirect
11. #11720991C2semidirect
13. #11720904C2semidirect
14. #11720903C2semidirect
15. #11720902C2semidirect
77. #63458D3semidirect
107. #6194Q8semidirect
114. #6189D4semidirect
201. C2×D3×C9C2×Q8semidirect
204. C2×C3×D9C2×Q8semidirect
211. C3⋊Dic9C2×Q8semidirect
233. #896D9semidirect
430. C2×D9D3×Q8semidirect
466. C3×C9D4×Q8semidirect
598. C2×D3Q8×D9semidirect
634. C9#5632semidirect
698. C3#10589734semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic182
C2×D9×Dic62
#117217442
C9×#8962
C3×#634582
#117210282
#117210242
#117210232
#117210122
#117209962
#117209912
#117209762
#117209042
#117209032
#117209022
#105943773
#105897343