Finite Group Databasebeta

← #13148759

Subgroups — #13148759

Order 1728.

914 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic18C211yesmaximal, characteristic, complemented
2C2×(C3⋊D9)⋊Q8C211yesmaximal, characteristic, complemented
3#11721752C211yesmaximal, characteristic, complemented
4C9×#896C211yesmaximal, characteristic, complemented
5C3×#63450C211yesmaximal, characteristic, complemented
6#11721030C211yesmaximal, characteristic
7#11721026C211yesmaximal, characteristic, complemented
8#11721018C211yesmaximal, characteristic, complemented
9#11721014C211yesmaximal, characteristic
10#11721013C211yesmaximal, characteristic
11#11720995C211yesmaximal, characteristic, complemented
12#11720985C211yesmaximal, characteristic, complemented
13#11720905C211yesmaximal, characteristic, complemented
14#11720903C211yesmaximal, characteristic, complemented
15#11720901C211yesmaximal, characteristic, complemented
16#10594378—31nomaximal
17#10589734—31nomaximal
18C2×C4×C3⋊D9C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×C4×D3×C9C2211yescharacteristic
21C2×C9×Dic6C2211yescharacteristic
22C2×C3×Dic18C2211yescharacteristic
23C2×C3×Dic18C2211yescharacteristic
24C2×#6195C2211yescharacteristic
25C2×D3×Dic9C2211yescharacteristic
26C2×D3×Dic9C2211yescharacteristic
27C2×(C3⋊D9)⋊C4C2211yescharacteristic
28C2×(C3⋊D9)⋊C4C2211yescharacteristic
29C2×#6189C2211yescharacteristic
30C2×#6189C2211yescharacteristic
31C2×#6189C2211yescharacteristic
32D3×Dic18—24no—
33(C3⋊D9)⋊Q8—24no—
34C3×C9×C4⋊C4C2211yescharacteristic
35#88536C2211yescharacteristic
36#88536C2211yescharacteristic
37#88534C2211yescharacteristic
38#88534C2211yescharacteristic
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C9×(C2×D3)⋊C4C2211yescharacteristic
41C9×Dic3⋊C4C2211yescharacteristic
42C9×Dic3⋊C4C2211yescharacteristic
43C3×C4⋊Dic9C2211yescharacteristic
44C3×Dic9⋊C4C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46C3×C4×Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48#88445C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic
50#88442C2211yescharacteristic
51Dic9⋊Dic3C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×#3797—31no—
56C2×D3×Dic6—31no—
57#64105—31no—
58C3×#896D311yescharacteristic
59C3×#888—31no—
60#63904—31no—
61#63899—31no—
62#63895—31no—
63#63888—31no—
64#63887—31no—
65#63881—31no—
66#63880—31no—
67#63840—31no—
68#63839—31no—
69#63837—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#63458—31no—
78#63458—61no—
79#63450—31no—
80#63450D311yescharacteristic, complemented
81#63449—31no—
82#611⋊C4—31no—
83#611⋊C4—31no—
84#63440—31no—
85#63440—31no—
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3⋊Dic9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C4×C3⋊D9—22no—
95#6226—22no—
96C2×C9×Dic3C2311yescharacteristic
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C4×D3×C9—22no—
104C9×Dic6—22no—
105C3×Dic18—22no—
106C3×Dic18—22no—
107#6195Q814yescomplemented
108D3×Dic9—22no—
109D3×Dic9—22no—
110(C3⋊D9)⋊C4—22no—
111(C3⋊D9)⋊C4—22no—
112#6189—22no—
113#6189—22no—
114#6189D414yescomplemented
115#5727—91no—
116#5632—91no—
117C2×C4×C3⋊D3—31no—
118C2×#634—31no—
119C2×C3×C4×D3C2×D311yescharacteristic
120C2×C3×Dic6—31no—
121C2×C3×Dic6—31no—
122C2×C3×Dic6C2×D311yescharacteristic
123C2×#627—31no—
124C2×#627—31no—
125C2×#627—31no—
126C2×#626—31no—
127C2×#624—31no—
128C2×#624—31no—
129C2×D3×Dic3—31no—
130C2×D3×Dic3—31no—
131#3797—64no—
132D3×Dic6—64no—
133C32×C4⋊C4C2×D311yescharacteristic
134#3752—31no—
135#3752—31no—
136#3750—31no—
137#3750—31no—
138C3×(C2×D3)⋊C4C2×D311yescharacteristic
139C3×(C2×D3)⋊C4C2×D311yescharacteristic
140C3×C4⋊Dic3—31no—
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4—31no—
143C3×Dic3⋊C4C2×D311yescharacteristic
144C3×Dic3⋊C4C2×D311yescharacteristic
145C3×C4×Dic3—31no—
146#3724—31no—
147Dic3⋊Dic3—31no—
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150#3722—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×D9—31no—
163C2×C4×D9—61no—
164C2×Dic18—31no—
165C2×Dic18—31no—
166C2×Dic18—31no—
167C2×Dic18—31no—
168C2×Dic18—64no—
169C2×Dic18—61no—
170C2×Dic18C2×D311yescharacteristic
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)⋊C4—31no—
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—61no—
183(C2×D9)⋊C4—61no—
184C4⋊Dic9—31no—
185C4⋊Dic9C2×D311yescharacteristic
186Dic9⋊C4—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—31no—
191Dic9⋊C4—61no—
192Dic9⋊C4—61no—
193Dic9⋊C4C2×D311yescharacteristic
194Dic9⋊C4C2×D311yescharacteristic
195C4×Dic9—31no—
196C4×Dic9—31no—
197C4×Dic9C2×D311yescharacteristic
198C22×C3×C9C2411yescharacteristic
199C2×C3⋊D9—21no—
200C2×C3⋊D9—21no—
201C2×C3⋊D9C2×Q812yescomplemented
202C2×D3×C9—21no—
203C2×D3×C9—21no—
204C2×D3×C9C2×Q812yescomplemented
205C3×C4×C9—21no—
206C3×C4×C9—21no—
207C3×C4×C9—21no—
208C3⋊Dic9—21no—
209C3⋊Dic9—21no—
210C3⋊Dic9C2×D412yes—
211C9×Dic3—21no—
212C9×Dic3—21no—
213C9×Dic3C2×D412yes—
214C3×Dic9—21no—
215C3×Dic9—21no—
216C3×Dic9C2×D412yes—
217C3×Dic9C2×Q812yescomplemented
218C2×D3×Q8—91no—
219C2×D3×Q8—91no—
220C2×D3×Q8—91no—
221C22×Dic6—91no—
222C3×C4⋊Q8—91no—
223C3×C22⋊Q8—31no—
224#946—91no—
225#946—91no—
226#944—91no—
227C4×#67—91no—
228#897—91no—
229#896—91no—
230#896—91no—
231#896—91no—
232#896—91no—
233#896—91no—
234#896—181no—
235#896D911yescharacteristic, complemented
236#893—91no—
237#893—91no—
238#888—31no—
239#888—91no—
240#888—91no—
241#888—91no—
242#887—91no—
243#67⋊C4—91no—
244#67⋊C4—91no—
245#878—91no—
246#878—91no—
247C4×D12—91no—
248C4×Dic6—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—
257C4×C3⋊D3—62no—
258#634—62no—
259C2×C3×Dic3—31no—
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×Dic6—22no—
268C3×Dic6—62no—
269C3×Dic6—62no—
270#627—34no—
271#627—62no—
272#627—62no—
273#626—34no—
274#624—62no—
275#624—62no—
276D3×Dic3—62no—
277D3×Dic3—62no—
278C23×C9—31no—
279C22×D9—31no—
280C22×D9—61no—
281Q8×C9—62no—
282C2×C4×C9—21no—
283C2×C4×C9—21no—
284C2×C4×C9—21no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—31no—
288C2×C4×C9—62no—
289C2×C4×C9C22×D311yescharacteristic
290C2×C4×C9C22×D311yescharacteristic
291C2×C4×C9C22×D311yescharacteristic
292#611—34no—
293C2×Dic9—31no—
294C2×Dic9—31no—
295C2×Dic9—31no—
296C2×Dic9—61no—
297C2×Dic9—61no—
298C2×Dic9—61no—
299C2×Dic9—62no—
300C2×Dic9—62no—
301C2×Dic9C22×D311yescharacteristic
302C2×Dic9C22×D311yescharacteristic
303C2×Dic9C22×D311yescharacteristic
304C2×Dic9C22×D311yescharacteristic
305C4×D9—62no—
306C4×D9—62no—
307C4×D9—62no—
308C4×D9—122no—
309Dic18—22no—
310Dic18—22no—
311Dic18—34no—
312Dic18—62no—
313Dic18—62no—
314Dic18—62no—
315Dic18—122no—
316D4×Q8—271noSylow
317C2×C3×C9C22×D411yescharacteristic
318C2×C3×C9C22×Q811yescharacteristic
319C2×C3×C92−1+411yescharacteristic
320C3⋊D9—22no—
321D3×C9—22no—
322C2×C3×Q8—31no—
323C2×C3×Q8—91no—
324C2×C3×Q8—91no—
325C22×C3×C4—31no—
326C2×#67—91no—
327C22×Dic3—91no—
328C22×Dic3—91no—
329D3×Q8—184no—
330D3×Q8—184no—
331D3×Q8—184no—
332C2×D12—91no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—181no—
342C2×C4×D3C2×D911yescharacteristic
343C2×Dic6—31no—
344C2×Dic6—31no—
345C2×Dic6—91no—
346C2×Dic6—91no—
347C2×Dic6—91no—
348C2×Dic6—91no—
349C2×Dic6—91no—
350C2×Dic6—91no—
351C2×Dic6—91no—
352C2×Dic6—91no—
353C2×Dic6—181no—
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⋊C4—91no—
362C3×C4⋊C4C2×D911yescharacteristic
363C3×C4⋊C4D3211yescharacteristic
364C3×C22⋊C4—31no—
365C3×C22⋊C4—31no—
366C3×C42—91no—
367#217—91no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—181no—
376(C2×D3)⋊C4—181no—
377(C2×D3)⋊C4C2×D911yescharacteristic
378(C2×D3)⋊C4C2×D911yescharacteristic
379C4⋊Dic3—31no—
380C4⋊Dic3—91no—
381C4⋊Dic3—91no—
382C4⋊Dic3—91no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—181no—
395Dic3⋊C4—181no—
396Dic3⋊C4C2×D911yescharacteristic
397Dic3⋊C4C2×D911yescharacteristic
398C4×Dic3—31no—
399C4×Dic3—91no—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C4×Dic3—91no—
403C22×C32C23×D311yescharacteristic
404C2×C3⋊D3—32no—
405C2×C3⋊D3—61no—
406C2×C3⋊D3—61no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3D3×Q812yes—
410C32×C4—21no—
411C32×C4—21no—
412C32×C4—21no—
413C3⋊Dic3—32no—
414C3⋊Dic3—61no—
415C3⋊Dic3—61no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—32no—
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—32no—
429C2×D9—62no—
430C2×D9—61no—
431C2×D9—61no—
432C2×D9—121no—
433C2×D9—121no—
434C4×C9—21no—
435C4×C9—21no—
436C4×C9—21no—
437C4×C9—32no—
438C4×C9—41no—
439C4×C9—41no—
440C4×C9—41no—
441C4×C9—61no—
442C4×C9—61no—
443Dic9—21no—
444Dic9—21no—
445Dic9—32no—
446Dic9—62no—
447Dic9—61no—
448Dic9—61no—
449Dic9—121no—
450Dic9—121no—
451Dic9D3×D412yes—
452Dic9D3×Q812yescomplemented
453C22×Q8—271no—
454C22×Q8—271no—
455C4⋊Q8—91no—
456C4⋊Q8—271no—
457C4⋊Q8—271no—
458C22⋊Q8—31no—
459C22⋊Q8—271no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462C22⋊Q8—271no—
463C22⋊Q8—271no—
464C4×Q8—271no—
465C4×D4—271no—
466C4×D4—271no—
467C4×D4—271no—
468C3×C9D4×Q811yescharacteristic, complemented, Sylow
469C23×C3—31no—
470C22×D3—91no—
471C22×D3—91no—
472C22×D3—181no—
473C22×D3C22×D911yescharacteristic
474C3×Q8—62no—
475C3×Q8—182no—
476C3×Q8—182no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—31no—
483C2×C3×C4—62no—
484C2×C3×C4—91no—
485C2×C3×C4—91no—
486C2×C3×C4—91no—
487C2×C3×C4—91no—
488C2×C3×C4C22×D911yescharacteristic
489C2×C3×C4C22×D911yescharacteristic
490C2×C3×C4C22×D911yescharacteristic
491C2×C3×C4C2×D3211yescharacteristic
492C2×C3×C4C2×D3211yescharacteristic
493C2×C3×C4C2×D3211yescharacteristic
494#67—94no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—91no—
500C2×Dic3—91no—
501C2×Dic3—91no—
502C2×Dic3—91no—
503C2×Dic3—91no—
504C2×Dic3—91no—
505C2×Dic3—181no—
506C2×Dic3—181no—
507C2×Dic3—181no—
508C2×Dic3—182no—
509C2×Dic3—182no—
510C2×Dic3C22×D911yescharacteristic
511C2×Dic3C22×D911yescharacteristic
512C2×Dic3C22×D911yescharacteristic
513D12—94no—
514C4×D3—22no—
515C4×D3—182no—
516C4×D3—182no—
517C4×D3—182no—
518C4×D3—182no—
519C4×D3—182no—
520C4×D3—182no—
521C4×D3—182no—
522C4×D3—182no—
523C4×D3—362no—
524Dic6—22no—
525Dic6—62no—
526Dic6—62no—
527Dic6—94no—
528Dic6—94no—
529Dic6—182no—
530Dic6—182no—
531Dic6—182no—
532Dic6—182no—
533Dic6—182no—
534Dic6—182no—
535Dic6—362no—
536C2×C32C2×D3×D411yescharacteristic
537C2×C32C2×D3×Q811yescharacteristic
538C2×C32#101011yescharacteristic
539C3⋊D3—62no—
540C3×D3—22no—
541C2×C9—21no—
542C2×C9—21no—
543C2×C9—21no—
544C2×C9—62no—
545C2×C9C2×D3×D411yescharacteristic
546C2×C9C2×D3×Q811yescharacteristic
547C2×C9#100711yescharacteristic
548D9—62no—
549D9—122no—
550C2×Q8—31no—
551C2×Q8—91no—
552C2×Q8—91no—
553C2×Q8—271no—
554C2×Q8—271no—
555C2×Q8—271no—
556C2×Q8—271no—
557C2×Q8—544no—
558C2×Q8—544no—
559C2×D4—271no—
560C22×C4—31no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4—271no—
565C22×C4—271no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—91no—
569C4⋊C4—91no—
570C4⋊C4—91no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C4⋊C4—271no—
575C4⋊C4—271no—
576C4⋊C4—271no—
577C4⋊C4D3×D911yescharacteristic
578C22⋊C4—31no—
579C22⋊C4—31no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C42—91no—
585C42—271no—
586C42—271no—
587C22×C3—21no—
588C22×C3—32no—
589C22×C3—61no—
590C22×C3—61no—
591C22×C3C23×D911yescharacteristic
592C22×C3C22×D3211yescharacteristic
593C2×D3—21no—
594C2×D3—21no—
595C2×D3—92no—
596C2×D3—92no—
597C2×D3—182no—
598C2×D3—181no—
599C2×D3—181no—
600C2×D3—181no—
601C2×D3—181no—
602C2×D3—361no—
603C2×D3—361no—
604C2×D3Q8×D912yescomplemented
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—32no—
612C3×C4—41no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4—61no—
616C3×C4—61no—
617C3×C4—92no—
618C3×C4—92no—
619C3×C4—181no—
620C3×C4—181no—
621Dic3—21no—
622Dic3—21no—
623Dic3—32no—
624Dic3—32no—
625Dic3—61no—
626Dic3—61no—
627Dic3—92no—
628Dic3—92no—
629Dic3—182no—
630Dic3—181no—
631Dic3—181no—
632Dic3—181no—
633Dic3—181no—
634Dic3—361no—
635Dic3—361no—
636Dic3D4×D912yes—
637C32#563211yescharacteristic
638C9—21no—
639C9#572711yescharacteristic, complemented
640C23—31no—
641C23—271no—
642Q8—62no—
643Q8—182no—
644Q8—182no—
645Q8—274no—
646Q8—542no—
647Q8—542no—
648Q8—542no—
649D4—274no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—62no—
654C2×C4—91no—
655C2×C4—91no—
656C2×C4—91no—
657C2×C4—91no—
658C2×C4—271no—
659C2×C4—271no—
660C2×C4—271no—
661C2×C4—542no—
662C2×C4—542no—
663C2×C4—542no—
664C2×C4—542no—
665C2×C4—542no—
666C2×C4C2×D3×D911yescharacteristic
667C2×C4C2×D3×D911yescharacteristic
668C2×C4C2×D3×D911yescharacteristic
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—62no—
673C2×C3C2×D4×D911yescharacteristic
674C2×C3C2×Q8×D911yescharacteristic
675C2×C3#6371611yescharacteristic
676C2×C3#6429711yescharacteristic
677C2×C3D32×D411yescharacteristic
678C2×C3D32×Q811yescharacteristic
679D3—22no—
680D3—182no—
681D3—182no—
682D3—362no—
683C22—32no—
684C22—61no—
685C22—61no—
686C22—272no—
687C22—541no—
688C22—541no—
689C22C22×D3×D911yescharacteristic
690C4—21no—
691C4—21no—
692C4—21no—
693C4—32no—
694C4—61no—
695C4—61no—
696C4—92no—
697C4—92no—
698C4—181no—
699C4—181no—
700C4—272no—
701C4—541no—
702C4—541no—
703C3—21no—
704C3#1058973411yescharacteristic, complemented
705C3#1059437811yescharacteristic
706C2—62no—
707C2—542no—
708C2#1172246411yescharacteristic
709C2D3×D4×D911yescharacteristic
710C2D3×Q8×D911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radicalC2×#6195C22
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×(C3⋊D9)⋊Q8C2semidirect
3. #11721752C2semidirect
4. C9×#896C2semidirect
5. C3×#63450C2semidirect
7. #11721026C2semidirect
8. #11721018C2semidirect
11. #11720995C2semidirect
12. #11720985C2semidirect
13. #11720905C2semidirect
14. #11720903C2semidirect
15. #11720901C2semidirect
80. #63450D3semidirect
107. #6195Q8semidirect
114. #6189D4semidirect
201. C2×C3⋊D9C2×Q8semidirect
204. C2×D3×C9C2×Q8semidirect
217. C3×Dic9C2×Q8semidirect
235. #896D9semidirect
452. Dic9D3×Q8semidirect
468. C3×C9D4×Q8semidirect
604. C2×D3Q8×D9semidirect
639. C9#5727semidirect
704. 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×(C3⋊D9)⋊Q82
#117217522
C9×#8962
C3×#634502
#117210302
#117210262
#117210182
#117210142
#117210132
#117209952
#117209852
#117209052
#117209032
#117209012
#105943783
#105897343