Finite Group Databasebeta

← #13148012

Subgroups — #13148012

Order 1728.

888 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88662C211yesmaximal, characteristic
2C2×(C3⋊D9)⋊Q8C211yesmaximal, characteristic, complemented
3#11721729C211yesmaximal, characteristic, complemented
4C9×#885C211yesmaximal, characteristic, complemented
5C3×#63440C211yesmaximal, characteristic, complemented
6#11721275C211yesmaximal, characteristic, complemented
7#11721263C211yesmaximal, characteristic, complemented
8#11721253C211yesmaximal, characteristic, complemented
9#11721023C211yesmaximal, characteristic, complemented
10#11721018C211yesmaximal, characteristic, complemented
11#11720970C211yesmaximal, characteristic, complemented
12#11720958C211yesmaximal, characteristic, complemented
13#11720957C211yesmaximal, characteristic, complemented
14#11720903C211yesmaximal, characteristic, complemented
15#11720898C211yesmaximal, characteristic, complemented
16#10594070—31nomaximal
17#10589777—31nomaximal
18C2×#6233C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C9×#67C2211yescharacteristic
21C22×C3×Dic9C2211yescharacteristic
22C2×C9×Dic6C2211yescharacteristic
23C2×C3×Dic18C2211yescharacteristic
24C2×#6195C2211yescharacteristic
25#88662—24no—
26C2×D3×Dic9C2211yescharacteristic
27C2×(C3⋊D9)⋊C4C2211yescharacteristic
28C2×(C3⋊D9)⋊C4C2211yescharacteristic
29C2×#6189C2211yescharacteristic
30C2×#6189C2211yescharacteristic
31C2×#6189C2211yescharacteristic
32(C3⋊D9)⋊Q8—24no—
33C3×C9×C22⋊C4C2211yescharacteristic
34#88551C2211yescharacteristic
35#88536C2211yescharacteristic
36C4⋊(C3⋊Dic9)C2211yescharacteristic
37#88534C2211yescharacteristic
38C9×#217C2211yescharacteristic
39C3×#3676C2211yescharacteristic
40C9×(C2×D3)⋊C4C2211yescharacteristic
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C4×C9×Dic3C2211yescharacteristic
43C3×C4⋊Dic9C2211yescharacteristic
44C3×Dic9⋊C4C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48#88445C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic9⋊Dic3C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×#3804—31no—
56C2×#3797—31no—
57#64092—31no—
58C3×#885D311yescharacteristic
59C3×#878—31no—
60#63975—31no—
61#63964—31no—
62#63959—31no—
63#63918—31no—
64#63893—31no—
65#63887—31no—
66#63854—31no—
67#63853—31no—
68#63839—31no—
69#63836—31no—
70C2×Q8×D9—31no—
71C2×#3699—31no—
72C9×#124—31no—
73#63506—31no—
74#63498—31no—
75#63445—31no—
76#63445—31no—
77#63445—31no—
78#63445—31no—
79#63445—61no—
80#63440—31no—
81#63440—31no—
82#63440—31no—
83#63440D311yescharacteristic, complemented
84#63434—31no—
85#63431—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91#6233—22no—
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C4×C3⋊D9—22no—
96C9×#67—22no—
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C3×Dic9—22no—
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C9×Dic6—22no—
106C3×Dic18—22no—
107#6195—22no—
108D3×Dic9—22no—
109(C3⋊D9)⋊C4—22no—
110(C3⋊D9)⋊C4D414yes—
111#6189—22no—
112#6189—22no—
113#6189—22no—
114#5675—91no—
115#5628—91no—
116C2×#638—31no—
117C2×C4×C3⋊D3—31no—
118C2×C3×#67C2×D311yescharacteristic
119C22×C3×Dic3—31no—
120C2×C3×Dic6—31no—
121C2×C3×Dic6C2×D311yescharacteristic
122C2×#627—31no—
123C2×#627—31no—
124C2×#627—31no—
125C2×#626—31no—
126C2×#624—31no—
127C2×#624—31no—
128#3804—64no—
129C2×D3×Dic3—31no—
130#3797—64no—
131C32×C22⋊C4C2×D311yescharacteristic
132#3757—31no—
133#3752—31no—
134C4⋊(C3⋊Dic3)—31no—
135#3750—31no—
136C3×#217—31no—
137C3×#217C2×D311yescharacteristic
138C3×(C2×D3)⋊C4C2×D311yescharacteristic
139C3×(C2×D3)⋊C4C2×D311yescharacteristic
140C3×C4⋊Dic3—31no—
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4—31no—
143C3×C4×Dic3C2×D311yescharacteristic
144#3724—31no—
145Dic3⋊Dic3—31no—
146Dic3⋊Dic3—31no—
147Dic3⋊Dic3—31no—
148Dic3⋊Dic3—31no—
149#3722—31no—
150(C2×D3)⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152Dic32—31no—
153C2×Q8×C9—31no—
154C2×D4×C9—31no—
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—61no—
158C22×Dic9—31no—
159C22×Dic9C2×D311yescharacteristic
160Q8×D9—64no—
161#3699—64no—
162C2×C4×D9—31no—
163C2×C4×D9—31no—
164C2×C4×D9—31no—
165C2×C4×D9—61no—
166C2×Dic18—31no—
167C2×Dic18—31no—
168C2×Dic18—31no—
169C2×Dic18C2×D311yescharacteristic
170C9×C22⋊C4—21no—
171C9×C22⋊C4—31no—
172C9×C22⋊C4—31no—
173C9×C22⋊C4—31no—
174C9×C22⋊C4C2×D311yescharacteristic
175C42×C9—31no—
176#3676—31no—
177#3676—31no—
178#3676—31no—
179#3676—61no—
180#3676C2×D311yescharacteristic
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4—61no—
184C4⋊Dic9—31no—
185C4⋊Dic9—31no—
186C4⋊Dic9—31no—
187C4⋊Dic9—61no—
188C4⋊Dic9C2×D311yescharacteristic
189Dic9⋊C4—31no—
190Dic9⋊C4—31no—
191Dic9⋊C4—31no—
192Dic9⋊C4—31no—
193Dic9⋊C4—61no—
194Dic9⋊C4C2×D311yescharacteristic
195Dic9⋊C4C2×D311yescharacteristic
196C4×Dic9—31no—
197C22×C3×C9—21no—
198C22×C3×C9—21no—
199C22×C3×C9—21no—
200C22×C3×C9C2411yescharacteristic
201C2×C3⋊D9—21no—
202C2×C3⋊D9—21no—
203C2×C3⋊D9C2×D412yes—
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×D3×C9—21no—
207C3×C4×C9—21no—
208C3×C4×C9—21no—
209C3⋊Dic9—21no—
210C3⋊Dic9—21no—
211C3⋊Dic9—21no—
212C9×Dic3—21no—
213C9×Dic3—21no—
214C9×Dic3C2×D412yes—
215C3×Dic9—21no—
216C3×Dic9—21no—
217C3×Dic9—21no—
218C3×Dic9C2×D412yes—
219C2×D3×Q8—91no—
220C2×D3×Q8—91no—
221C2×#237—91no—
222C2×#235—91no—
223C3×#124—31no—
224C3×C22⋊Q8—91no—
225#946—91no—
226#944—91no—
227#936—91no—
228#924—91no—
229#897—91no—
230#894—91no—
231#894—91no—
232#892—91no—
233#888—91no—
234#888—91no—
235#885—91no—
236#885D911yescharacteristic, complemented
237#883—91no—
238#883—91no—
239#883—91no—
240#883—91no—
241#883—91no—
242#883—91no—
243#883—181no—
244#878—31no—
245#878—91no—
246#878—91no—
247#878—91no—
248#872—91no—
249#869—91no—
250C23×C32C22×D311yescharacteristic
251C22×C3⋊D3—31no—
252C22×C3×D3C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255#638—62no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C4×C3⋊D3—62no—
260C3×#67—22no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—62no—
266C2×C3×Dic3C22×D311yescharacteristic
267C2×C3×Dic3C22×D311yescharacteristic
268C2×C3×Dic3C22×D311yescharacteristic
269C3×Dic6—22no—
270C3×Dic6—62no—
271#627—62no—
272#627—62no—
273#627—62no—
274#626—62no—
275#624—34no—
276#624—62no—
277D3×Dic3—62no—
278C23×C9—21no—
279C23×C9—31no—
280C23×C9C22×D311yescharacteristic
281C22×D9—31no—
282C22×D9—61no—
283Q8×C9—62no—
284D4×C9—62no—
285C2×C4×C9—21no—
286C2×C4×C9—21no—
287C2×C4×C9—31no—
288C2×C4×C9—31no—
289C2×C4×C9—31no—
290C2×C4×C9C22×D311yescharacteristic
291C2×C4×C9C22×D311yescharacteristic
292#611—62no—
293#611—62no—
294#611—122no—
295C2×Dic9—22no—
296C2×Dic9—31no—
297C2×Dic9—31no—
298C2×Dic9—31no—
299C2×Dic9—61no—
300C2×Dic9—61no—
301C2×Dic9—61no—
302C2×Dic9—62no—
303C2×Dic9C22×D311yescharacteristic
304C2×Dic9C22×D311yescharacteristic
305C2×Dic9C22×D311yescharacteristic
306C2×Dic9C22×D311yescharacteristic
307C4×D9—34no—
308C4×D9—62no—
309C4×D9—62no—
310C4×D9—122no—
311Dic18—22no—
312Dic18—62no—
313Dic18—62no—
314Dic18—62no—
315#536—271noSylow
316C2×C3×C9—41no—
317C2×C3×C9C22×D411yescharacteristic
318C2×C3×C92−1+411yescharacteristic
319C2×C3×C92−1+411yescharacteristic
320C3⋊D9—22no—
321D3×C9—41no—
322C2×C3×Q8—31no—
323C2×C3×Q8—91no—
324C2×C3×D4—31no—
325C22×C3×C4—91no—
326C2×#67—91no—
327C2×#67—91no—
328C2×#67—91no—
329C2×#67—181no—
330C2×#67C2×D911yescharacteristic
331C22×Dic3—31no—
332C22×Dic3—91no—
333D3×Q8—184no—
334D3×Q8—184no—
335#237—184no—
336#235—184no—
337C2×D12—91no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×C4×D3—91no—
344C2×C4×D3—91no—
345C2×C4×D3—181no—
346C2×Dic6—31no—
347C2×Dic6—91no—
348C2×Dic6—91no—
349C2×Dic6—91no—
350C2×Dic6—91no—
351C2×Dic6—91no—
352C2×Dic6—91no—
353C2×Dic6C2×D911yescharacteristic
354C3×C4⋊C4—91no—
355C3×C4⋊C4—91no—
356C3×C4⋊C4—91no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4C2×D911yescharacteristic
363C3×C22⋊C4D3211yescharacteristic
364C3×C42—31no—
365#217—31no—
366#217—91no—
367#217—91no—
368#217—91no—
369#217—91no—
370#217—181no—
371#217C2×D911yescharacteristic
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—91no—
377(C2×D3)⋊C4—91no—
378(C2×D3)⋊C4—181no—
379(C2×D3)⋊C4C2×D911yescharacteristic
380(C2×D3)⋊C4C2×D911yescharacteristic
381C4⋊Dic3—31no—
382C4⋊Dic3—91no—
383C4⋊Dic3—91no—
384C4⋊Dic3—91no—
385C4⋊Dic3—91no—
386C4⋊Dic3—91no—
387C4⋊Dic3—91no—
388C4⋊Dic3—181no—
389Dic3⋊C4—31no—
390Dic3⋊C4—31no—
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—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C4×Dic3C2×D911yescharacteristic
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32C23×D311yescharacteristic
407C2×C3⋊D3—32no—
408C2×C3⋊D3—61no—
409C2×C3⋊D3—61no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C32×C4—21no—
414C32×C4—21no—
415C3⋊Dic3—61no—
416C3⋊Dic3—61no—
417C3⋊Dic3—61no—
418C3×Dic3—21no—
419C3×Dic3—21no—
420C3×Dic3—32no—
421C3×Dic3—61no—
422C3×Dic3—61no—
423C3×Dic3—61no—
424C3×Dic3D3×D412yes—
425C22×C9—21no—
426C22×C9—21no—
427C22×C9—21no—
428C22×C9—21no—
429C22×C9—41no—
430C22×C9—41no—
431C22×C9—41no—
432C22×C9—61no—
433C22×C9—61no—
434C22×C9—61no—
435C22×C9C23×D311yescharacteristic
436C2×D9—32no—
437C2×D9—62no—
438C2×D9—61no—
439C2×D9—61no—
440C2×D9—121no—
441C2×D9—121no—
442C4×C9—21no—
443C4×C9—21no—
444C4×C9—32no—
445C4×C9—41no—
446C4×C9—41no—
447C4×C9—61no—
448C4×C9—61no—
449Dic9—21no—
450Dic9—21no—
451Dic9—21no—
452Dic9—61no—
453Dic9—61no—
454Dic9—61no—
455Dic9—121no—
456Dic9—121no—
457Dic9—121no—
458Dic9D3×D412yes—
459C2×#41—271no—
460C22×Q8—271no—
461C4⋊Q8—271no—
462C4⋊Q8—271no—
463#124—31no—
464#124—271no—
465#123—271no—
466#123—271no—
467#123—271no—
468#123—271no—
469C22⋊Q8—91no—
470C22⋊Q8—271no—
471C22⋊Q8—271no—
472C22⋊Q8—271no—
473#117—271no—
474C3×C9#53611yescharacteristic, complemented, Sylow
475C23×C3—21no—
476C23×C3—31no—
477C23×C3C22×D911yescharacteristic
478C23×C3C2×D3211yescharacteristic
479C22×D3—91no—
480C22×D3—91no—
481C22×D3—181no—
482C22×D3C22×D911yescharacteristic
483C3×Q8—62no—
484C3×Q8—182no—
485C3×D4—62no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—91no—
495C2×C3×C4—182no—
496C2×C3×C4C22×D911yescharacteristic
497C2×C3×C4C22×D911yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499C2×C3×C4C2×D3211yescharacteristic
500#67—22no—
501#67—182no—
502#67—182no—
503#67—182no—
504#67—362no—
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—62no—
510C2×Dic3—91no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—91no—
515C2×Dic3—91no—
516C2×Dic3—181no—
517C2×Dic3—181no—
518C2×Dic3—181no—
519C2×Dic3—182no—
520C2×Dic3C22×D911yescharacteristic
521C2×Dic3C22×D911yescharacteristic
522C2×Dic3C22×D911yescharacteristic
523D12—182no—
524C4×D3—94no—
525C4×D3—94no—
526C4×D3—182no—
527C4×D3—182no—
528C4×D3—182no—
529C4×D3—182no—
530C4×D3—182no—
531C4×D3—362no—
532Dic6—22no—
533Dic6—62no—
534Dic6—182no—
535Dic6—182no—
536Dic6—182no—
537Dic6—182no—
538Dic6—182no—
539Dic6—182no—
540C2×C32—41no—
541C2×C32C2×D3×D411yescharacteristic
542C2×C32#101011yescharacteristic
543C2×C32#101011yescharacteristic
544C3⋊D3—62no—
545C3×D3—41no—
546C2×C9—21no—
547C2×C9—21no—
548C2×C9—21no—
549C2×C9—41no—
550C2×C9—81no—
551C2×C9—121no—
552C2×C9C2×D3×D411yescharacteristic
553C2×C9#100711yescharacteristic
554C2×C9#101011yescharacteristic
555D9—62no—
556D9—122no—
557#41—544no—
558C2×Q8—31no—
559C2×Q8—91no—
560C2×Q8—271no—
561C2×Q8—271no—
562C2×Q8—271no—
563C2×Q8—544no—
564C2×D4—31no—
565C2×D4—271no—
566C2×D4—271no—
567C22×C4—91no—
568C22×C4—271no—
569C22×C4—271no—
570C22×C4—271no—
571C22×C4—271no—
572C4⋊C4—91no—
573C4⋊C4—91no—
574C4⋊C4—91no—
575C4⋊C4—271no—
576C4⋊C4—271no—
577C4⋊C4—271no—
578C4⋊C4—271no—
579C4⋊C4—271no—
580C4⋊C4—271no—
581C4⋊C4—271no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—31no—
585C22⋊C4—91no—
586C22⋊C4—271no—
587C22⋊C4—271no—
588C22⋊C4—271no—
589C22⋊C4—271no—
590C22⋊C4—271no—
591C22⋊C4D3×D911yescharacteristic
592C42—31no—
593C42—271no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—61no—
605C22×C3—61no—
606C22×C3—61no—
607C22×C3C23×D911yescharacteristic
608C22×C3C22×D3211yescharacteristic
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—21no—
612C2×D3—92no—
613C2×D3—92no—
614C2×D3—182no—
615C2×D3—181no—
616C2×D3—181no—
617C2×D3—181no—
618C2×D3—181no—
619C2×D3—361no—
620C2×D3—361no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—32no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—61no—
629C3×C4—61no—
630C3×C4—92no—
631C3×C4—181no—
632C3×C4—181no—
633C3×C4—181no—
634Dic3—21no—
635Dic3—21no—
636Dic3—32no—
637Dic3—61no—
638Dic3—61no—
639Dic3—61no—
640Dic3—181no—
641Dic3—181no—
642Dic3—181no—
643Dic3—181no—
644Dic3—181no—
645Dic3—181no—
646Dic3—361no—
647Dic3—361no—
648Dic3—361no—
649Dic3D4×D912yes—
650C32#567511yescharacteristic
651C9—21no—
652C9#562811yescharacteristic, complemented
653C23—31no—
654C23—271no—
655C23C2×D3×D911yescharacteristic
656Q8—62no—
657Q8—182no—
658Q8—542no—
659Q8—542no—
660Q8—542no—
661D4—62no—
662D4—542no—
663D4—542no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—91no—
668C2×C4—91no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—182no—
672C2×C4—274no—
673C2×C4—271no—
674C2×C4—271no—
675C2×C4—271no—
676C2×C4—542no—
677C2×C4—542no—
678C2×C4—542no—
679C2×C4C2×D3×D911yescharacteristic
680C2×C4C2×D3×D911yescharacteristic
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—41no—
685C2×C3—41no—
686C2×C3—81no—
687C2×C3—121no—
688C2×C3C2×D4×D911yescharacteristic
689C2×C3#6371611yescharacteristic
690C2×C3#6371611yescharacteristic
691C2×C3#6429711yescharacteristic
692C2×C3#6430911yescharacteristic
693C2×C3D32×D411yescharacteristic
694D3—41no—
695D3—182no—
696D3—182no—
697D3—362no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—61no—
702C22—61no—
703C22—61no—
704C22—272no—
705C22—541no—
706C22—541no—
707C22C22×D3×D911yescharacteristic
708C4—21no—
709C4—21no—
710C4—32no—
711C4—61no—
712C4—61no—
713C4—92no—
714C4—181no—
715C4—181no—
716C4—181no—
717C4—541no—
718C4—541no—
719C4—541no—
720C3—21no—
721C3#1058977711yescharacteristic, complemented
722C3#1059407011yescharacteristic
723C2—41no—
724C2—121no—
725C2—542no—
726C2#1172246411yescharacteristic
727C2#1172249411yescharacteristic
728C2D3×D4×D911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC2×#88662C2
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#536
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×(C3⋊D9)⋊Q8C2semidirect
3. #11721729C2semidirect
4. C9×#885C2semidirect
5. C3×#63440C2semidirect
6. #11721275C2semidirect
7. #11721263C2semidirect
8. #11721253C2semidirect
9. #11721023C2semidirect
10. #11721018C2semidirect
11. #11720970C2semidirect
12. #11720958C2semidirect
13. #11720957C2semidirect
14. #11720903C2semidirect
15. #11720898C2semidirect
83. #63440D3semidirect
236. #885D9semidirect
474. C3×C9#536semidirect
652. C9#5628semidirect
721. C3#10589777semidirect

Maximal subgroups

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

subgroupindex
C2×#886622
C2×(C3⋊D9)⋊Q82
#117217292
C9×#8852
C3×#634402
#117212752
#117212632
#117212532
#117210232
#117210182
#117209702
#117209582
#117209572
#117209032
#117208982
#105940703
#105897773