Finite Group Databasebeta

← #13147930

Subgroups — #13147930

Order 1728.

934 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6189C211yesmaximal, characteristic, complemented
2C2×(C3⋊D9)⋊Q8C211yesmaximal, characteristic, complemented
3#11721727C211yesmaximal, characteristic
4C9×#878C211yesmaximal, characteristic, complemented
5C3×#63440C211yesmaximal, characteristic, complemented
6#11721267C211yesmaximal, characteristic, complemented
7#11721241C211yesmaximal, characteristic
8#11721240C211yesmaximal, characteristic
9#11720995C211yesmaximal, characteristic, complemented
10#11720994C211yesmaximal, characteristic, complemented
11#11720971C211yesmaximal, characteristic, complemented
12#11720923C211yesmaximal, characteristic, complemented
13#11720904C211yesmaximal, characteristic, complemented
14#11720903C211yesmaximal, characteristic, complemented
15#11720902C211yesmaximal, characteristic, complemented
16#10594072—31nomaximal
17#10589734—31nomaximal
18C2×#6233C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C22×C9×Dic3C2211yescharacteristic
22C22×C3×Dic9C2211yescharacteristic
23C2×C9×Dic6C2211yescharacteristic
24C2×C3×Dic18C2211yescharacteristic
25C2×(C3⋊D9)⋊C4C2211yescharacteristic
26C2×(C3⋊D9)⋊C4C2211yescharacteristic
27C2×#6189—24no—
28C2×#6189C2211yescharacteristic
29C2×#6189C2211yescharacteristic
30C2×#6189C2211yescharacteristic
31C2×#6189C2211yescharacteristic
32C2×#6189C2211yescharacteristic
33(C3⋊D9)⋊Q8—24no—
34C3×C9×C22⋊C4C2211yescharacteristic
35#88536C2211yescharacteristic
36#88534C2211yescharacteristic
37C4×C3⋊Dic9C2211yescharacteristic
38C9×#217C2211yescharacteristic
39C3×#3676C2211yescharacteristic
40C9×C4⋊Dic3C2211yescharacteristic
41C9×Dic3⋊C4C2211yescharacteristic
42C9×Dic3⋊C4C2211yescharacteristic
43C3×C4⋊Dic9C2211yescharacteristic
44C3×Dic9⋊C4C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic
49#88442C2211yescharacteristic
50#88442C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C22×#627—31no—
56C2×#3797—31no—
57#64090—31no—
58C3×#878—31no—
59C3×#878D311yescharacteristic
60#63982—31no—
61#63952—31no—
62#63952—31no—
63#63919—31no—
64#63895—31no—
65#63895—31no—
66#63865—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#63458—31no—
78#63450—31no—
79#63450—31no—
80#63449—31no—
81#611⋊C4—31no—
82#611⋊C4—31no—
83#611⋊C4—61no—
84#63440—31no—
85#63440D311yescharacteristic, complemented
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90#6233Q814yescomplemented
91C2×C3⋊Dic9—22no—
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C4×C3⋊D9—22no—
96C2×C9×Dic3—22no—
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9—22no—
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C9×Dic6—22no—
107C3×Dic18—22no—
108(C3⋊D9)⋊C4—22no—
109(C3⋊D9)⋊C4—22no—
110#6189—22no—
111#6189—22no—
112#6189—22no—
113#6189—22no—
114#6189D414yescomplemented
115#5632—91no—
116#5632—91no—
117C2×#638—31no—
118C22×C3⋊Dic3—31no—
119C2×C4×C3⋊D3—31no—
120C22×C3×Dic3—31no—
121C22×C3×Dic3C2×D311yescharacteristic
122C2×C3×Dic6—31no—
123C2×C3×Dic6C2×D311yescharacteristic
124C2×#627—31no—
125C2×#627—31no—
126C2×#627—31no—
127C2×#627—31no—
128C2×#627—31no—
129C2×#627—64no—
130C2×#624—31no—
131C2×#624—31no—
132#3797—64no—
133C32×C22⋊C4C2×D311yescharacteristic
134#3752—31no—
135#3750—31no—
136C4×C3⋊Dic3—31no—
137C3×#217—31no—
138C3×#217C2×D311yescharacteristic
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4—31no—
143C3×Dic3⋊C4C2×D311yescharacteristic
144C3×Dic3⋊C4C2×D311yescharacteristic
145#3724—31no—
146#3724—31no—
147#3724—31no—
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150#3722—31no—
151#3722—31no—
152Dic32—31no—
153Dic32—31no—
154C2×Q8×C9—31no—
155C22×C4×C9—31no—
156C2×#611—31no—
157C2×#611—61no—
158C22×Dic9—31no—
159C22×Dic9—61no—
160C22×Dic9C2×D311yescharacteristic
161Q8×D9—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×Dic18—31no—
170C2×Dic18—31no—
171C2×Dic18—64no—
172C2×Dic18C2×D311yescharacteristic
173C9×C4⋊C4—31no—
174C9×C4⋊C4—31no—
175C9×C4⋊C4—31no—
176C9×C22⋊C4—21no—
177C9×C22⋊C4—31no—
178C9×C22⋊C4C2×D311yescharacteristic
179#3676C2×D311yescharacteristic
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—31no—
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⋊C4C2×D311yescharacteristic
193Dic9⋊C4C2×D311yescharacteristic
194C4×Dic9—31no—
195C4×Dic9—31no—
196C4×Dic9—31no—
197C4×Dic9—61no—
198C22×C3×C9—21no—
199C22×C3×C9—21no—
200C22×C3×C9C2×Q812yescomplemented
201C22×C3×C9C2411yescharacteristic
202C2×C3⋊D9—21no—
203C2×C3⋊D9—21no—
204C2×C3⋊D9C2×Q812yescomplemented
205C3×C4×C9—21no—
206C3×C4×C9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9C2×D412yes—
209C3⋊Dic9C2×Q812yescomplemented
210C9×Dic3—21no—
211C9×Dic3—21no—
212C9×Dic3—21no—
213C9×Dic3C2×D412yes—
214C3×Dic9—21no—
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—91no—
231#896—91no—
232#896—91no—
233#896—91no—
234#888—91no—
235#888—91no—
236#888—91no—
237#888—91no—
238#887—91no—
239#887—91no—
240#67⋊C4—91no—
241#67⋊C4—91no—
242#67⋊C4—91no—
243#67⋊C4—91no—
244#67⋊C4—181no—
245#878—31no—
246#878—91no—
247#878—91no—
248#878D911yescharacteristic, complemented
249C23×C32C22×D311yescharacteristic
250C22×C3⋊D3—31no—
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253#638—34no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—62no—
258C4×C3⋊D3—62no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—62no—
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C2×C3×Dic3C22×D311yescharacteristic
268C2×C3×Dic3C22×D311yescharacteristic
269C3×Dic6—22no—
270C3×Dic6—62no—
271#627—34no—
272#627—62no—
273#627—62no—
274#627—62no—
275#627—62no—
276#624—62no—
277#624—62no—
278C23×C9—21no—
279C23×C9C22×D311yescharacteristic
280C22×D9—31no—
281C22×D9—61no—
282Q8×C9—62no—
283C2×C4×C9—21no—
284C2×C4×C9—21no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—31no—
288C2×C4×C9—31no—
289C2×C4×C9—62no—
290C2×C4×C9C22×D311yescharacteristic
291C2×C4×C9C22×D311yescharacteristic
292#611—34no—
293#611—64no—
294C2×Dic9—22no—
295C2×Dic9—31no—
296C2×Dic9—31no—
297C2×Dic9—31no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—61no—
301C2×Dic9—62no—
302C2×Dic9—122no—
303C2×Dic9C22×D311yescharacteristic
304C2×Dic9C22×D311yescharacteristic
305C2×Dic9C22×D311yescharacteristic
306C2×Dic9C22×D311yescharacteristic
307C4×D9—62no—
308C4×D9—62no—
309C4×D9—62no—
310C4×D9—122no—
311Dic18—22no—
312Dic18—34no—
313Dic18—62no—
314Dic18—62no—
315Dic18—62no—
316Dic18—62no—
317D4×Q8—271noSylow
318C2×C3×C9—22no—
319C2×C3×C9C22×D411yescharacteristic
320C2×C3×C9C22×Q811yescharacteristic
321C2×C3×C92−1+411yescharacteristic
322C3⋊D9—22no—
323C2×C3×Q8—31no—
324C2×C3×Q8—91no—
325C22×C3×C4—31no—
326C22×C3×C4—91no—
327C2×#67—91no—
328C2×#67—91no—
329C2×#67—181no—
330C22×Dic3—31no—
331C22×Dic3—91no—
332C22×Dic3—91no—
333C22×Dic3—181no—
334C22×Dic3C2×D911yescharacteristic
335D3×Q8—184no—
336D3×Q8—184no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×C4×D3—181no—
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—91no—
354C2×Dic6—91no—
355C2×Dic6—184no—
356C2×Dic6—184no—
357C2×Dic6C2×D911yescharacteristic
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—91no—
362C3×C4⋊C4—91no—
363C3×C4⋊C4—91no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—91no—
367C3×C22⋊C4C2×D911yescharacteristic
368C3×C22⋊C4D3211yescharacteristic
369#217—31no—
370#217C2×D911yescharacteristic
371(C2×D3)⋊C4—91no—
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—181no—
378C4⋊Dic3—31no—
379C4⋊Dic3—91no—
380C4⋊Dic3—91no—
381C4⋊Dic3C2×D911yescharacteristic
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
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—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—181no—
395Dic3⋊C4C2×D911yescharacteristic
396Dic3⋊C4C2×D911yescharacteristic
397C4×Dic3—91no—
398C4×Dic3—91no—
399C4×Dic3—91no—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C4×Dic3—91no—
403C4×Dic3—181no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32D3×Q812yes—
407C22×C32C23×D311yescharacteristic
408C2×C3⋊D3—32no—
409C2×C3⋊D3—61no—
410C2×C3⋊D3—61no—
411C32×C4—21no—
412C32×C4—21no—
413C3⋊Dic3—32no—
414C3⋊Dic3—32no—
415C3⋊Dic3—61no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—32no—
420C3×Dic3—61no—
421C3×Dic3—61no—
422C3×Dic3—61no—
423C3×Dic3D3×D412yes—
424C22×C9—21no—
425C22×C9—21no—
426C22×C9—21no—
427C22×C9—22no—
428C22×C9—41no—
429C22×C9—41no—
430C22×C9D3×Q812yescomplemented
431C22×C9C23×D311yescharacteristic
432C2×D9—32no—
433C2×D9—62no—
434C2×D9—61no—
435C2×D9—61no—
436C2×D9—121no—
437C2×D9—121no—
438C4×C9—21no—
439C4×C9—21no—
440C4×C9—32no—
441C4×C9—41no—
442C4×C9—41no—
443C4×C9—61no—
444C4×C9—61no—
445C4×C9—61no—
446Dic9—21no—
447Dic9—21no—
448Dic9—21no—
449Dic9—32no—
450Dic9—32no—
451Dic9—62no—
452Dic9—62no—
453Dic9—61no—
454Dic9—121no—
455Dic9D3×D412yes—
456C22×Q8—271no—
457C22×Q8—271no—
458C4⋊Q8—271no—
459C4⋊Q8—271no—
460C4⋊Q8—271no—
461C22⋊Q8—31no—
462C22⋊Q8—91no—
463C22⋊Q8—271no—
464C22⋊Q8—271no—
465C22⋊Q8—271no—
466C22⋊Q8—271no—
467C4×Q8—271no—
468C4×D4—271no—
469C4×D4—271no—
470C4×D4—271no—
471C3×C9D4×Q811yescharacteristic, complemented, Sylow
472C23×C3—21no—
473C23×C3C22×D911yescharacteristic
474C23×C3C2×D3211yescharacteristic
475C22×D3—91no—
476C22×D3—91no—
477C22×D3—181no—
478C3×Q8—62no—
479C3×Q8—182no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—62no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4—91no—
491C2×C3×C4—182no—
492C2×C3×C4C22×D911yescharacteristic
493C2×C3×C4C22×D911yescharacteristic
494C2×C3×C4C2×D3211yescharacteristic
495C2×C3×C4C2×D3211yescharacteristic
496#67—94no—
497#67—94no—
498#67—184no—
499C2×Dic3—22no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—31no—
504C2×Dic3—62no—
505C2×Dic3—91no—
506C2×Dic3—91no—
507C2×Dic3—91no—
508C2×Dic3—91no—
509C2×Dic3—91no—
510C2×Dic3—91no—
511C2×Dic3—181no—
512C2×Dic3—181no—
513C2×Dic3—181no—
514C2×Dic3—182no—
515C2×Dic3—182no—
516C2×Dic3—362no—
517C2×Dic3C22×D911yescharacteristic
518C2×Dic3C22×D911yescharacteristic
519C2×Dic3C22×D911yescharacteristic
520C2×Dic3C22×D911yescharacteristic
521C4×D3—182no—
522C4×D3—182no—
523C4×D3—182no—
524C4×D3—182no—
525C4×D3—182no—
526C4×D3—182no—
527C4×D3—362no—
528Dic6—22no—
529Dic6—62no—
530Dic6—94no—
531Dic6—94no—
532Dic6—182no—
533Dic6—182no—
534Dic6—182no—
535Dic6—182no—
536Dic6—182no—
537Dic6—182no—
538Dic6—182no—
539Dic6—182no—
540C2×C32—22no—
541C2×C32C2×D3×D411yescharacteristic
542C2×C32C2×D3×Q811yescharacteristic
543C2×C32#101011yescharacteristic
544C3⋊D3—62no—
545C2×C9—22no—
546C2×C9—21no—
547C2×C9—21no—
548C2×C9—21no—
549C2×C9—42no—
550C2×C9C2×D3×D411yescharacteristic
551C2×C9C2×D3×Q811yescharacteristic
552C2×C9#101011yescharacteristic
553D9—62no—
554D9—122no—
555C2×Q8—31no—
556C2×Q8—91no—
557C2×Q8—271no—
558C2×Q8—271no—
559C2×Q8—271no—
560C2×Q8—271no—
561C2×Q8—271no—
562C2×Q8—544no—
563C2×Q8—544no—
564C2×D4—271no—
565C22×C4—31no—
566C22×C4—91no—
567C22×C4—271no—
568C22×C4—271no—
569C22×C4—271no—
570C22×C4—271no—
571C4⋊C4—31no—
572C4⋊C4—31no—
573C4⋊C4—31no—
574C4⋊C4—91no—
575C4⋊C4—91no—
576C4⋊C4—91no—
577C4⋊C4—271no—
578C4⋊C4—271no—
579C4⋊C4—271no—
580C4⋊C4—271no—
581C4⋊C4—271no—
582C4⋊C4—271no—
583C22⋊C4—31no—
584C22⋊C4—91no—
585C22⋊C4—271no—
586C22⋊C4—271no—
587C22⋊C4—271no—
588C22⋊C4D3×D911yescharacteristic
589C42—271no—
590C42—271no—
591C42—271no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—22no—
597C22×C3—21no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3Q8×D912yescomplemented
601C22×C3C23×D911yescharacteristic
602C22×C3#379712yes—
603C22×C3C22×D3211yescharacteristic
604C2×D3—92no—
605C2×D3—92no—
606C2×D3—182no—
607C2×D3—181no—
608C2×D3—181no—
609C2×D3—181no—
610C2×D3—181no—
611C2×D3—361no—
612C2×D3—361no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—32no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—61no—
621C3×C4—61no—
622C3×C4—61no—
623C3×C4—92no—
624C3×C4—181no—
625C3×C4—181no—
626C3×C4—181no—
627Dic3—21no—
628Dic3—21no—
629Dic3—21no—
630Dic3—32no—
631Dic3—61no—
632Dic3—61no—
633Dic3—61no—
634Dic3—92no—
635Dic3—92no—
636Dic3—92no—
637Dic3—92no—
638Dic3—182no—
639Dic3—182no—
640Dic3—181no—
641Dic3—181no—
642Dic3—361no—
643Dic3D4×D912yes—
644C32#563211yescharacteristic
645C9—21no—
646C9#563211yescharacteristic, complemented
647C23—271no—
648C23C2×D3×D911yescharacteristic
649Q8—62no—
650Q8—182no—
651Q8—274no—
652Q8—542no—
653Q8—542no—
654Q8—542no—
655Q8—542no—
656D4—274no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—62no—
662C2×C4—91no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—182no—
667C2×C4—271no—
668C2×C4—271no—
669C2×C4—271no—
670C2×C4—542no—
671C2×C4—542no—
672C2×C4—542no—
673C2×C4—542no—
674C2×C4C2×D3×D911yescharacteristic
675C2×C4C2×D3×D911yescharacteristic
676C2×C3—22no—
677C2×C3—22no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—42no—
682C2×C3C2×D4×D911yescharacteristic
683C2×C3C2×Q8×D911yescharacteristic
684C2×C3#6371611yescharacteristic
685C2×C3C2×#379711yescharacteristic
686C2×C3#6430911yescharacteristic
687C2×C3D32×D411yescharacteristic
688D3—182no—
689D3—182no—
690D3—362no—
691C22—21no—
692C22—21no—
693C22—272no—
694C22—541no—
695C22—541no—
696C22(C3⋊D9)⋊Q812yescomplemented
697C22C22×D3×D911yescharacteristic
698C4—21no—
699C4—21no—
700C4—32no—
701C4—61no—
702C4—61no—
703C4—61no—
704C4—92no—
705C4—181no—
706C4—181no—
707C4—181no—
708C4—272no—
709C4—272no—
710C4—541no—
711C3—21no—
712C3#1058973411yescharacteristic, complemented
713C3#1059407211yescharacteristic
714C2—22no—
715C2—542no—
716C2C2×(C3⋊D9)⋊Q811yescharacteristic
717C2#1172249411yescharacteristic
718C2D3×D4×D911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC2×#6233C22
hypercenterC22⋊C4D3×D9
hypocenterC3×C9D4×Q8
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6189C2semidirect
2. C2×(C3⋊D9)⋊Q8C2semidirect
4. C9×#878C2semidirect
5. C3×#63440C2semidirect
6. #11721267C2semidirect
9. #11720995C2semidirect
10. #11720994C2semidirect
11. #11720971C2semidirect
12. #11720923C2semidirect
13. #11720904C2semidirect
14. #11720903C2semidirect
15. #11720902C2semidirect
85. #63440D3semidirect
90. #6233Q8semidirect
114. #6189D4semidirect
200. C22×C3×C9C2×Q8semidirect
204. C2×C3⋊D9C2×Q8semidirect
209. C3⋊Dic9C2×Q8semidirect
248. #878D9semidirect
430. C22×C9D3×Q8semidirect
471. C3×C9D4×Q8semidirect
600. C22×C3Q8×D9semidirect
646. C9#5632semidirect
696. C22(C3⋊D9)⋊Q8semidirect
712. C3#10589734semidirect

Maximal subgroups

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

subgroupindex
C22×#61892
C2×(C3⋊D9)⋊Q82
#117217272
C9×#8782
C3×#634402
#117212672
#117212412
#117212402
#117209952
#117209942
#117209712
#117209232
#117209042
#117209032
#117209022
#105940723
#105897343