Finite Group Databasebeta

← D9×#896 #13148809

Subgroups — D9×#896 #13148809

Order 1728.

1040 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D9C211yesmaximal, characteristic
2C2×D9×Dic6C211yesmaximal, characteristic, complemented
3#11721752C211yesmaximal, characteristic, complemented
4C9×#896C211yesmaximal, characteristic, complemented
5C3×C4⋊C4×D9C211yesmaximal, characteristic, complemented
6D9×(C2×D3)⋊C4C211yesmaximal, characteristic
7D9×(C2×D3)⋊C4C211yesmaximal, characteristic
8#11721026C211yesmaximal, characteristic, complemented
9#11721024C211yesmaximal, characteristic, complemented
10#11720995C211yesmaximal, characteristic, complemented
11#11720986C211yesmaximal, characteristic, complemented
12D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
13D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
14#11720955C211yesmaximal, characteristic, complemented
15#11720923C211yesmaximal, characteristic, complemented
16D3×#896—31nomaximal
17D9×C22⋊Q8—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×#6226C2211yescharacteristic, complemented
21C2×C4×D3×C9C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×C9×Dic6C2211yescharacteristic, complemented
26C2×D3×Dic9C2211yescharacteristic
27C2×(C3⋊D9)⋊C4C2211yescharacteristic
28C2×Dic3×D9C2211yescharacteristic
29C2×Dic3×D9C2211yescharacteristic
30C2×Dic3×D9C2211yescharacteristic
31C2×#6189C2211yescharacteristic, complemented
32C2×#6189C2211yescharacteristic, complemented
33C4×D3×D9—24no—
34D9×Dic6—24no—
35C3×C9×C4⋊C4C2211yescharacteristic, complemented
36#88536C2211yescharacteristic
37#88536C2211yescharacteristic
38#88534C2211yescharacteristic, complemented
39#88534C2211yescharacteristic, complemented
40C9×(C2×D3)⋊C4C2211yescharacteristic
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C9×Dic3⋊C4C2211yescharacteristic, complemented
43C9×Dic3⋊C4C2211yescharacteristic, complemented
44C3×C4⋊Dic9C2211yescharacteristic, complemented
45C3×Dic9⋊C4C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49#88445C2211yescharacteristic
50#88445C2211yescharacteristic
51Dic3⋊Dic9C2211yescharacteristic, complemented
52Dic3⋊Dic9C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54#88442C2211yescharacteristic, complemented
55C2×C4×D32—31no—
56C2×D3×Dic6—31no—
57#64105—31no—
58C3×#896D311yescharacteristic
59C3×D3×C4⋊C4—31no—
60D3×(C2×D3)⋊C4—31no—
61D3×(C2×D3)⋊C4—31no—
62#63899—31no—
63#63896—31no—
64#63895—31no—
65#63888—31no—
66D3×Dic3⋊C4—31no—
67D3×Dic3⋊C4—31no—
68#63865—31no—
69#63851—31no—
70C2×Q8×D9—31no—
71C22×C4×D9—31no—
72C9×C22⋊Q8—31no—
73#63508—31no—
74#63486—31no—
75#63459—31no—
76#63458—31no—
77#63458—31no—
78#63458—61no—
79C4⋊C4×D9—31no—
80C4⋊C4×D9—31no—
81C4⋊C4×D9D311yescharacteristic, complemented
82C22⋊C4×D9—31no—
83C22⋊C4×D9—31no—
84#63440—31no—
85#63440—31no—
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C2×D3×D9—22no—
90C2×D3×D9—22no—
91C2×D3×D9Q814yescomplemented
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C4×C3⋊D9—22no—
99#6226—22no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C4×D3×C9—22no—
107C3×C4×D9—22no—
108C3×C4×D9—22no—
109C3×C4×D9—22no—
110C9×Dic6—22no—
111D3×Dic9—22no—
112(C3⋊D9)⋊C4—22no—
113Dic3×D9—22no—
114Dic3×D9—22no—
115Dic3×D9D414yes—
116#6189—22no—
117#6189—22no—
118D3×C22⋊Q8—91no—
119C2×#896—91no—
120C22×D32—31no—
121C2×C4×C3⋊D3—31no—
122C2×#634—31no—
123C2×C3×C4×D3—31no—
124C2×C3×C4×D3—31no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3C2×D311yescharacteristic
127C2×C3×Dic6C2×D311yescharacteristic
128C2×#627—31no—
129C2×#627—31no—
130C2×#624—31no—
131C2×D3×Dic3—31no—
132C2×D3×Dic3—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C4×D32—64no—
136D3×Dic6—64no—
137C23×D9—31no—
138C32×C4⋊C4C2×D311yescharacteristic
139#3752—31no—
140#3752—31no—
141#3750—31no—
142#3750—31no—
143C3×(C2×D3)⋊C4C2×D311yescharacteristic
144C3×(C2×D3)⋊C4C2×D311yescharacteristic
145C3×C4⋊Dic3—31no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4—31no—
148C3×Dic3⋊C4C2×D311yescharacteristic
149C3×Dic3⋊C4C2×D311yescharacteristic
150#3724—31no—
151#3724—31no—
152Dic3⋊Dic3—31no—
153Dic3⋊Dic3—31no—
154#3722—31no—
155#3722—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158C2×Q8×C9—31no—
159C22×C4×C9—31no—
160C22×Dic9—31no—
161Q8×D9—64no—
162C2×C4×D9—31no—
163C2×C4×D9—31no—
164C2×C4×D9—31no—
165C2×C4×D9—31no—
166C2×C4×D9—31no—
167C2×C4×D9—64no—
168C2×C4×D9—61no—
169C2×C4×D9C2×D311yescharacteristic
170C2×C4×D9C2×D311yescharacteristic
171C2×C4×D9C2×D311yescharacteristic
172C2×Dic18—31no—
173C2×Dic18—31no—
174C2×Dic18—31no—
175C2×Dic18—61no—
176C9×C4⋊C4—21no—
177C9×C4⋊C4—31no—
178C9×C4⋊C4—31no—
179C9×C4⋊C4C2×D311yescharacteristic, complemented
180C9×C22⋊C4—31no—
181C9×C22⋊C4—31no—
182#3676—31no—
183#3676—31no—
184(C2×D9)⋊C4—31no—
185(C2×D9)⋊C4—31no—
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—61no—
189(C2×D9)⋊C4—61no—
190C4⋊Dic9—31no—
191C4⋊Dic9—31no—
192C4⋊Dic9C2×D311yescharacteristic, complemented
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4—61no—
198Dic9⋊C4—61no—
199Dic9⋊C4C2×D311yescharacteristic, complemented
200Dic9⋊C4C2×D311yescharacteristic, complemented
201C22×C3×C9C2411yescharacteristic
202C2×C3⋊D9—21no—
203C2×C3⋊D9—21no—
204C2×C3⋊D9C2×Q812yescomplemented
205C2×D3×C9—21no—
206C2×D3×C9—21no—
207C2×D3×C9C2×Q812yescomplemented
208C2×C3×D9C2×D412yes—
209C2×C3×D9C2×Q812yes—
210C2×C3×D9#4112yes—
211D3×D9—28no—
212C3×C4×C9—21no—
213C3×C4×C9—21no—
214C3×C4×C9—21no—
215C3⋊Dic9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9C2×D412yes—
218C9×Dic3—21no—
219C9×Dic3—21no—
220C9×Dic3C2×D412yes—
221C3×Dic9—21no—
222C3×Dic9—21no—
223C3×Dic9—21no—
224C2×D3×Q8—91no—
225C22×C4×D3—91no—
226C22×C4×D3—91no—
227C22×Dic6—91no—
228C3×C22⋊Q8—31no—
229C2×C3×C4⋊C4—91no—
230#946—91no—
231C2×(C2×D3)⋊C4—91no—
232C2×(C2×D3)⋊C4—91no—
233#924—91no—
234C2×Dic3⋊C4—91no—
235C2×Dic3⋊C4—91no—
236#897—91no—
237#896—91no—
238#896—91no—
239#896—91no—
240#896—91no—
241#896—91no—
242#896—91no—
243#896—91no—
244#896—91no—
245#896—91no—
246#896—181no—
247#896D911yescharacteristic, direct product factor
248D3×C4⋊C4—31no—
249D3×C4⋊C4—91no—
250D3×C4⋊C4—91no—
251D3×C22⋊C4—91no—
252D3×C22⋊C4—91no—
253#878—91no—
254#878—91no—
255C22×C3⋊D3—31no—
256C22×C3×D3—31no—
257C22×C3×D3C22×D311yescharacteristic
258C2×D32—34no—
259C2×D32—62no—
260C2×D32—62no—
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—31no—
266C2×C3⋊Dic3—31no—
267C4×C3⋊D3—62no—
268#634—62no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C22×D311yescharacteristic
275C3×C4×D3—22no—
276C3×C4×D3—62no—
277C3×C4×D3—62no—
278C3×C4×D3—62no—
279C3×Dic6—22no—
280#627—62no—
281#627—62no—
282#624—62no—
283D3×Dic3—34no—
284D3×Dic3—62no—
285D3×Dic3—62no—
286D3×Dic3—62no—
287C23×C9—31no—
288C22×D9—31no—
289C22×D9—34no—
290C22×D9—61no—
291C22×D9—62no—
292C22×D9—62no—
293C22×D9C22×D311yescharacteristic
294Q8×C9—62no—
295C2×C4×C9—21no—
296C2×C4×C9—21no—
297C2×C4×C9—21no—
298C2×C4×C9—31no—
299C2×C4×C9—31no—
300C2×C4×C9—31no—
301C2×C4×C9—62no—
302C2×C4×C9C22×D311yescharacteristic
303C2×C4×C9C22×D311yescharacteristic
304C2×C4×C9C22×D311yescharacteristic
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—31no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9—61no—
311C2×Dic9—62no—
312C2×Dic9C22×D311yescharacteristic
313C2×Dic9C22×D311yescharacteristic
314C2×Dic9C22×D311yescharacteristic
315C4×D9—22no—
316C4×D9—22no—
317C4×D9—22no—
318C4×D9—34no—
319C4×D9—62no—
320C4×D9—62no—
321C4×D9—62no—
322C4×D9—62no—
323C4×D9—122no—
324Dic18—62no—
325Dic18—62no—
326Dic18—62no—
327Dic18—122no—
328C2×C22⋊Q8—271noSylow
329C2×C3×C9C22×D411yescharacteristic
330C2×C3×C9C22×Q811yescharacteristic
331C2×C3×C9C2×#4111yescharacteristic
332C3⋊D9—22no—
333D3×C9—22no—
334C3×D9C22⋊Q814yescomplemented
335C23×D3—91no—
336C23×D3—91no—
337C2×C3×Q8—31no—
338C22×C3×C4—31no—
339C22×C3×C4—91no—
340C22×C3×C4—91no—
341C22×C3×C4—91no—
342C22×Dic3—91no—
343C22×Dic3—91no—
344C22×Dic3—91no—
345C22×Dic3—91no—
346D3×Q8—184no—
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—91no—
351C2×C4×D3—91no—
352C2×C4×D3—91no—
353C2×C4×D3—91no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—91no—
358C2×C4×D3—181no—
359C2×C4×D3—184no—
360C2×C4×D3—184no—
361C2×C4×D3C2×D911yescharacteristic
362C2×Dic6—91no—
363C2×Dic6—91no—
364C2×Dic6—91no—
365C2×Dic6—91no—
366C2×Dic6—91no—
367C2×Dic6—91no—
368C2×Dic6—181no—
369C2×Dic6—184no—
370C2×Dic6C2×D911yescharacteristic, complemented
371C3×C4⋊C4—21no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—91no—
375C3×C4⋊C4—91no—
376C3×C4⋊C4—91no—
377C3×C4⋊C4C2×D911yescharacteristic, complemented
378C3×C4⋊C4D3211yescharacteristic
379C3×C22⋊C4—31no—
380C3×C22⋊C4—31no—
381#217—91no—
382#217—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—181no—
394(C2×D3)⋊C4—181no—
395(C2×D3)⋊C4C2×D911yescharacteristic
396(C2×D3)⋊C4C2×D911yescharacteristic
397C4⋊Dic3—31no—
398C4⋊Dic3—91no—
399C4⋊Dic3—91no—
400Dic3⋊C4—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—181no—
413Dic3⋊C4—181no—
414Dic3⋊C4C2×D911yescharacteristic, complemented
415Dic3⋊C4C2×D911yescharacteristic, complemented
416C22×C32C23×D311yescharacteristic
417C2×C3⋊D3—32no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—61no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—32no—
423C2×C3×D3—32no—
424C2×C3×D3—32no—
425C2×C3×D3D3×Q812yes—
426D32—68no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4—21no—
430C3⋊Dic3—32no—
431C3⋊Dic3—61no—
432C3⋊Dic3—61no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—61no—
436C3×Dic3—61no—
437C3×Dic3—61no—
438C3×Dic3D3×D412yes—
439C22×C9—21no—
440C22×C9—32no—
441C22×C9—61no—
442C22×C9—61no—
443C22×C9C23×D311yescharacteristic
444C2×D9—32no—
445C2×D9—62no—
446C2×D9—61no—
447C2×D9—61no—
448C2×D9—68no—
449C2×D9—121no—
450C2×D9—121no—
451C2×D9#23512yes—
452C2×D9D3×D412yes—
453C2×D9D3×Q812yes—
454C4×C9—21no—
455C4×C9—21no—
456C4×C9—21no—
457C4×C9—32no—
458C4×C9—41no—
459C4×C9—41no—
460C4×C9—41no—
461C4×C9—61no—
462C4×C9—61no—
463Dic9—21no—
464Dic9—21no—
465Dic9—21no—
466Dic9—32no—
467Dic9—62no—
468Dic9—61no—
469Dic9—61no—
470Dic9—121no—
471Dic9—121no—
472C22×Q8—271no—
473C23×C4—271no—
474C22⋊Q8—31no—
475C22⋊Q8—271no—
476C22⋊Q8—271no—
477C22⋊Q8—271no—
478C22⋊Q8—271no—
479C22⋊Q8—271no—
480C22⋊Q8—271no—
481C22⋊Q8—271no—
482C2×C4⋊C4—91no—
483C2×C4⋊C4—271no—
484C2×C4⋊C4—271no—
485C2×C22⋊C4—271no—
486C2×C22⋊C4—271no—
487C3×C9C2×C22⋊Q811yescharacteristic, complemented, Sylow
488C23×C3—31no—
489C23×C3—91no—
490C22×D3—31no—
491C22×D3—94no—
492C22×D3—91no—
493C22×D3—91no—
494C22×D3—94no—
495C22×D3—181no—
496C22×D3—182no—
497C22×D3—182no—
498C22×D3—182no—
499C22×D3—182no—
500C22×D3C22×D911yescharacteristic
501C3×Q8—62no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—62no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—182no—
513C2×C3×C4—182no—
514C2×C3×C4—182no—
515C2×C3×C4C22×D911yescharacteristic
516C2×C3×C4C22×D911yescharacteristic
517C2×C3×C4C22×D911yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520C2×C3×C4C2×D3211yescharacteristic
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—91no—
525C2×Dic3—91no—
526C2×Dic3—94no—
527C2×Dic3—91no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—181no—
532C2×Dic3—181no—
533C2×Dic3—181no—
534C2×Dic3—182no—
535C2×Dic3—182no—
536C2×Dic3—182no—
537C2×Dic3C22×D911yescharacteristic
538C2×Dic3C22×D911yescharacteristic
539C2×Dic3C22×D911yescharacteristic
540C4×D3—22no—
541C4×D3—62no—
542C4×D3—62no—
543C4×D3—62no—
544C4×D3—94no—
545C4×D3—182no—
546C4×D3—182no—
547C4×D3—182no—
548C4×D3—182no—
549C4×D3—182no—
550C4×D3—182no—
551C4×D3—182no—
552C4×D3—362no—
553Dic6—22no—
554Dic6—182no—
555Dic6—182no—
556Dic6—182no—
557Dic6—182no—
558Dic6—182no—
559Dic6—182no—
560Dic6—362no—
561C2×C32C2×D3×D411yescharacteristic
562C2×C32C2×D3×Q811yescharacteristic
563C2×C32D3×#4111yescharacteristic
564C3⋊D3—62no—
565C3×D3—22no—
566C3×D3—34no—
567C2×C9—21no—
568C2×C9—21no—
569C2×C9—21no—
570C2×C9—62no—
571C2×C9C2×#23511yescharacteristic
572C2×C9C2×D3×D411yescharacteristic
573C2×C9C2×D3×Q811yescharacteristic
574D9—62no—
575D9—122no—
576D9#89614yesdirect product factor
577C24—271no—
578C2×Q8—31no—
579C2×Q8—271no—
580C2×Q8—271no—
581C2×Q8—271no—
582C2×Q8—544no—
583C22×C4—31no—
584C22×C4—91no—
585C22×C4—91no—
586C22×C4—91no—
587C22×C4—271no—
588C22×C4—271no—
589C22×C4—271no—
590C22×C4—271no—
591C22×C4—271no—
592C22×C4—271no—
593C22×C4—544no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—91no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—271no—
600C4⋊C4—271no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4D3×D911yescharacteristic, complemented
606C22⋊C4—31no—
607C22⋊C4—31no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22×C3—21no—
615C22×C3—32no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—92no—
619C22×C3—92no—
620C22×C3—92no—
621C22×C3C23×D911yescharacteristic
622C22×C3C22×D3211yescharacteristic
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—32no—
626C2×D3—32no—
627C2×D3—32no—
628C2×D3—92no—
629C2×D3—92no—
630C2×D3—182no—
631C2×D3—188no—
632C2×D3—188no—
633C2×D3—181no—
634C2×D3—181no—
635C2×D3—181no—
636C2×D3—181no—
637C2×D3—361no—
638C2×D3—361no—
639C2×D3Q8×D912yescomplemented
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—32no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—61no—
651C3×C4—61no—
652C3×C4—181no—
653C3×C4—181no—
654C3×C4—181no—
655Dic3—21no—
656Dic3—21no—
657Dic3—61no—
658Dic3—61no—
659Dic3—61no—
660Dic3—92no—
661Dic3—92no—
662Dic3—182no—
663Dic3—181no—
664Dic3—181no—
665Dic3—181no—
666Dic3—181no—
667Dic3—361no—
668Dic3—361no—
669Dic3D4×D912yes—
670C32D3×C22⋊Q811yescharacteristic
671C9—21no—
672C9C2×#89611yescharacteristic, complemented
673C23—31no—
674C23—91no—
675C23—274no—
676C23—271no—
677C23—542no—
678C23—542no—
679Q8—62no—
680Q8—542no—
681Q8—542no—
682Q8—542no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—62no—
687C2×C4—91no—
688C2×C4—91no—
689C2×C4—91no—
690C2×C4—182no—
691C2×C4—182no—
692C2×C4—182no—
693C2×C4—274no—
694C2×C4—271no—
695C2×C4—271no—
696C2×C4—271no—
697C2×C4—542no—
698C2×C4—542no—
699C2×C4—542no—
700C2×C4—542no—
701C2×C4—542no—
702C2×C4C2×D3×D911yescharacteristic
703C2×C4C2×D3×D911yescharacteristic
704C2×C4C2×D3×D911yescharacteristic
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—62no—
709C2×C3—94no—
710C2×C3C2×D4×D911yescharacteristic
711C2×C3C2×Q8×D911yescharacteristic
712C2×C3#41×D911yescharacteristic
713C2×C3D3×#23511yescharacteristic
714C2×C3D32×D411yescharacteristic
715C2×C3D32×Q811yescharacteristic
716D3—22no—
717D3—34no—
718D3—182no—
719D3—182no—
720D3—362no—
721C22—32no—
722C22—61no—
723C22—61no—
724C22—92no—
725C22—92no—
726C22—92no—
727C22—272no—
728C22—548no—
729C22—541no—
730C22—541no—
731C22C22×D3×D911yescharacteristic
732C4—21no—
733C4—21no—
734C4—21no—
735C4—32no—
736C4—61no—
737C4—61no—
738C4—181no—
739C4—181no—
740C4—181no—
741C4—272no—
742C4—541no—
743C4—541no—
744C3—21no—
745C3D9×C22⋊Q811yescharacteristic, complemented
746C3D3×#89611yescharacteristic
747C2—62no—
748C2—94no—
749C2—542no—
750C2D9×#23511yescharacteristic
751C2D3×D4×D911yescharacteristic
752C2D3×Q8×D911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radicalC22×D3×D9C22
hypercenterC4⋊C4D3×D9
hypocenterC3×C9C2×C22⋊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
2. C2×D9×Dic6C2semidirect
3. #11721752C2semidirect
4. C9×#896C2semidirect
5. C3×C4⋊C4×D9C2semidirect
8. #11721026C2semidirect
9. #11721024C2semidirect
10. #11720995C2semidirect
11. #11720986C2semidirect
12. D9×Dic3⋊C4C2semidirect
13. D9×Dic3⋊C4C2semidirect
14. #11720955C2semidirect
15. #11720923C2semidirect
20. C2×#6226C22semidirect
25. C2×C9×Dic6C22semidirect
31. C2×#6189C22semidirect
32. C2×#6189C22semidirect
35. C3×C9×C4⋊C4C22semidirect
38. #88534C22semidirect
39. #88534C22semidirect
42. C9×Dic3⋊C4C22semidirect
43. C9×Dic3⋊C4C22semidirect
44. C3×C4⋊Dic9C22semidirect
45. C3×Dic9⋊C4C22semidirect
46. C3×Dic9⋊C4C22semidirect
51. Dic3⋊Dic9C22semidirect
52. Dic3⋊Dic9C22semidirect
53. #88442C22semidirect
54. #88442C22semidirect
81. C4⋊C4×D9D3semidirect
91. C2×D3×D9Q8semidirect
179. C9×C4⋊C4C2×D3semidirect
192. C4⋊Dic9C2×D3semidirect
199. Dic9⋊C4C2×D3semidirect
200. Dic9⋊C4C2×D3semidirect
204. C2×C3⋊D9C2×Q8semidirect
207. C2×D3×C9C2×Q8semidirect
247. #896D9direct (N × H)
334. C3×D9C22⋊Q8semidirect
370. C2×Dic6C2×D9semidirect
377. C3×C4⋊C4C2×D9semidirect
414. Dic3⋊C4C2×D9semidirect
415. Dic3⋊C4C2×D9semidirect
487. C3×C9C2×C22⋊Q8semidirect
576. D9#896direct (N × H)
605. C4⋊C4D3×D9semidirect
639. C2×D3Q8×D9semidirect
672. C9C2×#896semidirect
745. C3D9×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×D92
C2×D9×Dic62
#117217522
C9×#8962
C3×C4⋊C4×D92
D9×(C2×D3)⋊C42
#117210262
#117210242
#117209952
#117209862
D9×Dic3⋊C42
#117209552
#117209232
D3×#8963
D9×C22⋊Q83