Finite Group Databasebeta

← D3×#63440 #13148195

Subgroups — D3×#63440 #13148195

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
1C22×D3×Dic9C211yesmaximal, characteristic
2C2×D3×Dic18C211yesmaximal, characteristic, complemented
3#11721724C211yesmaximal, characteristic, complemented
4D3×C9×C22⋊C4C211yesmaximal, characteristic
5C3×#63440C211yesmaximal, characteristic, complemented
6D3×#3676C211yesmaximal, characteristic
7#11721267C211yesmaximal, characteristic, complemented
8#11721253C211yesmaximal, characteristic, complemented
9#11721026C211yesmaximal, characteristic, complemented
10#11721024C211yesmaximal, characteristic, complemented
11#11721023C211yesmaximal, characteristic, complemented
12D3×C4⋊Dic9C211yesmaximal, characteristic, complemented
13#11721018C211yesmaximal, characteristic, complemented
14D3×Dic9⋊C4C211yesmaximal, characteristic, complemented
15D3×Dic9⋊C4C211yesmaximal, characteristic, complemented
16D3×#878—31nomaximal
17C2×#63440—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×#6226C2211yescharacteristic, complemented
21C22×C3×Dic9C2211yescharacteristic
22C2×C4×D3×C9C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic
24C2×C3×Dic18C2211yescharacteristic, complemented
25C2×D3×Dic9—24no—
26C2×D3×Dic9C2211yescharacteristic
27C2×D3×Dic9C2211yescharacteristic
28C2×D3×Dic9C2211yescharacteristic
29C2×D3×Dic9C2211yescharacteristic
30C2×D3×Dic9C2211yescharacteristic
31C2×D3×Dic9C2211yescharacteristic
32C2×#6189C2211yescharacteristic, complemented
33C2×#6189C2211yescharacteristic, complemented
34D3×Dic18—24no—
35C3×C9×C22⋊C4C2211yescharacteristic
36#88551C2211yescharacteristic
37C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
38#88534C2211yescharacteristic, complemented
39#88534C2211yescharacteristic, complemented
40C9×#217C2211yescharacteristic
41C3×#3676C2211yescharacteristic
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C9×(C2×D3)⋊C4C2211yescharacteristic
44C3×C4⋊Dic9C2211yescharacteristic, complemented
45C3×Dic9⋊C4C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C22×D3×Dic3—31no—
56C2×D3×Dic6—31no—
57#64087—31no—
58C3×D3×C22⋊C4D311yescharacteristic
59C3×#878—31no—
60#63982—31no—
61D3×#217—31no—
62#63964—31no—
63#63899—31no—
64#63896—31no—
65#63893—31no—
66D3×C4⋊Dic3—31no—
67#63887—31no—
68D3×Dic3⋊C4—31no—
69D3×Dic3⋊C4—31no—
70C23×Dic9—31no—
71C22×Dic18—31no—
72C2×C9×C22⋊C4—31no—
73C2×#3676—31no—
74C2×C4⋊Dic9—31no—
75C2×Dic9⋊C4—31no—
76C2×Dic9⋊C4—31no—
77#63440—31no—
78#63440—31no—
79#63440—31no—
80#63440—31no—
81#63440—31no—
82#63440—31no—
83#63440—31no—
84#63440—61no—
85#63440D311yescharacteristic, direct product factor
86C23×C3×C9C2311yescharacteristic
87C22×D3×C9—22no—
88C22×D3×C9—22no—
89C22×D3×C9Q814yescomplemented
90C22×D3×C9C2311yescharacteristic
91C22×D3×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3⋊Dic9—22no—
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99#6226—22no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9—22no—
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C4×D3×C9—22no—
108C4×D3×C9—22no—
109C3×Dic18—22no—
110D3×Dic9—22no—
111D3×Dic9—22no—
112D3×Dic9—22no—
113D3×Dic9—22no—
114D3×Dic9—22no—
115D3×Dic9D414yes—
116#6189—22no—
117#6189—22no—
118D3×C22⋊Q8—91no—
119C2×#878—91no—
120C23×C3×D3C2×D311yescharacteristic
121C22×C3⋊Dic3—31no—
122C2×#634—31no—
123C22×C3×Dic3—31no—
124C2×C3×C4×D3C2×D311yescharacteristic
125C2×C3×C4×D3C2×D311yescharacteristic
126C2×C3×Dic6—31no—
127C2×#627—31no—
128C2×#627—31no—
129C2×D3×Dic3—31no—
130C2×D3×Dic3—31no—
131C2×D3×Dic3—31no—
132C2×D3×Dic3—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—64no—
136D3×Dic6—64no—
137C24×C9—31no—
138C32×C22⋊C4C2×D311yescharacteristic
139#3757—31no—
140C4⋊(C3⋊Dic3)—31no—
141#3750—31no—
142#3750—31no—
143C3×#217—31no—
144C3×#217C2×D311yescharacteristic
145C3×(C2×D3)⋊C4C2×D311yescharacteristic
146C3×(C2×D3)⋊C4C2×D311yescharacteristic
147C3×C4⋊Dic3—31no—
148C3×Dic3⋊C4—31no—
149C3×Dic3⋊C4—31no—
150#3724—31no—
151#3724—31no—
152Dic3⋊Dic3—31no—
153Dic3⋊Dic3—31no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158C22×C4×C9—31no—
159C22×C4×C9—31no—
160C22×Dic9—31no—
161C22×Dic9—31no—
162C22×Dic9—31no—
163C22×Dic9—31no—
164C22×Dic9—31no—
165C22×Dic9—31no—
166C22×Dic9—31no—
167C22×Dic9—64no—
168C22×Dic9—61no—
169C22×Dic9C2×D311yescharacteristic
170C2×Dic18—31no—
171C2×Dic18—31no—
172C2×Dic18—31no—
173C2×Dic18—64no—
174C2×Dic18—61no—
175C2×Dic18C2×D311yescharacteristic, complemented
176C9×C22⋊C4—21no—
177C9×C22⋊C4—31no—
178C9×C22⋊C4—31no—
179C9×C22⋊C4—31no—
180C9×C22⋊C4C2×D311yescharacteristic
181#3676—31no—
182#3676—31no—
183#3676—31no—
184#3676—61no—
185#3676C2×D311yescharacteristic
186C4⋊Dic9—31no—
187C4⋊Dic9—31no—
188C4⋊Dic9—31no—
189C4⋊Dic9—61no—
190C4⋊Dic9C2×D311yescharacteristic, complemented
191Dic9⋊C4—31no—
192Dic9⋊C4—31no—
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×C9—21no—
202C22×C3×C9—21no—
203C22×C3×C9C2×Q812yescomplemented
204C22×C3×C9C2411yescharacteristic
205C2×D3×C9—21no—
206C2×D3×C9—21no—
207C2×D3×C9—28no—
208C2×D3×C9C2×D412yes—
209C2×D3×C9C2×Q812yes—
210C2×D3×C9C2×Q812yescomplemented
211C2×D3×C9#4112yes—
212C3×C4×C9—21no—
213C3×C4×C9—21no—
214C3⋊Dic9—21no—
215C3⋊Dic9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9C2×D412yes—
218C9×Dic3—21no—
219C9×Dic3—21no—
220C3×Dic9—21no—
221C3×Dic9—21no—
222C3×Dic9—21no—
223C3×Dic9C2×D412yes—
224C23×Dic3—91no—
225C2×D3×Q8—91no—
226C22×C4×D3—91no—
227C22×Dic6—91no—
228C3×C22⋊Q8—91no—
229C2×C3×C22⋊C4—31no—
230C2×#217—91no—
231#946—91no—
232C2×C4⋊Dic3—91no—
233#924—91no—
234C2×Dic3⋊C4—91no—
235C2×Dic3⋊C4—91no—
236#897—91no—
237#896—91no—
238#896—91no—
239D3×C4⋊C4—91no—
240D3×C4⋊C4—91no—
241D3×C4⋊C4—91no—
242D3×C22⋊C4—91no—
243D3×C22⋊C4D911yescharacteristic
244#878—31no—
245#878—91no—
246#878—91no—
247#878—91no—
248#878—91no—
249#878—91no—
250#878—91no—
251#878—91no—
252#878—91no—
253#878—91no—
254#878—181no—
255C23×C32C22×D311yescharacteristic
256C22×C3×D3—22no—
257C22×C3×D3—22no—
258C22×C3×D3Dic614yes—
259C22×C3×D3C22×D311yescharacteristic
260C22×C3×D3C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—31no—
266C2×C3⋊Dic3—31no—
267C2×C3⋊Dic3—62no—
268#634—62no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—62no—
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D311yescharacteristic
276C3×C4×D3—22no—
277C3×C4×D3—22no—
278C3×Dic6—62no—
279#627—62no—
280#627—62no—
281D3×Dic3—34no—
282D3×Dic3—62no—
283D3×Dic3—62no—
284D3×Dic3—62no—
285D3×Dic3—62no—
286D3×Dic3—62no—
287C23×C9—21no—
288C23×C9—31no—
289C23×C9—34no—
290C23×C9—31no—
291C23×C9—62no—
292C23×C9—62no—
293C23×C9C22×D311yescharacteristic
294C2×C4×C9—21no—
295C2×C4×C9—21no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9—62no—
299C2×C4×C9—62no—
300C2×C4×C9C22×D311yescharacteristic
301C2×C4×C9C22×D311yescharacteristic
302C2×Dic9—22no—
303C2×Dic9—31no—
304C2×Dic9—34no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—31no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9—61no—
311C2×Dic9—61no—
312C2×Dic9—62no—
313C2×Dic9—62no—
314C2×Dic9—62no—
315C2×Dic9—62no—
316C2×Dic9—62no—
317C2×Dic9—62no—
318C2×Dic9—122no—
319C2×Dic9C22×D311yescharacteristic
320C2×Dic9C22×D311yescharacteristic
321C2×Dic9C22×D311yescharacteristic
322C2×Dic9C22×D311yescharacteristic
323Dic18—22no—
324Dic18—62no—
325Dic18—62no—
326Dic18—62no—
327Dic18—122no—
328C2×C22⋊Q8—271noSylow
329C2×C3×C9—22no—
330C2×C3×C9C22×D411yescharacteristic
331C2×C3×C9C22×Q811yescharacteristic
332C2×C3×C9C2×#4111yescharacteristic
333D3×C9—22no—
334D3×C9C22⋊Q814yescomplemented
335C24×C3—31no—
336C23×D3C2×D911yescharacteristic
337C2×C3×Q8—91no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—91no—
341C22×Dic3—31no—
342C22×Dic3—91no—
343C22×Dic3—91no—
344C22×Dic3—91no—
345C22×Dic3—91no—
346C22×Dic3—91no—
347C22×Dic3—91no—
348C22×Dic3—91no—
349C22×Dic3—91no—
350C22×Dic3—181no—
351C22×Dic3—184no—
352D3×Q8—184no—
353C2×C4×D3—91no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×C4×D3—184no—
360C2×C4×D3C2×D911yescharacteristic
361C2×C4×D3C2×D911yescharacteristic
362C2×Dic6—31no—
363C2×Dic6—91no—
364C2×Dic6—91no—
365C2×Dic6—91no—
366C2×Dic6—91no—
367C2×Dic6—91no—
368C2×Dic6—91no—
369C2×Dic6—181no—
370C2×Dic6—184no—
371C3×C4⋊C4—91no—
372C3×C4⋊C4—91no—
373C3×C4⋊C4—91no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4C2×D911yescharacteristic
380C3×C22⋊C4D3211yescharacteristic
381#217—31no—
382#217—91no—
383#217—91no—
384#217—91no—
385#217—91no—
386#217—181no—
387#217C2×D911yescharacteristic
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4C2×D911yescharacteristic
391(C2×D3)⋊C4C2×D911yescharacteristic
392C4⋊Dic3—31no—
393C4⋊Dic3—91no—
394C4⋊Dic3—91no—
395C4⋊Dic3—91no—
396C4⋊Dic3—91no—
397C4⋊Dic3—91no—
398C4⋊Dic3—91no—
399C4⋊Dic3—181no—
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—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—181no—
415Dic3⋊C4—181no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32C2×Dic612yes—
419C22×C32C23×D311yescharacteristic
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—28no—
423C2×C3×D3C2×Dic612yes—
424C2×C3×D3C2×Dic612yes—
425C2×C3×D3D3×D412yes—
426C2×C3×D3#23712yes—
427C32×C4—21no—
428C32×C4—21no—
429C3⋊Dic3—32no—
430C3⋊Dic3—61no—
431C3⋊Dic3—61no—
432C3⋊Dic3—61no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—32no—
436C3×Dic3—61no—
437C3×Dic3—61no—
438C3×Dic3—61no—
439C22×C9—21no—
440C22×C9—21no—
441C22×C9—21no—
442C22×C9—22no—
443C22×C9—32no—
444C22×C9—32no—
445C22×C9—32no—
446C22×C9—32no—
447C22×C9—41no—
448C22×C9—41no—
449C22×C9—68no—
450C22×C9—61no—
451C22×C9—61no—
452C22×C9D3×Q812yescomplemented
453C22×C9C23×D311yescharacteristic
454C4×C9—21no—
455C4×C9—21no—
456C4×C9—41no—
457C4×C9—41no—
458C4×C9—61no—
459C4×C9—61no—
460Dic9—21no—
461Dic9—21no—
462Dic9—21no—
463Dic9—32no—
464Dic9—62no—
465Dic9—61no—
466Dic9—61no—
467Dic9—61no—
468Dic9—121no—
469Dic9—121no—
470Dic9—121no—
471Dic9D3×D412yes—
472C22×Q8—271no—
473C23×C4—271no—
474C22⋊Q8—91no—
475C22⋊Q8—271no—
476C22⋊Q8—271no—
477C22⋊Q8—271no—
478C22⋊Q8—271no—
479C22⋊Q8—271no—
480C22⋊Q8—271no—
481C22⋊Q8—271no—
482C2×C4⋊C4—271no—
483C2×C4⋊C4—271no—
484C2×C4⋊C4—271no—
485C2×C22⋊C4—31no—
486C2×C22⋊C4—271no—
487C3×C9C2×C22⋊Q811yescharacteristic, complemented, Sylow
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—31no—
491C23×C3—34no—
492C23×C3—62no—
493C23×C3—62no—
494C23×C3C22×D911yescharacteristic
495C23×C3C2×D3211yescharacteristic
496C22×D3—22no—
497C22×D3—22no—
498C22×D3Dic1814yescomplemented
499C22×D3C22×D911yescharacteristic
500C22×D3C22×D911yescharacteristic
501C3×Q8—182no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—62no—
507C2×C3×C4—62no—
508C2×C3×C4—91no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—182no—
513C2×C3×C4C22×D911yescharacteristic
514C2×C3×C4C22×D911yescharacteristic
515C2×C3×C4C2×D3211yescharacteristic
516C2×C3×C4C2×D3211yescharacteristic
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—62no—
522C2×Dic3—94no—
523C2×Dic3—91no—
524C2×Dic3—91no—
525C2×Dic3—91no—
526C2×Dic3—91no—
527C2×Dic3—91no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—181no—
532C2×Dic3—181no—
533C2×Dic3—181no—
534C2×Dic3—181no—
535C2×Dic3—182no—
536C2×Dic3—182no—
537C2×Dic3—182no—
538C2×Dic3—182no—
539C2×Dic3—182no—
540C2×Dic3—182no—
541C2×Dic3—182no—
542C2×Dic3—362no—
543C2×Dic3C22×D911yescharacteristic
544C2×Dic3C22×D911yescharacteristic
545C4×D3—22no—
546C4×D3—22no—
547C4×D3—94no—
548C4×D3—182no—
549C4×D3—182no—
550C4×D3—182no—
551C4×D3—182no—
552C4×D3—182no—
553Dic6—62no—
554Dic6—182no—
555Dic6—182no—
556Dic6—182no—
557Dic6—182no—
558Dic6—182no—
559Dic6—182no—
560Dic6—362no—
561C2×C32—22no—
562C2×C32C22×Dic611yescharacteristic
563C2×C32C2×D3×D411yescharacteristic
564C2×C32C2×#23711yescharacteristic
565C3×D3—22no—
566C3×D3#87814yes—
567C2×C9—22no—
568C2×C9—21no—
569C2×C9—21no—
570C2×C9—21no—
571C2×C9—34no—
572C2×C9—42no—
573C2×C9—62no—
574C2×C9C2×D3×D411yescharacteristic
575C2×C9C2×D3×Q811yescharacteristic
576C2×C9D3×#4111yescharacteristic
577C24—31no—
578C2×Q8—91no—
579C2×Q8—271no—
580C2×Q8—271no—
581C2×Q8—271no—
582C2×Q8—544no—
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×C4—271no—
592C22×C4—271no—
593C22×C4—544no—
594C4⋊C4—91no—
595C4⋊C4—91no—
596C4⋊C4—91no—
597C4⋊C4—271no—
598C4⋊C4—271no—
599C4⋊C4—271no—
600C4⋊C4—271no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C22⋊C4—31no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—91no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4D3×D911yescharacteristic
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—22no—
619C22×C3—21no—
620C22×C3—32no—
621C22×C3—32no—
622C22×C3—32no—
623C22×C3—32no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—68no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3C2×Dic1812yescomplemented
630C22×C3C23×D911yescharacteristic
631C22×C3D3×Dic612yes—
632C22×C3C22×D3211yescharacteristic
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—28no—
636C2×D3C2×Dic1812yes—
637C2×D3C2×Dic1812yescomplemented
638C2×D3D4×D912yes—
639C2×D3#369912yes—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—92no—
649C3×C4—181no—
650C3×C4—181no—
651C3×C4—181no—
652Dic3—21no—
653Dic3—21no—
654Dic3—32no—
655Dic3—61no—
656Dic3—61no—
657Dic3—61no—
658Dic3—92no—
659Dic3—92no—
660Dic3—182no—
661Dic3—181no—
662Dic3—181no—
663Dic3—181no—
664Dic3—181no—
665Dic3—181no—
666Dic3—181no—
667Dic3—361no—
668Dic3—361no—
669Dic3—361no—
670C32C2×#87811yescharacteristic
671C9—21no—
672C9D3×C22⋊Q811yescharacteristic, complemented
673C23—31no—
674C23—34no—
675C23—31no—
676C23—62no—
677C23—62no—
678C23C2×D3×D911yescharacteristic
679Q8—182no—
680Q8—542no—
681Q8—542no—
682Q8—542no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—91no—
688C2×C4—91no—
689C2×C4—91no—
690C2×C4—91no—
691C2×C4—182no—
692C2×C4—274no—
693C2×C4—271no—
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×C4—542no—
703C2×C4C2×D3×D911yescharacteristic
704C2×C4C2×D3×D911yescharacteristic
705C2×C3—22no—
706C2×C3—22no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—34no—
711C2×C3—42no—
712C2×C3—62no—
713C2×C3C22×Dic1811yescharacteristic
714C2×C3C2×D4×D911yescharacteristic
715C2×C3C2×#369911yescharacteristic
716C2×C3C2×D3×Dic611yescharacteristic
717C2×C3D32×D411yescharacteristic
718C2×C3D3×#23711yescharacteristic
719D3—22no—
720D3#6344014yesdirect product factor
721C22—21no—
722C22—21no—
723C22—32no—
724C22—32no—
725C22—32no—
726C22—32no—
727C22—68no—
728C22—61no—
729C22—61no—
730C22D3×Dic1812yescomplemented
731C22C22×D3×D911yescharacteristic
732C4—21no—
733C4—21no—
734C4—61no—
735C4—61no—
736C4—92no—
737C4—181no—
738C4—181no—
739C4—181no—
740C4—272no—
741C4—541no—
742C4—541no—
743C4—541no—
744C3—21no—
745C3C2×#6344011yescharacteristic, complemented
746C3D3×#87811yescharacteristic
747C2—22no—
748C2—34no—
749C2—62no—
750C2C2×D3×Dic1811yescharacteristic
751C2D3×D4×D911yescharacteristic
752C2D3×#369911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC23×C3×D3C2×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9C2×C22⋊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
2. C2×D3×Dic18C2semidirect
3. #11721724C2semidirect
5. C3×#63440C2semidirect
7. #11721267C2semidirect
8. #11721253C2semidirect
9. #11721026C2semidirect
10. #11721024C2semidirect
11. #11721023C2semidirect
12. D3×C4⋊Dic9C2semidirect
13. #11721018C2semidirect
14. D3×Dic9⋊C4C2semidirect
15. D3×Dic9⋊C4C2semidirect
20. C2×#6226C22semidirect
24. C2×C3×Dic18C22semidirect
32. C2×#6189C22semidirect
33. C2×#6189C22semidirect
37. C4⋊(C3⋊Dic9)C22semidirect
38. #88534C22semidirect
39. #88534C22semidirect
44. C3×C4⋊Dic9C22semidirect
45. C3×Dic9⋊C4C22semidirect
46. C3×Dic9⋊C4C22semidirect
49. Dic3⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. #88442C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic9⋊Dic3C22semidirect
85. #63440D3direct (N × H)
89. C22×D3×C9Q8semidirect
175. C2×Dic18C2×D3semidirect
190. C4⋊Dic9C2×D3semidirect
199. Dic9⋊C4C2×D3semidirect
200. Dic9⋊C4C2×D3semidirect
203. C22×C3×C9C2×Q8semidirect
210. C2×D3×C9C2×Q8semidirect
334. D3×C9C22⋊Q8semidirect
452. C22×C9D3×Q8semidirect
487. C3×C9C2×C22⋊Q8semidirect
498. C22×D3Dic18semidirect
629. C22×C3C2×Dic18semidirect
637. C2×D3C2×Dic18semidirect
672. C9D3×C22⋊Q8semidirect
720. D3#63440direct (N × H)
730. C22D3×Dic18semidirect
745. C3C2×#63440semidirect

Maximal subgroups

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

subgroupindex
C22×D3×Dic92
C2×D3×Dic182
#117217242
D3×C9×C22⋊C42
C3×#634402
D3×#36762
#117212672
#117212532
#117210262
#117210242
#117210232
D3×C4⋊Dic92
#117210182
D3×Dic9⋊C42
D3×#8783
C2×#634403