Finite Group Databasebeta

← D3×#63445 #13148401

Subgroups — D3×#63445 #13148401

Order 1728.

1104 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#611C211yesmaximal, characteristic
2C2×C4×D3×D9C211yesmaximal, characteristic, complemented
3#11721729C211yesmaximal, characteristic, complemented
4D3×C9×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#63445C211yesmaximal, characteristic, complemented
6D3×#3676C211yesmaximal, characteristic, complemented
7#11721275C211yesmaximal, characteristic, complemented
8#11721269C211yesmaximal, characteristic, complemented
9D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
10#11721031C211yesmaximal, characteristic, complemented
11D3×C4⋊Dic9C211yesmaximal, characteristic, complemented
12D3×Dic9⋊C4C211yesmaximal, characteristic, complemented
13#11720989C211yesmaximal, characteristic, complemented
14#11720958C211yesmaximal, characteristic, complemented
15#11720957C211yesmaximal, characteristic, complemented
16D3×#883—31nomaximal
17C2×#63445—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C3×#611C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic, complemented
26D3×#611—24no—
27C2×#6195C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×D3×Dic9C2211yescharacteristic
30C2×D3×Dic9C2211yescharacteristic
31C2×D3×Dic9C2211yescharacteristic
32C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
33C2×Dic3×D9C2211yescharacteristic, complemented
34C4×D3×D9—24no—
35C3×C9×C22⋊C4C2211yescharacteristic, complemented
36#88551C2211yescharacteristic, complemented
37#88536C2211yescharacteristic, complemented
38C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
39#88534C2211yescharacteristic, complemented
40C9×#217C2211yescharacteristic, complemented
41C3×#3676C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C3×C4⋊Dic9C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52Dic3⋊Dic9C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×C4×D32—31no—
57#64092—31no—
58C3×#883—31no—
59C3×D3×C22⋊C4D311yescharacteristic
60#63975—31no—
61#63969—31no—
62D3×#217—31no—
63D3×(C2×D3)⋊C4—31no—
64#63905—31no—
65#63891—31no—
66D3×C4⋊Dic3—31no—
67D3×Dic3⋊C4—31no—
68#63854—31no—
69#63853—31no—
70C22×#611—31no—
71C22×C4×D9—31no—
72C2×C9×C22⋊C4—31no—
73C2×#3676—31no—
74C2×(C2×D9)⋊C4—31no—
75C2×C4⋊Dic9—31no—
76C2×Dic9⋊C4—31no—
77#63445—31no—
78#63445—31no—
79#63445—31no—
80#63445—31no—
81#63445—31no—
82#63445—31no—
83#63445—31no—
84#63445—61no—
85#63445D311yescharacteristic, direct product factor
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9—22no—
89C22×D3×C9—22no—
90C22×D3×C9—22no—
91C22×D3×C9C2311yescharacteristic
92C22×D3×C9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
94C2×D3×D9—22no—
95C2×D3×D9—22no—
96C2×D3×D9D414yes—
97C2×C3×C4×C9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99#6233—22no—
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103C4×C3⋊D9—22no—
104C3×#611—22no—
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C4×D3×C9—22no—
111C4×D3×C9—22no—
112C3×C4×D9—22no—
113#6195—22no—
114#6194—22no—
115D3×Dic9—22no—
116D3×Dic9—22no—
117D3×Dic9—22no—
118(C3⋊D9)⋊C4—22no—
119Dic3×D9—22no—
120D3×#123—91no—
121C2×#883—91no—
122C23×C3×D3C2×D311yescharacteristic
123C22×D32—31no—
124C2×#638—31no—
125C2×C4×C3⋊D3—31no—
126C2×C3×#67—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3C2×D311yescharacteristic
129C2×C3×C4×D3C2×D311yescharacteristic
130D3×#67—64no—
131C2×#626—31no—
132C2×#625—31no—
133C2×#624—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137C2×D3×Dic3—31no—
138C4×D32—64no—
139C24×C9—31no—
140C23×D9—31no—
141C32×C22⋊C4C2×D311yescharacteristic
142#3757—31no—
143#3752—31no—
144C4⋊(C3⋊Dic3)—31no—
145#3750—31no—
146C3×#217—31no—
147C3×#217C2×D311yescharacteristic
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4C2×D311yescharacteristic
150C3×(C2×D3)⋊C4C2×D311yescharacteristic
151C3×C4⋊Dic3—31no—
152C3×Dic3⋊C4—31no—
153#3724—31no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—31no—
156Dic3⋊Dic3—31no—
157#3722—31no—
158(C2×D3)⋊Dic3—31no—
159(C2×D3)⋊Dic3—31no—
160(C2×D3)⋊Dic3—31no—
161C22×C4×C9—31no—
162C22×C4×C9—31no—
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—31no—
166C2×#611—64no—
167C2×#611—61no—
168C2×#611C2×D311yescharacteristic
169C22×Dic9—31no—
170C22×Dic9—31no—
171C22×Dic9—31no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—31no—
175C2×C4×D9—64no—
176C2×C4×D9—61no—
177C2×C4×D9C2×D311yescharacteristic, complemented
178C9×C22⋊C4—21no—
179C9×C22⋊C4—31no—
180C9×C22⋊C4—31no—
181C9×C22⋊C4—31no—
182C9×C22⋊C4C2×D311yescharacteristic, complemented
183#3676—31no—
184#3676—31no—
185#3676—31no—
186#3676—61no—
187#3676C2×D311yescharacteristic, complemented
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—61no—
192(C2×D9)⋊C4C2×D311yescharacteristic, complemented
193C4⋊Dic9—31no—
194C4⋊Dic9—31no—
195C4⋊Dic9—31no—
196C4⋊Dic9—61no—
197C4⋊Dic9C2×D311yescharacteristic, complemented
198Dic9⋊C4—31no—
199Dic9⋊C4—31no—
200Dic9⋊C4—31no—
201Dic9⋊C4—61no—
202Dic9⋊C4C2×D311yescharacteristic, complemented
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9C2411yescharacteristic
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9C2×D412yes—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9—21no—
213C2×D3×C9—44no—
214C2×D3×C9C2×D412yes—
215C2×D3×C9#4112yes—
216C2×D3×C9#4112yes—
217C2×C3×D9—21no—
218C2×C3×D9—21no—
219C2×C3×D9C2×D412yes—
220D3×D9—28no—
221C3×C4×C9—21no—
222C3×C4×C9—21no—
223C3⋊Dic9—21no—
224C3⋊Dic9—21no—
225C3⋊Dic9—21no—
226C9×Dic3—21no—
227C9×Dic3—21no—
228C3×Dic9—21no—
229C3×Dic9—21no—
230C3×Dic9—21no—
231C22×#67—91no—
232C2×D3×D4—91no—
233C22×C4×D3—91no—
234C22×C4×D3—91no—
235C3×#123—91no—
236C2×C3×C22⋊C4—31no—
237C2×#217—91no—
238#935—91no—
239#929—91no—
240C2×(C2×D3)⋊C4—91no—
241C2×C4⋊Dic3—91no—
242C2×Dic3⋊C4—91no—
243#894—91no—
244#894—91no—
245D3×C4⋊C4—91no—
246D3×C4⋊C4—91no—
247#886—91no—
248#883—31no—
249#883—91no—
250#883—91no—
251#883—91no—
252#883—91no—
253#883—91no—
254#883—91no—
255#883—91no—
256#883—91no—
257#883—91no—
258#883—181no—
259D3×C22⋊C4—91no—
260D3×C22⋊C4—91no—
261D3×C22⋊C4D911yescharacteristic, complemented
262C23×C32C22×D311yescharacteristic
263C22×C3⋊D3—31no—
264C22×C3×D3—22no—
265C22×C3×D3—22no—
266C22×C3×D3—22no—
267C22×C3×D3—31no—
268C22×C3×D3C22×D311yescharacteristic
269C22×C3×D3C22×D311yescharacteristic
270C2×D32—34no—
271C2×D32—62no—
272C2×D32—62no—
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275#638—62no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—31no—
278C2×C3⋊Dic3—31no—
279C4×C3⋊D3—62no—
280C3×#67—62no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C3×C4×D3—22no—
287C3×C4×D3—22no—
288C3×C4×D3—62no—
289#626—62no—
290#625—62no—
291#624—62no—
292D3×Dic3—62no—
293D3×Dic3—62no—
294D3×Dic3—62no—
295D3×Dic3—62no—
296C23×C9—21no—
297C23×C9—31no—
298C23×C9—31no—
299C23×C9—62no—
300C23×C9—62no—
301C23×C9—62no—
302C23×C9C22×D311yescharacteristic
303C22×D9—31no—
304C22×D9—34no—
305C22×D9—61no—
306C22×D9—62no—
307C22×D9—62no—
308C22×D9C22×D311yescharacteristic
309C2×C4×C9—21no—
310C2×C4×C9—21no—
311C2×C4×C9—31no—
312C2×C4×C9—31no—
313C2×C4×C9—62no—
314C2×C4×C9—62no—
315C2×C4×C9C22×D311yescharacteristic
316C2×C4×C9C22×D311yescharacteristic
317#611—22no—
318#611—62no—
319#611—62no—
320#611—62no—
321#611—122no—
322C2×Dic9—31no—
323C2×Dic9—31no—
324C2×Dic9—31no—
325C2×Dic9—61no—
326C2×Dic9—61no—
327C2×Dic9—61no—
328C2×Dic9—62no—
329C2×Dic9—62no—
330C2×Dic9—62no—
331C2×Dic9C22×D311yescharacteristic
332C2×Dic9C22×D311yescharacteristic
333C2×Dic9C22×D311yescharacteristic
334C4×D9—22no—
335C4×D9—62no—
336C4×D9—62no—
337C4×D9—62no—
338C4×D9—122no—
339C2×#123—271noSylow
340C2×C3×C9—41no—
341C2×C3×C9C22×D411yescharacteristic
342C2×C3×C9C2×#4111yescharacteristic
343C2×C3×C9C2×#4111yescharacteristic
344C3⋊D9—22no—
345D3×C9—41no—
346D3×C9#12314yescomplemented
347C3×D9—22no—
348C24×C3—31no—
349C23×D3—91no—
350C23×D3—91no—
351C23×D3C2×D911yescharacteristic
352C2×C3×D4—91no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—91no—
356C2×#67—31no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—181no—
363C2×#67—184no—
364C22×Dic3—91no—
365C22×Dic3—91no—
366C22×Dic3—91no—
367C22×Dic3—91no—
368D3×D4—184no—
369C2×D12—91no—
370C2×C4×D3—31no—
371C2×C4×D3—91no—
372C2×C4×D3—91no—
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—181no—
380C2×C4×D3—184no—
381C2×C4×D3—184no—
382C2×C4×D3C2×D911yescharacteristic
383C2×C4×D3C2×D911yescharacteristic
384C3×C4⋊C4—91no—
385C3×C4⋊C4—91no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—31no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4—91no—
392C3×C22⋊C4C2×D911yescharacteristic, complemented
393C3×C22⋊C4D3211yescharacteristic
394#217—31no—
395#217—91no—
396#217—91no—
397#217—91no—
398#217—91no—
399#217—91no—
400#217—181no—
401#217C2×D911yescharacteristic, complemented
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—181no—
411(C2×D3)⋊C4C2×D911yescharacteristic, complemented
412(C2×D3)⋊C4C2×D911yescharacteristic, complemented
413C4⋊Dic3—31no—
414C4⋊Dic3—91no—
415C4⋊Dic3—91no—
416C4⋊Dic3—91no—
417C4⋊Dic3—91no—
418C4⋊Dic3—91no—
419C4⋊Dic3—181no—
420Dic3⋊C4—31no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4—91no—
428Dic3⋊C4—181no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32C23×D311yescharacteristic
433C2×C3⋊D3—32no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—32no—
440C2×C3×D3—44no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3#23512yes—
444C2×C3×D3D3×D412yes—
445C2×C3×D3#23712yes—
446D32—68no—
447C32×C4—21no—
448C32×C4—21no—
449C3⋊Dic3—61no—
450C3⋊Dic3—61no—
451C3⋊Dic3—61no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C22×C9—21no—
458C22×C9—21no—
459C22×C9—21no—
460C22×C9—21no—
461C22×C9—32no—
462C22×C9—32no—
463C22×C9—32no—
464C22×C9—41no—
465C22×C9—41no—
466C22×C9—41no—
467C22×C9—61no—
468C22×C9—61no—
469C22×C9—61no—
470C22×C9—124no—
471C22×C9C23×D311yescharacteristic
472C2×D9—21no—
473C2×D9—21no—
474C2×D9—32no—
475C2×D9—62no—
476C2×D9—68no—
477C2×D9—61no—
478C2×D9—61no—
479C2×D9—121no—
480C2×D9—121no—
481C2×D9D3×D412yes—
482C4×C9—21no—
483C4×C9—21no—
484C4×C9—41no—
485C4×C9—41no—
486C4×C9—61no—
487C4×C9—61no—
488Dic9—21no—
489Dic9—21no—
490Dic9—21no—
491Dic9—61no—
492Dic9—61no—
493Dic9—61no—
494Dic9—121no—
495Dic9—121no—
496Dic9—121no—
497C22×D4—271no—
498C23×C4—271no—
499#123—91no—
500#123—271no—
501#123—271no—
502#123—271no—
503#123—271no—
504#123—271no—
505#123—271no—
506#123—271no—
507C2×C4⋊C4—271no—
508C2×C4⋊C4—271no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—271no—
511C2×C22⋊C4—271no—
512C3×C9C2×#12311yescharacteristic, complemented, Sylow
513C23×C3—21no—
514C23×C3—31no—
515C23×C3—31no—
516C23×C3—62no—
517C23×C3—62no—
518C23×C3—62no—
519C23×C3—91no—
520C23×C3C22×D911yescharacteristic
521C23×C3C2×D3211yescharacteristic
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—31no—
526C22×D3—94no—
527C22×D3—91no—
528C22×D3—91no—
529C22×D3—94no—
530C22×D3—181no—
531C22×D3—182no—
532C22×D3—182no—
533C22×D3—182no—
534C22×D3—182no—
535C22×D3C22×D911yescharacteristic
536C22×D3C22×D911yescharacteristic
537C3×D4—182no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—62no—
543C2×C3×C4—62no—
544C2×C3×C4—91no—
545C2×C3×C4—91no—
546C2×C3×C4—91no—
547C2×C3×C4—182no—
548C2×C3×C4C22×D911yescharacteristic
549C2×C3×C4C22×D911yescharacteristic
550C2×C3×C4C2×D3211yescharacteristic
551C2×C3×C4C2×D3211yescharacteristic
552#67—62no—
553#67—182no—
554#67—182no—
555#67—182no—
556#67—182no—
557#67—182no—
558#67—362no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—181no—
569C2×Dic3—181no—
570C2×Dic3—181no—
571C2×Dic3—182no—
572C2×Dic3—182no—
573C2×Dic3—182no—
574C2×Dic3—182no—
575C2×Dic3C22×D911yescharacteristic
576C2×Dic3C22×D911yescharacteristic
577D12—182no—
578C4×D3—22no—
579C4×D3—22no—
580C4×D3—62no—
581C4×D3—182no—
582C4×D3—182no—
583C4×D3—182no—
584C4×D3—182no—
585C4×D3—182no—
586C4×D3—182no—
587C4×D3—182no—
588C4×D3—182no—
589C4×D3—362no—
590C2×C32—41no—
591C2×C32C2×#23511yescharacteristic
592C2×C32C2×D3×D411yescharacteristic
593C2×C32C2×#23711yescharacteristic
594C3⋊D3—62no—
595C3×D3—41no—
596C3×D3—62no—
597C3×D3#88314yes—
598C2×C9—21no—
599C2×C9—21no—
600C2×C9—21no—
601C2×C9—34no—
602C2×C9—41no—
603C2×C9—81no—
604C2×C9—121no—
605C2×C9C2×D3×D411yescharacteristic
606C2×C9D3×#4111yescharacteristic
607C2×C9D3×#4111yescharacteristic
608D9—22no—
609D9—62no—
610D9—122no—
611C24—31no—
612C24—271no—
613C2×D4—91no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—544no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—91no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—544no—
628C4⋊C4—91no—
629C4⋊C4—91no—
630C4⋊C4—271no—
631C4⋊C4—271no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4—271no—
635C4⋊C4—271no—
636C22⋊C4—31no—
637C22⋊C4—31no—
638C22⋊C4—31no—
639C22⋊C4—91no—
640C22⋊C4—91no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4D3×D911yescharacteristic, complemented
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—32no—
656C22×C3—32no—
657C22×C3—32no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—92no—
665C22×C3—124no—
666C22×C3—181no—
667C22×C3—181no—
668C22×C3C23×D911yescharacteristic
669C22×C3C22×D3211yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—32no—
674C2×D3—44no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—92no—
678C2×D3—92no—
679C2×D3—182no—
680C2×D3—188no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—181no—
684C2×D3—181no—
685C2×D3—188no—
686C2×D3—361no—
687C2×D3—361no—
688C2×D3#369712yes—
689C2×D3D4×D912yes—
690C2×D3#369912yes—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—61no—
698C3×C4—61no—
699C3×C4—181no—
700C3×C4—181no—
701C3×C4—181no—
702Dic3—21no—
703Dic3—21no—
704Dic3—61no—
705Dic3—61no—
706Dic3—61no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710Dic3—181no—
711Dic3—181no—
712Dic3—181no—
713Dic3—361no—
714Dic3—361no—
715Dic3—361no—
716C32C2×#88311yescharacteristic
717C9—21no—
718C9D3×#12311yescharacteristic, complemented
719C23—31no—
720C23—31no—
721C23—62no—
722C23—62no—
723C23—62no—
724C23—91no—
725C23—274no—
726C23—271no—
727C23—542no—
728C23—542no—
729C23C2×D3×D911yescharacteristic
730D4—182no—
731D4—542no—
732D4—542no—
733D4—542no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—91no—
739C2×C4—91no—
740C2×C4—91no—
741C2×C4—182no—
742C2×C4—271no—
743C2×C4—271no—
744C2×C4—271no—
745C2×C4—542no—
746C2×C4—542no—
747C2×C4—542no—
748C2×C4—542no—
749C2×C4—542no—
750C2×C4—542no—
751C2×C4C2×D3×D911yescharacteristic
752C2×C4C2×D3×D911yescharacteristic
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—34no—
757C2×C3—41no—
758C2×C3—41no—
759C2×C3—81no—
760C2×C3—121no—
761C2×C3—182no—
762C2×C3C2×#369711yescharacteristic
763C2×C3C2×D4×D911yescharacteristic
764C2×C3C2×#369911yescharacteristic
765C2×C3D3×#23511yescharacteristic
766C2×C3D32×D411yescharacteristic
767C2×C3D3×#23711yescharacteristic
768D3—41no—
769D3—62no—
770D3—182no—
771D3—182no—
772D3—362no—
773D3#6344514yesdirect product factor
774C22—21no—
775C22—21no—
776C22—21no—
777C22—32no—
778C22—32no—
779C22—32no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—92no—
784C22—124no—
785C22—181no—
786C22—181no—
787C22—272no—
788C22—548no—
789C22—541no—
790C22—541no—
791C22C22×D3×D911yescharacteristic
792C4—21no—
793C4—21no—
794C4—61no—
795C4—61no—
796C4—181no—
797C4—181no—
798C4—181no—
799C4—541no—
800C4—541no—
801C4—541no—
802C3—21no—
803C3C2×#6344511yescharacteristic, complemented
804C3D3×#88311yescharacteristic
805C2—34no—
806C2—41no—
807C2—121no—
808C2—182no—
809C2—542no—
810C2D3×#369711yescharacteristic
811C2D3×D4×D911yescharacteristic
812C2D3×#369911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC2×D3×#611C2
hypercenterC22⋊C4D3×D9
hypocenterC3×C9C2×#123
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×C4×D3×D9C2semidirect
3. #11721729C2semidirect
4. D3×C9×C22⋊C4C2semidirect
5. C3×#63445C2semidirect
6. D3×#3676C2semidirect
7. #11721275C2semidirect
8. #11721269C2semidirect
9. D3×(C2×D9)⋊C4C2semidirect
10. #11721031C2semidirect
11. D3×C4⋊Dic9C2semidirect
12. D3×Dic9⋊C4C2semidirect
13. #11720989C2semidirect
14. #11720958C2semidirect
15. #11720957C2semidirect
21. C2×C4×C3⋊D9C22semidirect
25. C2×C3×C4×D9C22semidirect
32. C2×(C3⋊D9)⋊C4C22semidirect
33. C2×Dic3×D9C22semidirect
35. C3×C9×C22⋊C4C22semidirect
36. #88551C22semidirect
37. #88536C22semidirect
38. C4⋊(C3⋊Dic9)C22semidirect
39. #88534C22semidirect
40. C9×#217C22semidirect
41. C3×#3676C22semidirect
42. C9×(C2×D3)⋊C4C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C3×C4⋊Dic9C22semidirect
46. C3×Dic9⋊C4C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. #88445C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. Dic3⋊Dic9C22semidirect
52. Dic3⋊Dic9C22semidirect
53. #88442C22semidirect
54. Dic9⋊Dic3C22semidirect
85. #63445D3direct (N × H)
177. C2×C4×D9C2×D3semidirect
182. C9×C22⋊C4C2×D3semidirect
187. #3676C2×D3semidirect
192. (C2×D9)⋊C4C2×D3semidirect
197. C4⋊Dic9C2×D3semidirect
202. Dic9⋊C4C2×D3semidirect
261. D3×C22⋊C4D9semidirect
346. D3×C9#123semidirect
392. C3×C22⋊C4C2×D9semidirect
401. #217C2×D9semidirect
411. (C2×D3)⋊C4C2×D9semidirect
412. (C2×D3)⋊C4C2×D9semidirect
512. C3×C9C2×#123semidirect
647. C22⋊C4D3×D9semidirect
718. C9D3×#123semidirect
773. D3#63445direct (N × H)
803. C3C2×#63445semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6112
C2×C4×D3×D92
#117217292
D3×C9×C22⋊C42
C3×#634452
D3×#36762
#117212752
#117212692
D3×(C2×D9)⋊C42
#117210312
D3×C4⋊Dic92
D3×Dic9⋊C42
#117209892
#117209582
#117209572
D3×#8833
C2×#634453