Finite Group Databasebeta

← D3×#63447 #13148200

Subgroups — D3×#63447 #13148200

Order 1728.

1066 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×D3×Dic18C211yesmaximal, characteristic, complemented
3#11721731C211yesmaximal, characteristic, complemented
4D3×C9×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#63447C211yesmaximal, characteristic, complemented
6D3×#3676C211yesmaximal, characteristic, complemented
7#11721257C211yesmaximal, characteristic, complemented
8#11721242C211yesmaximal, characteristic, complemented
9D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
10D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
11#11721044C211yesmaximal, characteristic, complemented
12#11721042C211yesmaximal, characteristic, complemented
13#11721035C211yesmaximal, characteristic, complemented
14C4×D3×Dic9C211yesmaximal, characteristic, complemented
15#11720956C211yesmaximal, characteristic, complemented
16D3×#885—31nomaximal
17C2×#63447—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6226C2211yescharacteristic, complemented
22C2×C3×#611C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic
25C2×C3×Dic18C2211yescharacteristic, complemented
26D3×#611—24no—
27C2×#6195C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×D3×Dic9C2211yescharacteristic
30C2×D3×Dic9C2211yescharacteristic
31C2×D3×Dic9C2211yescharacteristic
32C2×#6189C2211yescharacteristic, complemented
33C2×#6189C2211yescharacteristic, complemented
34D3×Dic18—24no—
35C3×C9×C22⋊C4C2211yescharacteristic, complemented
36#88551C2211yescharacteristic, complemented
37#88536C2211yescharacteristic, complemented
38#88536C2211yescharacteristic, complemented
39C4×C3⋊Dic9C2211yescharacteristic, complemented
40C9×#217C2211yescharacteristic, complemented
41C3×#3676C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×C4×Dic9C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic3×Dic9C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×D3×Dic6—31no—
57#64094—31no—
58C3×#885—31no—
59C3×D3×C22⋊C4D311yescharacteristic
60D3×#217—31no—
61#63959—31no—
62#63953—31no—
63D3×(C2×D3)⋊C4—31no—
64D3×(C2×D3)⋊C4—31no—
65#63915—31no—
66#63913—31no—
67#63907—31no—
68C4×D3×Dic3—31no—
69#63852—31no—
70C22×#611—31no—
71C22×Dic18—31no—
72C2×C9×C22⋊C4—31no—
73C2×#3676—31no—
74C2×(C2×D9)⋊C4—31no—
75C2×(C2×D9)⋊C4—31no—
76C2×C4×Dic9—31no—
77#63447—31no—
78#63447—31no—
79#63447—31no—
80#63447—31no—
81#63447—31no—
82#63447—31no—
83#63447—31no—
84#63447—61no—
85#63447D311yescharacteristic, 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×D9—22no—
97C2×C3×C4×C9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99#6233—22no—
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103#6226—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×Dic18—22no—
113#6195—22no—
114#6194—22no—
115D3×Dic9—22no—
116D3×Dic9—22no—
117D3×Dic9D414yes—
118#6189—22no—
119#6189—22no—
120D3×#124—91no—
121C2×#885—91no—
122C23×C3×D3C2×D311yescharacteristic
123C22×D32—31no—
124C2×#638—31no—
125C2×#634—31no—
126C2×C3×#67—31no—
127C2×C3×C4×D3C2×D311yescharacteristic
128C2×C3×C4×D3C2×D311yescharacteristic
129C2×C3×Dic6—31no—
130D3×#67—64no—
131C2×#627—31no—
132C2×#627—31no—
133C2×#626—31no—
134C2×#625—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137C2×D3×Dic3—31no—
138D3×Dic6—64no—
139C24×C9—31no—
140C23×D9—31no—
141C32×C22⋊C4C2×D311yescharacteristic
142#3757—31no—
143#3752—31no—
144#3752—31no—
145C4×C3⋊Dic3—31no—
146C3×#217—31no—
147C3×#217C2×D311yescharacteristic
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4—31no—
150C3×(C2×D3)⋊C4C2×D311yescharacteristic
151C3×(C2×D3)⋊C4C2×D311yescharacteristic
152C3×C4×Dic3—31no—
153#3722—31no—
154#3722—31no—
155(C2×D3)⋊Dic3—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159Dic32—31no—
160Dic32—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×Dic18—31no—
173C2×Dic18—31no—
174C2×Dic18—31no—
175C2×Dic18—64no—
176C2×Dic18—61no—
177C2×Dic18C2×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—31no—
192(C2×D9)⋊C4—31no—
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—61no—
195(C2×D9)⋊C4—61no—
196(C2×D9)⋊C4C2×D311yescharacteristic, complemented
197(C2×D9)⋊C4C2×D311yescharacteristic, complemented
198C4×Dic9—31no—
199C4×Dic9—31no—
200C4×Dic9—31no—
201C4×Dic9—61no—
202C4×Dic9C2×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⋊D9—21no—
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×D9—21no—
220D3×D9—44no—
221C3×C4×C9—21no—
222C3×C4×C9—21no—
223C3⋊Dic9—21no—
224C3⋊Dic9—21no—
225C3⋊Dic9C2×D412yes—
226C9×Dic3—21no—
227C9×Dic3—21no—
228C3×Dic9—21no—
229C3×Dic9—21no—
230C3×Dic9C2×D412yes—
231C22×#67—91no—
232C2×D3×Q8—91no—
233C2×D3×D4—91no—
234C22×Dic6—91no—
235C3×#124—91no—
236C2×C3×C22⋊C4—31no—
237C2×#217—91no—
238#947—91no—
239#936—91no—
240C2×(C2×D3)⋊C4—91no—
241C2×(C2×D3)⋊C4—91no—
242C2×C4×Dic3—91no—
243#885—31no—
244#885—91no—
245#885—91no—
246#885—91no—
247#885—91no—
248#885—91no—
249#885—91no—
250#885—91no—
251#885—91no—
252#885—91no—
253#885—91no—
254#885—91no—
255#885—181no—
256D3×C22⋊C4—91no—
257D3×C22⋊C4—91no—
258D3×C22⋊C4—91no—
259D3×C22⋊C4D911yescharacteristic, complemented
260#875—91no—
261C42×D3—91no—
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—62no—
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—
279#634—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×Dic6—62no—
289#627—62no—
290#627—62no—
291#626—62no—
292#625—62no—
293D3×Dic3—34no—
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—61no—
305C22×D9—62no—
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—34no—
324C2×Dic9—31no—
325C2×Dic9—31no—
326C2×Dic9—61no—
327C2×Dic9—61no—
328C2×Dic9—61no—
329C2×Dic9—62no—
330C2×Dic9—62no—
331C2×Dic9C22×D311yescharacteristic
332C2×Dic9C22×D311yescharacteristic
333C2×Dic9C22×D311yescharacteristic
334Dic18—22no—
335Dic18—62no—
336Dic18—62no—
337Dic18—62no—
338Dic18—122no—
339C2×#124—271noSylow
340C2×C3×C9—41no—
341C2×C3×C9C22×D411yescharacteristic
342C2×C3×C9C2×#4111yescharacteristic
343C2×C3×C9C2×#4111yescharacteristic
344C3⋊D9—41no—
345D3×C9—41no—
346D3×C9#12414yescomplemented
347C3×D9—41no—
348C24×C3—31no—
349C23×D3—91no—
350C23×D3—91no—
351C23×D3C2×D911yescharacteristic
352C2×C3×Q8—91no—
353C2×C3×D4—91no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
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—
367D3×Q8—184no—
368D3×D4—184no—
369C2×D12—91no—
370C2×C4×D3—91no—
371C2×C4×D3—91no—
372C2×C4×D3—91no—
373C2×C4×D3C2×D911yescharacteristic
374C2×C4×D3C2×D911yescharacteristic
375C2×Dic6—31no—
376C2×Dic6—91no—
377C2×Dic6—91no—
378C2×Dic6—91no—
379C2×Dic6—91no—
380C2×Dic6—91no—
381C2×Dic6—91no—
382C2×Dic6—181no—
383C2×Dic6—184no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4—31no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—91no—
389C3×C22⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4C2×D911yescharacteristic, complemented
392C3×C22⋊C4D3211yescharacteristic
393C3×C42—91no—
394#217—31no—
395#217—91no—
396#217—91no—
397#217—91no—
398#217—91no—
399#217—91no—
400#217—91no—
401#217—181no—
402#217C2×D911yescharacteristic, complemented
403(C2×D3)⋊C4—31no—
404(C2×D3)⋊C4—31no—
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—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415(C2×D3)⋊C4—91no—
416(C2×D3)⋊C4—91no—
417(C2×D3)⋊C4—181no—
418(C2×D3)⋊C4—181no—
419(C2×D3)⋊C4C2×D911yescharacteristic, complemented
420(C2×D3)⋊C4C2×D911yescharacteristic, complemented
421C4×Dic3—31no—
422C4×Dic3—91no—
423C4×Dic3—91no—
424C4×Dic3—91no—
425C4×Dic3—91no—
426C4×Dic3—91no—
427C4×Dic3—91no—
428C4×Dic3—181no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32C23×D311yescharacteristic
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—44no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3#23512yes—
444C2×C3×D3D3×D412yes—
445C2×C3×D3#23712yes—
446D32—124no—
447C32×C4—21no—
448C32×C4—21no—
449C3⋊Dic3—32no—
450C3⋊Dic3—61no—
451C3⋊Dic3—61no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—32no—
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—21no—
475C2×D9—61no—
476C2×D9—61no—
477C2×D9—61no—
478C2×D9—121no—
479C2×D9—121no—
480C2×D9—121no—
481C2×D9—124no—
482C4×C9—21no—
483C4×C9—21no—
484C4×C9—41no—
485C4×C9—41no—
486C4×C9—61no—
487C4×C9—61no—
488Dic9—21no—
489Dic9—21no—
490Dic9—32no—
491Dic9—62no—
492Dic9—61no—
493Dic9—61no—
494Dic9—121no—
495Dic9—121no—
496Dic9D3×D412yes—
497C22×Q8—271no—
498C22×D4—271no—
499#124—91no—
500#124—271no—
501#124—271no—
502#124—271no—
503#124—271no—
504#124—271no—
505#124—271no—
506#124—271no—
507C2×C22⋊C4—31no—
508C2×C22⋊C4—271no—
509C2×C22⋊C4—271no—
510C2×C22⋊C4—271no—
511C2×C42—271no—
512C3×C9C2×#12411yescharacteristic, 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—91no—
527C22×D3—91no—
528C22×D3—181no—
529C22×D3—182no—
530C22×D3—182no—
531C22×D3—182no—
532C22×D3—182no—
533C22×D3—182no—
534C22×D3—182no—
535C22×D3C22×D911yescharacteristic
536C22×D3C22×D911yescharacteristic
537C3×Q8—182no—
538C3×D4—182no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—62no—
544C2×C3×C4—62no—
545C2×C3×C4—91no—
546C2×C3×C4—91no—
547C2×C3×C4—91no—
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—94no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—91no—
569C2×Dic3—181no—
570C2×Dic3—181no—
571C2×Dic3—181no—
572C2×Dic3—182no—
573C2×Dic3—182no—
574C2×Dic3C22×D911yescharacteristic
575C2×Dic3C22×D911yescharacteristic
576D12—182no—
577C4×D3—22no—
578C4×D3—22no—
579C4×D3—94no—
580C4×D3—182no—
581C4×D3—182no—
582Dic6—62no—
583Dic6—182no—
584Dic6—182no—
585Dic6—182no—
586Dic6—182no—
587Dic6—182no—
588Dic6—182no—
589Dic6—362no—
590C2×C32—41no—
591C2×C32C2×#23511yescharacteristic
592C2×C32C2×D3×D411yescharacteristic
593C2×C32C2×#23711yescharacteristic
594C3⋊D3—121no—
595C3×D3—41no—
596C3×D3—121no—
597C3×D3#88514yes—
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—41no—
609D9—121no—
610D9—241no—
611C24—31no—
612C24—271no—
613C2×Q8—91no—
614C2×Q8—271no—
615C2×Q8—271no—
616C2×Q8—271no—
617C2×Q8—544no—
618C2×D4—91no—
619C2×D4—271no—
620C2×D4—271no—
621C2×D4—271no—
622C2×D4—544no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—271no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—31no—
631C22⋊C4—91no—
632C22⋊C4—91no—
633C22⋊C4—91no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4D3×D911yescharacteristic, complemented
644C42—91no—
645C42—271no—
646C42—271no—
647C42—271no—
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—124no—
665C22×C3—181no—
666C22×C3—181no—
667C22×C3—181no—
668C22×C3C23×D911yescharacteristic
669C22×C3C22×D3211yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—44no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—181no—
678C2×D3—181no—
679C2×D3—181no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—361no—
684C2×D3—361no—
685C2×D3—361no—
686C2×D3—364no—
687C2×D3—364no—
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—92no—
700C3×C4—181no—
701C3×C4—181no—
702Dic3—21no—
703Dic3—21no—
704Dic3—32no—
705Dic3—61no—
706Dic3—61no—
707Dic3—92no—
708Dic3—92no—
709Dic3—182no—
710Dic3—181no—
711Dic3—181no—
712Dic3—181no—
713Dic3—181no—
714Dic3—361no—
715Dic3—361no—
716C32C2×#88511yescharacteristic
717C9—21no—
718C9D3×#12411yescharacteristic, complemented
719C23—31no—
720C23—31no—
721C23—62no—
722C23—62no—
723C23—62no—
724C23—91no—
725C23—271no—
726C23—542no—
727C23—542no—
728C23—542no—
729C23C2×D3×D911yescharacteristic
730Q8—182no—
731Q8—542no—
732Q8—542no—
733Q8—542no—
734D4—182no—
735D4—542no—
736D4—542no—
737D4—542no—
738C2×C4—31no—
739C2×C4—31no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—91no—
743C2×C4—91no—
744C2×C4—91no—
745C2×C4—274no—
746C2×C4—271no—
747C2×C4—271no—
748C2×C4—271no—
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—361no—
762C2×C3C2×#369711yescharacteristic
763C2×C3C2×D4×D911yescharacteristic
764C2×C3C2×#369911yescharacteristic
765C2×C3D3×#23511yescharacteristic
766C2×C3D32×D411yescharacteristic
767C2×C3D3×#23711yescharacteristic
768D3—41no—
769D3—121no—
770D3—361no—
771D3—361no—
772D3—721no—
773D3#6344714yesdirect product factor
774C22—21no—
775C22—21no—
776C22—21no—
777C22—32no—
778C22—32no—
779C22—32no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—124no—
784C22—181no—
785C22—181no—
786C22—181no—
787C22—541no—
788C22—541no—
789C22—541no—
790C22—1084no—
791C22C22×D3×D911yescharacteristic
792C4—21no—
793C4—21no—
794C4—61no—
795C4—61no—
796C4—92no—
797C4—181no—
798C4—181no—
799C4—272no—
800C4—541no—
801C4—541no—
802C3—21no—
803C3C2×#6344711yescharacteristic, complemented
804C3D3×#88511yescharacteristic
805C2—34no—
806C2—41no—
807C2—121no—
808C2—361no—
809C2—1081no—
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×#124
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. #11721731C2semidirect
4. D3×C9×C22⋊C4C2semidirect
5. C3×#63447C2semidirect
6. D3×#3676C2semidirect
7. #11721257C2semidirect
8. #11721242C2semidirect
9. D3×(C2×D9)⋊C4C2semidirect
10. D3×(C2×D9)⋊C4C2semidirect
11. #11721044C2semidirect
12. #11721042C2semidirect
13. #11721035C2semidirect
14. C4×D3×Dic9C2semidirect
15. #11720956C2semidirect
21. C2×#6226C22semidirect
25. C2×C3×Dic18C22semidirect
32. C2×#6189C22semidirect
33. C2×#6189C22semidirect
35. C3×C9×C22⋊C4C22semidirect
36. #88551C22semidirect
37. #88536C22semidirect
38. #88536C22semidirect
39. C4×C3⋊Dic9C22semidirect
40. C9×#217C22semidirect
41. C3×#3676C22semidirect
42. C9×(C2×D3)⋊C4C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×C4×Dic9C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. #88445C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic3×Dic9C22semidirect
54. Dic3×Dic9C22semidirect
85. #63447D3direct (N × H)
177. C2×Dic18C2×D3semidirect
182. C9×C22⋊C4C2×D3semidirect
187. #3676C2×D3semidirect
196. (C2×D9)⋊C4C2×D3semidirect
197. (C2×D9)⋊C4C2×D3semidirect
202. C4×Dic9C2×D3semidirect
259. D3×C22⋊C4D9semidirect
346. D3×C9#124semidirect
391. C3×C22⋊C4C2×D9semidirect
402. #217C2×D9semidirect
419. (C2×D3)⋊C4C2×D9semidirect
420. (C2×D3)⋊C4C2×D9semidirect
512. C3×C9C2×#124semidirect
643. C22⋊C4D3×D9semidirect
718. C9D3×#124semidirect
773. D3#63447direct (N × H)
803. C3C2×#63447semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6112
C2×D3×Dic182
#117217312
D3×C9×C22⋊C42
C3×#634472
D3×#36762
#117212572
#117212422
D3×(C2×D9)⋊C42
#117210442
#117210422
#117210352
C4×D3×Dic92
#117209562
D3×#8853
C2×#634473