Finite Group Databasebeta

← #13148006

Subgroups — #13148006

Order 1728.

1068 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88662C211yesmaximal, characteristic, complemented
2C2×C4×D3×D9C211yesmaximal, characteristic, complemented
3#11721729C211yesmaximal, characteristic, complemented
4C9×#884C211yesmaximal, characteristic, complemented
5C3×#611⋊C4C211yesmaximal, characteristic, complemented
6#11721292C211yesmaximal, characteristic, complemented
7#67×Dic9C211yesmaximal, characteristic, complemented
8#11721270C211yesmaximal, characteristic, complemented
9#11721050C211yesmaximal, characteristic, complemented
10D12×Dic9C211yesmaximal, characteristic, complemented
11#11721012C211yesmaximal, characteristic, complemented
12#11720991C211yesmaximal, characteristic, complemented
13#11720957C211yesmaximal, characteristic, complemented
14#11720955C211yesmaximal, characteristic, complemented
15#11720899C211yesmaximal, characteristic, complemented
16#10594286—31nomaximal
17#10589708—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic, complemented
23C2×C3×#611C2211yescharacteristic
24C22×C3×Dic9C2211yescharacteristic, complemented
25C2×C9×D12C2211yescharacteristic
26C2×C4×D3×C9C2211yescharacteristic
27C2×C3×C4×D9C2211yescharacteristic
28C2×#6195C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30#88662—24no—
31C2×D3×Dic9C2211yescharacteristic
32C2×D3×Dic9C2211yescharacteristic, complemented
33C2×(C3⋊D9)⋊C4C2211yescharacteristic
34C2×Dic3×D9C2211yescharacteristic
35C2×#6189C2211yescharacteristic, complemented
36C4×D3×D9—24no—
37C3×C9×C22⋊C4C2211yescharacteristic, complemented
38#88551C2211yescharacteristic, complemented
39#88536C2211yescharacteristic
40C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
41#88534C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C9×Dic3⋊C4C2211yescharacteristic, complemented
45C3×Dic9⋊C4C2211yescharacteristic, complemented
46C3×C4×Dic9C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50#88445C2211yescharacteristic
51(C2×D9)⋊Dic3C2211yescharacteristic
52Dic3⋊Dic9C2211yescharacteristic, complemented
53Dic3⋊Dic9C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×#3804—31no—
56C2×C4×D32—31no—
57#64092—31no—
58C3×#884D311yescharacteristic
59C3×#67⋊C4—31no—
60#63983—31no—
61Dic3×#67—31no—
62#63970—31no—
63#63922—31no—
64#63893—31no—
65Dic3×D12—31no—
66#63879—31no—
67#63853—31no—
68#63851—31no—
69#63836—31no—
70C2×#3699—31no—
71C22×C4×D9—31no—
72C9×#121—31no—
73#63500—31no—
74#63499—31no—
75#63499—31no—
76D4×Dic9—31no—
77D4×Dic9—31no—
78#63486—31no—
79#63459—31no—
80#63454—31no—
81#63445—31no—
82#63445—31no—
83#63445—61no—
84#611⋊C4—31no—
85#611⋊C4D311yescharacteristic, complemented
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×D3×D9—22no—
92C2×D3×D9—22no—
93C2×D3×D9—22no—
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96#6233—22no—
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C4×C3⋊D9—22no—
101C9×#67—22no—
102C9×#67—22no—
103C3×#611—22no—
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C3×Dic9—22no—
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C9×D12—22no—
111C4×D3×C9—22no—
112C3×C4×D9—22no—
113#6195—22no—
114#6194—22no—
115D3×Dic9—22no—
116D3×Dic9—22no—
117(C3⋊D9)⋊C4D414yescomplemented
118Dic3×D9—22no—
119#6189—22no—
120#5606—91no—
121#5547—91no—
122C22×D32—31no—
123C2×#638—31no—
124C2×C4×C3⋊D3—31no—
125C2×C3×#67—31no—
126C2×C3×#67C2×D311yescharacteristic
127C2×C3×#67C2×D311yescharacteristic
128C22×C3×Dic3—31no—
129C2×C3×D12C2×D311yescharacteristic
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3C2×D311yescharacteristic
132C2×#627—31no—
133C2×#626—31no—
134C2×#625—31no—
135C2×#624—31no—
136#3804—64no—
137C2×D3×Dic3—31no—
138C2×D3×Dic3—31no—
139C2×D3×Dic3—31no—
140C4×D32—64no—
141C23×D9—31no—
142C32×C22⋊C4C2×D311yescharacteristic
143#3757—31no—
144#3752—31no—
145C4⋊(C3⋊Dic3)—31no—
146#3750—31no—
147C3×(C2×D3)⋊C4—31no—
148C3×(C2×D3)⋊C4C2×D311yescharacteristic
149C3×Dic3⋊C4—31no—
150C3×Dic3⋊C4C2×D311yescharacteristic
151C3×C4×Dic3—31no—
152Dic3⋊Dic3—31no—
153Dic3⋊Dic3—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—
160C2×D4×C9—31no—
161C2×D4×C9—31no—
162C2×D4×C9—31no—
163C22×C4×C9—31no—
164C2×#611—31no—
165C2×#611—31no—
166C2×#611—31no—
167C2×#611—61no—
168C2×#611C2×D311yescharacteristic
169C22×Dic9—31no—
170C22×Dic9—31no—
171C22×Dic9C2×D311yescharacteristic, complemented
172#3699—64no—
173C2×C4×D9—31no—
174C2×C4×D9—31no—
175C2×C4×D9—31no—
176C2×C4×D9—64no—
177C2×C4×D9—61no—
178C2×C4×D9C2×D311yescharacteristic
179C2×Dic18—31no—
180C9×C4⋊C4—31no—
181C9×C22⋊C4—21no—
182C9×C22⋊C4—31no—
183C9×C22⋊C4C2×D311yescharacteristic, complemented
184#3676—31no—
185#3676—31no—
186#3676—31no—
187#3676—31no—
188#3676—61no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—61no—
193(C2×D9)⋊C4C2×D311yescharacteristic
194C4⋊Dic9—31no—
195C4⋊Dic9—31no—
196C4⋊Dic9—31no—
197C4⋊Dic9—61no—
198Dic9⋊C4—31no—
199Dic9⋊C4—61no—
200Dic9⋊C4C2×D311yescharacteristic, complemented
201C4×Dic9—31no—
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⋊D9C2×D412yes—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9—21no—
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9#4112yescomplemented
216C2×C3×D9—21no—
217C2×C3×D9—21no—
218C2×C3×D9#4112yescomplemented
219D3×D9—28no—
220C3×C4×C9—21no—
221C3×C4×C9—21no—
222C3⋊Dic9—21no—
223C3⋊Dic9—21no—
224C3⋊Dic9—21no—
225C9×Dic3—21no—
226C9×Dic3C2×D412yes—
227C3×Dic9—21no—
228C3×Dic9—21no—
229C3×Dic9C2×D412yes—
230C2×#237—91no—
231C2×#235—91no—
232C22×C4×D3—91no—
233C22×C4×D3—91no—
234C3×#121—31no—
235C3×C4×D4—91no—
236#939—91no—
237#938—91no—
238#937—91no—
239#937—91no—
240#937—91no—
241D4×Dic3—91no—
242D4×Dic3—91no—
243C4×#67—91no—
244C4×#67—91no—
245#924—91no—
246#897—91no—
247#896—91no—
248#894—91no—
249#892—91no—
250#884D911yescharacteristic, complemented
251#883—91no—
252#883—91no—
253#883—91no—
254#883—181no—
255#882—91no—
256#67⋊C4—31no—
257#67⋊C4—91no—
258#878—91no—
259C4×D12—91no—
260#872—91no—
261C23×C32C22×D311yescharacteristic
262C22×C3⋊D3—31no—
263C22×C3×D3—31no—
264C22×C3×D3C22×D311yescharacteristic
265C22×C3×D3C22×D311yescharacteristic
266C2×D32—62no—
267C2×D32—62no—
268C2×D32—62no—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271#638—62no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C4×C3⋊D3—62no—
276C3×#67—22no—
277C3×#67—22no—
278C3×#67—62no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C3×D12—22no—
286C3×C4×D3—22no—
287C3×C4×D3—62no—
288#627—62no—
289#626—62no—
290#625—62no—
291#624—34no—
292D3×Dic3—62no—
293D3×Dic3—62no—
294D3×Dic3—62no—
295C23×C9—21no—
296C23×C9—31no—
297C23×C9—31no—
298C23×C9C22×D311yescharacteristic
299C22×D9—31no—
300C22×D9—61no—
301C22×D9—62no—
302C22×D9—62no—
303C22×D9—62no—
304C22×D9C22×D311yescharacteristic
305D4×C9—62no—
306D4×C9—62no—
307D4×C9—62no—
308C2×C4×C9—21no—
309C2×C4×C9—21no—
310C2×C4×C9—31no—
311C2×C4×C9—31no—
312C2×C4×C9—62no—
313C2×C4×C9C22×D311yescharacteristic
314C2×C4×C9C22×D311yescharacteristic
315#611—22no—
316#611—62no—
317#611—62no—
318#611—62no—
319#611—122no—
320C2×Dic9—22no—
321C2×Dic9—31no—
322C2×Dic9—31no—
323C2×Dic9—31no—
324C2×Dic9—61no—
325C2×Dic9—61no—
326C2×Dic9—61no—
327C2×Dic9—62no—
328C2×Dic9—62no—
329C2×Dic9C22×D311yescharacteristic
330C2×Dic9C22×D311yescharacteristic
331C2×Dic9C22×D311yescharacteristic
332C4×D9—22no—
333C4×D9—34no—
334C4×D9—62no—
335C4×D9—62no—
336C4×D9—122no—
337Dic18—62no—
338#525—271noSylow
339C2×C3×C9—41no—
340C2×C3×C9C22×D411yescharacteristic
341C2×C3×C9C2×#4111yescharacteristic
342C2×C3×C9C2×#4111yescharacteristic
343C3⋊D9—22no—
344D3×C9—22no—
345D3×C9—41no—
346C3×D9—22no—
347C23×D3—91no—
348C23×D3—91no—
349C2×C3×D4—31no—
350C2×C3×D4—31no—
351C2×C3×D4—31no—
352C2×C3×D4—91no—
353C22×C3×C4—31no—
354C22×C3×C4—91no—
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×#67C2×D911yescharacteristic
364C2×#67C2×D911yescharacteristic, complemented
365C22×Dic3—31no—
366C22×Dic3—91no—
367C22×Dic3—91no—
368C22×Dic3—91no—
369#237—184no—
370#235—184no—
371C2×D12—91no—
372C2×D12C2×D911yescharacteristic
373C2×C4×D3—31no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C2×C4×D3—181no—
382C2×C4×D3—184no—
383C2×C4×D3—184no—
384C2×C4×D3C2×D911yescharacteristic
385C2×Dic6—91no—
386C2×Dic6—91no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—91no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—91no—
392C3×C22⋊C4C2×D911yescharacteristic, complemented
393C3×C22⋊C4D3211yescharacteristic
394C3×C42—91no—
395#217—91no—
396#217—91no—
397#217—91no—
398#217—91no—
399#217—91no—
400#217—91no—
401#217—181no—
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—91no—
411(C2×D3)⋊C4—181no—
412(C2×D3)⋊C4C2×D911yescharacteristic, complemented
413C4⋊Dic3—91no—
414C4⋊Dic3—91no—
415C4⋊Dic3—91no—
416C4⋊Dic3—91no—
417C4⋊Dic3—181no—
418Dic3⋊C4—31no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—181no—
424Dic3⋊C4C2×D911yescharacteristic, complemented
425C4×Dic3—31no—
426C4×Dic3—91no—
427C4×Dic3—91no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32C23×D311yescharacteristic
432C2×C3⋊D3—32no—
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—32no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3#23712yes—
444D32—68no—
445C32×C4—21no—
446C32×C4—21no—
447C3⋊Dic3—61no—
448C3⋊Dic3—61no—
449C3⋊Dic3—61no—
450C3×Dic3—21no—
451C3×Dic3—32no—
452C3×Dic3—61no—
453C3×Dic3—61no—
454C3×Dic3D3×D412yes—
455C22×C9—21no—
456C22×C9—21no—
457C22×C9—21no—
458C22×C9—21no—
459C22×C9—32no—
460C22×C9—41no—
461C22×C9—41no—
462C22×C9—41no—
463C22×C9—61no—
464C22×C9—61no—
465C22×C9—61no—
466C22×C9—61no—
467C22×C9—61no—
468C22×C9C23×D311yescharacteristic
469C2×D9—21no—
470C2×D9—21no—
471C2×D9—32no—
472C2×D9—62no—
473C2×D9—68no—
474C2×D9—61no—
475C2×D9—61no—
476C2×D9—121no—
477C2×D9—121no—
478C2×D9#23512yescomplemented
479C4×C9—21no—
480C4×C9—21no—
481C4×C9—32no—
482C4×C9—41no—
483C4×C9—41no—
484C4×C9—61no—
485Dic9—21no—
486Dic9—21no—
487Dic9—61no—
488Dic9—61no—
489Dic9—61no—
490Dic9—121no—
491Dic9—121no—
492Dic9—121no—
493Dic9D3×D412yes—
494C2×#41—271no—
495C23×C4—271no—
496#123—271no—
497#123—271no—
498C22⋊Q8—271no—
499C22⋊Q8—271no—
500#121—31no—
501#121—271no—
502#120—271no—
503#120—271no—
504C4×D4—91no—
505C4×D4—271no—
506C4×D4—271no—
507C4×D4—271no—
508#117—271no—
509C3×C9#52511yescharacteristic, complemented, Sylow
510C23×C3—21no—
511C23×C3—31no—
512C23×C3—31no—
513C23×C3—91no—
514C23×C3C22×D911yescharacteristic
515C23×C3C2×D3211yescharacteristic
516C22×D3—31no—
517C22×D3—91no—
518C22×D3—91no—
519C22×D3—181no—
520C22×D3—182no—
521C22×D3—182no—
522C22×D3—182no—
523C22×D3—182no—
524C22×D3—182no—
525C22×D3—182no—
526C22×D3C22×D911yescharacteristic
527C22×D3C22×D911yescharacteristic
528C3×D4—62no—
529C3×D4—62no—
530C3×D4—62no—
531C3×D4—182no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—62no—
537C2×C3×C4—91no—
538C2×C3×C4—91no—
539C2×C3×C4—91no—
540C2×C3×C4—182no—
541C2×C3×C4—182no—
542C2×C3×C4C22×D911yescharacteristic
543C2×C3×C4C22×D911yescharacteristic
544C2×C3×C4C2×D3211yescharacteristic
545C2×C3×C4C2×D3211yescharacteristic
546#67—22no—
547#67—22no—
548#67—62no—
549#67—182no—
550#67—182no—
551#67—182no—
552#67—182no—
553#67—182no—
554#67—362no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—62no—
559C2×Dic3—91no—
560C2×Dic3—91no—
561C2×Dic3—91no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—181no—
566C2×Dic3—181no—
567C2×Dic3—181no—
568C2×Dic3—182no—
569C2×Dic3—182no—
570C2×Dic3—182no—
571C2×Dic3C22×D911yescharacteristic
572C2×Dic3C22×D911yescharacteristic
573D12—22no—
574D12—182no—
575C4×D3—22no—
576C4×D3—62no—
577C4×D3—94no—
578C4×D3—94no—
579C4×D3—182no—
580C4×D3—182no—
581C4×D3—182no—
582C4×D3—182no—
583C4×D3—182no—
584C4×D3—362no—
585Dic6—182no—
586Dic6—182no—
587C2×C32—41no—
588C2×C32C2×D3×D411yescharacteristic
589C2×C32C2×#23711yescharacteristic
590C2×C32D3×#4111yescharacteristic
591C3⋊D3—62no—
592C3×D3—22no—
593C3×D3—41no—
594C3×D3—62no—
595C2×C9—21no—
596C2×C9—21no—
597C2×C9—21no—
598C2×C9—41no—
599C2×C9—62no—
600C2×C9—81no—
601C2×C9—121no—
602C2×C9C2×#23511yescharacteristic
603C2×C9C2×D3×D411yescharacteristic
604C2×C9D3×#4111yescharacteristic
605D9—22no—
606D9—62no—
607D9—122no—
608C24—271no—
609#41—544no—
610C2×Q8—271no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—31no—
614C2×D4—91no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C22×C4—31no—
619C22×C4—91no—
620C22×C4—91no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—544no—
627C4⋊C4—31no—
628C4⋊C4—91no—
629C4⋊C4—271no—
630C4⋊C4—271no—
631C4⋊C4—271no—
632C4⋊C4—271no—
633C22⋊C4—31no—
634C22⋊C4—91no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4D3×D911yescharacteristic, complemented
643C42—91no—
644C42—271no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—32no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—92no—
662C22×C3—181no—
663C22×C3—181no—
664C22×C3C23×D911yescharacteristic
665C22×C3C22×D3211yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—32no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—92no—
675C2×D3—92no—
676C2×D3—182no—
677C2×D3—188no—
678C2×D3—188no—
679C2×D3—181no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—361no—
684C2×D3—361no—
685C2×D3#369912yescomplemented
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—32no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—61no—
694C3×C4—92no—
695C3×C4—181no—
696C3×C4—181no—
697Dic3—21no—
698Dic3—32no—
699Dic3—61no—
700Dic3—61no—
701Dic3—181no—
702Dic3—181no—
703Dic3—181no—
704Dic3—181no—
705Dic3—181no—
706Dic3—181no—
707Dic3—361no—
708Dic3—361no—
709Dic3—361no—
710Dic3D4×D912yes—
711C32#560611yescharacteristic
712C9—21no—
713C9#554711yescharacteristic, complemented
714C23—31no—
715C23—31no—
716C23—91no—
717C23—271no—
718C23—542no—
719C23—542no—
720C23—542no—
721C23C2×D3×D911yescharacteristic
722Q8—542no—
723D4—62no—
724D4—62no—
725D4—62no—
726D4—182no—
727D4—542no—
728D4—542no—
729D4—542no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—62no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—182no—
737C2×C4—182no—
738C2×C4—274no—
739C2×C4—271no—
740C2×C4—271no—
741C2×C4—271no—
742C2×C4—542no—
743C2×C4—542no—
744C2×C4—542no—
745C2×C4—542no—
746C2×C4C2×D3×D911yescharacteristic
747C2×C4C2×D3×D911yescharacteristic
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—41no—
752C2×C3—41no—
753C2×C3—62no—
754C2×C3—81no—
755C2×C3—121no—
756C2×C3—182no—
757C2×C3C2×D4×D911yescharacteristic
758C2×C3C2×#369911yescharacteristic
759C2×C3#41×D911yescharacteristic
760C2×C3D3×#23511yescharacteristic
761C2×C3D32×D411yescharacteristic
762C2×C3D3×#23711yescharacteristic
763D3—22no—
764D3—41no—
765D3—62no—
766D3—182no—
767D3—182no—
768D3—362no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—32no—
773C22—61no—
774C22—61no—
775C22—61no—
776C22—61no—
777C22—61no—
778C22—92no—
779C22—181no—
780C22—181no—
781C22—272no—
782C22—548no—
783C22—541no—
784C22—541no—
785C22C22×D3×D911yescharacteristic
786C4—21no—
787C4—21no—
788C4—32no—
789C4—61no—
790C4—92no—
791C4—181no—
792C4—181no—
793C4—541no—
794C4—541no—
795C4—541no—
796C3—21no—
797C3#1058970811yescharacteristic, complemented
798C3#1059428611yescharacteristic
799C2—41no—
800C2—62no—
801C2—121no—
802C2—182no—
803C2—542no—
804C2D9×#23511yescharacteristic
805C2D3×D4×D911yescharacteristic
806C2D3×#369911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#525
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. C2×#88662C2semidirect
2. C2×C4×D3×D9C2semidirect
3. #11721729C2semidirect
4. C9×#884C2semidirect
5. C3×#611⋊C4C2semidirect
6. #11721292C2semidirect
7. #67×Dic9C2semidirect
8. #11721270C2semidirect
9. #11721050C2semidirect
10. D12×Dic9C2semidirect
11. #11721012C2semidirect
12. #11720991C2semidirect
13. #11720957C2semidirect
14. #11720955C2semidirect
15. #11720899C2semidirect
22. C2×C9×#67C22semidirect
24. C22×C3×Dic9C22semidirect
32. C2×D3×Dic9C22semidirect
35. C2×#6189C22semidirect
37. C3×C9×C22⋊C4C22semidirect
38. #88551C22semidirect
40. C4⋊(C3⋊Dic9)C22semidirect
41. #88534C22semidirect
42. C9×(C2×D3)⋊C4C22semidirect
44. C9×Dic3⋊C4C22semidirect
45. C3×Dic9⋊C4C22semidirect
46. C3×C4×Dic9C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
52. Dic3⋊Dic9C22semidirect
53. Dic3⋊Dic9C22semidirect
54. Dic3×Dic9C22semidirect
85. #611⋊C4D3semidirect
117. (C3⋊D9)⋊C4D4semidirect
171. C22×Dic9C2×D3semidirect
183. C9×C22⋊C4C2×D3semidirect
200. Dic9⋊C4C2×D3semidirect
202. C4×Dic9C2×D3semidirect
215. C2×D3×C9#41semidirect
218. C2×C3×D9#41semidirect
250. #884D9semidirect
364. C2×#67C2×D9semidirect
392. C3×C22⋊C4C2×D9semidirect
412. (C2×D3)⋊C4C2×D9semidirect
424. Dic3⋊C4C2×D9semidirect
478. C2×D9#235semidirect
509. C3×C9#525semidirect
642. C22⋊C4D3×D9semidirect
685. C2×D3#3699semidirect
713. C9#5547semidirect
797. C3#10589708semidirect

Maximal subgroups

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

subgroupindex
C2×#886622
C2×C4×D3×D92
#117217292
C9×#8842
C3×#611⋊C42
#117212922
#67×Dic92
#117212702
#117210502
D12×Dic92
#117210122
#117209912
#117209572
#117209552
#117208992
#105942863
#105897083