Finite Group Databasebeta

← #13148408

Subgroups — #13148408

Order 1728.

1116 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#611C211yesmaximal, characteristic, complemented
2C2×#88646C211yesmaximal, characteristic, complemented
3#11721729C211yesmaximal, characteristic, complemented
4C9×#882C211yesmaximal, characteristic, complemented
5C3×#63446C211yesmaximal, characteristic, complemented
6#11721292C211yesmaximal, characteristic, complemented
7#11721286C211yesmaximal, characteristic, complemented
8#11721270C211yesmaximal, characteristic, complemented
9#11721050C211yesmaximal, characteristic, complemented
10D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#11721036C211yesmaximal, characteristic, complemented
12#11721021C211yesmaximal, characteristic, complemented
13#11721015C211yesmaximal, characteristic, complemented
14#11720982C211yesmaximal, characteristic, complemented
15#11720957C211yesmaximal, characteristic, complemented
16#10594263—31nomaximal
17#10589691—31nomaximal
18C23×D3×C9C2211yescharacteristic, complemented
19C22×D3×D9C2211yescharacteristic
20C22×D3×D9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic
22C2×C4×C3⋊D9C2211yescharacteristic, complemented
23C2×C9×#67C2211yescharacteristic, complemented
24C2×C3×#611C2211yescharacteristic, complemented
25C2×C3×#611C2211yescharacteristic, complemented
26C2×C9×D12C2211yescharacteristic
27C2×C9×D12C2211yescharacteristic, complemented
28C2×C3×D36C2211yescharacteristic, complemented
29C2×C3×C4×D9C2211yescharacteristic, complemented
30D3×#611—24no—
31C2×#6195C2211yescharacteristic
32C2×#6194C2211yescharacteristic
33C2×#6194C2211yescharacteristic, complemented
34C2×#6194C2211yescharacteristic, complemented
35C2×#6194C2211yescharacteristic, complemented
36C2×D3×Dic9C2211yescharacteristic, complemented
37C2×Dic3×D9C2211yescharacteristic, complemented
38#88646—24no—
39C3×C9×C22⋊C4C2211yescharacteristic, complemented
40#88551C2211yescharacteristic, complemented
41#88536C2211yescharacteristic, complemented
42C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
43#88534C2211yescharacteristic, complemented
44C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C3×Dic9⋊C4C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51(C2×D3)⋊Dic9C2211yescharacteristic, complemented
52#88445C2211yescharacteristic, complemented
53(C2×D9)⋊Dic3C2211yescharacteristic, complemented
54Dic3⋊Dic9C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3802—31no—
57#64092—31no—
58C3×#884—31no—
59C3×#882D311yescharacteristic
60#63983—31no—
61#63976—31no—
62#63970—31no—
63#63922—31no—
64D3×(C2×D3)⋊C4—31no—
65#63908—31no—
66#63891—31no—
67#63885—31no—
68#63884—31no—
69#63853—31no—
70C22×#611—31no—
71C2×D4×D9—31no—
72C9×#120—31no—
73#63515—31no—
74#63500—31no—
75#63500—31no—
76#63499—31no—
77#63499—31no—
78#63497—31no—
79#63448—31no—
80#63446—31no—
81#63446D311yescharacteristic, complemented
82#63445—31no—
83#63445—31no—
84#63445—61no—
85C22⋊C4×D9—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9—22no—
89C22×D3×C9—41no—
90C22×D3×C9—41no—
91C22×D3×C9C2311yescharacteristic
92C22×D3×C9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C22×C3×D9C2311yescharacteristic
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×D3×D9—41no—
99C2×D3×D9—41no—
100C2×D3×D9—41no—
101C2×D3×D9D414yescomplemented
102C2×C3×C4×C9C2311yescharacteristic
103C2×C3×C4×C9C2311yescharacteristic
104#6233—22no—
105C2×C3⋊Dic9C2311yescharacteristic
106C2×C3⋊Dic9C2311yescharacteristic
107C2×C3⋊Dic9C2311yescharacteristic
108C4×C3⋊D9—22no—
109C9×#67—41no—
110C3×#611—22no—
111C3×#611—41no—
112C2×C9×Dic3C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114C2×C3×Dic9C2311yescharacteristic
115C9×D12—22no—
116C9×D12—41no—
117C3×D36—22no—
118C3×C4×D9—41no—
119#6195—22no—
120#6194—22no—
121#6194—22no—
122#6194—22no—
123#6194—41no—
124D3×Dic9—22no—
125Dic3×D9—41no—
126#5605—91no—
127#5589—91no—
128C23×C3×D3C2×D311yescharacteristic
129C22×D32—31no—
130C22×D32—31no—
131C2×#638—31no—
132C2×C4×C3⋊D3—31no—
133C2×C3×#67—31no—
134C2×C3×#67—31no—
135C2×C3×#67C2×D311yescharacteristic
136C2×C3×D12—31no—
137C2×C3×D12C2×D311yescharacteristic
138C2×C3×D12C2×D311yescharacteristic
139C2×C3×C4×D3—31no—
140D3×#67—64no—
141C2×#626—31no—
142C2×#625—31no—
143C2×#625—31no—
144C2×#625—31no—
145C2×#625—31no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—31no—
148#3802—64no—
149C24×C9—31no—
150C23×D9—31no—
151C23×D9—31no—
152C32×C22⋊C4C2×D311yescharacteristic
153#3757—31no—
154#3752—31no—
155C4⋊(C3⋊Dic3)—31no—
156#3750—31no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4C2×D311yescharacteristic
159C3×(C2×D3)⋊C4C2×D311yescharacteristic
160C3×Dic3⋊C4—31no—
161Dic3⋊Dic3—31no—
162#3722—31no—
163(C2×D3)⋊Dic3—31no—
164(C2×D3)⋊Dic3—31no—
165(C2×D3)⋊Dic3—31no—
166(C2×D3)⋊Dic3—31no—
167(C2×D3)⋊Dic3—31no—
168C2×D4×C9—31no—
169C2×D4×C9—31no—
170C2×D4×C9—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—31no—
174C2×#611—31no—
175C2×#611—31no—
176C2×#611—31no—
177C2×#611—64no—
178C2×#611—61no—
179C2×#611C2×D311yescharacteristic, complemented
180C2×#611C2×D311yescharacteristic, complemented
181C22×Dic9—31no—
182D4×D9—64no—
183C2×D36C2×D311yescharacteristic, complemented
184C2×C4×D9—31no—
185C2×C4×D9—31no—
186C2×C4×D9—61no—
187C2×C4×D9C2×D311yescharacteristic, complemented
188C9×C22⋊C4—21no—
189C9×C22⋊C4—31no—
190C9×C22⋊C4—31no—
191C9×C22⋊C4C2×D311yescharacteristic, complemented
192#3676—31no—
193#3676—31no—
194#3676—31no—
195#3676—31no—
196#3676—31no—
197#3676—61no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—61no—
202(C2×D9)⋊C4C2×D311yescharacteristic, complemented
203C4⋊Dic9—31no—
204C4⋊Dic9—31no—
205C4⋊Dic9—61no—
206Dic9⋊C4—31no—
207Dic9⋊C4—61no—
208Dic9⋊C4C2×D311yescharacteristic, complemented
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9C2411yescharacteristic
213C2×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9C2×D412yes—
216C2×D3×C9—21no—
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
220C2×D3×C9—21no—
221C2×D3×C9—21no—
222C2×D3×C9—21no—
223C2×D3×C9—21no—
224C2×D3×C9—44no—
225C2×D3×C9C2×D412yes—
226C2×C3×D9—21no—
227C2×C3×D9—21no—
228C2×C3×D9—21no—
229C2×C3×D9—21no—
230C2×C3×D9—21no—
231C2×C3×D9C2×D412yes—
232D3×D9—44no—
233D3×D9—44no—
234C3×C4×C9—21no—
235C3×C4×C9—21no—
236C3⋊Dic9—21no—
237C3⋊Dic9—21no—
238C3⋊Dic9—21no—
239C9×Dic3—21no—
240C3×Dic9—21no—
241C3×Dic9—21no—
242C22×#67—91no—
243C2×D3×D4—91no—
244C2×D3×D4—91no—
245C2×D3×D4—91no—
246C3×#121—91no—
247C3×#120—31no—
248#953—91no—
249#939—91no—
250#939—91no—
251#938—91no—
252#938—91no—
253#937—91no—
254#937—91no—
255#937—91no—
256#937—91no—
257#935—91no—
258#930—91no—
259C2×(C2×D3)⋊C4—91no—
260#894—91no—
261#894—91no—
262#886—91no—
263#884—31no—
264#884—91no—
265#883—91no—
266#883—91no—
267#883—91no—
268#883—91no—
269#883—181no—
270#882—91no—
271#882D911yescharacteristic, complemented
272D3×C22⋊C4—91no—
273C23×C32C22×D311yescharacteristic
274C22×C3⋊D3—31no—
275C22×C3×D3—22no—
276C22×C3×D3—31no—
277C22×C3×D3—31no—
278C22×C3×D3—41no—
279C22×C3×D3—41no—
280C22×C3×D3C22×D311yescharacteristic
281C22×C3×D3C22×D311yescharacteristic
282C22×C3×D3C22×D311yescharacteristic
283C2×D32—34no—
284C2×D32—62no—
285C2×D32—121no—
286C2×D32—121no—
287C2×D32—121no—
288C2×D32—121no—
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291#638—62no—
292C2×C3⋊Dic3—31no—
293C2×C3⋊Dic3—31no—
294C2×C3⋊Dic3—31no—
295C4×C3⋊D3—62no—
296C3×#67—41no—
297C3×#67—62no—
298C3×#67—121no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3C22×D311yescharacteristic
302C3×D12—22no—
303C3×D12—41no—
304C3×D12—62no—
305C3×C4×D3—121no—
306#626—62no—
307#625—62no—
308#625—62no—
309#625—62no—
310#625—121no—
311D3×Dic3—62no—
312D3×Dic3—121no—
313C23×C9—21no—
314C23×C9—31no—
315C23×C9—31no—
316C23×C9—31no—
317C23×C9—62no—
318C23×C9—121no—
319C23×C9—121no—
320C23×C9C22×D311yescharacteristic
321C22×D9—31no—
322C22×D9—34no—
323C22×D9—61no—
324C22×D9—62no—
325C22×D9—121no—
326C22×D9—121no—
327C22×D9—121no—
328C22×D9—121no—
329C22×D9C22×D311yescharacteristic
330C22×D9C22×D311yescharacteristic
331D4×C9—62no—
332D4×C9—121no—
333D4×C9—121no—
334C2×C4×C9—21no—
335C2×C4×C9—21no—
336C2×C4×C9—31no—
337C2×C4×C9C22×D311yescharacteristic
338C2×C4×C9C22×D311yescharacteristic
339#611—22no—
340#611—41no—
341#611—62no—
342#611—62no—
343#611—62no—
344#611—62no—
345#611—62no—
346#611—122no—
347#611—121no—
348C2×Dic9—31no—
349C2×Dic9—31no—
350C2×Dic9—31no—
351C2×Dic9—61no—
352C2×Dic9—61no—
353C2×Dic9—61no—
354C2×Dic9—62no—
355C2×Dic9C22×D311yescharacteristic
356C2×Dic9C22×D311yescharacteristic
357D36—22no—
358C4×D9—41no—
359C4×D9—62no—
360C4×D9—122no—
361C4×D9—121no—
362#534—271noSylow
363C2×C3×C9—41no—
364C2×C3×C9C22×D411yescharacteristic
365C2×C3×C9H(5,𝔽2)11yescharacteristic
366C2×C3×C9H(5,𝔽2)11yescharacteristic
367C3⋊D9—22no—
368D3×C9—22no—
369D3×C9—41no—
370D3×C9—41no—
371C3×D9—22no—
372C3×D9—41no—
373C24×C3—31no—
374C23×D3—91no—
375C23×D3—91no—
376C23×D3—91no—
377C23×D3—91no—
378C23×D3C2×D911yescharacteristic, complemented
379C2×C3×D4—31no—
380C2×C3×D4—31no—
381C2×C3×D4—31no—
382C2×C3×D4—91no—
383C2×C3×D4—91no—
384C2×C3×D4—91no—
385C22×C3×C4—91no—
386C2×#67—31no—
387C2×#67—31no—
388C2×#67—91no—
389C2×#67—91no—
390C2×#67—91no—
391C2×#67—91no—
392C2×#67—91no—
393C2×#67—91no—
394C2×#67—91no—
395C2×#67—91no—
396C2×#67—91no—
397C2×#67—91no—
398C2×#67—91no—
399C2×#67—181no—
400C2×#67—184no—
401C2×#67C2×D911yescharacteristic, complemented
402C22×Dic3—91no—
403C22×Dic3—91no—
404D3×D4—184no—
405D3×D4—184no—
406D3×D4—184no—
407C2×D12—31no—
408C2×D12—91no—
409C2×D12C2×D911yescharacteristic
410C2×D12C2×D911yescharacteristic, complemented
411C2×C4×D3—31no—
412C2×C4×D3—91no—
413C2×C4×D3—91no—
414C2×C4×D3—91no—
415C2×C4×D3—91no—
416C2×C4×D3—181no—
417C3×C4⋊C4—91no—
418C3×C22⋊C4—21no—
419C3×C22⋊C4—31no—
420C3×C22⋊C4—31no—
421C3×C22⋊C4—91no—
422C3×C22⋊C4C2×D911yescharacteristic, complemented
423C3×C22⋊C4D3211yescharacteristic
424#217—91no—
425#217—91no—
426#217—91no—
427#217—91no—
428#217—91no—
429#217—91no—
430#217—91no—
431#217—181no—
432(C2×D3)⋊C4—31no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—181no—
443(C2×D3)⋊C4C2×D911yescharacteristic, complemented
444(C2×D3)⋊C4C2×D911yescharacteristic, complemented
445C4⋊Dic3—91no—
446C4⋊Dic3—91no—
447C4⋊Dic3—91no—
448C4⋊Dic3—181no—
449Dic3⋊C4—31no—
450Dic3⋊C4—91no—
451Dic3⋊C4—91no—
452Dic3⋊C4—91no—
453Dic3⋊C4—181no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32C23×D311yescharacteristic
458C2×C3⋊D3—32no—
459C2×C3⋊D3—61no—
460C2×C3⋊D3—61no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—32no—
470C2×C3×D3—44no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3D3×D412yes—
477D32—124no—
478D32—124no—
479C32×C4—21no—
480C32×C4—21no—
481C3⋊Dic3—61no—
482C3⋊Dic3—61no—
483C3⋊Dic3—61no—
484C3×Dic3—21no—
485C3×Dic3—61no—
486C3×Dic3—61no—
487C22×C9—21no—
488C22×C9—21no—
489C22×C9—21no—
490C22×C9—21no—
491C22×C9—32no—
492C22×C9—41no—
493C22×C9—41no—
494C22×C9—41no—
495C22×C9—61no—
496C22×C9—61no—
497C22×C9—61no—
498C22×C9—61no—
499C22×C9—61no—
500C22×C9—61no—
501C22×C9—61no—
502C22×C9—61no—
503C22×C9—124no—
504C22×C9C23×D311yescharacteristic
505C2×D9—21no—
506C2×D9—21no—
507C2×D9—21no—
508C2×D9—21no—
509C2×D9—21no—
510C2×D9—32no—
511C2×D9—62no—
512C2×D9—61no—
513C2×D9—61no—
514C2×D9—121no—
515C2×D9—121no—
516C2×D9—124no—
517C2×D9—124no—
518C2×D9D3×D412yes—
519C4×C9—21no—
520C4×C9—21no—
521C4×C9—41no—
522C4×C9—41no—
523C4×C9—61no—
524Dic9—21no—
525Dic9—21no—
526Dic9—61no—
527Dic9—61no—
528Dic9—61no—
529Dic9—121no—
530Dic9—121no—
531Dic9—121no—
532C22×D4—271no—
533C22×D4—271no—
534#123—271no—
535#123—271no—
536#123—271no—
537#123—271no—
538#121—91no—
539#121—271no—
540#121—271no—
541#121—271no—
542#120—31no—
543#120—271no—
544#120—271no—
545#120—271no—
546C2×C22⋊C4—271no—
547C3×C9#53411yescharacteristic, complemented, Sylow
548C23×C3—21no—
549C23×C3—31no—
550C23×C3—31no—
551C23×C3—31no—
552C23×C3—62no—
553C23×C3—91no—
554C23×C3—91no—
555C23×C3—121no—
556C23×C3—121no—
557C23×C3C22×D911yescharacteristic
558C23×C3C2×D3211yescharacteristic
559C22×D3—22no—
560C22×D3—31no—
561C22×D3—31no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—94no—
565C22×D3—91no—
566C22×D3—91no—
567C22×D3—94no—
568C22×D3—181no—
569C22×D3—182no—
570C22×D3—182no—
571C22×D3—361no—
572C22×D3—361no—
573C22×D3—361no—
574C22×D3—361no—
575C22×D3—361no—
576C22×D3—361no—
577C22×D3—361no—
578C22×D3—361no—
579C22×D3C22×D911yescharacteristic
580C22×D3C22×D911yescharacteristic
581C22×D3C22×D911yescharacteristic
582C3×D4—62no—
583C3×D4—121no—
584C3×D4—121no—
585C3×D4—182no—
586C3×D4—182no—
587C3×D4—361no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—31no—
591C2×C3×C4—91no—
592C2×C3×C4—91no—
593C2×C3×C4—361no—
594C2×C3×C4C22×D911yescharacteristic
595C2×C3×C4C22×D911yescharacteristic
596C2×C3×C4C2×D3211yescharacteristic
597C2×C3×C4C2×D3211yescharacteristic
598#67—41no—
599#67—62no—
600#67—121no—
601#67—182no—
602#67—182no—
603#67—182no—
604#67—182no—
605#67—182no—
606#67—182no—
607#67—182no—
608#67—182no—
609#67—182no—
610#67—362no—
611#67—361no—
612#67—361no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—91no—
616C2×Dic3—91no—
617C2×Dic3—91no—
618C2×Dic3—91no—
619C2×Dic3—91no—
620C2×Dic3—91no—
621C2×Dic3—181no—
622C2×Dic3—181no—
623C2×Dic3—181no—
624C2×Dic3—182no—
625C2×Dic3—361no—
626C2×Dic3C22×D911yescharacteristic
627D12—22no—
628D12—41no—
629D12—62no—
630D12—182no—
631C4×D3—121no—
632C4×D3—182no—
633C4×D3—182no—
634C4×D3—182no—
635C4×D3—362no—
636C4×D3—361no—
637C2×C32—41no—
638C2×C32C2×D3×D411yescharacteristic
639C2×C32#100411yescharacteristic
640C2×C32#100411yescharacteristic
641C3⋊D3—62no—
642C3×D3—22no—
643C3×D3—41no—
644C3×D3—41no—
645C3×D3—62no—
646C3×D3—121no—
647C2×C9—21no—
648C2×C9—21no—
649C2×C9—21no—
650C2×C9—41no—
651C2×C9—62no—
652C2×C9—81no—
653C2×C9—121no—
654C2×C9—121no—
655C2×C9C2×D3×D411yescharacteristic
656C2×C9#100411yescharacteristic
657C2×C9#100911yescharacteristic
658D9—22no—
659D9—41no—
660D9—62no—
661D9—122no—
662C24—31no—
663C24—271no—
664C24—271no—
665C2×D4—31no—
666C2×D4—31no—
667C2×D4—31no—
668C2×D4—91no—
669C2×D4—91no—
670C2×D4—91no—
671C2×D4—271no—
672C2×D4—271no—
673C2×D4—271no—
674C2×D4—271no—
675C2×D4—271no—
676C2×D4—271no—
677C2×D4—544no—
678C2×D4—544no—
679C22×C4—91no—
680C22×C4—271no—
681C22×C4—271no—
682C22×C4—271no—
683C4⋊C4—91no—
684C4⋊C4—271no—
685C4⋊C4—271no—
686C4⋊C4—271no—
687C22⋊C4—31no—
688C22⋊C4—31no—
689C22⋊C4—91no—
690C22⋊C4—271no—
691C22⋊C4—271no—
692C22⋊C4—271no—
693C22⋊C4—271no—
694C22⋊C4—271no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4D3×D911yescharacteristic, complemented
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—32no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—92no—
719C22×C3—124no—
720C22×C3—181no—
721C22×C3—181no—
722C22×C3—181no—
723C22×C3—181no—
724C22×C3—181no—
725C22×C3C23×D911yescharacteristic
726C22×C3C22×D3211yescharacteristic
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—32no—
736C2×D3—44no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—92no—
743C2×D3—92no—
744C2×D3—182no—
745C2×D3—181no—
746C2×D3—181no—
747C2×D3—181no—
748C2×D3—181no—
749C2×D3—361no—
750C2×D3—361no—
751C2×D3—364no—
752C2×D3—364no—
753C2×D3—364no—
754C2×D3—364no—
755C2×D3D4×D912yes—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—61no—
763C3×C4—181no—
764C3×C4—181no—
765Dic3—21no—
766Dic3—61no—
767Dic3—61no—
768Dic3—181no—
769Dic3—181no—
770Dic3—181no—
771Dic3—181no—
772Dic3—181no—
773Dic3—181no—
774Dic3—361no—
775Dic3—361no—
776Dic3—361no—
777C32#558911yescharacteristic
778C9—21no—
779C9#560511yescharacteristic, complemented
780C23—31no—
781C23—31no—
782C23—31no—
783C23—62no—
784C23—91no—
785C23—91no—
786C23—121no—
787C23—121no—
788C23—274no—
789C23—271no—
790C23—542no—
791C23—1081no—
792C23—1081no—
793C23—1081no—
794C23—1081no—
795C23C2×D3×D911yescharacteristic
796D4—62no—
797D4—121no—
798D4—121no—
799D4—182no—
800D4—182no—
801D4—361no—
802D4—542no—
803D4—542no—
804D4—542no—
805D4—542no—
806D4—542no—
807D4—1081no—
808C2×C4—31no—
809C2×C4—91no—
810C2×C4—91no—
811C2×C4—271no—
812C2×C4—271no—
813C2×C4—271no—
814C2×C4—361no—
815C2×C4—542no—
816C2×C4—542no—
817C2×C4—1081no—
818C2×C4C2×D3×D911yescharacteristic
819C2×C4C2×D3×D911yescharacteristic
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—41no—
824C2×C3—41no—
825C2×C3—62no—
826C2×C3—81no—
827C2×C3—121no—
828C2×C3—121no—
829C2×C3—182no—
830C2×C3—361no—
831C2×C3C2×D4×D911yescharacteristic
832C2×C3#6371011yescharacteristic
833C2×C3#6371011yescharacteristic
834C2×C3#6430711yescharacteristic
835C2×C3D32×D411yescharacteristic
836C2×C3#6431311yescharacteristic
837D3—22no—
838D3—41no—
839D3—41no—
840D3—62no—
841D3—121no—
842D3—182no—
843D3—182no—
844D3—362no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—32no—
849C22—61no—
850C22—61no—
851C22—61no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—61no—
857C22—92no—
858C22—124no—
859C22—181no—
860C22—181no—
861C22—181no—
862C22—181no—
863C22—181no—
864C22—272no—
865C22—541no—
866C22—541no—
867C22—1084no—
868C22—1084no—
869C22C22×D3×D911yescharacteristic
870C4—21no—
871C4—21no—
872C4—61no—
873C4—181no—
874C4—181no—
875C4—541no—
876C4—541no—
877C4—541no—
878C3—21no—
879C3#1058969111yescharacteristic, complemented
880C3#1059426311yescharacteristic
881C2—41no—
882C2—62no—
883C2—121no—
884C2—121no—
885C2—182no—
886C2—361no—
887C2—542no—
888C2#1172247611yescharacteristic
889C2D3×D4×D911yescharacteristic
890C2#1172249911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#534
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×D3×#611C2semidirect
2. C2×#88646C2semidirect
3. #11721729C2semidirect
4. C9×#882C2semidirect
5. C3×#63446C2semidirect
6. #11721292C2semidirect
7. #11721286C2semidirect
8. #11721270C2semidirect
9. #11721050C2semidirect
10. D9×(C2×D3)⋊C4C2semidirect
11. #11721036C2semidirect
12. #11721021C2semidirect
13. #11721015C2semidirect
14. #11720982C2semidirect
15. #11720957C2semidirect
18. C23×D3×C9C22semidirect
20. C22×D3×D9C22semidirect
22. C2×C4×C3⋊D9C22semidirect
23. C2×C9×#67C22semidirect
24. C2×C3×#611C22semidirect
25. C2×C3×#611C22semidirect
27. C2×C9×D12C22semidirect
28. C2×C3×D36C22semidirect
29. C2×C3×C4×D9C22semidirect
33. C2×#6194C22semidirect
34. C2×#6194C22semidirect
35. C2×#6194C22semidirect
36. C2×D3×Dic9C22semidirect
37. C2×Dic3×D9C22semidirect
39. C3×C9×C22⋊C4C22semidirect
40. #88551C22semidirect
41. #88536C22semidirect
42. C4⋊(C3⋊Dic9)C22semidirect
43. #88534C22semidirect
44. C9×(C2×D3)⋊C4C22semidirect
45. C9×(C2×D3)⋊C4C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C3×Dic9⋊C4C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
51. (C2×D3)⋊Dic9C22semidirect
52. #88445C22semidirect
53. (C2×D9)⋊Dic3C22semidirect
54. Dic3⋊Dic9C22semidirect
81. #63446D3semidirect
101. C2×D3×D9D4semidirect
179. C2×#611C2×D3semidirect
180. C2×#611C2×D3semidirect
183. C2×D36C2×D3semidirect
187. C2×C4×D9C2×D3semidirect
191. C9×C22⋊C4C2×D3semidirect
202. (C2×D9)⋊C4C2×D3semidirect
208. Dic9⋊C4C2×D3semidirect
271. #882D9semidirect
378. C23×D3C2×D9semidirect
401. C2×#67C2×D9semidirect
410. C2×D12C2×D9semidirect
422. C3×C22⋊C4C2×D9semidirect
443. (C2×D3)⋊C4C2×D9semidirect
444. (C2×D3)⋊C4C2×D9semidirect
547. C3×C9#534semidirect
698. C22⋊C4D3×D9semidirect
779. C9#5605semidirect
879. C3#10589691semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6112
C2×#886462
#117217292
C9×#8822
C3×#634462
#117212922
#117212862
#117212702
#117210502
D9×(C2×D3)⋊C42
#117210362
#117210212
#117210152
#117209822
#117209572
#105942633
#105896913