Finite Group Databasebeta

← #13148406

Subgroups — #13148406

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#611C211yesmaximal, characteristic, complemented
2C2×D9×D12C211yesmaximal, characteristic, complemented
3#11721730C211yesmaximal, characteristic, complemented
4C9×#882C211yesmaximal, characteristic, complemented
5C3×#63445C211yesmaximal, characteristic, complemented
6#11721292C211yesmaximal, characteristic, complemented
7#11721287C211yesmaximal, characteristic, complemented
8#11721262C211yesmaximal, characteristic, complemented
9#11721050C211yesmaximal, characteristic, complemented
10#11721048C211yesmaximal, characteristic, complemented
11#11721045C211yesmaximal, characteristic, complemented
12#11721039C211yesmaximal, characteristic, complemented
13#11721031C211yesmaximal, characteristic, complemented
14#11721020C211yesmaximal, characteristic, complemented
15#11721015C211yesmaximal, characteristic, complemented
16#10594262—31nomaximal
17#10589691—31nomaximal
18C23×D3×C9C2211yescharacteristic, complemented
19C22×D3×D9C2211yescharacteristic
20C22×D3×D9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
24C2×C4×C3⋊D9C2211yescharacteristic, complemented
25C2×C9×#67C2211yescharacteristic, complemented
26C2×C3×#611C2211yescharacteristic
27C2×C9×D12C2211yescharacteristic
28C2×C9×D12C2211yescharacteristic, complemented
29C2×C3×C4×D9C2211yescharacteristic, complemented
30D3×#611—24no—
31C2×#6195C2211yescharacteristic
32C2×#6195C2211yescharacteristic, complemented
33C2×#6195C2211yescharacteristic, complemented
34C2×#6195C2211yescharacteristic, complemented
35C2×#6194C2211yescharacteristic
36C2×D3×Dic9C2211yescharacteristic, complemented
37C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
38D9×D12—24no—
39C3×C9×C22⋊C4C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41#88534C2211yescharacteristic, complemented
42C3×#3676C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×C4⋊Dic9C2211yescharacteristic, 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×D3×D12—31no—
57#64093—31no—
58C3×#883—31no—
59C3×#882D311yescharacteristic
60#63983—31no—
61#63977—31no—
62#63958—31no—
63#63922—31no—
64#63921—31no—
65#63916—31no—
66#63910—31no—
67#63905—31no—
68#63890—31no—
69#63884—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#63446—31no—
82#63446—61no—
83#63445—31no—
84#63445D311yescharacteristic, complemented
85C22⋊C4×D9—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9—22no—
90C22×D3×C9—41no—
91C22×D3×C9—41no—
92C22×D3×C9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×D3×C9C2311yescharacteristic
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—
105#6233—41no—
106C2×C3⋊Dic9C2311yescharacteristic
107C2×C3⋊Dic9C2311yescharacteristic
108C4⋊(C3⋊D9)—22no—
109C4×C3⋊D9—41no—
110C9×#67—41no—
111C3×#611—22no—
112C2×C9×Dic3C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114C2×C3×Dic9C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C9×D12—22no—
117C9×D12—41no—
118C3×C4×D9—22no—
119#6195—22no—
120#6195—22no—
121#6195—22no—
122#6195—41no—
123#6194—22no—
124D3×Dic9—22no—
125(C3⋊D9)⋊C4—41no—
126#5653—91no—
127#5589—91no—
128C23×C3×D3C2×D311yescharacteristic
129C22×D32—31no—
130C22×D32—31no—
131C2×#638—31no—
132C2×#638—31no—
133C2×C4⋊(C3⋊D3)—31no—
134C2×C4×C3⋊D3—31no—
135C2×C3×#67—31no—
136C2×C3×#67C2×D311yescharacteristic
137C2×C3×D12C2×D311yescharacteristic
138C2×C3×D12C2×D311yescharacteristic
139C2×C3×C4×D3—31no—
140D3×#67—64no—
141C2×#626—31no—
142C2×#626—31no—
143C2×#626—31no—
144C2×#626—31no—
145C2×#625—31no—
146C2×#624—31no—
147C2×D3×Dic3—31no—
148D3×D12—64no—
149C24×C9—31no—
150C23×D9—31no—
151C23×D9—31no—
152C32×C22⋊C4C2×D311yescharacteristic
153#3752—31no—
154#3750—31no—
155C3×#217—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×(C2×D3)⋊C4C2×D311yescharacteristic
158C3×(C2×D3)⋊C4C2×D311yescharacteristic
159C3×C4⋊Dic3—31no—
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—31no—
178C2×#611—64no—
179C2×#611—61no—
180C2×#611—61no—
181C2×#611C2×D311yescharacteristic
182C22×Dic9—31no—
183D4×D9—64no—
184C2×D36—31no—
185C2×D36—61no—
186C2×C4×D9—31no—
187C2×C4×D9—31no—
188C2×C4×D9—61no—
189C2×C4×D9C2×D311yescharacteristic, complemented
190C9×C22⋊C4—21no—
191C9×C22⋊C4—31no—
192C9×C22⋊C4—31no—
193C9×C22⋊C4C2×D311yescharacteristic, complemented
194#3676—31no—
195#3676—31no—
196#3676—31no—
197#3676—31no—
198#3676C2×D311yescharacteristic, complemented
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—31no—
202(C2×D9)⋊C4—61no—
203(C2×D9)⋊C4C2×D311yescharacteristic, complemented
204C4⋊Dic9—31no—
205C4⋊Dic9C2×D311yescharacteristic, complemented
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⋊D9—21no—
216C2×C3⋊D9—21no—
217C2×C3⋊D9—21no—
218C2×C3⋊D9C2×D412yes—
219C2×D3×C9—21no—
220C2×D3×C9—21no—
221C2×D3×C9—21no—
222C2×D3×C9—21no—
223C2×D3×C9—21no—
224C2×D3×C9—21no—
225C2×D3×C9—21no—
226C2×D3×C9—21no—
227C2×D3×C9—44no—
228C2×D3×C9C2×D412yes—
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—
238C9×Dic3—21no—
239C3×Dic9—21no—
240C3×Dic9—21no—
241C3×Dic9—21no—
242C22×#67—91no—
243C2×D3×D4—91no—
244C2×D3×D4—91no—
245C22×D12—91no—
246C3×#123—91no—
247C3×#120—31no—
248#953—91no—
249#938—91no—
250#938—91no—
251#937—91no—
252#937—91no—
253#937—91no—
254#935—91no—
255#929—91no—
256#895—91no—
257#895—91no—
258#894—91no—
259#894—91no—
260#886—91no—
261#884—91no—
262#884—91no—
263#884—91no—
264#884—91no—
265#884—181no—
266#883—31no—
267#883—91no—
268#882—91no—
269#882—91no—
270#882D911yescharacteristic, complemented
271D3×C22⋊C4—91no—
272D3×C22⋊C4—91no—
273C23×C32C22×D311yescharacteristic
274C22×C3⋊D3—31no—
275C22×C3⋊D3—31no—
276C22×C3×D3—22no—
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—
292#638—121no—
293C2×C3⋊Dic3—31no—
294C2×C3⋊Dic3—31no—
295C4⋊(C3⋊D3)—62no—
296C4×C3⋊D3—121no—
297C3×#67—41no—
298C3×#67—62no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3C22×D311yescharacteristic
303C3×D12—22no—
304C3×D12—41no—
305C3×C4×D3—62no—
306#626—62no—
307#626—62no—
308#626—62no—
309#626—121no—
310#625—62no—
311#624—121no—
312D3×Dic3—62no—
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—31no—
324C22×D9—61no—
325C22×D9—61no—
326C22×D9—62no—
327C22×D9—121no—
328C22×D9—121no—
329C22×D9—121no—
330C22×D9—121no—
331C22×D9C22×D311yescharacteristic
332D4×C9—62no—
333D4×C9—121no—
334D4×C9—121no—
335C2×C4×C9—21no—
336C2×C4×C9—21no—
337C2×C4×C9—31no—
338C2×C4×C9C22×D311yescharacteristic
339C2×C4×C9C22×D311yescharacteristic
340#611—22no—
341#611—62no—
342#611—62no—
343#611—62no—
344#611—62no—
345#611—62no—
346#611—122no—
347#611—121no—
348#611—121no—
349#611—122no—
350C2×Dic9—31no—
351C2×Dic9—31no—
352C2×Dic9—61no—
353C2×Dic9—61no—
354C2×Dic9—62no—
355C2×Dic9C22×D311yescharacteristic
356C2×Dic9C22×D311yescharacteristic
357C2×Dic9C22×D311yescharacteristic
358D36—62no—
359D36—122no—
360C4×D9—22no—
361C4×D9—121no—
362C4×D9—121no—
363C4×D9—122no—
364#534—271noSylow
365C2×C3×C9—41no—
366C2×C3×C9C22×D411yescharacteristic
367C2×C3×C9H(5,𝔽2)11yescharacteristic
368C2×C3×C9H(5,𝔽2)11yescharacteristic
369C3⋊D9—22no—
370C3⋊D9—41no—
371D3×C9—22no—
372D3×C9—41no—
373D3×C9—41no—
374C3×D9—22no—
375C24×C3—31no—
376C23×D3—91no—
377C23×D3—91no—
378C23×D3—91no—
379C23×D3—91no—
380C23×D3C2×D911yescharacteristic, complemented
381C2×C3×D4—31no—
382C2×C3×D4—31no—
383C2×C3×D4—31no—
384C2×C3×D4—91no—
385C22×C3×C4—91no—
386C2×#67—31no—
387C2×#67—91no—
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—181no—
398C2×#67—181no—
399C2×#67—184no—
400C2×#67C2×D911yescharacteristic, complemented
401C22×Dic3—91no—
402D3×D4—184no—
403D3×D4—184no—
404C2×D12—91no—
405C2×D12—91no—
406C2×D12—91no—
407C2×D12—91no—
408C2×D12—91no—
409C2×D12—91no—
410C2×D12—181no—
411C2×D12—184no—
412C2×D12C2×D911yescharacteristic
413C2×D12C2×D911yescharacteristic, complemented
414C2×C4×D3—31no—
415C2×C4×D3—91no—
416C2×C4×D3—91no—
417C2×C4×D3—91no—
418C2×C4×D3—91no—
419C2×C4×D3—91no—
420C2×C4×D3—181no—
421C3×C4⋊C4—91no—
422C3×C4⋊C4—91no—
423C3×C22⋊C4—21no—
424C3×C22⋊C4—31no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—91no—
427C3×C22⋊C4—91no—
428C3×C22⋊C4C2×D911yescharacteristic, complemented
429C3×C22⋊C4D3211yescharacteristic
430#217—31no—
431#217—91no—
432#217—91no—
433#217—91no—
434#217—91no—
435#217—91no—
436(C2×D3)⋊C4—31no—
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—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—181no—
447(C2×D3)⋊C4C2×D911yescharacteristic, complemented
448(C2×D3)⋊C4C2×D911yescharacteristic, complemented
449C4⋊Dic3—31no—
450C4⋊Dic3—91no—
451Dic3⋊C4—31no—
452Dic3⋊C4—91no—
453Dic3⋊C4—91no—
454Dic3⋊C4—91no—
455Dic3⋊C4—181no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32C23×D311yescharacteristic
460C2×C3⋊D3—32no—
461C2×C3⋊D3—61no—
462C2×C3⋊D3—61no—
463C2×C3⋊D3—61no—
464C2×C3⋊D3—61no—
465C2×C3⋊D3—61no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—32no—
475C2×C3×D3—44no—
476C2×C3×D3—61no—
477C2×C3×D3—61no—
478C2×C3×D3D3×D412yes—
479D32—124no—
480D32—124no—
481C32×C4—21no—
482C32×C4—21no—
483C3⋊Dic3—61no—
484C3⋊Dic3—61no—
485C3×Dic3—21no—
486C3×Dic3—61no—
487C3×Dic3—61no—
488C3×Dic3—61no—
489C22×C9—21no—
490C22×C9—21no—
491C22×C9—21no—
492C22×C9—21no—
493C22×C9—32no—
494C22×C9—41no—
495C22×C9—41no—
496C22×C9—41no—
497C22×C9—61no—
498C22×C9—61no—
499C22×C9—61no—
500C22×C9—61no—
501C22×C9—61no—
502C22×C9—61no—
503C22×C9—61no—
504C22×C9—61no—
505C22×C9—124no—
506C22×C9C23×D311yescharacteristic
507C2×D9—21no—
508C2×D9—21no—
509C2×D9—32no—
510C2×D9—62no—
511C2×D9—61no—
512C2×D9—61no—
513C2×D9—61no—
514C2×D9—61no—
515C2×D9—61no—
516C2×D9—121no—
517C2×D9—121no—
518C2×D9—121no—
519C2×D9—121no—
520C2×D9—121no—
521C2×D9—124no—
522C2×D9—124no—
523C2×D9D3×D412yes—
524C4×C9—21no—
525C4×C9—21no—
526C4×C9—41no—
527C4×C9—41no—
528C4×C9—61no—
529Dic9—21no—
530Dic9—21no—
531Dic9—21no—
532Dic9—62no—
533Dic9—61no—
534Dic9—61no—
535Dic9—121no—
536C22×D4—271no—
537C22×D4—271no—
538#123—91no—
539#123—271no—
540#123—271no—
541#123—271no—
542#121—271no—
543#121—271no—
544#121—271no—
545#121—271no—
546#120—31no—
547#120—271no—
548#120—271no—
549#120—271no—
550C2×C22⋊C4—271no—
551C3×C9#53411yescharacteristic, complemented, Sylow
552C23×C3—21no—
553C23×C3—31no—
554C23×C3—31no—
555C23×C3—31no—
556C23×C3—62no—
557C23×C3—91no—
558C23×C3—121no—
559C23×C3—121no—
560C23×C3C22×D911yescharacteristic
561C23×C3C2×D3211yescharacteristic
562C22×D3—22no—
563C22×D3—31no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—94no—
567C22×D3—91no—
568C22×D3—91no—
569C22×D3—94no—
570C22×D3—91no—
571C22×D3—91no—
572C22×D3—181no—
573C22×D3—181no—
574C22×D3—182no—
575C22×D3—182no—
576C22×D3—361no—
577C22×D3—361no—
578C22×D3—361no—
579C22×D3—361no—
580C22×D3—361no—
581C22×D3—361no—
582C22×D3—361no—
583C22×D3—361no—
584C22×D3C22×D911yescharacteristic
585C22×D3C22×D911yescharacteristic
586C22×D3C22×D911yescharacteristic
587C3×D4—62no—
588C3×D4—121no—
589C3×D4—121no—
590C3×D4—182no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—31no—
594C2×C3×C4—91no—
595C2×C3×C4—91no—
596C2×C3×C4—91no—
597C2×C3×C4—182no—
598C2×C3×C4C22×D911yescharacteristic
599C2×C3×C4C22×D911yescharacteristic
600C2×C3×C4C2×D3211yescharacteristic
601C2×C3×C4C2×D3211yescharacteristic
602#67—41no—
603#67—62no—
604#67—182no—
605#67—182no—
606#67—182no—
607#67—182no—
608#67—182no—
609#67—182no—
610#67—182no—
611#67—362no—
612#67—361no—
613#67—361no—
614#67—361no—
615#67—362no—
616C2×Dic3—31no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—91no—
620C2×Dic3—91no—
621C2×Dic3—91no—
622C2×Dic3—91no—
623C2×Dic3—181no—
624C2×Dic3—181no—
625C2×Dic3—182no—
626C2×Dic3C22×D911yescharacteristic
627D12—22no—
628D12—41no—
629D12—182no—
630D12—182no—
631D12—182no—
632D12—182no—
633D12—182no—
634D12—362no—
635D12—361no—
636C4×D3—62no—
637C4×D3—182no—
638C4×D3—361no—
639C4×D3—361no—
640C4×D3—361no—
641C4×D3—361no—
642C4×D3—362no—
643C2×C32—41no—
644C2×C32C2×D3×D411yescharacteristic
645C2×C32#100411yescharacteristic
646C2×C32#100411yescharacteristic
647C3⋊D3—62no—
648C3⋊D3—121no—
649C3×D3—22no—
650C3×D3—41no—
651C3×D3—41no—
652C3×D3—62no—
653C2×C9—21no—
654C2×C9—21no—
655C2×C9—21no—
656C2×C9—41no—
657C2×C9—62no—
658C2×C9—81no—
659C2×C9—121no—
660C2×C9—121no—
661C2×C9C2×D3×D411yescharacteristic
662C2×C9#100911yescharacteristic
663C2×C9#100911yescharacteristic
664D9—22no—
665D9—62no—
666D9—122no—
667D9—121no—
668D9—241no—
669C24—31no—
670C24—271no—
671C24—271no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—91no—
676C2×D4—271no—
677C2×D4—271no—
678C2×D4—271no—
679C2×D4—271no—
680C2×D4—271no—
681C2×D4—271no—
682C2×D4—271no—
683C2×D4—271no—
684C2×D4—544no—
685C2×D4—544no—
686C22×C4—91no—
687C22×C4—271no—
688C22×C4—271no—
689C22×C4—271no—
690C4⋊C4—91no—
691C4⋊C4—91no—
692C4⋊C4—271no—
693C4⋊C4—271no—
694C22⋊C4—31no—
695C22⋊C4—31no—
696C22⋊C4—91no—
697C22⋊C4—91no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C22⋊C4—271no—
702C22⋊C4—271no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4D3×D911yescharacteristic, complemented
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—92no—
726C22×C3—124no—
727C22×C3—181no—
728C22×C3—181no—
729C22×C3C23×D911yescharacteristic
730C22×C3C22×D3211yescharacteristic
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—32no—
740C2×D3—44no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—92no—
744C2×D3—92no—
745C2×D3—182no—
746C2×D3—181no—
747C2×D3—181no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—181no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—181no—
754C2×D3—181no—
755C2×D3—181no—
756C2×D3—361no—
757C2×D3—361no—
758C2×D3—361no—
759C2×D3—361no—
760C2×D3—361no—
761C2×D3—364no—
762C2×D3—364no—
763C2×D3—364no—
764C2×D3—364no—
765C2×D3D4×D912yes—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—41no—
771C3×C4—41no—
772C3×C4—61no—
773C3×C4—181no—
774C3×C4—181no—
775C3×C4—181no—
776Dic3—21no—
777Dic3—61no—
778Dic3—61no—
779Dic3—61no—
780Dic3—182no—
781Dic3—181no—
782Dic3—181no—
783Dic3—181no—
784Dic3—181no—
785Dic3—361no—
786C32#558911yescharacteristic
787C9—21no—
788C9#565311yescharacteristic, complemented
789C23—31no—
790C23—31no—
791C23—31no—
792C23—62no—
793C23—91no—
794C23—121no—
795C23—121no—
796C23—274no—
797C23—271no—
798C23—271no—
799C23—542no—
800C23—1081no—
801C23—1081no—
802C23—1081no—
803C23—1081no—
804C23C2×D3×D911yescharacteristic
805D4—62no—
806D4—121no—
807D4—121no—
808D4—182no—
809D4—542no—
810D4—542no—
811D4—542no—
812D4—542no—
813D4—542no—
814D4—542no—
815D4—1081no—
816D4—1081no—
817C2×C4—31no—
818C2×C4—91no—
819C2×C4—91no—
820C2×C4—91no—
821C2×C4—182no—
822C2×C4—271no—
823C2×C4—271no—
824C2×C4—542no—
825C2×C4—1081no—
826C2×C4—1081no—
827C2×C4C2×D3×D911yescharacteristic
828C2×C4C2×D3×D911yescharacteristic
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—41no—
833C2×C3—41no—
834C2×C3—62no—
835C2×C3—81no—
836C2×C3—121no—
837C2×C3—121no—
838C2×C3—182no—
839C2×C3C2×D4×D911yescharacteristic
840C2×C3#6371011yescharacteristic
841C2×C3#6371011yescharacteristic
842C2×C3#6430711yescharacteristic
843C2×C3D32×D411yescharacteristic
844C2×C3#6431411yescharacteristic
845D3—22no—
846D3—41no—
847D3—41no—
848D3—62no—
849D3—182no—
850D3—182no—
851D3—362no—
852D3—361no—
853D3—361no—
854D3—721no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—32no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22—61no—
866C22—61no—
867C22—92no—
868C22—124no—
869C22—181no—
870C22—181no—
871C22—272no—
872C22—541no—
873C22—541no—
874C22—541no—
875C22—541no—
876C22—541no—
877C22—1084no—
878C22—1084no—
879C22C22×D3×D911yescharacteristic
880C4—21no—
881C4—21no—
882C4—61no—
883C4—181no—
884C4—181no—
885C4—181no—
886C4—541no—
887C4—541no—
888C3—21no—
889C3#1058969111yescharacteristic, complemented
890C3#1059426211yescharacteristic
891C2—41no—
892C2—62no—
893C2—121no—
894C2—121no—
895C2—182no—
896C2—542no—
897C2—1081no—
898C2#1172247611yescharacteristic
899C2D3×D4×D911yescharacteristic
900C2#1172250011yescharacteristic
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×D9×D12C2semidirect
3. #11721730C2semidirect
4. C9×#882C2semidirect
5. C3×#63445C2semidirect
6. #11721292C2semidirect
7. #11721287C2semidirect
8. #11721262C2semidirect
9. #11721050C2semidirect
10. #11721048C2semidirect
11. #11721045C2semidirect
12. #11721039C2semidirect
13. #11721031C2semidirect
14. #11721020C2semidirect
15. #11721015C2semidirect
18. C23×D3×C9C22semidirect
20. C22×D3×D9C22semidirect
21. C2×#6233C22semidirect
22. C2×#6233C22semidirect
23. C2×C4⋊(C3⋊D9)C22semidirect
24. C2×C4×C3⋊D9C22semidirect
25. C2×C9×#67C22semidirect
28. C2×C9×D12C22semidirect
29. C2×C3×C4×D9C22semidirect
32. C2×#6195C22semidirect
33. C2×#6195C22semidirect
34. C2×#6195C22semidirect
36. C2×D3×Dic9C22semidirect
37. C2×(C3⋊D9)⋊C4C22semidirect
39. C3×C9×C22⋊C4C22semidirect
40. #88536C22semidirect
41. #88534C22semidirect
42. C3×#3676C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C9×(C2×D3)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×C4⋊Dic9C22semidirect
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
84. #63445D3semidirect
101. C2×D3×D9D4semidirect
189. C2×C4×D9C2×D3semidirect
193. C9×C22⋊C4C2×D3semidirect
198. #3676C2×D3semidirect
203. (C2×D9)⋊C4C2×D3semidirect
205. C4⋊Dic9C2×D3semidirect
208. Dic9⋊C4C2×D3semidirect
270. #882D9semidirect
380. C23×D3C2×D9semidirect
400. C2×#67C2×D9semidirect
413. C2×D12C2×D9semidirect
428. C3×C22⋊C4C2×D9semidirect
447. (C2×D3)⋊C4C2×D9semidirect
448. (C2×D3)⋊C4C2×D9semidirect
551. C3×C9#534semidirect
705. C22⋊C4D3×D9semidirect
788. C9#5653semidirect
889. 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×D9×D122
#117217302
C9×#8822
C3×#634452
#117212922
#117212872
#117212622
#117210502
#117210482
#117210452
#117210392
#117210312
#117210202
#117210152
#105942623
#105896913