Finite Group Databasebeta

← #13150970

Subgroups — #13150970

Order 1728.

1514 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊D9C211yesmaximal, characteristic, complemented
2C2×#88668C211yesmaximal, characteristic, complemented
3C2×#88668C211yesmaximal, characteristic, complemented
4C22×(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
5C9×#939C211yesmaximal, characteristic, complemented
6C3×#63501C211yesmaximal, characteristic, complemented
7#11721288C211yesmaximal, characteristic, complemented
8#11721277C211yesmaximal, characteristic, complemented
9#11721274C211yesmaximal, characteristic, complemented
10#11721262C211yesmaximal, characteristic, complemented
11#11721256C211yesmaximal, characteristic, complemented
12#11721048C211yesmaximal, characteristic, complemented
13#11721039C211yesmaximal, characteristic, complemented
14#11721005C211yesmaximal, characteristic, complemented
15#11720980C211yesmaximal, characteristic, complemented
16#10595298—31nomaximal
17D9×#121—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C23×C3⋊D9C2211yescharacteristic
20C22×D3×D9C2211yescharacteristic
21C2×C3×D4×C9C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C2×#6233C2211yescharacteristic, complemented
24D4×C3⋊D9—24no—
25C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
26C2×C4×C3⋊D9C2211yescharacteristic
27C2×C9×#67C2211yescharacteristic, complemented
28C2×C9×#67C2211yescharacteristic, complemented
29C2×C3×#611C2211yescharacteristic, complemented
30C2×C3×#611C2211yescharacteristic, complemented
31C22×C9×Dic3C2211yescharacteristic, complemented
32C22×C3×Dic9C2211yescharacteristic, complemented
33#88668—24no—
34#88668—24no—
35C2×#6195C2211yescharacteristic, complemented
36C2×#6195C2211yescharacteristic, complemented
37C2×#6192C2211yescharacteristic, complemented
38C2×#6192C2211yescharacteristic, complemented
39C2×(C3⋊D9)⋊C4—24no—
40C2×(C3⋊D9)⋊C4C2211yescharacteristic
41C2×(C3⋊D9)⋊C4C2211yescharacteristic
42C2×(C3⋊D9)⋊C4C2211yescharacteristic
43C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
44C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
45C9×#217C2211yescharacteristic, complemented
46C3×#3676C2211yescharacteristic, complemented
47C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
49C9×Dic3⋊C4C2211yescharacteristic, complemented
50C3×Dic9⋊C4C2211yescharacteristic, complemented
51(C2×D3)⋊Dic9C2211yescharacteristic, complemented
52#88445C2211yescharacteristic, complemented
53#88445C2211yescharacteristic, complemented
54(C2×D9)⋊Dic3C2211yescharacteristic, complemented
55Dic3⋊Dic9C2211yescharacteristic, complemented
56Dic9⋊Dic3C2211yescharacteristic, complemented
57C2×D4×C3⋊D3—31no—
58C2×#3811—31no—
59C2×#3811—31no—
60C22×#624—31no—
61C3×#939—31no—
62C3×#939D311yescharacteristic
63#63978—31no—
64#63978—31no—
65#63974—31no—
66#63958—31no—
67#63958—31no—
68#63921—31no—
69#63910—31no—
70#63910—31no—
71#63883—31no—
72C2×D4×D9—31no—
73C2×D4×D9—31no—
74C2×D4×D9—31no—
75C2×D4×D9—61no—
76C22×C4×D9—31no—
77C9×#121—31no—
78#63501—31no—
79#63501D311yescharacteristic, complemented
80#63500—31no—
81#63492—31no—
82#63457—31no—
83C4⋊C4×D9—31no—
84#63446—31no—
85#63446—31no—
86C22⋊C4×D9—31no—
87C22⋊C4×D9—31no—
88C23×C3×C9C2311yescharacteristic
89C23×C3×C9C2311yescharacteristic
90C22×C3⋊D9—22no—
91C22×C3⋊D9—22no—
92C22×C3⋊D9—22no—
93C22×C3⋊D9—22no—
94C22×C3⋊D9—22no—
95C22×C3⋊D9D414yescomplemented
96C22×C3⋊D9C2311yescharacteristic
97C22×C3⋊D9C2311yescharacteristic
98C22×C3⋊D9C2311yescharacteristic
99C22×D3×C9C2311yescharacteristic
100C22×C3×D9C2311yescharacteristic
101C2×D3×D9—22no—
102C2×D3×D9—22no—
103C2×D3×D9—22no—
104C3×D4×C9—22no—
105C2×C3×C4×C9C2311yescharacteristic
106#6233—22no—
107#6233—22no—
108C2×C3⋊Dic9C2311yescharacteristic
109C4⋊(C3⋊D9)—22no—
110C4×C3⋊D9—22no—
111C9×#67—22no—
112C9×#67—22no—
113C3×#611—22no—
114C3×#611—22no—
115C2×C9×Dic3—22no—
116C2×C9×Dic3C2311yescharacteristic
117C2×C9×Dic3C2311yescharacteristic
118C2×C9×Dic3C2311yescharacteristic
119C2×C3×Dic9—22no—
120C2×C3×Dic9C2311yescharacteristic
121C2×C3×Dic9C2311yescharacteristic
122C2×C3×Dic9C2311yescharacteristic
123#6195—22no—
124#6195—22no—
125#6192—22no—
126#6192—22no—
127(C3⋊D9)⋊C4—22no—
128(C3⋊D9)⋊C4—22no—
129(C3⋊D9)⋊C4—22no—
130(C3⋊D9)⋊C4—22no—
131(C3⋊D9)⋊C4D414yescomplemented
132D3×#121—91no—
133D3×#121—91no—
134C23×C3⋊D3—31no—
135C23×C3⋊D3—31no—
136C22×D32—31no—
137C2×C32×D4C2×D311yescharacteristic
138C2×#638—31no—
139C2×#638—31no—
140D4×C3⋊D3—64no—
141C2×C4⋊(C3⋊D3)—31no—
142C2×C4×C3⋊D3—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67C2×D311yescharacteristic
146C2×C3×#67C2×D311yescharacteristic
147C22×C3×Dic3—31no—
148C22×C3×Dic3C2×D311yescharacteristic
149#3811—64no—
150#3811—64no—
151C2×#626—31no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#624—31no—
156C2×#624—31no—
157C2×#624—31no—
158C2×#624—31no—
159C2×#624—31no—
160C2×#624—64no—
161C23×D9—31no—
162C23×D9—31no—
163C23×D9—31no—
164C23×D9—61no—
165C23×D9—61no—
166C3×#217—31no—
167C3×#217C2×D311yescharacteristic
168C3×(C2×D3)⋊C4—31no—
169C3×(C2×D3)⋊C4C2×D311yescharacteristic
170C3×Dic3⋊C4—31no—
171C3×Dic3⋊C4C2×D311yescharacteristic
172Dic3⋊Dic3—31no—
173Dic3⋊Dic3—31no—
174#3722—31no—
175#3722—31no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178C2×D4×C9—21no—
179C2×D4×C9—31no—
180C2×D4×C9—31no—
181C2×D4×C9C2×D311yescharacteristic, complemented
182C22×C4×C9—31no—
183C2×#611—31no—
184C2×#611—31no—
185C2×#611—31no—
186C2×#611—31no—
187C2×#611—61no—
188C2×#611—61no—
189C2×#611C2×D311yescharacteristic, complemented
190C2×#611C2×D311yescharacteristic, complemented
191C22×Dic9C2×D311yescharacteristic, complemented
192D4×D9—64no—
193D4×D9—64no—
194D4×D9—64no—
195D4×D9—68no—
196C2×D36—31no—
197C2×D36—31no—
198C2×D36—31no—
199C2×D36—61no—
200C2×C4×D9—31no—
201C2×C4×D9—31no—
202C2×C4×D9—31no—
203C2×C4×D9—31no—
204C2×C4×D9—31no—
205C2×C4×D9—31no—
206C2×C4×D9—64no—
207C2×C4×D9—61no—
208C9×C4⋊C4—31no—
209C9×C22⋊C4—31no—
210C9×C22⋊C4—31no—
211#3676—31no—
212#3676C2×D311yescharacteristic, complemented
213(C2×D9)⋊C4—31no—
214(C2×D9)⋊C4—31no—
215(C2×D9)⋊C4—31no—
216(C2×D9)⋊C4C2×D311yescharacteristic, complemented
217C4⋊Dic9—31no—
218Dic9⋊C4—31no—
219Dic9⋊C4C2×D311yescharacteristic, complemented
220C22×C3×C9—21no—
221C22×C3×C9—21no—
222C22×C3×C9—21no—
223C22×C3×C9—21no—
224C22×C3×C9—21no—
225C22×C3×C9C2×D412yescomplemented
226C22×C3×C9C2411yescharacteristic
227C2×C3⋊D9—21no—
228C2×C3⋊D9—21no—
229C2×C3⋊D9—28no—
230C2×C3⋊D9—21no—
231C2×C3⋊D9—21no—
232C2×C3⋊D9—21no—
233C2×C3⋊D9—44no—
234C2×C3⋊D9C2×D412yes—
235C2×C3⋊D9C2×D412yes—
236C2×C3⋊D9C2×D412yescomplemented
237C2×C3⋊D9#4112yes—
238C2×D3×C9—21no—
239C2×D3×C9—21no—
240C2×D3×C9—21no—
241C2×C3×D9—21no—
242C2×C3×D9—21no—
243C2×C3×D9—21no—
244D3×D9—44no—
245C3×C4×C9—21no—
246C3⋊Dic9—21no—
247C9×Dic3—21no—
248C9×Dic3—21no—
249C9×Dic3C2×D412yescomplemented
250C3×Dic9—21no—
251C3×Dic9—21no—
252C3×Dic9C2×D412yescomplemented
253C2×D3×D4—91no—
254C2×D3×D4—91no—
255C2×D3×D4—91no—
256C2×D3×D4—91no—
257C2×D3×D4—91no—
258C2×D3×D4—91no—
259C2×D3×D4—181no—
260C22×C4×D3—91no—
261C22×C4×D3—91no—
262C3×#121—31no—
263C3×#121—91no—
264#939—31no—
265#939—91no—
266#939—91no—
267#939D911yescharacteristic, complemented
268#938—91no—
269#938—91no—
270#930—91no—
271#930—91no—
272#895—91no—
273#895—91no—
274D3×C4⋊C4—91no—
275D3×C4⋊C4—91no—
276#884—91no—
277#884—91no—
278#884—91no—
279#884—91no—
280D3×C22⋊C4—91no—
281D3×C22⋊C4—91no—
282D3×C22⋊C4—91no—
283D3×C22⋊C4—91no—
284C23×C32C22×D311yescharacteristic
285C23×C32C22×D311yescharacteristic
286C22×C3⋊D3—31no—
287C22×C3⋊D3—34no—
288C22×C3⋊D3—31no—
289C22×C3⋊D3—31no—
290C22×C3⋊D3—62no—
291C22×C3⋊D3—62no—
292C22×C3⋊D3—62no—
293C22×C3⋊D3—62no—
294C22×C3⋊D3—62no—
295C22×C3×D3—31no—
296C22×C3×D3C22×D311yescharacteristic
297C2×D32—62no—
298C2×D32—62no—
299C2×D32—62no—
300C32×D4—22no—
301C2×C32×C4C22×D311yescharacteristic
302#638—62no—
303#638—62no—
304C2×C3⋊Dic3—31no—
305C4⋊(C3⋊D3)—62no—
306C4×C3⋊D3—62no—
307C3×#67—22no—
308C3×#67—22no—
309C3×#67—62no—
310C3×#67—62no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—62no—
316C2×C3×Dic3C22×D311yescharacteristic
317C2×C3×Dic3C22×D311yescharacteristic
318C2×C3×Dic3C22×D311yescharacteristic
319#626—62no—
320#626—62no—
321#626—62no—
322#626—62no—
323#624—34no—
324#624—62no—
325#624—62no—
326#624—62no—
327#624—62no—
328C23×C9—21no—
329C23×C9—21no—
330C23×C9—31no—
331C23×C9C22×D311yescharacteristic
332C23×C9C22×D311yescharacteristic
333C22×D9—31no—
334C22×D9—34no—
335C22×D9—31no—
336C22×D9—31no—
337C22×D9—61no—
338C22×D9—61no—
339C22×D9—61no—
340C22×D9—64no—
341C22×D9—62no—
342C22×D9—62no—
343C22×D9—62no—
344C22×D9—62no—
345C22×D9—62no—
346C22×D9—62no—
347C22×D9—62no—
348C22×D9—62no—
349C22×D9—64no—
350C22×D9—122no—
351C22×D9—122no—
352C22×D9—122no—
353C22×D9—122no—
354C22×D9C22×D311yescharacteristic
355D4×C9—24no—
356D4×C9—22no—
357D4×C9—62no—
358D4×C9—62no—
359C2×C4×C9—21no—
360C2×C4×C9—31no—
361C2×C4×C9—31no—
362C2×C4×C9—31no—
363C2×C4×C9—62no—
364C2×C4×C9C22×D311yescharacteristic
365#611—22no—
366#611—22no—
367#611—62no—
368#611—62no—
369#611—64no—
370#611—64no—
371#611—62no—
372#611—62no—
373C2×Dic9—22no—
374C2×Dic9—31no—
375C2×Dic9—61no—
376C2×Dic9C22×D311yescharacteristic
377C2×Dic9C22×D311yescharacteristic
378C2×Dic9C22×D311yescharacteristic
379D36—62no—
380D36—64no—
381D36—62no—
382D36—62no—
383C4×D9—34no—
384C4×D9—62no—
385C4×D9—62no—
386C4×D9—62no—
387C4×D9—62no—
388C4×D9—64no—
389C4×D9—62no—
390C2×#121—271noSylow
391C2×C3×C9—22no—
392C2×C3×C9—41no—
393C2×C3×C9C22×D411yescharacteristic
394C2×C3×C9C22×D411yescharacteristic
395C2×C3×C9C2×#4111yescharacteristic
396C3⋊D9—22no—
397C3⋊D9—41no—
398C3⋊D9#12114yescomplemented
399D3×C9—41no—
400C3×D9—41no—
401C23×D3—91no—
402C23×D3—91no—
403C23×D3—91no—
404C23×D3—91no—
405C23×D3—91no—
406C23×D3—91no—
407C23×D3—181no—
408C23×D3—181no—
409C2×C3×D4—21no—
410C2×C3×D4—31no—
411C2×C3×D4—31no—
412C2×C3×D4—91no—
413C2×C3×D4—91no—
414C2×C3×D4C2×D911yescharacteristic, complemented
415C2×C3×D4D3211yescharacteristic
416C22×C3×C4—31no—
417C22×C3×C4—91no—
418C2×#67—31no—
419C2×#67—31no—
420C2×#67—91no—
421C2×#67—91no—
422C2×#67—91no—
423C2×#67—91no—
424C2×#67—91no—
425C2×#67—91no—
426C2×#67—91no—
427C2×#67—91no—
428C2×#67—181no—
429C2×#67—181no—
430C2×#67C2×D911yescharacteristic, complemented
431C2×#67C2×D911yescharacteristic, complemented
432C22×Dic3—31no—
433C22×Dic3C2×D911yescharacteristic, complemented
434D3×D4—184no—
435D3×D4—184no—
436D3×D4—184no—
437D3×D4—184no—
438D3×D4—184no—
439D3×D4—184no—
440D3×D4—188no—
441C2×D12—91no—
442C2×D12—91no—
443C2×D12—91no—
444C2×D12—91no—
445C2×D12—91no—
446C2×D12—91no—
447C2×D12—181no—
448C2×C4×D3—91no—
449C2×C4×D3—91no—
450C2×C4×D3—91no—
451C2×C4×D3—91no—
452C2×C4×D3—91no—
453C2×C4×D3—91no—
454C2×C4×D3—91no—
455C2×C4×D3—91no—
456C2×C4×D3—91no—
457C2×C4×D3—91no—
458C2×C4×D3—91no—
459C2×C4×D3—91no—
460C2×C4×D3—181no—
461C2×C4×D3—184no—
462C2×C4×D3—184no—
463C3×C4⋊C4—31no—
464C3×C4⋊C4—91no—
465C3×C22⋊C4—31no—
466C3×C22⋊C4—31no—
467C3×C22⋊C4—91no—
468C3×C22⋊C4—91no—
469#217—31no—
470#217—91no—
471#217—91no—
472#217C2×D911yescharacteristic, complemented
473(C2×D3)⋊C4—31no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—91no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4C2×D911yescharacteristic, complemented
481C4⋊Dic3—91no—
482C4⋊Dic3—91no—
483Dic3⋊C4—31no—
484Dic3⋊C4—91no—
485Dic3⋊C4—91no—
486Dic3⋊C4C2×D911yescharacteristic, complemented
487C22×C32—21no—
488C22×C32—21no—
489C22×C32—21no—
490C22×C32—21no—
491C22×C32—21no—
492C22×C32D3×D412yes—
493C22×C32C23×D311yescharacteristic
494C2×C3⋊D3—32no—
495C2×C3⋊D3—32no—
496C2×C3⋊D3—32no—
497C2×C3⋊D3—32no—
498C2×C3⋊D3—61no—
499C2×C3⋊D3—68no—
500C2×C3⋊D3—61no—
501C2×C3⋊D3—61no—
502C2×C3⋊D3—61no—
503C2×C3⋊D3—61no—
504C2×C3⋊D3—124no—
505C2×C3×D3—21no—
506C2×C3×D3—21no—
507C2×C3×D3—21no—
508C2×C3×D3—61no—
509C2×C3×D3—61no—
510C2×C3×D3—61no—
511D32—124no—
512C32×C4—21no—
513C3⋊Dic3—61no—
514C3×Dic3—21no—
515C3×Dic3—21no—
516C3×Dic3—32no—
517C3×Dic3—61no—
518C3×Dic3—61no—
519C3×Dic3D3×D412yes—
520C22×C9—21no—
521C22×C9—21no—
522C22×C9—22no—
523C22×C9—21no—
524C22×C9—21no—
525C22×C9—21no—
526C22×C9—21no—
527C22×C9—22no—
528C22×C9—41no—
529C22×C9—41no—
530C22×C9—41no—
531C22×C9—41no—
532C22×C9—61no—
533C22×C9—61no—
534C22×C9—61no—
535C22×C9D3×D412yescomplemented
536C22×C9C23×D311yescharacteristic
537C2×D9—21no—
538C2×D9—21no—
539C2×D9—21no—
540C2×D9—32no—
541C2×D9—32no—
542C2×D9—32no—
543C2×D9—32no—
544C2×D9—62no—
545C2×D9—62no—
546C2×D9—62no—
547C2×D9—62no—
548C2×D9—68no—
549C2×D9—61no—
550C2×D9—61no—
551C2×D9—62no—
552C2×D9—61no—
553C2×D9—61no—
554C2×D9—61no—
555C2×D9—128no—
556C2×D9—121no—
557C2×D9—121no—
558C2×D9—121no—
559C2×D9—121no—
560C2×D9—124no—
561C2×D9—124no—
562C2×D9—128no—
563C4×C9—22no—
564C4×C9—21no—
565C4×C9—32no—
566C4×C9—61no—
567C4×C9—61no—
568Dic9—21no—
569Dic9—21no—
570Dic9—62no—
571Dic9—61no—
572Dic9D3×D412yescomplemented
573C22×D4—271no—
574C22×D4—271no—
575C22×D4—271no—
576C23×C4—271no—
577#121—31no—
578#121—91no—
579#121—271no—
580#121—271no—
581#121—271no—
582#121—271no—
583#121—271no—
584#121—271no—
585C2×C4⋊C4—271no—
586C2×C22⋊C4—271no—
587C2×C22⋊C4—271no—
588C3×C9C2×#12111yescharacteristic, complemented, Sylow
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—31no—
592C23×C3—91no—
593C23×C3C22×D911yescharacteristic
594C23×C3C22×D911yescharacteristic
595C23×C3C2×D3211yescharacteristic
596C23×C3C2×D3211yescharacteristic
597C22×D3—31no—
598C22×D3—91no—
599C22×D3—91no—
600C22×D3—91no—
601C22×D3—94no—
602C22×D3—91no—
603C22×D3—94no—
604C22×D3—91no—
605C22×D3—91no—
606C22×D3—181no—
607C22×D3—181no—
608C22×D3—181no—
609C22×D3—184no—
610C22×D3—182no—
611C22×D3—182no—
612C22×D3—182no—
613C22×D3—182no—
614C22×D3—182no—
615C22×D3—182no—
616C22×D3—182no—
617C22×D3—182no—
618C22×D3—182no—
619C22×D3—182no—
620C22×D3—182no—
621C22×D3—182no—
622C22×D3—182no—
623C22×D3—182no—
624C22×D3—182no—
625C22×D3—182no—
626C22×D3—184no—
627C22×D3—362no—
628C22×D3—362no—
629C22×D3—362no—
630C22×D3—362no—
631C22×D3C22×D911yescharacteristic
632C3×D4—24no—
633C3×D4—22no—
634C3×D4—22no—
635C3×D4—62no—
636C3×D4—62no—
637C3×D4—182no—
638C3×D4—182no—
639C2×C3×C4—21no—
640C2×C3×C4—31no—
641C2×C3×C4—31no—
642C2×C3×C4—31no—
643C2×C3×C4—62no—
644C2×C3×C4—91no—
645C2×C3×C4—91no—
646C2×C3×C4—91no—
647C2×C3×C4—182no—
648C2×C3×C4C22×D911yescharacteristic
649C2×C3×C4C2×D3211yescharacteristic
650#67—22no—
651#67—22no—
652#67—62no—
653#67—62no—
654#67—182no—
655#67—182no—
656#67—182no—
657#67—182no—
658#67—182no—
659#67—184no—
660#67—184no—
661#67—182no—
662#67—182no—
663#67—182no—
664C2×Dic3—22no—
665C2×Dic3—31no—
666C2×Dic3—31no—
667C2×Dic3—31no—
668C2×Dic3—62no—
669C2×Dic3—91no—
670C2×Dic3—91no—
671C2×Dic3—181no—
672C2×Dic3C22×D911yescharacteristic
673C2×Dic3C22×D911yescharacteristic
674C2×Dic3C22×D911yescharacteristic
675D12—182no—
676D12—182no—
677D12—184no—
678D12—182no—
679D12—182no—
680D12—182no—
681D12—182no—
682C4×D3—94no—
683C4×D3—94no—
684C4×D3—182no—
685C4×D3—182no—
686C4×D3—182no—
687C4×D3—182no—
688C4×D3—182no—
689C4×D3—182no—
690C4×D3—182no—
691C4×D3—182no—
692C4×D3—182no—
693C4×D3—184no—
694C4×D3—182no—
695C2×C32—22no—
696C2×C32—41no—
697C2×C32C2×D3×D411yescharacteristic
698C2×C32C2×D3×D411yescharacteristic
699C2×C32D3×#4111yescharacteristic
700C3⋊D3—34no—
701C3⋊D3—62no—
702C3⋊D3—121no—
703C3×D3—41no—
704C3×D3—121no—
705C2×C9—22no—
706C2×C9—21no—
707C2×C9—21no—
708C2×C9—21no—
709C2×C9—42no—
710C2×C9—42no—
711C2×C9—41no—
712C2×C9—121no—
713C2×C9C2×D3×D411yescharacteristic
714C2×C9C2×D3×D411yescharacteristic
715C2×C9D3×#4111yescharacteristic
716D9—34no—
717D9—41no—
718D9—64no—
719D9—62no—
720D9—122no—
721D9—122no—
722D9—121no—
723C24—271no—
724C24—271no—
725C24—271no—
726C2×D4—31no—
727C2×D4—31no—
728C2×D4—91no—
729C2×D4—91no—
730C2×D4—271no—
731C2×D4—271no—
732C2×D4—271no—
733C2×D4—271no—
734C2×D4—271no—
735C2×D4—271no—
736C2×D4—271no—
737C2×D4—544no—
738C2×D4—544no—
739C2×D4—544no—
740C2×D4D3×D911yescharacteristic, complemented
741C22×C4—31no—
742C22×C4—91no—
743C22×C4—271no—
744C22×C4—271no—
745C22×C4—271no—
746C22×C4—271no—
747C22×C4—271no—
748C22×C4—271no—
749C22×C4—544no—
750C4⋊C4—31no—
751C4⋊C4—91no—
752C4⋊C4—271no—
753C4⋊C4—271no—
754C22⋊C4—31no—
755C22⋊C4—31no—
756C22⋊C4—91no—
757C22⋊C4—91no—
758C22⋊C4—271no—
759C22⋊C4—271no—
760C22⋊C4—271no—
761C22⋊C4—271no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—22no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—22no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—61no—
780C22×C3—61no—
781C22×C3—61no—
782C22×C3—181no—
783C22×C3—181no—
784C22×C3—181no—
785C22×C3D4×D912yescomplemented
786C22×C3C23×D911yescharacteristic
787C22×C3#381112yes—
788C22×C3C22×D3211yescharacteristic
789C2×D3—21no—
790C2×D3—21no—
791C2×D3—21no—
792C2×D3—61no—
793C2×D3—61no—
794C2×D3—61no—
795C2×D3—92no—
796C2×D3—92no—
797C2×D3—92no—
798C2×D3—92no—
799C2×D3—92no—
800C2×D3—92no—
801C2×D3—92no—
802C2×D3—92no—
803C2×D3—182no—
804C2×D3—182no—
805C2×D3—182no—
806C2×D3—182no—
807C2×D3—188no—
808C2×D3—188no—
809C2×D3—181no—
810C2×D3—181no—
811C2×D3—181no—
812C2×D3—181no—
813C2×D3—182no—
814C2×D3—181no—
815C2×D3—181no—
816C2×D3—181no—
817C2×D3—181no—
818C2×D3—181no—
819C2×D3—181no—
820C2×D3—368no—
821C2×D3—361no—
822C2×D3—361no—
823C2×D3—361no—
824C2×D3—361no—
825C2×D3—364no—
826C2×D3—364no—
827C2×D3—364no—
828C2×D3—364no—
829C2×D3—368no—
830C3×C4—22no—
831C3×C4—21no—
832C3×C4—21no—
833C3×C4—32no—
834C3×C4—61no—
835C3×C4—61no—
836C3×C4—92no—
837C3×C4—181no—
838C3×C4—181no—
839Dic3—21no—
840Dic3—21no—
841Dic3—32no—
842Dic3—61no—
843Dic3—61no—
844Dic3—182no—
845Dic3—181no—
846Dic3—181no—
847Dic3D4×D912yescomplemented
848C32D3×#12111yescharacteristic
849C9—21no—
850C9D3×#12111yescharacteristic, complemented
851C23—31no—
852C23—91no—
853C23—271no—
854C23—271no—
855C23—274no—
856C23—271no—
857C23—542no—
858C23—542no—
859C23—542no—
860C23—542no—
861C23—542no—
862C23—542no—
863C23—542no—
864C23—542no—
865C23C2×D3×D911yescharacteristic
866C23C2×D3×D911yescharacteristic
867D4—22no—
868D4—62no—
869D4—62no—
870D4—182no—
871D4—182no—
872D4—542no—
873D4—542no—
874D4—542no—
875D4—542no—
876D4—542no—
877D4—542no—
878D4—542no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—31no—
882C2×C4—62no—
883C2×C4—91no—
884C2×C4—91no—
885C2×C4—91no—
886C2×C4—182no—
887C2×C4—274no—
888C2×C4—271no—
889C2×C4—542no—
890C2×C4—542no—
891C2×C4—542no—
892C2×C4—542no—
893C2×C4—542no—
894C2×C4C2×D3×D911yescharacteristic
895C2×C3—22no—
896C2×C3—22no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—42no—
901C2×C3—42no—
902C2×C3—41no—
903C2×C3—41no—
904C2×C3—121no—
905C2×C3—361no—
906C2×C3C2×D4×D911yescharacteristic
907C2×C3C2×D4×D911yescharacteristic
908C2×C3#41×D911yescharacteristic
909C2×C3D32×D411yescharacteristic
910C2×C3#6431211yescharacteristic
911C2×C3C2×#381111yescharacteristic
912D3—41no—
913D3—94no—
914D3—94no—
915D3—121no—
916D3—184no—
917D3—182no—
918D3—182no—
919D3—362no—
920D3—362no—
921D3—361no—
922D3—361no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—61no—
929C22—61no—
930C22—61no—
931C22—181no—
932C22—181no—
933C22—181no—
934C22—272no—
935C22—272no—
936C22—272no—
937C22—272no—
938C22—548no—
939C22—541no—
940C22—541no—
941C22—541no—
942C22—541no—
943C22—541no—
944C22—1084no—
945C22—1084no—
946C22#8866812yescomplemented
947C22C22×D3×D911yescharacteristic
948C4—21no—
949C4—32no—
950C4—61no—
951C4—61no—
952C4—92no—
953C4—181no—
954C4—181no—
955C4—541no—
956C3—21no—
957C3D9×#12111yescharacteristic, complemented
958C3#1059529811yescharacteristic
959C2—22no—
960C2—41no—
961C2—121no—
962C2—274no—
963C2—361no—
964C2—542no—
965C2—1081no—
966C2D3×D4×D911yescharacteristic
967C2#1172249811yescharacteristic
968C2C2×#8866811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9C2×#121
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×D4×C3⋊D9C2semidirect
2. C2×#88668C2semidirect
3. C2×#88668C2semidirect
4. C22×(C3⋊D9)⋊C4C2semidirect
5. C9×#939C2semidirect
6. C3×#63501C2semidirect
7. #11721288C2semidirect
8. #11721277C2semidirect
9. #11721274C2semidirect
10. #11721262C2semidirect
11. #11721256C2semidirect
12. #11721048C2semidirect
13. #11721039C2semidirect
14. #11721005C2semidirect
15. #11720980C2semidirect
21. C2×C3×D4×C9C22semidirect
22. C2×#6233C22semidirect
23. C2×#6233C22semidirect
25. C2×C4⋊(C3⋊D9)C22semidirect
27. C2×C9×#67C22semidirect
28. C2×C9×#67C22semidirect
29. C2×C3×#611C22semidirect
30. C2×C3×#611C22semidirect
31. C22×C9×Dic3C22semidirect
32. C22×C3×Dic9C22semidirect
35. C2×#6195C22semidirect
36. C2×#6195C22semidirect
37. C2×#6192C22semidirect
38. C2×#6192C22semidirect
43. C2×(C3⋊D9)⋊C4C22semidirect
44. C2×(C3⋊D9)⋊C4C22semidirect
45. C9×#217C22semidirect
46. C3×#3676C22semidirect
47. C9×(C2×D3)⋊C4C22semidirect
48. C3×(C2×D9)⋊C4C22semidirect
49. C9×Dic3⋊C4C22semidirect
50. C3×Dic9⋊C4C22semidirect
51. (C2×D3)⋊Dic9C22semidirect
52. #88445C22semidirect
53. #88445C22semidirect
54. (C2×D9)⋊Dic3C22semidirect
55. Dic3⋊Dic9C22semidirect
56. Dic9⋊Dic3C22semidirect
79. #63501D3semidirect
95. C22×C3⋊D9D4semidirect
131. (C3⋊D9)⋊C4D4semidirect
181. C2×D4×C9C2×D3semidirect
189. C2×#611C2×D3semidirect
190. C2×#611C2×D3semidirect
191. C22×Dic9C2×D3semidirect
212. #3676C2×D3semidirect
216. (C2×D9)⋊C4C2×D3semidirect
219. Dic9⋊C4C2×D3semidirect
225. C22×C3×C9C2×D4semidirect
236. C2×C3⋊D9C2×D4semidirect
249. C9×Dic3C2×D4semidirect
252. C3×Dic9C2×D4semidirect
267. #939D9semidirect
398. C3⋊D9#121semidirect
414. C2×C3×D4C2×D9semidirect
430. C2×#67C2×D9semidirect
431. C2×#67C2×D9semidirect
433. C22×Dic3C2×D9semidirect
472. #217C2×D9semidirect
480. (C2×D3)⋊C4C2×D9semidirect
486. Dic3⋊C4C2×D9semidirect
535. C22×C9D3×D4semidirect
572. Dic9D3×D4semidirect
588. C3×C9C2×#121semidirect
740. C2×D4D3×D9semidirect
785. C22×C3D4×D9semidirect
847. Dic3D4×D9semidirect
850. C9D3×#121semidirect
946. C22#88668semidirect
957. C3D9×#121semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊D92
C2×#886682
C22×(C3⋊D9)⋊C42
C9×#9392
C3×#635012
#117212882
#117212772
#117212742
#117212622
#117212562
#117210482
#117210392
#117210052
#117209802
#105952983
D9×#1213