Finite Group Databasebeta

← #13150527

Subgroups — #13150527

Order 1728.

1146 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88668C211yesmaximal, characteristic
2C2×#88536C211yesmaximal, characteristic, complemented
3C4×C9×#67C211yesmaximal, characteristic, complemented
4C3×C4×#611C211yesmaximal, characteristic, complemented
5#67⋊Dic9C211yesmaximal, characteristic, complemented
6#11721274C211yesmaximal, characteristic, complemented
7#611⋊Dic3C211yesmaximal, characteristic, complemented
8D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721030C211yesmaximal, characteristic, complemented
11#11721013C211yesmaximal, characteristic, complemented
12#11721002C211yesmaximal, characteristic, complemented
13#11720977C211yesmaximal, characteristic, complemented
14#11720899C211yesmaximal, characteristic, complemented
15#11720898C211yesmaximal, characteristic, complemented
16#10595058—31nomaximal
17#10589647—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C22×C3×C4×C9C2211yescharacteristic, complemented
21C22×C3⋊Dic9C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic, complemented
25C2×C3×C4×D9C2211yescharacteristic, complemented
26#88668C418yescomplemented
27C2×#6195C2211yescharacteristic
28C2×D3×Dic9C2211yescharacteristic, complemented
29C2×#6192C2211yescharacteristic
30C2×(C3⋊D9)⋊C4C2211yescharacteristic
31C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
32C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
33C2×Dic3×D9C2211yescharacteristic, complemented
34#88536C2211yescharacteristic
35#88536C2211yescharacteristic
36#88536C2211yescharacteristic, complemented
37#88536C2211yescharacteristic, complemented
38C9×#217C2211yescharacteristic, complemented
39C3×#3676C2211yescharacteristic, complemented
40C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
42C9×Dic3⋊C4C2211yescharacteristic, complemented
43C4×C9×Dic3C2211yescharacteristic, complemented
44C3×Dic9⋊C4C2211yescharacteristic, complemented
45C3×C4×Dic9C2211yescharacteristic, complemented
46(C2×D3)⋊Dic9C2211yescharacteristic, complemented
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53Dic3×Dic9C2211yescharacteristic, complemented
54C2×#3811—31no—
55C2×#3752—31no—
56C3×C4×#67—31no—
57C3×C4×#67D311yescharacteristic
58#63974—31no—
59#67⋊Dic3—31no—
60#67⋊Dic3—31no—
61D3×(C2×D3)⋊C4—31no—
62D3×(C2×D3)⋊C4—31no—
63#63904—31no—
64#63904—31no—
65#63880—31no—
66#63880—31no—
67#63836—31no—
68#63836—31no—
69C2×D4×D9—31no—
70C4×D4×C9—31no—
71D4×Dic9—31no—
72C4×#611—31no—
73C4×#611D311yescharacteristic, complemented
74C2×(C2×D9)⋊C4—31no—
75C2×(C2×D9)⋊C4—31no—
76C2×(C2×D9)⋊C4—61no—
77#63455—31no—
78#63454—31no—
79#611⋊C4—31no—
80#611⋊C4—31no—
81C22⋊C4×D9—31no—
82C22⋊C4×D9—31no—
83C4×D36—31no—
84#63434—31no—
85C23×C3×C9C2311yescharacteristic
86C22×C3⋊D9—41no—
87C22×C3⋊D9—41no—
88C22×C3⋊D9C2×C414yescomplemented
89C22×C3⋊D9C2311yescharacteristic
90C22×C3⋊D9C2311yescharacteristic
91C22×D3×C9C2311yescharacteristic
92C22×C3×D9C2311yescharacteristic
93C2×D3×D9—41no—
94C2×D3×D9—41no—
95C2×D3×D9C2×C414yescomplemented
96C2×C3×C4×C9—41no—
97C2×C3×C4×C9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3⋊Dic9—41no—
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C9×#67C2×C414yescomplemented
103C3×#611C2×C414yescomplemented
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C4×D3×C9—41no—
111C3×C4×D9—41no—
112#6195C2×C414yescomplemented
113D3×Dic9—41no—
114#6192C2×C414yescomplemented
115(C3⋊D9)⋊C4—41no—
116(C3⋊D9)⋊C4—41no—
117(C3⋊D9)⋊C4C2×C414yescomplemented
118Dic3×D9—41no—
119#5545—91no—
120#5545—91no—
121C23×C3⋊D3—31no—
122C22×D32—31no—
123C22×C32×C4C2×D311yescharacteristic
124C22×C3⋊Dic3—31no—
125C2×C3×#67—31no—
126C2×C3×#67C2×D311yescharacteristic
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3C2×D311yescharacteristic
129#3811—38no—
130C2×#626—31no—
131C2×#626—31no—
132C2×#624—31no—
133C2×#624—31no—
134C2×#624—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137C23×D9—31no—
138C23×D9—31no—
139C23×D9—61no—
140#3752—31no—
141#3752—31no—
142#3752—31no—
143#3752—31no—
144C3×#217—31no—
145C3×#217C2×D311yescharacteristic
146C3×(C2×D3)⋊C4—31no—
147C3×(C2×D3)⋊C4C2×D311yescharacteristic
148C3×Dic3⋊C4—31no—
149C3×Dic3⋊C4C2×D311yescharacteristic
150C3×C4×Dic3—31no—
151C3×C4×Dic3C2×D311yescharacteristic
152Dic3⋊Dic3—31no—
153Dic3⋊Dic3—31no—
154#3722—31no—
155#3722—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158Dic32—31no—
159Dic32—31no—
160C2×D4×C9—31no—
161C22×C4×C9—21no—
162C22×C4×C9—31no—
163C22×C4×C9C2×D311yescharacteristic, complemented
164C2×#611—31no—
165C2×#611C2×D311yescharacteristic
166C22×Dic9—31no—
167C22×Dic9—31no—
168C22×Dic9—61no—
169D4×D9—38no—
170C2×D36—31no—
171C2×C4×D9—31no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—31no—
175C2×C4×D9C2×D311yescharacteristic, complemented
176C9×C4⋊C4—31no—
177C9×C22⋊C4—31no—
178C9×C22⋊C4—31no—
179C42×C9—31no—
180#3676—31no—
181#3676C2×D311yescharacteristic, complemented
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4—31no—
184(C2×D9)⋊C4—31no—
185(C2×D9)⋊C4—31no—
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—61no—
190(C2×D9)⋊C4—61no—
191(C2×D9)⋊C4—61no—
192(C2×D9)⋊C4—61no—
193(C2×D9)⋊C4C2×D311yescharacteristic, complemented
194C4⋊Dic9—31no—
195Dic9⋊C4—31no—
196Dic9⋊C4C2×D311yescharacteristic, complemented
197C4×Dic9—31no—
198C4×Dic9—31no—
199C4×Dic9C2×D311yescharacteristic, complemented
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9C22×C412yes—
203C22×C3×C9C2411yescharacteristic
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9—21no—
207C2×C3⋊D9—21no—
208C2×C3⋊D9—44no—
209C2×C3⋊D9C22×C412yes—
210C2×C3⋊D9C22×C412yes—
211C2×D3×C9—21no—
212C2×D3×C9—21no—
213C2×D3×C9C22×C412yes—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
216C2×C3×D9C22×C412yes—
217D3×D9—44no—
218C3×C4×C9—21no—
219C3×C4×C9—21no—
220C3⋊Dic9—21no—
221C3⋊Dic9—21no—
222C9×Dic3—21no—
223C9×Dic3—21no—
224C9×Dic3C22×C412yes—
225C3×Dic9—21no—
226C3×Dic9—21no—
227C3×Dic9C22×C412yes—
228C2×D3×D4—91no—
229C2×D3×D4—91no—
230C3×C4×D4—31no—
231C3×C4×D4—91no—
232D4×Dic3—91no—
233D4×Dic3—91no—
234C4×#67—31no—
235C4×#67—91no—
236C4×#67—91no—
237C4×#67D911yescharacteristic, complemented
238C2×(C2×D3)⋊C4—91no—
239C2×(C2×D3)⋊C4—91no—
240C2×(C2×D3)⋊C4—91no—
241C2×(C2×D3)⋊C4—91no—
242C2×(C2×D3)⋊C4—181no—
243#893—91no—
244#893—91no—
245#892—91no—
246#892—91no—
247#67⋊C4—91no—
248#67⋊C4—91no—
249#67⋊C4—91no—
250#67⋊C4—91no—
251D3×C22⋊C4—91no—
252D3×C22⋊C4—91no—
253D3×C22⋊C4—91no—
254D3×C22⋊C4—91no—
255C4×D12—91no—
256C4×D12—91no—
257#872—91no—
258#872—91no—
259C23×C32C22×D311yescharacteristic
260C22×C3⋊D3—31no—
261C22×C3⋊D3—31no—
262C22×C3⋊D3—34no—
263C22×C3⋊D3—121no—
264C22×C3⋊D3—121no—
265C22×C3×D3—31no—
266C22×C3×D3C22×D311yescharacteristic
267C2×D32—34no—
268C2×D32—121no—
269C2×D32—121no—
270C2×C32×C4—41no—
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—121no—
276C3×#67—34no—
277C3×#67C4×D314yes—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C3×C4×D3—41no—
285C3×C4×D3—121no—
286#626—34no—
287#626—34no—
288#624—34no—
289#624—121no—
290#624—121no—
291D3×Dic3—121no—
292D3×Dic3—121no—
293C23×C9—21no—
294C23×C9—31no—
295C23×C9C22×D311yescharacteristic
296C22×D9—31no—
297C22×D9—31no—
298C22×D9—34no—
299C22×D9—34no—
300C22×D9—61no—
301C22×D9—61no—
302C22×D9—64no—
303C22×D9—121no—
304C22×D9—121no—
305C22×D9—121no—
306C22×D9—121no—
307C22×D9—122no—
308C22×D9—122no—
309C22×D9C22×D311yescharacteristic
310D4×C9—34no—
311C2×C4×C9—21no—
312C2×C4×C9—21no—
313C2×C4×C9—31no—
314C2×C4×C9—31no—
315C2×C4×C9—31no—
316C2×C4×C9—41no—
317C2×C4×C9—42no—
318C2×C4×C9—121no—
319C2×C4×C9C22×D311yescharacteristic
320C2×C4×C9C22×D311yescharacteristic
321#611—34no—
322#611C4×D314yescomplemented
323C2×Dic9—31no—
324C2×Dic9—31no—
325C2×Dic9—61no—
326C2×Dic9—61no—
327C2×Dic9—121no—
328C2×Dic9—121no—
329C2×Dic9—122no—
330C2×Dic9C22×D311yescharacteristic
331C2×Dic9C22×D311yescharacteristic
332C2×Dic9C22×D311yescharacteristic
333D36—34no—
334C4×D9—34no—
335C4×D9—41no—
336C4×D9—121no—
337C4×D9—121no—
338C4×D9—121no—
339#518—271noSylow
340C2×C3×C9—22no—
341C2×C3×C9C23×C411yescharacteristic
342C2×C3×C9H(5,𝔽2)11yescharacteristic
343C2×C3×C9H(5,𝔽2)11yescharacteristic
344C3⋊D9—22no—
345C3⋊D9—22no—
346D3×C9—22no—
347C3×D9—22no—
348C23×D3—91no—
349C23×D3—91no—
350C23×D3—91no—
351C23×D3—91no—
352C23×D3—181no—
353C2×C3×D4—31no—
354C2×C3×D4—91no—
355C22×C3×C4—21no—
356C22×C3×C4—31no—
357C22×C3×C4—91no—
358C22×C3×C4C2×D911yescharacteristic, complemented
359C22×C3×C4D3211yescharacteristic
360C2×#67—31no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67C2×D911yescharacteristic
364C22×Dic3—91no—
365C22×Dic3—91no—
366C22×Dic3—91no—
367C22×Dic3—91no—
368C22×Dic3—181no—
369D3×D4—98no—
370D3×D4—98no—
371C2×D12—91no—
372C2×D12—91no—
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—91no—
382C2×C4×D3C2×D911yescharacteristic, complemented
383C3×C4⋊C4—31no—
384C3×C4⋊C4—91no—
385C3×C22⋊C4—31no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—91no—
388C3×C22⋊C4—91no—
389C3×C42—31no—
390C3×C42—91no—
391#217—31no—
392#217—91no—
393#217—91no—
394#217C2×D911yescharacteristic, complemented
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4—91no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
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—181no—
411(C2×D3)⋊C4—181no—
412(C2×D3)⋊C4—181no—
413(C2×D3)⋊C4—181no—
414(C2×D3)⋊C4C2×D911yescharacteristic, complemented
415C4⋊Dic3—91no—
416C4⋊Dic3—91no—
417Dic3⋊C4—31no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4C2×D911yescharacteristic, complemented
421C4×Dic3—31no—
422C4×Dic3—91no—
423C4×Dic3—91no—
424C4×Dic3—91no—
425C4×Dic3—91no—
426C4×Dic3C2×D911yescharacteristic, complemented
427C22×C32—21no—
428C22×C32—21no—
429C22×C32C2×C4×D312yes—
430C22×C32C23×D311yescharacteristic
431C2×C3⋊D3—32no—
432C2×C3⋊D3—32no—
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3⋊D3—61no—
437C2×C3⋊D3—124no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—32no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3C2×C4×D312yes—
444D32—124no—
445C32×C4—21no—
446C32×C4—21no—
447C3⋊Dic3—61no—
448C3⋊Dic3—61no—
449C3×Dic3—21no—
450C3×Dic3—21no—
451C3×Dic3—32no—
452C3×Dic3—61no—
453C3×Dic3—61no—
454C3×Dic3C2×C4×D312yes—
455C22×C9—22no—
456C22×C9—22no—
457C22×C9—21no—
458C22×C9—21no—
459C22×C9—21no—
460C22×C9—22no—
461C22×C9—32no—
462C22×C9—61no—
463C22×C9—61no—
464C22×C9C2×C4×D312yes—
465C22×C9C23×D311yescharacteristic
466C2×D9—21no—
467C2×D9—21no—
468C2×D9—32no—
469C2×D9—32no—
470C2×D9—62no—
471C2×D9—62no—
472C2×D9—61no—
473C2×D9—61no—
474C2×D9—61no—
475C2×D9—61no—
476C2×D9—121no—
477C2×D9—121no—
478C2×D9—121no—
479C2×D9—121no—
480C2×D9—124no—
481C2×D9—124no—
482C2×D9—128no—
483C2×D9C2×C4×D312yes—
484C4×C9—21no—
485C4×C9—21no—
486C4×C9—32no—
487C4×C9—41no—
488C4×C9—41no—
489C4×C9—61no—
490C4×C9—61no—
491Dic9—21no—
492Dic9—21no—
493Dic9—61no—
494Dic9—61no—
495Dic9—121no—
496Dic9—121no—
497Dic9C2×C4×D312yes—
498C22×D4—271no—
499C4×D4—31no—
500C4×D4—91no—
501C4×D4—271no—
502C4×D4—271no—
503C4×D4—271no—
504C4×D4—271no—
505C4×D4—271no—
506C4×D4—271no—
507#117—271no—
508#117—271no—
509C2×C22⋊C4—271no—
510C2×C22⋊C4—271no—
511C2×C22⋊C4—271no—
512C2×C22⋊C4—271no—
513C3×C9#51811yescharacteristic, complemented, Sylow
514C23×C3—21no—
515C23×C3—31no—
516C23×C3—91no—
517C23×C3C22×D911yescharacteristic
518C23×C3C2×D3211yescharacteristic
519C22×D3—31no—
520C22×D3—94no—
521C22×D3—91no—
522C22×D3—91no—
523C22×D3—91no—
524C22×D3—91no—
525C22×D3—94no—
526C22×D3—94no—
527C22×D3—94no—
528C22×D3—181no—
529C22×D3—181no—
530C22×D3—184no—
531C22×D3—361no—
532C22×D3—361no—
533C22×D3—361no—
534C22×D3—361no—
535C22×D3—361no—
536C22×D3—361no—
537C22×D3—361no—
538C22×D3—361no—
539C22×D3—362no—
540C22×D3—362no—
541C22×D3C22×D911yescharacteristic
542C3×D4—34no—
543C3×D4—94no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—42no—
552C2×C3×C4—91no—
553C2×C3×C4—91no—
554C2×C3×C4—91no—
555C2×C3×C4—121no—
556C2×C3×C4—361no—
557C2×C3×C4C22×D911yescharacteristic
558C2×C3×C4C22×D911yescharacteristic
559C2×C3×C4C2×D3211yescharacteristic
560C2×C3×C4C2×D3211yescharacteristic
561#67—34no—
562#67—94no—
563#67—94no—
564#67C4×D914yescomplemented
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—91no—
569C2×Dic3—91no—
570C2×Dic3—91no—
571C2×Dic3—91no—
572C2×Dic3—181no—
573C2×Dic3—181no—
574C2×Dic3—361no—
575C2×Dic3—361no—
576C2×Dic3—361no—
577C2×Dic3—361no—
578C2×Dic3—362no—
579C2×Dic3C22×D911yescharacteristic
580C2×Dic3C22×D911yescharacteristic
581C2×Dic3C22×D911yescharacteristic
582D12—94no—
583D12—94no—
584C4×D3—41no—
585C4×D3—94no—
586C4×D3—94no—
587C4×D3—121no—
588C4×D3—361no—
589C4×D3—361no—
590C4×D3—361no—
591C4×D3—361no—
592C4×D3—361no—
593C4×D3—361no—
594C2×C32—22no—
595C2×C32C22×C4×D311yescharacteristic
596C2×C32#100411yescharacteristic
597C2×C32#100911yescharacteristic
598C3⋊D3—62no—
599C3⋊D3—62no—
600C3×D3—22no—
601C3×D3—62no—
602C2×C9—24no—
603C2×C9—22no—
604C2×C9—21no—
605C2×C9—21no—
606C2×C9—21no—
607C2×C9—62no—
608C2×C9C22×C4×D311yescharacteristic
609C2×C9#100411yescharacteristic
610C2×C9#100911yescharacteristic
611D9—22no—
612D9—62no—
613D9—62no—
614D9—122no—
615D9—122no—
616C24—271no—
617C24—271no—
618C2×D4—31no—
619C2×D4—91no—
620C2×D4—271no—
621C2×D4—271no—
622C2×D4—278no—
623C22×C4—31no—
624C22×C4—91no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—271no—
628C22×C4—271no—
629C22×C4—271no—
630C22×C4—271no—
631C22×C4D3×D911yescharacteristic, complemented
632C4⋊C4—31no—
633C4⋊C4—91no—
634C4⋊C4—271no—
635C4⋊C4—271no—
636C22⋊C4—31no—
637C22⋊C4—31no—
638C22⋊C4—91no—
639C22⋊C4—91no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4—271no—
648C42—31no—
649C42—91no—
650C42—271no—
651C42—271no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—22no—
660C22×C3—32no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—92no—
664C22×C3—181no—
665C22×C3—181no—
666C22×C3C2×C4×D912yes—
667C22×C3C23×D911yescharacteristic
668C22×C3C4×D3212yes—
669C22×C3C22×D3211yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—32no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—92no—
676C2×D3—92no—
677C2×D3—92no—
678C2×D3—92no—
679C2×D3—182no—
680C2×D3—182no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—181no—
684C2×D3—181no—
685C2×D3—181no—
686C2×D3—181no—
687C2×D3—181no—
688C2×D3—181no—
689C2×D3—361no—
690C2×D3—361no—
691C2×D3—361no—
692C2×D3—361no—
693C2×D3—364no—
694C2×D3—364no—
695C2×D3—364no—
696C2×D3—364no—
697C2×D3—368no—
698C2×D3C2×C4×D912yes—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—32no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—61no—
707C3×C4—61no—
708C3×C4—92no—
709C3×C4—181no—
710C3×C4—181no—
711Dic3—21no—
712Dic3—21no—
713Dic3—32no—
714Dic3—61no—
715Dic3—61no—
716Dic3—181no—
717Dic3—181no—
718Dic3—181no—
719Dic3—181no—
720Dic3—361no—
721Dic3—361no—
722Dic3C2×C4×D912yes—
723C32#554511yescharacteristic
724C9—21no—
725C9#554511yescharacteristic, complemented
726C23—31no—
727C23—91no—
728C23—274no—
729C23—271no—
730C23—271no—
731C23—274no—
732C23—1081no—
733C23—1081no—
734C23—1081no—
735C23—1081no—
736C23C2×D3×D911yescharacteristic
737D4—34no—
738D4—94no—
739D4—274no—
740D4—274no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—41no—
745C2×C4—91no—
746C2×C4—91no—
747C2×C4—91no—
748C2×C4—121no—
749C2×C4—274no—
750C2×C4—271no—
751C2×C4—271no—
752C2×C4—361no—
753C2×C4—1081no—
754C2×C4—1081no—
755C2×C4—1081no—
756C2×C4—1081no—
757C2×C4—1081no—
758C2×C4C2×D3×D911yescharacteristic
759C2×C4C2×D3×D911yescharacteristic
760C2×C3—24no—
761C2×C3—22no—
762C2×C3—22no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—62no—
767C2×C3—182no—
768C2×C3C22×C4×D911yescharacteristic
769C2×C3#6371011yescharacteristic
770C2×C3#6371511yescharacteristic
771C2×C3C2×C4×D3211yescharacteristic
772C2×C3#6430811yescharacteristic
773C2×C3#6433011yescharacteristic
774D3—22no—
775D3—62no—
776D3—182no—
777D3—182no—
778D3—182no—
779D3—182no—
780D3—362no—
781D3—362no—
782C22—21no—
783C22—21no—
784C22—32no—
785C22—61no—
786C22—61no—
787C22—92no—
788C22—181no—
789C22—181no—
790C22—272no—
791C22—272no—
792C22—541no—
793C22—541no—
794C22—541no—
795C22—541no—
796C22—1084no—
797C22—1084no—
798C22C4×D3×D912yes—
799C22C22×D3×D911yescharacteristic
800C4—21no—
801C4—21no—
802C4—32no—
803C4—61no—
804C4—61no—
805C4—92no—
806C4—181no—
807C4—181no—
808C4—541no—
809C4—541no—
810C3—21no—
811C3#1058964711yescharacteristic, complemented
812C3#1059505811yescharacteristic
813C2—22no—
814C2—62no—
815C2—182no—
816C2—542no—
817C2—542no—
818C2C2×C4×D3×D911yescharacteristic
819C2#1172247811yescharacteristic
820C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
prime radicalC2×#88668C2
cosocleC22×C3×C9C24
hypercenterC22×C4D3×D9
hypocenterC3×C9#518
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#88536C2semidirect
3. C4×C9×#67C2semidirect
4. C3×C4×#611C2semidirect
5. #67⋊Dic9C2semidirect
6. #11721274C2semidirect
7. #611⋊Dic3C2semidirect
8. D3×(C2×D9)⋊C4C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721030C2semidirect
11. #11721013C2semidirect
12. #11721002C2semidirect
13. #11720977C2semidirect
14. #11720899C2semidirect
15. #11720898C2semidirect
20. C22×C3×C4×C9C22semidirect
21. C22×C3⋊Dic9C22semidirect
24. C2×C4×D3×C9C22semidirect
25. C2×C3×C4×D9C22semidirect
26. #88668C4semidirect
28. C2×D3×Dic9C22semidirect
31. C2×(C3⋊D9)⋊C4C22semidirect
32. C2×(C3⋊D9)⋊C4C22semidirect
33. C2×Dic3×D9C22semidirect
36. #88536C22semidirect
37. #88536C22semidirect
38. C9×#217C22semidirect
39. C3×#3676C22semidirect
40. C9×(C2×D3)⋊C4C22semidirect
41. C3×(C2×D9)⋊C4C22semidirect
42. C9×Dic3⋊C4C22semidirect
43. C4×C9×Dic3C22semidirect
44. C3×Dic9⋊C4C22semidirect
45. C3×C4×Dic9C22semidirect
46. (C2×D3)⋊Dic9C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. Dic3⋊Dic9C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
53. Dic3×Dic9C22semidirect
73. C4×#611D3semidirect
88. C22×C3⋊D9C2×C4semidirect
95. C2×D3×D9C2×C4semidirect
102. C9×#67C2×C4semidirect
103. C3×#611C2×C4semidirect
112. #6195C2×C4semidirect
114. #6192C2×C4semidirect
117. (C3⋊D9)⋊C4C2×C4semidirect
163. C22×C4×C9C2×D3semidirect
175. C2×C4×D9C2×D3semidirect
181. #3676C2×D3semidirect
193. (C2×D9)⋊C4C2×D3semidirect
196. Dic9⋊C4C2×D3semidirect
199. C4×Dic9C2×D3semidirect
237. C4×#67D9semidirect
322. #611C4×D3semidirect
358. C22×C3×C4C2×D9semidirect
382. C2×C4×D3C2×D9semidirect
394. #217C2×D9semidirect
414. (C2×D3)⋊C4C2×D9semidirect
420. Dic3⋊C4C2×D9semidirect
426. C4×Dic3C2×D9semidirect
513. C3×C9#518semidirect
564. #67C4×D9semidirect
631. C22×C4D3×D9semidirect
725. C9#5545semidirect
811. C3#10589647semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×#885362
C4×C9×#672
C3×C4×#6112
#67⋊Dic92
#117212742
#611⋊Dic32
D3×(C2×D9)⋊C42
D9×(C2×D3)⋊C42
#117210302
#117210132
#117210022
#117209772
#117208992
#117208982
#105950583
#105896473