Finite Group Databasebeta

← #13148411

Subgroups — #13148411

Order 1728.

1410 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88668C211yesmaximal, characteristic, complemented
2C2×#88668C211yesmaximal, characteristic, complemented
3C2×#88646C211yesmaximal, characteristic, complemented
4C2×C4×D3×D9C211yesmaximal, characteristic, complemented
5C22⋊C4×C3⋊D9C211yesmaximal, characteristic, complemented
6C9×#884C211yesmaximal, characteristic, complemented
7C3×#63446C211yesmaximal, characteristic, complemented
8#11721281C211yesmaximal, characteristic, complemented
9#11721270C211yesmaximal, characteristic, complemented
10#11721048C211yesmaximal, characteristic, complemented
11#11721034C211yesmaximal, characteristic, complemented
12#11721033C211yesmaximal, characteristic, complemented
13#11721017C211yesmaximal, characteristic, complemented
14#11720983C211yesmaximal, characteristic, complemented
15#11720980C211yesmaximal, characteristic, complemented
16#10594265—31nomaximal
17D9×#121—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C22×D3×D9C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic
22C2×C4×C3⋊D9C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic, complemented
24C2×C9×#67C2211yescharacteristic, complemented
25C2×C3×#611C2211yescharacteristic, complemented
26C2×C3×#611C2211yescharacteristic, complemented
27C2×C9×D12C2211yescharacteristic, complemented
28C2×C4×D3×C9C2211yescharacteristic, complemented
29C2×C3×D36C2211yescharacteristic, complemented
30C2×C3×C4×D9C2211yescharacteristic, complemented
31#88668—24no—
32#88668—24no—
33C2×#6195C2211yescharacteristic, complemented
34C2×#6195C2211yescharacteristic, complemented
35C2×#6194C2211yescharacteristic, complemented
36C2×#6194C2211yescharacteristic, complemented
37C2×D3×Dic9C2211yescharacteristic, complemented
38C2×#6192C2211yescharacteristic, complemented
39C2×#6192C2211yescharacteristic, complemented
40C2×(C3⋊D9)⋊C4C2211yescharacteristic
41C2×(C3⋊D9)⋊C4C2211yescharacteristic
42C2×Dic3×D9C2211yescharacteristic, complemented
43#88646—24no—
44C4×D3×D9—24no—
45C3×C9×C22⋊C4C2211yescharacteristic, complemented
46#88551C2211yescharacteristic, complemented
47#88536C2211yescharacteristic, complemented
48#88536C2211yescharacteristic, complemented
49C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
51C9×Dic3⋊C4C2211yescharacteristic, complemented
52C3×Dic9⋊C4C2211yescharacteristic, complemented
53(C2×D3)⋊Dic9C2211yescharacteristic, complemented
54(C2×D9)⋊Dic3C2211yescharacteristic, complemented
55Dic3⋊Dic9C2211yescharacteristic, complemented
56Dic9⋊Dic3C2211yescharacteristic, complemented
57C2×#3811—31no—
58C2×#3811—31no—
59C2×#3802—31no—
60C2×C4×D32—31no—
61C22⋊C4×C3⋊D3—31no—
62C3×#884—31no—
63C3×#884D311yescharacteristic
64#63970—31no—
65#63970—31no—
66#63921—31no—
67#63906—31no—
68#63906—31no—
69#63886—31no—
70#63886—31no—
71#63883—31no—
72C2×D4×D9—31no—
73C2×D4×D9—31no—
74C2×D4×D9—31no—
75C22×C4×D9—31no—
76C9×#121—31no—
77#63501—31no—
78#63501—31no—
79#63500—31no—
80#63492—31no—
81#63457—31no—
82C4⋊C4×D9—31no—
83#63446—31no—
84#63446D311yescharacteristic, complemented
85C22⋊C4×D9—31no—
86C22⋊C4×D9—31no—
87C22⋊C4×D9—61no—
88C23×C3×C9C2311yescharacteristic
89C22×C3⋊D9—22no—
90C22×C3⋊D9—22no—
91C22×C3⋊D9—22no—
92C22×C3⋊D9C2311yescharacteristic
93C22×C3⋊D9C2311yescharacteristic
94C22×D3×C9C2311yescharacteristic
95C22×D3×C9C2311yescharacteristic
96C22×C3×D9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98C2×D3×D9—22no—
99C2×D3×D9—22no—
100C2×D3×D9—22no—
101C2×D3×D9—22no—
102C2×D3×D9—22no—
103C2×D3×D9D414yescomplemented
104C2×C3×C4×C9C2311yescharacteristic
105C2×C3×C4×C9C2311yescharacteristic
106C2×C3⋊Dic9C2311yescharacteristic
107C2×C3⋊Dic9C2311yescharacteristic
108C4×C3⋊D9—22no—
109C4×C3⋊D9—22no—
110C9×#67—22no—
111C9×#67—22no—
112C3×#611—22no—
113C3×#611—22no—
114C2×C9×Dic3C2311yescharacteristic
115C2×C9×Dic3C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117C2×C3×Dic9C2311yescharacteristic
118C9×D12—22no—
119C4×D3×C9—22no—
120C3×D36—22no—
121C3×C4×D9—22no—
122#6195—22no—
123#6195—22no—
124#6194—22no—
125#6194—22no—
126D3×Dic9—22no—
127#6192—22no—
128#6192—22no—
129(C3⋊D9)⋊C4—22no—
130(C3⋊D9)⋊C4D414yescomplemented
131Dic3×D9—22no—
132D3×#121—91no—
133D3×#121—91no—
134C23×C3⋊D3—31no—
135C22×D32—31no—
136C22×D32—31no—
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3—31no—
139C2×C3×#67—31no—
140C2×C3×#67—31no—
141C2×C3×#67C2×D311yescharacteristic
142C2×C3×#67C2×D311yescharacteristic
143C2×C3×D12—31no—
144C2×C3×D12C2×D311yescharacteristic
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3C2×D311yescharacteristic
147#3811—64no—
148#3811—64no—
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—31no—
152C2×#626—31no—
153C2×#625—31no—
154C2×#625—31no—
155C2×#624—31no—
156C2×#624—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159#3802—64no—
160C4×D32—64no—
161C23×D9—31no—
162C23×D9—31no—
163C23×D9—31no—
164C23×D9—61no—
165C32×C22⋊C4C2×D311yescharacteristic
166#3757—31no—
167#3752—31no—
168#3752—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4C2×D311yescharacteristic
171C3×Dic3⋊C4—31no—
172C3×Dic3⋊C4C2×D311yescharacteristic
173Dic3⋊Dic3—31no—
174Dic3⋊Dic3—31no—
175(C2×D3)⋊Dic3—31no—
176(C2×D3)⋊Dic3—31no—
177C2×D4×C9—31no—
178C2×D4×C9—31no—
179C2×D4×C9—31no—
180C22×C4×C9—31no—
181C2×#611—31no—
182C2×#611—31no—
183C2×#611—31no—
184C2×#611—31no—
185C2×#611C2×D311yescharacteristic, complemented
186C2×#611C2×D311yescharacteristic, complemented
187C22×Dic9—31no—
188D4×D9—64no—
189D4×D9—64no—
190D4×D9—64no—
191C2×D36—31no—
192C2×D36—31no—
193C2×D36C2×D311yescharacteristic, complemented
194C2×C4×D9—31no—
195C2×C4×D9—31no—
196C2×C4×D9—31no—
197C2×C4×D9—31no—
198C2×C4×D9—31no—
199C2×C4×D9—64no—
200C2×C4×D9—61no—
201C2×C4×D9—61no—
202C2×C4×D9C2×D311yescharacteristic, complemented
203C9×C4⋊C4—31no—
204C9×C22⋊C4—21no—
205C9×C22⋊C4—31no—
206C9×C22⋊C4C2×D311yescharacteristic, complemented
207#3676—31no—
208#3676—31no—
209#3676—61no—
210(C2×D9)⋊C4—31no—
211(C2×D9)⋊C4—31no—
212(C2×D9)⋊C4—31no—
213(C2×D9)⋊C4—61no—
214(C2×D9)⋊C4—61no—
215(C2×D9)⋊C4C2×D311yescharacteristic, complemented
216C4⋊Dic9—31no—
217Dic9⋊C4—31no—
218Dic9⋊C4C2×D311yescharacteristic, complemented
219C22×C3×C9—21no—
220C22×C3×C9—21no—
221C22×C3×C9—21no—
222C22×C3×C9C2411yescharacteristic
223C2×C3⋊D9—21no—
224C2×C3⋊D9—21no—
225C2×C3⋊D9—21no—
226C2×C3⋊D9—44no—
227C2×C3⋊D9C2×D412yes—
228C2×C3⋊D9C2×D412yes—
229C2×C3⋊D9#4112yes—
230C2×D3×C9—21no—
231C2×D3×C9—21no—
232C2×D3×C9—21no—
233C2×D3×C9—21no—
234C2×D3×C9—21no—
235C2×D3×C9C2×D412yescomplemented
236C2×C3×D9—21no—
237C2×C3×D9—21no—
238C2×C3×D9—21no—
239C2×C3×D9—21no—
240C2×C3×D9—21no—
241C2×C3×D9C2×D412yescomplemented
242D3×D9—28no—
243D3×D9—44no—
244C3×C4×C9—21no—
245C3×C4×C9—21no—
246C3⋊Dic9—21no—
247C3⋊Dic9—21no—
248C9×Dic3—21no—
249C9×Dic3C2×D412yescomplemented
250C3×Dic9—21no—
251C3×Dic9C2×D412yescomplemented
252C2×D3×D4—91no—
253C2×D3×D4—91no—
254C2×D3×D4—91no—
255C2×D3×D4—91no—
256C2×D3×D4—91no—
257C2×D3×D4—91no—
258C22×C4×D3—91no—
259C22×C4×D3—91no—
260C3×#121—31no—
261C3×#121—91no—
262#939—91no—
263#939—91no—
264#939—91no—
265#939—91no—
266#938—91no—
267#938—91no—
268#930—91no—
269#930—91no—
270#895—91no—
271#895—91no—
272D3×C4⋊C4—91no—
273D3×C4⋊C4—91no—
274#884—31no—
275#884—91no—
276#884—91no—
277#884D911yescharacteristic, complemented
278D3×C22⋊C4—91no—
279D3×C22⋊C4—91no—
280D3×C22⋊C4—91no—
281D3×C22⋊C4—91no—
282D3×C22⋊C4—181no—
283C23×C32C22×D311yescharacteristic
284C22×C3⋊D3—31no—
285C22×C3⋊D3—31no—
286C22×C3⋊D3—62no—
287C22×C3⋊D3—62no—
288C22×C3⋊D3—62no—
289C22×C3×D3—31no—
290C22×C3×D3—31no—
291C22×C3×D3C22×D311yescharacteristic
292C22×C3×D3C22×D311yescharacteristic
293C2×D32—34no—
294C2×D32—62no—
295C2×D32—62no—
296C2×D32—62no—
297C2×D32—62no—
298C2×D32—62no—
299C2×C32×C4C22×D311yescharacteristic
300C2×C32×C4C22×D311yescharacteristic
301C2×C3⋊Dic3—31no—
302C2×C3⋊Dic3—31no—
303C4×C3⋊D3—62no—
304C4×C3⋊D3—62no—
305C3×#67—22no—
306C3×#67—22no—
307C3×#67—62no—
308C3×#67—62no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3C22×D311yescharacteristic
312C2×C3×Dic3C22×D311yescharacteristic
313C3×D12—22no—
314C3×D12—62no—
315C3×C4×D3—22no—
316C3×C4×D3—62no—
317#626—62no—
318#626—62no—
319#626—62no—
320#626—62no—
321#625—62no—
322#625—62no—
323#624—34no—
324#624—62no—
325D3×Dic3—62no—
326D3×Dic3—62no—
327C23×C9—21no—
328C23×C9—31no—
329C23×C9—31no—
330C23×C9C22×D311yescharacteristic
331C22×D9—31no—
332C22×D9—34no—
333C22×D9—31no—
334C22×D9—61no—
335C22×D9—61no—
336C22×D9—62no—
337C22×D9—62no—
338C22×D9—62no—
339C22×D9—62no—
340C22×D9—62no—
341C22×D9—62no—
342C22×D9—62no—
343C22×D9—62no—
344C22×D9—64no—
345C22×D9—122no—
346C22×D9—122no—
347C22×D9C22×D311yescharacteristic
348C22×D9C22×D311yescharacteristic
349D4×C9—62no—
350D4×C9—62no—
351D4×C9—62no—
352C2×C4×C9—21no—
353C2×C4×C9—21no—
354C2×C4×C9—31no—
355C2×C4×C9—31no—
356C2×C4×C9—62no—
357C2×C4×C9C22×D311yescharacteristic
358C2×C4×C9C22×D311yescharacteristic
359#611—22no—
360#611—22no—
361#611—62no—
362#611—62no—
363#611—62no—
364#611—62no—
365C2×Dic9—31no—
366C2×Dic9—31no—
367C2×Dic9—61no—
368C2×Dic9—61no—
369C2×Dic9—62no—
370C2×Dic9C22×D311yescharacteristic
371C2×Dic9C22×D311yescharacteristic
372D36—22no—
373D36—62no—
374D36—62no—
375C4×D9—22no—
376C4×D9—34no—
377C4×D9—62no—
378C4×D9—62no—
379C4×D9—62no—
380C4×D9—62no—
381C4×D9—122no—
382C4×D9—122no—
383C2×#121—271noSylow
384C2×C3×C9—41no—
385C2×C3×C9C22×D411yescharacteristic
386C2×C3×C9C22×D411yescharacteristic
387C2×C3×C9C2×#4111yescharacteristic
388C3⋊D9—41no—
389C3⋊D9#12114yescomplemented
390D3×C9—22no—
391D3×C9—41no—
392C3×D9—22no—
393C3×D9—41no—
394C23×D3—91no—
395C23×D3—91no—
396C23×D3—91no—
397C23×D3—91no—
398C23×D3—91no—
399C23×D3—91no—
400C23×D3—181no—
401C2×C3×D4—31no—
402C2×C3×D4—31no—
403C2×C3×D4—31no—
404C2×C3×D4—91no—
405C2×C3×D4—91no—
406C2×C3×D4—91no—
407C22×C3×C4—31no—
408C22×C3×C4—91no—
409C2×#67—31no—
410C2×#67—31no—
411C2×#67—91no—
412C2×#67—91no—
413C2×#67—91no—
414C2×#67—91no—
415C2×#67—91no—
416C2×#67—91no—
417C2×#67—91no—
418C2×#67—91no—
419C2×#67C2×D911yescharacteristic, complemented
420C2×#67C2×D911yescharacteristic, complemented
421C22×Dic3—91no—
422C22×Dic3—91no—
423D3×D4—184no—
424D3×D4—184no—
425D3×D4—184no—
426D3×D4—184no—
427D3×D4—184no—
428D3×D4—184no—
429C2×D12—31no—
430C2×D12—91no—
431C2×D12—91no—
432C2×D12—91no—
433C2×D12—91no—
434C2×D12C2×D911yescharacteristic, complemented
435C2×C4×D3—31no—
436C2×C4×D3—91no—
437C2×C4×D3—91no—
438C2×C4×D3—91no—
439C2×C4×D3—91no—
440C2×C4×D3—91no—
441C2×C4×D3—91no—
442C2×C4×D3—91no—
443C2×C4×D3—91no—
444C2×C4×D3—91no—
445C2×C4×D3—91no—
446C2×C4×D3—181no—
447C2×C4×D3—181no—
448C2×C4×D3—184no—
449C2×C4×D3—184no—
450C2×C4×D3C2×D911yescharacteristic, complemented
451C3×C4⋊C4—31no—
452C3×C4⋊C4—91no—
453C3×C22⋊C4—21no—
454C3×C22⋊C4—31no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4C2×D911yescharacteristic, complemented
457C3×C22⋊C4D3211yescharacteristic
458#217—91no—
459#217—91no—
460#217—91no—
461#217—91no—
462#217—181no—
463(C2×D3)⋊C4—31no—
464(C2×D3)⋊C4—91no—
465(C2×D3)⋊C4—91no—
466(C2×D3)⋊C4—91no—
467(C2×D3)⋊C4—91no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4—91no—
470(C2×D3)⋊C4—181no—
471(C2×D3)⋊C4—181no—
472(C2×D3)⋊C4C2×D911yescharacteristic, complemented
473C4⋊Dic3—91no—
474C4⋊Dic3—91no—
475Dic3⋊C4—31no—
476Dic3⋊C4—91no—
477Dic3⋊C4—91no—
478Dic3⋊C4C2×D911yescharacteristic, complemented
479C22×C32—21no—
480C22×C32—21no—
481C22×C32—21no—
482C22×C32C23×D311yescharacteristic
483C2×C3⋊D3—32no—
484C2×C3⋊D3—32no—
485C2×C3⋊D3—32no—
486C2×C3⋊D3—61no—
487C2×C3⋊D3—61no—
488C2×C3⋊D3—61no—
489C2×C3⋊D3—124no—
490C2×C3×D3—21no—
491C2×C3×D3—21no—
492C2×C3×D3—21no—
493C2×C3×D3—21no—
494C2×C3×D3—21no—
495C2×C3×D3—32no—
496C2×C3×D3—61no—
497C2×C3×D3—61no—
498C2×C3×D3—61no—
499C2×C3×D3—61no—
500C2×C3×D3—61no—
501C2×C3×D3D3×D412yes—
502D32—68no—
503D32—124no—
504C32×C4—21no—
505C32×C4—21no—
506C3⋊Dic3—61no—
507C3⋊Dic3—61no—
508C3×Dic3—21no—
509C3×Dic3—32no—
510C3×Dic3—61no—
511C3×Dic3D3×D412yes—
512C22×C9—22no—
513C22×C9—21no—
514C22×C9—21no—
515C22×C9—21no—
516C22×C9—21no—
517C22×C9—32no—
518C22×C9—41no—
519C22×C9—41no—
520C22×C9—61no—
521C22×C9—61no—
522C22×C9—61no—
523C22×C9—61no—
524C22×C9—61no—
525C22×C9C23×D311yescharacteristic
526C2×D9—21no—
527C2×D9—21no—
528C2×D9—21no—
529C2×D9—21no—
530C2×D9—21no—
531C2×D9—32no—
532C2×D9—32no—
533C2×D9—32no—
534C2×D9—62no—
535C2×D9—62no—
536C2×D9—62no—
537C2×D9—68no—
538C2×D9—62no—
539C2×D9—61no—
540C2×D9—61no—
541C2×D9—61no—
542C2×D9—121no—
543C2×D9—121no—
544C2×D9—124no—
545C2×D9—124no—
546C2×D9—128no—
547C2×D9D3×D412yescomplemented
548C4×C9—21no—
549C4×C9—21no—
550C4×C9—32no—
551C4×C9—41no—
552C4×C9—41no—
553C4×C9—61no—
554Dic9—21no—
555Dic9—61no—
556Dic9—61no—
557Dic9—121no—
558Dic9—121no—
559Dic9D3×D412yescomplemented
560C22×D4—271no—
561C22×D4—271no—
562C22×D4—271no—
563C23×C4—271no—
564#121—31no—
565#121—91no—
566#121—271no—
567#121—271no—
568#121—271no—
569#121—271no—
570#121—271no—
571#121—271no—
572C2×C4⋊C4—271no—
573C2×C22⋊C4—271no—
574C2×C22⋊C4—271no—
575C3×C9C2×#12111yescharacteristic, complemented, Sylow
576C23×C3—21no—
577C23×C3—31no—
578C23×C3—31no—
579C23×C3—91no—
580C23×C3—91no—
581C23×C3C22×D911yescharacteristic
582C23×C3C2×D3211yescharacteristic
583C22×D3—31no—
584C22×D3—31no—
585C22×D3—94no—
586C22×D3—91no—
587C22×D3—91no—
588C22×D3—94no—
589C22×D3—91no—
590C22×D3—91no—
591C22×D3—181no—
592C22×D3—181no—
593C22×D3—182no—
594C22×D3—182no—
595C22×D3—182no—
596C22×D3—182no—
597C22×D3—182no—
598C22×D3—182no—
599C22×D3—182no—
600C22×D3—182no—
601C22×D3—182no—
602C22×D3—182no—
603C22×D3—182no—
604C22×D3—182no—
605C22×D3—182no—
606C22×D3—182no—
607C22×D3—182no—
608C22×D3—182no—
609C22×D3—184no—
610C22×D3—362no—
611C22×D3—362no—
612C22×D3C22×D911yescharacteristic
613C22×D3C22×D911yescharacteristic
614C3×D4—62no—
615C3×D4—62no—
616C3×D4—62no—
617C3×D4—182no—
618C3×D4—182no—
619C3×D4—182no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—31no—
623C2×C3×C4—31no—
624C2×C3×C4—62no—
625C2×C3×C4—91no—
626C2×C3×C4—91no—
627C2×C3×C4—182no—
628C2×C3×C4C22×D911yescharacteristic
629C2×C3×C4C22×D911yescharacteristic
630C2×C3×C4C2×D3211yescharacteristic
631C2×C3×C4C2×D3211yescharacteristic
632#67—22no—
633#67—22no—
634#67—62no—
635#67—62no—
636#67—182no—
637#67—182no—
638#67—182no—
639#67—182no—
640#67—182no—
641#67—182no—
642#67—182no—
643#67—182no—
644C2×Dic3—31no—
645C2×Dic3—31no—
646C2×Dic3—91no—
647C2×Dic3—91no—
648C2×Dic3—91no—
649C2×Dic3—91no—
650C2×Dic3—181no—
651C2×Dic3—181no—
652C2×Dic3—182no—
653C2×Dic3—182no—
654C2×Dic3C22×D911yescharacteristic
655C2×Dic3C22×D911yescharacteristic
656D12—22no—
657D12—62no—
658D12—182no—
659D12—182no—
660D12—182no—
661D12—182no—
662C4×D3—22no—
663C4×D3—62no—
664C4×D3—94no—
665C4×D3—94no—
666C4×D3—182no—
667C4×D3—182no—
668C4×D3—182no—
669C4×D3—182no—
670C4×D3—182no—
671C4×D3—182no—
672C4×D3—182no—
673C4×D3—182no—
674C4×D3—362no—
675C4×D3—362no—
676C2×C32—41no—
677C2×C32C2×D3×D411yescharacteristic
678C2×C32C2×D3×D411yescharacteristic
679C2×C32D3×#4111yescharacteristic
680C3⋊D3—34no—
681C3⋊D3—121no—
682C3×D3—22no—
683C3×D3—41no—
684C3×D3—62no—
685C3×D3—121no—
686C2×C9—21no—
687C2×C9—21no—
688C2×C9—21no—
689C2×C9—42no—
690C2×C9—41no—
691C2×C9—62no—
692C2×C9—121no—
693C2×C9C2×D3×D411yescharacteristic
694C2×C9C2×D3×D411yescharacteristic
695C2×C9D3×#4111yescharacteristic
696D9—22no—
697D9—34no—
698D9—41no—
699D9—64no—
700D9—122no—
701D9—121no—
702C24—271no—
703C24—271no—
704C24—271no—
705C2×D4—31no—
706C2×D4—31no—
707C2×D4—31no—
708C2×D4—91no—
709C2×D4—91no—
710C2×D4—91no—
711C2×D4—271no—
712C2×D4—271no—
713C2×D4—271no—
714C2×D4—271no—
715C2×D4—271no—
716C2×D4—271no—
717C2×D4—544no—
718C2×D4—544no—
719C2×D4—544no—
720C22×C4—31no—
721C22×C4—91no—
722C22×C4—271no—
723C22×C4—271no—
724C22×C4—271no—
725C22×C4—271no—
726C22×C4—271no—
727C22×C4—271no—
728C22×C4—544no—
729C4⋊C4—31no—
730C4⋊C4—91no—
731C4⋊C4—271no—
732C4⋊C4—271no—
733C22⋊C4—31no—
734C22⋊C4—91no—
735C22⋊C4—271no—
736C22⋊C4—271no—
737C22⋊C4—271no—
738C22⋊C4—271no—
739C22⋊C4—271no—
740C22⋊C4D3×D911yescharacteristic, complemented
741C22×C3—22no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—32no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—61no—
753C22×C3—61no—
754C22×C3—61no—
755C22×C3—61no—
756C22×C3—61no—
757C22×C3—92no—
758C22×C3—181no—
759C22×C3—181no—
760C22×C3—181no—
761C22×C3—181no—
762C22×C3—181no—
763C22×C3C23×D911yescharacteristic
764C22×C3C22×D3211yescharacteristic
765C2×D3—21no—
766C2×D3—21no—
767C2×D3—21no—
768C2×D3—21no—
769C2×D3—21no—
770C2×D3—32no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—92no—
777C2×D3—92no—
778C2×D3—92no—
779C2×D3—92no—
780C2×D3—92no—
781C2×D3—92no—
782C2×D3—182no—
783C2×D3—182no—
784C2×D3—182no—
785C2×D3—188no—
786C2×D3—188no—
787C2×D3—182no—
788C2×D3—181no—
789C2×D3—181no—
790C2×D3—181no—
791C2×D3—181no—
792C2×D3—181no—
793C2×D3—181no—
794C2×D3—361no—
795C2×D3—361no—
796C2×D3—364no—
797C2×D3—364no—
798C2×D3—364no—
799C2×D3—364no—
800C2×D3—368no—
801C2×D3D4×D912yescomplemented
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—21no—
805C3×C4—21no—
806C3×C4—32no—
807C3×C4—41no—
808C3×C4—41no—
809C3×C4—61no—
810C3×C4—92no—
811C3×C4—181no—
812Dic3—21no—
813Dic3—32no—
814Dic3—61no—
815Dic3—181no—
816Dic3—181no—
817Dic3—181no—
818Dic3—181no—
819Dic3—361no—
820Dic3—361no—
821Dic3D4×D912yescomplemented
822C32D3×#12111yescharacteristic
823C9—21no—
824C9D3×#12111yescharacteristic, complemented
825C23—31no—
826C23—31no—
827C23—91no—
828C23—91no—
829C23—274no—
830C23—271no—
831C23—271no—
832C23—542no—
833C23—542no—
834C23—542no—
835C23—542no—
836C23—542no—
837C23—542no—
838C23—542no—
839C23—542no—
840C23C2×D3×D911yescharacteristic
841D4—62no—
842D4—62no—
843D4—62no—
844D4—182no—
845D4—182no—
846D4—182no—
847D4—542no—
848D4—542no—
849D4—542no—
850D4—542no—
851D4—542no—
852D4—542no—
853C2×C4—31no—
854C2×C4—31no—
855C2×C4—62no—
856C2×C4—91no—
857C2×C4—91no—
858C2×C4—182no—
859C2×C4—274no—
860C2×C4—271no—
861C2×C4—271no—
862C2×C4—542no—
863C2×C4—542no—
864C2×C4—542no—
865C2×C4—542no—
866C2×C4—542no—
867C2×C4C2×D3×D911yescharacteristic
868C2×C4C2×D3×D911yescharacteristic
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—42no—
873C2×C3—41no—
874C2×C3—41no—
875C2×C3—62no—
876C2×C3—121no—
877C2×C3—182no—
878C2×C3—361no—
879C2×C3C2×D4×D911yescharacteristic
880C2×C3C2×D4×D911yescharacteristic
881C2×C3#41×D911yescharacteristic
882C2×C3#6430611yescharacteristic
883C2×C3D32×D411yescharacteristic
884C2×C3D32×D411yescharacteristic
885D3—22no—
886D3—41no—
887D3—62no—
888D3—94no—
889D3—94no—
890D3—121no—
891D3—184no—
892D3—362no—
893D3—361no—
894D3—361no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—32no—
899C22—61no—
900C22—61no—
901C22—61no—
902C22—61no—
903C22—61no—
904C22—92no—
905C22—181no—
906C22—181no—
907C22—181no—
908C22—181no—
909C22—181no—
910C22—272no—
911C22—272no—
912C22—272no—
913C22—548no—
914C22—541no—
915C22—541no—
916C22—541no—
917C22—1084no—
918C22—1084no—
919C22C22×D3×D911yescharacteristic
920C4—21no—
921C4—21no—
922C4—32no—
923C4—61no—
924C4—92no—
925C4—181no—
926C4—541no—
927C4—541no—
928C3—21no—
929C3D9×#12111yescharacteristic, complemented
930C3#1059426511yescharacteristic
931C2—41no—
932C2—62no—
933C2—121no—
934C2—182no—
935C2—274no—
936C2—361no—
937C2—1081no—
938C2#1172247511yescharacteristic
939C2D3×D4×D911yescharacteristic
940C2D3×D4×D911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9C2×#121
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×#88668C2semidirect
2. C2×#88668C2semidirect
3. C2×#88646C2semidirect
4. C2×C4×D3×D9C2semidirect
5. C22⋊C4×C3⋊D9C2semidirect
6. C9×#884C2semidirect
7. C3×#63446C2semidirect
8. #11721281C2semidirect
9. #11721270C2semidirect
10. #11721048C2semidirect
11. #11721034C2semidirect
12. #11721033C2semidirect
13. #11721017C2semidirect
14. #11720983C2semidirect
15. #11720980C2semidirect
23. C2×C9×#67C22semidirect
24. C2×C9×#67C22semidirect
25. C2×C3×#611C22semidirect
26. C2×C3×#611C22semidirect
27. C2×C9×D12C22semidirect
28. C2×C4×D3×C9C22semidirect
29. C2×C3×D36C22semidirect
30. C2×C3×C4×D9C22semidirect
33. C2×#6195C22semidirect
34. C2×#6195C22semidirect
35. C2×#6194C22semidirect
36. C2×#6194C22semidirect
37. C2×D3×Dic9C22semidirect
38. C2×#6192C22semidirect
39. C2×#6192C22semidirect
42. C2×Dic3×D9C22semidirect
45. C3×C9×C22⋊C4C22semidirect
46. #88551C22semidirect
47. #88536C22semidirect
48. #88536C22semidirect
49. C9×(C2×D3)⋊C4C22semidirect
50. C3×(C2×D9)⋊C4C22semidirect
51. C9×Dic3⋊C4C22semidirect
52. C3×Dic9⋊C4C22semidirect
53. (C2×D3)⋊Dic9C22semidirect
54. (C2×D9)⋊Dic3C22semidirect
55. Dic3⋊Dic9C22semidirect
56. Dic9⋊Dic3C22semidirect
84. #63446D3semidirect
103. C2×D3×D9D4semidirect
130. (C3⋊D9)⋊C4D4semidirect
185. C2×#611C2×D3semidirect
186. C2×#611C2×D3semidirect
193. C2×D36C2×D3semidirect
202. C2×C4×D9C2×D3semidirect
206. C9×C22⋊C4C2×D3semidirect
215. (C2×D9)⋊C4C2×D3semidirect
218. Dic9⋊C4C2×D3semidirect
235. C2×D3×C9C2×D4semidirect
241. C2×C3×D9C2×D4semidirect
249. C9×Dic3C2×D4semidirect
251. C3×Dic9C2×D4semidirect
277. #884D9semidirect
389. C3⋊D9#121semidirect
419. C2×#67C2×D9semidirect
420. C2×#67C2×D9semidirect
434. C2×D12C2×D9semidirect
450. C2×C4×D3C2×D9semidirect
456. C3×C22⋊C4C2×D9semidirect
472. (C2×D3)⋊C4C2×D9semidirect
478. Dic3⋊C4C2×D9semidirect
547. C2×D9D3×D4semidirect
559. Dic9D3×D4semidirect
575. C3×C9C2×#121semidirect
740. C22⋊C4D3×D9semidirect
801. C2×D3D4×D9semidirect
821. Dic3D4×D9semidirect
824. C9D3×#121semidirect
929. C3D9×#121semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×#886462
C2×C4×D3×D92
C22⋊C4×C3⋊D92
C9×#8842
C3×#634462
#117212812
#117212702
#117210482
#117210342
#117210332
#117210172
#117209832
#117209802
#105942653
D9×#1213