Finite Group Databasebeta

← #13148141

Subgroups — #13148141

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88668C211yesmaximal, characteristic, complemented
2C2×#88635C211yesmaximal, characteristic, complemented
3#11721728C211yesmaximal, characteristic, complemented
4C9×#885C211yesmaximal, characteristic, complemented
5C3×#63445C211yesmaximal, characteristic, complemented
6#11721274C211yesmaximal, characteristic, complemented
7#11721271C211yesmaximal, characteristic, complemented
8#11721262C211yesmaximal, characteristic, complemented
9#11721051C211yesmaximal, characteristic, complemented
10D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#11721039C211yesmaximal, characteristic, complemented
12#11720993C211yesmaximal, characteristic, complemented
13#11720986C211yesmaximal, characteristic, complemented
14#11720977C211yesmaximal, characteristic, complemented
15#11720958C211yesmaximal, characteristic, complemented
16#10594282—31nomaximal
17#10589778—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic, complemented
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
23C2×C9×#67C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic, complemented
26C2×C9×Dic6C2211yescharacteristic, complemented
27#88668—24no—
28C2×#6195C2211yescharacteristic
29C2×#6195C2211yescharacteristic, complemented
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic, complemented
32C2×(C3⋊D9)⋊C4C2211yescharacteristic
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
35C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
36C2×Dic3×D9C2211yescharacteristic, complemented
37#88635—24no—
38C3×C9×C22⋊C4C2211yescharacteristic, complemented
39#88536C2211yescharacteristic
40#88536C2211yescharacteristic, complemented
41C9×#217C2211yescharacteristic, complemented
42C3×#3676C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C4×C9×Dic3C2211yescharacteristic, complemented
47C3×C4⋊Dic9C2211yescharacteristic, complemented
48C3×Dic9⋊C4C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50#88445C2211yescharacteristic
51#88445C2211yescharacteristic
52#88445C2211yescharacteristic, complemented
53Dic3⋊Dic9C2211yescharacteristic, complemented
54#88442C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×#3799—31no—
57#64091—31no—
58C3×#885D311yescharacteristic
59C3×#883—31no—
60#63974—31no—
61#63971—31no—
62#63958—31no—
63#63923—31no—
64D3×(C2×D3)⋊C4—31no—
65#63910—31no—
66#63894—31no—
67#63888—31no—
68#63880—31no—
69#63854—31no—
70C2×#3701—31no—
71C2×D4×D9—31no—
72C9×#124—31no—
73#63508—31no—
74#63500—31no—
75#63446—31no—
76#63446—31no—
77#63445—31no—
78#63445D311yescharacteristic, complemented
79#63444—31no—
80#63444—31no—
81#63444—61no—
82C22⋊C4×D9—31no—
83C22⋊C4×D9—31no—
84C4×D36—31no—
85C4×D36—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9—22no—
88C22×C3⋊D9—22no—
89C22×C3⋊D9—41no—
90C22×C3⋊D9C2311yescharacteristic
91C22×C3⋊D9C2311yescharacteristic
92C22×C3⋊D9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100#6233—41no—
101C2×C3⋊Dic9C2311yescharacteristic
102C4⋊(C3⋊D9)—22no—
103C4⋊(C3⋊D9)—22no—
104C9×#67—22no—
105C3×#611—22no—
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C3×C4×D9—22no—
113C9×Dic6—22no—
114#6195—22no—
115#6195—41no—
116#6192—22no—
117#6192D414yescomplemented
118(C3⋊D9)⋊C4—22no—
119(C3⋊D9)⋊C4—22no—
120(C3⋊D9)⋊C4—22no—
121(C3⋊D9)⋊C4—41no—
122Dic3×D9—41no—
123#5676—91no—
124#5654—91no—
125C23×C3⋊D3—31no—
126C22×D32—31no—
127C2×#638—31no—
128C2×C4⋊(C3⋊D3)—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C3×#67—31no—
131C2×C3×#67C2×D311yescharacteristic
132C2×C3×C4×D3—31no—
133C2×C3×Dic6C2×D311yescharacteristic
134#3811—64no—
135C2×#626—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#624—31no—
140C2×#624—31no—
141C2×#624—31no—
142C2×#624—31no—
143C2×D3×Dic3—31no—
144#3799—64no—
145C23×D9—31no—
146C23×D9—31no—
147C23×D9—61no—
148C32×C22⋊C4C2×D311yescharacteristic
149#3752—31no—
150#3752—31no—
151C3×#217—31no—
152C3×#217C2×D311yescharacteristic
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4C2×D311yescharacteristic
155C3×(C2×D3)⋊C4C2×D311yescharacteristic
156C3×C4⋊Dic3—31no—
157C3×Dic3⋊C4—31no—
158C3×C4×Dic3C2×D311yescharacteristic
159#3724—31no—
160Dic3⋊Dic3—31no—
161#3722—31no—
162#3722—31no—
163#3722—31no—
164(C2×D3)⋊Dic3—31no—
165C2×Q8×C9—31no—
166C2×D4×C9—31no—
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—61no—
171C2×#611C2×D311yescharacteristic
172#3701—64no—
173D4×D9—64no—
174C2×D36—31no—
175C2×D36—31no—
176C2×D36—31no—
177C2×D36—31no—
178C2×D36—61no—
179C2×D36—61no—
180C2×C4×D9—31no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—31no—
184C2×C4×D9—31no—
185C2×C4×D9C2×D311yescharacteristic, complemented
186C9×C22⋊C4—21no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4—31no—
189C9×C22⋊C4—31no—
190C9×C22⋊C4C2×D311yescharacteristic, complemented
191C42×C9—31no—
192#3676—31no—
193#3676C2×D311yescharacteristic, complemented
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—61no—
200(C2×D9)⋊C4—61no—
201(C2×D9)⋊C4C2×D311yescharacteristic, complemented
202C4⋊Dic9—31no—
203C4⋊Dic9C2×D311yescharacteristic, complemented
204Dic9⋊C4—31no—
205Dic9⋊C4C2×D311yescharacteristic, complemented
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9—21no—
209C22×C3×C9C2411yescharacteristic
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9—21no—
213C2×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9—21no—
216C2×C3⋊D9—21no—
217C2×C3⋊D9—44no—
218C2×C3⋊D9C2×D412yes—
219C2×C3⋊D9#4112yescomplemented
220C2×D3×C9—21no—
221C2×D3×C9—21no—
222C2×D3×C9—21no—
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9C2×D412yes—
226D3×D9—44no—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C9×Dic3—21no—
231C9×Dic3—21no—
232C9×Dic3C2×D412yes—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C2×#239—91no—
237C2×D3×D4—91no—
238C2×D3×D4—91no—
239C2×#235—91no—
240C3×#124—31no—
241C3×#123—91no—
242#946—91no—
243#939—91no—
244#938—91no—
245C2×(C2×D3)⋊C4—91no—
246#896—91no—
247#895—91no—
248#894—91no—
249#893—91no—
250#885D911yescharacteristic, complemented
251#884—91no—
252#884—91no—
253#884—91no—
254#883—31no—
255#883—91no—
256#882—91no—
257#882—91no—
258#882—91no—
259#882—91no—
260#882—181no—
261#67⋊C4—91no—
262D3×C22⋊C4—91no—
263D3×C22⋊C4—91no—
264D3×C22⋊C4—91no—
265C4×D12—91no—
266C4×D12—91no—
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
269C22×C3⋊D3—31no—
270C22×C3⋊D3—31no—
271C22×C3⋊D3—62no—
272C22×C3⋊D3—62no—
273C22×C3⋊D3—121no—
274C22×C3×D3—31no—
275C22×C3×D3C22×D311yescharacteristic
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—121no—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281#638—121no—
282C2×C3⋊Dic3—31no—
283C4⋊(C3⋊D3)—62no—
284C4⋊(C3⋊D3)—62no—
285C3×#67—22no—
286C3×#67—62no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D311yescharacteristic
292C2×C3×Dic3C22×D311yescharacteristic
293C3×C4×D3—62no—
294C3×Dic6—22no—
295#626—34no—
296#626—62no—
297#626—62no—
298#626—121no—
299#624—62no—
300#624—62no—
301#624—62no—
302#624—121no—
303D3×Dic3—121no—
304C23×C9—21no—
305C23×C9—31no—
306C23×C9C22×D311yescharacteristic
307C22×D9—31no—
308C22×D9—31no—
309C22×D9—31no—
310C22×D9—61no—
311C22×D9—61no—
312C22×D9—61no—
313C22×D9—62no—
314C22×D9—62no—
315C22×D9—62no—
316C22×D9—62no—
317C22×D9—122no—
318C22×D9—122no—
319C22×D9—121no—
320C22×D9—121no—
321C22×D9—122no—
322C22×D9C22×D311yescharacteristic
323Q8×C9—62no—
324D4×C9—62no—
325C2×C4×C9—21no—
326C2×C4×C9—21no—
327C2×C4×C9—31no—
328C2×C4×C9—31no—
329C2×C4×C9—31no—
330C2×C4×C9C22×D311yescharacteristic
331C2×C4×C9C22×D311yescharacteristic
332#611—22no—
333#611—62no—
334#611—121no—
335#611—121no—
336#611—122no—
337C2×Dic9—31no—
338C2×Dic9—61no—
339C2×Dic9C22×D311yescharacteristic
340C2×Dic9C22×D311yescharacteristic
341C2×Dic9C22×D311yescharacteristic
342D36—34no—
343D36—62no—
344D36—62no—
345D36—62no—
346D36—122no—
347D36—122no—
348C4×D9—22no—
349C4×D9—62no—
350C4×D9—62no—
351C4×D9—62no—
352C4×D9—121no—
353C4×D9—121no—
354#546—271noSylow
355C2×C3×C9—41no—
356C2×C3×C9C22×D411yescharacteristic
357C2×C3×C9C2×#4111yescharacteristic
358C2×C3×C9H(5,𝔽2)11yescharacteristic
359C3⋊D9—22no—
360C3⋊D9—22no—
361C3⋊D9—41no—
362D3×C9—41no—
363C3×D9—22no—
364C23×D3—91no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3—91no—
368C23×D3—181no—
369C2×C3×Q8—31no—
370C2×C3×D4—31no—
371C2×C3×D4—91no—
372C22×C3×C4—91no—
373C2×#67—31no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—181no—
381C2×#67C2×D911yescharacteristic
382C22×Dic3—91no—
383#239—184no—
384D3×D4—184no—
385D3×D4—184no—
386#235—184no—
387C2×D12—91no—
388C2×D12—91no—
389C2×D12—91no—
390C2×D12—91no—
391C2×D12—91no—
392C2×D12—91no—
393C2×D12—91no—
394C2×D12—91no—
395C2×D12—181no—
396C2×D12—181no—
397C2×C4×D3—31no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×C4×D3—91no—
407C2×Dic6C2×D911yescharacteristic, complemented
408C3×C4⋊C4—91no—
409C3×C4⋊C4—91no—
410C3×C22⋊C4—21no—
411C3×C22⋊C4—31no—
412C3×C22⋊C4—31no—
413C3×C22⋊C4—31no—
414C3×C22⋊C4—91no—
415C3×C22⋊C4—91no—
416C3×C22⋊C4C2×D911yescharacteristic, complemented
417C3×C22⋊C4D3211yescharacteristic
418C3×C42—31no—
419#217—31no—
420#217—91no—
421#217C2×D911yescharacteristic, complemented
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—181no—
435(C2×D3)⋊C4—181no—
436(C2×D3)⋊C4C2×D911yescharacteristic, complemented
437(C2×D3)⋊C4C2×D911yescharacteristic, complemented
438C4⋊Dic3—31no—
439C4⋊Dic3—91no—
440Dic3⋊C4—31no—
441Dic3⋊C4—91no—
442Dic3⋊C4—91no—
443Dic3⋊C4—91no—
444C4×Dic3C2×D911yescharacteristic, complemented
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32C23×D311yescharacteristic
449C2×C3⋊D3—32no—
450C2×C3⋊D3—32no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—61no—
453C2×C3⋊D3—61no—
454C2×C3⋊D3—61no—
455C2×C3⋊D3—61no—
456C2×C3⋊D3—61no—
457C2×C3⋊D3—61no—
458C2×C3⋊D3—124no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—32no—
463C2×C3×D3—61no—
464C2×C3×D3—61no—
465D32—124no—
466C32×C4—21no—
467C32×C4—21no—
468C3⋊Dic3—61no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C3×Dic3D3×D412yes—
475C22×C9—22no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—21no—
479C22×C9—21no—
480C22×C9—41no—
481C22×C9—41no—
482C22×C9—61no—
483C22×C9—61no—
484C22×C9—61no—
485C22×C9C23×D311yescharacteristic
486C2×D9—21no—
487C2×D9—21no—
488C2×D9—32no—
489C2×D9—32no—
490C2×D9—62no—
491C2×D9—62no—
492C2×D9—61no—
493C2×D9—61no—
494C2×D9—61no—
495C2×D9—61no—
496C2×D9—61no—
497C2×D9—61no—
498C2×D9—61no—
499C2×D9—121no—
500C2×D9—121no—
501C2×D9—121no—
502C2×D9—121no—
503C2×D9—121no—
504C2×D9—121no—
505C2×D9—121no—
506C2×D9—124no—
507C2×D9—124no—
508C2×D9—128no—
509C2×D9D3×D412yes—
510C4×C9—21no—
511C4×C9—21no—
512C4×C9—32no—
513C4×C9—41no—
514C4×C9—41no—
515C4×C9—61no—
516C4×C9—61no—
517Dic9—21no—
518Dic9—21no—
519Dic9—21no—
520Dic9—61no—
521Dic9—121no—
522C2×#41—271no—
523C22×D4—271no—
524#124—31no—
525#123—91no—
526#123—271no—
527C22⋊Q8—271no—
528#121—271no—
529#121—271no—
530#121—271no—
531#120—271no—
532#120—271no—
533C4×D4—271no—
534C4×D4—271no—
535C2×C22⋊C4—271no—
536C2×C22⋊C4—271no—
537C3×C9#54611yescharacteristic, complemented, Sylow
538C23×C3—21no—
539C23×C3—31no—
540C23×C3—91no—
541C23×C3C22×D911yescharacteristic
542C23×C3C2×D3211yescharacteristic
543C22×D3—31no—
544C22×D3—91no—
545C22×D3—91no—
546C22×D3—91no—
547C22×D3—91no—
548C22×D3—91no—
549C22×D3—91no—
550C22×D3—181no—
551C22×D3—181no—
552C22×D3—181no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—182no—
556C22×D3—182no—
557C22×D3—182no—
558C22×D3—182no—
559C22×D3—182no—
560C22×D3—182no—
561C22×D3—362no—
562C22×D3—362no—
563C22×D3—361no—
564C22×D3—361no—
565C22×D3—361no—
566C22×D3—361no—
567C22×D3—362no—
568C22×D3C22×D911yescharacteristic
569C3×Q8—62no—
570C3×D4—62no—
571C3×D4—182no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—91no—
578C2×C3×C4—91no—
579C2×C3×C4—91no—
580C2×C3×C4—182no—
581C2×C3×C4C22×D911yescharacteristic
582C2×C3×C4C22×D911yescharacteristic
583C2×C3×C4C2×D3211yescharacteristic
584C2×C3×C4C2×D3211yescharacteristic
585#67—22no—
586#67—62no—
587#67—94no—
588#67—182no—
589#67—182no—
590#67—361no—
591#67—361no—
592#67—361no—
593#67—362no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—181no—
600C2×Dic3—361no—
601C2×Dic3C22×D911yescharacteristic
602C2×Dic3C22×D911yescharacteristic
603C2×Dic3C22×D911yescharacteristic
604D12—94no—
605D12—182no—
606D12—182no—
607D12—182no—
608D12—182no—
609D12—182no—
610D12—182no—
611D12—362no—
612D12—362no—
613D12—361no—
614C4×D3—62no—
615C4×D3—182no—
616C4×D3—182no—
617C4×D3—182no—
618C4×D3—182no—
619C4×D3—182no—
620C4×D3—182no—
621C4×D3—361no—
622C4×D3—361no—
623C4×D3—361no—
624Dic6—22no—
625C2×C32—41no—
626C2×C32C2×D3×D411yescharacteristic
627C2×C32D3×#4111yescharacteristic
628C2×C32#100911yescharacteristic
629C3⋊D3—62no—
630C3⋊D3—62no—
631C3⋊D3—121no—
632C3×D3—41no—
633C3×D3—62no—
634C2×C9—21no—
635C2×C9—21no—
636C2×C9—21no—
637C2×C9—42no—
638C2×C9—41no—
639C2×C9—121no—
640C2×C9C2×D3×D411yescharacteristic
641C2×C9D3×#4111yescharacteristic
642C2×C9#100911yescharacteristic
643D9—22no—
644D9—62no—
645D9—62no—
646D9—122no—
647D9—122no—
648D9—121no—
649D9—241no—
650C24—271no—
651C24—271no—
652#41—544no—
653C2×Q8—31no—
654C2×D4—31no—
655C2×D4—91no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—271no—
659C2×D4—271no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—271no—
663C2×D4—544no—
664C22×C4—91no—
665C22×C4—271no—
666C22×C4—271no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C4⋊C4—91no—
671C4⋊C4—91no—
672C4⋊C4—271no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—31no—
677C22⋊C4—91no—
678C22⋊C4—91no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C22⋊C4—271no—
682C22⋊C4—271no—
683C22⋊C4—271no—
684C22⋊C4—271no—
685C22⋊C4D3×D911yescharacteristic, complemented
686C42—31no—
687C22×C3—22no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—61no—
698C22×C3—61no—
699C22×C3—61no—
700C22×C3—92no—
701C22×C3—181no—
702C22×C3—181no—
703C22×C3C23×D911yescharacteristic
704C22×C3C22×D3211yescharacteristic
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—32no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—92no—
712C2×D3—92no—
713C2×D3—92no—
714C2×D3—92no—
715C2×D3—182no—
716C2×D3—182no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—181no—
720C2×D3—181no—
721C2×D3—181no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—181no—
727C2×D3—181no—
728C2×D3—181no—
729C2×D3—181no—
730C2×D3—181no—
731C2×D3—361no—
732C2×D3—361no—
733C2×D3—361no—
734C2×D3—361no—
735C2×D3—361no—
736C2×D3—361no—
737C2×D3—361no—
738C2×D3—364no—
739C2×D3—364no—
740C2×D3—364no—
741C2×D3—364no—
742C2×D3—368no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—32no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—181no—
753C3×C4—181no—
754C3×C4—181no—
755Dic3—21no—
756Dic3—21no—
757Dic3—61no—
758Dic3—61no—
759Dic3—61no—
760Dic3—181no—
761Dic3—181no—
762Dic3—361no—
763Dic3D4×D912yes—
764C32#567611yescharacteristic
765C9—21no—
766C9#565411yescharacteristic, complemented
767C23—31no—
768C23—91no—
769C23—271no—
770C23—271no—
771C23—271no—
772C23—542no—
773C23—542no—
774C23—542no—
775C23—542no—
776C23—1081no—
777C23—1081no—
778C23C2×D3×D911yescharacteristic
779Q8—62no—
780D4—62no—
781D4—182no—
782D4—274no—
783D4—542no—
784D4—542no—
785D4—542no—
786D4—542no—
787D4—1081no—
788D4—1081no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—91no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—182no—
796C2×C4—271no—
797C2×C4—542no—
798C2×C4—542no—
799C2×C4—542no—
800C2×C4—1081no—
801C2×C4—1081no—
802C2×C4C2×D3×D911yescharacteristic
803C2×C4C2×D3×D911yescharacteristic
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—42no—
808C2×C3—41no—
809C2×C3—41no—
810C2×C3—121no—
811C2×C3—182no—
812C2×C3C2×D4×D911yescharacteristic
813C2×C3#41×D911yescharacteristic
814C2×C3#6371511yescharacteristic
815C2×C3#6430811yescharacteristic
816C2×C3D32×D411yescharacteristic
817C2×C3#6431211yescharacteristic
818D3—41no—
819D3—62no—
820D3—182no—
821D3—182no—
822D3—182no—
823D3—182no—
824D3—362no—
825D3—362no—
826D3—361no—
827D3—361no—
828D3—721no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—61no—
833C22—61no—
834C22—61no—
835C22—92no—
836C22—181no—
837C22—181no—
838C22—272no—
839C22—272no—
840C22—541no—
841C22—541no—
842C22—541no—
843C22—541no—
844C22—541no—
845C22—541no—
846C22—541no—
847C22—1084no—
848C22—1084no—
849C22C22×D3×D911yescharacteristic
850C4—21no—
851C4—21no—
852C4—32no—
853C4—61no—
854C4—61no—
855C4—181no—
856C4—181no—
857C4—181no—
858C4—541no—
859C3—21no—
860C3#1058977811yescharacteristic, complemented
861C3#1059428211yescharacteristic
862C2—41no—
863C2—121no—
864C2—182no—
865C2—542no—
866C2—542no—
867C2—1081no—
868C2#1172247811yescharacteristic
869C2D3×D4×D911yescharacteristic
870C2#1172249811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#546
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×#88635C2semidirect
3. #11721728C2semidirect
4. C9×#885C2semidirect
5. C3×#63445C2semidirect
6. #11721274C2semidirect
7. #11721271C2semidirect
8. #11721262C2semidirect
9. #11721051C2semidirect
10. D9×(C2×D3)⋊C4C2semidirect
11. #11721039C2semidirect
12. #11720993C2semidirect
13. #11720986C2semidirect
14. #11720977C2semidirect
15. #11720958C2semidirect
20. C2×#6233C22semidirect
22. C2×C4⋊(C3⋊D9)C22semidirect
25. C2×C3×C4×D9C22semidirect
26. C2×C9×Dic6C22semidirect
29. C2×#6195C22semidirect
31. C2×#6192C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
34. C2×(C3⋊D9)⋊C4C22semidirect
35. C2×(C3⋊D9)⋊C4C22semidirect
36. C2×Dic3×D9C22semidirect
38. C3×C9×C22⋊C4C22semidirect
40. #88536C22semidirect
41. C9×#217C22semidirect
42. C3×#3676C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C9×(C2×D3)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C4×C9×Dic3C22semidirect
47. C3×C4⋊Dic9C22semidirect
48. C3×Dic9⋊C4C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
52. #88445C22semidirect
53. Dic3⋊Dic9C22semidirect
54. #88442C22semidirect
78. #63445D3semidirect
117. #6192D4semidirect
185. C2×C4×D9C2×D3semidirect
190. C9×C22⋊C4C2×D3semidirect
193. #3676C2×D3semidirect
201. (C2×D9)⋊C4C2×D3semidirect
203. C4⋊Dic9C2×D3semidirect
205. Dic9⋊C4C2×D3semidirect
219. C2×C3⋊D9#41semidirect
250. #885D9semidirect
407. C2×Dic6C2×D9semidirect
416. C3×C22⋊C4C2×D9semidirect
421. #217C2×D9semidirect
436. (C2×D3)⋊C4C2×D9semidirect
437. (C2×D3)⋊C4C2×D9semidirect
444. C4×Dic3C2×D9semidirect
537. C3×C9#546semidirect
685. C22⋊C4D3×D9semidirect
766. C9#5654semidirect
860. C3#10589778semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×#886352
#117217282
C9×#8852
C3×#634452
#117212742
#117212712
#117212622
#117210512
D9×(C2×D3)⋊C42
#117210392
#117209932
#117209862
#117209772
#117209582
#105942823
#105897783