Finite Group Databasebeta

← #13148139

Subgroups — #13148139

Order 1728.

1080 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D9×#67C211yesmaximal, characteristic, complemented
2C2×#88634C211yesmaximal, characteristic, complemented
3#11721729C211yesmaximal, characteristic, complemented
4C9×#885C211yesmaximal, characteristic, complemented
5C3×#63444C211yesmaximal, characteristic, complemented
6#11721270C211yesmaximal, characteristic, complemented
7D9×#217C211yesmaximal, characteristic, complemented
8#11721256C211yesmaximal, characteristic, complemented
9#11721049C211yesmaximal, characteristic, complemented
10#11721048C211yesmaximal, characteristic, complemented
11Dic3×D36C211yesmaximal, characteristic, complemented
12#11720989C211yesmaximal, characteristic, complemented
13#11720984C211yesmaximal, characteristic, complemented
14#11720982C211yesmaximal, characteristic, complemented
15#11720977C211yesmaximal, characteristic, complemented
16#10594281—31nomaximal
17#10589778—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic, complemented
24C2×C3×D36C2211yescharacteristic
25C2×C3×D36C2211yescharacteristic, complemented
26C2×C9×Dic6C2211yescharacteristic, complemented
27D9×#67—24no—
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic, complemented
30C2×#6192C2211yescharacteristic
31C2×#6192C2211yescharacteristic, complemented
32C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
33C2×Dic3×D9C2211yescharacteristic
34C2×Dic3×D9C2211yescharacteristic, complemented
35C2×Dic3×D9C2211yescharacteristic, complemented
36C2×Dic3×D9C2211yescharacteristic, complemented
37#88634—24no—
38C3×C9×C22⋊C4C2211yescharacteristic, complemented
39#88551C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
42#88534C2211yescharacteristic, complemented
43C9×#217C2211yescharacteristic, complemented
44C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C3×(C2×D9)⋊C4C2211yescharacteristic
47C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
48C4×C9×Dic3C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic
51(C2×D9)⋊Dic3C2211yescharacteristic
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic3⋊Dic9C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3796—31no—
57#64092—31no—
58C3×#885D311yescharacteristic
59C3×#882—31no—
60#63970—31no—
61D3×#217—31no—
62#63958—31no—
63#63922—31no—
64#63921—31no—
65Dic3×D12—31no—
66#63891—31no—
67#63887—31no—
68#63885—31no—
69#63880—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#63445—31no—
79#63445—61no—
80#63444—31no—
81#63444D311yescharacteristic, complemented
82C22⋊C4×D9—31no—
83C22⋊C4×D9—31no—
84C4×D36—31no—
85C4×D36—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9—22no—
90C22×C3×D9—22no—
91C22×C3×D9—41no—
92C22×C3×D9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
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—22no—
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C4×C3⋊D9—22no—
105C9×#67—22no—
106C3×#611—41no—
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C3×D36—22no—
112C3×D36—22no—
113C9×Dic6—22no—
114#6194—22no—
115#6194—41no—
116#6192—22no—
117#6192D414yescomplemented
118(C3⋊D9)⋊C4—41no—
119Dic3×D9—22no—
120Dic3×D9—22no—
121Dic3×D9—22no—
122Dic3×D9—41no—
123#5676—91no—
124#5591—91no—
125C23×C3×D3—31no—
126C22×D32—31no—
127C2×#638—31no—
128C2×C4×C3⋊D3—31no—
129C2×C3×#67—31no—
130C2×C3×#67C2×D311yescharacteristic
131C2×C3×D12—31no—
132C2×C3×D12—31no—
133C2×C3×Dic6C2×D311yescharacteristic
134D3×#67—64no—
135C2×#626—31no—
136C2×#626—31no—
137C2×#625—31no—
138C2×#625—31no—
139C2×#624—31no—
140C2×D3×Dic3—31no—
141C2×D3×Dic3—31no—
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144#3796—64no—
145C23×D9—31no—
146C23×D9C2×D311yescharacteristic
147C32×C22⋊C4C2×D311yescharacteristic
148#3757—31no—
149#3752—31no—
150C4⋊(C3⋊Dic3)—31no—
151#3750—31no—
152C3×#217C2×D311yescharacteristic
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4—31no—
155C3×(C2×D3)⋊C4C2×D311yescharacteristic
156C3×(C2×D3)⋊C4C2×D311yescharacteristic
157C3×C4×Dic3C2×D311yescharacteristic
158Dic3⋊Dic3—31no—
159Dic3⋊Dic3—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164C2×Q8×C9—31no—
165C2×D4×C9—31no—
166C2×#611—31no—
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—61no—
170C2×#611C2×D311yescharacteristic, complemented
171#3701—64no—
172D4×D9—64no—
173C2×D36—31no—
174C2×D36—31no—
175C2×D36C2×D311yescharacteristic
176C2×D36C2×D311yescharacteristic, complemented
177C2×C4×D9—31no—
178C2×C4×D9—31no—
179C2×C4×D9—31no—
180C2×C4×D9—31no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—61no—
184C9×C22⋊C4—21no—
185C9×C22⋊C4—31no—
186C9×C22⋊C4—31no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4C2×D311yescharacteristic, complemented
189C42×C9—31no—
190#3676—31no—
191#3676—31no—
192#3676—61no—
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—61no—
198(C2×D9)⋊C4C2×D311yescharacteristic
199(C2×D9)⋊C4C2×D311yescharacteristic, complemented
200C4⋊Dic9—31no—
201C4⋊Dic9—31no—
202C4⋊Dic9—61no—
203Dic9⋊C4—31no—
204Dic9⋊C4—31no—
205Dic9⋊C4—61no—
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⋊D9C2×D412yes—
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9—21no—
216C2×C3×D9—21no—
217C2×C3×D9—21no—
218C2×C3×D9—21no—
219C2×C3×D9—21no—
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—44no—
224C2×C3×D9C2×D412yes—
225C2×C3×D9#4112yescomplemented
226D3×D9—44no—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C3⋊Dic9—21no—
232C9×Dic3—21no—
233C9×Dic3—21no—
234C9×Dic3C2×D412yes—
235C3×Dic9—21no—
236C22×#67—91no—
237C2×#239—91no—
238C2×#237—91no—
239C2×D3×D4—91no—
240C3×#124—31no—
241C3×#120—91no—
242C2×#217—91no—
243#946—91no—
244#939—91no—
245#939—91no—
246#938—91no—
247#938—91no—
248#937—91no—
249D4×Dic3—91no—
250#886—91no—
251#885D911yescharacteristic, complemented
252#884—91no—
253#884—91no—
254#883—91no—
255#883—91no—
256#883—91no—
257#883—181no—
258#882—31no—
259#882—91no—
260#67⋊C4—91no—
261D3×C22⋊C4—91no—
262D3×C22⋊C4—91no—
263D3×C22⋊C4—91no—
264#878—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—31no—
272C22×C3×D3—62no—
273C22×C3×D3—62no—
274C22×C3×D3—121no—
275C22×C3×D3C22×D311yescharacteristic
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—121no—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281#638—62no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C4×C3⋊D3—62no—
286C3×#67—22no—
287C3×#67—121no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D311yescharacteristic
292C3×D12—62no—
293C3×D12—62no—
294C3×Dic6—22no—
295#626—34no—
296#626—62no—
297#625—62no—
298#625—121no—
299#624—121no—
300D3×Dic3—62no—
301D3×Dic3—62no—
302D3×Dic3—62no—
303D3×Dic3—121no—
304C23×C9—21no—
305C23×C9—31no—
306C23×C9C22×D311yescharacteristic
307C22×D9—22no—
308C22×D9—22no—
309C22×D9—31no—
310C22×D9—41no—
311C22×D9—61no—
312C22×D9—62no—
313C22×D9—62no—
314C22×D9—121no—
315C22×D9C22×D311yescharacteristic
316C22×D9C22×D311yescharacteristic
317C22×D9C22×D311yescharacteristic
318Q8×C9—62no—
319D4×C9—62no—
320C2×C4×C9—21no—
321C2×C4×C9—21no—
322C2×C4×C9—31no—
323C2×C4×C9—31no—
324C2×C4×C9—31no—
325C2×C4×C9C22×D311yescharacteristic
326C2×C4×C9C22×D311yescharacteristic
327#611—41no—
328#611—62no—
329#611—62no—
330#611—122no—
331#611—121no—
332C2×Dic9—31no—
333C2×Dic9—31no—
334C2×Dic9—31no—
335C2×Dic9—61no—
336C2×Dic9—61no—
337C2×Dic9—61no—
338C2×Dic9C22×D311yescharacteristic
339D36—22no—
340D36—22no—
341D36—34no—
342D36—62no—
343C4×D9—62no—
344C4×D9—62no—
345C4×D9—62no—
346C4×D9—62no—
347C4×D9—122no—
348C4×D9—121no—
349C4×D9—121no—
350#546—271noSylow
351C2×C3×C9—41no—
352C2×C3×C9C22×D411yescharacteristic
353C2×C3×C9C2×#4111yescharacteristic
354C2×C3×C9H(5,𝔽2)11yescharacteristic
355C3⋊D9—22no—
356D3×C9—41no—
357C3×D9—22no—
358C3×D9—22no—
359C3×D9—41no—
360C24×C3—91no—
361C23×D3—31no—
362C23×D3—91no—
363C23×D3—91no—
364C2×C3×Q8—31no—
365C2×C3×D4—31no—
366C2×C3×D4—91no—
367C2×C3×D4—91no—
368C2×C3×D4—91no—
369C2×#67—31no—
370C2×#67—91no—
371C2×#67—91no—
372C2×#67—91no—
373C2×#67—91no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—181no—
379C2×#67—184no—
380C2×#67C2×D911yescharacteristic
381C22×Dic3—91no—
382C22×Dic3—91no—
383C22×Dic3—91no—
384C22×Dic3—91no—
385#239—184no—
386#237—184no—
387D3×D4—184no—
388C2×D12—31no—
389C2×D12—31no—
390C2×D12—91no—
391C2×D12—91no—
392C2×C4×D3—91no—
393C2×C4×D3—91no—
394C2×C4×D3—91no—
395C2×C4×D3—91no—
396C2×C4×D3—91no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—181no—
401C2×Dic6C2×D911yescharacteristic, complemented
402C3×C22⋊C4—21no—
403C3×C22⋊C4—31no—
404C3×C22⋊C4—31no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—91no—
407C3×C22⋊C4—91no—
408C3×C22⋊C4C2×D911yescharacteristic, complemented
409C3×C22⋊C4D3211yescharacteristic
410C3×C42—31no—
411#217—91no—
412#217—91no—
413#217—91no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—181no—
418#217C2×D911yescharacteristic, complemented
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4—91no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—181no—
428(C2×D3)⋊C4C2×D911yescharacteristic, complemented
429(C2×D3)⋊C4C2×D911yescharacteristic, complemented
430C4⋊Dic3—91no—
431C4⋊Dic3—91no—
432C4⋊Dic3—91no—
433C4⋊Dic3—91no—
434C4⋊Dic3—181no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—181no—
440C4×Dic3C2×D911yescharacteristic, complemented
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32C23×D311yescharacteristic
445C2×C3⋊D3—32no—
446C2×C3⋊D3—61no—
447C2×C3⋊D3—61no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—32no—
452C2×C3×D3—32no—
453C2×C3×D3—61no—
454C2×C3×D3—61no—
455C2×C3×D3—61no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—124no—
461D32—124no—
462C32×C4—21no—
463C32×C4—21no—
464C3⋊Dic3—61no—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3×Dic3—21no—
468C3×Dic3—21no—
469C3×Dic3—61no—
470C3×Dic3D3×D412yes—
471C22×C9—21no—
472C22×C9—21no—
473C22×C9—21no—
474C22×C9—21no—
475C22×C9—41no—
476C22×C9—41no—
477C22×C9—41no—
478C22×C9—61no—
479C22×C9—61no—
480C22×C9—61no—
481C22×C9C23×D311yescharacteristic
482C2×D9—21no—
483C2×D9—21no—
484C2×D9—21no—
485C2×D9—21no—
486C2×D9—21no—
487C2×D9—21no—
488C2×D9—21no—
489C2×D9—32no—
490C2×D9—44no—
491C2×D9—62no—
492C2×D9—61no—
493C2×D9—61no—
494C2×D9—121no—
495C2×D9—121no—
496C2×D9—124no—
497C2×D9D3×D412yes—
498C2×D9#23712yescomplemented
499C4×C9—21no—
500C4×C9—21no—
501C4×C9—32no—
502C4×C9—41no—
503C4×C9—41no—
504C4×C9—61no—
505C4×C9—61no—
506Dic9—21no—
507Dic9—61no—
508Dic9—61no—
509Dic9—61no—
510Dic9—121no—
511Dic9—121no—
512Dic9—121no—
513C2×#41—271no—
514C22×D4—271no—
515#124—31no—
516#123—271no—
517#123—271no—
518C22⋊Q8—271no—
519#121—271no—
520#121—271no—
521#121—271no—
522#120—91no—
523#120—271no—
524C4×D4—271no—
525C4×D4—271no—
526C2×C22⋊C4—271no—
527C2×C22⋊C4—271no—
528C3×C9#54611yescharacteristic, complemented, Sylow
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—91no—
532C23×C3—91no—
533C23×C3—91no—
534C23×C3—182no—
535C23×C3—182no—
536C23×C3—361no—
537C23×C3C22×D911yescharacteristic
538C23×C3C2×D3211yescharacteristic
539C22×D3—31no—
540C22×D3—31no—
541C22×D3—31no—
542C22×D3—62no—
543C22×D3—62no—
544C22×D3—91no—
545C22×D3—91no—
546C22×D3—121no—
547C22×D3—181no—
548C22×D3—182no—
549C22×D3—182no—
550C22×D3—182no—
551C22×D3—182no—
552C22×D3—361no—
553C22×D3—361no—
554C22×D3C22×D911yescharacteristic
555C3×Q8—62no—
556C3×D4—62no—
557C3×D4—182no—
558C3×D4—182no—
559C3×D4—361no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—91no—
566C2×C3×C4C22×D911yescharacteristic
567C2×C3×C4C22×D911yescharacteristic
568C2×C3×C4C2×D3211yescharacteristic
569C2×C3×C4C2×D3211yescharacteristic
570#67—22no—
571#67—94no—
572#67—121no—
573#67—182no—
574#67—182no—
575#67—182no—
576#67—182no—
577#67—182no—
578#67—362no—
579#67—361no—
580#67—361no—
581C2×Dic3—31no—
582C2×Dic3—91no—
583C2×Dic3—91no—
584C2×Dic3—91no—
585C2×Dic3—91no—
586C2×Dic3—91no—
587C2×Dic3—91no—
588C2×Dic3—181no—
589C2×Dic3—181no—
590C2×Dic3—181no—
591C2×Dic3—182no—
592C2×Dic3—182no—
593C2×Dic3—182no—
594C2×Dic3—361no—
595C2×Dic3C22×D911yescharacteristic
596C2×Dic3C22×D911yescharacteristic
597C2×Dic3C22×D911yescharacteristic
598D12—62no—
599D12—62no—
600D12—94no—
601D12—182no—
602C4×D3—182no—
603C4×D3—182no—
604C4×D3—182no—
605C4×D3—182no—
606C4×D3—182no—
607C4×D3—362no—
608C4×D3—361no—
609C4×D3—361no—
610C4×D3—361no—
611Dic6—22no—
612C2×C32—41no—
613C2×C32C2×D3×D411yescharacteristic
614C2×C32D3×#4111yescharacteristic
615C2×C32#100911yescharacteristic
616C3⋊D3—62no—
617C3×D3—41no—
618C3×D3—62no—
619C3×D3—62no—
620C3×D3—121no—
621C2×C9—21no—
622C2×C9—21no—
623C2×C9—21no—
624C2×C9—41no—
625C2×C9—81no—
626C2×C9—121no—
627C2×C9C2×D3×D411yescharacteristic
628C2×C9C2×#23711yescharacteristic
629C2×C9#100411yescharacteristic
630D9—22no—
631D9—22no—
632D9—41no—
633D9—62no—
634D9—122no—
635C24—91no—
636C24—271no—
637#41—544no—
638C2×Q8—31no—
639C2×D4—31no—
640C2×D4—91no—
641C2×D4—91no—
642C2×D4—91no—
643C2×D4—271no—
644C2×D4—271no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4—544no—
649C22×C4—271no—
650C22×C4—271no—
651C22×C4—271no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C4⋊C4—271no—
656C4⋊C4—271no—
657C4⋊C4—271no—
658C4⋊C4—271no—
659C22⋊C4—31no—
660C22⋊C4—31no—
661C22⋊C4—31no—
662C22⋊C4—91no—
663C22⋊C4—91no—
664C22⋊C4—271no—
665C22⋊C4—271no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4D3×D911yescharacteristic, complemented
671C42—31no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—92no—
686C22×C3—92no—
687C22×C3—181no—
688C22×C3—181no—
689C22×C3—181no—
690C22×C3—181no—
691C22×C3—181no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3—364no—
695C22×C3C23×D911yescharacteristic
696C22×C3C22×D3211yescharacteristic
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—32no—
701C2×D3—32no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—92no—
710C2×D3—92no—
711C2×D3—124no—
712C2×D3—182no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—361no—
718C2×D3—361no—
719C2×D3—364no—
720C2×D3—364no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—32no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—61no—
729C3×C4—61no—
730C3×C4—181no—
731Dic3—21no—
732Dic3—21no—
733Dic3—61no—
734Dic3—181no—
735Dic3—181no—
736Dic3—181no—
737Dic3—181no—
738Dic3—181no—
739Dic3—181no—
740Dic3—361no—
741Dic3—361no—
742Dic3—361no—
743Dic3D4×D912yes—
744C32#567611yescharacteristic
745C9—21no—
746C9#559111yescharacteristic, complemented
747C23—31no—
748C23—91no—
749C23—91no—
750C23—91no—
751C23—182no—
752C23—182no—
753C23—271no—
754C23—361no—
755C23—542no—
756C23—542no—
757C23—1081no—
758C23C2×D3×D911yescharacteristic
759Q8—62no—
760D4—62no—
761D4—182no—
762D4—182no—
763D4—274no—
764D4—361no—
765D4—542no—
766D4—542no—
767D4—542no—
768D4—1081no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—91no—
773C2×C4—271no—
774C2×C4—271no—
775C2×C4—271no—
776C2×C4—542no—
777C2×C4—542no—
778C2×C4—542no—
779C2×C4—542no—
780C2×C4—1081no—
781C2×C4—1081no—
782C2×C4C2×D3×D911yescharacteristic
783C2×C4C2×D3×D911yescharacteristic
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—41no—
788C2×C3—41no—
789C2×C3—81no—
790C2×C3—121no—
791C2×C3—182no—
792C2×C3—182no—
793C2×C3—361no—
794C2×C3C2×D4×D911yescharacteristic
795C2×C3#41×D911yescharacteristic
796C2×C3#6371511yescharacteristic
797C2×C3#6430711yescharacteristic
798C2×C3D32×D411yescharacteristic
799C2×C3D3×#23711yescharacteristic
800D3—41no—
801D3—62no—
802D3—62no—
803D3—121no—
804D3—182no—
805D3—182no—
806D3—362no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—92no—
814C22—92no—
815C22—181no—
816C22—181no—
817C22—181no—
818C22—181no—
819C22—181no—
820C22—181no—
821C22—181no—
822C22—272no—
823C22—364no—
824C22—541no—
825C22—541no—
826C22—1084no—
827C22C22×D3×D911yescharacteristic
828C4—21no—
829C4—21no—
830C4—32no—
831C4—61no—
832C4—61no—
833C4—181no—
834C4—541no—
835C4—541no—
836C4—541no—
837C3—21no—
838C3#1058977811yescharacteristic, complemented
839C3#1059428111yescharacteristic
840C2—41no—
841C2—121no—
842C2—182no—
843C2—182no—
844C2—361no—
845C2—542no—
846C2#1172247711yescharacteristic
847C2D3×D4×D911yescharacteristic
848C2D9×#23711yescharacteristic
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×D9×#67C2semidirect
2. C2×#88634C2semidirect
3. #11721729C2semidirect
4. C9×#885C2semidirect
5. C3×#63444C2semidirect
6. #11721270C2semidirect
7. D9×#217C2semidirect
8. #11721256C2semidirect
9. #11721049C2semidirect
10. #11721048C2semidirect
11. Dic3×D36C2semidirect
12. #11720989C2semidirect
13. #11720984C2semidirect
14. #11720982C2semidirect
15. #11720977C2semidirect
21. C2×C4×C3⋊D9C22semidirect
23. C2×C3×#611C22semidirect
25. C2×C3×D36C22semidirect
26. C2×C9×Dic6C22semidirect
29. C2×#6194C22semidirect
31. C2×#6192C22semidirect
32. C2×(C3⋊D9)⋊C4C22semidirect
34. C2×Dic3×D9C22semidirect
35. C2×Dic3×D9C22semidirect
36. C2×Dic3×D9C22semidirect
38. C3×C9×C22⋊C4C22semidirect
39. #88551C22semidirect
40. #88536C22semidirect
41. C4⋊(C3⋊Dic9)C22semidirect
42. #88534C22semidirect
43. C9×#217C22semidirect
44. C9×(C2×D3)⋊C4C22semidirect
45. C9×(C2×D3)⋊C4C22semidirect
47. C3×(C2×D9)⋊C4C22semidirect
48. C4×C9×Dic3C22semidirect
49. (C2×D3)⋊Dic9C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic3⋊Dic9C22semidirect
54. Dic9⋊Dic3C22semidirect
81. #63444D3semidirect
117. #6192D4semidirect
170. C2×#611C2×D3semidirect
176. C2×D36C2×D3semidirect
188. C9×C22⋊C4C2×D3semidirect
199. (C2×D9)⋊C4C2×D3semidirect
225. C2×C3×D9#41semidirect
251. #885D9semidirect
401. C2×Dic6C2×D9semidirect
408. C3×C22⋊C4C2×D9semidirect
418. #217C2×D9semidirect
428. (C2×D3)⋊C4C2×D9semidirect
429. (C2×D3)⋊C4C2×D9semidirect
440. C4×Dic3C2×D9semidirect
498. C2×D9#237semidirect
528. C3×C9#546semidirect
670. C22⋊C4D3×D9semidirect
746. C9#5591semidirect
838. C3#10589778semidirect

Maximal subgroups

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

subgroupindex
C2×D9×#672
C2×#886342
#117217292
C9×#8852
C3×#634442
#117212702
D9×#2172
#117212562
#117210492
#117210482
Dic3×D362
#117209892
#117209842
#117209822
#117209772
#105942813
#105897783