Finite Group Databasebeta

← D3×#41×D9 #13164774

Subgroups — D3×#41×D9 #13164774

Order 1728.

2834 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊D9C211yesmaximal, characteristic, complemented
2D3×C9×#41C211yesmaximal, characteristic, complemented
3C3×#41×D9C211yesmaximal, characteristic, complemented
4#11722514C211yesmaximal, characteristic, complemented
5D9×#239C211yesmaximal, characteristic, complemented
6D3×#3701C211yesmaximal, characteristic, complemented
7D3×Q8×D9C211yesmaximal, characteristic, complemented
8#11722498C213yesmaximal, complemented
9D9×#237C213yesmaximal, complemented
10D3×#3699C213yesmaximal, complemented
11D3×D4×D9C213yesmaximal, complemented
12#11722475C213yesmaximal, complemented
13D9×#235C213yesmaximal, complemented
14D3×#3697C213yesmaximal, complemented
15C2×C4×D3×D9C213yesmaximal, complemented
16D32×#41—31nomaximal
17C2×#41×D9—31nomaximal
18C22×D3×D9C2213yes—
19C3×C9×#41C2211yescharacteristic, complemented
20#88746C2211yescharacteristic, complemented
21Q8×C3⋊D9C2211yescharacteristic, complemented
22#88742C2213yescomplemented
23D4×C3⋊D9C2213yescomplemented
24#88736C2213yescomplemented
25C2×C4×C3⋊D9C2213yescomplemented
26C9×#239C2211yescharacteristic, complemented
27D3×Q8×C9C2211yescharacteristic, complemented
28C3×#3701C2211yescharacteristic, complemented
29C3×Q8×D9C2211yescharacteristic, complemented
30C9×#237C2213yescomplemented
31D3×D4×C9C2213yescomplemented
32C3×#3699C2213yescomplemented
33C3×D4×D9C2213yescomplemented
34C9×#235C2213yescomplemented
35C2×C4×D3×C9C2213yescomplemented
36C3×#3697C2213yescomplemented
37C2×C3×C4×D9C2213yescomplemented
38#88668C2216yescomplemented
39D9×#67C2216yescomplemented
40D3×#611C2216yescomplemented
41#88663C2216yescomplemented
42#88662C2216yescomplemented
43C2×D3×Dic9C2213yescomplemented
44C2×(C3⋊D9)⋊C4C2213yescomplemented
45#88658C2216yescomplemented
46C2×Dic3×D9C2213yescomplemented
47#88646C2213yescomplemented
48D9×D12C2213yescomplemented
49D3×D36C2213yescomplemented
50C4×D3×D9C2213yes—
51C4×D3×D9C2211yescharacteristic
52C4×D3×D9C2213yescomplemented
53C4×D3×D9C2213yescomplemented
54C4×D3×D9C2213yescomplemented
55C4×D3×D9C2213yescomplemented
56C4×D3×D9C2213yescomplemented
57C4×D3×D9C2213yescomplemented
58#88642C2213yescomplemented
59#88641C2213yescomplemented
60#88640C2216yescomplemented
61#88639C2213yescomplemented
62#88638C2213yescomplemented
63D3×Dic18C2213yescomplemented
64(C3⋊D9)⋊Q8C2213yescomplemented
65#88635C2213yescomplemented
66#88634C2213yescomplemented
67D9×Dic6C2213yescomplemented
68#41×C3⋊D3—31no—
69C3×D3×#41—31no—
70C3×D3×#41D311yescharacteristic
71#64319—31no—
72D3×#239—31no—
73D3×#239—31no—
74D32×Q8—31no—
75#64312—33no—
76D3×#237—33no—
77D3×#237—33no—
78D32×D4—33no—
79#64306—33no—
80D3×#235—33no—
81D3×#235—33no—
82C2×C4×D32—33no—
83C2×C9×#41—31no—
84#41×D9—31no—
85#41×D9—31no—
86#41×D9—31no—
87#41×D9—33no—
88#41×D9—33no—
89#41×D9—33no—
90#41×D9—33no—
91#41×D9—61no—
92#41×D9D311yescharacteristic, direct product factor
93C2×#3701—31no—
94C2×Q8×D9—31no—
95C2×#3699—33no—
96C2×D4×D9—33no—
97C2×#3697—33no—
98C22×C4×D9—33no—
99C22×C3⋊D9C2313yes—
100C22×D3×C9C2313yes—
101C22×C3×D9C2313yes—
102C2×D3×D9—212no—
103C2×D3×D9C2313yes—
104C2×D3×D9C2313yes—
105C2×D3×D9C2313yes—
106C2×D3×D9C2311yescharacteristic
107C3×Q8×C9C2311yescharacteristic, complemented
108C3×D4×C9C2313yescomplemented
109C2×C3×C4×C9C2313yescomplemented
110#6233C2316yescomplemented
111C2×C3⋊Dic9C2313yescomplemented
112C4⋊(C3⋊D9)C2313yescomplemented
113C4×C3⋊D9C2313yes—
114C4×C3⋊D9C2311yescharacteristic
115C4×C3⋊D9C2313yescomplemented
116C4×C3⋊D9C2313yescomplemented
117#6226C2313yescomplemented
118C9×#67C2316yescomplemented
119C3×#611C2316yescomplemented
120C2×C9×Dic3C2313yescomplemented
121C2×C3×Dic9C2313yescomplemented
122C9×D12C2313yescomplemented
123C4×D3×C9C2313yes—
124C4×D3×C9C2311yescharacteristic
125C4×D3×C9C2313yescomplemented
126C4×D3×C9C2313yescomplemented
127C3×D36C2313yescomplemented
128C3×C4×D9C2313yes—
129C3×C4×D9C2311yescharacteristic
130C3×C4×D9C2313yescomplemented
131C3×C4×D9C2313yescomplemented
132C9×Dic6C2313yescomplemented
133C3×Dic18C2313yescomplemented
134#6195C2316yescomplemented
135#6194C2316yescomplemented
136D3×Dic9C2313yes—
137D3×Dic9C2311yescharacteristic
138D3×Dic9C2313yescomplemented
139D3×Dic9C2313yescomplemented
140#6192C2316yescomplemented
141(C3⋊D9)⋊C4C2313yes—
142(C3⋊D9)⋊C4C2311yescharacteristic
143(C3⋊D9)⋊C4C2313yescomplemented
144(C3⋊D9)⋊C4C2313yescomplemented
145Dic3×D9C2313yes—
146Dic3×D9C2311yescharacteristic
147Dic3×D9C2313yescomplemented
148Dic3×D9C2313yescomplemented
149#6189C2316yescomplemented
150C2×D3×#41—91no—
151C2×D3×#41—91no—
152C22×D32—33no—
153C32×#41C2×D311yescharacteristic
154#3832—31no—
155Q8×C3⋊D3—31no—
156#3830—33no—
157D4×C3⋊D3—33no—
158#3828—33no—
159C2×C4×C3⋊D3—33no—
160C3×#239—31no—
161C3×#239C2×D311yescharacteristic
162C3×D3×Q8—31no—
163C3×D3×Q8C2×D311yescharacteristic
164C3×#237—33no—
165C3×#237C2×D313yes—
166C3×D3×D4—33no—
167C3×D3×D4C2×D313yes—
168C3×#235—33no—
169C3×#235C2×D313yes—
170C2×C3×C4×D3—33no—
171C2×C3×C4×D3C2×D313yes—
172#3811—36no—
173D3×#67—36no—
174D3×#67—36no—
175C2×#624—33no—
176#3805—36no—
177#3804—36no—
178#3804—36no—
179C2×D3×Dic3—33no—
180C2×D3×Dic3—33no—
181#3802—33no—
182D3×D12—33no—
183D3×D12—33no—
184C4×D32—31no—
185C4×D32—33no—
186C4×D32—33no—
187C4×D32—33no—
188C4×D32—33no—
189C4×D32—33no—
190C4×D32—33no—
191C4×D32—33no—
192#3799—33no—
193#3799—33no—
194#3798—36no—
195#3797—33no—
196#3796—33no—
197#3796—33no—
198#3795—33no—
199#3795—33no—
200D3×Dic6—33no—
201D3×Dic6—33no—
202C23×D9—33no—
203C9×#41—21no—
204C9×#41—31no—
205C9×#41—33no—
206C9×#41—33no—
207C9×#41C2×D311yescharacteristic, complemented
208C2×Q8×C9—31no—
209C2×D4×C9—33no—
210C22×C4×C9—33no—
211C2×#611—36no—
212C22×Dic9—33no—
213#3701—31no—
214#3701—33no—
215#3701—33no—
216#3701—61no—
217#3701C2×D311yescharacteristic, complemented
218Q8×D9—31no—
219Q8×D9—33no—
220Q8×D9—33no—
221Q8×D9—61no—
222Q8×D9C2×D311yescharacteristic, complemented
223#3699—33no—
224#3699—36no—
225#3699—36no—
226#3699—33no—
227#3699—33no—
228#3699—63no—
229#3699C2×D313yescomplemented
230D4×D9—36no—
231D4×D9—33no—
232D4×D9—36no—
233D4×D9—33no—
234D4×D9—33no—
235D4×D9—63no—
236D4×D9C2×D313yescomplemented
237#3697—33no—
238#3697—36no—
239#3697—33no—
240#3697—36no—
241#3697—33no—
242#3697—63no—
243#3697C2×D313yescomplemented
244C2×D36—33no—
245C2×C4×D9—33no—
246C2×C4×D9—33no—
247C2×C4×D9—33no—
248C2×C4×D9—31no—
249C2×C4×D9—33no—
250C2×C4×D9—33no—
251C2×C4×D9—33no—
252C2×C4×D9—33no—
253C2×C4×D9—33no—
254C2×C4×D9—33no—
255C2×C4×D9—33no—
256C2×C4×D9—63no—
257C2×C4×D9C2×D313yescomplemented
258C2×Dic18—33no—
259C22×C3×C9C2413yes—
260C2×C3⋊D9—26no—
261C2×C3⋊D9C2413yes—
262C2×C3⋊D9C2411yescharacteristic
263C2×D3×C9—26no—
264C2×D3×C9C2413yes—
265C2×D3×C9C2411yescharacteristic
266C2×C3×D9—26no—
267C2×C3×D9C2413yes—
268C2×C3×D9C2411yescharacteristic
269D3×D9—26no—
270D3×D9—26no—
271D3×D9—26no—
272D3×D9#4114yesdirect product factor
273C3×C4×C9C2413yes—
274C3×C4×C9C2411yescharacteristic
275C3⋊Dic9C2413yes—
276C3⋊Dic9C2411yescharacteristic
277C9×Dic3C2413yes—
278C9×Dic3C2411yescharacteristic
279C3×Dic9C2413yes—
280C3×Dic9C2411yescharacteristic
281C2×C3×#41—31no—
282C2×C3×#41—91no—
283D3×#41—31no—
284D3×#41—93no—
285D3×#41—93no—
286D3×#41—93no—
287D3×#41—93no—
288D3×#41—91no—
289D3×#41—91no—
290D3×#41—91no—
291D3×#41—91no—
292D3×#41—91no—
293D3×#41—91no—
294D3×#41—93no—
295D3×#41—93no—
296D3×#41—93no—
297D3×#41—93no—
298D3×#41—181no—
299D3×#41D911yescharacteristic, direct product factor
300C2×#239—91no—
301C2×#239—91no—
302C2×D3×Q8—91no—
303C2×D3×Q8—91no—
304C2×#237—93no—
305C2×#237—93no—
306C2×D3×D4—93no—
307C2×D3×D4—93no—
308C2×#235—93no—
309C2×#235—93no—
310C22×C4×D3—93no—
311C22×C4×D3—93no—
312C22×C3⋊D3—33no—
313C22×C3×D3—33no—
314C22×C3×D3C22×D313yes—
315C2×D32—31no—
316C2×D32—33no—
317C2×D32—33no—
318C2×D32—33no—
319C2×D32—612no—
320C32×Q8C22×D311yescharacteristic
321C32×D4C22×D313yes—
322C2×C32×C4C22×D313yes—
323#638—36no—
324C2×C3⋊Dic3—33no—
325C4⋊(C3⋊D3)—33no—
326C4×C3⋊D3—33no—
327C4×C3⋊D3—31no—
328C4×C3⋊D3—33no—
329C4×C3⋊D3—33no—
330#634—33no—
331C3×#67—36no—
332C3×#67C22×D316yes—
333C2×C3×Dic3—33no—
334C2×C3×Dic3C22×D313yes—
335C3×D12—33no—
336C3×D12C22×D313yes—
337C3×C4×D3—33no—
338C3×C4×D3—31no—
339C3×C4×D3—33no—
340C3×C4×D3—33no—
341C3×C4×D3C22×D313yes—
342C3×C4×D3C22×D311yescharacteristic
343C3×C4×D3C22×D313yes—
344C3×C4×D3C22×D313yes—
345C3×Dic6—33no—
346C3×Dic6C22×D313yes—
347#627—36no—
348#626—36no—
349#626—36no—
350#625—36no—
351#624—33no—
352#624—31no—
353#624—33no—
354#624—33no—
355D3×Dic3—33no—
356D3×Dic3—31no—
357D3×Dic3—33no—
358D3×Dic3—33no—
359D3×Dic3—33no—
360D3×Dic3—31no—
361D3×Dic3—33no—
362D3×Dic3—33no—
363C23×C9—33no—
364C22×D9—31no—
365C22×D9—33no—
366C22×D9—33no—
367C22×D9—33no—
368C22×D9—33no—
369C22×D9—63no—
370C22×D9—612no—
371C22×D9C22×D313yes—
372Q8×C9—21no—
373Q8×C9—33no—
374Q8×C9C22×D311yescharacteristic, complemented
375D4×C9—23no—
376D4×C9—36no—
377D4×C9—33no—
378D4×C9C22×D313yescomplemented
379C2×C4×C9—23no—
380C2×C4×C9—33no—
381C2×C4×C9—33no—
382C2×C4×C9—31no—
383C2×C4×C9—33no—
384C2×C4×C9—33no—
385C2×C4×C9C22×D313yescomplemented
386#611—36no—
387#611—36no—
388#611—36no—
389#611—66no—
390#611C22×D316yescomplemented
391C2×Dic9—33no—
392C2×Dic9—33no—
393C2×Dic9—31no—
394C2×Dic9—33no—
395C2×Dic9—33no—
396C2×Dic9—63no—
397C2×Dic9C22×D313yescomplemented
398D36—36no—
399D36—33no—
400D36—63no—
401D36C22×D313yescomplemented
402C4×D9—31no—
403C4×D9—33no—
404C4×D9—33no—
405C4×D9—33no—
406C4×D9—31no—
407C4×D9—33no—
408C4×D9—33no—
409C4×D9—33no—
410C4×D9—31no—
411C4×D9—33no—
412C4×D9—33no—
413C4×D9—33no—
414C4×D9—61no—
415C4×D9—63no—
416C4×D9—63no—
417C4×D9—63no—
418C4×D9C22×D311yescharacteristic
419C4×D9C22×D313yes—
420C4×D9C22×D313yescomplemented
421C4×D9C22×D313yescomplemented
422Dic18—33no—
423Dic18—36no—
424Dic18—63no—
425Dic18C22×D313yescomplemented
426C22×#41—271noSylow
427C2×C3×C9—23no—
428C2×C3×C9C2511yescharacteristic
429C3⋊D9—23no—
430C3⋊D9C2×#4112yescomplemented
431D3×C9—23no—
432D3×C9C2×#4112yescomplemented
433C3×D9—23no—
434C3×D9C2×#4112yescomplemented
435C23×D3—93no—
436C23×D3—93no—
437C3×#41—21no—
438C3×#41—31no—
439C3×#41—33no—
440C3×#41—33no—
441C3×#41—91no—
442C3×#41—93no—
443C3×#41—93no—
444C3×#41C2×D911yescharacteristic, complemented
445C3×#41D3211yescharacteristic
446C2×C3×Q8—31no—
447C2×C3×Q8—91no—
448C2×C3×D4—33no—
449C2×C3×D4—93no—
450C22×C3×C4—33no—
451C22×C3×C4—93no—
452C2×#67—96no—
453C2×#67—96no—
454C22×Dic3—93no—
455C22×Dic3—93no—
456#239—31no—
457#239—93no—
458#239—93no—
459#239—91no—
460#239—91no—
461#239—93no—
462#239—93no—
463#239—181no—
464#239C2×D911yescharacteristic, complemented
465D3×Q8—31no—
466D3×Q8—93no—
467D3×Q8—93no—
468D3×Q8—91no—
469D3×Q8—91no—
470D3×Q8—93no—
471D3×Q8—93no—
472D3×Q8—181no—
473D3×Q8C2×D911yescharacteristic, complemented
474#237—33no—
475#237—93no—
476#237—93no—
477#237—96no—
478#237—96no—
479#237—93no—
480#237—93no—
481#237—96no—
482#237—96no—
483#237—93no—
484#237—93no—
485#237—183no—
486#237C2×D913yescomplemented
487D3×D4—33no—
488D3×D4—93no—
489D3×D4—93no—
490D3×D4—96no—
491D3×D4—96no—
492D3×D4—96no—
493D3×D4—93no—
494D3×D4—93no—
495D3×D4—96no—
496D3×D4—93no—
497D3×D4—93no—
498D3×D4—183no—
499D3×D4C2×D913yescomplemented
500#235—33no—
501#235—93no—
502#235—96no—
503#235—93no—
504#235—96no—
505#235—93no—
506#235—93no—
507#235—96no—
508#235—93no—
509#235—96no—
510#235—93no—
511#235—183no—
512#235C2×D913yescomplemented
513C2×D12—93no—
514C2×D12—93no—
515C2×C4×D3—33no—
516C2×C4×D3—91no—
517C2×C4×D3—93no—
518C2×C4×D3—93no—
519C2×C4×D3—93no—
520C2×C4×D3—93no—
521C2×C4×D3—93no—
522C2×C4×D3—93no—
523C2×C4×D3—93no—
524C2×C4×D3—93no—
525C2×C4×D3—93no—
526C2×C4×D3—93no—
527C2×C4×D3—93no—
528C2×C4×D3—93no—
529C2×C4×D3—93no—
530C2×C4×D3—91no—
531C2×C4×D3—93no—
532C2×C4×D3—93no—
533C2×C4×D3—93no—
534C2×C4×D3—93no—
535C2×C4×D3—93no—
536C2×C4×D3—93no—
537C2×C4×D3—93no—
538C2×C4×D3—183no—
539C2×C4×D3C2×D913yescomplemented
540C2×Dic6—93no—
541C2×Dic6—93no—
542C22×C32C23×D313yes—
543C2×C3⋊D3—31no—
544C2×C3⋊D3—33no—
545C2×C3⋊D3—66no—
546C2×C3×D3—26no—
547C2×C3×D3—31no—
548C2×C3×D3—33no—
549C2×C3×D3—66no—
550C2×C3×D3C23×D313yes—
551C2×C3×D3C23×D311yescharacteristic
552D32—34no—
553D32—66no—
554D32—66no—
555D32—66no—
556C32×C4C23×D313yes—
557C32×C4C23×D311yescharacteristic
558C3⋊Dic3—31no—
559C3⋊Dic3—33no—
560C3×Dic3—31no—
561C3×Dic3—33no—
562C3×Dic3C23×D311yescharacteristic
563C3×Dic3C23×D313yes—
564C22×C9—23no—
565C22×C9—31no—
566C22×C9—33no—
567C22×C9—66no—
568C22×C9C23×D313yes—
569C2×D9—26no—
570C2×D9—31no—
571C2×D9—34no—
572C2×D9—33no—
573C2×D9—61no—
574C2×D9—63no—
575C2×D9—66no—
576C2×D9—66no—
577C2×D9—66no—
578C2×D9—66no—
579C2×D9—126no—
580C2×D9C23×D313yes—
581C2×D9C23×D311yescharacteristic
582C4×C9—23no—
583C4×C9—21no—
584C4×C9—33no—
585C4×C9—31no—
586C4×C9C23×D313yes—
587C4×C9C23×D311yescharacteristic
588Dic9—33no—
589Dic9—31no—
590Dic9—63no—
591Dic9—61no—
592Dic9C23×D313yes—
593Dic9C23×D311yescharacteristic
594C2×#41—31no—
595C2×#41—91no—
596C2×#41—273no—
597C2×#41—273no—
598C2×#41—273no—
599C2×#41—273no—
600C2×#41—271no—
601C2×#41—271no—
602C2×#41—271no—
603C2×#41—273no—
604C2×#41—273no—
605C2×#41—271no—
606C22×Q8—271no—
607C22×D4—273no—
608C23×C4—273no—
609C3×C9C22×#4111yescharacteristic, complemented, Sylow
610C23×C3—33no—
611C23×C3—93no—
612C22×D3—33no—
613C22×D3—91no—
614C22×D3—93no—
615C22×D3—93no—
616C22×D3—93no—
617C22×D3—91no—
618C22×D3—93no—
619C22×D3—93no—
620C22×D3—93no—
621C22×D3—93no—
622C22×D3—93no—
623C22×D3—183no—
624C22×D3—1812no—
625C22×D3—1812no—
626C22×D3C22×D913yes—
627C3×Q8—21no—
628C3×Q8—33no—
629C3×Q8—93no—
630C3×Q8C22×D911yescharacteristic, complemented
631C3×Q8C2×D3211yescharacteristic
632C3×D4—23no—
633C3×D4—36no—
634C3×D4—33no—
635C3×D4—96no—
636C3×D4—93no—
637C3×D4C22×D913yescomplemented
638C3×D4C2×D3213yes—
639C2×C3×C4—23no—
640C2×C3×C4—33no—
641C2×C3×C4—33no—
642C2×C3×C4—31no—
643C2×C3×C4—33no—
644C2×C3×C4—33no—
645C2×C3×C4—93no—
646C2×C3×C4—93no—
647C2×C3×C4—91no—
648C2×C3×C4—93no—
649C2×C3×C4—93no—
650C2×C3×C4C22×D913yescomplemented
651C2×C3×C4C2×D3213yes—
652#67—36no—
653#67—96no—
654#67—96no—
655#67—96no—
656#67—96no—
657#67—96no—
658#67—96no—
659#67—186no—
660#67C22×D916yescomplemented
661C2×Dic3—33no—
662C2×Dic3—93no—
663C2×Dic3—91no—
664C2×Dic3—93no—
665C2×Dic3—93no—
666C2×Dic3—93no—
667C2×Dic3—93no—
668C2×Dic3—93no—
669C2×Dic3—91no—
670C2×Dic3—93no—
671C2×Dic3—93no—
672C2×Dic3—183no—
673C2×Dic3C22×D913yescomplemented
674D12—33no—
675D12—96no—
676D12—96no—
677D12—93no—
678D12—93no—
679D12—183no—
680D12C22×D913yescomplemented
681C4×D3—31no—
682C4×D3—33no—
683C4×D3—33no—
684C4×D3—33no—
685C4×D3—91no—
686C4×D3—93no—
687C4×D3—93no—
688C4×D3—93no—
689C4×D3—91no—
690C4×D3—93no—
691C4×D3—93no—
692C4×D3—93no—
693C4×D3—91no—
694C4×D3—93no—
695C4×D3—93no—
696C4×D3—93no—
697C4×D3—91no—
698C4×D3—93no—
699C4×D3—93no—
700C4×D3—93no—
701C4×D3—91no—
702C4×D3—93no—
703C4×D3—93no—
704C4×D3—93no—
705C4×D3—91no—
706C4×D3—93no—
707C4×D3—93no—
708C4×D3—93no—
709C4×D3—181no—
710C4×D3—183no—
711C4×D3—183no—
712C4×D3—183no—
713C4×D3C22×D911yescharacteristic
714C4×D3C22×D913yes—
715C4×D3C22×D913yescomplemented
716C4×D3C22×D913yescomplemented
717Dic6—33no—
718Dic6—96no—
719Dic6—93no—
720Dic6—93no—
721Dic6—96no—
722Dic6—183no—
723Dic6C22×D913yescomplemented
724C2×C32—23no—
725C2×C32C24×D311yescharacteristic
726C3⋊D3—32no—
727C3⋊D3—63no—
728C3×D3—23no—
729C3×D3—32no—
730C3×D3—63no—
731C3×D3D3×#4112yes—
732C2×C9—23no—
733C2×C9—21no—
734C2×C9—32no—
735C2×C9—43no—
736C2×C9—63no—
737C2×C9C24×D311yescharacteristic
738D9—23no—
739D9—32no—
740D9—62no—
741D9—63no—
742D9—123no—
743D9D3×#4112yesdirect product factor
744C24—273no—
745#41—31no—
746#41—33no—
747#41—33no—
748#41—91no—
749#41—93no—
750#41—93no—
751#41—276no—
752#41—276no—
753#41—273no—
754#41—273no—
755#41—276no—
756#41—273no—
757#41—273no—
758#41—276no—
759#41—273no—
760#41—273no—
761#41—271no—
762#41—273no—
763#41—273no—
764#41D3×D911yescharacteristic, direct product factor
765C2×Q8—31no—
766C2×Q8—91no—
767C2×Q8—273no—
768C2×Q8—273no—
769C2×Q8—273no—
770C2×Q8—271no—
771C2×D4—33no—
772C2×D4—93no—
773C2×D4—273no—
774C2×D4—273no—
775C2×D4—276no—
776C2×D4—273no—
777C2×D4—276no—
778C2×D4—276no—
779C2×D4—273no—
780C22×C4—33no—
781C22×C4—93no—
782C22×C4—271no—
783C22×C4—273no—
784C22×C4—273no—
785C22×C4—273no—
786C22×C4—273no—
787C22×C4—273no—
788C22×C4—273no—
789C22×C4—273no—
790C22×C4—273no—
791C22×C4—273no—
792C22×C4—273no—
793C22×C4—273no—
794C22×C3—23no—
795C22×C3—31no—
796C22×C3—33no—
797C22×C3—66no—
798C22×C3—91no—
799C22×C3—93no—
800C22×C3—186no—
801C22×C3C23×D913yes—
802C22×C3C22×D3213yes—
803C2×D3—26no—
804C2×D3—31no—
805C2×D3—33no—
806C2×D3—66no—
807C2×D3—94no—
808C2×D3—91no—
809C2×D3—91no—
810C2×D3—94no—
811C2×D3—93no—
812C2×D3—93no—
813C2×D3—181no—
814C2×D3—183no—
815C2×D3—186no—
816C2×D3—186no—
817C2×D3—186no—
818C2×D3—186no—
819C2×D3—186no—
820C2×D3—186no—
821C2×D3—186no—
822C2×D3—186no—
823C2×D3—366no—
824C2×D3C23×D913yes—
825C2×D3C23×D911yescharacteristic
826C3×C4—23no—
827C3×C4—21no—
828C3×C4—33no—
829C3×C4—31no—
830C3×C4—93no—
831C3×C4—91no—
832C3×C4C23×D913yes—
833C3×C4C23×D911yescharacteristic
834C3×C4C22×D3213yes—
835C3×C4C22×D3211yescharacteristic
836Dic3—33no—
837Dic3—31no—
838Dic3—93no—
839Dic3—91no—
840Dic3—93no—
841Dic3—91no—
842Dic3—183no—
843Dic3—181no—
844Dic3C23×D913yes—
845Dic3C23×D911yescharacteristic
846C32C2×D3×#4111yescharacteristic
847C9—21no—
848C9C2×D3×#4111yescharacteristic, complemented
849C23—33no—
850C23—93no—
851C23—271no—
852C23—273no—
853C23—273no—
854C23—273no—
855C23—273no—
856C23—5412no—
857Q8—33no—
858Q8—93no—
859Q8—276no—
860Q8—273no—
861Q8C2×D3×D911yescharacteristic, complemented
862D4—36no—
863D4—33no—
864D4—96no—
865D4—93no—
866D4—276no—
867D4—276no—
868D4—276no—
869D4—276no—
870D4—273no—
871D4C2×D3×D913yescomplemented
872C2×C4—33no—
873C2×C4—33no—
874C2×C4—33no—
875C2×C4—31no—
876C2×C4—33no—
877C2×C4—93no—
878C2×C4—93no—
879C2×C4—93no—
880C2×C4—91no—
881C2×C4—93no—
882C2×C4—271no—
883C2×C4—273no—
884C2×C4—273no—
885C2×C4—273no—
886C2×C4—271no—
887C2×C4—273no—
888C2×C4—273no—
889C2×C4—273no—
890C2×C4—271no—
891C2×C4—273no—
892C2×C4—273no—
893C2×C4—273no—
894C2×C4—273no—
895C2×C4—273no—
896C2×C4—273no—
897C2×C4—271no—
898C2×C4—273no—
899C2×C4C2×D3×D913yescomplemented
900C2×C3—23no—
901C2×C3—23no—
902C2×C3—21no—
903C2×C3—32no—
904C2×C3—43no—
905C2×C3—63no—
906C2×C3—92no—
907C2×C3—183no—
908C2×C3C24×D911yescharacteristic
909C2×C3C23×D3211yescharacteristic
910D3—23no—
911D3—32no—
912D3—63no—
913D3—92no—
914D3—92no—
915D3—182no—
916D3—183no—
917D3—183no—
918D3—363no—
919D3#41×D912yesdirect product factor
920C22—31no—
921C22—33no—
922C22—66no—
923C22—91no—
924C22—93no—
925C22—186no—
926C22—274no—
927C22—271no—
928C22—273no—
929C22—546no—
930C22—546no—
931C22—546no—
932C22—546no—
933C22C22×D3×D913yes—
934C4—31no—
935C4—33no—
936C4—91no—
937C4—93no—
938C4—271no—
939C4—273no—
940C4C22×D3×D913yes—
941C4C22×D3×D911yescharacteristic
942C3—21no—
943C3C2×#41×D911yescharacteristic, complemented
944C3D32×#4111yescharacteristic
945C2—23no—
946C2—32no—
947C2—63no—
948C2—92no—
949C2—183no—
950C2—272no—
951C2—543no—
952C2C23×D3×D911yescharacteristic
subgroupG/H
centerC4C22×D3×D9
commutator, cosocleC2×C3×C9C25
FrattiniC2×C3C23×D32
FittingC3×C9×#41C22
socleC2×C32C24×D3
hypercenter#41D3×D9
hypocenterC3×C9C22×#41
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊D9C2semidirect
2. D3×C9×#41C2semidirect
3. C3×#41×D9C2semidirect
4. #11722514C2semidirect
5. D9×#239C2semidirect
6. D3×#3701C2semidirect
7. D3×Q8×D9C2semidirect
8. #11722498C2semidirect
9. D9×#237C2semidirect
10. D3×#3699C2semidirect
11. D3×D4×D9C2semidirect
12. #11722475C2semidirect
13. D9×#235C2semidirect
14. D3×#3697C2semidirect
15. C2×C4×D3×D9C2semidirect
19. C3×C9×#41C22semidirect
20. #88746C22semidirect
21. Q8×C3⋊D9C22semidirect
22. #88742C22semidirect
23. D4×C3⋊D9C22semidirect
24. #88736C22semidirect
25. C2×C4×C3⋊D9C22semidirect
26. C9×#239C22semidirect
27. D3×Q8×C9C22semidirect
28. C3×#3701C22semidirect
29. C3×Q8×D9C22semidirect
30. C9×#237C22semidirect
31. D3×D4×C9C22semidirect
32. C3×#3699C22semidirect
33. C3×D4×D9C22semidirect
34. C9×#235C22semidirect
35. C2×C4×D3×C9C22semidirect
36. C3×#3697C22semidirect
37. C2×C3×C4×D9C22semidirect
38. #88668C22semidirect
39. D9×#67C22semidirect
40. D3×#611C22semidirect
41. #88663C22semidirect
42. #88662C22semidirect
43. C2×D3×Dic9C22semidirect
44. C2×(C3⋊D9)⋊C4C22semidirect
45. #88658C22semidirect
46. C2×Dic3×D9C22semidirect
47. #88646C22semidirect
48. D9×D12C22semidirect
49. D3×D36C22semidirect
52. C4×D3×D9C22semidirect
53. C4×D3×D9C22semidirect
54. C4×D3×D9C22semidirect
55. C4×D3×D9C22semidirect
56. C4×D3×D9C22semidirect
57. C4×D3×D9C22semidirect
58. #88642C22semidirect
59. #88641C22semidirect
60. #88640C22semidirect
61. #88639C22semidirect
62. #88638C22semidirect
63. D3×Dic18C22semidirect
64. (C3⋊D9)⋊Q8C22semidirect
65. #88635C22semidirect
66. #88634C22semidirect
67. D9×Dic6C22semidirect
92. #41×D9D3direct (N × H)
107. C3×Q8×C9C23semidirect
108. C3×D4×C9C23semidirect
109. C2×C3×C4×C9C23semidirect
110. #6233C23semidirect
111. C2×C3⋊Dic9C23semidirect
112. C4⋊(C3⋊D9)C23semidirect
115. C4×C3⋊D9C23semidirect
116. C4×C3⋊D9C23semidirect
117. #6226C23semidirect
118. C9×#67C23semidirect
119. C3×#611C23semidirect
120. C2×C9×Dic3C23semidirect
121. C2×C3×Dic9C23semidirect
122. C9×D12C23semidirect
125. C4×D3×C9C23semidirect
126. C4×D3×C9C23semidirect
127. C3×D36C23semidirect
130. C3×C4×D9C23semidirect
131. C3×C4×D9C23semidirect
132. C9×Dic6C23semidirect
133. C3×Dic18C23semidirect
134. #6195C23semidirect
135. #6194C23semidirect
138. D3×Dic9C23semidirect
139. D3×Dic9C23semidirect
140. #6192C23semidirect
143. (C3⋊D9)⋊C4C23semidirect
144. (C3⋊D9)⋊C4C23semidirect
147. Dic3×D9C23semidirect
148. Dic3×D9C23semidirect
149. #6189C23semidirect
207. C9×#41C2×D3semidirect
217. #3701C2×D3semidirect
222. Q8×D9C2×D3semidirect
229. #3699C2×D3semidirect
236. D4×D9C2×D3semidirect
243. #3697C2×D3semidirect
257. C2×C4×D9C2×D3semidirect
272. D3×D9#41direct (N × H)
299. D3×#41D9direct (N × H)
374. Q8×C9C22×D3semidirect
378. D4×C9C22×D3semidirect
385. C2×C4×C9C22×D3semidirect
390. #611C22×D3semidirect
397. C2×Dic9C22×D3semidirect
401. D36C22×D3semidirect
420. C4×D9C22×D3semidirect
421. C4×D9C22×D3semidirect
425. Dic18C22×D3semidirect
430. C3⋊D9C2×#41semidirect
432. D3×C9C2×#41semidirect
434. C3×D9C2×#41semidirect
444. C3×#41C2×D9semidirect
464. #239C2×D9semidirect
473. D3×Q8C2×D9semidirect
486. #237C2×D9semidirect
499. D3×D4C2×D9semidirect
512. #235C2×D9semidirect
539. C2×C4×D3C2×D9semidirect
609. C3×C9C22×#41semidirect
630. C3×Q8C22×D9semidirect
637. C3×D4C22×D9semidirect
650. C2×C3×C4C22×D9semidirect
660. #67C22×D9semidirect
673. C2×Dic3C22×D9semidirect
680. D12C22×D9semidirect
715. C4×D3C22×D9semidirect
716. C4×D3C22×D9semidirect
723. Dic6C22×D9semidirect
743. D9D3×#41direct (N × H)
764. #41D3×D9direct (N × H)
848. C9C2×D3×#41semidirect
861. Q8C2×D3×D9semidirect
871. D4C2×D3×D9semidirect
899. C2×C4C2×D3×D9semidirect
919. D3#41×D9direct (N × H)
943. C3C2×#41×D9semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊D92
D3×C9×#412
C3×#41×D92
#117225142
D9×#2392
D3×#37012
D3×Q8×D92
#117224982
D9×#2372
D3×#36992
D3×D4×D92
#117224752
D9×#2352
D3×#36972
C2×C4×D3×D92
D32×#413
C2×#41×D93