Finite Group Databasebeta

← #13150473

Subgroups — #13150473

Order 1728.

1094 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88736C211yesmaximal, characteristic, complemented
2C2×#88640C211yesmaximal, characteristic, complemented
3C4×C9×#67C211yesmaximal, characteristic, complemented
4C3×C4×#611C211yesmaximal, characteristic, complemented
5#11721289C211yesmaximal, characteristic, complemented
6#11721262C211yesmaximal, characteristic, complemented
7#11721256C211yesmaximal, characteristic, complemented
8#11721242C211yesmaximal, characteristic, complemented
9#11721042C211yesmaximal, characteristic, complemented
10#11721039C211yesmaximal, characteristic, complemented
11C4×#6195C211yesmaximal, characteristic, complemented
12#11721005C211yesmaximal, characteristic, complemented
13C4×#6192C211yesmaximal, characteristic, complemented
14C4×(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
15#11720905C211yesmaximal, characteristic, complemented
16#10595017—31nomaximal
17#10589650—31nomaximal
18C22×C3×C4×C9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21#88736—24no—
22C2×C4⋊(C3⋊D9)C2211yescharacteristic
23C2×C4×C3⋊D9C2211yescharacteristic
24C2×C4×C3⋊D9C2211yescharacteristic
25C2×#6226C2211yescharacteristic
26C2×C9×#67C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic
28C2×C4×D3×C9C2211yescharacteristic
29C2×C3×C4×D9C2211yescharacteristic
30C2×#6195C2211yescharacteristic
31C2×#6195C2211yescharacteristic
32C2×#6194C2211yescharacteristic
33C2×#6192C2211yescharacteristic
34C2×#6192C2211yescharacteristic
35C2×(C3⋊D9)⋊C4C2211yescharacteristic
36C2×(C3⋊D9)⋊C4C2211yescharacteristic
37C2×#6189C2211yescharacteristic
38#88640—24no—
39C9×#217C2211yescharacteristic
40C3×#3676C2211yescharacteristic
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C9×Dic3⋊C4C2211yescharacteristic
44C4×C9×Dic3C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46C3×C4×Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51Dic3⋊Dic9C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×#3828—31no—
56C2×#3798—31no—
57C3×C4×#67—31no—
58C3×C4×#67D311yescharacteristic
59#63979—31no—
60#63958—31no—
61#63958—31no—
62#63953—31no—
63#63913—31no—
64#63910—31no—
65#63910—31no—
66C4×#626—31no—
67C4×#626—31no—
68C4×#624—31no—
69#63840—31no—
70C2×#3697—31no—
71C2×#3697—31no—
72C2×#3697—61no—
73C4×D4×C9—31no—
74#63502—31no—
75#63500—31no—
76C4×#611—31no—
77C4×#611D311yescharacteristic, complemented
78#63457—31no—
79#63450—31no—
80#63447—31no—
81#63447—31no—
82#63446—31no—
83#63446—31no—
84C4×D36—31no—
85C42×D9—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×C3×C4×C9—22no—
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94#6233—22no—
95#6233—22no—
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C4⋊(C3⋊D9)—22no—
99C4×C3⋊D9—22no—
100C4×C3⋊D9D414yescomplemented
101#6226—22no—
102C9×#67—22no—
103C3×#611—22no—
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C4×D3×C9—22no—
111C3×C4×D9—22no—
112#6195—22no—
113#6195—22no—
114#6194—22no—
115#6192—22no—
116#6192—22no—
117(C3⋊D9)⋊C4—22no—
118(C3⋊D9)⋊C4—22no—
119#6189—22no—
120#5548—91no—
121#5548—91no—
122C22×C32×C4C2×D311yescharacteristic
123C2×#638—31no—
124C2×#638—31no—
125#3828—64no—
126C2×C4⋊(C3⋊D3)—31no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3—31no—
129C2×#634—31no—
130C2×C3×#67—31no—
131C2×C3×#67C2×D311yescharacteristic
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×#627—31no—
135C2×#626—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#625—31no—
140C2×#624—31no—
141C2×#624—31no—
142#3798—64no—
143C3×#217—31no—
144C3×#217C2×D311yescharacteristic
145C3×(C2×D3)⋊C4—31no—
146C3×(C2×D3)⋊C4C2×D311yescharacteristic
147C3×Dic3⋊C4—31no—
148C3×Dic3⋊C4C2×D311yescharacteristic
149C3×C4×Dic3—31no—
150C3×C4×Dic3C2×D311yescharacteristic
151Dic3⋊Dic3—31no—
152Dic3⋊Dic3—31no—
153#3722—31no—
154#3722—31no—
155(C2×D3)⋊Dic3—31no—
156(C2×D3)⋊Dic3—31no—
157Dic32—31no—
158Dic32—31no—
159C2×D4×C9—31no—
160C22×C4×C9—21no—
161C22×C4×C9—31no—
162C22×C4×C9C2×D311yescharacteristic
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—31no—
166C2×#611—31no—
167C2×#611—31no—
168C2×#611—61no—
169C2×#611—61no—
170C2×#611C2×D311yescharacteristic
171#3697—64no—
172#3697—64no—
173#3697—68no—
174C2×D36—31no—
175C2×D36—31no—
176C2×D36—31no—
177C2×D36—61no—
178C2×C4×D9—31no—
179C2×C4×D9—31no—
180C2×C4×D9—31no—
181C2×C4×D9—31no—
182C2×C4×D9—61no—
183C2×C4×D9—61no—
184C2×C4×D9C2×D311yescharacteristic
185C2×Dic18—31no—
186C2×Dic18—31no—
187C2×Dic18—61no—
188C9×C4⋊C4—31no—
189C9×C22⋊C4—31no—
190C9×C22⋊C4—31no—
191C42×C9—31no—
192#3676—31no—
193#3676C2×D311yescharacteristic
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4C2×D311yescharacteristic
198C4⋊Dic9—31no—
199Dic9⋊C4—31no—
200Dic9⋊C4C2×D311yescharacteristic
201C4×Dic9—31no—
202C4×Dic9—31no—
203C4×Dic9C2×D311yescharacteristic
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9—21no—
207C22×C3×C9C2411yescharacteristic
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9—21no—
213C2×C3⋊D9C2×D412yes—
214C2×D3×C9—21no—
215C2×D3×C9—21no—
216C2×D3×C9—21no—
217C2×C3×D9—21no—
218C2×C3×D9—21no—
219C2×C3×D9—21no—
220C3×C4×C9—21no—
221C3×C4×C9C2×D412yes—
222C3⋊Dic9—21no—
223C3⋊Dic9C2×D412yes—
224C9×Dic3—21no—
225C9×Dic3—21no—
226C9×Dic3#4112yescomplemented
227C3×Dic9—21no—
228C3×Dic9—21no—
229C3×Dic9#4112yescomplemented
230C2×#235—91no—
231C2×#235—91no—
232C2×#235—91no—
233C2×#235—91no—
234C2×#235—181no—
235C3×C4×D4—31no—
236C3×C4×D4—91no—
237#940—91no—
238#940—91no—
239#938—91no—
240#938—91no—
241C4×#67—31no—
242C4×#67—91no—
243C4×#67—91no—
244C4×#67D911yescharacteristic, complemented
245#895—91no—
246#895—91no—
247#888—91no—
248#888—91no—
249#885—91no—
250#885—91no—
251#885—91no—
252#885—91no—
253#884—91no—
254#884—91no—
255#884—91no—
256#884—91no—
257C4×D12—91no—
258C4×D12—91no—
259C42×D3—91no—
260C42×D3—91no—
261C23×C32C22×D311yescharacteristic
262C22×C3⋊D3—31no—
263C22×C3⋊D3—31no—
264C22×C3×D3—31no—
265C22×C3×D3C22×D311yescharacteristic
266C2×C32×C4—22no—
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C22×D311yescharacteristic
269#638—62no—
270#638—62no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—31no—
273C4⋊(C3⋊D3)—62no—
274C4×C3⋊D3—34no—
275C4×C3⋊D3—62no—
276#634—62no—
277C3×#67—22no—
278C3×#67—62no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C3×C4×D3—22no—
286C3×C4×D3—62no—
287#627—62no—
288#626—62no—
289#626—62no—
290#626—62no—
291#626—62no—
292#625—62no—
293#624—62no—
294#624—62no—
295C23×C9—21no—
296C23×C9—31no—
297C23×C9C22×D311yescharacteristic
298C22×D9—31no—
299C22×D9—31no—
300C22×D9—61no—
301C22×D9—61no—
302C22×D9C22×D311yescharacteristic
303D4×C9—62no—
304C2×C4×C9—24no—
305C2×C4×C9—22no—
306C2×C4×C9—21no—
307C2×C4×C9—21no—
308C2×C4×C9—31no—
309C2×C4×C9—31no—
310C2×C4×C9—31no—
311C2×C4×C9—62no—
312C2×C4×C9C22×D311yescharacteristic
313C2×C4×C9C22×D311yescharacteristic
314#611—22no—
315#611—62no—
316#611—62no—
317#611—62no—
318#611—62no—
319#611—64no—
320#611—64no—
321#611—62no—
322C2×Dic9—31no—
323C2×Dic9—31no—
324C2×Dic9—61no—
325C2×Dic9—61no—
326C2×Dic9C22×D311yescharacteristic
327C2×Dic9C22×D311yescharacteristic
328C2×Dic9C22×D311yescharacteristic
329D36—62no—
330D36—64no—
331D36—62no—
332D36—62no—
333C4×D9—22no—
334C4×D9—34no—
335C4×D9—64no—
336C4×D9—62no—
337C4×D9—64no—
338C4×D9—62no—
339C4×D9—62no—
340Dic18—62no—
341Dic18—62no—
342Dic18—64no—
343#532—271noSylow
344C2×C3×C9—41no—
345C2×C3×C9C22×D411yescharacteristic
346C2×C3×C9C2×#4111yescharacteristic
347C2×C3×C9C2×#4111yescharacteristic
348C3⋊D9—22no—
349C3⋊D9—41no—
350D3×C9—41no—
351C3×D9—41no—
352C2×C3×D4—31no—
353C2×C3×D4—91no—
354C22×C3×C4—21no—
355C22×C3×C4—31no—
356C22×C3×C4—91no—
357C22×C3×C4C2×D911yescharacteristic
358C22×C3×C4D3211yescharacteristic
359C2×#67—31no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—91no—
365C2×#67—91no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—91no—
370C2×#67—181no—
371C2×#67—181no—
372C2×#67C2×D911yescharacteristic
373#235—184no—
374#235—184no—
375#235—184no—
376#235—184no—
377#235—188no—
378C2×D12—91no—
379C2×D12—91no—
380C2×D12—91no—
381C2×D12—91no—
382C2×D12—91no—
383C2×D12—91no—
384C2×D12—181no—
385C2×C4×D3—31no—
386C2×C4×D3—91no—
387C2×C4×D3—91no—
388C2×C4×D3—91no—
389C2×C4×D3—91no—
390C2×C4×D3—91no—
391C2×C4×D3—91no—
392C2×C4×D3—91no—
393C2×C4×D3—91no—
394C2×C4×D3—181no—
395C2×C4×D3—181no—
396C2×C4×D3C2×D911yescharacteristic
397C2×Dic6—91no—
398C2×Dic6—91no—
399C2×Dic6—91no—
400C2×Dic6—91no—
401C2×Dic6—181no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—91no—
404C3×C22⋊C4—31no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—91no—
407C3×C22⋊C4—91no—
408C3×C42—31no—
409C3×C42—91no—
410#217—31no—
411#217—91no—
412#217—91no—
413#217C2×D911yescharacteristic
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—91no—
416(C2×D3)⋊C4—91no—
417(C2×D3)⋊C4—91no—
418(C2×D3)⋊C4—91no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4C2×D911yescharacteristic
422C4⋊Dic3—91no—
423C4⋊Dic3—91no—
424Dic3⋊C4—31no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4C2×D911yescharacteristic
428C4×Dic3—31no—
429C4×Dic3—91no—
430C4×Dic3—91no—
431C4×Dic3—91no—
432C4×Dic3—91no—
433C4×Dic3C2×D911yescharacteristic
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32C23×D311yescharacteristic
438C2×C3⋊D3—32no—
439C2×C3⋊D3—61no—
440C2×C3⋊D3—61no—
441C2×C3⋊D3—61no—
442C2×C3⋊D3—61no—
443C2×C3⋊D3—61no—
444C2×C3×D3—21no—
445C2×C3×D3—21no—
446C2×C3×D3—21no—
447C2×C3×D3—61no—
448C2×C3×D3—61no—
449C2×C3×D3—61no—
450C32×C4—21no—
451C32×C4D3×D412yes—
452C3⋊Dic3—32no—
453C3⋊Dic3—61no—
454C3×Dic3—21no—
455C3×Dic3—21no—
456C3×Dic3—32no—
457C3×Dic3—61no—
458C3×Dic3—61no—
459C3×Dic3#23512yes—
460C22×C9—22no—
461C22×C9—21no—
462C22×C9—21no—
463C22×C9—21no—
464C22×C9—21no—
465C22×C9—41no—
466C22×C9—41no—
467C22×C9—61no—
468C22×C9—61no—
469C22×C9—61no—
470C22×C9C23×D311yescharacteristic
471C2×D9—21no—
472C2×D9—21no—
473C2×D9—21no—
474C2×D9—32no—
475C2×D9—62no—
476C2×D9—61no—
477C2×D9—61no—
478C2×D9—62no—
479C2×D9—61no—
480C2×D9—61no—
481C2×D9—61no—
482C2×D9—121no—
483C2×D9—121no—
484C2×D9—121no—
485C2×D9—121no—
486C4×C9—22no—
487C4×C9—21no—
488C4×C9—22no—
489C4×C9—32no—
490C4×C9—61no—
491C4×C9—61no—
492C4×C9D3×D412yes—
493Dic9—21no—
494Dic9—21no—
495Dic9—32no—
496Dic9—62no—
497Dic9—62no—
498Dic9—61no—
499Dic9#23512yescomplemented
500C2×#41—271no—
501C2×#41—271no—
502C4⋊Q8—271no—
503#127—271no—
504#124—271no—
505#124—271no—
506#121—271no—
507#121—271no—
508#121—271no—
509#121—271no—
510C4×D4—31no—
511C4×D4—91no—
512C4×D4—271no—
513C4×D4—271no—
514C2×C42—271no—
515C3×C9#53211yescharacteristic, complemented, Sylow
516C23×C3—21no—
517C23×C3—31no—
518C23×C3—91no—
519C23×C3C22×D911yescharacteristic
520C23×C3C2×D3211yescharacteristic
521C22×D3—31no—
522C22×D3—91no—
523C22×D3—91no—
524C22×D3—91no—
525C22×D3—91no—
526C22×D3—181no—
527C22×D3—181no—
528C22×D3C22×D911yescharacteristic
529C3×D4—62no—
530C3×D4—182no—
531C2×C3×C4—24no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—62no—
540C2×C3×C4—91no—
541C2×C3×C4—91no—
542C2×C3×C4—91no—
543C2×C3×C4—182no—
544C2×C3×C4C22×D911yescharacteristic
545C2×C3×C4C22×D911yescharacteristic
546C2×C3×C4C2×D3211yescharacteristic
547C2×C3×C4C2×D3211yescharacteristic
548#67—22no—
549#67—62no—
550#67—182no—
551#67—182no—
552#67—182no—
553#67—182no—
554#67—182no—
555#67—182no—
556#67—182no—
557#67—182no—
558#67—182no—
559#67—184no—
560#67—184no—
561#67—182no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—91no—
569C2×Dic3—181no—
570C2×Dic3—181no—
571C2×Dic3C22×D911yescharacteristic
572C2×Dic3C22×D911yescharacteristic
573C2×Dic3C22×D911yescharacteristic
574D12—182no—
575D12—182no—
576D12—184no—
577D12—182no—
578D12—182no—
579D12—182no—
580D12—182no—
581C4×D3—22no—
582C4×D3—62no—
583C4×D3—94no—
584C4×D3—94no—
585C4×D3—184no—
586C4×D3—182no—
587C4×D3—182no—
588C4×D3—182no—
589C4×D3—184no—
590C4×D3—182no—
591C4×D3—182no—
592C4×D3—182no—
593Dic6—182no—
594Dic6—182no—
595Dic6—182no—
596Dic6—182no—
597Dic6—184no—
598C2×C32—41no—
599C2×C32C2×#23511yescharacteristic
600C2×C32C2×D3×D411yescharacteristic
601C2×C32D3×#4111yescharacteristic
602C3⋊D3—62no—
603C3⋊D3—121no—
604C3×D3—41no—
605C3×D3—121no—
606C2×C9—21no—
607C2×C9—21no—
608C2×C9—21no—
609C2×C9—42no—
610C2×C9—41no—
611C2×C9—121no—
612C2×C9C2×#23511yescharacteristic
613C2×C9C2×D3×D411yescharacteristic
614C2×C9D3×#4111yescharacteristic
615D9—41no—
616D9—62no—
617D9—122no—
618D9—122no—
619D9—121no—
620#41—544no—
621#41—544no—
622C2×Q8—271no—
623C2×Q8—271no—
624C2×D4—31no—
625C2×D4—91no—
626C2×D4—271no—
627C2×D4—271no—
628C2×D4—271no—
629C2×D4—271no—
630C2×D4—271no—
631C2×D4—271no—
632C2×D4—271no—
633C2×D4—271no—
634C22×C4—31no—
635C22×C4—91no—
636C22×C4—271no—
637C22×C4—271no—
638C22×C4—271no—
639C22×C4—271no—
640C22×C4D3×D911yescharacteristic
641C4⋊C4—31no—
642C4⋊C4—91no—
643C4⋊C4—271no—
644C4⋊C4—271no—
645C22⋊C4—31no—
646C22⋊C4—31no—
647C22⋊C4—91no—
648C22⋊C4—91no—
649C22⋊C4—271no—
650C22⋊C4—271no—
651C22⋊C4—271no—
652C22⋊C4—271no—
653C42—31no—
654C42—91no—
655C42—271no—
656C42—271no—
657C22×C3—22no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—181no—
671C22×C3—181no—
672C22×C3—181no—
673C22×C3C23×D911yescharacteristic
674C22×C3C22×D3211yescharacteristic
675C2×D3—21no—
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—92no—
682C2×D3—92no—
683C2×D3—182no—
684C2×D3—181no—
685C2×D3—181no—
686C2×D3—181no—
687C2×D3—181no—
688C2×D3—182no—
689C2×D3—181no—
690C2×D3—181no—
691C2×D3—181no—
692C2×D3—181no—
693C2×D3—181no—
694C2×D3—181no—
695C2×D3—361no—
696C2×D3—361no—
697C2×D3—361no—
698C2×D3—361no—
699C3×C4—22no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—22no—
703C3×C4—32no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—92no—
707C3×C4—181no—
708C3×C4—181no—
709C3×C4D4×D912yes—
710C3×C4#381112yes—
711Dic3—21no—
712Dic3—21no—
713Dic3—32no—
714Dic3—61no—
715Dic3—61no—
716Dic3—92no—
717Dic3—92no—
718Dic3—182no—
719Dic3—182no—
720Dic3—181no—
721Dic3—181no—
722Dic3#369712yescomplemented
723C32#554811yescharacteristic
724C9—21no—
725C9#554811yescharacteristic, complemented
726C23—31no—
727C23—91no—
728C23—271no—
729C23—271no—
730C23C2×D3×D911yescharacteristic
731Q8—542no—
732Q8—542no—
733D4—62no—
734D4—182no—
735D4—542no—
736D4—542no—
737D4—542no—
738D4—542no—
739D4—542no—
740D4—542no—
741D4—542no—
742D4—542no—
743C2×C4—22no—
744C2×C4—31no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—62no—
748C2×C4—91no—
749C2×C4—91no—
750C2×C4—91no—
751C2×C4—182no—
752C2×C4—271no—
753C2×C4—274no—
754C2×C4—271no—
755C2×C4—542no—
756C2×C4—542no—
757C2×C4—542no—
758C2×C4C2×D3×D911yescharacteristic
759C2×C4C2×D3×D911yescharacteristic
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—42no—
764C2×C3—41no—
765C2×C3—41no—
766C2×C3—121no—
767C2×C3—361no—
768C2×C3C2×#369711yescharacteristic
769C2×C3C2×D4×D911yescharacteristic
770C2×C3#41×D911yescharacteristic
771C2×C3D3×#23511yescharacteristic
772C2×C3D3×#23511yescharacteristic
773C2×C3C2×#381111yescharacteristic
774D3—41no—
775D3—121no—
776D3—182no—
777D3—182no—
778D3—362no—
779D3—362no—
780D3—361no—
781D3—361no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—61no—
786C22—61no—
787C22—61no—
788C22—181no—
789C22—181no—
790C22—181no—
791C22—272no—
792C22—541no—
793C22—541no—
794C22—541no—
795C22—541no—
796C22—541no—
797C22C22×D3×D911yescharacteristic
798C4—21no—
799C4—32no—
800C4—61no—
801C4—61no—
802C4—92no—
803C4—181no—
804C4—181no—
805C4—272no—
806C4—541no—
807C4#8866812yes—
808C3—21no—
809C3#1058965011yescharacteristic, complemented
810C3#1059501711yescharacteristic
811C2—41no—
812C2—121no—
813C2—361no—
814C2—542no—
815C2—1081no—
816C2D3×#369711yescharacteristic
817C2D9×#23511yescharacteristic
818C2C2×#8866811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#532
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88736C2semidirect
2. C2×#88640C2semidirect
3. C4×C9×#67C2semidirect
4. C3×C4×#611C2semidirect
5. #11721289C2semidirect
6. #11721262C2semidirect
7. #11721256C2semidirect
8. #11721242C2semidirect
9. #11721042C2semidirect
10. #11721039C2semidirect
11. C4×#6195C2semidirect
12. #11721005C2semidirect
13. C4×#6192C2semidirect
14. C4×(C3⋊D9)⋊C4C2semidirect
15. #11720905C2semidirect
77. C4×#611D3semidirect
100. C4×C3⋊D9D4semidirect
226. C9×Dic3#41semidirect
229. C3×Dic9#41semidirect
244. C4×#67D9semidirect
499. Dic9#235semidirect
515. C3×C9#532semidirect
722. Dic3#3697semidirect
725. C9#5548semidirect
809. C3#10589650semidirect

Maximal subgroups

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

subgroupindex
C2×#887362
C2×#886402
C4×C9×#672
C3×C4×#6112
#117212892
#117212622
#117212562
#117212422
#117210422
#117210392
C4×#61952
#117210052
C4×#61922
C4×(C3⋊D9)⋊C42
#117209052
#105950173
#105896503