Finite Group Databasebeta

← #13150561

Subgroups — #13150561

Order 1728.

1154 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88736C211yesmaximal, characteristic, complemented
2C2×C4×D3×D9C211yesmaximal, characteristic, complemented
3C4×C9×#67C211yesmaximal, characteristic, complemented
4C3×C4×#611C211yesmaximal, characteristic, complemented
5#11721292C211yesmaximal, characteristic, complemented
6#11721282C211yesmaximal, characteristic, complemented
7#11721275C211yesmaximal, characteristic, complemented
8#11721271C211yesmaximal, characteristic, complemented
9#11721051C211yesmaximal, characteristic, complemented
10C4×#6195C211yesmaximal, characteristic, complemented
11#11721024C211yesmaximal, characteristic, complemented
12C4×#6192C211yesmaximal, characteristic, complemented
13#11720997C211yesmaximal, characteristic, complemented
14#11720996C211yesmaximal, characteristic, complemented
15#11720931C211yesmaximal, characteristic, complemented
16#10595076—31nomaximal
17#10589649—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic, complemented
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic, complemented
22#88736—24no—
23C2×C4⋊(C3⋊D9)C2211yescharacteristic
24C2×C4×C3⋊D9C2211yescharacteristic
25C2×C4×C3⋊D9C2211yescharacteristic, complemented
26C2×#6226C2211yescharacteristic, complemented
27C2×C9×#67C2211yescharacteristic
28C2×C3×#611C2211yescharacteristic
29C2×C4×D3×C9C2211yescharacteristic
30C2×C3×C4×D9C2211yescharacteristic
31C2×#6195C2211yescharacteristic
32C2×D3×Dic9C2211yescharacteristic
33C2×#6192C2211yescharacteristic
34C2×(C3⋊D9)⋊C4C2211yescharacteristic
35C2×Dic3×D9C2211yescharacteristic
36C4×D3×D9—24no—
37C9×#217C2211yescharacteristic, complemented
38C3×#3676C2211yescharacteristic, complemented
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C9×Dic3⋊C4C2211yescharacteristic, complemented
42C4×C9×Dic3C2211yescharacteristic, complemented
43C3×Dic9⋊C4C2211yescharacteristic, complemented
44C3×C4×Dic9C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic
51Dic3⋊Dic9C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×#3828—31no—
56C2×C4×D32—31no—
57C3×C4×#67—31no—
58C3×C4×#67D311yescharacteristic
59#63983—31no—
60#63975—31no—
61#63971—31no—
62#63971—31no—
63#63923—31no—
64C4×#626—31no—
65C4×#626—31no—
66#63897—31no—
67#63896—31no—
68#63896—31no—
69#63874—31no—
70C2×#3697—31no—
71C2×#3697—61no—
72C22×C4×D9—31no—
73C4×D4×C9—31no—
74#63501—31no—
75#63499—31no—
76C4×#611—31no—
77C4×#611D311yescharacteristic, complemented
78#63458—31no—
79#63456—31no—
80#63446—31no—
81#63445—31no—
82#63444—31no—
83#63440—31no—
84C4×D36—31no—
85#63434—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×D3×D9—22no—
92C2×D3×D9—22no—
93C2×D3×D9—22no—
94C2×C3×C4×C9—22no—
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97#6233—22no—
98#6233—22no—
99C2×C3⋊Dic9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C4⋊(C3⋊D9)—22no—
102C4×C3⋊D9—22no—
103C4×C3⋊D9D414yescomplemented
104#6226—22no—
105C9×#67—22no—
106C3×#611—22no—
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C4×D3×C9—22no—
114C3×C4×D9—22no—
115#6195—22no—
116D3×Dic9—22no—
117#6192—22no—
118(C3⋊D9)⋊C4—22no—
119Dic3×D9—22no—
120#5547—91no—
121#5547—91no—
122C22×D32—31no—
123C22×C32×C4C2×D311yescharacteristic
124C2×#638—31no—
125C2×#638—31no—
126#3828—64no—
127C2×C4⋊(C3⋊D3)—31no—
128C2×C4×C3⋊D3—31no—
129C2×C4×C3⋊D3—31no—
130C2×#634—31no—
131C2×C3×#67—31no—
132C2×C3×#67C2×D311yescharacteristic
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3C2×D311yescharacteristic
135C2×#626—31no—
136C2×#626—31no—
137C2×#624—31no—
138C2×D3×Dic3—31no—
139C2×D3×Dic3—31no—
140C4×D32—64no—
141C23×D9—31no—
142C3×#217—31no—
143C3×#217C2×D311yescharacteristic
144C3×(C2×D3)⋊C4—31no—
145C3×(C2×D3)⋊C4C2×D311yescharacteristic
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4C2×D311yescharacteristic
148C3×C4×Dic3—31no—
149C3×C4×Dic3C2×D311yescharacteristic
150#3724—31no—
151#3724—31no—
152Dic3⋊Dic3—31no—
153Dic3⋊Dic3—31no—
154#3722—31no—
155#3722—31no—
156#3722—31no—
157#3722—31no—
158(C2×D3)⋊Dic3—31no—
159(C2×D3)⋊Dic3—31no—
160C2×D4×C9—31no—
161C22×C4×C9—21no—
162C22×C4×C9—31no—
163C22×C4×C9C2×D311yescharacteristic, complemented
164C2×#611—31no—
165C2×#611—31no—
166C2×#611—31no—
167C2×#611—61no—
168C2×#611—61no—
169C2×#611C2×D311yescharacteristic
170C22×Dic9—31no—
171#3697—64no—
172#3697—68no—
173C2×D36—31no—
174C2×D36—31no—
175C2×D36—61no—
176C2×C4×D9—31no—
177C2×C4×D9—31no—
178C2×C4×D9—31no—
179C2×C4×D9—31no—
180C2×C4×D9—64no—
181C2×C4×D9—61no—
182C2×C4×D9—61no—
183C2×C4×D9C2×D311yescharacteristic
184C2×Dic18—31no—
185C2×Dic18—61no—
186C9×C4⋊C4—31no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4—31no—
189C42×C9—31no—
190#3676—31no—
191#3676C2×D311yescharacteristic, complemented
192(C2×D9)⋊C4—31no—
193(C2×D9)⋊C4—31no—
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⋊C4—31no—
201Dic9⋊C4—31no—
202Dic9⋊C4C2×D311yescharacteristic, complemented
203C4×Dic9C2×D311yescharacteristic, complemented
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#4112yescomplemented
217C2×C3×D9—21no—
218C2×C3×D9—21no—
219C2×C3×D9#4112yescomplemented
220D3×D9—28no—
221C3×C4×C9—21no—
222C3×C4×C9C2×D412yes—
223C3⋊Dic9—21no—
224C3⋊Dic9C2×D412yes—
225C9×Dic3—21no—
226C9×Dic3—21no—
227C9×Dic3—21no—
228C3×Dic9—21no—
229C3×Dic9—21no—
230C3×Dic9—21no—
231C2×#235—91no—
232C2×#235—91no—
233C2×#235—181no—
234C22×C4×D3—91no—
235C22×C4×D3—91no—
236C3×C4×D4—31no—
237C3×C4×D4—91no—
238#939—91no—
239#939—91no—
240#937—91no—
241#937—91no—
242C4×#67—31no—
243C4×#67—91no—
244C4×#67—91no—
245C4×#67D911yescharacteristic, complemented
246#896—91no—
247#896—91no—
248#894—91no—
249#894—91no—
250#884—91no—
251#884—91no—
252#883—91no—
253#883—91no—
254#882—91no—
255#882—91no—
256#878—91no—
257#878—91no—
258C4×D12—91no—
259C4×D12—91no—
260#872—91no—
261#872—91no—
262C23×C32C22×D311yescharacteristic
263C22×C3⋊D3—31no—
264C22×C3⋊D3—31no—
265C22×C3×D3—31no—
266C22×C3×D3C22×D311yescharacteristic
267C2×D32—62no—
268C2×D32—62no—
269C2×D32—62no—
270C2×C32×C4—22no—
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273#638—62no—
274#638—62no—
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—31no—
277C4⋊(C3⋊D3)—62no—
278C4×C3⋊D3—34no—
279C4×C3⋊D3—62no—
280#634—62no—
281C3×#67—22no—
282C3×#67—62no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D311yescharacteristic
289C3×C4×D3—22no—
290C3×C4×D3—62no—
291#626—62no—
292#626—62no—
293#624—62no—
294D3×Dic3—62no—
295D3×Dic3—62no—
296C23×C9—21no—
297C23×C9—31no—
298C23×C9C22×D311yescharacteristic
299C22×D9—31no—
300C22×D9—31no—
301C22×D9—61no—
302C22×D9—61no—
303C22×D9—62no—
304C22×D9—62no—
305C22×D9—62no—
306C22×D9C22×D311yescharacteristic
307D4×C9—62no—
308C2×C4×C9—24no—
309C2×C4×C9—22no—
310C2×C4×C9—21no—
311C2×C4×C9—21no—
312C2×C4×C9—31no—
313C2×C4×C9—31no—
314C2×C4×C9—31no—
315C2×C4×C9—62no—
316C2×C4×C9C22×D311yescharacteristic
317C2×C4×C9C22×D311yescharacteristic
318#611—22no—
319#611—62no—
320#611—62no—
321#611—62no—
322#611—64no—
323#611—64no—
324C2×Dic9—31no—
325C2×Dic9—31no—
326C2×Dic9—61no—
327C2×Dic9—61no—
328C2×Dic9—62no—
329C2×Dic9C22×D311yescharacteristic
330C2×Dic9C22×D311yescharacteristic
331C2×Dic9C22×D311yescharacteristic
332D36—62no—
333D36—64no—
334D36—62no—
335C4×D9—22no—
336C4×D9—34no—
337C4×D9—64no—
338C4×D9—62no—
339C4×D9—62no—
340C4×D9—64no—
341C4×D9—62no—
342Dic18—62no—
343Dic18—64no—
344#525—271noSylow
345C2×C3×C9—41no—
346C2×C3×C9C22×D411yescharacteristic
347C2×C3×C9C2×#4111yescharacteristic
348C2×C3×C9C2×#4111yescharacteristic
349C3⋊D9—22no—
350C3⋊D9—41no—
351D3×C9—22no—
352C3×D9—22no—
353C23×D3—91no—
354C23×D3—91no—
355C2×C3×D4—31no—
356C2×C3×D4—91no—
357C22×C3×C4—21no—
358C22×C3×C4—31no—
359C22×C3×C4—91no—
360C22×C3×C4C2×D911yescharacteristic, complemented
361C22×C3×C4D3211yescharacteristic
362C2×#67—31no—
363C2×#67—91no—
364C2×#67—91no—
365C2×#67—91no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—181no—
370C2×#67—181no—
371C2×#67C2×D911yescharacteristic
372C22×Dic3—91no—
373C22×Dic3—91no—
374#235—184no—
375#235—184no—
376#235—188no—
377C2×D12—91no—
378C2×D12—91no—
379C2×D12—91no—
380C2×D12—91no—
381C2×D12—181no—
382C2×C4×D3—31no—
383C2×C4×D3—91no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×C4×D3—91no—
387C2×C4×D3—91no—
388C2×C4×D3—91no—
389C2×C4×D3—91no—
390C2×C4×D3—91no—
391C2×C4×D3—181no—
392C2×C4×D3—181no—
393C2×C4×D3—184no—
394C2×C4×D3—184no—
395C2×C4×D3C2×D911yescharacteristic
396C2×Dic6—91no—
397C2×Dic6—91no—
398C2×Dic6—181no—
399C3×C4⋊C4—31no—
400C3×C4⋊C4—91no—
401C3×C22⋊C4—31no—
402C3×C22⋊C4—31no—
403C3×C22⋊C4—91no—
404C3×C22⋊C4—91no—
405C3×C42—31no—
406C3×C42—91no—
407#217—31no—
408#217—91no—
409#217—91no—
410#217C2×D911yescharacteristic, complemented
411(C2×D3)⋊C4—31no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
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)⋊C4—91no—
422(C2×D3)⋊C4C2×D911yescharacteristic
423C4⋊Dic3—91no—
424C4⋊Dic3—91no—
425Dic3⋊C4—31no—
426Dic3⋊C4—91no—
427Dic3⋊C4—91no—
428Dic3⋊C4—91no—
429Dic3⋊C4—91no—
430Dic3⋊C4—91no—
431Dic3⋊C4—91no—
432Dic3⋊C4C2×D911yescharacteristic, complemented
433C4×Dic3—31no—
434C4×Dic3C2×D911yescharacteristic, complemented
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—21no—
438C22×C32C23×D311yescharacteristic
439C2×C3⋊D3—32no—
440C2×C3⋊D3—61no—
441C2×C3⋊D3—61no—
442C2×C3⋊D3—61no—
443C2×C3⋊D3—61no—
444C2×C3⋊D3—61no—
445C2×C3×D3—21no—
446C2×C3×D3—21no—
447C2×C3×D3—32no—
448C2×C3×D3—61no—
449C2×C3×D3—61no—
450C2×C3×D3#23512yes—
451D32—68no—
452C32×C4—21no—
453C32×C4D3×D412yes—
454C3⋊Dic3—32no—
455C3⋊Dic3—61no—
456C3×Dic3—21no—
457C3×Dic3—21no—
458C3×Dic3—21no—
459C3×Dic3—61no—
460C3×Dic3—61no—
461C3×Dic3—61no—
462C22×C9—22no—
463C22×C9—21no—
464C22×C9—21no—
465C22×C9—21no—
466C22×C9—21no—
467C22×C9—32no—
468C22×C9—41no—
469C22×C9—41no—
470C22×C9—61no—
471C22×C9—61no—
472C22×C9C23×D311yescharacteristic
473C2×D9—21no—
474C2×D9—21no—
475C2×D9—32no—
476C2×D9—62no—
477C2×D9—68no—
478C2×D9—61no—
479C2×D9—61no—
480C2×D9—62no—
481C2×D9—61no—
482C2×D9—61no—
483C2×D9—61no—
484C2×D9—121no—
485C2×D9—121no—
486C2×D9—121no—
487C2×D9—121no—
488C2×D9#23512yescomplemented
489C4×C9—22no—
490C4×C9—21no—
491C4×C9—22no—
492C4×C9—61no—
493C4×C9—61no—
494C4×C9—61no—
495C4×C9D3×D412yes—
496Dic9—21no—
497Dic9—21no—
498Dic9—21no—
499Dic9—32no—
500Dic9—62no—
501Dic9—62no—
502Dic9—61no—
503C2×#41—271no—
504C23×C4—271no—
505#123—271no—
506#123—271no—
507C22⋊Q8—271no—
508C22⋊Q8—271no—
509#121—271no—
510#121—271no—
511#120—271no—
512#120—271no—
513C4×D4—31no—
514C4×D4—91no—
515C4×D4—271no—
516C4×D4—271no—
517#117—271no—
518C3×C9#52511yescharacteristic, complemented, Sylow
519C23×C3—21no—
520C23×C3—31no—
521C23×C3—91no—
522C23×C3C22×D911yescharacteristic
523C23×C3C2×D3211yescharacteristic
524C22×D3—31no—
525C22×D3—91no—
526C22×D3—91no—
527C22×D3—91no—
528C22×D3—91no—
529C22×D3—181no—
530C22×D3—181no—
531C22×D3—182no—
532C22×D3—182no—
533C22×D3—182no—
534C22×D3—182no—
535C22×D3—182no—
536C22×D3—182no—
537C22×D3C22×D911yescharacteristic
538C3×D4—62no—
539C3×D4—182no—
540C2×C3×C4—24no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—62no—
549C2×C3×C4—91no—
550C2×C3×C4—91no—
551C2×C3×C4—91no—
552C2×C3×C4—182no—
553C2×C3×C4C22×D911yescharacteristic
554C2×C3×C4C22×D911yescharacteristic
555C2×C3×C4C2×D3211yescharacteristic
556C2×C3×C4C2×D3211yescharacteristic
557#67—22no—
558#67—62no—
559#67—182no—
560#67—182no—
561#67—182no—
562#67—182no—
563#67—182no—
564#67—182no—
565#67—184no—
566#67—184no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—91no—
571C2×Dic3—91no—
572C2×Dic3—91no—
573C2×Dic3—91no—
574C2×Dic3—181no—
575C2×Dic3—181no—
576C2×Dic3—182no—
577C2×Dic3—182no—
578C2×Dic3C22×D911yescharacteristic
579C2×Dic3C22×D911yescharacteristic
580C2×Dic3C22×D911yescharacteristic
581D12—182no—
582D12—182no—
583D12—184no—
584D12—182no—
585D12—182no—
586C4×D3—22no—
587C4×D3—62no—
588C4×D3—94no—
589C4×D3—94no—
590C4×D3—184no—
591C4×D3—182no—
592C4×D3—182no—
593C4×D3—182no—
594C4×D3—182no—
595C4×D3—184no—
596C4×D3—182no—
597C4×D3—182no—
598Dic6—182no—
599Dic6—182no—
600Dic6—184no—
601C2×C32—41no—
602C2×C32C2×#23511yescharacteristic
603C2×C32C2×D3×D411yescharacteristic
604C2×C32D3×#4111yescharacteristic
605C3⋊D3—62no—
606C3⋊D3—121no—
607C3×D3—22no—
608C3×D3—62no—
609C2×C9—21no—
610C2×C9—21no—
611C2×C9—21no—
612C2×C9—42no—
613C2×C9—41no—
614C2×C9—62no—
615C2×C9C2×#23511yescharacteristic
616C2×C9C2×D3×D411yescharacteristic
617C2×C9D3×#4111yescharacteristic
618D9—22no—
619D9—62no—
620D9—122no—
621D9—122no—
622D9—121no—
623C24—271no—
624#41—544no—
625C2×Q8—271no—
626C2×D4—31no—
627C2×D4—91no—
628C2×D4—271no—
629C2×D4—271no—
630C2×D4—271no—
631C2×D4—271no—
632C2×D4—271no—
633C22×C4—31no—
634C22×C4—91no—
635C22×C4—271no—
636C22×C4—271no—
637C22×C4—271no—
638C22×C4—271no—
639C22×C4—271no—
640C22×C4—544no—
641C22×C4D3×D911yescharacteristic, complemented
642C4⋊C4—31no—
643C4⋊C4—91no—
644C4⋊C4—271no—
645C4⋊C4—271no—
646C4⋊C4—271no—
647C4⋊C4—271no—
648C22⋊C4—31no—
649C22⋊C4—31no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—271no—
653C22⋊C4—271no—
654C22⋊C4—271no—
655C22⋊C4—271no—
656C22⋊C4—271no—
657C22⋊C4—271no—
658C42—31no—
659C42—91no—
660C22×C3—22no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—32no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—92no—
674C22×C3—181no—
675C22×C3—181no—
676C22×C3C23×D911yescharacteristic
677C22×C3C22×D3211yescharacteristic
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—32no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—92no—
684C2×D3—92no—
685C2×D3—182no—
686C2×D3—188no—
687C2×D3—188no—
688C2×D3—181no—
689C2×D3—181no—
690C2×D3—181no—
691C2×D3—181no—
692C2×D3—182no—
693C2×D3—181no—
694C2×D3—181no—
695C2×D3—181no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—361no—
700C2×D3—361no—
701C2×D3—361no—
702C2×D3—361no—
703C2×D3#369712yescomplemented
704C3×C4—22no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—22no—
708C3×C4—61no—
709C3×C4—61no—
710C3×C4—61no—
711C3×C4—181no—
712C3×C4—181no—
713C3×C4—181no—
714C3×C4D4×D912yes—
715C3×C4#381112yes—
716Dic3—21no—
717Dic3—21no—
718Dic3—21no—
719Dic3—61no—
720Dic3—61no—
721Dic3—61no—
722Dic3—92no—
723Dic3—92no—
724Dic3—182no—
725Dic3—182no—
726Dic3—181no—
727Dic3—181no—
728C32#554711yescharacteristic
729C9—21no—
730C9#554711yescharacteristic, complemented
731C23—31no—
732C23—91no—
733C23—271no—
734C23—271no—
735C23—542no—
736C23—542no—
737C23—542no—
738C23C2×D3×D911yescharacteristic
739Q8—542no—
740D4—62no—
741D4—182no—
742D4—542no—
743D4—542no—
744D4—542no—
745D4—542no—
746D4—542no—
747C2×C4—22no—
748C2×C4—31no—
749C2×C4—31no—
750C2×C4—31no—
751C2×C4—62no—
752C2×C4—91no—
753C2×C4—91no—
754C2×C4—91no—
755C2×C4—182no—
756C2×C4—271no—
757C2×C4—274no—
758C2×C4—271no—
759C2×C4—542no—
760C2×C4—542no—
761C2×C4—542no—
762C2×C4—542no—
763C2×C4C2×D3×D911yescharacteristic
764C2×C4C2×D3×D911yescharacteristic
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—41no—
770C2×C3—41no—
771C2×C3—62no—
772C2×C3—182no—
773C2×C3C2×#369711yescharacteristic
774C2×C3C2×D4×D911yescharacteristic
775C2×C3#41×D911yescharacteristic
776C2×C3D3×#23511yescharacteristic
777C2×C3D3×#23511yescharacteristic
778C2×C3C2×#381111yescharacteristic
779D3—22no—
780D3—62no—
781D3—182no—
782D3—182no—
783D3—362no—
784D3—362no—
785D3—361no—
786D3—361no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—32no—
791C22—61no—
792C22—61no—
793C22—92no—
794C22—181no—
795C22—181no—
796C22—272no—
797C22—548no—
798C22—541no—
799C22—541no—
800C22—541no—
801C22—541no—
802C22—541no—
803C22C22×D3×D911yescharacteristic
804C4—21no—
805C4—61no—
806C4—61no—
807C4—61no—
808C4—181no—
809C4—181no—
810C4—181no—
811C4—272no—
812C4—541no—
813C4#8866812yes—
814C3—21no—
815C3#1058964911yescharacteristic, complemented
816C3#1059507611yescharacteristic
817C2—41no—
818C2—62no—
819C2—182no—
820C2—542no—
821C2—1081no—
822C2D3×#369711yescharacteristic
823C2D9×#23511yescharacteristic
824C2C2×#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#525
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×C4×D3×D9C2semidirect
3. C4×C9×#67C2semidirect
4. C3×C4×#611C2semidirect
5. #11721292C2semidirect
6. #11721282C2semidirect
7. #11721275C2semidirect
8. #11721271C2semidirect
9. #11721051C2semidirect
10. C4×#6195C2semidirect
11. #11721024C2semidirect
12. C4×#6192C2semidirect
13. #11720997C2semidirect
14. #11720996C2semidirect
15. #11720931C2semidirect
19. C22×C3×C4×C9C22semidirect
21. C2×#6233C22semidirect
25. C2×C4×C3⋊D9C22semidirect
26. C2×#6226C22semidirect
37. C9×#217C22semidirect
38. C3×#3676C22semidirect
41. C9×Dic3⋊C4C22semidirect
42. C4×C9×Dic3C22semidirect
43. C3×Dic9⋊C4C22semidirect
44. C3×C4×Dic9C22semidirect
48. #88445C22semidirect
49. #88445C22semidirect
51. Dic3⋊Dic9C22semidirect
52. #88442C22semidirect
53. #88442C22semidirect
54. Dic9⋊Dic3C22semidirect
77. C4×#611D3semidirect
103. C4×C3⋊D9D4semidirect
163. C22×C4×C9C2×D3semidirect
191. #3676C2×D3semidirect
202. Dic9⋊C4C2×D3semidirect
203. C4×Dic9C2×D3semidirect
216. C2×D3×C9#41semidirect
219. C2×C3×D9#41semidirect
245. C4×#67D9semidirect
360. C22×C3×C4C2×D9semidirect
410. #217C2×D9semidirect
432. Dic3⋊C4C2×D9semidirect
434. C4×Dic3C2×D9semidirect
488. C2×D9#235semidirect
518. C3×C9#525semidirect
641. C22×C4D3×D9semidirect
703. C2×D3#3697semidirect
730. C9#5547semidirect
815. C3#10589649semidirect

Maximal subgroups

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

subgroupindex
C2×#887362
C2×C4×D3×D92
C4×C9×#672
C3×C4×#6112
#117212922
#117212822
#117212752
#117212712
#117210512
C4×#61952
#117210242
C4×#61922
#117209972
#117209962
#117209312
#105950763
#105896493