Finite Group Databasebeta

← #13153919

Subgroups — #13153919

Order 1728.

1650 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88736C211yesmaximal, characteristic, complemented
2C22×C4×C3⋊D9C211yesmaximal, characteristic, complemented
3C3×C4×D4×C9C211yesmaximal, characteristic, complemented
4#11721839C211yesmaximal, characteristic, complemented
5#11721837C211yesmaximal, characteristic, complemented
6C4×#6233C211yesmaximal, characteristic, complemented
7C4×#6233C211yesmaximal, characteristic, complemented
8#11721752C211yesmaximal, characteristic, complemented
9#11721750C211yesmaximal, characteristic, complemented
10#11721730C211yesmaximal, characteristic, complemented
11#11721729C211yesmaximal, characteristic, complemented
12#11721728C211yesmaximal, characteristic, complemented
13#11721724C211yesmaximal, characteristic, complemented
14C4×C4⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
15#11721709C211yesmaximal, characteristic, complemented
16#10596018—31nomaximal
17#10589649—33nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic
20C22×C3×C4×C9C2211yescharacteristic
21C22×C3×C4×C9C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic
23C2×#6233C2211yescharacteristic
24C2×#6233C2211yescharacteristic
25C2×#6233C2211yescharacteristic, complemented
26C22×C3⋊Dic9C2211yescharacteristic
27#88736—24no—
28C2×C4⋊(C3⋊D9)C2211yescharacteristic
29C2×C4⋊(C3⋊D9)C2211yescharacteristic
30C2×C4×C3⋊D9—24no—
31C2×C4×C3⋊D9C2211yescharacteristic
32C2×C4×C3⋊D9C2211yescharacteristic
33C2×C4×C3⋊D9C2211yescharacteristic
34C2×C4×C3⋊D9C2211yescharacteristic
35C2×C4×C3⋊D9C2211yescharacteristic, complemented
36C2×#6226C2211yescharacteristic, complemented
37C3×C9×C4⋊C4C2211yescharacteristic, complemented
38C3×C9×C22⋊C4C2211yescharacteristic
39C3×C9×C22⋊C4C2211yescharacteristic, complemented
40C3×C42×C9C2211yescharacteristic, complemented
41#88551C2211yescharacteristic
42#88551C2211yescharacteristic, complemented
43#88536C2211yescharacteristic
44#88536C2211yescharacteristic
45#88536C2211yescharacteristic
46#88536C2211yescharacteristic
47#88536C2211yescharacteristic, complemented
48#88536C2211yescharacteristic, complemented
49C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
50#88534C2211yescharacteristic, complemented
51#88534C2211yescharacteristic, complemented
52#88534C2211yescharacteristic, complemented
53#88534C2211yescharacteristic, complemented
54C4×C3⋊Dic9C2211yescharacteristic, complemented
55C2×#3828—31no—
56C22×C4×C3⋊D3—31no—
57C32×C4×D4D311yescharacteristic
58#64148—31no—
59#64146—31no—
60C4×#638—31no—
61C4×#638—31no—
62#64105—31no—
63#64103—31no—
64#64093—31no—
65#64092—31no—
66#64091—31no—
67#64087—31no—
68C4×C4⋊(C3⋊D3)—31no—
69#64081—31no—
70C2×#3697—33no—
71C22×C4×D9—33no—
72C4×D4×C9D313yescomplemented
73#63501—33no—
74#63499—33no—
75C4×#611—33no—
76C4×#611—33no—
77#63458—33no—
78#63456—33no—
79#63446—33no—
80#63445—33no—
81#63444—33no—
82#63440—33no—
83C4×D36—33no—
84#63434—33no—
85C23×C3×C9C2311yescharacteristic
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9—22no—
88C22×C3⋊D9—22no—
89C22×C3⋊D9—22no—
90C22×C3⋊D9C2311yescharacteristic
91C22×C3⋊D9C2311yescharacteristic
92C22×C3⋊D9C2311yescharacteristic
93C3×D4×C9—22no—
94C2×C3×C4×C9—22no—
95C2×C3×C4×C9—22no—
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3×C4×C9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3×C4×C9C2311yescharacteristic
101#6233—22no—
102#6233—22no—
103#6233—22no—
104#6233—22no—
105C2×C3⋊Dic9—22no—
106C2×C3⋊Dic9C2311yescharacteristic
107C2×C3⋊Dic9C2311yescharacteristic
108C2×C3⋊Dic9C2311yescharacteristic
109C2×C3⋊Dic9C2311yescharacteristic
110C2×C3⋊Dic9C2311yescharacteristic
111C4⋊(C3⋊D9)—22no—
112C4⋊(C3⋊D9)—22no—
113C4×C3⋊D9—22no—
114C4×C3⋊D9—22no—
115C4×C3⋊D9—22no—
116C4×C3⋊D9—22no—
117C4×C3⋊D9D414yescomplemented
118#6226—22no—
119#5547—93no—
120#5547—91no—
121C23×C3⋊D3—31no—
122C2×C32×D4C2×D311yescharacteristic
123C22×C32×C4C2×D311yescharacteristic
124C22×C32×C4C2×D311yescharacteristic
125C2×#638—31no—
126C2×#638—31no—
127C2×#638—31no—
128C2×#638—31no—
129C22×C3⋊Dic3—31no—
130#3828—64no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4⋊(C3⋊D3)—31no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3—31no—
136C2×C4×C3⋊D3—31no—
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3—64no—
139C2×#634—31no—
140C23×D9—33no—
141C32×C4⋊C4C2×D311yescharacteristic
142C32×C22⋊C4C2×D311yescharacteristic
143C32×C22⋊C4C2×D311yescharacteristic
144C32×C42C2×D311yescharacteristic
145#3757—31no—
146#3757—31no—
147#3752—31no—
148#3752—31no—
149#3752—31no—
150#3752—31no—
151#3752—31no—
152#3752—31no—
153C4⋊(C3⋊Dic3)—31no—
154#3750—31no—
155#3750—31no—
156#3750—31no—
157#3750—31no—
158C4×C3⋊Dic3—31no—
159C2×D4×C9C2×D313yes—
160C22×C4×C9C2×D313yes—
161C22×C4×C9C2×D313yescomplemented
162C2×#611—33no—
163C2×#611—33no—
164C2×#611—33no—
165C2×#611—33no—
166C22×Dic9—33no—
167#3697—612no—
168C2×D36—33no—
169C2×D36—33no—
170C2×C4×D9—33no—
171C2×C4×D9—33no—
172C2×C4×D9—33no—
173C2×C4×D9—33no—
174C2×C4×D9—33no—
175C2×C4×D9—612no—
176C2×Dic18—33no—
177C9×C4⋊C4C2×D313yescomplemented
178C9×C22⋊C4C2×D313yes—
179C9×C22⋊C4C2×D313yescomplemented
180C42×C9C2×D313yescomplemented
181#3676—33no—
182#3676—33no—
183(C2×D9)⋊C4—33no—
184(C2×D9)⋊C4—33no—
185(C2×D9)⋊C4—33no—
186(C2×D9)⋊C4—33no—
187(C2×D9)⋊C4—33no—
188(C2×D9)⋊C4—33no—
189C4⋊Dic9—33no—
190Dic9⋊C4—33no—
191Dic9⋊C4—33no—
192Dic9⋊C4—33no—
193Dic9⋊C4—33no—
194C4×Dic9—33no—
195C22×C3×C9—21no—
196C22×C3×C9—21no—
197C22×C3×C9—21no—
198C22×C3×C9—21no—
199C22×C3×C9—21no—
200C22×C3×C9#4112yescomplemented
201C22×C3×C9C2411yescharacteristic
202C2×C3⋊D9—28no—
203C2×C3⋊D9—21no—
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9—21no—
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
210C2×C3⋊D9C2×D412yes—
211C2×C3⋊D9#4112yescomplemented
212C3×C4×C9—21no—
213C3×C4×C9—21no—
214C3×C4×C9—21no—
215C3×C4×C9—21no—
216C3×C4×C9C2×D412yes—
217C3⋊Dic9—21no—
218C3⋊Dic9—21no—
219C3⋊Dic9—21no—
220C3⋊Dic9—21no—
221C3⋊Dic9C2×D412yes—
222C2×#235—93no—
223C2×#235—91no—
224C22×C4×D3—93no—
225C22×C4×D3—91no—
226C3×C4×D4D913yescomplemented
227C3×C4×D4C3⋊D311yescharacteristic
228#939—93no—
229#939—91no—
230#937—93no—
231#937—91no—
232C4×#67—93no—
233C4×#67—93no—
234C4×#67—91no—
235C4×#67—91no—
236#896—93no—
237#896—91no—
238#894—93no—
239#894—91no—
240#884—93no—
241#884—91no—
242#883—93no—
243#883—91no—
244#882—93no—
245#882—91no—
246#878—93no—
247#878—91no—
248C4×D12—93no—
249C4×D12—91no—
250#872—93no—
251#872—91no—
252C23×C32C22×D311yescharacteristic
253C23×C32C22×D311yescharacteristic
254C22×C3⋊D3—31no—
255C22×C3⋊D3—31no—
256C22×C3⋊D3—31no—
257C22×C3⋊D3—62no—
258C22×C3⋊D3—62no—
259C22×C3⋊D3—62no—
260C32×D4—22no—
261C2×C32×C4—22no—
262C2×C32×C4—22no—
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268#638—62no—
269#638—62no—
270#638—62no—
271#638—62no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—62no—
278C4⋊(C3⋊D3)—62no—
279C4⋊(C3⋊D3)—62no—
280C4×C3⋊D3—34no—
281C4×C3⋊D3—62no—
282C4×C3⋊D3—62no—
283C4×C3⋊D3—62no—
284C4×C3⋊D3—62no—
285#634—62no—
286C23×C9C22×D313yes—
287C23×C9C22×D313yes—
288C22×D9—33no—
289C22×D9—33no—
290C22×D9—33no—
291C22×D9—66no—
292C22×D9—66no—
293C22×D9—66no—
294D4×C9—26no—
295C2×C4×C9—26no—
296C2×C4×C9—26no—
297C2×C4×C9C22×D313yes—
298C2×C4×C9C22×D313yes—
299C2×C4×C9C22×D313yes—
300C2×C4×C9C22×D313yes—
301C2×C4×C9C22×D313yes—
302#611—66no—
303#611—66no—
304#611—66no—
305#611—66no—
306C2×Dic9—33no—
307C2×Dic9—33no—
308C2×Dic9—33no—
309C2×Dic9—33no—
310C2×Dic9—33no—
311C2×Dic9—66no—
312D36—66no—
313D36—66no—
314C4×D9—312no—
315C4×D9—66no—
316C4×D9—66no—
317C4×D9—66no—
318C4×D9—66no—
319Dic18—66no—
320#525—271noSylow
321C2×C3×C9—22no—
322C2×C3×C9—41no—
323C2×C3×C9C22×D411yescharacteristic
324C2×C3×C9C2×#4111yescharacteristic
325C2×C3×C9C2×#4111yescharacteristic
326C3⋊D9—22no—
327C3⋊D9—22no—
328C3⋊D9—41no—
329C23×D3—93no—
330C23×D3—91no—
331C2×C3×D4C2×D913yes—
332C2×C3×D4C2×C3⋊D311yescharacteristic
333C22×C3×C4C2×D913yes—
334C22×C3×C4C2×D913yescomplemented
335C22×C3×C4C2×C3⋊D311yescharacteristic
336C22×C3×C4C2×C3⋊D311yescharacteristic
337C2×#67—93no—
338C2×#67—93no—
339C2×#67—93no—
340C2×#67—93no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C22×Dic3—93no—
346C22×Dic3—91no—
347#235—184no—
348#235—1812no—
349C2×D12—93no—
350C2×D12—93no—
351C2×D12—91no—
352C2×D12—91no—
353C2×C4×D3—93no—
354C2×C4×D3—91no—
355C2×C4×D3—93no—
356C2×C4×D3—93no—
357C2×C4×D3—93no—
358C2×C4×D3—93no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×C4×D3—184no—
364C2×C4×D3—1812no—
365C2×Dic6—93no—
366C2×Dic6—91no—
367C3×C4⋊C4C2×D913yescomplemented
368C3×C4⋊C4C2×C3⋊D311yescharacteristic
369C3×C22⋊C4C2×D913yes—
370C3×C22⋊C4C2×D913yescomplemented
371C3×C22⋊C4C2×C3⋊D311yescharacteristic
372C3×C22⋊C4C2×C3⋊D311yescharacteristic
373C3×C42C2×D913yescomplemented
374C3×C42C2×C3⋊D311yescharacteristic
375#217—93no—
376#217—93no—
377#217—91no—
378#217—91no—
379(C2×D3)⋊C4—93no—
380(C2×D3)⋊C4—93no—
381(C2×D3)⋊C4—93no—
382(C2×D3)⋊C4—93no—
383(C2×D3)⋊C4—93no—
384(C2×D3)⋊C4—93no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391C4⋊Dic3—93no—
392C4⋊Dic3—91no—
393Dic3⋊C4—93no—
394Dic3⋊C4—93no—
395Dic3⋊C4—93no—
396Dic3⋊C4—93no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401C4×Dic3—93no—
402C4×Dic3—91no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32#23512yes—
409C22×C32C23×D311yescharacteristic
410C2×C3⋊D3—32no—
411C2×C3⋊D3—32no—
412C2×C3⋊D3—68no—
413C2×C3⋊D3—61no—
414C2×C3⋊D3—61no—
415C2×C3⋊D3—61no—
416C2×C3⋊D3—61no—
417C2×C3⋊D3—61no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—61no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4D3×D412yes—
425C3⋊Dic3—32no—
426C3⋊Dic3—61no—
427C3⋊Dic3—61no—
428C3⋊Dic3—61no—
429C3⋊Dic3—61no—
430C22×C9—23no—
431C22×C9—23no—
432C22×C9—23no—
433C22×C9—23no—
434C22×C9—23no—
435C22×C9#23516yescomplemented
436C22×C9C23×D313yes—
437C2×D9—36no—
438C2×D9—36no—
439C2×D9—624no—
440C2×D9—63no—
441C2×D9—63no—
442C2×D9—63no—
443C2×D9—63no—
444C2×D9—63no—
445C2×D9—63no—
446C2×D9—63no—
447C4×C9—23no—
448C4×C9—23no—
449C4×C9—23no—
450C4×C9—23no—
451C4×C9D3×D416yes—
452Dic9—36no—
453Dic9—63no—
454Dic9—63no—
455Dic9—63no—
456Dic9—63no—
457C2×#41—271no—
458C23×C4—271no—
459#123—271no—
460#123—271no—
461C22⋊Q8—271no—
462C22⋊Q8—271no—
463#121—271no—
464#121—271no—
465#120—271no—
466#120—271no—
467C4×D4—271no—
468C4×D4—271no—
469C4×D4—271no—
470C4×D4C3⋊D911yescharacteristic, complemented
471#117—271no—
472C3×C9#52511yescharacteristic, complemented, Sylow
473C23×C3C22×D913yes—
474C23×C3C22×D913yes—
475C23×C3C22×C3⋊D311yescharacteristic
476C23×C3C22×C3⋊D311yescharacteristic
477C22×D3—91no—
478C22×D3—91no—
479C22×D3—93no—
480C22×D3—93no—
481C22×D3—91no—
482C22×D3—93no—
483C22×D3—182no—
484C22×D3—182no—
485C22×D3—186no—
486C22×D3—186no—
487C22×D3—186no—
488C22×D3—182no—
489C3×D4—26no—
490C3×D4—22no—
491C2×C3×C4—26no—
492C2×C3×C4—26no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4C22×D913yes—
496C2×C3×C4C22×D913yes—
497C2×C3×C4C22×D913yes—
498C2×C3×C4C22×D913yes—
499C2×C3×C4C22×D913yes—
500C2×C3×C4C22×C3⋊D311yescharacteristic
501C2×C3×C4C22×C3⋊D311yescharacteristic
502C2×C3×C4C22×C3⋊D311yescharacteristic
503C2×C3×C4C22×C3⋊D311yescharacteristic
504C2×C3×C4C22×C3⋊D311yescharacteristic
505#67—182no—
506#67—186no—
507#67—182no—
508#67—182no—
509#67—186no—
510#67—186no—
511#67—186no—
512#67—182no—
513C2×Dic3—91no—
514C2×Dic3—93no—
515C2×Dic3—91no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—91no—
519C2×Dic3—93no—
520C2×Dic3—93no—
521C2×Dic3—93no—
522C2×Dic3—93no—
523C2×Dic3—182no—
524C2×Dic3—186no—
525D12—182no—
526D12—182no—
527D12—186no—
528D12—186no—
529C4×D3—912no—
530C4×D3—94no—
531C4×D3—182no—
532C4×D3—186no—
533C4×D3—182no—
534C4×D3—186no—
535C4×D3—186no—
536C4×D3—186no—
537C4×D3—182no—
538C4×D3—182no—
539Dic6—182no—
540Dic6—186no—
541C2×C32—22no—
542C2×C32—41no—
543C2×C32C2×#23511yescharacteristic
544C2×C32C2×D3×D411yescharacteristic
545C2×C32D3×#4111yescharacteristic
546C3⋊D3—62no—
547C3⋊D3—62no—
548C3⋊D3—121no—
549C2×C9—26no—
550C2×C9—43no—
551C2×C9C2×#23513yes—
552C2×C9C2×D3×D413yes—
553C2×C9D3×#4113yes—
554D9—66no—
555D9—66no—
556D9—123no—
557C24—271no—
558#41—544no—
559C2×Q8—271no—
560C2×D4—271no—
561C2×D4—271no—
562C2×D4—271no—
563C2×D4—271no—
564C2×D4—271no—
565C2×D4—271no—
566C2×D4C2×C3⋊D911yescharacteristic
567C22×C4—271no—
568C22×C4—271no—
569C22×C4—271no—
570C22×C4—271no—
571C22×C4—271no—
572C22×C4—271no—
573C22×C4—544no—
574C22×C4C2×C3⋊D911yescharacteristic
575C22×C4C2×C3⋊D911yescharacteristic, complemented
576C4⋊C4—271no—
577C4⋊C4—271no—
578C4⋊C4—271no—
579C4⋊C4—271no—
580C4⋊C4—271no—
581C4⋊C4C2×C3⋊D911yescharacteristic, complemented
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4—271no—
586C22⋊C4—271no—
587C22⋊C4—271no—
588C22⋊C4—271no—
589C22⋊C4—271no—
590C22⋊C4C2×C3⋊D911yescharacteristic
591C22⋊C4C2×C3⋊D911yescharacteristic, complemented
592C42—271no—
593C42C2×C3⋊D911yescharacteristic, complemented
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—23no—
597C22×C3—23no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—23no—
602C22×C3—23no—
603C22×C3—23no—
604C22×C3#369716yescomplemented
605C22×C3C23×D913yes—
606C22×C3#382812yes—
607C22×C3C23×C3⋊D311yescharacteristic
608C2×D3—92no—
609C2×D3—92no—
610C2×D3—96no—
611C2×D3—96no—
612C2×D3—188no—
613C2×D3—1824no—
614C2×D3—181no—
615C2×D3—181no—
616C2×D3—181no—
617C2×D3—181no—
618C2×D3—183no—
619C2×D3—183no—
620C2×D3—183no—
621C2×D3—183no—
622C2×D3—181no—
623C2×D3—181no—
624C2×D3—181no—
625C2×D3—183no—
626C2×D3—183no—
627C2×D3—183no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—23no—
633C3×C4—23no—
634C3×C4—23no—
635C3×C4—23no—
636C3×C4D4×D916yes—
637C3×C4D4×C3⋊D312yes—
638Dic3—92no—
639Dic3—96no—
640Dic3—181no—
641Dic3—181no—
642Dic3—181no—
643Dic3—181no—
644Dic3—183no—
645Dic3—183no—
646Dic3—183no—
647Dic3—183no—
648C32#554711yescharacteristic
649C9#554713yescomplemented
650C23—271no—
651C23—271no—
652C23—271no—
653C23—542no—
654C23—542no—
655C23—542no—
656C23C22×C3⋊D911yescharacteristic
657C23C22×C3⋊D911yescharacteristic
658Q8—542no—
659D4—22no—
660D4—542no—
661D4—542no—
662D4—542no—
663D4—542no—
664D4—542no—
665D4—542no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—271no—
669C2×C4—274no—
670C2×C4—271no—
671C2×C4—271no—
672C2×C4—271no—
673C2×C4—271no—
674C2×C4—542no—
675C2×C4—542no—
676C2×C4—542no—
677C2×C4—542no—
678C2×C4—542no—
679C2×C4C22×C3⋊D911yescharacteristic
680C2×C4C22×C3⋊D911yescharacteristic
681C2×C4C22×C3⋊D911yescharacteristic
682C2×C4C22×C3⋊D911yescharacteristic
683C2×C4C22×C3⋊D911yescharacteristic
684C2×C3—22no—
685C2×C3—26no—
686C2×C3—41no—
687C2×C3—43no—
688C2×C3C2×#369713yes—
689C2×C3C2×D4×D913yes—
690C2×C3#41×D913yes—
691C2×C3C2×#382811yescharacteristic
692C2×C3C2×D4×C3⋊D311yescharacteristic
693C2×C3#41×C3⋊D311yescharacteristic
694D3—182no—
695D3—182no—
696D3—186no—
697D3—186no—
698D3—361no—
699D3—363no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—272no—
706C22—272no—
707C22—548no—
708C22—541no—
709C22—541no—
710C22—541no—
711C22—541no—
712C22—541no—
713C22—541no—
714C22—541no—
715C22#8873612yescomplemented
716C22C23×C3⋊D911yescharacteristic
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—272no—
722C4—541no—
723C4—541no—
724C4—541no—
725C4—541no—
726C4D4×C3⋊D912yes—
727C3#1058964913yescomplemented
728C3#1059601811yescharacteristic
729C2—22no—
730C2—41no—
731C2—542no—
732C2—542no—
733C2—1081no—
734C2C2×#8873611yescharacteristic
735C2C2×D4×C3⋊D911yescharacteristic
736C2#41×C3⋊D911yescharacteristic
subgroupG/H
centerC2×C4C22×C3⋊D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C23×C3⋊D3
FittingC3×C4×D4×C9C2
socleC22×C32C23×D3
hypercenterC4×D4C3⋊D9
hypocenterC3×C9#525
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#88736C2semidirect
2. C22×C4×C3⋊D9C2semidirect
3. C3×C4×D4×C9C2semidirect
4. #11721839C2semidirect
5. #11721837C2semidirect
6. C4×#6233C2semidirect
7. C4×#6233C2semidirect
8. #11721752C2semidirect
9. #11721750C2semidirect
10. #11721730C2semidirect
11. #11721729C2semidirect
12. #11721728C2semidirect
13. #11721724C2semidirect
14. C4×C4⋊(C3⋊D9)C2semidirect
15. #11721709C2semidirect
21. C22×C3×C4×C9C22semidirect
25. C2×#6233C22semidirect
35. C2×C4×C3⋊D9C22semidirect
36. C2×#6226C22semidirect
37. C3×C9×C4⋊C4C22semidirect
39. C3×C9×C22⋊C4C22semidirect
40. C3×C42×C9C22semidirect
42. #88551C22semidirect
47. #88536C22semidirect
48. #88536C22semidirect
49. C4⋊(C3⋊Dic9)C22semidirect
50. #88534C22semidirect
51. #88534C22semidirect
52. #88534C22semidirect
53. #88534C22semidirect
54. C4×C3⋊Dic9C22semidirect
72. C4×D4×C9D3semidirect
117. C4×C3⋊D9D4semidirect
161. C22×C4×C9C2×D3semidirect
177. C9×C4⋊C4C2×D3semidirect
179. C9×C22⋊C4C2×D3semidirect
180. C42×C9C2×D3semidirect
200. C22×C3×C9#41semidirect
211. C2×C3⋊D9#41semidirect
226. C3×C4×D4D9semidirect
334. C22×C3×C4C2×D9semidirect
367. C3×C4⋊C4C2×D9semidirect
370. C3×C22⋊C4C2×D9semidirect
373. C3×C42C2×D9semidirect
435. C22×C9#235semidirect
470. C4×D4C3⋊D9semidirect
472. C3×C9#525semidirect
575. C22×C4C2×C3⋊D9semidirect
581. C4⋊C4C2×C3⋊D9semidirect
591. C22⋊C4C2×C3⋊D9semidirect
593. C42C2×C3⋊D9semidirect
604. C22×C3#3697semidirect
649. C9#5547semidirect
715. C22#88736semidirect
727. C3#10589649semidirect

Maximal subgroups

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

subgroupindex
C2×#887362
C22×C4×C3⋊D92
C3×C4×D4×C92
#117218392
#117218372
C4×#62332
#117217522
#117217502
#117217302
#117217292
#117217282
#117217242
C4×C4⋊(C3⋊D9)2
#117217092
#105960183
#105896493