Finite Group Databasebeta

← #13148979

Subgroups — #13148979

Order 1728.

968 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88640C211yesmaximal, characteristic, complemented
2C2×#88634C211yesmaximal, characteristic, complemented
3C4⋊C4×C3⋊D9C211yesmaximal, characteristic, complemented
4C9×#896C211yesmaximal, characteristic, complemented
5C3×#63456C211yesmaximal, characteristic, complemented
6#11721041C211yesmaximal, characteristic, complemented
7#11720991C211yesmaximal, characteristic, complemented
8#11720989C211yesmaximal, characteristic, complemented
9#11720982C211yesmaximal, characteristic, complemented
10#11720978C211yesmaximal, characteristic, complemented
11#11720976C211yesmaximal, characteristic, complemented
12D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
13#11720957C211yesmaximal, characteristic, complemented
14#11720941C211yesmaximal, characteristic, complemented
15#11720903C211yesmaximal, characteristic, complemented
16#10594371—31nomaximal
17#10589733—31nomaximal
18C2×C4×C3⋊D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C4×D3×C9C2211yescharacteristic
22C2×C3×D36C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×C9×Dic6C2211yescharacteristic
25C2×#6195C2211yescharacteristic
26C2×#6194C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×Dic3×D9C2211yescharacteristic
31C2×Dic3×D9C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33C2×#6189C2211yescharacteristic
34#88640—24no—
35#88634—24no—
36C3×C9×C4⋊C4C2211yescharacteristic
37C4⋊(C3⋊Dic9)C2211yescharacteristic
38#88534C2211yescharacteristic
39#88534C2211yescharacteristic
40C9×(C2×D3)⋊C4C2211yescharacteristic
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×(C2×D9)⋊C4C2211yescharacteristic
45C9×Dic3⋊C4C2211yescharacteristic
46C9×Dic3⋊C4C2211yescharacteristic
47C3×Dic9⋊C4C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49#88445C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51Dic3⋊Dic9C2211yescharacteristic
52#88442C2211yescharacteristic
53Dic9⋊Dic3C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×#3798—31no—
56C2×#3796—31no—
57C4⋊C4×C3⋊D3—31no—
58C3×#896D311yescharacteristic
59C3×#894—31no—
60#63912—31no—
61#63893—31no—
62#63891—31no—
63#63885—31no—
64#63881—31no—
65#63879—31no—
66D3×Dic3⋊C4—31no—
67#63853—31no—
68#63853—31no—
69#63839—31no—
70C2×#3701—31no—
71C2×#3697—31no—
72C9×C22⋊Q8—31no—
73#63506—31no—
74C4×#611—31no—
75#63459—31no—
76#63456—31no—
77#63456D311yescharacteristic, complemented
78#63455—31no—
79C4⋊C4×D9—31no—
80C4⋊C4×D9—31no—
81C4⋊C4×D9—61no—
82#63446—31no—
83#63446—31no—
84#63445—31no—
85#63445—31no—
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C4×C3⋊D9—22no—
97C4×C3⋊D9—22no—
98C4×C3⋊D9—22no—
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C4×D3×C9—22no—
105C3×D36—22no—
106C3×C4×D9—22no—
107C9×Dic6—22no—
108#6195—22no—
109#6194—22no—
110#6194—22no—
111#6192—22no—
112#6192D414yescomplemented
113Dic3×D9—22no—
114Dic3×D9—22no—
115Dic3×D9—22no—
116#6189—22no—
117#5655—91no—
118#5631—91no—
119C2×C4×C3⋊D3—31no—
120C2×C4×C3⋊D3—31no—
121C2×C4×C3⋊D3—31no—
122C2×C3×D12—31no—
123C2×C3×C4×D3—31no—
124C2×C3×C4×D3C2×D311yescharacteristic
125C2×C3×Dic6C2×D311yescharacteristic
126C2×#627—31no—
127C2×#626—31no—
128C2×#626—31no—
129C2×#626—31no—
130C2×#625—31no—
131C2×#625—31no—
132C2×D3×Dic3—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135#3798—64no—
136#3796—64no—
137C32×C4⋊C4C2×D311yescharacteristic
138C4⋊(C3⋊Dic3)—31no—
139#3750—31no—
140#3750—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4—31no—
144C3×(C2×D3)⋊C4C2×D311yescharacteristic
145C3×(C2×D3)⋊C4C2×D311yescharacteristic
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4C2×D311yescharacteristic
148C3×Dic3⋊C4C2×D311yescharacteristic
149#3724—31no—
150Dic3⋊Dic3—31no—
151Dic3⋊Dic3—31no—
152#3722—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155Dic32—31no—
156C2×Q8×C9—31no—
157C22×C4×C9—31no—
158C2×#611—31no—
159C2×#611—31no—
160C2×#611—31no—
161#3701—64no—
162#3697—64no—
163C2×D36—31no—
164C2×D36—31no—
165C2×D36C2×D311yescharacteristic
166C2×C4×D9—31no—
167C2×C4×D9—31no—
168C2×C4×D9—31no—
169C2×C4×D9—31no—
170C2×C4×D9—31no—
171C2×C4×D9—31no—
172C2×C4×D9—61no—
173C2×C4×D9—61no—
174C2×C4×D9—61no—
175C2×C4×D9C2×D311yescharacteristic
176C2×Dic18—31no—
177C9×C4⋊C4—21no—
178C9×C4⋊C4—31no—
179C9×C4⋊C4—31no—
180C9×C4⋊C4C2×D311yescharacteristic
181C9×C22⋊C4—31no—
182C9×C22⋊C4—31no—
183#3676—31no—
184(C2×D9)⋊C4—31no—
185(C2×D9)⋊C4—31no—
186(C2×D9)⋊C4C2×D311yescharacteristic
187(C2×D9)⋊C4C2×D311yescharacteristic
188(C2×D9)⋊C4C2×D311yescharacteristic
189C4⋊Dic9—31no—
190C4⋊Dic9—31no—
191C4⋊Dic9—61no—
192Dic9⋊C4—31no—
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4—31no—
196Dic9⋊C4—61no—
197Dic9⋊C4—61no—
198Dic9⋊C4C2×D311yescharacteristic
199C4×Dic9—31no—
200C22×C3×C9C2411yescharacteristic
201C2×C3⋊D9—21no—
202C2×C3⋊D9—21no—
203C2×C3⋊D9C2×D412yes—
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×D3×C9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9C2×D412yes—
213C3×C4×C9—21no—
214C3×C4×C9—21no—
215C3×C4×C9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9—21no—
218C3⋊Dic9#4112yescomplemented
219C9×Dic3—21no—
220C9×Dic3—21no—
221C9×Dic3C2×D412yes—
222C3×Dic9—21no—
223C3×Dic9—21no—
224C2×#239—91no—
225C2×#237—91no—
226C2×#235—91no—
227C2×#235—91no—
228C3×#123—91no—
229C3×C22⋊Q8—31no—
230#944—91no—
231#939—91no—
232C4×#67—91no—
233C2×Dic3⋊C4—91no—
234#897—91no—
235#896D911yescharacteristic, complemented
236#894—31no—
237#894—91no—
238#894—91no—
239#893—91no—
240D3×C4⋊C4—91no—
241D3×C4⋊C4—91no—
242D3×C4⋊C4—91no—
243D3×C4⋊C4—181no—
244#888—91no—
245#886—91no—
246#884—91no—
247#884—91no—
248#884—91no—
249#883—91no—
250#883—91no—
251#883—91no—
252#67⋊C4—91no—
253#67⋊C4—91no—
254#878—91no—
255C22×C3⋊D3—31no—
256C22×C3×D3—31no—
257C22×C3×D3—31no—
258C22×C3×D3C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C4×C3⋊D3—62no—
266C4×C3⋊D3—62no—
267C4×C3⋊D3—62no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C22×D311yescharacteristic
272C2×C3×Dic3C22×D311yescharacteristic
273C3×D12—62no—
274C3×C4×D3—22no—
275C3×C4×D3—62no—
276C3×Dic6—22no—
277#627—62no—
278#626—34no—
279#626—62no—
280#626—62no—
281#625—62no—
282#625—62no—
283D3×Dic3—62no—
284D3×Dic3—62no—
285D3×Dic3—62no—
286C23×C9—31no—
287C22×D9—31no—
288C22×D9—61no—
289C22×D9C22×D311yescharacteristic
290C22×D9C22×D311yescharacteristic
291Q8×C9—62no—
292C2×C4×C9—21no—
293C2×C4×C9—21no—
294C2×C4×C9—21no—
295C2×C4×C9—31no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9—62no—
299C2×C4×C9C22×D311yescharacteristic
300C2×C4×C9C22×D311yescharacteristic
301C2×C4×C9C22×D311yescharacteristic
302#611—62no—
303#611—62no—
304#611—62no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—31no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9—61no—
311C2×Dic9C22×D311yescharacteristic
312C2×Dic9C22×D311yescharacteristic
313D36—22no—
314D36—34no—
315D36—62no—
316C4×D9—22no—
317C4×D9—62no—
318C4×D9—62no—
319C4×D9—62no—
320C4×D9—62no—
321C4×D9—64no—
322C4×D9—62no—
323C4×D9—62no—
324C4×D9—122no—
325C4×D9—122no—
326Dic18—62no—
327#547—271noSylow
328C2×C3×C9C22×D411yescharacteristic
329C2×C3×C9C2×#4111yescharacteristic
330C2×C3×C92−1+411yescharacteristic
331C3⋊D9—22no—
332D3×C9—41no—
333C3×D9—22no—
334C3×D9—41no—
335C2×C3×Q8—31no—
336C2×C3×D4—91no—
337C22×C3×C4—31no—
338C22×C3×C4—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C22×Dic3—91no—
347C22×Dic3—91no—
348C22×Dic3—91no—
349#239—184no—
350#237—184no—
351#235—184no—
352#235—184no—
353C2×D12—31no—
354C2×D12—91no—
355C2×D12—91no—
356C2×D12—91no—
357C2×C4×D3—31no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×C4×D3—91no—
364C2×C4×D3—91no—
365C2×C4×D3—91no—
366C2×C4×D3—91no—
367C2×C4×D3—181no—
368C2×C4×D3—181no—
369C2×C4×D3—181no—
370C2×C4×D3C2×D911yescharacteristic
371C2×Dic6—91no—
372C2×Dic6—91no—
373C2×Dic6C2×D911yescharacteristic
374C3×C4⋊C4—21no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—91no—
378C3×C4⋊C4C2×D911yescharacteristic
379C3×C4⋊C4D3211yescharacteristic
380C3×C22⋊C4—31no—
381C3×C22⋊C4—31no—
382C3×C22⋊C4—91no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—91no—
385#217—91no—
386#217—91no—
387(C2×D3)⋊C4—31no—
388(C2×D3)⋊C4—31no—
389(C2×D3)⋊C4—31no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4C2×D911yescharacteristic
395(C2×D3)⋊C4C2×D911yescharacteristic
396C4⋊Dic3—91no—
397C4⋊Dic3—91no—
398C4⋊Dic3—91no—
399C4⋊Dic3—91no—
400C4⋊Dic3—181no—
401Dic3⋊C4—31no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—181no—
411Dic3⋊C4—181no—
412Dic3⋊C4C2×D911yescharacteristic
413Dic3⋊C4C2×D911yescharacteristic
414C4×Dic3—91no—
415C4×Dic3—91no—
416C22×C32C23×D311yescharacteristic
417C2×C3⋊D3—32no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—61no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—32no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C2×C3×D3—61no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—21no—
432C3⋊Dic3—32no—
433C3⋊Dic3—61no—
434C3⋊Dic3—61no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—61no—
438C3×Dic3—61no—
439C3×Dic3D3×D412yes—
440C22×C9—21no—
441C22×C9—61no—
442C22×C9—61no—
443C22×C9—61no—
444C22×C9C23×D311yescharacteristic
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—21no—
450C2×D9—32no—
451C2×D9—62no—
452C2×D9—62no—
453C2×D9—62no—
454C2×D9—61no—
455C2×D9—61no—
456C2×D9D3×D412yes—
457C4×C9—22no—
458C4×C9—21no—
459C4×C9—21no—
460C4×C9—21no—
461C4×C9—32no—
462C4×C9—41no—
463C4×C9—41no—
464C4×C9—61no—
465C4×C9—61no—
466Dic9—21no—
467Dic9—21no—
468Dic9—32no—
469Dic9—62no—
470Dic9—61no—
471Dic9—61no—
472Dic9—121no—
473Dic9—121no—
474C2×#41—271no—
475C2×#41—271no—
476C4⋊Q8—271no—
477#123—91no—
478#123—271no—
479#123—271no—
480#123—271no—
481C22⋊Q8—31no—
482C22⋊Q8—271no—
483#121—271no—
484#121—271no—
485C4×D4—271no—
486C4×D4—271no—
487C2×C4⋊C4—271no—
488C2×C4⋊C4—271no—
489C3×C9#54711yescharacteristic, complemented, Sylow
490C23×C3—31no—
491C23×C3—91no—
492C23×C3—91no—
493C22×D3—31no—
494C22×D3—31no—
495C22×D3—91no—
496C22×D3—91no—
497C22×D3—181no—
498C22×D3C22×D911yescharacteristic
499C3×Q8—62no—
500C3×D4—182no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—62no—
508C2×C3×C4—91no—
509C2×C3×C4—91no—
510C2×C3×C4—182no—
511C2×C3×C4C22×D911yescharacteristic
512C2×C3×C4C22×D911yescharacteristic
513C2×C3×C4C22×D911yescharacteristic
514C2×C3×C4C2×D3211yescharacteristic
515C2×C3×C4C2×D3211yescharacteristic
516C2×C3×C4C2×D3211yescharacteristic
517#67—94no—
518#67—182no—
519#67—182no—
520#67—182no—
521#67—182no—
522#67—182no—
523#67—182no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—91no—
527C2×Dic3—91no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—181no—
533C2×Dic3—181no—
534C2×Dic3—181no—
535C2×Dic3—182no—
536C2×Dic3—182no—
537C2×Dic3—182no—
538C2×Dic3C22×D911yescharacteristic
539C2×Dic3C22×D911yescharacteristic
540C2×Dic3C22×D911yescharacteristic
541D12—62no—
542D12—94no—
543D12—182no—
544D12—182no—
545C4×D3—22no—
546C4×D3—62no—
547C4×D3—182no—
548C4×D3—182no—
549C4×D3—182no—
550C4×D3—182no—
551C4×D3—182no—
552C4×D3—182no—
553C4×D3—182no—
554C4×D3—184no—
555C4×D3—182no—
556C4×D3—182no—
557C4×D3—362no—
558C4×D3—362no—
559Dic6—22no—
560Dic6—182no—
561Dic6—182no—
562C2×C32C2×D3×D411yescharacteristic
563C2×C32#100711yescharacteristic
564C2×C32D3×#4111yescharacteristic
565C3⋊D3—62no—
566C3×D3—41no—
567C3×D3—62no—
568C3×D3—121no—
569C2×C9—21no—
570C2×C9—21no—
571C2×C9—21no—
572C2×C9—121no—
573C2×C9C2×D3×D411yescharacteristic
574C2×C9D3×#4111yescharacteristic
575C2×C9#101011yescharacteristic
576D9—22no—
577D9—41no—
578D9—64no—
579D9—62no—
580#41—544no—
581#41—544no—
582C2×Q8—31no—
583C2×Q8—271no—
584C2×D4—91no—
585C2×D4—271no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C2×D4—271no—
590C22×C4—31no—
591C22×C4—91no—
592C22×C4—271no—
593C22×C4—271no—
594C22×C4—271no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—91no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C4⋊C4D3×D911yescharacteristic
608C22⋊C4—31no—
609C22⋊C4—31no—
610C22⋊C4—91no—
611C22⋊C4—91no—
612C22⋊C4—91no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C42—271no—
617C22×C3—21no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—92no—
622C22×C3—181no—
623C22×C3—181no—
624C22×C3—181no—
625C22×C3—181no—
626C22×C3—181no—
627C22×C3C23×D911yescharacteristic
628C22×C3C22×D3211yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—32no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—92no—
639C2×D3—92no—
640C2×D3—182no—
641C2×D3—182no—
642C2×D3—182no—
643C2×D3—181no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—181no—
647C3×C4—22no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—32no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—181no—
660C3×C4—181no—
661Dic3—21no—
662Dic3—21no—
663Dic3—61no—
664Dic3—61no—
665Dic3—92no—
666Dic3—92no—
667Dic3—182no—
668Dic3—181no—
669Dic3—181no—
670Dic3—181no—
671Dic3—181no—
672Dic3—361no—
673Dic3—361no—
674Dic3D4×D912yes—
675C32#563111yescharacteristic
676C9—21no—
677C9#565511yescharacteristic, complemented
678C23—31no—
679C23—91no—
680C23—91no—
681C23—271no—
682Q8—62no—
683Q8—542no—
684D4—182no—
685D4—274no—
686D4—542no—
687D4—542no—
688D4—542no—
689D4—542no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—62no—
694C2×C4—91no—
695C2×C4—91no—
696C2×C4—182no—
697C2×C4—271no—
698C2×C4—271no—
699C2×C4—271no—
700C2×C4—542no—
701C2×C4—542no—
702C2×C4—542no—
703C2×C4—542no—
704C2×C4—542no—
705C2×C4—542no—
706C2×C4C2×D3×D911yescharacteristic
707C2×C4C2×D3×D911yescharacteristic
708C2×C4C2×D3×D911yescharacteristic
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—121no—
713C2×C3—182no—
714C2×C3—361no—
715C2×C3C2×D4×D911yescharacteristic
716C2×C3#6371311yescharacteristic
717C2×C3#41×D911yescharacteristic
718C2×C3#6430611yescharacteristic
719C2×C3D32×D411yescharacteristic
720C2×C3#6431511yescharacteristic
721D3—41no—
722D3—62no—
723D3—121no—
724D3—184no—
725D3—182no—
726D3—182no—
727C22—61no—
728C22—61no—
729C22—61no—
730C22—92no—
731C22—181no—
732C22—181no—
733C22—181no—
734C22—181no—
735C22—181no—
736C22—272no—
737C22—541no—
738C22—541no—
739C22C22×D3×D911yescharacteristic
740C4—21no—
741C4—21no—
742C4—21no—
743C4—32no—
744C4—61no—
745C4—61no—
746C4—181no—
747C4—181no—
748C4—272no—
749C4—541no—
750C4—541no—
751C3—21no—
752C3#1058973311yescharacteristic, complemented
753C3#1059437111yescharacteristic
754C2—121no—
755C2—182no—
756C2—361no—
757C2—542no—
758C2#1172247511yescharacteristic
759C2D3×D4×D911yescharacteristic
760C2#1172251011yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#547
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#88640C2semidirect
2. C2×#88634C2semidirect
3. C4⋊C4×C3⋊D9C2semidirect
4. C9×#896C2semidirect
5. C3×#63456C2semidirect
6. #11721041C2semidirect
7. #11720991C2semidirect
8. #11720989C2semidirect
9. #11720982C2semidirect
10. #11720978C2semidirect
11. #11720976C2semidirect
12. D9×Dic3⋊C4C2semidirect
13. #11720957C2semidirect
14. #11720941C2semidirect
15. #11720903C2semidirect
77. #63456D3semidirect
112. #6192D4semidirect
218. C3⋊Dic9#41semidirect
235. #896D9semidirect
489. C3×C9#547semidirect
677. C9#5655semidirect
752. C3#10589733semidirect

Maximal subgroups

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

subgroupindex
C2×#886402
C2×#886342
C4⋊C4×C3⋊D92
C9×#8962
C3×#634562
#117210412
#117209912
#117209892
#117209822
#117209782
#117209762
D9×Dic3⋊C42
#117209572
#117209412
#117209032
#105943713
#105897333