Finite Group Databasebeta

← #13150177

Subgroups — #13150177

Order 1728.

954 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3697C211yesmaximal, characteristic, complemented
2C2×#88658C211yesmaximal, characteristic, complemented
3#11721818C211yesmaximal, characteristic, complemented
4C2×C9×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#11721277C211yesmaximal, characteristic, complemented
6Dic3×#611C211yesmaximal, characteristic, complemented
7#11721259C211yesmaximal, characteristic, complemented
8#11721002C211yesmaximal, characteristic, complemented
9#11720985C211yesmaximal, characteristic, complemented
10#11720983C211yesmaximal, characteristic, complemented
11#11720981C211yesmaximal, characteristic, complemented
12D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
13#11720939C211yesmaximal, characteristic, complemented
14#11720938C211yesmaximal, characteristic, complemented
15#11720904C211yesmaximal, characteristic, complemented
16#10594885—31nomaximal
17#10589609—31nomaximal
18C22×C3×C4×C9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C22×C9×Dic3C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C3×#3697—24no—
25C2×C3×D36C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic
27C2×C3×C4×D9C2211yescharacteristic
28C2×C3×Dic18C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6192C2211yescharacteristic
31C2×(C3⋊D9)⋊C4C2211yescharacteristic
32#88658—24no—
33C2×Dic3×D9C2211yescharacteristic
34C2×Dic3×D9C2211yescharacteristic
35C2×#6189C2211yescharacteristic
36#88551C2211yescharacteristic
37#88536C2211yescharacteristic
38#88536C2211yescharacteristic
39#88534C2211yescharacteristic
40#88534C2211yescharacteristic
41C9×Dic3⋊C4C2211yescharacteristic
42C9×Dic3⋊C4C2211yescharacteristic
43C9×Dic3⋊C4C2211yescharacteristic
44C9×Dic3⋊C4C2211yescharacteristic
45#88445C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic
51#88442C2211yescharacteristic
52#88442C2211yescharacteristic
53Dic9⋊Dic3C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×C3×#235—31no—
56C2×#3804—31no—
57#64138—31no—
58C2×C3×Dic3⋊C4D311yescharacteristic
59#63978—31no—
60Dic3×#67—31no—
61#63961—31no—
62#63904—31no—
63#63888—31no—
64#63886—31no—
65#63884—31no—
66D3×Dic3⋊C4—31no—
67#63851—31no—
68#63850—31no—
69#63839—31no—
70C2×#3697—31no—
71C2×#3697D311yescharacteristic, complemented
72C2×C9×C4⋊C4—31no—
73#63492—31no—
74#63491—31no—
75#63491—31no—
76#63491—61no—
77C4×#611—31no—
78#63458—31no—
79#63458—31no—
80#63457—31no—
81#63456—31no—
82#63456—31no—
83#63455—31no—
84C4⋊C4×D9—31no—
85#63450—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×C3×C4×C9—22no—
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93#6233—22no—
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C3×#611—22no—
98C3×#611D414yescomplemented
99C2×C9×Dic3—22no—
100C2×C9×Dic3—22no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C3×D36—22no—
108C3×C4×D9—22no—
109C3×C4×D9—22no—
110C3×Dic18—22no—
111#6192—22no—
112#6192—22no—
113(C3⋊D9)⋊C4—22no—
114Dic3×D9—22no—
115Dic3×D9—22no—
116#6189—22no—
117#5824—91no—
118#5507—91no—
119C22×C32×C4C2×D311yescharacteristic
120C2×#638—31no—
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C22×C3×Dic3C2×D311yescharacteristic
124C22×C3×Dic3C2×D311yescharacteristic
125C3×#235—64no—
126C2×C3×D12—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—31no—
129C2×C3×Dic6—31no—
130C2×#627—31no—
131C2×#626—31no—
132C2×#626—31no—
133C2×#624—31no—
134#3804—64no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137#3757—31no—
138#3752—31no—
139#3752—31no—
140#3750—31no—
141#3750—31no—
142C3×Dic3⋊C4C2×D311yescharacteristic
143C3×Dic3⋊C4C2×D311yescharacteristic
144C3×Dic3⋊C4C2×D311yescharacteristic
145C3×Dic3⋊C4C2×D311yescharacteristic
146#3724—31no—
147#3724—31no—
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150#3722—31no—
151(C2×D3)⋊Dic3—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155Dic32—31no—
156C22×C4×C9—21no—
157C22×C4×C9—31no—
158C22×C4×C9—31no—
159C22×C4×C9C2×D311yescharacteristic
160C2×#611—31no—
161C2×#611—61no—
162C2×#611C2×D311yescharacteristic
163C2×#611C2×D311yescharacteristic
164#3697—24no—
165#3697—64no—
166C2×D36—31no—
167C2×D36—31no—
168C2×D36C2×D311yescharacteristic
169C2×C4×D9—31no—
170C2×C4×D9—31no—
171C2×C4×D9—31no—
172C2×C4×D9C2×D311yescharacteristic
173C2×C4×D9C2×D311yescharacteristic
174C2×Dic18—31no—
175C2×Dic18C2×D311yescharacteristic
176C9×C4⋊C4—31no—
177C9×C4⋊C4—31no—
178C9×C4⋊C4—31no—
179C9×C4⋊C4—31no—
180#3676—31no—
181#3676—61no—
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4—31no—
184(C2×D9)⋊C4—31no—
185(C2×D9)⋊C4—31no—
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—61no—
190(C2×D9)⋊C4—61no—
191C4⋊Dic9—31no—
192Dic9⋊C4—31no—
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4—61no—
198Dic9⋊C4—61no—
199C4×Dic9—31no—
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9C2×D412yes—
203C22×C3×C9C2411yescharacteristic
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×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9C2×D412yes—
213C3×C4×C9—21no—
214C3×C4×C9—21no—
215C3⋊Dic9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9—21no—
218C9×Dic3—21no—
219C9×Dic3—21no—
220C9×Dic3—21no—
221C9×Dic3#4112yescomplemented
222C3×Dic9—21no—
223C3×Dic9C2×D412yes—
224C2×C3×#41—91no—
225C2×#237—91no—
226C2×#235—31no—
227C2×#235—91no—
228C2×C3×C4⋊C4—31no—
229#946—91no—
230#944—91no—
231#939—91no—
232#939—91no—
233#935—91no—
234#935—91no—
235D4×Dic3—91no—
236#930—91no—
237#929—91no—
238#929—91no—
239#929—91no—
240#929—91no—
241#929—181no—
242C4×#67—91no—
243C4×#67—91no—
244#924—91no—
245C2×Dic3⋊C4—91no—
246C2×Dic3⋊C4D911yescharacteristic, complemented
247#896—91no—
248#896—91no—
249#895—91no—
250#894—91no—
251#894—91no—
252#893—91no—
253D3×C4⋊C4—91no—
254#888—91no—
255C23×C32C22×D311yescharacteristic
256C22×C3⋊D3—31no—
257C22×C3×D3—31no—
258C22×C3×D3—31no—
259C2×C32×C4—22no—
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262#638—62no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—31no—
266C3×#67—34no—
267C3×#67—62no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D311yescharacteristic
276C3×D12—62no—
277C3×C4×D3—62no—
278C3×C4×D3—62no—
279C3×Dic6—62no—
280#627—62no—
281#626—62no—
282#626—62no—
283#624—62no—
284D3×Dic3—62no—
285D3×Dic3—62no—
286C23×C9—21no—
287C23×C9C22×D311yescharacteristic
288C22×D9—31no—
289C22×D9—61no—
290C22×D9C22×D311yescharacteristic
291C22×D9C22×D311yescharacteristic
292C2×C4×C9—22no—
293C2×C4×C9—21no—
294C2×C4×C9—21no—
295C2×C4×C9—31no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9—31no—
299C2×C4×C9—42no—
300C2×C4×C9—62no—
301C2×C4×C9—62no—
302C2×C4×C9C22×D311yescharacteristic
303C2×C4×C9C22×D311yescharacteristic
304#611—22no—
305#611—62no—
306#611—122no—
307#611#6714yescomplemented
308C2×Dic9—31no—
309C2×Dic9—31no—
310C2×Dic9—31no—
311C2×Dic9—61no—
312C2×Dic9—61no—
313C2×Dic9—61no—
314C2×Dic9C22×D311yescharacteristic
315C2×Dic9C22×D311yescharacteristic
316D36—22no—
317D36—62no—
318D36—62no—
319C4×D9—22no—
320C4×D9—22no—
321C4×D9—62no—
322C4×D9—62no—
323C4×D9—62no—
324Dic18—22no—
325Dic18—62no—
326#547—271noSylow
327C2×C3×C9—22no—
328C2×C3×C9C22×D411yescharacteristic
329C2×C3×C9C2×#4111yescharacteristic
330C2×C3×C92−1+411yescharacteristic
331C3⋊D9—41no—
332C3×D9—22no—
333C3×D9—41no—
334C3×#41—184no—
335C2×C3×Q8—91no—
336C2×C3×D4—91no—
337C2×C3×D4—91no—
338C2×C3×D4—91no—
339C22×C3×C4—21no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—91no—
343C22×C3×C4—91no—
344C22×C3×C4C2×D911yescharacteristic
345C22×C3×C4D3211yescharacteristic
346C2×#67—31no—
347C2×#67—31no—
348C2×#67—91no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67—91no—
352C2×#67—181no—
353C22×Dic3—91no—
354C22×Dic3—91no—
355C22×Dic3C2×D911yescharacteristic
356C22×Dic3C2×D911yescharacteristic
357#237—184no—
358#235—64no—
359#235—184no—
360C2×D12—31no—
361C2×D12—91no—
362C2×D12—91no—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—91no—
366C2×C4×D3—91no—
367C2×C4×D3—91no—
368C2×C4×D3—91no—
369C2×Dic6—31no—
370C2×Dic6—91no—
371C2×Dic6—91no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376#217—91no—
377#217—91no—
378#217—91no—
379#217—91no—
380#217—91no—
381#217—91no—
382#217—181no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
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—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—181no—
394(C2×D3)⋊C4—181no—
395C4⋊Dic3—91no—
396C4⋊Dic3—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—181no—
408Dic3⋊C4—181no—
409Dic3⋊C4C2×D911yescharacteristic
410Dic3⋊C4C2×D911yescharacteristic
411Dic3⋊C4C2×D911yescharacteristic
412Dic3⋊C4C2×D911yescharacteristic
413C4×Dic3—91no—
414C4×Dic3—91no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32D3×D412yes—
418C22×C32C23×D311yescharacteristic
419C2×C3⋊D3—61no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
422C2×C3×D3—32no—
423C2×C3×D3—61no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C32×C4—21no—
429C32×C4—21no—
430C3⋊Dic3—61no—
431C3⋊Dic3—61no—
432C3⋊Dic3—61no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—32no—
437C3×Dic3—61no—
438C3×Dic3#23512yes—
439C22×C9—21no—
440C22×C9—21no—
441C22×C9—21no—
442C22×C9—22no—
443C22×C9—41no—
444C22×C9—41no—
445C22×C9C2×#6712yes—
446C22×C9C23×D311yescharacteristic
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—21no—
450C2×D9—21no—
451C2×D9—21no—
452C2×D9—61no—
453C2×D9—61no—
454C2×D9—61no—
455C2×D9—121no—
456C2×D9—121no—
457C2×D9—121no—
458C2×D9C2×#6712yes—
459C4×C9—21no—
460C4×C9—21no—
461C4×C9—32no—
462C4×C9—41no—
463C4×C9—41no—
464C4×C9—61no—
465C4×C9—61no—
466C4×C9—61no—
467Dic9—21no—
468Dic9—61no—
469Dic9—61no—
470Dic9—61no—
471Dic9—121no—
472Dic9—121no—
473Dic9—121no—
474Dic9C2×#6712yes—
475C2×#41—91no—
476C2×#41—271no—
477C4⋊Q8—271no—
478#123—271no—
479#123—271no—
480#123—271no—
481#123—271no—
482C22⋊Q8—271no—
483C22⋊Q8—271no—
484#121—271no—
485#121—271no—
486C4×D4—271no—
487C4×D4—271no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—271no—
490C3×C9#54711yescharacteristic, complemented, Sylow
491C23×C3—21no—
492C23×C3—91no—
493C23×C3—91no—
494C23×C3C22×D911yescharacteristic
495C23×C3C2×D3211yescharacteristic
496C22×D3—31no—
497C22×D3—31no—
498C22×D3—91no—
499C22×D3—91no—
500C22×D3—181no—
501C3×Q8—182no—
502C3×D4—94no—
503C3×D4—182no—
504C3×D4—182no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—42no—
514C2×C3×C4—62no—
515C2×C3×C4—62no—
516C2×C3×C4—91no—
517C2×C3×C4—91no—
518C2×C3×C4—182no—
519C2×C3×C4—182no—
520C2×C3×C4C22×D911yescharacteristic
521C2×C3×C4C22×D911yescharacteristic
522C2×C3×C4C2×D3211yescharacteristic
523C2×C3×C4C2×D3211yescharacteristic
524#67—34no—
525#67—62no—
526#67—182no—
527#67—182no—
528#67—182no—
529#67—182no—
530#67—362no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—181no—
542C2×Dic3—181no—
543C2×Dic3—181no—
544C2×Dic3—182no—
545C2×Dic3—182no—
546C2×Dic3C22×D911yescharacteristic
547C2×Dic3C22×D911yescharacteristic
548C2×Dic3C22×D911yescharacteristic
549C2×Dic3C22×D911yescharacteristic
550D12—62no—
551D12—182no—
552D12—182no—
553C4×D3—62no—
554C4×D3—62no—
555C4×D3—182no—
556C4×D3—182no—
557C4×D3—182no—
558C4×D3—182no—
559Dic6—62no—
560Dic6—182no—
561Dic6—182no—
562C2×C32—22no—
563C2×C32C2×#23511yescharacteristic
564C2×C32C2×D3×D411yescharacteristic
565C2×C32#100711yescharacteristic
566C3⋊D3—121no—
567C3×D3—62no—
568C3×D3—121no—
569C2×C9—22no—
570C2×C9—21no—
571C2×C9—21no—
572C2×C9—21no—
573C2×C9—42no—
574C2×C9D3×#4111yescharacteristic
575C2×C9#101011yescharacteristic
576C2×C9C22×#6711yescharacteristic
577D9—22no—
578D9—41no—
579D9—121no—
580D9—241no—
581#41—184no—
582#41—544no—
583C2×Q8—91no—
584C2×Q8—271no—
585C2×D4—91no—
586C2×D4—91no—
587C2×D4—91no—
588C2×D4—271no—
589C2×D4—271no—
590C2×D4—271no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—91no—
594C22×C4—91no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C22×C4D3×D911yescharacteristic
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C4⋊C4—271no—
608C4⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C42—271no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—22no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—92no—
627C22×C3—181no—
628C22×C3—181no—
629C22×C3—181no—
630C22×C3—181no—
631C22×C3—181no—
632C22×C3D4×D912yes—
633C22×C3C23×D911yescharacteristic
634C22×C3D3×#6712yes—
635C22×C3C22×D3211yescharacteristic
636C2×D3—32no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—181no—
643C2×D3—181no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—361no—
649C2×D3—361no—
650C2×D3—361no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—32no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—92no—
662C3×C4—181no—
663Dic3—21no—
664Dic3—21no—
665Dic3—21no—
666Dic3—32no—
667Dic3—61no—
668Dic3—181no—
669Dic3—181no—
670Dic3—181no—
671Dic3—181no—
672Dic3—181no—
673Dic3—181no—
674Dic3—361no—
675Dic3—361no—
676Dic3—361no—
677Dic3#369712yescomplemented
678C32#550711yescharacteristic
679C9—21no—
680C9#582411yescharacteristic, complemented
681C23—91no—
682C23—91no—
683C23—271no—
684C23C2×D3×D911yescharacteristic
685Q8—182no—
686Q8—542no—
687D4—94no—
688D4—182no—
689D4—182no—
690D4—542no—
691D4—542no—
692D4—542no—
693C2×C4—22no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—91no—
701C2×C4—91no—
702C2×C4—182no—
703C2×C4—182no—
704C2×C4—271no—
705C2×C4—271no—
706C2×C4—271no—
707C2×C4—542no—
708C2×C4—542no—
709C2×C4—542no—
710C2×C4C2×D3×D911yescharacteristic
711C2×C4C2×D3×D911yescharacteristic
712C2×C3—22no—
713C2×C3—22no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—42no—
718C2×C3—182no—
719C2×C3—361no—
720C2×C3C2×#369711yescharacteristic
721C2×C3C2×D4×D911yescharacteristic
722C2×C3#6371311yescharacteristic
723C2×C3#6429711yescharacteristic
724C2×C3D3×#23511yescharacteristic
725C2×C3C2×D3×#6711yescharacteristic
726D3—62no—
727D3—121no—
728D3—361no—
729D3—361no—
730D3—721no—
731C22—21no—
732C22—21no—
733C22—92no—
734C22—181no—
735C22—181no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22—541no—
740C22—541no—
741C22—541no—
742C22D9×#6712yes—
743C22C22×D3×D911yescharacteristic
744C4—21no—
745C4—21no—
746C4—32no—
747C4—61no—
748C4—61no—
749C4—61no—
750C4—92no—
751C4—181no—
752C4—541no—
753C4—541no—
754C4—541no—
755C3—21no—
756C3#1058960911yescharacteristic, complemented
757C3#1059488511yescharacteristic
758C2—22no—
759C2—182no—
760C2—361no—
761C2—1081no—
762C2#1172245811yescharacteristic
763C2D3×#369711yescharacteristic
764C2C2×D9×#6711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#547
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3697C2semidirect
2. C2×#88658C2semidirect
3. #11721818C2semidirect
4. C2×C9×Dic3⋊C4C2semidirect
5. #11721277C2semidirect
6. Dic3×#611C2semidirect
7. #11721259C2semidirect
8. #11721002C2semidirect
9. #11720985C2semidirect
10. #11720983C2semidirect
11. #11720981C2semidirect
12. D9×Dic3⋊C4C2semidirect
13. #11720939C2semidirect
14. #11720938C2semidirect
15. #11720904C2semidirect
71. C2×#3697D3semidirect
98. C3×#611D4semidirect
221. C9×Dic3#41semidirect
246. C2×Dic3⋊C4D9semidirect
307. #611#67semidirect
490. C3×C9#547semidirect
677. Dic3#3697semidirect
680. C9#5824semidirect
756. C3#10589609semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#36972
C2×#886582
#117218182
C2×C9×Dic3⋊C42
#117212772
Dic3×#6112
#117212592
#117210022
#117209852
#117209832
#117209812
D9×Dic3⋊C42
#117209392
#117209382
#117209042
#105948853
#105896093