Finite Group Databasebeta

← #13150908

Subgroups — #13150908

Order 1728.

964 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88663C211yesmaximal, characteristic, complemented
2C22×#6189C211yesmaximal, characteristic, complemented
3D4×C3⋊Dic9C211yesmaximal, characteristic, complemented
4C9×#939C211yesmaximal, characteristic, complemented
5C3×#63501C211yesmaximal, characteristic, complemented
6#11721290C211yesmaximal, characteristic, complemented
7#67×Dic9C211yesmaximal, characteristic, complemented
8Dic3×#611C211yesmaximal, characteristic, complemented
9#11721267C211yesmaximal, characteristic, complemented
10#11721263C211yesmaximal, characteristic, complemented
11#11721257C211yesmaximal, characteristic, complemented
12#11721044C211yesmaximal, characteristic, complemented
13#11721023C211yesmaximal, characteristic, complemented
14#11720991C211yesmaximal, characteristic, complemented
15#11720902C211yesmaximal, characteristic, complemented
16#10595142—31nomaximal
17#10589700—31nomaximal
18C2×C3×D4×C9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C22×C9×Dic3C2211yescharacteristic
26C22×C3×Dic9C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28#88663—24no—
29C2×D3×Dic9C2211yescharacteristic
30C2×Dic3×D9C2211yescharacteristic
31C2×#6189—24no—
32C2×#6189C2211yescharacteristic
33C2×#6189C2211yescharacteristic
34C2×#6189C2211yescharacteristic
35C2×#6189C2211yescharacteristic
36#88551C2211yescharacteristic
37#88551C2211yescharacteristic
38C4⋊(C3⋊Dic9)C2211yescharacteristic
39C4×C3⋊Dic9C2211yescharacteristic
40C9×#217C2211yescharacteristic
41C3×#3676C2211yescharacteristic
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C9×Dic3⋊C4C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C22×#627—31no—
56C2×#3805—31no—
57D4×C3⋊Dic3—31no—
58C3×#939—31no—
59C3×#939D311yescharacteristic
60#63982—31no—
61#63980—31no—
62Dic3×#67—31no—
63Dic3×#67—31no—
64#63959—31no—
65#63959—31no—
66#63915—31no—
67#63893—31no—
68#63893—31no—
69#63838—31no—
70C2×#3699—31no—
71C22×Dic18—31no—
72C9×#121—31no—
73#63501—31no—
74#63501D311yescharacteristic, complemented
75#63498—31no—
76D4×Dic9—31no—
77D4×Dic9—31no—
78D4×Dic9—61no—
79C4×#611—31no—
80#63459—31no—
81#63449—31no—
82#63447—31no—
83#63447—31no—
84#63440—31no—
85#63440—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C3×D4×C9—22no—
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3⋊Dic9—22no—
93C2×C3⋊Dic9—22no—
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C9×#67—22no—
99C9×#67—22no—
100C3×#611—22no—
101C3×#611—22no—
102C2×C9×Dic3—22no—
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C3×Dic9—22no—
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110#6194—22no—
111D3×Dic9—22no—
112Dic3×D9—22no—
113#6189—22no—
114#6189—22no—
115#6189—22no—
116#6189D414yescomplemented
117#5598—91no—
118#5598—91no—
119C2×C32×D4C2×D311yescharacteristic
120C22×C3⋊Dic3—31no—
121C22×C3⋊Dic3—31no—
122C2×C3×#67—31no—
123C2×C3×#67—31no—
124C2×C3×#67C2×D311yescharacteristic
125C2×C3×#67C2×D311yescharacteristic
126C22×C3×Dic3—31no—
127C22×C3×Dic3C2×D311yescharacteristic
128C2×#627—31no—
129C2×#627—31no—
130C2×#627—31no—
131C2×#627—31no—
132C2×#627—64no—
133C2×#625—31no—
134#3805—64no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137#3757—31no—
138#3757—31no—
139C4⋊(C3⋊Dic3)—31no—
140C4×C3⋊Dic3—31no—
141C3×#217—31no—
142C3×#217C2×D311yescharacteristic
143C3×(C2×D3)⋊C4—31no—
144C3×(C2×D3)⋊C4C2×D311yescharacteristic
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4C2×D311yescharacteristic
147#3724—31no—
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154Dic32—31no—
155Dic32—31no—
156C2×D4×C9—21no—
157C2×D4×C9—31no—
158C2×D4×C9—31no—
159C2×D4×C9C2×D311yescharacteristic
160C22×C4×C9—31no—
161C2×#611—31no—
162C2×#611C2×D311yescharacteristic
163C2×#611C2×D311yescharacteristic
164C22×Dic9—31no—
165C22×Dic9—31no—
166C22×Dic9—31no—
167C22×Dic9—61no—
168C22×Dic9—61no—
169C22×Dic9C2×D311yescharacteristic
170#3699—64no—
171C2×C4×D9—31no—
172C2×Dic18—31no—
173C2×Dic18—31no—
174C2×Dic18—31no—
175C2×Dic18—31no—
176C2×Dic18—64no—
177C9×C4⋊C4—31no—
178C9×C22⋊C4—31no—
179C9×C22⋊C4—31no—
180#3676—31no—
181#3676—31no—
182#3676—31no—
183#3676—31no—
184#3676—61no—
185#3676—61no—
186#3676C2×D311yescharacteristic
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4C2×D311yescharacteristic
190C4⋊Dic9—31no—
191C4⋊Dic9—31no—
192C4⋊Dic9—61no—
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4C2×D311yescharacteristic
196C4×Dic9—31no—
197C4×Dic9—31no—
198C4×Dic9—31no—
199C4×Dic9—61no—
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9—21no—
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9#4112yescomplemented
206C22×C3×C9C2411yescharacteristic
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C3×C4×C9—21no—
214C3⋊Dic9—21no—
215C3⋊Dic9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9C2×D412yes—
218C9×Dic3—21no—
219C9×Dic3—21no—
220C9×Dic3C2×D412yes—
221C3×Dic9—21no—
222C3×Dic9—21no—
223C3×Dic9C2×D412yes—
224C2×#237—91no—
225C2×#237—91no—
226C22×Dic6—91no—
227C22×Dic6—91no—
228C3×#121—31no—
229C3×#121—91no—
230#939—31no—
231#939—91no—
232#939—91no—
233#939D911yescharacteristic, complemented
234#936—91no—
235#936—91no—
236D4×Dic3—91no—
237D4×Dic3—91no—
238D4×Dic3—91no—
239D4×Dic3—91no—
240D4×Dic3—181no—
241C4×#67—91no—
242C4×#67—91no—
243#897—91no—
244#897—91no—
245#887—91no—
246#887—91no—
247#885—91no—
248#885—91no—
249#885—91no—
250#885—91no—
251#878—91no—
252#878—91no—
253#878—91no—
254#878—91no—
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C22×C3×D3—31no—
258C22×C3×D3C22×D311yescharacteristic
259C32×D4—22no—
260C2×C32×C4C22×D311yescharacteristic
261C2×C3⋊Dic3—31no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—62no—
266C2×C3⋊Dic3—62no—
267C3×#67—22no—
268C3×#67—22no—
269C3×#67—62no—
270C3×#67—62no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3C22×D311yescharacteristic
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C22×D311yescharacteristic
279#627—34no—
280#627—62no—
281#627—62no—
282#627—62no—
283#625—62no—
284D3×Dic3—62no—
285D3×Dic3—62no—
286C23×C9—21no—
287C23×C9—21no—
288C23×C9—31no—
289C23×C9C22×D311yescharacteristic
290C23×C9C22×D311yescharacteristic
291C22×D9C22×D311yescharacteristic
292D4×C9—24no—
293D4×C9—22no—
294D4×C9—62no—
295D4×C9—62no—
296C2×C4×C9—21no—
297C2×C4×C9—31no—
298C2×C4×C9—31no—
299C2×C4×C9—31no—
300C2×C4×C9—62no—
301C2×C4×C9C22×D311yescharacteristic
302#611—22no—
303#611—22no—
304#611—62no—
305C2×Dic9—22no—
306C2×Dic9—31no—
307C2×Dic9—31no—
308C2×Dic9—31no—
309C2×Dic9—31no—
310C2×Dic9—61no—
311C2×Dic9—61no—
312C2×Dic9—61no—
313C2×Dic9—61no—
314C2×Dic9—62no—
315C2×Dic9—62no—
316C2×Dic9—62no—
317C2×Dic9—122no—
318C2×Dic9—122no—
319C2×Dic9C22×D311yescharacteristic
320C2×Dic9C22×D311yescharacteristic
321C2×Dic9C22×D311yescharacteristic
322C4×D9—62no—
323Dic18—34no—
324Dic18—62no—
325Dic18—62no—
326Dic18—62no—
327#548—271noSylow
328C2×C3×C9—22no—
329C2×C3×C9—41no—
330C2×C3×C9C22×D411yescharacteristic
331C2×C3×C9C2×#4111yescharacteristic
332C2×C3×C92−1+411yescharacteristic
333D3×C9—41no—
334C3×D9—41no—
335C2×C3×D4—21no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—91no—
339C2×C3×D4—91no—
340C2×C3×D4C2×D911yescharacteristic
341C2×C3×D4D3211yescharacteristic
342C22×C3×C4—31no—
343C22×C3×C4—91no—
344C2×#67—31no—
345C2×#67—31no—
346C2×#67—91no—
347C2×#67—91no—
348C2×#67C2×D911yescharacteristic
349C2×#67C2×D911yescharacteristic
350C22×Dic3—31no—
351C22×Dic3—91no—
352C22×Dic3—91no—
353C22×Dic3—91no—
354C22×Dic3—91no—
355C22×Dic3—91no—
356C22×Dic3—91no—
357C22×Dic3—181no—
358C22×Dic3—181no—
359C22×Dic3C2×D911yescharacteristic
360#237—184no—
361#237—184no—
362C2×C4×D3—91no—
363C2×C4×D3—91no—
364C2×Dic6—91no—
365C2×Dic6—91no—
366C2×Dic6—91no—
367C2×Dic6—91no—
368C2×Dic6—91no—
369C2×Dic6—91no—
370C2×Dic6—91no—
371C2×Dic6—91no—
372C2×Dic6—184no—
373C2×Dic6—184no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—91no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380#217—31no—
381#217—91no—
382#217—91no—
383#217—91no—
384#217—91no—
385#217—91no—
386#217—91no—
387#217—91no—
388#217—91no—
389#217—181no—
390#217—181no—
391#217C2×D911yescharacteristic
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4C2×D911yescharacteristic
398C4⋊Dic3—91no—
399C4⋊Dic3—91no—
400C4⋊Dic3—91no—
401C4⋊Dic3—91no—
402C4⋊Dic3—181no—
403Dic3⋊C4—31no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4C2×D911yescharacteristic
409C4×Dic3—91no—
410C4×Dic3—91no—
411C4×Dic3—91no—
412C4×Dic3—91no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C4×Dic3—181no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32#23712yes—
422C22×C32C23×D311yescharacteristic
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C2×C3×D3—61no—
429C32×C4—21no—
430C3⋊Dic3—32no—
431C3⋊Dic3—61no—
432C3⋊Dic3—61no—
433C3⋊Dic3—61no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—32no—
437C3×Dic3—61no—
438C3×Dic3—61no—
439C3×Dic3D3×D412yes—
440C22×C9—21no—
441C22×C9—21no—
442C22×C9—22no—
443C22×C9—21no—
444C22×C9—21no—
445C22×C9—21no—
446C22×C9—21no—
447C22×C9—22no—
448C22×C9—41no—
449C22×C9—41no—
450C22×C9—41no—
451C22×C9—41no—
452C22×C9—61no—
453C22×C9—61no—
454C22×C9—61no—
455C22×C9#23712yescomplemented
456C22×C9C23×D311yescharacteristic
457C2×D9—21no—
458C2×D9—21no—
459C2×D9—21no—
460C4×C9—22no—
461C4×C9—21no—
462C4×C9—32no—
463C4×C9—61no—
464C4×C9—61no—
465Dic9—21no—
466Dic9—21no—
467Dic9—32no—
468Dic9—62no—
469Dic9—61no—
470Dic9—61no—
471Dic9—61no—
472Dic9—121no—
473Dic9—121no—
474Dic9—121no—
475Dic9D3×D412yes—
476C2×#41—271no—
477C22×Q8—271no—
478#124—271no—
479#124—271no—
480#124—271no—
481C22⋊Q8—271no—
482C22⋊Q8—271no—
483C22⋊Q8—271no—
484#121—31no—
485#121—91no—
486#121—271no—
487C4×Q8—271no—
488C4×D4—271no—
489C4×D4—271no—
490C4×D4—271no—
491C3×C9#54811yescharacteristic, complemented, Sylow
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—91no—
496C23×C3C22×D911yescharacteristic
497C23×C3C22×D911yescharacteristic
498C23×C3C2×D3211yescharacteristic
499C23×C3C2×D3211yescharacteristic
500C22×D3—31no—
501C22×D3C22×D911yescharacteristic
502C3×D4—24no—
503C3×D4—22no—
504C3×D4—22no—
505C3×D4—62no—
506C3×D4—62no—
507C3×D4—182no—
508C3×D4—182no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—62no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—182no—
518C2×C3×C4C22×D911yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520#67—22no—
521#67—22no—
522#67—62no—
523#67—62no—
524#67—182no—
525#67—182no—
526C2×Dic3—22no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—62no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—181no—
540C2×Dic3—181no—
541C2×Dic3—181no—
542C2×Dic3—181no—
543C2×Dic3—182no—
544C2×Dic3—182no—
545C2×Dic3—182no—
546C2×Dic3—182no—
547C2×Dic3—182no—
548C2×Dic3—182no—
549C2×Dic3—362no—
550C2×Dic3—362no—
551C2×Dic3C22×D911yescharacteristic
552C2×Dic3C22×D911yescharacteristic
553C2×Dic3C22×D911yescharacteristic
554C4×D3—182no—
555C4×D3—182no—
556Dic6—94no—
557Dic6—94no—
558Dic6—182no—
559Dic6—182no—
560Dic6—182no—
561Dic6—182no—
562Dic6—182no—
563Dic6—182no—
564C2×C32—22no—
565C2×C32—41no—
566C2×C32C2×D3×D411yescharacteristic
567C2×C32C2×#23711yescharacteristic
568C2×C32#101011yescharacteristic
569C3×D3—41no—
570C3×D3—121no—
571C2×C9—22no—
572C2×C9—21no—
573C2×C9—21no—
574C2×C9—21no—
575C2×C9—42no—
576C2×C9—42no—
577C2×C9—41no—
578C2×C9—121no—
579C2×C9C2×D3×D411yescharacteristic
580C2×C9C2×#23711yescharacteristic
581C2×C9#101011yescharacteristic
582D9—41no—
583#41—544no—
584C2×Q8—271no—
585C2×Q8—271no—
586C2×Q8—271no—
587C2×Q8—271no—
588C2×Q8—544no—
589C2×D4—31no—
590C2×D4—31no—
591C2×D4—91no—
592C2×D4—91no—
593C2×D4—271no—
594C2×D4D3×D911yescharacteristic
595C22×C4—31no—
596C22×C4—91no—
597C22×C4—271no—
598C22×C4—271no—
599C22×C4—271no—
600C22×C4—271no—
601C4⋊C4—31no—
602C4⋊C4—91no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C42—271no—
618C42—271no—
619C42—271no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—22no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—181no—
641C22×C3—181no—
642C22×C3—181no—
643C22×C3#369912yescomplemented
644C22×C3C23×D911yescharacteristic
645C22×C3#380512yes—
646C22×C3C22×D3211yescharacteristic
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—61no—
651C2×D3—61no—
652C2×D3—61no—
653C3×C4—22no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—32no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—92no—
660C3×C4—181no—
661C3×C4—181no—
662Dic3—21no—
663Dic3—21no—
664Dic3—32no—
665Dic3—61no—
666Dic3—61no—
667Dic3—92no—
668Dic3—92no—
669Dic3—182no—
670Dic3—181no—
671Dic3—181no—
672Dic3—181no—
673Dic3—181no—
674Dic3—181no—
675Dic3—181no—
676Dic3—361no—
677Dic3—361no—
678Dic3—361no—
679Dic3D4×D912yes—
680C32#559811yescharacteristic
681C9—21no—
682C9#559811yescharacteristic, complemented
683C23—31no—
684C23—91no—
685C23C2×D3×D911yescharacteristic
686C23C2×D3×D911yescharacteristic
687Q8—274no—
688Q8—542no—
689Q8—542no—
690Q8—542no—
691D4—22no—
692D4—62no—
693D4—62no—
694D4—182no—
695D4—182no—
696D4—542no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—62no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—91no—
704C2×C4—182no—
705C2×C4—271no—
706C2×C4—271no—
707C2×C4—271no—
708C2×C4—271no—
709C2×C4—542no—
710C2×C4—542no—
711C2×C4—542no—
712C2×C4—542no—
713C2×C4C2×D3×D911yescharacteristic
714C2×C3—22no—
715C2×C3—22no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—42no—
720C2×C3—42no—
721C2×C3—41no—
722C2×C3—41no—
723C2×C3—121no—
724C2×C3—361no—
725C2×C3C2×D4×D911yescharacteristic
726C2×C3C2×#369911yescharacteristic
727C2×C3#6371611yescharacteristic
728C2×C3#6430911yescharacteristic
729C2×C3D32×D411yescharacteristic
730C2×C3C2×#380511yescharacteristic
731D3—41no—
732D3—121no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—181no—
742C22—181no—
743C22—181no—
744C22#8866312yescomplemented
745C22C22×D3×D911yescharacteristic
746C4—21no—
747C4—32no—
748C4—61no—
749C4—61no—
750C4—92no—
751C4—181no—
752C4—181no—
753C4—272no—
754C4—541no—
755C4—541no—
756C4—541no—
757C3—21no—
758C3#1058970011yescharacteristic, complemented
759C3#1059514211yescharacteristic
760C2—22no—
761C2—41no—
762C2—121no—
763C2—361no—
764C2#1172249411yescharacteristic
765C2D3×D4×D911yescharacteristic
766C2C2×#8866311yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#548
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#88663C2semidirect
2. C22×#6189C2semidirect
3. D4×C3⋊Dic9C2semidirect
4. C9×#939C2semidirect
5. C3×#63501C2semidirect
6. #11721290C2semidirect
7. #67×Dic9C2semidirect
8. Dic3×#611C2semidirect
9. #11721267C2semidirect
10. #11721263C2semidirect
11. #11721257C2semidirect
12. #11721044C2semidirect
13. #11721023C2semidirect
14. #11720991C2semidirect
15. #11720902C2semidirect
74. #63501D3semidirect
116. #6189D4semidirect
205. C22×C3×C9#41semidirect
233. #939D9semidirect
455. C22×C9#237semidirect
491. C3×C9#548semidirect
643. C22×C3#3699semidirect
682. C9#5598semidirect
744. C22#88663semidirect
758. C3#10589700semidirect

Maximal subgroups

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

subgroupindex
C2×#886632
C22×#61892
D4×C3⋊Dic92
C9×#9392
C3×#635012
#117212902
#67×Dic92
Dic3×#6112
#117212672
#117212632
#117212572
#117210442
#117210232
#117209912
#117209022
#105951423
#105897003