Finite Group Databasebeta

← #13150503

Subgroups — #13150503

Order 1728.

844 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6233C211yesmaximal, characteristic, complemented
2C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C3×C4×#611C211yesmaximal, characteristic, complemented
4#11721287C211yesmaximal, characteristic, complemented
5#11721286C211yesmaximal, characteristic, complemented
6#11721277C211yesmaximal, characteristic, complemented
7#11721249C211yesmaximal, characteristic, complemented
8#11721044C211yesmaximal, characteristic, complemented
9#11721041C211yesmaximal, characteristic, complemented
10#11721033C211yesmaximal, characteristic, complemented
11#11721031C211yesmaximal, characteristic, complemented
12#11720966C211yesmaximal, characteristic, complemented
13#11720963C211yesmaximal, characteristic, complemented
14#11720957C211yesmaximal, characteristic, complemented
15#11720956C211yesmaximal, characteristic, complemented
16#10595036—31nomaximal
17#10589596—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic, complemented
25C2×#6195C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6192C2211yescharacteristic, complemented
30C2×#6189C2211yescharacteristic, complemented
31#88551C2211yescharacteristic
32#88536C2211yescharacteristic, complemented
33#88534C2211yescharacteristic, complemented
34C4×C3⋊Dic9C2211yescharacteristic, complemented
35C3×#3676C2211yescharacteristic
36C9×(C2×D3)⋊C4C2211yescharacteristic
37C9×(C2×D3)⋊C4C2211yescharacteristic
38C9×(C2×D3)⋊C4C2211yescharacteristic
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
41C3×Dic9⋊C4C2211yescharacteristic, complemented
42C3×C4×Dic9C2211yescharacteristic, complemented
43(C2×D3)⋊Dic9C2211yescharacteristic
44(C2×D3)⋊Dic9C2211yescharacteristic
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic
47#88445C2211yescharacteristic, complemented
48(C2×D9)⋊Dic3C2211yescharacteristic, complemented
49Dic3⋊Dic9C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53C4×#638—31no—
54C3×C4×#67—31no—
55C2×C3×(C2×D3)⋊C4D311yescharacteristic
56#63978—31no—
57#63977—31no—
58#63976—31no—
59#63964—31no—
60#63915—31no—
61#63912—31no—
62#63906—31no—
63#63905—31no—
64#63862—31no—
65#63859—31no—
66#63853—31no—
67#63852—31no—
68C2×C9×C22⋊C4—31no—
69#63515—31no—
70#63515—31no—
71#63492—31no—
72C4×#611—31no—
73C4×#611—61no—
74C4×#611D311yescharacteristic, complemented
75#63486—31no—
76#63447—31no—
77#63447—31no—
78#63446—31no—
79#63446—31no—
80#63445—31no—
81#63445—31no—
82#63441—31no—
83#63441—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9—22no—
87C22×D3×C9—41no—
88C22×D3×C9—41no—
89C22×D3×C9C2311yescharacteristic
90C22×D3×C9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C2×C3×C4×C9—41no—
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95#6233—22no—
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C4×C3⋊D9—41no—
100C3×#611—22no—
101C2×C9×Dic3—41no—
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C3×C4×D9—41no—
108#6195—41no—
109#6195—41no—
110#6194—41no—
111#6194—41no—
112#6192—41no—
113#6189—41no—
114#5560—91no—
115#5494—91no—
116C23×C3×D3C2×D311yescharacteristic
117C22×C32×C4C2×D311yescharacteristic
118C2×#638—31no—
119C2×C4×C3⋊D3—31no—
120C2×C3×#67—31no—
121C22×C3×Dic3C2×D311yescharacteristic
122C2×C3×C4×D3—31no—
123C2×#627—31no—
124C2×#626—31no—
125C2×#626—31no—
126C2×#626—31no—
127C2×#625—31no—
128C2×#625—31no—
129C24×C9—31no—
130#3757—31no—
131#3752—31no—
132#3750—31no—
133C4×C3⋊Dic3—31no—
134C3×#217—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4C2×D311yescharacteristic
137C3×(C2×D3)⋊C4C2×D311yescharacteristic
138C3×(C2×D3)⋊C4C2×D311yescharacteristic
139C3×(C2×D3)⋊C4C2×D311yescharacteristic
140C3×Dic3⋊C4—31no—
141C3×C4×Dic3—31no—
142#3724—31no—
143Dic3⋊Dic3—31no—
144Dic3⋊Dic3—31no—
145Dic3⋊Dic3—31no—
146#3722—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152C22×C4×C9—21no—
153C22×C4×C9—31no—
154C22×C4×C9C2×D311yescharacteristic
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—31no—
158C2×#611—31no—
159C2×#611—31no—
160C2×#611—61no—
161C2×#611C2×D311yescharacteristic
162C2×D36—31no—
163C2×C4×D9—31no—
164C2×C4×D9—61no—
165C2×C4×D9C2×D311yescharacteristic, complemented
166C2×Dic18—31no—
167C9×C22⋊C4—31no—
168C9×C22⋊C4—31no—
169C9×C22⋊C4—31no—
170C9×C22⋊C4—31no—
171#3676—31no—
172#3676—31no—
173#3676—31no—
174#3676—31no—
175#3676—31no—
176#3676—61no—
177#3676C2×D311yescharacteristic
178(C2×D9)⋊C4—31no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—61no—
182(C2×D9)⋊C4C2×D311yescharacteristic, complemented
183C4⋊Dic9—31no—
184C4⋊Dic9—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—61no—
189Dic9⋊C4C2×D311yescharacteristic, complemented
190C4×Dic9—31no—
191C4×Dic9—61no—
192C4×Dic9C2×D311yescharacteristic, complemented
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9#4112yes—
196C22×C3×C9C2411yescharacteristic
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9—21no—
200C2×D3×C9—21no—
201C2×D3×C9—21no—
202C2×D3×C9—21no—
203C2×D3×C9—21no—
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×D3×C9—44no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9—21no—
214C3⋊Dic9—21no—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×C4×D4—91no—
221C2×C3×C22⋊C4—31no—
222#953—91no—
223#953—91no—
224#939—91no—
225#937—91no—
226#930—91no—
227#930—91no—
228#929—91no—
229C4×#67—31no—
230C4×#67—91no—
231C4×#67—91no—
232C4×#67—181no—
233C2×(C2×D3)⋊C4D911yescharacteristic, complemented
234#924—91no—
235#898—91no—
236#894—91no—
237#885—91no—
238#885—91no—
239#885—91no—
240#884—91no—
241#884—91no—
242#884—91no—
243#883—91no—
244#883—91no—
245#882—91no—
246#879—91no—
247#879—91no—
248#878—91no—
249#876—91no—
250#875—91no—
251C23×C32C22×D311yescharacteristic
252C22×C3⋊D3—31no—
253C22×C3×D3—22no—
254C22×C3×D3—31no—
255C22×C3×D3—41no—
256C22×C3×D3—41no—
257C22×C3×D3C22×D311yescharacteristic
258C22×C3×D3C22×D311yescharacteristic
259C2×C32×C4—41no—
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262#638—62no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—31no—
266C4×C3⋊D3—121no—
267C3×#67—62no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—41no—
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C3×C4×D3—121no—
275#627—121no—
276#626—121no—
277#626—121no—
278#626—121no—
279#625—121no—
280#625—121no—
281C23×C9—21no—
282C23×C9—31no—
283C23×C9—31no—
284C23×C9—62no—
285C23×C9—121no—
286C23×C9—121no—
287C23×C9C22×D311yescharacteristic
288C22×D9—31no—
289C22×D9—61no—
290C22×D9C22×D311yescharacteristic
291C2×C4×C9—21no—
292C2×C4×C9—21no—
293C2×C4×C9—31no—
294C2×C4×C9—31no—
295C2×C4×C9—41no—
296C2×C4×C9—42no—
297C2×C4×C9—121no—
298C2×C4×C9C22×D311yescharacteristic
299C2×C4×C9C22×D311yescharacteristic
300#611—22no—
301#611—64no—
302#611—62no—
303#611—121no—
304#611—121no—
305#611—121no—
306#611—121no—
307C2×Dic9—31no—
308C2×Dic9—31no—
309C2×Dic9—31no—
310C2×Dic9—61no—
311C2×Dic9—61no—
312C2×Dic9—61no—
313C2×Dic9C22×D311yescharacteristic
314C2×Dic9C22×D311yescharacteristic
315C2×Dic9C22×D311yescharacteristic
316D36—121no—
317C4×D9—41no—
318C4×D9—121no—
319C4×D9—122no—
320Dic18—121no—
321#538—271noSylow
322C2×C3×C9—22no—
323C2×C3×C9C2×#4111yescharacteristic
324C2×C3×C9H(5,𝔽2)11yescharacteristic
325C2×C3×C9H(5,𝔽2)11yescharacteristic
326C3⋊D9—41no—
327D3×C9—41no—
328D3×C9—41no—
329C3×D9—41no—
330C24×C3—31no—
331C23×D3C2×D911yescharacteristic
332C2×C3×D4—91no—
333C22×C3×C4—21no—
334C22×C3×C4—31no—
335C22×C3×C4—91no—
336C22×C3×C4C2×D911yescharacteristic
337C22×C3×C4D3211yescharacteristic
338C2×#67—31no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—91no—
347C2×#67—91no—
348C2×#67—181no—
349C22×Dic3C2×D911yescharacteristic
350C2×D12—91no—
351C2×D12—91no—
352C2×D12—91no—
353C2×C4×D3—31no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—181no—
357C2×Dic6—91no—
358C2×Dic6—91no—
359C3×C4⋊C4—91no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—31no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4—91no—
366C3×C42—91no—
367#217—31no—
368#217—91no—
369#217—91no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—91no—
374#217—91no—
375#217—181no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—91no—
378(C2×D3)⋊C4—91no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—181no—
387(C2×D3)⋊C4C2×D911yescharacteristic
388(C2×D3)⋊C4C2×D911yescharacteristic
389(C2×D3)⋊C4C2×D911yescharacteristic
390(C2×D3)⋊C4C2×D911yescharacteristic
391C4⋊Dic3—91no—
392C4⋊Dic3—91no—
393C4⋊Dic3—91no—
394Dic3⋊C4—31no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—181no—
403C4×Dic3—31no—
404C4×Dic3—91no—
405C4×Dic3—91no—
406C4×Dic3—181no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32#23512yes—
410C22×C32C23×D311yescharacteristic
411C2×C3⋊D3—61no—
412C2×C3⋊D3—61no—
413C2×C3⋊D3—61no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—44no—
421C2×C3×D3—61no—
422C2×C3×D3—61no—
423C2×C3×D3—61no—
424C32×C4—21no—
425C32×C4—21no—
426C3⋊Dic3—61no—
427C3⋊Dic3—61no—
428C3⋊Dic3—61no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—61no—
432C3×Dic3—61no—
433C3×Dic3—61no—
434C22×C9—21no—
435C22×C9—21no—
436C22×C9—21no—
437C22×C9—22no—
438C22×C9—41no—
439C22×C9—41no—
440C22×C9—61no—
441C22×C9—61no—
442C22×C9—61no—
443C22×C9—61no—
444C22×C9—61no—
445C22×C9—61no—
446C22×C9—124no—
447C22×C9#23512yes—
448C22×C9C23×D311yescharacteristic
449C2×D9—21no—
450C2×D9—21no—
451C2×D9—21no—
452C2×D9—62no—
453C2×D9—61no—
454C2×D9—61no—
455C2×D9—61no—
456C2×D9—121no—
457C2×D9—121no—
458C4×C9—22no—
459C4×C9—21no—
460C4×C9—21no—
461C4×C9—41no—
462C4×C9—61no—
463C4×C9—61no—
464Dic9—21no—
465Dic9—21no—
466Dic9—21no—
467Dic9—62no—
468Dic9—61no—
469Dic9—61no—
470Dic9—61no—
471Dic9—121no—
472Dic9—121no—
473#126—271no—
474#126—271no—
475#124—271no—
476#124—271no—
477#123—271no—
478#123—271no—
479C22⋊Q8—271no—
480#121—271no—
481#121—271no—
482#121—271no—
483#120—271no—
484#120—271no—
485C4×D4—91no—
486C4×D4—271no—
487C2×C22⋊C4—31no—
488C3×C9#53811yescharacteristic, complemented, Sylow
489C23×C3—21no—
490C23×C3—31no—
491C23×C3—31no—
492C23×C3—62no—
493C23×C3—91no—
494C23×C3—121no—
495C23×C3—121no—
496C23×C3C22×D911yescharacteristic
497C23×C3C2×D3211yescharacteristic
498C22×D3—22no—
499C22×D3—31no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—91no—
503C22×D3—91no—
504C22×D3—181no—
505C22×D3C22×D911yescharacteristic
506C22×D3C22×D911yescharacteristic
507C3×D4—182no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—42no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—91no—
518C2×C3×C4—121no—
519C2×C3×C4—361no—
520C2×C3×C4C22×D911yescharacteristic
521C2×C3×C4C22×D911yescharacteristic
522C2×C3×C4C2×D3211yescharacteristic
523C2×C3×C4C2×D3211yescharacteristic
524#67—62no—
525#67—184no—
526#67—182no—
527#67—182no—
528#67—361no—
529#67—361no—
530#67—361no—
531#67—361no—
532#67—361no—
533#67—361no—
534#67—361no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—41no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—91no—
544C2×Dic3—91no—
545C2×Dic3—181no—
546C2×Dic3—181no—
547C2×Dic3—181no—
548C2×Dic3C22×D911yescharacteristic
549C2×Dic3C22×D911yescharacteristic
550D12—361no—
551D12—361no—
552D12—361no—
553C4×D3—121no—
554C4×D3—361no—
555C4×D3—361no—
556C4×D3—362no—
557Dic6—361no—
558Dic6—361no—
559C2×C32—22no—
560C2×C32C2×#23511yescharacteristic
561C2×C32#100411yescharacteristic
562C2×C32#100411yescharacteristic
563C3⋊D3—121no—
564C3×D3—41no—
565C3×D3—41no—
566C3×D3—121no—
567C2×C9—22no—
568C2×C9—21no—
569C2×C9—21no—
570C2×C9—21no—
571C2×C9—42no—
572C2×C9—121no—
573C2×C9—121no—
574C2×C9C2×#23511yescharacteristic
575C2×C9#100411yescharacteristic
576C2×C9#100911yescharacteristic
577D9—41no—
578D9—122no—
579D9—121no—
580C24—31no—
581C2×Q8—271no—
582C2×D4—91no—
583C2×D4—271no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C22×C4—31no—
590C22×C4—91no—
591C22×C4—271no—
592C22×C4D3×D911yescharacteristic
593C4⋊C4—91no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C4⋊C4—271no—
598C4⋊C4—271no—
599C22⋊C4—31no—
600C22⋊C4—31no—
601C22⋊C4—31no—
602C22⋊C4—31no—
603C22⋊C4—91no—
604C22⋊C4—91no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C42—91no—
614C42—271no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—22no—
620C22×C3—21no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—124no—
630C22×C3—181no—
631C22×C3—181no—
632C22×C3—181no—
633C22×C3#369712yes—
634C22×C3C23×D911yescharacteristic
635C22×C3#379812yes—
636C22×C3C22×D3211yescharacteristic
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—44no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—182no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—181no—
651C2×D3—181no—
652C2×D3—181no—
653C2×D3—181no—
654C2×D3—361no—
655C2×D3—361no—
656C3×C4—22no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—41no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—181no—
665C3×C4—181no—
666C3×C4—181no—
667Dic3—21no—
668Dic3—21no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—182no—
673Dic3—181no—
674Dic3—181no—
675Dic3—181no—
676Dic3—181no—
677Dic3—181no—
678Dic3—181no—
679Dic3—361no—
680Dic3—361no—
681C32#549411yescharacteristic
682C9—21no—
683C9#556011yescharacteristic, complemented
684C23—31no—
685C23—31no—
686C23—62no—
687C23—91no—
688C23—121no—
689C23—121no—
690C23—271no—
691C23C2×D3×D911yescharacteristic
692Q8—1081no—
693D4—182no—
694D4—542no—
695D4—1081no—
696D4—1081no—
697D4—1081no—
698D4—1081no—
699D4—1081no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—41no—
703C2×C4—91no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—121no—
707C2×C4—271no—
708C2×C4—271no—
709C2×C4—271no—
710C2×C4—361no—
711C2×C4—1081no—
712C2×C4C2×D3×D911yescharacteristic
713C2×C4C2×D3×D911yescharacteristic
714C2×C3—22no—
715C2×C3—22no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—42no—
720C2×C3—121no—
721C2×C3—121no—
722C2×C3—361no—
723C2×C3C2×#369711yescharacteristic
724C2×C3#6371011yescharacteristic
725C2×C3#6371011yescharacteristic
726C2×C3C2×#379811yescharacteristic
727C2×C3#6430711yescharacteristic
728C2×C3#6433011yescharacteristic
729D3—41no—
730D3—41no—
731D3—121no—
732D3—362no—
733D3—361no—
734D3—361no—
735C22—21no—
736C22—21no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—61no—
742C22—61no—
743C22—124no—
744C22—181no—
745C22—181no—
746C22—181no—
747C22—541no—
748C22—541no—
749C22—541no—
750C22#8864012yes—
751C22C22×D3×D911yescharacteristic
752C4—21no—
753C4—21no—
754C4—61no—
755C4—61no—
756C4—181no—
757C4—181no—
758C4—181no—
759C4—541no—
760C4—541no—
761C4—541no—
762C3—21no—
763C3#1058959611yescharacteristic, complemented
764C3#1059503611yescharacteristic
765C2—22no—
766C2—121no—
767C2—121no—
768C2—361no—
769C2—1081no—
770C2C2×#8864011yescharacteristic
771C2#1172247611yescharacteristic
772C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#538
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. C4×#6233C2semidirect
2. C2×C9×(C2×D3)⋊C4C2semidirect
3. C3×C4×#611C2semidirect
4. #11721287C2semidirect
5. #11721286C2semidirect
6. #11721277C2semidirect
7. #11721249C2semidirect
8. #11721044C2semidirect
9. #11721041C2semidirect
10. #11721033C2semidirect
11. #11721031C2semidirect
12. #11720966C2semidirect
13. #11720963C2semidirect
14. #11720957C2semidirect
15. #11720956C2semidirect
21. C2×C4×C3⋊D9C22semidirect
24. C2×C3×C4×D9C22semidirect
29. C2×#6192C22semidirect
30. C2×#6189C22semidirect
32. #88536C22semidirect
33. #88534C22semidirect
34. C4×C3⋊Dic9C22semidirect
40. C3×(C2×D9)⋊C4C22semidirect
41. C3×Dic9⋊C4C22semidirect
42. C3×C4×Dic9C22semidirect
47. #88445C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. Dic3⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. Dic9⋊Dic3C22semidirect
74. C4×#611D3semidirect
165. C2×C4×D9C2×D3semidirect
182. (C2×D9)⋊C4C2×D3semidirect
189. Dic9⋊C4C2×D3semidirect
192. C4×Dic9C2×D3semidirect
233. C2×(C2×D3)⋊C4D9semidirect
488. C3×C9#538semidirect
683. C9#5560semidirect
763. C3#10589596semidirect

Maximal subgroups

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

subgroupindex
C4×#62332
C2×C9×(C2×D3)⋊C42
C3×C4×#6112
#117212872
#117212862
#117212772
#117212492
#117210442
#117210412
#117210332
#117210312
#117209662
#117209632
#117209572
#117209562
#105950363
#105895963