Finite Group Databasebeta

← #13148322

Subgroups — #13148322

Order 1728.

818 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721724C211yesmaximal, characteristic, complemented
2C9×#886C211yesmaximal, characteristic, complemented
3C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
4#11721285C211yesmaximal, characteristic
5#67⋊Dic9C211yesmaximal, characteristic, complemented
6C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic, complemented
7#11721244C211yesmaximal, characteristic, complemented
8#11721042C211yesmaximal, characteristic, complemented
9#11721031C211yesmaximal, characteristic, complemented
10#11721021C211yesmaximal, characteristic, complemented
11#11721012C211yesmaximal, characteristic, complemented
12#11720946C211yesmaximal, characteristic, complemented
13#11720946C211yesmaximal, characteristic, complemented
14#11720945C211yesmaximal, characteristic, complemented
15#11720907C211yesmaximal, characteristic, complemented
16#10594211—31nomaximal
17#10589760—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×#6226C2211yescharacteristic, complemented
21C2×C9×#67C2211yescharacteristic
22C22×C9×Dic3C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×#6194C2211yescharacteristic
26C2×#6194C2211yescharacteristic
27C2×D3×Dic9C2211yescharacteristic, complemented
28C3×C9×C22⋊C4C2211yescharacteristic
29#88551C2211yescharacteristic
30C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
31#88534C2211yescharacteristic, complemented
32#88534C2211yescharacteristic, complemented
33C3×#3676C2211yescharacteristic
34C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C9×C4⋊Dic3C2211yescharacteristic, complemented
39C9×C4⋊Dic3C2211yescharacteristic, complemented
40(C2×D3)⋊Dic9C2211yescharacteristic, complemented
41(C2×D9)⋊Dic3C2211yescharacteristic
42(C2×D9)⋊Dic3C2211yescharacteristic
43(C2×D9)⋊Dic3C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic, complemented
48Dic3⋊Dic9C2211yescharacteristic, complemented
49Dic3⋊Dic9C2211yescharacteristic, complemented
50Dic3×Dic9C2211yescharacteristic, complemented
51Dic3×Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64087—31no—
54C3×#886D311yescharacteristic
55C3×D3×C22⋊C4—31no—
56#63976—31no—
57#67⋊Dic3—31no—
58C2×(C2×D3)⋊Dic3—31no—
59#63955—31no—
60#63913—31no—
61#63905—31no—
62#63891—31no—
63#63879—31no—
64#63858—31no—
65#63858—31no—
66#63857—31no—
67#63841—31no—
68C9×#123—31no—
69#63499—31no—
70D4×Dic9—31no—
71C2×(C2×D9)⋊C4—31no—
72#63488—31no—
73#63460—31no—
74#63460—31no—
75#63459—31no—
76#63454—31no—
77#63448—31no—
78#63447—31no—
79#63445—31no—
80#611⋊C4—31no—
81C22⋊C4×D9D311yescharacteristic, complemented
82#63440—31no—
83#63440—61no—
84C23×C3×C9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×C3×D9—22no—
87C22×C3×D9—22no—
88C22×C3×D9—41no—
89C22×C3×D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9—41no—
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98#6226—41no—
99C9×#67—22no—
100C2×C9×Dic3—22no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C3×C4×D9—22no—
107C3×C4×D9—41no—
108#6194—22no—
109#6194—41no—
110D3×Dic9—41no—
111#5658—91no—
112#5495—91no—
113C23×C3×D3—31no—
114C22×C3⋊Dic3—31no—
115C2×#634—31no—
116C2×C3×#67C2×D311yescharacteristic
117C22×C3×Dic3C2×D311yescharacteristic
118C2×C3×C4×D3—31no—
119C2×C3×C4×D3—31no—
120C2×#625—31no—
121C2×#625—31no—
122C2×D3×Dic3—31no—
123C23×D9C2×D311yescharacteristic
124C32×C22⋊C4C2×D311yescharacteristic
125#3757—31no—
126C4⋊(C3⋊Dic3)—31no—
127#3750—31no—
128#3750—31no—
129C3×#217—31no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4C2×D311yescharacteristic
133C3×(C2×D3)⋊C4C2×D311yescharacteristic
134C3×C4⋊Dic3C2×D311yescharacteristic
135C3×C4⋊Dic3C2×D311yescharacteristic
136Dic3⋊Dic3—31no—
137Dic3⋊Dic3—31no—
138Dic3⋊Dic3—31no—
139(C2×D3)⋊Dic3—31no—
140(C2×D3)⋊Dic3—31no—
141(C2×D3)⋊Dic3—31no—
142(C2×D3)⋊Dic3—31no—
143(C2×D3)⋊Dic3—31no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146Dic32—31no—
147Dic32—31no—
148Dic32—31no—
149C2×D4×C9—31no—
150C22×C4×C9—31no—
151C2×#611—31no—
152C2×#611—31no—
153C22×Dic9—31no—
154C22×Dic9—31no—
155C22×Dic9—61no—
156C2×C4×D9C2×D311yescharacteristic
157C2×C4×D9C2×D311yescharacteristic
158C2×Dic18—31no—
159C2×Dic18—61no—
160C9×C4⋊C4—31no—
161C9×C4⋊C4—31no—
162C9×C22⋊C4—21no—
163C9×C22⋊C4—31no—
164C9×C22⋊C4—31no—
165C9×C22⋊C4C2×D311yescharacteristic
166#3676—31no—
167#3676—31no—
168#3676—61no—
169#3676C2×D311yescharacteristic
170(C2×D9)⋊C4—31no—
171(C2×D9)⋊C4—31no—
172(C2×D9)⋊C4—31no—
173(C2×D9)⋊C4—31no—
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4—31no—
176(C2×D9)⋊C4C2×D311yescharacteristic
177(C2×D9)⋊C4C2×D311yescharacteristic
178C4⋊Dic9—31no—
179C4⋊Dic9—31no—
180C4⋊Dic9—31no—
181C4⋊Dic9—31no—
182C4⋊Dic9—61no—
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—61no—
186Dic9⋊C4—61no—
187C4×Dic9—31no—
188C4×Dic9—31no—
189C4×Dic9—31no—
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9#4112yes—
193C22×C3×C9C2411yescharacteristic
194C2×D3×C9—21no—
195C2×D3×C9—21no—
196C2×D3×C9—21no—
197C2×C3×D9—21no—
198C2×C3×D9—21no—
199C2×C3×D9—21no—
200C2×C3×D9—21no—
201C2×C3×D9—21no—
202C2×C3×D9—44no—
203C2×C3×D9#4112yes—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9—21no—
209C3⋊Dic9—21no—
210C9×Dic3—21no—
211C9×Dic3—21no—
212C9×Dic3—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×#123—31no—
216C2×C3×C22⋊C4—91no—
217#953—91no—
218C2×#217—91no—
219#937—91no—
220D4×Dic3—91no—
221#929—91no—
222C4×#67—91no—
223C2×(C2×D3)⋊C4—91no—
224#926—91no—
225#926—91no—
226#924—91no—
227#898—91no—
228#898—91no—
229#897—91no—
230#892—91no—
231#886—91no—
232#886D911yescharacteristic, complemented
233#885—91no—
234#885—91no—
235#883—91no—
236#883—91no—
237#67⋊C4—91no—
238#67⋊C4—91no—
239D3×C22⋊C4—31no—
240#879—91no—
241#879—91no—
242#878—91no—
243#878—91no—
244#878—181no—
245#877—91no—
246C23×C32C22×D311yescharacteristic
247C22×C3×D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3—62no—
250C22×C3×D3—62no—
251C22×C3×D3—121no—
252C22×C3×D3C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—121no—
260#634—121no—
261C3×#67—22no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C2×C3×Dic3C22×D311yescharacteristic
268C3×C4×D3—62no—
269C3×C4×D3—121no—
270#625—62no—
271#625—121no—
272D3×Dic3—121no—
273C23×C9—21no—
274C23×C9—31no—
275C23×C9C22×D311yescharacteristic
276C22×D9—22no—
277C22×D9—22no—
278C22×D9—41no—
279C22×D9C22×D311yescharacteristic
280C22×D9C22×D311yescharacteristic
281D4×C9—62no—
282C2×C4×C9—21no—
283C2×C4×C9—21no—
284C2×C4×C9—31no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—62no—
288C2×C4×C9C22×D311yescharacteristic
289C2×C4×C9C22×D311yescharacteristic
290#611—62no—
291#611—121no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—31no—
295C2×Dic9—31no—
296C2×Dic9—61no—
297C2×Dic9—61no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—121no—
301C2×Dic9—121no—
302C2×Dic9—122no—
303C2×Dic9C22×D311yescharacteristic
304C2×Dic9C22×D311yescharacteristic
305C4×D9—22no—
306C4×D9—41no—
307Dic18—121no—
308Dic18—122no—
309#551—271noSylow
310C2×C3×C9—22no—
311C2×C3×C9C2×#4111yescharacteristic
312C2×C3×C9C2×#4111yescharacteristic
313C2×C3×C9H(5,𝔽2)11yescharacteristic
314D3×C9—41no—
315C3×D9—22no—
316C3×D9—41no—
317C24×C3—91no—
318C23×D3—31no—
319C2×C3×D4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—91no—
322C22×C3×C4—91no—
323C2×#67—91no—
324C2×#67—91no—
325C2×#67—91no—
326C2×#67—91no—
327C2×#67C2×D911yescharacteristic
328C22×Dic3—91no—
329C22×Dic3—91no—
330C22×Dic3—91no—
331C22×Dic3—181no—
332C22×Dic3C2×D911yescharacteristic
333C2×C4×D3—31no—
334C2×C4×D3—31no—
335C2×C4×D3—91no—
336C2×Dic6—91no—
337C2×Dic6—91no—
338C2×Dic6—181no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C22⋊C4—21no—
342C3×C22⋊C4—31no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—91no—
345C3×C22⋊C4—91no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4C2×D911yescharacteristic
348C3×C22⋊C4D3211yescharacteristic
349#217—31no—
350#217—91no—
351#217—91no—
352#217—91no—
353#217—91no—
354#217—91no—
355#217—91no—
356#217—91no—
357#217—91no—
358#217—91no—
359#217—181no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4C2×D911yescharacteristic, complemented
370(C2×D3)⋊C4C2×D911yescharacteristic, complemented
371C4⋊Dic3—91no—
372C4⋊Dic3—91no—
373C4⋊Dic3—91no—
374C4⋊Dic3—91no—
375C4⋊Dic3—91no—
376C4⋊Dic3—181no—
377C4⋊Dic3C2×D911yescharacteristic, complemented
378C4⋊Dic3C2×D911yescharacteristic, complemented
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—181no—
387Dic3⋊C4—181no—
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32#23712yes—
397C22×C32C23×D311yescharacteristic
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C2×C3×D3—32no—
402C2×C3×D3—61no—
403C2×C3×D3—61no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406C2×C3×D3—61no—
407C2×C3×D3—124no—
408C32×C4—21no—
409C32×C4—21no—
410C3⋊Dic3—61no—
411C3⋊Dic3—61no—
412C3⋊Dic3—61no—
413C3⋊Dic3—61no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C22×C9—21no—
420C22×C9—21no—
421C22×C9—21no—
422C22×C9—22no—
423C22×C9—41no—
424C22×C9—41no—
425C22×C9—61no—
426C22×C9—61no—
427C22×C9—61no—
428C22×C9#23512yes—
429C22×C9C23×D311yescharacteristic
430C2×D9—21no—
431C2×D9—21no—
432C2×D9—21no—
433C2×D9—21no—
434C2×D9—21no—
435C2×D9—44no—
436C2×D9#23712yes—
437C4×C9—21no—
438C4×C9—21no—
439C4×C9—41no—
440C4×C9—41no—
441C4×C9—61no—
442C4×C9—61no—
443C4×C9—61no—
444Dic9—21no—
445Dic9—21no—
446Dic9—62no—
447Dic9—61no—
448Dic9—61no—
449Dic9—61no—
450Dic9—61no—
451Dic9—121no—
452Dic9—121no—
453Dic9—121no—
454#126—271no—
455#126—271no—
456#124—271no—
457#123—31no—
458#123—271no—
459#123—271no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462#120—271no—
463C4×D4—271no—
464C4×D4—271no—
465#117—271no—
466#117—271no—
467C2×C22⋊C4—91no—
468C2×C22⋊C4—271no—
469C3×C9#55111yescharacteristic, complemented, Sylow
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—91no—
473C23×C3—91no—
474C23×C3—182no—
475C23×C3—182no—
476C23×C3—361no—
477C23×C3C22×D911yescharacteristic
478C23×C3C2×D3211yescharacteristic
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—62no—
482C22×D3—62no—
483C22×D3—121no—
484C22×D3C22×D911yescharacteristic
485C3×D4—62no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—62no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—182no—
495C2×C3×C4—361no—
496C2×C3×C4C22×D911yescharacteristic
497C2×C3×C4C22×D911yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499C2×C3×C4C2×D3211yescharacteristic
500#67—22no—
501#67—182no—
502#67—182no—
503#67—361no—
504#67—361no—
505C2×Dic3—22no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—91no—
509C2×Dic3—91no—
510C2×Dic3—91no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—91no—
515C2×Dic3—91no—
516C2×Dic3—181no—
517C2×Dic3—181no—
518C2×Dic3—181no—
519C2×Dic3—181no—
520C2×Dic3—361no—
521C2×Dic3—361no—
522C2×Dic3—361no—
523C2×Dic3—362no—
524C2×Dic3C22×D911yescharacteristic
525C2×Dic3C22×D911yescharacteristic
526C2×Dic3C22×D911yescharacteristic
527C4×D3—62no—
528C4×D3—121no—
529C4×D3—361no—
530Dic6—361no—
531Dic6—361no—
532Dic6—362no—
533C2×C32—22no—
534C2×C32C2×#23711yescharacteristic
535C2×C32D3×#4111yescharacteristic
536C2×C32#100911yescharacteristic
537C3×D3—41no—
538C3×D3—62no—
539C3×D3—121no—
540C2×C9—22no—
541C2×C9—21no—
542C2×C9—21no—
543C2×C9—21no—
544C2×C9—42no—
545C2×C9—121no—
546C2×C9C2×#23511yescharacteristic
547C2×C9C2×#23711yescharacteristic
548C2×C9#100411yescharacteristic
549D9—22no—
550D9—41no—
551C24—91no—
552C2×Q8—271no—
553C2×D4—31no—
554C2×D4—271no—
555C2×D4—271no—
556C22×C4—31no—
557C22×C4—91no—
558C22×C4—91no—
559C22×C4—271no—
560C22×C4—271no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C22⋊C4—31no—
570C22⋊C4—31no—
571C22⋊C4—91no—
572C22⋊C4—91no—
573C22⋊C4—91no—
574C22⋊C4—271no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4D3×D911yescharacteristic
583C42—271no—
584C42—271no—
585C42—271no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—22no—
591C22×C3—21no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—61no—
595C22×C3—61no—
596C22×C3—61no—
597C22×C3—92no—
598C22×C3—181no—
599C22×C3—181no—
600C22×C3—181no—
601C22×C3—181no—
602C22×C3—181no—
603C22×C3—364no—
604C22×C3#369912yes—
605C22×C3C23×D911yescharacteristic
606C22×C3#379512yes—
607C22×C3C22×D3211yescharacteristic
608C2×D3—21no—
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—32no—
612C2×D3—61no—
613C2×D3—61no—
614C2×D3—61no—
615C2×D3—61no—
616C2×D3—61no—
617C2×D3—124no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—61no—
625C3×C4—61no—
626C3×C4—61no—
627C3×C4—181no—
628C3×C4—181no—
629Dic3—21no—
630Dic3—21no—
631Dic3—21no—
632Dic3—61no—
633Dic3—61no—
634Dic3—182no—
635Dic3—181no—
636Dic3—181no—
637Dic3—181no—
638Dic3—181no—
639Dic3—181no—
640Dic3—181no—
641Dic3—181no—
642Dic3—181no—
643Dic3—361no—
644Dic3—361no—
645Dic3—361no—
646C32#565811yescharacteristic
647C9—21no—
648C9#549511yescharacteristic, complemented
649C23—31no—
650C23—91no—
651C23—91no—
652C23—182no—
653C23—182no—
654C23—361no—
655C23C2×D3×D911yescharacteristic
656Q8—1081no—
657D4—62no—
658D4—542no—
659D4—1081no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—62no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—182no—
667C2×C4—271no—
668C2×C4—271no—
669C2×C4—271no—
670C2×C4—271no—
671C2×C4—361no—
672C2×C4—1081no—
673C2×C4—1081no—
674C2×C4C2×D3×D911yescharacteristic
675C2×C4C2×D3×D911yescharacteristic
676C2×C3—22no—
677C2×C3—22no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—42no—
682C2×C3—121no—
683C2×C3—182no—
684C2×C3—361no—
685C2×C3C2×#369911yescharacteristic
686C2×C3#41×D911yescharacteristic
687C2×C3#6371511yescharacteristic
688C2×C3C2×#379511yescharacteristic
689C2×C3D3×#23711yescharacteristic
690C2×C3#6431411yescharacteristic
691D3—41no—
692D3—62no—
693D3—121no—
694C22—21no—
695C22—21no—
696C22—61no—
697C22—61no—
698C22—61no—
699C22—92no—
700C22—181no—
701C22—181no—
702C22—181no—
703C22—181no—
704C22—181no—
705C22—364no—
706C22#8863812yes—
707C22C22×D3×D911yescharacteristic
708C4—21no—
709C4—21no—
710C4—61no—
711C4—61no—
712C4—61no—
713C4—181no—
714C4—181no—
715C4—541no—
716C4—541no—
717C4—541no—
718C4—541no—
719C3—21no—
720C3#1058976011yescharacteristic, complemented
721C3#1059421111yescharacteristic
722C2—22no—
723C2—121no—
724C2—182no—
725C2—361no—
726C2C2×#8863811yescharacteristic
727C2D9×#23711yescharacteristic
728C2#1172250111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radical#11721285C2
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#551
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. #11721724C2semidirect
2. C9×#886C2semidirect
3. C3×C22⋊C4×D9C2semidirect
5. #67⋊Dic9C2semidirect
6. C2×(C2×D9)⋊Dic3C2semidirect
7. #11721244C2semidirect
8. #11721042C2semidirect
9. #11721031C2semidirect
10. #11721021C2semidirect
11. #11721012C2semidirect
12. #11720946C2semidirect
13. #11720946C2semidirect
14. #11720945C2semidirect
15. #11720907C2semidirect
20. C2×#6226C22semidirect
27. C2×D3×Dic9C22semidirect
30. C4⋊(C3⋊Dic9)C22semidirect
31. #88534C22semidirect
32. #88534C22semidirect
34. C9×(C2×D3)⋊C4C22semidirect
35. C9×(C2×D3)⋊C4C22semidirect
38. C9×C4⋊Dic3C22semidirect
39. C9×C4⋊Dic3C22semidirect
40. (C2×D3)⋊Dic9C22semidirect
47. Dic3⋊Dic9C22semidirect
48. Dic3⋊Dic9C22semidirect
49. Dic3⋊Dic9C22semidirect
50. Dic3×Dic9C22semidirect
51. Dic3×Dic9C22semidirect
52. Dic3×Dic9C22semidirect
81. C22⋊C4×D9D3semidirect
232. #886D9semidirect
369. (C2×D3)⋊C4C2×D9semidirect
370. (C2×D3)⋊C4C2×D9semidirect
377. C4⋊Dic3C2×D9semidirect
378. C4⋊Dic3C2×D9semidirect
469. C3×C9#551semidirect
648. C9#5495semidirect
720. C3#10589760semidirect

Maximal subgroups

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

subgroupindex
#117217242
C9×#8862
C3×C22⋊C4×D92
#117212852
#67⋊Dic92
C2×(C2×D9)⋊Dic32
#117212442
#117210422
#117210312
#117210212
#117210122
#117209462
#117209452
#117209072
#105942113
#105897603