Finite Group Databasebeta

← #13148368

Subgroups — #13148368

Order 1728.

876 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊C4×C3⋊D9C211yesmaximal, characteristic, complemented
2C9×#886C211yesmaximal, characteristic, complemented
3C3×#63440C211yesmaximal, characteristic, complemented
4#11721291C211yesmaximal, characteristic
5#67×Dic9C211yesmaximal, characteristic, complemented
6C2×#88445C211yesmaximal, characteristic, complemented
7#11721244C211yesmaximal, characteristic, complemented
8#11721035C211yesmaximal, characteristic, complemented
9#11721020C211yesmaximal, characteristic, complemented
10#11721014C211yesmaximal, characteristic, complemented
11#11720957C211yesmaximal, characteristic, complemented
12#11720936C211yesmaximal, characteristic, complemented
13#11720922C211yesmaximal, characteristic, complemented
14#11720920C211yesmaximal, characteristic, complemented
15#11720920C211yesmaximal, characteristic, complemented
16#10594164—31nomaximal
17#10589760—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C22×C9×Dic3C2211yescharacteristic
23C22×C3×Dic9C2211yescharacteristic
24C2×C3×Dic18C2211yescharacteristic, complemented
25C2×#6195C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×D3×Dic9C2211yescharacteristic, complemented
28C3×C9×C22⋊C4C2211yescharacteristic
29#88551C2211yescharacteristic
30#88536C2211yescharacteristic
31#88536C2211yescharacteristic
32C3×#3676C2211yescharacteristic
33C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
34C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C9×C4⋊Dic3C2211yescharacteristic, complemented
36C9×C4⋊Dic3C2211yescharacteristic, complemented
37C3×C4⋊Dic9C2211yescharacteristic, complemented
38C3×Dic9⋊C4C2211yescharacteristic, complemented
39C3×Dic9⋊C4C2211yescharacteristic, complemented
40(C2×D3)⋊Dic9C2211yescharacteristic, complemented
41#88445C2211yescharacteristic
42#88445C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic, complemented
48Dic3⋊Dic9C2211yescharacteristic, complemented
49Dic3⋊Dic9C2211yescharacteristic, complemented
50Dic3×Dic9C2211yescharacteristic, complemented
51Dic3×Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53C22⋊C4×C3⋊D3—31no—
54C3×#886D311yescharacteristic
55C3×#878—31no—
56#63981—31no—
57Dic3×#67—31no—
58C2×#3722—31no—
59#63955—31no—
60#63907—31no—
61#63890—31no—
62#63881—31no—
63#63871—31no—
64#63853—31no—
65#63849—31no—
66#63848—31no—
67#63848—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×D9—31no—
82C22⋊C4×D9—61no—
83#63440D311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9—22no—
86C22×C3⋊D9—22no—
87C22×C3⋊D9—41no—
88C22×C3⋊D9C2311yescharacteristic
89C22×C3⋊D9C2311yescharacteristic
90C22×D3×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C4×C3⋊D9—22no—
96C4×C3⋊D9—41no—
97C9×#67—22no—
98C2×C9×Dic3—22no—
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9—41no—
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C3×Dic18—41no—
108#6195—22no—
109#6195—41no—
110D3×Dic9—41no—
111#5658—91no—
112#5637—91no—
113C23×C3⋊D3—31no—
114C2×C4×C3⋊D3—31no—
115C2×C4×C3⋊D3—31no—
116C2×C3×#67C2×D311yescharacteristic
117C22×C3×Dic3—31no—
118C22×C3×Dic3C2×D311yescharacteristic
119C2×C3×Dic6—31no—
120C2×#626—31no—
121C2×#626—31no—
122C2×D3×Dic3—31no—
123C23×D9—31no—
124C23×D9—61no—
125C32×C22⋊C4C2×D311yescharacteristic
126#3757—31no—
127#3752—31no—
128#3752—31no—
129C3×#217—31no—
130C3×(C2×D3)⋊C4C2×D311yescharacteristic
131C3×(C2×D3)⋊C4C2×D311yescharacteristic
132C3×C4⋊Dic3—31no—
133C3×C4⋊Dic3C2×D311yescharacteristic
134C3×C4⋊Dic3C2×D311yescharacteristic
135C3×Dic3⋊C4—31no—
136C3×Dic3⋊C4—31no—
137Dic3⋊Dic3—31no—
138Dic3⋊Dic3—31no—
139Dic3⋊Dic3—31no—
140#3722—31no—
141#3722—31no—
142#3722—31no—
143#3722—31no—
144#3722—31no—
145#3722—31no—
146(C2×D3)⋊Dic3—31no—
147Dic32—31no—
148Dic32—31no—
149Dic32—31no—
150C2×D4×C9—31no—
151C22×C4×C9—31no—
152C2×#611—31no—
153C2×#611—31no—
154C22×Dic9—31no—
155C22×Dic9C2×D311yescharacteristic
156C2×C4×D9—31no—
157C2×C4×D9—31no—
158C2×C4×D9—61no—
159C2×C4×D9—61no—
160C2×Dic18C2×D311yescharacteristic, complemented
161C9×C4⋊C4—31no—
162C9×C4⋊C4—31no—
163C9×C22⋊C4—21no—
164C9×C22⋊C4—31no—
165C9×C22⋊C4—31no—
166C9×C22⋊C4C2×D311yescharacteristic
167#3676—31no—
168#3676—31no—
169#3676—61no—
170#3676C2×D311yescharacteristic
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)⋊C4—31no—
177(C2×D9)⋊C4—31no—
178(C2×D9)⋊C4—31no—
179(C2×D9)⋊C4—61no—
180(C2×D9)⋊C4—61no—
181C4⋊Dic9—31no—
182C4⋊Dic9—31no—
183C4⋊Dic9—31no—
184C4⋊Dic9C2×D311yescharacteristic, complemented
185Dic9⋊C4C2×D311yescharacteristic, complemented
186Dic9⋊C4C2×D311yescharacteristic, complemented
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×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9—21no—
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9—44no—
200C2×C3⋊D9#4112yes—
201C2×D3×C9—21no—
202C2×D3×C9—21no—
203C2×D3×C9—21no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C9×Dic3—21no—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C3×Dic9—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×#123—31no—
216C3×C22⋊Q8—91no—
217#947—91no—
218#946—91no—
219#937—91no—
220D4×Dic3—91no—
221C4×#67—91no—
222C2×(C2×D3)⋊C4—91no—
223C2×(C2×D3)⋊C4—91no—
224#926—91no—
225#898—91no—
226#898—91no—
227#898—91no—
228#898—91no—
229#897—91no—
230#894—91no—
231#894—91no—
232#893—91no—
233#892—91no—
234#892—91no—
235#886—91no—
236#886D911yescharacteristic, complemented
237#885—91no—
238#883—91no—
239#882—91no—
240#67⋊C4—91no—
241D3×C22⋊C4—91no—
242D3×C22⋊C4—91no—
243D3×C22⋊C4—181no—
244#878—31no—
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—
257C4×C3⋊D3—62no—
258C4×C3⋊D3—121no—
259C3×#67—22no—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—121no—
266C2×C3×Dic3C22×D311yescharacteristic
267C2×C3×Dic3C22×D311yescharacteristic
268C2×C3×Dic3C22×D311yescharacteristic
269C3×Dic6—121no—
270#626—62no—
271#626—121no—
272D3×Dic3—121no—
273C23×C9—21no—
274C23×C9—31no—
275C23×C9C22×D311yescharacteristic
276C22×D9—31no—
277C22×D9—31no—
278C22×D9—61no—
279C22×D9—61no—
280C22×D9—62no—
281C22×D9—64no—
282C22×D9—62no—
283C22×D9—122no—
284C22×D9—121no—
285C22×D9—122no—
286D4×C9—62no—
287C2×C4×C9—21no—
288C2×C4×C9—21no—
289C2×C4×C9—31no—
290C2×C4×C9—31no—
291C2×C4×C9—31no—
292C2×C4×C9—62no—
293C2×C4×C9C22×D311yescharacteristic
294C2×C4×C9C22×D311yescharacteristic
295#611—62no—
296#611—121no—
297C2×Dic9—31no—
298C2×Dic9—31no—
299C2×Dic9—41no—
300C2×Dic9—61no—
301C2×Dic9—61no—
302C2×Dic9—121no—
303C2×Dic9C22×D311yescharacteristic
304C2×Dic9C22×D311yescharacteristic
305C2×Dic9C22×D311yescharacteristic
306C2×Dic9C22×D311yescharacteristic
307C4×D9—62no—
308C4×D9—122no—
309C4×D9—121no—
310C4×D9—122no—
311Dic18—41no—
312#551—271noSylow
313C2×C3×C9—22no—
314C2×C3×C9C2×#4111yescharacteristic
315C2×C3×C9C2×#4111yescharacteristic
316C2×C3×C9H(5,𝔽2)11yescharacteristic
317C3⋊D9—22no—
318C3⋊D9—41no—
319D3×C9—41no—
320C23×D3—91no—
321C23×D3—91no—
322C23×D3—181no—
323C2×C3×Q8—91no—
324C2×C3×D4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—91no—
327C2×#67—91no—
328C2×#67—91no—
329C2×#67C2×D911yescharacteristic
330C22×Dic3—31no—
331C22×Dic3—91no—
332C22×Dic3C2×D911yescharacteristic
333C2×D12—91no—
334C2×D12—91no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C2×C4×D3—181no—
341C2×C4×D3—181no—
342C2×Dic6—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—91no—
346C3×C4⋊C4—91no—
347C3×C4⋊C4—91no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—91no—
352C3×C22⋊C4C2×D911yescharacteristic
353C3×C22⋊C4D3211yescharacteristic
354#217—31no—
355#217—91no—
356#217—91no—
357#217—91no—
358#217—181no—
359(C2×D3)⋊C4—91no—
360(C2×D3)⋊C4—91no—
361(C2×D3)⋊C4—91no—
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)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—181no—
377(C2×D3)⋊C4—181no—
378(C2×D3)⋊C4C2×D911yescharacteristic, complemented
379(C2×D3)⋊C4C2×D911yescharacteristic, complemented
380C4⋊Dic3—31no—
381C4⋊Dic3—91no—
382C4⋊Dic3—91no—
383C4⋊Dic3—91no—
384C4⋊Dic3C2×D911yescharacteristic, complemented
385C4⋊Dic3C2×D911yescharacteristic, complemented
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3—91no—
395C4×Dic3—91no—
396C4×Dic3—91no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32#23712yes—
400C22×C32C23×D311yescharacteristic
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—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C32×C4—21no—
412C32×C4—21no—
413C3⋊Dic3—61no—
414C3⋊Dic3—61no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—61no—
419C3×Dic3—61no—
420C3×Dic3—61no—
421C3×Dic3—61no—
422C22×C9—21no—
423C22×C9—21no—
424C22×C9—21no—
425C22×C9—22no—
426C22×C9—41no—
427C22×C9—41no—
428C22×C9—61no—
429C22×C9—61no—
430C22×C9—61no—
431C22×C9#23912yes—
432C22×C9C23×D311yescharacteristic
433C2×D9—32no—
434C2×D9—62no—
435C2×D9—62no—
436C2×D9—62no—
437C2×D9—61no—
438C2×D9—61no—
439C2×D9—62no—
440C2×D9—61no—
441C2×D9—61no—
442C2×D9—61no—
443C2×D9—121no—
444C2×D9—121no—
445C2×D9—124no—
446C2×D9—128no—
447C4×C9—21no—
448C4×C9—21no—
449C4×C9—41no—
450C4×C9—41no—
451C4×C9—61no—
452C4×C9—61no—
453C4×C9—61no—
454Dic9—21no—
455Dic9—21no—
456Dic9—21no—
457Dic9—21no—
458Dic9—61no—
459Dic9—61no—
460Dic9—121no—
461Dic9—121no—
462#126—271no—
463#126—271no—
464#124—271no—
465#123—31no—
466#123—271no—
467#123—271no—
468C22⋊Q8—91no—
469C22⋊Q8—271no—
470#120—271no—
471C4×D4—271no—
472C4×D4—271no—
473#117—271no—
474#117—271no—
475C2×C22⋊C4—271no—
476C2×C22⋊C4—271no—
477C3×C9#55111yescharacteristic, complemented, Sylow
478C23×C3—21no—
479C23×C3—31no—
480C23×C3C22×D911yescharacteristic
481C23×C3C2×D3211yescharacteristic
482C22×D3—91no—
483C22×D3—91no—
484C22×D3—91no—
485C22×D3—91no—
486C22×D3—181no—
487C22×D3—181no—
488C22×D3—182no—
489C22×D3—182no—
490C22×D3—184no—
491C22×D3—182no—
492C22×D3—182no—
493C22×D3—362no—
494C22×D3—361no—
495C22×D3—361no—
496C22×D3—362no—
497C22×D3C22×D911yescharacteristic
498C3×Q8—361no—
499C3×D4—62no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—62no—
506C2×C3×C4—91no—
507C2×C3×C4—91no—
508C2×C3×C4—91no—
509C2×C3×C4—91no—
510C2×C3×C4—361no—
511C2×C3×C4C22×D911yescharacteristic
512C2×C3×C4C22×D911yescharacteristic
513C2×C3×C4C2×D3211yescharacteristic
514C2×C3×C4C2×D3211yescharacteristic
515#67—22no—
516#67—182no—
517#67—361no—
518C2×Dic3—22no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—91no—
524C2×Dic3—91no—
525C2×Dic3—91no—
526C2×Dic3—91no—
527C2×Dic3—121no—
528C2×Dic3—181no—
529C2×Dic3—181no—
530C2×Dic3—361no—
531C2×Dic3C22×D911yescharacteristic
532C2×Dic3C22×D911yescharacteristic
533C2×Dic3C22×D911yescharacteristic
534D12—182no—
535D12—361no—
536C4×D3—182no—
537C4×D3—182no—
538C4×D3—362no—
539C4×D3—361no—
540C4×D3—361no—
541C4×D3—361no—
542C4×D3—362no—
543Dic6—121no—
544C2×C32—22no—
545C2×C32C2×#23711yescharacteristic
546C2×C32D3×#4111yescharacteristic
547C2×C32#100911yescharacteristic
548C3⋊D3—62no—
549C3⋊D3—121no—
550C3×D3—41no—
551C2×C9—22no—
552C2×C9—21no—
553C2×C9—21no—
554C2×C9—21no—
555C2×C9—42no—
556C2×C9—121no—
557C2×C9#100411yescharacteristic
558C2×C9C2×#23911yescharacteristic
559C2×C9D3×#4111yescharacteristic
560D9—64no—
561D9—62no—
562D9—122no—
563D9—121no—
564C24—271no—
565C2×Q8—91no—
566C2×D4—31no—
567C2×D4—271no—
568C2×D4—271no—
569C22×C4—31no—
570C22×C4—91no—
571C22×C4—271no—
572C22×C4—271no—
573C22×C4—271no—
574C4⋊C4—31no—
575C4⋊C4—31no—
576C4⋊C4—91no—
577C4⋊C4—91no—
578C4⋊C4—91no—
579C4⋊C4—271no—
580C4⋊C4—271no—
581C4⋊C4—271no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—91no—
585C22⋊C4—271no—
586C22⋊C4—271no—
587C22⋊C4—271no—
588C22⋊C4—271no—
589C22⋊C4—271no—
590C22⋊C4—271no—
591C22⋊C4—271no—
592C22⋊C4—271no—
593C22⋊C4—271no—
594C22⋊C4—271no—
595C22⋊C4D3×D911yescharacteristic
596C42—271no—
597C42—271no—
598C42—271no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—22no—
604C22×C3—21no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—61no—
608C22×C3—61no—
609C22×C3—61no—
610C22×C3#369912yes—
611C22×C3C23×D911yescharacteristic
612C22×C3#379612yes—
613C22×C3C22×D3211yescharacteristic
614C2×D3—21no—
615C2×D3—21no—
616C2×D3—21no—
617C2×D3—92no—
618C2×D3—92no—
619C2×D3—182no—
620C2×D3—182no—
621C2×D3—182no—
622C2×D3—181no—
623C2×D3—181no—
624C2×D3—181no—
625C2×D3—181no—
626C2×D3—182no—
627C2×D3—181no—
628C2×D3—181no—
629C2×D3—181no—
630C2×D3—181no—
631C2×D3—181no—
632C2×D3—181no—
633C2×D3—361no—
634C2×D3—361no—
635C2×D3—364no—
636C2×D3—364no—
637C2×D3—368no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—181no—
648C3×C4—181no—
649C3×C4—181no—
650C3×C4—181no—
651Dic3—21no—
652Dic3—21no—
653Dic3—21no—
654Dic3—61no—
655Dic3—61no—
656Dic3—61no—
657Dic3—61no—
658Dic3—181no—
659Dic3—181no—
660Dic3—181no—
661Dic3—181no—
662Dic3—361no—
663Dic3—361no—
664C32#565811yescharacteristic
665C9—21no—
666C9#563711yescharacteristic, complemented
667C23—31no—
668C23—271no—
669C23—271no—
670C23—542no—
671C23—542no—
672C23—1081no—
673C23C2×D3×D911yescharacteristic
674Q8—361no—
675D4—62no—
676D4—542no—
677D4—1081no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—62no—
682C2×C4—91no—
683C2×C4—91no—
684C2×C4—91no—
685C2×C4—91no—
686C2×C4—271no—
687C2×C4—271no—
688C2×C4—361no—
689C2×C4—542no—
690C2×C4—1081no—
691C2×C4—1081no—
692C2×C4C2×D3×D911yescharacteristic
693C2×C4C2×D3×D911yescharacteristic
694C2×C3—22no—
695C2×C3—22no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—42no—
700C2×C3—121no—
701C2×C3C2×#369911yescharacteristic
702C2×C3#41×D911yescharacteristic
703C2×C3#6371511yescharacteristic
704C2×C3C2×#379611yescharacteristic
705C2×C3#6431211yescharacteristic
706C2×C3#6431411yescharacteristic
707D3—41no—
708D3—184no—
709D3—182no—
710D3—182no—
711D3—362no—
712D3—361no—
713D3—361no—
714C22—21no—
715C22—21no—
716C22—61no—
717C22—61no—
718C22—61no—
719C22—272no—
720C22—541no—
721C22—541no—
722C22—541no—
723C22—541no—
724C22—541no—
725C22—1084no—
726C22#8863912yes—
727C22C22×D3×D911yescharacteristic
728C4—21no—
729C4—21no—
730C4—61no—
731C4—61no—
732C4—61no—
733C4—181no—
734C4—181no—
735C4—181no—
736C4—181no—
737C4—541no—
738C4—541no—
739C3—21no—
740C3#1058976011yescharacteristic, complemented
741C3#1059416411yescharacteristic
742C2—22no—
743C2—121no—
744C2—542no—
745C2—1081no—
746C2C2×#8863911yescharacteristic
747C2#1172249811yescharacteristic
748C2#1172250111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radical#11721291C2
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. C22⋊C4×C3⋊D9C2semidirect
2. C9×#886C2semidirect
3. C3×#63440C2semidirect
5. #67×Dic9C2semidirect
6. C2×#88445C2semidirect
7. #11721244C2semidirect
8. #11721035C2semidirect
9. #11721020C2semidirect
10. #11721014C2semidirect
11. #11720957C2semidirect
12. #11720936C2semidirect
13. #11720922C2semidirect
14. #11720920C2semidirect
15. #11720920C2semidirect
24. C2×C3×Dic18C22semidirect
27. C2×D3×Dic9C22semidirect
33. C9×(C2×D3)⋊C4C22semidirect
34. C9×(C2×D3)⋊C4C22semidirect
35. C9×C4⋊Dic3C22semidirect
36. C9×C4⋊Dic3C22semidirect
37. C3×C4⋊Dic9C22semidirect
38. C3×Dic9⋊C4C22semidirect
39. C3×Dic9⋊C4C22semidirect
40. (C2×D3)⋊Dic9C22semidirect
47. Dic3⋊Dic9C22semidirect
48. Dic3⋊Dic9C22semidirect
49. Dic3⋊Dic9C22semidirect
50. Dic3×Dic9C22semidirect
51. Dic3×Dic9C22semidirect
52. Dic3×Dic9C22semidirect
83. #63440D3semidirect
160. C2×Dic18C2×D3semidirect
184. C4⋊Dic9C2×D3semidirect
185. Dic9⋊C4C2×D3semidirect
186. Dic9⋊C4C2×D3semidirect
236. #886D9semidirect
378. (C2×D3)⋊C4C2×D9semidirect
379. (C2×D3)⋊C4C2×D9semidirect
384. C4⋊Dic3C2×D9semidirect
385. C4⋊Dic3C2×D9semidirect
477. C3×C9#551semidirect
666. C9#5637semidirect
740. C3#10589760semidirect

Maximal subgroups

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

subgroupindex
C22⋊C4×C3⋊D92
C9×#8862
C3×#634402
#117212912
#67×Dic92
C2×#884452
#117212442
#117210352
#117210202
#117210142
#117209572
#117209362
#117209222
#117209202
#105941643
#105897603