Finite Group Databasebeta

← #13149351

Subgroups — #13149351

Order 1728.

820 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721748C211yesmaximal, characteristic, complemented
2C9×#898C211yesmaximal, characteristic, complemented
3C3×#63456C211yesmaximal, characteristic, complemented
4#11721049C211yesmaximal, characteristic
5#11721048C211yesmaximal, characteristic, complemented
6D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#11721044C211yesmaximal, characteristic, complemented
8#11720998C211yesmaximal, characteristic, complemented
9#11720994C211yesmaximal, characteristic, complemented
10#11720991C211yesmaximal, characteristic, complemented
11#11720989C211yesmaximal, characteristic, complemented
12#11720977C211yesmaximal, characteristic, complemented
13#11720966C211yesmaximal, characteristic, complemented
14#11720943C211yesmaximal, characteristic, complemented
15#11720941C211yesmaximal, characteristic, complemented
16#10594648—31nomaximal
17#10589807—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C3×D36C2211yescharacteristic
21C2×C3×C4×D9C2211yescharacteristic
22C2×#6194C2211yescharacteristic
23C2×#6192C2211yescharacteristic
24C2×(C3⋊D9)⋊C4C2211yescharacteristic
25C2×Dic3×D9C2211yescharacteristic
26C2×Dic3×D9C2211yescharacteristic, complemented
27C2×#6189C2211yescharacteristic, complemented
28C3×C9×C4⋊C4C2211yescharacteristic, complemented
29#88536C2211yescharacteristic
30#88536C2211yescharacteristic
31C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
32C4×C3⋊Dic9C2211yescharacteristic, complemented
33C4×C3⋊Dic9C2211yescharacteristic, complemented
34C9×(C2×D3)⋊C4C2211yescharacteristic
35C9×(C2×D3)⋊C4C2211yescharacteristic
36C9×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
39C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
40C9×C4⋊Dic3C2211yescharacteristic, complemented
41C9×Dic3⋊C4C2211yescharacteristic, complemented
42C4×C9×Dic3C2211yescharacteristic, complemented
43C3×Dic9⋊C4C2211yescharacteristic, complemented
44(C2×D3)⋊Dic9C2211yescharacteristic
45(C2×D3)⋊Dic9C2211yescharacteristic
46#88445C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53#64101—31no—
54C3×#898D311yescharacteristic
55C3×#894—31no—
56#63922—31no—
57#63921—31no—
58D3×(C2×D3)⋊C4—31no—
59#63915—31no—
60#63898—31no—
61#63895—31no—
62#63893—31no—
63#63891—31no—
64#63880—31no—
65#63862—31no—
66#63855—31no—
67#63853—31no—
68C9×#126—31no—
69#63459—31no—
70#63458—31no—
71#63456—31no—
72#63456D311yescharacteristic, complemented
73#63455—31no—
74#63454—31no—
75#63454—61no—
76#63447—31no—
77#63445—31no—
78#63444—31no—
79C22⋊C4×D9—31no—
80C22⋊C4×D9—31no—
81#63441—31no—
82C4×D36—31no—
83#63434—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×D3×D9—22no—
89C2×D3×D9—22no—
90C2×D3×D9—41no—
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C4×C3⋊D9—22no—
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C3×D36—22no—
104C3×C4×D9—22no—
105#6194—41no—
106#6192—22no—
107(C3⋊D9)⋊C4—41no—
108Dic3×D9—41no—
109Dic3×D9—41no—
110#6189—41no—
111#5705—91no—
112#5658—91no—
113C22×D32—31no—
114C2×C4×C3⋊D3—31no—
115C2×C3×D12—31no—
116C2×C3×C4×D3—31no—
117C2×#627—31no—
118C2×#626—31no—
119C2×#625—31no—
120C2×#624—31no—
121C2×D3×Dic3—31no—
122C2×D3×Dic3—31no—
123C23×D9—31no—
124C32×C4⋊C4C2×D311yescharacteristic
125#3752—31no—
126#3752—31no—
127C4⋊(C3⋊Dic3)—31no—
128C4×C3⋊Dic3—31no—
129C4×C3⋊Dic3—31no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4—31no—
133C3×(C2×D3)⋊C4C2×D311yescharacteristic
134C3×(C2×D3)⋊C4C2×D311yescharacteristic
135C3×(C2×D3)⋊C4C2×D311yescharacteristic
136C3×C4⋊Dic3C2×D311yescharacteristic
137C3×Dic3⋊C4—31no—
138C3×Dic3⋊C4C2×D311yescharacteristic
139C3×C4×Dic3C2×D311yescharacteristic
140Dic3⋊Dic3—31no—
141Dic3⋊Dic3—31no—
142Dic3⋊Dic3—31no—
143#3722—31no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149C2×#611—31no—
150C2×D36—31no—
151C2×D36C2×D311yescharacteristic
152C2×C4×D9—31no—
153C2×C4×D9—31no—
154C2×C4×D9—31no—
155C2×C4×D9—31no—
156C2×C4×D9—61no—
157C2×C4×D9C2×D311yescharacteristic
158C2×Dic18—31no—
159C9×C4⋊C4—21no—
160C9×C4⋊C4—31no—
161C9×C4⋊C4—31no—
162C9×C4⋊C4C2×D311yescharacteristic, complemented
163C9×C22⋊C4—31no—
164C9×C22⋊C4—31no—
165C9×C22⋊C4—31no—
166C42×C9—31no—
167#3676—31no—
168#3676—31no—
169(C2×D9)⋊C4—31no—
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—61no—
176(C2×D9)⋊C4—61no—
177(C2×D9)⋊C4C2×D311yescharacteristic
178(C2×D9)⋊C4C2×D311yescharacteristic, complemented
179(C2×D9)⋊C4C2×D311yescharacteristic, complemented
180C4⋊Dic9—31no—
181C4⋊Dic9—31no—
182C4⋊Dic9—61no—
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4C2×D311yescharacteristic, complemented
186C4×Dic9—31no—
187C4×Dic9—31no—
188C4×Dic9—61no—
189C4×Dic9—61no—
190C22×C3×C9C2411yescharacteristic
191C2×C3⋊D9—21no—
192C2×C3⋊D9—21no—
193C2×C3⋊D9#4112yes—
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#4112yes—
203D3×D9—44no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3×C4×C9—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×#126—31no—
216C3×#123—91no—
217#937—91no—
218D4×Dic3—91no—
219C2×(C2×D3)⋊C4—91no—
220#926—91no—
221#898—91no—
222#898D911yescharacteristic, complemented
223#897—91no—
224#897—91no—
225#896—91no—
226#894—31no—
227#894—91no—
228#893—91no—
229#892—91no—
230#892—91no—
231#892—181no—
232#886—91no—
233#885—91no—
234#885—91no—
235#883—91no—
236#883—91no—
237#882—91no—
238#67⋊C4—91no—
239D3×C22⋊C4—91no—
240D3×C22⋊C4—91no—
241D3×C22⋊C4—91no—
242#879—91no—
243#878—91no—
244C4×D12—91no—
245#872—91no—
246C22×C3⋊D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3C22×D311yescharacteristic
250C2×D32—62no—
251C2×D32—62no—
252C2×D32—121no—
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C4×C3⋊D3—62no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3C22×D311yescharacteristic
263C2×C3×Dic3C22×D311yescharacteristic
264C2×C3×Dic3C22×D311yescharacteristic
265C3×D12—62no—
266C3×C4×D3—62no—
267#627—121no—
268#626—62no—
269#625—121no—
270#624—121no—
271D3×Dic3—121no—
272D3×Dic3—121no—
273C23×C9—31no—
274C22×D9—31no—
275C22×D9—61no—
276C22×D9—62no—
277C22×D9—62no—
278C22×D9—121no—
279C22×D9C22×D311yescharacteristic
280C22×D9C22×D311yescharacteristic
281C2×C4×C9—21no—
282C2×C4×C9—21no—
283C2×C4×C9—21no—
284C2×C4×C9—31no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9C22×D311yescharacteristic
288C2×C4×C9C22×D311yescharacteristic
289C2×C4×C9C22×D311yescharacteristic
290#611—121no—
291C2×Dic9—31no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—61no—
295C2×Dic9—61no—
296C2×Dic9—61no—
297C2×Dic9C22×D311yescharacteristic
298C2×Dic9C22×D311yescharacteristic
299D36—22no—
300D36—62no—
301C4×D9—22no—
302C4×D9—62no—
303C4×D9—64no—
304C4×D9—121no—
305C4×D9—121no—
306C4×D9—121no—
307Dic18—121no—
308#551—271noSylow
309C2×C3×C9C2×#4111yescharacteristic
310C2×C3×C9C2×#4111yescharacteristic
311C2×C3×C9H(5,𝔽2)11yescharacteristic
312C3⋊D9—22no—
313D3×C9—41no—
314C3×D9—22no—
315C3×D9—41no—
316C23×D3—91no—
317C23×D3—91no—
318C2×C3×D4—91no—
319C22×C3×C4—91no—
320C2×#67—91no—
321C2×#67—91no—
322C2×#67—91no—
323C22×Dic3—91no—
324C22×Dic3—91no—
325C2×D12—31no—
326C2×D12—91no—
327C2×C4×D3—31no—
328C2×C4×D3—91no—
329C2×C4×D3—91no—
330C2×C4×D3—91no—
331C2×C4×D3—91no—
332C2×C4×D3—91no—
333C2×C4×D3—91no—
334C2×C4×D3—181no—
335C2×Dic6—91no—
336C2×Dic6—91no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—91no—
341C3×C4⋊C4C2×D911yescharacteristic, complemented
342C3×C4⋊C4D3211yescharacteristic
343C3×C22⋊C4—31no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4—91no—
349C3×C42—31no—
350#217—91no—
351#217—91no—
352#217—91no—
353#217—91no—
354#217—91no—
355(C2×D3)⋊C4—31no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—91no—
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—181no—
370(C2×D3)⋊C4—181no—
371(C2×D3)⋊C4C2×D911yescharacteristic
372(C2×D3)⋊C4C2×D911yescharacteristic
373(C2×D3)⋊C4C2×D911yescharacteristic
374C4⋊Dic3—91no—
375C4⋊Dic3—91no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—181no—
380C4⋊Dic3C2×D911yescharacteristic, complemented
381Dic3⋊C4—31no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4C2×D911yescharacteristic, complemented
386C4×Dic3—91no—
387C4×Dic3—91no—
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—181no—
391C4×Dic3—181no—
392C4×Dic3C2×D911yescharacteristic, complemented
393C22×C32C23×D311yescharacteristic
394C2×C3⋊D3—32no—
395C2×C3⋊D3—61no—
396C2×C3⋊D3—61no—
397C2×C3×D3—21no—
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—32no—
401C2×C3×D3—61no—
402C2×C3×D3—61no—
403C2×C3×D3—61no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406D32—124no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—21no—
410C3⋊Dic3—61no—
411C3⋊Dic3—61no—
412C3⋊Dic3—61no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C22×C9—21no—
419C22×C9—61no—
420C22×C9—61no—
421C22×C9—61no—
422C22×C9C23×D311yescharacteristic
423C2×D9—21no—
424C2×D9—21no—
425C2×D9—21no—
426C2×D9—21no—
427C2×D9—21no—
428C2×D9—32no—
429C2×D9—62no—
430C2×D9—61no—
431C2×D9—61no—
432C2×D9—121no—
433C2×D9—121no—
434C2×D9—124no—
435C2×D9#23712yes—
436C4×C9—22no—
437C4×C9—21no—
438C4×C9—21no—
439C4×C9—21no—
440C4×C9—41no—
441C4×C9—41no—
442C4×C9—61no—
443C4×C9—61no—
444C4×C9—61no—
445Dic9—21no—
446Dic9—21no—
447Dic9—62no—
448Dic9—61no—
449Dic9—61no—
450Dic9—61no—
451Dic9—121no—
452Dic9—121no—
453#126—31no—
454#126—271no—
455#124—271no—
456#123—91no—
457#123—271no—
458#123—271no—
459C22⋊Q8—271no—
460C22⋊Q8—271no—
461#120—271no—
462C4×D4—271no—
463C4×D4—271no—
464#117—271no—
465#117—271no—
466C2×C22⋊C4—271no—
467C2×C22⋊C4—271no—
468C3×C9#55111yescharacteristic, complemented, Sylow
469C23×C3—31no—
470C23×C3—91no—
471C23×C3—91no—
472C22×D3—31no—
473C22×D3—31no—
474C22×D3—91no—
475C22×D3—91no—
476C22×D3—181no—
477C22×D3—182no—
478C22×D3—182no—
479C22×D3—182no—
480C22×D3—182no—
481C22×D3—361no—
482C22×D3—361no—
483C22×D3C22×D911yescharacteristic
484C3×D4—182no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—182no—
494C2×C3×C4C22×D911yescharacteristic
495C2×C3×C4C22×D911yescharacteristic
496C2×C3×C4C22×D911yescharacteristic
497C2×C3×C4C2×D3211yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499C2×C3×C4C2×D3211yescharacteristic
500#67—182no—
501#67—361no—
502#67—361no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—91no—
506C2×Dic3—91no—
507C2×Dic3—91no—
508C2×Dic3—91no—
509C2×Dic3—91no—
510C2×Dic3—91no—
511C2×Dic3—181no—
512C2×Dic3—181no—
513C2×Dic3—181no—
514C2×Dic3—361no—
515C2×Dic3—361no—
516C2×Dic3C22×D911yescharacteristic
517C2×Dic3C22×D911yescharacteristic
518C2×Dic3C22×D911yescharacteristic
519D12—62no—
520D12—182no—
521C4×D3—62no—
522C4×D3—182no—
523C4×D3—182no—
524C4×D3—184no—
525C4×D3—361no—
526C4×D3—361no—
527C4×D3—361no—
528C4×D3—361no—
529Dic6—361no—
530Dic6—361no—
531C2×C32D3×#4111yescharacteristic
532C2×C32D3×#4111yescharacteristic
533C2×C32#100911yescharacteristic
534C3⋊D3—62no—
535C3×D3—41no—
536C3×D3—62no—
537C3×D3—121no—
538C2×C9—21no—
539C2×C9—21no—
540C2×C9—21no—
541C2×C9—121no—
542C2×C9C2×#23711yescharacteristic
543C2×C9D3×#4111yescharacteristic
544C2×C9#100911yescharacteristic
545D9—22no—
546D9—41no—
547D9—62no—
548D9—122no—
549C24—271no—
550C2×Q8—271no—
551C2×D4—91no—
552C2×D4—271no—
553C2×D4—271no—
554C22×C4—91no—
555C22×C4—271no—
556C22×C4—271no—
557C22×C4—271no—
558C22×C4—271no—
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—91no—
562C4⋊C4—271no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4D3×D911yescharacteristic, complemented
567C22⋊C4—31no—
568C22⋊C4—31no—
569C22⋊C4—31no—
570C22⋊C4—91no—
571C22⋊C4—91no—
572C22⋊C4—91no—
573C22⋊C4—271no—
574C22⋊C4—271no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C42—31no—
582C42—271no—
583C42—271no—
584C22×C3—21no—
585C22×C3—61no—
586C22×C3—61no—
587C22×C3—61no—
588C22×C3—92no—
589C22×C3—181no—
590C22×C3—181no—
591C22×C3—181no—
592C22×C3—181no—
593C22×C3—181no—
594C22×C3C23×D911yescharacteristic
595C22×C3C22×D3211yescharacteristic
596C2×D3—21no—
597C2×D3—21no—
598C2×D3—21no—
599C2×D3—32no—
600C2×D3—61no—
601C2×D3—61no—
602C2×D3—61no—
603C2×D3—61no—
604C2×D3—61no—
605C2×D3—92no—
606C2×D3—92no—
607C2×D3—182no—
608C2×D3—181no—
609C2×D3—181no—
610C2×D3—181no—
611C2×D3—181no—
612C2×D3—361no—
613C2×D3—361no—
614C2×D3—364no—
615C2×D3—364no—
616C3×C4—22no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—61no—
626C3×C4—61no—
627C3×C4—61no—
628C3×C4—181no—
629C3×C4—181no—
630Dic3—21no—
631Dic3—21no—
632Dic3—21no—
633Dic3—61no—
634Dic3—61no—
635Dic3—182no—
636Dic3—181no—
637Dic3—181no—
638Dic3—181no—
639Dic3—181no—
640Dic3—181no—
641Dic3—181no—
642Dic3—361no—
643Dic3—361no—
644C32#570511yescharacteristic
645C9—21no—
646C9#565811yescharacteristic, complemented
647C23—31no—
648C23—91no—
649C23—91no—
650C23—271no—
651C23—542no—
652C23—542no—
653C23—1081no—
654Q8—1081no—
655D4—182no—
656D4—542no—
657D4—1081no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—91no—
662C2×C4—91no—
663C2×C4—182no—
664C2×C4—271no—
665C2×C4—271no—
666C2×C4—271no—
667C2×C4—542no—
668C2×C4—1081no—
669C2×C4—1081no—
670C2×C4—1081no—
671C2×C4C2×D3×D911yescharacteristic
672C2×C4C2×D3×D911yescharacteristic
673C2×C4C2×D3×D911yescharacteristic
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—121no—
678C2×C3—182no—
679C2×C3—361no—
680C2×C3#41×D911yescharacteristic
681C2×C3#41×D911yescharacteristic
682C2×C3#6371511yescharacteristic
683C2×C3#6430611yescharacteristic
684C2×C3D3×#23711yescharacteristic
685C2×C3#6432011yescharacteristic
686D3—41no—
687D3—62no—
688D3—121no—
689D3—182no—
690D3—182no—
691D3—362no—
692C22—61no—
693C22—61no—
694C22—61no—
695C22—92no—
696C22—181no—
697C22—181no—
698C22—181no—
699C22—181no—
700C22—181no—
701C22—272no—
702C22—541no—
703C22—541no—
704C22—1084no—
705C22C22×D3×D911yescharacteristic
706C4—21no—
707C4—21no—
708C4—21no—
709C4—61no—
710C4—61no—
711C4—61no—
712C4—181no—
713C4—181no—
714C4—541no—
715C4—541no—
716C4—541no—
717C3—21no—
718C3#1058980711yescharacteristic, complemented
719C3#1059464811yescharacteristic
720C2—121no—
721C2—182no—
722C2—361no—
723C2—542no—
724C2#1172247511yescharacteristic
725C2D9×#23711yescharacteristic
726C2#1172251511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radical#11721049C2
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#551
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721748C2semidirect
2. C9×#898C2semidirect
3. C3×#63456C2semidirect
5. #11721048C2semidirect
6. D9×(C2×D3)⋊C4C2semidirect
7. #11721044C2semidirect
8. #11720998C2semidirect
9. #11720994C2semidirect
10. #11720991C2semidirect
11. #11720989C2semidirect
12. #11720977C2semidirect
13. #11720966C2semidirect
14. #11720943C2semidirect
15. #11720941C2semidirect
26. C2×Dic3×D9C22semidirect
27. C2×#6189C22semidirect
28. C3×C9×C4⋊C4C22semidirect
31. C4⋊(C3⋊Dic9)C22semidirect
32. C4×C3⋊Dic9C22semidirect
33. C4×C3⋊Dic9C22semidirect
38. C3×(C2×D9)⋊C4C22semidirect
39. C3×(C2×D9)⋊C4C22semidirect
40. C9×C4⋊Dic3C22semidirect
41. C9×Dic3⋊C4C22semidirect
42. C4×C9×Dic3C22semidirect
43. C3×Dic9⋊C4C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. Dic3⋊Dic9C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic9⋊Dic3C22semidirect
72. #63456D3semidirect
162. C9×C4⋊C4C2×D3semidirect
178. (C2×D9)⋊C4C2×D3semidirect
179. (C2×D9)⋊C4C2×D3semidirect
185. Dic9⋊C4C2×D3semidirect
222. #898D9semidirect
341. C3×C4⋊C4C2×D9semidirect
380. C4⋊Dic3C2×D9semidirect
385. Dic3⋊C4C2×D9semidirect
392. C4×Dic3C2×D9semidirect
468. C3×C9#551semidirect
566. C4⋊C4D3×D9semidirect
646. C9#5658semidirect
718. C3#10589807semidirect

Maximal subgroups

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

subgroupindex
#117217482
C9×#8982
C3×#634562
#117210492
#117210482
D9×(C2×D3)⋊C42
#117210442
#117209982
#117209942
#117209912
#117209892
#117209772
#117209662
#117209432
#117209412
#105946483
#105898073