Finite Group Databasebeta

← #13151166

Subgroups — #13151166

Order 1728.

838 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C3⋊Dic9C211yesmaximal, characteristic, complemented
2C9×#937C211yesmaximal, characteristic
3C3×#63497C211yesmaximal, characteristic, complemented
4#67⋊Dic9C211yesmaximal, characteristic, complemented
5#11721280C211yesmaximal, characteristic, complemented
6D3×#3676C211yesmaximal, characteristic, complemented
7#11721267C211yesmaximal, characteristic, complemented
8#11721266C211yesmaximal, characteristic, complemented
9C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
10#11721263C211yesmaximal, characteristic, complemented
11#11721245C211yesmaximal, characteristic, complemented
12#11721023C211yesmaximal, characteristic, complemented
13#11721011C211yesmaximal, characteristic, complemented
14#11720966C211yesmaximal, characteristic, complemented
15#11720965C211yesmaximal, characteristic, complemented
16#10595177—31nomaximal
17#10589689—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C22×C3⋊Dic9C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic
24C22×C3×Dic9C2211yescharacteristic
25C2×D3×Dic9C2211yescharacteristic
26C2×D3×Dic9C2211yescharacteristic
27C2×#6189C2211yescharacteristic, complemented
28#88551C2211yescharacteristic
29#88551C2211yescharacteristic, complemented
30C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
31C4×C3⋊Dic9C2211yescharacteristic, complemented
32C9×#217C2211yescharacteristic
33C3×#3676C2211yescharacteristic
34C3×#3676C2211yescharacteristic, complemented
35C3×#3676C2211yescharacteristic, complemented
36C9×(C2×D3)⋊C4C2211yescharacteristic
37C9×(C2×D3)⋊C4C2211yescharacteristic
38C3×Dic9⋊C4C2211yescharacteristic, complemented
39C3×Dic9⋊C4C2211yescharacteristic, complemented
40(C2×D3)⋊Dic9C2211yescharacteristic
41(C2×D3)⋊Dic9C2211yescharacteristic
42(C2×D3)⋊Dic9C2211yescharacteristic
43(C2×D3)⋊Dic9C2211yescharacteristic
44(C2×D3)⋊Dic9C2211yescharacteristic
45(C2×D3)⋊Dic9C2211yescharacteristic
46Dic3⋊Dic9C2211yescharacteristic, complemented
47#88442C2211yescharacteristic, complemented
48Dic9⋊Dic3C2211yescharacteristic, complemented
49Dic9⋊Dic3C2211yescharacteristic, complemented
50Dic9⋊Dic3C2211yescharacteristic, complemented
51Dic3×Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53D4×C3⋊Dic3—31no—
54C3×#937D311yescharacteristic
55C3×#935—31no—
56#63982—31no—
57#67⋊Dic3—31no—
58#63969—31no—
59D3×#217—31no—
60#63962—31no—
61C2×(C2×D3)⋊Dic3—31no—
62#63959—31no—
63#63955—31no—
64#63893—31no—
65#63878—31no—
66#63862—31no—
67#63861—31no—
68C9×#120—31no—
69C2×#3676—31no—
70C2×#3676—31no—
71#63498—31no—
72#63497—31no—
73#63497—31no—
74#63497D311yescharacteristic, complemented
75D4×Dic9—31no—
76D4×Dic9—31no—
77D4×Dic9—61no—
78#63441—31no—
79#63441—31no—
80#63440—31no—
81#63440—31no—
82#63439—31no—
83#63439—31no—
84C23×C3×C9C2311yescharacteristic
85C23×C3×C9C2311yescharacteristic
86C22×D3×C9—22no—
87C22×D3×C9—22no—
88C22×D3×C9—41no—
89C22×D3×C9C2311yescharacteristic
90C22×D3×C9C2311yescharacteristic
91C3×D4×C9—22no—
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9—41no—
94C2×C3⋊Dic9—41no—
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C9×#67—22no—
100C9×#67—41no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9—22no—
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108D3×Dic9—22no—
109D3×Dic9—41no—
110#6189—41no—
111#5658—91no—
112#5587—91no—
113C23×C3×D3C2×D311yescharacteristic
114C2×C32×D4C2×D311yescharacteristic
115C22×C3⋊Dic3—31no—
116C22×C3⋊Dic3—31no—
117C2×C3×#67C2×D311yescharacteristic
118C2×C3×#67C2×D311yescharacteristic
119C22×C3×Dic3—31no—
120C2×#627—31no—
121C2×D3×Dic3—31no—
122C2×D3×Dic3—31no—
123C24×C9—31no—
124#3757—31no—
125#3757—31no—
126C4⋊(C3⋊Dic3)—31no—
127C4×C3⋊Dic3—31no—
128C3×#217—31no—
129C3×#217—31no—
130C3×#217—31no—
131C3×#217C2×D311yescharacteristic
132C3×(C2×D3)⋊C4C2×D311yescharacteristic
133C3×(C2×D3)⋊C4C2×D311yescharacteristic
134C3×Dic3⋊C4—31no—
135C3×Dic3⋊C4—31no—
136#3724—31no—
137Dic3⋊Dic3—31no—
138Dic3⋊Dic3—31no—
139Dic3⋊Dic3—31no—
140Dic3⋊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—
146(C2×D3)⋊Dic3—31no—
147Dic32—31no—
148Dic32—31no—
149C2×D4×C9—21no—
150C2×D4×C9—31no—
151C2×D4×C9—31no—
152C2×D4×C9C2×D311yescharacteristic
153C22×Dic9—31no—
154C22×Dic9—31no—
155C22×Dic9—31no—
156C22×Dic9—31no—
157C22×Dic9—61no—
158C22×Dic9—61no—
159C22×Dic9C2×D311yescharacteristic
160C2×Dic18—31no—
161C9×C22⋊C4—31no—
162C9×C22⋊C4—31no—
163C9×C22⋊C4—31no—
164#3676—31no—
165#3676—31no—
166#3676—31no—
167#3676—31no—
168#3676—31no—
169#3676—31no—
170#3676—31no—
171#3676—31no—
172#3676—61no—
173#3676—61no—
174#3676C2×D311yescharacteristic
175#3676C2×D311yescharacteristic, complemented
176#3676C2×D311yescharacteristic, complemented
177C4⋊Dic9—31no—
178C4⋊Dic9—31no—
179C4⋊Dic9—61no—
180Dic9⋊C4—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4C2×D311yescharacteristic, complemented
185Dic9⋊C4C2×D311yescharacteristic, complemented
186C4×Dic9—31no—
187C4×Dic9—31no—
188C4×Dic9—31no—
189C4×Dic9—61no—
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9—21no—
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9#4112yes—
196C22×C3×C9C2411yescharacteristic
197C2×D3×C9—21no—
198C2×D3×C9—21no—
199C2×D3×C9—21no—
200C2×D3×C9—21no—
201C2×D3×C9—21no—
202C2×D3×C9—44no—
203C2×D3×C9#4112yes—
204C3×C4×C9—21no—
205C3⋊Dic9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9—21no—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C3×Dic9—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×#123—91no—
216C3×#120—31no—
217C2×#217—91no—
218C2×#217—91no—
219#937D911yescharacteristic
220#936—91no—
221#935—31no—
222#935—91no—
223#935—91no—
224D4×Dic3—91no—
225D4×Dic3—91no—
226D4×Dic3—91no—
227D4×Dic3—181no—
228C2×(C2×D3)⋊C4—91no—
229#926—91no—
230#898—91no—
231#898—91no—
232#897—91no—
233#892—91no—
234#886—91no—
235#885—91no—
236#883—91no—
237#67⋊C4—91no—
238D3×C22⋊C4—91no—
239#879—91no—
240#879—91no—
241#878—91no—
242#878—91no—
243#878—91no—
244#877—91no—
245#877—91no—
246C23×C32C22×D311yescharacteristic
247C23×C32C22×D311yescharacteristic
248C22×C3×D3—22no—
249C22×C3×D3—22no—
250C22×C3×D3—41no—
251C22×C3×D3C22×D311yescharacteristic
252C22×C3×D3C22×D311yescharacteristic
253C32×D4—22no—
254C2×C32×C4C22×D311yescharacteristic
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—121no—
260C2×C3⋊Dic3—121no—
261C3×#67—22no—
262C3×#67—41no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—62no—
268C2×C3×Dic3C22×D311yescharacteristic
269C2×C3×Dic3C22×D311yescharacteristic
270#627—121no—
271D3×Dic3—62no—
272D3×Dic3—121no—
273C23×C9—21no—
274C23×C9—21no—
275C23×C9—31no—
276C23×C9—31no—
277C23×C9—62no—
278C23×C9—62no—
279C23×C9—121no—
280C23×C9C22×D311yescharacteristic
281C23×C9C22×D311yescharacteristic
282D4×C9—24no—
283D4×C9—22no—
284D4×C9—62no—
285D4×C9—121no—
286C2×C4×C9—21no—
287C2×C4×C9—31no—
288C2×C4×C9—31no—
289C2×C4×C9C22×D311yescharacteristic
290C2×Dic9—22no—
291C2×Dic9—31no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—31no—
295C2×Dic9—61no—
296C2×Dic9—61no—
297C2×Dic9—61no—
298C2×Dic9—61no—
299C2×Dic9—62no—
300C2×Dic9—121no—
301C2×Dic9—121no—
302C2×Dic9—121no—
303C2×Dic9—122no—
304C2×Dic9—122no—
305C2×Dic9C22×D311yescharacteristic
306C2×Dic9C22×D311yescharacteristic
307C2×Dic9C22×D311yescharacteristic
308C2×Dic9C22×D311yescharacteristic
309Dic18—121no—
310#551—271noSylow
311C2×C3×C9—22no—
312C2×C3×C9—41no—
313C2×C3×C9C2×#4111yescharacteristic
314C2×C3×C9C2×#4111yescharacteristic
315C2×C3×C9H(5,𝔽2)11yescharacteristic
316D3×C9—22no—
317D3×C9—41no—
318C24×C3—31no—
319C23×D3C2×D911yescharacteristic
320C2×C3×D4—21no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4C2×D911yescharacteristic
324C2×C3×D4D3211yescharacteristic
325C22×C3×C4—91no—
326C2×#67C2×D911yescharacteristic
327C2×#67C2×D911yescharacteristic
328C22×Dic3—31no—
329C22×Dic3—91no—
330C22×Dic3—91no—
331C22×Dic3—91no—
332C22×Dic3—91no—
333C22×Dic3—91no—
334C22×Dic3—91no—
335C22×Dic3—181no—
336C22×Dic3—181no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×Dic6—91no—
340C2×Dic6—91no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4—91no—
349#217—31no—
350#217—31no—
351#217—31no—
352#217—91no—
353#217—91no—
354#217—91no—
355#217—91no—
356#217—91no—
357#217—91no—
358#217—91no—
359#217—91no—
360#217—91no—
361#217—91no—
362#217—181no—
363#217—181no—
364#217C2×D911yescharacteristic
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)⋊C4C2×D911yescharacteristic
372(C2×D3)⋊C4C2×D911yescharacteristic
373C4⋊Dic3—91no—
374C4⋊Dic3—91no—
375C4⋊Dic3—91no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—181no—
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3—181no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32#23712yes—
401C22×C32C23×D311yescharacteristic
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—44no—
408C2×C3×D3#23712yes—
409C32×C4—21no—
410C3⋊Dic3—61no—
411C3⋊Dic3—61no—
412C3⋊Dic3—61no—
413C3⋊Dic3—61no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C3×Dic3—61no—
420C22×C9—21no—
421C22×C9—21no—
422C22×C9—22no—
423C22×C9—21no—
424C22×C9—21no—
425C22×C9—21no—
426C22×C9—21no—
427C22×C9—22no—
428C22×C9—32no—
429C22×C9—41no—
430C22×C9—41no—
431C22×C9—41no—
432C22×C9—41no—
433C22×C9—61no—
434C22×C9—61no—
435C22×C9—61no—
436C22×C9—61no—
437C22×C9—61no—
438C22×C9—124no—
439C22×C9#23712yes—
440C22×C9C23×D311yescharacteristic
441C4×C9—22no—
442C4×C9—21no—
443C4×C9—61no—
444C4×C9—61no—
445Dic9—21no—
446Dic9—21no—
447Dic9—21no—
448Dic9—21no—
449Dic9—62no—
450Dic9—61no—
451Dic9—61no—
452Dic9—61no—
453Dic9—61no—
454Dic9—121no—
455Dic9—121no—
456Dic9—121no—
457#126—271no—
458#126—271no—
459#124—271no—
460#123—91no—
461#123—271no—
462#123—271no—
463C22⋊Q8—271no—
464C22⋊Q8—271no—
465#120—31no—
466C4×D4—271no—
467C4×D4—271no—
468#117—271no—
469#117—271no—
470C2×C22⋊C4—271no—
471C2×C22⋊C4—271no—
472C3×C9#55111yescharacteristic, complemented, Sylow
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3—31no—
477C23×C3—62no—
478C23×C3—62no—
479C23×C3—121no—
480C23×C3C22×D911yescharacteristic
481C23×C3C22×D911yescharacteristic
482C23×C3C2×D3211yescharacteristic
483C23×C3C2×D3211yescharacteristic
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—41no—
487C22×D3C22×D911yescharacteristic
488C22×D3C22×D911yescharacteristic
489C3×D4—24no—
490C3×D4—22no—
491C3×D4—22no—
492C3×D4—62no—
493C3×D4—121no—
494C2×C3×C4—21no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—91no—
498C2×C3×C4—91no—
499C2×C3×C4—91no—
500C2×C3×C4—91no—
501C2×C3×C4—182no—
502C2×C3×C4C22×D911yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504#67—22no—
505#67—41no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—62no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—91no—
515C2×Dic3—91no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—91no—
519C2×Dic3—181no—
520C2×Dic3—181no—
521C2×Dic3—181no—
522C2×Dic3—181no—
523C2×Dic3—182no—
524C2×Dic3—361no—
525C2×Dic3—361no—
526C2×Dic3—361no—
527C2×Dic3—361no—
528C2×Dic3—361no—
529C2×Dic3—362no—
530C2×Dic3—362no—
531C2×Dic3C22×D911yescharacteristic
532C2×Dic3C22×D911yescharacteristic
533C4×D3—182no—
534C4×D3—361no—
535Dic6—361no—
536Dic6—361no—
537C2×C32—22no—
538C2×C32—41no—
539C2×C32C2×#23711yescharacteristic
540C2×C32C2×#23711yescharacteristic
541C2×C32#100411yescharacteristic
542C3×D3—22no—
543C3×D3—41no—
544C2×C9—22no—
545C2×C9—21no—
546C2×C9—21no—
547C2×C9—21no—
548C2×C9—42no—
549C2×C9—42no—
550C2×C9—41no—
551C2×C9—62no—
552C2×C9—121no—
553C2×C9C2×#23711yescharacteristic
554C2×C9D3×#4111yescharacteristic
555C2×C9#100911yescharacteristic
556C24—31no—
557C2×Q8—271no—
558C2×D4—31no—
559C2×D4—31no—
560C2×D4D3×D911yescharacteristic
561C22×C4—91no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4—271no—
565C22×C4—271no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C22⋊C4—31no—
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—91no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4—271no—
586C22⋊C4—271no—
587C22⋊C4—271no—
588C42—271no—
589C42—271no—
590C42—271no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—22no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—22no—
604C22×C3—32no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—61no—
610C22×C3—61no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—124no—
615C22×C3#369912yes—
616C22×C3C23×D911yescharacteristic
617C22×C3#380512yes—
618C22×C3C22×D3211yescharacteristic
619C2×D3—21no—
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—44no—
625C2×D3#369912yes—
626C3×C4—22no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—61no—
630C3×C4—61no—
631C3×C4—181no—
632C3×C4—181no—
633C3×C4—181no—
634C3×C4—181no—
635Dic3—21no—
636Dic3—21no—
637Dic3—61no—
638Dic3—61no—
639Dic3—61no—
640Dic3—61no—
641Dic3—182no—
642Dic3—181no—
643Dic3—181no—
644Dic3—181no—
645Dic3—181no—
646Dic3—181no—
647Dic3—181no—
648Dic3—181no—
649Dic3—181no—
650Dic3—361no—
651Dic3—361no—
652Dic3—361no—
653C32#558711yescharacteristic
654C9—21no—
655C9#565811yescharacteristic, complemented
656C23—31no—
657C23—31no—
658C23—62no—
659C23—62no—
660C23—121no—
661C23C2×D3×D911yescharacteristic
662C23C2×D3×D911yescharacteristic
663Q8—1081no—
664D4—22no—
665D4—62no—
666D4—121no—
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—91no—
673C2×C4—182no—
674C2×C4—271no—
675C2×C4—271no—
676C2×C4—271no—
677C2×C4—271no—
678C2×C4—542no—
679C2×C4—1081no—
680C2×C4—1081no—
681C2×C4—1081no—
682C2×C4C2×D3×D911yescharacteristic
683C2×C3—22no—
684C2×C3—22no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—42no—
689C2×C3—42no—
690C2×C3—41no—
691C2×C3—41no—
692C2×C3—62no—
693C2×C3—121no—
694C2×C3C2×#369911yescharacteristic
695C2×C3C2×#369911yescharacteristic
696C2×C3#6371011yescharacteristic
697C2×C3D3×#23711yescharacteristic
698C2×C3#6431411yescharacteristic
699C2×C3C2×#380511yescharacteristic
700D3—22no—
701D3—41no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—32no—
708C22—61no—
709C22—61no—
710C22—61no—
711C22—61no—
712C22—61no—
713C22—124no—
714C22#8866312yes—
715C22C22×D3×D911yescharacteristic
716C4—21no—
717C4—61no—
718C4—61no—
719C4—181no—
720C4—181no—
721C4—181no—
722C4—181no—
723C4—541no—
724C4—541no—
725C4—541no—
726C4—541no—
727C3—21no—
728C3#1058968911yescharacteristic, complemented
729C3#1059517711yescharacteristic
730C2—22no—
731C2—41no—
732C2—62no—
733C2—121no—
734C2D3×#369911yescharacteristic
735C2#1172250011yescharacteristic
736C2C2×#8866311yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
prime radicalC3×#937D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#551
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. D4×C3⋊Dic9C2semidirect
3. C3×#63497C2semidirect
4. #67⋊Dic9C2semidirect
5. #11721280C2semidirect
6. D3×#3676C2semidirect
7. #11721267C2semidirect
8. #11721266C2semidirect
9. C2×(C2×D3)⋊Dic9C2semidirect
10. #11721263C2semidirect
11. #11721245C2semidirect
12. #11721023C2semidirect
13. #11721011C2semidirect
14. #11720966C2semidirect
15. #11720965C2semidirect
21. C22×C3⋊Dic9C22semidirect
27. C2×#6189C22semidirect
29. #88551C22semidirect
30. C4⋊(C3⋊Dic9)C22semidirect
31. C4×C3⋊Dic9C22semidirect
34. C3×#3676C22semidirect
35. C3×#3676C22semidirect
38. C3×Dic9⋊C4C22semidirect
39. C3×Dic9⋊C4C22semidirect
46. Dic3⋊Dic9C22semidirect
47. #88442C22semidirect
48. Dic9⋊Dic3C22semidirect
49. Dic9⋊Dic3C22semidirect
50. Dic9⋊Dic3C22semidirect
51. Dic3×Dic9C22semidirect
52. Dic3×Dic9C22semidirect
74. #63497D3semidirect
175. #3676C2×D3semidirect
176. #3676C2×D3semidirect
184. Dic9⋊C4C2×D3semidirect
185. Dic9⋊C4C2×D3semidirect
472. C3×C9#551semidirect
655. C9#5658semidirect
728. C3#10589689semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊Dic92
C9×#9372
C3×#634972
#67⋊Dic92
#117212802
D3×#36762
#117212672
#117212662
C2×(C2×D3)⋊Dic92
#117212632
#117212452
#117210232
#117210112
#117209662
#117209652
#105951773
#105896893