Finite Group Databasebeta

← #13148236

Subgroups — #13148236

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×#882C211yesmaximal, characteristic
3C3×#63439C211yesmaximal, characteristic, complemented
4#67⋊Dic9C211yesmaximal, characteristic, complemented
5D3×#3676C211yesmaximal, characteristic, complemented
6#11721265C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
8#11721024C211yesmaximal, characteristic, complemented
9D12×Dic9C211yesmaximal, characteristic, complemented
10#11721015C211yesmaximal, characteristic, complemented
11#11721015C211yesmaximal, characteristic, complemented
12#11721010C211yesmaximal, characteristic, complemented
13#11720965C211yesmaximal, characteristic, complemented
14#11720964C211yesmaximal, characteristic, complemented
15#11720963C211yesmaximal, characteristic, complemented
16#10594117—31nomaximal
17#10589689—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×#6226C2211yescharacteristic, complemented
21C2×C9×#67C2211yescharacteristic
22C22×C3×Dic9C2211yescharacteristic
23C2×C9×D12C2211yescharacteristic
24C2×C9×D12C2211yescharacteristic
25C2×D3×Dic9C2211yescharacteristic
26C2×D3×Dic9C2211yescharacteristic
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
35C9×(C2×D3)⋊C4C2211yescharacteristic
36C3×Dic9⋊C4C2211yescharacteristic, complemented
37C3×Dic9⋊C4C2211yescharacteristic, complemented
38C3×C4×Dic9C2211yescharacteristic, complemented
39C3×C4×Dic9C2211yescharacteristic, 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
46(C2×D3)⋊Dic9C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49Dic3⋊Dic9C2211yescharacteristic, complemented
50#88442C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64087—31no—
54C3×#882D311yescharacteristic
55C3×#877—31no—
56#67⋊Dic3—31no—
57D3×#217—31no—
58#63961—31no—
59C2×(C2×D3)⋊Dic3—31no—
60#63896—31no—
61Dic3×D12—31no—
62#63884—31no—
63#63884—31no—
64#63877—31no—
65#63861—31no—
66#63860—31no—
67#63859—31no—
68C9×#120—31no—
69C2×#3676—31no—
70C2×#3676—31no—
71#63498—31no—
72#63497—31no—
73#63497—31no—
74#63497—31no—
75D4×Dic9—31no—
76D4×Dic9—31no—
77#63441—31no—
78#63441—31no—
79#63440—31no—
80#63440—31no—
81#63440—61no—
82#63439—31no—
83#63439D311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×D3×C9—22no—
86C22×D3×C9—22no—
87C22×D3×C9—41no—
88C22×D3×C9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×D3×C9C2311yescharacteristic
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×Dic3C2311yescharacteristic
101C2×C3×Dic9—22no—
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C9×D12—22no—
107C9×D12—41no—
108D3×Dic9—22no—
109D3×Dic9—41no—
110D3×Dic9—41no—
111#5587—91no—
112#5527—91no—
113C23×C3×D3C2×D311yescharacteristic
114C22×C3⋊Dic3—31no—
115C2×#634—31no—
116C2×C3×#67C2×D311yescharacteristic
117C22×C3×Dic3—31no—
118C2×C3×D12C2×D311yescharacteristic
119C2×C3×D12C2×D311yescharacteristic
120C2×D3×Dic3—31no—
121C2×D3×Dic3—31no—
122C2×D3×Dic3—31no—
123C24×C9—31no—
124C32×C22⋊C4C2×D311yescharacteristic
125#3757—31no—
126C4⋊(C3⋊Dic3)—31no—
127#3750—31no—
128#3750—31no—
129C3×#217—31no—
130C3×(C2×D3)⋊C4C2×D311yescharacteristic
131C3×(C2×D3)⋊C4C2×D311yescharacteristic
132C3×Dic3⋊C4—31no—
133C3×Dic3⋊C4—31no—
134C3×C4×Dic3—31no—
135C3×C4×Dic3—31no—
136#3724—31no—
137#3724—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—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148Dic32—31no—
149C2×D4×C9—31no—
150C2×D4×C9—31no—
151C2×D4×C9—31no—
152C22×Dic9—31no—
153C22×Dic9—31no—
154C22×Dic9—31no—
155C22×Dic9—31no—
156C22×Dic9—61no—
157C22×Dic9C2×D311yescharacteristic
158C2×Dic18—31no—
159C2×Dic18—61no—
160C9×C22⋊C4—21no—
161C9×C22⋊C4—31no—
162C9×C22⋊C4—31no—
163C9×C22⋊C4C2×D311yescharacteristic
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—31no—
173#3676—31no—
174#3676—61no—
175#3676C2×D311yescharacteristic
176C4⋊Dic9—31no—
177C4⋊Dic9—31no—
178C4⋊Dic9—61no—
179Dic9⋊C4—31no—
180Dic9⋊C4—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—61no—
184Dic9⋊C4—61no—
185Dic9⋊C4C2×D311yescharacteristic, complemented
186Dic9⋊C4C2×D311yescharacteristic, complemented
187C4×Dic9—31no—
188C4×Dic9C2×D311yescharacteristic, complemented
189C4×Dic9C2×D311yescharacteristic, complemented
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×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×C4×C9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9—21no—
209C3⋊Dic9—21no—
210C9×Dic3—21no—
211C3×Dic9—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×#120—31no—
216C3×#117—91no—
217C2×#217—91no—
218C2×#217—91no—
219#936—91no—
220#935—91no—
221#935—91no—
222#935—91no—
223D4×Dic3—91no—
224D4×Dic3—91no—
225#929—91no—
226C2×(C2×D3)⋊C4—91no—
227#898—91no—
228#896—91no—
229#894—91no—
230#894—91no—
231#882D911yescharacteristic
232#67⋊C4—91no—
233D3×C22⋊C4—91no—
234#879—91no—
235#879—91no—
236#878—91no—
237#878—91no—
238#878—91no—
239#878—181no—
240#877—31no—
241#877—91no—
242#876—91no—
243#875—91no—
244C4×D12—91no—
245#872—91no—
246C23×C32C22×D311yescharacteristic
247C22×C3×D3—22no—
248C22×C3×D3—22no—
249C22×C3×D3—41no—
250C22×C3×D3C22×D311yescharacteristic
251C22×C3×D3C22×D311yescharacteristic
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—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—62no—
267C2×C3×Dic3C22×D311yescharacteristic
268C3×D12—22no—
269C3×D12—41no—
270D3×Dic3—62no—
271D3×Dic3—121no—
272D3×Dic3—121no—
273C23×C9—21no—
274C23×C9—31no—
275C23×C9—31no—
276C23×C9—31no—
277C23×C9—62no—
278C23×C9—62no—
279C23×C9—121no—
280C23×C9C22×D311yescharacteristic
281D4×C9—62no—
282D4×C9—62no—
283D4×C9—121no—
284C2×C4×C9—21no—
285C2×C4×C9—21no—
286C2×C4×C9—31no—
287C2×C4×C9C22×D311yescharacteristic
288C2×C4×C9C22×D311yescharacteristic
289C2×Dic9—22no—
290C2×Dic9—31no—
291C2×Dic9—31no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—61no—
295C2×Dic9—61no—
296C2×Dic9—61no—
297C2×Dic9—61no—
298C2×Dic9—62no—
299C2×Dic9—121no—
300C2×Dic9—121no—
301C2×Dic9—121no—
302C2×Dic9—122no—
303C2×Dic9C22×D311yescharacteristic
304C2×Dic9C22×D311yescharacteristic
305C2×Dic9C22×D311yescharacteristic
306C2×Dic9C22×D311yescharacteristic
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—22no—
315D3×C9—41no—
316D3×C9—41no—
317C24×C3—31no—
318C23×D3C2×D911yescharacteristic
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C22×C3×C4—91no—
323C2×#67C2×D911yescharacteristic
324C22×Dic3—31no—
325C22×Dic3—91no—
326C22×Dic3—91no—
327C22×Dic3—91no—
328C22×Dic3—91no—
329C22×Dic3—91no—
330C22×Dic3—181no—
331C2×D12C2×D911yescharacteristic
332C2×D12C2×D911yescharacteristic
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3—91no—
336C2×Dic6—91no—
337C2×Dic6—91no—
338C2×Dic6—181no—
339C3×C4⋊C4—91no—
340C3×C4⋊C4—91no—
341C3×C22⋊C4—21no—
342C3×C22⋊C4—31no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—91no—
345C3×C22⋊C4C2×D911yescharacteristic
346C3×C22⋊C4D3211yescharacteristic
347C3×C42—91no—
348C3×C42—91no—
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—91no—
360#217—91no—
361#217—181no—
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)⋊C4C2×D911yescharacteristic
372(C2×D3)⋊C4C2×D911yescharacteristic
373C4⋊Dic3—91no—
374C4⋊Dic3—91no—
375C4⋊Dic3—91no—
376C4⋊Dic3—181no—
377Dic3⋊C4—31no—
378Dic3⋊C4—31no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—181no—
389Dic3⋊C4—181no—
390C4×Dic3—31no—
391C4×Dic3—31no—
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—21no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—44no—
407C2×C3×D3#23712yes—
408C32×C4—21no—
409C32×C4—21no—
410C3⋊Dic3—61no—
411C3⋊Dic3—61no—
412C3⋊Dic3—61no—
413C3⋊Dic3—61no—
414C3×Dic3—21no—
415C3×Dic3—61no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C22×C9—21no—
420C22×C9—21no—
421C22×C9—21no—
422C22×C9—22no—
423C22×C9—32no—
424C22×C9—41no—
425C22×C9—41no—
426C22×C9—61no—
427C22×C9—61no—
428C22×C9—61no—
429C22×C9—61no—
430C22×C9—61no—
431C22×C9—61no—
432C22×C9—61no—
433C22×C9—61no—
434C22×C9—124no—
435C22×C9#23512yes—
436C22×C9C23×D311yescharacteristic
437C4×C9—21no—
438C4×C9—21no—
439C4×C9—41no—
440C4×C9—41no—
441C4×C9—61no—
442Dic9—21no—
443Dic9—21no—
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—271no—
458#123—271no—
459#123—271no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462#120—31no—
463C4×D4—271no—
464C4×D4—271no—
465#117—91no—
466#117—271no—
467C2×C22⋊C4—271no—
468C2×C22⋊C4—271no—
469C3×C9#55111yescharacteristic, complemented, Sylow
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—31no—
473C23×C3—31no—
474C23×C3—62no—
475C23×C3—62no—
476C23×C3—121no—
477C23×C3C22×D911yescharacteristic
478C23×C3C2×D3211yescharacteristic
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—41no—
482C22×D3C22×D911yescharacteristic
483C22×D3C22×D911yescharacteristic
484C22×D3C22×D911yescharacteristic
485C3×D4—62no—
486C3×D4—62no—
487C3×D4—121no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—31no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—91no—
495C2×C3×C4—182no—
496C2×C3×C4C22×D911yescharacteristic
497C2×C3×C4C22×D911yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499C2×C3×C4C2×D3211yescharacteristic
500#67—22no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—62no—
506C2×Dic3—91no—
507C2×Dic3—91no—
508C2×Dic3—91no—
509C2×Dic3—91no—
510C2×Dic3—91no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—181no—
515C2×Dic3—181no—
516C2×Dic3—181no—
517C2×Dic3—181no—
518C2×Dic3—182no—
519C2×Dic3—361no—
520C2×Dic3—361no—
521C2×Dic3—361no—
522C2×Dic3—361no—
523C2×Dic3—362no—
524C2×Dic3C22×D911yescharacteristic
525D12—22no—
526D12—41no—
527C4×D3—182no—
528C4×D3—361no—
529C4×D3—361no—
530Dic6—361no—
531Dic6—361no—
532Dic6—362no—
533C2×C32—22no—
534C2×C32C2×#23711yescharacteristic
535C2×C32C2×#23711yescharacteristic
536C2×C32#100411yescharacteristic
537C3×D3—22no—
538C3×D3—41no—
539C3×D3—41no—
540C2×C9—22no—
541C2×C9—21no—
542C2×C9—21no—
543C2×C9—21no—
544C2×C9—42no—
545C2×C9—62no—
546C2×C9—121no—
547C2×C9—121no—
548C2×C9C2×#23511yescharacteristic
549C2×C9D3×#4111yescharacteristic
550C2×C9#100911yescharacteristic
551C24—31no—
552C2×Q8—271no—
553C2×D4—31no—
554C2×D4—31no—
555C2×D4—31no—
556C22×C4—91no—
557C22×C4—271no—
558C22×C4—271no—
559C22×C4—271no—
560C22×C4—271no—
561C4⋊C4—91no—
562C4⋊C4—91no—
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—271no—
573C22⋊C4—271no—
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—91no—
584C42—91no—
585C42—271no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—22no—
591C22×C3—21no—
592C22×C3—32no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—61no—
596C22×C3—61no—
597C22×C3—61no—
598C22×C3—61no—
599C22×C3—61no—
600C22×C3—61no—
601C22×C3—61no—
602C22×C3—61no—
603C22×C3—124no—
604C22×C3#369912yes—
605C22×C3C23×D911yescharacteristic
606C22×C3#379512yes—
607C22×C3C22×D3211yescharacteristic
608C2×D3—21no—
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—21no—
612C2×D3—21no—
613C2×D3—21no—
614C2×D3—21no—
615C2×D3—21no—
616C2×D3—44no—
617C2×D3#369912yes—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—61no—
625C3×C4—181no—
626C3×C4—181no—
627C3×C4—181no—
628C3×C4—181no—
629Dic3—21no—
630Dic3—61no—
631Dic3—61no—
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#558711yescharacteristic
647C9—21no—
648C9#552711yescharacteristic, complemented
649C23—31no—
650C23—31no—
651C23—31no—
652C23—62no—
653C23—62no—
654C23—121no—
655C23C2×D3×D911yescharacteristic
656Q8—1081no—
657D4—62no—
658D4—62no—
659D4—121no—
660C2×C4—31no—
661C2×C4—91no—
662C2×C4—91no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—182no—
666C2×C4—271no—
667C2×C4—271no—
668C2×C4—271no—
669C2×C4—271no—
670C2×C4—542no—
671C2×C4—1081no—
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—62no—
683C2×C3—121no—
684C2×C3—121no—
685C2×C3C2×#369911yescharacteristic
686C2×C3C2×#369911yescharacteristic
687C2×C3#6371011yescharacteristic
688C2×C3C2×#379511yescharacteristic
689C2×C3D3×#23711yescharacteristic
690C2×C3#6431411yescharacteristic
691D3—22no—
692D3—41no—
693D3—41no—
694C22—21no—
695C22—21no—
696C22—32no—
697C22—61no—
698C22—61no—
699C22—61no—
700C22—61no—
701C22—61no—
702C22—61no—
703C22—61no—
704C22—61no—
705C22—124no—
706C22#8863812yes—
707C22C22×D3×D911yescharacteristic
708C4—21no—
709C4—21no—
710C4—61no—
711C4—181no—
712C4—181no—
713C4—181no—
714C4—181no—
715C4—541no—
716C4—541no—
717C4—541no—
718C4—541no—
719C3—21no—
720C3#1058968911yescharacteristic, complemented
721C3#1059411711yescharacteristic
722C2—22no—
723C2—62no—
724C2—121no—
725C2—121no—
726C2C2×#8863811yescharacteristic
727C2D3×#369911yescharacteristic
728C2#1172250011yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC3×#882D3
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
3. C3×#63439C2semidirect
4. #67⋊Dic9C2semidirect
5. D3×#3676C2semidirect
6. #11721265C2semidirect
7. C2×(C2×D3)⋊Dic9C2semidirect
8. #11721024C2semidirect
9. D12×Dic9C2semidirect
10. #11721015C2semidirect
11. #11721015C2semidirect
12. #11721010C2semidirect
13. #11720965C2semidirect
14. #11720964C2semidirect
15. #11720963C2semidirect
20. C2×#6226C22semidirect
27. C2×D3×Dic9C22semidirect
30. C4⋊(C3⋊Dic9)C22semidirect
31. #88534C22semidirect
32. #88534C22semidirect
36. C3×Dic9⋊C4C22semidirect
37. C3×Dic9⋊C4C22semidirect
38. C3×C4×Dic9C22semidirect
39. C3×C4×Dic9C22semidirect
46. (C2×D3)⋊Dic9C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. Dic3⋊Dic9C22semidirect
50. #88442C22semidirect
51. #88442C22semidirect
52. Dic3×Dic9C22semidirect
83. #63439D3semidirect
185. Dic9⋊C4C2×D3semidirect
186. Dic9⋊C4C2×D3semidirect
188. C4×Dic9C2×D3semidirect
189. C4×Dic9C2×D3semidirect
469. C3×C9#551semidirect
648. C9#5527semidirect
720. C3#10589689semidirect

Maximal subgroups

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

subgroupindex
#117217242
C9×#8822
C3×#634392
#67⋊Dic92
D3×#36762
#117212652
C2×(C2×D3)⋊Dic92
#117210242
D12×Dic92
#117210152
#117210102
#117209652
#117209642
#117209632
#105941173
#105896893