Finite Group Databasebeta

← #13147986

Subgroups — #13147986

Order 1728.

1006 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88663C211yesmaximal, characteristic
2#11721723C211yesmaximal, characteristic, complemented
3C9×#67⋊C4C211yesmaximal, characteristic, complemented
4C3×#611⋊C4C211yesmaximal, characteristic, complemented
5#67×Dic9C211yesmaximal, characteristic, complemented
6Dic3×#611C211yesmaximal, characteristic, complemented
7C2×Dic3×Dic9C211yesmaximal, characteristic, complemented
8#11721012C211yesmaximal, characteristic, complemented
9#11721011C211yesmaximal, characteristic, complemented
10C4×D3×Dic9C211yesmaximal, characteristic, complemented
11#11720976C211yesmaximal, characteristic, complemented
12#11720975C211yesmaximal, characteristic, complemented
13C4×Dic3×D9C211yesmaximal, characteristic, complemented
14#11720901C211yesmaximal, characteristic, complemented
15#11720900C211yesmaximal, characteristic, complemented
16#10594050—31nomaximal
17C4×#3699—31nomaximal
18C22×C3⋊Dic9C2211yescharacteristic
19C2×C9×#67C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C22×C9×Dic3C2211yescharacteristic
22C22×C3×Dic9C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×#6194C2211yescharacteristic
26#88663C418yescomplemented
27C2×D3×Dic9C2211yescharacteristic
28C2×D3×Dic9C2211yescharacteristic
29C2×Dic3×D9C2211yescharacteristic
30C2×Dic3×D9C2211yescharacteristic
31C2×#6189C2211yescharacteristic
32C3×C9×C22⋊C4C2211yescharacteristic
33#88551C2211yescharacteristic
34#88534C2211yescharacteristic
35#88534C2211yescharacteristic
36C4×C3⋊Dic9C2211yescharacteristic
37C4×C3⋊Dic9C2211yescharacteristic
38C9×(C2×D3)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C9×Dic3⋊C4C2211yescharacteristic
41C4×C9×Dic3C2211yescharacteristic
42C3×Dic9⋊C4C2211yescharacteristic
43C3×C4×Dic9C2211yescharacteristic
44(C2×D3)⋊Dic9C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46Dic3⋊Dic9C2211yescharacteristic
47Dic9⋊Dic3C2211yescharacteristic
48Dic3×Dic9C2211yescharacteristic
49Dic3×Dic9C2211yescharacteristic
50Dic3×Dic9C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54C2×#3805—31no—
55#64086—31no—
56C3×#67⋊C4—31no—
57C3×#67⋊C4D311yescharacteristic
58Dic3×#67—31no—
59Dic3×#67—31no—
60C2×Dic32—31no—
61#63879—31no—
62#63879—31no—
63#63878—31no—
64#63878—31no—
65C4×D3×Dic3—31no—
66C4×D3×Dic3—31no—
67#63837—31no—
68#63837—31no—
69C2×#3699—31no—
70C4×D4×C9—31no—
71D4×Dic9—31no—
72C4×#611—31no—
73C4×#611—31no—
74C2×C4×Dic9—31no—
75C2×C4×Dic9—31no—
76#63454—31no—
77#63449—31no—
78#611⋊C4—31no—
79#611⋊C4D311yescharacteristic, complemented
80#63439—31no—
81#63439—31no—
82#63439—61no—
83C42×D9—31no—
84C4×Dic18—31no—
85C23×C3×C9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3⋊Dic9C2×C414yescomplemented
91C2×C3⋊Dic9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C9×#67C2×C414yescomplemented
96C3×#611C2×C414yescomplemented
97C2×C9×Dic3—22no—
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9—22no—
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C4×D3×C9—22no—
106C3×C4×D9—22no—
107#6194C2×C414yescomplemented
108D3×Dic9—22no—
109D3×Dic9C2×C414yescomplemented
110Dic3×D9—22no—
111Dic3×D9C2×C414yescomplemented
112#6189C2×C414yescomplemented
113C4×#237—91no—
114C4×#237—91no—
115C22×C3⋊Dic3—31no—
116C2×C3×#67—31no—
117C2×C3×#67C2×D311yescharacteristic
118C22×C3×Dic3—31no—
119C22×C3×Dic3C2×D311yescharacteristic
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3C2×D311yescharacteristic
122C2×#627—31no—
123C2×#625—31no—
124#3805—38no—
125C2×D3×Dic3—31no—
126C2×D3×Dic3—31no—
127C2×D3×Dic3—31no—
128C2×D3×Dic3—31no—
129C32×C22⋊C4C2×D311yescharacteristic
130#3757—31no—
131#3750—31no—
132#3750—31no—
133C4×C3⋊Dic3—31no—
134C4×C3⋊Dic3—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4C2×D311yescharacteristic
137C3×Dic3⋊C4—31no—
138C3×Dic3⋊C4C2×D311yescharacteristic
139C3×C4×Dic3—31no—
140C3×C4×Dic3C2×D311yescharacteristic
141Dic3⋊Dic3—31no—
142Dic3⋊Dic3—31no—
143(C2×D3)⋊Dic3—31no—
144(C2×D3)⋊Dic3—31no—
145Dic32—31no—
146Dic32—31no—
147Dic32—31no—
148Dic32—31no—
149Dic32—31no—
150Dic32—31no—
151C2×D4×C9—31no—
152C22×C4×C9—31no—
153C22×C4×C9—31no—
154C2×#611—31no—
155C2×#611C2×D311yescharacteristic
156C22×Dic9—31no—
157C22×Dic9—31no—
158C22×Dic9—31no—
159C22×Dic9—61no—
160C22×Dic9C2×D311yescharacteristic
161#3699—38no—
162C2×C4×D9—31no—
163C2×C4×D9—31no—
164C2×C4×D9C2×D311yescharacteristic
165C2×Dic18—31no—
166C9×C4⋊C4—31no—
167C9×C22⋊C4—21no—
168C9×C22⋊C4—31no—
169C9×C22⋊C4C2×D311yescharacteristic
170C42×C9—31no—
171#3676—31no—
172#3676—31no—
173#3676—61no—
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4C2×D311yescharacteristic
176C4⋊Dic9—31no—
177Dic9⋊C4—31no—
178Dic9⋊C4—31no—
179Dic9⋊C4—31no—
180Dic9⋊C4—61no—
181Dic9⋊C4—61no—
182Dic9⋊C4C2×D311yescharacteristic
183C4×Dic9—31no—
184C4×Dic9—31no—
185C4×Dic9—31no—
186C4×Dic9—31no—
187C4×Dic9—31no—
188C4×Dic9—31no—
189C4×Dic9—31no—
190C4×Dic9—31no—
191C4×Dic9—61no—
192C4×Dic9—61no—
193C4×Dic9C2×D311yescharacteristic
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9C22×C412yes—
197C22×C3×C9C2411yescharacteristic
198C2×D3×C9—21no—
199C2×D3×C9—21no—
200C2×D3×C9C22×C412yes—
201C2×C3×D9—21no—
202C2×C3×D9—21no—
203C2×C3×D9C22×C412yes—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9C22×C412yes—
209C3⋊Dic9C22×C412yes—
210C9×Dic3—21no—
211C9×Dic3C22×C412yes—
212C9×Dic3#4112yescomplemented
213C3×Dic9—21no—
214C3×Dic9C22×C412yes—
215C3×Dic9#4112yescomplemented
216C2×#237—91no—
217C2×#237—91no—
218C3×C4×D4—31no—
219C3×C4×D4—91no—
220D4×Dic3—91no—
221D4×Dic3—91no—
222C4×#67—91no—
223C4×#67—91no—
224C4×#67—91no—
225C4×#67—91no—
226C2×C4×Dic3—91no—
227C2×C4×Dic3—91no—
228C2×C4×Dic3—91no—
229C2×C4×Dic3—91no—
230#892—91no—
231#892—91no—
232#887—91no—
233#887—91no—
234#67⋊C4—31no—
235#67⋊C4—91no—
236#67⋊C4—91no—
237#67⋊C4D911yescharacteristic, complemented
238#877—91no—
239#877—91no—
240#877—91no—
241#877—91no—
242#877—181no—
243C42×D3—91no—
244C42×D3—91no—
245C4×Dic6—91no—
246C4×Dic6—91no—
247C23×C32C22×D311yescharacteristic
248C22×C3×D3—31no—
249C22×C3×D3C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C3⋊Dic3—34no—
253C2×C3⋊Dic3—31no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C3×#67—34no—
258C3×#67C4×D314yes—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—62no—
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C3×C4×D3—22no—
268C3×C4×D3—62no—
269#627—34no—
270#625—34no—
271D3×Dic3—34no—
272D3×Dic3—34no—
273D3×Dic3—62no—
274D3×Dic3—62no—
275C23×C9—21no—
276C23×C9—31no—
277C23×C9C22×D311yescharacteristic
278C22×D9C22×D311yescharacteristic
279D4×C9—34no—
280C2×C4×C9—21no—
281C2×C4×C9—21no—
282C2×C4×C9—31no—
283C2×C4×C9—31no—
284C2×C4×C9—31no—
285C2×C4×C9—62no—
286C2×C4×C9—62no—
287C2×C4×C9C22×D311yescharacteristic
288C2×C4×C9C22×D311yescharacteristic
289#611—34no—
290#611C4×D314yescomplemented
291C2×Dic9—22no—
292C2×Dic9—34no—
293C2×Dic9—31no—
294C2×Dic9—31no—
295C2×Dic9—34no—
296C2×Dic9—31no—
297C2×Dic9—31no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—64no—
301C2×Dic9—61no—
302C2×Dic9—61no—
303C2×Dic9—62no—
304C2×Dic9C22×D311yescharacteristic
305C2×Dic9C22×D311yescharacteristic
306C2×Dic9C22×D311yescharacteristic
307C4×D9—22no—
308C4×D9—34no—
309C4×D9—62no—
310Dic18—34no—
311C4×#41—271noSylow
312C2×C3×C9—22no—
313C2×C3×C9C23×C411yescharacteristic
314C2×C3×C9C2×#4111yescharacteristic
315C2×C3×C9C2×#4111yescharacteristic
316D3×C9—22no—
317C3×D9—22no—
318C2×C3×D4—31no—
319C2×C3×D4—91no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—91no—
323C22×C3×C4—91no—
324C2×#67—31no—
325C2×#67—91no—
326C2×#67—91no—
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×Dic3C2×D911yescharacteristic
337#237—98no—
338#237—98no—
339C2×C4×D3—31no—
340C2×C4×D3—91no—
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×C4×D3—91no—
344C2×C4×D3C2×D911yescharacteristic
345C2×Dic6—91no—
346C2×Dic6—91no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—91no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—91no—
352C3×C22⋊C4C2×D911yescharacteristic
353C3×C22⋊C4D3211yescharacteristic
354C3×C42—31no—
355C3×C42—91no—
356#217—91no—
357#217—91no—
358#217—91no—
359#217—91no—
360#217—181no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4C2×D911yescharacteristic
365C4⋊Dic3—91no—
366C4⋊Dic3—91no—
367Dic3⋊C4—31no—
368Dic3⋊C4—91no—
369Dic3⋊C4—91no—
370Dic3⋊C4—91no—
371Dic3⋊C4—91no—
372Dic3⋊C4—91no—
373Dic3⋊C4—91no—
374Dic3⋊C4—181no—
375Dic3⋊C4—181no—
376Dic3⋊C4C2×D911yescharacteristic
377C4×Dic3—31no—
378C4×Dic3—91no—
379C4×Dic3—91no—
380C4×Dic3—91no—
381C4×Dic3—91no—
382C4×Dic3—91no—
383C4×Dic3—91no—
384C4×Dic3—91no—
385C4×Dic3—91no—
386C4×Dic3—91no—
387C4×Dic3—91no—
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3—181no—
395C4×Dic3—181no—
396C4×Dic3C2×D911yescharacteristic
397C22×C32—21no—
398C22×C32—21no—
399C22×C32C2×C4×D312yes—
400C22×C32C23×D311yescharacteristic
401C2×C3×D3—21no—
402C2×C3×D3—21no—
403C2×C3×D3—32no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406C2×C3×D3C2×C4×D312yes—
407C32×C4—21no—
408C32×C4—21no—
409C3⋊Dic3—32no—
410C3⋊Dic3—32no—
411C3⋊Dic3—61no—
412C3⋊Dic3—61no—
413C3×Dic3—21no—
414C3×Dic3—32no—
415C3×Dic3—32no—
416C3×Dic3—61no—
417C3×Dic3C2×C4×D312yes—
418C3×Dic3#23712yes—
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×C9C2×C4×D312yes—
429C22×C9C23×D311yescharacteristic
430C2×D9—21no—
431C2×D9—21no—
432C2×D9C2×C4×D312yes—
433C4×C9—21no—
434C4×C9—21no—
435C4×C9—32no—
436C4×C9—32no—
437C4×C9—41no—
438C4×C9—41no—
439C4×C9—61no—
440Dic9—21no—
441Dic9—32no—
442Dic9—32no—
443Dic9—62no—
444Dic9—62no—
445Dic9—61no—
446Dic9—61no—
447Dic9—121no—
448Dic9—121no—
449Dic9C2×C4×D312yes—
450Dic9#23712yescomplemented
451C2×#41—271no—
452C4×Q8—271no—
453C4×Q8—271no—
454C4×D4—31no—
455C4×D4—91no—
456C4×D4—271no—
457C4×D4—271no—
458C4×D4—271no—
459C4×D4—271no—
460#117—271no—
461#117—271no—
462#117—271no—
463C2×C42—271no—
464C2×C42—271no—
465C2×C42—271no—
466C3×C9C4×#4111yescharacteristic, complemented, Sylow
467C23×C3—21no—
468C23×C3—31no—
469C23×C3—91no—
470C23×C3C22×D911yescharacteristic
471C23×C3C2×D3211yescharacteristic
472C22×D3—31no—
473C22×D3C22×D911yescharacteristic
474C3×D4—34no—
475C3×D4—94no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—62no—
482C2×C3×C4—62no—
483C2×C3×C4—91no—
484C2×C3×C4—91no—
485C2×C3×C4—91no—
486C2×C3×C4—182no—
487C2×C3×C4—182no—
488C2×C3×C4C22×D911yescharacteristic
489C2×C3×C4C22×D911yescharacteristic
490C2×C3×C4C2×D3211yescharacteristic
491C2×C3×C4C2×D3211yescharacteristic
492#67—34no—
493#67—94no—
494#67—94no—
495#67C4×D914yescomplemented
496C2×Dic3—22no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—62no—
501C2×Dic3—94no—
502C2×Dic3—91no—
503C2×Dic3—91no—
504C2×Dic3—94no—
505C2×Dic3—91no—
506C2×Dic3—91no—
507C2×Dic3—94no—
508C2×Dic3—94no—
509C2×Dic3—91no—
510C2×Dic3—91no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—181no—
514C2×Dic3—181no—
515C2×Dic3—184no—
516C2×Dic3—181no—
517C2×Dic3—181no—
518C2×Dic3—182no—
519C2×Dic3—182no—
520C2×Dic3C22×D911yescharacteristic
521C2×Dic3C22×D911yescharacteristic
522C2×Dic3C22×D911yescharacteristic
523C4×D3—22no—
524C4×D3—62no—
525C4×D3—94no—
526C4×D3—94no—
527C4×D3—182no—
528C4×D3—182no—
529Dic6—94no—
530Dic6—94no—
531C2×C32—22no—
532C2×C32C22×C4×D311yescharacteristic
533C2×C32C2×#23711yescharacteristic
534C2×C32D3×#4111yescharacteristic
535C3×D3—22no—
536C3×D3—62no—
537C2×C9—22no—
538C2×C9—21no—
539C2×C9—21no—
540C2×C9—21no—
541C2×C9—42no—
542C2×C9—62no—
543C2×C9C22×C4×D311yescharacteristic
544C2×C9C2×#23711yescharacteristic
545C2×C9D3×#4111yescharacteristic
546D9—22no—
547#41—278no—
548C2×Q8—271no—
549C2×D4—31no—
550C2×D4—91no—
551C2×D4—271no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—91no—
555C22×C4—91no—
556C22×C4—271no—
557C22×C4—271no—
558C22×C4—271no—
559C22×C4—271no—
560C22×C4—271no—
561C4⋊C4—31no—
562C4⋊C4—91no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C22⋊C4—31no—
568C22⋊C4—91no—
569C22⋊C4—271no—
570C22⋊C4—271no—
571C22⋊C4—271no—
572C22⋊C4D3×D911yescharacteristic
573C42—31no—
574C42—91no—
575C42—271no—
576C42—271no—
577C42—271no—
578C42—271no—
579C42—271no—
580C42—271no—
581C42—271no—
582C42—271no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—22no—
589C22×C3—32no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—61no—
593C22×C3—61no—
594C22×C3—92no—
595C22×C3—181no—
596C22×C3—181no—
597C22×C3C2×C4×D912yes—
598C22×C3C23×D911yescharacteristic
599C22×C3C4×D3212yes—
600C22×C3C22×D3211yescharacteristic
601C2×D3—21no—
602C2×D3—21no—
603C2×D3—32no—
604C2×D3—61no—
605C2×D3—61no—
606C2×D3C2×C4×D912yes—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—32no—
612C3×C4—32no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4—61no—
616C3×C4—92no—
617C3×C4—92no—
618C3×C4—181no—
619Dic3—21no—
620Dic3—32no—
621Dic3—32no—
622Dic3—61no—
623Dic3—92no—
624Dic3—92no—
625Dic3—92no—
626Dic3—92no—
627Dic3—182no—
628Dic3—182no—
629Dic3—181no—
630Dic3—181no—
631Dic3—181no—
632Dic3—181no—
633Dic3—361no—
634Dic3—361no—
635Dic3C2×C4×D912yes—
636Dic3#369912yescomplemented
637C32C4×#23711yescharacteristic
638C9—21no—
639C9C4×#23711yescharacteristic, complemented
640C23—31no—
641C23—91no—
642C23C2×D3×D911yescharacteristic
643Q8—274no—
644D4—34no—
645D4—94no—
646D4—274no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—91no—
653C2×C4—91no—
654C2×C4—91no—
655C2×C4—182no—
656C2×C4—182no—
657C2×C4—274no—
658C2×C4—274no—
659C2×C4—271no—
660C2×C4—271no—
661C2×C4—274no—
662C2×C4—271no—
663C2×C4—271no—
664C2×C4—542no—
665C2×C4—542no—
666C2×C4C2×D3×D911yescharacteristic
667C2×C4C2×D3×D911yescharacteristic
668C2×C3—22no—
669C2×C3—22no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—42no—
674C2×C3—62no—
675C2×C3—182no—
676C2×C3C22×C4×D911yescharacteristic
677C2×C3C2×#369911yescharacteristic
678C2×C3#41×D911yescharacteristic
679C2×C3C2×C4×D3211yescharacteristic
680C2×C3D3×#23711yescharacteristic
681C2×C3D3×#23711yescharacteristic
682D3—22no—
683D3—62no—
684C22—21no—
685C22—21no—
686C22—32no—
687C22—61no—
688C22—61no—
689C22—92no—
690C22—181no—
691C22—181no—
692C22C4×D3×D912yes—
693C22C22×D3×D911yescharacteristic
694C4—21no—
695C4—21no—
696C4—32no—
697C4—32no—
698C4—61no—
699C4—92no—
700C4—92no—
701C4—181no—
702C4—272no—
703C4—272no—
704C4—541no—
705C4—541no—
706C3—21no—
707C3C4×#369911yescharacteristic, complemented
708C3#1059405011yescharacteristic
709C2—22no—
710C2—62no—
711C2—182no—
712C2C2×C4×D3×D911yescharacteristic
713C2D3×#369911yescharacteristic
714C2D9×#23711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC2×#88663C2
cosocleC22×C3×C9C24
hypercenterC22⋊C4D3×D9
hypocenterC3×C9C4×#41
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #11721723C2semidirect
3. C9×#67⋊C4C2semidirect
4. C3×#611⋊C4C2semidirect
5. #67×Dic9C2semidirect
6. Dic3×#611C2semidirect
7. C2×Dic3×Dic9C2semidirect
8. #11721012C2semidirect
9. #11721011C2semidirect
10. C4×D3×Dic9C2semidirect
11. #11720976C2semidirect
12. #11720975C2semidirect
13. C4×Dic3×D9C2semidirect
14. #11720901C2semidirect
15. #11720900C2semidirect
26. #88663C4semidirect
79. #611⋊C4D3semidirect
90. C2×C3⋊Dic9C2×C4semidirect
95. C9×#67C2×C4semidirect
96. C3×#611C2×C4semidirect
107. #6194C2×C4semidirect
109. D3×Dic9C2×C4semidirect
111. Dic3×D9C2×C4semidirect
112. #6189C2×C4semidirect
212. C9×Dic3#41semidirect
215. C3×Dic9#41semidirect
237. #67⋊C4D9semidirect
290. #611C4×D3semidirect
450. Dic9#237semidirect
466. C3×C9C4×#41semidirect
495. #67C4×D9semidirect
636. Dic3#3699semidirect
639. C9C4×#237semidirect
707. C3C4×#3699semidirect

Maximal subgroups

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

subgroupindex
C2×#886632
#117217232
C9×#67⋊C42
C3×#611⋊C42
#67×Dic92
Dic3×#6112
C2×Dic3×Dic92
#117210122
#117210112
C4×D3×Dic92
#117209762
#117209752
C4×Dic3×D92
#117209012
#117209002
#105940503
C4×#36993