Finite Group Databasebeta

← C4×#88663 #13150168

Subgroups — C4×#88663 #13150168

Order 1728.

1038 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88663C211yesmaximal, characteristic
2C2×C4×C3⋊Dic9C211yesmaximal, characteristic, complemented
3C4×C9×#67C211yesmaximal, characteristic, complemented
4C3×C4×#611C211yesmaximal, characteristic, complemented
5#67⋊Dic9C211yesmaximal, characteristic, complemented
6#611⋊Dic3C211yesmaximal, characteristic, complemented
7#11721248C211yesmaximal, characteristic, complemented
8#11721028C211yesmaximal, characteristic, complemented
9C4×#6194C211yesmaximal, characteristic, complemented
10#11721011C211yesmaximal, characteristic, complemented
11C4×D3×Dic9C211yesmaximal, characteristic, complemented
12#11720975C211yesmaximal, characteristic, complemented
13C4×Dic3×D9C211yesmaximal, characteristic, complemented
14C4×#6189C211yesmaximal, characteristic, complemented
15#11720902C211yesmaximal, characteristic, complemented
16C4×#3805—31nomaximal
17C4×#3699—31nomaximal
18C22×C3×C4×C9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×#6194C2211yescharacteristic
26#88663C418yesdirect product factor
27C2×D3×Dic9C2211yescharacteristic
28C2×D3×Dic9C2211yescharacteristic
29C2×Dic3×D9C2211yescharacteristic
30C2×Dic3×D9C2211yescharacteristic
31C2×#6189C2211yescharacteristic
32C4×C3⋊Dic9C2211yescharacteristic
33C4×C3⋊Dic9C2211yescharacteristic
34C4×C3⋊Dic9C2211yescharacteristic
35C4×C3⋊Dic9C2211yescharacteristic
36C9×#217C2211yescharacteristic
37C3×#3676C2211yescharacteristic
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
47#88442C2211yescharacteristic
48#88442C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic3×Dic9C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54C2×#3805—31no—
55C2×C4×C3⋊Dic3—31no—
56C3×C4×#67—31no—
57C3×C4×#67D311yescharacteristic
58#67⋊Dic3—31no—
59#67⋊Dic3—31no—
60#63957—31no—
61C4×#627—31no—
62#63902—31no—
63C4×#625—31no—
64#63878—31no—
65#63878—31no—
66C4×D3×Dic3—31no—
67C4×D3×Dic3—31no—
68#63838—31no—
69C2×#3699—31no—
70C4×D4×C9—31no—
71D4×Dic9—31no—
72C4×#611—31no—
73C4×#611D311yescharacteristic, complemented
74C2×C4×Dic9—31no—
75C2×C4×Dic9—31no—
76C2×C4×Dic9—61no—
77#63454—31no—
78#63449—31no—
79#611⋊C4—31no—
80#611⋊C4—31no—
81#63439—31no—
82#63439—31no—
83C42×D9—31no—
84C4×Dic18—31no—
85C23×C3×C9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×C3×C4×C9—22no—
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3⋊Dic9—22no—
92C2×C3⋊Dic9C2×C414yescomplemented
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C9×#67C2×C414yescomplemented
98C3×#611C2×C414yescomplemented
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
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×C32×C4C2×D311yescharacteristic
116C22×C3⋊Dic3—31no—
117C22×C3⋊Dic3—31no—
118C2×C3×#67—31no—
119C2×C3×#67C2×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—
129C4×C3⋊Dic3—31no—
130C4×C3⋊Dic3—31no—
131C4×C3⋊Dic3—31no—
132C4×C3⋊Dic3—31no—
133C3×#217—31no—
134C3×#217C2×D311yescharacteristic
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
141#3724—31no—
142#3724—31no—
143Dic3⋊Dic3—31no—
144Dic3⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147Dic32—31no—
148Dic32—31no—
149Dic32—31no—
150Dic32—31no—
151C2×D4×C9—31no—
152C22×C4×C9—21no—
153C22×C4×C9—31no—
154C22×C4×C9C2×D311yescharacteristic
155C2×#611—31no—
156C2×#611C2×D311yescharacteristic
157C22×Dic9—31no—
158C22×Dic9—31no—
159C22×Dic9—31no—
160C22×Dic9—31no—
161C22×Dic9—61no—
162C22×Dic9—61no—
163#3699—38no—
164C2×C4×D9—31no—
165C2×C4×D9—31no—
166C2×C4×D9C2×D311yescharacteristic
167C2×Dic18—31no—
168C9×C4⋊C4—31no—
169C9×C22⋊C4—31no—
170C9×C22⋊C4—31no—
171C42×C9—31no—
172#3676—31no—
173#3676C2×D311yescharacteristic
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4C2×D311yescharacteristic
176C4⋊Dic9—31no—
177Dic9⋊C4—31no—
178Dic9⋊C4—31no—
179Dic9⋊C4—31no—
180Dic9⋊C4C2×D311yescharacteristic
181C4×Dic9—31no—
182C4×Dic9—31no—
183C4×Dic9—31no—
184C4×Dic9—31no—
185C4×Dic9—31no—
186C4×Dic9—31no—
187C4×Dic9—31no—
188C4×Dic9—31no—
189C4×Dic9—61no—
190C4×Dic9—61no—
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#4112yescomplemented
206C3⋊Dic9—21no—
207C3⋊Dic9C22×C412yes—
208C3⋊Dic9C22×C412yes—
209C3⋊Dic9#4112yescomplemented
210C9×Dic3—21no—
211C9×Dic3—21no—
212C9×Dic3C22×C412yes—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×Dic9C22×C412yes—
216C2×#237—91no—
217C2×#237—91no—
218C3×C4×D4—31no—
219C3×C4×D4—91no—
220D4×Dic3—91no—
221D4×Dic3—91no—
222C4×#67—31no—
223C4×#67—91no—
224C4×#67—91no—
225C4×#67D911yescharacteristic, complemented
226C2×C4×Dic3—91no—
227C2×C4×Dic3—91no—
228C2×C4×Dic3—91no—
229C2×C4×Dic3—91no—
230C2×C4×Dic3—181no—
231#892—91no—
232#892—91no—
233#887—91no—
234#887—91no—
235#67⋊C4—91no—
236#67⋊C4—91no—
237#67⋊C4—91no—
238#67⋊C4—91no—
239#877—91no—
240#877—91no—
241#877—91no—
242#877—91no—
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×C4—22no—
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C3⋊Dic3—34no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—62no—
259C3×#67—34no—
260C3×#67C4×D314yes—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
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—24no—
281C2×C4×C9—22no—
282C2×C4×C9—21no—
283C2×C4×C9—21no—
284C2×C4×C9—31no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—62no—
288C2×C4×C9C22×D311yescharacteristic
289C2×C4×C9C22×D311yescharacteristic
290#611—34no—
291#611C4×D314yescomplemented
292C2×Dic9—34no—
293C2×Dic9—31no—
294C2×Dic9—31no—
295C2×Dic9—31no—
296C2×Dic9—34no—
297C2×Dic9—31no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—61no—
301C2×Dic9—61no—
302C2×Dic9—64no—
303C2×Dic9—62no—
304C2×Dic9—62no—
305C2×Dic9—64no—
306C2×Dic9C22×D311yescharacteristic
307C2×Dic9C22×D311yescharacteristic
308C2×Dic9C22×D311yescharacteristic
309C4×D9—22no—
310C4×D9—34no—
311C4×D9—62no—
312Dic18—34no—
313C4×#41—271noSylow
314C2×C3×C9—22no—
315C2×C3×C9C23×C411yescharacteristic
316C2×C3×C9C2×#4111yescharacteristic
317C2×C3×C9C2×#4111yescharacteristic
318D3×C9—22no—
319C3×D9—22no—
320C2×C3×D4—31no—
321C2×C3×D4—91no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—91no—
325C22×C3×C4C2×D911yescharacteristic
326C22×C3×C4D3211yescharacteristic
327C2×#67—31no—
328C2×#67—91no—
329C2×#67—91no—
330C2×#67C2×D911yescharacteristic
331C22×Dic3—91no—
332C22×Dic3—91no—
333C22×Dic3—91no—
334C22×Dic3—91no—
335C22×Dic3—91no—
336C22×Dic3—91no—
337C22×Dic3—91no—
338C22×Dic3—91no—
339C22×Dic3—181no—
340C22×Dic3—181no—
341#237—98no—
342#237—98no—
343C2×C4×D3—31no—
344C2×C4×D3—91no—
345C2×C4×D3—91no—
346C2×C4×D3—91no—
347C2×C4×D3—91no—
348C2×C4×D3C2×D911yescharacteristic
349C2×Dic6—91no—
350C2×Dic6—91no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—91no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—91no—
356C3×C22⋊C4—91no—
357C3×C42—31no—
358C3×C42—91no—
359#217—31no—
360#217—91no—
361#217—91no—
362#217C2×D911yescharacteristic
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4C2×D911yescharacteristic
367C4⋊Dic3—91no—
368C4⋊Dic3—91no—
369Dic3⋊C4—31no—
370Dic3⋊C4—91no—
371Dic3⋊C4—91no—
372Dic3⋊C4—91no—
373Dic3⋊C4—91no—
374Dic3⋊C4—91no—
375Dic3⋊C4—91no—
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×Dic3—181no—
397C4×Dic3—181no—
398C4×Dic3C2×D911yescharacteristic
399C22×C32—21no—
400C22×C32—21no—
401C22×C32C2×C4×D312yes—
402C22×C32C23×D311yescharacteristic
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—32no—
406C2×C3×D3—61no—
407C2×C3×D3—61no—
408C2×C3×D3C2×C4×D312yes—
409C32×C4—21no—
410C32×C4#23712yes—
411C3⋊Dic3—32no—
412C3⋊Dic3—32no—
413C3⋊Dic3—32no—
414C3⋊Dic3—61no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—32no—
418C3×Dic3—61no—
419C3×Dic3—61no—
420C3×Dic3C2×C4×D312yes—
421C22×C9—22no—
422C22×C9—22no—
423C22×C9—21no—
424C22×C9—21no—
425C22×C9—21no—
426C22×C9—22no—
427C22×C9—32no—
428C22×C9—61no—
429C22×C9—61no—
430C22×C9C2×C4×D312yes—
431C22×C9C23×D311yescharacteristic
432C2×D9—21no—
433C2×D9—21no—
434C2×D9C2×C4×D312yes—
435C4×C9—22no—
436C4×C9—21no—
437C4×C9—22no—
438C4×C9—32no—
439C4×C9—61no—
440C4×C9—61no—
441C4×C9#23712yescomplemented
442Dic9—21no—
443Dic9—21no—
444Dic9—32no—
445Dic9—32no—
446Dic9—32no—
447Dic9—62no—
448Dic9—62no—
449Dic9—62no—
450Dic9—62no—
451Dic9—61no—
452Dic9C2×C4×D312yes—
453C2×#41—271no—
454C4×Q8—271no—
455C4×Q8—271no—
456C4×D4—31no—
457C4×D4—91no—
458C4×D4—271no—
459C4×D4—271no—
460C4×D4—271no—
461C4×D4—271no—
462#117—271no—
463#117—271no—
464#117—271no—
465C2×C42—271no—
466C2×C42—271no—
467C2×C42—271no—
468C3×C9C4×#4111yescharacteristic, complemented, Sylow
469C23×C3—21no—
470C23×C3—31no—
471C23×C3—91no—
472C23×C3C22×D911yescharacteristic
473C23×C3C2×D3211yescharacteristic
474C22×D3—31no—
475C22×D3C22×D911yescharacteristic
476C3×D4—34no—
477C3×D4—94no—
478C2×C3×C4—24no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—62no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4—182no—
491C2×C3×C4C22×D911yescharacteristic
492C2×C3×C4C22×D911yescharacteristic
493C2×C3×C4C2×D3211yescharacteristic
494C2×C3×C4C2×D3211yescharacteristic
495#67—34no—
496#67—94no—
497#67—94no—
498#67C4×D914yescomplemented
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—94no—
503C2×Dic3—91no—
504C2×Dic3—91no—
505C2×Dic3—91no—
506C2×Dic3—94no—
507C2×Dic3—91no—
508C2×Dic3—91no—
509C2×Dic3—91no—
510C2×Dic3—94no—
511C2×Dic3—94no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—181no—
515C2×Dic3—181no—
516C2×Dic3—181no—
517C2×Dic3—181no—
518C2×Dic3—184no—
519C2×Dic3—182no—
520C2×Dic3—182no—
521C2×Dic3—182no—
522C2×Dic3—182no—
523C2×Dic3—184no—
524C2×Dic3C22×D911yescharacteristic
525C2×Dic3C22×D911yescharacteristic
526C2×Dic3C22×D911yescharacteristic
527C4×D3—22no—
528C4×D3—62no—
529C4×D3—94no—
530C4×D3—94no—
531C4×D3—182no—
532C4×D3—182no—
533Dic6—94no—
534Dic6—94no—
535C2×C32—22no—
536C2×C32C22×C4×D311yescharacteristic
537C2×C32C2×#23711yescharacteristic
538C2×C32D3×#4111yescharacteristic
539C3×D3—22no—
540C3×D3—62no—
541C2×C9—24no—
542C2×C9—22no—
543C2×C9—21no—
544C2×C9—21no—
545C2×C9—21no—
546C2×C9—62no—
547C2×C9C22×C4×D311yescharacteristic
548C2×C9C2×#23711yescharacteristic
549C2×C9D3×#4111yescharacteristic
550D9—22no—
551#41—278no—
552C2×Q8—271no—
553C2×D4—31no—
554C2×D4—91no—
555C2×D4—271no—
556C22×C4—31no—
557C22×C4—91no—
558C22×C4—271no—
559C22×C4—271no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4D3×D911yescharacteristic
565C4⋊C4—31no—
566C4⋊C4—91no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C22⋊C4—31no—
572C22⋊C4—31no—
573C22⋊C4—91no—
574C22⋊C4—91no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C42—31no—
578C42—91no—
579C42—271no—
580C42—271no—
581C42—271no—
582C42—271no—
583C42—271no—
584C42—271no—
585C42—271no—
586C42—271no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—22no—
595C22×C3—32no—
596C22×C3—61no—
597C22×C3—61no—
598C22×C3—92no—
599C22×C3—181no—
600C22×C3—181no—
601C22×C3C2×C4×D912yes—
602C22×C3C23×D911yescharacteristic
603C22×C3C4×D3212yes—
604C22×C3C22×D3211yescharacteristic
605C2×D3—21no—
606C2×D3—21no—
607C2×D3—32no—
608C2×D3—61no—
609C2×D3—61no—
610C2×D3C2×C4×D912yes—
611C3×C4—22no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—22no—
615C3×C4—32no—
616C3×C4—61no—
617C3×C4—61no—
618C3×C4—92no—
619C3×C4—181no—
620C3×C4—181no—
621C3×C4#369912yescomplemented
622C3×C4#380512yes—
623Dic3—21no—
624Dic3—21no—
625Dic3—32no—
626Dic3—61no—
627Dic3—61no—
628Dic3—92no—
629Dic3—92no—
630Dic3—92no—
631Dic3—92no—
632Dic3—92no—
633Dic3—92no—
634Dic3—182no—
635Dic3—182no—
636Dic3—182no—
637Dic3—182no—
638Dic3—181no—
639Dic3—181no—
640Dic3C2×C4×D912yes—
641C32C4×#23711yescharacteristic
642C9—21no—
643C9C4×#23711yescharacteristic, complemented
644C23—31no—
645C23—91no—
646C23C2×D3×D911yescharacteristic
647Q8—274no—
648D4—34no—
649D4—94no—
650D4—274no—
651C2×C4—22no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—62no—
656C2×C4—91no—
657C2×C4—91no—
658C2×C4—91no—
659C2×C4—182no—
660C2×C4—274no—
661C2×C4—274no—
662C2×C4—271no—
663C2×C4—271no—
664C2×C4—271no—
665C2×C4—274no—
666C2×C4—271no—
667C2×C4—542no—
668C2×C4—542no—
669C2×C4—542no—
670C2×C4C2×D3×D911yescharacteristic
671C2×C4C2×D3×D911yescharacteristic
672C2×C3—24no—
673C2×C3—22no—
674C2×C3—22no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—62no—
679C2×C3—182no—
680C2×C3C22×C4×D911yescharacteristic
681C2×C3C2×#369911yescharacteristic
682C2×C3#41×D911yescharacteristic
683C2×C3C2×C4×D3211yescharacteristic
684C2×C3#6430611yescharacteristic
685C2×C3C2×#380511yescharacteristic
686D3—22no—
687D3—62no—
688C22—21no—
689C22—21no—
690C22—32no—
691C22—61no—
692C22—61no—
693C22—92no—
694C22—181no—
695C22—181no—
696C22C4×D3×D912yes—
697C22C22×D3×D911yescharacteristic
698C4—21no—
699C4—32no—
700C4—61no—
701C4—61no—
702C4—92no—
703C4—181no—
704C4—181no—
705C4—272no—
706C4—272no—
707C4—272no—
708C4—541no—
709C4#8866312yesdirect product factor
710C3—21no—
711C3C4×#369911yescharacteristic, complemented
712C3C4×#380511yescharacteristic
713C2—22no—
714C2—62no—
715C2—182no—
716C2C2×C4×D3×D911yescharacteristic
717C2#1172247511yescharacteristic
718C2C2×#8866311yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
prime radicalC2×#88663C2
cosocleC22×C3×C9C24
hypercenterC22×C4D3×D9
hypocenterC3×C9C4×#41
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C3⋊Dic9C2semidirect
3. C4×C9×#67C2semidirect
4. C3×C4×#611C2semidirect
5. #67⋊Dic9C2semidirect
6. #611⋊Dic3C2semidirect
7. #11721248C2semidirect
8. #11721028C2semidirect
9. C4×#6194C2semidirect
10. #11721011C2semidirect
11. C4×D3×Dic9C2semidirect
12. #11720975C2semidirect
13. C4×Dic3×D9C2semidirect
14. C4×#6189C2semidirect
15. #11720902C2semidirect
26. #88663C4direct (N × H)
73. C4×#611D3semidirect
92. C2×C3⋊Dic9C2×C4semidirect
97. C9×#67C2×C4semidirect
98. C3×#611C2×C4semidirect
107. #6194C2×C4semidirect
109. D3×Dic9C2×C4semidirect
111. Dic3×D9C2×C4semidirect
112. #6189C2×C4semidirect
205. C3×C4×C9#41semidirect
209. C3⋊Dic9#41semidirect
225. C4×#67D9semidirect
291. #611C4×D3semidirect
441. C4×C9#237semidirect
468. C3×C9C4×#41semidirect
498. #67C4×D9semidirect
621. C3×C4#3699semidirect
643. C9C4×#237semidirect
709. C4#88663direct (N × H)
711. C3C4×#3699semidirect

Maximal subgroups

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

subgroupindex
C2×#886632
C2×C4×C3⋊Dic92
C4×C9×#672
C3×C4×#6112
#67⋊Dic92
#611⋊Dic32
#117212482
#117210282
C4×#61942
#117210112
C4×D3×Dic92
#117209752
C4×Dic3×D92
C4×#61892
#117209022
C4×#38053
C4×#36993