Finite Group Databasebeta

← C4×#88662 #13150356

Subgroups — C4×#88662 #13150356

Order 1728.

1024 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88662C211yesmaximal, characteristic
2C4×#6233C211yesmaximal, characteristic, complemented
3C4×C9×#67C211yesmaximal, characteristic, complemented
4C2×C3×C4×Dic9C211yesmaximal, characteristic, complemented
5#67×Dic9C211yesmaximal, characteristic, complemented
6#11721245C211yesmaximal, characteristic, complemented
7#11721241C211yesmaximal, characteristic, complemented
8C4×#6195C211yesmaximal, characteristic, complemented
9#11721013C211yesmaximal, characteristic, complemented
10#11721010C211yesmaximal, characteristic, complemented
11C4×D3×Dic9C211yesmaximal, characteristic, complemented
12C4×(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
13C4×#6189C211yesmaximal, characteristic, complemented
14#11720901C211yesmaximal, characteristic, complemented
15#11720899C211yesmaximal, characteristic, complemented
16C4×#3804—31nomaximal
17C4×#3699—31nomaximal
18C22×C3×C4×C9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C22×C3×Dic9C2211yescharacteristic
23C22×C3×Dic9C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic
25C2×#6195C2211yescharacteristic
26#88662C418yesdirect product factor
27C2×D3×Dic9C2211yescharacteristic
28C2×D3×Dic9C2211yescharacteristic
29C2×(C3⋊D9)⋊C4C2211yescharacteristic
30C2×(C3⋊D9)⋊C4C2211yescharacteristic
31C2×#6189C2211yescharacteristic
32#88551C2211yescharacteristic
33#88536C2211yescharacteristic
34#88534C2211yescharacteristic
35C4×C3⋊Dic9C2211yescharacteristic
36C9×#217C2211yescharacteristic
37C9×(C2×D3)⋊C4C2211yescharacteristic
38C9×Dic3⋊C4C2211yescharacteristic
39C4×C9×Dic3C2211yescharacteristic
40C3×C4×Dic9C2211yescharacteristic
41C3×C4×Dic9C2211yescharacteristic
42C3×C4×Dic9C2211yescharacteristic
43C3×C4×Dic9C2211yescharacteristic
44(C2×D3)⋊Dic9C2211yescharacteristic
45#88445C2211yescharacteristic
46Dic3⋊Dic9C2211yescharacteristic
47#88442C2211yescharacteristic
48Dic9⋊Dic3C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic3×Dic9C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54C2×#3804—31no—
55C4×#638—31no—
56C3×C4×#67D311yescharacteristic
57C2×C3×C4×Dic3—31no—
58Dic3×#67—31no—
59#63955—31no—
60#63952—31no—
61C4×#627—31no—
62C4×#626—31no—
63C4×#624—31no—
64#63880—31no—
65#63877—31no—
66C4×D3×Dic3—31no—
67#63837—31no—
68#63836—31no—
69C2×#3699—31no—
70C4×D4×C9—31no—
71D4×Dic9—31no—
72C4×#611—31no—
73C4×#611—31no—
74C4×#611—61no—
75C2×C4×Dic9—31no—
76C2×C4×Dic9D311yescharacteristic, complemented
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×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C2×C3×C4×C9—22no—
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91#6233C2×C414yescomplemented
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C4×C3⋊D9—22no—
96C9×#67C2×C414yescomplemented
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C3×Dic9—22no—
101C2×C3×Dic9C2×C414yescomplemented
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C4×D3×C9—22no—
107#6195C2×C414yescomplemented
108D3×Dic9—22no—
109D3×Dic9C2×C414yescomplemented
110(C3⋊D9)⋊C4—22no—
111(C3⋊D9)⋊C4C2×C414yescomplemented
112#6189C2×C414yescomplemented
113C4×#237—91no—
114C4×#235—91no—
115C22×C32×C4C2×D311yescharacteristic
116C2×#638—31no—
117C2×C4×C3⋊D3—31no—
118C2×C3×#67C2×D311yescharacteristic
119C22×C3×Dic3—31no—
120C22×C3×Dic3—31no—
121C2×C3×C4×D3C2×D311yescharacteristic
122C2×#627—31no—
123C2×#626—31no—
124C2×#624—31no—
125C2×#624—31no—
126#3804—38no—
127C2×D3×Dic3—31no—
128C2×D3×Dic3—31no—
129#3757—31no—
130#3752—31no—
131#3750—31no—
132C4×C3⋊Dic3—31no—
133C3×#217C2×D311yescharacteristic
134C3×(C2×D3)⋊C4C2×D311yescharacteristic
135C3×Dic3⋊C4C2×D311yescharacteristic
136C3×C4×Dic3—31no—
137C3×C4×Dic3—31no—
138C3×C4×Dic3—31no—
139C3×C4×Dic3—31no—
140C3×C4×Dic3C2×D311yescharacteristic
141#3724—31no—
142Dic3⋊Dic3—31no—
143Dic3⋊Dic3—31no—
144Dic3⋊Dic3—31no—
145#3722—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×#611—31no—
157C2×#611—61no—
158C22×Dic9—31no—
159C22×Dic9—31no—
160C22×Dic9C2×D311yescharacteristic
161C22×Dic9C2×D311yescharacteristic
162#3699—38no—
163C2×C4×D9—31no—
164C2×C4×D9—31no—
165C2×C4×D9—31no—
166C2×C4×D9—61no—
167C2×Dic18—31no—
168C9×C4⋊C4—31no—
169C9×C22⋊C4—31no—
170C9×C22⋊C4—31no—
171C42×C9—31no—
172#3676—31no—
173#3676—31no—
174#3676—61no—
175(C2×D9)⋊C4—31no—
176(C2×D9)⋊C4—31no—
177(C2×D9)⋊C4—61no—
178C4⋊Dic9—31no—
179Dic9⋊C4—31no—
180Dic9⋊C4—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—61no—
184C4×Dic9—31no—
185C4×Dic9—31no—
186C4×Dic9—31no—
187C4×Dic9—31no—
188C4×Dic9—31no—
189C4×Dic9—61no—
190C4×Dic9C2×D311yescharacteristic
191C4×Dic9C2×D311yescharacteristic
192C4×Dic9C2×D311yescharacteristic
193C4×Dic9C2×D311yescharacteristic
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9C22×C412yes—
197C22×C3×C9C2411yescharacteristic
198C2×C3⋊D9—21no—
199C2×C3⋊D9—21no—
200C2×C3⋊D9C22×C412yes—
201C2×D3×C9—21no—
202C2×D3×C9—21no—
203C2×D3×C9C22×C412yes—
204C3×C4×C9—21no—
205C3×C4×C9#4112yescomplemented
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9C22×C412yes—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C9×Dic3C22×C412yes—
212C3×Dic9—21no—
213C3×Dic9C22×C412yes—
214C3×Dic9C22×C412yes—
215C3×Dic9#4112yescomplemented
216C2×#237—91no—
217C2×#235—91no—
218C3×C4×D4—31no—
219C2×C3×C42—91no—
220D4×Dic3—91no—
221C4×#67—91no—
222C4×#67—91no—
223C4×#67—91no—
224C4×#67—91no—
225C4×#67—91no—
226C4×#67—181no—
227C4×#67D911yescharacteristic, complemented
228#926—91no—
229C2×C4×Dic3—31no—
230C2×C4×Dic3—91no—
231#892—91no—
232#887—91no—
233#67⋊C4—91no—
234#67⋊C4—91no—
235#877—91no—
236#877—91no—
237C4×D12—91no—
238C4×D12—91no—
239#872—91no—
240#872—91no—
241C42×D3—91no—
242C42×D3—91no—
243C42×D3—91no—
244C4×Dic6—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
253#638—34no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C4×C3⋊D3—62no—
258C3×#67C4×D314yes—
259C2×C3×Dic3—34no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—62no—
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C2×C3×Dic3C22×D311yescharacteristic
268C3×C4×D3—22no—
269#627—34no—
270#626—34no—
271#624—34no—
272#624—62no—
273D3×Dic3—34no—
274D3×Dic3—62no—
275C23×C9—21no—
276C23×C9—31no—
277C23×C9C22×D311yescharacteristic
278C22×D9—31no—
279C22×D9—61no—
280D4×C9—34no—
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—42no—
288C2×C4×C9—62no—
289C2×C4×C9C22×D311yescharacteristic
290C2×C4×C9C22×D311yescharacteristic
291#611—34no—
292#611—34no—
293#611—64no—
294C2×Dic9—22no—
295C2×Dic9—31no—
296C2×Dic9—34no—
297C2×Dic9—31no—
298C2×Dic9—31no—
299C2×Dic9—61no—
300C2×Dic9—61no—
301C2×Dic9—61no—
302C2×Dic9—62no—
303C2×Dic9C4×D314yescomplemented
304C2×Dic9C22×D311yescharacteristic
305C2×Dic9C22×D311yescharacteristic
306C2×Dic9C22×D311yescharacteristic
307C2×Dic9C22×D311yescharacteristic
308C4×D9—34no—
309C4×D9—62no—
310C4×D9—62no—
311C4×D9—122no—
312Dic18—34no—
313C4×#41—271noSylow
314C2×C3×C9—22no—
315C2×C3×C9C23×C411yescharacteristic
316C2×C3×C9C2×#4111yescharacteristic
317C2×C3×C9C2×#4111yescharacteristic
318C3⋊D9—22no—
319D3×C9—22no—
320C2×C3×D4—31no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—91no—
324C22×C3×C4—91no—
325C22×C3×C4C2×D911yescharacteristic
326C22×C3×C4D3211yescharacteristic
327C2×#67—91no—
328C2×#67—91no—
329C2×#67—91no—
330C2×#67—181no—
331C2×#67C2×D911yescharacteristic
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—91no—
335C22×Dic3—91no—
336#237—98no—
337#235—98no—
338C2×D12—91no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×C4×D3—91no—
344C2×C4×D3—91no—
345C2×C4×D3—91no—
346C2×C4×D3—91no—
347C2×C4×D3—181no—
348C2×C4×D3C2×D911yescharacteristic
349C2×Dic6—91no—
350C2×Dic6—91no—
351C3×C4⋊C4—31no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C42—31no—
355C3×C42—91no—
356C3×C42—91no—
357C3×C42—91no—
358C3×C42—91no—
359#217—91no—
360#217—91no—
361#217—91no—
362#217—181no—
363#217C2×D911yescharacteristic
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)⋊C4C2×D911yescharacteristic
371C4⋊Dic3—91no—
372C4⋊Dic3—91no—
373C4⋊Dic3—91no—
374Dic3⋊C4—91no—
375Dic3⋊C4—91no—
376Dic3⋊C4—91no—
377Dic3⋊C4—91no—
378Dic3⋊C4—91no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—181no—
382Dic3⋊C4C2×D911yescharacteristic
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—91no—
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3—91no—
395C4×Dic3—91no—
396C4×Dic3—91no—
397C4×Dic3—181no—
398C4×Dic3C2×D911yescharacteristic
399C22×C32—21no—
400C22×C32—21no—
401C22×C32C2×C4×D312yes—
402C22×C32C23×D311yescharacteristic
403C2×C3⋊D3—32no—
404C2×C3⋊D3—61no—
405C2×C3⋊D3—61no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3C2×C4×D312yes—
409C32×C4—21no—
410C32×C4#23712yes—
411C3⋊Dic3—32no—
412C3⋊Dic3—61no—
413C3⋊Dic3—61no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—32no—
417C3×Dic3—32no—
418C3×Dic3—32no—
419C3×Dic3—61no—
420C3×Dic3C2×C4×D312yes—
421C22×C9—21no—
422C22×C9—21no—
423C22×C9—21no—
424C22×C9—22no—
425C22×C9—32no—
426C22×C9—41no—
427C22×C9—41no—
428C22×C9—61no—
429C22×C9—61no—
430C22×C9C2×C4×D312yes—
431C22×C9C23×D311yescharacteristic
432C2×D9—32no—
433C2×D9—62no—
434C2×D9—61no—
435C2×D9—61no—
436C2×D9—121no—
437C2×D9—121no—
438C4×C9—21no—
439C4×C9—22no—
440C4×C9—32no—
441C4×C9—41no—
442C4×C9—61no—
443C4×C9—61no—
444C4×C9#23512yescomplemented
445Dic9—21no—
446Dic9—32no—
447Dic9—62no—
448Dic9—61no—
449Dic9—61no—
450Dic9—121no—
451Dic9—121no—
452Dic9C2×C4×D312yes—
453Dic9C2×C4×D312yes—
454Dic9#23512yescomplemented
455C2×#41—271no—
456C4×Q8—271no—
457C4×Q8—271no—
458C4×D4—31no—
459C4×D4—271no—
460C4×D4—271no—
461C4×D4—271no—
462C4×D4—271no—
463C4×D4—271no—
464#117—271no—
465#117—271no—
466#117—271no—
467C2×C42—91no—
468C2×C42—271no—
469C2×C42—271no—
470C3×C9C4×#4111yescharacteristic, complemented, Sylow
471C23×C3—21no—
472C23×C3—31no—
473C23×C3C22×D911yescharacteristic
474C23×C3C2×D3211yescharacteristic
475C22×D3—91no—
476C22×D3—91no—
477C22×D3—181no—
478C22×D3C22×D911yescharacteristic
479C3×D4—34no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—42no—
488C2×C3×C4—62no—
489C2×C3×C4—94no—
490C2×C3×C4—91no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—182no—
495C2×C3×C4C22×D911yescharacteristic
496C2×C3×C4C22×D911yescharacteristic
497C2×C3×C4C2×D3211yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499#67—94no—
500#67—94no—
501#67—94no—
502#67—184no—
503#67C4×D914yescomplemented
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—34no—
508C2×Dic3—31no—
509C2×Dic3—62no—
510C2×Dic3—94no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—91no—
515C2×Dic3—91no—
516C2×Dic3—91no—
517C2×Dic3—181no—
518C2×Dic3—181no—
519C2×Dic3—181no—
520C2×Dic3—182no—
521C2×Dic3C22×D911yescharacteristic
522C2×Dic3C22×D911yescharacteristic
523C2×Dic3C22×D911yescharacteristic
524D12—94no—
525C4×D3—22no—
526C4×D3—94no—
527C4×D3—94no—
528C4×D3—94no—
529C4×D3—182no—
530C4×D3—182no—
531C4×D3—182no—
532C4×D3—182no—
533C4×D3—182no—
534C4×D3—362no—
535Dic6—94no—
536Dic6—94no—
537C2×C32—22no—
538C2×C32C22×C4×D311yescharacteristic
539C2×C32C2×#23711yescharacteristic
540C2×C32D3×#4111yescharacteristic
541C3⋊D3—62no—
542C3×D3—22no—
543C2×C9—22no—
544C2×C9—21no—
545C2×C9—21no—
546C2×C9—21no—
547C2×C9—42no—
548C2×C9—62no—
549C2×C9C22×C4×D311yescharacteristic
550C2×C9C2×#23511yescharacteristic
551C2×C9C2×#23511yescharacteristic
552D9—62no—
553D9—122no—
554#41—278no—
555C2×Q8—271no—
556C2×D4—31no—
557C2×D4—271no—
558C2×D4—271no—
559C22×C4—31no—
560C22×C4—91no—
561C22×C4—91no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4—271no—
565C22×C4—271no—
566C22×C4—271no—
567C22×C4D3×D911yescharacteristic
568C4⋊C4—31no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C22⋊C4—31no—
575C22⋊C4—31no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C42—31no—
581C42—91no—
582C42—91no—
583C42—91no—
584C42—91no—
585C42—271no—
586C42—271no—
587C42—271no—
588C42—271no—
589C42—271no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—22no—
596C22×C3—32no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—61no—
600C22×C3—61no—
601C22×C3C2×C4×D912yes—
602C22×C3C23×D911yescharacteristic
603C22×C3C4×D3212yes—
604C22×C3C22×D3211yescharacteristic
605C2×D3—21no—
606C2×D3—21no—
607C2×D3—92no—
608C2×D3—92no—
609C2×D3—182no—
610C2×D3—181no—
611C2×D3—181no—
612C2×D3—181no—
613C2×D3—181no—
614C2×D3—361no—
615C2×D3—361no—
616C2×D3C2×C4×D912yes—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—22no—
620C3×C4—32no—
621C3×C4—41no—
622C3×C4—61no—
623C3×C4—61no—
624C3×C4—92no—
625C3×C4—92no—
626C3×C4—92no—
627C3×C4—181no—
628C3×C4#369912yescomplemented
629C3×C4#380412yes—
630Dic3—21no—
631Dic3—21no—
632Dic3—32no—
633Dic3—32no—
634Dic3—32no—
635Dic3—61no—
636Dic3—92no—
637Dic3—92no—
638Dic3—182no—
639Dic3—181no—
640Dic3—181no—
641Dic3—181no—
642Dic3—181no—
643Dic3—361no—
644Dic3—361no—
645Dic3C2×C4×D912yes—
646C32C4×#23711yescharacteristic
647C9—21no—
648C9C4×#23511yescharacteristic, complemented
649C23—31no—
650C23—271no—
651C23C2×D3×D911yescharacteristic
652Q8—274no—
653D4—34no—
654D4—274no—
655D4—274no—
656C2×C4—22no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—62no—
661C2×C4—91no—
662C2×C4—91no—
663C2×C4—91no—
664C2×C4—94no—
665C2×C4—91no—
666C2×C4—182no—
667C2×C4—274no—
668C2×C4—274no—
669C2×C4—271no—
670C2×C4—271no—
671C2×C4—271no—
672C2×C4—542no—
673C2×C4—542no—
674C2×C4—542no—
675C2×C4C2×D3×D911yescharacteristic
676C2×C4C2×D3×D911yescharacteristic
677C2×C3—22no—
678C2×C3—22no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—42no—
683C2×C3—62no—
684C2×C3C22×C4×D911yescharacteristic
685C2×C3C2×#369911yescharacteristic
686C2×C3#41×D911yescharacteristic
687C2×C3C2×C4×D3211yescharacteristic
688C2×C3D3×#23511yescharacteristic
689C2×C3C2×#380411yescharacteristic
690D3—22no—
691D3—182no—
692D3—182no—
693D3—362no—
694C22—21no—
695C22—21no—
696C22—32no—
697C22—61no—
698C22—61no—
699C22—272no—
700C22—541no—
701C22—541no—
702C22C4×D3×D912yes—
703C22C22×D3×D911yescharacteristic
704C4—21no—
705C4—32no—
706C4—61no—
707C4—61no—
708C4—92no—
709C4—92no—
710C4—92no—
711C4—181no—
712C4—272no—
713C4—541no—
714C4—541no—
715C4#8866212yesdirect product factor
716C3—21no—
717C3C4×#369911yescharacteristic, complemented
718C3C4×#380411yescharacteristic
719C2—22no—
720C2—62no—
721C2—542no—
722C2C2×C4×D3×D911yescharacteristic
723C2D9×#23511yescharacteristic
724C2C2×#8866211yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
prime radicalC2×#88662C2
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. C4×#6233C2semidirect
3. C4×C9×#67C2semidirect
4. C2×C3×C4×Dic9C2semidirect
5. #67×Dic9C2semidirect
6. #11721245C2semidirect
7. #11721241C2semidirect
8. C4×#6195C2semidirect
9. #11721013C2semidirect
10. #11721010C2semidirect
11. C4×D3×Dic9C2semidirect
12. C4×(C3⋊D9)⋊C4C2semidirect
13. C4×#6189C2semidirect
14. #11720901C2semidirect
15. #11720899C2semidirect
26. #88662C4direct (N × H)
76. C2×C4×Dic9D3semidirect
91. #6233C2×C4semidirect
96. C9×#67C2×C4semidirect
101. C2×C3×Dic9C2×C4semidirect
107. #6195C2×C4semidirect
109. D3×Dic9C2×C4semidirect
111. (C3⋊D9)⋊C4C2×C4semidirect
112. #6189C2×C4semidirect
205. C3×C4×C9#41semidirect
215. C3×Dic9#41semidirect
227. C4×#67D9semidirect
303. C2×Dic9C4×D3semidirect
444. C4×C9#235semidirect
454. Dic9#235semidirect
470. C3×C9C4×#41semidirect
503. #67C4×D9semidirect
628. C3×C4#3699semidirect
648. C9C4×#235semidirect
715. C4#88662direct (N × H)
717. C3C4×#3699semidirect

Maximal subgroups

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

subgroupindex
C2×#886622
C4×#62332
C4×C9×#672
C2×C3×C4×Dic92
#67×Dic92
#117212452
#117212412
C4×#61952
#117210132
#117210102
C4×D3×Dic92
C4×(C3⋊D9)⋊C42
C4×#61892
#117209012
#117208992
C4×#38043
C4×#36993