Finite Group Databasebeta

← #13148194

Subgroups — #13148194

Order 1728.

976 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
2#11721727C211yesmaximal, characteristic, complemented
3C9×#67⋊C4C211yesmaximal, characteristic, complemented
4C3×#63439C211yesmaximal, characteristic, complemented
5#67⋊Dic9C211yesmaximal, characteristic, complemented
6C2×Dic9⋊Dic3C211yesmaximal, characteristic, complemented
7#11721240C211yesmaximal, characteristic, complemented
8C4×#6195C211yesmaximal, characteristic, complemented
9#11721013C211yesmaximal, characteristic, complemented
10#11721011C211yesmaximal, characteristic, complemented
11D3×Dic9⋊C4C211yesmaximal, characteristic, complemented
12#11720980C211yesmaximal, characteristic, complemented
13C4×#6189C211yesmaximal, characteristic, complemented
14#11720901C211yesmaximal, characteristic, complemented
15#11720898C211yesmaximal, characteristic, complemented
16#10594049—31nomaximal
17#10589648—31nomaximal
18C2×#6233C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C22×C9×Dic3C2211yescharacteristic
23C22×C3×Dic9C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic
25C2×#6195C2211yescharacteristic
26#88662C418yescomplemented
27C2×D3×Dic9C2211yescharacteristic
28C2×D3×Dic9C2211yescharacteristic
29C2×(C3⋊D9)⋊C4C2211yescharacteristic
30C2×(C3⋊D9)⋊C4C2211yescharacteristic
31C2×#6189C2211yescharacteristic
32C3×C9×C22⋊C4C2211yescharacteristic
33#88536C2211yescharacteristic
34#88534C2211yescharacteristic
35C4×C3⋊Dic9C2211yescharacteristic
36C3×#3676C2211yescharacteristic
37C9×(C2×D3)⋊C4C2211yescharacteristic
38C9×Dic3⋊C4C2211yescharacteristic
39C4×C9×Dic3C2211yescharacteristic
40C3×Dic9⋊C4C2211yescharacteristic
41C3×Dic9⋊C4C2211yescharacteristic
42C3×C4×Dic9C2211yescharacteristic
43C3×C4×Dic9C2211yescharacteristic
44(C2×D3)⋊Dic9C2211yescharacteristic
45#88445C2211yescharacteristic
46Dic3⋊Dic9C2211yescharacteristic
47#88442C2211yescharacteristic
48Dic9⋊Dic3C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic9⋊Dic3C2211yescharacteristic
51Dic9⋊Dic3C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54C2×#3804—31no—
55#64090—31no—
56C3×#67⋊C4D311yescharacteristic
57C3×#877—31no—
58#67⋊Dic3—31no—
59C2×Dic3⋊Dic3—31no—
60#63952—31no—
61C4×#627—31no—
62C4×#626—31no—
63#63883—31no—
64#63880—31no—
65#63878—31no—
66D3×Dic3⋊C4—31no—
67#63837—31no—
68#63836—31no—
69C2×#3699—31no—
70C4×D4×C9—31no—
71D4×Dic9—31no—
72C4×#611—31no—
73C4×#611—31no—
74C2×Dic9⋊C4—31no—
75C2×Dic9⋊C4—31no—
76C4⋊C4×D9—31no—
77#63449—31no—
78#611⋊C4—31no—
79#611⋊C4—31no—
80#611⋊C4—61no—
81#63439—31no—
82#63439D311yescharacteristic, complemented
83#63434—31no—
84C4×Dic18—31no—
85C23×C3×C9C2311yescharacteristic
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90#6233C2×C414yescomplemented
91C2×C3⋊Dic9—41no—
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C4×C3⋊D9—41no—
96C9×#67C2×C414yescomplemented
97C2×C9×Dic3—41no—
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9C2×C414yescomplemented
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C4×D3×C9—41no—
107#6195C2×C414yescomplemented
108D3×Dic9—41no—
109D3×Dic9C2×C414yescomplemented
110(C3⋊D9)⋊C4—41no—
111(C3⋊D9)⋊C4C2×C414yescomplemented
112#6189C2×C414yescomplemented
113#5546—91no—
114#5523—91no—
115C2×#638—31no—
116C22×C3⋊Dic3—31no—
117C2×C4×C3⋊D3—31no—
118C2×C3×#67C2×D311yescharacteristic
119C22×C3×Dic3—31no—
120C22×C3×Dic3C2×D311yescharacteristic
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—
129C32×C22⋊C4C2×D311yescharacteristic
130#3752—31no—
131#3750—31no—
132C4×C3⋊Dic3—31no—
133C3×#217—31no—
134C3×(C2×D3)⋊C4C2×D311yescharacteristic
135C3×Dic3⋊C4—31no—
136C3×Dic3⋊C4—31no—
137C3×Dic3⋊C4C2×D311yescharacteristic
138C3×C4×Dic3—31no—
139C3×C4×Dic3—31no—
140C3×C4×Dic3C2×D311yescharacteristic
141#3724—31no—
142Dic3⋊Dic3—31no—
143Dic3⋊Dic3—31no—
144Dic3⋊Dic3—31no—
145Dic3⋊Dic3—31no—
146Dic3⋊Dic3—31no—
147#3722—31no—
148(C2×D3)⋊Dic3—31no—
149Dic32—31no—
150Dic32—31no—
151C2×D4×C9—31no—
152C22×C4×C9—31no—
153C22×C4×C9—31no—
154C2×#611—31no—
155C2×#611—31no—
156C2×#611—61no—
157C22×Dic9—31no—
158C22×Dic9—31no—
159C22×Dic9—31no—
160C22×Dic9—61no—
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—21no—
170C9×C22⋊C4—31no—
171C9×C22⋊C4C2×D311yescharacteristic
172C42×C9—31no—
173#3676—31no—
174#3676C2×D311yescharacteristic
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—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—61no—
186Dic9⋊C4C2×D311yescharacteristic
187Dic9⋊C4C2×D311yescharacteristic
188C4×Dic9—31no—
189C4×Dic9—31no—
190C4×Dic9—31no—
191C4×Dic9—61no—
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—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9C22×C412yes—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C9×Dic3C22×C412yes—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×Dic9C22×C412yes—
215C3×Dic9C22×C412yes—
216C2×#237—91no—
217C2×#235—91no—
218C3×C4×D4—31no—
219C3×#117—91no—
220D4×Dic3—91no—
221C4×#67—91no—
222C4×#67—91no—
223C2×C4⋊Dic3—91no—
224C2×Dic3⋊C4—91no—
225C2×Dic3⋊C4—91no—
226#892—91no—
227#892—91no—
228D3×C4⋊C4—91no—
229D3×C4⋊C4—91no—
230D3×C4⋊C4—91no—
231#887—91no—
232#67⋊C4—91no—
233#67⋊C4—91no—
234#67⋊C4—91no—
235#67⋊C4—91no—
236#67⋊C4—91no—
237#67⋊C4—181no—
238#67⋊C4D911yescharacteristic, complemented
239#877—31no—
240#877—91no—
241C4×D12—91no—
242C4×D12—91no—
243#872—91no—
244C4×Dic6—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
252#638—34no—
253C2×C3⋊Dic3—31no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—121no—
257C4×C3⋊D3—121no—
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—41no—
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C2×C3×Dic3C22×D311yescharacteristic
268C3×C4×D3—41no—
269#627—34no—
270#626—34no—
271#624—34no—
272#624—121no—
273D3×Dic3—34no—
274D3×Dic3—121no—
275C23×C9—21no—
276C23×C9—31no—
277C23×C9C22×D311yescharacteristic
278C22×D9—31no—
279C22×D9—61no—
280D4×C9—34no—
281C2×C4×C9—21no—
282C2×C4×C9—21no—
283C2×C4×C9—31no—
284C2×C4×C9—31no—
285C2×C4×C9—31no—
286C2×C4×C9—121no—
287C2×C4×C9—121no—
288C2×C4×C9C22×D311yescharacteristic
289C2×C4×C9C22×D311yescharacteristic
290#611—34no—
291#611—34no—
292#611—64no—
293C2×Dic9—31no—
294C2×Dic9—34no—
295C2×Dic9—31no—
296C2×Dic9—31no—
297C2×Dic9—61no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—121no—
301C2×Dic9—121no—
302C2×Dic9—122no—
303C2×Dic9C4×D314yescomplemented
304C2×Dic9C22×D311yescharacteristic
305C2×Dic9C22×D311yescharacteristic
306C2×Dic9C22×D311yescharacteristic
307C2×Dic9C22×D311yescharacteristic
308C4×D9—34no—
309C4×D9—121no—
310C4×D9—121no—
311C4×D9—122no—
312Dic18—34no—
313#520—271noSylow
314C2×C3×C9—22no—
315C2×C3×C9C23×C411yescharacteristic
316C2×C3×C9H(5,𝔽2)11yescharacteristic
317C2×C3×C92−1+411yescharacteristic
318C3⋊D9—22no—
319D3×C9—22no—
320C2×C3×D4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—91no—
324C2×#67—91no—
325C2×#67—91no—
326C2×#67—91no—
327C2×#67—181no—
328C2×#67C2×D911yescharacteristic
329C22×Dic3—31no—
330C22×Dic3—91no—
331C22×Dic3—91no—
332C22×Dic3—91no—
333C22×Dic3—91no—
334C22×Dic3—181no—
335C22×Dic3C2×D911yescharacteristic
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×C4⋊C4—91no—
353C3×C4⋊C4—91no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—91no—
357C3×C22⋊C4C2×D911yescharacteristic
358C3×C22⋊C4D3211yescharacteristic
359C3×C42—31no—
360C3×C42—91no—
361C3×C42—91no—
362#217—31no—
363#217—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—181no—
370(C2×D3)⋊C4C2×D911yescharacteristic
371C4⋊Dic3—91no—
372C4⋊Dic3—91no—
373C4⋊Dic3—91no—
374C4⋊Dic3—91no—
375C4⋊Dic3—91no—
376Dic3⋊C4—31no—
377Dic3⋊C4—31no—
378Dic3⋊C4—91no—
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—181no—
388Dic3⋊C4C2×D911yescharacteristic
389C4×Dic3—31no—
390C4×Dic3—31no—
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—21no—
411C3⋊Dic3—32no—
412C3⋊Dic3—61no—
413C3⋊Dic3—61no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—32no—
417C3×Dic3—32no—
418C3×Dic3—61no—
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—21no—
440C4×C9—32no—
441C4×C9—41no—
442C4×C9—41no—
443C4×C9—61no—
444C4×C9—61no—
445Dic9—21no—
446Dic9—21no—
447Dic9—32no—
448Dic9—62no—
449Dic9—62no—
450Dic9—61no—
451Dic9—61no—
452Dic9—121no—
453Dic9C2×C4×D312yes—
454Dic9C2×C4×D312yes—
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—91no—
465#117—271no—
466#117—271no—
467C2×C4⋊C4—271no—
468C2×C4⋊C4—271no—
469C2×C4⋊C4—271no—
470C3×C9#52011yescharacteristic, 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—21no—
481C2×C3×C4—21no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—94no—
486C2×C3×C4—91no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4—121no—
491C2×C3×C4—121no—
492C2×C3×C4C22×D911yescharacteristic
493C2×C3×C4C22×D911yescharacteristic
494C2×C3×C4C2×D3211yescharacteristic
495C2×C3×C4C2×D3211yescharacteristic
496#67—94no—
497#67—94no—
498#67—94no—
499#67—184no—
500#67C4×D914yescomplemented
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—34no—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—41no—
507C2×Dic3—94no—
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—361no—
518C2×Dic3—361no—
519C2×Dic3—361no—
520C2×Dic3—362no—
521C2×Dic3C22×D911yescharacteristic
522C2×Dic3C22×D911yescharacteristic
523C2×Dic3C22×D911yescharacteristic
524D12—94no—
525C4×D3—41no—
526C4×D3—94no—
527C4×D3—94no—
528C4×D3—94no—
529C4×D3—361no—
530C4×D3—361no—
531C4×D3—361no—
532C4×D3—361no—
533C4×D3—362no—
534C4×D3—361no—
535Dic6—94no—
536Dic6—94no—
537C2×C32—22no—
538C2×C32C22×C4×D311yescharacteristic
539C2×C32#100411yescharacteristic
540C2×C32#101011yescharacteristic
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×C9#100911yescharacteristic
551C2×C9#101011yescharacteristic
552D9—62no—
553D9—122no—
554#41—278no—
555C2×Q8—271no—
556C2×D4—31no—
557C2×D4—271no—
558C2×D4—271no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—91no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4—271no—
565C22×C4—271no—
566C22×C4—271no—
567C22×C4—271no—
568C4⋊C4—31no—
569C4⋊C4—91no—
570C4⋊C4—91no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C4⋊C4—271no—
575C4⋊C4—271no—
576C4⋊C4—271no—
577C4⋊C4—271no—
578C22⋊C4—31no—
579C22⋊C4—91no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4D3×D911yescharacteristic
584C42—31no—
585C42—91no—
586C42—91no—
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—21no—
620C3×C4—21no—
621C3×C4—32no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—61no—
625C3×C4—61no—
626C3×C4—92no—
627C3×C4—92no—
628C3×C4—181no—
629C3×C4—181no—
630Dic3—21no—
631Dic3—21no—
632Dic3—32no—
633Dic3—32no—
634Dic3—61no—
635Dic3—61no—
636Dic3—92no—
637Dic3—92no—
638Dic3—182no—
639Dic3—182no—
640Dic3—181no—
641Dic3—181no—
642Dic3—181no—
643Dic3—181no—
644Dic3—361no—
645Dic3C2×C4×D912yes—
646C32#554611yescharacteristic
647C9—21no—
648C9#552311yescharacteristic, complemented
649C23—31no—
650C23—271no—
651C23C2×D3×D911yescharacteristic
652Q8—274no—
653D4—34no—
654D4—274no—
655D4—274no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—91no—
660C2×C4—91no—
661C2×C4—94no—
662C2×C4—91no—
663C2×C4—91no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4—274no—
667C2×C4—274no—
668C2×C4—271no—
669C2×C4—271no—
670C2×C4—271no—
671C2×C4—1081no—
672C2×C4—1081no—
673C2×C4—1081no—
674C2×C4—1081no—
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×C3#6371011yescharacteristic
686C2×C3#6371611yescharacteristic
687C2×C3C2×C4×D3211yescharacteristic
688C2×C3#6430911yescharacteristic
689C2×C3#6431411yescharacteristic
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—21no—
706C4—32no—
707C4—61no—
708C4—61no—
709C4—92no—
710C4—92no—
711C4—181no—
712C4—181no—
713C4—272no—
714C4—541no—
715C4—541no—
716C3—21no—
717C3#1058964811yescharacteristic, complemented
718C3#1059404911yescharacteristic
719C2—22no—
720C2—62no—
721C2—542no—
722C2C2×C4×D3×D911yescharacteristic
723C2#1172249411yescharacteristic
724C2#1172250011yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC2×#88662C2
cosocleC22×C3×C9C24
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#520
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. #11721727C2semidirect
3. C9×#67⋊C4C2semidirect
4. C3×#63439C2semidirect
5. #67⋊Dic9C2semidirect
6. C2×Dic9⋊Dic3C2semidirect
7. #11721240C2semidirect
8. C4×#6195C2semidirect
9. #11721013C2semidirect
10. #11721011C2semidirect
11. D3×Dic9⋊C4C2semidirect
12. #11720980C2semidirect
13. C4×#6189C2semidirect
14. #11720901C2semidirect
15. #11720898C2semidirect
26. #88662C4semidirect
82. #63439D3semidirect
90. #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
238. #67⋊C4D9semidirect
303. C2×Dic9C4×D3semidirect
470. C3×C9#520semidirect
500. #67C4×D9semidirect
648. C9#5523semidirect
717. C3#10589648semidirect

Maximal subgroups

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

subgroupindex
C2×#886622
#117217272
C9×#67⋊C42
C3×#634392
#67⋊Dic92
C2×Dic9⋊Dic32
#117212402
C4×#61952
#117210132
#117210112
D3×Dic9⋊C42
#117209802
C4×#61892
#117209012
#117208982
#105940493
#105896483