Finite Group Databasebeta

← #13150345

Subgroups — #13150345

Order 1728.

882 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88536C211yesmaximal, characteristic, complemented
2C4×C9×#67C211yesmaximal, characteristic, complemented
3C3×C4×#611C211yesmaximal, characteristic, complemented
4#11721291C211yesmaximal, characteristic, complemented
5#11721290C211yesmaximal, characteristic, complemented
6#11721278C211yesmaximal, characteristic, complemented
7#11721267C211yesmaximal, characteristic, complemented
8#11721034C211yesmaximal, characteristic, complemented
9#11721033C211yesmaximal, characteristic, complemented
10#11720956C211yesmaximal, characteristic, complemented
11#11720954C211yesmaximal, characteristic, complemented
12#11720940C211yesmaximal, characteristic, complemented
13#11720938C211yesmaximal, characteristic, complemented
14#11720934C211yesmaximal, characteristic, complemented
15#11720926C211yesmaximal, characteristic, complemented
16#10595039—31nomaximal
17#10589662—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic, complemented
24C2×C3×C4×D9C2211yescharacteristic, complemented
25C2×#6195C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×#6194C2211yescharacteristic, complemented
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×#6189C2211yescharacteristic, complemented
31#88536C2211yescharacteristic
32#88536C2211yescharacteristic
33#88536C2211yescharacteristic
34#88536C2211yescharacteristic
35C9×#217C2211yescharacteristic
36C3×#3676C2211yescharacteristic
37C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
39C9×Dic3⋊C4C2211yescharacteristic, complemented
40C4×C9×Dic3C2211yescharacteristic, complemented
41C3×Dic9⋊C4C2211yescharacteristic, complemented
42C3×C4×Dic9C2211yescharacteristic, complemented
43(C2×D3)⋊Dic9C2211yescharacteristic, complemented
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic, complemented
49Dic3⋊Dic9C2211yescharacteristic, complemented
50#88442C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53C2×#3752—31no—
54C3×C4×#67—31no—
55C3×C4×#67D311yescharacteristic
56#63982—31no—
57#63981—31no—
58#63981—31no—
59#63980—31no—
60#63906—31no—
61#63906—31no—
62#63868—31no—
63#63868—31no—
64#63852—31no—
65#63852—31no—
66#63850—31no—
67#63850—31no—
68C4×D4×C9—31no—
69#63501—31no—
70#63499—31no—
71#63492—31no—
72#63491—31no—
73C4×#611D311yescharacteristic, complemented
74C2×(C2×D9)⋊C4—31no—
75C2×(C2×D9)⋊C4—61no—
76#63460—31no—
77#63456—31no—
78#63447—31no—
79#63446—31no—
80#63444—31no—
81#63440—31no—
82#63438—31no—
83#63437—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9—22no—
86C22×C3⋊D9—41no—
87C22×C3⋊D9—41no—
88C22×C3⋊D9C2311yescharacteristic
89C22×C3⋊D9C2311yescharacteristic
90C22×D3×C9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C2×C3×C4×C9—41no—
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3⋊Dic9—41no—
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C9×#67—22no—
99C3×#611—22no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C4×D3×C9—41no—
107C3×C4×D9—41no—
108#6195—41no—
109#6195—41no—
110#6194—41no—
111#6192—41no—
112#6192—41no—
113#6189—41no—
114#5560—91no—
115#5560—91no—
116C23×C3⋊D3—31no—
117C22×C32×C4C2×D311yescharacteristic
118C22×C3⋊Dic3—31no—
119C2×C3×#67—31no—
120C2×C3×#67C2×D311yescharacteristic
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3C2×D311yescharacteristic
123C2×#627—31no—
124C2×#626—31no—
125C2×#626—31no—
126C2×#626—31no—
127C2×#626—31no—
128C2×#625—31no—
129C23×D9—31no—
130C23×D9—61no—
131#3752—31no—
132#3752—31no—
133#3752—31no—
134#3752—31no—
135C3×#217—31no—
136C3×#217C2×D311yescharacteristic
137C3×(C2×D3)⋊C4—31no—
138C3×(C2×D3)⋊C4C2×D311yescharacteristic
139C3×Dic3⋊C4—31no—
140C3×Dic3⋊C4C2×D311yescharacteristic
141C3×C4×Dic3—31no—
142C3×C4×Dic3C2×D311yescharacteristic
143#3724—31no—
144#3724—31no—
145Dic3⋊Dic3—31no—
146Dic3⋊Dic3—31no—
147#3722—31no—
148#3722—31no—
149#3722—31no—
150#3722—31no—
151(C2×D3)⋊Dic3—31no—
152(C2×D3)⋊Dic3—31no—
153C2×D4×C9—31no—
154C22×C4×C9—21no—
155C22×C4×C9—31no—
156C22×C4×C9C2×D311yescharacteristic
157C2×#611—31no—
158C2×#611—31no—
159C2×#611—31no—
160C2×#611C2×D311yescharacteristic
161C22×Dic9—31no—
162C22×Dic9—61no—
163C2×D36—31no—
164C2×D36—31no—
165C2×C4×D9C2×D311yescharacteristic, complemented
166C2×Dic18—31no—
167C9×C4⋊C4—31no—
168C9×C22⋊C4—31no—
169C9×C22⋊C4—31no—
170C42×C9—31no—
171#3676—31no—
172#3676C2×D311yescharacteristic
173(C2×D9)⋊C4—31no—
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4—31no—
176(C2×D9)⋊C4—31no—
177(C2×D9)⋊C4—31no—
178(C2×D9)⋊C4—31no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—61no—
183(C2×D9)⋊C4—61no—
184(C2×D9)⋊C4—61no—
185(C2×D9)⋊C4—61no—
186(C2×D9)⋊C4C2×D311yescharacteristic, complemented
187C4⋊Dic9—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—31no—
191Dic9⋊C4C2×D311yescharacteristic, complemented
192C4×Dic9C2×D311yescharacteristic, complemented
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9#4112yes—
196C22×C3×C9C2411yescharacteristic
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9—21no—
200C2×C3⋊D9—21no—
201C2×C3⋊D9—21no—
202C2×C3⋊D9—21no—
203C2×C3⋊D9—44no—
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×D3×C9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9—21no—
214C9×Dic3—21no—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×C4×D4—31no—
221C3×C4×D4—91no—
222#939—91no—
223#939—91no—
224#937—91no—
225#937—91no—
226#930—91no—
227#930—91no—
228#929—91no—
229#929—91no—
230C4×#67—31no—
231C4×#67D911yescharacteristic, complemented
232C2×(C2×D3)⋊C4—91no—
233C2×(C2×D3)⋊C4—91no—
234C2×(C2×D3)⋊C4—181no—
235#898—91no—
236#898—91no—
237#894—91no—
238#894—91no—
239#885—91no—
240#885—91no—
241#884—91no—
242#884—91no—
243#882—91no—
244#882—91no—
245#878—91no—
246#878—91no—
247#876—91no—
248#876—91no—
249#875—91no—
250#875—91no—
251C23×C32C22×D311yescharacteristic
252C22×C3⋊D3—31no—
253C22×C3⋊D3—31no—
254C22×C3⋊D3—62no—
255C22×C3⋊D3—121no—
256C22×C3⋊D3—121no—
257C22×C3×D3—31no—
258C22×C3×D3C22×D311yescharacteristic
259C2×C32×C4—41no—
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—121no—
265C3×#67—22no—
266C3×#67—62no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C22×D311yescharacteristic
272C2×C3×Dic3C22×D311yescharacteristic
273C3×C4×D3—41no—
274C3×C4×D3—121no—
275#627—121no—
276#626—121no—
277#626—121no—
278#626—121no—
279#626—121no—
280#625—121no—
281C23×C9—21no—
282C23×C9—31no—
283C23×C9C22×D311yescharacteristic
284C22×D9—31no—
285C22×D9—31no—
286C22×D9—61no—
287C22×D9—61no—
288C22×D9—64no—
289C22×D9—62no—
290C22×D9—121no—
291C22×D9—121no—
292C22×D9—122no—
293C22×D9—122no—
294C22×D9C22×D311yescharacteristic
295D4×C9—62no—
296C2×C4×C9—21no—
297C2×C4×C9—21no—
298C2×C4×C9—31no—
299C2×C4×C9—31no—
300C2×C4×C9—31no—
301C2×C4×C9—41no—
302C2×C4×C9—42no—
303C2×C4×C9—121no—
304C2×C4×C9C22×D311yescharacteristic
305C2×C4×C9C22×D311yescharacteristic
306#611—22no—
307#611—121no—
308#611—121no—
309#611—121no—
310C2×Dic9—31no—
311C2×Dic9—31no—
312C2×Dic9—61no—
313C2×Dic9—61no—
314C2×Dic9—121no—
315C2×Dic9—122no—
316C2×Dic9C22×D311yescharacteristic
317C2×Dic9C22×D311yescharacteristic
318C2×Dic9C22×D311yescharacteristic
319D36—121no—
320D36—121no—
321C4×D9—41no—
322Dic18—121no—
323#538—271noSylow
324C2×C3×C9—22no—
325C2×C3×C9C2×#4111yescharacteristic
326C2×C3×C9H(5,𝔽2)11yescharacteristic
327C2×C3×C9H(5,𝔽2)11yescharacteristic
328C3⋊D9—41no—
329C3⋊D9—41no—
330D3×C9—41no—
331C3×D9—41no—
332C23×D3—91no—
333C23×D3—91no—
334C23×D3—181no—
335C2×C3×D4—31no—
336C2×C3×D4—91no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—91no—
340C22×C3×C4C2×D911yescharacteristic
341C22×C3×C4D3211yescharacteristic
342C2×#67—31no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—91no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67C2×D911yescharacteristic
350C22×Dic3—91no—
351C22×Dic3—91no—
352C22×Dic3—181no—
353C2×D12—91no—
354C2×D12—91no—
355C2×D12—91no—
356C2×D12—91no—
357C2×C4×D3—31no—
358C2×C4×D3C2×D911yescharacteristic, complemented
359C2×Dic6—91no—
360C2×Dic6—91no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—91no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367C3×C42—31no—
368C3×C42—91no—
369#217—31no—
370#217—91no—
371#217—91no—
372#217C2×D911yescharacteristic
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—91no—
377(C2×D3)⋊C4—91no—
378(C2×D3)⋊C4—91no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—181no—
393(C2×D3)⋊C4—181no—
394(C2×D3)⋊C4—181no—
395(C2×D3)⋊C4—181no—
396(C2×D3)⋊C4C2×D911yescharacteristic, complemented
397C4⋊Dic3—91no—
398C4⋊Dic3—91no—
399Dic3⋊C4—31no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4C2×D911yescharacteristic, complemented
407C4×Dic3—31no—
408C4×Dic3C2×D911yescharacteristic, complemented
409C22×C32—21no—
410C22×C32—21no—
411C22×C32#23512yes—
412C22×C32C23×D311yescharacteristic
413C2×C3⋊D3—61no—
414C2×C3⋊D3—61no—
415C2×C3⋊D3—61no—
416C2×C3⋊D3—61no—
417C2×C3⋊D3—61no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—124no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—61no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C32×C4—21no—
427C32×C4—21no—
428C3⋊Dic3—61no—
429C3⋊Dic3—61no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—61no—
434C3×Dic3—61no—
435C3×Dic3—61no—
436C22×C9—22no—
437C22×C9—22no—
438C22×C9—21no—
439C22×C9—21no—
440C22×C9—21no—
441C22×C9—22no—
442C22×C9—61no—
443C22×C9—61no—
444C22×C9—61no—
445C22×C9#23512yes—
446C22×C9C23×D311yescharacteristic
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—21no—
450C2×D9—62no—
451C2×D9—62no—
452C2×D9—61no—
453C2×D9—61no—
454C2×D9—61no—
455C2×D9—61no—
456C2×D9—61no—
457C2×D9—61no—
458C2×D9—121no—
459C2×D9—121no—
460C2×D9—121no—
461C2×D9—121no—
462C2×D9—128no—
463C2×D9—124no—
464C4×C9—21no—
465C4×C9—21no—
466C4×C9—41no—
467C4×C9—41no—
468C4×C9—61no—
469C4×C9—61no—
470C4×C9—61no—
471Dic9—21no—
472Dic9—21no—
473Dic9—21no—
474Dic9—61no—
475Dic9—61no—
476Dic9—121no—
477Dic9—121no—
478#126—271no—
479#126—271no—
480#124—271no—
481#124—271no—
482#123—271no—
483#123—271no—
484C22⋊Q8—271no—
485#121—271no—
486#121—271no—
487#121—271no—
488#120—271no—
489#120—271no—
490C4×D4—31no—
491C4×D4—91no—
492C2×C22⋊C4—271no—
493C3×C9#53811yescharacteristic, complemented, Sylow
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—91no—
497C23×C3C22×D911yescharacteristic
498C23×C3C2×D3211yescharacteristic
499C22×D3—31no—
500C22×D3—91no—
501C22×D3—91no—
502C22×D3—91no—
503C22×D3—91no—
504C22×D3—181no—
505C22×D3—181no—
506C22×D3—184no—
507C22×D3—182no—
508C22×D3—182no—
509C22×D3—361no—
510C22×D3—361no—
511C22×D3—361no—
512C22×D3—361no—
513C22×D3—362no—
514C22×D3—362no—
515C22×D3C22×D911yescharacteristic
516C3×D4—62no—
517C3×D4—182no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—42no—
526C2×C3×C4—91no—
527C2×C3×C4—91no—
528C2×C3×C4—91no—
529C2×C3×C4—121no—
530C2×C3×C4—361no—
531C2×C3×C4C22×D911yescharacteristic
532C2×C3×C4C22×D911yescharacteristic
533C2×C3×C4C2×D3211yescharacteristic
534C2×C3×C4C2×D3211yescharacteristic
535#67—22no—
536#67—62no—
537#67—361no—
538#67—361no—
539#67—361no—
540#67—361no—
541#67—361no—
542#67—361no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—91no—
547C2×Dic3—91no—
548C2×Dic3—91no—
549C2×Dic3—91no—
550C2×Dic3—181no—
551C2×Dic3—181no—
552C2×Dic3—361no—
553C2×Dic3—361no—
554C2×Dic3—362no—
555C2×Dic3C22×D911yescharacteristic
556C2×Dic3C22×D911yescharacteristic
557C2×Dic3C22×D911yescharacteristic
558D12—361no—
559D12—361no—
560D12—361no—
561D12—361no—
562C4×D3—41no—
563C4×D3—121no—
564Dic6—361no—
565Dic6—361no—
566C2×C32—22no—
567C2×C32C2×#23511yescharacteristic
568C2×C32#100411yescharacteristic
569C2×C32#100911yescharacteristic
570C3⋊D3—121no—
571C3⋊D3—121no—
572C3×D3—41no—
573C3×D3—121no—
574C2×C9—24no—
575C2×C9—22no—
576C2×C9—21no—
577C2×C9—21no—
578C2×C9—21no—
579C2×C9—121no—
580C2×C9C2×#23511yescharacteristic
581C2×C9#100411yescharacteristic
582C2×C9#100911yescharacteristic
583D9—41no—
584D9—122no—
585D9—122no—
586D9—121no—
587D9—121no—
588C24—271no—
589C2×Q8—271no—
590C2×D4—31no—
591C2×D4—91no—
592C2×D4—271no—
593C2×D4—271no—
594C2×D4—271no—
595C2×D4—271no—
596C2×D4—271no—
597C22×C4—31no—
598C22×C4—91no—
599C22×C4—271no—
600C22×C4D3×D911yescharacteristic
601C4⋊C4—31no—
602C4⋊C4—91no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C22⋊C4—271no—
618C22⋊C4—271no—
619C22⋊C4—271no—
620C22⋊C4—271no—
621C42—31no—
622C42—91no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—181no—
635C22×C3—181no—
636C22×C3—181no—
637C22×C3#369712yes—
638C22×C3C23×D911yescharacteristic
639C22×C3#379812yes—
640C22×C3C22×D3211yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—182no—
648C2×D3—182no—
649C2×D3—181no—
650C2×D3—181no—
651C2×D3—181no—
652C2×D3—181no—
653C2×D3—181no—
654C2×D3—181no—
655C2×D3—181no—
656C2×D3—181no—
657C2×D3—181no—
658C2×D3—181no—
659C2×D3—181no—
660C2×D3—181no—
661C2×D3—361no—
662C2×D3—361no—
663C2×D3—361no—
664C2×D3—361no—
665C2×D3—364no—
666C2×D3—368no—
667C2×D3—364no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—181no—
678C3×C4—181no—
679C3×C4—181no—
680Dic3—21no—
681Dic3—21no—
682Dic3—21no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—181no—
687Dic3—181no—
688Dic3—181no—
689Dic3—181no—
690Dic3—361no—
691Dic3—361no—
692C32#556011yescharacteristic
693C9—21no—
694C9#556011yescharacteristic, complemented
695C23—31no—
696C23—91no—
697C23—271no—
698C23—271no—
699C23—542no—
700C23—1081no—
701C23—1081no—
702C23C2×D3×D911yescharacteristic
703Q8—1081no—
704D4—62no—
705D4—182no—
706D4—1081no—
707D4—1081no—
708D4—1081no—
709D4—1081no—
710D4—1081no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—41no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—91no—
718C2×C4—121no—
719C2×C4—271no—
720C2×C4—271no—
721C2×C4—361no—
722C2×C4—1081no—
723C2×C4C2×D3×D911yescharacteristic
724C2×C4C2×D3×D911yescharacteristic
725C2×C3—24no—
726C2×C3—22no—
727C2×C3—22no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—121no—
732C2×C3—361no—
733C2×C3C2×#369711yescharacteristic
734C2×C3#6371011yescharacteristic
735C2×C3#6371511yescharacteristic
736C2×C3C2×#379811yescharacteristic
737C2×C3#6430811yescharacteristic
738C2×C3#6433011yescharacteristic
739D3—41no—
740D3—121no—
741D3—362no—
742D3—362no—
743D3—361no—
744D3—361no—
745D3—361no—
746D3—361no—
747C22—21no—
748C22—21no—
749C22—61no—
750C22—61no—
751C22—61no—
752C22—181no—
753C22—181no—
754C22—181no—
755C22—541no—
756C22—541no—
757C22—541no—
758C22—541no—
759C22—541no—
760C22—541no—
761C22—1084no—
762C22#8864012yes—
763C22C22×D3×D911yescharacteristic
764C4—21no—
765C4—21no—
766C4—61no—
767C4—61no—
768C4—61no—
769C4—181no—
770C4—181no—
771C4—181no—
772C4—541no—
773C4—541no—
774C3—21no—
775C3#1058966211yescharacteristic, complemented
776C3#1059503911yescharacteristic
777C2—22no—
778C2—121no—
779C2—361no—
780C2—1081no—
781C2—1081no—
782C2C2×#8864011yescharacteristic
783C2#1172247811yescharacteristic
784C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#538
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. C2×#88536C2semidirect
2. C4×C9×#67C2semidirect
3. C3×C4×#611C2semidirect
4. #11721291C2semidirect
5. #11721290C2semidirect
6. #11721278C2semidirect
7. #11721267C2semidirect
8. #11721034C2semidirect
9. #11721033C2semidirect
10. #11720956C2semidirect
11. #11720954C2semidirect
12. #11720940C2semidirect
13. #11720938C2semidirect
14. #11720934C2semidirect
15. #11720926C2semidirect
23. C2×C4×D3×C9C22semidirect
24. C2×C3×C4×D9C22semidirect
27. C2×#6194C22semidirect
30. C2×#6189C22semidirect
37. C9×(C2×D3)⋊C4C22semidirect
38. C3×(C2×D9)⋊C4C22semidirect
39. C9×Dic3⋊C4C22semidirect
40. C4×C9×Dic3C22semidirect
41. C3×Dic9⋊C4C22semidirect
42. C3×C4×Dic9C22semidirect
43. (C2×D3)⋊Dic9C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. Dic3⋊Dic9C22semidirect
50. #88442C22semidirect
51. #88442C22semidirect
52. Dic9⋊Dic3C22semidirect
73. C4×#611D3semidirect
165. C2×C4×D9C2×D3semidirect
186. (C2×D9)⋊C4C2×D3semidirect
191. Dic9⋊C4C2×D3semidirect
192. C4×Dic9C2×D3semidirect
231. C4×#67D9semidirect
358. C2×C4×D3C2×D9semidirect
396. (C2×D3)⋊C4C2×D9semidirect
406. Dic3⋊C4C2×D9semidirect
408. C4×Dic3C2×D9semidirect
493. C3×C9#538semidirect
694. C9#5560semidirect
775. C3#10589662semidirect

Maximal subgroups

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

subgroupindex
C2×#885362
C4×C9×#672
C3×C4×#6112
#117212912
#117212902
#117212782
#117212672
#117210342
#117210332
#117209562
#117209542
#117209402
#117209382
#117209342
#117209262
#105950393
#105896623