Finite Group Databasebeta

← C3×#10589769 #13153022

Subgroups — C3×#10589769 #13153022

Order 1728.

738 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#123C211yesmaximal, characteristic, complemented
2C3×#63501C211yesmaximal, characteristic, complemented
3C3×#63500C211yesmaximal, characteristic, complemented
4C3×#63492C211yesmaximal, characteristic, complemented
5C3×#63486C211yesmaximal, characteristic, complemented
6C3×#63459C211yesmaximal, characteristic, complemented
7C3×#63458C211yesmaximal, characteristic, complemented
8C3×#63456C211yesmaximal, characteristic, complemented
9C3×#63452C211yesmaximal, characteristic, complemented
10C3×#63448C211yesmaximal, characteristic, complemented
11C3×#63447C211yesmaximal, characteristic, complemented
12C3×#63447C211yesmaximal, characteristic, complemented
13C3×#63446C211yesmaximal, characteristic, complemented
14C3×#63445C211yesmaximal, characteristic, complemented
15C3×#63440C211yesmaximal, characteristic, complemented
16C3×#5667—31nomaximal
17#10589769C311yesmaximal, characteristic, direct product factor
18C2×C3×D4×C9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C22×C3×Dic9C2211yescharacteristic
25C2×C3×D36C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic
27C2×C3×C4×D9C2211yescharacteristic
28C2×C3×Dic18C2211yescharacteristic
29C2×C3×Dic18C2211yescharacteristic
30C3×C9×C4⋊C4C2211yescharacteristic
31C3×C9×C4⋊C4C2211yescharacteristic
32C3×C9×C22⋊C4C2211yescharacteristic
33C3×C9×C22⋊C4C2211yescharacteristic
34C3×C9×C22⋊C4C2211yescharacteristic
35C3×#3676C2211yescharacteristic
36C3×#3676C2211yescharacteristic
37C3×#3676C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×C4⋊Dic9C2211yescharacteristic
45C3×C4⋊Dic9C2211yescharacteristic
46C3×C4⋊Dic9C2211yescharacteristic
47C3×C4⋊Dic9C2211yescharacteristic
48C3×Dic9⋊C4C2211yescharacteristic
49C3×Dic9⋊C4C2211yescharacteristic
50C3×Dic9⋊C4C2211yescharacteristic
51C3×Dic9⋊C4C2211yescharacteristic
52C3×C4×Dic9C2211yescharacteristic
53C32×#123D311yescharacteristic
54C3×#939—31no—
55C3×#938—31no—
56C3×#930—31no—
57C3×#924—31no—
58C3×#897—31no—
59C3×#896—31no—
60C3×#894—31no—
61C3×#890—31no—
62C3×#886—31no—
63C3×#885—31no—
64C3×#885—31no—
65C3×#884—31no—
66C3×#883—31no—
67C3×#878—31no—
68C9×#123—21no—
69C9×#123C2×C311yescharacteristic, complemented
70#63501C2×C311yescharacteristic, complemented
71#63500C2×C311yescharacteristic, complemented
72#63492C2×C311yescharacteristic, complemented
73#63486C2×C311yescharacteristic, complemented
74#63459C2×C311yescharacteristic, complemented
75#63458C2×C311yescharacteristic, complemented
76#63456C2×C311yescharacteristic, complemented
77#63452C2×C311yescharacteristic, complemented
78#63448C2×C311yescharacteristic, complemented
79#63447C2×C311yescharacteristic, complemented
80#63447C2×C311yescharacteristic, complemented
81#63446C2×C311yescharacteristic, complemented
82#63445C2×C311yescharacteristic, complemented
83#63440C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C23×C3×C9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C3×D4×C9—41no—
89C2×C3×C4×C9—41no—
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C3×#611—41no—
96C3×#611—41no—
97C3×#611—41no—
98C3×#611—41no—
99C2×C3×Dic9—41no—
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C3×D36—41no—
107C3×C4×D9—41no—
108C3×C4×D9—41no—
109C3×Dic18—41no—
110C3×Dic18—41no—
111C3×#562—91no—
112#5667—31no—
113C2×C32×D4C2×D311yescharacteristic
114C22×C32×C4C2×D311yescharacteristic
115C2×C3×#67—31no—
116C2×C3×#67—31no—
117C2×C3×#67—31no—
118C2×C3×#67—31no—
119C22×C3×Dic3—31no—
120C2×C3×D12—31no—
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3—31no—
123C2×C3×Dic6—31no—
124C2×C3×Dic6—31no—
125C32×C4⋊C4C2×D311yescharacteristic
126C32×C4⋊C4C2×D311yescharacteristic
127C32×C22⋊C4C2×D311yescharacteristic
128C32×C22⋊C4C2×D311yescharacteristic
129C32×C22⋊C4C2×D311yescharacteristic
130C3×#217—31no—
131C3×#217—31no—
132C3×#217—31no—
133C3×(C2×D3)⋊C4—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4—31no—
137C3×(C2×D3)⋊C4—31no—
138C3×(C2×D3)⋊C4—31no—
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3—31no—
141C3×C4⋊Dic3—31no—
142C3×C4⋊Dic3—31no—
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4—31no—
147C3×C4×Dic3—31no—
148C2×D4×C9—21no—
149C2×D4×C9C22×C311yescharacteristic
150C22×C4×C9—21no—
151C22×C4×C9C22×C311yescharacteristic
152C2×#611C22×C311yescharacteristic
153C2×#611C22×C311yescharacteristic
154C2×#611C22×C311yescharacteristic
155C2×#611C22×C311yescharacteristic
156C22×Dic9C22×C311yescharacteristic
157C2×D36C22×C311yescharacteristic
158C2×C4×D9C22×C311yescharacteristic
159C2×C4×D9C22×C311yescharacteristic
160C2×Dic18C22×C311yescharacteristic
161C2×Dic18C22×C311yescharacteristic
162C9×C4⋊C4—21no—
163C9×C4⋊C4—21no—
164C9×C4⋊C4C22×C311yescharacteristic
165C9×C4⋊C4C22×C311yescharacteristic
166C9×C22⋊C4—21no—
167C9×C22⋊C4—21no—
168C9×C22⋊C4—21no—
169C9×C22⋊C4C22×C311yescharacteristic
170C9×C22⋊C4C22×C311yescharacteristic
171C9×C22⋊C4C22×C311yescharacteristic
172#3676C22×C311yescharacteristic
173#3676C22×C311yescharacteristic
174#3676C22×C311yescharacteristic
175(C2×D9)⋊C4C22×C311yescharacteristic
176(C2×D9)⋊C4C22×C311yescharacteristic
177(C2×D9)⋊C4C22×C311yescharacteristic
178(C2×D9)⋊C4C22×C311yescharacteristic
179(C2×D9)⋊C4C22×C311yescharacteristic
180(C2×D9)⋊C4C22×C311yescharacteristic
181C4⋊Dic9C22×C311yescharacteristic
182C4⋊Dic9C22×C311yescharacteristic
183C4⋊Dic9C22×C311yescharacteristic
184C4⋊Dic9C22×C311yescharacteristic
185Dic9⋊C4C22×C311yescharacteristic
186Dic9⋊C4C22×C311yescharacteristic
187Dic9⋊C4C22×C311yescharacteristic
188Dic9⋊C4C22×C311yescharacteristic
189C4×Dic9C22×C311yescharacteristic
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9—21no—
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
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—
203C3×C4×C9—21no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3×C4×C9—21no—
207C3×C4×C9—21no—
208C3×Dic9—21no—
209C3×Dic9—21no—
210C3×Dic9—21no—
211C3×Dic9—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×#125—91no—
215C3×#124—91no—
216C3×#124—91no—
217C3×#123—21no—
218C3×#123—91no—
219C3×#123—91no—
220C3×#123—91no—
221C3×#123D911yescharacteristic, complemented
222C3×#123C3×D311yescharacteristic
223C3×C22⋊Q8—91no—
224C3×C22⋊Q8—91no—
225C3×C22⋊Q8—91no—
226C3×C22⋊Q8—91no—
227C3×#121—91no—
228C3×#121—91no—
229C3×#121—91no—
230C3×#121—91no—
231#939—31no—
232#938—31no—
233#930—31no—
234#924—31no—
235#897—31no—
236#896—31no—
237#894—31no—
238#890—31no—
239#886—31no—
240#885—31no—
241#885—31no—
242#884—31no—
243#883—31no—
244#878—31no—
245C23×C32C22×D311yescharacteristic
246C23×C32C22×D311yescharacteristic
247C22×C3×D3—31no—
248C22×C3×D3—31no—
249C32×D4—41no—
250C2×C32×C4—41no—
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C3×#67—121no—
257C3×#67—121no—
258C3×#67—121no—
259C3×#67—121no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—121no—
267C3×D12—121no—
268C3×C4×D3—121no—
269C3×C4×D3—121no—
270C3×Dic6—121no—
271C3×Dic6—121no—
272C23×C9—21no—
273C23×C9—21no—
274C23×C9C23×C311yescharacteristic
275C23×C9C23×C311yescharacteristic
276C22×D9C23×C311yescharacteristic
277C22×D9C23×C311yescharacteristic
278D4×C9—41no—
279D4×C9—42no—
280C2×C4×C9—21no—
281C2×C4×C9—21no—
282C2×C4×C9—21no—
283C2×C4×C9—21no—
284C2×C4×C9—21no—
285C2×C4×C9—41no—
286C2×C4×C9—42no—
287C2×C4×C9C23×C311yescharacteristic
288C2×C4×C9C23×C311yescharacteristic
289C2×C4×C9C23×C311yescharacteristic
290C2×C4×C9C23×C311yescharacteristic
291C2×C4×C9C23×C311yescharacteristic
292#611—41no—
293#611—41no—
294#611—41no—
295#611—41no—
296C2×Dic9—41no—
297C2×Dic9C23×C311yescharacteristic
298C2×Dic9C23×C311yescharacteristic
299C2×Dic9C23×C311yescharacteristic
300C2×Dic9C23×C311yescharacteristic
301C2×Dic9C23×C311yescharacteristic
302C2×Dic9C23×C311yescharacteristic
303D36—41no—
304C4×D9—41no—
305C4×D9—41no—
306Dic18—41no—
307Dic18—41no—
308#562—91noSylow
309C2×C3×C9—41no—
310C2×C3×C9—41no—
311C2×C3×C9H(5,𝔽2)11yescharacteristic
312C2×C3×C9H(5,𝔽2)11yescharacteristic
313C2×C3×C92−1+411yescharacteristic
314C3×D9—41no—
315C3×D9—41no—
316C2×C3×Q8—91no—
317C2×C3×Q8—91no—
318C2×C3×D4—21no—
319C2×C3×D4—91no—
320C2×C3×D4—91no—
321C2×C3×D4—91no—
322C2×C3×D4—91no—
323C2×C3×D4—91no—
324C2×C3×D4C2×D911yescharacteristic
325C2×C3×D4C2×C3×D311yescharacteristic
326C22×C3×C4—21no—
327C22×C3×C4—91no—
328C22×C3×C4—91no—
329C22×C3×C4—91no—
330C22×C3×C4C2×D911yescharacteristic
331C22×C3×C4C2×C3×D311yescharacteristic
332C2×#67—31no—
333C2×#67—31no—
334C2×#67—31no—
335C2×#67—31no—
336C22×Dic3—31no—
337C2×D12—31no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×Dic6—31no—
341C2×Dic6—31no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—91no—
345C3×C4⋊C4—91no—
346C3×C4⋊C4—91no—
347C3×C4⋊C4—91no—
348C3×C4⋊C4—91no—
349C3×C4⋊C4—91no—
350C3×C4⋊C4—91no—
351C3×C4⋊C4—91no—
352C3×C4⋊C4C2×D911yescharacteristic
353C3×C4⋊C4C2×D911yescharacteristic
354C3×C4⋊C4C2×C3×D311yescharacteristic
355C3×C4⋊C4C2×C3×D311yescharacteristic
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—91no—
360C3×C22⋊C4—91no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367C3×C22⋊C4—91no—
368C3×C22⋊C4C2×D911yescharacteristic
369C3×C22⋊C4C2×D911yescharacteristic
370C3×C22⋊C4C2×D911yescharacteristic
371C3×C22⋊C4C2×C3×D311yescharacteristic
372C3×C22⋊C4C2×C3×D311yescharacteristic
373C3×C22⋊C4C2×C3×D311yescharacteristic
374C3×C42—91no—
375#217—31no—
376#217—31no—
377#217—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—31no—
391Dic3⋊C4—31no—
392C4×Dic3—31no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32C23×D311yescharacteristic
400C2×C3×D3—61no—
401C2×C3×D3—61no—
402C2×C3×D3—61no—
403C2×C3×D3—61no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—21no—
411C3×Dic3—61no—
412C3×Dic3—61no—
413C3×Dic3—61no—
414C3×Dic3—61no—
415C3×Dic3—61no—
416C3×Dic3—61no—
417C22×C9—22no—
418C22×C9—21no—
419C22×C9—21no—
420C22×C9—21no—
421C22×C9—21no—
422C22×C9—21no—
423C22×C9—21no—
424C22×C9—21no—
425C22×C9—41no—
426C22×C9—41no—
427C22×C9—41no—
428C22×C9—41no—
429C22×C9—41no—
430C22×C9C24×C311yescharacteristic
431C2×D9—21no—
432C2×D9—21no—
433C2×D9—21no—
434C2×D9—21no—
435C2×D9—21no—
436C2×D9—21no—
437C4×C9—21no—
438C4×C9—21no—
439C4×C9—21no—
440C4×C9—21no—
441C4×C9—21no—
442C4×C9—41no—
443C4×C9—41no—
444C4×C9—41no—
445C4×C9—41no—
446C4×C9—41no—
447Dic9—21no—
448Dic9—21no—
449Dic9—21no—
450Dic9—21no—
451Dic9—21no—
452Dic9—21no—
453#125—91no—
454#124—91no—
455#124—91no—
456#123—91no—
457#123—91no—
458#123—91no—
459#123C3×D911yescharacteristic, complemented
460C22⋊Q8—91no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463C22⋊Q8—91no—
464#121—91no—
465#121—91no—
466#121—91no—
467#121—91no—
468C3×C9#56211yescharacteristic, complemented, Sylow
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—91no—
472C23×C3—91no—
473C23×C3C22×D911yescharacteristic
474C23×C3C22×D911yescharacteristic
475C23×C3C22×C3×D311yescharacteristic
476C23×C3C22×C3×D311yescharacteristic
477C22×D3—31no—
478C22×D3—31no—
479C3×Q8—361no—
480C3×Q8—361no—
481C3×D4—41no—
482C3×D4—41no—
483C3×D4—42no—
484C3×D4—361no—
485C3×D4—361no—
486C3×D4—361no—
487C3×D4—361no—
488C3×D4—361no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—42no—
497C2×C3×C4—91no—
498C2×C3×C4—91no—
499C2×C3×C4—91no—
500C2×C3×C4—91no—
501C2×C3×C4—91no—
502C2×C3×C4—91no—
503C2×C3×C4—361no—
504C2×C3×C4—361no—
505C2×C3×C4—361no—
506C2×C3×C4C22×D911yescharacteristic
507C2×C3×C4C22×D911yescharacteristic
508C2×C3×C4C22×D911yescharacteristic
509C2×C3×C4C22×D911yescharacteristic
510C2×C3×C4C22×D911yescharacteristic
511C2×C3×C4C22×C3×D311yescharacteristic
512C2×C3×C4C22×C3×D311yescharacteristic
513C2×C3×C4C22×C3×D311yescharacteristic
514C2×C3×C4C22×C3×D311yescharacteristic
515C2×C3×C4C22×C3×D311yescharacteristic
516#67—121no—
517#67—121no—
518#67—121no—
519#67—121no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—121no—
527D12—121no—
528C4×D3—121no—
529C4×D3—121no—
530Dic6—121no—
531Dic6—121no—
532C2×C32—41no—
533C2×C32—41no—
534C2×C32#100411yescharacteristic
535C2×C32#100911yescharacteristic
536C2×C32#101011yescharacteristic
537C3×D3—121no—
538C3×D3—121no—
539C2×C9—21no—
540C2×C9—21no—
541C2×C9—21no—
542C2×C9—42no—
543C2×C9—41no—
544C2×C9—41no—
545C2×C9—81no—
546C2×C9C3×H(5,𝔽2)11yescharacteristic
547C2×C9C3×H(5,𝔽2)11yescharacteristic
548C2×C9C3×2−1+411yescharacteristic
549D9—41no—
550D9—41no—
551C2×Q8—91no—
552C2×Q8—91no—
553C2×D4—91no—
554C2×D4—91no—
555C2×D4—91no—
556C2×D4—91no—
557C2×D4—91no—
558C2×D4C2×C3×D911yescharacteristic
559C22×C4—91no—
560C22×C4—91no—
561C22×C4—91no—
562C22×C4C2×C3×D911yescharacteristic
563C4⋊C4—91no—
564C4⋊C4—91no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—91no—
569C4⋊C4—91no—
570C4⋊C4—91no—
571C4⋊C4C2×C3×D911yescharacteristic
572C4⋊C4C2×C3×D911yescharacteristic
573C22⋊C4—91no—
574C22⋊C4—91no—
575C22⋊C4—91no—
576C22⋊C4—91no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—91no—
580C22⋊C4—91no—
581C22⋊C4—91no—
582C22⋊C4C2×C3×D911yescharacteristic
583C22⋊C4C2×C3×D911yescharacteristic
584C22⋊C4C2×C3×D911yescharacteristic
585C42—91no—
586C22×C3—22no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—181no—
606C22×C3—181no—
607C22×C3—181no—
608C22×C3—181no—
609C22×C3—181no—
610C22×C3—181no—
611C22×C3C23×D911yescharacteristic
612C22×C3C23×C3×D311yescharacteristic
613C2×D3—61no—
614C2×D3—61no—
615C2×D3—61no—
616C2×D3—61no—
617C2×D3—61no—
618C2×D3—61no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—181no—
635C3×C4—181no—
636C3×C4—181no—
637C3×C4—181no—
638C3×C4—181no—
639C3×C4—181no—
640Dic3—61no—
641Dic3—61no—
642Dic3—61no—
643Dic3—61no—
644Dic3—61no—
645Dic3—61no—
646C32#566711yescharacteristic
647C9—21no—
648C9C3×#56211yescharacteristic, complemented
649C23—91no—
650C23—91no—
651C23C22×C3×D911yescharacteristic
652C23C22×C3×D911yescharacteristic
653Q8—361no—
654Q8—361no—
655D4—41no—
656D4—361no—
657D4—361no—
658D4—361no—
659D4—361no—
660D4—361no—
661C2×C4—41no—
662C2×C4—91no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—91no—
667C2×C4—91no—
668C2×C4—361no—
669C2×C4—361no—
670C2×C4—361no—
671C2×C4C22×C3×D911yescharacteristic
672C2×C4C22×C3×D911yescharacteristic
673C2×C4C22×C3×D911yescharacteristic
674C2×C4C22×C3×D911yescharacteristic
675C2×C4C22×C3×D911yescharacteristic
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—42no—
680C2×C3—41no—
681C2×C3—41no—
682C2×C3—41no—
683C2×C3—41no—
684C2×C3—81no—
685C2×C3—361no—
686C2×C3—361no—
687C2×C3#6371011yescharacteristic
688C2×C3#6371511yescharacteristic
689C2×C3#6371611yescharacteristic
690C2×C3C3×#100411yescharacteristic
691C2×C3C3×#100911yescharacteristic
692C2×C3C3×#101011yescharacteristic
693D3—121no—
694D3—121no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—181no—
702C22—181no—
703C22—181no—
704C22—181no—
705C22—181no—
706C22—181no—
707C22C23×C3×D911yescharacteristic
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—21no—
713C4—181no—
714C4—181no—
715C4—181no—
716C4—181no—
717C4—181no—
718C4—181no—
719C3—21no—
720C3#1058976911yescharacteristic, direct product factor
721C3C3×#566711yescharacteristic
722C2—41no—
723C2—41no—
724C2—361no—
725C2—361no—
726C2C3×#6371011yescharacteristic
727C2C3×#6371511yescharacteristic
728C2C3×#6371611yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#123C2
socleC22×C32C23×D3
hypercenterC3×#123D9
hypocenterC9C3×#562
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×#123

Complements

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

NH ≅ G/Ntype
1. C3×C9×#123C2semidirect
2. C3×#63501C2semidirect
3. C3×#63500C2semidirect
4. C3×#63492C2semidirect
5. C3×#63486C2semidirect
6. C3×#63459C2semidirect
7. C3×#63458C2semidirect
8. C3×#63456C2semidirect
9. C3×#63452C2semidirect
10. C3×#63448C2semidirect
11. C3×#63447C2semidirect
12. C3×#63447C2semidirect
13. C3×#63446C2semidirect
14. C3×#63445C2semidirect
15. C3×#63440C2semidirect
17. #10589769C3direct (N × H)
69. C9×#123C2×C3semidirect
70. #63501C2×C3semidirect
71. #63500C2×C3semidirect
72. #63492C2×C3semidirect
73. #63486C2×C3semidirect
74. #63459C2×C3semidirect
75. #63458C2×C3semidirect
76. #63456C2×C3semidirect
77. #63452C2×C3semidirect
78. #63448C2×C3semidirect
79. #63447C2×C3semidirect
80. #63447C2×C3semidirect
81. #63446C2×C3semidirect
82. #63445C2×C3semidirect
83. #63440C2×C3semidirect
221. C3×#123D9semidirect
459. #123C3×D9semidirect
468. C3×C9#562semidirect
648. C9C3×#562semidirect
720. C3#10589769direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1232
C3×#635012
C3×#635002
C3×#634922
C3×#634862
C3×#634592
C3×#634582
C3×#634562
C3×#634522
C3×#634482
C3×#634472
C3×#634462
C3×#634452
C3×#634402
C3×#56673
#105897693