Finite Group Databasebeta

← C3×#10595251 #13174755

Subgroups — C3×#10595251 #13174755

Order 1728.

1294 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64149C211yesmaximal, characteristic, complemented
2C32×#939C211yesmaximal, characteristic, complemented
3C32×#935C211yesmaximal, characteristic, complemented
4C3×#63978C211yesmaximal, characteristic, complemented
5C3×#63975C211yesmaximal, characteristic, complemented
6C3×#63971C211yesmaximal, characteristic, complemented
7C3×#63971C211yesmaximal, characteristic, complemented
8C3×#63966C211yesmaximal, characteristic, complemented
9C3×#63958C211yesmaximal, characteristic, complemented
10C3×#63952C211yesmaximal, characteristic, complemented
11C3×#63952C211yesmaximal, characteristic, complemented
12C3×#63910C211yesmaximal, characteristic, complemented
13C3×#63897C211yesmaximal, characteristic, complemented
14C3×#63878C211yesmaximal, characteristic, complemented
15C3×#63870C211yesmaximal, characteristic, complemented
16C3×#5663—31nomaximal
17C3×#5615—31nomaximal
18#10595251C311yesmaximal, characteristic, direct product factor
19C2×C33×D4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic
27C22×C32×Dic3C2211yescharacteristic
28C22×C32×Dic3C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic
31C2×C3×#624C2211yescharacteristic
32C2×C3×#624C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34C3×C4×C3⋊Dic3C2211yescharacteristic
35C32×#217C2211yescharacteristic
36C32×#217C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×#217C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×#123—31no—
55C32×#121—31no—
56#64149C2×C311yescharacteristic, complemented
57C3×#940—31no—
58C3×#940—31no—
59C3×#940—61no—
60C3×#939—21no—
61C3×#939—31no—
62C3×#939—31no—
63C3×#939—31no—
64C3×#939D311yescharacteristic, complemented
65C3×#939C2×C311yescharacteristic, complemented
66C3×#938—31no—
67C3×#935—21no—
68C3×#935D311yescharacteristic, complemented
69C3×#935C2×C311yescharacteristic, complemented
70C3×#930—31no—
71C3×#929—31no—
72C3×C4×#67—31no—
73C3×C4×#67—31no—
74C3×#895—31no—
75C3×#894—31no—
76C3×#894—31no—
77C3×#892—31no—
78C3×#889—31no—
79C3×#889—31no—
80C3×#886—31no—
81C3×#884—31no—
82C3×#884—31no—
83C3×#884—31no—
84C3×#884—31no—
85C3×#883—31no—
86C3×#883—31no—
87C3×#67⋊C4—31no—
88C3×#67⋊C4—31no—
89C3×#877—31no—
90#63978C2×C311yescharacteristic, complemented
91#63975C2×C311yescharacteristic, complemented
92#63971C2×C311yescharacteristic, complemented
93#63971C2×C311yescharacteristic, complemented
94#63966C2×C311yescharacteristic, complemented
95#63958C2×C311yescharacteristic, complemented
96#63952C2×C311yescharacteristic, complemented
97#63952C2×C311yescharacteristic, complemented
98#63910C2×C311yescharacteristic, complemented
99#63897C2×C311yescharacteristic, complemented
100#63878C2×C311yescharacteristic, complemented
101#63870C2×C311yescharacteristic, complemented
102C23×C33C2311yescharacteristic
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C33×D4—41no—
108C2×C33×C4C2311yescharacteristic
109C3×#638—22no—
110C3×#638—22no—
111C3×#638—41no—
112C3×#638—41no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C3×C4⋊(C3⋊D3)—41no—
116C32×#67—41no—
117C32×#67—41no—
118C2×C32×Dic3—41no—
119C2×C32×Dic3—41no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C3×#626—41no—
128C3×#626—41no—
129C3×#624—41no—
130C3×#624—41no—
131C3×D3×Dic3—22no—
132C3×#540—91no—
133#5663—31no—
134#5615—31no—
135C2×C32×D4—21no—
136C2×C32×D4—21no—
137C2×C32×D4—21no—
138C2×C32×D4—31no—
139C2×C32×D4—31no—
140C2×C32×D4—41no—
141C2×C32×D4C2×D311yescharacteristic
142C2×C32×D4C2×D311yescharacteristic
143C2×C32×D4C22×C311yescharacteristic
144C22×C32×C4—31no—
145C22×C32×C4—31no—
146C2×#638C22×C311yescharacteristic
147C2×#638C22×C311yescharacteristic
148C2×#638C22×C311yescharacteristic
149C2×#638C22×C311yescharacteristic
150C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
151C2×C3×#67—21no—
152C2×C3×#67—21no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—61no—
164C2×C3×#67—61no—
165C2×C3×#67—61no—
166C2×C3×#67—61no—
167C2×C3×#67C2×D311yescharacteristic
168C2×C3×#67C2×D311yescharacteristic
169C2×C3×#67C22×C311yescharacteristic
170C2×C3×#67C22×C311yescharacteristic
171C22×C3×Dic3—21no—
172C22×C3×Dic3—21no—
173C22×C3×Dic3—31no—
174C22×C3×Dic3C2×D311yescharacteristic
175C22×C3×Dic3C2×D311yescharacteristic
176C22×C3×Dic3C22×C311yescharacteristic
177C22×C3×Dic3C22×C311yescharacteristic
178C2×C3×D12—31no—
179C2×C3×D12—31no—
180C2×C3×D12—31no—
181C2×C3×D12—31no—
182C2×C3×D12—61no—
183C2×C3×C4×D3—31no—
184C2×C3×C4×D3—31no—
185C2×C3×C4×D3—31no—
186C2×C3×C4×D3—31no—
187C2×C3×C4×D3—31no—
188C2×#626C22×C311yescharacteristic
189C2×#626C22×C311yescharacteristic
190C2×#624C22×C311yescharacteristic
191C2×#624C22×C311yescharacteristic
192C2×D3×Dic3C22×C311yescharacteristic
193C32×C4⋊C4—31no—
194C32×C4⋊C4—31no—
195C32×C4⋊C4—31no—
196C32×C22⋊C4—31no—
197C32×C22⋊C4—31no—
198C32×C22⋊C4—31no—
199C32×C22⋊C4—31no—
200C32×C22⋊C4—31no—
201C4×C3⋊Dic3C22×C311yescharacteristic
202C3×#217—21no—
203C3×#217—21no—
204C3×#217—21no—
205C3×#217—21no—
206C3×#217—31no—
207C3×#217C2×D311yescharacteristic
208C3×#217C2×D311yescharacteristic
209C3×#217C2×D311yescharacteristic
210C3×#217C2×D311yescharacteristic
211C3×#217C22×C311yescharacteristic
212C3×#217C22×C311yescharacteristic
213C3×#217C22×C311yescharacteristic
214C3×#217C22×C311yescharacteristic
215C3×(C2×D3)⋊C4—21no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4C2×D311yescharacteristic
226C3×(C2×D3)⋊C4C22×C311yescharacteristic
227C3×C4⋊Dic3—31no—
228C3×C4⋊Dic3—31no—
229C3×C4⋊Dic3—31no—
230C3×Dic3⋊C4—21no—
231C3×Dic3⋊C4—21no—
232C3×Dic3⋊C4—21no—
233C3×Dic3⋊C4—31no—
234C3×Dic3⋊C4—31no—
235C3×Dic3⋊C4—31no—
236C3×Dic3⋊C4—31no—
237C3×Dic3⋊C4—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4C2×D311yescharacteristic
241C3×Dic3⋊C4C2×D311yescharacteristic
242C3×Dic3⋊C4C2×D311yescharacteristic
243C3×Dic3⋊C4C22×C311yescharacteristic
244C3×Dic3⋊C4C22×C311yescharacteristic
245C3×Dic3⋊C4C22×C311yescharacteristic
246C3×C4×Dic3—31no—
247C3×C4×Dic3—31no—
248C3×C4×Dic3—31no—
249C3×C4×Dic3—31no—
250C3×C4×Dic3—61no—
251#3724C22×C311yescharacteristic
252#3724C22×C311yescharacteristic
253Dic3⋊Dic3C22×C311yescharacteristic
254Dic3⋊Dic3C22×C311yescharacteristic
255Dic3⋊Dic3C22×C311yescharacteristic
256#3722C22×C311yescharacteristic
257#3722C22×C311yescharacteristic
258#3722C22×C311yescharacteristic
259#3722C22×C311yescharacteristic
260(C2×D3)⋊Dic3C22×C311yescharacteristic
261Dic32C22×C311yescharacteristic
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33—21no—
266C22×C33—21no—
267C22×C33—21no—
268C22×C33C2411yescharacteristic
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C33×C4—21no—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3#4112yes—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C3×#127—91no—
289C3×#125—91no—
290C3×#123—31no—
291C3×#123—31no—
292C3×#123—61no—
293C3×#123—91no—
294C3×#123—91no—
295C3×#123—91no—
296C3×#121—31no—
297C3×#121—31no—
298C3×#121—61no—
299C3×#121—91no—
300C3×#121—91no—
301C3×#121—91no—
302C3×#121—91no—
303C3×#121—91no—
304C3×C4×D4—91no—
305C3×C4×D4—91no—
306C3×#117—91no—
307#940—31no—
308#940—31no—
309#940—61no—
310#939—31no—
311#939—31no—
312#939—31no—
313#939C3×D311yescharacteristic, complemented
314#938—31no—
315#935C3×D311yescharacteristic, complemented
316#930—31no—
317#929—31no—
318C4×#67—31no—
319C4×#67—31no—
320#895—31no—
321#894—31no—
322#894—31no—
323#892—31no—
324#889—31no—
325#889—31no—
326#886—31no—
327#884—31no—
328#884—31no—
329#884—31no—
330#884—31no—
331#883—31no—
332#883—31no—
333#67⋊C4—31no—
334#67⋊C4—31no—
335#877—31no—
336C23×C32—21no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—21no—
341C23×C32—21no—
342C23×C32—31no—
343C23×C32—41no—
344C23×C32—41no—
345C23×C32C22×D311yescharacteristic
346C23×C32C22×D311yescharacteristic
347C23×C32C22×D311yescharacteristic
348C23×C32C22×D311yescharacteristic
349C23×C32C23×C311yescharacteristic
350C23×C32C23×C311yescharacteristic
351C22×C3⋊D3C23×C311yescharacteristic
352C22×C3⋊D3C23×C311yescharacteristic
353C22×C3×D3—21no—
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—61no—
359C22×C3×D3—61no—
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C23×C311yescharacteristic
362C32×D4—41no—
363C32×D4—41no—
364C32×D4—41no—
365C32×D4—42no—
366C32×D4—42no—
367C32×D4—42no—
368C32×D4—44no—
369C32×D4—121no—
370C32×D4—121no—
371C2×C32×C4—21no—
372C2×C32×C4—21no—
373C2×C32×C4—21no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—31no—
381C2×C32×C4—41no—
382C2×C32×C4—121no—
383C2×C32×C4—121no—
384C2×C32×C4C22×D311yescharacteristic
385C2×C32×C4C22×D311yescharacteristic
386C2×C32×C4C23×C311yescharacteristic
387#638—22no—
388#638—22no—
389#638—41no—
390#638—41no—
391C2×C3⋊Dic3C23×C311yescharacteristic
392C2×C3⋊Dic3C23×C311yescharacteristic
393C4⋊(C3⋊D3)—41no—
394C3×#67—41no—
395C3×#67—41no—
396C3×#67—41no—
397C3×#67—41no—
398C3×#67—42no—
399C3×#67—42no—
400C3×#67—62no—
401C3×#67—62no—
402C3×#67—62no—
403C3×#67—62no—
404C3×#67—122no—
405C3×#67—122no—
406C3×#67—121no—
407C3×#67—121no—
408C3×#67—121no—
409C3×#67—121no—
410C3×#67—121no—
411C3×#67—121no—
412C3×#67—122no—
413C3×#67—122no—
414C2×C3×Dic3—21no—
415C2×C3×Dic3—21no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—21no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—41no—
426C2×C3×Dic3—41no—
427C2×C3×Dic3—41no—
428C2×C3×Dic3—41no—
429C2×C3×Dic3—42no—
430C2×C3×Dic3—42no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—62no—
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C23×C311yescharacteristic
442C2×C3×Dic3C23×C311yescharacteristic
443C2×C3×Dic3C23×C311yescharacteristic
444C2×C3×Dic3C23×C311yescharacteristic
445C2×C3×Dic3C23×C311yescharacteristic
446C2×C3×Dic3C23×C311yescharacteristic
447C2×C3×Dic3C23×C311yescharacteristic
448C3×D12—121no—
449C3×D12—121no—
450C3×D12—122no—
451C3×D12—121no—
452C3×D12—121no—
453C3×C4×D3—62no—
454C3×C4×D3—121no—
455C3×C4×D3—121no—
456C3×C4×D3—121no—
457C3×C4×D3—121no—
458#626—41no—
459#626—41no—
460#624—41no—
461#624—41no—
462D3×Dic3—22no—
463#540—91noSylow
464C2×C33—41no—
465C2×C33—41no—
466C2×C33C2×#4111yescharacteristic
467C2×C33H(5,𝔽2)11yescharacteristic
468C2×C33H(5,𝔽2)11yescharacteristic
469C3×C3⋊D3—41no—
470C3×C3⋊D3—41no—
471C32×D3—41no—
472C2×C3×D4—21no—
473C2×C3×D4—21no—
474C2×C3×D4—21no—
475C2×C3×D4—31no—
476C2×C3×D4—31no—
477C2×C3×D4—31no—
478C2×C3×D4—31no—
479C2×C3×D4—41no—
480C2×C3×D4—61no—
481C2×C3×D4—61no—
482C2×C3×D4—91no—
483C2×C3×D4—91no—
484C2×C3×D4—91no—
485C2×C3×D4—91no—
486C2×C3×D4—91no—
487C2×C3×D4—91no—
488C2×C3×D4—91no—
489C2×C3×D4D3211yescharacteristic
490C2×C3×D4C2×C3×D311yescharacteristic
491C2×C3×D4C2×C3×D311yescharacteristic
492C22×C3×C4—31no—
493C22×C3×C4—31no—
494C22×C3×C4—31no—
495C22×C3×C4—31no—
496C22×C3×C4—61no—
497C22×C3×C4—61no—
498C22×C3×C4—91no—
499C22×C3×C4—91no—
500C22×C3×C4—91no—
501C2×#67—31no—
502C2×#67—31no—
503C2×#67—31no—
504C2×#67—31no—
505C2×#67—31no—
506C2×#67—31no—
507C2×#67—31no—
508C2×#67—31no—
509C2×#67—31no—
510C2×#67—31no—
511C2×#67—61no—
512C2×#67—61no—
513C2×#67—61no—
514C2×#67—61no—
515C2×#67C2×C3×D311yescharacteristic
516C2×#67C2×C3×D311yescharacteristic
517C22×Dic3—31no—
518C22×Dic3C2×C3×D311yescharacteristic
519C22×Dic3C2×C3×D311yescharacteristic
520C2×D12—31no—
521C2×D12—31no—
522C2×D12—31no—
523C2×D12—31no—
524C2×D12—61no—
525C2×C4×D3—31no—
526C2×C4×D3—31no—
527C2×C4×D3—31no—
528C2×C4×D3—31no—
529C2×C4×D3—31no—
530C3×C4⋊C4—31no—
531C3×C4⋊C4—31no—
532C3×C4⋊C4—31no—
533C3×C4⋊C4—31no—
534C3×C4⋊C4—31no—
535C3×C4⋊C4—31no—
536C3×C4⋊C4—61no—
537C3×C4⋊C4—61no—
538C3×C4⋊C4—61no—
539C3×C4⋊C4—91no—
540C3×C4⋊C4—91no—
541C3×C4⋊C4—91no—
542C3×C4⋊C4—91no—
543C3×C4⋊C4—91no—
544C3×C22⋊C4—31no—
545C3×C22⋊C4—31no—
546C3×C22⋊C4—31no—
547C3×C22⋊C4—31no—
548C3×C22⋊C4—31no—
549C3×C22⋊C4—31no—
550C3×C22⋊C4—31no—
551C3×C22⋊C4—31no—
552C3×C22⋊C4—31no—
553C3×C22⋊C4—31no—
554C3×C22⋊C4—61no—
555C3×C22⋊C4—61no—
556C3×C22⋊C4—61no—
557C3×C22⋊C4—61no—
558C3×C22⋊C4—61no—
559C3×C22⋊C4—91no—
560C3×C22⋊C4—91no—
561C3×C22⋊C4—91no—
562C3×C22⋊C4—91no—
563C3×C22⋊C4—91no—
564C3×C42—91no—
565C3×C42—91no—
566#217—31no—
567#217C2×C3×D311yescharacteristic
568#217C2×C3×D311yescharacteristic
569#217C2×C3×D311yescharacteristic
570#217C2×C3×D311yescharacteristic
571(C2×D3)⋊C4—31no—
572(C2×D3)⋊C4—31no—
573(C2×D3)⋊C4—31no—
574(C2×D3)⋊C4—31no—
575(C2×D3)⋊C4—31no—
576(C2×D3)⋊C4—31no—
577(C2×D3)⋊C4—31no—
578(C2×D3)⋊C4—31no—
579(C2×D3)⋊C4—31no—
580(C2×D3)⋊C4C2×C3×D311yescharacteristic
581C4⋊Dic3—31no—
582C4⋊Dic3—31no—
583C4⋊Dic3—31no—
584Dic3⋊C4—31no—
585Dic3⋊C4—31no—
586Dic3⋊C4—31no—
587Dic3⋊C4—31no—
588Dic3⋊C4—31no—
589Dic3⋊C4—31no—
590Dic3⋊C4—31no—
591Dic3⋊C4C2×C3×D311yescharacteristic
592Dic3⋊C4C2×C3×D311yescharacteristic
593Dic3⋊C4C2×C3×D311yescharacteristic
594C4×Dic3—31no—
595C4×Dic3—31no—
596C4×Dic3—31no—
597C4×Dic3—31no—
598C4×Dic3—61no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—22no—
602C22×C32—22no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—21no—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32—21no—
612C22×C32—21no—
613C22×C32—21no—
614C22×C32—21no—
615C22×C32—21no—
616C22×C32—21no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—41no—
623C22×C32—41no—
624C22×C32—41no—
625C22×C32—41no—
626C22×C32—41no—
627C22×C32—42no—
628C22×C32—42no—
629C22×C32—41no—
630C22×C32—41no—
631C22×C32—41no—
632C22×C32—41no—
633C22×C32—41no—
634C22×C32—41no—
635C22×C32—41no—
636C22×C32—41no—
637C22×C32—41no—
638C22×C32—41no—
639C22×C32—41no—
640C22×C32—41no—
641C22×C32—61no—
642C22×C32—61no—
643C22×C32—61no—
644C22×C32—81no—
645C22×C32—81no—
646C22×C32—81no—
647C22×C32—81no—
648C22×C32C23×D311yescharacteristic
649C22×C32C23×D311yescharacteristic
650C22×C32C24×C311yescharacteristic
651C2×C3⋊D3—21no—
652C2×C3⋊D3—21no—
653C2×C3⋊D3—21no—
654C2×C3⋊D3—21no—
655C2×C3⋊D3—21no—
656C2×C3⋊D3—21no—
657C2×C3×D3—21no—
658C2×C3×D3—21no—
659C2×C3×D3—21no—
660C2×C3×D3—21no—
661C2×C3×D3—21no—
662C2×C3×D3—21no—
663C2×C3×D3—41no—
664C2×C3×D3—41no—
665C2×C3×D3—41no—
666C2×C3×D3—61no—
667C2×C3×D3—61no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—61no—
671C2×C3×D3—61no—
672C2×C3×D3—61no—
673C2×C3×D3—61no—
674C2×C3×D3—61no—
675C2×C3×D3—61no—
676C2×C3×D3—61no—
677C2×C3×D3—61no—
678C2×C3×D3—121no—
679C2×C3×D3—121no—
680C2×C3×D3—121no—
681C2×C3×D3—121no—
682C2×C3×D3—121no—
683C2×C3×D3—121no—
684C32×C4—21no—
685C32×C4—22no—
686C32×C4—21no—
687C32×C4—21no—
688C32×C4—41no—
689C32×C4—41no—
690C32×C4—42no—
691C32×C4—61no—
692C32×C4—61no—
693C32×C4—61no—
694C32×C4—61no—
695C32×C4—61no—
696C32×C4—61no—
697C32×C4—61no—
698C3⋊Dic3—21no—
699C3⋊Dic3C3×#4112yes—
700C3×Dic3—22no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—21no—
710C3×Dic3—21no—
711C3×Dic3—21no—
712C3×Dic3—21no—
713C3×Dic3—21no—
714C3×Dic3—21no—
715C3×Dic3—32no—
716C3×Dic3—32no—
717C3×Dic3—41no—
718C3×Dic3—41no—
719C3×Dic3—41no—
720C3×Dic3—41no—
721C3×Dic3—41no—
722C3×Dic3—41no—
723C3×Dic3—62no—
724C3×Dic3—62no—
725C3×Dic3—61no—
726C3×Dic3—61no—
727#127—91no—
728#125—91no—
729#123—31no—
730#123—91no—
731#123—91no—
732#123—91no—
733#121—31no—
734#121—91no—
735#121—91no—
736#121—91no—
737#121—91no—
738#121—91no—
739C4×D4—91no—
740C4×D4—91no—
741#117—91no—
742C33#54011yescharacteristic, complemented, Sylow
743C23×C3—21no—
744C23×C3—21no—
745C23×C3—21no—
746C23×C3—21no—
747C23×C3—21no—
748C23×C3—21no—
749C23×C3—31no—
750C23×C3—31no—
751C23×C3—41no—
752C23×C3—41no—
753C23×C3—61no—
754C23×C3—91no—
755C23×C3—91no—
756C23×C3C2×D3211yescharacteristic
757C23×C3C2×D3211yescharacteristic
758C23×C3C22×C3×D311yescharacteristic
759C23×C3C22×C3×D311yescharacteristic
760C23×C3C22×C3×D311yescharacteristic
761C23×C3C22×C3×D311yescharacteristic
762C22×D3—31no—
763C22×D3—31no—
764C22×D3—31no—
765C22×D3—31no—
766C22×D3—61no—
767C22×D3—61no—
768C22×D3C22×C3×D311yescharacteristic
769C3×D4—41no—
770C3×D4—41no—
771C3×D4—41no—
772C3×D4—42no—
773C3×D4—42no—
774C3×D4—42no—
775C3×D4—44no—
776C3×D4—121no—
777C3×D4—121no—
778C3×D4—121no—
779C3×D4—121no—
780C3×D4—122no—
781C3×D4—122no—
782C3×D4—182no—
783C3×D4—182no—
784C3×D4—361no—
785C3×D4—361no—
786C3×D4—361no—
787C3×D4—361no—
788C3×D4—361no—
789C2×C3×C4—21no—
790C2×C3×C4—21no—
791C2×C3×C4—21no—
792C2×C3×C4—31no—
793C2×C3×C4—31no—
794C2×C3×C4—31no—
795C2×C3×C4—31no—
796C2×C3×C4—31no—
797C2×C3×C4—31no—
798C2×C3×C4—31no—
799C2×C3×C4—31no—
800C2×C3×C4—31no—
801C2×C3×C4—31no—
802C2×C3×C4—31no—
803C2×C3×C4—31no—
804C2×C3×C4—31no—
805C2×C3×C4—31no—
806C2×C3×C4—41no—
807C2×C3×C4—61no—
808C2×C3×C4—61no—
809C2×C3×C4—61no—
810C2×C3×C4—61no—
811C2×C3×C4—61no—
812C2×C3×C4—61no—
813C2×C3×C4—61no—
814C2×C3×C4—91no—
815C2×C3×C4—91no—
816C2×C3×C4—121no—
817C2×C3×C4—121no—
818C2×C3×C4—121no—
819C2×C3×C4—121no—
820C2×C3×C4—122no—
821C2×C3×C4—122no—
822C2×C3×C4—182no—
823C2×C3×C4—361no—
824C2×C3×C4—361no—
825C2×C3×C4C2×D3211yescharacteristic
826C2×C3×C4C22×C3×D311yescharacteristic
827C2×C3×C4C22×C3×D311yescharacteristic
828#67—41no—
829#67—41no—
830#67—62no—
831#67—62no—
832#67—62no—
833#67—62no—
834#67—122no—
835#67—122no—
836#67—121no—
837#67—121no—
838#67—121no—
839#67—121no—
840#67—121no—
841#67—121no—
842#67—122no—
843#67—122no—
844C2×Dic3—31no—
845C2×Dic3—31no—
846C2×Dic3—31no—
847C2×Dic3—31no—
848C2×Dic3—41no—
849C2×Dic3—41no—
850C2×Dic3—61no—
851C2×Dic3—61no—
852C2×Dic3—62no—
853C2×Dic3C22×C3×D311yescharacteristic
854C2×Dic3C22×C3×D311yescharacteristic
855C2×Dic3C22×C3×D311yescharacteristic
856C2×Dic3C22×C3×D311yescharacteristic
857C2×Dic3C22×C3×D311yescharacteristic
858C2×Dic3C22×C3×D311yescharacteristic
859C2×Dic3C22×C3×D311yescharacteristic
860D12—121no—
861D12—121no—
862D12—122no—
863D12—121no—
864D12—121no—
865C4×D3—62no—
866C4×D3—121no—
867C4×D3—121no—
868C4×D3—121no—
869C4×D3—121no—
870C2×C32—21no—
871C2×C32—21no—
872C2×C32—21no—
873C2×C32—21no—
874C2×C32—21no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—21no—
878C2×C32—21no—
879C2×C32—41no—
880C2×C32—41no—
881C2×C32—41no—
882C2×C32—41no—
883C2×C32—41no—
884C2×C32—42no—
885C2×C32—42no—
886C2×C32—41no—
887C2×C32—41no—
888C2×C32—41no—
889C2×C32—41no—
890C2×C32—81no—
891C2×C32—81no—
892C2×C32—81no—
893C2×C32—81no—
894C2×C32—82no—
895C2×C32—82no—
896C2×C32—121no—
897C2×C32#100411yescharacteristic
898C2×C32#100411yescharacteristic
899C2×C32#100411yescharacteristic
900C2×C32D3×#4111yescharacteristic
901C2×C32D3×#4111yescharacteristic
902C2×C32#100911yescharacteristic
903C2×C32C2×C3×#4111yescharacteristic
904C2×C32C3×H(5,𝔽2)11yescharacteristic
905C2×C32C3×H(5,𝔽2)11yescharacteristic
906C3⋊D3—41no—
907C3⋊D3—41no—
908C3×D3—41no—
909C3×D3—41no—
910C3×D3—81no—
911C3×D3—121no—
912C3×D3—121no—
913C3×D3—121no—
914C3×D3—121no—
915C3×D3—241no—
916C3×D3—241no—
917C2×D4—31no—
918C2×D4—31no—
919C2×D4—91no—
920C2×D4—91no—
921C2×D4—91no—
922C2×D4—91no—
923C2×D4—91no—
924C2×D4—91no—
925C2×D4—91no—
926C2×D4C3×D3211yescharacteristic
927C22×C4—31no—
928C22×C4—31no—
929C22×C4—91no—
930C22×C4—91no—
931C22×C4—91no—
932C4⋊C4—31no—
933C4⋊C4—31no—
934C4⋊C4—31no—
935C4⋊C4—91no—
936C4⋊C4—91no—
937C4⋊C4—91no—
938C4⋊C4—91no—
939C4⋊C4—91no—
940C22⋊C4—31no—
941C22⋊C4—31no—
942C22⋊C4—31no—
943C22⋊C4—31no—
944C22⋊C4—31no—
945C22⋊C4—91no—
946C22⋊C4—91no—
947C22⋊C4—91no—
948C22⋊C4—91no—
949C22⋊C4—91no—
950C42—91no—
951C42—91no—
952C22×C3—22no—
953C22×C3—22no—
954C22×C3—21no—
955C22×C3—21no—
956C22×C3—21no—
957C22×C3—21no—
958C22×C3—21no—
959C22×C3—21no—
960C22×C3—21no—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—21no—
970C22×C3—21no—
971C22×C3—21no—
972C22×C3—21no—
973C22×C3—21no—
974C22×C3—21no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—41no—
978C22×C3—41no—
979C22×C3—41no—
980C22×C3—41no—
981C22×C3—41no—
982C22×C3—41no—
983C22×C3—41no—
984C22×C3—41no—
985C22×C3—41no—
986C22×C3—41no—
987C22×C3—41no—
988C22×C3—41no—
989C22×C3—41no—
990C22×C3—41no—
991C22×C3—42no—
992C22×C3—42no—
993C22×C3—41no—
994C22×C3—61no—
995C22×C3—61no—
996C22×C3—61no—
997C22×C3—61no—
998C22×C3—61no—
999C22×C3—61no—
1000C22×C3—81no—
1001C22×C3—81no—
1002C22×C3—81no—
1003C22×C3—81no—
1004C22×C3—121no—
1005C22×C3—121no—
1006C22×C3—121no—
1007C22×C3—181no—
1008C22×C3—181no—
1009C22×C3—181no—
1010C22×C3—181no—
1011C22×C3—181no—
1012C22×C3—181no—
1013C22×C3C22×D3211yescharacteristic
1014C22×C3C23×C3×D311yescharacteristic
1015C22×C3C23×C3×D311yescharacteristic
1016C2×D3—21no—
1017C2×D3—21no—
1018C2×D3—21no—
1019C2×D3—61no—
1020C2×D3—61no—
1021C2×D3—61no—
1022C2×D3—61no—
1023C2×D3—61no—
1024C2×D3—61no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—61no—
1030C2×D3—61no—
1031C2×D3—121no—
1032C2×D3—121no—
1033C2×D3—121no—
1034C2×D3—121no—
1035C2×D3—121no—
1036C2×D3—121no—
1037C3×C4—22no—
1038C3×C4—21no—
1039C3×C4—21no—
1040C3×C4—21no—
1041C3×C4—41no—
1042C3×C4—41no—
1043C3×C4—42no—
1044C3×C4—62no—
1045C3×C4—61no—
1046C3×C4—61no—
1047C3×C4—61no—
1048C3×C4—61no—
1049C3×C4—61no—
1050C3×C4—61no—
1051C3×C4—61no—
1052C3×C4—61no—
1053C3×C4—61no—
1054C3×C4—61no—
1055C3×C4—61no—
1056C3×C4—61no—
1057C3×C4—61no—
1058C3×C4—61no—
1059C3×C4—92no—
1060C3×C4—121no—
1061C3×C4—121no—
1062C3×C4—121no—
1063C3×C4—121no—
1064C3×C4—121no—
1065C3×C4—121no—
1066C3×C4—181no—
1067Dic3—21no—
1068Dic3—21no—
1069Dic3—21no—
1070Dic3—21no—
1071Dic3—21no—
1072Dic3—21no—
1073Dic3—21no—
1074Dic3—32no—
1075Dic3—32no—
1076Dic3—62no—
1077Dic3—62no—
1078Dic3—61no—
1079Dic3—61no—
1080C32—21no—
1081C32—21no—
1082C32—21no—
1083C32—41no—
1084C32#561511yescharacteristic, complemented
1085C32#566311yescharacteristic, complemented
1086C32C3×#54011yescharacteristic, complemented
1087C23—31no—
1088C23—91no—
1089C23—91no—
1090C23C2×C3×D3211yescharacteristic
1091C23C2×C3×D3211yescharacteristic
1092D4—41no—
1093D4—121no—
1094D4—121no—
1095D4—182no—
1096D4—182no—
1097D4—361no—
1098D4—361no—
1099D4—361no—
1100D4—361no—
1101D4—361no—
1102C2×C4—31no—
1103C2×C4—31no—
1104C2×C4—31no—
1105C2×C4—31no—
1106C2×C4—31no—
1107C2×C4—31no—
1108C2×C4—31no—
1109C2×C4—91no—
1110C2×C4—91no—
1111C2×C4—121no—
1112C2×C4—121no—
1113C2×C4—182no—
1114C2×C4—361no—
1115C2×C4—361no—
1116C2×C4C2×C3×D3211yescharacteristic
1117C2×C3—21no—
1118C2×C3—21no—
1119C2×C3—21no—
1120C2×C3—21no—
1121C2×C3—21no—
1122C2×C3—21no—
1123C2×C3—21no—
1124C2×C3—21no—
1125C2×C3—21no—
1126C2×C3—42no—
1127C2×C3—42no—
1128C2×C3—41no—
1129C2×C3—41no—
1130C2×C3—41no—
1131C2×C3—41no—
1132C2×C3—41no—
1133C2×C3—41no—
1134C2×C3—41no—
1135C2×C3—41no—
1136C2×C3—41no—
1137C2×C3—81no—
1138C2×C3—81no—
1139C2×C3—81no—
1140C2×C3—81no—
1141C2×C3—82no—
1142C2×C3—82no—
1143C2×C3—121no—
1144C2×C3—121no—
1145C2×C3—241no—
1146C2×C3—361no—
1147C2×C3—361no—
1148C2×C3#6431211yescharacteristic
1149C2×C3#6431411yescharacteristic
1150C2×C3#6433011yescharacteristic
1151C2×C3C3×#100411yescharacteristic
1152C2×C3C3×#100411yescharacteristic
1153C2×C3C3×#100411yescharacteristic
1154C2×C3C3×D3×#4111yescharacteristic
1155C2×C3C3×D3×#4111yescharacteristic
1156C2×C3C3×#100911yescharacteristic
1157D3—41no—
1158D3—121no—
1159D3—121no—
1160D3—121no—
1161D3—121no—
1162D3—241no—
1163D3—241no—
1164C22—21no—
1165C22—21no—
1166C22—21no—
1167C22—21no—
1168C22—21no—
1169C22—21no—
1170C22—61no—
1171C22—61no—
1172C22—61no—
1173C22—181no—
1174C22—181no—
1175C22—181no—
1176C22—181no—
1177C22—181no—
1178C22—181no—
1179C22C22×C3×D3211yescharacteristic
1180C4—21no—
1181C4—61no—
1182C4—61no—
1183C4—61no—
1184C4—61no—
1185C4—61no—
1186C4—61no—
1187C4—61no—
1188C4—92no—
1189C4—181no—
1190C3—21no—
1191C3—21no—
1192C3—21no—
1193C3—41no—
1194C3#1059525111yescharacteristic, direct product factor
1195C3C3×#561511yescharacteristic, complemented
1196C3C3×#566311yescharacteristic, complemented
1197C2—41no—
1198C2—41no—
1199C2—121no—
1200C2—361no—
1201C2—361no—
1202C2C3×#6431211yescharacteristic
1203C2C3×#6431411yescharacteristic
1204C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#540
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C3×#64149C2semidirect
2. C32×#939C2semidirect
3. C32×#935C2semidirect
4. C3×#63978C2semidirect
5. C3×#63975C2semidirect
6. C3×#63971C2semidirect
7. C3×#63971C2semidirect
8. C3×#63966C2semidirect
9. C3×#63958C2semidirect
10. C3×#63952C2semidirect
11. C3×#63952C2semidirect
12. C3×#63910C2semidirect
13. C3×#63897C2semidirect
14. C3×#63878C2semidirect
15. C3×#63870C2semidirect
18. #10595251C3direct (N × H)
56. #64149C2×C3semidirect
64. C3×#939D3semidirect
65. C3×#939C2×C3semidirect
68. C3×#935D3semidirect
69. C3×#935C2×C3semidirect
90. #63978C2×C3semidirect
91. #63975C2×C3semidirect
92. #63971C2×C3semidirect
93. #63971C2×C3semidirect
94. #63966C2×C3semidirect
95. #63958C2×C3semidirect
96. #63952C2×C3semidirect
97. #63952C2×C3semidirect
98. #63910C2×C3semidirect
99. #63897C2×C3semidirect
100. #63878C2×C3semidirect
101. #63870C2×C3semidirect
313. #939C3×D3semidirect
315. #935C3×D3semidirect
742. C33#540semidirect
1084. C32#5615semidirect
1085. C32#5663semidirect
1086. C32C3×#540semidirect
1194. C3#10595251direct (N × H)
1195. C3C3×#5615semidirect
1196. C3C3×#5663semidirect

Maximal subgroups

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

subgroupindex
C3×#641492
C32×#9392
C32×#9352
C3×#639782
C3×#639752
C3×#639712
C3×#639662
C3×#639582
C3×#639522
C3×#639102
C3×#638972
C3×#638782
C3×#638702
C3×#56633
C3×#56153
#105952513