Finite Group Databasebeta

← C3×#73377 #11812965

Subgroups — C3×#73377 #11812965

Order 1152.

1385 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C2×C3×C4×#67C211yesmaximal, characteristic, complemented
3C2×C32×#95C211yesmaximal, characteristic, complemented
4C3×#5213C211yesmaximal, characteristic, complemented
5C3×#5213C211yesmaximal, characteristic, complemented
6C3×#5213C211yesmaximal, characteristic, complemented
7C3×#5210C211yesmaximal, characteristic, complemented
8C3×#4675C211yesmaximal, characteristic, complemented
9C3×#4675C211yesmaximal, characteristic, complemented
10C3×#4672C211yesmaximal, characteristic, complemented
11C3×#4669C211yesmaximal, characteristic, complemented
12C3×#4665C211yesmaximal, characteristic, complemented
13C3×#4664C211yesmaximal, characteristic, complemented
14C3×#4660C211yesmaximal, characteristic, complemented
15C3×#4655C211yesmaximal, characteristic, complemented
16C3×#2444—31nomaximal
17#73377C311yesmaximal, characteristic, direct product factor
18C23×C32×C4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C3×#930—24no—
28C3×C4×#67—24no—
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C32×#95C2211yescharacteristic
44C32×#95C2211yescharacteristic
45C32×#95C2211yescharacteristic
46C32×#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C2×C3×#121—31no—
56C2×C3×C4×D4—31no—
57C2×#930C2×C311yescharacteristic
58C2×C4×#67C2×C311yescharacteristic, complemented
59C3×#400—31no—
60C3×#397—31no—
61C3×#397—31no—
62C3×#394—31no—
63C3×#388—31no—
64C3×#387—31no—
65C3×#386—31no—
66C3×#386—31no—
67C3×#386—31no—
68C3×#386—31no—
69C3×#385—31no—
70C3×#381—31no—
71C2×C3×#95—21no—
72C2×C3×#95D311yescharacteristic, complemented
73C2×C3×#95C2×C311yescharacteristic, complemented
74#5213C2×C311yescharacteristic, complemented
75#5213C2×C311yescharacteristic, complemented
76#5213C2×C311yescharacteristic, complemented
77#5210C2×C311yescharacteristic, complemented
78#4675C2×C311yescharacteristic, complemented
79#4675C2×C311yescharacteristic, complemented
80#4672C2×C311yescharacteristic, complemented
81#4669C2×C311yescharacteristic, complemented
82#4665C2×C311yescharacteristic, complemented
83#4664C2×C311yescharacteristic, complemented
84#4660C2×C311yescharacteristic, complemented
85#4655C2×C311yescharacteristic, complemented
86C24×C32C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4—22no—
90C22×C32×C4—22no—
91C22×C32×C4—22no—
92C22×C32×C4—22no—
93C22×C32×C4—22no—
94C22×C32×C4—41no—
95C22×C32×C4—41no—
96C22×C32×C4—41no—
97C22×C32×C4—41no—
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67D414yes—
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C2×C3×D12—22no—
117C2×C3×D12—22no—
118C2×C3×D12—41no—
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—41no—
122C3×#217—22no—
123C3×#217—22no—
124C3×(C2×D3)⋊C4—22no—
125C3×(C2×D3)⋊C4—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—41no—
129C3×(C2×D3)⋊C4—41no—
130C3×(C2×D3)⋊C4—41no—
131C3×(C2×D3)⋊C4—41no—
132C3×(C2×D3)⋊C4—41no—
133C3×C4⋊Dic3—22no—
134C3×Dic3⋊C4—22no—
135C3×Dic3⋊C4—22no—
136C3×Dic3⋊C4—41no—
137C3×C4×Dic3—22no—
138#2444—31noSylow
139C22×C3×D4—31no—
140C22×C3×D4—31no—
141C22×C3×D4—31no—
142C23×C3×C4—21no—
143C23×C3×C4—21no—
144C23×C3×C4—21no—
145C23×C3×C4—31no—
146C23×C3×C4C2×D311yescharacteristic
147C23×C3×C4C2×D311yescharacteristic
148C23×C3×C4C2×D311yescharacteristic
149C23×C3×C4C22×C311yescharacteristic
150C23×C3×C4C22×C311yescharacteristic
151C23×C3×C4C22×C311yescharacteristic
152C22×#67C22×C311yescharacteristic
153C22×#67C22×C311yescharacteristic
154C22×D12C22×C311yescharacteristic
155C22×C4×D3C22×C311yescharacteristic
156C3×#121—64no—
157C3×C4×D4—64no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C42—31no—
174C2×#217C22×C311yescharacteristic
175C2×#217C22×C311yescharacteristic
176#930—24no—
177C4×#67—24no—
178C2×(C2×D3)⋊C4C22×C311yescharacteristic
179C2×(C2×D3)⋊C4C22×C311yescharacteristic
180C2×(C2×D3)⋊C4C22×C311yescharacteristic
181C2×(C2×D3)⋊C4C22×C311yescharacteristic
182C2×(C2×D3)⋊C4C22×C311yescharacteristic
183C2×(C2×D3)⋊C4C22×C311yescharacteristic
184C2×(C2×D3)⋊C4C22×C311yescharacteristic
185C2×(C2×D3)⋊C4C22×C311yescharacteristic
186C2×(C2×D3)⋊C4C22×C311yescharacteristic
187C2×C4⋊Dic3C22×C311yescharacteristic
188C2×Dic3⋊C4C22×C311yescharacteristic
189C2×Dic3⋊C4C22×C311yescharacteristic
190C2×Dic3⋊C4C22×C311yescharacteristic
191C2×C4×Dic3C22×C311yescharacteristic
192C3×#95—21no—
193C3×#95—21no—
194C3×#95—21no—
195C3×#95—21no—
196C3×#95—31no—
197C3×#95—31no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95C2×D311yescharacteristic
205C3×#95C2×D311yescharacteristic
206C3×#95C2×D311yescharacteristic
207C3×#95C2×D311yescharacteristic
208C3×#95C22×C311yescharacteristic
209C3×#95C22×C311yescharacteristic
210C3×#95C22×C311yescharacteristic
211C3×#95C22×C311yescharacteristic
212C3⋊#95C22×C311yescharacteristic
213C3⋊#95C22×C311yescharacteristic
214C3⋊#95C22×C311yescharacteristic
215C3⋊#95C22×C311yescharacteristic
216C3⋊#95C22×C311yescharacteristic
217C3⋊#95C22×C311yescharacteristic
218C3⋊#95C22×C311yescharacteristic
219C3⋊#95C22×C311yescharacteristic
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32C2×D412yes—
225C23×C32#4112yes—
226C23×C32#4112yes—
227C23×C32C2411yescharacteristic
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D412yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—44no—
259C2×C32×C4—44no—
260C2×C32×C4—44no—
261C2×C32×C4#4112yes—
262C2×C32×C4#4112yes—
263C3×#67—28no—
264C3×#67—44no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D412yes—
283C3×D12—44no—
284C3×C4×D3—44no—
285C2×#121—31no—
286C2×C4×D4—31no—
287#400—31no—
288#397—31no—
289#397—31no—
290#394—31no—
291#388—31no—
292#387—31no—
293#386—31no—
294#386—31no—
295#386—31no—
296#386—31no—
297#385—31no—
298#381—31no—
299C2×#95C3×D311yescharacteristic, complemented
300C24×C3—21no—
301C24×C3—31no—
302C24×C3—31no—
303C24×C3C22×D311yescharacteristic
304C24×C3C23×C311yescharacteristic
305C23×D3C23×C311yescharacteristic
306C23×D3C23×C311yescharacteristic
307C2×C3×D4—34no—
308C2×C3×D4—62no—
309C2×C3×D4—62no—
310C2×C3×D4—62no—
311C2×C3×D4—62no—
312C2×C3×D4—62no—
313C2×C3×D4—62no—
314C2×C3×D4—62no—
315C2×C3×D4—121no—
316C22×C3×C4—24no—
317C22×C3×C4—24no—
318C22×C3×C4—24no—
319C22×C3×C4—22no—
320C22×C3×C4—22no—
321C22×C3×C4—22no—
322C22×C3×C4—22no—
323C22×C3×C4—22no—
324C22×C3×C4—22no—
325C22×C3×C4—22no—
326C22×C3×C4—22no—
327C22×C3×C4—22no—
328C22×C3×C4—22no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—42no—
342C22×C3×C4—42no—
343C22×C3×C4—41no—
344C22×C3×C4—41no—
345C22×C3×C4—41no—
346C22×C3×C4—41no—
347C22×C3×C4—41no—
348C22×C3×C4—41no—
349C22×C3×C4—41no—
350C22×C3×C4—41no—
351C22×C3×C4—42no—
352C22×C3×C4—42no—
353C22×C3×C4—42no—
354C22×C3×C4—42no—
355C22×C3×C4—62no—
356C22×C3×C4—62no—
357C22×C3×C4—121no—
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C23×C311yescharacteristic
365C22×C3×C4C23×C311yescharacteristic
366C22×C3×C4C23×C311yescharacteristic
367C22×C3×C4C23×C311yescharacteristic
368C22×C3×C4C23×C311yescharacteristic
369C22×C3×C4C23×C311yescharacteristic
370C2×#67—22no—
371C2×#67—22no—
372C2×#67—22no—
373C2×#67—22no—
374C2×#67—22no—
375C2×#67C3×D414yes—
376C22×Dic3C23×C311yescharacteristic
377C22×Dic3C23×C311yescharacteristic
378C22×Dic3C23×C311yescharacteristic
379C22×Dic3C23×C311yescharacteristic
380C22×Dic3C23×C311yescharacteristic
381C22×Dic3C23×C311yescharacteristic
382C2×D12—22no—
383C2×D12—22no—
384C2×D12—41no—
385C2×C4×D3—22no—
386C2×C4×D3—22no—
387C2×C4×D3—41no—
388C3×C4⋊C4—62no—
389C3×C4⋊C4—62no—
390C3×C4⋊C4—62no—
391C3×C4⋊C4—121no—
392C3×C22⋊C4—62no—
393C3×C22⋊C4—62no—
394C3×C22⋊C4—62no—
395C3×C22⋊C4—62no—
396C3×C22⋊C4—62no—
397C3×C22⋊C4—62no—
398C3×C22⋊C4—121no—
399C3×C22⋊C4—121no—
400C3×C22⋊C4—121no—
401C3×C22⋊C4—121no—
402C3×C22⋊C4—121no—
403C3×C42—62no—
404#217—22no—
405#217—22no—
406(C2×D3)⋊C4—22no—
407(C2×D3)⋊C4—22no—
408(C2×D3)⋊C4—22no—
409(C2×D3)⋊C4—22no—
410(C2×D3)⋊C4—41no—
411(C2×D3)⋊C4—41no—
412(C2×D3)⋊C4—41no—
413(C2×D3)⋊C4—41no—
414(C2×D3)⋊C4—41no—
415C4⋊Dic3—22no—
416Dic3⋊C4—22no—
417Dic3⋊C4—22no—
418Dic3⋊C4—41no—
419C4×Dic3—22no—
420C22×C32—22no—
421C22×C32—22no—
422C22×C32—22no—
423C22×C32—22no—
424C22×C32—22no—
425C22×C32—22no—
426C22×C32#12314yes—
427C22×C32C22×D411yescharacteristic
428C22×C32C2×#4111yescharacteristic
429C22×C32C2×#4111yescharacteristic
430C22×C32C2×#4111yescharacteristic
431C22×C32C2×#4111yescharacteristic
432C22×C32H(5,𝔽2)11yescharacteristic
433C22×C32H(5,𝔽2)11yescharacteristic
434C2×C3×D3—22no—
435C2×C3×D3—22no—
436C2×C3×D3—22no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C32×C4—22no—
449C32×C4—22no—
450C32×C4—41no—
451C32×C4—41no—
452C32×C4—41no—
453C32×C4—41no—
454C3×Dic3—22no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3—41no—
460C22×D4—31no—
461C22×D4—31no—
462C22×D4—31no—
463C23×C4—31no—
464C23×C4C2×C3×D311yescharacteristic
465C23×C4C2×C3×D311yescharacteristic
466C23×C4C2×C3×D311yescharacteristic
467#121—64no—
468C4×D4—64no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—31no—
471C2×C4⋊C4—31no—
472C2×C4⋊C4—31no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—31no—
475C2×C22⋊C4—31no—
476C2×C22⋊C4—31no—
477C2×C22⋊C4—31no—
478C2×C22⋊C4—31no—
479C2×C22⋊C4—31no—
480C2×C22⋊C4—31no—
481C2×C22⋊C4—31no—
482C2×C22⋊C4—31no—
483C2×C22⋊C4—31no—
484C2×C42—31no—
485#95—31no—
486#95—31no—
487#95—31no—
488#95—31no—
489#95—31no—
490#95—31no—
491#95—31no—
492#95—31no—
493#95C2×C3×D311yescharacteristic
494#95C2×C3×D311yescharacteristic
495#95C2×C3×D311yescharacteristic
496#95C2×C3×D311yescharacteristic
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—32no—
514C23×C3—61no—
515C23×C3—61no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3#23512yes—
528C23×C3D3×D412yes—
529C23×C3#23912yes—
530C23×C3C2×C3×D412yes—
531C23×C3C3×#4112yes—
532C23×C3C3×#4112yes—
533C23×C3C23×D311yescharacteristic
534C23×C3C24×C311yescharacteristic
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3C2×C3×D412yes—
549C3×D4—68no—
550C3×D4—124no—
551C3×D4—124no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—32no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—44no—
604C2×C3×C4—44no—
605C2×C3×C4—44no—
606C2×C3×C4—44no—
607C2×C3×C4—48no—
608C2×C3×C4—48no—
609C2×C3×C4—48no—
610C2×C3×C4—44no—
611C2×C3×C4—44no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—124no—
630C2×C3×C4#23512yes—
631C2×C3×C4#23512yes—
632C2×C3×C4C3×#4112yes—
633C2×C3×C4C3×#4112yes—
634#67—28no—
635#67—44no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3C2×C3×D412yes—
654D12—44no—
655C4×D3—44no—
656C2×C32—24no—
657C2×C32C2×#12311yescharacteristic
658C2×C32#52911yescharacteristic
659C2×C32#53811yescharacteristic
660C2×C32#54611yescharacteristic
661C2×C32#54611yescharacteristic
662C2×C32#55311yescharacteristic
663C2×C32#55311yescharacteristic
664C3×D3—42no—
665C3×D3—81no—
666C24—31no—
667C24—31no—
668C24C22×C3×D311yescharacteristic
669C2×D4—34no—
670C2×D4—62no—
671C2×D4—62no—
672C2×D4—62no—
673C2×D4—62no—
674C2×D4—62no—
675C2×D4—62no—
676C2×D4—62no—
677C2×D4—121no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—41no—
693C22×C4—62no—
694C22×C4—62no—
695C22×C4—121no—
696C22×C4C22×C3×D311yescharacteristic
697C22×C4C22×C3×D311yescharacteristic
698C22×C4C22×C3×D311yescharacteristic
699C22×C4C22×C3×D311yescharacteristic
700C22×C4C22×C3×D311yescharacteristic
701C22×C4C22×C3×D311yescharacteristic
702C4⋊C4—62no—
703C4⋊C4—62no—
704C4⋊C4—62no—
705C4⋊C4—121no—
706C22⋊C4—62no—
707C22⋊C4—62no—
708C22⋊C4—62no—
709C22⋊C4—62no—
710C22⋊C4—62no—
711C22⋊C4—62no—
712C22⋊C4—121no—
713C22⋊C4—121no—
714C22⋊C4—121no—
715C22⋊C4—121no—
716C22⋊C4—121no—
717C42—62no—
718C22×C3—24no—
719C22×C3—24no—
720C22×C3—24no—
721C22×C3—24no—
722C22×C3—24no—
723C22×C3—24no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—24no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—62no—
745C22×C3—62no—
746C22×C3—62no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3#89414yes—
759C22×C3C3×#12314yes—
760C22×C3C2×#23511yescharacteristic
761C22×C3C2×#23511yescharacteristic
762C22×C3C2×#23511yescharacteristic
763C22×C3C2×D3×D411yescharacteristic
764C22×C3#100411yescharacteristic
765C22×C3#100411yescharacteristic
766C22×C3C2×#23911yescharacteristic
767C22×C3C22×C3×D411yescharacteristic
768C22×C3C2×C3×#4111yescharacteristic
769C22×C3C2×C3×#4111yescharacteristic
770C22×C3C2×C3×#4111yescharacteristic
771C22×C3C2×C3×#4111yescharacteristic
772C22×C3C3×H(5,𝔽2)11yescharacteristic
773C22×C3C3×H(5,𝔽2)11yescharacteristic
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C3×C4—22no—
789C3×C4—22no—
790C3×C4—22no—
791C3×C4—22no—
792C3×C4—42no—
793C3×C4—42no—
794C3×C4—42no—
795C3×C4—42no—
796C3×C4—42no—
797C3×C4—42no—
798C3×C4—41no—
799C3×C4—41no—
800C3×C4—41no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—41no—
805C3×C4—41no—
806C3×C4—62no—
807C3×C4—121no—
808C3×C4—121no—
809C3×C4—121no—
810C3×C4—121no—
811C3×C4—121no—
812Dic3—22no—
813Dic3—41no—
814Dic3—41no—
815Dic3—41no—
816Dic3—41no—
817Dic3—41no—
818C32#244411yescharacteristic, complemented, Sylow
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—32no—
824C23—61no—
825C23—61no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23C3×#23512yes—
838C23C3×D3×D412yes—
839C23C3×#23912yes—
840C23C23×C3×D311yescharacteristic
841D4—68no—
842D4—124no—
843D4—124no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—32no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—124no—
882C2×C4C3×#23512yes—
883C2×C4C3×#23512yes—
884C2×C3—28no—
885C2×C3—24no—
886C2×C3—24no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—122no—
895C2×C3—241no—
896C2×C3#547911yescharacteristic
897C2×C3#549011yescharacteristic
898C2×C3#549011yescharacteristic
899C2×C3#549411yescharacteristic
900C2×C3C2×#89411yescharacteristic
901C2×C3#551411yescharacteristic
902C2×C3#551411yescharacteristic
903C2×C3C2×C3×#12311yescharacteristic
904C2×C3C3×#52911yescharacteristic
905C2×C3C3×#53811yescharacteristic
906C2×C3C3×#54611yescharacteristic
907C2×C3C3×#54611yescharacteristic
908C2×C3C3×#55311yescharacteristic
909C2×C3C3×#55311yescharacteristic
910D3—42no—
911D3—81no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—22no—
916C22—22no—
917C22—22no—
918C22—62no—
919C22—62no—
920C22—62no—
921C22—121no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—121no—
926C22—121no—
927C22—121no—
928C22—121no—
929C22—121no—
930C22—121no—
931C22—121no—
932C22C3×#89414yes—
933C22C2×C3×#23511yescharacteristic
934C22C2×C3×#23511yescharacteristic
935C22C2×C3×#23511yescharacteristic
936C22C2×C3×D3×D411yescharacteristic
937C22C3×#100411yescharacteristic
938C22C3×#100411yescharacteristic
939C22C2×C3×#23911yescharacteristic
940C4—22no—
941C4—22no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—62no—
947C4—121no—
948C4—121no—
949C4—121no—
950C4—121no—
951C4—121no—
952C3—21no—
953C3#7337711yescharacteristic, direct product factor
954C3C3×#244411yescharacteristic, complemented
955C2—24no—
956C2—122no—
957C2—241no—
958C2C3×#547911yescharacteristic
959C2C3×#549011yescharacteristic
960C2C3×#549011yescharacteristic
961C2C3×#549411yescharacteristic
962C2C2×C3×#89411yescharacteristic
963C2C3×#551411yescharacteristic
964C2C3×#551411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#95C2
socleC23×C32C24
prime radicalC2×C3×#930C2
hypercenterC2×C3×#95D3
hypocenterC3C3×#2444
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×#67C2semidirect
3. C2×C32×#95C2semidirect
4. C3×#5213C2semidirect
5. C3×#5213C2semidirect
6. C3×#5213C2semidirect
7. C3×#5210C2semidirect
8. C3×#4675C2semidirect
9. C3×#4675C2semidirect
10. C3×#4672C2semidirect
11. C3×#4669C2semidirect
12. C3×#4665C2semidirect
13. C3×#4664C2semidirect
14. C3×#4660C2semidirect
15. C3×#4655C2semidirect
17. #73377C3direct (N × H)
58. C2×C4×#67C2×C3semidirect
72. C2×C3×#95D3semidirect
73. C2×C3×#95C2×C3semidirect
74. #5213C2×C3semidirect
75. #5213C2×C3semidirect
76. #5213C2×C3semidirect
77. #5210C2×C3semidirect
78. #4675C2×C3semidirect
79. #4675C2×C3semidirect
80. #4672C2×C3semidirect
81. #4669C2×C3semidirect
82. #4665C2×C3semidirect
83. #4664C2×C3semidirect
84. #4660C2×C3semidirect
85. #4655C2×C3semidirect
299. C2×#95C3×D3semidirect
818. C32#2444semidirect
953. C3#73377direct (N × H)
954. C3C3×#2444semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C2×C3×C4×#672
C2×C32×#952
C3×#52132
C3×#52102
C3×#46752
C3×#46722
C3×#46692
C3×#46652
C3×#46642
C3×#46602
C3×#46552
C3×#24443
#733773