Finite Group Databasebeta

← C3×#74883 #11807706

Subgroups — C3×#74883 #11807706

Order 1152.

1295 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C32×#386C211yesmaximal, characteristic, complemented
3C3×#5220C211yesmaximal, characteristic, complemented
4C3×#5213C211yesmaximal, characteristic, complemented
5C3×#5210C211yesmaximal, characteristic, complemented
6C3×#4958C211yesmaximal, characteristic, complemented
7C3×#4957C211yesmaximal, characteristic, complemented
8C3×#4957C211yesmaximal, characteristic, complemented
9C3×#4946C211yesmaximal, characteristic, complemented
10C3×#4945C211yesmaximal, characteristic, complemented
11C3×#4944C211yesmaximal, characteristic, complemented
12C3×#4667C211yesmaximal, characteristic, complemented
13C3×#4664C211yesmaximal, characteristic, complemented
14C3×#4654C211yesmaximal, characteristic, complemented
15C3×#4653C211yesmaximal, characteristic, complemented
16C3×#2377—31nomaximal
17#74883C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C3×#938C418yescomplemented
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C32×#95C2211yescharacteristic
45C32×#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C2×C3×#121—31no—
55C2×#938C2×C311yescharacteristic
56C3×#390—31no—
57C3×#390—31no—
58C3×#388—31no—
59C3×#388—31no—
60C3×#387—31no—
61C3×#387—31no—
62C3×#386—21no—
63C3×#386—31no—
64C3×#386—31no—
65C3×#386—31no—
66C3×#386D311yescharacteristic, complemented
67C3×#386C2×C311yescharacteristic, complemented
68C3×#385—31no—
69C3×#385—31no—
70C3×#381—31no—
71C3×#380—31no—
72#5220C2×C311yescharacteristic, complemented
73#5213C2×C311yescharacteristic, complemented
74#5210C2×C311yescharacteristic, complemented
75#4958C2×C311yescharacteristic, complemented
76#4957C2×C311yescharacteristic, complemented
77#4957C2×C311yescharacteristic, complemented
78#4946C2×C311yescharacteristic, complemented
79#4945C2×C311yescharacteristic, complemented
80#4944C2×C311yescharacteristic, complemented
81#4667C2×C311yescharacteristic, complemented
82#4664C2×C311yescharacteristic, complemented
83#4654C2×C311yescharacteristic, complemented
84#4653C2×C311yescharacteristic, complemented
85C24×C32C2311yescharacteristic
86C24×C32C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C2×C32×D4—41no—
89C2×C32×D4—41no—
90C2×C32×D4C2×C414yes—
91C22×C32×C4—41no—
92C22×C32×C4—41no—
93C22×C32×C4—41no—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×C3×#67—41no—
100C2×C3×#67—41no—
101C2×C3×#67—41no—
102C2×C3×#67—41no—
103C2×C3×#67C2×C414yescomplemented
104C2×C3×#67C2×C414yescomplemented
105C22×C3×Dic3—41no—
106C22×C3×Dic3—41no—
107C22×C3×Dic3—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×C3×C4×D3—41no—
116C2×C3×C4×D3—41no—
117C2×C3×C4×D3C2×C414yescomplemented
118C32×C22⋊C4—41no—
119C32×C22⋊C4—41no—
120C32×C22⋊C4—41no—
121C3×#217—41no—
122C3×#217—41no—
123C3×#217—41no—
124C3×#217C2×C414yescomplemented
125C3×#217C2×C414yescomplemented
126C3×(C2×D3)⋊C4—41no—
127C3×(C2×D3)⋊C4—41no—
128C3×(C2×D3)⋊C4—41no—
129C3×(C2×D3)⋊C4—41no—
130C3×C4⋊Dic3C2×C414yescomplemented
131C3×Dic3⋊C4—41no—
132C3×Dic3⋊C4—41no—
133C3×Dic3⋊C4—41no—
134C3×Dic3⋊C4—41no—
135C3×C4×Dic3—41no—
136C3×C4×Dic3—41no—
137#2377—31noSylow
138C22×C3×D4—21no—
139C22×C3×D4—31no—
140C22×C3×D4—31no—
141C22×C3×D4C2×D311yescharacteristic
142C22×C3×D4C22×C311yescharacteristic
143C23×C3×C4—21no—
144C23×C3×C4—31no—
145C23×C3×C4—31no—
146C23×C3×C4C2×D311yescharacteristic
147C23×C3×C4C22×C311yescharacteristic
148C22×#67C22×C311yescharacteristic
149C22×#67C22×C311yescharacteristic
150C23×Dic3C22×C311yescharacteristic
151C22×C4×D3C22×C311yescharacteristic
152C3×#121—38no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—21no—
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊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⋊C4C2×D311yescharacteristic
171C2×C3×C22⋊C4C2×D311yescharacteristic
172C2×C3×C22⋊C4C2×D311yescharacteristic
173C2×C3×C22⋊C4C22×C311yescharacteristic
174C2×C3×C22⋊C4C22×C311yescharacteristic
175C2×C3×C22⋊C4C22×C311yescharacteristic
176C2×C3×C42—31no—
177C2×C3×C42—31no—
178C2×#217C22×C311yescharacteristic
179C2×#217C22×C311yescharacteristic
180C2×#217C22×C311yescharacteristic
181C2×#217C22×C311yescharacteristic
182C2×#217C22×C311yescharacteristic
183#938C3×C418yescomplemented
184C2×(C2×D3)⋊C4C22×C311yescharacteristic
185C2×(C2×D3)⋊C4C22×C311yescharacteristic
186C2×(C2×D3)⋊C4C22×C311yescharacteristic
187C2×(C2×D3)⋊C4C22×C311yescharacteristic
188C2×C4⋊Dic3C22×C311yescharacteristic
189C2×Dic3⋊C4C22×C311yescharacteristic
190C2×Dic3⋊C4C22×C311yescharacteristic
191C2×Dic3⋊C4C22×C311yescharacteristic
192C2×Dic3⋊C4C22×C311yescharacteristic
193C2×C4×Dic3C22×C311yescharacteristic
194C2×C4×Dic3C22×C311yescharacteristic
195C3×#95—21no—
196C3×#95—21no—
197C3×#95—31no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95—31no—
205C3×#95C2×D311yescharacteristic
206C3×#95C2×D311yescharacteristic
207C3×#95C22×C311yescharacteristic
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
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32—21no—
228C23×C32—21no—
229C23×C32C22×C412yes—
230C23×C32C22×C412yes—
231C23×C32C2411yescharacteristic
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×D3C22×C412yes—
239C32×D4—44no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
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—44no—
255C2×C32×C4C22×C412yes—
256C3×#67—44no—
257C3×#67—44no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
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—44no—
277C2×C3×Dic3C22×C412yes—
278C2×C3×Dic3C22×C412yes—
279C2×C3×Dic3C22×C412yes—
280C3×C4×D3—44no—
281C2×#121—31no—
282#390—31no—
283#390—31no—
284#388—31no—
285#388—31no—
286#387—31no—
287#387—31no—
288#386—31no—
289#386—31no—
290#386—31no—
291#386C3×D311yescharacteristic, complemented
292#385—31no—
293#385—31no—
294#381—31no—
295#380—31no—
296C24×C3—21no—
297C24×C3—21no—
298C24×C3—31no—
299C24×C3C22×D311yescharacteristic
300C24×C3C22×D311yescharacteristic
301C24×C3C23×C311yescharacteristic
302C24×C3C23×C311yescharacteristic
303C23×D3C23×C311yescharacteristic
304C2×C3×D4—24no—
305C2×C3×D4—34no—
306C2×C3×D4—34no—
307C2×C3×D4—41no—
308C2×C3×D4—41no—
309C2×C3×D4—41no—
310C2×C3×D4—41no—
311C2×C3×D4—42no—
312C2×C3×D4—42no—
313C2×C3×D4—121no—
314C2×C3×D4—121no—
315C2×C3×D4—121no—
316C2×C3×D4—121no—
317C2×C3×D4C4×D314yes—
318C2×C3×D4C2×C3×C414yes—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—34no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—41no—
333C22×C3×C4—41no—
334C22×C3×C4—41no—
335C22×C3×C4—41no—
336C22×C3×C4—41no—
337C22×C3×C4—41no—
338C22×C3×C4—42no—
339C22×C3×C4—42no—
340C22×C3×C4—42no—
341C22×C3×C4—121no—
342C22×C3×C4—121no—
343C22×C3×C4—121no—
344C22×C3×C4—121no—
345C22×C3×C4—121no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C23×C311yescharacteristic
352C22×C3×C4C23×C311yescharacteristic
353C22×C3×C4C23×C311yescharacteristic
354C22×C3×C4C23×C311yescharacteristic
355C22×C3×C4C23×C311yescharacteristic
356C2×#67—41no—
357C2×#67—41no—
358C2×#67—41no—
359C2×#67—41no—
360C2×#67C2×C3×C414yescomplemented
361C2×#67C2×C3×C414yescomplemented
362C22×Dic3—41no—
363C22×Dic3—41no—
364C22×Dic3—41no—
365C22×Dic3C23×C311yescharacteristic
366C22×Dic3C23×C311yescharacteristic
367C22×Dic3C23×C311yescharacteristic
368C22×Dic3C23×C311yescharacteristic
369C22×Dic3C23×C311yescharacteristic
370C22×Dic3C23×C311yescharacteristic
371C22×Dic3C23×C311yescharacteristic
372C2×C4×D3—41no—
373C2×C4×D3—41no—
374C2×C4×D3C2×C3×C414yescomplemented
375C3×C4⋊C4—34no—
376C3×C4⋊C4—121no—
377C3×C4⋊C4—121no—
378C3×C4⋊C4—121no—
379C3×C4⋊C4—121no—
380C3×C22⋊C4—34no—
381C3×C22⋊C4—34no—
382C3×C22⋊C4—41no—
383C3×C22⋊C4—41no—
384C3×C22⋊C4—41no—
385C3×C22⋊C4—41no—
386C3×C22⋊C4—41no—
387C3×C22⋊C4—41no—
388C3×C22⋊C4—42no—
389C3×C22⋊C4—42no—
390C3×C22⋊C4—42no—
391C3×C22⋊C4—121no—
392C3×C22⋊C4—121no—
393C3×C22⋊C4—121no—
394C3×C22⋊C4—121no—
395C3×C22⋊C4—121no—
396C3×C22⋊C4—121no—
397C3×C22⋊C4—121no—
398C3×C42—121no—
399C3×C42—121no—
400#217—41no—
401#217—41no—
402#217—41no—
403#217C2×C3×C414yescomplemented
404#217C2×C3×C414yescomplemented
405(C2×D3)⋊C4—41no—
406(C2×D3)⋊C4—41no—
407(C2×D3)⋊C4—41no—
408(C2×D3)⋊C4—41no—
409C4⋊Dic3C2×C3×C414yescomplemented
410Dic3⋊C4—41no—
411Dic3⋊C4—41no—
412Dic3⋊C4—41no—
413Dic3⋊C4—41no—
414C4×Dic3—41no—
415C4×Dic3—41no—
416C22×C32—22no—
417C22×C32—22no—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—22no—
421C22×C32—22no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32C23×C411yescharacteristic
431C22×C32H(5,𝔽2)11yescharacteristic
432C22×C32H(5,𝔽2)11yescharacteristic
433C22×C32H(5,𝔽2)11yescharacteristic
434C22×C32H(5,𝔽2)11yescharacteristic
435C22×C32H(5,𝔽2)11yescharacteristic
436C22×C322−1+411yescharacteristic
437C2×C3×D3—22no—
438C2×C3×D3—22no—
439C2×C3×D3—22no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C32×C4—22no—
445C32×C4—41no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4—41no—
449C3×Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C22×D4—31no—
457C22×D4—31no—
458C22×D4C2×C3×D311yescharacteristic
459C23×C4—31no—
460C23×C4—31no—
461C23×C4C2×C3×D311yescharacteristic
462#121—38no—
463C2×C4⋊C4—31no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4—31no—
468C2×C22⋊C4—31no—
469C2×C22⋊C4—31no—
470C2×C22⋊C4—31no—
471C2×C22⋊C4—31no—
472C2×C22⋊C4—31no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—31no—
475C2×C22⋊C4—31no—
476C2×C22⋊C4—31no—
477C2×C22⋊C4C2×C3×D311yescharacteristic
478C2×C22⋊C4C2×C3×D311yescharacteristic
479C2×C22⋊C4C2×C3×D311yescharacteristic
480C2×C42—31no—
481C2×C42—31no—
482#95—31no—
483#95—31no—
484#95—31no—
485#95—31no—
486#95—31no—
487#95—31no—
488#95—31no—
489#95—31no—
490#95C2×C3×D311yescharacteristic
491#95C2×C3×D311yescharacteristic
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
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—21no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—32no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3C2×C4×D312yes—
539C23×C3C2×C4×D312yes—
540C23×C3C22×C3×C412yes—
541C23×C3C22×C3×C412yes—
542C23×C3C23×D311yescharacteristic
543C23×C3C24×C311yescharacteristic
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3C22×C3×C412yes—
551C3×D4—44no—
552C3×D4—44no—
553C3×D4—48no—
554C3×D4—124no—
555C3×D4—124no—
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—21no—
563C2×C3×C4—21no—
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—22no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—41no—
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—48no—
603C2×C3×C4—44no—
604C2×C3×C4—44no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
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—124no—
624C2×C3×C4—124no—
625C2×C3×C4C2×C4×D312yes—
626C2×C3×C4C22×C3×C412yes—
627#67—44no—
628#67—44no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
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—44no—
648C2×Dic3C22×C3×C412yes—
649C2×Dic3C22×C3×C412yes—
650C2×Dic3C22×C3×C412yes—
651C4×D3—44no—
652C2×C32—42no—
653C2×C32—42no—
654C2×C32#51811yescharacteristic
655C2×C32#51811yescharacteristic
656C2×C32#52011yescharacteristic
657C2×C32#56011yescharacteristic
658C2×C32#56011yescharacteristic
659C2×C32#56211yescharacteristic
660C2×C32#56211yescharacteristic
661C3×D3—42no—
662C24—31no—
663C24C22×C3×D311yescharacteristic
664C24C22×C3×D311yescharacteristic
665C2×D4—34no—
666C2×D4—34no—
667C2×D4—41no—
668C2×D4—41no—
669C2×D4—121no—
670C2×D4—121no—
671C2×D4—121no—
672C2×D4—121no—
673C2×D4C3×C4×D314yes—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—34no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—121no—
686C22×C4—121no—
687C22×C4—121no—
688C22×C4—121no—
689C22×C4—121no—
690C22×C4C22×C3×D311yescharacteristic
691C22×C4C22×C3×D311yescharacteristic
692C22×C4C22×C3×D311yescharacteristic
693C22×C4C22×C3×D311yescharacteristic
694C22×C4C22×C3×D311yescharacteristic
695C4⋊C4—34no—
696C4⋊C4—121no—
697C4⋊C4—121no—
698C4⋊C4—121no—
699C4⋊C4—121no—
700C22⋊C4—34no—
701C22⋊C4—34no—
702C22⋊C4—41no—
703C22⋊C4—41no—
704C22⋊C4—41no—
705C22⋊C4—121no—
706C22⋊C4—121no—
707C22⋊C4—121no—
708C22⋊C4—121no—
709C22⋊C4—121no—
710C22⋊C4—121no—
711C22⋊C4—121no—
712C42—121no—
713C42—121no—
714C22×C3—24no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—42no—
735C22×C3—42no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—81no—
763C22×C3—81no—
764C22×C3—81no—
765C22×C3—81no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3C22×C4×D311yescharacteristic
771C22×C3#100411yescharacteristic
772C22×C3#100411yescharacteristic
773C22×C3#100411yescharacteristic
774C22×C3#100411yescharacteristic
775C22×C3#100911yescharacteristic
776C22×C3#101011yescharacteristic
777C22×C3C23×C3×C411yescharacteristic
778C22×C3C3×H(5,𝔽2)11yescharacteristic
779C22×C3C3×H(5,𝔽2)11yescharacteristic
780C22×C3C3×H(5,𝔽2)11yescharacteristic
781C22×C3C3×H(5,𝔽2)11yescharacteristic
782C22×C3C3×H(5,𝔽2)11yescharacteristic
783C22×C3C3×2−1+411yescharacteristic
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C3×C4—22no—
792C3×C4—22no—
793C3×C4—42no—
794C3×C4—42no—
795C3×C4—42no—
796C3×C4—41no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—41no—
800C3×C4—41no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4—62no—
807C3×C4—81no—
808C3×C4—81no—
809C3×C4—121no—
810C3×C4—121no—
811C3×C4—121no—
812C3×C4—121no—
813Dic3—22no—
814Dic3—22no—
815Dic3—22no—
816Dic3—41no—
817Dic3—41no—
818Dic3—41no—
819Dic3—41no—
820C32#237711yescharacteristic, complemented, Sylow
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—32no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23C2×C3×C4×D312yes—
841C23C2×C3×C4×D312yes—
842C23C23×C3×D311yescharacteristic
843D4—44no—
844D4—124no—
845D4—124no—
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—32no—
862C2×C4—32no—
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—61no—
882C2×C4—124no—
883C2×C4—124no—
884C2×C4C2×C3×C4×D312yes—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—44no—
893C2×C3—42no—
894C2×C3—42no—
895C2×C3—42no—
896C2×C3—42no—
897C2×C3—82no—
898C2×C3—122no—
899C2×C3#548611yescharacteristic
900C2×C3#554511yescharacteristic
901C2×C3#554611yescharacteristic
902C2×C3#559511yescharacteristic
903C2×C3#562011yescharacteristic
904C2×C3#562111yescharacteristic
905C2×C3#566711yescharacteristic
906C2×C3C3×#51811yescharacteristic
907C2×C3C3×#51811yescharacteristic
908C2×C3C3×#52011yescharacteristic
909C2×C3C3×#56011yescharacteristic
910C2×C3C3×#56011yescharacteristic
911C2×C3C3×#56211yescharacteristic
912C2×C3C3×#56211yescharacteristic
913D3—42no—
914C22—22no—
915C22—22no—
916C22—22no—
917C22—22no—
918C22—22no—
919C22—22no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—62no—
929C22—62no—
930C22—62no—
931C22—121no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22C22×C3×C4×D311yescharacteristic
936C22C3×#100411yescharacteristic
937C22C3×#100411yescharacteristic
938C22C3×#100411yescharacteristic
939C22C3×#100411yescharacteristic
940C22C3×#100911yescharacteristic
941C22C3×#101011yescharacteristic
942C4—22no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—62no—
948C4—62no—
949C4—62no—
950C4—121no—
951C4—121no—
952C4—121no—
953C4—121no—
954C3—21no—
955C3#7488311yescharacteristic, direct product factor
956C3C3×#237711yescharacteristic, complemented
957C2—42no—
958C2—42no—
959C2—122no—
960C2C3×#548611yescharacteristic
961C2C3×#554511yescharacteristic
962C2C3×#554611yescharacteristic
963C2C3×#559511yescharacteristic
964C2C3×#562011yescharacteristic
965C2C3×#562111yescharacteristic
966C2C3×#566711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#386C2
socleC23×C32C24
prime radicalC2×C3×#938C2
cosocleC23×C3C24×C3
hypercenterC3×#386D3
hypocenterC3C3×#2377
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
2. C32×#386C2semidirect
3. C3×#5220C2semidirect
4. C3×#5213C2semidirect
5. C3×#5210C2semidirect
6. C3×#4958C2semidirect
7. C3×#4957C2semidirect
8. C3×#4957C2semidirect
9. C3×#4946C2semidirect
10. C3×#4945C2semidirect
11. C3×#4944C2semidirect
12. C3×#4667C2semidirect
13. C3×#4664C2semidirect
14. C3×#4654C2semidirect
15. C3×#4653C2semidirect
17. #74883C3direct (N × H)
32. C3×#938C4semidirect
66. C3×#386D3semidirect
67. C3×#386C2×C3semidirect
72. #5220C2×C3semidirect
73. #5213C2×C3semidirect
74. #5210C2×C3semidirect
75. #4958C2×C3semidirect
76. #4957C2×C3semidirect
77. #4957C2×C3semidirect
78. #4946C2×C3semidirect
79. #4945C2×C3semidirect
80. #4944C2×C3semidirect
81. #4667C2×C3semidirect
82. #4664C2×C3semidirect
83. #4654C2×C3semidirect
84. #4653C2×C3semidirect
103. C2×C3×#67C2×C4semidirect
104. C2×C3×#67C2×C4semidirect
117. C2×C3×C4×D3C2×C4semidirect
124. C3×#217C2×C4semidirect
125. C3×#217C2×C4semidirect
130. C3×C4⋊Dic3C2×C4semidirect
183. #938C3×C4semidirect
291. #386C3×D3semidirect
360. C2×#67C2×C3×C4semidirect
361. C2×#67C2×C3×C4semidirect
374. C2×C4×D3C2×C3×C4semidirect
403. #217C2×C3×C4semidirect
404. #217C2×C3×C4semidirect
409. C4⋊Dic3C2×C3×C4semidirect
820. C32#2377semidirect
955. C3#74883direct (N × H)
956. C3C3×#2377semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C32×#3862
C3×#52202
C3×#52132
C3×#52102
C3×#49582
C3×#49572
C3×#49462
C3×#49452
C3×#49442
C3×#46672
C3×#46642
C3×#46542
C3×#46532
C3×#23773
#748833