Finite Group Databasebeta

← C3×#75313 #11807715

Subgroups — C3×#75313 #11807715

Order 1152.

1229 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic
2C32×#387C211yesmaximal, characteristic, complemented
3C3×#4989C211yesmaximal, characteristic, complemented
4C3×#4988C211yesmaximal, characteristic, complemented
5C3×#4980C211yesmaximal, characteristic, complemented
6C3×#4940C211yesmaximal, characteristic, complemented
7C3×#4939C211yesmaximal, characteristic, complemented
8C3×#4669C211yesmaximal, characteristic, complemented
9C3×#4668C211yesmaximal, characteristic, complemented
10C3×#4667C211yesmaximal, characteristic, complemented
11C3×#4665C211yesmaximal, characteristic, complemented
12C3×#4665C211yesmaximal, characteristic, complemented
13C3×#4665C211yesmaximal, characteristic, complemented
14C3×#4665C211yesmaximal, characteristic, complemented
15C3×#4664C211yesmaximal, characteristic, complemented
16C3×#2377—31nomaximal
17#75313C311yesmaximal, characteristic, direct product factor
18C22×C3×D12C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C42C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#895C418yescomplemented
44C32×#95C2211yescharacteristic
45C32×#95C2211yescharacteristic
46C32×#95C2211yescharacteristic
47C32×#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C2×C3×#121—31no—
55C2×#895C2×C311yescharacteristic
56C3×#390—31no—
57C3×#390—31no—
58C3×#388—31no—
59C3×#388—31no—
60C3×#387—21no—
61C3×#387—31no—
62C3×#387D311yescharacteristic, complemented
63C3×#387C2×C311yescharacteristic, complemented
64C3×#386—31no—
65C3×#386—31no—
66C3×#386—31no—
67C3×#386—31no—
68C3×#385—31no—
69C3×#385—31no—
70C3×#381—31no—
71C3×#380—31no—
72#4989C2×C311yescharacteristic, complemented
73#4988C2×C311yescharacteristic, complemented
74#4980C2×C311yescharacteristic, complemented
75#4940C2×C311yescharacteristic, complemented
76#4939C2×C311yescharacteristic, complemented
77#4669C2×C311yescharacteristic, complemented
78#4668C2×C311yescharacteristic, complemented
79#4667C2×C311yescharacteristic, complemented
80#4665C2×C311yescharacteristic, complemented
81#4665C2×C311yescharacteristic, complemented
82#4665C2×C311yescharacteristic, complemented
83#4665C2×C311yescharacteristic, complemented
84#4664C2×C311yescharacteristic, complemented
85C23×C3×D3C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×C3×D12—41no—
101C2×C3×D12—41no—
102C2×C3×D12—41no—
103C2×C3×D12—41no—
104C2×C3×D12—41no—
105C2×C3×D12—41no—
106C2×C3×D12C2×C414yes—
107C2×C3×D12C2×C414yescomplemented
108C2×C3×D12C2×C414yescomplemented
109C2×C3×C4×D3—41no—
110C2×C3×C4×D3—41no—
111C2×C3×C4×D3—41no—
112C2×C3×C4×D3—41no—
113C2×C3×C4×D3—41no—
114C2×C3×C4×D3—41no—
115C2×C3×C4×D3—41no—
116C2×C3×C4×D3—41no—
117C2×C3×C4×D3C2×C414yescomplemented
118C32×C4⋊C4—41no—
119C32×C4⋊C4C2×C414yescomplemented
120C32×C42—41no—
121C3×(C2×D3)⋊C4—41no—
122C3×(C2×D3)⋊C4—41no—
123C3×(C2×D3)⋊C4—41no—
124C3×(C2×D3)⋊C4—41no—
125C3×(C2×D3)⋊C4—41no—
126C3×(C2×D3)⋊C4—41no—
127C3×(C2×D3)⋊C4—41no—
128C3×(C2×D3)⋊C4—41no—
129C3×(C2×D3)⋊C4—41no—
130C3×(C2×D3)⋊C4—41no—
131C3×(C2×D3)⋊C4C2×C414yescomplemented
132C3×(C2×D3)⋊C4C2×C414yescomplemented
133C3×C4⋊Dic3—41no—
134C3×Dic3⋊C4—41no—
135C3×Dic3⋊C4—41no—
136C3×C4×Dic3—41no—
137#2377—31noSylow
138C22×C3×D4—31no—
139C22×C3×D4—31no—
140C22×C3×D4—31no—
141C23×C3×C4—31no—
142C23×C3×C4—31no—
143C23×C3×C4—31no—
144C22×D12C22×C311yescharacteristic
145C22×D12C22×C311yescharacteristic
146C22×D12C22×C311yescharacteristic
147C22×C4×D3C22×C311yescharacteristic
148C22×C4×D3C22×C311yescharacteristic
149C22×C4×D3C22×C311yescharacteristic
150C3×#121—38no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4—21no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4C2×D311yescharacteristic
157C2×C3×C4⋊C4C2×D311yescharacteristic
158C2×C3×C4⋊C4C22×C311yescharacteristic
159C2×C3×C4⋊C4C22×C311yescharacteristic
160C2×C3×C22⋊C4—31no—
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⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C42—21no—
173C2×C3×C42—31no—
174C2×C3×C42C2×D311yescharacteristic
175C2×C3×C42C22×C311yescharacteristic
176C2×(C2×D3)⋊C4C22×C311yescharacteristic
177C2×(C2×D3)⋊C4C22×C311yescharacteristic
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×(C2×D3)⋊C4C22×C311yescharacteristic
188C2×C4⋊Dic3C22×C311yescharacteristic
189C2×Dic3⋊C4C22×C311yescharacteristic
190C2×Dic3⋊C4C22×C311yescharacteristic
191C2×C4×Dic3C22×C311yescharacteristic
192#895C3×C418yescomplemented
193C3×#95—21no—
194C3×#95—21no—
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×#95C2×D311yescharacteristic
204C3×#95C2×D311yescharacteristic
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×C32C2411yescharacteristic
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
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×D3C22×C412yes—
237C22×C3×D3C22×C412yes—
238C22×C3×D3C22×C412yes—
239C2×C32×C4—21no—
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—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C22×C412yes—
258C2×C32×C4C22×C412yes—
259C2×C32×C4C22×C412yes—
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×Dic3C22×C412yes—
275C3×D12—44no—
276C3×D12—44no—
277C3×D12—44no—
278C3×C4×D3—44no—
279C3×C4×D3—44no—
280C3×C4×D3—44no—
281C2×#121—31no—
282#390—31no—
283#390—31no—
284#388—31no—
285#388—31no—
286#387—31no—
287#387C3×D311yescharacteristic, complemented
288#386—31no—
289#386—31no—
290#386—31no—
291#386—31no—
292#385—31no—
293#385—31no—
294#381—31no—
295#380—31no—
296C24×C3—31no—
297C24×C3—31no—
298C24×C3—31no—
299C23×D3C23×C311yescharacteristic
300C23×D3C23×C311yescharacteristic
301C23×D3C23×C311yescharacteristic
302C2×C3×D4—34no—
303C2×C3×D4—34no—
304C2×C3×D4—34no—
305C2×C3×D4—121no—
306C2×C3×D4—121no—
307C2×C3×D4—121no—
308C2×C3×D4—121no—
309C2×C3×D4—121no—
310C2×C3×D4—121no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—31no—
319C22×C3×C4—34no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—121no—
325C22×C3×C4—121no—
326C22×C3×C4—121no—
327C22×C3×C4—121no—
328C22×C3×C4—121no—
329C22×C3×C4—121no—
330C22×C3×C4—121no—
331C22×C3×C4—121no—
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C23×C311yescharacteristic
340C22×C3×C4C23×C311yescharacteristic
341C22×C3×C4C23×C311yescharacteristic
342C22×C3×C4C23×C311yescharacteristic
343C22×C3×C4C23×C311yescharacteristic
344C22×C3×C4C23×C311yescharacteristic
345C22×C3×C4C23×C311yescharacteristic
346C22×Dic3C23×C311yescharacteristic
347C22×Dic3C23×C311yescharacteristic
348C22×Dic3C23×C311yescharacteristic
349C22×Dic3C23×C311yescharacteristic
350C22×Dic3C23×C311yescharacteristic
351C2×D12—41no—
352C2×D12—41no—
353C2×D12—41no—
354C2×D12—41no—
355C2×D12—41no—
356C2×D12—41no—
357C2×D12C2×C3×C414yes—
358C2×D12C2×C3×C414yescomplemented
359C2×D12C2×C3×C414yescomplemented
360C2×C4×D3—41no—
361C2×C4×D3—41no—
362C2×C4×D3—41no—
363C2×C4×D3—41no—
364C2×C4×D3—41no—
365C2×C4×D3—41no—
366C2×C4×D3—41no—
367C2×C4×D3—41no—
368C2×C4×D3C2×C3×C414yescomplemented
369C3×C4⋊C4—24no—
370C3×C4⋊C4—41no—
371C3×C4⋊C4—41no—
372C3×C4⋊C4—42no—
373C3×C4⋊C4—121no—
374C3×C4⋊C4—121no—
375C3×C4⋊C4—121no—
376C3×C4⋊C4C4×D314yescomplemented
377C3×C4⋊C4C2×C3×C414yescomplemented
378C3×C22⋊C4—34no—
379C3×C22⋊C4—34no—
380C3×C22⋊C4—121no—
381C3×C22⋊C4—121no—
382C3×C22⋊C4—121no—
383C3×C22⋊C4—121no—
384C3×C22⋊C4—121no—
385C3×C22⋊C4—121no—
386C3×C22⋊C4—121no—
387C3×C22⋊C4—121no—
388C3×C22⋊C4—121no—
389C3×C22⋊C4—121no—
390C3×C42—41no—
391C3×C42—41no—
392C3×C42—42no—
393C3×C42—121no—
394(C2×D3)⋊C4—41no—
395(C2×D3)⋊C4—41no—
396(C2×D3)⋊C4—41no—
397(C2×D3)⋊C4—41no—
398(C2×D3)⋊C4—41no—
399(C2×D3)⋊C4—41no—
400(C2×D3)⋊C4—41no—
401(C2×D3)⋊C4—41no—
402(C2×D3)⋊C4—41no—
403(C2×D3)⋊C4—41no—
404(C2×D3)⋊C4C2×C3×C414yescomplemented
405(C2×D3)⋊C4C2×C3×C414yescomplemented
406C4⋊Dic3—41no—
407Dic3⋊C4—41no—
408Dic3⋊C4—41no—
409C4×Dic3—41no—
410C22×C32C23×C411yescharacteristic
411C22×C32H(5,𝔽2)11yescharacteristic
412C22×C32H(5,𝔽2)11yescharacteristic
413C22×C32H(5,𝔽2)11yescharacteristic
414C22×C32H(5,𝔽2)11yescharacteristic
415C22×C32H(5,𝔽2)11yescharacteristic
416C22×C322−1+411yescharacteristic
417C2×C3×D3—22no—
418C2×C3×D3—22no—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C32×C4—22no—
439C32×C4—22no—
440C32×C4—22no—
441C32×C4—41no—
442C32×C4—41no—
443C32×C4—41no—
444C32×C4—41no—
445C3×Dic3—22no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C22×D4—31no—
451C22×D4—31no—
452C22×D4—31no—
453C23×C4—31no—
454C23×C4—31no—
455C23×C4—31no—
456#121—38no—
457C2×C4⋊C4—31no—
458C2×C4⋊C4—31no—
459C2×C4⋊C4—31no—
460C2×C4⋊C4C2×C3×D311yescharacteristic
461C2×C4⋊C4C2×C3×D311yescharacteristic
462C2×C22⋊C4—31no—
463C2×C22⋊C4—31no—
464C2×C22⋊C4—31no—
465C2×C22⋊C4—31no—
466C2×C22⋊C4—31no—
467C2×C22⋊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×C42—31no—
475C2×C42C2×C3×D311yescharacteristic
476#95—31no—
477#95—31no—
478#95—31no—
479#95—31no—
480#95—31no—
481#95—31no—
482#95C2×C3×D311yescharacteristic
483#95C2×C3×D311yescharacteristic
484#95C2×C3×D311yescharacteristic
485#95C2×C3×D311yescharacteristic
486C23×C3—21no—
487C23×C3—32no—
488C23×C3—32no—
489C23×C3—32no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3—61no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—61no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3—61no—
508C23×C3C23×D311yescharacteristic
509C23×C3C24×C311yescharacteristic
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3C22×C3×C412yes—
529C22×D3C22×C3×C412yes—
530C22×D3C22×C3×C412yes—
531C3×D4—124no—
532C3×D4—124no—
533C3×D4—124no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
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—21no—
561C2×C3×C4—21no—
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—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—32no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—124no—
607C2×C3×C4—124no—
608C2×C3×C4—124no—
609C2×C3×C4C2×C4×D312yes—
610C2×C3×C4C2×C4×D312yes—
611C2×C3×C4C2×C4×D312yes—
612C2×C3×C4C22×C3×C412yes—
613C2×C3×C4C22×C3×C412yes—
614C2×C3×C4C22×C3×C412yes—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3C22×C3×C412yes—
630D12—44no—
631D12—44no—
632D12—44no—
633C4×D3—44no—
634C4×D3—44no—
635C4×D3—44no—
636C2×C32#51811yescharacteristic
637C2×C32#51811yescharacteristic
638C2×C32#52011yescharacteristic
639C2×C32#56011yescharacteristic
640C2×C32#56011yescharacteristic
641C2×C32#56211yescharacteristic
642C2×C32#56211yescharacteristic
643C3×D3—42no—
644C3×D3—42no—
645C3×D3—42no—
646C24—31no—
647C24—31no—
648C24—31no—
649C2×D4—34no—
650C2×D4—34no—
651C2×D4—34no—
652C2×D4—121no—
653C2×D4—121no—
654C2×D4—121no—
655C2×D4—121no—
656C2×D4—121no—
657C2×D4—121no—
658C22×C4—31no—
659C22×C4—34no—
660C22×C4—31no—
661C22×C4—31no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—121no—
665C22×C4—121no—
666C22×C4—121no—
667C22×C4—121no—
668C22×C4—121no—
669C22×C4—121no—
670C22×C4—121no—
671C22×C4—121no—
672C22×C4C22×C3×D311yescharacteristic
673C22×C4C22×C3×D311yescharacteristic
674C22×C4C22×C3×D311yescharacteristic
675C22×C4C22×C3×D311yescharacteristic
676C22×C4C22×C3×D311yescharacteristic
677C22×C4C22×C3×D311yescharacteristic
678C22×C4C22×C3×D311yescharacteristic
679C4⋊C4—41no—
680C4⋊C4—121no—
681C4⋊C4—121no—
682C4⋊C4—121no—
683C4⋊C4C3×C4×D314yescomplemented
684C22⋊C4—34no—
685C22⋊C4—34no—
686C22⋊C4—121no—
687C22⋊C4—121no—
688C22⋊C4—121no—
689C22⋊C4—121no—
690C22⋊C4—121no—
691C22⋊C4—121no—
692C22⋊C4—121no—
693C22⋊C4—121no—
694C22⋊C4—121no—
695C22⋊C4—121no—
696C42—41no—
697C42—121no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—62no—
706C22×C3—62no—
707C22×C3—62no—
708C22×C3—62no—
709C22×C3—62no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3—62no—
713C22×C3—62no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3C22×C4×D311yescharacteristic
727C22×C3#100411yescharacteristic
728C22×C3#100711yescharacteristic
729C22×C3#100911yescharacteristic
730C22×C3#100911yescharacteristic
731C22×C3#100911yescharacteristic
732C22×C3#100911yescharacteristic
733C22×C3C23×C3×C411yescharacteristic
734C22×C3C3×H(5,𝔽2)11yescharacteristic
735C22×C3C3×H(5,𝔽2)11yescharacteristic
736C22×C3C3×H(5,𝔽2)11yescharacteristic
737C22×C3C3×H(5,𝔽2)11yescharacteristic
738C22×C3C3×H(5,𝔽2)11yescharacteristic
739C22×C3C3×2−1+411yescharacteristic
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—22no—
767C3×C4—42no—
768C3×C4—42no—
769C3×C4—42no—
770C3×C4—42no—
771C3×C4—42no—
772C3×C4—41no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—41no—
778C3×C4—41no—
779C3×C4—41no—
780C3×C4—62no—
781C3×C4—81no—
782C3×C4—81no—
783C3×C4—121no—
784C3×C4—121no—
785C3×C4—121no—
786C3×C4—121no—
787Dic3—22no—
788Dic3—41no—
789Dic3—41no—
790Dic3—41no—
791Dic3—41no—
792C32#237711yescharacteristic, complemented, Sylow
793C23—32no—
794C23—32no—
795C23—32no—
796C23—61no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—61no—
803C23—61no—
804C23—61no—
805C23—61no—
806C23—61no—
807C23—61no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—61no—
813C23—61no—
814C23C23×C3×D311yescharacteristic
815D4—124no—
816D4—124no—
817D4—124no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—32no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—124no—
852C2×C4—124no—
853C2×C4—124no—
854C2×C4C2×C3×C4×D312yes—
855C2×C4C2×C3×C4×D312yes—
856C2×C4C2×C3×C4×D312yes—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—122no—
865C2×C3—122no—
866C2×C3—122no—
867C2×C3#552111yescharacteristic
868C2×C3#554511yescharacteristic
869C2×C3#557411yescharacteristic
870C2×C3#564711yescharacteristic
871C2×C3#566611yescharacteristic
872C2×C3#570011yescharacteristic
873C2×C3#571111yescharacteristic
874C2×C3C3×#51811yescharacteristic
875C2×C3C3×#51811yescharacteristic
876C2×C3C3×#52011yescharacteristic
877C2×C3C3×#56011yescharacteristic
878C2×C3C3×#56011yescharacteristic
879C2×C3C3×#56211yescharacteristic
880C2×C3C3×#56211yescharacteristic
881D3—42no—
882D3—42no—
883D3—42no—
884C22—62no—
885C22—62no—
886C22—62no—
887C22—62no—
888C22—62no—
889C22—62no—
890C22—62no—
891C22—62no—
892C22—62no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22C22×C3×C4×D311yescharacteristic
906C22C3×#100411yescharacteristic
907C22C3×#100711yescharacteristic
908C22C3×#100911yescharacteristic
909C22C3×#100911yescharacteristic
910C22C3×#100911yescharacteristic
911C22C3×#100911yescharacteristic
912C4—22no—
913C4—22no—
914C4—22no—
915C4—41no—
916C4—41no—
917C4—41no—
918C4—41no—
919C4—62no—
920C4—121no—
921C4—121no—
922C4—121no—
923C4—121no—
924C3—21no—
925C3#7531311yescharacteristic, direct product factor
926C3C3×#237711yescharacteristic, complemented
927C2—122no—
928C2—122no—
929C2—122no—
930C2C3×#552111yescharacteristic
931C2C3×#554511yescharacteristic
932C2C3×#557411yescharacteristic
933C2C3×#564711yescharacteristic
934C2C3×#566611yescharacteristic
935C2C3×#570011yescharacteristic
936C2C3×#571111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#387C2
socleC23×C32C24
prime radicalC2×C3×#895C2
cosocleC23×C3C24×C3
hypercenterC3×#387D3
hypocenterC3C3×#2377
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#387

Complements

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

NH ≅ G/Ntype
2. C32×#387C2semidirect
3. C3×#4989C2semidirect
4. C3×#4988C2semidirect
5. C3×#4980C2semidirect
6. C3×#4940C2semidirect
7. C3×#4939C2semidirect
8. C3×#4669C2semidirect
9. C3×#4668C2semidirect
10. C3×#4667C2semidirect
11. C3×#4665C2semidirect
12. C3×#4665C2semidirect
13. C3×#4665C2semidirect
14. C3×#4665C2semidirect
15. C3×#4664C2semidirect
17. #75313C3direct (N × H)
43. C3×#895C4semidirect
62. C3×#387D3semidirect
63. C3×#387C2×C3semidirect
72. #4989C2×C3semidirect
73. #4988C2×C3semidirect
74. #4980C2×C3semidirect
75. #4940C2×C3semidirect
76. #4939C2×C3semidirect
77. #4669C2×C3semidirect
78. #4668C2×C3semidirect
79. #4667C2×C3semidirect
80. #4665C2×C3semidirect
81. #4665C2×C3semidirect
82. #4665C2×C3semidirect
83. #4665C2×C3semidirect
84. #4664C2×C3semidirect
107. C2×C3×D12C2×C4semidirect
108. C2×C3×D12C2×C4semidirect
117. C2×C3×C4×D3C2×C4semidirect
119. C32×C4⋊C4C2×C4semidirect
131. C3×(C2×D3)⋊C4C2×C4semidirect
132. C3×(C2×D3)⋊C4C2×C4semidirect
192. #895C3×C4semidirect
287. #387C3×D3semidirect
358. C2×D12C2×C3×C4semidirect
359. C2×D12C2×C3×C4semidirect
368. C2×C4×D3C2×C3×C4semidirect
376. C3×C4⋊C4C4×D3semidirect
377. C3×C4⋊C4C2×C3×C4semidirect
404. (C2×D3)⋊C4C2×C3×C4semidirect
405. (C2×D3)⋊C4C2×C3×C4semidirect
683. C4⋊C4C3×C4×D3semidirect
792. C32#2377semidirect
925. C3#75313direct (N × H)
926. C3C3×#2377semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C32×#3872
C3×#49892
C3×#49882
C3×#49802
C3×#49402
C3×#49392
C3×#46692
C3×#46682
C3×#46672
C3×#46652
C3×#46642
C3×#23773
#753133