Finite Group Databasebeta

← C3×#77111 #11810276

Subgroups — C3×#77111 #11810276

Order 1152.

1719 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#937C211yesmaximal, characteristic
2C2×C3×#935C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
5C32×#394C211yesmaximal, characteristic, complemented
6C3×#4993C211yesmaximal, characteristic, complemented
7C3×#4989C211yesmaximal, characteristic, complemented
8C3×#4959C211yesmaximal, characteristic, complemented
9C3×#4958C211yesmaximal, characteristic, complemented
10C3×#4956C211yesmaximal, characteristic, complemented
11C3×#4955C211yesmaximal, characteristic, complemented
12C3×#4952C211yesmaximal, characteristic, complemented
13C3×#4945C211yesmaximal, characteristic, complemented
14C3×#4669C211yesmaximal, characteristic, complemented
15C3×#4667C211yesmaximal, characteristic, complemented
16C3×#2418—31nomaximal
17#77111C311yesmaximal, characteristic, direct product factor
18C24×C3×D3C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic, complemented
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic, complemented
29C2×C32×C22⋊C4C2211yescharacteristic, complemented
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic, complemented
34C3×#937—24no—
35C3×#935—24no—
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×C4×Dic3C2211yescharacteristic, complemented
49C3×#67⋊C4—24no—
50C3×D3×C22⋊C4—24no—
51C32×#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57C2×C3×#123—31no—
58C2×C3×#120—31no—
59C2×C3×C4×D4—31no—
60C22×C3×C22⋊C4—31no—
61C2×#937C2×C311yescharacteristic
62C2×#935C2×C311yescharacteristic, complemented
63C2×#67⋊C4C2×C311yescharacteristic, complemented
64C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
65C3×#399—31no—
66C3×#397—31no—
67C3×#394—21no—
68C3×#394—31no—
69C3×#394D311yescharacteristic, complemented
70C3×#394C2×C311yescharacteristic, complemented
71C3×#388—31no—
72C3×#388—31no—
73C3×#386—31no—
74C3×#386—31no—
75C3×#385—31no—
76C3×#380—31no—
77C3×#379—31no—
78#4993C2×C311yescharacteristic, complemented
79#4989C2×C311yescharacteristic, complemented
80#4959C2×C311yescharacteristic, complemented
81#4958C2×C311yescharacteristic, complemented
82#4956C2×C311yescharacteristic, complemented
83#4955C2×C311yescharacteristic, complemented
84#4952C2×C311yescharacteristic, complemented
85#4945C2×C311yescharacteristic, complemented
86#4669C2×C311yescharacteristic, complemented
87#4667C2×C311yescharacteristic, complemented
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—22no—
95C23×C3×D3—41no—
96C23×C3×D3—41no—
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C2×C32×D4—22no—
100C2×C32×D4—22no—
101C2×C32×D4—41no—
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67—41no—
112C2×C3×#67D414yes—
113C22×C3×Dic3—22no—
114C22×C3×Dic3—22no—
115C22×C3×Dic3—41no—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3—22no—
124C2×C3×C4×D3—22no—
125C2×C3×C4×D3—22no—
126C2×C3×C4×D3—41no—
127C2×C3×C4×D3—41no—
128C32×C4⋊C4—41no—
129C32×C22⋊C4—22no—
130C32×C22⋊C4—22no—
131C32×C22⋊C4—41no—
132C32×C22⋊C4—41no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217—22no—
136C3×#217D414yescomplemented
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—22no—
140C3×(C2×D3)⋊C4—22no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—41no—
145C3×Dic3⋊C4—22no—
146C3×Dic3⋊C4—22no—
147C3×Dic3⋊C4—22no—
148C3×Dic3⋊C4—41no—
149C3×C4×Dic3—22no—
150#2418—31noSylow
151C25×C3—31no—
152C24×D3C22×C311yescharacteristic
153C22×C3×D4—21no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C22×C3×D4C2×D311yescharacteristic
157C22×C3×D4C22×C311yescharacteristic
158C23×C3×C4—31no—
159C23×C3×C4—31no—
160C23×C3×C4—31no—
161C22×#67C22×C311yescharacteristic
162C22×#67C22×C311yescharacteristic
163C23×Dic3C22×C311yescharacteristic, complemented
164C22×C4×D3C22×C311yescharacteristic
165C22×C4×D3C22×C311yescharacteristic
166C3×#123—64no—
167C3×#120—64no—
168C3×C4×D4—64no—
169C2×C3×C4⋊C4—21no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
175C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4—21no—
178C2×C3×C22⋊C4—21no—
179C2×C3×C22⋊C4—21no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—64no—
193C2×C3×C22⋊C4C2×D311yescharacteristic
194C2×C3×C22⋊C4C2×D311yescharacteristic
195C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
196C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
197C2×C3×C22⋊C4C22×C311yescharacteristic
198C2×C3×C22⋊C4C22×C311yescharacteristic
199C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
200C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
201C2×C3×C42—31no—
202C2×#217C22×C311yescharacteristic
203C2×#217C22×C311yescharacteristic
204C2×#217C22×C311yescharacteristic
205C2×#217C22×C311yescharacteristic, complemented
206#937—24no—
207#935—24no—
208C2×(C2×D3)⋊C4C22×C311yescharacteristic
209C2×(C2×D3)⋊C4C22×C311yescharacteristic
210C2×(C2×D3)⋊C4C22×C311yescharacteristic
211C2×(C2×D3)⋊C4C22×C311yescharacteristic
212C2×(C2×D3)⋊C4C22×C311yescharacteristic
213C2×(C2×D3)⋊C4C22×C311yescharacteristic
214C2×(C2×D3)⋊C4C22×C311yescharacteristic
215C2×(C2×D3)⋊C4C22×C311yescharacteristic
216C2×Dic3⋊C4C22×C311yescharacteristic, complemented
217C2×Dic3⋊C4C22×C311yescharacteristic, complemented
218C2×Dic3⋊C4C22×C311yescharacteristic, complemented
219C2×Dic3⋊C4C22×C311yescharacteristic, complemented
220C2×C4×Dic3C22×C311yescharacteristic, complemented
221#67⋊C4—24no—
222D3×C22⋊C4—24no—
223C3×#95—21no—
224C3×#95—31no—
225C3×#95—31no—
226C3×#95—31no—
227C3×#95—31no—
228C3×#95—31no—
229C3×#95C2×D311yescharacteristic, complemented
230C3×#95C22×C311yescharacteristic, complemented
231C3⋊#95C22×C311yescharacteristic, complemented
232C3⋊#95C22×C311yescharacteristic, complemented
233C3⋊#95C22×C311yescharacteristic, complemented
234C3⋊#95C22×C311yescharacteristic, complemented
235C3⋊#95C22×C311yescharacteristic, complemented
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32C2×D412yes—
249C23×C32C2×D412yes—
250C23×C32C2411yescharacteristic
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—28no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3—44no—
268C22×C3×D3C2×D412yes—
269C22×C3×D3#4112yes—
270C22×C3×D3#4112yes—
271C22×C3×D3#4112yes—
272C32×D4—44no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C3×#67—28no—
289C3×#67—44no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—44no—
306C2×C3×Dic3C2×D412yes—
307C2×C3×Dic3C2×D412yes—
308C2×C3×Dic3C2×D412yes—
309C3×C4×D3—44no—
310C3×C4×D3—44no—
311C2×#123—31no—
312C2×#120—31no—
313C2×C4×D4—31no—
314C22×C22⋊C4—31no—
315#399—31no—
316#397—31no—
317#394—31no—
318#394C3×D311yescharacteristic, complemented
319#388—31no—
320#388—31no—
321#386—31no—
322#386—31no—
323#385—31no—
324#380—31no—
325#379—31no—
326C24×C3—21no—
327C24×C3—21no—
328C24×C3—31no—
329C24×C3—31no—
330C24×C3—62no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—121no—
336C24×C3—121no—
337C24×C3C22×D311yescharacteristic
338C24×C3C22×D311yescharacteristic
339C24×C3C23×C311yescharacteristic
340C24×C3C23×C311yescharacteristic
341C23×D3—22no—
342C23×D3—22no—
343C23×D3—22no—
344C23×D3—22no—
345C23×D3—22no—
346C23×D3—41no—
347C23×D3—41no—
348C23×D3C23×C311yescharacteristic
349C23×D3C23×C311yescharacteristic
350C2×C3×D4—22no—
351C2×C3×D4—22no—
352C2×C3×D4—22no—
353C2×C3×D4—22no—
354C2×C3×D4—34no—
355C2×C3×D4—42no—
356C2×C3×D4—42no—
357C2×C3×D4—41no—
358C2×C3×D4—41no—
359C2×C3×D4—42no—
360C2×C3×D4—62no—
361C2×C3×D4—62no—
362C2×C3×D4—62no—
363C2×C3×D4—62no—
364C2×C3×D4—121no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—62no—
377C22×C3×C4—62no—
378C22×C3×C4—62no—
379C22×C3×C4—62no—
380C22×C3×C4—62no—
381C22×C3×C4—62no—
382C22×C3×C4—121no—
383C22×C3×C4—121no—
384C22×C3×C4—121no—
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C23×C311yescharacteristic
391C22×C3×C4C23×C311yescharacteristic
392C22×C3×C4C23×C311yescharacteristic
393C22×C3×C4C23×C311yescharacteristic
394C22×C3×C4C23×C311yescharacteristic
395C2×#67—22no—
396C2×#67—22no—
397C2×#67—22no—
398C2×#67—22no—
399C2×#67—41no—
400C2×#67C3×D414yes—
401C22×Dic3—22no—
402C22×Dic3—22no—
403C22×Dic3—41no—
404C22×Dic3C23×C311yescharacteristic
405C22×Dic3C23×C311yescharacteristic
406C22×Dic3C23×C311yescharacteristic
407C22×Dic3C23×C311yescharacteristic
408C22×Dic3C23×C311yescharacteristic
409C22×Dic3C23×C311yescharacteristic
410C2×C4×D3—22no—
411C2×C4×D3—22no—
412C2×C4×D3—22no—
413C2×C4×D3—22no—
414C2×C4×D3—41no—
415C2×C4×D3—41no—
416C3×C4⋊C4—41no—
417C3×C4⋊C4—41no—
418C3×C4⋊C4—42no—
419C3×C4⋊C4—62no—
420C3×C4⋊C4—62no—
421C3×C4⋊C4—62no—
422C3×C4⋊C4—121no—
423C3×C22⋊C4—22no—
424C3×C22⋊C4—22no—
425C3×C22⋊C4—22no—
426C3×C22⋊C4—22no—
427C3×C22⋊C4—34no—
428C3×C22⋊C4—42no—
429C3×C22⋊C4—42no—
430C3×C22⋊C4—41no—
431C3×C22⋊C4—41no—
432C3×C22⋊C4—41no—
433C3×C22⋊C4—41no—
434C3×C22⋊C4—42no—
435C3×C22⋊C4—42no—
436C3×C22⋊C4—62no—
437C3×C22⋊C4—62no—
438C3×C22⋊C4—62no—
439C3×C22⋊C4—62no—
440C3×C22⋊C4—62no—
441C3×C22⋊C4—62no—
442C3×C22⋊C4—62no—
443C3×C22⋊C4—62no—
444C3×C22⋊C4—62no—
445C3×C22⋊C4—62no—
446C3×C22⋊C4—121no—
447C3×C42—62no—
448#217—22no—
449#217—22no—
450#217—22no—
451#217C3×D414yescomplemented
452(C2×D3)⋊C4—22no—
453(C2×D3)⋊C4—22no—
454(C2×D3)⋊C4—22no—
455(C2×D3)⋊C4—22no—
456(C2×D3)⋊C4—22no—
457(C2×D3)⋊C4—22no—
458(C2×D3)⋊C4—22no—
459(C2×D3)⋊C4—41no—
460Dic3⋊C4—22no—
461Dic3⋊C4—22no—
462Dic3⋊C4—22no—
463Dic3⋊C4—41no—
464C4×Dic3—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32C22×D411yescharacteristic
480C22×C32C22×D411yescharacteristic
481C22×C32C2×#4111yescharacteristic
482C22×C32C2×#4111yescharacteristic
483C22×C32C2×#4111yescharacteristic
484C22×C32H(5,𝔽2)11yescharacteristic
485C22×C32H(5,𝔽2)11yescharacteristic
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—416no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C2×C3×D3#12314yescomplemented
501C32×C4—41no—
502C32×C4—41no—
503C32×C4—41no—
504C32×C4—41no—
505C32×C4—41no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—41no—
510C3×Dic3—41no—
511C3×Dic3—41no—
512C25—31no—
513C22×D4—31no—
514C22×D4—31no—
515C22×D4C2×C3×D311yescharacteristic
516C23×C4—31no—
517C23×C4—31no—
518C23×C4—31no—
519#123—64no—
520#120—64no—
521C4×D4—64no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—31no—
526C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4—31no—
539C2×C22⋊C4—64no—
540C2×C22⋊C4C2×C3×D311yescharacteristic
541C2×C22⋊C4C2×C3×D311yescharacteristic
542C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
543C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
544C2×C42—31no—
545#95—31no—
546#95—31no—
547#95—31no—
548#95—31no—
549#95—31no—
550#95C2×C3×D311yescharacteristic, complemented
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—32no—
579C23×C3—32no—
580C23×C3—32no—
581C23×C3—32no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—68no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—124no—
606C23×C3—124no—
607C23×C3—124no—
608C23×C3—124no—
609C23×C3—124no—
610C23×C3—124no—
611C23×C3D3×D412yes—
612C23×C3D3×D412yes—
613C23×C3C2×C3×D412yes—
614C23×C3C2×C3×D412yes—
615C23×C3C23×D311yescharacteristic
616C23×C3C24×C311yescharacteristic
617C22×D3—21no—
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—28no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—44no—
629C22×D3—44no—
630C22×D3—44no—
631C22×D3—44no—
632C22×D3—44no—
633C22×D3—44no—
634C22×D3C2×C3×D412yes—
635C22×D3C3×#4112yes—
636C22×D3C3×#4112yes—
637C22×D3C3×#4112yes—
638C3×D4—44no—
639C3×D4—44no—
640C3×D4—48no—
641C3×D4—68no—
642C3×D4—124no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—32no—
676C2×C3×C4—32no—
677C2×C3×C4—32no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4—61no—
706C2×C3×C4—124no—
707C2×C3×C4—124no—
708C2×C3×C4—124no—
709#67—28no—
710#67—44no—
711C2×Dic3—21no—
712C2×Dic3—21no—
713C2×Dic3—21no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—21no—
721C2×Dic3—21no—
722C2×Dic3—21no—
723C2×Dic3—21no—
724C2×Dic3—21no—
725C2×Dic3—21no—
726C2×Dic3—44no—
727C2×Dic3C2×C3×D412yes—
728C2×Dic3C2×C3×D412yes—
729C2×Dic3C2×C3×D412yes—
730C4×D3—44no—
731C4×D3—44no—
732C2×C32—42no—
733C2×C32—42no—
734C2×C32C2×#12311yescharacteristic
735C2×C32#52511yescharacteristic
736C2×C32#53811yescharacteristic
737C2×C32D4211yescharacteristic
738C2×C32#54611yescharacteristic
739C2×C32#54611yescharacteristic
740C2×C32#55111yescharacteristic
741C3×D3—24no—
742C3×D3—42no—
743C24—31no—
744C24—31no—
745C24—62no—
746C24—62no—
747C24—62no—
748C24—62no—
749C24—62no—
750C24—121no—
751C24—121no—
752C24C22×C3×D311yescharacteristic
753C24C22×C3×D311yescharacteristic
754C2×D4—22no—
755C2×D4—22no—
756C2×D4—34no—
757C2×D4—41no—
758C2×D4—62no—
759C2×D4—62no—
760C2×D4—62no—
761C2×D4—62no—
762C2×D4—121no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—31no—
769C22×C4—62no—
770C22×C4—62no—
771C22×C4—62no—
772C22×C4—62no—
773C22×C4—62no—
774C22×C4—62no—
775C22×C4—121no—
776C22×C4—121no—
777C22×C4—121no—
778C22×C4C22×C3×D311yescharacteristic
779C22×C4C22×C3×D311yescharacteristic
780C22×C4C22×C3×D311yescharacteristic
781C22×C4C22×C3×D311yescharacteristic
782C22×C4C22×C3×D311yescharacteristic
783C4⋊C4—41no—
784C4⋊C4—62no—
785C4⋊C4—62no—
786C4⋊C4—62no—
787C4⋊C4—121no—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—34no—
791C22⋊C4—41no—
792C22⋊C4—41no—
793C22⋊C4—62no—
794C22⋊C4—62no—
795C22⋊C4—62no—
796C22⋊C4—62no—
797C22⋊C4—62no—
798C22⋊C4—62no—
799C22⋊C4—62no—
800C22⋊C4—62no—
801C22⋊C4—62no—
802C22⋊C4—62no—
803C22⋊C4—121no—
804C42—62no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—34no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—62no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—81no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—81no—
860C22×C3—81no—
861C22×C3—81no—
862C22×C3—81no—
863C22×C3—81no—
864C22×C3—1216no—
865C22×C3—121no—
866C22×C3—121no—
867C22×C3—121no—
868C22×C3—121no—
869C22×C3C2×D3×D411yescharacteristic
870C22×C3C2×D3×D411yescharacteristic
871C22×C3#100411yescharacteristic
872C22×C3#100411yescharacteristic
873C22×C3D3×#4111yescharacteristic
874C22×C3D3×#4111yescharacteristic
875C22×C3D3×#4111yescharacteristic
876C22×C3C22×C3×D411yescharacteristic
877C22×C3C22×C3×D411yescharacteristic
878C22×C3C2×C3×#4111yescharacteristic
879C22×C3C2×C3×#4111yescharacteristic
880C22×C3C2×C3×#4111yescharacteristic
881C22×C3C3×H(5,𝔽2)11yescharacteristic
882C22×C3C3×H(5,𝔽2)11yescharacteristic
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—22no—
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—22no—
890C2×D3—22no—
891C2×D3—22no—
892C2×D3—416no—
893C2×D3—41no—
894C2×D3—41no—
895C2×D3—41no—
896C2×D3—41no—
897C2×D3C3×#12314yescomplemented
898C3×C4—42no—
899C3×C4—42no—
900C3×C4—41no—
901C3×C4—41no—
902C3×C4—41no—
903C3×C4—41no—
904C3×C4—41no—
905C3×C4—41no—
906C3×C4—41no—
907C3×C4—41no—
908C3×C4—41no—
909C3×C4—41no—
910C3×C4—62no—
911C3×C4—62no—
912C3×C4—62no—
913C3×C4—81no—
914C3×C4—81no—
915C3×C4—81no—
916C3×C4—121no—
917C3×C4—121no—
918C3×C4—121no—
919Dic3—22no—
920Dic3—22no—
921Dic3—22no—
922Dic3—41no—
923Dic3—41no—
924Dic3—41no—
925C32#241811yescharacteristic, complemented, Sylow
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—32no—
939C23—32no—
940C23—32no—
941C23—32no—
942C23—68no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—61no—
948C23—61no—
949C23—61no—
950C23—61no—
951C23—61no—
952C23—61no—
953C23—124no—
954C23—124no—
955C23—124no—
956C23—124no—
957C23—124no—
958C23—124no—
959C23C3×D3×D412yes—
960C23C3×D3×D412yes—
961C23C23×C3×D311yescharacteristic
962D4—44no—
963D4—68no—
964D4—124no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—32no—
981C2×C4—32no—
982C2×C4—32no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—61no—
993C2×C4—61no—
994C2×C4—61no—
995C2×C4—61no—
996C2×C4—61no—
997C2×C4—61no—
998C2×C4—124no—
999C2×C4—124no—
1000C2×C4—124no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—42no—
1009C2×C3—42no—
1010C2×C3—42no—
1011C2×C3—42no—
1012C2×C3—64no—
1013C2×C3—82no—
1014C2×C3—82no—
1015C2×C3—122no—
1016C2×C3#559011yescharacteristic
1017C2×C3#561011yescharacteristic
1018C2×C3#561011yescharacteristic
1019C2×C3#561311yescharacteristic
1020C2×C3D3×#12311yescharacteristic
1021C2×C3#565611yescharacteristic
1022C2×C3#567911yescharacteristic
1023C2×C3C2×C3×#12311yescharacteristic
1024C2×C3C3×#52511yescharacteristic
1025C2×C3C3×#53811yescharacteristic
1026C2×C3C3×D4211yescharacteristic
1027C2×C3C3×#54611yescharacteristic
1028C2×C3C3×#54611yescharacteristic
1029C2×C3C3×#55111yescharacteristic
1030D3—24no—
1031D3—42no—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—22no—
1037C22—22no—
1038C22—34no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—62no—
1053C22—62no—
1054C22—62no—
1055C22—62no—
1056C22—1216no—
1057C22—121no—
1058C22—121no—
1059C22—121no—
1060C22—121no—
1061C22C2×C3×D3×D411yescharacteristic
1062C22C2×C3×D3×D411yescharacteristic
1063C22C3×#100411yescharacteristic
1064C22C3×#100411yescharacteristic
1065C22C3×D3×#4111yescharacteristic
1066C22C3×D3×#4111yescharacteristic
1067C22C3×D3×#4111yescharacteristic
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—41no—
1072C4—41no—
1073C4—62no—
1074C4—62no—
1075C4—62no—
1076C4—121no—
1077C4—121no—
1078C4—121no—
1079C3—21no—
1080C3#7711111yescharacteristic, direct product factor
1081C3C3×#241811yescharacteristic, complemented
1082C2—42no—
1083C2—42no—
1084C2—64no—
1085C2—122no—
1086C2C3×#559011yescharacteristic
1087C2C3×#561011yescharacteristic
1088C2C3×#561011yescharacteristic
1089C2C3×#561311yescharacteristic
1090C2C3×D3×#12311yescharacteristic
1091C2C3×#565611yescharacteristic
1092C2C3×#567911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#394C2
socleC23×C32C24
prime radicalC2×C3×#937C2
hypercenterC3×#394D3
hypocenterC3C3×#2418
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#394

Complements

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

NH ≅ G/Ntype
2. C2×C3×#935C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C2×C3×D3×C22⋊C4C2semidirect
5. C32×#394C2semidirect
6. C3×#4993C2semidirect
7. C3×#4989C2semidirect
8. C3×#4959C2semidirect
9. C3×#4958C2semidirect
10. C3×#4956C2semidirect
11. C3×#4955C2semidirect
12. C3×#4952C2semidirect
13. C3×#4945C2semidirect
14. C3×#4669C2semidirect
15. C3×#4667C2semidirect
17. #77111C3direct (N × H)
22. C23×C3×Dic3C22semidirect
25. C2×C32×C4⋊C4C22semidirect
28. C2×C32×C22⋊C4C22semidirect
29. C2×C32×C22⋊C4C22semidirect
33. C2×C3×#217C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×C4×Dic3C22semidirect
51. C32×#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
62. C2×#935C2×C3semidirect
63. C2×#67⋊C4C2×C3semidirect
64. C2×D3×C22⋊C4C2×C3semidirect
69. C3×#394D3semidirect
70. C3×#394C2×C3semidirect
78. #4993C2×C3semidirect
79. #4989C2×C3semidirect
80. #4959C2×C3semidirect
81. #4958C2×C3semidirect
82. #4956C2×C3semidirect
83. #4955C2×C3semidirect
84. #4952C2×C3semidirect
85. #4945C2×C3semidirect
86. #4669C2×C3semidirect
87. #4667C2×C3semidirect
136. C3×#217D4semidirect
163. C23×Dic3C22×C3semidirect
174. C2×C3×C4⋊C4C2×D3semidirect
175. C2×C3×C4⋊C4C22×C3semidirect
195. C2×C3×C22⋊C4C2×D3semidirect
196. C2×C3×C22⋊C4C2×D3semidirect
199. C2×C3×C22⋊C4C22×C3semidirect
200. C2×C3×C22⋊C4C22×C3semidirect
205. C2×#217C22×C3semidirect
216. C2×Dic3⋊C4C22×C3semidirect
217. C2×Dic3⋊C4C22×C3semidirect
218. C2×Dic3⋊C4C22×C3semidirect
219. C2×Dic3⋊C4C22×C3semidirect
220. C2×C4×Dic3C22×C3semidirect
229. C3×#95C2×D3semidirect
230. C3×#95C22×C3semidirect
231. C3⋊#95C22×C3semidirect
232. C3⋊#95C22×C3semidirect
233. C3⋊#95C22×C3semidirect
234. C3⋊#95C22×C3semidirect
235. C3⋊#95C22×C3semidirect
318. #394C3×D3semidirect
451. #217C3×D4semidirect
500. C2×C3×D3#123semidirect
526. C2×C4⋊C4C2×C3×D3semidirect
542. C2×C22⋊C4C2×C3×D3semidirect
543. C2×C22⋊C4C2×C3×D3semidirect
550. #95C2×C3×D3semidirect
897. C2×D3C3×#123semidirect
925. C32#2418semidirect
1080. C3#77111direct (N × H)
1081. C3C3×#2418semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9372
C2×C3×#9352
C2×C3×#67⋊C42
C2×C3×D3×C22⋊C42
C32×#3942
C3×#49932
C3×#49892
C3×#49592
C3×#49582
C3×#49562
C3×#49552
C3×#49522
C3×#49452
C3×#46692
C3×#46672
C3×#24183
#771113