Finite Group Databasebeta

← #13156855

Subgroups — #13156855

Order 1728.

1666 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6292C211yesmaximal, characteristic
2C2×#88814C211yesmaximal, characteristic, complemented
3C2×#88804C211yesmaximal, characteristic, complemented
4C2×#88804C211yesmaximal, characteristic, complemented
5C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C2×C3×#3722C211yesmaximal, characteristic, complemented
7C2×C3×Dic32C211yesmaximal, characteristic, complemented
8#10591384—31nomaximal
9#10591383—31nomaximal
10#10591320—31nomaximal
11C23×C3⋊(C3⋊D3)C2211yescharacteristic
12C23×C3×C3⋊D3C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×#6292—22no—
19C2×#6292—22no—
20C2×#6292C414yescomplemented
21#88814—22no—
22#88804—22no—
23#88804—22no—
24C3×Dic3⋊Dic3—22no—
25C3×#3722—22no—
26C3×Dic32—22no—
27C22×C4⋊(C3⋊D3)—31no—
28C22×#626—31no—
29C22×#626—31no—
30C22×#626—61no—
31C2×#3752—31no—
32C2×#3752—31no—
33C2×C3×(C2×D3)⋊C4—31no—
34C2×C3×(C2×D3)⋊C4—31no—
35C2×C3×C4⋊Dic3—31no—
36C2×C3×Dic3⋊C4—31no—
37C2×C3×C4×Dic3—31no—
38C2×C3×C4×Dic3—31no—
39C2×Dic3⋊Dic3D311yescharacteristic, complemented
40C2×#3722—31no—
41C2×#3722—31no—
42C2×#3722—31no—
43C2×#3722—31no—
44C2×#3722—31no—
45C2×#3722—61no—
46C2×#3722—61no—
47C2×#3722D311yescharacteristic, complemented
48C2×(C2×D3)⋊Dic3—31no—
49C2×(C2×D3)⋊Dic3—31no—
50C2×Dic32D311yescharacteristic, complemented
51C23×C33C2311yescharacteristic
52C22×C3⋊(C3⋊D3)—21no—
53C22×C3⋊(C3⋊D3)—21no—
54C22×C3⋊(C3⋊D3)—21no—
55C22×C3⋊(C3⋊D3)—21no—
56C22×C3⋊(C3⋊D3)—21no—
57C22×C3⋊(C3⋊D3)—21no—
58C22×C3⋊(C3⋊D3)C2×C412yes—
59C22×C3×C3⋊D3—21no—
60C22×C3×C3⋊D3—21no—
61C22×C3×C3⋊D3—21no—
62C22×C3×C3⋊D3—21no—
63C22×C3×C3⋊D3—21no—
64C22×C3×C3⋊D3—21no—
65C22×C3×C3⋊D3C2×C412yes—
66C2×C3×C3⋊Dic3—21no—
67C2×C3×C3⋊Dic3—21no—
68C2×C3×C3⋊Dic3—21no—
69C2×C3×C3⋊Dic3—21no—
70C2×C3×C3⋊Dic3—21no—
71C2×C3×C3⋊Dic3D412yescomplemented
72C2×C32×Dic3—21no—
73C2×C32×Dic3—21no—
74C2×C32×Dic3—21no—
75C2×C32×Dic3—21no—
76C2×C32×Dic3—21no—
77C2×C32×Dic3C2×C412yes—
78C2×C32×Dic3D412yes—
79C2×C32×Dic3D412yes—
80C2×C32×Dic3D412yescomplemented
81#6292—28no—
82#4988—91no—
83#4957—91no—
84#4939—91no—
85C23×C3⋊D3—31no—
86C23×C3⋊D3—31no—
87C23×C3⋊D3—31no—
88C23×C3⋊D3—61no—
89C23×C3⋊D3—61no—
90C23×C3⋊D3—61no—
91C23×C3⋊D3—121no—
92C23×C3⋊D3C2×D311yescharacteristic
93C23×C3×D3—31no—
94C23×C3×D3—31no—
95C23×C3×D3—61no—
96C22×C32×C4—31no—
97C22×C32×C4—31no—
98C22×C32×C4—31no—
99C22×C3⋊Dic3C2×D311yescharacteristic
100C22×C3⋊Dic3C2×D311yescharacteristic
101C2×C4⋊(C3⋊D3)—34no—
102C2×C4⋊(C3⋊D3)—62no—
103C2×C4⋊(C3⋊D3)—62no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C22×C3×Dic3—21no—
107C22×C3×Dic3—31no—
108C22×C3×Dic3—31no—
109C22×C3×Dic3—31no—
110C22×C3×Dic3—31no—
111C22×C3×Dic3—61no—
112C22×C3×Dic3—61no—
113C22×C3×Dic3C2×D311yescharacteristic
114C22×C3×Dic3C2×D311yescharacteristic
115C22×C3×Dic3C2×D311yescharacteristic
116C22×C3×Dic3C2×D311yescharacteristic
117C22×C3×Dic3C2×D311yescharacteristic
118C22×C3×Dic3C2×D311yescharacteristic
119C2×#626—34no—
120C2×#626—34no—
121C2×#626—64no—
122C2×#626—64no—
123C2×#626—64no—
124C2×#626—62no—
125C2×#626—62no—
126C2×#626—62no—
127C2×#626—62no—
128#3752—62no—
129#3752—62no—
130C3×(C2×D3)⋊C4—62no—
131C3×(C2×D3)⋊C4—62no—
132C3×C4⋊Dic3—62no—
133C3×Dic3⋊C4—62no—
134C3×C4×Dic3—62no—
135C3×C4×Dic3—62no—
136Dic3⋊Dic3—22no—
137#3722—22no—
138#3722—62no—
139#3722—62no—
140#3722—64no—
141#3722—64no—
142#3722—62no—
143#3722—62no—
144#3722—62no—
145(C2×D3)⋊Dic3—62no—
146(C2×D3)⋊Dic3—62no—
147Dic32—22no—
148C22×C33C22×C411yescharacteristic
149C22×C33C2×D411yescharacteristic
150C22×C33C2×D411yescharacteristic
151C22×C33C2×D411yescharacteristic
152C22×C33C2×D411yescharacteristic
153C22×C33#4111yescharacteristic
154C22×C33#4111yescharacteristic
155C2×C3⋊(C3⋊D3)—22no—
156C2×C3⋊(C3⋊D3)—22no—
157C2×C3⋊(C3⋊D3)—22no—
158C2×C3⋊(C3⋊D3)—41no—
159C2×C3⋊(C3⋊D3)—41no—
160C2×C3⋊(C3⋊D3)—41no—
161C2×C3⋊(C3⋊D3)—41no—
162C2×C3×C3⋊D3—22no—
163C2×C3×C3⋊D3—22no—
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3—41no—
166C2×C3×C3⋊D3—41no—
167C2×C3×C3⋊D3—41no—
168C2×C3×C3⋊D3—41no—
169C3×C3⋊Dic3—22no—
170C3×C3⋊Dic3—41no—
171C32×Dic3—22no—
172C32×Dic3—41no—
173C32×Dic3C22⋊C414yescomplemented
174C22×#67—91no—
175C22×D12—91no—
176C22×D12—91no—
177C22×D12—181no—
178C2×C3×C4⋊C4—91no—
179C2×C3×C22⋊C4—91no—
180C2×C3×C42—91no—
181C2×#217—91no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—91no—
185C2×(C2×D3)⋊C4—91no—
186C2×(C2×D3)⋊C4—91no—
187C2×(C2×D3)⋊C4—91no—
188C2×(C2×D3)⋊C4—91no—
189C2×(C2×D3)⋊C4—91no—
190C2×(C2×D3)⋊C4—91no—
191C2×(C2×D3)⋊C4—91no—
192C2×(C2×D3)⋊C4—181no—
193C2×(C2×D3)⋊C4—181no—
194C2×C4⋊Dic3—31no—
195C2×Dic3⋊C4—31no—
196C2×C4×Dic3—31no—
197C2×C4×Dic3—31no—
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—21no—
201C23×C32—41no—
202C23×C32C22×D311yescharacteristic
203C23×C32C22×D311yescharacteristic
204C23×C32C22×D311yescharacteristic
205C22×C3⋊D3—21no—
206C22×C3⋊D3—21no—
207C22×C3⋊D3—21no—
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—21no—
211C22×C3⋊D3—32no—
212C22×C3⋊D3—32no—
213C22×C3⋊D3—32no—
214C22×C3⋊D3—62no—
215C22×C3⋊D3—62no—
216C22×C3⋊D3—62no—
217C22×C3⋊D3—61no—
218C22×C3⋊D3—61no—
219C22×C3⋊D3—61no—
220C22×C3⋊D3—61no—
221C22×C3⋊D3—61no—
222C22×C3⋊D3—61no—
223C22×C3⋊D3—62no—
224C22×C3⋊D3—62no—
225C22×C3⋊D3—62no—
226C22×C3⋊D3—62no—
227C22×C3⋊D3—62no—
228C22×C3⋊D3—62no—
229C22×C3⋊D3—61no—
230C22×C3⋊D3—61no—
231C22×C3⋊D3—61no—
232C22×C3⋊D3—61no—
233C22×C3⋊D3—61no—
234C22×C3⋊D3—61no—
235C22×C3⋊D3—61no—
236C22×C3⋊D3—61no—
237C22×C3⋊D3—61no—
238C22×C3⋊D3—61no—
239C22×C3⋊D3—61no—
240C22×C3⋊D3—61no—
241C22×C3⋊D3—122no—
242C22×C3⋊D3—121no—
243C22×C3⋊D3—121no—
244C22×C3⋊D3—121no—
245C22×C3⋊D3—121no—
246C22×C3⋊D3—121no—
247C22×C3⋊D3—121no—
248C22×C3⋊D3—121no—
249C22×C3⋊D3—121no—
250C22×C3⋊D3—121no—
251C22×C3⋊D3—121no—
252C22×C3⋊D3—121no—
253C22×C3⋊D3—121no—
254C22×C3⋊D3—122no—
255C22×C3⋊D3—122no—
256C22×C3⋊D3—122no—
257C22×C3⋊D3—122no—
258C22×C3⋊D3—122no—
259C22×C3⋊D3—122no—
260C22×C3⋊D3C4×D312yes—
261C22×C3×D3—32no—
262C22×C3×D3—32no—
263C22×C3×D3—62no—
264C22×C3×D3—62no—
265C22×C3×D3—62no—
266C22×C3×D3—61no—
267C22×C3×D3—61no—
268C22×C3×D3—61no—
269C22×C3×D3—61no—
270C22×C3×D3—61no—
271C22×C3×D3—61no—
272C22×C3×D3—61no—
273C22×C3×D3—61no—
274C22×C3×D3—61no—
275C22×C3×D3—61no—
276C22×C3×D3—61no—
277C22×C3×D3—61no—
278C22×C3×D3—121no—
279C22×C3×D3—121no—
280C22×C3×D3—121no—
281C22×C3×D3—121no—
282C2×C32×C4—32no—
283C2×C32×C4—32no—
284C2×C32×C4—32no—
285C2×C32×C4—32no—
286C2×C32×C4—61no—
287C2×C32×C4—61no—
288C2×C32×C4—61no—
289C2×C32×C4—61no—
290C2×C32×C4—61no—
291C2×C3⋊Dic3—21no—
292C2×C3⋊Dic3—21no—
293C2×C3⋊Dic3—21no—
294C2×C3⋊Dic3—21no—
295C2×C3⋊Dic3—21no—
296C2×C3⋊Dic3D1212yescomplemented
297C4⋊(C3⋊D3)—68no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—32no—
314C2×C3×Dic3—32no—
315C2×C3×Dic3—41no—
316C2×C3×Dic3—41no—
317C2×C3×Dic3—41no—
318C2×C3×Dic3—41no—
319C2×C3×Dic3—62no—
320C2×C3×Dic3—61no—
321C2×C3×Dic3—61no—
322C2×C3×Dic3—61no—
323C2×C3×Dic3—61no—
324C2×C3×Dic3—62no—
325C2×C3×Dic3—61no—
326C2×C3×Dic3—61no—
327C2×C3×Dic3—61no—
328C2×C3×Dic3—61no—
329C2×C3×Dic3—61no—
330C2×C3×Dic3—61no—
331C2×C3×Dic3—121no—
332C2×C3×Dic3—121no—
333C2×C3×Dic3—121no—
334C2×C3×Dic3—121no—
335C2×C3×Dic3C4×D312yes—
336C2×C3×Dic3C4×D312yes—
337C2×C3×Dic3D1212yes—
338C2×C3×Dic3D1212yes—
339C2×C3×Dic3D1212yescomplemented
340C2×C3×Dic3#6712yes—
341C2×C3×Dic3#6712yes—
342C2×C3×Dic3#6712yescomplemented
343#626—616no—
344#626—68no—
345#626—68no—
346#390—271noSylow
347C2×C33C2×C22⋊C411yescharacteristic
348C2×C33C4×D411yescharacteristic
349C2×C33C4×D411yescharacteristic
350C2×C33#12111yescharacteristic
351C2×C33#12111yescharacteristic
352C2×C33#12411yescharacteristic
353C2×C33#12711yescharacteristic
354C3⋊(C3⋊D3)—42no—
355C3×C3⋊D3—42no—
356C24×C3—91no—
357C23×D3—31no—
358C23×D3—31no—
359C23×D3—61no—
360C23×D3—91no—
361C23×D3—91no—
362C23×D3—91no—
363C23×D3—181no—
364C23×D3—181no—
365C23×D3—181no—
366C23×D3—361no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—61no—
374C22×C3×C4—61no—
375C22×C3×C4—61no—
376C22×C3×C4—91no—
377C22×C3×C4—91no—
378C2×#67—94no—
379C2×#67—182no—
380C2×#67—182no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3D3211yescharacteristic
388C22×Dic3D3211yescharacteristic
389C22×Dic3D3211yescharacteristic
390C2×D12—94no—
391C2×D12—94no—
392C2×D12—184no—
393C2×D12—182no—
394C2×D12—182no—
395C2×D12—182no—
396C2×D12—182no—
397C2×D12—184no—
398C2×D12—184no—
399C3×C4⋊C4—182no—
400C3×C22⋊C4—182no—
401C3×C42—182no—
402#217—182no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—182no—
406(C2×D3)⋊C4—182no—
407(C2×D3)⋊C4—182no—
408(C2×D3)⋊C4—182no—
409(C2×D3)⋊C4—182no—
410(C2×D3)⋊C4—182no—
411(C2×D3)⋊C4—184no—
412(C2×D3)⋊C4—184no—
413(C2×D3)⋊C4—182no—
414(C2×D3)⋊C4—182no—
415C4⋊Dic3—62no—
416Dic3⋊C4—62no—
417C4×Dic3—62no—
418C4×Dic3—62no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—21no—
438C22×C32—21no—
439C22×C32—21no—
440C22×C32—41no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32C2×C4×D311yescharacteristic
448C22×C32C2×C4×D311yescharacteristic
449C22×C32C2×C4×D311yescharacteristic
450C22×C32C2×D1211yescharacteristic
451C22×C32C2×D1211yescharacteristic
452C22×C32C2×D1211yescharacteristic
453C22×C32C2×D1211yescharacteristic
454C22×C32#23511yescharacteristic
455C22×C32#23511yescharacteristic
456C22×C32#23511yescharacteristic
457C22×C32D3×D411yescharacteristic
458C22×C32D3×D411yescharacteristic
459C22×C32D3×D411yescharacteristic
460C22×C32D3×D411yescharacteristic
461C22×C32D3×D411yescharacteristic
462C22×C32#23711yescharacteristic
463C22×C32#23911yescharacteristic
464C22×C32#23911yescharacteristic
465C22×C32C2×#6711yescharacteristic
466C22×C32C2×#6711yescharacteristic
467C22×C32C2×#6711yescharacteristic
468C2×C3⋊D3—22no—
469C2×C3⋊D3—22no—
470C2×C3⋊D3—22no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—62no—
476C2×C3⋊D3—62no—
477C2×C3⋊D3—62no—
478C2×C3⋊D3—64no—
479C2×C3⋊D3—64no—
480C2×C3⋊D3—64no—
481C2×C3⋊D3—62no—
482C2×C3⋊D3—62no—
483C2×C3⋊D3—62no—
484C2×C3⋊D3—62no—
485C2×C3⋊D3—62no—
486C2×C3⋊D3—62no—
487C2×C3⋊D3—122no—
488C2×C3⋊D3—122no—
489C2×C3⋊D3—122no—
490C2×C3⋊D3—122no—
491C2×C3⋊D3—122no—
492C2×C3⋊D3—122no—
493C2×C3⋊D3—124no—
494C2×C3⋊D3—124no—
495C2×C3⋊D3—124no—
496C2×C3⋊D3—122no—
497C2×C3⋊D3—122no—
498C2×C3⋊D3—122no—
499C2×C3⋊D3—122no—
500C2×C3⋊D3—122no—
501C2×C3⋊D3—122no—
502C2×C3⋊D3—122no—
503C2×C3⋊D3—122no—
504C2×C3⋊D3—122no—
505C2×C3⋊D3—122no—
506C2×C3⋊D3—122no—
507C2×C3⋊D3—122no—
508C2×C3⋊D3—124no—
509C2×C3⋊D3—124no—
510C2×C3⋊D3—124no—
511C2×C3⋊D3—124no—
512C2×C3⋊D3—121no—
513C2×C3⋊D3—121no—
514C2×C3⋊D3—121no—
515C2×C3⋊D3—121no—
516C2×C3⋊D3—121no—
517C2×C3⋊D3—121no—
518C2×C3⋊D3—121no—
519C2×C3⋊D3—121no—
520C2×C3⋊D3—121no—
521C2×C3⋊D3—121no—
522C2×C3⋊D3—121no—
523C2×C3⋊D3—121no—
524C2×C3×D3—64no—
525C2×C3×D3—62no—
526C2×C3×D3—62no—
527C2×C3×D3—62no—
528C2×C3×D3—62no—
529C2×C3×D3—62no—
530C2×C3×D3—62no—
531C2×C3×D3—122no—
532C2×C3×D3—122no—
533C2×C3×D3—122no—
534C2×C3×D3—122no—
535C2×C3×D3—122no—
536C2×C3×D3—122no—
537C2×C3×D3—121no—
538C2×C3×D3—121no—
539C2×C3×D3—121no—
540C2×C3×D3—121no—
541C2×C3×D3—121no—
542C2×C3×D3—121no—
543C2×C3×D3—121no—
544C2×C3×D3—121no—
545C32×C4—34no—
546C32×C4—62no—
547C32×C4—121no—
548C3⋊Dic3—22no—
549C3⋊Dic3—41no—
550C3×Dic3—22no—
551C3×Dic3—22no—
552C3×Dic3—24no—
553C3×Dic3—42no—
554C3×Dic3—42no—
555C3×Dic3—41no—
556C3×Dic3—41no—
557C3×Dic3—62no—
558C3×Dic3—62no—
559C3×Dic3—122no—
560C3×Dic3—122no—
561C3×Dic3—121no—
562C3×Dic3—121no—
563C3×Dic3(C2×D3)⋊C414yescomplemented
564C3×Dic3(C2×D3)⋊C414yescomplemented
565C22×D4—271no—
566C2×C4⋊C4—91no—
567C2×C22⋊C4—91no—
568C2×C22⋊C4—271no—
569C2×C22⋊C4—271no—
570C2×C22⋊C4—271no—
571C2×C42—91no—
572C33#39011yescharacteristic, complemented, Sylow
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—41no—
577C23×C3—92no—
578C23×C3—181no—
579C23×C3—181no—
580C23×C3—181no—
581C23×C3—181no—
582C23×C3—181no—
583C23×C3—181no—
584C23×C3C2×D3211yescharacteristic
585C23×C3C2×D3211yescharacteristic
586C23×C3C2×D3211yescharacteristic
587C22×D3—32no—
588C22×D3—32no—
589C22×D3—62no—
590C22×D3—62no—
591C22×D3—62no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—92no—
605C22×D3—92no—
606C22×D3—92no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—182no—
612C22×D3—182no—
613C22×D3—182no—
614C22×D3—182no—
615C22×D3—182no—
616C22×D3—182no—
617C22×D3—182no—
618C22×D3—182no—
619C22×D3—182no—
620C22×D3—181no—
621C22×D3—181no—
622C22×D3—181no—
623C22×D3—181no—
624C22×D3—181no—
625C22×D3—181no—
626C22×D3—181no—
627C22×D3—181no—
628C22×D3—181no—
629C22×D3—181no—
630C22×D3—181no—
631C22×D3—181no—
632C22×D3—181no—
633C22×D3—181no—
634C22×D3—181no—
635C22×D3—181no—
636C22×D3—181no—
637C22×D3—181no—
638C22×D3—362no—
639C22×D3—361no—
640C22×D3—361no—
641C22×D3—361no—
642C22×D3—361no—
643C22×D3—361no—
644C22×D3—361no—
645C22×D3—361no—
646C22×D3—361no—
647C22×D3—361no—
648C22×D3—361no—
649C22×D3—361no—
650C22×D3—361no—
651C22×D3—362no—
652C22×D3—362no—
653C22×D3—362no—
654C22×D3—362no—
655C22×D3—362no—
656C22×D3—362no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—32no—
662C2×C3×C4—32no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—62no—
666C2×C3×C4—62no—
667C2×C3×C4—62no—
668C2×C3×C4—62no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—62no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—92no—
681C2×C3×C4—121no—
682C2×C3×C4—121no—
683C2×C3×C4—121no—
684C2×C3×C4—121no—
685C2×C3×C4—181no—
686C2×C3×C4—181no—
687C2×C3×C4—181no—
688C2×C3×C4—181no—
689C2×C3×C4—181no—
690#67—188no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—32no—
697C2×Dic3—32no—
698C2×Dic3—62no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—62no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—121no—
711C2×Dic3—121no—
712C2×Dic3—121no—
713C2×Dic3—121no—
714C2×Dic3#62412yes—
715C2×Dic3#62612yes—
716C2×Dic3#62612yes—
717C2×Dic3#62612yescomplemented
718D12—188no—
719D12—188no—
720D12—1816no—
721C2×C32—21no—
722C2×C32—21no—
723C2×C32—21no—
724C2×C32—21no—
725C2×C32—21no—
726C2×C32—21no—
727C2×C32—21no—
728C2×C32—21no—
729C2×C32—21no—
730C2×C32—21no—
731C2×C32—21no—
732C2×C32—21no—
733C2×C32—21no—
734C2×C32—21no—
735C2×C32—21no—
736C2×C32—21no—
737C2×C32—21no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—41no—
743C2×C32—41no—
744C2×C32—41no—
745C2×C32—41no—
746C2×C32—41no—
747C2×C32—41no—
748C2×C32—41no—
749C2×C32C4×D1211yescharacteristic
750C2×C32C4×D1211yescharacteristic
751C2×C32#87411yescharacteristic
752C2×C32#87511yescharacteristic
753C2×C32D3×C22⋊C411yescharacteristic
754C2×C32#67⋊C411yescharacteristic
755C2×C32#88411yescharacteristic
756C2×C32#88511yescharacteristic
757C2×C32#89311yescharacteristic
758C2×C32#89311yescharacteristic
759C2×C32#89511yescharacteristic
760C2×C32#89511yescharacteristic
761C2×C32C2×(C2×D3)⋊C411yescharacteristic
762C2×C32C2×(C2×D3)⋊C411yescharacteristic
763C2×C32C4×#6711yescharacteristic
764C2×C32#93011yescharacteristic
765C2×C32#93011yescharacteristic
766C2×C32#93911yescharacteristic
767C2×C32#94011yescharacteristic
768C2×C32#94011yescharacteristic
769C2×C32#94711yescharacteristic
770C3⋊D3—42no—
771C3⋊D3—124no—
772C3⋊D3—124no—
773C3⋊D3—124no—
774C3⋊D3—128no—
775C3⋊D3—122no—
776C3⋊D3—122no—
777C3⋊D3—122no—
778C3×D3—124no—
779C3×D3—122no—
780C3×D3—122no—
781C24—91no—
782C24—271no—
783C2×D4—274no—
784C2×D4—542no—
785C2×D4—542no—
786C22×C4—31no—
787C22×C4—31no—
788C22×C4—31no—
789C22×C4—91no—
790C22×C4—91no—
791C4⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—542no—
794C22⋊C4—542no—
795C22⋊C4—542no—
796C42—182no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—182no—
826C22×C3—182no—
827C22×C3—182no—
828C22×C3—361no—
829C22×C3—361no—
830C22×C3—361no—
831C22×C3—361no—
832C22×C3#379611yescharacteristic
833C22×C3#379811yescharacteristic
834C22×C3#379911yescharacteristic
835C22×C3#379911yescharacteristic
836C22×C3#379911yescharacteristic
837C22×C3C4×D3211yescharacteristic
838C22×C3C4×D3211yescharacteristic
839C22×C3D3×D1211yescharacteristic
840C22×C3D3×D1211yescharacteristic
841C22×C3D3×D1211yescharacteristic
842C22×C3D3×D1211yescharacteristic
843C22×C3D3×D1211yescharacteristic
844C22×C3#380411yescharacteristic
845C22×C3C2×#62411yescharacteristic
846C22×C3C2×#62611yescharacteristic
847C22×C3C2×#62611yescharacteristic
848C22×C3C2×#62611yescharacteristic
849C22×C3D3×#6711yescharacteristic
850C22×C3D3×#6711yescharacteristic
851C22×C3D3×#6711yescharacteristic
852C22×C3#381111yescharacteristic
853C2×D3—64no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—62no—
857C2×D3—62no—
858C2×D3—62no—
859C2×D3—62no—
860C2×D3—122no—
861C2×D3—122no—
862C2×D3—122no—
863C2×D3—122no—
864C2×D3—122no—
865C2×D3—122no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—184no—
875C2×D3—184no—
876C2×D3—184no—
877C2×D3—182no—
878C2×D3—182no—
879C2×D3—182no—
880C2×D3—182no—
881C2×D3—182no—
882C2×D3—182no—
883C2×D3—182no—
884C2×D3—182no—
885C2×D3—182no—
886C2×D3—362no—
887C2×D3—362no—
888C2×D3—362no—
889C2×D3—362no—
890C2×D3—362no—
891C2×D3—362no—
892C2×D3—364no—
893C2×D3—364no—
894C2×D3—364no—
895C2×D3—362no—
896C2×D3—362no—
897C2×D3—362no—
898C2×D3—362no—
899C2×D3—362no—
900C2×D3—362no—
901C2×D3—362no—
902C2×D3—362no—
903C2×D3—362no—
904C2×D3—362no—
905C2×D3—362no—
906C2×D3—362no—
907C2×D3—364no—
908C2×D3—364no—
909C2×D3—364no—
910C2×D3—364no—
911C2×D3—361no—
912C2×D3—361no—
913C2×D3—361no—
914C2×D3—361no—
915C2×D3—361no—
916C2×D3—361no—
917C2×D3—361no—
918C2×D3—361no—
919C2×D3—361no—
920C2×D3—361no—
921C2×D3—361no—
922C2×D3—361no—
923C3×C4—34no—
924C3×C4—34no—
925C3×C4—64no—
926C3×C4—62no—
927C3×C4—62no—
928C3×C4—122no—
929C3×C4—122no—
930C3×C4—121no—
931C3×C4—121no—
932C3×C4—182no—
933C3×C4—361no—
934Dic3—22no—
935Dic3—41no—
936Dic3—62no—
937Dic3—62no—
938Dic3—122no—
939Dic3—122no—
940Dic3—121no—
941Dic3—121no—
942Dic3#372214yescomplemented
943C32—21no—
944C32—21no—
945C32—21no—
946C32—41no—
947C32#493911yescharacteristic, complemented
948C32#495711yescharacteristic, complemented
949C32#498811yescharacteristic, complemented
950C23—92no—
951C23—181no—
952C23—181no—
953C23—181no—
954C23—181no—
955C23—181no—
956C23—181no—
957C23—272no—
958C23—541no—
959C23—541no—
960C23—541no—
961C23—541no—
962C23—541no—
963C23—541no—
964C23D3311yescharacteristic
965D4—548no—
966C2×C4—32no—
967C2×C4—32no—
968C2×C4—32no—
969C2×C4—32no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—92no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—41no—
1003C2×C3—41no—
1004C2×C3—41no—
1005C2×C3—41no—
1006C2×C3—41no—
1007C2×C3—41no—
1008C2×C3—41no—
1009C2×C3—362no—
1010C2×C3#6385211yescharacteristic
1011C2×C3#6386411yescharacteristic
1012C2×C3#6388011yescharacteristic
1013C2×C3#6388111yescharacteristic
1014C2×C3#6388611yescharacteristic
1015C2×C3#6389411yescharacteristic
1016C2×C3#6389411yescharacteristic
1017C2×C3C4×#62611yescharacteristic
1018C2×C3#6390411yescharacteristic
1019C2×C3#6390611yescharacteristic
1020C2×C3#6390711yescharacteristic
1021C2×C3#6390911yescharacteristic
1022C2×C3#6390911yescharacteristic
1023C2×C3#6391011yescharacteristic
1024C2×C3#6391111yescharacteristic
1025C2×C3#6391111yescharacteristic
1026C2×C3D3×(C2×D3)⋊C411yescharacteristic
1027C2×C3D3×(C2×D3)⋊C411yescharacteristic
1028C2×C3C2×#372211yescharacteristic
1029C2×C3#6397811yescharacteristic
1030C2×C3#6397911yescharacteristic
1031D3—124no—
1032D3—122no—
1033D3—122no—
1034D3—364no—
1035D3—364no—
1036D3—364no—
1037D3—368no—
1038D3—362no—
1039D3—362no—
1040D3—362no—
1041C22—182no—
1042C22—182no—
1043C22—182no—
1044C22—361no—
1045C22—361no—
1046C22—361no—
1047C22—361no—
1048C22—542no—
1049C22—542no—
1050C22—542no—
1051C22—1081no—
1052C22—1081no—
1053C22—1081no—
1054C22—1081no—
1055C22D3×#62411yescharacteristic
1056C22D3×#62611yescharacteristic
1057C22D3×#62611yescharacteristic
1058C22D3×#62611yescharacteristic
1059C22#8895511yescharacteristic
1060C22#8896211yescharacteristic
1061C22#8896511yescharacteristic
1062C4—34no—
1063C4—62no—
1064C4—121no—
1065C4—182no—
1066C4—361no—
1067C3—21no—
1068C3—21no—
1069C3—21no—
1070C3—41no—
1071C3#1059132011yescharacteristic, complemented
1072C3#1059138311yescharacteristic, complemented
1073C3#1059138411yescharacteristic, complemented
1074C2—362no—
1075C2—1082no—
1076C2D3×#372211yescharacteristic
1077C2#1172293311yescharacteristic
1078C2#1172293711yescharacteristic
1079C2#1172295911yescharacteristic
1080C2#1172296111yescharacteristic
1081C2#1172300311yescharacteristic
1082C2#1172303011yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, cosocleC23×C33C23
prime radicalC22×#6292C2
hypocenterC33#390
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#88814C2semidirect
3. C2×#88804C2semidirect
4. C2×#88804C2semidirect
5. C2×C3×Dic3⋊Dic3C2semidirect
6. C2×C3×#3722C2semidirect
7. C2×C3×Dic32C2semidirect
20. C2×#6292C4semidirect
39. C2×Dic3⋊Dic3D3semidirect
47. C2×#3722D3semidirect
50. C2×Dic32D3semidirect
71. C2×C3×C3⋊Dic3D4semidirect
80. C2×C32×Dic3D4semidirect
173. C32×Dic3C22⋊C4semidirect
296. C2×C3⋊Dic3D12semidirect
339. C2×C3×Dic3D12semidirect
342. C2×C3×Dic3#67semidirect
563. C3×Dic3(C2×D3)⋊C4semidirect
564. C3×Dic3(C2×D3)⋊C4semidirect
572. C33#390semidirect
717. C2×Dic3#626semidirect
942. Dic3#3722semidirect
947. C32#4939semidirect
948. C32#4957semidirect
949. C32#4988semidirect
1071. C3#10591320semidirect
1072. C3#10591383semidirect
1073. C3#10591384semidirect

Maximal subgroups

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

subgroupindex
C22×#62922
C2×#888142
C2×#888042
C2×C3×Dic3⋊Dic32
C2×C3×#37222
C2×C3×Dic322
#105913843
#105913833
#105913203