Finite Group Databasebeta

← #13156772

Subgroups — #13156772

Order 1728.

1882 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6291C211yesmaximal, characteristic
2C22×#6289C211yesmaximal, characteristic, complemented
3C2×#88804C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
6#11722082C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8#10591722—31nomaximal
9#10591387—31nomaximal
10#10591275—31nomaximal
11C23×C3⋊(C3⋊D3)C2211yescharacteristic
12C23×C32×D3C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×#6291—22no—
19C2×#6291—22no—
20C2×#6291C414yescomplemented
21C2×#6289—22no—
22C2×#6289—22no—
23C2×#6289—22no—
24#88804—22no—
25C3×(C2×D3)⋊Dic3—22no—
26C3×(C2×D3)⋊Dic3—22no—
27C22×#638—31no—
28C22×C4×C3⋊D3—31no—
29C22×#626—31no—
30C22×#626—31no—
31C22×#626—61no—
32C22×#624—31no—
33C22×#624—31no—
34C22×#624—61no—
35C2×#3752—31no—
36C2×C3×#217—31no—
37C2×C3×#217—31no—
38C2×C3×(C2×D3)⋊C4—31no—
39C2×C3×(C2×D3)⋊C4—31no—
40C2×#3722—31no—
41C2×#3722—31no—
42C2×#3722—61no—
43C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
44C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
45C3×C3⋊#95—31no—
46C3×C3⋊#95—31no—
47#63579—31no—
48#63579—31no—
49#63579—31no—
50#63579D311yescharacteristic, 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)C2×C412yes—
57C22×C3⋊(C3⋊D3)D412yes—
58C22×C3⋊(C3⋊D3)D412yes—
59C22×C32×D3—21no—
60C22×C32×D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3—21no—
63C22×C32×D3—21no—
64C22×C32×D3—21no—
65C22×C32×D3C2×C412yescomplemented
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⋊Dic3—21no—
72C2×C3×C3⋊Dic3—21no—
73C2×C3×C3⋊Dic3C2×C412yescomplemented
74C2×C3×C3⋊Dic3D412yescomplemented
75C2×C32×Dic3—21no—
76C2×C32×Dic3—21no—
77C2×C32×Dic3—21no—
78C2×C32×Dic3—21no—
79C2×C32×Dic3—21no—
80C2×C32×Dic3D412yescomplemented
81#6291—28no—
82#6289—28no—
83#4956—91no—
84#4956—91no—
85#4665—91no—
86C24×C32—31no—
87C23×C3⋊D3—31no—
88C23×C3⋊D3—31no—
89C23×C3⋊D3—31no—
90C23×C3⋊D3—61no—
91C23×C3⋊D3—61no—
92C23×C3⋊D3—61no—
93C23×C3⋊D3—121no—
94C23×C3×D3—21no—
95C23×C3×D3C2×D311yescharacteristic
96C23×C3×D3C2×D311yescharacteristic
97C22×C32×C4—31no—
98C22×C32×C4—31no—
99C2×#638—34no—
100C2×#638—62no—
101C2×#638—62no—
102C22×C3⋊Dic3C2×D311yescharacteristic
103C22×C3⋊Dic3C2×D311yescharacteristic
104C22×C3⋊Dic3C2×D311yescharacteristic
105C2×C4×C3⋊D3—62no—
106C2×C4×C3⋊D3—62no—
107C2×C4×C3⋊D3—62no—
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3—31no—
111C22×C3×Dic3—31no—
112C22×C3×Dic3—31no—
113C22×C3×Dic3—31no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—31no—
116C22×C3×Dic3—61no—
117C22×C3×Dic3—61no—
118C22×C3×Dic3—61no—
119C22×C3×Dic3C2×D311yescharacteristic
120C22×C3×Dic3C2×D311yescharacteristic
121C22×C3×Dic3C2×D311yescharacteristic
122C22×C3×Dic3C2×D311yescharacteristic
123C2×#626—34no—
124C2×#626—34no—
125C2×#626—62no—
126C2×#626—62no—
127C2×#626—62no—
128C2×#626—62no—
129C2×#626—64no—
130C2×#626—64no—
131C2×#626—64no—
132C2×#624—62no—
133C2×#624—62no—
134C2×#624—62no—
135C2×#624—62no—
136C2×#624—64no—
137C2×#624—64no—
138C2×#624—64no—
139C2×#624—62no—
140C2×#624—62no—
141#3752—62no—
142C3×#217—62no—
143C3×#217—62no—
144C3×(C2×D3)⋊C4—62no—
145C3×(C2×D3)⋊C4—62no—
146#3722—62no—
147#3722—62no—
148#3722—64no—
149(C2×D3)⋊Dic3—22no—
150(C2×D3)⋊Dic3—22no—
151C22×C33C22×C411yescharacteristic
152C22×C33C2×D411yescharacteristic
153C22×C33C2×D411yescharacteristic
154C22×C33C2×D411yescharacteristic
155C22×C33C2×D411yescharacteristic
156C22×C33#4111yescharacteristic
157C22×C33#4111yescharacteristic
158C2×C3⋊(C3⋊D3)—22no—
159C2×C3⋊(C3⋊D3)—22no—
160C2×C3⋊(C3⋊D3)—22no—
161C2×C3⋊(C3⋊D3)—22no—
162C2×C3⋊(C3⋊D3)—22no—
163C2×C3⋊(C3⋊D3)—22no—
164C2×C3⋊(C3⋊D3)C22⋊C414yescomplemented
165C2×C32×D3—22no—
166C2×C32×D3—22no—
167C2×C32×D3—22no—
168C2×C32×D3—41no—
169C2×C32×D3—41no—
170C2×C32×D3—41no—
171C2×C32×D3—41no—
172C3×C3⋊Dic3—22no—
173C3×C3⋊Dic3—22no—
174C3×C3⋊Dic3—41no—
175C32×Dic3—22no—
176C32×Dic3—41no—
177C22×#67—91no—
178C22×#67—91no—
179C22×#67—181no—
180C22×D12—91no—
181C22×C4×D3—91no—
182C22×C4×D3—91no—
183C22×C4×D3—91no—
184C22×C4×D3—181no—
185C2×C3×C22⋊C4—91no—
186C2×C3×C22⋊C4—91no—
187C2×#217—31no—
188C2×#217—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—91no—
192C2×(C2×D3)⋊C4—91no—
193C2×(C2×D3)⋊C4—91no—
194C2×(C2×D3)⋊C4—181no—
195C3×#95—91no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—91no—
199C3⋊#95—91no—
200C3⋊#95—91no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32—32no—
205C23×C32—41no—
206C23×C32—61no—
207C23×C32—61no—
208C23×C32—61no—
209C23×C32—61no—
210C23×C32—61no—
211C23×C32—61no—
212C23×C32C22×D311yescharacteristic
213C23×C32C22×D311yescharacteristic
214C23×C32C22×D311yescharacteristic
215C22×C3⋊D3—32no—
216C22×C3⋊D3—32no—
217C22×C3⋊D3—32no—
218C22×C3⋊D3—32no—
219C22×C3⋊D3—32no—
220C22×C3⋊D3—32no—
221C22×C3⋊D3—32no—
222C22×C3⋊D3—32no—
223C22×C3⋊D3—32no—
224C22×C3⋊D3—62no—
225C22×C3⋊D3—62no—
226C22×C3⋊D3—62no—
227C22×C3⋊D3—62no—
228C22×C3⋊D3—62no—
229C22×C3⋊D3—62no—
230C22×C3⋊D3—62no—
231C22×C3⋊D3—62no—
232C22×C3⋊D3—62no—
233C22×C3⋊D3—61no—
234C22×C3⋊D3—61no—
235C22×C3⋊D3—61no—
236C22×C3⋊D3—61no—
237C22×C3⋊D3—62no—
238C22×C3⋊D3—62no—
239C22×C3⋊D3—62no—
240C22×C3⋊D3—62no—
241C22×C3⋊D3—61no—
242C22×C3⋊D3—61no—
243C22×C3⋊D3—61no—
244C22×C3⋊D3—61no—
245C22×C3⋊D3—61no—
246C22×C3⋊D3—61no—
247C22×C3⋊D3—61no—
248C22×C3⋊D3—61no—
249C22×C3⋊D3—122no—
250C22×C3⋊D3—122no—
251C22×C3⋊D3—122no—
252C22×C3⋊D3—121no—
253C22×C3⋊D3—121no—
254C22×C3⋊D3—121no—
255C22×C3⋊D3—121no—
256C22×C3⋊D3—121no—
257C22×C3⋊D3—121no—
258C22×C3⋊D3—121no—
259C22×C3⋊D3—121no—
260C22×C3⋊D3—122no—
261C22×C3⋊D3—122no—
262C22×C3⋊D3—122no—
263C22×C3⋊D3—122no—
264C22×C3×D3—22no—
265C22×C3×D3—22no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—21no—
271C22×C3×D3—21no—
272C22×C3×D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—21no—
277C22×C3×D3—21no—
278C22×C3×D3—22no—
279C22×C3×D3—41no—
280C22×C3×D3—41no—
281C22×C3×D3—41no—
282C22×C3×D3—41no—
283C22×C3×D3C4×D312yescomplemented
284C22×C3×D3C4×D312yescomplemented
285C2×C32×C4—32no—
286C2×C32×C4—61no—
287C2×C32×C4—61no—
288C2×C32×C4—61no—
289C2×C32×C4—61no—
290C2×C32×C4—61no—
291#638—68no—
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⋊Dic3C4×D312yescomplemented
300C2×C3⋊Dic3#6712yescomplemented
301C4×C3⋊D3—68no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3—21no—
314C2×C3×Dic3—21no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—32no—
317C2×C3×Dic3—32no—
318C2×C3×Dic3—32no—
319C2×C3×Dic3—32no—
320C2×C3×Dic3—41no—
321C2×C3×Dic3—41no—
322C2×C3×Dic3—62no—
323C2×C3×Dic3—62no—
324C2×C3×Dic3—62no—
325C2×C3×Dic3—62no—
326C2×C3×Dic3—62no—
327C2×C3×Dic3—62no—
328C2×C3×Dic3—61no—
329C2×C3×Dic3—61no—
330C2×C3×Dic3—61no—
331C2×C3×Dic3—61no—
332C2×C3×Dic3—61no—
333C2×C3×Dic3—61no—
334C2×C3×Dic3—61no—
335C2×C3×Dic3—61no—
336C2×C3×Dic3—62no—
337C2×C3×Dic3—61no—
338C2×C3×Dic3—61no—
339C2×C3×Dic3—61no—
340C2×C3×Dic3—61no—
341C2×C3×Dic3—61no—
342C2×C3×Dic3—61no—
343C2×C3×Dic3—121no—
344C2×C3×Dic3—121no—
345C2×C3×Dic3D1212yescomplemented
346C2×C3×Dic3#6712yescomplemented
347#626—68no—
348#626—68no—
349#626—616no—
350#624—616no—
351#624—68no—
352#624—68no—
353#386—271noSylow
354C2×C33C2×C22⋊C411yescharacteristic
355C2×C33C4×D411yescharacteristic
356C2×C33C4×D411yescharacteristic
357C2×C33#12011yescharacteristic
358C2×C33#12111yescharacteristic
359C2×C33#12111yescharacteristic
360C2×C33#12311yescharacteristic
361C3⋊(C3⋊D3)—24no—
362C32×D3—42no—
363C24×C3—31no—
364C24×C3—31no—
365C24×C3—61no—
366C23×D3—91no—
367C23×D3—91no—
368C23×D3—91no—
369C23×D3—181no—
370C23×D3—181no—
371C23×D3—181no—
372C23×D3—361no—
373C23×D3D3211yescharacteristic
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—61no—
379C22×C3×C4—61no—
380C22×C3×C4—91no—
381C22×C3×C4—91no—
382C22×C3×C4—91no—
383C2×#67—94no—
384C2×#67—94no—
385C2×#67—184no—
386C2×#67—182no—
387C2×#67—182no—
388C2×#67—182no—
389C2×#67—182no—
390C2×#67—184no—
391C2×#67—184no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—31no—
398C22×Dic3—61no—
399C22×Dic3—61no—
400C22×Dic3—61no—
401C22×Dic3D3211yescharacteristic
402C22×Dic3D3211yescharacteristic
403C2×D12—94no—
404C2×D12—182no—
405C2×D12—182no—
406C2×C4×D3—182no—
407C2×C4×D3—182no—
408C2×C4×D3—182no—
409C2×C4×D3—182no—
410C2×C4×D3—182no—
411C2×C4×D3—182no—
412C2×C4×D3—182no—
413C2×C4×D3—182no—
414C2×C4×D3—184no—
415C2×C4×D3—184no—
416C2×C4×D3—184no—
417C2×C4×D3—182no—
418C3×C22⋊C4—182no—
419C3×C22⋊C4—182no—
420#217—62no—
421#217—62no—
422(C2×D3)⋊C4—62no—
423(C2×D3)⋊C4—62no—
424(C2×D3)⋊C4—182no—
425(C2×D3)⋊C4—182no—
426(C2×D3)⋊C4—182no—
427(C2×D3)⋊C4—184no—
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—21no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32—62no—
457C22×C32—62no—
458C22×C32—62no—
459C22×C32—121no—
460C22×C32—121no—
461C22×C32—121no—
462C22×C32—121no—
463C22×C32C2×C4×D311yescharacteristic
464C22×C32C2×C4×D311yescharacteristic
465C22×C32C2×C4×D311yescharacteristic
466C22×C32C2×D1211yescharacteristic
467C22×C32#23511yescharacteristic
468C22×C32#23511yescharacteristic
469C22×C32#23511yescharacteristic
470C22×C32D3×D411yescharacteristic
471C22×C32D3×D411yescharacteristic
472C22×C32D3×D411yescharacteristic
473C22×C32D3×D411yescharacteristic
474C22×C32D3×D411yescharacteristic
475C22×C32D3×D411yescharacteristic
476C22×C32D3×D411yescharacteristic
477C22×C32D3×D411yescharacteristic
478C22×C32D3×D411yescharacteristic
479C22×C32#23711yescharacteristic
480C22×C32#23711yescharacteristic
481C22×C32#23911yescharacteristic
482C22×C32C2×#6711yescharacteristic
483C22×C32C2×#6711yescharacteristic
484C2×C3⋊D3—34no—
485C2×C3⋊D3—34no—
486C2×C3⋊D3—34no—
487C2×C3⋊D3—64no—
488C2×C3⋊D3—64no—
489C2×C3⋊D3—64no—
490C2×C3⋊D3—62no—
491C2×C3⋊D3—62no—
492C2×C3⋊D3—62no—
493C2×C3⋊D3—62no—
494C2×C3⋊D3—62no—
495C2×C3⋊D3—62no—
496C2×C3⋊D3—64no—
497C2×C3⋊D3—64no—
498C2×C3⋊D3—64no—
499C2×C3⋊D3—64no—
500C2×C3⋊D3—64no—
501C2×C3⋊D3—64no—
502C2×C3⋊D3—62no—
503C2×C3⋊D3—62no—
504C2×C3⋊D3—62no—
505C2×C3⋊D3—62no—
506C2×C3⋊D3—62no—
507C2×C3⋊D3—62no—
508C2×C3⋊D3—62no—
509C2×C3⋊D3—62no—
510C2×C3⋊D3—62no—
511C2×C3⋊D3—62no—
512C2×C3⋊D3—62no—
513C2×C3⋊D3—62no—
514C2×C3⋊D3—124no—
515C2×C3⋊D3—122no—
516C2×C3⋊D3—122no—
517C2×C3⋊D3—122no—
518C2×C3⋊D3—122no—
519C2×C3⋊D3—122no—
520C2×C3⋊D3—122no—
521C2×C3⋊D3—122no—
522C2×C3⋊D3—122no—
523C2×C3⋊D3—122no—
524C2×C3⋊D3—122no—
525C2×C3⋊D3—122no—
526C2×C3⋊D3—122no—
527C2×C3⋊D3—124no—
528C2×C3⋊D3—124no—
529C2×C3⋊D3—124no—
530C2×C3⋊D3—124no—
531C2×C3⋊D3—124no—
532C2×C3⋊D3—124no—
533C2×C3×D3—24no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3—22no—
539C2×C3×D3—22no—
540C2×C3×D3—42no—
541C2×C3×D3—42no—
542C2×C3×D3—42no—
543C2×C3×D3—42no—
544C2×C3×D3—42no—
545C2×C3×D3—42no—
546C2×C3×D3—41no—
547C2×C3×D3—41no—
548C2×C3×D3—41no—
549C2×C3×D3—41no—
550C2×C3×D3—41no—
551C2×C3×D3—41no—
552C2×C3×D3—41no—
553C2×C3×D3—41no—
554C32×C4—62no—
555C32×C4—121no—
556C3⋊Dic3—22no—
557C3⋊Dic3—22no—
558C3⋊Dic3—41no—
559C3×Dic3—24no—
560C3×Dic3—22no—
561C3×Dic3—22no—
562C3×Dic3—42no—
563C3×Dic3—41no—
564C3×Dic3—41no—
565C3×Dic3—64no—
566C3×Dic3—64no—
567C3×Dic3—62no—
568C3×Dic3—62no—
569C3×Dic3—62no—
570C3×Dic3—62no—
571C3×Dic3—122no—
572C3×Dic3—121no—
573C3×Dic3—121no—
574C22×D4—271no—
575C23×C4—271no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4—91no—
578C2×C22⋊C4—271no—
579#95—91no—
580#95—271no—
581C33#38611yescharacteristic, complemented, Sylow
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—32no—
586C23×C3—32no—
587C23×C3—41no—
588C23×C3—62no—
589C23×C3—62no—
590C23×C3—62no—
591C23×C3—61no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—61no—
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—121no—
604C23×C3—121no—
605C23×C3—121no—
606C23×C3—121no—
607C23×C3C2×D3211yescharacteristic
608C23×C3C2×D3211yescharacteristic
609C23×C3C2×D3211yescharacteristic
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—92no—
617C22×D3—92no—
618C22×D3—92no—
619C22×D3—92no—
620C22×D3—92no—
621C22×D3—92no—
622C22×D3—92no—
623C22×D3—92no—
624C22×D3—92no—
625C22×D3—182no—
626C22×D3—182no—
627C22×D3—182no—
628C22×D3—182no—
629C22×D3—182no—
630C22×D3—182no—
631C22×D3—182no—
632C22×D3—182no—
633C22×D3—182no—
634C22×D3—182no—
635C22×D3—182no—
636C22×D3—182no—
637C22×D3—182no—
638C22×D3—181no—
639C22×D3—181no—
640C22×D3—181no—
641C22×D3—181no—
642C22×D3—181no—
643C22×D3—181no—
644C22×D3—181no—
645C22×D3—181no—
646C22×D3—181no—
647C22×D3—181no—
648C22×D3—181no—
649C22×D3—181no—
650C22×D3—362no—
651C22×D3—362no—
652C22×D3—362no—
653C22×D3—361no—
654C22×D3—361no—
655C22×D3—361no—
656C22×D3—361no—
657C22×D3—361no—
658C22×D3—361no—
659C22×D3—361no—
660C22×D3—361no—
661C22×D3—362no—
662C22×D3—362no—
663C22×D3—362no—
664C22×D3—362no—
665C22×D3#62412yescomplemented
666C2×C3×C4—32no—
667C2×C3×C4—32no—
668C2×C3×C4—62no—
669C2×C3×C4—62no—
670C2×C3×C4—62no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—62no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—92no—
683C2×C3×C4—92no—
684C2×C3×C4—121no—
685C2×C3×C4—121no—
686C2×C3×C4—181no—
687C2×C3×C4—181no—
688C2×C3×C4—181no—
689C2×C3×C4—181no—
690C2×C3×C4—181no—
691C2×C3×C4—181no—
692C2×C3×C4—181no—
693#67—188no—
694#67—188no—
695#67—1816no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—21no—
699C2×Dic3—21no—
700C2×Dic3—21no—
701C2×Dic3—32no—
702C2×Dic3—32no—
703C2×Dic3—32no—
704C2×Dic3—32no—
705C2×Dic3—62no—
706C2×Dic3—62no—
707C2×Dic3—62no—
708C2×Dic3—62no—
709C2×Dic3—62no—
710C2×Dic3—62no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—62no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—121no—
727C2×Dic3—121no—
728C2×Dic3#62612yescomplemented
729D12—188no—
730C4×D3—188no—
731C4×D3—1816no—
732C4×D3—188no—
733C4×D3—188no—
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—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—41no—
756C2×C32—41no—
757C2×C32—41no—
758C2×C32—41no—
759C2×C32—41no—
760C2×C32—41no—
761C2×C32—41no—
762C2×C32—122no—
763C2×C32C4×D1211yescharacteristic
764C2×C32D3×C22⋊C411yescharacteristic
765C2×C32D3×C22⋊C411yescharacteristic
766C2×C32D3×C22⋊C411yescharacteristic
767C2×C32#67⋊C411yescharacteristic
768C2×C32#67⋊C411yescharacteristic
769C2×C32#88211yescharacteristic
770C2×C32#88311yescharacteristic
771C2×C32#88311yescharacteristic
772C2×C32#88411yescharacteristic
773C2×C32#88411yescharacteristic
774C2×C32#88411yescharacteristic
775C2×C32#89311yescharacteristic
776C2×C32#89411yescharacteristic
777C2×C32#89511yescharacteristic
778C2×C32C4×#6711yescharacteristic
779C2×C32C4×#6711yescharacteristic
780C2×C32#93711yescharacteristic
781C2×C32#93711yescharacteristic
782C2×C32#93811yescharacteristic
783C2×C32#93811yescharacteristic
784C3⋊D3—64no—
785C3⋊D3—68no—
786C3⋊D3—64no—
787C3⋊D3—64no—
788C3⋊D3—124no—
789C3⋊D3—124no—
790C3⋊D3—128no—
791C3×D3—44no—
792C3×D3—42no—
793C3×D3—42no—
794C24—31no—
795C24—271no—
796C2×D4—274no—
797C2×D4—542no—
798C2×D4—542no—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—91no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—542no—
805C22×C4—542no—
806C22×C4—542no—
807C22⋊C4—182no—
808C22⋊C4—182no—
809C22⋊C4—542no—
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—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—64no—
839C22×C3—62no—
840C22×C3—62no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—122no—
846C22×C3—122no—
847C22×C3—122no—
848C22×C3—122no—
849C22×C3—122no—
850C22×C3—122no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3—121no—
857C22×C3—121no—
858C22×C3—121no—
859C22×C3#379611yescharacteristic
860C22×C3#379811yescharacteristic
861C22×C3#379911yescharacteristic
862C22×C3C4×D3211yescharacteristic
863C22×C3C4×D3211yescharacteristic
864C22×C3D3×D1211yescharacteristic
865C22×C3#380211yescharacteristic
866C22×C3#380211yescharacteristic
867C22×C3#380411yescharacteristic
868C22×C3#380411yescharacteristic
869C22×C3#380411yescharacteristic
870C22×C3C2×#62411yescharacteristic
871C22×C3C2×#62611yescharacteristic
872C22×C3D3×#6711yescharacteristic
873C22×C3D3×#6711yescharacteristic
874C22×C3D3×#6711yescharacteristic
875C22×C3#381111yescharacteristic
876C22×C3#381111yescharacteristic
877C22×C3#381111yescharacteristic
878C22×C3#381111yescharacteristic
879C22×C3#381111yescharacteristic
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—41no—
884C2×D3—41no—
885C2×D3—41no—
886C2×D3—41no—
887C2×D3—94no—
888C2×D3—94no—
889C2×D3—94no—
890C2×D3—184no—
891C2×D3—184no—
892C2×D3—184no—
893C2×D3—184no—
894C2×D3—184no—
895C2×D3—184no—
896C2×D3—184no—
897C2×D3—184no—
898C2×D3—184no—
899C2×D3—182no—
900C2×D3—182no—
901C2×D3—182no—
902C2×D3—182no—
903C2×D3—182no—
904C2×D3—182no—
905C2×D3—182no—
906C2×D3—182no—
907C2×D3—182no—
908C2×D3—182no—
909C2×D3—182no—
910C2×D3—182no—
911C2×D3—182no—
912C2×D3—182no—
913C2×D3—182no—
914C2×D3—182no—
915C2×D3—182no—
916C2×D3—182no—
917C2×D3—364no—
918C2×D3—362no—
919C2×D3—362no—
920C2×D3—362no—
921C2×D3—362no—
922C2×D3—362no—
923C2×D3—362no—
924C2×D3—362no—
925C2×D3—362no—
926C2×D3—362no—
927C2×D3—362no—
928C2×D3—362no—
929C2×D3—362no—
930C2×D3—364no—
931C2×D3—364no—
932C2×D3—364no—
933C2×D3—364no—
934C2×D3—364no—
935C2×D3—364no—
936C3×C4—64no—
937C3×C4—62no—
938C3×C4—62no—
939C3×C4—122no—
940C3×C4—121no—
941C3×C4—121no—
942C3×C4—182no—
943C3×C4—182no—
944C3×C4—361no—
945Dic3—22no—
946Dic3—41no—
947Dic3—64no—
948Dic3—64no—
949Dic3—62no—
950Dic3—62no—
951Dic3—62no—
952Dic3—62no—
953Dic3—122no—
954Dic3—121no—
955Dic3—121no—
956C32—21no—
957C32—21no—
958C32—21no—
959C32—41no—
960C32#466511yescharacteristic, complemented
961C32#495611yescharacteristic, complemented
962C32#495611yescharacteristic, complemented
963C23—32no—
964C23—61no—
965C23—61no—
966C23—61no—
967C23—61no—
968C23—61no—
969C23—61no—
970C23—272no—
971C23—272no—
972C23—272no—
973C23—541no—
974C23—541no—
975C23—541no—
976C23—541no—
977C23D3311yescharacteristic
978D4—548no—
979C2×C4—32no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—92no—
986C2×C4—92no—
987C2×C4—181no—
988C2×C4—181no—
989C2×C4—181no—
990C2×C4—181no—
991C2×C4—181no—
992C2×C4—181no—
993C2×C4—181no—
994C2×C4—548no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—21no—
1015C2×C3—21no—
1016C2×C3—41no—
1017C2×C3—41no—
1018C2×C3—41no—
1019C2×C3—41no—
1020C2×C3—41no—
1021C2×C3—41no—
1022C2×C3—41no—
1023C2×C3—124no—
1024C2×C3—122no—
1025C2×C3—122no—
1026C2×C3#6385311yescharacteristic
1027C2×C3#6385411yescharacteristic
1028C2×C3#6388011yescharacteristic
1029C2×C3#6388111yescharacteristic
1030C2×C3C4×#62611yescharacteristic
1031C2×C3#6390411yescharacteristic
1032C2×C3#6391011yescharacteristic
1033C2×C3#6391211yescharacteristic
1034C2×C3#6391611yescharacteristic
1035C2×C3#6392111yescharacteristic
1036C2×C3#6392111yescharacteristic
1037C2×C3#6392211yescharacteristic
1038C2×C3#6395211yescharacteristic
1039C2×C3#6395211yescharacteristic
1040C2×C3#6395811yescharacteristic
1041C2×C3#6395811yescharacteristic
1042C2×C3#6395811yescharacteristic
1043C2×C3#6397411yescharacteristic
1044C2×C3#6397511yescharacteristic
1045C2×C3#6398111yescharacteristic
1046C2×C3#6398311yescharacteristic
1047D3—42no—
1048D3—188no—
1049D3—184no—
1050D3—184no—
1051D3—184no—
1052D3—364no—
1053D3—364no—
1054D3—368no—
1055C22—62no—
1056C22—62no—
1057C22—62no—
1058C22—121no—
1059C22—121no—
1060C22—121no—
1061C22—121no—
1062C22—274no—
1063C22—542no—
1064C22—542no—
1065C22—542no—
1066C22—542no—
1067C22—542no—
1068C22—542no—
1069C22D3×#62411yescharacteristic
1070C22D3×#62611yescharacteristic
1071C22#8895211yescharacteristic
1072C22#8895411yescharacteristic
1073C22#8895411yescharacteristic
1074C22#8895911yescharacteristic
1075C22#8896211yescharacteristic
1076C4—62no—
1077C4—121no—
1078C4—182no—
1079C4—182no—
1080C4—361no—
1081C3—21no—
1082C3—21no—
1083C3—21no—
1084C3—41no—
1085C3#1059127511yescharacteristic, complemented
1086C3#1059138711yescharacteristic, complemented
1087C3#1059172211yescharacteristic, complemented
1088C2—122no—
1089C2—544no—
1090C2#1172290611yescharacteristic
1091C2#1172293211yescharacteristic
1092C2#1172293511yescharacteristic
1093C2#1172294911yescharacteristic
1094C2#1172296311yescharacteristic
1095C2#1172296411yescharacteristic
1096C2#1172299611yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, cosocleC23×C33C23
prime radicalC22×#6291C2
hypocenterC33#386
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C22×#6289C2semidirect
3. C2×#88804C2semidirect
4. C2×C3×(C2×D3)⋊Dic3C2semidirect
5. C2×C3×(C2×D3)⋊Dic3C2semidirect
6. #11722082C2semidirect
7. C3×#63579C2semidirect
20. C2×#6291C4semidirect
43. C2×(C2×D3)⋊Dic3D3semidirect
44. C2×(C2×D3)⋊Dic3D3semidirect
50. #63579D3semidirect
65. C22×C32×D3C2×C4semidirect
73. C2×C3×C3⋊Dic3C2×C4semidirect
74. C2×C3×C3⋊Dic3D4semidirect
80. C2×C32×Dic3D4semidirect
164. C2×C3⋊(C3⋊D3)C22⋊C4semidirect
283. C22×C3×D3C4×D3semidirect
284. C22×C3×D3C4×D3semidirect
299. C2×C3⋊Dic3C4×D3semidirect
300. C2×C3⋊Dic3#67semidirect
345. C2×C3×Dic3D12semidirect
346. C2×C3×Dic3#67semidirect
581. C33#386semidirect
665. C22×D3#624semidirect
728. C2×Dic3#626semidirect
960. C32#4665semidirect
961. C32#4956semidirect
962. C32#4956semidirect
1085. C3#10591275semidirect
1086. C3#10591387semidirect
1087. C3#10591722semidirect

Maximal subgroups

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

subgroupindex
C22×#62912
C22×#62892
C2×#888042
C2×C3×(C2×D3)⋊Dic32
#117220822
C3×#635792
#105917223
#105913873
#105912753