Finite Group Databasebeta

← #13156830

Subgroups — #13156830

Order 1728.

1130 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88814C211yesmaximal, characteristic
2C2×#88803C211yesmaximal, characteristic
3C2×Dic3×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C3×#3722C211yesmaximal, characteristic
6#11722061C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8#10591284—31nomaximal
9#10591283—31nomaximal
10#10591266—31nomaximal
11C23×C3×C3⋊D3C2211yescharacteristic
12C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18#88814—22no—
19#88803C414yescomplemented
20Dic3×C3⋊Dic3—22no—
21C3×Dic3⋊Dic3—22no—
22C3×#3722—22no—
23C2×#3752—31no—
24C2×C4×C3⋊Dic3—31no—
25C2×C3×(C2×D3)⋊C4—31no—
26C2×C3×(C2×D3)⋊C4—31no—
27C2×C3×C4⋊Dic3—31no—
28C2×C3×Dic3⋊C4—31no—
29C2×Dic3⋊Dic3D311yescharacteristic, complemented
30C2×#3722—31no—
31C2×#3722D311yescharacteristic
32C2×(C2×D3)⋊Dic3—31no—
33C2×(C2×D3)⋊Dic3—31no—
34C2×(C2×D3)⋊Dic3—31no—
35C2×(C2×D3)⋊Dic3—31no—
36C2×(C2×D3)⋊Dic3—61no—
37C2×Dic32—31no—
38C2×Dic32—31no—
39C2×Dic32—61no—
40#63658—31no—
41C3×C3⋊#95—31no—
42C3×C3⋊#95—31no—
43#63579—31no—
44#63579—31no—
45#63579—61no—
46#63579D311yescharacteristic, complemented
47C23×C33C2311yescharacteristic
48C22×C3×C3⋊D3—21no—
49C22×C3×C3⋊D3—21no—
50C22×C3×C3⋊D3—21no—
51C22×C3×C3⋊D3—21no—
52C22×C3×C3⋊D3—21no—
53C22×C3×C3⋊D3—21no—
54C22×C3×C3⋊D3C2×C412yes—
55C2×C3⋊(C3⋊Dic3)—21no—
56C2×C3⋊(C3⋊Dic3)—21no—
57C2×C3⋊(C3⋊Dic3)C2×C412yes—
58C2×C3×C3⋊Dic3—21no—
59C2×C3×C3⋊Dic3—21no—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3—21no—
63C2×C3×C3⋊Dic3D412yes—
64C2×C32×Dic3—21no—
65C2×C32×Dic3—21no—
66C2×C32×Dic3—21no—
67C2×C32×Dic3—21no—
68C2×C32×Dic3—21no—
69C2×C32×Dic3—21no—
70C2×C32×Dic3—21no—
71C2×C32×Dic3C2×C412yes—
72C2×C32×Dic3D412yes—
73#4990—91no—
74#4945—91no—
75#4670—91no—
76C23×C3⋊D3C2×D311yescharacteristic
77C23×C3×D3—31no—
78C23×C3×D3—31no—
79C23×C3×D3—61no—
80C22×C32×C4—31no—
81C22×C32×C4—31no—
82C22×C32×C4—31no—
83C22×C3⋊Dic3—31no—
84C22×C3⋊Dic3—31no—
85C22×C3⋊Dic3—31no—
86C22×C3⋊Dic3—61no—
87C22×C3⋊Dic3—61no—
88C22×C3⋊Dic3—61no—
89C22×C3⋊Dic3—121no—
90C22×C3⋊Dic3C2×D311yescharacteristic
91C22×C3⋊Dic3C2×D311yescharacteristic
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—61no—
100C22×C3×Dic3—61no—
101C22×C3×Dic3C2×D311yescharacteristic
102C22×C3×Dic3C2×D311yescharacteristic
103C22×C3×Dic3C2×D311yescharacteristic
104C22×C3×Dic3C2×D311yescharacteristic
105C22×C3×Dic3C2×D311yescharacteristic
106C22×C3×Dic3C2×D311yescharacteristic
107#3752—34no—
108C4×C3⋊Dic3—62no—
109C3×(C2×D3)⋊C4—62no—
110C3×(C2×D3)⋊C4—62no—
111C3×C4⋊Dic3—62no—
112C3×Dic3⋊C4—62no—
113Dic3⋊Dic3—22no—
114#3722—22no—
115#3722—62no—
116(C2×D3)⋊Dic3—34no—
117(C2×D3)⋊Dic3—34no—
118(C2×D3)⋊Dic3—64no—
119(C2×D3)⋊Dic3—62no—
120(C2×D3)⋊Dic3—62no—
121Dic32—62no—
122Dic32—62no—
123Dic32—64no—
124C22×C33C22×C411yescharacteristic
125C22×C33C2×D411yescharacteristic
126C22×C33C2×D411yescharacteristic
127C22×C33#4111yescharacteristic
128C22×C33#4111yescharacteristic
129C22×C33#4111yescharacteristic
130C22×C33#4111yescharacteristic
131C2×C3×C3⋊D3—22no—
132C2×C3×C3⋊D3—22no—
133C2×C3×C3⋊D3—22no—
134C2×C3×C3⋊D3—41no—
135C2×C3×C3⋊D3—41no—
136C2×C3×C3⋊D3—41no—
137C2×C3×C3⋊D3—41no—
138C3⋊(C3⋊Dic3)—22no—
139C3×C3⋊Dic3—22no—
140C3×C3⋊Dic3—41no—
141C32×Dic3—22no—
142C32×Dic3—22no—
143C32×Dic3—41no—
144C2×C3×C4⋊C4—91no—
145C2×C3×C22⋊C4—91no—
146C2×#217—91no—
147C2×#217—91no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—91no—
151C2×(C2×D3)⋊C4—91no—
152C2×(C2×D3)⋊C4—91no—
153C2×(C2×D3)⋊C4—91no—
154C2×(C2×D3)⋊C4—181no—
155C2×C4⋊Dic3—31no—
156C2×Dic3⋊C4—31no—
157C2×C4×Dic3—91no—
158C2×C4×Dic3—91no—
159C2×C4×Dic3—91no—
160C2×C4×Dic3—181no—
161C3×#95—91no—
162C3⋊#95—31no—
163C3⋊#95—31no—
164C3⋊#95—91no—
165C3⋊#95—91no—
166C3⋊#95—91no—
167C3⋊#95—181no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—41no—
172C23×C32C22×D311yescharacteristic
173C23×C32C22×D311yescharacteristic
174C23×C32C22×D311yescharacteristic
175C22×C3⋊D3—21no—
176C22×C3⋊D3—21no—
177C22×C3⋊D3—21no—
178C22×C3⋊D3—21no—
179C22×C3⋊D3—21no—
180C22×C3⋊D3—21no—
181C22×C3⋊D3C4×D312yes—
182C22×C3×D3—32no—
183C22×C3×D3—32no—
184C22×C3×D3—62no—
185C22×C3×D3—62no—
186C22×C3×D3—62no—
187C22×C3×D3—61no—
188C22×C3×D3—61no—
189C22×C3×D3—61no—
190C22×C3×D3—61no—
191C22×C3×D3—61no—
192C22×C3×D3—61no—
193C22×C3×D3—61no—
194C22×C3×D3—61no—
195C22×C3×D3—61no—
196C22×C3×D3—61no—
197C22×C3×D3—61no—
198C22×C3×D3—61no—
199C22×C3×D3—121no—
200C22×C3×D3—121no—
201C22×C3×D3—121no—
202C22×C3×D3—121no—
203C2×C32×C4—32no—
204C2×C32×C4—32no—
205C2×C32×C4—61no—
206C2×C32×C4—61no—
207C2×C32×C4—61no—
208C2×C32×C4—61no—
209C2×C32×C4—61no—
210C2×C32×C4—61no—
211C2×C32×C4—61no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3—21no—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—32no—
218C2×C3⋊Dic3—32no—
219C2×C3⋊Dic3—32no—
220C2×C3⋊Dic3—62no—
221C2×C3⋊Dic3—62no—
222C2×C3⋊Dic3—62no—
223C2×C3⋊Dic3—61no—
224C2×C3⋊Dic3—61no—
225C2×C3⋊Dic3—62no—
226C2×C3⋊Dic3—62no—
227C2×C3⋊Dic3—61no—
228C2×C3⋊Dic3—61no—
229C2×C3⋊Dic3—61no—
230C2×C3⋊Dic3—61no—
231C2×C3⋊Dic3—122no—
232C2×C3⋊Dic3—121no—
233C2×C3⋊Dic3—121no—
234C2×C3⋊Dic3—121no—
235C2×C3⋊Dic3—121no—
236C2×C3⋊Dic3—122no—
237C2×C3⋊Dic3—122no—
238C2×C3⋊Dic3D1212yes—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—22no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—22no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—32no—
259C2×C3×Dic3—32no—
260C2×C3×Dic3—41no—
261C2×C3×Dic3—41no—
262C2×C3×Dic3—41no—
263C2×C3×Dic3—41no—
264C2×C3×Dic3—62no—
265C2×C3×Dic3—62no—
266C2×C3×Dic3—62no—
267C2×C3×Dic3—61no—
268C2×C3×Dic3—61no—
269C2×C3×Dic3—61no—
270C2×C3×Dic3—61no—
271C2×C3×Dic3—62no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—121no—
279C2×C3×Dic3—121no—
280C2×C3×Dic3C4×D312yes—
281C2×C3×Dic3C4×D312yes—
282C2×C3×Dic3#6712yes—
283C2×C3×Dic3#6712yes—
284#388—271noSylow
285C2×C33#11711yescharacteristic
286C2×C33C4×D411yescharacteristic
287C2×C33C4×D411yescharacteristic
288C2×C33#12111yescharacteristic
289C2×C33#12311yescharacteristic
290C2×C33#12411yescharacteristic
291C2×C33#12611yescharacteristic
292C3×C3⋊D3—42no—
293C24×C3—91no—
294C23×D3—31no—
295C23×D3—31no—
296C23×D3—61no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—91no—
307C22×C3×C4—91no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—91no—
315C22×Dic3—91no—
316C22×Dic3—91no—
317C22×Dic3—181no—
318C22×Dic3—181no—
319C22×Dic3—181no—
320C22×Dic3—361no—
321C22×Dic3D3211yescharacteristic
322C22×Dic3D3211yescharacteristic
323C22×Dic3D3211yescharacteristic
324C3×C4⋊C4—182no—
325C3×C22⋊C4—182no—
326#217—94no—
327#217—182no—
328(C2×D3)⋊C4—62no—
329(C2×D3)⋊C4—62no—
330(C2×D3)⋊C4—94no—
331(C2×D3)⋊C4—94no—
332(C2×D3)⋊C4—184no—
333(C2×D3)⋊C4—182no—
334(C2×D3)⋊C4—182no—
335C4⋊Dic3—62no—
336Dic3⋊C4—62no—
337C4×Dic3—182no—
338C4×Dic3—182no—
339C4×Dic3—182no—
340C4×Dic3—184no—
341C22×C32—21no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—21no—
346C22×C32—21no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32—21no—
353C22×C32—21no—
354C22×C32—21no—
355C22×C32—21no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—41no—
363C22×C32—41no—
364C22×C32—41no—
365C22×C32—41no—
366C22×C32—41no—
367C22×C32—41no—
368C22×C32—41no—
369C22×C32C2×C4×D311yescharacteristic
370C22×C32C2×C4×D311yescharacteristic
371C22×C32C2×C4×D311yescharacteristic
372C22×C32C2×D1211yescharacteristic
373C22×C32#23511yescharacteristic
374C22×C32#23511yescharacteristic
375C22×C32#23511yescharacteristic
376C22×C32D3×D411yescharacteristic
377C22×C32D3×D411yescharacteristic
378C22×C32D3×D411yescharacteristic
379C22×C32#23711yescharacteristic
380C22×C32#23711yescharacteristic
381C22×C32#23711yescharacteristic
382C22×C32#23711yescharacteristic
383C22×C32#23711yescharacteristic
384C22×C32#23711yescharacteristic
385C22×C32#23911yescharacteristic
386C22×C32#23911yescharacteristic
387C22×C32#23911yescharacteristic
388C22×C32C2×#6711yescharacteristic
389C22×C32C2×#6711yescharacteristic
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—22no—
393C2×C3⋊D3—41no—
394C2×C3⋊D3—41no—
395C2×C3⋊D3—41no—
396C2×C3⋊D3—41no—
397C2×C3×D3—64no—
398C2×C3×D3—62no—
399C2×C3×D3—62no—
400C2×C3×D3—62no—
401C2×C3×D3—62no—
402C2×C3×D3—62no—
403C2×C3×D3—62no—
404C2×C3×D3—122no—
405C2×C3×D3—122no—
406C2×C3×D3—122no—
407C2×C3×D3—122no—
408C2×C3×D3—122no—
409C2×C3×D3—122no—
410C2×C3×D3—121no—
411C2×C3×D3—121no—
412C2×C3×D3—121no—
413C2×C3×D3—121no—
414C2×C3×D3—121no—
415C2×C3×D3—121no—
416C2×C3×D3—121no—
417C2×C3×D3—121no—
418C32×C4—62no—
419C32×C4—62no—
420C32×C4—121no—
421C3⋊Dic3—22no—
422C3⋊Dic3—41no—
423C3⋊Dic3—62no—
424C3⋊Dic3—64no—
425C3⋊Dic3—62no—
426C3⋊Dic3—62no—
427C3⋊Dic3—122no—
428C3⋊Dic3—122no—
429C3⋊Dic3—124no—
430C3×Dic3—24no—
431C3×Dic3—22no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—42no—
436C3×Dic3—42no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—64no—
440C3×Dic3—62no—
441C3×Dic3—62no—
442C3×Dic3—122no—
443C3×Dic3—121no—
444C3×Dic3—121no—
445C2×C4⋊C4—91no—
446C2×C22⋊C4—91no—
447C2×C22⋊C4—271no—
448C2×C22⋊C4—271no—
449C2×C42—271no—
450#95—91no—
451#95—271no—
452C33#38811yescharacteristic, complemented, Sylow
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—41no—
457C23×C3—92no—
458C23×C3—181no—
459C23×C3—181no—
460C23×C3—181no—
461C23×C3—181no—
462C23×C3—181no—
463C23×C3—181no—
464C23×C3C2×D3211yescharacteristic
465C23×C3C2×D3211yescharacteristic
466C23×C3C2×D3211yescharacteristic
467C22×D3—32no—
468C22×D3—32no—
469C22×D3—62no—
470C22×D3—62no—
471C22×D3—62no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—121no—
485C22×D3—121no—
486C22×D3—121no—
487C22×D3—121no—
488C2×C3×C4—32no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—62no—
493C2×C3×C4—62no—
494C2×C3×C4—62no—
495C2×C3×C4—62no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—62no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—92no—
512C2×C3×C4—121no—
513C2×C3×C4—121no—
514C2×C3×C4—121no—
515C2×C3×C4—121no—
516C2×C3×C4—181no—
517C2×C3×C4—181no—
518C2×C3×C4—181no—
519C2×C3×C4—181no—
520C2×C3×C4—181no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—32no—
529C2×Dic3—32no—
530C2×Dic3—62no—
531C2×Dic3—62no—
532C2×Dic3—62no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—62no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—92no—
545C2×Dic3—92no—
546C2×Dic3—92no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—182no—
550C2×Dic3—182no—
551C2×Dic3—182no—
552C2×Dic3—182no—
553C2×Dic3—182no—
554C2×Dic3—181no—
555C2×Dic3—181no—
556C2×Dic3—181no—
557C2×Dic3—181no—
558C2×Dic3—181no—
559C2×Dic3—181no—
560C2×Dic3—362no—
561C2×Dic3—361no—
562C2×Dic3—361no—
563C2×Dic3—361no—
564C2×Dic3—361no—
565C2×Dic3—362no—
566C2×Dic3—362no—
567C2×Dic3#62412yes—
568C2×Dic3#62512yes—
569C2×C32—21no—
570C2×C32—21no—
571C2×C32—21no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—21no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—21no—
588C2×C32—21no—
589C2×C32—21no—
590C2×C32—41no—
591C2×C32—41no—
592C2×C32—41no—
593C2×C32—41no—
594C2×C32—41no—
595C2×C32—41no—
596C2×C32—41no—
597C2×C32C4×D1211yescharacteristic
598C2×C32#87711yescharacteristic
599C2×C32#87911yescharacteristic
600C2×C32#67⋊C411yescharacteristic
601C2×C32#67⋊C411yescharacteristic
602C2×C32#88311yescharacteristic
603C2×C32#88511yescharacteristic
604C2×C32#88611yescharacteristic
605C2×C32#89211yescharacteristic
606C2×C32#89211yescharacteristic
607C2×C32#89311yescharacteristic
608C2×C32#89411yescharacteristic
609C2×C32#89511yescharacteristic
610C2×C32#89811yescharacteristic
611C2×C32#89811yescharacteristic
612C2×C32C4×#6711yescharacteristic
613C2×C32C4×#6711yescharacteristic
614C2×C32#93611yescharacteristic
615C2×C32#93911yescharacteristic
616C2×C32#93911yescharacteristic
617C2×C32#94711yescharacteristic
618C3⋊D3—42no—
619C3×D3—124no—
620C3×D3—122no—
621C3×D3—122no—
622C24—91no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—91no—
627C22×C4—91no—
628C22×C4—271no—
629C4⋊C4—182no—
630C22⋊C4—182no—
631C22⋊C4—274no—
632C22⋊C4—542no—
633C42—542no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—182no—
663C22×C3—182no—
664C22×C3—182no—
665C22×C3—361no—
666C22×C3—361no—
667C22×C3—361no—
668C22×C3—361no—
669C22×C3#379511yescharacteristic
670C22×C3#379611yescharacteristic
671C22×C3#379611yescharacteristic
672C22×C3#379611yescharacteristic
673C22×C3#379611yescharacteristic
674C22×C3#379611yescharacteristic
675C22×C3#379811yescharacteristic
676C22×C3#379911yescharacteristic
677C22×C3C4×D3211yescharacteristic
678C22×C3C4×D3211yescharacteristic
679C22×C3D3×D1211yescharacteristic
680C22×C3D3×D1211yescharacteristic
681C22×C3#380411yescharacteristic
682C22×C3#380411yescharacteristic
683C22×C3#380511yescharacteristic
684C22×C3#380511yescharacteristic
685C22×C3C2×#62411yescharacteristic
686C22×C3C2×#62511yescharacteristic
687C22×C3D3×#6711yescharacteristic
688C22×C3D3×#6711yescharacteristic
689C22×C3#381111yescharacteristic
690C2×D3—64no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—62no—
694C2×D3—62no—
695C2×D3—62no—
696C2×D3—62no—
697C2×D3—122no—
698C2×D3—122no—
699C2×D3—122no—
700C2×D3—122no—
701C2×D3—122no—
702C2×D3—122no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C3×C4—64no—
712C3×C4—62no—
713C3×C4—62no—
714C3×C4—62no—
715C3×C4—62no—
716C3×C4—122no—
717C3×C4—122no—
718C3×C4—121no—
719C3×C4—121no—
720C3×C4—182no—
721C3×C4—361no—
722Dic3—22no—
723Dic3—22no—
724Dic3—41no—
725Dic3—64no—
726Dic3—62no—
727Dic3—62no—
728Dic3—122no—
729Dic3—121no—
730Dic3—121no—
731Dic3—184no—
732Dic3—182no—
733Dic3—182no—
734Dic3—182no—
735Dic3—362no—
736Dic3—362no—
737Dic3—364no—
738C32—21no—
739C32—21no—
740C32—21no—
741C32—41no—
742C32#467011yescharacteristic, complemented
743C32#494511yescharacteristic, complemented
744C32#499011yescharacteristic, complemented
745C23—92no—
746C23—181no—
747C23—181no—
748C23—181no—
749C23—181no—
750C23—181no—
751C23—181no—
752C23D3311yescharacteristic
753C2×C4—32no—
754C2×C4—32no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—92no—
763C2×C4—181no—
764C2×C4—181no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4—181no—
768C2×C4—272no—
769C2×C4—541no—
770C2×C4—541no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—41no—
795C2×C3—41no—
796C2×C3—41no—
797C2×C3—41no—
798C2×C3—41no—
799C2×C3—362no—
800C2×C3#6384811yescharacteristic
801C2×C3#6384911yescharacteristic
802C2×C3#6385311yescharacteristic
803C2×C3#6385811yescharacteristic
804C2×C3#6386211yescharacteristic
805C2×C3#6386311yescharacteristic
806C2×C3#6387811yescharacteristic
807C2×C3#6387811yescharacteristic
808C2×C3#6387911yescharacteristic
809C2×C3#6388011yescharacteristic
810C2×C3#6388111yescharacteristic
811C2×C3#6388611yescharacteristic
812C2×C3#6388611yescharacteristic
813C2×C3#6389011yescharacteristic
814C2×C3#6389111yescharacteristic
815C2×C3#6389411yescharacteristic
816C2×C3C4×#62511yescharacteristic
817C2×C3#6390711yescharacteristic
818C2×C3#6395211yescharacteristic
819C2×C3#6395911yescharacteristic
820C2×C3#6398011yescharacteristic
821D3—124no—
822D3—122no—
823D3—122no—
824C22—182no—
825C22—182no—
826C22—182no—
827C22—361no—
828C22—361no—
829C22—361no—
830C22—361no—
831C22D3×#62411yescharacteristic
832C22D3×#62511yescharacteristic
833C22#8895511yescharacteristic
834C22#8896011yescharacteristic
835C22#8896211yescharacteristic
836C22#8896411yescharacteristic
837C22#8896411yescharacteristic
838C4—62no—
839C4—62no—
840C4—121no—
841C4—182no—
842C4—361no—
843C4—542no—
844C3—21no—
845C3—21no—
846C3—21no—
847C3—41no—
848C3#1059126611yescharacteristic, complemented
849C3#1059128311yescharacteristic, complemented
850C3#1059128411yescharacteristic, complemented
851C2—362no—
852C2#1172292111yescharacteristic
853C2#1172293011yescharacteristic
854C2#1172293711yescharacteristic
855C2#1172295511yescharacteristic
856C2#1172299711yescharacteristic
857C2#1172300111yescharacteristic
858C2#1172302511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, cosocleC23×C33C23
prime radicalC23×C3×C3⋊D3C22
hypocenterC33#388
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
3. C2×Dic3×C3⋊Dic3C2semidirect
4. C2×C3×Dic3⋊Dic3C2semidirect
6. #11722061C2semidirect
7. C3×#63579C2semidirect
19. #88803C4semidirect
29. C2×Dic3⋊Dic3D3semidirect
46. #63579D3semidirect
452. C33#388semidirect
742. C32#4670semidirect
743. C32#4945semidirect
744. C32#4990semidirect
848. C3#10591266semidirect
849. C3#10591283semidirect
850. C3#10591284semidirect

Maximal subgroups

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

subgroupindex
C2×#888142
C2×#888032
C2×Dic3×C3⋊Dic32
C2×C3×Dic3⋊Dic32
C2×C3×#37222
#117220612
C3×#635792
#105912843
#105912833
#105912663