Finite Group Databasebeta

← #13170753

Subgroups — #13170753

Order 1728.

1592 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88960C211yesmaximal, characteristic, complemented
2C2×#88949C211yesmaximal, characteristic, complemented
3#11723701C211yesmaximal, characteristic, complemented
4#11723523C211yesmaximal, characteristic, complemented
5#11723483C211yesmaximal, characteristic, complemented
6Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
7C3×#63910C211yesmaximal, characteristic, complemented
8C3×#63880C211yesmaximal, characteristic, complemented
9C3×#63836C211yesmaximal, characteristic, complemented
10#11722997C211yesmaximal, characteristic, complemented
11#11722972C211yesmaximal, characteristic, complemented
12#11722962C211yesmaximal, characteristic, complemented
13#11722951C211yesmaximal, characteristic, complemented
14#11722934C211yesmaximal, characteristic, complemented
15Dic3×#626C211yesmaximal, characteristic, complemented
16#10594626—31nomaximal
17#10594286—31nomaximal
18#10593997—31nomaximal
19C22×#1113C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6293C2211yescharacteristic, complemented
24C2×#6290C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
29C2×C3×#626C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic, complemented
32C2×C3×#624C2211yescharacteristic
33C2×C3×#624C2211yescharacteristic
34C2×C3×#624C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic, complemented
36#88960—24no—
37#88949—24no—
38C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43C32×C4×Dic3C2211yescharacteristic, complemented
44#88814C2211yescharacteristic
45#88807C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic, complemented
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic
54C3×#3722C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×#3804—31no—
57C2×C4×D32—31no—
58C2×C4×D32—31no—
59C2×C4×D32—31no—
60C2×#3798—31no—
61C2×#3795—31no—
62#64106—31no—
63#64092—31no—
64C4×C4⋊(C3⋊D3)—31no—
65C3×#895—31no—
66C3×#892—31no—
67C3×#884—31no—
68C3×#67⋊C4—31no—
69C3×C4×D12—31no—
70C3×#872—31no—
71#63983—31no—
72Dic3×#67—31no—
73#63970—31no—
74#63923—31no—
75#63922—31no—
76#63922—31no—
77#63922—31no—
78#63922—31no—
79#63916—31no—
80#63910D311yescharacteristic, complemented
81C4×#626—31no—
82C4×#626—31no—
83#63895—31no—
84#63893—31no—
85#63893—31no—
86#63893—61no—
87Dic3×D12—31no—
88Dic3×D12—31no—
89Dic3×D12—31no—
90Dic3×D12—61no—
91#63891—31no—
92#63891—31no—
93#63891—31no—
94#63891—61no—
95#63890—31no—
96#63886—31no—
97#63880—31no—
98#63880D311yescharacteristic, complemented
99#63879—31no—
100#63857—31no—
101#63853—31no—
102#63851—31no—
103#63836D311yescharacteristic, complemented
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×#1113—22no—
110C2×#1113—22no—
111C2×#1113—22no—
112C2×C33×C4C2311yescharacteristic
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4⋊(C3⋊D3)—22no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6295—22no—
124#6295—22no—
125#6293—22no—
126#6290—22no—
127Dic3×C3⋊D3—22no—
128Dic3×C3⋊D3—22no—
129Dic3×C3⋊D3—22no—
130Dic3×C3⋊D3—22no—
131C3×#626—22no—
132C3×#626—22no—
133C3×#626—22no—
134C3×#624—22no—
135C3×#624—22no—
136C3×#624D414yescomplemented
137C3×D3×Dic3—22no—
138#5606—91no—
139#5547—91no—
140#5524—91no—
141C22×D32—31no—
142C22×D32—31no—
143C22×D32—31no—
144C2×#638—31no—
145C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
146C2×C4×C3⋊D3—31no—
147C2×C4×C3⋊D3—31no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—31no—
150C2×#634—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C22×C3×Dic3—31no—
155C2×C3×D12—31no—
156C2×C3×D12—31no—
157C2×C3×D12—31no—
158C2×C3×D12—31no—
159C2×C3×D12—31no—
160C2×C3×D12—61no—
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×#627—31no—
169C2×#627—31no—
170C2×#627—61no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626C2×D311yescharacteristic
176C2×#626C2×D311yescharacteristic
177C2×#626C2×D311yescharacteristic, complemented
178C2×#625—31no—
179C2×#625—31no—
180C2×#625—31no—
181C2×#625—31no—
182C2×#625—61no—
183C2×#624C2×D311yescharacteristic
184C2×#624C2×D311yescharacteristic
185C2×#624C2×D311yescharacteristic
186#3804—64no—
187C2×D3×Dic3—31no—
188C2×D3×Dic3—31no—
189C2×D3×Dic3—31no—
190C2×D3×Dic3—31no—
191C2×D3×Dic3—31no—
192C2×D3×Dic3—31no—
193C2×D3×Dic3—31no—
194C2×D3×Dic3—31no—
195C2×D3×Dic3—61no—
196C2×D3×Dic3—61no—
197C2×D3×Dic3—61no—
198C2×D3×Dic3—61no—
199C2×D3×Dic3C2×D311yescharacteristic, complemented
200C4×D32—64no—
201C4×D32—64no—
202C4×D32—64no—
203#3798—64no—
204#3795—64no—
205C32×C4⋊C4—31no—
206C32×C22⋊C4—31no—
207C32×C42—31no—
208#3757—31no—
209#3752—31no—
210#3752—31no—
211#3752—31no—
212#3752C2×D311yescharacteristic
213#3752C2×D311yescharacteristic
214C4⋊(C3⋊Dic3)—31no—
215C4⋊(C3⋊Dic3)—31no—
216C4⋊(C3⋊Dic3)—31no—
217C4⋊(C3⋊Dic3)—31no—
218C4⋊(C3⋊Dic3)—61no—
219C4⋊(C3⋊Dic3)—61no—
220C4⋊(C3⋊Dic3)—61no—
221C4⋊(C3⋊Dic3)—121no—
222#3750—31no—
223C3×(C2×D3)⋊C4—21no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—31no—
227C3×(C2×D3)⋊C4—31no—
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—61no—
233C3×(C2×D3)⋊C4—61no—
234C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
235C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
236C3×C4⋊Dic3—31no—
237C3×C4⋊Dic3—31no—
238C3×Dic3⋊C4—21no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4C2×D311yescharacteristic, complemented
242C3×Dic3⋊C4C2×D311yescharacteristic, complemented
243C3×C4×Dic3—21no—
244C3×C4×Dic3—31no—
245C3×C4×Dic3—31no—
246C3×C4×Dic3C2×D311yescharacteristic, complemented
247C3×C4×Dic3C2×D311yescharacteristic, complemented
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—61no—
253Dic3⋊Dic3—61no—
254Dic3⋊Dic3C2×D311yescharacteristic, complemented
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722C2×D311yescharacteristic
258#3722C2×D311yescharacteristic, complemented
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3—61no—
272(C2×D3)⋊Dic3—61no—
273Dic32C2×D311yescharacteristic, complemented
274C22×C33C2411yescharacteristic
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—21no—
278C2×C3×C3⋊D3—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3—21no—
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3C2×D412yes—
285C2×C3×C3⋊D3#4112yescomplemented
286C2×C3×C3⋊D3#4112yescomplemented
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3—21no—
290#1113—28no—
291C33×C4—21no—
292C3⋊(C3⋊Dic3)—21no—
293C3⋊(C3⋊Dic3)—21no—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3—21no—
296C32×Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3C2×D412yes—
300C32×Dic3C2×D412yes—
301C2×#237—91no—
302C2×#235—91no—
303C2×#235—91no—
304C22×C4×D3—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×#121—91no—
308C3×C4×D4—91no—
309C3×#117—91no—
310#939—91no—
311#938—91no—
312#937—91no—
313#937—91no—
314#937—91no—
315D4×Dic3—91no—
316D4×Dic3—91no—
317C4×#67—91no—
318C4×#67—91no—
319#924—91no—
320#897—91no—
321#897—91no—
322#897—91no—
323#897—181no—
324#896—91no—
325#895—31no—
326#895—91no—
327#894—91no—
328#892—31no—
329#886—91no—
330#886—91no—
331#884—31no—
332#883—91no—
333#883—91no—
334#883—91no—
335#883—181no—
336#882—91no—
337#882—91no—
338#882—91no—
339#67⋊C4—31no—
340#67⋊C4—91no—
341#878—91no—
342C4×D12—31no—
343C4×D12—91no—
344C4×D12—91no—
345C4×D12—91no—
346C4×D12—91no—
347C4×D12—181no—
348#872—31no—
349C23×C32—31no—
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3⋊D3C22×D311yescharacteristic
352C22×C3⋊D3C22×D311yescharacteristic
353C22×C3⋊D3C22×D311yescharacteristic
354C22×C3×D3—21no—
355C22×C3×D3—31no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—31no—
359C22×C3×D3—31no—
360C22×C3×D3—31no—
361C22×C3×D3—31no—
362C22×C3×D3—31no—
363C22×C3×D3—61no—
364C22×C3×D3—61no—
365C22×C3×D3—61no—
366C22×C3×D3—61no—
367C22×C3×D3C22×D311yescharacteristic
368C22×C3×D3C22×D311yescharacteristic
369C2×D32—62no—
370C2×D32—62no—
371C2×D32—62no—
372C2×D32—62no—
373C2×D32—62no—
374C2×D32—62no—
375C2×D32—62no—
376C2×D32—62no—
377C2×D32—62no—
378C2×C32×C4—21no—
379C2×C32×C4—21no—
380C2×C32×C4—21no—
381C2×C32×C4—31no—
382C2×C32×C4—31no—
383C2×C32×C4—31no—
384C2×C32×C4—31no—
385C2×C32×C4—31no—
386C2×C32×C4—41no—
387C2×C32×C4C22×D311yescharacteristic
388C2×C32×C4C22×D311yescharacteristic
389C2×C32×C4C22×D311yescharacteristic
390#638—62no—
391C2×C3⋊Dic3—31no—
392C2×C3⋊Dic3—31no—
393C2×C3⋊Dic3—31no—
394C2×C3⋊Dic3—31no—
395C2×C3⋊Dic3—31no—
396C2×C3⋊Dic3—31no—
397C2×C3⋊Dic3—61no—
398C2×C3⋊Dic3—61no—
399C2×C3⋊Dic3—61no—
400C2×C3⋊Dic3—61no—
401C2×C3⋊Dic3—61no—
402C2×C3⋊Dic3—61no—
403C2×C3⋊Dic3—121no—
404C2×C3⋊Dic3—121no—
405C2×C3⋊Dic3C22×D311yescharacteristic
406C2×C3⋊Dic3C22×D311yescharacteristic
407C4⋊(C3⋊D3)—22no—
408C4×C3⋊D3—62no—
409C4×C3⋊D3—62no—
410C4×C3⋊D3—62no—
411C4×C3⋊D3—62no—
412#634—62no—
413C3×#67—62no—
414C3×#67—62no—
415C3×#67—62no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—21no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—62no—
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C3×D12—62no—
439C3×D12—62no—
440C3×D12—64no—
441C3×D12—62no—
442C3×D12—62no—
443C3×D12—62no—
444C3×C4×D3—34no—
445C3×C4×D3—34no—
446C3×C4×D3—62no—
447C3×C4×D3—62no—
448C3×C4×D3—62no—
449C3×C4×D3—62no—
450C3×C4×D3—62no—
451#627—62no—
452#627—62no—
453#627—122no—
454#626—22no—
455#626—22no—
456#626—22no—
457#626—62no—
458#626—62no—
459#626—62no—
460#626—62no—
461#625—62no—
462#625—62no—
463#625—62no—
464#625—62no—
465#625—122no—
466#624—22no—
467#624—22no—
468#624D1214yescomplemented
469D3×Dic3—22no—
470D3×Dic3—62no—
471D3×Dic3—62no—
472D3×Dic3—62no—
473D3×Dic3—62no—
474D3×Dic3—62no—
475D3×Dic3—62no—
476D3×Dic3—62no—
477D3×Dic3—62no—
478D3×Dic3—122no—
479D3×Dic3—122no—
480D3×Dic3—122no—
481D3×Dic3—122no—
482#525—271noSylow
483C2×C33C22×D411yescharacteristic
484C2×C33C2×#4111yescharacteristic
485C2×C33C2×#4111yescharacteristic
486C3×C3⋊D3—22no—
487C3×C3⋊D3—22no—
488C3×C3⋊D3—22no—
489C3×C3⋊D3—41no—
490C32×D3—41no—
491C23×D3—91no—
492C23×D3—91no—
493C23×D3—91no—
494C2×C3×D4—91no—
495C2×C3×D4—91no—
496C2×C3×D4—91no—
497C2×C3×D4—91no—
498C22×C3×C4—91no—
499C22×C3×C4—91no—
500C22×C3×C4—91no—
501C22×C3×C4—91no—
502C2×#67—31no—
503C2×#67—31no—
504C2×#67—31no—
505C2×#67—91no—
506C2×#67—91no—
507C2×#67—91no—
508C2×#67—91no—
509C2×#67—91no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—181no—
513C22×Dic3—31no—
514C22×Dic3—91no—
515C22×Dic3—91no—
516C22×Dic3—91no—
517C22×Dic3—91no—
518#237—184no—
519#235—184no—
520#235—184no—
521C2×D12—31no—
522C2×D12—31no—
523C2×D12—31no—
524C2×D12—31no—
525C2×D12—31no—
526C2×D12—61no—
527C2×D12—91no—
528C2×D12—91no—
529C2×C4×D3—31no—
530C2×C4×D3—31no—
531C2×C4×D3—31no—
532C2×C4×D3—31no—
533C2×C4×D3—31no—
534C2×C4×D3—31no—
535C2×C4×D3—31no—
536C2×C4×D3—91no—
537C2×C4×D3—91no—
538C2×C4×D3—91no—
539C2×C4×D3—91no—
540C2×C4×D3—91no—
541C2×C4×D3—91no—
542C2×C4×D3—91no—
543C2×C4×D3—91no—
544C2×C4×D3—181no—
545C2×C4×D3—181no—
546C2×C4×D3—181no—
547C2×C4×D3—181no—
548C2×C4×D3—184no—
549C2×C4×D3—184no—
550C2×C4×D3—184no—
551C2×Dic6—91no—
552C2×Dic6—91no—
553C2×Dic6—91no—
554C2×Dic6—181no—
555C3×C4⋊C4—31no—
556C3×C4⋊C4—31no—
557C3×C4⋊C4—61no—
558C3×C4⋊C4—91no—
559C3×C4⋊C4—91no—
560C3×C22⋊C4—31no—
561C3×C22⋊C4—31no—
562C3×C22⋊C4—61no—
563C3×C22⋊C4—91no—
564C3×C22⋊C4—91no—
565C3×C22⋊C4—91no—
566C3×C22⋊C4—91no—
567C3×C42—31no—
568C3×C42—31no—
569C3×C42—61no—
570C3×C42—91no—
571#217—91no—
572#217—91no—
573#217—91no—
574#217—91no—
575#217—91no—
576#217—91no—
577#217—181no—
578(C2×D3)⋊C4—31no—
579(C2×D3)⋊C4—31no—
580(C2×D3)⋊C4—31no—
581(C2×D3)⋊C4—31no—
582(C2×D3)⋊C4—31no—
583(C2×D3)⋊C4—31no—
584(C2×D3)⋊C4—31no—
585(C2×D3)⋊C4—31no—
586(C2×D3)⋊C4—61no—
587(C2×D3)⋊C4—61no—
588(C2×D3)⋊C4—91no—
589(C2×D3)⋊C4—91no—
590(C2×D3)⋊C4—91no—
591(C2×D3)⋊C4—91no—
592(C2×D3)⋊C4—91no—
593(C2×D3)⋊C4—91no—
594(C2×D3)⋊C4—91no—
595(C2×D3)⋊C4—91no—
596(C2×D3)⋊C4—91no—
597(C2×D3)⋊C4—181no—
598(C2×D3)⋊C4—181no—
599(C2×D3)⋊C4—181no—
600(C2×D3)⋊C4D3211yescharacteristic, complemented
601C4⋊Dic3—31no—
602C4⋊Dic3—31no—
603C4⋊Dic3—91no—
604C4⋊Dic3—91no—
605C4⋊Dic3—91no—
606C4⋊Dic3—91no—
607C4⋊Dic3—91no—
608C4⋊Dic3—91no—
609C4⋊Dic3—181no—
610C4⋊Dic3—181no—
611C4⋊Dic3—181no—
612C4⋊Dic3—181no—
613C4⋊Dic3—361no—
614Dic3⋊C4—31no—
615Dic3⋊C4—31no—
616Dic3⋊C4—91no—
617Dic3⋊C4—91no—
618Dic3⋊C4—91no—
619Dic3⋊C4—181no—
620Dic3⋊C4D3211yescharacteristic, complemented
621C4×Dic3—31no—
622C4×Dic3—31no—
623C4×Dic3D3211yescharacteristic, complemented
624C22×C32—21no—
625C22×C32—21no—
626C22×C32—21no—
627C22×C32—41no—
628C22×C32—61no—
629C22×C32—61no—
630C22×C32—61no—
631C22×C32C23×D311yescharacteristic
632C22×C32C23×D311yescharacteristic
633C22×C32C23×D311yescharacteristic
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3⋊D3—21no—
638C2×C3⋊D3—21no—
639C2×C3⋊D3—21no—
640C2×C3⋊D3—21no—
641C2×C3⋊D3—21no—
642C2×C3⋊D3—21no—
643C2×C3⋊D3C2×D1212yes—
644C2×C3⋊D3#23512yescomplemented
645C2×C3⋊D3#23712yescomplemented
646C2×C3×D3—21no—
647C2×C3×D3—21no—
648C2×C3×D3—21no—
649C2×C3×D3—21no—
650C2×C3×D3—21no—
651C2×C3×D3—21no—
652C2×C3×D3—32no—
653C2×C3×D3—32no—
654C2×C3×D3—32no—
655C2×C3×D3—32no—
656C2×C3×D3—32no—
657C2×C3×D3—32no—
658C2×C3×D3—41no—
659C2×C3×D3—41no—
660C2×C3×D3—41no—
661C2×C3×D3—62no—
662C2×C3×D3—62no—
663C2×C3×D3—62no—
664C2×C3×D3—61no—
665C2×C3×D3—61no—
666C2×C3×D3—61no—
667C2×C3×D3—61no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—61no—
671C2×C3×D3—61no—
672C2×C3×D3—61no—
673C2×C3×D3—61no—
674C2×C3×D3—61no—
675C2×C3×D3—61no—
676C2×C3×D3—62no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—61no—
683C2×C3×D3—121no—
684C2×C3×D3—121no—
685C2×C3×D3—121no—
686C2×C3×D3—121no—
687C2×C3×D3—121no—
688C2×C3×D3—121no—
689C2×C3×D3—121no—
690C2×C3×D3—121no—
691D32—68no—
692D32—68no—
693D32—68no—
694C32×C4—21no—
695C32×C4—22no—
696C32×C4—21no—
697C32×C4—21no—
698C32×C4—32no—
699C32×C4—32no—
700C32×C4—41no—
701C32×C4—41no—
702C32×C4—42no—
703C32×C4—61no—
704C32×C4—61no—
705C32×C4—61no—
706C3⋊Dic3—21no—
707C3⋊Dic3—21no—
708C3⋊Dic3—61no—
709C3⋊Dic3—61no—
710C3⋊Dic3—61no—
711C3⋊Dic3—61no—
712C3⋊Dic3—61no—
713C3⋊Dic3—61no—
714C3⋊Dic3—121no—
715C3⋊Dic3—121no—
716C3⋊Dic3—121no—
717C3⋊Dic3—121no—
718C3⋊Dic3—121no—
719C3⋊Dic3—121no—
720C3⋊Dic3—241no—
721C3⋊Dic3—241no—
722C3×Dic3—21no—
723C3×Dic3—21no—
724C3×Dic3—21no—
725C3×Dic3—21no—
726C3×Dic3—21no—
727C3×Dic3—21no—
728C3×Dic3—22no—
729C3×Dic3—22no—
730C3×Dic3—41no—
731C3×Dic3—41no—
732C3×Dic3—41no—
733C3×Dic3—61no—
734C3×Dic3—61no—
735C3×Dic3—61no—
736C3×Dic3—61no—
737C3×Dic3—121no—
738C3×Dic3—121no—
739C3×Dic3C2×D1212yes—
740C3×Dic3C2×D1212yes—
741C3×Dic3D3×D412yes—
742C3×Dic3D3×D412yes—
743C2×#41—271no—
744C23×C4—271no—
745#123—271no—
746#123—271no—
747C22⋊Q8—271no—
748C22⋊Q8—271no—
749#121—91no—
750#121—271no—
751#120—271no—
752#120—271no—
753C4×D4—91no—
754C4×D4—271no—
755C4×D4—271no—
756C4×D4—271no—
757#117—91no—
758C33#52511yescharacteristic, complemented, Sylow
759C23×C3—31no—
760C23×C3—31no—
761C23×C3—61no—
762C23×C3—91no—
763C23×C3—91no—
764C23×C3—91no—
765C23×C3—91no—
766C22×D3—31no—
767C22×D3—31no—
768C22×D3—31no—
769C22×D3—31no—
770C22×D3—31no—
771C22×D3—31no—
772C22×D3—31no—
773C22×D3—31no—
774C22×D3—61no—
775C22×D3—61no—
776C22×D3—61no—
777C22×D3—61no—
778C22×D3—182no—
779C22×D3—182no—
780C22×D3—182no—
781C22×D3—182no—
782C22×D3—182no—
783C22×D3—182no—
784C22×D3—182no—
785C22×D3—182no—
786C22×D3—182no—
787C22×D3C2×D3211yescharacteristic
788C3×D4—182no—
789C3×D4—182no—
790C3×D4—182no—
791C3×D4—182no—
792C2×C3×C4—21no—
793C2×C3×C4—21no—
794C2×C3×C4—21no—
795C2×C3×C4—31no—
796C2×C3×C4—31no—
797C2×C3×C4—31no—
798C2×C3×C4—31no—
799C2×C3×C4—31no—
800C2×C3×C4—31no—
801C2×C3×C4—31no—
802C2×C3×C4—31no—
803C2×C3×C4—31no—
804C2×C3×C4—31no—
805C2×C3×C4—41no—
806C2×C3×C4—61no—
807C2×C3×C4—61no—
808C2×C3×C4—61no—
809C2×C3×C4—61no—
810C2×C3×C4—61no—
811C2×C3×C4—94no—
812C2×C3×C4—91no—
813C2×C3×C4—91no—
814C2×C3×C4—182no—
815C2×C3×C4—182no—
816C2×C3×C4—182no—
817C2×C3×C4C2×D3211yescharacteristic
818C2×C3×C4C2×D3211yescharacteristic
819C2×C3×C4C2×D3211yescharacteristic
820#67—62no—
821#67—62no—
822#67—62no—
823#67—182no—
824#67—182no—
825#67—182no—
826#67—182no—
827#67—182no—
828#67—182no—
829#67—182no—
830#67—362no—
831C2×Dic3—31no—
832C2×Dic3—31no—
833C2×Dic3—31no—
834C2×Dic3—31no—
835C2×Dic3—61no—
836C2×Dic3—61no—
837C2×Dic3—62no—
838C2×Dic3—91no—
839C2×Dic3—91no—
840C2×Dic3—91no—
841C2×Dic3—91no—
842C2×Dic3—91no—
843C2×Dic3—91no—
844C2×Dic3—181no—
845C2×Dic3—181no—
846C2×Dic3—181no—
847C2×Dic3—181no—
848C2×Dic3—181no—
849C2×Dic3—181no—
850C2×Dic3—182no—
851C2×Dic3—182no—
852C2×Dic3—182no—
853C2×Dic3—182no—
854C2×Dic3—361no—
855C2×Dic3—361no—
856C2×Dic3C2×D3211yescharacteristic
857C2×Dic3C2×D3211yescharacteristic
858C2×Dic3C2×D3211yescharacteristic
859C2×Dic3C2×D3211yescharacteristic
860C2×Dic3C2×D3211yescharacteristic
861D12—62no—
862D12—62no—
863D12—64no—
864D12—62no—
865D12—62no—
866D12—62no—
867D12—182no—
868D12—182no—
869C4×D3—34no—
870C4×D3—34no—
871C4×D3—62no—
872C4×D3—62no—
873C4×D3—62no—
874C4×D3—62no—
875C4×D3—62no—
876C4×D3—182no—
877C4×D3—182no—
878C4×D3—182no—
879C4×D3—182no—
880C4×D3—182no—
881C4×D3—182no—
882C4×D3—182no—
883C4×D3—182no—
884C4×D3—362no—
885C4×D3—362no—
886C4×D3—362no—
887C4×D3—362no—
888Dic6—182no—
889Dic6—182no—
890Dic6—182no—
891Dic6—362no—
892C2×C32—21no—
893C2×C32—21no—
894C2×C32—21no—
895C2×C32—21no—
896C2×C32—21no—
897C2×C32—21no—
898C2×C32—21no—
899C2×C32—21no—
900C2×C32—21no—
901C2×C32—41no—
902C2×C32—41no—
903C2×C32—41no—
904C2×C32—121no—
905C2×C32C22×D1211yescharacteristic
906C2×C32C2×#23511yescharacteristic
907C2×C32C2×D3×D411yescharacteristic
908C2×C32C2×D3×D411yescharacteristic
909C2×C32C2×#23711yescharacteristic
910C2×C32D3×#4111yescharacteristic
911C2×C32D3×#4111yescharacteristic
912C2×C32D3×#4111yescharacteristic
913C2×C32D3×#4111yescharacteristic
914C3⋊D3—22no—
915C3⋊D3—22no—
916C3⋊D3—22no—
917C3⋊D3—41no—
918C3×D3—41no—
919C3×D3—41no—
920C3×D3—62no—
921C3×D3—62no—
922C3×D3—62no—
923C3×D3—62no—
924C3×D3—62no—
925C3×D3—62no—
926C3×D3—81no—
927C3×D3—122no—
928C3×D3—122no—
929C3×D3—122no—
930C3×D3—122no—
931C3×D3—121no—
932C3×D3—121no—
933C24—271no—
934#41—544no—
935C2×Q8—271no—
936C2×D4—91no—
937C2×D4—91no—
938C2×D4—91no—
939C2×D4—91no—
940C2×D4—271no—
941C2×D4—271no—
942C2×D4—271no—
943C22×C4—91no—
944C22×C4—91no—
945C22×C4—91no—
946C22×C4—91no—
947C22×C4—271no—
948C22×C4—271no—
949C22×C4—271no—
950C22×C4—271no—
951C22×C4—544no—
952C4⋊C4—31no—
953C4⋊C4—91no—
954C4⋊C4—91no—
955C4⋊C4—271no—
956C4⋊C4—271no—
957C4⋊C4—271no—
958C22⋊C4—31no—
959C22⋊C4—91no—
960C22⋊C4—91no—
961C22⋊C4—91no—
962C22⋊C4—91no—
963C22⋊C4—271no—
964C22⋊C4—271no—
965C22⋊C4—271no—
966C22⋊C4—271no—
967C22⋊C4—271no—
968C42—31no—
969C42—91no—
970C22×C3—21no—
971C22×C3—21no—
972C22×C3—21no—
973C22×C3—41no—
974C22×C3—61no—
975C22×C3—61no—
976C22×C3—61no—
977C22×C3—61no—
978C22×C3—61no—
979C22×C3—61no—
980C22×C3—92no—
981C22×C3—92no—
982C22×C3—92no—
983C22×C3—121no—
984C22×C3—121no—
985C22×C3—121no—
986C22×C3—181no—
987C22×C3—181no—
988C22×C3—181no—
989C22×C3—181no—
990C22×C3—181no—
991C22×C3—181no—
992C22×C3—181no—
993C22×C3—181no—
994C22×C3—181no—
995C22×C3C22×D3211yescharacteristic
996C22×C3C22×D3211yescharacteristic
997C22×C3C22×D3211yescharacteristic
998C2×D3—21no—
999C2×D3—21no—
1000C2×D3—21no—
1001C2×D3—32no—
1002C2×D3—32no—
1003C2×D3—32no—
1004C2×D3—32no—
1005C2×D3—32no—
1006C2×D3—32no—
1007C2×D3—62no—
1008C2×D3—62no—
1009C2×D3—62no—
1010C2×D3—61no—
1011C2×D3—61no—
1012C2×D3—61no—
1013C2×D3—61no—
1014C2×D3—61no—
1015C2×D3—61no—
1016C2×D3—61no—
1017C2×D3—61no—
1018C2×D3—61no—
1019C2×D3—61no—
1020C2×D3—61no—
1021C2×D3—61no—
1022C2×D3—62no—
1023C2×D3—61no—
1024C2×D3—61no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—121no—
1030C2×D3—121no—
1031C2×D3—121no—
1032C2×D3—121no—
1033C2×D3—121no—
1034C2×D3—121no—
1035C2×D3—121no—
1036C2×D3—121no—
1037C2×D3—188no—
1038C2×D3—188no—
1039C2×D3—188no—
1040C3×C4—22no—
1041C3×C4—21no—
1042C3×C4—21no—
1043C3×C4—21no—
1044C3×C4—32no—
1045C3×C4—32no—
1046C3×C4—32no—
1047C3×C4—32no—
1048C3×C4—41no—
1049C3×C4—41no—
1050C3×C4—42no—
1051C3×C4—62no—
1052C3×C4—62no—
1053C3×C4—61no—
1054C3×C4—61no—
1055C3×C4—61no—
1056C3×C4—61no—
1057C3×C4—61no—
1058C3×C4—61no—
1059C3×C4—121no—
1060C3×C4—121no—
1061C3×C4—121no—
1062C3×C4—181no—
1063C3×C4—181no—
1064Dic3—21no—
1065Dic3—21no—
1066Dic3—21no—
1067Dic3—61no—
1068Dic3—61no—
1069Dic3—61no—
1070Dic3—61no—
1071Dic3—121no—
1072Dic3—121no—
1073Dic3—181no—
1074Dic3—181no—
1075Dic3—181no—
1076Dic3—181no—
1077Dic3—181no—
1078Dic3—181no—
1079Dic3—361no—
1080Dic3—361no—
1081Dic3—361no—
1082Dic3—361no—
1083Dic3—361no—
1084Dic3—361no—
1085Dic3—721no—
1086Dic3—721no—
1087Dic3D3×D1212yes—
1088Dic3D3×D1212yes—
1089C32—21no—
1090C32—21no—
1091C32—21no—
1092C32—41no—
1093C32#552411yescharacteristic, complemented
1094C32#554711yescharacteristic, complemented
1095C32#560611yescharacteristic, complemented
1096C23—31no—
1097C23—91no—
1098C23—91no—
1099C23—91no—
1100C23—91no—
1101C23—542no—
1102C23—542no—
1103C23—542no—
1104Q8—542no—
1105D4—182no—
1106D4—182no—
1107D4—182no—
1108D4—182no—
1109D4—542no—
1110D4—542no—
1111D4—542no—
1112C2×C4—31no—
1113C2×C4—31no—
1114C2×C4—31no—
1115C2×C4—31no—
1116C2×C4—31no—
1117C2×C4—94no—
1118C2×C4—91no—
1119C2×C4—91no—
1120C2×C4—182no—
1121C2×C4—182no—
1122C2×C4—182no—
1123C2×C4—271no—
1124C2×C4—271no—
1125C2×C4—542no—
1126C2×C4—542no—
1127C2×C4—542no—
1128C2×C4—542no—
1129C2×C4D3311yescharacteristic
1130C2×C3—21no—
1131C2×C3—21no—
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—21no—
1135C2×C3—21no—
1136C2×C3—21no—
1137C2×C3—21no—
1138C2×C3—21no—
1139C2×C3—41no—
1140C2×C3—41no—
1141C2×C3—41no—
1142C2×C3—121no—
1143C2×C3—121no—
1144C2×C3—182no—
1145C2×C3—182no—
1146C2×C3—182no—
1147C2×C3—241no—
1148C2×C3—361no—
1149C2×C3C2×D3×D1211yescharacteristic
1150C2×C3C2×D3×D1211yescharacteristic
1151C2×C3D3×#23511yescharacteristic
1152C2×C3D3×#23511yescharacteristic
1153C2×C3#6430611yescharacteristic
1154C2×C3D32×D411yescharacteristic
1155C2×C3D3×#23711yescharacteristic
1156C2×C3D3×#23711yescharacteristic
1157C2×C3#6431911yescharacteristic
1158D3—41no—
1159D3—62no—
1160D3—62no—
1161D3—62no—
1162D3—62no—
1163D3—62no—
1164D3—62no—
1165D3—122no—
1166D3—122no—
1167D3—122no—
1168D3—122no—
1169D3—121no—
1170D3—121no—
1171C22—61no—
1172C22—61no—
1173C22—61no—
1174C22—92no—
1175C22—92no—
1176C22—92no—
1177C22—181no—
1178C22—181no—
1179C22—181no—
1180C22—181no—
1181C22—181no—
1182C22—181no—
1183C22—181no—
1184C22—181no—
1185C22—181no—
1186C22—548no—
1187C22C2×D3311yescharacteristic
1188C4—21no—
1189C4—32no—
1190C4—32no—
1191C4—61no—
1192C4—61no—
1193C4—61no—
1194C4—181no—
1195C4—181no—
1196C4—541no—
1197C4—541no—
1198C3—21no—
1199C3—21no—
1200C3—21no—
1201C3—41no—
1202C3#1059399711yescharacteristic, complemented
1203C3#1059428611yescharacteristic, complemented
1204C3#1059462611yescharacteristic, complemented
1205C2—121no—
1206C2—182no—
1207C2—182no—
1208C2—182no—
1209C2—361no—
1210C2#1172438911yescharacteristic
1211C2D32×D1211yescharacteristic
1212C2#1172440711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88960C2semidirect
2. C2×#88949C2semidirect
3. #11723701C2semidirect
4. #11723523C2semidirect
5. #11723483C2semidirect
6. Dic3×C4⋊(C3⋊D3)C2semidirect
7. C3×#63910C2semidirect
8. C3×#63880C2semidirect
9. C3×#63836C2semidirect
10. #11722997C2semidirect
11. #11722972C2semidirect
12. #11722962C2semidirect
13. #11722951C2semidirect
14. #11722934C2semidirect
15. Dic3×#626C2semidirect
23. C2×#6293C22semidirect
28. C2×Dic3×C3⋊D3C22semidirect
31. C2×C3×#626C22semidirect
35. C2×C3×D3×Dic3C22semidirect
38. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
41. C32×(C2×D3)⋊C4C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. C32×C4×Dic3C22semidirect
45. #88807C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88803C22semidirect
50. (C2×D3)⋊(C3⋊Dic3)C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
54. C3×#3722C22semidirect
55. C3×Dic32C22semidirect
80. #63910D3semidirect
98. #63880D3semidirect
103. #63836D3semidirect
136. C3×#624D4semidirect
177. C2×#626C2×D3semidirect
199. C2×D3×Dic3C2×D3semidirect
234. C3×(C2×D3)⋊C4C2×D3semidirect
235. C3×(C2×D3)⋊C4C2×D3semidirect
241. C3×Dic3⋊C4C2×D3semidirect
242. C3×Dic3⋊C4C2×D3semidirect
246. C3×C4×Dic3C2×D3semidirect
247. C3×C4×Dic3C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
258. #3722C2×D3semidirect
273. Dic32C2×D3semidirect
285. C2×C3×C3⋊D3#41semidirect
286. C2×C3×C3⋊D3#41semidirect
468. #624D12semidirect
600. (C2×D3)⋊C4D32semidirect
620. Dic3⋊C4D32semidirect
623. C4×Dic3D32semidirect
644. C2×C3⋊D3#235semidirect
645. C2×C3⋊D3#237semidirect
758. C33#525semidirect
1093. C32#5524semidirect
1094. C32#5547semidirect
1095. C32#5606semidirect
1202. C3#10593997semidirect
1203. C3#10594286semidirect
1204. C3#10594626semidirect

Maximal subgroups

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

subgroupindex
C2×#889602
C2×#889492
#117237012
#117235232
#117234832
Dic3×C4⋊(C3⋊D3)2
C3×#639102
C3×#638802
C3×#638362
#117229972
#117229722
#117229622
#117229512
#117229342
Dic3×#6262
#105946263
#105942863
#105939973