Finite Group Databasebeta

← #13170735

Subgroups — #13170735

Order 1728.

1620 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88959C211yesmaximal, characteristic, complemented
2C2×D32×Dic3C211yesmaximal, characteristic, complemented
3#11723692C211yesmaximal, characteristic, complemented
4#11723479C211yesmaximal, characteristic, complemented
5#11723475C211yesmaximal, characteristic, complemented
6#11723471C211yesmaximal, characteristic, complemented
7C3×#63922C211yesmaximal, characteristic, complemented
8C3×Dic3×D12C211yesmaximal, characteristic, complemented
9C3×#63877C211yesmaximal, characteristic, complemented
10#11722989C211yesmaximal, characteristic, complemented
11#11722981C211yesmaximal, characteristic, complemented
12#11722966C211yesmaximal, characteristic, complemented
13#11722948C211yesmaximal, characteristic, complemented
14#11722932C211yesmaximal, characteristic, complemented
15Dic3×#626C211yesmaximal, characteristic, complemented
16#10595129—31nomaximal
17#10594078—31nomaximal
18#10593997—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6296C2211yescharacteristic, complemented
22C2×#6294C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6291C2211yescharacteristic, complemented
27C2×#6289C2211yescharacteristic, complemented
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic
30C2×D3×C3⋊Dic3C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic
32C2×C3×#625C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic, complemented
36#88959—24no—
37D32×Dic3—24no—
38#88859C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic
40C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41C3×#3750C2211yescharacteristic, complemented
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×C4×Dic3C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88814C2211yescharacteristic
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48#88804C2211yescharacteristic, complemented
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
50C3×#3724C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×#3804—31no—
57C2×#3804—31no—
58C22×D3×Dic3—31no—
59C22×D3×Dic3—31no—
60C2×C4×D32—31no—
61C2×#3798—31no—
62#64148—31no—
63#64095—31no—
64C4×C4⋊(C3⋊D3)—31no—
65C3×#937—31no—
66C3×D4×Dic3—31no—
67C3×#882—31no—
68C3×#877—31no—
69C3×C4×D12—31no—
70C3×#872—31no—
71#63982—31no—
72#63977—31no—
73#63977—31no—
74Dic3×#67—31no—
75#63971—31no—
76#63969—31no—
77#63962—31no—
78#63952—31no—
79#63923—31no—
80#63922D311yescharacteristic, complemented
81#63910—31no—
82C4×#626—31no—
83C4×#626—31no—
84#63899—31no—
85#63895—31no—
86#63893—31no—
87#63893—31no—
88#63893—31no—
89Dic3×D12—31no—
90Dic3×D12D311yescharacteristic, complemented
91#63891—31no—
92#63890—31no—
93#63890—31no—
94#63890—61no—
95#63886—31no—
96#63886—31no—
97#63886—31no—
98#63886—61no—
99#63880—31no—
100#63880—31no—
101#63880—31no—
102#63880—61no—
103#63877D311yescharacteristic, complemented
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×C3×D32—22no—
110C2×C3×D32—22no—
111C2×C3×D32—22no—
112C2×C33×C4C2311yescharacteristic
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C32×D12—22no—
123#6296—22no—
124#6294—22no—
125#6292—22no—
126#6291—22no—
127#6291—22no—
128#6291—22no—
129#6289—22no—
130Dic3×C3⋊D3—22no—
131D3×C3⋊Dic3—22no—
132D3×C3⋊Dic3—22no—
133C3×#626—22no—
134C3×#625—22no—
135C3×D3×Dic3—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3D414yescomplemented
138#5586—91no—
139#5547—91no—
140#5524—91no—
141C23×C3×D3—31no—
142C23×C3×D3—31no—
143C22×D32C2×D311yescharacteristic
144C2×C32×D4—31no—
145C2×#638—31no—
146C2×#638—31no—
147C2×#638—31no—
148C22×C3⋊Dic3—31no—
149C22×C3⋊Dic3—31no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C2×C3×D12—21no—
160C2×C3×D12—31no—
161C2×C3×D12C2×D311yescharacteristic
162C2×C3×D12C2×D311yescharacteristic
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×#627—31no—
167C2×#627—31no—
168C2×#627—31no—
169C2×#626—31no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—61no—
178C2×#626—61no—
179C2×#626—61no—
180C2×#626—61no—
181C2×#626C2×D311yescharacteristic
182C2×#625C2×D311yescharacteristic
183C2×#624—31no—
184C2×#624—31no—
185C2×#624—31no—
186C2×#624—61no—
187#3804—64no—
188#3804—64no—
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—31no—
196C2×D3×Dic3—31no—
197C2×D3×Dic3—64no—
198C2×D3×Dic3—64no—
199C2×D3×Dic3—61no—
200C2×D3×Dic3—61no—
201C2×D3×Dic3—61no—
202C2×D3×Dic3C2×D311yescharacteristic
203C2×D3×Dic3C2×D311yescharacteristic
204C2×D3×Dic3C2×D311yescharacteristic, complemented
205C4×D32—64no—
206#3798—64no—
207C32×C22⋊C4—31no—
208C32×C42—31no—
209#3757—31no—
210#3752—31no—
211#3752—31no—
212#3752—31no—
213#3752—31no—
214#3752—61no—
215#3752—61no—
216#3752—61no—
217#3752—121no—
218#3752C2×D311yescharacteristic
219C4⋊(C3⋊Dic3)—31no—
220C4⋊(C3⋊Dic3)—31no—
221C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
222#3750C2×D311yescharacteristic, complemented
223C3×#217—31no—
224C3×#217—31no—
225C3×#217—31no—
226C3×#217—31no—
227C3×(C2×D3)⋊C4—21no—
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—61no—
235C3×(C2×D3)⋊C4C2×D311yescharacteristic
236C3×(C2×D3)⋊C4C2×D311yescharacteristic
237C3×C4⋊Dic3—31no—
238C3×C4⋊Dic3—31no—
239C3×C4⋊Dic3—61no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—61no—
245C3×C4×Dic3—21no—
246C3×C4×Dic3—31no—
247C3×C4×Dic3—31no—
248C3×C4×Dic3C2×D311yescharacteristic, complemented
249C3×C4×Dic3C2×D311yescharacteristic, complemented
250#3724—31no—
251#3724C2×D311yescharacteristic, complemented
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—31no—
257Dic3⋊Dic3—31no—
258Dic3⋊Dic3—61no—
259Dic3⋊Dic3—61no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—61no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3C2×D311yescharacteristic
270(C2×D3)⋊Dic3C2×D311yescharacteristic
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
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#4112yescomplemented
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C2×C32×D3—21no—
285C2×C32×D3—21no—
286C2×C32×D3—21no—
287C2×C32×D3—21no—
288C2×C32×D3C2×D412yes—
289C2×C32×D3#4112yescomplemented
290C3×D32—28no—
291C33×C4—21no—
292C3⋊(C3⋊Dic3)—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3—21no—
296C3×C3⋊Dic3—21no—
297C3×C3⋊Dic3C2×D412yes—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3C2×D412yes—
301C23×Dic3—91no—
302C2×#237—91no—
303C2×#235—91no—
304C2×#235—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×#120—91no—
308C3×C4×D4—91no—
309C3×#117—91no—
310#953—91no—
311#939—91no—
312#939—91no—
313#939—91no—
314#939—181no—
315#937—31no—
316#935—91no—
317D4×Dic3—31no—
318D4×Dic3—91no—
319C4×#67—91no—
320C4×#67—91no—
321#897—91no—
322#897—91no—
323#896—91no—
324#895—91no—
325#895—91no—
326#894—91no—
327#886—91no—
328#886—91no—
329#886—91no—
330#886—181no—
331#884—91no—
332#883—91no—
333#882—31no—
334#882—91no—
335#882—91no—
336#67⋊C4—91no—
337#67⋊C4—91no—
338#878—91no—
339#878—91no—
340#878—91no—
341#877—31no—
342C4×D12—31no—
343C4×D12—91no—
344C4×D12—91no—
345C4×D12—91no—
346C4×D12—91no—
347C4×D12—181no—
348#872—31no—
349C23×C32—31no—
350C23×C32—31no—
351C23×C32—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—31no—
355C22×C3⋊D3—61no—
356C22×C3⋊D3—61no—
357C22×C3⋊D3—61no—
358C22×C3⋊D3—121no—
359C22×C3⋊D3C22×D311yescharacteristic
360C22×C3×D3—21no—
361C22×C3×D3—21no—
362C22×C3×D3—21no—
363C22×C3×D3—31no—
364C22×C3×D3—31no—
365C22×C3×D3—61no—
366C22×C3×D3—62no—
367C22×C3×D3—62no—
368C22×C3×D3—62no—
369C22×C3×D3—62no—
370C22×C3×D3—62no—
371C22×C3×D3—62no—
372C22×C3×D3C22×D311yescharacteristic
373C22×C3×D3C22×D311yescharacteristic
374C22×C3×D3C22×D311yescharacteristic
375C22×C3×D3C22×D311yescharacteristic
376C22×C3×D3C22×D311yescharacteristic
377C22×C3×D3C22×D311yescharacteristic
378C2×D32—22no—
379C2×D32—22no—
380C2×D32—22no—
381C32×D4—62no—
382C2×C32×C4—21no—
383C2×C32×C4—21no—
384C2×C32×C4—21no—
385C2×C32×C4—31no—
386C2×C32×C4—31no—
387C2×C32×C4—31no—
388C2×C32×C4—41no—
389C2×C32×C4C22×D311yescharacteristic
390C2×C32×C4C22×D311yescharacteristic
391C2×C32×C4C22×D311yescharacteristic
392#638—62no—
393#638—62no—
394#638—62no—
395C2×C3⋊Dic3—31no—
396C2×C3⋊Dic3—31no—
397C2×C3⋊Dic3—31no—
398C2×C3⋊Dic3—61no—
399C2×C3⋊Dic3—61no—
400C2×C3⋊Dic3—61no—
401C2×C3⋊Dic3—62no—
402C2×C3⋊Dic3—62no—
403C2×C3⋊Dic3—121no—
404C2×C3⋊Dic3C22×D311yescharacteristic
405C2×C3⋊Dic3C22×D311yescharacteristic
406C2×C3⋊Dic3C22×D311yescharacteristic
407C2×C3⋊Dic3C22×D311yescharacteristic
408C2×C3⋊Dic3C22×D311yescharacteristic
409C4⋊(C3⋊D3)—62no—
410C4×C3⋊D3—62no—
411C4×C3⋊D3—62no—
412C3×#67—62no—
413C3×#67—62no—
414C3×#67—62no—
415C2×C3×Dic3—21no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—34no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—62no—
435C2×C3×Dic3—62no—
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C3×D12—22no—
443C3×D12—22no—
444C3×D12—42no—
445C3×D12—62no—
446C3×C4×D3—34no—
447C3×C4×D3—62no—
448C3×C4×D3—62no—
449#627—62no—
450#627—62no—
451#627—62no—
452#626—22no—
453#626—62no—
454#626—62no—
455#626—64no—
456#626—62no—
457#626—62no—
458#626—62no—
459#626—62no—
460#626—62no—
461#626—62no—
462#626—122no—
463#626—122no—
464#626—122no—
465#625—22no—
466#624—62no—
467#624—62no—
468#624—62no—
469#624—122no—
470D3×Dic3—22no—
471D3×Dic3—22no—
472D3×Dic3—62no—
473D3×Dic3—62no—
474D3×Dic3—62no—
475D3×Dic3—62no—
476D3×Dic3—62no—
477D3×Dic3—62no—
478D3×Dic3—62no—
479D3×Dic3—62no—
480D3×Dic3—122no—
481D3×Dic3—122no—
482D3×Dic3—122no—
483D3×Dic3D1214yescomplemented
484#525—271noSylow
485C2×C33C22×D411yescharacteristic
486C2×C33C2×#4111yescharacteristic
487C2×C33C2×#4111yescharacteristic
488C3⋊(C3⋊D3)—41no—
489C3×C3⋊D3—22no—
490C32×D3—22no—
491C32×D3—22no—
492C32×D3—41no—
493C24×C3—91no—
494C23×D3—31no—
495C23×D3—31no—
496C2×C3×D4—31no—
497C2×C3×D4—31no—
498C2×C3×D4—61no—
499C2×C3×D4—91no—
500C2×C3×D4—91no—
501C22×C3×C4—91no—
502C22×C3×C4—91no—
503C22×C3×C4—91no—
504C2×#67—31no—
505C2×#67—31no—
506C2×#67—31no—
507C2×#67—91no—
508C2×#67—91no—
509C2×#67—91no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—181no—
515C2×#67—181no—
516C2×#67—181no—
517C22×Dic3—31no—
518C22×Dic3—31no—
519C22×Dic3—31no—
520C22×Dic3—91no—
521C22×Dic3—91no—
522C22×Dic3—91no—
523C22×Dic3—91no—
524C22×Dic3—91no—
525C22×Dic3—91no—
526C22×Dic3—181no—
527C22×Dic3—181no—
528C22×Dic3—184no—
529#237—184no—
530#235—184no—
531#235—184no—
532C2×D12—31no—
533C2×D12—91no—
534C2×D12—91no—
535C2×D12—91no—
536C2×D12—91no—
537C2×D12—91no—
538C2×D12—181no—
539C2×D12D3211yescharacteristic
540C2×C4×D3—31no—
541C2×C4×D3—31no—
542C2×C4×D3—31no—
543C2×C4×D3—91no—
544C2×C4×D3—91no—
545C2×C4×D3—91no—
546C2×C4×D3—91no—
547C2×C4×D3—91no—
548C2×C4×D3—91no—
549C2×C4×D3—91no—
550C2×C4×D3—91no—
551C2×C4×D3—91no—
552C2×C4×D3—181no—
553C2×C4×D3—181no—
554C2×C4×D3—184no—
555C2×C4×D3—184no—
556C2×Dic6—91no—
557C2×Dic6—91no—
558C2×Dic6—91no—
559C3×C4⋊C4—91no—
560C3×C4⋊C4—91no—
561C3×C4⋊C4—91no—
562C3×C22⋊C4—31no—
563C3×C22⋊C4—31no—
564C3×C22⋊C4—61no—
565C3×C22⋊C4—91no—
566C3×C22⋊C4—91no—
567C3×C22⋊C4—91no—
568C3×C22⋊C4—91no—
569C3×C22⋊C4—91no—
570C3×C42—31no—
571C3×C42—31no—
572C3×C42—61no—
573C3×C42—91no—
574#217—31no—
575#217—31no—
576#217—31no—
577#217—31no—
578#217—91no—
579#217—91no—
580#217—91no—
581#217—181no—
582(C2×D3)⋊C4—31no—
583(C2×D3)⋊C4—31no—
584(C2×D3)⋊C4—31no—
585(C2×D3)⋊C4—31no—
586(C2×D3)⋊C4—31no—
587(C2×D3)⋊C4—31no—
588(C2×D3)⋊C4—61no—
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—91no—
598(C2×D3)⋊C4—181no—
599(C2×D3)⋊C4—181no—
600(C2×D3)⋊C4—181no—
601(C2×D3)⋊C4—181no—
602(C2×D3)⋊C4—361no—
603(C2×D3)⋊C4D3211yescharacteristic
604C4⋊Dic3—31no—
605C4⋊Dic3—31no—
606C4⋊Dic3—61no—
607C4⋊Dic3—91no—
608C4⋊Dic3—91no—
609C4⋊Dic3—91no—
610C4⋊Dic3—91no—
611C4⋊Dic3—91no—
612C4⋊Dic3—181no—
613C4⋊Dic3—181no—
614Dic3⋊C4—31no—
615Dic3⋊C4—31no—
616Dic3⋊C4—31no—
617Dic3⋊C4—31no—
618Dic3⋊C4—61no—
619Dic3⋊C4—91no—
620Dic3⋊C4—91no—
621Dic3⋊C4—91no—
622Dic3⋊C4—91no—
623C4×Dic3—31no—
624C4×Dic3—31no—
625C4×Dic3D3211yescharacteristic, complemented
626C22×C32—21no—
627C22×C32—21no—
628C22×C32—21no—
629C22×C32—32no—
630C22×C32—32no—
631C22×C32—41no—
632C22×C32—61no—
633C22×C32—61no—
634C22×C32—61no—
635C22×C32—61no—
636C22×C32—61no—
637C22×C32—61no—
638C22×C32—61no—
639C22×C32C23×D311yescharacteristic
640C22×C32C23×D311yescharacteristic
641C22×C32C23×D311yescharacteristic
642C2×C3⋊D3—21no—
643C2×C3⋊D3—21no—
644C2×C3⋊D3—61no—
645C2×C3⋊D3—62no—
646C2×C3⋊D3—61no—
647C2×C3⋊D3—61no—
648C2×C3⋊D3—61no—
649C2×C3⋊D3—61no—
650C2×C3⋊D3—61no—
651C2×C3⋊D3—61no—
652C2×C3⋊D3—61no—
653C2×C3⋊D3—61no—
654C2×C3⋊D3—121no—
655C2×C3⋊D3—121no—
656C2×C3⋊D3—122no—
657C2×C3⋊D3—121no—
658C2×C3⋊D3—121no—
659C2×C3⋊D3—121no—
660C2×C3⋊D3—121no—
661C2×C3⋊D3—121no—
662C2×C3⋊D3—121no—
663C2×C3⋊D3—241no—
664C2×C3⋊D3—241no—
665C2×C3⋊D3#23712yescomplemented
666C2×C3×D3—21no—
667C2×C3×D3—21no—
668C2×C3×D3—21no—
669C2×C3×D3—21no—
670C2×C3×D3—21no—
671C2×C3×D3—21no—
672C2×C3×D3—21no—
673C2×C3×D3—21no—
674C2×C3×D3—21no—
675C2×C3×D3—21no—
676C2×C3×D3—21no—
677C2×C3×D3—21no—
678C2×C3×D3—21no—
679C2×C3×D3—21no—
680C2×C3×D3—22no—
681C2×C3×D3—22no—
682C2×C3×D3—32no—
683C2×C3×D3—32no—
684C2×C3×D3—41no—
685C2×C3×D3—41no—
686C2×C3×D3—41no—
687C2×C3×D3—41no—
688C2×C3×D3—41no—
689C2×C3×D3—41no—
690C2×C3×D3—41no—
691C2×C3×D3—62no—
692C2×C3×D3—68no—
693C2×C3×D3—68no—
694C2×C3×D3—61no—
695C2×C3×D3—61no—
696C2×C3×D3—61no—
697C2×C3×D3—61no—
698C2×C3×D3—121no—
699C2×C3×D3—121no—
700C2×C3×D3C2×D1212yes—
701C2×C3×D3#23512yescomplemented
702C2×C3×D3D3×D412yes—
703C2×C3×D3#23712yescomplemented
704D32—28no—
705C32×C4—21no—
706C32×C4—21no—
707C32×C4—21no—
708C32×C4—32no—
709C32×C4—41no—
710C32×C4—41no—
711C32×C4—41no—
712C32×C4—61no—
713C32×C4—61no—
714C32×C4—81no—
715C3⋊Dic3—21no—
716C3⋊Dic3—21no—
717C3⋊Dic3—21no—
718C3⋊Dic3—21no—
719C3⋊Dic3—61no—
720C3⋊Dic3—61no—
721C3⋊Dic3—61no—
722C3⋊Dic3—121no—
723C3⋊Dic3—121no—
724C3⋊Dic3—121no—
725C3⋊Dic3—241no—
726C3⋊Dic3C2×D1212yes—
727C3×Dic3—22no—
728C3×Dic3—21no—
729C3×Dic3—21no—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—22no—
733C3×Dic3—32no—
734C3×Dic3—32no—
735C3×Dic3—41no—
736C3×Dic3—62no—
737C3×Dic3—61no—
738C3×Dic3—61no—
739C3×Dic3—61no—
740C3×Dic3—61no—
741C3×Dic3—61no—
742C3×Dic3—61no—
743C3×Dic3—61no—
744C3×Dic3—61no—
745C3×Dic3—121no—
746C3×Dic3—121no—
747C3×Dic3—121no—
748C3×Dic3—121no—
749C3×Dic3C2×D1212yes—
750C3×Dic3D3×D412yes—
751C2×#41—271no—
752C23×C4—271no—
753#123—271no—
754#123—271no—
755C22⋊Q8—271no—
756C22⋊Q8—271no—
757#121—271no—
758#121—271no—
759#120—91no—
760#120—271no—
761C4×D4—91no—
762C4×D4—271no—
763C4×D4—271no—
764C4×D4—271no—
765#117—91no—
766C33#52511yescharacteristic, complemented, Sylow
767C23×C3—31no—
768C23×C3—31no—
769C23×C3—31no—
770C23×C3—31no—
771C23×C3—31no—
772C23×C3—31no—
773C23×C3—61no—
774C23×C3—61no—
775C23×C3—61no—
776C23×C3—91no—
777C23×C3—182no—
778C23×C3—182no—
779C23×C3—182no—
780C22×D3—31no—
781C22×D3—31no—
782C22×D3—61no—
783C22×D3—62no—
784C22×D3—62no—
785C22×D3—62no—
786C22×D3—62no—
787C22×D3—62no—
788C22×D3—62no—
789C22×D3—91no—
790C22×D3—91no—
791C22×D3—91no—
792C22×D3—181no—
793C22×D3—181no—
794C22×D3—181no—
795C22×D3—361no—
796C22×D3C2×D3211yescharacteristic
797C22×D3C2×D3211yescharacteristic
798C22×D3C2×D3211yescharacteristic
799C3×D4—62no—
800C3×D4—62no—
801C3×D4—122no—
802C3×D4—182no—
803C3×D4—182no—
804C2×C3×C4—21no—
805C2×C3×C4—21no—
806C2×C3×C4—21no—
807C2×C3×C4—31no—
808C2×C3×C4—31no—
809C2×C3×C4—31no—
810C2×C3×C4—31no—
811C2×C3×C4—31no—
812C2×C3×C4—31no—
813C2×C3×C4—41no—
814C2×C3×C4—61no—
815C2×C3×C4—61no—
816C2×C3×C4—61no—
817C2×C3×C4—94no—
818C2×C3×C4—91no—
819C2×C3×C4—91no—
820C2×C3×C4—91no—
821C2×C3×C4—91no—
822C2×C3×C4—91no—
823C2×C3×C4—182no—
824C2×C3×C4—182no—
825C2×C3×C4C2×D3211yescharacteristic
826C2×C3×C4C2×D3211yescharacteristic
827C2×C3×C4C2×D3211yescharacteristic
828#67—62no—
829#67—62no—
830#67—62no—
831#67—182no—
832#67—182no—
833#67—182no—
834#67—182no—
835#67—182no—
836#67—182no—
837#67—182no—
838#67—362no—
839#67—362no—
840#67—362no—
841C2×Dic3—31no—
842C2×Dic3—31no—
843C2×Dic3—34no—
844C2×Dic3—31no—
845C2×Dic3—31no—
846C2×Dic3—31no—
847C2×Dic3—31no—
848C2×Dic3—31no—
849C2×Dic3—31no—
850C2×Dic3—31no—
851C2×Dic3—31no—
852C2×Dic3—61no—
853C2×Dic3—61no—
854C2×Dic3—61no—
855C2×Dic3—61no—
856C2×Dic3—61no—
857C2×Dic3—62no—
858C2×Dic3—62no—
859C2×Dic3—91no—
860C2×Dic3—91no—
861C2×Dic3—91no—
862C2×Dic3—181no—
863C2×Dic3—181no—
864C2×Dic3—181no—
865C2×Dic3—182no—
866C2×Dic3—182no—
867C2×Dic3—182no—
868C2×Dic3—182no—
869C2×Dic3—182no—
870C2×Dic3—182no—
871C2×Dic3—361no—
872C2×Dic3—362no—
873C2×Dic3—362no—
874C2×Dic3C2×D3211yescharacteristic
875C2×Dic3C2×D3211yescharacteristic
876C2×Dic3C2×D3211yescharacteristic
877D12—22no—
878D12—62no—
879D12—182no—
880D12—182no—
881D12—184no—
882D12—182no—
883D12—182no—
884D12—182no—
885C4×D3—34no—
886C4×D3—62no—
887C4×D3—62no—
888C4×D3—182no—
889C4×D3—182no—
890C4×D3—182no—
891C4×D3—182no—
892C4×D3—182no—
893C4×D3—182no—
894C4×D3—182no—
895C4×D3—182no—
896C4×D3—182no—
897C4×D3—362no—
898C4×D3—362no—
899Dic6—182no—
900Dic6—182no—
901Dic6—182no—
902C2×C32—21no—
903C2×C32—21no—
904C2×C32—21no—
905C2×C32—21no—
906C2×C32—21no—
907C2×C32—21no—
908C2×C32—21no—
909C2×C32—21no—
910C2×C32—21no—
911C2×C32—41no—
912C2×C32—41no—
913C2×C32—41no—
914C2×C32—62no—
915C2×C32—62no—
916C2×C32—121no—
917C2×C32C22×D1211yescharacteristic
918C2×C32C2×#23511yescharacteristic
919C2×C32C2×D3×D411yescharacteristic
920C2×C32C2×D3×D411yescharacteristic
921C2×C32C2×#23711yescharacteristic
922C2×C32C2×#23711yescharacteristic
923C2×C32D3×#4111yescharacteristic
924C2×C32D3×#4111yescharacteristic
925C2×C32D3×#4111yescharacteristic
926C3⋊D3—22no—
927C3⋊D3—121no—
928C3⋊D3—122no—
929C3⋊D3—121no—
930C3⋊D3—121no—
931C3⋊D3—241no—
932C3⋊D3—241no—
933C3⋊D3—242no—
934C3×D3—22no—
935C3×D3—22no—
936C3×D3—22no—
937C3×D3—22no—
938C3×D3—42no—
939C3×D3—42no—
940C3×D3—41no—
941C3×D3—41no—
942C3×D3—62no—
943C3×D3—62no—
944C3×D3—81no—
945C3×D3—122no—
946C24—91no—
947#41—544no—
948C2×Q8—271no—
949C2×D4—31no—
950C2×D4—91no—
951C2×D4—91no—
952C2×D4—271no—
953C2×D4—271no—
954C2×D4—271no—
955C2×D4—271no—
956C22×C4—91no—
957C22×C4—91no—
958C22×C4—91no—
959C22×C4—271no—
960C22×C4—271no—
961C22×C4—271no—
962C22×C4—271no—
963C22×C4—271no—
964C22×C4—544no—
965C4⋊C4—91no—
966C4⋊C4—91no—
967C4⋊C4—91no—
968C4⋊C4—271no—
969C4⋊C4—271no—
970C4⋊C4—271no—
971C22⋊C4—31no—
972C22⋊C4—91no—
973C22⋊C4—91no—
974C22⋊C4—91no—
975C22⋊C4—91no—
976C22⋊C4—91no—
977C22⋊C4—271no—
978C22⋊C4—271no—
979C22⋊C4—271no—
980C22⋊C4—271no—
981C42—31no—
982C42—91no—
983C22×C3—21no—
984C22×C3—21no—
985C22×C3—21no—
986C22×C3—32no—
987C22×C3—32no—
988C22×C3—32no—
989C22×C3—32no—
990C22×C3—41no—
991C22×C3—62no—
992C22×C3—62no—
993C22×C3—61no—
994C22×C3—61no—
995C22×C3—61no—
996C22×C3—61no—
997C22×C3—61no—
998C22×C3—61no—
999C22×C3—61no—
1000C22×C3—61no—
1001C22×C3—61no—
1002C22×C3—61no—
1003C22×C3—61no—
1004C22×C3—61no—
1005C22×C3—61no—
1006C22×C3—61no—
1007C22×C3—92no—
1008C22×C3—121no—
1009C22×C3—121no—
1010C22×C3—121no—
1011C22×C3—121no—
1012C22×C3—121no—
1013C22×C3—121no—
1014C22×C3—121no—
1015C22×C3—188no—
1016C22×C3—181no—
1017C22×C3—181no—
1018C22×C3C22×D3211yescharacteristic
1019C22×C3C22×D3211yescharacteristic
1020C22×C3C22×D3211yescharacteristic
1021C2×D3—21no—
1022C2×D3—21no—
1023C2×D3—21no—
1024C2×D3—21no—
1025C2×D3—21no—
1026C2×D3—21no—
1027C2×D3—21no—
1028C2×D3—32no—
1029C2×D3—32no—
1030C2×D3—62no—
1031C2×D3—68no—
1032C2×D3—68no—
1033C2×D3—61no—
1034C2×D3—61no—
1035C2×D3—61no—
1036C2×D3—61no—
1037C2×D3—121no—
1038C2×D3—121no—
1039C2×D3—182no—
1040C2×D3—181no—
1041C2×D3—181no—
1042C2×D3—181no—
1043C2×D3—181no—
1044C2×D3—181no—
1045C2×D3—181no—
1046C2×D3—181no—
1047C2×D3—181no—
1048C2×D3—181no—
1049C2×D3—361no—
1050C2×D3—361no—
1051C2×D3—361no—
1052C2×D3—361no—
1053C2×D3—361no—
1054C2×D3—361no—
1055C2×D3—361no—
1056C2×D3—361no—
1057C2×D3—362no—
1058C2×D3—721no—
1059C2×D3—721no—
1060C2×D3D3×D1212yes—
1061C2×D3#380412yescomplemented
1062C3×C4—21no—
1063C3×C4—21no—
1064C3×C4—21no—
1065C3×C4—32no—
1066C3×C4—32no—
1067C3×C4—41no—
1068C3×C4—41no—
1069C3×C4—41no—
1070C3×C4—62no—
1071C3×C4—62no—
1072C3×C4—61no—
1073C3×C4—61no—
1074C3×C4—61no—
1075C3×C4—61no—
1076C3×C4—81no—
1077C3×C4—92no—
1078C3×C4—121no—
1079C3×C4—181no—
1080C3×C4—181no—
1081C3×C4—181no—
1082C3×C4—181no—
1083Dic3—21no—
1084Dic3—21no—
1085Dic3—32no—
1086Dic3—32no—
1087Dic3—62no—
1088Dic3—61no—
1089Dic3—61no—
1090Dic3—61no—
1091Dic3—61no—
1092Dic3—61no—
1093Dic3—61no—
1094Dic3—61no—
1095Dic3—61no—
1096Dic3—121no—
1097Dic3—121no—
1098Dic3—121no—
1099Dic3—121no—
1100Dic3—181no—
1101Dic3—181no—
1102Dic3—181no—
1103Dic3—361no—
1104Dic3—361no—
1105Dic3—361no—
1106Dic3—721no—
1107Dic3D3×D1212yes—
1108C32—21no—
1109C32—21no—
1110C32—21no—
1111C32—41no—
1112C32#552411yescharacteristic, complemented
1113C32#554711yescharacteristic, complemented
1114C32#558611yescharacteristic, complemented
1115C23—31no—
1116C23—31no—
1117C23—31no—
1118C23—91no—
1119C23—182no—
1120C23—182no—
1121C23—182no—
1122C23—271no—
1123Q8—542no—
1124D4—62no—
1125D4—182no—
1126D4—182no—
1127D4—542no—
1128D4—542no—
1129D4—542no—
1130D4—542no—
1131C2×C4—31no—
1132C2×C4—31no—
1133C2×C4—31no—
1134C2×C4—94no—
1135C2×C4—91no—
1136C2×C4—91no—
1137C2×C4—91no—
1138C2×C4—91no—
1139C2×C4—91no—
1140C2×C4—182no—
1141C2×C4—182no—
1142C2×C4—271no—
1143C2×C4—542no—
1144C2×C4—542no—
1145C2×C4—542no—
1146C2×C4—542no—
1147C2×C4—542no—
1148C2×C4D3311yescharacteristic
1149C2×C3—21no—
1150C2×C3—21no—
1151C2×C3—21no—
1152C2×C3—21no—
1153C2×C3—21no—
1154C2×C3—21no—
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—21no—
1158C2×C3—41no—
1159C2×C3—41no—
1160C2×C3—41no—
1161C2×C3—62no—
1162C2×C3—62no—
1163C2×C3—62no—
1164C2×C3—62no—
1165C2×C3—122no—
1166C2×C3—122no—
1167C2×C3—121no—
1168C2×C3—121no—
1169C2×C3—182no—
1170C2×C3—241no—
1171C2×C3C2×D3×D1211yescharacteristic
1172C2×C3C2×D3×D1211yescharacteristic
1173C2×C3D3×#23511yescharacteristic
1174C2×C3#6430611yescharacteristic
1175C2×C3D32×D411yescharacteristic
1176C2×C3D3×#23711yescharacteristic
1177C2×C3D3×#23711yescharacteristic
1178C2×C3D3×#23711yescharacteristic
1179C2×C3C2×#380411yescharacteristic
1180D3—22no—
1181D3—22no—
1182D3—41no—
1183D3—62no—
1184D3—62no—
1185D3—122no—
1186D3—362no—
1187D3—361no—
1188D3—361no—
1189D3—361no—
1190D3—721no—
1191D3—721no—
1192D3—722no—
1193C22—32no—
1194C22—32no—
1195C22—61no—
1196C22—61no—
1197C22—61no—
1198C22—61no—
1199C22—61no—
1200C22—61no—
1201C22—61no—
1202C22—92no—
1203C22—188no—
1204C22—181no—
1205C22—181no—
1206C22—541no—
1207C22—541no—
1208C22—541no—
1209C22C2×D3311yescharacteristic
1210C4—21no—
1211C4—32no—
1212C4—61no—
1213C4—61no—
1214C4—92no—
1215C4—181no—
1216C4—181no—
1217C4—181no—
1218C4—181no—
1219C4—541no—
1220C3—21no—
1221C3—21no—
1222C3—21no—
1223C3—41no—
1224C3#1059399711yescharacteristic, complemented
1225C3#1059407811yescharacteristic, complemented
1226C3#1059512911yescharacteristic, complemented
1227C2—62no—
1228C2—62no—
1229C2—121no—
1230C2—182no—
1231C2—1081no—
1232C2#1172437311yescharacteristic
1233C2D32×D1211yescharacteristic
1234C2D3×#380411yescharacteristic
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×#88959C2semidirect
2. C2×D32×Dic3C2semidirect
3. #11723692C2semidirect
4. #11723479C2semidirect
5. #11723475C2semidirect
6. #11723471C2semidirect
7. C3×#63922C2semidirect
8. C3×Dic3×D12C2semidirect
9. C3×#63877C2semidirect
10. #11722989C2semidirect
11. #11722981C2semidirect
12. #11722966C2semidirect
13. #11722948C2semidirect
14. #11722932C2semidirect
15. Dic3×#626C2semidirect
21. C2×#6296C22semidirect
26. C2×#6291C22semidirect
27. C2×#6289C22semidirect
35. C2×C3×D3×Dic3C22semidirect
38. #88859C22semidirect
40. C3×C4⋊(C3⋊Dic3)C22semidirect
41. C3×#3750C22semidirect
43. C32×C4×Dic3C22semidirect
44. #88815C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
48. #88804C22semidirect
49. (C2×D3)⋊(C3⋊Dic3)C22semidirect
50. C3×#3724C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
80. #63922D3semidirect
90. Dic3×D12D3semidirect
103. #63877D3semidirect
137. C3×D3×Dic3D4semidirect
204. C2×D3×Dic3C2×D3semidirect
221. C4⋊(C3⋊Dic3)C2×D3semidirect
222. #3750C2×D3semidirect
248. C3×C4×Dic3C2×D3semidirect
249. C3×C4×Dic3C2×D3semidirect
251. #3724C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. Dic32C2×D3semidirect
280. C2×C3×C3⋊D3#41semidirect
289. C2×C32×D3#41semidirect
483. D3×Dic3D12semidirect
625. C4×Dic3D32semidirect
665. C2×C3⋊D3#237semidirect
701. C2×C3×D3#235semidirect
703. C2×C3×D3#237semidirect
766. C33#525semidirect
1061. C2×D3#3804semidirect
1112. C32#5524semidirect
1113. C32#5547semidirect
1114. C32#5586semidirect
1224. C3#10593997semidirect
1225. C3#10594078semidirect
1226. C3#10595129semidirect

Maximal subgroups

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

subgroupindex
C2×#889592
C2×D32×Dic32
#117236922
#117234792
#117234752
#117234712
C3×#639222
C3×Dic3×D122
C3×#638772
#117229892
#117229812
#117229662
#117229482
#117229322
Dic3×#6262
#105951293
#105940783
#105939973