Finite Group Databasebeta

← #13170795

Subgroups — #13170795

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×#89041C211yesmaximal, characteristic, complemented
2C2×D32×Dic3C211yesmaximal, characteristic, complemented
3#11723507C211yesmaximal, characteristic, complemented
4#11723488C211yesmaximal, characteristic, complemented
5#11723487C211yesmaximal, characteristic, complemented
6C3×#63923C211yesmaximal, characteristic, complemented
7C3×#63896C211yesmaximal, characteristic, complemented
8C3×#63881C211yesmaximal, characteristic, complemented
9#11722997C211yesmaximal, characteristic, complemented
10#11722960C211yesmaximal, characteristic, complemented
11#11722955C211yesmaximal, characteristic, complemented
12#11722947C211yesmaximal, characteristic, complemented
13#11722928C211yesmaximal, characteristic, complemented
14#11722927C211yesmaximal, characteristic, complemented
15#11722922C211yesmaximal, characteristic, complemented
16#10594623—31nomaximal
17#10594055—31nomaximal
18#10594054—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C3×#634C2211yescharacteristic, complemented
23C2×#6295C2211yescharacteristic
24C2×#6295C2211yescharacteristic, complemented
25C2×#6294C2211yescharacteristic
26C2×#6294C2211yescharacteristic, complemented
27#89041—24no—
28C2×#6290C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C2×D3×C3⋊Dic3C2211yescharacteristic
31C2×D3×C3⋊Dic3C2211yescharacteristic
32C2×C3×#626C2211yescharacteristic
33C2×C3×#626C2211yescharacteristic
34C2×C3×#626C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36C2×C3×D3×Dic3C2211yescharacteristic
37D32×Dic3—24no—
38#88857C2211yescharacteristic, complemented
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44#88803C2211yescharacteristic
45#88803C2211yescharacteristic, complemented
46#88803C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49Dic3×C3⋊Dic3C2211yescharacteristic, complemented
50C3×#3724C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic
53C3×#3722C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×Dic32C2211yescharacteristic, complemented
56C22×D3×Dic3—31no—
57C22×D3×Dic3—31no—
58C2×C4×D32—31no—
59C2×#3799—31no—
60C2×#3796—31no—
61C2×#3795—31no—
62#64103—31no—
63#64090—31no—
64#64087—31no—
65C3×#896—31no—
66C3×#893—31no—
67C3×#882—31no—
68C3×#882—31no—
69C3×#67⋊C4—31no—
70C3×#878—31no—
71#63980—31no—
72#63978—31no—
73#63977—31no—
74#63976—31no—
75#67⋊Dic3—31no—
76Dic3×#67—31no—
77#63923D311yescharacteristic, complemented
78#63922—31no—
79#63906—31no—
80#63904—31no—
81#63898—31no—
82#63896D311yescharacteristic, complemented
83Dic3×D12—31no—
84#63891—31no—
85#63890—31no—
86#63887—31no—
87#63887—31no—
88#63887—61no—
89#63886—31no—
90#63886—31no—
91#63885—31no—
92#63884—31no—
93#63884—31no—
94#63884—61no—
95#63881D311yescharacteristic, complemented
96#63880—31no—
97#63879—31no—
98#63879—31no—
99#63879—61no—
100#63878—31no—
101#63877—31no—
102#63853—31no—
103#63836—31no—
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊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⋊Dic3)C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C3×C4⋊(C3⋊D3)—22no—
119C3×C4×C3⋊D3—22no—
120C3×#634—22no—
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6295—22no—
126#6295—22no—
127#6294—22no—
128#6294D414yescomplemented
129#6290—22no—
130Dic3×C3⋊D3—22no—
131D3×C3⋊Dic3—22no—
132D3×C3⋊Dic3—22no—
133C3×#626—22no—
134C3×#626—22no—
135C3×#626—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5627—91no—
139#5586—91no—
140#5547—91no—
141C23×C3×D3—31no—
142C23×C3×D3—31no—
143C22×D32C2×D311yescharacteristic
144C2×#638—31no—
145C22×C3⋊Dic3—31no—
146C22×C3⋊Dic3—31no—
147C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
150C2×#634C2×D311yescharacteristic, complemented
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C22×C3×Dic3—31no—
155C22×C3×Dic3—31no—
156C2×C3×D12—31no—
157C2×C3×D12—31no—
158C2×C3×D12—31no—
159C2×C3×D12—31no—
160C2×C3×D12—31no—
161C2×C3×D12—61no—
162C2×C3×C4×D3—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—61no—
167C2×C3×Dic6—31no—
168C2×C3×Dic6—31no—
169C2×C3×Dic6—61no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626C2×D311yescharacteristic
175C2×#626C2×D311yescharacteristic
176C2×#626C2×D311yescharacteristic
177C2×#625—31no—
178C2×#625—31no—
179C2×#625—31no—
180C2×#625—31no—
181C2×#625—61no—
182C2×#624—31no—
183C2×#624—31no—
184C2×D3×Dic3—31no—
185C2×D3×Dic3—31no—
186C2×D3×Dic3—31no—
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—64no—
195C2×D3×Dic3—64no—
196C2×D3×Dic3—61no—
197C2×D3×Dic3—61no—
198C2×D3×Dic3—61no—
199C2×D3×Dic3C2×D311yescharacteristic
200C2×D3×Dic3C2×D311yescharacteristic
201C4×D32—64no—
202#3799—64no—
203#3796—64no—
204#3795—64no—
205C32×C4⋊C4—31no—
206C32×C22⋊C4—31no—
207C32×C22⋊C4—31no—
208#3757—31no—
209#3752—31no—
210#3752—31no—
211#3752—31no—
212#3752—31no—
213C4⋊(C3⋊Dic3)—31no—
214#3750—31no—
215#3750—31no—
216#3750—31no—
217#3750—31no—
218#3750—61no—
219#3750—61no—
220#3750—61no—
221#3750—121no—
222C4×C3⋊Dic3—31no—
223C3×#217—31no—
224C3×(C2×D3)⋊C4—21no—
225C3×(C2×D3)⋊C4—21no—
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)⋊C4C2×D311yescharacteristic
232C3×(C2×D3)⋊C4C2×D311yescharacteristic
233C3×(C2×D3)⋊C4C2×D311yescharacteristic
234C3×(C2×D3)⋊C4C2×D311yescharacteristic
235C3×C4⋊Dic3—31no—
236C3×Dic3⋊C4—21no—
237C3×Dic3⋊C4—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4C2×D311yescharacteristic, complemented
241C3×Dic3⋊C4C2×D311yescharacteristic, complemented
242C3×C4×Dic3—31no—
243C3×C4×Dic3—31no—
244#3724C2×D311yescharacteristic, complemented
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—61no—
250Dic3⋊Dic3—61no—
251Dic3⋊Dic3C2×D311yescharacteristic, complemented
252#3722C2×D311yescharacteristic
253#3722C2×D311yescharacteristic, complemented
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—31no—
258(C2×D3)⋊Dic3—31no—
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—61no—
265(C2×D3)⋊Dic3—61no—
266(C2×D3)⋊Dic3—61no—
267(C2×D3)⋊Dic3—61no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3C2×D311yescharacteristic
270Dic32—31no—
271Dic32—31no—
272Dic32—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⋊D3C2×D412yes—
284C2×C32×D3—21no—
285C2×C32×D3—21no—
286C2×C32×D3—21no—
287C2×C32×D3—21no—
288C2×C32×D3#4112yescomplemented
289C2×C32×D3#4112yescomplemented
290C3×D32—28no—
291C33×C4—21no—
292C3⋊(C3⋊Dic3)—21no—
293C3⋊(C3⋊Dic3)—21no—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3C2×D412yes—
296C3×C3⋊Dic3C2×D412yes—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C23×Dic3—91no—
302C2×#239—91no—
303C2×#237—91no—
304C2×#235—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×C22⋊Q8—91no—
308C3×#120—91no—
309C3×C4×D4—91no—
310#953—91no—
311#946—91no—
312#939—91no—
313#939—91no—
314#939—91no—
315#937—91no—
316#935—91no—
317D4×Dic3—91no—
318D4×Dic3—91no—
319#930—91no—
320C4×#67—91no—
321C4×#67—91no—
322#896—31no—
323#895—91no—
324#894—91no—
325#894—91no—
326#894—91no—
327#894—181no—
328#893—31no—
329#893—91no—
330#892—91no—
331#886—91no—
332#884—91no—
333#883—91no—
334#882—31no—
335#882—31no—
336#882—91no—
337#67⋊C4—31no—
338#67⋊C4—91no—
339#67⋊C4—91no—
340#67⋊C4—91no—
341#67⋊C4—181no—
342#878—31no—
343#878—91no—
344#878—91no—
345#878—181no—
346#877—91no—
347C4×D12—91no—
348#872—91no—
349C23×C32—31no—
350C23×C32—31no—
351C22×C3⋊D3C22×D311yescharacteristic
352C22×C3⋊D3C22×D311yescharacteristic
353C22×C3⋊D3C22×D311yescharacteristic
354C22×C3×D3—21no—
355C22×C3×D3—21no—
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—61no—
363C22×C3×D3—61no—
364C22×C3×D3—61no—
365C22×C3×D3—62no—
366C22×C3×D3—62no—
367C22×C3×D3—62no—
368C22×C3×D3—62no—
369C22×C3×D3—62no—
370C22×C3×D3—62no—
371C22×C3×D3C22×D311yescharacteristic
372C22×C3×D3C22×D311yescharacteristic
373C22×C3×D3C22×D311yescharacteristic
374C22×C3×D3C22×D311yescharacteristic
375C2×D32—22no—
376C2×D32—22no—
377C2×D32—22no—
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—41no—
386C2×C32×C4C22×D311yescharacteristic
387C2×C32×C4C22×D311yescharacteristic
388C2×C32×C4C22×D311yescharacteristic
389#638—62no—
390C2×C3⋊Dic3—31no—
391C2×C3⋊Dic3—31no—
392C2×C3⋊Dic3—31no—
393C2×C3⋊Dic3—31no—
394C2×C3⋊Dic3—31no—
395C2×C3⋊Dic3—31no—
396C2×C3⋊Dic3—61no—
397C2×C3⋊Dic3—61no—
398C2×C3⋊Dic3—61no—
399C2×C3⋊Dic3—61no—
400C2×C3⋊Dic3—61no—
401C2×C3⋊Dic3—61no—
402C2×C3⋊Dic3—62no—
403C2×C3⋊Dic3—62no—
404C2×C3⋊Dic3—121no—
405C2×C3⋊Dic3—121no—
406C2×C3⋊Dic3C22×D311yescharacteristic
407C2×C3⋊Dic3C22×D311yescharacteristic
408C2×C3⋊Dic3C22×D311yescharacteristic
409C4⋊(C3⋊D3)—22no—
410C4×C3⋊D3—22no—
411C4×C3⋊D3—62no—
412#634—22no—
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—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—62no—
430C2×C3×Dic3—62no—
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
438C2×C3×Dic3C22×D311yescharacteristic
439C3×D12—62no—
440C3×D12—62no—
441C3×D12—62no—
442C3×D12—62no—
443C3×D12—62no—
444C3×D12—122no—
445C3×C4×D3—62no—
446C3×C4×D3—62no—
447C3×C4×D3—62no—
448C3×C4×D3—62no—
449C3×C4×D3—122no—
450C3×Dic6—62no—
451C3×Dic6—62no—
452C3×Dic6—122no—
453#626—22no—
454#626—22no—
455#626—22no—
456#626—62no—
457#626—62no—
458#626—62no—
459#626—62no—
460#625—62no—
461#625—64no—
462#625—62no—
463#625—62no—
464#625—62no—
465#624—34no—
466#624—62no—
467D3×Dic3—22no—
468D3×Dic3—22no—
469D3×Dic3—34no—
470D3×Dic3—34no—
471D3×Dic3—62no—
472D3×Dic3—62no—
473D3×Dic3—62no—
474D3×Dic3—62no—
475D3×Dic3—62no—
476D3×Dic3—62no—
477D3×Dic3—62no—
478D3×Dic3—62no—
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—41no—
488C3×C3⋊D3—41no—
489C32×D3—22no—
490C32×D3—22no—
491C24×C3—91no—
492C23×D3—31no—
493C23×D3—31no—
494C2×C3×Q8—91no—
495C2×C3×D4—91no—
496C2×C3×D4—91no—
497C2×C3×D4—91no—
498C2×C3×D4—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—31no—
515C22×Dic3—91no—
516C22×Dic3—91no—
517C22×Dic3—91no—
518C22×Dic3—91no—
519C22×Dic3—91no—
520C22×Dic3—91no—
521C22×Dic3—91no—
522C22×Dic3—181no—
523C22×Dic3—181no—
524C22×Dic3—184no—
525#239—184no—
526#237—184no—
527#235—184no—
528C2×D12—31no—
529C2×D12—31no—
530C2×D12—31no—
531C2×D12—31no—
532C2×D12—31no—
533C2×D12—61no—
534C2×D12—91no—
535C2×D12—91no—
536C2×C4×D3—31no—
537C2×C4×D3—31no—
538C2×C4×D3—31no—
539C2×C4×D3—31no—
540C2×C4×D3—61no—
541C2×C4×D3—91no—
542C2×C4×D3—91no—
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—181no—
550C2×C4×D3—184no—
551C2×C4×D3—184no—
552C2×Dic6—31no—
553C2×Dic6—31no—
554C2×Dic6—61no—
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—31no—
563C3×C22⋊C4—31no—
564C3×C22⋊C4—61no—
565C3×C22⋊C4—61no—
566C3×C22⋊C4—91no—
567C3×C22⋊C4—91no—
568C3×C22⋊C4—91no—
569C3×C42—91no—
570#217—31no—
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—91no—
584(C2×D3)⋊C4—91no—
585(C2×D3)⋊C4—91no—
586(C2×D3)⋊C4—91no—
587(C2×D3)⋊C4—91no—
588(C2×D3)⋊C4—91no—
589(C2×D3)⋊C4—91no—
590(C2×D3)⋊C4—91no—
591(C2×D3)⋊C4—91no—
592(C2×D3)⋊C4—181no—
593(C2×D3)⋊C4—181no—
594(C2×D3)⋊C4—181no—
595(C2×D3)⋊C4—181no—
596(C2×D3)⋊C4D3211yescharacteristic
597(C2×D3)⋊C4D3211yescharacteristic
598C4⋊Dic3—31no—
599C4⋊Dic3—91no—
600C4⋊Dic3—91no—
601C4⋊Dic3—91no—
602C4⋊Dic3—181no—
603Dic3⋊C4—31no—
604Dic3⋊C4—31no—
605Dic3⋊C4—31no—
606Dic3⋊C4—91no—
607Dic3⋊C4—91no—
608Dic3⋊C4—91no—
609Dic3⋊C4—91no—
610Dic3⋊C4—91no—
611Dic3⋊C4—91no—
612Dic3⋊C4—181no—
613Dic3⋊C4—181no—
614Dic3⋊C4—181no—
615Dic3⋊C4—181no—
616Dic3⋊C4—361no—
617Dic3⋊C4D3211yescharacteristic, complemented
618C4×Dic3—31no—
619C4×Dic3—31no—
620C4×Dic3—91no—
621C4×Dic3—91no—
622C4×Dic3—91no—
623C4×Dic3—181no—
624C22×C32—21no—
625C22×C32—21no—
626C22×C32—21no—
627C22×C32—32no—
628C22×C32—32no—
629C22×C32—41no—
630C22×C32—61no—
631C22×C32—61no—
632C22×C32—61no—
633C22×C32—61no—
634C22×C32C23×D311yescharacteristic
635C22×C32C23×D311yescharacteristic
636C22×C32C23×D311yescharacteristic
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⋊D3—21no—
644C2×C3⋊D3—21no—
645C2×C3⋊D3D3×D412yes—
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—21no—
653C2×C3×D3—21no—
654C2×C3×D3—22no—
655C2×C3×D3—22no—
656C2×C3×D3—32no—
657C2×C3×D3—32no—
658C2×C3×D3—41no—
659C2×C3×D3—41no—
660C2×C3×D3—41no—
661C2×C3×D3—41no—
662C2×C3×D3—62no—
663C2×C3×D3—68no—
664C2×C3×D3—68no—
665C2×C3×D3—61no—
666C2×C3×D3—61no—
667C2×C3×D3—61no—
668C2×C3×D3—61no—
669C2×C3×D3—62no—
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—61no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—121no—
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#23512yescomplemented
690C2×C3×D3#23712yescomplemented
691C2×C3×D3#23712yescomplemented
692C2×C3×D3#23912yescomplemented
693D32—28no—
694C32×C4—21no—
695C32×C4—21no—
696C32×C4—21no—
697C32×C4—41no—
698C32×C4—41no—
699C32×C4—41no—
700C32×C4—61no—
701C32×C4—61no—
702C32×C4—61no—
703C32×C4—61no—
704C32×C4—81no—
705C3⋊Dic3—21no—
706C3⋊Dic3—61no—
707C3⋊Dic3—62no—
708C3⋊Dic3—61no—
709C3⋊Dic3—61no—
710C3⋊Dic3—61no—
711C3⋊Dic3—61no—
712C3⋊Dic3—61no—
713C3⋊Dic3—121no—
714C3⋊Dic3—121no—
715C3⋊Dic3—122no—
716C3⋊Dic3—121no—
717C3⋊Dic3—121no—
718C3⋊Dic3—121no—
719C3⋊Dic3—241no—
720C3⋊Dic3D3×D412yes—
721C3⋊Dic3D3×D412yes—
722C3×Dic3—21no—
723C3×Dic3—21no—
724C3×Dic3—21no—
725C3×Dic3—21no—
726C3×Dic3—21no—
727C3×Dic3—21no—
728C3×Dic3—21no—
729C3×Dic3—21no—
730C3×Dic3—32no—
731C3×Dic3—32no—
732C3×Dic3—32no—
733C3×Dic3—32no—
734C3×Dic3—41no—
735C3×Dic3—41no—
736C3×Dic3—41no—
737C3×Dic3—41no—
738C3×Dic3—62no—
739C3×Dic3—62no—
740C3×Dic3—61no—
741C3×Dic3—61no—
742C3×Dic3—121no—
743C2×#41—271no—
744C23×C4—271no—
745#123—271no—
746#123—271no—
747C22⋊Q8—91no—
748C22⋊Q8—271no—
749#121—271no—
750#121—271no—
751#120—91no—
752#120—271no—
753C4×D4—91no—
754C4×D4—271no—
755C4×D4—271no—
756C4×D4—271no—
757#117—271no—
758C33#52511yescharacteristic, complemented, Sylow
759C23×C3—31no—
760C23×C3—31no—
761C23×C3—31no—
762C23×C3—31no—
763C23×C3—61no—
764C23×C3—61no—
765C23×C3—91no—
766C23×C3—91no—
767C23×C3—91no—
768C23×C3—182no—
769C23×C3—182no—
770C23×C3—182no—
771C22×D3—31no—
772C22×D3—31no—
773C22×D3—31no—
774C22×D3—31no—
775C22×D3—31no—
776C22×D3—31no—
777C22×D3—61no—
778C22×D3—61no—
779C22×D3—61no—
780C22×D3—62no—
781C22×D3—62no—
782C22×D3—62no—
783C22×D3—62no—
784C22×D3—62no—
785C22×D3—62no—
786C22×D3C2×D3211yescharacteristic
787C22×D3C2×D3211yescharacteristic
788C3×Q8—182no—
789C3×D4—182no—
790C3×D4—182no—
791C3×D4—182no—
792C3×D4—182no—
793C2×C3×C4—21no—
794C2×C3×C4—21no—
795C2×C3×C4—21no—
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—41no—
805C2×C3×C4—61no—
806C2×C3×C4—61no—
807C2×C3×C4—61no—
808C2×C3×C4—61no—
809C2×C3×C4—91no—
810C2×C3×C4—91no—
811C2×C3×C4—91no—
812C2×C3×C4—182no—
813C2×C3×C4—182no—
814C2×C3×C4—182no—
815C2×C3×C4C2×D3211yescharacteristic
816C2×C3×C4C2×D3211yescharacteristic
817C2×C3×C4C2×D3211yescharacteristic
818#67—62no—
819#67—62no—
820#67—62no—
821#67—182no—
822#67—182no—
823#67—182no—
824#67—182no—
825#67—182no—
826#67—182no—
827#67—184no—
828#67—182no—
829C2×Dic3—31no—
830C2×Dic3—31no—
831C2×Dic3—31no—
832C2×Dic3—31no—
833C2×Dic3—31no—
834C2×Dic3—31no—
835C2×Dic3—61no—
836C2×Dic3—61no—
837C2×Dic3—61no—
838C2×Dic3—62no—
839C2×Dic3—62no—
840C2×Dic3—94no—
841C2×Dic3—91no—
842C2×Dic3—91no—
843C2×Dic3—91no—
844C2×Dic3—91no—
845C2×Dic3—91no—
846C2×Dic3—91no—
847C2×Dic3—181no—
848C2×Dic3—181no—
849C2×Dic3—181no—
850C2×Dic3—181no—
851C2×Dic3—181no—
852C2×Dic3—181no—
853C2×Dic3—182no—
854C2×Dic3—182no—
855C2×Dic3—182no—
856C2×Dic3—182no—
857C2×Dic3—182no—
858C2×Dic3—182no—
859C2×Dic3—361no—
860C2×Dic3—361no—
861C2×Dic3—362no—
862C2×Dic3—362no—
863C2×Dic3C2×D3211yescharacteristic
864C2×Dic3C2×D3211yescharacteristic
865C2×Dic3C2×D3211yescharacteristic
866C2×Dic3C2×D3211yescharacteristic
867D12—62no—
868D12—62no—
869D12—62no—
870D12—62no—
871D12—62no—
872D12—122no—
873D12—182no—
874D12—182no—
875C4×D3—62no—
876C4×D3—62no—
877C4×D3—62no—
878C4×D3—62no—
879C4×D3—94no—
880C4×D3—94no—
881C4×D3—122no—
882C4×D3—182no—
883C4×D3—182no—
884C4×D3—182no—
885C4×D3—182no—
886C4×D3—182no—
887C4×D3—182no—
888C4×D3—362no—
889Dic6—62no—
890Dic6—62no—
891Dic6—122no—
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—62no—
905C2×C32—62no—
906C2×C32C2×#23511yescharacteristic
907C2×C32C2×D3×D411yescharacteristic
908C2×C32C2×D3×D411yescharacteristic
909C2×C32C2×D3×D411yescharacteristic
910C2×C32C2×#23711yescharacteristic
911C2×C32C2×#23711yescharacteristic
912C2×C32C2×#23911yescharacteristic
913C2×C32D3×#4111yescharacteristic
914C2×C32D3×#4111yescharacteristic
915C3⋊D3—22no—
916C3⋊D3—41no—
917C3⋊D3—41no—
918C3×D3—22no—
919C3×D3—22no—
920C3×D3—22no—
921C3×D3—22no—
922C3×D3—42no—
923C3×D3—42no—
924C3×D3—62no—
925C3×D3—62no—
926C3×D3—122no—
927C3×D3—122no—
928C3×D3—121no—
929C3×D3—121no—
930C3×D3—121no—
931C3×D3—121no—
932C3×D3—241no—
933C24—91no—
934#41—544no—
935C2×Q8—91no—
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—271no—
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—31no—
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—91no—
969C42—271no—
970C22×C3—21no—
971C22×C3—21no—
972C22×C3—21no—
973C22×C3—32no—
974C22×C3—32no—
975C22×C3—32no—
976C22×C3—32no—
977C22×C3—41no—
978C22×C3—62no—
979C22×C3—62no—
980C22×C3—61no—
981C22×C3—61no—
982C22×C3—61no—
983C22×C3—61no—
984C22×C3—61no—
985C22×C3—61no—
986C22×C3—61no—
987C22×C3—61no—
988C22×C3—92no—
989C22×C3—121no—
990C22×C3—121no—
991C22×C3—121no—
992C22×C3—121no—
993C22×C3—188no—
994C22×C3—181no—
995C22×C3—181no—
996C22×C3—181no—
997C22×C3—181no—
998C22×C3—181no—
999C22×C3—181no—
1000C22×C3—181no—
1001C22×C3—181no—
1002C22×C3C22×D3211yescharacteristic
1003C22×C3C22×D3211yescharacteristic
1004C22×C3C22×D3211yescharacteristic
1005C2×D3—21no—
1006C2×D3—21no—
1007C2×D3—21no—
1008C2×D3—21no—
1009C2×D3—32no—
1010C2×D3—32no—
1011C2×D3—62no—
1012C2×D3—68no—
1013C2×D3—68no—
1014C2×D3—61no—
1015C2×D3—61no—
1016C2×D3—61no—
1017C2×D3—61no—
1018C2×D3—62no—
1019C2×D3—61no—
1020C2×D3—61no—
1021C2×D3—61no—
1022C2×D3—61no—
1023C2×D3—61no—
1024C2×D3—61no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—61no—
1030C2×D3—61no—
1031C2×D3—121no—
1032C2×D3—121no—
1033C2×D3—121no—
1034C2×D3—121no—
1035C2×D3—121no—
1036C2×D3—121no—
1037C2×D3—121no—
1038C2×D3#379512yescomplemented
1039C2×D3#379612yescomplemented
1040C3×C4—21no—
1041C3×C4—21no—
1042C3×C4—21no—
1043C3×C4—41no—
1044C3×C4—41no—
1045C3×C4—41no—
1046C3×C4—61no—
1047C3×C4—61no—
1048C3×C4—61no—
1049C3×C4—61no—
1050C3×C4—61no—
1051C3×C4—61no—
1052C3×C4—61no—
1053C3×C4—61no—
1054C3×C4—81no—
1055C3×C4—92no—
1056C3×C4—92no—
1057C3×C4—121no—
1058C3×C4—121no—
1059C3×C4—121no—
1060C3×C4—121no—
1061C3×C4—181no—
1062Dic3—21no—
1063Dic3—21no—
1064Dic3—21no—
1065Dic3—21no—
1066Dic3—32no—
1067Dic3—32no—
1068Dic3—32no—
1069Dic3—32no—
1070Dic3—62no—
1071Dic3—62no—
1072Dic3—61no—
1073Dic3—61no—
1074Dic3—121no—
1075Dic3—182no—
1076Dic3—181no—
1077Dic3—181no—
1078Dic3—181no—
1079Dic3—181no—
1080Dic3—181no—
1081Dic3—181no—
1082Dic3—361no—
1083Dic3—361no—
1084Dic3—361no—
1085Dic3—361no—
1086Dic3—361no—
1087Dic3—362no—
1088Dic3—721no—
1089C32—21no—
1090C32—21no—
1091C32—21no—
1092C32—41no—
1093C32#554711yescharacteristic, complemented
1094C32#558611yescharacteristic, complemented
1095C32#562711yescharacteristic, complemented
1096C23—31no—
1097C23—31no—
1098C23—91no—
1099C23—91no—
1100C23—91no—
1101C23—182no—
1102C23—182no—
1103C23—182no—
1104Q8—182no—
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—91no—
1117C2×C4—91no—
1118C2×C4—91no—
1119C2×C4—182no—
1120C2×C4—182no—
1121C2×C4—182no—
1122C2×C4—274no—
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—62no—
1143C2×C3—62no—
1144C2×C3—62no—
1145C2×C3—62no—
1146C2×C3—122no—
1147C2×C3—122no—
1148C2×C3—182no—
1149C2×C3—361no—
1150C2×C3—361no—
1151C2×C3C2×#379511yescharacteristic
1152C2×C3C2×#379611yescharacteristic
1153C2×C3D3×#23511yescharacteristic
1154C2×C3D32×D411yescharacteristic
1155C2×C3D32×D411yescharacteristic
1156C2×C3D32×D411yescharacteristic
1157C2×C3D3×#23711yescharacteristic
1158C2×C3D3×#23711yescharacteristic
1159C2×C3D3×#23911yescharacteristic
1160D3—22no—
1161D3—22no—
1162D3—62no—
1163D3—62no—
1164D3—122no—
1165D3—122no—
1166D3—121no—
1167D3—121no—
1168D3—121no—
1169D3—121no—
1170D3—241no—
1171C22—32no—
1172C22—32no—
1173C22—61no—
1174C22—61no—
1175C22—61no—
1176C22—61no—
1177C22—92no—
1178C22—188no—
1179C22—181no—
1180C22—181no—
1181C22—181no—
1182C22—181no—
1183C22—181no—
1184C22—181no—
1185C22—181no—
1186C22—181no—
1187C22C2×D3311yescharacteristic
1188C4—21no—
1189C4—61no—
1190C4—61no—
1191C4—61no—
1192C4—61no—
1193C4—92no—
1194C4—92no—
1195C4—181no—
1196C4—541no—
1197C4—541no—
1198C3—21no—
1199C3—21no—
1200C3—21no—
1201C3—41no—
1202C3#1059405411yescharacteristic, complemented
1203C3#1059405511yescharacteristic, complemented
1204C3#1059462311yescharacteristic, complemented
1205C2—62no—
1206C2—62no—
1207C2—182no—
1208C2—361no—
1209C2—361no—
1210C2D3×#379511yescharacteristic
1211C2D3×#379611yescharacteristic
1212C2#1172444011yescharacteristic
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×#89041C2semidirect
2. C2×D32×Dic3C2semidirect
3. #11723507C2semidirect
4. #11723488C2semidirect
5. #11723487C2semidirect
6. C3×#63923C2semidirect
7. C3×#63896C2semidirect
8. C3×#63881C2semidirect
9. #11722997C2semidirect
10. #11722960C2semidirect
11. #11722955C2semidirect
12. #11722947C2semidirect
13. #11722928C2semidirect
14. #11722927C2semidirect
15. #11722922C2semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
22. C2×C3×#634C22semidirect
24. C2×#6295C22semidirect
26. C2×#6294C22semidirect
38. #88857C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88807C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
45. #88803C22semidirect
46. #88803C22semidirect
47. #88803C22semidirect
49. Dic3×C3⋊Dic3C22semidirect
50. C3×#3724C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
53. C3×#3722C22semidirect
55. C3×Dic32C22semidirect
77. #63923D3semidirect
82. #63896D3semidirect
95. #63881D3semidirect
128. #6294D4semidirect
149. C2×C4×C3⋊D3C2×D3semidirect
150. C2×#634C2×D3semidirect
240. C3×Dic3⋊C4C2×D3semidirect
241. C3×Dic3⋊C4C2×D3semidirect
244. #3724C2×D3semidirect
251. Dic3⋊Dic3C2×D3semidirect
253. #3722C2×D3semidirect
273. Dic32C2×D3semidirect
288. C2×C32×D3#41semidirect
289. C2×C32×D3#41semidirect
617. Dic3⋊C4D32semidirect
689. C2×C3×D3#235semidirect
690. C2×C3×D3#237semidirect
691. C2×C3×D3#237semidirect
692. C2×C3×D3#239semidirect
758. C33#525semidirect
1038. C2×D3#3795semidirect
1039. C2×D3#3796semidirect
1093. C32#5547semidirect
1094. C32#5586semidirect
1095. C32#5627semidirect
1202. C3#10594054semidirect
1203. C3#10594055semidirect
1204. C3#10594623semidirect

Maximal subgroups

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

subgroupindex
C2×#890412
C2×D32×Dic32
#117235072
#117234882
#117234872
C3×#639232
C3×#638962
C3×#638812
#117229972
#117229602
#117229552
#117229472
#117229282
#117229272
#117229222
#105946233
#105940553
#105940543