Finite Group Databasebeta

← #13170738

Subgroups — #13170738

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×#88962C211yesmaximal, characteristic, complemented
2C2×D32×Dic3C211yesmaximal, characteristic, complemented
3#11723691C211yesmaximal, characteristic, complemented
4#11723482C211yesmaximal, characteristic, complemented
5#11723479C211yesmaximal, characteristic, complemented
6#11723461C211yesmaximal, characteristic, complemented
7C3×#63923C211yesmaximal, characteristic, complemented
8C3×#63893C211yesmaximal, characteristic, complemented
9C3×#63878C211yesmaximal, characteristic, complemented
10#11722990C211yesmaximal, characteristic, complemented
11#11722974C211yesmaximal, characteristic, complemented
12#11722959C211yesmaximal, characteristic, complemented
13#11722948C211yesmaximal, characteristic, complemented
14#11722937C211yesmaximal, characteristic, complemented
15#11722928C211yesmaximal, characteristic, complemented
16#10594627—31nomaximal
17#10594078—31nomaximal
18#10594055—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6294C2211yescharacteristic, complemented
23C2×#6292C2211yescharacteristic
24C2×#6292C2211yescharacteristic, complemented
25C2×#6291C2211yescharacteristic
26C2×#6291C2211yescharacteristic
27C2×#6289C2211yescharacteristic, complemented
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic
30C2×D3×C3⋊Dic3C2211yescharacteristic
31C2×C3×#627C2211yescharacteristic, complemented
32C2×C3×#626C2211yescharacteristic
33C2×C3×#626C2211yescharacteristic
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36#88962—24no—
37D32×Dic3—24no—
38#88859C2211yescharacteristic, complemented
39C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic, complemented
44#88814C2211yescharacteristic
45#88814C2211yescharacteristic, complemented
46#88807C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48#88804C2211yescharacteristic, complemented
49#88803C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×Dic32C2211yescharacteristic, complemented
56C2×#3804—31no—
57C22×D3×Dic3—31no—
58C22×D3×Dic3—31no—
59C2×C4×D32—31no—
60C2×#3799—31no—
61C2×#3796—31no—
62#64104—31no—
63#64095—31no—
64#64090—31no—
65C3×#897—31no—
66C3×#892—31no—
67C3×#882—31no—
68C3×#882—31no—
69C3×#878—31no—
70C3×#877—31no—
71#63978—31no—
72#63977—31no—
73#63977—31no—
74#67⋊Dic3—31no—
75#63962—31no—
76#63923—31no—
77#63923D311yescharacteristic, complemented
78#63909—31no—
79#63898—31no—
80#63894—31no—
81#63894—31no—
82#63893—31no—
83#63893D311yescharacteristic, complemented
84Dic3×D12—31no—
85Dic3×D12—31no—
86#63890—31no—
87#63890—31no—
88#63890—31no—
89#63890—61no—
90#63887—31no—
91#63886—31no—
92#63886—31no—
93#63886—31no—
94#63886—61no—
95#63884—31no—
96#63881—31no—
97#63880—31no—
98#63880—31no—
99#63880—31no—
100#63880—31no—
101#63880—61no—
102#63878D311yescharacteristic, complemented
103#63871—31no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
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⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C3×C4⋊(C3⋊D3)—22no—
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6294—22no—
124#6294—22no—
125#6292—22no—
126#6292—22no—
127#6291—22no—
128#6291—22no—
129#6289—22no—
130Dic3×C3⋊D3—22no—
131D3×C3⋊Dic3—22no—
132D3×C3⋊Dic3—22no—
133C3×#627—22no—
134C3×#626—22no—
135C3×#626—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3D414yescomplemented
138#5627—91no—
139#5586—91no—
140#5524—91no—
141C23×C3×D3—31no—
142C23×C3×D3—31no—
143C22×D32C2×D311yescharacteristic
144C2×#638—31no—
145C2×#638—31no—
146C22×C3⋊Dic3—31no—
147C22×C3⋊Dic3—31no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C22×C3×Dic3—31no—
156C22×C3×Dic3—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×Dic6—31no—
165C2×C3×Dic6—31no—
166C2×#627C2×D311yescharacteristic, complemented
167C2×#626—31no—
168C2×#626—31no—
169C2×#626—31no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—61no—
176C2×#626—61no—
177C2×#626—61no—
178C2×#626—61no—
179C2×#626C2×D311yescharacteristic
180C2×#626C2×D311yescharacteristic
181C2×#624—31no—
182C2×#624—31no—
183C2×#624—31no—
184C2×#624—31no—
185C2×#624—61no—
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—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
204C4×D32—64no—
205#3799—64no—
206#3796—64no—
207C32×C4⋊C4—31no—
208C32×C22⋊C4—31no—
209C32×C22⋊C4—31no—
210#3752—31no—
211#3752—31no—
212#3752—31no—
213#3752—31no—
214#3752—31no—
215#3752—61no—
216#3752—61no—
217#3752—61no—
218#3752—121no—
219C4⋊(C3⋊Dic3)—31no—
220C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
221#3750—31no—
222C4×C3⋊Dic3C2×D311yescharacteristic, complemented
223C3×#217—31no—
224C3×#217—31no—
225C3×(C2×D3)⋊C4—21no—
226C3×(C2×D3)⋊C4—21no—
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×C4⋊Dic3—31no—
237C3×C4⋊Dic3—31no—
238C3×C4⋊Dic3—31no—
239C3×C4⋊Dic3—61no—
240C3×Dic3⋊C4—21no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4C2×D311yescharacteristic, complemented
244C3×Dic3⋊C4C2×D311yescharacteristic, complemented
245C3×C4×Dic3—31no—
246C3×C4×Dic3—31no—
247C3×C4×Dic3—31no—
248C3×C4×Dic3—31no—
249C3×C4×Dic3—61no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—61no—
255Dic3⋊Dic3—61no—
256Dic3⋊Dic3C2×D311yescharacteristic, complemented
257Dic3⋊Dic3C2×D311yescharacteristic, complemented
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—61no—
263#3722C2×D311yescharacteristic
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—31no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272(C2×D3)⋊Dic3C2×D311yescharacteristic
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#4112yescomplemented
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⋊Dic3C2×D412yes—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3C2×D412yes—
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×#117—91no—
310#953—91no—
311#946—91no—
312#939—91no—
313#939—91no—
314#935—91no—
315D4×Dic3—91no—
316D4×Dic3—91no—
317#930—91no—
318#897—31no—
319#897—91no—
320#895—91no—
321#895—91no—
322#895—91no—
323#895—181no—
324#894—91no—
325#894—91no—
326#893—91no—
327#893—91no—
328#892—31no—
329#886—91no—
330#886—91no—
331#886—91no—
332#886—181no—
333#882—31no—
334#882—31no—
335#882—91no—
336#882—91no—
337#67⋊C4—91no—
338#67⋊C4—91no—
339#67⋊C4—91no—
340#67⋊C4—91no—
341#67⋊C4—181no—
342#878—31no—
343#878—91no—
344#877—31no—
345C4×D12—91no—
346C4×D12—91no—
347C4×D12—91no—
348C4×D12—91no—
349C23×C32—31no—
350C23×C32—31no—
351C22×C3⋊D3—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—61no—
355C22×C3⋊D3—61no—
356C22×C3⋊D3—61no—
357C22×C3⋊D3—121no—
358C22×C3⋊D3C22×D311yescharacteristic
359C22×C3⋊D3C22×D311yescharacteristic
360C22×C3×D3—21no—
361C22×C3×D3—21no—
362C22×C3×D3—31no—
363C22×C3×D3—31no—
364C22×C3×D3—31no—
365C22×C3×D3—31no—
366C22×C3×D3—61no—
367C22×C3×D3—61no—
368C22×C3×D3—62no—
369C22×C3×D3—62no—
370C22×C3×D3—62no—
371C22×C3×D3—62no—
372C22×C3×D3—62no—
373C22×C3×D3—62no—
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—
381C2×C32×C4—21no—
382C2×C32×C4—21no—
383C2×C32×C4—21no—
384C2×C32×C4—31no—
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—
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—62no—
401C2×C3⋊Dic3—62no—
402C2×C3⋊Dic3—121no—
403C2×C3⋊Dic3C22×D311yescharacteristic
404C2×C3⋊Dic3C22×D311yescharacteristic
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—
412C3×#67—62no—
413C3×#67—62no—
414C2×C3×Dic3—21no—
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—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—62no—
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
439C2×C3×Dic3C22×D311yescharacteristic
440C3×D12—62no—
441C3×D12—62no—
442C3×D12—62no—
443C3×D12—62no—
444C3×D12—122no—
445C3×C4×D3—34no—
446C3×C4×D3—62no—
447C3×Dic6—62no—
448C3×Dic6—62no—
449#627—22no—
450#626—22no—
451#626—22no—
452#626—62no—
453#626—62no—
454#626—64no—
455#626—62no—
456#626—62no—
457#626—62no—
458#626—62no—
459#626—62no—
460#626—62no—
461#626—122no—
462#626—122no—
463#626—122no—
464#624—62no—
465#624—62no—
466#624—62no—
467#624—62no—
468#624—122no—
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—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—
490C3×C3⋊D3—41no—
491C32×D3—22no—
492C32×D3—22no—
493C24×C3—91no—
494C23×D3—31no—
495C23×D3—31no—
496C2×C3×Q8—91no—
497C2×C3×D4—91no—
498C2×C3×D4—91no—
499C2×C3×D4—91no—
500C22×C3×C4—91no—
501C22×C3×C4—91no—
502C2×#67—31no—
503C2×#67—31no—
504C2×#67—91no—
505C2×#67—91no—
506C2×#67—91no—
507C2×#67—91no—
508C2×#67—91no—
509C2×#67—91no—
510C2×#67—181no—
511C2×#67—181no—
512C22×Dic3—31no—
513C22×Dic3—31no—
514C22×Dic3—91no—
515C22×Dic3—91no—
516C22×Dic3—91no—
517C22×Dic3—91no—
518C22×Dic3—91no—
519C22×Dic3—91no—
520C22×Dic3—91no—
521C22×Dic3—181no—
522C22×Dic3—181no—
523C22×Dic3—184no—
524#239—184no—
525#237—184no—
526#235—184no—
527C2×D12—31no—
528C2×D12—31no—
529C2×D12—31no—
530C2×D12—31no—
531C2×D12—61no—
532C2×D12—91no—
533C2×D12—91no—
534C2×D12—91no—
535C2×D12—91no—
536C2×D12—91no—
537C2×D12—91no—
538C2×D12—181no—
539C2×D12—181no—
540C2×C4×D3—31no—
541C2×C4×D3—31no—
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—91no—
550C2×C4×D3—91no—
551C2×C4×D3—91no—
552C2×C4×D3—91no—
553C2×C4×D3—181no—
554C2×C4×D3—181no—
555C2×C4×D3—184no—
556C2×C4×D3—184no—
557C2×Dic6—31no—
558C2×Dic6—31no—
559C3×C4⋊C4—31no—
560C3×C4⋊C4—31no—
561C3×C4⋊C4—61no—
562C3×C4⋊C4—91no—
563C3×C4⋊C4—91no—
564C3×C4⋊C4—91no—
565C3×C22⋊C4—31no—
566C3×C22⋊C4—31no—
567C3×C22⋊C4—31no—
568C3×C22⋊C4—31no—
569C3×C22⋊C4—61no—
570C3×C22⋊C4—61no—
571C3×C22⋊C4—91no—
572C3×C22⋊C4—91no—
573C3×C22⋊C4—91no—
574C3×C42—91no—
575C3×C42—91no—
576#217—31no—
577#217—31no—
578#217—91no—
579#217—91no—
580#217—91no—
581(C2×D3)⋊C4—31no—
582(C2×D3)⋊C4—31no—
583(C2×D3)⋊C4—31no—
584(C2×D3)⋊C4—31no—
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—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)⋊C4—181no—
601(C2×D3)⋊C4—181no—
602(C2×D3)⋊C4—361no—
603(C2×D3)⋊C4D3211yescharacteristic
604(C2×D3)⋊C4D3211yescharacteristic
605C4⋊Dic3—31no—
606C4⋊Dic3—31no—
607C4⋊Dic3—31no—
608C4⋊Dic3—31no—
609C4⋊Dic3—61no—
610C4⋊Dic3—91no—
611C4⋊Dic3—91no—
612C4⋊Dic3—91no—
613C4⋊Dic3—181no—
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×Dic3—31no—
624C4×Dic3—31no—
625C4×Dic3—61no—
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×C32C23×D311yescharacteristic
637C22×C32C23×D311yescharacteristic
638C22×C32C23×D311yescharacteristic
639C2×C3⋊D3—21no—
640C2×C3⋊D3—21no—
641C2×C3⋊D3—21no—
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—22no—
675C2×C3×D3—22no—
676C2×C3×D3—32no—
677C2×C3×D3—32no—
678C2×C3×D3—41no—
679C2×C3×D3—41no—
680C2×C3×D3—41no—
681C2×C3×D3—41no—
682C2×C3×D3—62no—
683C2×C3×D3—68no—
684C2×C3×D3—68no—
685C2×C3×D3—61no—
686C2×C3×D3—61no—
687C2×C3×D3—61no—
688C2×C3×D3—61no—
689C2×C3×D3—61no—
690C2×C3×D3—61no—
691C2×C3×D3—61no—
692C2×C3×D3—61no—
693C2×C3×D3—61no—
694C2×C3×D3—61no—
695C2×C3×D3—121no—
696C2×C3×D3—121no—
697C2×C3×D3—121no—
698C2×C3×D3—121no—
699C2×C3×D3—121no—
700C2×C3×D3C2×D1212yes—
701C2×C3×D3D3×D412yes—
702C2×C3×D3#23712yescomplemented
703C2×C3×D3#23912yescomplemented
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—61no—
715C32×C4—81no—
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—21no—
728C3×Dic3—21no—
729C3×Dic3—21no—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—22no—
734C3×Dic3—32no—
735C3×Dic3—32no—
736C3×Dic3—41no—
737C3×Dic3—41no—
738C3×Dic3—41no—
739C3×Dic3—62no—
740C3×Dic3—62no—
741C3×Dic3—61no—
742C3×Dic3—61no—
743C3×Dic3—61no—
744C3×Dic3—61no—
745C3×Dic3—61no—
746C3×Dic3—61no—
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—91no—
756C22⋊Q8—271no—
757#121—271no—
758#121—271no—
759#120—91no—
760#120—271no—
761C4×D4—271no—
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—61no—
772C23×C3—61no—
773C23×C3—91no—
774C23×C3—91no—
775C23×C3—182no—
776C23×C3—182no—
777C23×C3—182no—
778C22×D3—31no—
779C22×D3—31no—
780C22×D3—31no—
781C22×D3—31no—
782C22×D3—61no—
783C22×D3—61no—
784C22×D3—62no—
785C22×D3—62no—
786C22×D3—62no—
787C22×D3—62no—
788C22×D3—62no—
789C22×D3—62no—
790C22×D3—91no—
791C22×D3—91no—
792C22×D3—91no—
793C22×D3—181no—
794C22×D3—181no—
795C22×D3—181no—
796C22×D3—361no—
797C22×D3C2×D3211yescharacteristic
798C22×D3C2×D3211yescharacteristic
799C3×Q8—182no—
800C3×D4—182no—
801C3×D4—182no—
802C3×D4—182no—
803C2×C3×C4—21no—
804C2×C3×C4—21no—
805C2×C3×C4—21no—
806C2×C3×C4—31no—
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—31no—
814C2×C3×C4—41no—
815C2×C3×C4—61no—
816C2×C3×C4—61no—
817C2×C3×C4—61no—
818C2×C3×C4—61no—
819C2×C3×C4—94no—
820C2×C3×C4—91no—
821C2×C3×C4—91no—
822C2×C3×C4—91no—
823C2×C3×C4—91no—
824C2×C3×C4—182no—
825C2×C3×C4C2×D3211yescharacteristic
826C2×C3×C4C2×D3211yescharacteristic
827C2×C3×C4C2×D3211yescharacteristic
828#67—62no—
829#67—62no—
830#67—182no—
831#67—182no—
832#67—182no—
833#67—182no—
834#67—182no—
835#67—184no—
836#67—182no—
837#67—362no—
838C2×Dic3—31no—
839C2×Dic3—31no—
840C2×Dic3—34no—
841C2×Dic3—31no—
842C2×Dic3—31no—
843C2×Dic3—31no—
844C2×Dic3—31no—
845C2×Dic3—31no—
846C2×Dic3—31no—
847C2×Dic3—61no—
848C2×Dic3—61no—
849C2×Dic3—61no—
850C2×Dic3—61no—
851C2×Dic3—62no—
852C2×Dic3—91no—
853C2×Dic3—91no—
854C2×Dic3—91no—
855C2×Dic3—181no—
856C2×Dic3—181no—
857C2×Dic3—181no—
858C2×Dic3—182no—
859C2×Dic3—182no—
860C2×Dic3—182no—
861C2×Dic3—182no—
862C2×Dic3—182no—
863C2×Dic3—182no—
864C2×Dic3—182no—
865C2×Dic3—361no—
866C2×Dic3—362no—
867C2×Dic3—362no—
868C2×Dic3C2×D3211yescharacteristic
869C2×Dic3C2×D3211yescharacteristic
870C2×Dic3C2×D3211yescharacteristic
871C2×Dic3C2×D3211yescharacteristic
872D12—62no—
873D12—62no—
874D12—62no—
875D12—62no—
876D12—122no—
877D12—182no—
878D12—182no—
879D12—182no—
880D12—182no—
881D12—182no—
882D12—182no—
883D12—362no—
884D12—362no—
885C4×D3—34no—
886C4×D3—62no—
887C4×D3—182no—
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—182no—
898C4×D3—362no—
899C4×D3—362no—
900Dic6—62no—
901Dic6—62no—
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×C32C22×D1211yescharacteristic
917C2×C32C2×D3×D411yescharacteristic
918C2×C32C2×D3×D411yescharacteristic
919C2×C32C2×#23711yescharacteristic
920C2×C32C2×#23711yescharacteristic
921C2×C32C2×#23911yescharacteristic
922C2×C32D3×#4111yescharacteristic
923C2×C32D3×#4111yescharacteristic
924C2×C32D3×#4111yescharacteristic
925C3⋊D3—22no—
926C3⋊D3—41no—
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—62no—
941C3×D3—62no—
942C3×D3—122no—
943C3×D3—121no—
944C3×D3—121no—
945C3×D3—241no—
946C24—91no—
947#41—544no—
948C2×Q8—91no—
949C2×D4—91no—
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—271no—
959C22×C4—271no—
960C22×C4—271no—
961C22×C4—271no—
962C22×C4—271no—
963C22×C4—271no—
964C22×C4—544no—
965C4⋊C4—31no—
966C4⋊C4—91no—
967C4⋊C4—91no—
968C4⋊C4—91no—
969C4⋊C4—271no—
970C4⋊C4—271no—
971C22⋊C4—31no—
972C22⋊C4—31no—
973C22⋊C4—91no—
974C22⋊C4—91no—
975C22⋊C4—91no—
976C22⋊C4—271no—
977C22⋊C4—271no—
978C22⋊C4—271no—
979C22⋊C4—271no—
980C22⋊C4—271no—
981C42—91no—
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—92no—
1002C22×C3—121no—
1003C22×C3—121no—
1004C22×C3—121no—
1005C22×C3—121no—
1006C22×C3—188no—
1007C22×C3—181no—
1008C22×C3—181no—
1009C22×C3—181no—
1010C22×C3—181no—
1011C22×C3—181no—
1012C22×C3C22×D3211yescharacteristic
1013C22×C3C22×D3211yescharacteristic
1014C22×C3C22×D3211yescharacteristic
1015C2×D3—21no—
1016C2×D3—21no—
1017C2×D3—21no—
1018C2×D3—21no—
1019C2×D3—32no—
1020C2×D3—32no—
1021C2×D3—62no—
1022C2×D3—68no—
1023C2×D3—68no—
1024C2×D3—61no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—61no—
1030C2×D3—61no—
1031C2×D3—61no—
1032C2×D3—61no—
1033C2×D3—61no—
1034C2×D3—121no—
1035C2×D3—121no—
1036C2×D3—121no—
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×D3#379612yescomplemented
1061C2×D3D3×D1212yes—
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—61no—
1072C3×C4—61no—
1073C3×C4—61no—
1074C3×C4—61no—
1075C3×C4—61no—
1076C3×C4—61no—
1077C3×C4—81no—
1078C3×C4—92no—
1079C3×C4—121no—
1080C3×C4—121no—
1081C3×C4—121no—
1082C3×C4—181no—
1083C3×C4—181no—
1084C3×C4—181no—
1085Dic3—21no—
1086Dic3—21no—
1087Dic3—21no—
1088Dic3—32no—
1089Dic3—32no—
1090Dic3—62no—
1091Dic3—62no—
1092Dic3—61no—
1093Dic3—61no—
1094Dic3—61no—
1095Dic3—61no—
1096Dic3—61no—
1097Dic3—61no—
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#558611yescharacteristic, complemented
1114C32#562711yescharacteristic, complemented
1115C23—31no—
1116C23—31no—
1117C23—91no—
1118C23—91no—
1119C23—182no—
1120C23—182no—
1121C23—182no—
1122C23—271no—
1123Q8—182no—
1124D4—182no—
1125D4—182no—
1126D4—182no—
1127D4—542no—
1128D4—542no—
1129D4—542no—
1130D4—542no—
1131C2×C4—31no—
1132C2×C4—31no—
1133C2×C4—31no—
1134C2×C4—31no—
1135C2×C4—94no—
1136C2×C4—91no—
1137C2×C4—91no—
1138C2×C4—91no—
1139C2×C4—91no—
1140C2×C4—182no—
1141C2×C4—271no—
1142C2×C4—542no—
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—182no—
1168C2×C3—361no—
1169C2×C3C2×#379611yescharacteristic
1170C2×C3C2×D3×D1211yescharacteristic
1171C2×C3C2×D3×D1211yescharacteristic
1172C2×C3D32×D411yescharacteristic
1173C2×C3D3×#23711yescharacteristic
1174C2×C3D3×#23711yescharacteristic
1175C2×C3D3×#23711yescharacteristic
1176C2×C3#6431211yescharacteristic
1177C2×C3D3×#23911yescharacteristic
1178D3—22no—
1179D3—22no—
1180D3—62no—
1181D3—62no—
1182D3—122no—
1183D3—121no—
1184D3—121no—
1185D3—241no—
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—92no—
1200C22—188no—
1201C22—181no—
1202C22—181no—
1203C22—181no—
1204C22—181no—
1205C22—181no—
1206C22—541no—
1207C22—541no—
1208C22—541no—
1209C22C2×D3311yescharacteristic
1210C4—21no—
1211C4—32no—
1212C4—61no—
1213C4—61no—
1214C4—61no—
1215C4—92no—
1216C4—181no—
1217C4—181no—
1218C4—181no—
1219C4—541no—
1220C3—21no—
1221C3—21no—
1222C3—21no—
1223C3—41no—
1224C3#1059405511yescharacteristic, complemented
1225C3#1059407811yescharacteristic, complemented
1226C3#1059462711yescharacteristic, complemented
1227C2—62no—
1228C2—62no—
1229C2—182no—
1230C2—361no—
1231C2—1081no—
1232C2D3×#379611yescharacteristic
1233C2D32×D1211yescharacteristic
1234C2#1172440811yescharacteristic
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×#88962C2semidirect
2. C2×D32×Dic3C2semidirect
3. #11723691C2semidirect
4. #11723482C2semidirect
5. #11723479C2semidirect
6. #11723461C2semidirect
7. C3×#63923C2semidirect
8. C3×#63893C2semidirect
9. C3×#63878C2semidirect
10. #11722990C2semidirect
11. #11722974C2semidirect
12. #11722959C2semidirect
13. #11722948C2semidirect
14. #11722937C2semidirect
15. #11722928C2semidirect
22. C2×#6294C22semidirect
24. C2×#6292C22semidirect
27. C2×#6289C22semidirect
31. C2×C3×#627C22semidirect
38. #88859C22semidirect
39. C3×C4⋊(C3⋊Dic3)C22semidirect
40. C3×C4×C3⋊Dic3C22semidirect
43. C32×Dic3⋊C4C22semidirect
45. #88814C22semidirect
46. #88807C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
48. #88804C22semidirect
49. #88803C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
77. #63923D3semidirect
83. #63893D3semidirect
102. #63878D3semidirect
137. C3×D3×Dic3D4semidirect
166. C2×#627C2×D3semidirect
220. C4⋊(C3⋊Dic3)C2×D3semidirect
222. C4×C3⋊Dic3C2×D3semidirect
243. C3×Dic3⋊C4C2×D3semidirect
244. C3×Dic3⋊C4C2×D3semidirect
256. Dic3⋊Dic3C2×D3semidirect
257. Dic3⋊Dic3C2×D3semidirect
273. Dic32C2×D3semidirect
283. C2×C3×C3⋊D3#41semidirect
289. C2×C32×D3#41semidirect
483. D3×Dic3D12semidirect
620. Dic3⋊C4D32semidirect
665. C2×C3⋊D3#237semidirect
702. C2×C3×D3#237semidirect
703. C2×C3×D3#239semidirect
766. C33#525semidirect
1060. C2×D3#3796semidirect
1112. C32#5524semidirect
1113. C32#5586semidirect
1114. C32#5627semidirect
1224. C3#10594055semidirect
1225. C3#10594078semidirect
1226. C3#10594627semidirect

Maximal subgroups

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

subgroupindex
C2×#889622
C2×D32×Dic32
#117236912
#117234822
#117234792
#117234612
C3×#639232
C3×#638932
C3×#638782
#117229902
#117229742
#117229592
#117229482
#117229372
#117229282
#105946273
#105940783
#105940553