Finite Group Databasebeta

← #13170743

Subgroups — #13170743

Order 1728.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88959C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723692C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic, complemented
5#11723525C211yesmaximal, characteristic, complemented
6#11723484C211yesmaximal, characteristic, complemented
7C3×#63891C211yesmaximal, characteristic, complemented
8C3×#63880C211yesmaximal, characteristic, complemented
9C3×#63877C211yesmaximal, characteristic, complemented
10#11722987C211yesmaximal, characteristic, complemented
11#11722982C211yesmaximal, characteristic, complemented
12#11722966C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14#11722933C211yesmaximal, characteristic, complemented
15#11722932C211yesmaximal, characteristic, complemented
16#10594266—31nomaximal
17#10594079—31nomaximal
18#10593997—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×#6296C2211yescharacteristic, complemented
22C2×#6294C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6291C2211yescharacteristic, complemented
27C2×#6289C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×#6289C2211yescharacteristic, complemented
30C2×C3×#626C2211yescharacteristic
31C2×C3×#625C2211yescharacteristic
32C2×C3×#624C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic, complemented
36#88959—24no—
37D3×#624—24no—
38C3×#3752C2211yescharacteristic
39C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40C3×#3750C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C32×C4×Dic3C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88814C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50C3×#3724C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C22×#624—31no—
57C2×#3804—31no—
58C2×#3804—31no—
59C2×C4×D32—31no—
60C2×C4×D32—31no—
61C2×#3798—31no—
62#64093—31no—
63#64091—31no—
64C4×C4⋊(C3⋊D3)—31no—
65C3×#886—31no—
66C3×#883—31no—
67C3×#67⋊C4—31no—
68C3×#877—31no—
69C3×C4×D12—31no—
70C3×#872—31no—
71#63983—31no—
72#63981—31no—
73#63971—31no—
74#63966—31no—
75#63952—31no—
76#63923—31no—
77#63923—31no—
78#63923—61no—
79#63922—31no—
80#63910—31no—
81#63910—31no—
82#63910—31no—
83#63910—61no—
84#63904—31no—
85C4×#626—31no—
86C4×#626—31no—
87#63899—31no—
88#63895—31no—
89#63895—31no—
90#63895—31no—
91#63894—31no—
92#63894—31no—
93#63894—31no—
94#63894—61no—
95#63893—31no—
96#63891D311yescharacteristic, complemented
97#63890—31no—
98#63886—31no—
99#63880—31no—
100#63880D311yescharacteristic, complemented
101#63877D311yescharacteristic, complemented
102#63865—31no—
103#63850—31no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×D3×C3⋊D3—22no—
110C2×D3×C3⋊D3—22no—
111C2×D3×C3⋊D3—22no—
112C2×C33×C4C2311yescharacteristic
113C4⋊(C3⋊(C3⋊D3))—22no—
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
122C2×C32×Dic3C2311yescharacteristic
123#6296—22no—
124#6294—22no—
125#6292—22no—
126#6291—22no—
127#6291—22no—
128#6291—22no—
129#6289—22no—
130#6289—22no—
131#6289—22no—
132C3×#626—22no—
133C3×#625—22no—
134C3×#624—22no—
135C3×D3×Dic3—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3D414yescomplemented
138#5656—91no—
139#5547—91no—
140#5524—91no—
141C23×C3⋊D3—31no—
142C22×D32—31no—
143C22×D32—31no—
144C22×D32—61no—
145C2×#638—31no—
146C2×#638—31no—
147C2×#638—31no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4⋊(C3⋊D3)—31no—
152C2×C4⋊(C3⋊D3)—61no—
153C2×C4⋊(C3⋊D3)—61no—
154C2×C4⋊(C3⋊D3)—61no—
155C2×C4⋊(C3⋊D3)—121no—
156C2×C4×C3⋊D3—31no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—31no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C22×C3×Dic3—31no—
163C22×C3×Dic3—31no—
164C22×C3×Dic3—31no—
165C2×C3×D12—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×C3×C4×D3—31no—
171C2×#627—31no—
172C2×#627—31no—
173C2×#627—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—31no—
178C2×#626—31no—
179C2×#626—31no—
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—61no—
183C2×#626—61no—
184C2×#626—61no—
185C2×#626—61no—
186C2×#626C2×D311yescharacteristic
187C2×#625C2×D311yescharacteristic
188C2×#624—31no—
189C2×#624—31no—
190C2×#624—31no—
191C2×#624—31no—
192C2×#624—31no—
193C2×#624—31no—
194C2×#624—31no—
195C2×#624—64no—
196C2×#624—61no—
197C2×#624—61no—
198C2×#624—61no—
199C2×#624C2×D311yescharacteristic
200#3804—64no—
201#3804—64no—
202C2×D3×Dic3—31no—
203C2×D3×Dic3—31no—
204C2×D3×Dic3C2×D311yescharacteristic
205C2×D3×Dic3C2×D311yescharacteristic
206C2×D3×Dic3C2×D311yescharacteristic, complemented
207C4×D32—64no—
208C4×D32—64no—
209#3798—64no—
210C32×C22⋊C4—31no—
211C32×C22⋊C4—31no—
212C32×C42—31no—
213#3752—31no—
214#3752—31no—
215#3752—31no—
216#3752—31no—
217#3752C2×D311yescharacteristic
218C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
219#3750C2×D311yescharacteristic, complemented
220C3×#217—31no—
221C3×#217—31no—
222C3×(C2×D3)⋊C4—21no—
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—61no—
229C3×(C2×D3)⋊C4C2×D311yescharacteristic
230C3×(C2×D3)⋊C4C2×D311yescharacteristic
231C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
232C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
233C3×C4⋊Dic3—31no—
234C3×C4⋊Dic3—31no—
235C3×C4⋊Dic3—31no—
236C3×C4⋊Dic3—31no—
237C3×C4⋊Dic3—61no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
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⋊Dic3C2×D311yescharacteristic, complemented
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265#3722—61no—
266#3722—61no—
267#3722—61no—
268#3722—61no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
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×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×D3—21no—
289C2×C32×D3C2×D412yes—
290D3×C3⋊D3—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—
301C2×#237—91no—
302C2×#235—91no—
303C2×#235—91no—
304C22×C4×D3—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×#123—91no—
308C3×C4×D4—91no—
309C3×#117—91no—
310#939—91no—
311#937—91no—
312#937—91no—
313#929—91no—
314C4×#67—91no—
315C4×#67—91no—
316#897—91no—
317#897—91no—
318#896—91no—
319#896—91no—
320#896—91no—
321#895—91no—
322#895—91no—
323#894—91no—
324#893—91no—
325#893—91no—
326#886—31no—
327#886—91no—
328#884—91no—
329#884—91no—
330#884—91no—
331#884—181no—
332#883—31no—
333#882—91no—
334#882—91no—
335#882—91no—
336#882—91no—
337#882—181no—
338#67⋊C4—31no—
339#67⋊C4—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—
351C22×C3⋊D3—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—31no—
355C22×C3⋊D3—31no—
356C22×C3⋊D3—31no—
357C22×C3⋊D3—61no—
358C22×C3⋊D3—61no—
359C22×C3⋊D3—61no—
360C22×C3⋊D3—61no—
361C22×C3⋊D3—61no—
362C22×C3⋊D3—61no—
363C22×C3⋊D3—62no—
364C22×C3⋊D3—62no—
365C22×C3⋊D3—62no—
366C22×C3⋊D3—121no—
367C22×C3⋊D3—121no—
368C22×C3⋊D3C22×D311yescharacteristic
369C22×C3×D3—21no—
370C22×C3×D3—21no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—61no—
374C22×C3×D3C22×D311yescharacteristic
375C22×C3×D3C22×D311yescharacteristic
376C22×C3×D3C22×D311yescharacteristic
377C22×C3×D3C22×D311yescharacteristic
378C2×D32—62no—
379C2×D32—62no—
380C2×D32—62no—
381C2×D32—62no—
382C2×D32—62no—
383C2×D32—62no—
384C2×D32—122no—
385C2×D32—122no—
386C2×D32—122no—
387C2×C32×C4—21no—
388C2×C32×C4—21no—
389C2×C32×C4—21no—
390C2×C32×C4—31no—
391C2×C32×C4—31no—
392C2×C32×C4—31no—
393C2×C32×C4—31no—
394C2×C32×C4—41no—
395C2×C32×C4C22×D311yescharacteristic
396C2×C32×C4C22×D311yescharacteristic
397C2×C32×C4C22×D311yescharacteristic
398#638—62no—
399#638—62no—
400#638—62no—
401C2×C3⋊Dic3C22×D311yescharacteristic
402C2×C3⋊Dic3C22×D311yescharacteristic
403C2×C3⋊Dic3C22×D311yescharacteristic
404C2×C3⋊Dic3C22×D311yescharacteristic
405C2×C3⋊Dic3C22×D311yescharacteristic
406C4⋊(C3⋊D3)—62no—
407C4⋊(C3⋊D3)—62no—
408C4⋊(C3⋊D3)—62no—
409C4⋊(C3⋊D3)—64no—
410C4⋊(C3⋊D3)—62no—
411C4⋊(C3⋊D3)—122no—
412C4⋊(C3⋊D3)—122no—
413C4⋊(C3⋊D3)—124no—
414C4×C3⋊D3—62no—
415C4×C3⋊D3—62no—
416C4×C3⋊D3—62no—
417C3×#67—62no—
418C3×#67—62no—
419C3×#67—62no—
420C2×C3×Dic3—21no—
421C2×C3×Dic3—21no—
422C2×C3×Dic3—21no—
423C2×C3×Dic3—21no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—34no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—31no—
433C2×C3×Dic3—31no—
434C2×C3×Dic3—31no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—61no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—61no—
439C2×C3×Dic3—61no—
440C2×C3×Dic3—62no—
441C2×C3×Dic3—62no—
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C3×D12—62no—
451C3×C4×D3—34no—
452C3×C4×D3—62no—
453C3×C4×D3—62no—
454C3×C4×D3—62no—
455C3×C4×D3—62no—
456#627—62no—
457#627—62no—
458#627—62no—
459#626—22no—
460#626—62no—
461#626—62no—
462#626—62no—
463#626—62no—
464#626—62no—
465#626—62no—
466#626—62no—
467#626—62no—
468#626—122no—
469#626—122no—
470#626—122no—
471#626—122no—
472#625—22no—
473#624—22no—
474#624—62no—
475#624—62no—
476#624—62no—
477#624—62no—
478#624—62no—
479#624—62no—
480#624—62no—
481#624—122no—
482#624—122no—
483#624—122no—
484D3×Dic3—22no—
485D3×Dic3—22no—
486D3×Dic3—62no—
487D3×Dic3—62no—
488D3×Dic3D1214yescomplemented
489#525—271noSylow
490C2×C33C22×D411yescharacteristic
491C2×C33C2×#4111yescharacteristic
492C2×C33C2×#4111yescharacteristic
493C3⋊(C3⋊D3)—22no—
494C3⋊(C3⋊D3)—41no—
495C3×C3⋊D3—22no—
496C32×D3—22no—
497C32×D3—41no—
498C23×D3—91no—
499C23×D3—91no—
500C23×D3—91no—
501C23×D3—181no—
502C2×C3×D4—91no—
503C2×C3×D4—91no—
504C22×C3×C4—91no—
505C22×C3×C4—91no—
506C22×C3×C4—91no—
507C22×C3×C4—91no—
508C2×#67—31no—
509C2×#67—31no—
510C2×#67—31no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—91no—
517C2×#67—91no—
518C2×#67—181no—
519C2×#67—181no—
520C2×#67—181no—
521C22×Dic3—31no—
522C22×Dic3—31no—
523C22×Dic3—31no—
524C22×Dic3—91no—
525#237—184no—
526#235—184no—
527#235—184no—
528C2×D12—31no—
529C2×D12—91no—
530C2×D12—91no—
531C2×D12—91no—
532C2×D12—91no—
533C2×D12—91no—
534C2×D12—91no—
535C2×D12—91no—
536C2×D12—91no—
537C2×D12—181no—
538C2×D12—181no—
539C2×D12—181no—
540C2×D12—181no—
541C2×D12—361no—
542C2×C4×D3—31no—
543C2×C4×D3—31no—
544C2×C4×D3—31no—
545C2×C4×D3—31no—
546C2×C4×D3—31no—
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—91no—
554C2×C4×D3—91no—
555C2×C4×D3—91no—
556C2×C4×D3—91no—
557C2×C4×D3—91no—
558C2×C4×D3—181no—
559C2×C4×D3—181no—
560C2×C4×D3—181no—
561C2×C4×D3—184no—
562C2×C4×D3—184no—
563C2×C4×D3—184no—
564C2×Dic6—91no—
565C2×Dic6—91no—
566C2×Dic6—91no—
567C3×C4⋊C4—91no—
568C3×C4⋊C4—91no—
569C3×C4⋊C4—91no—
570C3×C4⋊C4—91no—
571C3×C4⋊C4—91no—
572C3×C22⋊C4—31no—
573C3×C22⋊C4—31no—
574C3×C22⋊C4—31no—
575C3×C22⋊C4—31no—
576C3×C22⋊C4—61no—
577C3×C22⋊C4—61no—
578C3×C22⋊C4—91no—
579C3×C22⋊C4—91no—
580C3×C22⋊C4—91no—
581C3×C42—31no—
582C3×C42—31no—
583C3×C42—61no—
584C3×C42—91no—
585#217—31no—
586#217—31no—
587#217—91no—
588(C2×D3)⋊C4—31no—
589(C2×D3)⋊C4—31no—
590(C2×D3)⋊C4—31no—
591(C2×D3)⋊C4—31no—
592(C2×D3)⋊C4—61no—
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—91no—
599(C2×D3)⋊C4—91no—
600(C2×D3)⋊C4—91no—
601(C2×D3)⋊C4—91no—
602(C2×D3)⋊C4—91no—
603(C2×D3)⋊C4—91no—
604(C2×D3)⋊C4—91no—
605(C2×D3)⋊C4—91no—
606(C2×D3)⋊C4—91no—
607(C2×D3)⋊C4—181no—
608(C2×D3)⋊C4—181no—
609(C2×D3)⋊C4—181no—
610(C2×D3)⋊C4—181no—
611(C2×D3)⋊C4D3211yescharacteristic
612(C2×D3)⋊C4D3211yescharacteristic, complemented
613C4⋊Dic3—31no—
614C4⋊Dic3—31no—
615C4⋊Dic3—31no—
616C4⋊Dic3—31no—
617C4⋊Dic3—61no—
618C4⋊Dic3—91no—
619Dic3⋊C4—31no—
620Dic3⋊C4—31no—
621Dic3⋊C4—31no—
622Dic3⋊C4—31no—
623Dic3⋊C4—31no—
624Dic3⋊C4—31no—
625Dic3⋊C4—61no—
626Dic3⋊C4—91no—
627Dic3⋊C4—91no—
628C4×Dic3—31no—
629C4×Dic3—31no—
630C4×Dic3D3211yescharacteristic, complemented
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—32no—
635C22×C32—41no—
636C22×C32—61no—
637C22×C32—61no—
638C22×C32—61no—
639C22×C32—61no—
640C22×C32—61no—
641C22×C32C23×D311yescharacteristic
642C22×C32C23×D311yescharacteristic
643C22×C32C23×D311yescharacteristic
644C2×C3⋊D3—21no—
645C2×C3⋊D3—21no—
646C2×C3⋊D3—32no—
647C2×C3⋊D3—32no—
648C2×C3⋊D3—32no—
649C2×C3⋊D3—62no—
650C2×C3⋊D3—62no—
651C2×C3⋊D3—62no—
652C2×C3⋊D3—61no—
653C2×C3⋊D3—68no—
654C2×C3⋊D3—61no—
655C2×C3⋊D3—61no—
656C2×C3⋊D3—61no—
657C2×C3⋊D3—61no—
658C2×C3⋊D3—61no—
659C2×C3⋊D3—61no—
660C2×C3⋊D3—62no—
661C2×C3⋊D3—61no—
662C2×C3⋊D3—61no—
663C2×C3⋊D3—61no—
664C2×C3⋊D3—61no—
665C2×C3⋊D3—61no—
666C2×C3⋊D3—61no—
667C2×C3⋊D3—61no—
668C2×C3⋊D3—61no—
669C2×C3⋊D3—122no—
670C2×C3⋊D3—121no—
671C2×C3⋊D3—121no—
672C2×C3⋊D3—122no—
673C2×C3⋊D3—121no—
674C2×C3⋊D3—121no—
675C2×C3⋊D3—121no—
676C2×C3⋊D3—121no—
677C2×C3⋊D3—121no—
678C2×C3⋊D3—121no—
679C2×C3⋊D3—121no—
680C2×C3⋊D3—121no—
681C2×C3⋊D3—121no—
682C2×C3⋊D3—121no—
683C2×C3⋊D3—121no—
684C2×C3⋊D3—121no—
685C2×C3⋊D3—241no—
686C2×C3⋊D3—241no—
687C2×C3⋊D3—241no—
688C2×C3⋊D3—241no—
689C2×C3⋊D3#23512yescomplemented
690C2×C3×D3—21no—
691C2×C3×D3—21no—
692C2×C3×D3—21no—
693C2×C3×D3—21no—
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—21no—
697C2×C3×D3—21no—
698C2×C3×D3—21no—
699C2×C3×D3—21no—
700C2×C3×D3—22no—
701C2×C3×D3—32no—
702C2×C3×D3—32no—
703C2×C3×D3—41no—
704C2×C3×D3—41no—
705C2×C3×D3—41no—
706C2×C3×D3—41no—
707C2×C3×D3—41no—
708C2×C3×D3—62no—
709C2×C3×D3—61no—
710C2×C3×D3—61no—
711C2×C3×D3—61no—
712C2×C3×D3—61no—
713C2×C3×D3—121no—
714C2×C3×D3—121no—
715C2×C3×D3C2×D1212yes—
716C2×C3×D3D3×D412yes—
717D32—68no—
718D32—68no—
719D32—128no—
720C32×C4—21no—
721C32×C4—22no—
722C32×C4—21no—
723C32×C4—21no—
724C32×C4—32no—
725C32×C4—41no—
726C32×C4—41no—
727C32×C4—42no—
728C32×C4—61no—
729C32×C4—61no—
730C32×C4—61no—
731C3⋊Dic3—21no—
732C3⋊Dic3—21no—
733C3⋊Dic3—21no—
734C3⋊Dic3—21no—
735C3⋊Dic3C2×D1212yes—
736C3×Dic3—21no—
737C3×Dic3—21no—
738C3×Dic3—21no—
739C3×Dic3—21no—
740C3×Dic3—21no—
741C3×Dic3—21no—
742C3×Dic3—22no—
743C3×Dic3—32no—
744C3×Dic3—32no—
745C3×Dic3—41no—
746C3×Dic3—41no—
747C3×Dic3—41no—
748C3×Dic3—62no—
749C3×Dic3—61no—
750C3×Dic3—61no—
751C3×Dic3—61no—
752C3×Dic3—61no—
753C3×Dic3—61no—
754C3×Dic3—61no—
755C3×Dic3—61no—
756C3×Dic3—61no—
757C3×Dic3—121no—
758C3×Dic3—121no—
759C3×Dic3—121no—
760C3×Dic3—121no—
761C3×Dic3C2×D1212yes—
762C3×Dic3D3×D412yes—
763C2×#41—271no—
764C23×C4—271no—
765#123—91no—
766#123—271no—
767C22⋊Q8—271no—
768C22⋊Q8—271no—
769#121—271no—
770#121—271no—
771#120—271no—
772#120—271no—
773C4×D4—91no—
774C4×D4—271no—
775C4×D4—271no—
776C4×D4—271no—
777#117—91no—
778C33#52511yescharacteristic, complemented, Sylow
779C23×C3—31no—
780C23×C3—31no—
781C23×C3—31no—
782C23×C3—31no—
783C23×C3—61no—
784C23×C3—61no—
785C23×C3—91no—
786C22×D3—31no—
787C22×D3—31no—
788C22×D3—61no—
789C22×D3—91no—
790C22×D3—91no—
791C22×D3—91no—
792C22×D3—91no—
793C22×D3—91no—
794C22×D3—91no—
795C22×D3—181no—
796C22×D3—181no—
797C22×D3—181no—
798C22×D3—181no—
799C22×D3—181no—
800C22×D3—181no—
801C22×D3—182no—
802C22×D3—182no—
803C22×D3—182no—
804C22×D3—182no—
805C22×D3—182no—
806C22×D3—182no—
807C22×D3—182no—
808C22×D3—182no—
809C22×D3—182no—
810C22×D3—361no—
811C22×D3—361no—
812C22×D3—362no—
813C22×D3—362no—
814C22×D3—362no—
815C22×D3C2×D3211yescharacteristic
816C22×D3C2×D3211yescharacteristic
817C3×D4—182no—
818C3×D4—182no—
819C2×C3×C4—21no—
820C2×C3×C4—21no—
821C2×C3×C4—21no—
822C2×C3×C4—31no—
823C2×C3×C4—31no—
824C2×C3×C4—31no—
825C2×C3×C4—31no—
826C2×C3×C4—31no—
827C2×C3×C4—31no—
828C2×C3×C4—31no—
829C2×C3×C4—31no—
830C2×C3×C4—41no—
831C2×C3×C4—61no—
832C2×C3×C4—61no—
833C2×C3×C4—61no—
834C2×C3×C4—61no—
835C2×C3×C4—94no—
836C2×C3×C4—91no—
837C2×C3×C4—91no—
838C2×C3×C4—91no—
839C2×C3×C4—91no—
840C2×C3×C4—91no—
841C2×C3×C4—182no—
842C2×C3×C4—182no—
843C2×C3×C4—182no—
844C2×C3×C4C2×D3211yescharacteristic
845C2×C3×C4C2×D3211yescharacteristic
846C2×C3×C4C2×D3211yescharacteristic
847#67—62no—
848#67—62no—
849#67—62no—
850#67—182no—
851#67—182no—
852#67—182no—
853#67—182no—
854#67—182no—
855#67—182no—
856#67—182no—
857#67—362no—
858#67—362no—
859#67—362no—
860C2×Dic3—31no—
861C2×Dic3—31no—
862C2×Dic3—34no—
863C2×Dic3—31no—
864C2×Dic3—31no—
865C2×Dic3—31no—
866C2×Dic3—31no—
867C2×Dic3—31no—
868C2×Dic3—31no—
869C2×Dic3—31no—
870C2×Dic3—31no—
871C2×Dic3—61no—
872C2×Dic3—61no—
873C2×Dic3—61no—
874C2×Dic3—61no—
875C2×Dic3—61no—
876C2×Dic3—62no—
877C2×Dic3—62no—
878C2×Dic3—182no—
879C2×Dic3C2×D3211yescharacteristic
880C2×Dic3C2×D3211yescharacteristic
881C2×Dic3C2×D3211yescharacteristic
882C2×Dic3C2×D3211yescharacteristic
883D12—62no—
884D12—182no—
885D12—182no—
886D12—182no—
887D12—184no—
888D12—182no—
889D12—182no—
890D12—182no—
891D12—182no—
892D12—182no—
893D12—362no—
894D12—362no—
895D12—364no—
896D12—362no—
897C4×D3—34no—
898C4×D3—62no—
899C4×D3—62no—
900C4×D3—62no—
901C4×D3—62no—
902C4×D3—182no—
903C4×D3—182no—
904C4×D3—182no—
905C4×D3—182no—
906C4×D3—182no—
907C4×D3—182no—
908C4×D3—182no—
909C4×D3—182no—
910C4×D3—182no—
911C4×D3—182no—
912C4×D3—182no—
913C4×D3—362no—
914C4×D3—362no—
915C4×D3—362no—
916Dic6—182no—
917Dic6—182no—
918Dic6—182no—
919C2×C32—21no—
920C2×C32—21no—
921C2×C32—21no—
922C2×C32—21no—
923C2×C32—21no—
924C2×C32—21no—
925C2×C32—21no—
926C2×C32—21no—
927C2×C32—21no—
928C2×C32—41no—
929C2×C32—41no—
930C2×C32—41no—
931C2×C32—62no—
932C2×C32—121no—
933C2×C32C22×D1211yescharacteristic
934C2×C32C2×#23511yescharacteristic
935C2×C32C2×D3×D411yescharacteristic
936C2×C32C2×D3×D411yescharacteristic
937C2×C32D3×#4111yescharacteristic
938C2×C32D3×#4111yescharacteristic
939C2×C32D3×#4111yescharacteristic
940C2×C32D3×#4111yescharacteristic
941C2×C32D3×#4111yescharacteristic
942C3⋊D3—22no—
943C3⋊D3—62no—
944C3⋊D3—62no—
945C3⋊D3—62no—
946C3⋊D3—122no—
947C3⋊D3—122no—
948C3⋊D3—122no—
949C3⋊D3—121no—
950C3⋊D3—122no—
951C3⋊D3—121no—
952C3⋊D3—121no—
953C3⋊D3—242no—
954C3⋊D3—241no—
955C3⋊D3—241no—
956C3⋊D3—242no—
957C3×D3—22no—
958C3×D3—22no—
959C3×D3—42no—
960C3×D3—41no—
961C3×D3—41no—
962C3×D3—62no—
963C3×D3—62no—
964C3×D3—81no—
965C3×D3—122no—
966C24—271no—
967#41—544no—
968C2×Q8—271no—
969C2×D4—91no—
970C2×D4—91no—
971C2×D4—271no—
972C2×D4—271no—
973C2×D4—271no—
974C2×D4—271no—
975C2×D4—271no—
976C22×C4—91no—
977C22×C4—91no—
978C22×C4—91no—
979C22×C4—91no—
980C22×C4—271no—
981C22×C4—271no—
982C22×C4—271no—
983C22×C4—271no—
984C22×C4—544no—
985C4⋊C4—91no—
986C4⋊C4—91no—
987C4⋊C4—91no—
988C4⋊C4—91no—
989C4⋊C4—91no—
990C4⋊C4—271no—
991C22⋊C4—31no—
992C22⋊C4—31no—
993C22⋊C4—91no—
994C22⋊C4—91no—
995C22⋊C4—91no—
996C22⋊C4—271no—
997C22⋊C4—271no—
998C22⋊C4—271no—
999C22⋊C4—271no—
1000C22⋊C4—271no—
1001C42—31no—
1002C42—91no—
1003C22×C3—21no—
1004C22×C3—21no—
1005C22×C3—21no—
1006C22×C3—32no—
1007C22×C3—32no—
1008C22×C3—41no—
1009C22×C3—62no—
1010C22×C3—61no—
1011C22×C3—61no—
1012C22×C3—61no—
1013C22×C3—61no—
1014C22×C3—61no—
1015C22×C3—61no—
1016C22×C3—61no—
1017C22×C3—61no—
1018C22×C3—61no—
1019C22×C3—61no—
1020C22×C3—92no—
1021C22×C3—121no—
1022C22×C3—121no—
1023C22×C3—121no—
1024C22×C3—121no—
1025C22×C3—121no—
1026C22×C3—181no—
1027C22×C3—181no—
1028C22×C3C22×D3211yescharacteristic
1029C22×C3C22×D3211yescharacteristic
1030C22×C3C22×D3211yescharacteristic
1031C2×D3—21no—
1032C2×D3—21no—
1033C2×D3—21no—
1034C2×D3—21no—
1035C2×D3—21no—
1036C2×D3—32no—
1037C2×D3—32no—
1038C2×D3—62no—
1039C2×D3—61no—
1040C2×D3—61no—
1041C2×D3—61no—
1042C2×D3—61no—
1043C2×D3—92no—
1044C2×D3—92no—
1045C2×D3—92no—
1046C2×D3—121no—
1047C2×D3—121no—
1048C2×D3—182no—
1049C2×D3—182no—
1050C2×D3—182no—
1051C2×D3—188no—
1052C2×D3—188no—
1053C2×D3—188no—
1054C2×D3—181no—
1055C2×D3—181no—
1056C2×D3—181no—
1057C2×D3—181no—
1058C2×D3—181no—
1059C2×D3—181no—
1060C2×D3—182no—
1061C2×D3—181no—
1062C2×D3—181no—
1063C2×D3—181no—
1064C2×D3—181no—
1065C2×D3—181no—
1066C2×D3—181no—
1067C2×D3—181no—
1068C2×D3—181no—
1069C2×D3—181no—
1070C2×D3—362no—
1071C2×D3—368no—
1072C2×D3—361no—
1073C2×D3—361no—
1074C2×D3—361no—
1075C2×D3—361no—
1076C2×D3—361no—
1077C2×D3—361no—
1078C2×D3—361no—
1079C2×D3—361no—
1080C2×D3—361no—
1081C2×D3—361no—
1082C2×D3—361no—
1083C2×D3—361no—
1084C2×D3—361no—
1085C2×D3—361no—
1086C2×D3—362no—
1087C2×D3—721no—
1088C2×D3—721no—
1089C2×D3—721no—
1090C2×D3—721no—
1091C2×D3D3×D1212yes—
1092C3×C4—22no—
1093C3×C4—21no—
1094C3×C4—21no—
1095C3×C4—21no—
1096C3×C4—32no—
1097C3×C4—32no—
1098C3×C4—41no—
1099C3×C4—41no—
1100C3×C4—42no—
1101C3×C4—62no—
1102C3×C4—61no—
1103C3×C4—61no—
1104C3×C4—61no—
1105C3×C4—61no—
1106C3×C4—61no—
1107C3×C4—61no—
1108C3×C4—92no—
1109C3×C4—121no—
1110C3×C4—121no—
1111C3×C4—121no—
1112C3×C4—181no—
1113C3×C4—181no—
1114C3×C4—181no—
1115C3×C4—181no—
1116Dic3—21no—
1117Dic3—21no—
1118Dic3—21no—
1119Dic3—32no—
1120Dic3—32no—
1121Dic3—62no—
1122Dic3—61no—
1123Dic3—61no—
1124Dic3—61no—
1125Dic3—61no—
1126Dic3—61no—
1127Dic3—61no—
1128Dic3—61no—
1129Dic3—61no—
1130Dic3—121no—
1131Dic3—121no—
1132Dic3—121no—
1133Dic3—121no—
1134Dic3D3×D1212yes—
1135C32—21no—
1136C32—21no—
1137C32—21no—
1138C32—41no—
1139C32#552411yescharacteristic, complemented
1140C32#554711yescharacteristic, complemented
1141C32#565611yescharacteristic, complemented
1142C23—31no—
1143C23—31no—
1144C23—91no—
1145C23—271no—
1146C23—271no—
1147C23—542no—
1148C23—542no—
1149C23—542no—
1150Q8—542no—
1151D4—182no—
1152D4—182no—
1153D4—542no—
1154D4—542no—
1155D4—542no—
1156D4—542no—
1157D4—542no—
1158C2×C4—31no—
1159C2×C4—31no—
1160C2×C4—31no—
1161C2×C4—31no—
1162C2×C4—94no—
1163C2×C4—91no—
1164C2×C4—91no—
1165C2×C4—91no—
1166C2×C4—91no—
1167C2×C4—91no—
1168C2×C4—182no—
1169C2×C4—182no—
1170C2×C4—182no—
1171C2×C4—542no—
1172C2×C4—542no—
1173C2×C4—542no—
1174C2×C4—542no—
1175C2×C4D3311yescharacteristic
1176C2×C3—21no—
1177C2×C3—21no—
1178C2×C3—21no—
1179C2×C3—21no—
1180C2×C3—21no—
1181C2×C3—21no—
1182C2×C3—21no—
1183C2×C3—21no—
1184C2×C3—21no—
1185C2×C3—41no—
1186C2×C3—41no—
1187C2×C3—41no—
1188C2×C3—62no—
1189C2×C3—62no—
1190C2×C3—122no—
1191C2×C3—121no—
1192C2×C3—121no—
1193C2×C3—182no—
1194C2×C3—241no—
1195C2×C3C2×D3×D1211yescharacteristic
1196C2×C3C2×D3×D1211yescharacteristic
1197C2×C3D3×#23511yescharacteristic
1198C2×C3D3×#23511yescharacteristic
1199C2×C3#6430611yescharacteristic
1200C2×C3D32×D411yescharacteristic
1201C2×C3#6431211yescharacteristic
1202C2×C3#6431211yescharacteristic
1203C2×C3#6431211yescharacteristic
1204D3—22no—
1205D3—41no—
1206D3—62no—
1207D3—62no—
1208D3—122no—
1209D3—182no—
1210D3—182no—
1211D3—182no—
1212D3—362no—
1213D3—362no—
1214D3—362no—
1215D3—362no—
1216D3—361no—
1217D3—361no—
1218D3—361no—
1219D3—722no—
1220D3—721no—
1221D3—721no—
1222D3—722no—
1223C22—32no—
1224C22—61no—
1225C22—61no—
1226C22—61no—
1227C22—61no—
1228C22—61no—
1229C22—92no—
1230C22—181no—
1231C22—181no—
1232C22—272no—
1233C22—548no—
1234C22—541no—
1235C22—541no—
1236C22—541no—
1237C22—541no—
1238C22—541no—
1239C22C2×D3311yescharacteristic
1240C4—21no—
1241C4—32no—
1242C4—61no—
1243C4—61no—
1244C4—61no—
1245C4—92no—
1246C4—181no—
1247C4—181no—
1248C4—181no—
1249C4—181no—
1250C3—21no—
1251C3—21no—
1252C3—21no—
1253C3—41no—
1254C3#1059399711yescharacteristic, complemented
1255C3#1059407911yescharacteristic, complemented
1256C3#1059426611yescharacteristic, complemented
1257C2—62no—
1258C2—121no—
1259C2—182no—
1260C2—542no—
1261C2—1081no—
1262C2#1172438811yescharacteristic
1263C2D32×D1211yescharacteristic
1264C2#1172441111yescharacteristic
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×D3×#624C2semidirect
3. #11723692C2semidirect
4. #11723542C2semidirect
5. #11723525C2semidirect
6. #11723484C2semidirect
7. C3×#63891C2semidirect
8. C3×#63880C2semidirect
9. C3×#63877C2semidirect
10. #11722987C2semidirect
11. #11722982C2semidirect
12. #11722966C2semidirect
13. #11722949C2semidirect
14. #11722933C2semidirect
15. #11722932C2semidirect
21. C2×#6296C22semidirect
26. C2×#6291C22semidirect
29. C2×#6289C22semidirect
35. C2×C3×D3×Dic3C22semidirect
39. C3×C4⋊(C3⋊Dic3)C22semidirect
40. C3×#3750C22semidirect
42. C32×(C2×D3)⋊C4C22semidirect
43. C32×C4×Dic3C22semidirect
44. #88815C22semidirect
48. #88804C22semidirect
49. #88804C22semidirect
50. C3×#3724C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
96. #63891D3semidirect
100. #63880D3semidirect
101. #63877D3semidirect
137. C3×D3×Dic3D4semidirect
206. C2×D3×Dic3C2×D3semidirect
218. C4⋊(C3⋊Dic3)C2×D3semidirect
219. #3750C2×D3semidirect
231. C3×(C2×D3)⋊C4C2×D3semidirect
232. C3×(C2×D3)⋊C4C2×D3semidirect
248. C3×C4×Dic3C2×D3semidirect
249. C3×C4×Dic3C2×D3semidirect
251. #3724C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. Dic32C2×D3semidirect
280. C2×C3⋊(C3⋊D3)#41semidirect
283. C2×C3×C3⋊D3#41semidirect
488. D3×Dic3D12semidirect
612. (C2×D3)⋊C4D32semidirect
630. C4×Dic3D32semidirect
689. C2×C3⋊D3#235semidirect
778. C33#525semidirect
1139. C32#5524semidirect
1140. C32#5547semidirect
1141. C32#5656semidirect
1254. C3#10593997semidirect
1255. C3#10594079semidirect
1256. C3#10594266semidirect

Maximal subgroups

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

subgroupindex
C2×#889592
C2×D3×#6242
#117236922
#117235422
#117235252
#117234842
C3×#638912
C3×#638802
C3×#638772
#117229872
#117229822
#117229662
#117229492
#117229332
#117229322
#105942663
#105940793
#105939973