Finite Group Databasebeta

← #13170790

Subgroups — #13170790

Order 1728.

1638 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88962C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723691C211yesmaximal, characteristic, complemented
4#11723541C211yesmaximal, characteristic, complemented
5#11723469C211yesmaximal, characteristic, complemented
6#11723422C211yesmaximal, characteristic, complemented
7C3×#63910C211yesmaximal, characteristic, complemented
8C3×#63902C211yesmaximal, characteristic, complemented
9C3×#63893C211yesmaximal, characteristic, complemented
10#11723000C211yesmaximal, characteristic, complemented
11#11722970C211yesmaximal, characteristic, complemented
12#11722956C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14#11722936C211yesmaximal, characteristic, complemented
15#11722927C211yesmaximal, characteristic, complemented
16#10594632—31nomaximal
17#10594286—31nomaximal
18#10594066—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6294C2211yescharacteristic, complemented
23C2×#6292C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×C3×#627C2211yescharacteristic, complemented
29C2×C3×#626C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic, complemented
31C2×C3×#625C2211yescharacteristic
32C2×C3×#624C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic, complemented
36#88962—24no—
37D3×#624—24no—
38#88859C2211yescharacteristic
39C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C32×Dic3⋊C4C2211yescharacteristic, complemented
44#88814C2211yescharacteristic
45#88814C2211yescharacteristic, complemented
46#88806C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48#88804C2211yescharacteristic
49#88803C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52C3×#3724C2211yescharacteristic, complemented
53C3×Dic3⋊Dic3C2211yescharacteristic, complemented
54C3×#3722C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic
56C22×#624—31no—
57C2×#3804—31no—
58C2×C4×D32—31no—
59C2×C4×D32—31no—
60C2×#3799—31no—
61C2×#3796—31no—
62#64101—31no—
63#64092—31no—
64#64091—31no—
65C3×#897—31no—
66C3×#895—31no—
67C3×#884—31no—
68C3×#67⋊C4—31no—
69C3×#67⋊C4—31no—
70C3×#878—31no—
71#63983—31no—
72#63981—31no—
73#63978—31no—
74Dic3×#67—31no—
75#63970—31no—
76#63952—31no—
77#63922—31no—
78#63922—31no—
79#63922—31no—
80#63922—61no—
81#63910D311yescharacteristic, complemented
82#63908—31no—
83#63904—31no—
84#63902—31no—
85#63902D311yescharacteristic, complemented
86#63898—31no—
87#63898—31no—
88#63897—31no—
89#63894—31no—
90#63893D311yescharacteristic, complemented
91Dic3×D12—31no—
92#63888—31no—
93#63879—31no—
94#63856—31no—
95#63854—31no—
96#63854—31no—
97#63854—31no—
98#63854—61no—
99#63853—31no—
100#63851—31no—
101#63836—31no—
102#63836—31no—
103#63836—61no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
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
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#6291—22no—
127#6290—22no—
128#6289—22no—
129#6289D414yescomplemented
130C3×#627—22no—
131C3×#626—22no—
132C3×#626—22no—
133C3×#625—22no—
134C3×#624—22no—
135C3×D3×Dic3—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5627—91no—
139#5606—91no—
140#5547—91no—
141C23×C3⋊D3—31no—
142C22×D32—31no—
143C22×D32—31no—
144C22×D32—61no—
145C2×#638—31no—
146C2×#638—31no—
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C22×C3×Dic3—31no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—31no—
158C2×C3×D12—31no—
159C2×C3×D12—31no—
160C2×C3×D12—31no—
161C2×C3×D12—31no—
162C2×C3×D12—61no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×C3×Dic6—31no—
169C2×C3×Dic6—31no—
170C2×#627C2×D311yescharacteristic, complemented
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—61no—
176C2×#626—61no—
177C2×#626C2×D311yescharacteristic
178C2×#626C2×D311yescharacteristic, complemented
179C2×#625—31no—
180C2×#625—31no—
181C2×#625—61no—
182C2×#625C2×D311yescharacteristic
183C2×#624—31no—
184C2×#624—31no—
185C2×#624—31no—
186C2×#624—31no—
187C2×#624—31no—
188C2×#624—31no—
189C2×#624—64no—
190C2×#624—61no—
191C2×#624—61no—
192C2×#624C2×D311yescharacteristic
193#3804—64no—
194C2×D3×Dic3—31no—
195C2×D3×Dic3—31no—
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3C2×D311yescharacteristic
199C2×D3×Dic3C2×D311yescharacteristic
200C2×D3×Dic3C2×D311yescharacteristic, complemented
201C4×D32—64no—
202C4×D32—64no—
203#3799—64no—
204#3796—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—
213#3752—31no—
214#3752—61no—
215#3752—61no—
216#3752—61no—
217#3752—121no—
218C4⋊(C3⋊Dic3)—31no—
219C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
220#3750—31no—
221C4×C3⋊Dic3—31no—
222C4×C3⋊Dic3C2×D311yescharacteristic, complemented
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)⋊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—61no—
237C3×Dic3⋊C4—21no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4C2×D311yescharacteristic, complemented
242C3×Dic3⋊C4C2×D311yescharacteristic, complemented
243C3×C4×Dic3—31no—
244C3×C4×Dic3—31no—
245C3×C4×Dic3—61no—
246#3724—31no—
247#3724—31no—
248#3724—61no—
249#3724C2×D311yescharacteristic, complemented
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—61no—
253Dic3⋊Dic3C2×D311yescharacteristic, complemented
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—61no—
259#3722C2×D311yescharacteristic, complemented
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3C2×D311yescharacteristic
271Dic32—31no—
272Dic32—31no—
273Dic32—61no—
274C22×C33C2411yescharacteristic
275C2×C3⋊(C3⋊D3)—21no—
276C2×C3⋊(C3⋊D3)—21no—
277C2×C3⋊(C3⋊D3)C2×D412yes—
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×D3—21no—
289C2×C32×D3#4112yescomplemented
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×#239—91no—
302C2×#237—91no—
303C2×#235—91no—
304C22×C4×D3—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×C22⋊Q8—91no—
308C3×#121—91no—
309C3×C4×D4—91no—
310#946—91no—
311#939—91no—
312#938—91no—
313#937—91no—
314#937—91no—
315#937—91no—
316D4×Dic3—91no—
317D4×Dic3—91no—
318#930—91no—
319C4×#67—91no—
320C4×#67—91no—
321#924—91no—
322#897—31no—
323#896—91no—
324#895—31no—
325#894—91no—
326#894—91no—
327#894—91no—
328#893—91no—
329#893—91no—
330#892—91no—
331#892—91no—
332#892—181no—
333#884—31no—
334#883—91no—
335#883—91no—
336#883—91no—
337#883—181no—
338#882—91no—
339#882—91no—
340#882—91no—
341#882—181no—
342#67⋊C4—31no—
343#67⋊C4—31no—
344#67⋊C4—91no—
345#67⋊C4—91no—
346#878—31no—
347C4×D12—91no—
348#872—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—62no—
358C22×C3⋊D3—62no—
359C22×C3⋊D3—62no—
360C22×C3⋊D3—121no—
361C22×C3⋊D3C22×D311yescharacteristic
362C22×C3⋊D3C22×D311yescharacteristic
363C22×C3×D3—21no—
364C22×C3×D3—21no—
365C22×C3×D3—31no—
366C22×C3×D3—31no—
367C22×C3×D3—31no—
368C22×C3×D3—31no—
369C22×C3×D3—61no—
370C22×C3×D3—61no—
371C22×C3×D3C22×D311yescharacteristic
372C22×C3×D3C22×D311yescharacteristic
373C22×C3×D3C22×D311yescharacteristic
374C22×C3×D3C22×D311yescharacteristic
375C2×D32—62no—
376C2×D32—62no—
377C2×D32—62no—
378C2×D32—62no—
379C2×D32—62no—
380C2×D32—62no—
381C2×D32—122no—
382C2×D32—122no—
383C2×D32—122no—
384C2×C32×C4—21no—
385C2×C32×C4—21no—
386C2×C32×C4—21no—
387C2×C32×C4—31no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390C2×C32×C4—31no—
391C2×C32×C4—41no—
392C2×C32×C4C22×D311yescharacteristic
393C2×C32×C4C22×D311yescharacteristic
394C2×C32×C4C22×D311yescharacteristic
395#638—62no—
396#638—62no—
397C2×C3⋊Dic3—31no—
398C2×C3⋊Dic3—31no—
399C2×C3⋊Dic3—31no—
400C2×C3⋊Dic3—61no—
401C2×C3⋊Dic3—61no—
402C2×C3⋊Dic3—61no—
403C2×C3⋊Dic3—121no—
404C2×C3⋊Dic3C22×D311yescharacteristic
405C2×C3⋊Dic3C22×D311yescharacteristic
406C2×C3⋊Dic3C22×D311yescharacteristic
407C2×C3⋊Dic3C22×D311yescharacteristic
408C4⋊(C3⋊D3)—22no—
409C4⋊(C3⋊D3)—62no—
410C4×C3⋊D3—34no—
411C4×C3⋊D3—62no—
412C3×#67—62no—
413C3×#67—62no—
414C3×#67—62no—
415C3×#67—62no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—31no—
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—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—62no—
433C2×C3×Dic3—62no—
434C2×C3×Dic3—62no—
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C3×D12—62no—
444C3×D12—62no—
445C3×D12—62no—
446C3×D12—62no—
447C3×D12—122no—
448C3×C4×D3—62no—
449C3×C4×D3—62no—
450C3×C4×D3—62no—
451C3×C4×D3—62no—
452C3×C4×D3—62no—
453C3×Dic6—62no—
454C3×Dic6—62no—
455#627—22no—
456#626—22no—
457#626—22no—
458#626—62no—
459#626—62no—
460#626—62no—
461#626—62no—
462#626—122no—
463#626—122no—
464#625—22no—
465#625—62no—
466#625—62no—
467#625—122no—
468#624—22no—
469#624—34no—
470#624—34no—
471#624—64no—
472#624—62no—
473#624—62no—
474#624—62no—
475#624—62no—
476#624—122no—
477D3×Dic3—22no—
478D3×Dic3—22no—
479D3×Dic3—22no—
480D3×Dic3—62no—
481D3×Dic3—62no—
482D3×Dic3—62no—
483D3×Dic3—62no—
484#525—271noSylow
485C2×C33C22×D411yescharacteristic
486C2×C33C2×#4111yescharacteristic
487C2×C33C2×#4111yescharacteristic
488C3⋊(C3⋊D3)—22no—
489C3×C3⋊D3—22no—
490C3×C3⋊D3—41no—
491C32×D3—22no—
492C32×D3—41no—
493C23×D3—91no—
494C23×D3—91no—
495C23×D3—91no—
496C23×D3—181no—
497C2×C3×Q8—91no—
498C2×C3×D4—91no—
499C2×C3×D4—91no—
500C2×C3×D4—91no—
501C2×C3×D4—91no—
502C22×C3×C4—91no—
503C22×C3×C4—91no—
504C22×C3×C4—91no—
505C22×C3×C4—91no—
506C2×#67—31no—
507C2×#67—31no—
508C2×#67—31no—
509C2×#67—31no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—181no—
517C2×#67—181no—
518C22×Dic3—31no—
519C22×Dic3—31no—
520C22×Dic3—31no—
521C22×Dic3—91no—
522C22×Dic3—91no—
523#239—184no—
524#237—184no—
525#235—184no—
526C2×D12—31no—
527C2×D12—31no—
528C2×D12—31no—
529C2×D12—31no—
530C2×D12—61no—
531C2×D12—91no—
532C2×D12—91no—
533C2×D12—91no—
534C2×D12—181no—
535C2×C4×D3—31no—
536C2×C4×D3—31no—
537C2×C4×D3—31no—
538C2×C4×D3—31no—
539C2×C4×D3—31no—
540C2×C4×D3—91no—
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—91no—
550C2×C4×D3—181no—
551C2×C4×D3—181no—
552C2×C4×D3—184no—
553C2×C4×D3—184no—
554C2×C4×D3—184no—
555C2×Dic6—31no—
556C2×Dic6—31no—
557C3×C4⋊C4—31no—
558C3×C4⋊C4—31no—
559C3×C4⋊C4—61no—
560C3×C4⋊C4—91no—
561C3×C4⋊C4—91no—
562C3×C4⋊C4—91no—
563C3×C22⋊C4—31no—
564C3×C22⋊C4—31no—
565C3×C22⋊C4—31no—
566C3×C22⋊C4—31no—
567C3×C22⋊C4—61no—
568C3×C22⋊C4—61no—
569C3×C22⋊C4—91no—
570C3×C22⋊C4—91no—
571C3×C42—91no—
572#217—31no—
573#217—91no—
574#217—91no—
575#217—91no—
576#217—91no—
577#217—91no—
578#217—181no—
579(C2×D3)⋊C4—31no—
580(C2×D3)⋊C4—31no—
581(C2×D3)⋊C4—31no—
582(C2×D3)⋊C4—91no—
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—91no—
593(C2×D3)⋊C4—91no—
594(C2×D3)⋊C4—91no—
595(C2×D3)⋊C4—181no—
596(C2×D3)⋊C4—181no—
597(C2×D3)⋊C4—181no—
598(C2×D3)⋊C4—181no—
599(C2×D3)⋊C4—181no—
600(C2×D3)⋊C4—361no—
601(C2×D3)⋊C4D3211yescharacteristic
602(C2×D3)⋊C4D3211yescharacteristic, complemented
603C4⋊Dic3—31no—
604C4⋊Dic3—31no—
605C4⋊Dic3—31no—
606C4⋊Dic3—61no—
607C4⋊Dic3—91no—
608C4⋊Dic3—91no—
609C4⋊Dic3—181no—
610Dic3⋊C4—31no—
611Dic3⋊C4—31no—
612Dic3⋊C4—31no—
613Dic3⋊C4—91no—
614Dic3⋊C4—91no—
615Dic3⋊C4—91no—
616Dic3⋊C4—91no—
617Dic3⋊C4—181no—
618Dic3⋊C4D3211yescharacteristic, complemented
619C4×Dic3—31no—
620C4×Dic3—31no—
621C4×Dic3—61no—
622C4×Dic3—91no—
623C4×Dic3—91no—
624C4×Dic3—91no—
625C4×Dic3—181no—
626C22×C32—21no—
627C22×C32—21no—
628C22×C32—21no—
629C22×C32—32no—
630C22×C32—41no—
631C22×C32—61no—
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—32no—
645C2×C3⋊D3—32no—
646C2×C3⋊D3—32no—
647C2×C3⋊D3—62no—
648C2×C3⋊D3—62no—
649C2×C3⋊D3—62no—
650C2×C3⋊D3—68no—
651C2×C3⋊D3—61no—
652C2×C3⋊D3—61no—
653C2×C3⋊D3—61no—
654C2×C3⋊D3—61no—
655C2×C3⋊D3—61no—
656C2×C3⋊D3—61no—
657C2×C3⋊D3—122no—
658C2×C3⋊D3—121no—
659C2×C3⋊D3—121no—
660C2×C3⋊D3—121no—
661C2×C3⋊D3—121no—
662C2×C3⋊D3—121no—
663C2×C3⋊D3—121no—
664C2×C3⋊D3—241no—
665C2×C3⋊D3—241no—
666C2×C3⋊D3#23712yescomplemented
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—22no—
678C2×C3×D3—32no—
679C2×C3×D3—32no—
680C2×C3×D3—41no—
681C2×C3×D3—41no—
682C2×C3×D3—41no—
683C2×C3×D3—41no—
684C2×C3×D3—41no—
685C2×C3×D3—62no—
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—61no—
696C2×C3×D3—121no—
697C2×C3×D3—121no—
698C2×C3×D3—121no—
699C2×C3×D3—121no—
700C2×C3×D3—121no—
701C2×C3×D3#23512yescomplemented
702C2×C3×D3#23912yescomplemented
703D32—68no—
704D32—68no—
705D32—128no—
706C32×C4—21no—
707C32×C4—21no—
708C32×C4—21no—
709C32×C4—32no—
710C32×C4—41no—
711C32×C4—41no—
712C32×C4—41no—
713C32×C4—61no—
714C32×C4—61no—
715C32×C4—61no—
716C32×C4—81no—
717C3⋊Dic3—21no—
718C3⋊Dic3—21no—
719C3⋊Dic3—21no—
720C3⋊Dic3—61no—
721C3⋊Dic3—61no—
722C3⋊Dic3—61no—
723C3⋊Dic3—121no—
724C3⋊Dic3—121no—
725C3⋊Dic3—121no—
726C3⋊Dic3—241no—
727C3⋊Dic3D3×D412yes—
728C3×Dic3—21no—
729C3×Dic3—21no—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—21no—
734C3×Dic3—22no—
735C3×Dic3—32no—
736C3×Dic3—32no—
737C3×Dic3—41no—
738C3×Dic3—41no—
739C3×Dic3—41no—
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×Dic3—121no—
750C3×Dic3D3×D412yes—
751C3×Dic3D3×D412yes—
752C2×#41—271no—
753C23×C4—271no—
754#123—271no—
755#123—271no—
756C22⋊Q8—91no—
757C22⋊Q8—271no—
758#121—91no—
759#121—271no—
760#120—271no—
761#120—271no—
762C4×D4—91no—
763C4×D4—271no—
764C4×D4—271no—
765C4×D4—271no—
766#117—271no—
767C33#52511yescharacteristic, complemented, Sylow
768C23×C3—31no—
769C23×C3—31no—
770C23×C3—31no—
771C23×C3—31no—
772C23×C3—61no—
773C23×C3—61no—
774C23×C3—91no—
775C23×C3—91no—
776C22×D3—31no—
777C22×D3—31no—
778C22×D3—31no—
779C22×D3—31no—
780C22×D3—61no—
781C22×D3—61no—
782C22×D3—91no—
783C22×D3—91no—
784C22×D3—91no—
785C22×D3—181no—
786C22×D3—181no—
787C22×D3—181no—
788C22×D3—182no—
789C22×D3—182no—
790C22×D3—182no—
791C22×D3—182no—
792C22×D3—182no—
793C22×D3—182no—
794C22×D3—182no—
795C22×D3—182no—
796C22×D3—182no—
797C22×D3—361no—
798C22×D3—362no—
799C22×D3—362no—
800C22×D3—362no—
801C22×D3C2×D3211yescharacteristic
802C22×D3C2×D3211yescharacteristic
803C3×Q8—182no—
804C3×D4—182no—
805C3×D4—182no—
806C3×D4—182no—
807C3×D4—182no—
808C2×C3×C4—21no—
809C2×C3×C4—21no—
810C2×C3×C4—21no—
811C2×C3×C4—31no—
812C2×C3×C4—31no—
813C2×C3×C4—31no—
814C2×C3×C4—31no—
815C2×C3×C4—31no—
816C2×C3×C4—31no—
817C2×C3×C4—31no—
818C2×C3×C4—31no—
819C2×C3×C4—41no—
820C2×C3×C4—61no—
821C2×C3×C4—61no—
822C2×C3×C4—61no—
823C2×C3×C4—61no—
824C2×C3×C4—91no—
825C2×C3×C4—91no—
826C2×C3×C4—91no—
827C2×C3×C4—91no—
828C2×C3×C4—182no—
829C2×C3×C4—182no—
830C2×C3×C4—182no—
831C2×C3×C4—182no—
832C2×C3×C4C2×D3211yescharacteristic
833C2×C3×C4C2×D3211yescharacteristic
834C2×C3×C4C2×D3211yescharacteristic
835#67—62no—
836#67—62no—
837#67—62no—
838#67—62no—
839#67—182no—
840#67—182no—
841#67—182no—
842#67—182no—
843#67—182no—
844#67—182no—
845#67—362no—
846#67—362no—
847C2×Dic3—31no—
848C2×Dic3—31no—
849C2×Dic3—31no—
850C2×Dic3—31no—
851C2×Dic3—31no—
852C2×Dic3—31no—
853C2×Dic3—31no—
854C2×Dic3—31no—
855C2×Dic3—61no—
856C2×Dic3—61no—
857C2×Dic3—61no—
858C2×Dic3—61no—
859C2×Dic3—62no—
860C2×Dic3—62no—
861C2×Dic3—62no—
862C2×Dic3—91no—
863C2×Dic3—91no—
864C2×Dic3—91no—
865C2×Dic3—181no—
866C2×Dic3—181no—
867C2×Dic3—181no—
868C2×Dic3—182no—
869C2×Dic3—182no—
870C2×Dic3—361no—
871C2×Dic3C2×D3211yescharacteristic
872C2×Dic3C2×D3211yescharacteristic
873C2×Dic3C2×D3211yescharacteristic
874C2×Dic3C2×D3211yescharacteristic
875D12—62no—
876D12—62no—
877D12—62no—
878D12—62no—
879D12—122no—
880D12—182no—
881D12—182no—
882D12—182no—
883D12—362no—
884C4×D3—62no—
885C4×D3—62no—
886C4×D3—62no—
887C4×D3—62no—
888C4×D3—62no—
889C4×D3—94no—
890C4×D3—94no—
891C4×D3—94no—
892C4×D3—184no—
893C4×D3—182no—
894C4×D3—182no—
895C4×D3—182no—
896C4×D3—182no—
897C4×D3—182no—
898C4×D3—182no—
899C4×D3—182no—
900C4×D3—362no—
901Dic6—62no—
902Dic6—62no—
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—21no—
912C2×C32—41no—
913C2×C32—41no—
914C2×C32—41no—
915C2×C32—62no—
916C2×C32—121no—
917C2×C32C2×#23511yescharacteristic
918C2×C32C2×D3×D411yescharacteristic
919C2×C32C2×D3×D411yescharacteristic
920C2×C32C2×D3×D411yescharacteristic
921C2×C32C2×#23711yescharacteristic
922C2×C32C2×#23911yescharacteristic
923C2×C32D3×#4111yescharacteristic
924C2×C32D3×#4111yescharacteristic
925C2×C32D3×#4111yescharacteristic
926C3⋊D3—22no—
927C3⋊D3—41no—
928C3⋊D3—62no—
929C3⋊D3—62no—
930C3⋊D3—62no—
931C3⋊D3—122no—
932C3⋊D3—122no—
933C3⋊D3—122no—
934C3⋊D3—242no—
935C3×D3—22no—
936C3×D3—22no—
937C3×D3—42no—
938C3×D3—41no—
939C3×D3—41no—
940C3×D3—62no—
941C3×D3—62no—
942C3×D3—81no—
943C3×D3—122no—
944C3×D3—121no—
945C3×D3—121no—
946C3×D3—241no—
947C24—271no—
948#41—544no—
949C2×Q8—91no—
950C2×D4—91no—
951C2×D4—91no—
952C2×D4—91no—
953C2×D4—91no—
954C2×D4—271no—
955C2×D4—271no—
956C2×D4—271no—
957C22×C4—91no—
958C22×C4—91no—
959C22×C4—91no—
960C22×C4—91no—
961C22×C4—271no—
962C22×C4—271no—
963C22×C4—271no—
964C22×C4—271no—
965C22×C4—544no—
966C4⋊C4—31no—
967C4⋊C4—91no—
968C4⋊C4—91no—
969C4⋊C4—91no—
970C4⋊C4—271no—
971C4⋊C4—271no—
972C22⋊C4—31no—
973C22⋊C4—31no—
974C22⋊C4—91no—
975C22⋊C4—91no—
976C22⋊C4—271no—
977C22⋊C4—271no—
978C22⋊C4—271no—
979C22⋊C4—271no—
980C22⋊C4—271no—
981C22⋊C4—271no—
982C42—91no—
983C42—271no—
984C22×C3—21no—
985C22×C3—21no—
986C22×C3—21no—
987C22×C3—32no—
988C22×C3—32no—
989C22×C3—41no—
990C22×C3—62no—
991C22×C3—61no—
992C22×C3—61no—
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—121no—
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—21no—
1020C2×D3—32no—
1021C2×D3—32no—
1022C2×D3—62no—
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—61no—
1032C2×D3—61no—
1033C2×D3—92no—
1034C2×D3—92no—
1035C2×D3—92no—
1036C2×D3—121no—
1037C2×D3—121no—
1038C2×D3—121no—
1039C2×D3—121no—
1040C2×D3—121no—
1041C2×D3—182no—
1042C2×D3—182no—
1043C2×D3—182no—
1044C2×D3—188no—
1045C2×D3—188no—
1046C2×D3—188no—
1047C2×D3—181no—
1048C2×D3—181no—
1049C2×D3—181no—
1050C2×D3—181no—
1051C2×D3—181no—
1052C2×D3—181no—
1053C2×D3—362no—
1054C2×D3—368no—
1055C2×D3—361no—
1056C2×D3—361no—
1057C2×D3—361no—
1058C2×D3—361no—
1059C2×D3—361no—
1060C2×D3—361no—
1061C2×D3—721no—
1062C2×D3—721no—
1063C2×D3#379912yescomplemented
1064C3×C4—21no—
1065C3×C4—21no—
1066C3×C4—21no—
1067C3×C4—32no—
1068C3×C4—32no—
1069C3×C4—41no—
1070C3×C4—41no—
1071C3×C4—41no—
1072C3×C4—62no—
1073C3×C4—61no—
1074C3×C4—61no—
1075C3×C4—61no—
1076C3×C4—61no—
1077C3×C4—61no—
1078C3×C4—61no—
1079C3×C4—81no—
1080C3×C4—92no—
1081C3×C4—121no—
1082C3×C4—121no—
1083C3×C4—121no—
1084C3×C4—181no—
1085C3×C4—181no—
1086C3×C4—181no—
1087Dic3—21no—
1088Dic3—21no—
1089Dic3—21no—
1090Dic3—32no—
1091Dic3—32no—
1092Dic3—62no—
1093Dic3—61no—
1094Dic3—61no—
1095Dic3—61no—
1096Dic3—61no—
1097Dic3—61no—
1098Dic3—61no—
1099Dic3—121no—
1100Dic3—121no—
1101Dic3—121no—
1102Dic3—181no—
1103Dic3—181no—
1104Dic3—181no—
1105Dic3—361no—
1106Dic3—361no—
1107Dic3—361no—
1108Dic3—721no—
1109Dic3#380212yes—
1110C32—21no—
1111C32—21no—
1112C32—21no—
1113C32—41no—
1114C32#554711yescharacteristic, complemented
1115C32#560611yescharacteristic, complemented
1116C32#562711yescharacteristic, complemented
1117C23—31no—
1118C23—31no—
1119C23—91no—
1120C23—91no—
1121C23—271no—
1122C23—542no—
1123C23—542no—
1124C23—542no—
1125Q8—182no—
1126D4—182no—
1127D4—182no—
1128D4—182no—
1129D4—182no—
1130D4—542no—
1131D4—542no—
1132D4—542no—
1133C2×C4—31no—
1134C2×C4—31no—
1135C2×C4—31no—
1136C2×C4—31no—
1137C2×C4—91no—
1138C2×C4—91no—
1139C2×C4—91no—
1140C2×C4—91no—
1141C2×C4—182no—
1142C2×C4—182no—
1143C2×C4—182no—
1144C2×C4—182no—
1145C2×C4—274no—
1146C2×C4—271no—
1147C2×C4—542no—
1148C2×C4—542no—
1149C2×C4—542no—
1150C2×C4D3311yescharacteristic
1151C2×C3—21no—
1152C2×C3—21no—
1153C2×C3—21no—
1154C2×C3—21no—
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—21no—
1158C2×C3—21no—
1159C2×C3—21no—
1160C2×C3—41no—
1161C2×C3—41no—
1162C2×C3—41no—
1163C2×C3—62no—
1164C2×C3—62no—
1165C2×C3—122no—
1166C2×C3—121no—
1167C2×C3—121no—
1168C2×C3—182no—
1169C2×C3—241no—
1170C2×C3—361no—
1171C2×C3C2×#379911yescharacteristic
1172C2×C3C2×#380211yescharacteristic
1173C2×C3D3×#23511yescharacteristic
1174C2×C3D32×D411yescharacteristic
1175C2×C3D32×D411yescharacteristic
1176C2×C3D3×#23711yescharacteristic
1177C2×C3D3×#23711yescharacteristic
1178C2×C3#6431211yescharacteristic
1179C2×C3D3×#23911yescharacteristic
1180D3—22no—
1181D3—41no—
1182D3—62no—
1183D3—62no—
1184D3—122no—
1185D3—121no—
1186D3—121no—
1187D3—182no—
1188D3—182no—
1189D3—182no—
1190D3—241no—
1191D3—362no—
1192D3—362no—
1193D3—362no—
1194D3—722no—
1195C22—32no—
1196C22—61no—
1197C22—61no—
1198C22—61no—
1199C22—61no—
1200C22—61no—
1201C22—92no—
1202C22—181no—
1203C22—181no—
1204C22—181no—
1205C22—181no—
1206C22—181no—
1207C22—272no—
1208C22—548no—
1209C22—541no—
1210C22—541no—
1211C22C2×D3311yescharacteristic
1212C4—21no—
1213C4—32no—
1214C4—61no—
1215C4—61no—
1216C4—61no—
1217C4—92no—
1218C4—181no—
1219C4—181no—
1220C4—181no—
1221C4—541no—
1222C3—21no—
1223C3—21no—
1224C3—21no—
1225C3—41no—
1226C3#1059406611yescharacteristic, complemented
1227C3#1059428611yescharacteristic, complemented
1228C3#1059463211yescharacteristic, complemented
1229C2—62no—
1230C2—121no—
1231C2—182no—
1232C2—361no—
1233C2—542no—
1234C2D3×#379911yescharacteristic
1235C2D3×#380211yescharacteristic
1236C2#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×D3×#624C2semidirect
3. #11723691C2semidirect
4. #11723541C2semidirect
5. #11723469C2semidirect
6. #11723422C2semidirect
7. C3×#63910C2semidirect
8. C3×#63902C2semidirect
9. C3×#63893C2semidirect
10. #11723000C2semidirect
11. #11722970C2semidirect
12. #11722956C2semidirect
13. #11722949C2semidirect
14. #11722936C2semidirect
15. #11722927C2semidirect
22. C2×#6294C22semidirect
28. C2×C3×#627C22semidirect
30. C2×C3×#626C22semidirect
35. C2×C3×D3×Dic3C22semidirect
39. C3×C4⋊(C3⋊Dic3)C22semidirect
40. C3×C4×C3⋊Dic3C22semidirect
42. C32×(C2×D3)⋊C4C22semidirect
43. C32×Dic3⋊C4C22semidirect
45. #88814C22semidirect
46. #88806C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
50. (C2×D3)⋊(C3⋊Dic3)C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. C3×#3724C22semidirect
53. C3×Dic3⋊Dic3C22semidirect
54. C3×#3722C22semidirect
81. #63910D3semidirect
85. #63902D3semidirect
90. #63893D3semidirect
129. #6289D4semidirect
170. C2×#627C2×D3semidirect
178. C2×#626C2×D3semidirect
200. C2×D3×Dic3C2×D3semidirect
219. C4⋊(C3⋊Dic3)C2×D3semidirect
222. C4×C3⋊Dic3C2×D3semidirect
231. C3×(C2×D3)⋊C4C2×D3semidirect
232. C3×(C2×D3)⋊C4C2×D3semidirect
241. C3×Dic3⋊C4C2×D3semidirect
242. C3×Dic3⋊C4C2×D3semidirect
249. #3724C2×D3semidirect
253. Dic3⋊Dic3C2×D3semidirect
259. #3722C2×D3semidirect
283. C2×C3×C3⋊D3#41semidirect
289. C2×C32×D3#41semidirect
602. (C2×D3)⋊C4D32semidirect
618. Dic3⋊C4D32semidirect
666. C2×C3⋊D3#237semidirect
701. C2×C3×D3#235semidirect
702. C2×C3×D3#239semidirect
767. C33#525semidirect
1063. C2×D3#3799semidirect
1114. C32#5547semidirect
1115. C32#5606semidirect
1116. C32#5627semidirect
1226. C3#10594066semidirect
1227. C3#10594286semidirect
1228. C3#10594632semidirect

Maximal subgroups

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

subgroupindex
C2×#889622
C2×D3×#6242
#117236912
#117235412
#117234692
#117234222
C3×#639102
C3×#639022
C3×#638932
#117230002
#117229702
#117229562
#117229492
#117229362
#117229272
#105946323
#105942863
#105940663