Finite Group Databasebeta

← #13170793

Subgroups — #13170793

Order 1728.

1614 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×#88964C211yesmaximal, characteristic, complemented
2C2×#88949C211yesmaximal, characteristic, complemented
3#11723701C211yesmaximal, characteristic, complemented
4#11723508C211yesmaximal, characteristic, complemented
5#11723501C211yesmaximal, characteristic, complemented
6#11723466C211yesmaximal, characteristic, complemented
7C3×#63910C211yesmaximal, characteristic, complemented
8C3×#63895C211yesmaximal, characteristic, complemented
9C3×#63854C211yesmaximal, characteristic, complemented
10#11722995C211yesmaximal, characteristic, complemented
11#11722970C211yesmaximal, characteristic, complemented
12#11722957C211yesmaximal, characteristic, complemented
13#11722951C211yesmaximal, characteristic, complemented
14#11722938C211yesmaximal, characteristic, complemented
15#11722929C211yesmaximal, characteristic, complemented
16#10594632—31nomaximal
17#10594615—31nomaximal
18#10594267—31nomaximal
19C22×#1113C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6290C2211yescharacteristic
24C2×Dic3×C3⋊D3C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
28C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
29C2×C3×#627C2211yescharacteristic, complemented
30C2×C3×#626C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic
32C2×C3×#626C2211yescharacteristic, complemented
33C2×C3×#624C2211yescharacteristic
34C2×C3×#624C2211yescharacteristic
35C2×C3×#624C2211yescharacteristic
36#88964—24no—
37#88949—24no—
38C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C32×C4⋊Dic3C2211yescharacteristic, complemented
43C32×Dic3⋊C4C2211yescharacteristic, complemented
44#88814C2211yescharacteristic
45#88806C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic, complemented
50Dic3×C3⋊Dic3C2211yescharacteristic, complemented
51C3×#3724C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic
54C3×#3722C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×#3805—31no—
57C2×C4×D32—31no—
58C2×C4×D32—31no—
59C2×C4×D32—31no—
60C2×#3796—31no—
61C2×#3796—31no—
62#64102—31no—
63#64101—31no—
64#64090—31no—
65C3×#897—31no—
66C3×#896—31no—
67C3×#895—31no—
68C3×#894—31no—
69C3×#884—31no—
70C3×#883—31no—
71#63983—31no—
72#67⋊Dic3—31no—
73#63958—31no—
74#63923—31no—
75#63922—31no—
76#63922—31no—
77#63922—31no—
78#63922—31no—
79#63910D311yescharacteristic, complemented
80#63908—31no—
81#63906—31no—
82#63905—31no—
83#63902—31no—
84#63902—31no—
85#63902—31no—
86#63902—61no—
87#63898—31no—
88#63898—31no—
89#63898—31no—
90#63898—61no—
91#63895D311yescharacteristic, complemented
92#63888—31no—
93#63881—31no—
94#63881—31no—
95#63881—31no—
96#63878—31no—
97#63878—31no—
98#63878—61no—
99#63856—31no—
100#63854—31no—
101#63854D311yescharacteristic, complemented
102#63851—31no—
103#63850—31no—
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×#1113—22no—
110C2×#1113—22no—
111C2×#1113—22no—
112C2×C33×C4C2311yescharacteristic
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4⋊(C3⋊D3)—22no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6295—22no—
124#6295—22no—
125#6290—22no—
126Dic3×C3⋊D3—22no—
127Dic3×C3⋊D3—22no—
128Dic3×C3⋊D3—22no—
129Dic3×C3⋊D3D414yescomplemented
130D3×C3⋊Dic3—22no—
131C3×#627—22no—
132C3×#626—22no—
133C3×#626—22no—
134C3×#626—22no—
135C3×#624—22no—
136C3×#624—22no—
137C3×#624—22no—
138#5656—91no—
139#5627—91no—
140#5606—91no—
141C22×D32—31no—
142C22×D32—31no—
143C22×D32—31no—
144C2×#638—31no—
145C22×C3⋊Dic3—31no—
146C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
147C2×C4×C3⋊D3—31no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×D12—31no—
155C2×C3×D12—31no—
156C2×C3×D12—31no—
157C2×C3×D12—31no—
158C2×C3×D12—31no—
159C2×C3×D12—61no—
160C2×C3×C4×D3—31no—
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×Dic6—31no—
167C2×C3×Dic6—31no—
168C2×#627C2×D311yescharacteristic, complemented
169C2×#626—31no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626C2×D311yescharacteristic
174C2×#626C2×D311yescharacteristic
175C2×#626C2×D311yescharacteristic, complemented
176C2×#625—31no—
177C2×#625—31no—
178C2×#625—31no—
179C2×#625—31no—
180C2×#625—61no—
181C2×#624C2×D311yescharacteristic
182C2×#624C2×D311yescharacteristic
183C2×#624C2×D311yescharacteristic
184#3805—64no—
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—31no—
195C2×D3×Dic3—61no—
196C2×D3×Dic3—61no—
197C2×D3×Dic3—61no—
198C2×D3×Dic3—61no—
199C2×D3×Dic3—61no—
200C4×D32—64no—
201C4×D32—64no—
202C4×D32—64no—
203#3796—64no—
204#3796—64no—
205C32×C4⋊C4—31no—
206C32×C4⋊C4—31no—
207C32×C22⋊C4—31no—
208#3752—31no—
209#3752—31no—
210#3752—31no—
211#3752C2×D311yescharacteristic
212#3752C2×D311yescharacteristic
213C4⋊(C3⋊Dic3)—31no—
214#3750—31no—
215C4×C3⋊Dic3—31no—
216C4×C3⋊Dic3—31no—
217C4×C3⋊Dic3—31no—
218C4×C3⋊Dic3—31no—
219C4×C3⋊Dic3—61no—
220C4×C3⋊Dic3—61no—
221C4×C3⋊Dic3—61no—
222C4×C3⋊Dic3—121no—
223C3×#217—31no—
224C3×(C2×D3)⋊C4—21no—
225C3×(C2×D3)⋊C4—31no—
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)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—61no—
235C3×(C2×D3)⋊C4—61no—
236C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
237C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
238C3×C4⋊Dic3—21no—
239C3×C4⋊Dic3—31no—
240C3×C4⋊Dic3C2×D311yescharacteristic, complemented
241C3×C4⋊Dic3C2×D311yescharacteristic, complemented
242C3×Dic3⋊C4—21no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—31no—
245C3×Dic3⋊C4—31no—
246C3×Dic3⋊C4C2×D311yescharacteristic, complemented
247C3×Dic3⋊C4C2×D311yescharacteristic, complemented
248#3724—31no—
249#3724—31no—
250#3724—61no—
251#3724C2×D311yescharacteristic, complemented
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—61no—
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722C2×D311yescharacteristic
258#3722C2×D311yescharacteristic, complemented
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—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—61no—
268(C2×D3)⋊Dic3—61no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
271Dic32—31no—
272Dic32—31no—
273Dic32—61no—
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—21no—
284C2×C3×C3⋊D3C2×D412yes—
285C2×C3×C3⋊D3#4112yescomplemented
286C2×C3×C3⋊D3#4112yescomplemented
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3—21no—
290#1113—28no—
291C33×C4—21no—
292C3⋊(C3⋊Dic3)—21no—
293C3⋊(C3⋊Dic3)C2×D412yes—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3—21no—
296C32×Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3C2×D412yes—
301C2×#239—91no—
302C2×#237—91no—
303C2×#237—91no—
304C22×C4×D3—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×#123—91no—
308C3×C22⋊Q8—91no—
309C3×#121—91no—
310#946—91no—
311#938—91no—
312#937—91no—
313#937—91no—
314#937—91no—
315D4×Dic3—91no—
316D4×Dic3—91no—
317#930—91no—
318#929—91no—
319#924—91no—
320#897—31no—
321#896—31no—
322#896—91no—
323#895—31no—
324#894—31no—
325#894—91no—
326#893—91no—
327#893—91no—
328#893—91no—
329#893—91no—
330#893—181no—
331#892—91no—
332#892—91no—
333#892—181no—
334#884—31no—
335#884—91no—
336#883—31no—
337#883—91no—
338#882—91no—
339#882—91no—
340#882—91no—
341#67⋊C4—91no—
342#67⋊C4—91no—
343#67⋊C4—91no—
344#67⋊C4—91no—
345#67⋊C4—91no—
346#67⋊C4—91no—
347#67⋊C4—181no—
348#877—91no—
349C23×C32—31no—
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3⋊D3C22×D311yescharacteristic
352C22×C3⋊D3C22×D311yescharacteristic
353C22×C3⋊D3C22×D311yescharacteristic
354C22×C3×D3—21no—
355C22×C3×D3—31no—
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—31no—
363C22×C3×D3—61no—
364C22×C3×D3—61no—
365C22×C3×D3—61no—
366C22×C3×D3—61no—
367C22×C3×D3C22×D311yescharacteristic
368C22×C3×D3C22×D311yescharacteristic
369C2×D32—62no—
370C2×D32—62no—
371C2×D32—62no—
372C2×D32—62no—
373C2×D32—62no—
374C2×D32—62no—
375C2×D32—62no—
376C2×D32—62no—
377C2×D32—62no—
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—31no—
386C2×C32×C4—41no—
387C2×C32×C4C22×D311yescharacteristic
388C2×C32×C4C22×D311yescharacteristic
389C2×C32×C4C22×D311yescharacteristic
390#638—62no—
391C2×C3⋊Dic3—31no—
392C2×C3⋊Dic3—31no—
393C2×C3⋊Dic3—31no—
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—61no—
401C2×C3⋊Dic3—61no—
402C2×C3⋊Dic3—61no—
403C2×C3⋊Dic3—62no—
404C2×C3⋊Dic3—121no—
405C2×C3⋊Dic3—121no—
406C2×C3⋊Dic3C22×D311yescharacteristic
407C2×C3⋊Dic3C22×D311yescharacteristic
408C4⋊(C3⋊D3)—22no—
409C4×C3⋊D3—34no—
410C4×C3⋊D3—62no—
411C4×C3⋊D3—62no—
412C4×C3⋊D3—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—21no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C3×D12—62no—
438C3×D12—62no—
439C3×D12—64no—
440C3×D12—62no—
441C3×D12—62no—
442C3×D12—62no—
443C3×C4×D3—62no—
444C3×C4×D3—62no—
445C3×C4×D3—62no—
446C3×C4×D3—62no—
447C3×C4×D3—62no—
448C3×C4×D3—62no—
449C3×Dic6—62no—
450C3×Dic6—62no—
451#627—22no—
452#626—22no—
453#626—22no—
454#626—22no—
455#626—62no—
456#626—62no—
457#626—62no—
458#626—62no—
459#625—62no—
460#625—62no—
461#625—62no—
462#625—62no—
463#625—64no—
464#624—22no—
465#624—22no—
466#624—22no—
467D3×Dic3—34no—
468D3×Dic3—34no—
469D3×Dic3—64no—
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—122no—
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—22no—
488C3×C3⋊D3—22no—
489C3×C3⋊D3—41no—
490C32×D3—41no—
491C23×D3—91no—
492C23×D3—91no—
493C23×D3—91no—
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—91no—
514C22×Dic3—91no—
515C22×Dic3—91no—
516C22×Dic3—91no—
517C22×Dic3—91no—
518C22×Dic3—91no—
519C22×Dic3—181no—
520#239—184no—
521#237—184no—
522#237—184no—
523C2×D12—31no—
524C2×D12—31no—
525C2×D12—31no—
526C2×D12—31no—
527C2×D12—31no—
528C2×D12—61no—
529C2×D12—91no—
530C2×D12—91no—
531C2×C4×D3—31no—
532C2×C4×D3—31no—
533C2×C4×D3—31no—
534C2×C4×D3—31no—
535C2×C4×D3—31no—
536C2×C4×D3—31no—
537C2×C4×D3—91no—
538C2×C4×D3—91no—
539C2×C4×D3—91no—
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—181no—
547C2×C4×D3—181no—
548C2×C4×D3—181no—
549C2×C4×D3—181no—
550C2×C4×D3—184no—
551C2×C4×D3—184no—
552C2×C4×D3—184no—
553C2×Dic6—31no—
554C2×Dic6—31no—
555C3×C4⋊C4—31no—
556C3×C4⋊C4—31no—
557C3×C4⋊C4—31no—
558C3×C4⋊C4—31no—
559C3×C4⋊C4—61no—
560C3×C4⋊C4—61no—
561C3×C4⋊C4—91no—
562C3×C4⋊C4—91no—
563C3×C22⋊C4—31no—
564C3×C22⋊C4—31no—
565C3×C22⋊C4—61no—
566C3×C22⋊C4—91no—
567C3×C22⋊C4—91no—
568C3×C22⋊C4—91no—
569C3×C22⋊C4—91no—
570C3×C22⋊C4—91no—
571#217—31no—
572#217—91no—
573#217—91no—
574#217—91no—
575#217—91no—
576(C2×D3)⋊C4—31no—
577(C2×D3)⋊C4—31no—
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—31no—
584(C2×D3)⋊C4—31no—
585(C2×D3)⋊C4—61no—
586(C2×D3)⋊C4—61no—
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)⋊C4D3211yescharacteristic, complemented
599C4⋊Dic3—31no—
600C4⋊Dic3—91no—
601C4⋊Dic3—91no—
602C4⋊Dic3—181no—
603C4⋊Dic3D3211yescharacteristic, complemented
604Dic3⋊C4—31no—
605Dic3⋊C4—31no—
606Dic3⋊C4—31no—
607Dic3⋊C4—91no—
608Dic3⋊C4—91no—
609Dic3⋊C4—91no—
610Dic3⋊C4—91no—
611Dic3⋊C4—181no—
612Dic3⋊C4D3211yescharacteristic, complemented
613C4×Dic3—91no—
614C4×Dic3—91no—
615C4×Dic3—91no—
616C4×Dic3—91no—
617C4×Dic3—91no—
618C4×Dic3—91no—
619C4×Dic3—181no—
620C4×Dic3—181no—
621C4×Dic3—181no—
622C4×Dic3—181no—
623C4×Dic3—361no—
624C22×C32—21no—
625C22×C32—21no—
626C22×C32—21no—
627C22×C32—41no—
628C22×C32—61no—
629C22×C32—61no—
630C22×C32—61no—
631C22×C32C23×D311yescharacteristic
632C22×C32C23×D311yescharacteristic
633C22×C32C23×D311yescharacteristic
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
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⋊D3D3×D412yes—
644C2×C3⋊D3#23712yescomplemented
645C2×C3⋊D3#23912yescomplemented
646C2×C3×D3—22no—
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—32no—
654C2×C3×D3—32no—
655C2×C3×D3—32no—
656C2×C3×D3—32no—
657C2×C3×D3—32no—
658C2×C3×D3—32no—
659C2×C3×D3—41no—
660C2×C3×D3—41no—
661C2×C3×D3—62no—
662C2×C3×D3—62no—
663C2×C3×D3—62no—
664C2×C3×D3—61no—
665C2×C3×D3—61no—
666C2×C3×D3—61no—
667C2×C3×D3—61no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
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—62no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—61no—
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—121no—
690C2×C3×D3—121no—
691D32—68no—
692D32—68no—
693D32—68no—
694C32×C4—21no—
695C32×C4—22no—
696C32×C4—21no—
697C32×C4—21no—
698C32×C4—32no—
699C32×C4—41no—
700C32×C4—41no—
701C32×C4—42no—
702C32×C4—61no—
703C32×C4—61no—
704C32×C4—61no—
705C32×C4—61no—
706C3⋊Dic3—21no—
707C3⋊Dic3—21no—
708C3⋊Dic3—32no—
709C3⋊Dic3—32no—
710C3⋊Dic3—32no—
711C3⋊Dic3—62no—
712C3⋊Dic3—62no—
713C3⋊Dic3—62no—
714C3⋊Dic3—61no—
715C3⋊Dic3—62no—
716C3⋊Dic3—61no—
717C3⋊Dic3—61no—
718C3⋊Dic3—122no—
719C3⋊Dic3—121no—
720C3⋊Dic3—121no—
721C3⋊Dic3—122no—
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—22no—
731C3×Dic3—41no—
732C3×Dic3—41no—
733C3×Dic3—41no—
734C3×Dic3—41no—
735C3×Dic3—61no—
736C3×Dic3—61no—
737C3×Dic3—61no—
738C3×Dic3—61no—
739C3×Dic3—121no—
740C3×Dic3—121no—
741C3×Dic3D3×D412yes—
742C3×Dic3D3×D412yes—
743C2×#41—271no—
744C23×C4—271no—
745#123—91no—
746#123—271no—
747C22⋊Q8—91no—
748C22⋊Q8—271no—
749#121—91no—
750#121—271no—
751#120—271no—
752#120—271no—
753C4×D4—271no—
754C4×D4—271no—
755C4×D4—271no—
756C4×D4—271no—
757#117—271no—
758C33#52511yescharacteristic, complemented, Sylow
759C23×C3—31no—
760C23×C3—31no—
761C23×C3—61no—
762C23×C3—91no—
763C23×C3—91no—
764C23×C3—91no—
765C23×C3—91no—
766C22×D3—31no—
767C22×D3—31no—
768C22×D3—31no—
769C22×D3—31no—
770C22×D3—31no—
771C22×D3—31no—
772C22×D3—31no—
773C22×D3—31no—
774C22×D3—61no—
775C22×D3—61no—
776C22×D3—61no—
777C22×D3—61no—
778C22×D3—182no—
779C22×D3—182no—
780C22×D3—182no—
781C22×D3—182no—
782C22×D3—182no—
783C22×D3—182no—
784C22×D3—182no—
785C22×D3—182no—
786C22×D3—182no—
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—31no—
805C2×C3×C4—31no—
806C2×C3×C4—41no—
807C2×C3×C4—61no—
808C2×C3×C4—61no—
809C2×C3×C4—61no—
810C2×C3×C4—61no—
811C2×C3×C4—61no—
812C2×C3×C4—91no—
813C2×C3×C4—91no—
814C2×C3×C4—182no—
815C2×C3×C4—182no—
816C2×C3×C4—182no—
817C2×C3×C4C2×D3211yescharacteristic
818C2×C3×C4C2×D3211yescharacteristic
819C2×C3×C4C2×D3211yescharacteristic
820#67—62no—
821#67—62no—
822#67—62no—
823#67—182no—
824#67—182no—
825#67—182no—
826#67—182no—
827#67—182no—
828#67—182no—
829#67—182no—
830#67—184no—
831C2×Dic3—31no—
832C2×Dic3—31no—
833C2×Dic3—31no—
834C2×Dic3—31no—
835C2×Dic3—61no—
836C2×Dic3—61no—
837C2×Dic3—91no—
838C2×Dic3—91no—
839C2×Dic3—91no—
840C2×Dic3—94no—
841C2×Dic3—91no—
842C2×Dic3—91no—
843C2×Dic3—91no—
844C2×Dic3—181no—
845C2×Dic3—181no—
846C2×Dic3—181no—
847C2×Dic3—181no—
848C2×Dic3—181no—
849C2×Dic3—181no—
850C2×Dic3—182no—
851C2×Dic3—182no—
852C2×Dic3—182no—
853C2×Dic3—182no—
854C2×Dic3—182no—
855C2×Dic3—361no—
856C2×Dic3—361no—
857C2×Dic3—362no—
858C2×Dic3C2×D3211yescharacteristic
859C2×Dic3C2×D3211yescharacteristic
860C2×Dic3C2×D3211yescharacteristic
861C2×Dic3C2×D3211yescharacteristic
862C2×Dic3C2×D3211yescharacteristic
863D12—62no—
864D12—62no—
865D12—64no—
866D12—62no—
867D12—62no—
868D12—62no—
869D12—182no—
870D12—182no—
871C4×D3—62no—
872C4×D3—62no—
873C4×D3—62no—
874C4×D3—62no—
875C4×D3—62no—
876C4×D3—62no—
877C4×D3—94no—
878C4×D3—94no—
879C4×D3—184no—
880C4×D3—182no—
881C4×D3—182no—
882C4×D3—182no—
883C4×D3—182no—
884C4×D3—182no—
885C4×D3—182no—
886C4×D3—182no—
887C4×D3—362no—
888C4×D3—362no—
889C4×D3—362no—
890Dic6—62no—
891Dic6—62no—
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—121no—
905C2×C32C2×D3×D411yescharacteristic
906C2×C32C2×D3×D411yescharacteristic
907C2×C32C2×D3×D411yescharacteristic
908C2×C32C2×#23711yescharacteristic
909C2×C32C2×#23911yescharacteristic
910C2×C32D3×#4111yescharacteristic
911C2×C32D3×#4111yescharacteristic
912C2×C32D3×#4111yescharacteristic
913C2×C32D3×#4111yescharacteristic
914C3⋊D3—22no—
915C3⋊D3—22no—
916C3⋊D3—22no—
917C3⋊D3—41no—
918C3×D3—42no—
919C3×D3—41no—
920C3×D3—41no—
921C3×D3—62no—
922C3×D3—62no—
923C3×D3—62no—
924C3×D3—62no—
925C3×D3—62no—
926C3×D3—62no—
927C3×D3—122no—
928C3×D3—122no—
929C3×D3—122no—
930C3×D3—122no—
931C3×D3—121no—
932C3×D3—121no—
933C24—271no—
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—31no—
954C4⋊C4—91no—
955C4⋊C4—91no—
956C4⋊C4—271no—
957C4⋊C4—271no—
958C22⋊C4—31no—
959C22⋊C4—91no—
960C22⋊C4—91no—
961C22⋊C4—91no—
962C22⋊C4—91no—
963C22⋊C4—91no—
964C22⋊C4—271no—
965C22⋊C4—271no—
966C22⋊C4—271no—
967C22⋊C4—271no—
968C42—271no—
969C42—271no—
970C22×C3—21no—
971C22×C3—21no—
972C22×C3—21no—
973C22×C3—41no—
974C22×C3—62no—
975C22×C3—61no—
976C22×C3—61no—
977C22×C3—61no—
978C22×C3—61no—
979C22×C3—61no—
980C22×C3—61no—
981C22×C3—92no—
982C22×C3—92no—
983C22×C3—92no—
984C22×C3—121no—
985C22×C3—121no—
986C22×C3—181no—
987C22×C3—181no—
988C22×C3—181no—
989C22×C3—181no—
990C22×C3—181no—
991C22×C3—181no—
992C22×C3—181no—
993C22×C3—181no—
994C22×C3—181no—
995C22×C3C22×D3211yescharacteristic
996C22×C3C22×D3211yescharacteristic
997C22×C3C22×D3211yescharacteristic
998C2×D3—21no—
999C2×D3—21no—
1000C2×D3—21no—
1001C2×D3—32no—
1002C2×D3—32no—
1003C2×D3—32no—
1004C2×D3—32no—
1005C2×D3—32no—
1006C2×D3—32no—
1007C2×D3—62no—
1008C2×D3—62no—
1009C2×D3—62no—
1010C2×D3—61no—
1011C2×D3—61no—
1012C2×D3—61no—
1013C2×D3—61no—
1014C2×D3—61no—
1015C2×D3—61no—
1016C2×D3—61no—
1017C2×D3—61no—
1018C2×D3—61no—
1019C2×D3—61no—
1020C2×D3—61no—
1021C2×D3—61no—
1022C2×D3—62no—
1023C2×D3—61no—
1024C2×D3—61no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—121no—
1030C2×D3—121no—
1031C2×D3—121no—
1032C2×D3—121no—
1033C2×D3—121no—
1034C2×D3—121no—
1035C2×D3—121no—
1036C2×D3—121no—
1037C2×D3—188no—
1038C2×D3—188no—
1039C2×D3—188no—
1040C3×C4—22no—
1041C3×C4—21no—
1042C3×C4—21no—
1043C3×C4—21no—
1044C3×C4—32no—
1045C3×C4—32no—
1046C3×C4—41no—
1047C3×C4—41no—
1048C3×C4—42no—
1049C3×C4—62no—
1050C3×C4—61no—
1051C3×C4—61no—
1052C3×C4—61no—
1053C3×C4—61no—
1054C3×C4—61no—
1055C3×C4—61no—
1056C3×C4—61no—
1057C3×C4—61no—
1058C3×C4—121no—
1059C3×C4—121no—
1060C3×C4—121no—
1061C3×C4—121no—
1062C3×C4—181no—
1063C3×C4—181no—
1064Dic3—21no—
1065Dic3—21no—
1066Dic3—21no—
1067Dic3—21no—
1068Dic3—61no—
1069Dic3—61no—
1070Dic3—61no—
1071Dic3—61no—
1072Dic3—92no—
1073Dic3—92no—
1074Dic3—92no—
1075Dic3—121no—
1076Dic3—121no—
1077Dic3—182no—
1078Dic3—182no—
1079Dic3—182no—
1080Dic3—182no—
1081Dic3—181no—
1082Dic3—181no—
1083Dic3—181no—
1084Dic3—362no—
1085Dic3—361no—
1086Dic3—361no—
1087Dic3—362no—
1088Dic3#380212yes—
1089C32—21no—
1090C32—21no—
1091C32—21no—
1092C32—41no—
1093C32#560611yescharacteristic, complemented
1094C32#562711yescharacteristic, complemented
1095C32#565611yescharacteristic, complemented
1096C23—31no—
1097C23—91no—
1098C23—91no—
1099C23—91no—
1100C23—91no—
1101C23—542no—
1102C23—542no—
1103C23—542no—
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—31no—
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—122no—
1143C2×C3—121no—
1144C2×C3—121no—
1145C2×C3—182no—
1146C2×C3—182no—
1147C2×C3—182no—
1148C2×C3—361no—
1149C2×C3C2×#380211yescharacteristic
1150C2×C3#6430611yescharacteristic
1151C2×C3#6430611yescharacteristic
1152C2×C3D32×D411yescharacteristic
1153C2×C3D32×D411yescharacteristic
1154C2×C3D3×#23711yescharacteristic
1155C2×C3D3×#23711yescharacteristic
1156C2×C3D3×#23911yescharacteristic
1157C2×C3D3×#23911yescharacteristic
1158D3—41no—
1159D3—62no—
1160D3—62no—
1161D3—62no—
1162D3—62no—
1163D3—62no—
1164D3—62no—
1165D3—122no—
1166D3—122no—
1167D3—122no—
1168D3—122no—
1169D3—121no—
1170D3—121no—
1171C22—61no—
1172C22—61no—
1173C22—61no—
1174C22—92no—
1175C22—92no—
1176C22—92no—
1177C22—181no—
1178C22—181no—
1179C22—181no—
1180C22—181no—
1181C22—181no—
1182C22—181no—
1183C22—181no—
1184C22—181no—
1185C22—181no—
1186C22—548no—
1187C22C2×D3311yescharacteristic
1188C4—21no—
1189C4—32no—
1190C4—61no—
1191C4—61no—
1192C4—61no—
1193C4—61no—
1194C4—181no—
1195C4—181no—
1196C4—272no—
1197C4—541no—
1198C3—21no—
1199C3—21no—
1200C3—21no—
1201C3—41no—
1202C3#1059426711yescharacteristic, complemented
1203C3#1059461511yescharacteristic, complemented
1204C3#1059463211yescharacteristic, complemented
1205C2—121no—
1206C2—182no—
1207C2—182no—
1208C2—182no—
1209C2—361no—
1210C2#1172439111yescharacteristic
1211C2D3×#380211yescharacteristic
1212C2#1172440711yescharacteristic
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×#88964C2semidirect
2. C2×#88949C2semidirect
3. #11723701C2semidirect
4. #11723508C2semidirect
5. #11723501C2semidirect
6. #11723466C2semidirect
7. C3×#63910C2semidirect
8. C3×#63895C2semidirect
9. C3×#63854C2semidirect
10. #11722995C2semidirect
11. #11722970C2semidirect
12. #11722957C2semidirect
13. #11722951C2semidirect
14. #11722938C2semidirect
15. #11722929C2semidirect
27. C2×Dic3×C3⋊D3C22semidirect
28. C2×D3×C3⋊Dic3C22semidirect
29. C2×C3×#627C22semidirect
32. C2×C3×#626C22semidirect
38. C4×C3⋊(C3⋊Dic3)C22semidirect
41. C32×(C2×D3)⋊C4C22semidirect
42. C32×C4⋊Dic3C22semidirect
43. C32×Dic3⋊C4C22semidirect
45. #88806C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88803C22semidirect
50. Dic3×C3⋊Dic3C22semidirect
51. C3×#3724C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
54. C3×#3722C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
79. #63910D3semidirect
91. #63895D3semidirect
101. #63854D3semidirect
129. Dic3×C3⋊D3D4semidirect
168. C2×#627C2×D3semidirect
175. C2×#626C2×D3semidirect
236. C3×(C2×D3)⋊C4C2×D3semidirect
237. C3×(C2×D3)⋊C4C2×D3semidirect
240. C3×C4⋊Dic3C2×D3semidirect
241. C3×C4⋊Dic3C2×D3semidirect
246. C3×Dic3⋊C4C2×D3semidirect
247. C3×Dic3⋊C4C2×D3semidirect
251. #3724C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
258. #3722C2×D3semidirect
270. (C2×D3)⋊Dic3C2×D3semidirect
285. C2×C3×C3⋊D3#41semidirect
286. C2×C3×C3⋊D3#41semidirect
598. (C2×D3)⋊C4D32semidirect
603. C4⋊Dic3D32semidirect
612. Dic3⋊C4D32semidirect
644. C2×C3⋊D3#237semidirect
645. C2×C3⋊D3#239semidirect
758. C33#525semidirect
1093. C32#5606semidirect
1094. C32#5627semidirect
1095. C32#5656semidirect
1202. C3#10594267semidirect
1203. C3#10594615semidirect
1204. C3#10594632semidirect

Maximal subgroups

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

subgroupindex
C2×#889642
C2×#889492
#117237012
#117235082
#117235012
#117234662
C3×#639102
C3×#638952
C3×#638542
#117229952
#117229702
#117229572
#117229512
#117229382
#117229292
#105946323
#105946153
#105942673