Finite Group Databasebeta

← #13172920

Subgroups — #13172920

Order 1728.

1652 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6294C211yesmaximal, characteristic, complemented
2C2×#88961C211yesmaximal, characteristic, complemented
3#11723641C211yesmaximal, characteristic, complemented
4#11723634C211yesmaximal, characteristic, complemented
5#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×#63980C211yesmaximal, characteristic, complemented
8C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
9#11722998C211yesmaximal, characteristic, complemented
10#11722994C211yesmaximal, characteristic, complemented
11#11722984C211yesmaximal, characteristic, complemented
12#11722965C211yesmaximal, characteristic, complemented
13#11722936C211yesmaximal, characteristic, complemented
14#11722928C211yesmaximal, characteristic, complemented
15#11722922C211yesmaximal, characteristic, complemented
16#10595138—31nomaximal
17#10595130—31nomaximal
18#10594054—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×#6294—24no—
25C2×#6294C2211yescharacteristic
26C2×#6294C2211yescharacteristic
27C2×#6294C2211yescharacteristic
28C2×#6294C2211yescharacteristic
29C2×#6293C2211yescharacteristic, complemented
30C2×#6290C2211yescharacteristic
31C2×#6290C2211yescharacteristic
32C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
33C2×C3×#626C2211yescharacteristic
34C2×C3×#626C2211yescharacteristic
35C2×C3×#625C2211yescharacteristic, complemented
36C2×C3×D3×Dic3C2211yescharacteristic, complemented
37#88961—24no—
38#88864C2211yescharacteristic
39C32×#217C2211yescharacteristic
40#88807C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44#88803C2211yescharacteristic
45#88803C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C22×#624—31no—
57C2×#3805—31no—
58C2×#3804—31no—
59C22×D3×Dic3—31no—
60C22×D3×Dic3—31no—
61C2×#3795—31no—
62#64146—31no—
63D4×C3⋊Dic3—31no—
64#64087—31no—
65C3×#939—31no—
66C3×#939—31no—
67C3×#937—31no—
68C3×D4×Dic3—31no—
69C3×#882—31no—
70C3×#67⋊C4—31no—
71#63981D311yescharacteristic, complemented
72#63980D311yescharacteristic, complemented
73#63976—31no—
74#63976—31no—
75#63976—61no—
76#63975—31no—
77#67⋊Dic3—31no—
78#67⋊Dic3D311yescharacteristic, complemented
79Dic3×#67—31no—
80Dic3×#67—31no—
81Dic3×#67—61no—
82#63970—31no—
83#63969—31no—
84#63964—31no—
85#63964—31no—
86#63964—61no—
87#63958—31no—
88#63952—31no—
89#63902—31no—
90#63896—31no—
91#63895—31no—
92#63893—31no—
93Dic3×D12—31no—
94#63891—31no—
95#63891—31no—
96#63885—31no—
97#63884—31no—
98#63880—31no—
99#63879—31no—
100#63878—31no—
101#63877—31no—
102#63854—31no—
103#63836—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—22no—
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C32×D3C2311yescharacteristic
111C22×C32×D3C2311yescharacteristic
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3×C3⋊Dic3—22no—
115C2×C3×C3⋊Dic3—22no—
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C32×#67—22no—
121C32×#67—22no—
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126#6294—22no—
127#6294—22no—
128#6294—22no—
129#6294D414yescomplemented
130#6293—22no—
131#6290—22no—
132#6290—22no—
133D3×C3⋊Dic3—22no—
134C3×#626—22no—
135C3×#626—22no—
136C3×#625—22no—
137C3×D3×Dic3—22no—
138#5606—91no—
139#5586—91no—
140#5547—91no—
141C23×C3⋊D3C2×D311yescharacteristic
142C23×C3×D3—31no—
143C23×C3×D3—31no—
144C23×C3×D3—61no—
145C2×C32×D4—31no—
146C2×C32×D4—31no—
147C2×#638—31no—
148C2×#638—31no—
149C22×C3⋊Dic3—31no—
150C22×C3⋊Dic3C2×D311yescharacteristic
151C22×C3⋊Dic3C2×D311yescharacteristic
152C2×#634—31no—
153C2×C3×#67—21no—
154C2×C3×#67—21no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67C2×D311yescharacteristic
160C2×C3×#67C2×D311yescharacteristic
161C2×C3×#67C2×D311yescharacteristic
162C2×C3×#67C2×D311yescharacteristic
163C22×C3×Dic3—31no—
164C22×C3×Dic3—31no—
165C22×C3×Dic3—31no—
166C22×C3×Dic3—31no—
167C22×C3×Dic3—31no—
168C22×C3×Dic3—61no—
169C22×C3×Dic3—61no—
170C2×C3×D12—31no—
171C2×C3×D12—31no—
172C2×C3×C4×D3—31no—
173C2×#627—31no—
174C2×#627—31no—
175C2×#627—61no—
176C2×#626C2×D311yescharacteristic
177C2×#626C2×D311yescharacteristic
178C2×#625—31no—
179C2×#625—31no—
180C2×#625—31no—
181C2×#625—31no—
182C2×#625—61no—
183C2×#625—61no—
184C2×#625C2×D311yescharacteristic, complemented
185C2×#624—31no—
186C2×#624—31no—
187C2×#624—31no—
188C2×#624—31no—
189C2×#624—64no—
190#3805—64no—
191#3804—64no—
192C2×D3×Dic3—31no—
193C2×D3×Dic3—31no—
194C2×D3×Dic3—31no—
195C2×D3×Dic3—31no—
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—31no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3—31no—
201C2×D3×Dic3—31no—
202C2×D3×Dic3—64no—
203C2×D3×Dic3—64no—
204C2×D3×Dic3—61no—
205C2×D3×Dic3C2×D311yescharacteristic, complemented
206#3795—64no—
207C32×C22⋊C4—31no—
208#3757—31no—
209#3757—31no—
210#3757—31no—
211#3757—31no—
212#3757—61no—
213#3757—61no—
214#3757—61no—
215#3757—121no—
216#3752—31no—
217#3752—31no—
218C4⋊(C3⋊Dic3)—31no—
219C4⋊(C3⋊Dic3)—31no—
220#3750—31no—
221#3750—31no—
222C4×C3⋊Dic3—31no—
223C3×#217—21no—
224C3×#217—31no—
225C3×#217—31no—
226C3×#217—31no—
227C3×#217C2×D311yescharacteristic
228C3×#217C2×D311yescharacteristic
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—31no—
235C3×(C2×D3)⋊C4—31no—
236C3×C4⋊Dic3—31no—
237C3×Dic3⋊C4—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×C4×Dic3—31no—
241C3×C4×Dic3—31no—
242#3724—31no—
243#3724—31no—
244#3724—61no—
245#3724C2×D311yescharacteristic, complemented
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—61no—
253Dic3⋊Dic3—61no—
254Dic3⋊Dic3—61no—
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722C2×D311yescharacteristic
257#3722C2×D311yescharacteristic
258(C2×D3)⋊Dic3—31no—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—61no—
265(C2×D3)⋊Dic3—61no—
266(C2×D3)⋊Dic3—61no—
267(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
268(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
269(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
270Dic32—31no—
271Dic32—31no—
272Dic32—61no—
273Dic32C2×D311yescharacteristic, complemented
274C22×C33—21no—
275C22×C33—21no—
276C22×C33#4112yescomplemented
277C22×C33C2411yescharacteristic
278C2×C3×C3⋊D3—28no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3—21no—
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3C2×D412yes—
284C2×C3×C3⋊D3#4112yescomplemented
285C2×C32×D3—21no—
286C2×C32×D3—21no—
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3—21no—
290C2×C32×D3—21no—
291C3⋊(C3⋊Dic3)—21no—
292C3⋊(C3⋊Dic3)—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3C2×D412yes—
296C3×C3⋊Dic3C2×D412yes—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C23×Dic3—91no—
302C2×#237—91no—
303C2×#237—91no—
304C2×#235—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×#121—91no—
308C3×#120—91no—
309C3×C4×D4—91no—
310#953—91no—
311#939—31no—
312#939—31no—
313#939—91no—
314#938—91no—
315#937—31no—
316#937—91no—
317#937—91no—
318#937—181no—
319#935—91no—
320D4×Dic3—31no—
321D4×Dic3—91no—
322D4×Dic3—91no—
323D4×Dic3—91no—
324D4×Dic3—181no—
325C4×#67—91no—
326C4×#67—91no—
327#924—91no—
328#897—91no—
329#896—91no—
330#894—91no—
331#892—91no—
332#886—91no—
333#884—91no—
334#883—91no—
335#883—91no—
336#883—91no—
337#882—31no—
338#67⋊C4—31no—
339#67⋊C4—91no—
340#67⋊C4—91no—
341#67⋊C4—91no—
342#878—91no—
343#878—91no—
344#878—91no—
345#878—181no—
346#877—91no—
347C4×D12—91no—
348#872—91no—
349C23×C32—21no—
350C23×C32—21no—
351C23×C32—21no—
352C23×C32—31no—
353C23×C32—31no—
354C23×C32—41no—
355C23×C32C22×D311yescharacteristic
356C23×C32C22×D311yescharacteristic
357C23×C32C22×D311yescharacteristic
358C22×C3⋊D3—22no—
359C22×C3⋊D3—22no—
360C22×C3⋊D3—22no—
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×D3—62no—
372C22×C3×D3—62no—
373C22×C3×D3—62no—
374C22×C3×D3—62no—
375C22×C3×D3—62no—
376C22×C3×D3—62no—
377C22×C3×D3—122no—
378C22×C3×D3—122no—
379C22×C3×D3—122no—
380C22×C3×D3C22×D311yescharacteristic
381C22×C3×D3C22×D311yescharacteristic
382C22×C3×D3C22×D311yescharacteristic
383C22×C3×D3C22×D311yescharacteristic
384C32×D4—62no—
385C32×D4—62no—
386C2×C32×C4—31no—
387C2×C32×C4—31no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390#638—62no—
391#638—62no—
392C2×C3⋊Dic3—22no—
393C2×C3⋊Dic3—22no—
394C2×C3⋊Dic3—31no—
395C2×C3⋊Dic3—31no—
396C2×C3⋊Dic3—31no—
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—61no—
404C2×C3⋊Dic3—61no—
405C2×C3⋊Dic3—61no—
406C2×C3⋊Dic3—62no—
407C2×C3⋊Dic3—121no—
408C2×C3⋊Dic3—121no—
409C2×C3⋊Dic3C22×D311yescharacteristic
410C2×C3⋊Dic3C22×D311yescharacteristic
411C2×C3⋊Dic3C22×D311yescharacteristic
412C2×C3⋊Dic3C22×D311yescharacteristic
413#634—62no—
414C3×#67—24no—
415C3×#67—22no—
416C3×#67—22no—
417C3×#67—22no—
418C3×#67—22no—
419C3×#67—42no—
420C3×#67—62no—
421C3×#67—62no—
422C3×#67—62no—
423C3×#67—62no—
424C2×C3×Dic3—21no—
425C2×C3×Dic3—21no—
426C2×C3×Dic3—21no—
427C2×C3×Dic3—21no—
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—31no—
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×Dic3—62no—
443C2×C3×Dic3—62no—
444C2×C3×Dic3—62no—
445C2×C3×Dic3—122no—
446C2×C3×Dic3—122no—
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C2×C3×Dic3C22×D311yescharacteristic
451C2×C3×Dic3C22×D311yescharacteristic
452C2×C3×Dic3C22×D311yescharacteristic
453C2×C3×Dic3C22×D311yescharacteristic
454C2×C3×Dic3C22×D311yescharacteristic
455C3×D12—62no—
456C3×D12—62no—
457C3×C4×D3—62no—
458#627—62no—
459#627—62no—
460#627—122no—
461#626—22no—
462#626—22no—
463#625—22no—
464#625—62no—
465#625—62no—
466#625—62no—
467#625—62no—
468#625—122no—
469#625—122no—
470#624—34no—
471#624—62no—
472#624—62no—
473#624—62no—
474D3×Dic3—22no—
475D3×Dic3—34no—
476D3×Dic3—34no—
477D3×Dic3—62no—
478D3×Dic3—62no—
479D3×Dic3—62no—
480D3×Dic3—62no—
481D3×Dic3—62no—
482D3×Dic3—62no—
483D3×Dic3—62no—
484D3×Dic3—62no—
485D3×Dic3—122no—
486#525—271noSylow
487C2×C33—22no—
488C2×C33C22×D411yescharacteristic
489C2×C33C2×#4111yescharacteristic
490C2×C33C2×#4111yescharacteristic
491C3×C3⋊D3—22no—
492C3×C3⋊D3—22no—
493C32×D3—41no—
494C32×D3—41no—
495C24×C3—91no—
496C23×D3—31no—
497C23×D3—31no—
498C23×D3—61no—
499C2×C3×D4—31no—
500C2×C3×D4—31no—
501C2×C3×D4—31no—
502C2×C3×D4—31no—
503C2×C3×D4—61no—
504C2×C3×D4—61no—
505C2×C3×D4—91no—
506C2×C3×D4—91no—
507C2×C3×D4—91no—
508C22×C3×C4—91no—
509C22×C3×C4—91no—
510C22×C3×C4—91no—
511C2×#67—31no—
512C2×#67—31no—
513C2×#67—31no—
514C2×#67—31no—
515C2×#67—91no—
516C2×#67—91no—
517C2×#67—91no—
518C2×#67—91no—
519C2×#67—91no—
520C2×#67—91no—
521C2×#67—181no—
522C2×#67—181no—
523C2×#67D3211yescharacteristic
524C2×#67D3211yescharacteristic
525C22×Dic3—31no—
526C22×Dic3—31no—
527C22×Dic3—31no—
528C22×Dic3—31no—
529C22×Dic3—31no—
530C22×Dic3—61no—
531C22×Dic3—61no—
532C22×Dic3—91no—
533C22×Dic3—91no—
534C22×Dic3—91no—
535C22×Dic3—91no—
536C22×Dic3—91no—
537C22×Dic3—91no—
538C22×Dic3—181no—
539C22×Dic3—184no—
540#237—184no—
541#237—184no—
542#235—184no—
543C2×D12—31no—
544C2×D12—31no—
545C2×C4×D3—31no—
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—91no—
554C2×C4×D3—91no—
555C2×C4×D3—184no—
556C2×C4×D3—184no—
557C2×Dic6—91no—
558C2×Dic6—91no—
559C2×Dic6—91no—
560C2×Dic6—181no—
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—
571C3×C42—91no—
572#217—31no—
573#217—31no—
574#217—31no—
575#217—91no—
576#217—91no—
577#217—91no—
578#217—91no—
579#217—91no—
580#217—91no—
581#217—91no—
582#217—181no—
583#217—181no—
584#217—181no—
585#217—181no—
586#217—361no—
587#217D3211yescharacteristic
588(C2×D3)⋊C4—31no—
589(C2×D3)⋊C4—31no—
590(C2×D3)⋊C4—31no—
591(C2×D3)⋊C4—31no—
592(C2×D3)⋊C4—31no—
593(C2×D3)⋊C4—31no—
594(C2×D3)⋊C4—31no—
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—181no—
601(C2×D3)⋊C4—181no—
602C4⋊Dic3—31no—
603C4⋊Dic3—91no—
604C4⋊Dic3—91no—
605C4⋊Dic3—91no—
606C4⋊Dic3—91no—
607C4⋊Dic3—91no—
608C4⋊Dic3—181no—
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—91no—
618Dic3⋊C4—91no—
619Dic3⋊C4—91no—
620Dic3⋊C4—181no—
621Dic3⋊C4—181no—
622C4×Dic3—31no—
623C4×Dic3—31no—
624C4×Dic3—91no—
625C4×Dic3—91no—
626C4×Dic3—91no—
627C4×Dic3—181no—
628C22×C32—21no—
629C22×C32—21no—
630C22×C32—21no—
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—21no—
637C22×C32—22no—
638C22×C32—22no—
639C22×C32—22no—
640C22×C32—41no—
641C22×C32—42no—
642C22×C32—41no—
643C22×C32—41no—
644C22×C32—41no—
645C22×C32—41no—
646C22×C32—41no—
647C22×C32—41no—
648C22×C32—61no—
649C22×C32—61no—
650C22×C32—61no—
651C22×C32—61no—
652C22×C32—61no—
653C22×C32—61no—
654C22×C32—81no—
655C22×C32—81no—
656C22×C32#23512yescomplemented
657C22×C32#23712yescomplemented
658C22×C32#23712yescomplemented
659C22×C32C23×D311yescharacteristic
660C22×C32C23×D311yescharacteristic
661C22×C32C23×D311yescharacteristic
662C2×C3⋊D3—28no—
663C2×C3⋊D3—21no—
664C2×C3⋊D3—21no—
665C2×C3⋊D3—21no—
666C2×C3⋊D3—21no—
667C2×C3⋊D3D3×D412yes—
668C2×C3⋊D3#23712yescomplemented
669C2×C3×D3—22no—
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—21no—
678C2×C3×D3—21no—
679C2×C3×D3—21no—
680C2×C3×D3—21no—
681C2×C3×D3—21no—
682C2×C3×D3—32no—
683C2×C3×D3—32no—
684C2×C3×D3—32no—
685C2×C3×D3—32no—
686C2×C3×D3—41no—
687C2×C3×D3—41no—
688C2×C3×D3—41no—
689C2×C3×D3—41no—
690C2×C3×D3—41no—
691C2×C3×D3—62no—
692C2×C3×D3—62no—
693C2×C3×D3—68no—
694C2×C3×D3—68no—
695C2×C3×D3—61no—
696C2×C3×D3—61no—
697C2×C3×D3—61no—
698C2×C3×D3—61no—
699C2×C3×D3—61no—
700C2×C3×D3—61no—
701C2×C3×D3—61no—
702C2×C3×D3—61no—
703C2×C3×D3—121no—
704C2×C3×D3—121no—
705C2×C3×D3—121no—
706C2×C3×D3—121no—
707C2×C3×D3—128no—
708C32×C4—61no—
709C32×C4—61no—
710C32×C4—61no—
711C32×C4—61no—
712C3⋊Dic3—21no—
713C3⋊Dic3—21no—
714C3⋊Dic3—61no—
715C3⋊Dic3—61no—
716C3⋊Dic3—61no—
717C3⋊Dic3—61no—
718C3⋊Dic3—61no—
719C3⋊Dic3—61no—
720C3⋊Dic3—121no—
721C3⋊Dic3—121no—
722C3⋊Dic3—121no—
723C3⋊Dic3—121no—
724C3⋊Dic3—121no—
725C3⋊Dic3—121no—
726C3⋊Dic3—241no—
727C3⋊Dic3—241no—
728C3⋊Dic3D3×D412yes—
729C3⋊Dic3D3×D412yes—
730C3×Dic3—22no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—21no—
734C3×Dic3—21no—
735C3×Dic3—21no—
736C3×Dic3—21no—
737C3×Dic3—21no—
738C3×Dic3—21no—
739C3×Dic3—32no—
740C3×Dic3—32no—
741C3×Dic3—32no—
742C3×Dic3—32no—
743C3×Dic3—41no—
744C3×Dic3—41no—
745C3×Dic3—41no—
746C3×Dic3—62no—
747C3×Dic3—62no—
748C3×Dic3—61no—
749C3×Dic3—61no—
750C3×Dic3—61no—
751C3×Dic3—61no—
752C3×Dic3—121no—
753C3×Dic3—121no—
754C2×#41—271no—
755C23×C4—271no—
756#123—271no—
757#123—271no—
758C22⋊Q8—271no—
759C22⋊Q8—271no—
760#121—91no—
761#121—271no—
762#120—91no—
763#120—271no—
764C4×D4—91no—
765C4×D4—271no—
766C4×D4—271no—
767C4×D4—271no—
768#117—271no—
769C33#52511yescharacteristic, complemented, Sylow
770C23×C3—21no—
771C23×C3—21no—
772C23×C3—21no—
773C23×C3—31no—
774C23×C3—31no—
775C23×C3—31no—
776C23×C3—31no—
777C23×C3—41no—
778C23×C3—61no—
779C23×C3—61no—
780C23×C3—91no—
781C23×C3—91no—
782C23×C3—182no—
783C23×C3—182no—
784C23×C3—182no—
785C23×C3C2×D3211yescharacteristic
786C23×C3C2×D3211yescharacteristic
787C23×C3C2×D3211yescharacteristic
788C22×D3—31no—
789C22×D3—31no—
790C22×D3—31no—
791C22×D3—31no—
792C22×D3—61no—
793C22×D3—61no—
794C22×D3—62no—
795C22×D3—62no—
796C22×D3—62no—
797C22×D3—62no—
798C22×D3—62no—
799C22×D3—62no—
800C22×D3—122no—
801C22×D3—122no—
802C22×D3—122no—
803C22×D3C2×D3211yescharacteristic
804C22×D3C2×D3211yescharacteristic
805C3×D4—64no—
806C3×D4—62no—
807C3×D4—62no—
808C3×D4—62no—
809C3×D4—62no—
810C3×D4—122no—
811C3×D4—182no—
812C3×D4—182no—
813C3×D4—182no—
814C2×C3×C4—31no—
815C2×C3×C4—31no—
816C2×C3×C4—31no—
817C2×C3×C4—31no—
818C2×C3×C4—31no—
819C2×C3×C4—31no—
820C2×C3×C4—31no—
821C2×C3×C4—31no—
822C2×C3×C4—61no—
823C2×C3×C4—61no—
824C2×C3×C4—61no—
825C2×C3×C4—61no—
826C2×C3×C4—91no—
827C2×C3×C4—91no—
828C2×C3×C4—91no—
829C2×C3×C4—91no—
830C2×C3×C4—182no—
831C2×C3×C4—182no—
832C2×C3×C4—182no—
833#67—22no—
834#67—22no—
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—62no—
863C2×Dic3—62no—
864C2×Dic3—94no—
865C2×Dic3—91no—
866C2×Dic3—91no—
867C2×Dic3—91no—
868C2×Dic3—91no—
869C2×Dic3—91no—
870C2×Dic3—91no—
871C2×Dic3—122no—
872C2×Dic3—122no—
873C2×Dic3—181no—
874C2×Dic3—181no—
875C2×Dic3—181no—
876C2×Dic3—181no—
877C2×Dic3—181no—
878C2×Dic3—181no—
879C2×Dic3—182no—
880C2×Dic3—182no—
881C2×Dic3—182no—
882C2×Dic3—182no—
883C2×Dic3—182no—
884C2×Dic3—361no—
885C2×Dic3—361no—
886C2×Dic3—362no—
887C2×Dic3C2×D3211yescharacteristic
888C2×Dic3C2×D3211yescharacteristic
889C2×Dic3C2×D3211yescharacteristic
890C2×Dic3C2×D3211yescharacteristic
891D12—62no—
892D12—62no—
893C4×D3—62no—
894C4×D3—94no—
895C4×D3—94no—
896C4×D3—182no—
897C4×D3—182no—
898C4×D3—182no—
899C4×D3—182no—
900C4×D3—182no—
901C4×D3—182no—
902C4×D3—182no—
903Dic6—182no—
904Dic6—182no—
905Dic6—182no—
906Dic6—362no—
907C2×C32—22no—
908C2×C32—22no—
909C2×C32—22no—
910C2×C32—21no—
911C2×C32—21no—
912C2×C32—21no—
913C2×C32—21no—
914C2×C32—21no—
915C2×C32—21no—
916C2×C32—21no—
917C2×C32—21no—
918C2×C32—21no—
919C2×C32—41no—
920C2×C32—41no—
921C2×C32—41no—
922C2×C32—42no—
923C2×C32—42no—
924C2×C32—42no—
925C2×C32—82no—
926C2×C32—121no—
927C2×C32—121no—
928C2×C32C2×#23511yescharacteristic
929C2×C32C2×D3×D411yescharacteristic
930C2×C32C2×D3×D411yescharacteristic
931C2×C32C2×D3×D411yescharacteristic
932C2×C32C2×#23711yescharacteristic
933C2×C32C2×#23711yescharacteristic
934C2×C32C2×#23711yescharacteristic
935C2×C32D3×#4111yescharacteristic
936C2×C32D3×#4111yescharacteristic
937C3⋊D3—22no—
938C3⋊D3—22no—
939C3×D3—42no—
940C3×D3—41no—
941C3×D3—41no—
942C3×D3—41no—
943C3×D3—41no—
944C3×D3—62no—
945C3×D3—62no—
946C3×D3—62no—
947C3×D3—62no—
948C3×D3—81no—
949C3×D3—122no—
950C3×D3—122no—
951C24—91no—
952#41—544no—
953C2×Q8—271no—
954C2×D4—31no—
955C2×D4—31no—
956C2×D4—91no—
957C2×D4—91no—
958C2×D4—91no—
959C2×D4—271no—
960C2×D4—271no—
961C22×C4—91no—
962C22×C4—91no—
963C22×C4—91no—
964C22×C4—271no—
965C22×C4—271no—
966C22×C4—271no—
967C22×C4—271no—
968C22×C4—271no—
969C22×C4—544no—
970C4⋊C4—91no—
971C4⋊C4—91no—
972C4⋊C4—271no—
973C4⋊C4—271no—
974C4⋊C4—271no—
975C4⋊C4—271no—
976C22⋊C4—31no—
977C22⋊C4—91no—
978C22⋊C4—91no—
979C22⋊C4—91no—
980C22⋊C4—91no—
981C22⋊C4—91no—
982C22⋊C4—271no—
983C22⋊C4—271no—
984C22⋊C4—271no—
985C22⋊C4—271no—
986C42—91no—
987C42—271no—
988C22×C3—21no—
989C22×C3—21no—
990C22×C3—21no—
991C22×C3—21no—
992C22×C3—21no—
993C22×C3—21no—
994C22×C3—21no—
995C22×C3—21no—
996C22×C3—21no—
997C22×C3—22no—
998C22×C3—22no—
999C22×C3—22no—
1000C22×C3—41no—
1001C22×C3—41no—
1002C22×C3—41no—
1003C22×C3—41no—
1004C22×C3—41no—
1005C22×C3—41no—
1006C22×C3—41no—
1007C22×C3—42no—
1008C22×C3—62no—
1009C22×C3—61no—
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—61no—
1021C22×C3—81no—
1022C22×C3—81no—
1023C22×C3—92no—
1024C22×C3—92no—
1025C22×C3—121no—
1026C22×C3—121no—
1027C22×C3—121no—
1028C22×C3—121no—
1029C22×C3—121no—
1030C22×C3—188no—
1031C22×C3—181no—
1032C22×C3—181no—
1033C22×C3—181no—
1034C22×C3—181no—
1035C22×C3#379512yescomplemented
1036C22×C3#380412yescomplemented
1037C22×C3#380512yescomplemented
1038C22×C3C22×D3211yescharacteristic
1039C22×C3C22×D3211yescharacteristic
1040C22×C3C22×D3211yescharacteristic
1041C2×D3—21no—
1042C2×D3—21no—
1043C2×D3—21no—
1044C2×D3—21no—
1045C2×D3—21no—
1046C2×D3—21no—
1047C2×D3—32no—
1048C2×D3—32no—
1049C2×D3—32no—
1050C2×D3—32no—
1051C2×D3—62no—
1052C2×D3—62no—
1053C2×D3—68no—
1054C2×D3—68no—
1055C2×D3—61no—
1056C2×D3—61no—
1057C2×D3—61no—
1058C2×D3—61no—
1059C2×D3—61no—
1060C2×D3—61no—
1061C2×D3—61no—
1062C2×D3—61no—
1063C2×D3—121no—
1064C2×D3—121no—
1065C2×D3—121no—
1066C2×D3—121no—
1067C2×D3—128no—
1068C3×C4—62no—
1069C3×C4—61no—
1070C3×C4—61no—
1071C3×C4—61no—
1072C3×C4—61no—
1073C3×C4—61no—
1074C3×C4—61no—
1075C3×C4—61no—
1076C3×C4—61no—
1077C3×C4—92no—
1078C3×C4—92no—
1079C3×C4—121no—
1080C3×C4—121no—
1081C3×C4—121no—
1082C3×C4—181no—
1083C3×C4—181no—
1084Dic3—21no—
1085Dic3—21no—
1086Dic3—21no—
1087Dic3—21no—
1088Dic3—32no—
1089Dic3—32no—
1090Dic3—32no—
1091Dic3—32no—
1092Dic3—62no—
1093Dic3—62no—
1094Dic3—61no—
1095Dic3—61no—
1096Dic3—61no—
1097Dic3—61no—
1098Dic3—121no—
1099Dic3—121no—
1100Dic3—181no—
1101Dic3—181no—
1102Dic3—181no—
1103Dic3—181no—
1104Dic3—181no—
1105Dic3—181no—
1106Dic3—361no—
1107Dic3—361no—
1108Dic3—361no—
1109Dic3—361no—
1110Dic3—361no—
1111Dic3—361no—
1112Dic3—721no—
1113Dic3—721no—
1114C32—21no—
1115C32—21no—
1116C32—21no—
1117C32—41no—
1118C32#554711yescharacteristic, complemented
1119C32#558611yescharacteristic, complemented
1120C32#560611yescharacteristic, complemented
1121C23—31no—
1122C23—31no—
1123C23—91no—
1124C23—91no—
1125C23—182no—
1126C23—182no—
1127C23—182no—
1128C23D3311yescharacteristic
1129Q8—542no—
1130D4—62no—
1131D4—62no—
1132D4—182no—
1133D4—182no—
1134D4—182no—
1135D4—542no—
1136D4—542no—
1137C2×C4—31no—
1138C2×C4—31no—
1139C2×C4—31no—
1140C2×C4—31no—
1141C2×C4—91no—
1142C2×C4—91no—
1143C2×C4—91no—
1144C2×C4—91no—
1145C2×C4—182no—
1146C2×C4—182no—
1147C2×C4—182no—
1148C2×C4—274no—
1149C2×C4—271no—
1150C2×C4—271no—
1151C2×C4—542no—
1152C2×C4—542no—
1153C2×C4—542no—
1154C2×C4—542no—
1155C2×C3—22no—
1156C2×C3—22no—
1157C2×C3—22no—
1158C2×C3—21no—
1159C2×C3—21no—
1160C2×C3—21no—
1161C2×C3—21no—
1162C2×C3—21no—
1163C2×C3—21no—
1164C2×C3—21no—
1165C2×C3—21no—
1166C2×C3—21no—
1167C2×C3—42no—
1168C2×C3—42no—
1169C2×C3—42no—
1170C2×C3—41no—
1171C2×C3—41no—
1172C2×C3—41no—
1173C2×C3—82no—
1174C2×C3—122no—
1175C2×C3—121no—
1176C2×C3—121no—
1177C2×C3—121no—
1178C2×C3—121no—
1179C2×C3—182no—
1180C2×C3—182no—
1181C2×C3—241no—
1182C2×C3C2×#379511yescharacteristic
1183C2×C3D32×D411yescharacteristic
1184C2×C3D32×D411yescharacteristic
1185C2×C3D32×D411yescharacteristic
1186C2×C3D3×#23711yescharacteristic
1187C2×C3D3×#23711yescharacteristic
1188C2×C3#6431211yescharacteristic
1189C2×C3C2×#380411yescharacteristic
1190C2×C3C2×#380511yescharacteristic
1191D3—41no—
1192D3—41no—
1193D3—62no—
1194D3—62no—
1195D3—62no—
1196D3—62no—
1197D3—122no—
1198D3—122no—
1199C22—21no—
1200C22—21no—
1201C22—61no—
1202C22—61no—
1203C22—61no—
1204C22—61no—
1205C22—61no—
1206C22—61no—
1207C22—92no—
1208C22—92no—
1209C22—188no—
1210C22—181no—
1211C22—181no—
1212C22—181no—
1213C22—181no—
1214C22#8896112yescomplemented
1215C22C2×D3311yescharacteristic
1216C4—61no—
1217C4—61no—
1218C4—61no—
1219C4—61no—
1220C4—92no—
1221C4—92no—
1222C4—181no—
1223C4—181no—
1224C4—541no—
1225C4—541no—
1226C3—21no—
1227C3—21no—
1228C3—21no—
1229C3—41no—
1230C3#1059405411yescharacteristic, complemented
1231C3#1059513011yescharacteristic, complemented
1232C3#1059513811yescharacteristic, complemented
1233C2—22no—
1234C2—121no—
1235C2—121no—
1236C2—182no—
1237C2—182no—
1238C2#1172440811yescharacteristic
1239C2C2×#8896111yescharacteristic
1240C2#1172444011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#6294C2semidirect
2. C2×#88961C2semidirect
3. #11723641C2semidirect
4. #11723634C2semidirect
5. #67×C3⋊Dic3C2semidirect
6. C3×#63981C2semidirect
7. C3×#63980C2semidirect
8. C3×#67⋊Dic3C2semidirect
9. #11722998C2semidirect
10. #11722994C2semidirect
11. #11722984C2semidirect
12. #11722965C2semidirect
13. #11722936C2semidirect
14. #11722928C2semidirect
15. #11722922C2semidirect
29. C2×#6293C22semidirect
32. C2×D3×C3⋊Dic3C22semidirect
35. C2×C3×#625C22semidirect
36. C2×C3×D3×Dic3C22semidirect
40. #88807C22semidirect
41. #88806C22semidirect
42. Dic3⋊(C3⋊Dic3)C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
46. (C2×D3)⋊(C3⋊Dic3)C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. C3×#3724C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
71. #63981D3semidirect
72. #63980D3semidirect
78. #67⋊Dic3D3semidirect
129. #6294D4semidirect
184. C2×#625C2×D3semidirect
205. C2×D3×Dic3C2×D3semidirect
245. #3724C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
267. (C2×D3)⋊Dic3C2×D3semidirect
268. (C2×D3)⋊Dic3C2×D3semidirect
269. (C2×D3)⋊Dic3C2×D3semidirect
273. Dic32C2×D3semidirect
276. C22×C33#41semidirect
284. C2×C3×C3⋊D3#41semidirect
656. C22×C32#235semidirect
657. C22×C32#237semidirect
658. C22×C32#237semidirect
668. C2×C3⋊D3#237semidirect
769. C33#525semidirect
1035. C22×C3#3795semidirect
1036. C22×C3#3804semidirect
1037. C22×C3#3805semidirect
1118. C32#5547semidirect
1119. C32#5586semidirect
1120. C32#5606semidirect
1214. C22#88961semidirect
1230. C3#10594054semidirect
1231. C3#10595130semidirect
1232. C3#10595138semidirect

Maximal subgroups

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

subgroupindex
C22×#62942
C2×#889612
#117236412
#117236342
#67×C3⋊Dic32
C3×#639812
C3×#639802
C3×#67⋊Dic32
#117229982
#117229942
#117229842
#117229652
#117229362
#117229282
#117229222
#105951383
#105951303
#105940543