Finite Group Databasebeta

← #13170757

Subgroups — #13170757

Order 1728.

1670 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89014C211yesmaximal, characteristic, complemented
2C2×D32×Dic3C211yesmaximal, characteristic, complemented
3#11723684C211yesmaximal, characteristic, complemented
4#11723497C211yesmaximal, characteristic, complemented
5#11723496C211yesmaximal, characteristic, complemented
6C3×#63922C211yesmaximal, characteristic, complemented
7C3×#63884C211yesmaximal, characteristic, complemented
8C3×#63881C211yesmaximal, characteristic, complemented
9#11722988C211yesmaximal, characteristic, complemented
10#11722967C211yesmaximal, characteristic, complemented
11#11722954C211yesmaximal, characteristic, complemented
12#11722947C211yesmaximal, characteristic, complemented
13#11722928C211yesmaximal, characteristic, complemented
14#11722924C211yesmaximal, characteristic, complemented
15#11722916C211yesmaximal, characteristic, complemented
16#10595160—31nomaximal
17#10594614—31nomaximal
18#10594054—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×#6308C2211yescharacteristic, complemented
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C32×D12C2211yescharacteristic
23C2×#6295C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×#6290C2211yescharacteristic, complemented
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×D3×C3⋊Dic3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic
30C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
31#89014—24no—
32C2×C3×#626C2211yescharacteristic
33C2×C3×#626C2211yescharacteristic
34C2×C3×#625C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36C2×C3×D3×Dic3C2211yescharacteristic
37D32×Dic3—24no—
38C3×#3752C2211yescharacteristic
39C3×#3750C2211yescharacteristic, complemented
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42#88814C2211yescharacteristic, complemented
43#88813C2211yescharacteristic, complemented
44#88807C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46#88806C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48#88803C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50C3×#3722C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×#3830—31no—
57C22×D3×Dic3—31no—
58C22×D3×Dic3—31no—
59C2×C4×D32—31no—
60C2×#3795—31no—
61C2×#3795—31no—
62C2×#3795—61no—
63#64105—31no—
64#64087—31no—
65C3×#937—31no—
66C3×#935—31no—
67C3×#894—31no—
68C3×#893—31no—
69C3×#882—31no—
70C3×#67⋊C4—31no—
71#63980—31no—
72#63977—31no—
73#63976—31no—
74#67⋊Dic3—31no—
75#67⋊Dic3—31no—
76Dic3×#67—31no—
77#63971—31no—
78#63971—31no—
79#63966—31no—
80#63957—31no—
81#63922—31no—
82#63922D311yescharacteristic, complemented
83#63912—31no—
84#63905—31no—
85#63904—31no—
86#63896—31no—
87#63896—31no—
88#63896—31no—
89#63896—31no—
90#63896—61no—
91#63896—61no—
92Dic3×D12—31no—
93#63891—31no—
94#63885—31no—
95#63885—31no—
96#63884D311yescharacteristic, complemented
97#63881—31no—
98#63881D311yescharacteristic, complemented
99#63880—31no—
100#63879—31no—
101#63879—31no—
102#63877—31no—
103#63877—31no—
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×C3×D32—22no—
110C2×C3×D32—22no—
111C2×C3×D32—22no—
112C2×C33×C4C2311yescharacteristic
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
115#6308—22no—
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C3×C4×C3⋊D3—22no—
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C32×D12—22no—
125#6295—22no—
126#6294—22no—
127#6290—22no—
128#6290—22no—
129Dic3×C3⋊D3—22no—
130D3×C3⋊Dic3—22no—
131D3×C3⋊Dic3—22no—
132D3×C3⋊Dic3D414yescomplemented
133C3×#626—22no—
134C3×#626—22no—
135C3×#625—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5656—91no—
139#5586—91no—
140#5547—91no—
141C23×C3×D3—31no—
142C23×C3×D3—31no—
143C22×D32C2×D311yescharacteristic
144C2×C32×D4—31no—
145C2×#638—31no—
146C2×#638—31no—
147C22×C3⋊Dic3—31no—
148C22×C3⋊Dic3—31no—
149C22×C3⋊Dic3—31no—
150#3830—64no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
153C2×#634—31no—
154C2×#634—31no—
155C2×#634—31no—
156C2×#634—61no—
157C2×#634—61no—
158C2×#634—61no—
159C2×#634—121no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C22×C3×Dic3—31no—
165C22×C3×Dic3—31no—
166C2×C3×D12—21no—
167C2×C3×D12—31no—
168C2×C3×D12—31no—
169C2×C3×D12C2×D311yescharacteristic
170C2×C3×D12C2×D311yescharacteristic
171C2×C3×C4×D3—31no—
172C2×C3×C4×D3—31no—
173C2×C3×C4×D3—31no—
174C2×C3×C4×D3—31no—
175C2×C3×C4×D3—61no—
176C2×#626—31no—
177C2×#626—31no—
178C2×#626C2×D311yescharacteristic
179C2×#626C2×D311yescharacteristic
180C2×#625—31no—
181C2×#625—31no—
182C2×#625—31no—
183C2×#625—31no—
184C2×#625—31no—
185C2×#625—61no—
186C2×#625—61no—
187C2×#625C2×D311yescharacteristic
188C2×#624—31no—
189C2×D3×Dic3—31no—
190C2×D3×Dic3—31no—
191C2×D3×Dic3—31no—
192C2×D3×Dic3—31no—
193C2×D3×Dic3—31no—
194C2×D3×Dic3—31no—
195C2×D3×Dic3—31no—
196C2×D3×Dic3—31no—
197C2×D3×Dic3—31no—
198C2×D3×Dic3—31no—
199C2×D3×Dic3—64no—
200C2×D3×Dic3—64no—
201C2×D3×Dic3—61no—
202C2×D3×Dic3—61no—
203C2×D3×Dic3—61no—
204C2×D3×Dic3—61no—
205C2×D3×Dic3C2×D311yescharacteristic
206C2×D3×Dic3C2×D311yescharacteristic
207C4×D32—64no—
208#3795—64no—
209#3795—64no—
210#3795—68no—
211C32×C4⋊C4—31no—
212C32×C22⋊C4—31no—
213#3757—31no—
214#3752—31no—
215#3752C2×D311yescharacteristic
216C4⋊(C3⋊Dic3)—31no—
217#3750—31no—
218#3750—31no—
219#3750—31no—
220#3750C2×D311yescharacteristic, complemented
221C3×#217—31no—
222C3×#217—31no—
223C3×#217—31no—
224C3×#217—31no—
225C3×(C2×D3)⋊C4—21no—
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)⋊C4C2×D311yescharacteristic
236C3×(C2×D3)⋊C4C2×D311yescharacteristic
237C3×Dic3⋊C4—21no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—61no—
241C3×Dic3⋊C4C2×D311yescharacteristic, complemented
242C3×Dic3⋊C4C2×D311yescharacteristic, complemented
243C3×C4×Dic3—31no—
244C3×C4×Dic3—31no—
245#3724—31no—
246#3724—31no—
247#3724—31no—
248#3724—31no—
249#3724—61no—
250#3724—61no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—61no—
256Dic3⋊Dic3—61no—
257#3722—31no—
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—61no—
266(C2×D3)⋊Dic3—61no—
267(C2×D3)⋊Dic3C2×D311yescharacteristic
268(C2×D3)⋊Dic3C2×D311yescharacteristic
269(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
270(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
271Dic32—31no—
272Dic32—31no—
273Dic32—31no—
274Dic32C2×D311yescharacteristic, complemented
275C22×C33C2411yescharacteristic
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#4112yescomplemented
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C2×C32×D3—21no—
285C2×C32×D3—21no—
286C2×C32×D3—21no—
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3C2×D412yes—
290C2×C32×D3#4112yescomplemented
291C3×D32—28no—
292C33×C4—21no—
293C3⋊(C3⋊Dic3)—21no—
294C3⋊(C3⋊Dic3)C2×D412yes—
295C3×C3⋊Dic3—21no—
296C3×C3⋊Dic3—21no—
297C3×C3⋊Dic3—21no—
298C3×C3⋊Dic3C2×D412yes—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C32×Dic3—21no—
302C23×Dic3—91no—
303C2×#237—91no—
304C2×#237—91no—
305C2×#237—181no—
306C2×#235—91no—
307C22×C4×D3—91no—
308C22×C4×D3—91no—
309C3×#123—91no—
310C3×#120—91no—
311C3×C4×D4—91no—
312#953—91no—
313#939—91no—
314#939—91no—
315#939—91no—
316#937—31no—
317#937—91no—
318#935—31no—
319D4×Dic3—91no—
320D4×Dic3—91no—
321#929—91no—
322C4×#67—91no—
323C4×#67—91no—
324#896—91no—
325#896—91no—
326#896—91no—
327#896—181no—
328#894—31no—
329#893—31no—
330#893—91no—
331#886—91no—
332#884—91no—
333#884—91no—
334#884—91no—
335#883—91no—
336#882—31no—
337#882—91no—
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—
347#877—91no—
348C4×D12—91no—
349#872—91no—
350C23×C32—31no—
351C23×C32—31no—
352C23×C32—31no—
353C22×C3⋊D3C22×D311yescharacteristic
354C22×C3⋊D3C22×D311yescharacteristic
355C22×C3×D3—21no—
356C22×C3×D3—21no—
357C22×C3×D3—21no—
358C22×C3×D3—31no—
359C22×C3×D3—31no—
360C22×C3×D3—31no—
361C22×C3×D3—31no—
362C22×C3×D3—61no—
363C22×C3×D3—61no—
364C22×C3×D3—62no—
365C22×C3×D3—62no—
366C22×C3×D3—62no—
367C22×C3×D3—62no—
368C22×C3×D3—62no—
369C22×C3×D3—62no—
370C22×C3×D3C22×D311yescharacteristic
371C22×C3×D3C22×D311yescharacteristic
372C22×C3×D3C22×D311yescharacteristic
373C22×C3×D3C22×D311yescharacteristic
374C22×C3×D3C22×D311yescharacteristic
375C22×C3×D3C22×D311yescharacteristic
376C2×D32—22no—
377C2×D32—22no—
378C2×D32—22no—
379C32×D4—62no—
380C2×C32×C4—21no—
381C2×C32×C4—21no—
382C2×C32×C4—21no—
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—
391#638—62no—
392C2×C3⋊Dic3—31no—
393C2×C3⋊Dic3—31no—
394C2×C3⋊Dic3—31no—
395C2×C3⋊Dic3—34no—
396C2×C3⋊Dic3—31no—
397C2×C3⋊Dic3—31no—
398C2×C3⋊Dic3—31no—
399C2×C3⋊Dic3—61no—
400C2×C3⋊Dic3—61no—
401C2×C3⋊Dic3—61no—
402C2×C3⋊Dic3—61no—
403C2×C3⋊Dic3—61no—
404C2×C3⋊Dic3—61no—
405C2×C3⋊Dic3—62no—
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
413C4×C3⋊D3—22no—
414C4×C3⋊D3—62no—
415#634—62no—
416#634—62no—
417#634—62no—
418#634—64no—
419#634—122no—
420#634—122no—
421#634—124no—
422C3×#67—62no—
423C3×#67—62no—
424C3×#67—62no—
425C3×#67—62no—
426C2×C3×Dic3—21no—
427C2×C3×Dic3—21no—
428C2×C3×Dic3—21no—
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—31no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—61no—
439C2×C3×Dic3—61no—
440C2×C3×Dic3—61no—
441C2×C3×Dic3—62no—
442C2×C3×Dic3—62no—
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C3×D12—24no—
450C3×D12—22no—
451C3×D12—22no—
452C3×D12—62no—
453C3×D12—62no—
454C3×C4×D3—62no—
455C3×C4×D3—62no—
456C3×C4×D3—62no—
457C3×C4×D3—64no—
458C3×C4×D3—62no—
459#626—22no—
460#626—22no—
461#626—62no—
462#626—62no—
463#625—22no—
464#625—62no—
465#625—62no—
466#625—62no—
467#625—64no—
468#625—64no—
469#625—62no—
470#625—62no—
471#624—62no—
472D3×Dic3—22no—
473D3×Dic3—22no—
474D3×Dic3—34no—
475D3×Dic3—34no—
476D3×Dic3—64no—
477D3×Dic3—62no—
478D3×Dic3—62no—
479D3×Dic3—62no—
480D3×Dic3—62no—
481D3×Dic3—62no—
482D3×Dic3—62no—
483D3×Dic3—62no—
484D3×Dic3—64no—
485D3×Dic3—62no—
486D3×Dic3—122no—
487D3×Dic3—122no—
488#525—271noSylow
489C2×C33C22×D411yescharacteristic
490C2×C33C2×#4111yescharacteristic
491C2×C33C2×#4111yescharacteristic
492C3×C3⋊D3—22no—
493C3×C3⋊D3—41no—
494C32×D3—22no—
495C32×D3—22no—
496C32×D3—41no—
497C24×C3—91no—
498C23×D3—31no—
499C23×D3—31no—
500C2×C3×D4—31no—
501C2×C3×D4—31no—
502C2×C3×D4—61no—
503C2×C3×D4—91no—
504C2×C3×D4—91no—
505C2×C3×D4—91no—
506C22×C3×C4—91no—
507C22×C3×C4—91no—
508C22×C3×C4—91no—
509C2×#67—31no—
510C2×#67—31no—
511C2×#67—31no—
512C2×#67—31no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—91no—
517C2×#67—91no—
518C2×#67—91no—
519C2×#67—91no—
520C2×#67—91no—
521C2×#67—181no—
522C2×#67—181no—
523C22×Dic3—31no—
524C22×Dic3—31no—
525C22×Dic3—91no—
526C22×Dic3—91no—
527C22×Dic3—91no—
528C22×Dic3—91no—
529C22×Dic3—91no—
530C22×Dic3—91no—
531C22×Dic3—91no—
532C22×Dic3—91no—
533C22×Dic3—181no—
534C22×Dic3—181no—
535C22×Dic3—181no—
536C22×Dic3—184no—
537#237—184no—
538#237—184no—
539#237—188no—
540#235—184no—
541C2×D12—31no—
542C2×D12—31no—
543C2×D12—91no—
544C2×D12D3211yescharacteristic
545C2×C4×D3—31no—
546C2×C4×D3—31no—
547C2×C4×D3—31no—
548C2×C4×D3—31no—
549C2×C4×D3—61no—
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—181no—
558C2×C4×D3—184no—
559C2×C4×D3—184no—
560C2×Dic6—91no—
561C2×Dic6—91no—
562C2×Dic6—91no—
563C2×Dic6—181no—
564C2×Dic6—181no—
565C2×Dic6—181no—
566C2×Dic6—361no—
567C3×C4⋊C4—31no—
568C3×C4⋊C4—31no—
569C3×C4⋊C4—61no—
570C3×C4⋊C4—91no—
571C3×C22⋊C4—31no—
572C3×C22⋊C4—31no—
573C3×C22⋊C4—61no—
574C3×C22⋊C4—91no—
575C3×C22⋊C4—91no—
576C3×C22⋊C4—91no—
577C3×C22⋊C4—91no—
578C3×C22⋊C4—91no—
579C3×C22⋊C4—91no—
580C3×C42—91no—
581#217—31no—
582#217—31no—
583#217—31no—
584#217—31no—
585#217—91no—
586#217—91no—
587#217—91no—
588#217—91no—
589#217—181no—
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—31no—
596(C2×D3)⋊C4—31no—
597(C2×D3)⋊C4—31no—
598(C2×D3)⋊C4—61no—
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—181no—
605(C2×D3)⋊C4D3211yescharacteristic
606C4⋊Dic3—91no—
607C4⋊Dic3—91no—
608C4⋊Dic3—91no—
609C4⋊Dic3—181no—
610Dic3⋊C4—31no—
611Dic3⋊C4—31no—
612Dic3⋊C4—61no—
613Dic3⋊C4—91no—
614Dic3⋊C4—91no—
615Dic3⋊C4—91no—
616Dic3⋊C4—91no—
617Dic3⋊C4—91no—
618Dic3⋊C4—91no—
619Dic3⋊C4—91no—
620Dic3⋊C4—91no—
621Dic3⋊C4—91no—
622Dic3⋊C4—181no—
623Dic3⋊C4—181no—
624Dic3⋊C4—181no—
625Dic3⋊C4D3211yescharacteristic, complemented
626C4×Dic3—31no—
627C4×Dic3—31no—
628C4×Dic3—91no—
629C4×Dic3—91no—
630C4×Dic3—91no—
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—32no—
635C22×C32—32no—
636C22×C32—41no—
637C22×C32—61no—
638C22×C32—61no—
639C22×C32—61no—
640C22×C32—61no—
641C22×C32—61no—
642C22×C32—61no—
643C22×C32—61no—
644C22×C32C23×D311yescharacteristic
645C22×C32C23×D311yescharacteristic
646C22×C32C23×D311yescharacteristic
647C2×C3⋊D3—21no—
648C2×C3⋊D3—21no—
649C2×C3⋊D3—21no—
650C2×C3⋊D3—21no—
651C2×C3⋊D3—21no—
652C2×C3⋊D3#23712yescomplemented
653C2×C3×D3—21no—
654C2×C3×D3—21no—
655C2×C3×D3—21no—
656C2×C3×D3—21no—
657C2×C3×D3—21no—
658C2×C3×D3—21no—
659C2×C3×D3—21no—
660C2×C3×D3—21no—
661C2×C3×D3—22no—
662C2×C3×D3—21no—
663C2×C3×D3—21no—
664C2×C3×D3—21no—
665C2×C3×D3—21no—
666C2×C3×D3—21no—
667C2×C3×D3—21no—
668C2×C3×D3—22no—
669C2×C3×D3—22no—
670C2×C3×D3—32no—
671C2×C3×D3—32no—
672C2×C3×D3—41no—
673C2×C3×D3—41no—
674C2×C3×D3—41no—
675C2×C3×D3—41no—
676C2×C3×D3—41no—
677C2×C3×D3—41no—
678C2×C3×D3—62no—
679C2×C3×D3—68no—
680C2×C3×D3—68no—
681C2×C3×D3—61no—
682C2×C3×D3—61no—
683C2×C3×D3—61no—
684C2×C3×D3—61no—
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—121no—
693C2×C3×D3—121no—
694C2×C3×D3—121no—
695C2×C3×D3—121no—
696C2×C3×D3#23512yescomplemented
697C2×C3×D3D3×D412yes—
698C2×C3×D3D3×D412yes—
699C2×C3×D3#23712yescomplemented
700D32—28no—
701C32×C4—21no—
702C32×C4—22no—
703C32×C4—21no—
704C32×C4—21no—
705C32×C4—41no—
706C32×C4—41no—
707C32×C4—42no—
708C32×C4—61no—
709C32×C4—61no—
710C32×C4—61no—
711C3⋊Dic3—21no—
712C3⋊Dic3—21no—
713C3⋊Dic3—21no—
714C3⋊Dic3—32no—
715C3⋊Dic3—32no—
716C3⋊Dic3—32no—
717C3⋊Dic3—62no—
718C3⋊Dic3—62no—
719C3⋊Dic3—62no—
720C3⋊Dic3—61no—
721C3⋊Dic3—62no—
722C3⋊Dic3—61no—
723C3⋊Dic3—61no—
724C3⋊Dic3—122no—
725C3⋊Dic3—121no—
726C3⋊Dic3—121no—
727C3⋊Dic3—122no—
728C3⋊Dic3D3×D412yes—
729C3×Dic3—21no—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—21no—
734C3×Dic3—21no—
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—
750C2×#41—271no—
751C23×C4—271no—
752#123—91no—
753#123—271no—
754C22⋊Q8—271no—
755C22⋊Q8—271no—
756#121—271no—
757#121—271no—
758#120—91no—
759#120—271no—
760C4×D4—91no—
761C4×D4—271no—
762C4×D4—271no—
763C4×D4—271no—
764#117—271no—
765C33#52511yescharacteristic, complemented, Sylow
766C23×C3—31no—
767C23×C3—31no—
768C23×C3—31no—
769C23×C3—31no—
770C23×C3—31no—
771C23×C3—31no—
772C23×C3—61no—
773C23×C3—61no—
774C23×C3—61no—
775C23×C3—91no—
776C23×C3—91no—
777C23×C3—182no—
778C23×C3—182no—
779C23×C3—182no—
780C22×D3—31no—
781C22×D3—31no—
782C22×D3—31no—
783C22×D3—31no—
784C22×D3—61no—
785C22×D3—61no—
786C22×D3—62no—
787C22×D3—62no—
788C22×D3—62no—
789C22×D3—62no—
790C22×D3—62no—
791C22×D3—62no—
792C22×D3C2×D3211yescharacteristic
793C22×D3C2×D3211yescharacteristic
794C22×D3C2×D3211yescharacteristic
795C3×D4—62no—
796C3×D4—62no—
797C3×D4—64no—
798C3×D4—182no—
799C3×D4—182no—
800C3×D4—182no—
801C2×C3×C4—21no—
802C2×C3×C4—21no—
803C2×C3×C4—21no—
804C2×C3×C4—31no—
805C2×C3×C4—31no—
806C2×C3×C4—31no—
807C2×C3×C4—31no—
808C2×C3×C4—31no—
809C2×C3×C4—31no—
810C2×C3×C4—41no—
811C2×C3×C4—61no—
812C2×C3×C4—61no—
813C2×C3×C4—61no—
814C2×C3×C4—91no—
815C2×C3×C4—91no—
816C2×C3×C4—91no—
817C2×C3×C4—91no—
818C2×C3×C4—182no—
819C2×C3×C4—182no—
820C2×C3×C4—182no—
821C2×C3×C4C2×D3211yescharacteristic
822C2×C3×C4C2×D3211yescharacteristic
823C2×C3×C4C2×D3211yescharacteristic
824#67—62no—
825#67—62no—
826#67—62no—
827#67—62no—
828#67—182no—
829#67—182no—
830#67—182no—
831#67—182no—
832#67—182no—
833#67—182no—
834#67—182no—
835#67—184no—
836#67—184no—
837#67—182no—
838C2×Dic3—31no—
839C2×Dic3—31no—
840C2×Dic3—31no—
841C2×Dic3—31no—
842C2×Dic3—31no—
843C2×Dic3—31no—
844C2×Dic3—31no—
845C2×Dic3—31no—
846C2×Dic3—61no—
847C2×Dic3—61no—
848C2×Dic3—61no—
849C2×Dic3—61no—
850C2×Dic3—62no—
851C2×Dic3—62no—
852C2×Dic3—94no—
853C2×Dic3—94no—
854C2×Dic3—91no—
855C2×Dic3—91no—
856C2×Dic3—91no—
857C2×Dic3—91no—
858C2×Dic3—91no—
859C2×Dic3—91no—
860C2×Dic3—184no—
861C2×Dic3—181no—
862C2×Dic3—181no—
863C2×Dic3—181no—
864C2×Dic3—181no—
865C2×Dic3—181no—
866C2×Dic3—181no—
867C2×Dic3—182no—
868C2×Dic3—182no—
869C2×Dic3—182no—
870C2×Dic3—182no—
871C2×Dic3—182no—
872C2×Dic3—182no—
873C2×Dic3—184no—
874C2×Dic3—361no—
875C2×Dic3—361no—
876C2×Dic3—362no—
877C2×Dic3C2×D3211yescharacteristic
878C2×Dic3C2×D3211yescharacteristic
879C2×Dic3C2×D3211yescharacteristic
880D12—22no—
881D12—62no—
882D12—62no—
883D12—182no—
884C4×D3—62no—
885C4×D3—62no—
886C4×D3—62no—
887C4×D3—64no—
888C4×D3—62no—
889C4×D3—94no—
890C4×D3—182no—
891C4×D3—182no—
892C4×D3—182no—
893C4×D3—182no—
894C4×D3—182no—
895C4×D3—182no—
896C4×D3—362no—
897Dic6—182no—
898Dic6—182no—
899Dic6—182no—
900Dic6—184no—
901Dic6—362no—
902Dic6—362no—
903Dic6—364no—
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—21no—
913C2×C32—41no—
914C2×C32—41no—
915C2×C32—41no—
916C2×C32—62no—
917C2×C32—62no—
918C2×C32—121no—
919C2×C32C2×#23511yescharacteristic
920C2×C32C2×D3×D411yescharacteristic
921C2×C32C2×D3×D411yescharacteristic
922C2×C32C2×D3×D411yescharacteristic
923C2×C32C2×#23711yescharacteristic
924C2×C32C2×#23711yescharacteristic
925C2×C32D3×#4111yescharacteristic
926C2×C32D3×#4111yescharacteristic
927C2×C32D3×#4111yescharacteristic
928C3⋊D3—22no—
929C3⋊D3—41no—
930C3×D3—22no—
931C3×D3—22no—
932C3×D3—22no—
933C3×D3—22no—
934C3×D3—42no—
935C3×D3—42no—
936C3×D3—42no—
937C3×D3—41no—
938C3×D3—41no—
939C3×D3—62no—
940C3×D3—62no—
941C3×D3—122no—
942C3×D3—122no—
943C3×D3—121no—
944C3×D3—121no—
945C24—91no—
946#41—544no—
947C2×Q8—271no—
948C2×D4—31no—
949C2×D4—91no—
950C2×D4—91no—
951C2×D4—91no—
952C2×D4—271no—
953C2×D4—271no—
954C2×D4—271no—
955C22×C4—91no—
956C22×C4—91no—
957C22×C4—91no—
958C22×C4—271no—
959C22×C4—271no—
960C22×C4—271no—
961C22×C4—271no—
962C22×C4—271no—
963C22×C4—544no—
964C4⋊C4—31no—
965C4⋊C4—91no—
966C4⋊C4—271no—
967C4⋊C4—271no—
968C4⋊C4—271no—
969C4⋊C4—271no—
970C22⋊C4—31no—
971C22⋊C4—91no—
972C22⋊C4—91no—
973C22⋊C4—91no—
974C22⋊C4—91no—
975C22⋊C4—91no—
976C22⋊C4—91no—
977C22⋊C4—271no—
978C22⋊C4—271no—
979C22⋊C4—271no—
980C42—91no—
981C42—271no—
982C22×C3—21no—
983C22×C3—21no—
984C22×C3—21no—
985C22×C3—32no—
986C22×C3—32no—
987C22×C3—32no—
988C22×C3—32no—
989C22×C3—41no—
990C22×C3—62no—
991C22×C3—62no—
992C22×C3—62no—
993C22×C3—61no—
994C22×C3—61no—
995C22×C3—61no—
996C22×C3—61no—
997C22×C3—61no—
998C22×C3—61no—
999C22×C3—61no—
1000C22×C3—61no—
1001C22×C3—61no—
1002C22×C3—61no—
1003C22×C3—61no—
1004C22×C3—61no—
1005C22×C3—61no—
1006C22×C3—61no—
1007C22×C3—92no—
1008C22×C3—121no—
1009C22×C3—121no—
1010C22×C3—121no—
1011C22×C3—121no—
1012C22×C3—121no—
1013C22×C3—121no—
1014C22×C3—188no—
1015C22×C3—181no—
1016C22×C3—181no—
1017C22×C3—181no—
1018C22×C3—181no—
1019C22×C3—181no—
1020C22×C3C22×D3211yescharacteristic
1021C22×C3C22×D3211yescharacteristic
1022C22×C3C22×D3211yescharacteristic
1023C2×D3—21no—
1024C2×D3—21no—
1025C2×D3—21no—
1026C2×D3—21no—
1027C2×D3—21no—
1028C2×D3—21no—
1029C2×D3—21no—
1030C2×D3—32no—
1031C2×D3—32no—
1032C2×D3—62no—
1033C2×D3—68no—
1034C2×D3—68no—
1035C2×D3—61no—
1036C2×D3—61no—
1037C2×D3—61no—
1038C2×D3—61no—
1039C2×D3—62no—
1040C2×D3—61no—
1041C2×D3—61no—
1042C2×D3—61no—
1043C2×D3—61no—
1044C2×D3—61no—
1045C2×D3—61no—
1046C2×D3—121no—
1047C2×D3—121no—
1048C2×D3—121no—
1049C2×D3—121no—
1050C2×D3#379512yescomplemented
1051C2×D3#381112yes—
1052C3×C4—22no—
1053C3×C4—21no—
1054C3×C4—21no—
1055C3×C4—21no—
1056C3×C4—41no—
1057C3×C4—41no—
1058C3×C4—42no—
1059C3×C4—61no—
1060C3×C4—61no—
1061C3×C4—61no—
1062C3×C4—61no—
1063C3×C4—61no—
1064C3×C4—61no—
1065C3×C4—92no—
1066C3×C4—121no—
1067C3×C4—121no—
1068C3×C4—121no—
1069C3×C4—181no—
1070C3×C4—181no—
1071C3×C4—181no—
1072Dic3—21no—
1073Dic3—21no—
1074Dic3—21no—
1075Dic3—32no—
1076Dic3—32no—
1077Dic3—62no—
1078Dic3—61no—
1079Dic3—61no—
1080Dic3—61no—
1081Dic3—61no—
1082Dic3—61no—
1083Dic3—61no—
1084Dic3—92no—
1085Dic3—92no—
1086Dic3—92no—
1087Dic3—121no—
1088Dic3—121no—
1089Dic3—121no—
1090Dic3—182no—
1091Dic3—182no—
1092Dic3—182no—
1093Dic3—182no—
1094Dic3—181no—
1095Dic3—181no—
1096Dic3—181no—
1097Dic3—362no—
1098Dic3—361no—
1099Dic3—361no—
1100Dic3—362no—
1101C32—21no—
1102C32—21no—
1103C32—21no—
1104C32—41no—
1105C32#554711yescharacteristic, complemented
1106C32#558611yescharacteristic, complemented
1107C32#565611yescharacteristic, complemented
1108C23—31no—
1109C23—31no—
1110C23—31no—
1111C23—91no—
1112C23—91no—
1113C23—182no—
1114C23—182no—
1115C23—182no—
1116Q8—542no—
1117D4—62no—
1118D4—182no—
1119D4—182no—
1120D4—182no—
1121D4—542no—
1122D4—542no—
1123D4—542no—
1124C2×C4—31no—
1125C2×C4—31no—
1126C2×C4—31no—
1127C2×C4—91no—
1128C2×C4—91no—
1129C2×C4—91no—
1130C2×C4—91no—
1131C2×C4—182no—
1132C2×C4—182no—
1133C2×C4—182no—
1134C2×C4—274no—
1135C2×C4—271no—
1136C2×C4—271no—
1137C2×C4—542no—
1138C2×C4—542no—
1139C2×C4—542no—
1140C2×C4—542no—
1141C2×C4D3311yescharacteristic
1142C2×C3—21no—
1143C2×C3—21no—
1144C2×C3—21no—
1145C2×C3—21no—
1146C2×C3—21no—
1147C2×C3—21no—
1148C2×C3—21no—
1149C2×C3—21no—
1150C2×C3—21no—
1151C2×C3—41no—
1152C2×C3—41no—
1153C2×C3—41no—
1154C2×C3—62no—
1155C2×C3—62no—
1156C2×C3—62no—
1157C2×C3—62no—
1158C2×C3—122no—
1159C2×C3—122no—
1160C2×C3—122no—
1161C2×C3—121no—
1162C2×C3—121no—
1163C2×C3—182no—
1164C2×C3—361no—
1165C2×C3C2×#379511yescharacteristic
1166C2×C3D3×#23511yescharacteristic
1167C2×C3D32×D411yescharacteristic
1168C2×C3D32×D411yescharacteristic
1169C2×C3D3×#23711yescharacteristic
1170C2×C3D3×#23711yescharacteristic
1171C2×C3D3×#23711yescharacteristic
1172C2×C3#6431911yescharacteristic
1173C2×C3C2×#381111yescharacteristic
1174D3—22no—
1175D3—22no—
1176D3—41no—
1177D3—62no—
1178D3—62no—
1179D3—122no—
1180D3—122no—
1181D3—121no—
1182D3—121no—
1183C22—32no—
1184C22—32no—
1185C22—61no—
1186C22—61no—
1187C22—61no—
1188C22—61no—
1189C22—61no—
1190C22—61no—
1191C22—61no—
1192C22—92no—
1193C22—188no—
1194C22—181no—
1195C22—181no—
1196C22—181no—
1197C22—181no—
1198C22—181no—
1199C22C2×D3311yescharacteristic
1200C4—21no—
1201C4—61no—
1202C4—61no—
1203C4—61no—
1204C4—92no—
1205C4—181no—
1206C4—181no—
1207C4—181no—
1208C4—272no—
1209C4—541no—
1210C3—21no—
1211C3—21no—
1212C3—21no—
1213C3—41no—
1214C3#1059405411yescharacteristic, complemented
1215C3#1059461411yescharacteristic, complemented
1216C3#1059516011yescharacteristic, complemented
1217C2—62no—
1218C2—62no—
1219C2—121no—
1220C2—182no—
1221C2—361no—
1222C2D3×#379511yescharacteristic
1223C2#1172437411yescharacteristic
1224C2D3×#381111yescharacteristic
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×#89014C2semidirect
2. C2×D32×Dic3C2semidirect
3. #11723684C2semidirect
4. #11723497C2semidirect
5. #11723496C2semidirect
6. C3×#63922C2semidirect
7. C3×#63884C2semidirect
8. C3×#63881C2semidirect
9. #11722988C2semidirect
10. #11722967C2semidirect
11. #11722954C2semidirect
12. #11722947C2semidirect
13. #11722928C2semidirect
14. #11722924C2semidirect
15. #11722916C2semidirect
20. C2×#6308C22semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
26. C2×#6290C22semidirect
30. C2×D3×C3⋊Dic3C22semidirect
39. C3×#3750C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88814C22semidirect
43. #88813C22semidirect
44. #88807C22semidirect
45. #88806C22semidirect
46. #88806C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
50. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
82. #63922D3semidirect
96. #63884D3semidirect
98. #63881D3semidirect
132. D3×C3⋊Dic3D4semidirect
152. C2×C4×C3⋊D3C2×D3semidirect
220. #3750C2×D3semidirect
241. C3×Dic3⋊C4C2×D3semidirect
242. C3×Dic3⋊C4C2×D3semidirect
258. #3722C2×D3semidirect
269. (C2×D3)⋊Dic3C2×D3semidirect
270. (C2×D3)⋊Dic3C2×D3semidirect
274. Dic32C2×D3semidirect
281. C2×C3×C3⋊D3#41semidirect
290. C2×C32×D3#41semidirect
625. Dic3⋊C4D32semidirect
652. C2×C3⋊D3#237semidirect
696. C2×C3×D3#235semidirect
699. C2×C3×D3#237semidirect
765. C33#525semidirect
1050. C2×D3#3795semidirect
1105. C32#5547semidirect
1106. C32#5586semidirect
1107. C32#5656semidirect
1214. C3#10594054semidirect
1215. C3#10594614semidirect
1216. C3#10595160semidirect

Maximal subgroups

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

subgroupindex
C2×#890142
C2×D32×Dic32
#117236842
#117234972
#117234962
C3×#639222
C3×#638842
C3×#638812
#117229882
#117229672
#117229542
#117229472
#117229282
#117229242
#117229162
#105951603
#105946143
#105940543