Finite Group Databasebeta

← #13168045

Subgroups — #13168045

Order 1728.

1254 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723683C211yesmaximal, characteristic, complemented
2#11723497C211yesmaximal, characteristic, complemented
3#11723496C211yesmaximal, characteristic, complemented
4#11723429C211yesmaximal, characteristic, complemented
5C3×#63922C211yesmaximal, characteristic
6C3×#63884C211yesmaximal, characteristic, complemented
7C3×#63878C211yesmaximal, characteristic, complemented
8#11723026C211yesmaximal, characteristic, complemented
9#11723020C211yesmaximal, characteristic, complemented
10#11722994C211yesmaximal, characteristic, complemented
11#11722985C211yesmaximal, characteristic, complemented
12Dic3×#626C211yesmaximal, characteristic, complemented
13#11722924C211yesmaximal, characteristic, complemented
14#11722902C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10595178—31nomaximal
17#10594644—31nomaximal
18#10594117—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×#6308C2211yescharacteristic, complemented
21C2×C32×D12C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×Dic3×C3⋊D3C2211yescharacteristic
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×C3×#626C2211yescharacteristic
26C2×C3×#625C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic, complemented
29C3×#3752C2211yescharacteristic
30C3×#3750C2211yescharacteristic, complemented
31C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×Dic3⋊C4C2211yescharacteristic, complemented
34#88815C2211yescharacteristic, complemented
35#88814C2211yescharacteristic
36#88813C2211yescharacteristic, complemented
37#88807C2211yescharacteristic, complemented
38#88806C2211yescharacteristic, complemented
39#88806C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41#88803C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64145—31no—
55#64105—31no—
56#64087—31no—
57C3×#937—31no—
58C3×#935—31no—
59C3×#894—31no—
60C3×#892—31no—
61C3×#882—31no—
62C3×#877—31no—
63#67⋊Dic3—31no—
64Dic3×#67—31no—
65Dic3×#67—31no—
66#63969—31no—
67#63969—31no—
68D3×#217—31no—
69D3×#217—31no—
70D3×#217—31no—
71#63961—31no—
72C2×(C2×D3)⋊Dic3—31no—
73#63956—31no—
74#63956—31no—
75#63922D311yescharacteristic
76#63921—31no—
77D3×(C2×D3)⋊C4—31no—
78#63905—31no—
79C4×#626—31no—
80#63896—31no—
81#63896—31no—
82#63896—31no—
83#63896—31no—
84#63896—61no—
85#63896—61no—
86Dic3×D12—31no—
87#63884—31no—
88#63884D311yescharacteristic, complemented
89#63879—31no—
90#63878—31no—
91#63878D311yescharacteristic, complemented
92#63877—31no—
93#63861—31no—
94#63860—31no—
95#63860—31no—
96#63860—61no—
97#63859—31no—
98#63859—31no—
99#63858—31no—
100#63854—31no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C3×D32—22no—
107C2×C3×D32—22no—
108C2×C3×D32—41no—
109C2×C33×C4C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112#6308—41no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C32×D12—41no—
122#6294—22no—
123Dic3×C3⋊D3—41no—
124D3×C3⋊Dic3—41no—
125C3×#626—22no—
126C3×#625—22no—
127C3×D3×Dic3—22no—
128C3×D3×Dic3—41no—
129#5659—91no—
130#5587—91no—
131#5527—91no—
132C23×C3×D3—31no—
133C23×C3×D3—31no—
134C22×D32C2×D311yescharacteristic
135C2×C32×D4—31no—
136C22×C3⋊Dic3—31no—
137C2×C4×C3⋊D3—31no—
138C2×#634—31no—
139C2×#634—31no—
140C2×#634—31no—
141C2×#634—61no—
142C2×#634—61no—
143C2×#634—61no—
144C2×#634—121no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—31no—
150C2×C3×D12—21no—
151C2×C3×D12—31no—
152C2×C3×D12C2×D311yescharacteristic
153C2×C3×D12C2×D311yescharacteristic
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×#626C2×D311yescharacteristic
157C2×#625C2×D311yescharacteristic
158C2×#624—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—31no—
163C2×D3×Dic3—31no—
164C2×D3×Dic3—31no—
165C2×D3×Dic3—61no—
166C2×D3×Dic3—61no—
167C2×D3×Dic3C2×D311yescharacteristic
168C2×D3×Dic3C2×D311yescharacteristic, complemented
169C32×C4⋊C4—31no—
170C32×C22⋊C4—31no—
171#3757—31no—
172#3757—31no—
173#3757—31no—
174#3757—31no—
175#3757—31no—
176#3752—31no—
177#3752C2×D311yescharacteristic
178C4⋊(C3⋊Dic3)—31no—
179#3750—31no—
180#3750—31no—
181#3750—31no—
182#3750C2×D311yescharacteristic, complemented
183C4×C3⋊Dic3C2×D311yescharacteristic, complemented
184C3×#217—31no—
185C3×#217—31no—
186C3×#217—31no—
187C3×#217—31no—
188C3×#217—31no—
189C3×(C2×D3)⋊C4—21no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—31no—
193C3×(C2×D3)⋊C4—31no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—61no—
198C3×(C2×D3)⋊C4C2×D311yescharacteristic
199C3×(C2×D3)⋊C4C2×D311yescharacteristic
200C3×C4⋊Dic3—31no—
201C3×Dic3⋊C4—21no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—61no—
206C3×Dic3⋊C4C2×D311yescharacteristic, complemented
207C3×Dic3⋊C4C2×D311yescharacteristic, complemented
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211C3×C4×Dic3—31no—
212C3×C4×Dic3—61no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—61no—
219#3724—61no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3C2×D311yescharacteristic, complemented
229#3722—31no—
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—61no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3—61no—
247(C2×D3)⋊Dic3—61no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252(C2×D3)⋊Dic3C2×D311yescharacteristic
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
255Dic32—31no—
256Dic32—31no—
257Dic32—31no—
258Dic32C2×D311yescharacteristic, complemented
259C22×C33C2411yescharacteristic
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3#4112yes—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C2×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3#4112yes—
272C3×D32—44no—
273C33×C4—21no—
274C3⋊(C3⋊Dic3)—21no—
275C3⋊(C3⋊Dic3)—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#123—91no—
285C3×#120—91no—
286C3×#117—91no—
287C2×#217—91no—
288C2×#217—91no—
289#937—31no—
290#936—91no—
291#936—91no—
292#936—181no—
293#935—31no—
294#935—91no—
295#935—91no—
296D4×Dic3—91no—
297D4×Dic3—91no—
298#929—91no—
299C4×#67—91no—
300C4×#67—91no—
301C2×(C2×D3)⋊C4—91no—
302#898—91no—
303#896—91no—
304#896—91no—
305#896—91no—
306#896—181no—
307#894—31no—
308#894—91no—
309#892—31no—
310#892—91no—
311#883—91no—
312#883—91no—
313#882—31no—
314#67⋊C4—91no—
315D3×C22⋊C4—91no—
316D3×C22⋊C4—91no—
317D3×C22⋊C4—91no—
318#879—91no—
319#879—91no—
320#879—91no—
321#879—91no—
322#878—91no—
323#878—91no—
324#878—91no—
325#878—181no—
326#877—31no—
327#877—91no—
328#876—91no—
329#875—91no—
330C4×D12—91no—
331#872—91no—
332C23×C32—31no—
333C23×C32—31no—
334C23×C32—31no—
335C22×C3⋊D3C22×D311yescharacteristic
336C22×C3×D3—21no—
337C22×C3×D3—21no—
338C22×C3×D3—21no—
339C22×C3×D3—31no—
340C22×C3×D3—31no—
341C22×C3×D3—61no—
342C22×C3×D3—62no—
343C22×C3×D3—62no—
344C22×C3×D3—62no—
345C22×C3×D3—62no—
346C22×C3×D3—121no—
347C22×C3×D3—121no—
348C22×C3×D3C22×D311yescharacteristic
349C22×C3×D3C22×D311yescharacteristic
350C22×C3×D3C22×D311yescharacteristic
351C22×C3×D3C22×D311yescharacteristic
352C22×C3×D3C22×D311yescharacteristic
353C22×C3×D3C22×D311yescharacteristic
354C2×D32—22no—
355C2×D32—22no—
356C2×D32—41no—
357C32×D4—121no—
358C2×C32×C4—21no—
359C2×C32×C4—21no—
360C2×C32×C4—21no—
361C2×C32×C4—31no—
362C2×C32×C4—31no—
363C2×C32×C4—31no—
364C2×C32×C4—41no—
365C2×C32×C4C22×D311yescharacteristic
366C2×C32×C4C22×D311yescharacteristic
367C2×C32×C4C22×D311yescharacteristic
368C2×C3⋊Dic3—31no—
369C2×C3⋊Dic3—31no—
370C2×C3⋊Dic3—31no—
371C2×C3⋊Dic3—31no—
372C2×C3⋊Dic3—31no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—61no—
375C2×C3⋊Dic3—61no—
376C2×C3⋊Dic3—61no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—121no—
381C2×C3⋊Dic3—121no—
382C2×C3⋊Dic3—121no—
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C4×C3⋊D3—121no—
389#634—121no—
390#634—121no—
391#634—121no—
392#634—122no—
393#634—122no—
394#634—122no—
395#634—124no—
396C3×#67—62no—
397C3×#67—62no—
398C3×#67—62no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—62no—
418C2×C3×Dic3—121no—
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C3×D12—41no—
426C3×D12—41no—
427C3×D12—42no—
428C3×D12—62no—
429C3×C4×D3—62no—
430C3×C4×D3—121no—
431#626—22no—
432#625—22no—
433#624—62no—
434D3×Dic3—22no—
435D3×Dic3—41no—
436D3×Dic3—62no—
437D3×Dic3—62no—
438D3×Dic3—121no—
439D3×Dic3—121no—
440D3×Dic3—122no—
441D3×Dic3—121no—
442D3×Dic3—121no—
443D3×Dic3—122no—
444#551—271noSylow
445C2×C33C2×#4111yescharacteristic
446C2×C33C2×#4111yescharacteristic
447C2×C33H(5,𝔽2)11yescharacteristic
448C3×C3⋊D3—22no—
449C32×D3—22no—
450C32×D3—41no—
451C32×D3—41no—
452C24×C3—91no—
453C23×D3—31no—
454C23×D3—31no—
455C2×C3×D4—31no—
456C2×C3×D4—31no—
457C2×C3×D4—61no—
458C2×C3×D4—91no—
459C2×C3×D4—91no—
460C22×C3×C4—91no—
461C22×C3×C4—91no—
462C2×#67—31no—
463C2×#67—31no—
464C2×#67—31no—
465C22×Dic3—31no—
466C22×Dic3—31no—
467C22×Dic3—91no—
468C22×Dic3—91no—
469C22×Dic3—91no—
470C22×Dic3—91no—
471C22×Dic3—181no—
472C2×D12—31no—
473C2×D12D3211yescharacteristic
474C2×C4×D3—31no—
475C2×C4×D3—31no—
476C2×C4×D3—91no—
477C2×C4×D3—91no—
478C2×C4×D3—91no—
479C2×C4×D3—91no—
480C2×C4×D3—91no—
481C2×C4×D3—181no—
482C2×Dic6—91no—
483C2×Dic6—91no—
484C2×Dic6—91no—
485C2×Dic6—181no—
486C2×Dic6—181no—
487C2×Dic6—181no—
488C2×Dic6—361no—
489C3×C4⋊C4—31no—
490C3×C4⋊C4—31no—
491C3×C4⋊C4—61no—
492C3×C4⋊C4—91no—
493C3×C4⋊C4—91no—
494C3×C22⋊C4—31no—
495C3×C22⋊C4—31no—
496C3×C22⋊C4—61no—
497C3×C22⋊C4—91no—
498C3×C22⋊C4—91no—
499C3×C22⋊C4—91no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C22⋊C4—91no—
503C3×C42—91no—
504C3×C42—91no—
505#217—31no—
506#217—31no—
507#217—31no—
508#217—31no—
509#217—31no—
510#217—91no—
511#217—91no—
512#217—91no—
513#217—91no—
514#217—91no—
515#217—91no—
516#217—91no—
517#217—91no—
518#217—91no—
519#217—91no—
520#217—91no—
521#217—91no—
522#217—181no—
523#217—181no—
524#217—181no—
525#217—181no—
526#217—181no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4—31no—
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—61no—
535(C2×D3)⋊C4—91no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—91no—
538(C2×D3)⋊C4—91no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543(C2×D3)⋊C4—91no—
544(C2×D3)⋊C4—181no—
545(C2×D3)⋊C4D3211yescharacteristic
546C4⋊Dic3—31no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—181no—
552Dic3⋊C4—31no—
553Dic3⋊C4—31no—
554Dic3⋊C4—31no—
555Dic3⋊C4—61no—
556Dic3⋊C4—91no—
557Dic3⋊C4—91no—
558Dic3⋊C4—91no—
559Dic3⋊C4—91no—
560Dic3⋊C4—91no—
561Dic3⋊C4—91no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—91no—
565Dic3⋊C4—91no—
566Dic3⋊C4—91no—
567Dic3⋊C4—181no—
568Dic3⋊C4—181no—
569Dic3⋊C4—181no—
570Dic3⋊C4D3211yescharacteristic, complemented
571C4×Dic3—31no—
572C4×Dic3—31no—
573C4×Dic3—31no—
574C4×Dic3—31no—
575C4×Dic3—61no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C22×C32—21no—
580C22×C32—21no—
581C22×C32—21no—
582C22×C32—32no—
583C22×C32—41no—
584C22×C32—61no—
585C22×C32—61no—
586C22×C32—61no—
587C22×C32—61no—
588C22×C32—61no—
589C22×C32—61no—
590C22×C32—61no—
591C22×C32—61no—
592C22×C32C23×D311yescharacteristic
593C22×C32C23×D311yescharacteristic
594C22×C32C23×D311yescharacteristic
595C2×C3⋊D3—21no—
596C2×C3⋊D3—21no—
597C2×C3⋊D3#23712yes—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—21no—
601C2×C3×D3—21no—
602C2×C3×D3—21no—
603C2×C3×D3—21no—
604C2×C3×D3—21no—
605C2×C3×D3—21no—
606C2×C3×D3—21no—
607C2×C3×D3—21no—
608C2×C3×D3—21no—
609C2×C3×D3—21no—
610C2×C3×D3—21no—
611C2×C3×D3—21no—
612C2×C3×D3—21no—
613C2×C3×D3—21no—
614C2×C3×D3—22no—
615C2×C3×D3—32no—
616C2×C3×D3—32no—
617C2×C3×D3—41no—
618C2×C3×D3—41no—
619C2×C3×D3—41no—
620C2×C3×D3—41no—
621C2×C3×D3—41no—
622C2×C3×D3—41no—
623C2×C3×D3—41no—
624C2×C3×D3—41no—
625C2×C3×D3—62no—
626C2×C3×D3—61no—
627C2×C3×D3—61no—
628C2×C3×D3—61no—
629C2×C3×D3—61no—
630C2×C3×D3—121no—
631C2×C3×D3—121no—
632C2×C3×D3—124no—
633C2×C3×D3—124no—
634C2×C3×D3#23512yes—
635C2×C3×D3#23712yes—
636D32—44no—
637C32×C4—21no—
638C32×C4—22no—
639C32×C4—21no—
640C32×C4—21no—
641C32×C4—41no—
642C32×C4—41no—
643C32×C4—42no—
644C32×C4—61no—
645C32×C4—61no—
646C32×C4—61no—
647C3⋊Dic3—21no—
648C3⋊Dic3—21no—
649C3⋊Dic3—21no—
650C3⋊Dic3—21no—
651C3⋊Dic3—21no—
652C3⋊Dic3—61no—
653C3⋊Dic3—61no—
654C3⋊Dic3—62no—
655C3⋊Dic3—62no—
656C3⋊Dic3—61no—
657C3⋊Dic3—61no—
658C3⋊Dic3—61no—
659C3⋊Dic3—61no—
660C3⋊Dic3—121no—
661C3⋊Dic3—121no—
662C3⋊Dic3—121no—
663C3⋊Dic3—121no—
664C3⋊Dic3—122no—
665C3⋊Dic3—122no—
666C3×Dic3—21no—
667C3×Dic3—21no—
668C3×Dic3—21no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—41no—
673C3×Dic3—41no—
674C3×Dic3—41no—
675C3×Dic3—61no—
676C3×Dic3—61no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—61no—
680C3×Dic3—61no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—121no—
686C3×Dic3—121no—
687C3×Dic3—121no—
688C3×Dic3—121no—
689C3×Dic3—121no—
690#126—271no—
691#126—271no—
692#124—271no—
693#123—91no—
694#123—271no—
695#123—271no—
696C22⋊Q8—271no—
697C22⋊Q8—271no—
698#120—91no—
699C4×D4—271no—
700C4×D4—271no—
701#117—91no—
702#117—271no—
703C2×C22⋊C4—271no—
704C2×C22⋊C4—271no—
705C33#55111yescharacteristic, complemented, Sylow
706C23×C3—31no—
707C23×C3—31no—
708C23×C3—31no—
709C23×C3—31no—
710C23×C3—31no—
711C23×C3—31no—
712C23×C3—61no—
713C23×C3—61no—
714C23×C3—61no—
715C23×C3—91no—
716C23×C3—182no—
717C23×C3—182no—
718C23×C3—361no—
719C22×D3—31no—
720C22×D3—31no—
721C22×D3—61no—
722C22×D3—62no—
723C22×D3—62no—
724C22×D3—62no—
725C22×D3—62no—
726C22×D3—121no—
727C22×D3—121no—
728C22×D3C2×D3211yescharacteristic
729C22×D3C2×D3211yescharacteristic
730C22×D3C2×D3211yescharacteristic
731C3×D4—121no—
732C3×D4—121no—
733C3×D4—122no—
734C3×D4—182no—
735C3×D4—182no—
736C2×C3×C4—21no—
737C2×C3×C4—21no—
738C2×C3×C4—21no—
739C2×C3×C4—31no—
740C2×C3×C4—31no—
741C2×C3×C4—31no—
742C2×C3×C4—31no—
743C2×C3×C4—31no—
744C2×C3×C4—31no—
745C2×C3×C4—41no—
746C2×C3×C4—61no—
747C2×C3×C4—61no—
748C2×C3×C4—61no—
749C2×C3×C4—91no—
750C2×C3×C4—91no—
751C2×C3×C4—91no—
752C2×C3×C4—91no—
753C2×C3×C4—91no—
754C2×C3×C4—182no—
755C2×C3×C4—361no—
756C2×C3×C4C2×D3211yescharacteristic
757C2×C3×C4C2×D3211yescharacteristic
758C2×C3×C4C2×D3211yescharacteristic
759#67—62no—
760#67—62no—
761#67—62no—
762C2×Dic3—31no—
763C2×Dic3—31no—
764C2×Dic3—31no—
765C2×Dic3—31no—
766C2×Dic3—31no—
767C2×Dic3—31no—
768C2×Dic3—31no—
769C2×Dic3—31no—
770C2×Dic3—31no—
771C2×Dic3—31no—
772C2×Dic3—61no—
773C2×Dic3—61no—
774C2×Dic3—61no—
775C2×Dic3—61no—
776C2×Dic3—61no—
777C2×Dic3—62no—
778C2×Dic3—91no—
779C2×Dic3—91no—
780C2×Dic3—91no—
781C2×Dic3—91no—
782C2×Dic3—91no—
783C2×Dic3—91no—
784C2×Dic3—121no—
785C2×Dic3—181no—
786C2×Dic3—181no—
787C2×Dic3—181no—
788C2×Dic3—181no—
789C2×Dic3—181no—
790C2×Dic3—181no—
791C2×Dic3—182no—
792C2×Dic3—361no—
793C2×Dic3—361no—
794C2×Dic3—361no—
795C2×Dic3—361no—
796C2×Dic3—361no—
797C2×Dic3—362no—
798C2×Dic3C2×D3211yescharacteristic
799C2×Dic3C2×D3211yescharacteristic
800C2×Dic3C2×D3211yescharacteristic
801D12—41no—
802D12—62no—
803C4×D3—62no—
804C4×D3—121no—
805C4×D3—182no—
806C4×D3—182no—
807C4×D3—361no—
808C4×D3—361no—
809C4×D3—362no—
810C4×D3—361no—
811Dic6—361no—
812Dic6—361no—
813Dic6—361no—
814Dic6—362no—
815Dic6—362no—
816Dic6—362no—
817Dic6—364no—
818C2×C32—21no—
819C2×C32—21no—
820C2×C32—21no—
821C2×C32—21no—
822C2×C32—21no—
823C2×C32—21no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—41no—
828C2×C32—41no—
829C2×C32—41no—
830C2×C32—62no—
831C2×C32—121no—
832C2×C32—121no—
833C2×C32C2×#23511yescharacteristic
834C2×C32C2×#23711yescharacteristic
835C2×C32C2×#23711yescharacteristic
836C2×C32#100411yescharacteristic
837C2×C32#100411yescharacteristic
838C2×C32D3×#4111yescharacteristic
839C2×C32D3×#4111yescharacteristic
840C2×C32D3×#4111yescharacteristic
841C2×C32#100911yescharacteristic
842C3⋊D3—22no—
843C3×D3—22no—
844C3×D3—22no—
845C3×D3—42no—
846C3×D3—41no—
847C3×D3—41no—
848C3×D3—41no—
849C3×D3—41no—
850C3×D3—62no—
851C3×D3—62no—
852C3×D3—81no—
853C3×D3—81no—
854C3×D3—122no—
855C24—91no—
856C2×Q8—271no—
857C2×D4—31no—
858C2×D4—91no—
859C2×D4—91no—
860C22×C4—91no—
861C22×C4—91no—
862C22×C4—271no—
863C22×C4—271no—
864C22×C4—271no—
865C4⋊C4—31no—
866C4⋊C4—91no—
867C4⋊C4—91no—
868C4⋊C4—271no—
869C4⋊C4—271no—
870C4⋊C4—271no—
871C4⋊C4—271no—
872C4⋊C4—271no—
873C22⋊C4—31no—
874C22⋊C4—91no—
875C22⋊C4—91no—
876C22⋊C4—91no—
877C22⋊C4—91no—
878C22⋊C4—91no—
879C22⋊C4—91no—
880C22⋊C4—271no—
881C22⋊C4—271no—
882C22⋊C4—271no—
883C22⋊C4—271no—
884C22⋊C4—271no—
885C22⋊C4—271no—
886C22⋊C4—271no—
887C42—91no—
888C42—91no—
889C42—271no—
890C22×C3—21no—
891C22×C3—21no—
892C22×C3—21no—
893C22×C3—32no—
894C22×C3—32no—
895C22×C3—41no—
896C22×C3—62no—
897C22×C3—61no—
898C22×C3—61no—
899C22×C3—61no—
900C22×C3—61no—
901C22×C3—61no—
902C22×C3—61no—
903C22×C3—61no—
904C22×C3—61no—
905C22×C3—61no—
906C22×C3—61no—
907C22×C3—61no—
908C22×C3—61no—
909C22×C3—61no—
910C22×C3—61no—
911C22×C3—61no—
912C22×C3—61no—
913C22×C3—92no—
914C22×C3—121no—
915C22×C3—121no—
916C22×C3—121no—
917C22×C3—121no—
918C22×C3—121no—
919C22×C3—121no—
920C22×C3—121no—
921C22×C3—121no—
922C22×C3—181no—
923C22×C3—181no—
924C22×C3—364no—
925C22×C3C22×D3211yescharacteristic
926C22×C3C22×D3211yescharacteristic
927C22×C3C22×D3211yescharacteristic
928C2×D3—21no—
929C2×D3—21no—
930C2×D3—21no—
931C2×D3—21no—
932C2×D3—21no—
933C2×D3—21no—
934C2×D3—21no—
935C2×D3—21no—
936C2×D3—32no—
937C2×D3—32no—
938C2×D3—62no—
939C2×D3—61no—
940C2×D3—61no—
941C2×D3—61no—
942C2×D3—61no—
943C2×D3—121no—
944C2×D3—121no—
945C2×D3—124no—
946C2×D3—124no—
947C2×D3#379512yes—
948C3×C4—22no—
949C3×C4—21no—
950C3×C4—21no—
951C3×C4—21no—
952C3×C4—41no—
953C3×C4—41no—
954C3×C4—42no—
955C3×C4—61no—
956C3×C4—61no—
957C3×C4—61no—
958C3×C4—61no—
959C3×C4—61no—
960C3×C4—61no—
961C3×C4—121no—
962C3×C4—121no—
963C3×C4—121no—
964C3×C4—181no—
965C3×C4—181no—
966C3×C4—181no—
967C3×C4—181no—
968C3×C4—181no—
969Dic3—21no—
970Dic3—21no—
971Dic3—21no—
972Dic3—61no—
973Dic3—61no—
974Dic3—61no—
975Dic3—61no—
976Dic3—61no—
977Dic3—61no—
978Dic3—61no—
979Dic3—61no—
980Dic3—61no—
981Dic3—61no—
982Dic3—121no—
983Dic3—121no—
984Dic3—121no—
985Dic3—121no—
986Dic3—121no—
987Dic3—182no—
988Dic3—182no—
989Dic3—181no—
990Dic3—181no—
991Dic3—181no—
992Dic3—181no—
993Dic3—181no—
994Dic3—181no—
995Dic3—361no—
996Dic3—361no—
997Dic3—361no—
998Dic3—361no—
999Dic3—362no—
1000Dic3—362no—
1001C32—21no—
1002C32—21no—
1003C32—21no—
1004C32—41no—
1005C32#552711yescharacteristic, complemented
1006C32#558711yescharacteristic, complemented
1007C32#565911yescharacteristic, complemented
1008C23—31no—
1009C23—31no—
1010C23—31no—
1011C23—91no—
1012C23—182no—
1013C23—182no—
1014C23—361no—
1015Q8—1081no—
1016D4—121no—
1017D4—182no—
1018D4—182no—
1019C2×C4—31no—
1020C2×C4—31no—
1021C2×C4—31no—
1022C2×C4—91no—
1023C2×C4—91no—
1024C2×C4—91no—
1025C2×C4—91no—
1026C2×C4—91no—
1027C2×C4—182no—
1028C2×C4—271no—
1029C2×C4—271no—
1030C2×C4—361no—
1031C2×C4—542no—
1032C2×C4—1081no—
1033C2×C4—1081no—
1034C2×C4D3311yescharacteristic
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—21no—
1038C2×C3—21no—
1039C2×C3—21no—
1040C2×C3—21no—
1041C2×C3—21no—
1042C2×C3—21no—
1043C2×C3—21no—
1044C2×C3—41no—
1045C2×C3—41no—
1046C2×C3—41no—
1047C2×C3—62no—
1048C2×C3—62no—
1049C2×C3—122no—
1050C2×C3—121no—
1051C2×C3—121no—
1052C2×C3—121no—
1053C2×C3—121no—
1054C2×C3—182no—
1055C2×C3—241no—
1056C2×C3—241no—
1057C2×C3C2×#379511yescharacteristic
1058C2×C3D3×#23511yescharacteristic
1059C2×C3D3×#23711yescharacteristic
1060C2×C3D3×#23711yescharacteristic
1061C2×C3D3×#23711yescharacteristic
1062C2×C3#6431411yescharacteristic
1063C2×C3#6431411yescharacteristic
1064C2×C3#6431911yescharacteristic
1065C2×C3#6433011yescharacteristic
1066D3—22no—
1067D3—41no—
1068D3—41no—
1069D3—62no—
1070D3—62no—
1071D3—122no—
1072C22—32no—
1073C22—61no—
1074C22—61no—
1075C22—61no—
1076C22—61no—
1077C22—61no—
1078C22—61no—
1079C22—61no—
1080C22—61no—
1081C22—92no—
1082C22—181no—
1083C22—181no—
1084C22—364no—
1085C22C2×D3311yescharacteristic
1086C4—21no—
1087C4—61no—
1088C4—61no—
1089C4—61no—
1090C4—181no—
1091C4—181no—
1092C4—181no—
1093C4—181no—
1094C4—181no—
1095C4—541no—
1096C4—541no—
1097C3—21no—
1098C3—21no—
1099C3—21no—
1100C3—41no—
1101C3#1059411711yescharacteristic, complemented
1102C3#1059464411yescharacteristic, complemented
1103C3#1059517811yescharacteristic, complemented
1104C2—62no—
1105C2—121no—
1106C2—121no—
1107C2—182no—
1108C2D3×#379511yescharacteristic
1109C2#1172437411yescharacteristic
1110C2#1172441911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC3×#63922C2
hypercenterC2×C4D33
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723683C2semidirect
2. #11723497C2semidirect
3. #11723496C2semidirect
4. #11723429C2semidirect
6. C3×#63884C2semidirect
7. C3×#63878C2semidirect
8. #11723026C2semidirect
9. #11723020C2semidirect
10. #11722994C2semidirect
11. #11722985C2semidirect
12. Dic3×#626C2semidirect
13. #11722924C2semidirect
14. #11722902C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
20. C2×#6308C22semidirect
28. C2×C3×D3×Dic3C22semidirect
30. C3×#3750C22semidirect
31. C3×C4×C3⋊Dic3C22semidirect
33. C32×Dic3⋊C4C22semidirect
34. #88815C22semidirect
36. #88813C22semidirect
37. #88807C22semidirect
38. #88806C22semidirect
39. #88806C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
45. (C2×D3)⋊(C3⋊Dic3)C22semidirect
46. (C2×D3)⋊(C3⋊Dic3)C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
88. #63884D3semidirect
91. #63878D3semidirect
168. C2×D3×Dic3C2×D3semidirect
182. #3750C2×D3semidirect
183. C4×C3⋊Dic3C2×D3semidirect
206. C3×Dic3⋊C4C2×D3semidirect
207. C3×Dic3⋊C4C2×D3semidirect
228. Dic3⋊Dic3C2×D3semidirect
254. (C2×D3)⋊Dic3C2×D3semidirect
258. Dic32C2×D3semidirect
570. Dic3⋊C4D32semidirect
705. C33#551semidirect
1005. C32#5527semidirect
1006. C32#5587semidirect
1007. C32#5659semidirect
1101. C3#10594117semidirect
1102. C3#10594644semidirect
1103. C3#10595178semidirect

Maximal subgroups

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

subgroupindex
#117236832
#117234972
#117234962
#117234292
C3×#639222
C3×#638842
C3×#638782
#117230262
#117230202
#117229942
#117229852
Dic3×#6262
#117229242
#117229022
D3×(C2×D3)⋊Dic32
#105951783
#105946443
#105941173