Finite Group Databasebeta

← #13168112

Subgroups — #13168112

Order 1728.

1232 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723673C211yesmaximal, characteristic, complemented
2#11723518C211yesmaximal, characteristic, complemented
3#11723459C211yesmaximal, characteristic, complemented
4#11723428C211yesmaximal, characteristic, complemented
5C3×#63921C211yesmaximal, characteristic, complemented
6C3×#63915C211yesmaximal, characteristic, complemented
7C3×#63902C211yesmaximal, characteristic, complemented
8#11723022C211yesmaximal, characteristic, complemented
9#11722989C211yesmaximal, characteristic, complemented
10#11722985C211yesmaximal, characteristic, complemented
11#11722970C211yesmaximal, characteristic, complemented
12#11722969C211yesmaximal, characteristic, complemented
13#11722946C211yesmaximal, characteristic
14#11722930C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10594300—31nomaximal
17#10594209—31nomaximal
18#10594092—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×#6290C2211yescharacteristic
22C2×D3×C3⋊Dic3C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic, complemented
24C2×C3×#625C2211yescharacteristic
25C2×C3×#625C2211yescharacteristic
26C2×C3×#624C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic, complemented
29#88857C2211yescharacteristic, complemented
30C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
31C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
35#88815C2211yescharacteristic, complemented
36#88815C2211yescharacteristic, complemented
37#88814C2211yescharacteristic
38#88814C2211yescharacteristic
39#88806C2211yescharacteristic, complemented
40#88806C2211yescharacteristic, complemented
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43#88803C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48Dic3×C3⋊Dic3C2211yescharacteristic, complemented
49C3×#3724C2211yescharacteristic, complemented
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64092—31no—
55#64088—31no—
56#64086—31no—
57C3×#885—31no—
58C3×#885—31no—
59C3×#67⋊C4—31no—
60C3×#67⋊C4—31no—
61C3×D3×C22⋊C4—31no—
62C3×D3×C22⋊C4—31no—
63#63983—31no—
64#63976—31no—
65#63976—31no—
66#63969—31no—
67#63969—31no—
68D3×#217—31no—
69#63964—31no—
70#63962—31no—
71#63961—31no—
72C2×(C2×D3)⋊Dic3—31no—
73#63956—31no—
74#63952—31no—
75#63921D311yescharacteristic, complemented
76D3×(C2×D3)⋊C4—31no—
77#63915D311yescharacteristic, complemented
78#63905—31no—
79#63905—31no—
80#63905—31no—
81#63905—61no—
82#63902D311yescharacteristic, complemented
83C4×#625—31no—
84#63891—31no—
85#63888—31no—
86#63887—31no—
87#63879—31no—
88#63877—31no—
89#63877—31no—
90#63877—61no—
91#63874—31no—
92#63862—31no—
93#63861—31no—
94#63859—31no—
95#63859—31no—
96#63859—61no—
97#63856—31no—
98#63856—31no—
99#63855—31no—
100#63855—31no—
101#63851—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
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4×C3⋊D3—22no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6290—22no—
122D3×C3⋊Dic3—22no—
123C3×#627—41no—
124C3×#625—22no—
125C3×#625—41no—
126C3×#624—41no—
127C3×D3×Dic3—41no—
128C3×D3×Dic3—41no—
129#5679—91no—
130#5556—91no—
131#5495—91no—
132C23×C3×D3—31no—
133C23×C3×D3—31no—
134C22×D32C2×D311yescharacteristic
135C2×#638—31no—
136C22×C3⋊Dic3—31no—
137C2×C4×C3⋊D3C2×D311yescharacteristic
138C2×C3×#67—31no—
139C2×C3×#67—31no—
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—61no—
151C2×C3×Dic6—31no—
152C2×C3×Dic6—31no—
153C2×#627C2×D311yescharacteristic, complemented
154C2×#625—31no—
155C2×#625—31no—
156C2×#625—61no—
157C2×#625C2×D311yescharacteristic
158C2×#625C2×D311yescharacteristic
159C2×#624C2×D311yescharacteristic
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—61no—
163C2×D3×Dic3C2×D311yescharacteristic
164C2×D3×Dic3C2×D311yescharacteristic, complemented
165C32×C22⋊C4—31no—
166C32×C22⋊C4—31no—
167C32×C22⋊C4—31no—
168#3757—31no—
169#3757—31no—
170#3757—31no—
171#3757—31no—
172#3752—31no—
173C4⋊(C3⋊Dic3)—31no—
174C4⋊(C3⋊Dic3)—31no—
175#3750—31no—
176#3750—31no—
177#3750—31no—
178#3750—31no—
179#3750—31no—
180#3750—61no—
181#3750—61no—
182#3750—61no—
183#3750—121no—
184C4×C3⋊Dic3—31no—
185C4×C3⋊Dic3C2×D311yescharacteristic, complemented
186C4×C3⋊Dic3C2×D311yescharacteristic, complemented
187C3×#217—31no—
188C3×#217—31no—
189C3×#217—31no—
190C3×#217—31no—
191C3×(C2×D3)⋊C4—21no—
192C3×(C2×D3)⋊C4—21no—
193C3×(C2×D3)⋊C4—21no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4C2×D311yescharacteristic
199C3×(C2×D3)⋊C4C2×D311yescharacteristic
200C3×(C2×D3)⋊C4C2×D311yescharacteristic
201C3×(C2×D3)⋊C4C2×D311yescharacteristic
202C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
203C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×C4×Dic3—31no—
207C3×C4×Dic3—31no—
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—61no—
211C3×C4×Dic3—61no—
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—61no—
219#3724—61no—
220#3724C2×D311yescharacteristic, complemented
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—61no—
230Dic3⋊Dic3—61no—
231#3722—31no—
232#3722—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—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—61no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3C2×D311yescharacteristic
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254(C2×D3)⋊Dic3C2×D311yescharacteristic
255(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
256Dic32—31no—
257Dic32—31no—
258Dic32—61no—
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×#124—91no—
285C3×C4×D4—91no—
286C2×C3×C22⋊C4—91no—
287#953—91no—
288C2×#217—91no—
289#946—91no—
290#946—91no—
291#937—91no—
292#937—91no—
293#935—91no—
294#935—91no—
295#929—91no—
296#929—91no—
297C4×#67—91no—
298C4×#67—91no—
299C2×(C2×D3)⋊C4—91no—
300#926—91no—
301#924—91no—
302#924—91no—
303#898—91no—
304#896—91no—
305#886—91no—
306#885—31no—
307#885—31no—
308#883—91no—
309#883—91no—
310#883—91no—
311#883—91no—
312#883—181no—
313#67⋊C4—31no—
314#67⋊C4—31no—
315#67⋊C4—91no—
316D3×C22⋊C4—31no—
317D3×C22⋊C4—31no—
318D3×C22⋊C4—91no—
319#879—91no—
320#879—91no—
321#879—91no—
322#879—91no—
323#879—181no—
324#878—91no—
325#877—91no—
326#877—91no—
327#877—181no—
328#876—91no—
329#872—91no—
330#872—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—
357C2×C32×C4—21no—
358C2×C32×C4—21no—
359C2×C32×C4—21no—
360C2×C32×C4—31no—
361C2×C32×C4—31no—
362C2×C32×C4—31no—
363C2×C32×C4—41no—
364C2×C32×C4C22×D311yescharacteristic
365C2×C32×C4C22×D311yescharacteristic
366C2×C32×C4C22×D311yescharacteristic
367#638—62no—
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—62no—
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—22no—
389C3×#67—62no—
390C3×#67—62no—
391C3×#67—121no—
392C3×#67—121no—
393C2×C3×Dic3—21no—
394C2×C3×Dic3—21no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—61no—
408C2×C3×Dic3—61no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—121no—
412C2×C3×Dic3—121no—
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C3×C4×D3—62no—
420C3×C4×D3—62no—
421C3×C4×D3—122no—
422C3×C4×D3—121no—
423C3×C4×D3—121no—
424C3×C4×D3—121no—
425C3×C4×D3—121no—
426C3×Dic6—121no—
427C3×Dic6—121no—
428#627—41no—
429#625—22no—
430#625—41no—
431#625—62no—
432#625—62no—
433#625—122no—
434#624—41no—
435D3×Dic3—41no—
436D3×Dic3—41no—
437D3×Dic3—64no—
438D3×Dic3—62no—
439D3×Dic3—62no—
440#551—271noSylow
441C2×C33C2×#4111yescharacteristic
442C2×C33C2×#4111yescharacteristic
443C2×C33H(5,𝔽2)11yescharacteristic
444C3×C3⋊D3—22no—
445C32×D3—22no—
446C32×D3—41no—
447C32×D3—41no—
448C24×C3—91no—
449C23×D3—31no—
450C23×D3—31no—
451C2×C3×Q8—91no—
452C2×C3×D4—91no—
453C2×C3×D4—91no—
454C22×C3×C4—91no—
455C22×C3×C4—91no—
456C22×C3×C4—91no—
457C22×C3×C4—91no—
458C2×#67—31no—
459C2×#67—31no—
460C2×#67—31no—
461C2×#67—31no—
462C2×#67—91no—
463C2×#67—91no—
464C2×#67—91no—
465C2×#67—181no—
466C22×Dic3—31no—
467C22×Dic3—31no—
468C22×Dic3—91no—
469C22×Dic3—91no—
470C22×Dic3—181no—
471C2×C4×D3—31no—
472C2×C4×D3—31no—
473C2×C4×D3—31no—
474C2×C4×D3—31no—
475C2×C4×D3—31no—
476C2×C4×D3—31no—
477C2×C4×D3—61no—
478C2×C4×D3—91no—
479C2×Dic6—31no—
480C2×Dic6—31no—
481C3×C4⋊C4—91no—
482C3×C22⋊C4—31no—
483C3×C22⋊C4—31no—
484C3×C22⋊C4—31no—
485C3×C22⋊C4—31no—
486C3×C22⋊C4—31no—
487C3×C22⋊C4—31no—
488C3×C22⋊C4—61no—
489C3×C22⋊C4—61no—
490C3×C22⋊C4—61no—
491C3×C22⋊C4—91no—
492C3×C22⋊C4—91no—
493C3×C22⋊C4—91no—
494C3×C22⋊C4—91no—
495C3×C42—91no—
496C3×C42—91no—
497#217—31no—
498#217—31no—
499#217—31no—
500#217—31no—
501#217—91no—
502#217—91no—
503#217—91no—
504#217—91no—
505#217—91no—
506#217—91no—
507#217—91no—
508#217—91no—
509#217—91no—
510#217—91no—
511#217—91no—
512#217—181no—
513#217—181no—
514#217—181no—
515#217—181no—
516(C2×D3)⋊C4—31no—
517(C2×D3)⋊C4—31no—
518(C2×D3)⋊C4—31no—
519(C2×D3)⋊C4—31no—
520(C2×D3)⋊C4—91no—
521(C2×D3)⋊C4—91no—
522(C2×D3)⋊C4—91no—
523(C2×D3)⋊C4—91no—
524(C2×D3)⋊C4—91no—
525(C2×D3)⋊C4—91no—
526(C2×D3)⋊C4—91no—
527(C2×D3)⋊C4—91no—
528(C2×D3)⋊C4—91no—
529(C2×D3)⋊C4—91no—
530(C2×D3)⋊C4—181no—
531(C2×D3)⋊C4D3211yescharacteristic
532(C2×D3)⋊C4D3211yescharacteristic
533(C2×D3)⋊C4D3211yescharacteristic, complemented
534C4⋊Dic3—91no—
535C4⋊Dic3—91no—
536C4⋊Dic3—91no—
537C4⋊Dic3—91no—
538C4⋊Dic3—91no—
539C4⋊Dic3—91no—
540C4⋊Dic3—181no—
541C4⋊Dic3—181no—
542Dic3⋊C4—31no—
543Dic3⋊C4—31no—
544Dic3⋊C4—91no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—91no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—91no—
555Dic3⋊C4—91no—
556Dic3⋊C4—91no—
557Dic3⋊C4—91no—
558Dic3⋊C4—91no—
559Dic3⋊C4—181no—
560Dic3⋊C4—181no—
561Dic3⋊C4—181no—
562Dic3⋊C4—181no—
563Dic3⋊C4—181no—
564Dic3⋊C4—361no—
565C4×Dic3—31no—
566C4×Dic3—31no—
567C4×Dic3—31no—
568C4×Dic3—31no—
569C4×Dic3—61no—
570C4×Dic3—61no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—181no—
575C22×C32—21no—
576C22×C32—21no—
577C22×C32—21no—
578C22×C32—32no—
579C22×C32—41no—
580C22×C32—61no—
581C22×C32—61no—
582C22×C32—61no—
583C22×C32—61no—
584C22×C32—61no—
585C22×C32—61no—
586C22×C32—61no—
587C22×C32—61no—
588C22×C32C23×D311yescharacteristic
589C22×C32C23×D311yescharacteristic
590C22×C32C23×D311yescharacteristic
591C2×C3⋊D3—21no—
592C2×C3⋊D3—21no—
593C2×C3⋊D3#23712yes—
594C2×C3×D3—21no—
595C2×C3×D3—21no—
596C2×C3×D3—21no—
597C2×C3×D3—21no—
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—22no—
611C2×C3×D3—32no—
612C2×C3×D3—32no—
613C2×C3×D3—41no—
614C2×C3×D3—41no—
615C2×C3×D3—41no—
616C2×C3×D3—41no—
617C2×C3×D3—41no—
618C2×C3×D3—41no—
619C2×C3×D3—41no—
620C2×C3×D3—41no—
621C2×C3×D3—62no—
622C2×C3×D3—61no—
623C2×C3×D3—61no—
624C2×C3×D3—61no—
625C2×C3×D3—61no—
626C2×C3×D3—121no—
627C2×C3×D3—121no—
628C2×C3×D3—124no—
629C2×C3×D3—124no—
630C2×C3×D3#23512yes—
631C2×C3×D3#23512yes—
632D32—44no—
633C32×C4—21no—
634C32×C4—21no—
635C32×C4—21no—
636C32×C4—41no—
637C32×C4—41no—
638C32×C4—41no—
639C32×C4—61no—
640C32×C4—61no—
641C32×C4—61no—
642C32×C4—81no—
643C3⋊Dic3—21no—
644C3⋊Dic3—21no—
645C3⋊Dic3—21no—
646C3⋊Dic3—21no—
647C3⋊Dic3—21no—
648C3⋊Dic3—61no—
649C3⋊Dic3—62no—
650C3⋊Dic3—61no—
651C3⋊Dic3—61no—
652C3⋊Dic3—61no—
653C3⋊Dic3—61no—
654C3⋊Dic3—61no—
655C3⋊Dic3—121no—
656C3⋊Dic3—121no—
657C3⋊Dic3—122no—
658C3⋊Dic3—121no—
659C3⋊Dic3—121no—
660C3⋊Dic3—121no—
661C3⋊Dic3—241no—
662C3×Dic3—21no—
663C3×Dic3—21no—
664C3×Dic3—21no—
665C3×Dic3—21no—
666C3×Dic3—21no—
667C3×Dic3—21no—
668C3×Dic3—41no—
669C3×Dic3—41no—
670C3×Dic3—41no—
671C3×Dic3—62no—
672C3×Dic3—61no—
673C3×Dic3—61no—
674C3×Dic3—61no—
675C3×Dic3—61no—
676C3×Dic3—61no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—61no—
680C3×Dic3—61no—
681C3×Dic3—61no—
682C3×Dic3—121no—
683C3×Dic3—121no—
684C3×Dic3—121no—
685C3×Dic3—121no—
686#126—271no—
687#126—271no—
688#124—91no—
689#123—271no—
690#123—271no—
691#123—271no—
692C22⋊Q8—271no—
693C22⋊Q8—271no—
694#120—271no—
695C4×D4—91no—
696C4×D4—271no—
697#117—271no—
698#117—271no—
699C2×C22⋊C4—91no—
700C2×C22⋊C4—271no—
701C33#55111yescharacteristic, complemented, Sylow
702C23×C3—31no—
703C23×C3—31no—
704C23×C3—31no—
705C23×C3—31no—
706C23×C3—31no—
707C23×C3—31no—
708C23×C3—61no—
709C23×C3—61no—
710C23×C3—61no—
711C23×C3—91no—
712C23×C3—182no—
713C23×C3—182no—
714C23×C3—361no—
715C22×D3—31no—
716C22×D3—31no—
717C22×D3—61no—
718C22×D3—62no—
719C22×D3—62no—
720C22×D3—62no—
721C22×D3—62no—
722C22×D3—121no—
723C22×D3—121no—
724C22×D3C2×D3211yescharacteristic
725C22×D3C2×D3211yescharacteristic
726C22×D3C2×D3211yescharacteristic
727C3×Q8—361no—
728C3×D4—182no—
729C3×D4—361no—
730C2×C3×C4—21no—
731C2×C3×C4—21no—
732C2×C3×C4—21no—
733C2×C3×C4—31no—
734C2×C3×C4—31no—
735C2×C3×C4—31no—
736C2×C3×C4—31no—
737C2×C3×C4—31no—
738C2×C3×C4—31no—
739C2×C3×C4—41no—
740C2×C3×C4—61no—
741C2×C3×C4—61no—
742C2×C3×C4—61no—
743C2×C3×C4—91no—
744C2×C3×C4—91no—
745C2×C3×C4—91no—
746C2×C3×C4—91no—
747C2×C3×C4—91no—
748C2×C3×C4—182no—
749C2×C3×C4—361no—
750C2×C3×C4—361no—
751C2×C3×C4—361no—
752C2×C3×C4C2×D3211yescharacteristic
753C2×C3×C4C2×D3211yescharacteristic
754C2×C3×C4C2×D3211yescharacteristic
755#67—62no—
756#67—62no—
757#67—121no—
758#67—121no—
759#67—182no—
760#67—182no—
761#67—182no—
762#67—362no—
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—31no—
773C2×Dic3—61no—
774C2×Dic3—61no—
775C2×Dic3—61no—
776C2×Dic3—61no—
777C2×Dic3—61no—
778C2×Dic3—91no—
779C2×Dic3—91no—
780C2×Dic3—91no—
781C2×Dic3—91no—
782C2×Dic3—91no—
783C2×Dic3—91no—
784C2×Dic3—121no—
785C2×Dic3—121no—
786C2×Dic3—181no—
787C2×Dic3—181no—
788C2×Dic3—181no—
789C2×Dic3—181no—
790C2×Dic3—181no—
791C2×Dic3—181no—
792C2×Dic3—182no—
793C2×Dic3—182no—
794C2×Dic3—184no—
795C2×Dic3—361no—
796C2×Dic3—361no—
797C2×Dic3C2×D3211yescharacteristic
798C2×Dic3C2×D3211yescharacteristic
799C2×Dic3C2×D3211yescharacteristic
800C4×D3—62no—
801C4×D3—62no—
802C4×D3—122no—
803C4×D3—121no—
804C4×D3—121no—
805C4×D3—121no—
806C4×D3—121no—
807C4×D3—182no—
808Dic6—121no—
809Dic6—121no—
810C2×C32—21no—
811C2×C32—21no—
812C2×C32—21no—
813C2×C32—21no—
814C2×C32—21no—
815C2×C32—21no—
816C2×C32—21no—
817C2×C32—21no—
818C2×C32—21no—
819C2×C32—41no—
820C2×C32—41no—
821C2×C32—41no—
822C2×C32—62no—
823C2×C32—121no—
824C2×C32—121no—
825C2×C32C2×#23511yescharacteristic
826C2×C32C2×#23511yescharacteristic
827C2×C32C2×#23711yescharacteristic
828C2×C32#100411yescharacteristic
829C2×C32#100411yescharacteristic
830C2×C32#100411yescharacteristic
831C2×C32D3×#4111yescharacteristic
832C2×C32D3×#4111yescharacteristic
833C2×C32D3×#4111yescharacteristic
834C3⋊D3—22no—
835C3×D3—22no—
836C3×D3—22no—
837C3×D3—42no—
838C3×D3—41no—
839C3×D3—41no—
840C3×D3—41no—
841C3×D3—41no—
842C3×D3—62no—
843C3×D3—62no—
844C3×D3—81no—
845C3×D3—81no—
846C3×D3—122no—
847C24—91no—
848C2×Q8—91no—
849C2×D4—91no—
850C2×D4—91no—
851C2×D4—271no—
852C22×C4—91no—
853C22×C4—91no—
854C22×C4—91no—
855C22×C4—91no—
856C22×C4—271no—
857C4⋊C4—91no—
858C4⋊C4—271no—
859C4⋊C4—271no—
860C4⋊C4—271no—
861C4⋊C4—271no—
862C4⋊C4—271no—
863C4⋊C4—271no—
864C4⋊C4—271no—
865C22⋊C4—31no—
866C22⋊C4—31no—
867C22⋊C4—31no—
868C22⋊C4—91no—
869C22⋊C4—91no—
870C22⋊C4—91no—
871C22⋊C4—91no—
872C22⋊C4—271no—
873C22⋊C4—271no—
874C22⋊C4—271no—
875C22⋊C4—271no—
876C22⋊C4—271no—
877C22⋊C4—271no—
878C22⋊C4—271no—
879C42—91no—
880C42—91no—
881C42—271no—
882C22×C3—21no—
883C22×C3—21no—
884C22×C3—21no—
885C22×C3—32no—
886C22×C3—32no—
887C22×C3—41no—
888C22×C3—62no—
889C22×C3—61no—
890C22×C3—61no—
891C22×C3—61no—
892C22×C3—61no—
893C22×C3—61no—
894C22×C3—61no—
895C22×C3—61no—
896C22×C3—61no—
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—92no—
906C22×C3—121no—
907C22×C3—121no—
908C22×C3—121no—
909C22×C3—121no—
910C22×C3—121no—
911C22×C3—121no—
912C22×C3—121no—
913C22×C3—121no—
914C22×C3—181no—
915C22×C3—181no—
916C22×C3—364no—
917C22×C3C22×D3211yescharacteristic
918C22×C3C22×D3211yescharacteristic
919C22×C3C22×D3211yescharacteristic
920C2×D3—21no—
921C2×D3—21no—
922C2×D3—21no—
923C2×D3—21no—
924C2×D3—21no—
925C2×D3—21no—
926C2×D3—21no—
927C2×D3—21no—
928C2×D3—32no—
929C2×D3—32no—
930C2×D3—62no—
931C2×D3—61no—
932C2×D3—61no—
933C2×D3—61no—
934C2×D3—61no—
935C2×D3—121no—
936C2×D3—121no—
937C2×D3—124no—
938C2×D3—124no—
939C2×D3#379812yes—
940C3×C4—21no—
941C3×C4—21no—
942C3×C4—21no—
943C3×C4—41no—
944C3×C4—41no—
945C3×C4—41no—
946C3×C4—61no—
947C3×C4—61no—
948C3×C4—61no—
949C3×C4—61no—
950C3×C4—61no—
951C3×C4—61no—
952C3×C4—81no—
953C3×C4—121no—
954C3×C4—121no—
955C3×C4—121no—
956C3×C4—181no—
957C3×C4—181no—
958C3×C4—181no—
959C3×C4—181no—
960C3×C4—181no—
961Dic3—21no—
962Dic3—21no—
963Dic3—21no—
964Dic3—62no—
965Dic3—61no—
966Dic3—61no—
967Dic3—61no—
968Dic3—61no—
969Dic3—61no—
970Dic3—61no—
971Dic3—61no—
972Dic3—61no—
973Dic3—61no—
974Dic3—61no—
975Dic3—121no—
976Dic3—121no—
977Dic3—121no—
978Dic3—121no—
979Dic3—182no—
980Dic3—181no—
981Dic3—181no—
982Dic3—181no—
983Dic3—181no—
984Dic3—181no—
985Dic3—181no—
986Dic3—361no—
987Dic3—361no—
988Dic3—361no—
989Dic3—361no—
990Dic3—361no—
991Dic3—362no—
992Dic3—721no—
993C32—21no—
994C32—21no—
995C32—21no—
996C32—41no—
997C32#549511yescharacteristic, complemented
998C32#555611yescharacteristic, complemented
999C32#567911yescharacteristic, complemented
1000C23—31no—
1001C23—31no—
1002C23—31no—
1003C23—91no—
1004C23—182no—
1005C23—182no—
1006C23—361no—
1007Q8—361no—
1008D4—182no—
1009D4—361no—
1010D4—542no—
1011C2×C4—31no—
1012C2×C4—31no—
1013C2×C4—31no—
1014C2×C4—91no—
1015C2×C4—91no—
1016C2×C4—91no—
1017C2×C4—91no—
1018C2×C4—91no—
1019C2×C4—182no—
1020C2×C4—271no—
1021C2×C4—271no—
1022C2×C4—361no—
1023C2×C4—361no—
1024C2×C4—361no—
1025C2×C4—542no—
1026C2×C4D3311yescharacteristic
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—41no—
1037C2×C3—41no—
1038C2×C3—41no—
1039C2×C3—62no—
1040C2×C3—62no—
1041C2×C3—122no—
1042C2×C3—121no—
1043C2×C3—121no—
1044C2×C3—121no—
1045C2×C3—121no—
1046C2×C3—182no—
1047C2×C3—241no—
1048C2×C3—241no—
1049C2×C3C2×#379811yescharacteristic
1050C2×C3D3×#23511yescharacteristic
1051C2×C3D3×#23511yescharacteristic
1052C2×C3D3×#23711yescharacteristic
1053C2×C3D3×#23711yescharacteristic
1054C2×C3#6431211yescharacteristic
1055C2×C3#6431311yescharacteristic
1056C2×C3#6431311yescharacteristic
1057C2×C3#6431311yescharacteristic
1058D3—22no—
1059D3—41no—
1060D3—41no—
1061D3—62no—
1062D3—62no—
1063D3—122no—
1064C22—32no—
1065C22—61no—
1066C22—61no—
1067C22—61no—
1068C22—61no—
1069C22—61no—
1070C22—61no—
1071C22—61no—
1072C22—61no—
1073C22—92no—
1074C22—181no—
1075C22—181no—
1076C22—364no—
1077C22C2×D3311yescharacteristic
1078C4—21no—
1079C4—61no—
1080C4—61no—
1081C4—61no—
1082C4—181no—
1083C4—181no—
1084C4—181no—
1085C4—181no—
1086C4—181no—
1087C4—541no—
1088C4—541no—
1089C3—21no—
1090C3—21no—
1091C3—21no—
1092C3—41no—
1093C3#1059409211yescharacteristic, complemented
1094C3#1059420911yescharacteristic, complemented
1095C3#1059430011yescharacteristic, complemented
1096C2—62no—
1097C2—121no—
1098C2—121no—
1099C2—182no—
1100C2D3×#379811yescharacteristic
1101C2#1172438211yescharacteristic
1102C2#1172440811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722946C2
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. #11723673C2semidirect
2. #11723518C2semidirect
3. #11723459C2semidirect
4. #11723428C2semidirect
5. C3×#63921C2semidirect
6. C3×#63915C2semidirect
7. C3×#63902C2semidirect
8. #11723022C2semidirect
9. #11722989C2semidirect
10. #11722985C2semidirect
11. #11722970C2semidirect
12. #11722969C2semidirect
14. #11722930C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
23. C2×C3×#627C22semidirect
28. C2×C3×D3×Dic3C22semidirect
29. #88857C22semidirect
30. C3×C4×C3⋊Dic3C22semidirect
31. C3×C4×C3⋊Dic3C22semidirect
34. C32×(C2×D3)⋊C4C22semidirect
35. #88815C22semidirect
36. #88815C22semidirect
39. #88806C22semidirect
40. #88806C22semidirect
41. Dic3⋊(C3⋊Dic3)C22semidirect
42. Dic3⋊(C3⋊Dic3)C22semidirect
47. (C2×D3)⋊(C3⋊Dic3)C22semidirect
48. Dic3×C3⋊Dic3C22semidirect
49. C3×#3724C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
75. #63921D3semidirect
77. #63915D3semidirect
82. #63902D3semidirect
153. C2×#627C2×D3semidirect
164. C2×D3×Dic3C2×D3semidirect
185. C4×C3⋊Dic3C2×D3semidirect
186. C4×C3⋊Dic3C2×D3semidirect
202. C3×(C2×D3)⋊C4C2×D3semidirect
203. C3×(C2×D3)⋊C4C2×D3semidirect
220. #3724C2×D3semidirect
255. (C2×D3)⋊Dic3C2×D3semidirect
533. (C2×D3)⋊C4D32semidirect
701. C33#551semidirect
997. C32#5495semidirect
998. C32#5556semidirect
999. C32#5679semidirect
1093. C3#10594092semidirect
1094. C3#10594209semidirect
1095. C3#10594300semidirect

Maximal subgroups

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

subgroupindex
#117236732
#117235182
#117234592
#117234282
C3×#639212
C3×#639152
C3×#639022
#117230222
#117229892
#117229852
#117229702
#117229692
#117229462
#117229302
D3×(C2×D3)⋊Dic32
#105943003
#105942093
#105940923