Finite Group Databasebeta

← #13172072

Subgroups — #13172072

Order 1728.

1272 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723716C211yesmaximal, characteristic, complemented
2#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4#11723603C211yesmaximal, characteristic, complemented
5C3×#63970C211yesmaximal, characteristic, complemented
6C3×#63970C211yesmaximal, characteristic, complemented
7C3×#63970C211yesmaximal, characteristic, complemented
8#11723019C211yesmaximal, characteristic, complemented
9#11723013C211yesmaximal, characteristic, complemented
10#11722989C211yesmaximal, characteristic, complemented
11#11722953C211yesmaximal, characteristic, complemented
12#11722924C211yesmaximal, characteristic, complemented
13Dic3×#625C211yesmaximal, characteristic, complemented
14#11722914C211yesmaximal, characteristic, complemented
15D3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
16#10595245—31nomaximal
17#10595189—31nomaximal
18#10595179—31nomaximal
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×D3×C3⋊Dic3C2211yescharacteristic
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×C3×#625C2211yescharacteristic
26C2×C3×#625C2211yescharacteristic
27C2×C3×#625C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29C2×C3×D3×Dic3C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34#88815C2211yescharacteristic
35#88815C2211yescharacteristic
36#88815C2211yescharacteristic
37#88813C2211yescharacteristic
38#88807C2211yescharacteristic
39#88807C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic
47Dic3×C3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54#64144—31no—
55D4×C3⋊Dic3—31no—
56D4×C3⋊Dic3—31no—
57C3×#939—31no—
58C3×#939—31no—
59C3×#939—31no—
60C3×#938—31no—
61C3×#938—31no—
62C3×#938—31no—
63#63980—31no—
64#67⋊Dic3—31no—
65#67⋊Dic3—31no—
66#67⋊Dic3—31no—
67#67⋊Dic3—31no—
68#67⋊Dic3—31no—
69#67⋊Dic3—61no—
70#67⋊Dic3—61no—
71Dic3×#67—31no—
72Dic3×#67—31no—
73Dic3×#67—31no—
74#63970—31no—
75#63970—31no—
76#63970D311yescharacteristic, complemented
77#63970D311yescharacteristic, complemented
78#63970D311yescharacteristic, complemented
79#63969—31no—
80C2×Dic3⋊Dic3—31no—
81#63962—31no—
82#63962—31no—
83#63962—31no—
84#63962—61no—
85#63956—31no—
86#63956—31no—
87#63956—31no—
88#63956—31no—
89#63955—31no—
90C4×#625—31no—
91#63891—31no—
92D3×C4⋊Dic3—31no—
93#63879—31no—
94#63878—31no—
95D3×Dic3⋊C4—31no—
96#63872—31no—
97#63862—31no—
98#63858—31no—
99#63846—31no—
100#63845—31no—
101#63841—31no—
102C23×C33C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)—41no—
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C32×#67—22no—
116C32×#67—22no—
117C32×#67—41no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121D3×C3⋊Dic3—41no—
122D3×C3⋊Dic3—41no—
123C3×#625—22no—
124C3×#625—22no—
125C3×#625—41no—
126C3×D3×Dic3—22no—
127C3×D3×Dic3—22no—
128C3×D3×Dic3—41no—
129#5618—91no—
130#5614—91no—
131#5601—91no—
132C2×C32×D4—31no—
133C2×C32×D4—31no—
134C2×C32×D4—31no—
135C22×C3⋊Dic3—31no—
136C22×C3⋊Dic3—31no—
137C22×C3⋊Dic3—31no—
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—31no—
140C22×C3⋊Dic3—61no—
141C22×C3⋊Dic3—61no—
142C22×C3⋊Dic3—61no—
143C22×C3⋊Dic3—121no—
144C2×C3×#67—21no—
145C2×C3×#67—21no—
146C2×C3×#67—21no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67C2×D311yescharacteristic
154C2×C3×#67C2×D311yescharacteristic
155C2×C3×#67C2×D311yescharacteristic
156C2×C3×#67C2×D311yescharacteristic
157C2×C3×#67C2×D311yescharacteristic
158C2×C3×#67C2×D311yescharacteristic
159C22×C3×Dic3—31no—
160C22×C3×Dic3—31no—
161C22×C3×Dic3—31no—
162C2×C3×C4×D3—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×#625C2×D311yescharacteristic
166C2×#625C2×D311yescharacteristic
167C2×#625C2×D311yescharacteristic
168C2×D3×Dic3—31no—
169C2×D3×Dic3—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—61no—
173C2×D3×Dic3—61no—
174C2×D3×Dic3C2×D311yescharacteristic
175C2×D3×Dic3C2×D311yescharacteristic
176C2×D3×Dic3C2×D311yescharacteristic
177#3757—31no—
178#3757—31no—
179#3757—31no—
180#3757—31no—
181#3757C2×D311yescharacteristic
182#3757C2×D311yescharacteristic
183#3757C2×D311yescharacteristic
184C4⋊(C3⋊Dic3)—31no—
185C4⋊(C3⋊Dic3)—31no—
186#3750—31no—
187#3750—31no—
188C4×C3⋊Dic3—31no—
189C4×C3⋊Dic3—31no—
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—31no—
199C3×#217—61no—
200C3×#217—61no—
201C3×#217—61no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×C4⋊Dic3—31no—
206C3×C4⋊Dic3—31no—
207C3×C4⋊Dic3—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—61no—
229Dic3⋊Dic3—61no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3C2×D311yescharacteristic
233Dic3⋊Dic3C2×D311yescharacteristic
234Dic3⋊Dic3C2×D311yescharacteristic
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—61no—
244(C2×D3)⋊Dic3—61no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3—61no—
247(C2×D3)⋊Dic3C2×D311yescharacteristic
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—61no—
258Dic32—61no—
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
262C22×C33C2411yescharacteristic
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⋊(C3⋊Dic3)—21no—
273C3⋊(C3⋊Dic3)—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—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3#4112yes—
283C3×#121—91no—
284C3×#121—91no—
285C3×#121—91no—
286#939—31no—
287#939—31no—
288#939—31no—
289#939—91no—
290#939—91no—
291#938—31no—
292#938—31no—
293#938—31no—
294#938—91no—
295#935—91no—
296#935—91no—
297#935—91no—
298#935—181no—
299D4×Dic3—91no—
300D4×Dic3—91no—
301D4×Dic3—91no—
302D4×Dic3—91no—
303D4×Dic3—91no—
304D4×Dic3—91no—
305D4×Dic3—181no—
306D4×Dic3—181no—
307C4×#67—91no—
308C4×#67—91no—
309C4×#67—91no—
310#926—91no—
311C2×C4⋊Dic3—91no—
312C2×Dic3⋊C4—91no—
313#898—91no—
314#892—91no—
315D3×C4⋊C4—91no—
316#890—91no—
317#890—91no—
318#889—91no—
319#886—91no—
320#886—91no—
321#883—91no—
322#67⋊C4—91no—
323#67⋊C4—91no—
324#67⋊C4—91no—
325#879—91no—
326#879—91no—
327#879—91no—
328#879—91no—
329#879—91no—
330#877—91no—
331C23×C32—21no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—31no—
335C23×C32—31no—
336C23×C32—31no—
337C23×C32—41no—
338C23×C32C22×D311yescharacteristic
339C23×C32C22×D311yescharacteristic
340C23×C32C22×D311yescharacteristic
341C22×C3×D3—21no—
342C22×C3×D3—21no—
343C22×C3×D3—21no—
344C22×C3×D3C22×D311yescharacteristic
345C22×C3×D3C22×D311yescharacteristic
346C22×C3×D3C22×D311yescharacteristic
347C22×C3×D3C22×D311yescharacteristic
348C22×C3×D3C22×D311yescharacteristic
349C22×C3×D3C22×D311yescharacteristic
350C32×D4—62no—
351C32×D4—62no—
352C32×D4—121no—
353C2×C32×C4—31no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—31no—
358C2×C3⋊Dic3—31no—
359C2×C3⋊Dic3—31no—
360C2×C3⋊Dic3—31no—
361C2×C3⋊Dic3—31no—
362C2×C3⋊Dic3—61no—
363C2×C3⋊Dic3—61no—
364C2×C3⋊Dic3—61no—
365C2×C3⋊Dic3—61no—
366C2×C3⋊Dic3—61no—
367C2×C3⋊Dic3—61no—
368C2×C3⋊Dic3—121no—
369C2×C3⋊Dic3—121no—
370C2×C3⋊Dic3—121no—
371C2×C3⋊Dic3—121no—
372C2×C3⋊Dic3—121no—
373C2×C3⋊Dic3—121no—
374C2×C3⋊Dic3—121no—
375C2×C3⋊Dic3—122no—
376C2×C3⋊Dic3—122no—
377C2×C3⋊Dic3—122no—
378C2×C3⋊Dic3—124no—
379C2×C3⋊Dic3C22×D311yescharacteristic
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C3×#67—24no—
386C3×#67—24no—
387C3×#67—22no—
388C3×#67—22no—
389C3×#67—22no—
390C3×#67—22no—
391C3×#67—41no—
392C3×#67—41no—
393C3×#67—42no—
394C3×#67—62no—
395C3×#67—62no—
396C3×#67—62no—
397C3×#67—62no—
398C3×#67—121no—
399C3×#67—121no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—21no—
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—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—62no—
422C2×C3×Dic3—62no—
423C2×C3×Dic3—121no—
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C3×C4×D3—62no—
431C3×C4×D3—62no—
432C3×C4×D3—121no—
433#625—22no—
434#625—22no—
435#625—41no—
436D3×Dic3—22no—
437D3×Dic3—22no—
438D3×Dic3—41no—
439D3×Dic3—121no—
440D3×Dic3—121no—
441D3×Dic3—121no—
442D3×Dic3—121no—
443D3×Dic3—122no—
444D3×Dic3—122no—
445#553—271noSylow
446C2×C33—41no—
447C2×C33C2×#4111yescharacteristic
448C2×C33C2×#4111yescharacteristic
449C2×C33H(5,𝔽2)11yescharacteristic
450C32×D3—22no—
451C32×D3—41no—
452C32×D3—41no—
453C2×C3×D4—31no—
454C2×C3×D4—31no—
455C2×C3×D4—31no—
456C2×C3×D4—31no—
457C2×C3×D4—31no—
458C2×C3×D4—31no—
459C2×C3×D4—61no—
460C2×C3×D4—61no—
461C2×C3×D4—61no—
462C2×C3×D4—91no—
463C2×C3×D4—91no—
464C2×C3×D4—91no—
465C22×C3×C4—91no—
466C22×C3×C4—91no—
467C22×C3×C4—91no—
468C2×#67—31no—
469C2×#67—31no—
470C2×#67—31no—
471C2×#67—31no—
472C2×#67—31no—
473C2×#67—31no—
474C2×#67D3211yescharacteristic
475C2×#67D3211yescharacteristic
476C2×#67D3211yescharacteristic
477C22×Dic3—31no—
478C22×Dic3—31no—
479C22×Dic3—31no—
480C22×Dic3—91no—
481C22×Dic3—91no—
482C22×Dic3—91no—
483C22×Dic3—91no—
484C22×Dic3—91no—
485C22×Dic3—91no—
486C22×Dic3—91no—
487C22×Dic3—181no—
488C22×Dic3—181no—
489C22×Dic3—181no—
490C22×Dic3—181no—
491C22×Dic3—181no—
492C22×Dic3—361no—
493C2×C4×D3—31no—
494C2×C4×D3—31no—
495C2×C4×D3—31no—
496C2×C4×D3—91no—
497C2×C4×D3—91no—
498C3×C4⋊C4—91no—
499C3×C4⋊C4—91no—
500C3×C4⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C22⋊C4—91no—
503C3×C22⋊C4—91no—
504C3×C22⋊C4—91no—
505C3×C22⋊C4—91no—
506C3×C22⋊C4—91no—
507#217—31no—
508#217—31no—
509#217—31no—
510#217—31no—
511#217—31no—
512#217—31no—
513#217—31no—
514#217—31no—
515#217—31no—
516#217—61no—
517#217—61no—
518#217—61no—
519#217—91no—
520#217—91no—
521#217—91no—
522#217—91no—
523#217—91no—
524#217—91no—
525#217—91no—
526#217—91no—
527#217—181no—
528#217—181no—
529#217—181no—
530#217—181no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—91no—
535(C2×D3)⋊C4—91no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—91no—
538C4⋊Dic3—31no—
539C4⋊Dic3—31no—
540C4⋊Dic3—31no—
541C4⋊Dic3—91no—
542C4⋊Dic3—91no—
543C4⋊Dic3—91no—
544C4⋊Dic3—91no—
545C4⋊Dic3—91no—
546C4⋊Dic3—91no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—181no—
551C4⋊Dic3—181no—
552Dic3⋊C4—31no—
553Dic3⋊C4—31no—
554Dic3⋊C4—31no—
555Dic3⋊C4—91no—
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—
569C4×Dic3—91no—
570C4×Dic3—91no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—181no—
579C4×Dic3—181no—
580C22×C32—21no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—22no—
584C22×C32—22no—
585C22×C32—22no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—21no—
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—32no—
596C22×C32—41no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—41no—
603C22×C32—42no—
604C22×C32—42no—
605C22×C32—42no—
606C22×C32—61no—
607C22×C32—61no—
608C22×C32—61no—
609C22×C32—61no—
610C22×C32—61no—
611C22×C32—61no—
612C22×C32—61no—
613C22×C32—61no—
614C22×C32C23×D311yescharacteristic
615C22×C32C23×D311yescharacteristic
616C22×C32C23×D311yescharacteristic
617C2×C3×D3—21no—
618C2×C3×D3—21no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—22no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—21no—
627C2×C3×D3—21no—
628C2×C3×D3—21no—
629C2×C3×D3—21no—
630C2×C3×D3—21no—
631C2×C3×D3—21no—
632C2×C3×D3—21no—
633C2×C3×D3—21no—
634C2×C3×D3—22no—
635C2×C3×D3—41no—
636C2×C3×D3—41no—
637C2×C3×D3—41no—
638C2×C3×D3—41no—
639C2×C3×D3—41no—
640C2×C3×D3—41no—
641C2×C3×D3—41no—
642C2×C3×D3#23712yes—
643C2×C3×D3#23712yes—
644C32×C4—32no—
645C32×C4—61no—
646C32×C4—61no—
647C3⋊Dic3—21no—
648C3⋊Dic3—21no—
649C3⋊Dic3—21no—
650C3⋊Dic3—21no—
651C3⋊Dic3—21no—
652C3⋊Dic3—21no—
653C3⋊Dic3—61no—
654C3⋊Dic3—61no—
655C3⋊Dic3—62no—
656C3⋊Dic3—62no—
657C3⋊Dic3—61no—
658C3⋊Dic3—61no—
659C3⋊Dic3—61no—
660C3⋊Dic3—61no—
661C3⋊Dic3—121no—
662C3⋊Dic3—121no—
663C3⋊Dic3—121no—
664C3⋊Dic3—121no—
665C3⋊Dic3—122no—
666C3⋊Dic3—122no—
667C3×Dic3—22no—
668C3×Dic3—21no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—22no—
673C3×Dic3—41no—
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—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—121no—
687C3×Dic3—121no—
688C3×Dic3—121no—
689C3×Dic3—121no—
690C3×Dic3—121no—
691C3×Dic3—121no—
692C3×Dic3#23712yes—
693C3×Dic3#23712yes—
694#126—271no—
695#126—271no—
696#125—271no—
697#123—271no—
698#123—271no—
699#121—91no—
700#121—91no—
701#121—91no—
702#121—271no—
703C4×D4—271no—
704C4×D4—271no—
705C4×D4—271no—
706C4×D4—271no—
707#117—271no—
708C2×C4⋊C4—271no—
709C33#55311yescharacteristic, complemented, Sylow
710C23×C3—21no—
711C23×C3—21no—
712C23×C3—21no—
713C23×C3—31no—
714C23×C3—31no—
715C23×C3—31no—
716C23×C3—31no—
717C23×C3—31no—
718C23×C3—31no—
719C23×C3—41no—
720C23×C3—61no—
721C23×C3—61no—
722C23×C3—61no—
723C23×C3C2×D3211yescharacteristic
724C23×C3C2×D3211yescharacteristic
725C23×C3C2×D3211yescharacteristic
726C22×D3C2×D3211yescharacteristic
727C22×D3C2×D3211yescharacteristic
728C22×D3C2×D3211yescharacteristic
729C3×D4—62no—
730C3×D4—62no—
731C3×D4—62no—
732C3×D4—62no—
733C3×D4—64no—
734C3×D4—64no—
735C3×D4—121no—
736C3×D4—121no—
737C3×D4—122no—
738C3×D4—182no—
739C3×D4—182no—
740C3×D4—361no—
741C2×C3×C4—31no—
742C2×C3×C4—31no—
743C2×C3×C4—31no—
744C2×C3×C4—31no—
745C2×C3×C4—31no—
746C2×C3×C4—31no—
747C2×C3×C4—61no—
748C2×C3×C4—61no—
749C2×C3×C4—61no—
750C2×C3×C4—91no—
751C2×C3×C4—91no—
752C2×C3×C4—91no—
753C2×C3×C4—91no—
754C2×C3×C4—91no—
755C2×C3×C4—91no—
756C2×C3×C4—182no—
757C2×C3×C4—182no—
758C2×C3×C4—361no—
759#67—22no—
760#67—22no—
761#67—41no—
762#67—62no—
763#67—62no—
764#67—62no—
765#67—62no—
766#67—121no—
767#67—121no—
768C2×Dic3—31no—
769C2×Dic3—31no—
770C2×Dic3—31no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—61no—
781C2×Dic3—61no—
782C2×Dic3—61no—
783C2×Dic3—61no—
784C2×Dic3—61no—
785C2×Dic3—61no—
786C2×Dic3—62no—
787C2×Dic3—62no—
788C2×Dic3—91no—
789C2×Dic3—91no—
790C2×Dic3—91no—
791C2×Dic3—91no—
792C2×Dic3—91no—
793C2×Dic3—91no—
794C2×Dic3—121no—
795C2×Dic3—181no—
796C2×Dic3—181no—
797C2×Dic3—181no—
798C2×Dic3—181no—
799C2×Dic3—181no—
800C2×Dic3—181no—
801C2×Dic3—361no—
802C2×Dic3—361no—
803C2×Dic3—361no—
804C2×Dic3—361no—
805C2×Dic3—361no—
806C2×Dic3—361no—
807C2×Dic3—362no—
808C2×Dic3—362no—
809C2×Dic3—361no—
810C2×Dic3—361no—
811C2×Dic3—361no—
812C2×Dic3—362no—
813C2×Dic3—362no—
814C2×Dic3—362no—
815C2×Dic3—364no—
816C2×Dic3C2×D3211yescharacteristic
817C2×Dic3C2×D3211yescharacteristic
818C2×Dic3C2×D3211yescharacteristic
819C4×D3—62no—
820C4×D3—62no—
821C4×D3—121no—
822C4×D3—361no—
823C4×D3—361no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—21no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—41no—
834C2×C32—41no—
835C2×C32—41no—
836C2×C32—42no—
837C2×C32—42no—
838C2×C32—42no—
839C2×C32—44no—
840C2×C32—41no—
841C2×C32—41no—
842C2×C32—41no—
843C2×C32—62no—
844C2×C32—121no—
845C2×C32—121no—
846C2×C32C2×#23711yescharacteristic
847C2×C32C2×#23711yescharacteristic
848C2×C32C2×#23711yescharacteristic
849C2×C32C2×#23711yescharacteristic
850C2×C32#100411yescharacteristic
851C2×C32#100411yescharacteristic
852C2×C32D3×#4111yescharacteristic
853C2×C32D3×#4111yescharacteristic
854C2×C32#100911yescharacteristic
855C3×D3—22no—
856C3×D3—22no—
857C3×D3—42no—
858C3×D3—42no—
859C3×D3—41no—
860C3×D3—41no—
861C3×D3—41no—
862C3×D3—41no—
863C3×D3—81no—
864C2×D4—31no—
865C2×D4—31no—
866C2×D4—31no—
867C2×D4—91no—
868C2×D4—91no—
869C2×D4—91no—
870C22×C4—91no—
871C22×C4—91no—
872C22×C4—91no—
873C22×C4—271no—
874C22×C4—271no—
875C22×C4—271no—
876C4⋊C4—91no—
877C4⋊C4—91no—
878C4⋊C4—91no—
879C4⋊C4—271no—
880C4⋊C4—271no—
881C4⋊C4—271no—
882C4⋊C4—271no—
883C4⋊C4—271no—
884C4⋊C4—271no—
885C4⋊C4—271no—
886C22⋊C4—91no—
887C22⋊C4—91no—
888C22⋊C4—91no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C22⋊C4—91no—
892C22⋊C4—271no—
893C22⋊C4—271no—
894C22⋊C4—271no—
895C22⋊C4—271no—
896C42—271no—
897C42—271no—
898C42—271no—
899C22×C3—22no—
900C22×C3—22no—
901C22×C3—22no—
902C22×C3—21no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—21no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—21no—
912C22×C3—21no—
913C22×C3—21no—
914C22×C3—32no—
915C22×C3—32no—
916C22×C3—41no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—41no—
921C22×C3—41no—
922C22×C3—42no—
923C22×C3—42no—
924C22×C3—42no—
925C22×C3—41no—
926C22×C3—62no—
927C22×C3—62no—
928C22×C3—61no—
929C22×C3—61no—
930C22×C3—61no—
931C22×C3—61no—
932C22×C3—61no—
933C22×C3—61no—
934C22×C3—61no—
935C22×C3—61no—
936C22×C3—61no—
937C22×C3—61no—
938C22×C3—61no—
939C22×C3—61no—
940C22×C3—61no—
941C22×C3—61no—
942C22×C3—61no—
943C22×C3—61no—
944C22×C3—121no—
945C22×C3—121no—
946C22×C3—121no—
947C22×C3—121no—
948C22×C3—121no—
949C22×C3—121no—
950C22×C3—121no—
951C22×C3C22×D3211yescharacteristic
952C22×C3C22×D3211yescharacteristic
953C22×C3C22×D3211yescharacteristic
954C2×D3—21no—
955C2×D3—21no—
956C2×D3—21no—
957C2×D3—21no—
958C2×D3—21no—
959C2×D3—21no—
960C2×D3—21no—
961C2×D3—21no—
962C2×D3#380512yes—
963C3×C4—32no—
964C3×C4—32no—
965C3×C4—62no—
966C3×C4—62no—
967C3×C4—61no—
968C3×C4—61no—
969C3×C4—61no—
970C3×C4—61no—
971C3×C4—121no—
972C3×C4—181no—
973C3×C4—181no—
974C3×C4—181no—
975C3×C4—181no—
976C3×C4—181no—
977C3×C4—181no—
978Dic3—21no—
979Dic3—21no—
980Dic3—61no—
981Dic3—61no—
982Dic3—61no—
983Dic3—61no—
984Dic3—61no—
985Dic3—61no—
986Dic3—61no—
987Dic3—61no—
988Dic3—61no—
989Dic3—61no—
990Dic3—61no—
991Dic3—61no—
992Dic3—121no—
993Dic3—121no—
994Dic3—121no—
995Dic3—121no—
996Dic3—121no—
997Dic3—121no—
998Dic3—182no—
999Dic3—182no—
1000Dic3—181no—
1001Dic3—181no—
1002Dic3—181no—
1003Dic3—181no—
1004Dic3—181no—
1005Dic3—181no—
1006Dic3—361no—
1007Dic3—361no—
1008Dic3—361no—
1009Dic3—361no—
1010Dic3—362no—
1011Dic3—362no—
1012Dic3#380512yes—
1013C32—21no—
1014C32—21no—
1015C32—21no—
1016C32—41no—
1017C32#560111yescharacteristic, complemented
1018C32#561411yescharacteristic, complemented
1019C32#561811yescharacteristic, complemented
1020C23—31no—
1021C23—31no—
1022C23—31no—
1023C23D3311yescharacteristic
1024D4—62no—
1025D4—62no—
1026D4—121no—
1027D4—182no—
1028D4—182no—
1029D4—361no—
1030C2×C4—31no—
1031C2×C4—31no—
1032C2×C4—31no—
1033C2×C4—91no—
1034C2×C4—91no—
1035C2×C4—91no—
1036C2×C4—91no—
1037C2×C4—91no—
1038C2×C4—91no—
1039C2×C4—182no—
1040C2×C4—182no—
1041C2×C4—271no—
1042C2×C4—271no—
1043C2×C4—361no—
1044C2×C4—1081no—
1045C2×C4—1081no—
1046C2×C4—1081no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—42no—
1057C2×C3—42no—
1058C2×C3—42no—
1059C2×C3—44no—
1060C2×C3—41no—
1061C2×C3—41no—
1062C2×C3—41no—
1063C2×C3—41no—
1064C2×C3—41no—
1065C2×C3—41no—
1066C2×C3—62no—
1067C2×C3—62no—
1068C2×C3—122no—
1069C2×C3—122no—
1070C2×C3—121no—
1071C2×C3—121no—
1072C2×C3—121no—
1073C2×C3—121no—
1074C2×C3—241no—
1075C2×C3D3×#23711yescharacteristic
1076C2×C3D3×#23711yescharacteristic
1077C2×C3D3×#23711yescharacteristic
1078C2×C3D3×#23711yescharacteristic
1079C2×C3#6431411yescharacteristic
1080C2×C3#6431411yescharacteristic
1081C2×C3C2×#380511yescharacteristic
1082C2×C3C2×#380511yescharacteristic
1083C2×C3#6433011yescharacteristic
1084D3—22no—
1085D3—41no—
1086D3—41no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—32no—
1091C22—61no—
1092C22—61no—
1093C22—61no—
1094C22—61no—
1095C22—61no—
1096C22—61no—
1097C22—61no—
1098C22—61no—
1099C22C2×D3311yescharacteristic
1100C4—32no—
1101C4—61no—
1102C4—61no—
1103C4—181no—
1104C4—181no—
1105C4—181no—
1106C4—181no—
1107C4—181no—
1108C4—181no—
1109C4—541no—
1110C4—541no—
1111C3—21no—
1112C3—21no—
1113C3—21no—
1114C3—41no—
1115C3#1059517911yescharacteristic, complemented
1116C3#1059518911yescharacteristic, complemented
1117C3#1059524511yescharacteristic, complemented
1118C2—41no—
1119C2—62no—
1120C2—121no—
1121C2—121no—
1122C2D3×#380511yescharacteristic
1123C2D3×#380511yescharacteristic
1124C2#1172441911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723716C2semidirect
2. #67⋊(C3⋊Dic3)C2semidirect
3. #67⋊(C3⋊Dic3)C2semidirect
4. #11723603C2semidirect
5. C3×#63970C2semidirect
6. C3×#63970C2semidirect
7. C3×#63970C2semidirect
8. #11723019C2semidirect
9. #11723013C2semidirect
10. #11722989C2semidirect
11. #11722953C2semidirect
12. #11722924C2semidirect
13. Dic3×#625C2semidirect
14. #11722914C2semidirect
15. D3×Dic3⋊Dic3C2semidirect
76. #63970D3semidirect
77. #63970D3semidirect
78. #63970D3semidirect
709. C33#553semidirect
1017. C32#5601semidirect
1018. C32#5614semidirect
1019. C32#5618semidirect
1115. C3#10595179semidirect
1116. C3#10595189semidirect
1117. C3#10595245semidirect

Maximal subgroups

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

subgroupindex
#117237162
#67⋊(C3⋊Dic3)2
#117236032
C3×#639702
#117230192
#117230132
#117229892
#117229532
#117229242
Dic3×#6252
#117229142
D3×Dic3⋊Dic32
#105952453
#105951893
#105951793