Finite Group Databasebeta

← #13168406

Subgroups — #13168406

Order 1728.

1246 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723694C211yesmaximal, characteristic, complemented
2#11723523C211yesmaximal, characteristic, complemented
3#11723491C211yesmaximal, characteristic, complemented
4#11723404C211yesmaximal, characteristic, complemented
5C3×#63921C211yesmaximal, characteristic, complemented
6C3×#63890C211yesmaximal, characteristic, complemented
7C3×#63858C211yesmaximal, characteristic, complemented
8#11723019C211yesmaximal, characteristic, complemented
9#11723009C211yesmaximal, characteristic, complemented
10#11722972C211yesmaximal, characteristic, complemented
11#11722947C211yesmaximal, characteristic
12#11722934C211yesmaximal, characteristic, complemented
13#11722929C211yesmaximal, characteristic, complemented
14#11722913C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#10594648—31nomaximal
17#10594211—31nomaximal
18#10594093—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6293C2211yescharacteristic, complemented
23C2×#6290C2211yescharacteristic
24C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×C3×#626C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
30C3×#3752C2211yescharacteristic, complemented
31C3×#3750C2211yescharacteristic, complemented
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×C4⋊Dic3C2211yescharacteristic, complemented
35#88815C2211yescharacteristic, complemented
36#88814C2211yescharacteristic
37#88814C2211yescharacteristic, complemented
38#88807C2211yescharacteristic, complemented
39#88807C2211yescharacteristic, complemented
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic, complemented
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54#64101—31no—
55#64092—31no—
56#64087—31no—
57C3×#898—31no—
58C3×#894—31no—
59C3×#886—31no—
60C3×D3×C22⋊C4—31no—
61C3×D3×C22⋊C4—31no—
62C3×#879—31no—
63#63977—31no—
64#63976—31no—
65#67⋊Dic3—31no—
66D3×#217—31no—
67C2×(C2×D3)⋊Dic3—31no—
68#63956—31no—
69#63955—31no—
70#63953—31no—
71#63922—31no—
72#63921D311yescharacteristic, complemented
73D3×(C2×D3)⋊C4—31no—
74#63915—31no—
75#63913—31no—
76#63905—31no—
77C4×#626—31no—
78#63898—31no—
79#63895—31no—
80#63893—31no—
81#63893—31no—
82#63893—61no—
83#63891—31no—
84#63891—31no—
85#63891—61no—
86#63890D311yescharacteristic, complemented
87#63881—31no—
88#63880—31no—
89#63879—31no—
90#63877—31no—
91#63862—31no—
92#63858—31no—
93#63858D311yescharacteristic, complemented
94#63857—31no—
95#63855—31no—
96#63853—31no—
97#63851—31no—
98#63850—31no—
99#63841—31no—
100#63841—31no—
101#63841—61no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊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
116C3×C4×C3⋊D3—22no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6295—22no—
122#6293—41no—
123#6290—41no—
124Dic3×C3⋊D3—41no—
125D3×C3⋊Dic3—41no—
126C3×#626—22no—
127C3×#624—41no—
128C3×D3×Dic3—22no—
129#5705—91no—
130#5658—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⋊D3—31no—
138C2×C4×C3⋊D3C2×D311yescharacteristic
139C2×#634—31no—
140C2×C3×#67—31no—
141C22×C3×Dic3—31no—
142C2×C3×D12—31no—
143C2×C3×C4×D3—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—61no—
149C2×#627—31no—
150C2×#627—31no—
151C2×#627—61no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#626C2×D311yescharacteristic
155C2×#625—31no—
156C2×#625—31no—
157C2×#625—31no—
158C2×#625—61no—
159C2×#624C2×D311yescharacteristic
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—31no—
163C2×D3×Dic3—31no—
164C2×D3×Dic3—61no—
165C2×D3×Dic3—61no—
166C2×D3×Dic3C2×D311yescharacteristic
167C32×C4⋊C4—31no—
168C32×C22⋊C4—31no—
169C32×C22⋊C4—31no—
170#3757—31no—
171#3757—31no—
172#3752—31no—
173#3752—31no—
174#3752C2×D311yescharacteristic, complemented
175C4⋊(C3⋊Dic3)—31no—
176C4⋊(C3⋊Dic3)—31no—
177C4⋊(C3⋊Dic3)—31no—
178C4⋊(C3⋊Dic3)—61no—
179C4⋊(C3⋊Dic3)—61no—
180C4⋊(C3⋊Dic3)—61no—
181C4⋊(C3⋊Dic3)—121no—
182#3750—31no—
183#3750—31no—
184#3750C2×D311yescharacteristic, complemented
185C4×C3⋊Dic3—31no—
186C4×C3⋊Dic3—31no—
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—31no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—61no—
202C3×(C2×D3)⋊C4C2×D311yescharacteristic
203C3×(C2×D3)⋊C4C2×D311yescharacteristic
204C3×(C2×D3)⋊C4C2×D311yescharacteristic
205C3×(C2×D3)⋊C4C2×D311yescharacteristic
206C3×C4⋊Dic3—21no—
207C3×C4⋊Dic3—31no—
208C3×C4⋊Dic3—31no—
209C3×C4⋊Dic3C2×D311yescharacteristic, complemented
210C3×C4⋊Dic3C2×D311yescharacteristic, complemented
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—61no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—31no—
218#3724—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3C2×D311yescharacteristic, complemented
228Dic3⋊Dic3C2×D311yescharacteristic, complemented
229#3722—31no—
230#3722—31no—
231#3722C2×D311yescharacteristic, complemented
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)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251(C2×D3)⋊Dic3C2×D311yescharacteristic
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—61no—
257Dic32—61no—
258Dic32C2×D311yescharacteristic, complemented
259C22×C33C2411yescharacteristic
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3#4112yes—
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—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#126—91no—
285C3×#123—91no—
286C2×C3×C22⋊C4—91no—
287#953—91no—
288C2×#217—91no—
289#937—91no—
290D4×Dic3—91no—
291#929—91no—
292C4×#67—91no—
293C2×(C2×D3)⋊C4—91no—
294#926—91no—
295#926—91no—
296#924—91no—
297#898—31no—
298#898—91no—
299#897—91no—
300#897—91no—
301#896—91no—
302#894—31no—
303#894—91no—
304#893—91no—
305#892—91no—
306#892—91no—
307#892—181no—
308#886—31no—
309#886—91no—
310#885—91no—
311#885—91no—
312#885—91no—
313#883—91no—
314#883—91no—
315#883—91no—
316#883—181no—
317#882—91no—
318#67⋊C4—91no—
319#67⋊C4—91no—
320D3×C22⋊C4—31no—
321D3×C22⋊C4—31no—
322D3×C22⋊C4—91no—
323#879—31no—
324#879—91no—
325#879—91no—
326#878—91no—
327#878—91no—
328#878—181no—
329#877—91no—
330C4×D12—91no—
331#872—91no—
332C23×C32—31no—
333C23×C32—31no—
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3⋊D3C22×D311yescharacteristic
336C22×C3×D3—21no—
337C22×C3×D3—21no—
338C22×C3×D3—31no—
339C22×C3×D3—31no—
340C22×C3×D3—31no—
341C22×C3×D3—31no—
342C22×C3×D3—61no—
343C22×C3×D3—61no—
344C22×C3×D3—62no—
345C22×C3×D3—62no—
346C22×C3×D3—62no—
347C22×C3×D3—62no—
348C22×C3×D3—121no—
349C22×C3×D3—121no—
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—31no—
364C2×C32×C4—41no—
365C2×C32×C4C22×D311yescharacteristic
366C2×C32×C4C22×D311yescharacteristic
367C2×C32×C4C22×D311yescharacteristic
368#638—121no—
369C2×C3⋊Dic3—31no—
370C2×C3⋊Dic3—31no—
371C2×C3⋊Dic3—31no—
372C2×C3⋊Dic3—31no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—31no—
375C2×C3⋊Dic3—61no—
376C2×C3⋊Dic3—61no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—121no—
382C2×C3⋊Dic3—121no—
383C2×C3⋊Dic3—121no—
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C2×C3⋊Dic3C22×D311yescharacteristic
388C4×C3⋊D3—22no—
389C4×C3⋊D3—121no—
390#634—121no—
391C3×#67—62no—
392C2×C3×Dic3—21no—
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—61no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—61no—
408C2×C3×Dic3—62no—
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C3×D12—62no—
418C3×C4×D3—62no—
419C3×C4×D3—62no—
420C3×C4×D3—64no—
421C3×C4×D3—62no—
422C3×C4×D3—121no—
423C3×C4×D3—121no—
424#627—121no—
425#627—121no—
426#627—122no—
427#626—22no—
428#626—62no—
429#626—62no—
430#625—62no—
431#625—121no—
432#625—121no—
433#625—122no—
434#624—41no—
435D3×Dic3—22no—
436D3×Dic3—121no—
437D3×Dic3—121no—
438D3×Dic3—122no—
439D3×Dic3—121no—
440D3×Dic3—121no—
441D3×Dic3—122no—
442#551—271noSylow
443C2×C33C2×#4111yescharacteristic
444C2×C33C2×#4111yescharacteristic
445C2×C33H(5,𝔽2)11yescharacteristic
446C3×C3⋊D3—22no—
447C3×C3⋊D3—41no—
448C32×D3—22no—
449C32×D3—41no—
450C24×C3—91no—
451C23×D3—31no—
452C23×D3—31no—
453C2×C3×D4—91no—
454C22×C3×C4—91no—
455C22×C3×C4—91no—
456C22×C3×C4—91no—
457C2×#67—31no—
458C2×#67—91no—
459C2×#67—91no—
460C2×#67—91no—
461C2×#67—91no—
462C2×#67—91no—
463C2×#67—181no—
464C22×Dic3—31no—
465C22×Dic3—91no—
466C22×Dic3—91no—
467C22×Dic3—91no—
468C22×Dic3—181no—
469C2×D12—31no—
470C2×D12—91no—
471C2×C4×D3—31no—
472C2×C4×D3—31no—
473C2×C4×D3—31no—
474C2×C4×D3—31no—
475C2×C4×D3—31no—
476C2×C4×D3—61no—
477C2×C4×D3—91no—
478C2×C4×D3—91no—
479C2×C4×D3—91no—
480C2×C4×D3—181no—
481C2×Dic6—91no—
482C2×Dic6—91no—
483C2×Dic6—91no—
484C2×Dic6—181no—
485C3×C4⋊C4—31no—
486C3×C4⋊C4—31no—
487C3×C4⋊C4—61no—
488C3×C4⋊C4—91no—
489C3×C4⋊C4—91no—
490C3×C4⋊C4—91no—
491C3×C22⋊C4—31no—
492C3×C22⋊C4—31no—
493C3×C22⋊C4—31no—
494C3×C22⋊C4—31no—
495C3×C22⋊C4—61no—
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—
504#217—31no—
505#217—31no—
506#217—31no—
507#217—31no—
508#217—91no—
509#217—91no—
510#217—91no—
511#217—91no—
512#217—91no—
513#217—91no—
514#217—91no—
515#217—91no—
516#217—181no—
517#217—181no—
518(C2×D3)⋊C4—31no—
519(C2×D3)⋊C4—31no—
520(C2×D3)⋊C4—31no—
521(C2×D3)⋊C4—31no—
522(C2×D3)⋊C4—31no—
523(C2×D3)⋊C4—31no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—61no—
527(C2×D3)⋊C4—91no—
528(C2×D3)⋊C4—91no—
529(C2×D3)⋊C4—91no—
530(C2×D3)⋊C4—91no—
531(C2×D3)⋊C4—91no—
532(C2×D3)⋊C4—91no—
533(C2×D3)⋊C4—91no—
534(C2×D3)⋊C4—91no—
535(C2×D3)⋊C4—91no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—181no—
538(C2×D3)⋊C4—181no—
539(C2×D3)⋊C4D3211yescharacteristic
540(C2×D3)⋊C4D3211yescharacteristic
541C4⋊Dic3—31no—
542C4⋊Dic3—31no—
543C4⋊Dic3—91no—
544C4⋊Dic3—91no—
545C4⋊Dic3—91no—
546C4⋊Dic3—91no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—181no—
550C4⋊Dic3—181no—
551C4⋊Dic3—181no—
552C4⋊Dic3—361no—
553C4⋊Dic3D3211yescharacteristic, complemented
554Dic3⋊C4—31no—
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
557Dic3⋊C4—31no—
558Dic3⋊C4—61no—
559Dic3⋊C4—91no—
560Dic3⋊C4—91no—
561Dic3⋊C4—91no—
562Dic3⋊C4—91no—
563Dic3⋊C4—91no—
564Dic3⋊C4—91no—
565Dic3⋊C4—181no—
566Dic3⋊C4—181no—
567C4×Dic3—31no—
568C4×Dic3—31no—
569C4×Dic3—91no—
570C4×Dic3—91no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—181no—
576C4×Dic3—181no—
577C22×C32—21no—
578C22×C32—21no—
579C22×C32—21no—
580C22×C32—32no—
581C22×C32—41no—
582C22×C32—61no—
583C22×C32—61no—
584C22×C32—61no—
585C22×C32—61no—
586C22×C32—61no—
587C22×C32C23×D311yescharacteristic
588C22×C32C23×D311yescharacteristic
589C22×C32C23×D311yescharacteristic
590C2×C3⋊D3—21no—
591C2×C3⋊D3—21no—
592C2×C3⋊D3—21no—
593C2×C3⋊D3—21no—
594C2×C3⋊D3—21no—
595C2×C3⋊D3#23712yes—
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—22no—
607C2×C3×D3—32no—
608C2×C3×D3—32no—
609C2×C3×D3—41no—
610C2×C3×D3—41no—
611C2×C3×D3—41no—
612C2×C3×D3—41no—
613C2×C3×D3—41no—
614C2×C3×D3—62no—
615C2×C3×D3—61no—
616C2×C3×D3—61no—
617C2×C3×D3—61no—
618C2×C3×D3—61no—
619C2×C3×D3—62no—
620C2×C3×D3—61no—
621C2×C3×D3—61no—
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—121no—
629C2×C3×D3—121no—
630C2×C3×D3—124no—
631C2×C3×D3—124no—
632C2×C3×D3#23512yes—
633C2×C3×D3#23712yes—
634D32—44no—
635C32×C4—21no—
636C32×C4—22no—
637C32×C4—21no—
638C32×C4—21no—
639C32×C4—41no—
640C32×C4—41no—
641C32×C4—42no—
642C32×C4—61no—
643C32×C4—61no—
644C32×C4—61no—
645C32×C4—61no—
646C3⋊Dic3—21no—
647C3⋊Dic3—21no—
648C3⋊Dic3—21no—
649C3⋊Dic3—21no—
650C3⋊Dic3—61no—
651C3⋊Dic3—61no—
652C3⋊Dic3—61no—
653C3⋊Dic3—61no—
654C3⋊Dic3—61no—
655C3⋊Dic3—61no—
656C3⋊Dic3—121no—
657C3⋊Dic3—121no—
658C3⋊Dic3—121no—
659C3⋊Dic3—121no—
660C3⋊Dic3—121no—
661C3⋊Dic3—121no—
662C3⋊Dic3—241no—
663C3⋊Dic3—241no—
664C3×Dic3—21no—
665C3×Dic3—21no—
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—41no—
676C3×Dic3—62no—
677C3×Dic3—62no—
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—
688#126—91no—
689#126—271no—
690#124—271no—
691#123—91no—
692#123—271no—
693#123—271no—
694C22⋊Q8—271no—
695C22⋊Q8—271no—
696#120—271no—
697C4×D4—271no—
698C4×D4—271no—
699#117—271no—
700#117—271no—
701C2×C22⋊C4—91no—
702C2×C22⋊C4—271no—
703C33#55111yescharacteristic, complemented, Sylow
704C23×C3—31no—
705C23×C3—31no—
706C23×C3—31no—
707C23×C3—31no—
708C23×C3—61no—
709C23×C3—61no—
710C23×C3—91no—
711C23×C3—91no—
712C23×C3—182no—
713C23×C3—182no—
714C23×C3—361no—
715C22×D3—31no—
716C22×D3—31no—
717C22×D3—31no—
718C22×D3—31no—
719C22×D3—61no—
720C22×D3—61no—
721C22×D3—62no—
722C22×D3—62no—
723C22×D3—62no—
724C22×D3—62no—
725C22×D3—121no—
726C22×D3—121no—
727C22×D3C2×D3211yescharacteristic
728C22×D3C2×D3211yescharacteristic
729C3×D4—182no—
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—31no—
740C2×C3×C4—31no—
741C2×C3×C4—41no—
742C2×C3×C4—61no—
743C2×C3×C4—61no—
744C2×C3×C4—61no—
745C2×C3×C4—61no—
746C2×C3×C4—91no—
747C2×C3×C4—91no—
748C2×C3×C4—91no—
749C2×C3×C4—91no—
750C2×C3×C4—182no—
751C2×C3×C4—182no—
752C2×C3×C4—361no—
753C2×C3×C4C2×D3211yescharacteristic
754C2×C3×C4C2×D3211yescharacteristic
755C2×C3×C4C2×D3211yescharacteristic
756#67—62no—
757#67—182no—
758#67—182no—
759#67—361no—
760#67—361no—
761#67—361no—
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—61no—
772C2×Dic3—61no—
773C2×Dic3—61no—
774C2×Dic3—61no—
775C2×Dic3—62no—
776C2×Dic3—91no—
777C2×Dic3—91no—
778C2×Dic3—91no—
779C2×Dic3—91no—
780C2×Dic3—91no—
781C2×Dic3—91no—
782C2×Dic3—181no—
783C2×Dic3—181no—
784C2×Dic3—181no—
785C2×Dic3—181no—
786C2×Dic3—181no—
787C2×Dic3—181no—
788C2×Dic3—361no—
789C2×Dic3—361no—
790C2×Dic3—361no—
791C2×Dic3—361no—
792C2×Dic3—361no—
793C2×Dic3—362no—
794C2×Dic3C2×D3211yescharacteristic
795C2×Dic3C2×D3211yescharacteristic
796C2×Dic3C2×D3211yescharacteristic
797C2×Dic3C2×D3211yescharacteristic
798D12—62no—
799D12—182no—
800C4×D3—62no—
801C4×D3—62no—
802C4×D3—64no—
803C4×D3—62no—
804C4×D3—121no—
805C4×D3—121no—
806C4×D3—361no—
807C4×D3—361no—
808C4×D3—361no—
809C4×D3—362no—
810Dic6—361no—
811Dic6—361no—
812Dic6—361no—
813Dic6—362no—
814C2×C32—21no—
815C2×C32—21no—
816C2×C32—21no—
817C2×C32—21no—
818C2×C32—21no—
819C2×C32—21no—
820C2×C32—21no—
821C2×C32—21no—
822C2×C32—21no—
823C2×C32—41no—
824C2×C32—41no—
825C2×C32—41no—
826C2×C32—62no—
827C2×C32—121no—
828C2×C32C2×#23511yescharacteristic
829C2×C32C2×#23711yescharacteristic
830C2×C32C2×#23711yescharacteristic
831C2×C32#100411yescharacteristic
832C2×C32D3×#4111yescharacteristic
833C2×C32D3×#4111yescharacteristic
834C2×C32D3×#4111yescharacteristic
835C2×C32#100911yescharacteristic
836C2×C32#100911yescharacteristic
837C3⋊D3—22no—
838C3⋊D3—41no—
839C3×D3—22no—
840C3×D3—22no—
841C3×D3—42no—
842C3×D3—41no—
843C3×D3—41no—
844C3×D3—62no—
845C3×D3—62no—
846C3×D3—81no—
847C3×D3—122no—
848C3×D3—122no—
849C3×D3—121no—
850C3×D3—121no—
851C24—91no—
852C2×Q8—271no—
853C2×D4—91no—
854C2×D4—271no—
855C2×D4—271no—
856C22×C4—91no—
857C22×C4—91no—
858C22×C4—91no—
859C22×C4—271no—
860C22×C4—271no—
861C4⋊C4—31no—
862C4⋊C4—91no—
863C4⋊C4—91no—
864C4⋊C4—91no—
865C4⋊C4—271no—
866C4⋊C4—271no—
867C4⋊C4—271no—
868C4⋊C4—271no—
869C22⋊C4—31no—
870C22⋊C4—31no—
871C22⋊C4—91no—
872C22⋊C4—91no—
873C22⋊C4—91no—
874C22⋊C4—91no—
875C22⋊C4—91no—
876C22⋊C4—91no—
877C22⋊C4—271no—
878C22⋊C4—271no—
879C22⋊C4—271no—
880C22⋊C4—271no—
881C22⋊C4—271no—
882C22⋊C4—271no—
883C42—91no—
884C42—271no—
885C42—271no—
886C22×C3—21no—
887C22×C3—21no—
888C22×C3—21no—
889C22×C3—32no—
890C22×C3—32no—
891C22×C3—41no—
892C22×C3—62no—
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—92no—
904C22×C3—121no—
905C22×C3—121no—
906C22×C3—121no—
907C22×C3—121no—
908C22×C3—121no—
909C22×C3—181no—
910C22×C3—181no—
911C22×C3—181no—
912C22×C3—181no—
913C22×C3—181no—
914C22×C3—364no—
915C22×C3C22×D3211yescharacteristic
916C22×C3C22×D3211yescharacteristic
917C22×C3C22×D3211yescharacteristic
918C2×D3—21no—
919C2×D3—21no—
920C2×D3—21no—
921C2×D3—21no—
922C2×D3—21no—
923C2×D3—32no—
924C2×D3—32no—
925C2×D3—62no—
926C2×D3—61no—
927C2×D3—61no—
928C2×D3—61no—
929C2×D3—61no—
930C2×D3—62no—
931C2×D3—61no—
932C2×D3—61no—
933C2×D3—61no—
934C2×D3—61no—
935C2×D3—61no—
936C2×D3—61no—
937C2×D3—121no—
938C2×D3—121no—
939C2×D3—121no—
940C2×D3—121no—
941C2×D3—124no—
942C2×D3—124no—
943C2×D3#379512yes—
944C3×C4—22no—
945C3×C4—21no—
946C3×C4—21no—
947C3×C4—21no—
948C3×C4—41no—
949C3×C4—41no—
950C3×C4—42no—
951C3×C4—61no—
952C3×C4—61no—
953C3×C4—61no—
954C3×C4—61no—
955C3×C4—61no—
956C3×C4—61no—
957C3×C4—61no—
958C3×C4—61no—
959C3×C4—121no—
960C3×C4—121no—
961C3×C4—121no—
962C3×C4—121no—
963C3×C4—181no—
964C3×C4—181no—
965C3×C4—181no—
966C3×C4—181no—
967Dic3—21no—
968Dic3—21no—
969Dic3—21no—
970Dic3—21no—
971Dic3—62no—
972Dic3—62no—
973Dic3—61no—
974Dic3—61no—
975Dic3—61no—
976Dic3—61no—
977Dic3—61no—
978Dic3—61no—
979Dic3—61no—
980Dic3—61no—
981Dic3—121no—
982Dic3—121no—
983Dic3—181no—
984Dic3—181no—
985Dic3—181no—
986Dic3—181no—
987Dic3—181no—
988Dic3—181no—
989Dic3—361no—
990Dic3—361no—
991Dic3—361no—
992Dic3—361no—
993Dic3—361no—
994Dic3—361no—
995Dic3—721no—
996Dic3—721no—
997C32—21no—
998C32—21no—
999C32—21no—
1000C32—41no—
1001C32#549511yescharacteristic, complemented
1002C32#565811yescharacteristic, complemented
1003C32#570511yescharacteristic, complemented
1004C23—31no—
1005C23—31no—
1006C23—91no—
1007C23—91no—
1008C23—182no—
1009C23—182no—
1010C23—361no—
1011Q8—1081no—
1012D4—182no—
1013D4—542no—
1014D4—1081no—
1015C2×C4—31no—
1016C2×C4—31no—
1017C2×C4—31no—
1018C2×C4—31no—
1019C2×C4—91no—
1020C2×C4—91no—
1021C2×C4—91no—
1022C2×C4—91no—
1023C2×C4—182no—
1024C2×C4—182no—
1025C2×C4—271no—
1026C2×C4—271no—
1027C2×C4—361no—
1028C2×C4—1081no—
1029C2×C4—1081no—
1030C2×C4D3311yescharacteristic
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—21no—
1038C2×C3—21no—
1039C2×C3—21no—
1040C2×C3—41no—
1041C2×C3—41no—
1042C2×C3—41no—
1043C2×C3—62no—
1044C2×C3—62no—
1045C2×C3—122no—
1046C2×C3—121no—
1047C2×C3—121no—
1048C2×C3—182no—
1049C2×C3—241no—
1050C2×C3—361no—
1051C2×C3C2×#379511yescharacteristic
1052C2×C3D3×#23511yescharacteristic
1053C2×C3#6430611yescharacteristic
1054C2×C3D3×#23711yescharacteristic
1055C2×C3D3×#23711yescharacteristic
1056C2×C3D3×#23711yescharacteristic
1057C2×C3#6431411yescharacteristic
1058C2×C3#6431411yescharacteristic
1059C2×C3#6432011yescharacteristic
1060D3—22no—
1061D3—41no—
1062D3—62no—
1063D3—62no—
1064D3—122no—
1065D3—122no—
1066D3—121no—
1067D3—121no—
1068C22—32no—
1069C22—61no—
1070C22—61no—
1071C22—61no—
1072C22—61no—
1073C22—61no—
1074C22—92no—
1075C22—181no—
1076C22—181no—
1077C22—181no—
1078C22—181no—
1079C22—181no—
1080C22—364no—
1081C22C2×D3311yescharacteristic
1082C4—21no—
1083C4—61no—
1084C4—61no—
1085C4—61no—
1086C4—61no—
1087C4—181no—
1088C4—181no—
1089C4—181no—
1090C4—181no—
1091C4—541no—
1092C4—541no—
1093C3—21no—
1094C3—21no—
1095C3—21no—
1096C3—41no—
1097C3#1059409311yescharacteristic, complemented
1098C3#1059421111yescharacteristic, complemented
1099C3#1059464811yescharacteristic, complemented
1100C2—62no—
1101C2—121no—
1102C2—182no—
1103C2—361no—
1104C2D3×#379511yescharacteristic
1105C2#1172438611yescharacteristic
1106C2#1172440711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722947C2
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. #11723694C2semidirect
2. #11723523C2semidirect
3. #11723491C2semidirect
4. #11723404C2semidirect
5. C3×#63921C2semidirect
6. C3×#63890C2semidirect
7. C3×#63858C2semidirect
8. #11723019C2semidirect
9. #11723009C2semidirect
10. #11722972C2semidirect
12. #11722934C2semidirect
13. #11722929C2semidirect
14. #11722913C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
22. C2×#6293C22semidirect
24. C2×Dic3×C3⋊D3C22semidirect
29. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
30. C3×#3752C22semidirect
31. C3×#3750C22semidirect
34. C32×C4⋊Dic3C22semidirect
35. #88815C22semidirect
37. #88814C22semidirect
38. #88807C22semidirect
39. #88807C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×#3722C22semidirect
53. C3×Dic32C22semidirect
72. #63921D3semidirect
86. #63890D3semidirect
93. #63858D3semidirect
174. #3752C2×D3semidirect
184. #3750C2×D3semidirect
209. C3×C4⋊Dic3C2×D3semidirect
210. C3×C4⋊Dic3C2×D3semidirect
227. Dic3⋊Dic3C2×D3semidirect
228. Dic3⋊Dic3C2×D3semidirect
231. #3722C2×D3semidirect
258. Dic32C2×D3semidirect
553. C4⋊Dic3D32semidirect
703. C33#551semidirect
1001. C32#5495semidirect
1002. C32#5658semidirect
1003. C32#5705semidirect
1097. C3#10594093semidirect
1098. C3#10594211semidirect
1099. C3#10594648semidirect

Maximal subgroups

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

subgroupindex
#117236942
#117235232
#117234912
#117234042
C3×#639212
C3×#638902
C3×#638582
#117230192
#117230092
#117229722
#117229472
#117229342
#117229292
#117229132
D3×(C2×D3)⋊Dic32
#105946483
#105942113
#105940933