Finite Group Databasebeta

← #13168575

Subgroups — #13168575

Order 1728.

1252 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723701C211yesmaximal, characteristic
2#11723501C211yesmaximal, characteristic, complemented
3#11723466C211yesmaximal, characteristic, complemented
4#11723433C211yesmaximal, characteristic, complemented
5C3×#63897C211yesmaximal, characteristic, complemented
6C3×#63895C211yesmaximal, characteristic, complemented
7C3×#63848C211yesmaximal, characteristic, complemented
8#11723007C211yesmaximal, characteristic, complemented
9#11722997C211yesmaximal, characteristic, complemented
10#11722997C211yesmaximal, characteristic, complemented
11#11722974C211yesmaximal, characteristic, complemented
12#11722934C211yesmaximal, characteristic, complemented
13#11722915C211yesmaximal, characteristic, complemented
14#11722905C211yesmaximal, characteristic, complemented
15#11722905C211yesmaximal, characteristic, complemented
16#10594655—31nomaximal
17#10594648—31nomaximal
18#10594647—31nomaximal
19C22×#1113C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×Dic3×C3⋊D3C2211yescharacteristic
24C2×Dic3×C3⋊D3C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
26C2×C3×#627C2211yescharacteristic, complemented
27C2×C3×#624C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic
29C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C3×#3752C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C32×C4⋊Dic3C2211yescharacteristic, complemented
33C32×Dic3⋊C4C2211yescharacteristic, complemented
34C32×Dic3⋊C4C2211yescharacteristic, complemented
35#88814C2211yescharacteristic
36#88807C2211yescharacteristic, complemented
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39#88803C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic, complemented
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×#3722C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64107—31no—
55#64102—31no—
56#64101—31no—
57C3×#898—31no—
58C3×#898—31no—
59C3×#897—31no—
60C3×#896—31no—
61C3×#894—31no—
62C3×#894—31no—
63#63923—31no—
64#63922—31no—
65#63922—31no—
66#63921—31no—
67#63921—31no—
68D3×(C2×D3)⋊C4—31no—
69D3×(C2×D3)⋊C4—31no—
70D3×(C2×D3)⋊C4—31no—
71D3×(C2×D3)⋊C4—31no—
72#63915—31no—
73#63907—31no—
74#63907—31no—
75C4×#626—31no—
76#63898—31no—
77#63898—31no—
78#63898—61no—
79#63897D311yescharacteristic, complemented
80#63895D311yescharacteristic, complemented
81#63893—31no—
82#63891—31no—
83#63891—31no—
84#63890—31no—
85#63890—31no—
86#63887—31no—
87#63880—31no—
88#63879—31no—
89#63878—31no—
90#63878—31no—
91#63878—61no—
92#63871—31no—
93#63862—31no—
94#63862—31no—
95#63862—61no—
96#63855—31no—
97#63853—31no—
98#63853—31no—
99#63848D311yescharacteristic, complemented
100#63841—31no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C2×#1113—22no—
107C2×#1113—22no—
108C2×#1113—41no—
109C2×C33×C4C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C3×C4⋊(C3⋊D3)—22no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6295—22no—
122#6295—41no—
123Dic3×C3⋊D3—22no—
124Dic3×C3⋊D3—41no—
125Dic3×C3⋊D3—41no—
126C3×#627—41no—
127C3×#624—22no—
128C3×#624—41no—
129#5705—91no—
130#5658—91no—
131#5637—91no—
132C22×D32—31no—
133C22×D32—31no—
134C22×D32—31no—
135C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
136C2×C4×C3⋊D3—31no—
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3—31no—
139C2×C3×D12—31no—
140C2×C3×D12—31no—
141C2×C3×D12—61no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×Dic6—31no—
147C2×C3×Dic6—31no—
148C2×#627C2×D311yescharacteristic, complemented
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—31no—
152C2×#626—31no—
153C2×#625—31no—
154C2×#625—31no—
155C2×#624C2×D311yescharacteristic
156C2×#624C2×D311yescharacteristic
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—31no—
163C2×D3×Dic3—61no—
164C2×D3×Dic3—61no—
165C2×D3×Dic3—61no—
166C32×C4⋊C4—31no—
167C32×C4⋊C4—31no—
168C32×C4⋊C4—31no—
169#3752—31no—
170#3752—31no—
171#3752—31no—
172#3752—31no—
173#3752—31no—
174#3752C2×D311yescharacteristic
175#3752C2×D311yescharacteristic
176C4⋊(C3⋊Dic3)—31no—
177C4⋊(C3⋊Dic3)—31no—
178#3750—31no—
179C4×C3⋊Dic3—31no—
180C4×C3⋊Dic3—31no—
181C4×C3⋊Dic3—31no—
182C4×C3⋊Dic3—31no—
183C4×C3⋊Dic3—61no—
184C4×C3⋊Dic3—61no—
185C4×C3⋊Dic3—61no—
186C4×C3⋊Dic3—121no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
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—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—61no—
204C3×(C2×D3)⋊C4—61no—
205C3×C4⋊Dic3—21no—
206C3×C4⋊Dic3—31no—
207C3×C4⋊Dic3—31no—
208C3×C4⋊Dic3C2×D311yescharacteristic, complemented
209C3×C4⋊Dic3C2×D311yescharacteristic, complemented
210C3×Dic3⋊C4—21no—
211C3×Dic3⋊C4—21no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4C2×D311yescharacteristic, complemented
215C3×Dic3⋊C4C2×D311yescharacteristic, complemented
216C3×Dic3⋊C4C2×D311yescharacteristic, complemented
217C3×Dic3⋊C4C2×D311yescharacteristic, complemented
218C3×C4×Dic3—31no—
219C3×C4×Dic3—31no—
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⋊Dic3—61no—
229Dic3⋊Dic3C2×D311yescharacteristic, complemented
230Dic3⋊Dic3C2×D311yescharacteristic, complemented
231#3722—31no—
232#3722C2×D311yescharacteristic
233#3722C2×D311yescharacteristic
234#3722C2×D311yescharacteristic
235#3722C2×D311yescharacteristic
236#3722C2×D311yescharacteristic, complemented
237#3722C2×D311yescharacteristic, complemented
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—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3—61no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3—61no—
255Dic32—31no—
256Dic32—31no—
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—21no—
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3#4112yes—
271C2×C3×C3⋊D3#4112yes—
272#1113—44no—
273C33×C4—21no—
274C3⋊(C3⋊Dic3)—21no—
275C3⋊(C3⋊Dic3)—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C32×Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#126—91no—
285C3×#123—91no—
286C3×C22⋊Q8—91no—
287#947—91no—
288#946—91no—
289#937—91no—
290D4×Dic3—91no—
291C4×#67—91no—
292C2×(C2×D3)⋊C4—91no—
293C2×(C2×D3)⋊C4—91no—
294#926—91no—
295#898—31no—
296#898—31no—
297#898—91no—
298#898—91no—
299#898—181no—
300#897—31no—
301#897—91no—
302#896—31no—
303#894—31no—
304#894—31no—
305#894—91no—
306#894—91no—
307#893—91no—
308#893—91no—
309#893—181no—
310#892—91no—
311#892—91no—
312#892—91no—
313#892—181no—
314#886—91no—
315#886—91no—
316#885—91no—
317#885—91no—
318#883—91no—
319#883—91no—
320#882—91no—
321#882—91no—
322#67⋊C4—91no—
323D3×C22⋊C4—91no—
324D3×C22⋊C4—91no—
325D3×C22⋊C4—91no—
326D3×C22⋊C4—91no—
327#879—91no—
328#878—91no—
329#877—91no—
330C4×D12—91no—
331#872—91no—
332C22×C3⋊D3C22×D311yescharacteristic
333C22×C3⋊D3C22×D311yescharacteristic
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3⋊D3C22×D311yescharacteristic
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—31no—
339C22×C3×D3—31no—
340C22×C3×D3—31no—
341C22×C3×D3—31no—
342C22×C3×D3—31no—
343C22×C3×D3—31no—
344C22×C3×D3—61no—
345C22×C3×D3—61no—
346C22×C3×D3—61no—
347C22×C3×D3—61no—
348C2×D32—62no—
349C2×D32—62no—
350C2×D32—62no—
351C2×D32—62no—
352C2×D32—62no—
353C2×D32—62no—
354C2×D32—121no—
355C2×D32—121no—
356C2×D32—121no—
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—31no—
365C2×C32×C4—31no—
366C2×C32×C4—41no—
367C2×C32×C4C22×D311yescharacteristic
368C2×C32×C4C22×D311yescharacteristic
369C2×C32×C4C22×D311yescharacteristic
370C2×C3⋊Dic3—31no—
371C2×C3⋊Dic3—31no—
372C2×C3⋊Dic3—31no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—31no—
375C2×C3⋊Dic3—31no—
376C2×C3⋊Dic3—61no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—61no—
382C2×C3⋊Dic3—121no—
383C2×C3⋊Dic3—121no—
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C4⋊(C3⋊D3)—22no—
387C4×C3⋊D3—62no—
388C4×C3⋊D3—121no—
389C4×C3⋊D3—121no—
390C2×C3×Dic3—21no—
391C2×C3×Dic3—21no—
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—61no—
401C2×C3×Dic3—61no—
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C3×D12—62no—
415C3×D12—62no—
416C3×D12—64no—
417C3×C4×D3—62no—
418C3×C4×D3—62no—
419C3×C4×D3—121no—
420C3×C4×D3—121no—
421C3×Dic6—121no—
422C3×Dic6—121no—
423#627—41no—
424#626—62no—
425#626—62no—
426#626—121no—
427#626—121no—
428#625—62no—
429#625—121no—
430#624—22no—
431#624—41no—
432D3×Dic3—62no—
433D3×Dic3—62no—
434D3×Dic3—64no—
435D3×Dic3—121no—
436D3×Dic3—121no—
437D3×Dic3—121no—
438D3×Dic3—121no—
439D3×Dic3—122no—
440D3×Dic3—122no—
441#551—271noSylow
442C2×C33C2×#4111yescharacteristic
443C2×C33C2×#4111yescharacteristic
444C2×C33H(5,𝔽2)11yescharacteristic
445C3×C3⋊D3—22no—
446C3×C3⋊D3—22no—
447C3×C3⋊D3—41no—
448C3×C3⋊D3—41no—
449C23×D3—91no—
450C23×D3—91no—
451C23×D3—91no—
452C2×C3×Q8—91no—
453C2×C3×D4—91no—
454C22×C3×C4—91no—
455C22×C3×C4—91no—
456C2×#67—91no—
457C2×#67—91no—
458C2×#67—91no—
459C2×#67—91no—
460C22×Dic3—91no—
461C22×Dic3—91no—
462C22×Dic3—91no—
463C2×D12—31no—
464C2×D12—31no—
465C2×D12—61no—
466C2×D12—91no—
467C2×D12—91no—
468C2×C4×D3—31no—
469C2×C4×D3—31no—
470C2×C4×D3—31no—
471C2×C4×D3—31no—
472C2×C4×D3—91no—
473C2×C4×D3—91no—
474C2×C4×D3—91no—
475C2×C4×D3—91no—
476C2×C4×D3—91no—
477C2×C4×D3—91no—
478C2×C4×D3—181no—
479C2×C4×D3—181no—
480C2×C4×D3—181no—
481C2×Dic6—31no—
482C2×Dic6—31no—
483C3×C4⋊C4—31no—
484C3×C4⋊C4—31no—
485C3×C4⋊C4—31no—
486C3×C4⋊C4—31no—
487C3×C4⋊C4—31no—
488C3×C4⋊C4—31no—
489C3×C4⋊C4—61no—
490C3×C4⋊C4—61no—
491C3×C4⋊C4—61no—
492C3×C4⋊C4—91no—
493C3×C4⋊C4—91no—
494C3×C22⋊C4—91no—
495C3×C22⋊C4—91no—
496C3×C22⋊C4—91no—
497C3×C22⋊C4—91no—
498C3×C22⋊C4—91no—
499C3×C22⋊C4—91no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C42—91no—
503#217—91no—
504#217—91no—
505#217—91no—
506#217—91no—
507#217—91no—
508#217—91no—
509(C2×D3)⋊C4—31no—
510(C2×D3)⋊C4—31no—
511(C2×D3)⋊C4—31no—
512(C2×D3)⋊C4—31no—
513(C2×D3)⋊C4—31no—
514(C2×D3)⋊C4—31no—
515(C2×D3)⋊C4—31no—
516(C2×D3)⋊C4—31no—
517(C2×D3)⋊C4—31no—
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—61no—
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—91no—
538(C2×D3)⋊C4—91no—
539(C2×D3)⋊C4—181no—
540(C2×D3)⋊C4—181no—
541(C2×D3)⋊C4—181no—
542(C2×D3)⋊C4—181no—
543(C2×D3)⋊C4—181no—
544C4⋊Dic3—31no—
545C4⋊Dic3—31no—
546C4⋊Dic3—91no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—181no—
552C4⋊Dic3—181no—
553C4⋊Dic3D3211yescharacteristic, complemented
554Dic3⋊C4—31no—
555Dic3⋊C4—31no—
556Dic3⋊C4—91no—
557Dic3⋊C4—91no—
558Dic3⋊C4—91no—
559Dic3⋊C4—91no—
560Dic3⋊C4—181no—
561Dic3⋊C4D3211yescharacteristic, complemented
562Dic3⋊C4D3211yescharacteristic, complemented
563C4×Dic3—31no—
564C4×Dic3—31no—
565C4×Dic3—91no—
566C4×Dic3—91no—
567C4×Dic3—91no—
568C4×Dic3—91no—
569C4×Dic3—91no—
570C4×Dic3—91no—
571C4×Dic3—181no—
572C4×Dic3—181no—
573C4×Dic3—181no—
574C4×Dic3—181no—
575C4×Dic3—361no—
576C22×C32—21no—
577C22×C32—21no—
578C22×C32—21no—
579C22×C32—41no—
580C22×C32C23×D311yescharacteristic
581C22×C32C23×D311yescharacteristic
582C22×C32C23×D311yescharacteristic
583C2×C3⋊D3—21no—
584C2×C3⋊D3—21no—
585C2×C3⋊D3—21no—
586C2×C3⋊D3—21no—
587C2×C3⋊D3—21no—
588C2×C3⋊D3—21no—
589C2×C3⋊D3—21no—
590C2×C3⋊D3—21no—
591C2×C3⋊D3—21no—
592C2×C3⋊D3—21no—
593C2×C3⋊D3#23712yes—
594C2×C3⋊D3#23912yes—
595C2×C3×D3—32no—
596C2×C3×D3—32no—
597C2×C3×D3—32no—
598C2×C3×D3—32no—
599C2×C3×D3—62no—
600C2×C3×D3—62no—
601C2×C3×D3—61no—
602C2×C3×D3—61no—
603C2×C3×D3—61no—
604C2×C3×D3—61no—
605C2×C3×D3—61no—
606C2×C3×D3—61no—
607C2×C3×D3—61no—
608C2×C3×D3—61no—
609C2×C3×D3—62no—
610C2×C3×D3—61no—
611C2×C3×D3—61no—
612C2×C3×D3—61no—
613C2×C3×D3—61no—
614C2×C3×D3—61no—
615C2×C3×D3—61no—
616C2×C3×D3—61no—
617C2×C3×D3—61no—
618C2×C3×D3—61no—
619C2×C3×D3—61no—
620C2×C3×D3—61no—
621C2×C3×D3—61no—
622C2×C3×D3—121no—
623C2×C3×D3—121no—
624C2×C3×D3—121no—
625C2×C3×D3—121no—
626C2×C3×D3—121no—
627C2×C3×D3—121no—
628C2×C3×D3—121no—
629C2×C3×D3—121no—
630C2×C3×D3—121no—
631D32—124no—
632D32—124no—
633D32—124no—
634C32×C4—21no—
635C32×C4—22no—
636C32×C4—21no—
637C32×C4—21no—
638C32×C4—41no—
639C32×C4—41no—
640C32×C4—42no—
641C32×C4—61no—
642C32×C4—61no—
643C32×C4—61no—
644C32×C4—61no—
645C32×C4—61no—
646C32×C4—61no—
647C3⋊Dic3—21no—
648C3⋊Dic3—21no—
649C3⋊Dic3—61no—
650C3⋊Dic3—61no—
651C3⋊Dic3—62no—
652C3⋊Dic3—62no—
653C3⋊Dic3—61no—
654C3⋊Dic3—61no—
655C3⋊Dic3—61no—
656C3⋊Dic3—61no—
657C3⋊Dic3—121no—
658C3⋊Dic3—121no—
659C3⋊Dic3—121no—
660C3⋊Dic3—121no—
661C3⋊Dic3—122no—
662C3⋊Dic3—122no—
663C3×Dic3—22no—
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—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—41no—
677C3×Dic3—41no—
678C3×Dic3—41no—
679C3×Dic3—41no—
680C3×Dic3—41no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—121no—
686C3×Dic3—121no—
687#126—91no—
688#126—271no—
689#124—271no—
690#123—91no—
691#123—271no—
692#123—271no—
693C22⋊Q8—91no—
694C22⋊Q8—271no—
695#120—271no—
696C4×D4—271no—
697C4×D4—271no—
698#117—271no—
699#117—271no—
700C2×C22⋊C4—271no—
701C2×C22⋊C4—271no—
702C33#55111yescharacteristic, complemented, Sylow
703C23×C3—91no—
704C23×C3—91no—
705C23×C3—91no—
706C23×C3—91no—
707C22×D3—31no—
708C22×D3—31no—
709C22×D3—31no—
710C22×D3—31no—
711C22×D3—31no—
712C22×D3—31no—
713C22×D3—31no—
714C22×D3—31no—
715C22×D3—61no—
716C22×D3—61no—
717C22×D3—61no—
718C22×D3—61no—
719C22×D3—182no—
720C22×D3—182no—
721C22×D3—182no—
722C22×D3—182no—
723C22×D3—182no—
724C22×D3—182no—
725C22×D3—361no—
726C22×D3—361no—
727C22×D3—361no—
728C3×Q8—361no—
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—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—61no—
750C2×C3×C4—61no—
751C2×C3×C4—61no—
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—182no—
760#67—182no—
761#67—361no—
762#67—361no—
763C2×Dic3—31no—
764C2×Dic3—31no—
765C2×Dic3—31no—
766C2×Dic3—31no—
767C2×Dic3—61no—
768C2×Dic3—61no—
769C2×Dic3—91no—
770C2×Dic3—91no—
771C2×Dic3—91no—
772C2×Dic3—91no—
773C2×Dic3—91no—
774C2×Dic3—91no—
775C2×Dic3—181no—
776C2×Dic3—181no—
777C2×Dic3—181no—
778C2×Dic3—181no—
779C2×Dic3—181no—
780C2×Dic3—181no—
781C2×Dic3—182no—
782C2×Dic3—361no—
783C2×Dic3—361no—
784C2×Dic3—361no—
785C2×Dic3—361no—
786C2×Dic3C2×D3211yescharacteristic
787C2×Dic3C2×D3211yescharacteristic
788C2×Dic3C2×D3211yescharacteristic
789C2×Dic3C2×D3211yescharacteristic
790C2×Dic3C2×D3211yescharacteristic
791C2×Dic3C2×D3211yescharacteristic
792D12—62no—
793D12—62no—
794D12—64no—
795D12—182no—
796D12—361no—
797C4×D3—62no—
798C4×D3—62no—
799C4×D3—121no—
800C4×D3—121no—
801C4×D3—182no—
802C4×D3—182no—
803C4×D3—184no—
804C4×D3—361no—
805C4×D3—361no—
806C4×D3—361no—
807C4×D3—361no—
808C4×D3—362no—
809C4×D3—362no—
810Dic6—121no—
811Dic6—121no—
812C2×C32—21no—
813C2×C32—21no—
814C2×C32—21no—
815C2×C32—21no—
816C2×C32—21no—
817C2×C32—21no—
818C2×C32—21no—
819C2×C32—21no—
820C2×C32—21no—
821C2×C32—41no—
822C2×C32—41no—
823C2×C32—41no—
824C2×C32C2×#23711yescharacteristic
825C2×C32#100411yescharacteristic
826C2×C32C2×#23911yescharacteristic
827C2×C32D3×#4111yescharacteristic
828C2×C32D3×#4111yescharacteristic
829C2×C32D3×#4111yescharacteristic
830C2×C32D3×#4111yescharacteristic
831C2×C32#100911yescharacteristic
832C2×C32#100911yescharacteristic
833C3⋊D3—22no—
834C3⋊D3—22no—
835C3⋊D3—41no—
836C3⋊D3—41no—
837C3×D3—62no—
838C3×D3—62no—
839C3×D3—62no—
840C3×D3—62no—
841C3×D3—122no—
842C3×D3—122no—
843C3×D3—122no—
844C3×D3—121no—
845C3×D3—121no—
846C3×D3—121no—
847C3×D3—121no—
848C3×D3—241no—
849C24—271no—
850C2×Q8—91no—
851C2×D4—91no—
852C2×D4—271no—
853C2×D4—271no—
854C22×C4—91no—
855C22×C4—91no—
856C22×C4—271no—
857C22×C4—271no—
858C22×C4—271no—
859C4⋊C4—31no—
860C4⋊C4—31no—
861C4⋊C4—31no—
862C4⋊C4—91no—
863C4⋊C4—91no—
864C4⋊C4—271no—
865C4⋊C4—271no—
866C4⋊C4—271no—
867C22⋊C4—91no—
868C22⋊C4—91no—
869C22⋊C4—91no—
870C22⋊C4—91no—
871C22⋊C4—91no—
872C22⋊C4—91no—
873C22⋊C4—91no—
874C22⋊C4—91no—
875C22⋊C4—271no—
876C22⋊C4—271no—
877C22⋊C4—271no—
878C22⋊C4—271no—
879C22⋊C4—271no—
880C22⋊C4—271no—
881C42—91no—
882C42—271no—
883C42—271no—
884C22×C3—21no—
885C22×C3—21no—
886C22×C3—21no—
887C22×C3—41no—
888C22×C3—92no—
889C22×C3—92no—
890C22×C3—181no—
891C22×C3—181no—
892C22×C3—181no—
893C22×C3—181no—
894C22×C3—181no—
895C22×C3—181no—
896C22×C3—181no—
897C22×C3—181no—
898C22×C3—181no—
899C22×C3—181no—
900C22×C3C22×D3211yescharacteristic
901C22×C3C22×D3211yescharacteristic
902C22×C3C22×D3211yescharacteristic
903C2×D3—32no—
904C2×D3—32no—
905C2×D3—32no—
906C2×D3—32no—
907C2×D3—62no—
908C2×D3—62no—
909C2×D3—61no—
910C2×D3—61no—
911C2×D3—61no—
912C2×D3—61no—
913C2×D3—61no—
914C2×D3—61no—
915C2×D3—61no—
916C2×D3—61no—
917C2×D3—62no—
918C2×D3—61no—
919C2×D3—61no—
920C2×D3—61no—
921C2×D3—61no—
922C2×D3—61no—
923C2×D3—61no—
924C2×D3—61no—
925C2×D3—61no—
926C2×D3—61no—
927C2×D3—61no—
928C2×D3—61no—
929C2×D3—61no—
930C2×D3—121no—
931C2×D3—121no—
932C2×D3—121no—
933C2×D3—121no—
934C2×D3—121no—
935C2×D3—121no—
936C2×D3—121no—
937C2×D3—121no—
938C2×D3—121no—
939C2×D3—364no—
940C2×D3—364no—
941C2×D3—364no—
942C3×C4—22no—
943C3×C4—21no—
944C3×C4—21no—
945C3×C4—21no—
946C3×C4—41no—
947C3×C4—41no—
948C3×C4—42no—
949C3×C4—62no—
950C3×C4—61no—
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—61no—
960C3×C4—61no—
961C3×C4—61no—
962C3×C4—121no—
963C3×C4—121no—
964C3×C4—121no—
965C3×C4—121no—
966C3×C4—121no—
967C3×C4—181no—
968C3×C4—181no—
969Dic3—21no—
970Dic3—21no—
971Dic3—21no—
972Dic3—21no—
973Dic3—21no—
974Dic3—21no—
975Dic3—61no—
976Dic3—61no—
977Dic3—61no—
978Dic3—61no—
979Dic3—121no—
980Dic3—121no—
981Dic3—182no—
982Dic3—182no—
983Dic3—181no—
984Dic3—181no—
985Dic3—181no—
986Dic3—181no—
987Dic3—181no—
988Dic3—181no—
989Dic3—361no—
990Dic3—361no—
991Dic3—361no—
992Dic3—361no—
993Dic3—362no—
994Dic3—362no—
995C32—21no—
996C32—21no—
997C32—21no—
998C32—41no—
999C32#563711yescharacteristic, complemented
1000C32#565811yescharacteristic, complemented
1001C32#570511yescharacteristic, complemented
1002C23—91no—
1003C23—91no—
1004C23—91no—
1005C23—91no—
1006C23—542no—
1007C23—542no—
1008C23—1081no—
1009Q8—361no—
1010D4—182no—
1011D4—542no—
1012D4—1081no—
1013C2×C4—31no—
1014C2×C4—31no—
1015C2×C4—31no—
1016C2×C4—31no—
1017C2×C4—31no—
1018C2×C4—31no—
1019C2×C4—91no—
1020C2×C4—91no—
1021C2×C4—182no—
1022C2×C4—271no—
1023C2×C4—271no—
1024C2×C4—361no—
1025C2×C4—542no—
1026C2×C4—1081no—
1027C2×C4—1081no—
1028C2×C4D3311yescharacteristic
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—21no—
1038C2×C3—41no—
1039C2×C3—41no—
1040C2×C3—41no—
1041C2×C3—182no—
1042C2×C3—182no—
1043C2×C3—361no—
1044C2×C3—361no—
1045C2×C3#6430611yescharacteristic
1046C2×C3#6430611yescharacteristic
1047C2×C3#6430711yescharacteristic
1048C2×C3D3×#23711yescharacteristic
1049C2×C3D3×#23711yescharacteristic
1050C2×C3#6431411yescharacteristic
1051C2×C3D3×#23911yescharacteristic
1052C2×C3D3×#23911yescharacteristic
1053C2×C3#6432011yescharacteristic
1054D3—62no—
1055D3—62no—
1056D3—62no—
1057D3—62no—
1058D3—122no—
1059D3—122no—
1060D3—122no—
1061D3—121no—
1062D3—121no—
1063D3—121no—
1064D3—121no—
1065D3—241no—
1066C22—92no—
1067C22—92no—
1068C22—181no—
1069C22—181no—
1070C22—181no—
1071C22—181no—
1072C22—181no—
1073C22—181no—
1074C22—181no—
1075C22—181no—
1076C22—181no—
1077C22—181no—
1078C22—1084no—
1079C22C2×D3311yescharacteristic
1080C4—21no—
1081C4—61no—
1082C4—61no—
1083C4—61no—
1084C4—61no—
1085C4—61no—
1086C4—61no—
1087C4—181no—
1088C4—181no—
1089C4—541no—
1090C4—541no—
1091C3—21no—
1092C3—21no—
1093C3—21no—
1094C3—41no—
1095C3#1059464711yescharacteristic, complemented
1096C3#1059464811yescharacteristic, complemented
1097C3#1059465511yescharacteristic, complemented
1098C2—182no—
1099C2—182no—
1100C2—361no—
1101C2—361no—
1102C2#1172438511yescharacteristic
1103C2#1172439111yescharacteristic
1104C2#1172440711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11723701C2
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
2. #11723501C2semidirect
3. #11723466C2semidirect
4. #11723433C2semidirect
5. C3×#63897C2semidirect
6. C3×#63895C2semidirect
7. C3×#63848C2semidirect
8. #11723007C2semidirect
9. #11722997C2semidirect
10. #11722997C2semidirect
11. #11722974C2semidirect
12. #11722934C2semidirect
13. #11722915C2semidirect
14. #11722905C2semidirect
15. #11722905C2semidirect
25. C2×Dic3×C3⋊D3C22semidirect
26. C2×C3×#627C22semidirect
29. C4×C3⋊(C3⋊Dic3)C22semidirect
32. C32×C4⋊Dic3C22semidirect
33. C32×Dic3⋊C4C22semidirect
34. C32×Dic3⋊C4C22semidirect
36. #88807C22semidirect
37. Dic3⋊(C3⋊Dic3)C22semidirect
38. Dic3⋊(C3⋊Dic3)C22semidirect
43. #88803C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
51. C3×#3722C22semidirect
52. C3×#3722C22semidirect
53. C3×Dic32C22semidirect
79. #63897D3semidirect
80. #63895D3semidirect
99. #63848D3semidirect
148. C2×#627C2×D3semidirect
208. C3×C4⋊Dic3C2×D3semidirect
209. C3×C4⋊Dic3C2×D3semidirect
214. C3×Dic3⋊C4C2×D3semidirect
215. C3×Dic3⋊C4C2×D3semidirect
216. C3×Dic3⋊C4C2×D3semidirect
217. C3×Dic3⋊C4C2×D3semidirect
229. Dic3⋊Dic3C2×D3semidirect
230. Dic3⋊Dic3C2×D3semidirect
236. #3722C2×D3semidirect
237. #3722C2×D3semidirect
258. Dic32C2×D3semidirect
553. C4⋊Dic3D32semidirect
561. Dic3⋊C4D32semidirect
562. Dic3⋊C4D32semidirect
702. C33#551semidirect
999. C32#5637semidirect
1000. C32#5658semidirect
1001. C32#5705semidirect
1095. C3#10594647semidirect
1096. C3#10594648semidirect
1097. C3#10594655semidirect

Maximal subgroups

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

subgroupindex
#117237012
#117235012
#117234662
#117234332
C3×#638972
C3×#638952
C3×#638482
#117230072
#117229972
#117229742
#117229342
#117229152
#117229052
#105946553
#105946483
#105946473