Finite Group Databasebeta

← C3×#10594422 #13173977

Subgroups — C3×#10594422 #13173977

Order 1728.

1172 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64103C211yesmaximal, characteristic, complemented
2C32×#892C211yesmaximal, characteristic, complemented
3C32×#889C211yesmaximal, characteristic, complemented
4C3×#63910C211yesmaximal, characteristic
5C3×#63904C211yesmaximal, characteristic, complemented
6C3×#63904C211yesmaximal, characteristic, complemented
7C3×#63895C211yesmaximal, characteristic, complemented
8C3×#63894C211yesmaximal, characteristic, complemented
9C3×C4×#624C211yesmaximal, characteristic, complemented
10C3×#63858C211yesmaximal, characteristic, complemented
11C3×#63853C211yesmaximal, characteristic, complemented
12C3×#63852C211yesmaximal, characteristic, complemented
13C3×#63848C211yesmaximal, characteristic, complemented
14C3×#63837C211yesmaximal, characteristic, complemented
15C3×#63836C211yesmaximal, characteristic, complemented
16C3×#5691—31nomaximal
17C3×#5528—31nomaximal
18#10594422C311yesmaximal, characteristic, direct product factor
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×C3×#627C2211yescharacteristic
23C2×C3×#626C2211yescharacteristic
24C2×C3×#626C2211yescharacteristic
25C2×C3×#624C2211yescharacteristic
26C2×C3×#624C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C3×#3750C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×C4⋊Dic3C2211yescharacteristic
36C32×C4⋊Dic3C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic
41C32×C4×Dic3C2211yescharacteristic
42C32×C4×Dic3C2211yescharacteristic
43C32×C4×Dic3C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×#3722C2211yescharacteristic
47C3×#3722C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×#125—31no—
55C32×#117—31no—
56#64103C2×C311yescharacteristic, complemented
57C3×C4×#67—31no—
58C3×C4×#67—31no—
59C3×#898—31no—
60C3×#898—31no—
61C3×#898—31no—
62C3×#897—31no—
63C3×#896—31no—
64C3×#895—31no—
65C3×#894—31no—
66C3×#894—31no—
67C3×#894—31no—
68C3×#894—61no—
69C3×#893—31no—
70C3×#893—31no—
71C3×#893—31no—
72C3×#892—21no—
73C3×#892—31no—
74C3×#892D311yescharacteristic, complemented
75C3×#892C2×C311yescharacteristic, complemented
76C3×#889—21no—
77C3×#889D311yescharacteristic, complemented
78C3×#889C2×C311yescharacteristic, complemented
79C3×#887—31no—
80C3×#885—31no—
81C3×#884—31no—
82C3×#883—31no—
83C3×#879—31no—
84C3×#875—31no—
85C3×C4×D12—31no—
86C3×#872—31no—
87C3×C42×D3—31no—
88C3×C42×D3—31no—
89C3×C4×Dic6—31no—
90#63910C2×C311yescharacteristic
91#63904C2×C311yescharacteristic, complemented
92#63904C2×C311yescharacteristic, complemented
93#63895C2×C311yescharacteristic, complemented
94#63894C2×C311yescharacteristic, complemented
95C4×#624C2×C311yescharacteristic, complemented
96#63858C2×C311yescharacteristic, complemented
97#63853C2×C311yescharacteristic, complemented
98#63852C2×C311yescharacteristic, complemented
99#63848C2×C311yescharacteristic, complemented
100#63837C2×C311yescharacteristic, complemented
101#63836C2×C311yescharacteristic, complemented
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C3×C4⋊(C3⋊D3)—22no—
111C3×C4×C3⋊D3—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C32×C4×D3—22no—
120C3×#627—22no—
121C3×#626—22no—
122C3×#626—22no—
123C3×#624—22no—
124C3×#624—22no—
125C3×#624—22no—
126C3×#529—91no—
127#5691—31no—
128#5528—31no—
129C22×C32×C4—31no—
130C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
131C2×C4×C3⋊D3C22×C311yescharacteristic
132C2×C3×#67—31no—
133C2×C3×#67—31no—
134C2×C3×D12—31no—
135C2×C3×D12—31no—
136C2×C3×D12—31no—
137C2×C3×D12—31no—
138C2×C3×D12—61no—
139C2×C3×C4×D3—21no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3—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×C3×C4×D3C2×D311yescharacteristic
150C2×C3×C4×D3C22×C311yescharacteristic
151C2×C3×Dic6—31no—
152C2×C3×Dic6—31no—
153C2×#627C22×C311yescharacteristic
154C2×#626C22×C311yescharacteristic
155C2×#626C22×C311yescharacteristic
156C2×#624C22×C311yescharacteristic
157C2×#624C22×C311yescharacteristic
158C2×#624C22×C311yescharacteristic
159C32×C4⋊C4—21no—
160C32×C4⋊C4—21no—
161C32×C4⋊C4—21no—
162C32×C4⋊C4—31no—
163C32×C4⋊C4—31no—
164C32×C4⋊C4—31no—
165C32×C4⋊C4—31no—
166C32×C4⋊C4—31no—
167C32×C4⋊C4—31no—
168C32×C4⋊C4—41no—
169C32×C4⋊C4C2×D311yescharacteristic
170C32×C4⋊C4C2×D311yescharacteristic
171C32×C4⋊C4C22×C311yescharacteristic
172C32×C22⋊C4—31no—
173C32×C22⋊C4—31no—
174C32×C42—31no—
175C32×C42—31no—
176C32×C42—31no—
177#3752C22×C311yescharacteristic
178#3752C22×C311yescharacteristic
179#3752C22×C311yescharacteristic
180#3750C22×C311yescharacteristic
181C3×#217—31no—
182C3×#217—31no—
183C3×(C2×D3)⋊C4—21no—
184C3×(C2×D3)⋊C4—21no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
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—61no—
200C3×(C2×D3)⋊C4—61no—
201C3×(C2×D3)⋊C4—61no—
202C3×(C2×D3)⋊C4C2×D311yescharacteristic
203C3×(C2×D3)⋊C4C2×D311yescharacteristic
204C3×(C2×D3)⋊C4C22×C311yescharacteristic
205C3×(C2×D3)⋊C4C22×C311yescharacteristic
206C3×C4⋊Dic3—21no—
207C3×C4⋊Dic3—21no—
208C3×C4⋊Dic3—31no—
209C3×C4⋊Dic3—31no—
210C3×C4⋊Dic3C2×D311yescharacteristic
211C3×C4⋊Dic3C2×D311yescharacteristic
212C3×C4⋊Dic3C22×C311yescharacteristic
213C3×C4⋊Dic3C22×C311yescharacteristic
214C3×Dic3⋊C4—21no—
215C3×Dic3⋊C4—21no—
216C3×Dic3⋊C4—21no—
217C3×Dic3⋊C4—21no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—61no—
223C3×Dic3⋊C4C2×D311yescharacteristic
224C3×Dic3⋊C4C2×D311yescharacteristic
225C3×Dic3⋊C4C2×D311yescharacteristic
226C3×Dic3⋊C4C2×D311yescharacteristic
227C3×Dic3⋊C4C22×C311yescharacteristic
228C3×Dic3⋊C4C22×C311yescharacteristic
229C3×Dic3⋊C4C22×C311yescharacteristic
230C3×Dic3⋊C4C22×C311yescharacteristic
231C3×C4×Dic3—21no—
232C3×C4×Dic3—21no—
233C3×C4×Dic3—21no—
234C3×C4×Dic3—31no—
235C3×C4×Dic3—31no—
236C3×C4×Dic3—31no—
237C3×C4×Dic3—31no—
238C3×C4×Dic3—31no—
239C3×C4×Dic3—31no—
240C3×C4×Dic3C2×D311yescharacteristic
241C3×C4×Dic3C2×D311yescharacteristic
242C3×C4×Dic3C2×D311yescharacteristic
243C3×C4×Dic3C22×C311yescharacteristic
244C3×C4×Dic3C22×C311yescharacteristic
245C3×C4×Dic3C22×C311yescharacteristic
246Dic3⋊Dic3C22×C311yescharacteristic
247Dic3⋊Dic3C22×C311yescharacteristic
248#3722C22×C311yescharacteristic
249#3722C22×C311yescharacteristic
250#3722C22×C311yescharacteristic
251(C2×D3)⋊Dic3C22×C311yescharacteristic
252(C2×D3)⋊Dic3C22×C311yescharacteristic
253Dic32C22×C311yescharacteristic
254Dic32C22×C311yescharacteristic
255Dic32C22×C311yescharacteristic
256C22×C33C2411yescharacteristic
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3—21no—
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—
266C33×C4—21no—
267C33×C4—21no—
268C33×C4—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3#4112yes—
277C32×Dic3#4112yes—
278C3×#126—91no—
279C3×#126—91no—
280C3×#125—31no—
281C3×#125—31no—
282C3×#125—61no—
283C3×#124—91no—
284C3×#123—91no—
285C3×#123—91no—
286C3×C22⋊Q8—91no—
287C3×#121—91no—
288C3×C4×Q8—91no—
289C3×C4×D4—91no—
290C3×C4×D4—91no—
291C3×C4×D4—91no—
292C3×#117—31no—
293C3×#117—31no—
294C3×#117—61no—
295C3×#117—91no—
296C2×C3×C42—91no—
297C4×#67—31no—
298C4×#67—31no—
299#898—31no—
300#898—31no—
301#898—31no—
302#897—31no—
303#896—31no—
304#895—31no—
305#894—31no—
306#894—31no—
307#894—31no—
308#894—61no—
309#893—31no—
310#893—31no—
311#893—31no—
312#892—31no—
313#892C3×D311yescharacteristic, complemented
314#889C3×D311yescharacteristic, complemented
315#887—31no—
316#885—31no—
317#884—31no—
318#883—31no—
319#879—31no—
320#875—31no—
321C4×D12—31no—
322#872—31no—
323C42×D3—31no—
324C42×D3—31no—
325C4×Dic6—31no—
326C23×C32—31no—
327C22×C3⋊D3C23×C311yescharacteristic
328C22×C3⋊D3C23×C311yescharacteristic
329C22×C3×D3—21no—
330C22×C3×D3—31no—
331C22×C3×D3—31no—
332C22×C3×D3—31no—
333C22×C3×D3—31no—
334C22×C3×D3—61no—
335C22×C3×D3—61no—
336C22×C3×D3C22×D311yescharacteristic
337C22×C3×D3C23×C311yescharacteristic
338C2×C32×C4—21no—
339C2×C32×C4—21no—
340C2×C32×C4—21no—
341C2×C32×C4—21no—
342C2×C32×C4—21no—
343C2×C32×C4—21no—
344C2×C32×C4—21no—
345C2×C32×C4—21no—
346C2×C32×C4—21no—
347C2×C32×C4—31no—
348C2×C32×C4—31no—
349C2×C32×C4—31no—
350C2×C32×C4—31no—
351C2×C32×C4—31no—
352C2×C32×C4—31no—
353C2×C32×C4—31no—
354C2×C32×C4—41no—
355C2×C32×C4—41no—
356C2×C32×C4—41no—
357C2×C32×C4—62no—
358C2×C32×C4C22×D311yescharacteristic
359C2×C32×C4C22×D311yescharacteristic
360C2×C32×C4C22×D311yescharacteristic
361C2×C32×C4C22×D311yescharacteristic
362C2×C32×C4C22×D311yescharacteristic
363C2×C32×C4C22×D311yescharacteristic
364C2×C32×C4C23×C311yescharacteristic
365C2×C32×C4C23×C311yescharacteristic
366C2×C32×C4C23×C311yescharacteristic
367C2×C3⋊Dic3C23×C311yescharacteristic
368C2×C3⋊Dic3C23×C311yescharacteristic
369C4⋊(C3⋊D3)—22no—
370C4×C3⋊D3—22no—
371C3×#67—62no—
372C3×#67—62no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—21no—
377C2×C3×Dic3—21no—
378C2×C3×Dic3—21no—
379C2×C3×Dic3—21no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C23×C311yescharacteristic
394C2×C3×Dic3C23×C311yescharacteristic
395C2×C3×Dic3C23×C311yescharacteristic
396C2×C3×Dic3C23×C311yescharacteristic
397C2×C3×Dic3C23×C311yescharacteristic
398C2×C3×Dic3C23×C311yescharacteristic
399C2×C3×Dic3C23×C311yescharacteristic
400C3×D12—62no—
401C3×D12—62no—
402C3×D12—62no—
403C3×D12—62no—
404C3×D12—122no—
405C3×C4×D3—24no—
406C3×C4×D3—22no—
407C3×C4×D3—22no—
408C3×C4×D3—62no—
409C3×C4×D3—62no—
410C3×C4×D3—62no—
411C3×C4×D3—62no—
412C3×C4×D3—62no—
413C3×C4×D3—62no—
414C3×C4×D3—62no—
415C3×C4×D3—62no—
416C3×C4×D3—122no—
417C3×Dic6—62no—
418C3×Dic6—62no—
419#627—22no—
420#626—22no—
421#626—22no—
422#624—22no—
423#624—22no—
424#624—22no—
425#529—91noSylow
426C2×C33C2×#4111yescharacteristic
427C2×C33C2×#4111yescharacteristic
428C2×C33C2×#4111yescharacteristic
429C3×C3⋊D3—22no—
430C3×C3⋊D3—41no—
431C32×D3—41no—
432C2×C3×Q8—91no—
433C2×C3×D4—91no—
434C2×C3×D4—91no—
435C2×C3×D4—91no—
436C22×C3×C4—31no—
437C22×C3×C4—31no—
438C22×C3×C4—61no—
439C22×C3×C4—91no—
440C22×C3×C4—91no—
441C22×C3×C4—91no—
442C22×C3×C4—91no—
443C2×#67—31no—
444C2×#67—31no—
445C2×D12—31no—
446C2×D12—31no—
447C2×D12—31no—
448C2×D12—31no—
449C2×D12—61no—
450C2×C4×D3—31no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—31no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—31no—
457C2×C4×D3—31no—
458C2×C4×D3—61no—
459C2×C4×D3C2×C3×D311yescharacteristic
460C2×Dic6—31no—
461C2×Dic6—31no—
462C3×C4⋊C4—21no—
463C3×C4⋊C4—21no—
464C3×C4⋊C4—21no—
465C3×C4⋊C4—31no—
466C3×C4⋊C4—31no—
467C3×C4⋊C4—31no—
468C3×C4⋊C4—31no—
469C3×C4⋊C4—31no—
470C3×C4⋊C4—31no—
471C3×C4⋊C4—31no—
472C3×C4⋊C4—31no—
473C3×C4⋊C4—31no—
474C3×C4⋊C4—31no—
475C3×C4⋊C4—31no—
476C3×C4⋊C4—31no—
477C3×C4⋊C4—41no—
478C3×C4⋊C4—61no—
479C3×C4⋊C4—61no—
480C3×C4⋊C4—61no—
481C3×C4⋊C4—61no—
482C3×C4⋊C4—61no—
483C3×C4⋊C4—61no—
484C3×C4⋊C4—91no—
485C3×C4⋊C4—91no—
486C3×C4⋊C4—91no—
487C3×C4⋊C4D3211yescharacteristic
488C3×C4⋊C4C2×C3×D311yescharacteristic
489C3×C4⋊C4C2×C3×D311yescharacteristic
490C3×C22⋊C4—31no—
491C3×C22⋊C4—31no—
492C3×C22⋊C4—31no—
493C3×C22⋊C4—31no—
494C3×C22⋊C4—61no—
495C3×C22⋊C4—61no—
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×C22⋊C4—91no—
503C3×C22⋊C4—91no—
504C3×C42—31no—
505C3×C42—31no—
506C3×C42—31no—
507C3×C42—31no—
508C3×C42—31no—
509C3×C42—31no—
510C3×C42—61no—
511C3×C42—61no—
512C3×C42—61no—
513C3×C42—91no—
514C3×C42—91no—
515C3×C42—91no—
516#217—31no—
517#217—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—31no—
526(C2×D3)⋊C4—31no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4—31no—
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—61no—
533(C2×D3)⋊C4—61no—
534(C2×D3)⋊C4—61no—
535(C2×D3)⋊C4C2×C3×D311yescharacteristic
536(C2×D3)⋊C4C2×C3×D311yescharacteristic
537C4⋊Dic3—31no—
538C4⋊Dic3—31no—
539C4⋊Dic3C2×C3×D311yescharacteristic
540C4⋊Dic3C2×C3×D311yescharacteristic
541Dic3⋊C4—31no—
542Dic3⋊C4—31no—
543Dic3⋊C4—31no—
544Dic3⋊C4—31no—
545Dic3⋊C4—61no—
546Dic3⋊C4C2×C3×D311yescharacteristic
547Dic3⋊C4C2×C3×D311yescharacteristic
548Dic3⋊C4C2×C3×D311yescharacteristic
549Dic3⋊C4C2×C3×D311yescharacteristic
550C4×Dic3—31no—
551C4×Dic3—31no—
552C4×Dic3—31no—
553C4×Dic3—31no—
554C4×Dic3—31no—
555C4×Dic3—31no—
556C4×Dic3C2×C3×D311yescharacteristic
557C4×Dic3C2×C3×D311yescharacteristic
558C4×Dic3C2×C3×D311yescharacteristic
559C22×C32—21no—
560C22×C32—21no—
561C22×C32—21no—
562C22×C32—41no—
563C22×C32—61no—
564C22×C32—61no—
565C22×C32—61no—
566C22×C32C23×D311yescharacteristic
567C22×C32C23×D311yescharacteristic
568C22×C32C24×C311yescharacteristic
569C2×C3⋊D3—21no—
570C2×C3⋊D3—21no—
571C2×C3⋊D3—21no—
572C2×C3⋊D3—21no—
573C2×C3⋊D3—21no—
574C2×C3⋊D3C3×#4112yes—
575C2×C3×D3—22no—
576C2×C3×D3—21no—
577C2×C3×D3—21no—
578C2×C3×D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—21no—
581C2×C3×D3—21no—
582C2×C3×D3—32no—
583C2×C3×D3—32no—
584C2×C3×D3—41no—
585C2×C3×D3—41no—
586C2×C3×D3—62no—
587C2×C3×D3—61no—
588C2×C3×D3—61no—
589C2×C3×D3—61no—
590C2×C3×D3—61no—
591C2×C3×D3—61no—
592C2×C3×D3—61no—
593C2×C3×D3—61no—
594C2×C3×D3—61no—
595C2×C3×D3—61no—
596C2×C3×D3—61no—
597C2×C3×D3—121no—
598C2×C3×D3—121no—
599C2×C3×D3—121no—
600C2×C3×D3—121no—
601C2×C3×D3—121no—
602C32×C4—21no—
603C32×C4—22no—
604C32×C4—21no—
605C32×C4—21no—
606C32×C4—21no—
607C32×C4—21no—
608C32×C4—21no—
609C32×C4—21no—
610C32×C4—21no—
611C32×C4—21no—
612C32×C4—32no—
613C32×C4—32no—
614C32×C4—41no—
615C32×C4—41no—
616C32×C4—42no—
617C32×C4—41no—
618C32×C4—41no—
619C32×C4—41no—
620C32×C4—41no—
621C32×C4—41no—
622C32×C4—41no—
623C32×C4—61no—
624C32×C4—61no—
625C32×C4—61no—
626C32×C4—61no—
627C32×C4—61no—
628C32×C4—81no—
629C32×C4—81no—
630C3⋊Dic3—21no—
631C3⋊Dic3—21no—
632C3×Dic3—21no—
633C3×Dic3—21no—
634C3×Dic3—21no—
635C3×Dic3—21no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—22no—
643C3×Dic3—22no—
644C3×Dic3—41no—
645C3×Dic3—41no—
646C3×Dic3—41no—
647C3×Dic3—41no—
648C3×Dic3—41no—
649C3×Dic3—61no—
650C3×Dic3—61no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—121no—
654C3×Dic3—121no—
655C3×Dic3#23512yes—
656C3×Dic3#23912yes—
657C3×Dic3C3×#4112yes—
658C3×Dic3C3×#4112yes—
659#126—91no—
660#126—91no—
661#125—31no—
662#124—91no—
663#123—91no—
664#123—91no—
665C22⋊Q8—91no—
666#121—91no—
667C4×Q8—91no—
668C4×D4—91no—
669C4×D4—91no—
670C4×D4—91no—
671#117—31no—
672#117—91no—
673C2×C42—91no—
674C33#52911yescharacteristic, complemented, Sylow
675C23×C3—31no—
676C23×C3—31no—
677C23×C3—61no—
678C23×C3—91no—
679C23×C3—91no—
680C22×D3—31no—
681C22×D3—31no—
682C22×D3—31no—
683C22×D3—31no—
684C22×D3—61no—
685C22×D3—61no—
686C22×D3C22×C3×D311yescharacteristic
687C3×Q8—182no—
688C3×D4—182no—
689C3×D4—182no—
690C3×D4—182no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—21no—
697C2×C3×C4—21no—
698C2×C3×C4—21no—
699C2×C3×C4—21no—
700C2×C3×C4—31no—
701C2×C3×C4—31no—
702C2×C3×C4—31no—
703C2×C3×C4—31no—
704C2×C3×C4—31no—
705C2×C3×C4—31no—
706C2×C3×C4—31no—
707C2×C3×C4—31no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—31no—
711C2×C3×C4—31no—
712C2×C3×C4—31no—
713C2×C3×C4—31no—
714C2×C3×C4—41no—
715C2×C3×C4—41no—
716C2×C3×C4—41no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—61no—
722C2×C3×C4—61no—
723C2×C3×C4—61no—
724C2×C3×C4—62no—
725C2×C3×C4—62no—
726C2×C3×C4—64no—
727C2×C3×C4—91no—
728C2×C3×C4—91no—
729C2×C3×C4—182no—
730C2×C3×C4—182no—
731C2×C3×C4—182no—
732C2×C3×C4—182no—
733C2×C3×C4C2×D3211yescharacteristic
734C2×C3×C4C2×D3211yescharacteristic
735C2×C3×C4C2×D3211yescharacteristic
736C2×C3×C4C22×C3×D311yescharacteristic
737C2×C3×C4C22×C3×D311yescharacteristic
738C2×C3×C4C22×C3×D311yescharacteristic
739C2×C3×C4C22×C3×D311yescharacteristic
740C2×C3×C4C22×C3×D311yescharacteristic
741C2×C3×C4C22×C3×D311yescharacteristic
742#67—62no—
743#67—62no—
744C2×Dic3—31no—
745C2×Dic3—31no—
746C2×Dic3—31no—
747C2×Dic3—31no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3C22×C3×D311yescharacteristic
751C2×Dic3C22×C3×D311yescharacteristic
752C2×Dic3C22×C3×D311yescharacteristic
753C2×Dic3C22×C3×D311yescharacteristic
754C2×Dic3C22×C3×D311yescharacteristic
755C2×Dic3C22×C3×D311yescharacteristic
756C2×Dic3C22×C3×D311yescharacteristic
757D12—62no—
758D12—62no—
759D12—62no—
760D12—62no—
761D12—122no—
762C4×D3—22no—
763C4×D3—62no—
764C4×D3—62no—
765C4×D3—62no—
766C4×D3—62no—
767C4×D3—62no—
768C4×D3—62no—
769C4×D3—62no—
770C4×D3—62no—
771C4×D3—122no—
772Dic6—62no—
773Dic6—62no—
774C2×C32—21no—
775C2×C32—21no—
776C2×C32—21no—
777C2×C32—21no—
778C2×C32—21no—
779C2×C32—21no—
780C2×C32—21no—
781C2×C32—21no—
782C2×C32—21no—
783C2×C32—41no—
784C2×C32—41no—
785C2×C32—41no—
786C2×C32—121no—
787C2×C32C2×#23511yescharacteristic
788C2×C32C2×#23911yescharacteristic
789C2×C32D3×#4111yescharacteristic
790C2×C32D3×#4111yescharacteristic
791C2×C32D3×#4111yescharacteristic
792C2×C32D3×#4111yescharacteristic
793C2×C32C2×C3×#4111yescharacteristic
794C2×C32C2×C3×#4111yescharacteristic
795C2×C32C2×C3×#4111yescharacteristic
796C3⋊D3—22no—
797C3⋊D3—41no—
798C3×D3—42no—
799C3×D3—41no—
800C3×D3—41no—
801C3×D3—62no—
802C3×D3—62no—
803C3×D3—122no—
804C3×D3—121no—
805C3×D3—121no—
806C3×D3—241no—
807C2×Q8—91no—
808C2×D4—91no—
809C2×D4—91no—
810C2×D4—91no—
811C22×C4—31no—
812C22×C4—91no—
813C22×C4—91no—
814C22×C4—91no—
815C22×C4—91no—
816C4⋊C4—31no—
817C4⋊C4—31no—
818C4⋊C4—31no—
819C4⋊C4—31no—
820C4⋊C4—31no—
821C4⋊C4—31no—
822C4⋊C4—91no—
823C4⋊C4—91no—
824C4⋊C4—91no—
825C4⋊C4C3×D3211yescharacteristic
826C22⋊C4—31no—
827C22⋊C4—31no—
828C22⋊C4—91no—
829C22⋊C4—91no—
830C22⋊C4—91no—
831C22⋊C4—91no—
832C22⋊C4—91no—
833C22⋊C4—91no—
834C22⋊C4—91no—
835C22⋊C4—91no—
836C42—31no—
837C42—31no—
838C42—31no—
839C42—91no—
840C42—91no—
841C42—91no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—41no—
846C22×C3—62no—
847C22×C3—61no—
848C22×C3—61no—
849C22×C3—61no—
850C22×C3—61no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—92no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3—181no—
857C22×C3—181no—
858C22×C3—181no—
859C22×C3—181no—
860C22×C3—181no—
861C22×C3C22×D3211yescharacteristic
862C22×C3C23×C3×D311yescharacteristic
863C22×C3C23×C3×D311yescharacteristic
864C2×D3—21no—
865C2×D3—21no—
866C2×D3—21no—
867C2×D3—32no—
868C2×D3—32no—
869C2×D3—62no—
870C2×D3—61no—
871C2×D3—61no—
872C2×D3—61no—
873C2×D3—61no—
874C2×D3—61no—
875C2×D3—61no—
876C2×D3—61no—
877C2×D3—61no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C3×C4—22no—
886C3×C4—21no—
887C3×C4—21no—
888C3×C4—21no—
889C3×C4—21no—
890C3×C4—21no—
891C3×C4—21no—
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—32no—
896C3×C4—32no—
897C3×C4—32no—
898C3×C4—32no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—41no—
902C3×C4—41no—
903C3×C4—41no—
904C3×C4—41no—
905C3×C4—41no—
906C3×C4—41no—
907C3×C4—42no—
908C3×C4—62no—
909C3×C4—62no—
910C3×C4—61no—
911C3×C4—61no—
912C3×C4—61no—
913C3×C4—61no—
914C3×C4—61no—
915C3×C4—61no—
916C3×C4—61no—
917C3×C4—61no—
918C3×C4—61no—
919C3×C4—61no—
920C3×C4—81no—
921C3×C4—81no—
922C3×C4—121no—
923C3×C4—121no—
924C3×C4—121no—
925C3×C4—121no—
926C3×C4—121no—
927C3×C4—181no—
928C3×C4—181no—
929Dic3—21no—
930Dic3—21no—
931Dic3—21no—
932Dic3—21no—
933Dic3—21no—
934Dic3—61no—
935Dic3—61no—
936Dic3—61no—
937Dic3—61no—
938Dic3—121no—
939Dic3—121no—
940Dic3C3×#23512yes—
941Dic3C3×#23912yes—
942C32—21no—
943C32—21no—
944C32—21no—
945C32—41no—
946C32#552811yescharacteristic, complemented
947C32#569111yescharacteristic, complemented
948C32C3×#52911yescharacteristic, complemented
949C23—31no—
950C23—91no—
951C23—91no—
952Q8—182no—
953D4—182no—
954D4—182no—
955D4—182no—
956C2×C4—31no—
957C2×C4—31no—
958C2×C4—31no—
959C2×C4—31no—
960C2×C4—31no—
961C2×C4—31no—
962C2×C4—31no—
963C2×C4—62no—
964C2×C4—91no—
965C2×C4—91no—
966C2×C4—182no—
967C2×C4—182no—
968C2×C4—182no—
969C2×C4—182no—
970C2×C4C2×C3×D3211yescharacteristic
971C2×C4C2×C3×D3211yescharacteristic
972C2×C4C2×C3×D3211yescharacteristic
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—41no—
983C2×C3—41no—
984C2×C3—41no—
985C2×C3—122no—
986C2×C3—121no—
987C2×C3—121no—
988C2×C3—182no—
989C2×C3—361no—
990C2×C3D3×#23511yescharacteristic
991C2×C3#6431211yescharacteristic
992C2×C3D3×#23911yescharacteristic
993C2×C3C2×C3×#23511yescharacteristic
994C2×C3C2×C3×#23911yescharacteristic
995C2×C3C3×D3×#4111yescharacteristic
996C2×C3C3×D3×#4111yescharacteristic
997C2×C3C3×D3×#4111yescharacteristic
998C2×C3C3×D3×#4111yescharacteristic
999D3—41no—
1000D3—62no—
1001D3—62no—
1002D3—122no—
1003D3—121no—
1004D3—121no—
1005D3—241no—
1006C22—61no—
1007C22—61no—
1008C22—61no—
1009C22—92no—
1010C22—181no—
1011C22—181no—
1012C22—181no—
1013C22—181no—
1014C22—181no—
1015C22C22×C3×D3211yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—32no—
1020C4—32no—
1021C4—61no—
1022C4—61no—
1023C4—61no—
1024C4—61no—
1025C4—61no—
1026C4—181no—
1027C4—181no—
1028C3—21no—
1029C3—21no—
1030C3—21no—
1031C3—41no—
1032C3#1059442211yescharacteristic, direct product factor
1033C3C3×#552811yescharacteristic, complemented
1034C3C3×#569111yescharacteristic, complemented
1035C2—121no—
1036C2—182no—
1037C2—361no—
1038C2C3×D3×#23511yescharacteristic
1039C2C3×#6431211yescharacteristic
1040C2C3×D3×#23911yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC3×#63910C2
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64103C2semidirect
2. C32×#892C2semidirect
3. C32×#889C2semidirect
5. C3×#63904C2semidirect
6. C3×#63904C2semidirect
7. C3×#63895C2semidirect
8. C3×#63894C2semidirect
9. C3×C4×#624C2semidirect
10. C3×#63858C2semidirect
11. C3×#63853C2semidirect
12. C3×#63852C2semidirect
13. C3×#63848C2semidirect
14. C3×#63837C2semidirect
15. C3×#63836C2semidirect
18. #10594422C3direct (N × H)
56. #64103C2×C3semidirect
74. C3×#892D3semidirect
75. C3×#892C2×C3semidirect
77. C3×#889D3semidirect
78. C3×#889C2×C3semidirect
91. #63904C2×C3semidirect
92. #63904C2×C3semidirect
93. #63895C2×C3semidirect
94. #63894C2×C3semidirect
95. C4×#624C2×C3semidirect
96. #63858C2×C3semidirect
97. #63853C2×C3semidirect
98. #63852C2×C3semidirect
99. #63848C2×C3semidirect
100. #63837C2×C3semidirect
101. #63836C2×C3semidirect
313. #892C3×D3semidirect
314. #889C3×D3semidirect
674. C33#529semidirect
946. C32#5528semidirect
947. C32#5691semidirect
948. C32C3×#529semidirect
1032. C3#10594422direct (N × H)
1033. C3C3×#5528semidirect
1034. C3C3×#5691semidirect

Maximal subgroups

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

subgroupindex
C3×#641032
C32×#8922
C32×#8892
C3×#639102
C3×#639042
C3×#638952
C3×#638942
C3×C4×#6242
C3×#638582
C3×#638532
C3×#638522
C3×#638482
C3×#638372
C3×#638362
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