Finite Group Databasebeta

← C3×#10594446 #13173992

Subgroups — C3×#10594446 #13173992

Order 1728.

978 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64098C211yesmaximal, characteristic, complemented
2C32×#898C211yesmaximal, characteristic
3C32×#888C211yesmaximal, characteristic, complemented
4C3×#63887C211yesmaximal, characteristic
5C3×#63887C211yesmaximal, characteristic
6C3×#63877C211yesmaximal, characteristic
7C3×#63867C211yesmaximal, characteristic, complemented
8C3×#63867C211yesmaximal, characteristic, complemented
9C3×#63862C211yesmaximal, characteristic
10C3×#63861C211yesmaximal, characteristic
11C3×#63858C211yesmaximal, characteristic
12C3×#63847C211yesmaximal, characteristic, complemented
13C3×#63846C211yesmaximal, characteristic, complemented
14C3×#63843C211yesmaximal, characteristic, complemented
15C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
16C3×#5731—31nomaximal
17C3×#5701—31nomaximal
18#10594446C311yesmaximal, characteristic, direct product factor
19C2×C32×Dic6C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic
21C2×C3×D3×Dic3C2211yescharacteristic
22C33×C4⋊C4C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×#3750C2211yescharacteristic
25C3×#3750C2211yescharacteristic
26C3×#3750C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C32×(C2×D3)⋊C4C2211yescharacteristic
30C32×(C2×D3)⋊C4C2211yescharacteristic
31C32×(C2×D3)⋊C4C2211yescharacteristic
32C32×C4⋊Dic3C2211yescharacteristic
33C32×C4⋊Dic3C2211yescharacteristic
34C32×Dic3⋊C4C2211yescharacteristic
35C32×Dic3⋊C4C2211yescharacteristic
36C32×Dic3⋊C4C2211yescharacteristic
37C32×C4×Dic3C2211yescharacteristic
38C32×C4×Dic3C2211yescharacteristic
39C3×#3724C2211yescharacteristic
40C3×#3724C2211yescharacteristic
41C3×Dic3⋊Dic3C2211yescharacteristic
42C3×Dic3⋊Dic3C2211yescharacteristic
43C3×Dic3⋊Dic3C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×C4⋊Q8—31no—
55C32×#126—31no—
56#64098C2×C311yescharacteristic, complemented
57C3×#946—31no—
58C3×#946—31no—
59C3×Q8×Dic3—31no—
60C3×Q8×Dic3—31no—
61C3×#898—21no—
62C3×#898—31no—
63C3×#898—31no—
64C3×#898—31no—
65C3×#898D311yescharacteristic
66C3×#898C2×C311yescharacteristic
67C3×#890—31no—
68C3×#889—31no—
69C3×#889—31no—
70C3×#889—31no—
71C3×#889—31no—
72C3×#889—31no—
73C3×#889—31no—
74C3×#889—31no—
75C3×#889—61no—
76C3×#888—21no—
77C3×#888D311yescharacteristic, complemented
78C3×#888C2×C311yescharacteristic, complemented
79C3×#887—31no—
80C3×#879—31no—
81C3×#879—31no—
82C3×#879—31no—
83C3×#878—31no—
84C3×#878—31no—
85C3×#877—31no—
86C3×#872—31no—
87C3×#870—31no—
88C3×#870—31no—
89C3×C4×Dic6—31no—
90#63887C2×C311yescharacteristic
91#63887C2×C311yescharacteristic
92#63877C2×C311yescharacteristic
93#63867C2×C311yescharacteristic, complemented
94#63867C2×C311yescharacteristic, complemented
95#63862C2×C311yescharacteristic
96#63861C2×C311yescharacteristic
97#63858C2×C311yescharacteristic
98#63847C2×C311yescharacteristic, complemented
99#63846C2×C311yescharacteristic, complemented
100#63843C2×C311yescharacteristic, complemented
101Dic3×Dic6C2×C311yescharacteristic, complemented
102C22×C32×D3C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×Dic6—22no—
118C32×Dic6—22no—
119C3×D3×Dic3—22no—
120C3×#541—91no—
121#5731—31no—
122#5701—31no—
123C2×C32×Q8—31no—
124C2×C32×Q8—31no—
125C22×C3×Dic3—31no—
126C2×C3×C4×D3—31no—
127C2×C3×Dic6—21no—
128C2×C3×Dic6—21no—
129C2×C3×Dic6C2×D311yescharacteristic
130C2×C3×Dic6C2×D311yescharacteristic
131C2×C3×Dic6C22×C311yescharacteristic
132C2×C3×Dic6C22×C311yescharacteristic
133C2×D3×Dic3C22×C311yescharacteristic
134C32×C4⋊C4—21no—
135C32×C4⋊C4—21no—
136C32×C4⋊C4—21no—
137C32×C4⋊C4—31no—
138C32×C4⋊C4—31no—
139C32×C4⋊C4—31no—
140C32×C4⋊C4—31no—
141C32×C4⋊C4—31no—
142C32×C4⋊C4—41no—
143C32×C4⋊C4C2×D311yescharacteristic
144C32×C4⋊C4C2×D311yescharacteristic
145C32×C4⋊C4C22×C311yescharacteristic
146C32×C22⋊C4—31no—
147C32×C22⋊C4—31no—
148C32×C22⋊C4—31no—
149C32×C42—31no—
150C32×C42—31no—
151C4⋊(C3⋊Dic3)C22×C311yescharacteristic
152#3750C22×C311yescharacteristic
153#3750C22×C311yescharacteristic
154#3750C22×C311yescharacteristic
155#3750C22×C311yescharacteristic
156C4×C3⋊Dic3C22×C311yescharacteristic
157C3×#217—31no—
158C3×#217—31no—
159C3×#217—31no—
160C3×(C2×D3)⋊C4—21no—
161C3×(C2×D3)⋊C4—21no—
162C3×(C2×D3)⋊C4—21no—
163C3×(C2×D3)⋊C4—31no—
164C3×(C2×D3)⋊C4—31no—
165C3×(C2×D3)⋊C4—31no—
166C3×(C2×D3)⋊C4C2×D311yescharacteristic
167C3×(C2×D3)⋊C4C2×D311yescharacteristic
168C3×(C2×D3)⋊C4C2×D311yescharacteristic
169C3×(C2×D3)⋊C4C22×C311yescharacteristic
170C3×(C2×D3)⋊C4C22×C311yescharacteristic
171C3×(C2×D3)⋊C4C22×C311yescharacteristic
172C3×C4⋊Dic3—21no—
173C3×C4⋊Dic3—21no—
174C3×C4⋊Dic3—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—61no—
184C3×C4⋊Dic3C2×D311yescharacteristic
185C3×C4⋊Dic3C2×D311yescharacteristic
186C3×C4⋊Dic3C22×C311yescharacteristic
187C3×C4⋊Dic3C22×C311yescharacteristic
188C3×Dic3⋊C4—21no—
189C3×Dic3⋊C4—21no—
190C3×Dic3⋊C4—21no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—61no—
211C3×Dic3⋊C4—61no—
212C3×Dic3⋊C4—61no—
213C3×Dic3⋊C4—61no—
214C3×Dic3⋊C4C2×D311yescharacteristic
215C3×Dic3⋊C4C2×D311yescharacteristic
216C3×Dic3⋊C4C2×D311yescharacteristic
217C3×Dic3⋊C4C22×C311yescharacteristic
218C3×Dic3⋊C4C22×C311yescharacteristic
219C3×Dic3⋊C4C22×C311yescharacteristic
220C3×C4×Dic3—21no—
221C3×C4×Dic3—21no—
222C3×C4×Dic3—31no—
223C3×C4×Dic3—31no—
224C3×C4×Dic3—31no—
225C3×C4×Dic3—31no—
226C3×C4×Dic3—31no—
227C3×C4×Dic3—31no—
228C3×C4×Dic3—31no—
229C3×C4×Dic3—31no—
230C3×C4×Dic3—61no—
231C3×C4×Dic3C2×D311yescharacteristic
232C3×C4×Dic3C2×D311yescharacteristic
233C3×C4×Dic3C22×C311yescharacteristic
234C3×C4×Dic3C22×C311yescharacteristic
235#3724C22×C311yescharacteristic
236#3724C22×C311yescharacteristic
237Dic3⋊Dic3C22×C311yescharacteristic
238Dic3⋊Dic3C22×C311yescharacteristic
239Dic3⋊Dic3C22×C311yescharacteristic
240Dic3⋊Dic3C22×C311yescharacteristic
241Dic3⋊Dic3C22×C311yescharacteristic
242Dic3⋊Dic3C22×C311yescharacteristic
243Dic3⋊Dic3C22×C311yescharacteristic
244(C2×D3)⋊Dic3C22×C311yescharacteristic
245(C2×D3)⋊Dic3C22×C311yescharacteristic
246(C2×D3)⋊Dic3C22×C311yescharacteristic
247Dic32C22×C311yescharacteristic
248Dic32C22×C311yescharacteristic
249Dic32C22×C311yescharacteristic
250C22×C33C2411yescharacteristic
251C2×C32×D3—21no—
252C2×C32×D3—21no—
253C2×C32×D3—21no—
254C33×C4—21no—
255C33×C4—21no—
256C33×C4—21no—
257C3×C3⋊Dic3—21no—
258C3×C3⋊Dic3—21no—
259C3×C3⋊Dic3—21no—
260C3×C3⋊Dic3—21no—
261C32×Dic3—21no—
262C32×Dic3—21no—
263C32×Dic3—21no—
264C32×Dic3—21no—
265C32×Dic3—21no—
266C32×Dic3—21no—
267C32×Dic3#4112yes—
268C3×C4⋊Q8—31no—
269C3×C4⋊Q8—31no—
270C3×C4⋊Q8—61no—
271C3×#126—31no—
272C3×#126—31no—
273C3×#126—61no—
274C3×#126—91no—
275C3×#126—91no—
276C3×#126—91no—
277C3×#125—91no—
278C3×#125—91no—
279C3×#125—91no—
280C3×#125—91no—
281C3×#125—91no—
282C3×C22⋊Q8—91no—
283C3×C22⋊Q8—91no—
284C3×C4×Q8—91no—
285C3×C4×Q8—91no—
286C3×#117—91no—
287#946—31no—
288#946—31no—
289Q8×Dic3—31no—
290Q8×Dic3—31no—
291#898—31no—
292#898—31no—
293#898—31no—
294#898C3×D311yescharacteristic
295#890—31no—
296#889—31no—
297#889—31no—
298#889—31no—
299#889—31no—
300#889—31no—
301#889—31no—
302#889—31no—
303#889—61no—
304#888C3×D311yescharacteristic, complemented
305#887—31no—
306#879—31no—
307#879—31no—
308#879—31no—
309#878—31no—
310#878—31no—
311#877—31no—
312#872—31no—
313#870—31no—
314#870—31no—
315C4×Dic6—31no—
316C23×C32—31no—
317C22×C3×D3—21no—
318C22×C3×D3C22×D311yescharacteristic
319C22×C3×D3C23×C311yescharacteristic
320C32×Q8—62no—
321C32×Q8—62no—
322C2×C32×C4—21no—
323C2×C32×C4—21no—
324C2×C32×C4—21no—
325C2×C32×C4—21no—
326C2×C32×C4—21no—
327C2×C32×C4—21no—
328C2×C32×C4—21no—
329C2×C32×C4—21no—
330C2×C32×C4—21no—
331C2×C32×C4—31no—
332C2×C32×C4—31no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—41no—
339C2×C32×C4—41no—
340C2×C32×C4—41no—
341C2×C32×C4C22×D311yescharacteristic
342C2×C32×C4C22×D311yescharacteristic
343C2×C32×C4C22×D311yescharacteristic
344C2×C32×C4C22×D311yescharacteristic
345C2×C32×C4C22×D311yescharacteristic
346C2×C32×C4C22×D311yescharacteristic
347C2×C32×C4C23×C311yescharacteristic
348C2×C32×C4C23×C311yescharacteristic
349C2×C32×C4C23×C311yescharacteristic
350C2×C3⋊Dic3C23×C311yescharacteristic
351C2×C3⋊Dic3C23×C311yescharacteristic
352C2×C3⋊Dic3C23×C311yescharacteristic
353C2×C3⋊Dic3C23×C311yescharacteristic
354C2×C3×Dic3—21no—
355C2×C3×Dic3—21no—
356C2×C3×Dic3—21no—
357C2×C3×Dic3—21no—
358C2×C3×Dic3—21no—
359C2×C3×Dic3—21no—
360C2×C3×Dic3—21no—
361C2×C3×Dic3—31no—
362C2×C3×Dic3—31no—
363C2×C3×Dic3—31no—
364C2×C3×Dic3—31no—
365C2×C3×Dic3—31no—
366C2×C3×Dic3—31no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—61no—
370C2×C3×Dic3—61no—
371C2×C3×Dic3—61no—
372C2×C3×Dic3—61no—
373C2×C3×Dic3—62no—
374C2×C3×Dic3C22×D311yescharacteristic
375C2×C3×Dic3C22×D311yescharacteristic
376C2×C3×Dic3C22×D311yescharacteristic
377C2×C3×Dic3C22×D311yescharacteristic
378C2×C3×Dic3C22×D311yescharacteristic
379C2×C3×Dic3C22×D311yescharacteristic
380C2×C3×Dic3C22×D311yescharacteristic
381C2×C3×Dic3C23×C311yescharacteristic
382C2×C3×Dic3C23×C311yescharacteristic
383C2×C3×Dic3C23×C311yescharacteristic
384C2×C3×Dic3C23×C311yescharacteristic
385C2×C3×Dic3C23×C311yescharacteristic
386C2×C3×Dic3C23×C311yescharacteristic
387C2×C3×Dic3C23×C311yescharacteristic
388C3×C4×D3—62no—
389C3×Dic6—22no—
390C3×Dic6—22no—
391C3×Dic6—22no—
392C3×Dic6—22no—
393C3×Dic6—42no—
394C3×Dic6—42no—
395D3×Dic3—22no—
396#541—91noSylow
397C2×C33C2×#4111yescharacteristic
398C2×C332−1+411yescharacteristic
399C2×C332−1+411yescharacteristic
400C32×D3—41no—
401C2×C3×Q8—31no—
402C2×C3×Q8—31no—
403C2×C3×Q8—31no—
404C2×C3×Q8—31no—
405C2×C3×Q8—61no—
406C2×C3×Q8—61no—
407C22×C3×C4—91no—
408C22×Dic3—31no—
409C2×C4×D3—31no—
410C2×Dic6C2×C3×D311yescharacteristic
411C2×Dic6C2×C3×D311yescharacteristic
412C3×C4⋊C4—21no—
413C3×C4⋊C4—21no—
414C3×C4⋊C4—21no—
415C3×C4⋊C4—31no—
416C3×C4⋊C4—31no—
417C3×C4⋊C4—31no—
418C3×C4⋊C4—31no—
419C3×C4⋊C4—31no—
420C3×C4⋊C4—31no—
421C3×C4⋊C4—31no—
422C3×C4⋊C4—31no—
423C3×C4⋊C4—31no—
424C3×C4⋊C4—31no—
425C3×C4⋊C4—41no—
426C3×C4⋊C4—61no—
427C3×C4⋊C4—61no—
428C3×C4⋊C4—61no—
429C3×C4⋊C4—61no—
430C3×C4⋊C4—61no—
431C3×C4⋊C4—91no—
432C3×C4⋊C4—91no—
433C3×C4⋊C4—91no—
434C3×C4⋊C4—91no—
435C3×C4⋊C4—91no—
436C3×C4⋊C4—91no—
437C3×C4⋊C4—91no—
438C3×C4⋊C4—91no—
439C3×C4⋊C4—91no—
440C3×C4⋊C4—91no—
441C3×C4⋊C4—91no—
442C3×C4⋊C4—91no—
443C3×C4⋊C4—91no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4D3211yescharacteristic
446C3×C4⋊C4C2×C3×D311yescharacteristic
447C3×C4⋊C4C2×C3×D311yescharacteristic
448C3×C22⋊C4—31no—
449C3×C22⋊C4—31no—
450C3×C22⋊C4—31no—
451C3×C22⋊C4—31no—
452C3×C22⋊C4—31no—
453C3×C22⋊C4—31no—
454C3×C22⋊C4—61no—
455C3×C22⋊C4—61no—
456C3×C22⋊C4—61no—
457C3×C22⋊C4—91no—
458C3×C22⋊C4—91no—
459C3×C22⋊C4—91no—
460C3×C42—31no—
461C3×C42—31no—
462C3×C42—31no—
463C3×C42—31no—
464C3×C42—61no—
465C3×C42—61no—
466C3×C42—91no—
467C3×C42—91no—
468C3×C42—91no—
469C3×C42—91no—
470#217—31no—
471#217—31no—
472#217—31no—
473(C2×D3)⋊C4—31no—
474(C2×D3)⋊C4—31no—
475(C2×D3)⋊C4—31no—
476(C2×D3)⋊C4C2×C3×D311yescharacteristic
477(C2×D3)⋊C4C2×C3×D311yescharacteristic
478(C2×D3)⋊C4C2×C3×D311yescharacteristic
479C4⋊Dic3—31no—
480C4⋊Dic3—31no—
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—31no—
487C4⋊Dic3—31no—
488C4⋊Dic3—61no—
489C4⋊Dic3C2×C3×D311yescharacteristic
490C4⋊Dic3C2×C3×D311yescharacteristic
491Dic3⋊C4—31no—
492Dic3⋊C4—31no—
493Dic3⋊C4—31no—
494Dic3⋊C4—31no—
495Dic3⋊C4—31no—
496Dic3⋊C4—31no—
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—31no—
508Dic3⋊C4—31no—
509Dic3⋊C4—31no—
510Dic3⋊C4—61no—
511Dic3⋊C4—61no—
512Dic3⋊C4—61no—
513Dic3⋊C4—61no—
514Dic3⋊C4C2×C3×D311yescharacteristic
515Dic3⋊C4C2×C3×D311yescharacteristic
516Dic3⋊C4C2×C3×D311yescharacteristic
517C4×Dic3—31no—
518C4×Dic3—31no—
519C4×Dic3—31no—
520C4×Dic3—31no—
521C4×Dic3—31no—
522C4×Dic3—31no—
523C4×Dic3—31no—
524C4×Dic3—31no—
525C4×Dic3—61no—
526C4×Dic3C2×C3×D311yescharacteristic
527C4×Dic3C2×C3×D311yescharacteristic
528C22×C32—21no—
529C22×C32—21no—
530C22×C32—21no—
531C22×C32—41no—
532C22×C32—61no—
533C22×C32—61no—
534C22×C32—61no—
535C22×C32C23×D311yescharacteristic
536C22×C32C23×D311yescharacteristic
537C22×C32C24×C311yescharacteristic
538C2×C3×D3—21no—
539C2×C3×D3—21no—
540C2×C3×D3—21no—
541C2×C3×D3—21no—
542C2×C3×D3—21no—
543C2×C3×D3—21no—
544C2×C3×D3—41no—
545C2×C3×D3—41no—
546C2×C3×D3—41no—
547C32×C4—21no—
548C32×C4—22no—
549C32×C4—21no—
550C32×C4—21no—
551C32×C4—21no—
552C32×C4—21no—
553C32×C4—21no—
554C32×C4—21no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4—32no—
558C32×C4—41no—
559C32×C4—41no—
560C32×C4—42no—
561C32×C4—41no—
562C32×C4—41no—
563C32×C4—41no—
564C32×C4—41no—
565C32×C4—41no—
566C32×C4—41no—
567C32×C4—61no—
568C32×C4—61no—
569C32×C4—61no—
570C32×C4—61no—
571C32×C4—61no—
572C32×C4—61no—
573C32×C4—81no—
574C32×C4—81no—
575C3⋊Dic3—21no—
576C3⋊Dic3—21no—
577C3⋊Dic3—21no—
578C3⋊Dic3—21no—
579C3×Dic3—22no—
580C3×Dic3—21no—
581C3×Dic3—21no—
582C3×Dic3—21no—
583C3×Dic3—21no—
584C3×Dic3—21no—
585C3×Dic3—21no—
586C3×Dic3—21no—
587C3×Dic3—21no—
588C3×Dic3—21no—
589C3×Dic3—21no—
590C3×Dic3—21no—
591C3×Dic3—21no—
592C3×Dic3—22no—
593C3×Dic3—41no—
594C3×Dic3—41no—
595C3×Dic3—41no—
596C3×Dic3—41no—
597C3×Dic3—41no—
598C3×Dic3—62no—
599C3×Dic3—61no—
600C3×Dic3—61no—
601C3×Dic3—61no—
602C3×Dic3—61no—
603C3×Dic3—61no—
604C3×Dic3—61no—
605C3×Dic3—61no—
606C3×Dic3—61no—
607C3×Dic3—121no—
608C3×Dic3—121no—
609C3×Dic3—121no—
610C3×Dic3#23712yes—
611C3×Dic3C3×#4112yes—
612C4⋊Q8—31no—
613#126—31no—
614#126—91no—
615#126—91no—
616#126—91no—
617#125—91no—
618#125—91no—
619#125—91no—
620#125—91no—
621#125—91no—
622C22⋊Q8—91no—
623C22⋊Q8—91no—
624C4×Q8—91no—
625C4×Q8—91no—
626#117—91no—
627C33#54111yescharacteristic, complemented, Sylow
628C23×C3—31no—
629C23×C3—31no—
630C23×C3—61no—
631C22×D3C22×C3×D311yescharacteristic
632C3×Q8—62no—
633C3×Q8—62no—
634C3×Q8—62no—
635C3×Q8—62no—
636C3×Q8—122no—
637C3×Q8—122no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—31no—
648C2×C3×C4—31no—
649C2×C3×C4—31no—
650C2×C3×C4—31no—
651C2×C3×C4—31no—
652C2×C3×C4—31no—
653C2×C3×C4—31no—
654C2×C3×C4—31no—
655C2×C3×C4—31no—
656C2×C3×C4—31no—
657C2×C3×C4—31no—
658C2×C3×C4—31no—
659C2×C3×C4—31no—
660C2×C3×C4—31no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—91no—
672C2×C3×C4—91no—
673C2×C3×C4—91no—
674C2×C3×C4—91no—
675C2×C3×C4—182no—
676C2×C3×C4C2×D3211yescharacteristic
677C2×C3×C4C2×D3211yescharacteristic
678C2×C3×C4C2×D3211yescharacteristic
679C2×C3×C4C22×C3×D311yescharacteristic
680C2×C3×C4C22×C3×D311yescharacteristic
681C2×C3×C4C22×C3×D311yescharacteristic
682C2×C3×C4C22×C3×D311yescharacteristic
683C2×C3×C4C22×C3×D311yescharacteristic
684C2×C3×C4C22×C3×D311yescharacteristic
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—31no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—62no—
698C2×Dic3C22×C3×D311yescharacteristic
699C2×Dic3C22×C3×D311yescharacteristic
700C2×Dic3C22×C3×D311yescharacteristic
701C2×Dic3C22×C3×D311yescharacteristic
702C2×Dic3C22×C3×D311yescharacteristic
703C2×Dic3C22×C3×D311yescharacteristic
704C2×Dic3C22×C3×D311yescharacteristic
705C4×D3—62no—
706Dic6—22no—
707Dic6—22no—
708C2×C32—21no—
709C2×C32—21no—
710C2×C32—21no—
711C2×C32—21no—
712C2×C32—21no—
713C2×C32—21no—
714C2×C32—21no—
715C2×C32—21no—
716C2×C32—21no—
717C2×C32—41no—
718C2×C32—41no—
719C2×C32—41no—
720C2×C32—121no—
721C2×C32C2×#23711yescharacteristic
722C2×C32#100711yescharacteristic
723C2×C32#100711yescharacteristic
724C2×C32D3×#4111yescharacteristic
725C2×C32#101011yescharacteristic
726C2×C32#101011yescharacteristic
727C2×C32C2×C3×#4111yescharacteristic
728C2×C32C3×2−1+411yescharacteristic
729C2×C32C3×2−1+411yescharacteristic
730C3×D3—41no—
731C3×D3—41no—
732C3×D3—81no—
733C2×Q8—31no—
734C2×Q8—31no—
735C22×C4—91no—
736C4⋊C4—31no—
737C4⋊C4—31no—
738C4⋊C4—31no—
739C4⋊C4—31no—
740C4⋊C4—31no—
741C4⋊C4—91no—
742C4⋊C4—91no—
743C4⋊C4—91no—
744C4⋊C4—91no—
745C4⋊C4—91no—
746C4⋊C4—91no—
747C4⋊C4—91no—
748C4⋊C4—91no—
749C4⋊C4—91no—
750C4⋊C4—91no—
751C4⋊C4—91no—
752C4⋊C4—91no—
753C4⋊C4—91no—
754C4⋊C4—91no—
755C4⋊C4C3×D3211yescharacteristic
756C22⋊C4—31no—
757C22⋊C4—31no—
758C22⋊C4—31no—
759C22⋊C4—91no—
760C22⋊C4—91no—
761C22⋊C4—91no—
762C42—31no—
763C42—31no—
764C42—91no—
765C42—91no—
766C42—91no—
767C42—91no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—41no—
772C22×C3—61no—
773C22×C3—61no—
774C22×C3—61no—
775C22×C3—61no—
776C22×C3—61no—
777C22×C3—61no—
778C22×C3—121no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3C22×D3211yescharacteristic
782C22×C3C23×C3×D311yescharacteristic
783C22×C3C23×C3×D311yescharacteristic
784C2×D3—21no—
785C2×D3—21no—
786C2×D3—21no—
787C3×C4—22no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—32no—
798C3×C4—32no—
799C3×C4—41no—
800C3×C4—41no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—41no—
805C3×C4—41no—
806C3×C4—41no—
807C3×C4—42no—
808C3×C4—62no—
809C3×C4—62no—
810C3×C4—61no—
811C3×C4—61no—
812C3×C4—61no—
813C3×C4—61no—
814C3×C4—61no—
815C3×C4—61no—
816C3×C4—61no—
817C3×C4—61no—
818C3×C4—61no—
819C3×C4—61no—
820C3×C4—61no—
821C3×C4—61no—
822C3×C4—81no—
823C3×C4—81no—
824C3×C4—121no—
825C3×C4—121no—
826C3×C4—121no—
827C3×C4—121no—
828C3×C4—121no—
829C3×C4—181no—
830C3×C4—181no—
831C3×C4—181no—
832C3×C4—181no—
833Dic3—21no—
834Dic3—21no—
835Dic3—21no—
836Dic3—21no—
837Dic3—21no—
838Dic3—21no—
839Dic3—62no—
840Dic3—61no—
841Dic3—61no—
842Dic3—61no—
843Dic3—61no—
844Dic3—61no—
845Dic3—61no—
846Dic3—61no—
847Dic3—61no—
848Dic3—121no—
849Dic3—121no—
850Dic3—121no—
851Dic3C3×#23712yes—
852C32—21no—
853C32—21no—
854C32—21no—
855C32—41no—
856C32#570111yescharacteristic, complemented
857C32#573111yescharacteristic, complemented
858C32C3×#54111yescharacteristic, complemented
859C23—31no—
860Q8—62no—
861Q8—62no—
862C2×C4—31no—
863C2×C4—31no—
864C2×C4—31no—
865C2×C4—31no—
866C2×C4—31no—
867C2×C4—31no—
868C2×C4—31no—
869C2×C4—91no—
870C2×C4—91no—
871C2×C4—91no—
872C2×C4—91no—
873C2×C4—182no—
874C2×C4C2×C3×D3211yescharacteristic
875C2×C4C2×C3×D3211yescharacteristic
876C2×C4C2×C3×D3211yescharacteristic
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—41no—
887C2×C3—41no—
888C2×C3—41no—
889C2×C3—121no—
890C2×C3—121no—
891C2×C3—241no—
892C2×C3#6429711yescharacteristic
893C2×C3D3×#23711yescharacteristic
894C2×C3#6431511yescharacteristic
895C2×C3C2×C3×#23711yescharacteristic
896C2×C3C3×#100711yescharacteristic
897C2×C3C3×#100711yescharacteristic
898C2×C3C3×D3×#4111yescharacteristic
899C2×C3C3×#101011yescharacteristic
900C2×C3C3×#101011yescharacteristic
901D3—41no—
902C22—61no—
903C22—61no—
904C22—61no—
905C22C22×C3×D3211yescharacteristic
906C4—21no—
907C4—21no—
908C4—21no—
909C4—32no—
910C4—61no—
911C4—61no—
912C4—61no—
913C4—61no—
914C4—61no—
915C4—61no—
916C4—181no—
917C4—181no—
918C4—181no—
919C4—181no—
920C3—21no—
921C3—21no—
922C3—21no—
923C3—41no—
924C3#1059444611yescharacteristic, direct product factor
925C3C3×#570111yescharacteristic, complemented
926C3C3×#573111yescharacteristic, complemented
927C2—121no—
928C2C3×#6429711yescharacteristic
929C2C3×D3×#23711yescharacteristic
930C2C3×#6431511yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC22×C32×D3C23
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#541
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×#64098C2semidirect
3. C32×#888C2semidirect
7. C3×#63867C2semidirect
8. C3×#63867C2semidirect
12. C3×#63847C2semidirect
13. C3×#63846C2semidirect
14. C3×#63843C2semidirect
15. C3×Dic3×Dic6C2semidirect
18. #10594446C3direct (N × H)
56. #64098C2×C3semidirect
77. C3×#888D3semidirect
78. C3×#888C2×C3semidirect
93. #63867C2×C3semidirect
94. #63867C2×C3semidirect
98. #63847C2×C3semidirect
99. #63846C2×C3semidirect
100. #63843C2×C3semidirect
101. Dic3×Dic6C2×C3semidirect
304. #888C3×D3semidirect
627. C33#541semidirect
856. C32#5701semidirect
857. C32#5731semidirect
858. C32C3×#541semidirect
924. C3#10594446direct (N × H)
925. C3C3×#5701semidirect
926. C3C3×#5731semidirect

Maximal subgroups

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

subgroupindex
C3×#640982
C32×#8982
C32×#8882
C3×#638872
C3×#638772
C3×#638672
C3×#638622
C3×#638612
C3×#638582
C3×#638472
C3×#638462
C3×#638432
C3×Dic3×Dic62
C3×#57313
C3×#57013
#105944463