Finite Group Databasebeta

← C3×#10594421 #13173975

Subgroups — C3×#10594421 #13173975

Order 1728.

1064 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64107C211yesmaximal, characteristic, complemented
2C32×#898C211yesmaximal, characteristic, complemented
3C32×#887C211yesmaximal, characteristic, complemented
4C3×#63918C211yesmaximal, characteristic, complemented
5C3×C4×#627C211yesmaximal, characteristic, complemented
6C3×#63888C211yesmaximal, characteristic, complemented
7C3×#63887C211yesmaximal, characteristic, complemented
8C3×#63880C211yesmaximal, characteristic
9C3×#63878C211yesmaximal, characteristic, complemented
10C3×#63861C211yesmaximal, characteristic, complemented
11C3×#63852C211yesmaximal, characteristic
12C3×#63852C211yesmaximal, characteristic
13C3×#63848C211yesmaximal, characteristic, complemented
14C3×#63837C211yesmaximal, characteristic, complemented
15C3×#63836C211yesmaximal, characteristic, complemented
16C3×#5702—31nomaximal
17C3×#5584—31nomaximal
18#10594421C311yesmaximal, characteristic, direct product factor
19C2×C32×Dic6C2211yescharacteristic
20C2×C3×#627C2211yescharacteristic
21C2×C3×#627C2211yescharacteristic
22C2×C3×#626C2211yescharacteristic
23C2×C3×#624C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C33×C4⋊C4C2211yescharacteristic
26C3×#3752C2211yescharacteristic
27C3×#3752C2211yescharacteristic
28C3×#3752C2211yescharacteristic
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×C4×C3⋊Dic3C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×C4⋊Dic3C2211yescharacteristic
36C32×Dic3⋊C4C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×C4×Dic3C2211yescharacteristic
40C32×C4×Dic3C2211yescharacteristic
41C32×C4×Dic3C2211yescharacteristic
42C32×C4×Dic3C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×#126—31no—
55C32×C4×Q8—31no—
56#64107C2×C311yescharacteristic, complemented
57C3×#946—31no—
58C3×#946—31no—
59C3×#898—21no—
60C3×#898—31no—
61C3×#898—31no—
62C3×#898—31no—
63C3×#898—31no—
64C3×#898—31no—
65C3×#898—61no—
66C3×#898D311yescharacteristic, complemented
67C3×#898C2×C311yescharacteristic, complemented
68C3×#896—31no—
69C3×#892—31no—
70C3×#892—31no—
71C3×#888—31no—
72C3×#887—21no—
73C3×#887—31no—
74C3×#887D311yescharacteristic, complemented
75C3×#887C2×C311yescharacteristic, complemented
76C3×#885—31no—
77C3×#885—31no—
78C3×#67⋊C4—31no—
79C3×#879—31no—
80C3×#878—31no—
81C3×#877—31no—
82C3×#875—31no—
83C3×#875—31no—
84C3×C4×D12—31no—
85C3×#872—31no—
86C3×#869—31no—
87C3×C4×Dic6—31no—
88C3×C4×Dic6—31no—
89C3×C4×Dic6—31no—
90#63918C2×C311yescharacteristic, complemented
91C4×#627C2×C311yescharacteristic, complemented
92#63888C2×C311yescharacteristic, complemented
93#63887C2×C311yescharacteristic, complemented
94#63880C2×C311yescharacteristic
95#63878C2×C311yescharacteristic, complemented
96#63861C2×C311yescharacteristic, complemented
97#63852C2×C311yescharacteristic
98#63852C2×C311yescharacteristic
99#63848C2×C311yescharacteristic, complemented
100#63837C2×C311yescharacteristic, complemented
101#63836C2×C311yescharacteristic, complemented
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
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—
118C3×#627—22no—
119C3×#627—22no—
120C3×#626—22no—
121C3×#624—22no—
122C3×D3×Dic3—22no—
123C3×#556—91no—
124#5702—31no—
125#5584—31no—
126C2×C32×Q8—31no—
127C2×C3×#67—31no—
128C22×C3×Dic3—31no—
129C2×C3×D12—31no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×Dic6—21no—
134C2×C3×Dic6—31no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×C3×Dic6—31no—
138C2×C3×Dic6C2×D311yescharacteristic
139C2×C3×Dic6C22×C311yescharacteristic
140C2×#627C22×C311yescharacteristic
141C2×#627C22×C311yescharacteristic
142C2×#626C22×C311yescharacteristic
143C2×#624C22×C311yescharacteristic
144C2×D3×Dic3C22×C311yescharacteristic
145C32×C4⋊C4—21no—
146C32×C4⋊C4—21no—
147C32×C4⋊C4—21no—
148C32×C4⋊C4—31no—
149C32×C4⋊C4—31no—
150C32×C4⋊C4—31no—
151C32×C4⋊C4—31no—
152C32×C4⋊C4—41no—
153C32×C4⋊C4C2×D311yescharacteristic
154C32×C4⋊C4C2×D311yescharacteristic
155C32×C4⋊C4C22×C311yescharacteristic
156C32×C22⋊C4—31no—
157C32×C22⋊C4—31no—
158C32×C22⋊C4—31no—
159C32×C42—31no—
160C32×C42—31no—
161C32×C42—31no—
162C32×C42—31no—
163#3752C22×C311yescharacteristic
164#3752C22×C311yescharacteristic
165#3752C22×C311yescharacteristic
166C4⋊(C3⋊Dic3)C22×C311yescharacteristic
167#3750C22×C311yescharacteristic
168C4×C3⋊Dic3C22×C311yescharacteristic
169C3×#217—31no—
170C3×#217—31no—
171C3×(C2×D3)⋊C4—21no—
172C3×(C2×D3)⋊C4—21no—
173C3×(C2×D3)⋊C4—21no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—61no—
187C3×(C2×D3)⋊C4—61no—
188C3×(C2×D3)⋊C4—61no—
189C3×(C2×D3)⋊C4C2×D311yescharacteristic
190C3×(C2×D3)⋊C4C2×D311yescharacteristic
191C3×(C2×D3)⋊C4C2×D311yescharacteristic
192C3×(C2×D3)⋊C4C22×C311yescharacteristic
193C3×(C2×D3)⋊C4C22×C311yescharacteristic
194C3×(C2×D3)⋊C4C22×C311yescharacteristic
195C3×C4⋊Dic3—21no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—31no—
199C3×C4⋊Dic3—31no—
200C3×C4⋊Dic3—31no—
201C3×C4⋊Dic3—31no—
202C3×C4⋊Dic3—61no—
203C3×C4⋊Dic3C2×D311yescharacteristic
204C3×C4⋊Dic3C22×C311yescharacteristic
205C3×Dic3⋊C4—21no—
206C3×Dic3⋊C4—21no—
207C3×Dic3⋊C4—21no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—61no—
217C3×Dic3⋊C4C2×D311yescharacteristic
218C3×Dic3⋊C4C2×D311yescharacteristic
219C3×Dic3⋊C4C2×D311yescharacteristic
220C3×Dic3⋊C4C22×C311yescharacteristic
221C3×Dic3⋊C4C22×C311yescharacteristic
222C3×Dic3⋊C4C22×C311yescharacteristic
223C3×C4×Dic3—21no—
224C3×C4×Dic3—21no—
225C3×C4×Dic3—21no—
226C3×C4×Dic3—21no—
227C3×C4×Dic3—31no—
228C3×C4×Dic3—31no—
229C3×C4×Dic3—31no—
230C3×C4×Dic3—31no—
231C3×C4×Dic3—31no—
232C3×C4×Dic3—31no—
233C3×C4×Dic3—61no—
234C3×C4×Dic3C2×D311yescharacteristic
235C3×C4×Dic3C2×D311yescharacteristic
236C3×C4×Dic3C2×D311yescharacteristic
237C3×C4×Dic3C2×D311yescharacteristic
238C3×C4×Dic3C22×C311yescharacteristic
239C3×C4×Dic3C22×C311yescharacteristic
240C3×C4×Dic3C22×C311yescharacteristic
241C3×C4×Dic3C22×C311yescharacteristic
242#3724C22×C311yescharacteristic
243Dic3⋊Dic3C22×C311yescharacteristic
244Dic3⋊Dic3C22×C311yescharacteristic
245Dic3⋊Dic3C22×C311yescharacteristic
246Dic3⋊Dic3C22×C311yescharacteristic
247#3722C22×C311yescharacteristic
248#3722C22×C311yescharacteristic
249(C2×D3)⋊Dic3C22×C311yescharacteristic
250(C2×D3)⋊Dic3C22×C311yescharacteristic
251Dic32C22×C311yescharacteristic
252Dic32C22×C311yescharacteristic
253C22×C33C2411yescharacteristic
254C2×C3×C3⋊D3—21no—
255C2×C3×C3⋊D3—21no—
256C2×C3×C3⋊D3—21no—
257C2×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×D3—21no—
260C33×C4—21no—
261C33×C4—21no—
262C33×C4—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C32×Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3#4112yes—
272C32×Dic3#4112yes—
273C3×C4⋊Q8—91no—
274C3×#126—31no—
275C3×#126—31no—
276C3×#126—61no—
277C3×#126—91no—
278C3×#126—91no—
279C3×#126—91no—
280C3×#124—91no—
281C3×#124—91no—
282C3×C22⋊Q8—91no—
283C3×C22⋊Q8—91no—
284C3×C4×Q8—31no—
285C3×C4×Q8—31no—
286C3×C4×Q8—61no—
287C3×C4×Q8—91no—
288C3×C4×Q8—91no—
289C3×C4×D4—91no—
290C3×#117—91no—
291C3×#117—91no—
292#946—31no—
293#946—31no—
294#898—31no—
295#898—31no—
296#898—31no—
297#898—31no—
298#898—31no—
299#898—61no—
300#898C3×D311yescharacteristic, complemented
301#896—31no—
302#892—31no—
303#892—31no—
304#888—31no—
305#887—31no—
306#887C3×D311yescharacteristic, complemented
307#885—31no—
308#885—31no—
309#67⋊C4—31no—
310#879—31no—
311#878—31no—
312#877—31no—
313#875—31no—
314#875—31no—
315C4×D12—31no—
316#872—31no—
317#869—31no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C4×Dic6—31no—
321C23×C32—31no—
322C22×C3⋊D3C23×C311yescharacteristic
323C22×C3×D3—21no—
324C22×C3×D3—31no—
325C22×C3×D3—31no—
326C22×C3×D3—61no—
327C22×C3×D3C22×D311yescharacteristic
328C22×C3×D3C23×C311yescharacteristic
329C32×Q8—62no—
330C2×C32×C4—21no—
331C2×C32×C4—21no—
332C2×C32×C4—21no—
333C2×C32×C4—21no—
334C2×C32×C4—21no—
335C2×C32×C4—21no—
336C2×C32×C4—21no—
337C2×C32×C4—21no—
338C2×C32×C4—21no—
339C2×C32×C4—31no—
340C2×C32×C4—31no—
341C2×C32×C4—31no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—41no—
347C2×C32×C4—41no—
348C2×C32×C4—41no—
349C2×C32×C4C22×D311yescharacteristic
350C2×C32×C4C22×D311yescharacteristic
351C2×C32×C4C22×D311yescharacteristic
352C2×C32×C4C22×D311yescharacteristic
353C2×C32×C4C22×D311yescharacteristic
354C2×C32×C4C22×D311yescharacteristic
355C2×C32×C4C23×C311yescharacteristic
356C2×C32×C4C23×C311yescharacteristic
357C2×C32×C4C23×C311yescharacteristic
358C2×C3⋊Dic3C23×C311yescharacteristic
359C2×C3⋊Dic3C23×C311yescharacteristic
360C2×C3⋊Dic3C23×C311yescharacteristic
361C3×#67—62no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—21no—
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—62no—
379C2×C3×Dic3C22×D311yescharacteristic
380C2×C3×Dic3C22×D311yescharacteristic
381C2×C3×Dic3C22×D311yescharacteristic
382C2×C3×Dic3C22×D311yescharacteristic
383C2×C3×Dic3C22×D311yescharacteristic
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C23×C311yescharacteristic
387C2×C3×Dic3C23×C311yescharacteristic
388C2×C3×Dic3C23×C311yescharacteristic
389C2×C3×Dic3C23×C311yescharacteristic
390C2×C3×Dic3C23×C311yescharacteristic
391C2×C3×Dic3C23×C311yescharacteristic
392C2×C3×Dic3C23×C311yescharacteristic
393C3×D12—62no—
394C3×C4×D3—62no—
395C3×C4×D3—62no—
396C3×C4×D3—62no—
397C3×Dic6—24no—
398C3×Dic6—22no—
399C3×Dic6—22no—
400C3×Dic6—62no—
401C3×Dic6—62no—
402C3×Dic6—62no—
403C3×Dic6—62no—
404#627—22no—
405#627—22no—
406#626—22no—
407#624—22no—
408D3×Dic3—22no—
409#556—91noSylow
410C2×C33C2×#4111yescharacteristic
411C2×C33C2×#4111yescharacteristic
412C2×C332−1+411yescharacteristic
413C3×C3⋊D3—41no—
414C32×D3—41no—
415C2×C3×Q8—31no—
416C2×C3×Q8—31no—
417C2×C3×Q8—61no—
418C2×C3×Q8—91no—
419C2×C3×Q8—91no—
420C2×C3×D4—91no—
421C22×C3×C4—91no—
422C22×C3×C4—91no—
423C2×#67—31no—
424C22×Dic3—31no—
425C2×D12—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×Dic6—31no—
430C2×Dic6—31no—
431C2×Dic6—31no—
432C2×Dic6—31no—
433C2×Dic6C2×C3×D311yescharacteristic
434C3×C4⋊C4—21no—
435C3×C4⋊C4—21no—
436C3×C4⋊C4—21no—
437C3×C4⋊C4—31no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4—41no—
446C3×C4⋊C4—61no—
447C3×C4⋊C4—61no—
448C3×C4⋊C4—61no—
449C3×C4⋊C4—61no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C4⋊C4—91no—
453C3×C4⋊C4—91no—
454C3×C4⋊C4—91no—
455C3×C4⋊C4—91no—
456C3×C4⋊C4—91no—
457C3×C4⋊C4D3211yescharacteristic
458C3×C4⋊C4C2×C3×D311yescharacteristic
459C3×C4⋊C4C2×C3×D311yescharacteristic
460C3×C22⋊C4—31no—
461C3×C22⋊C4—31no—
462C3×C22⋊C4—31no—
463C3×C22⋊C4—31no—
464C3×C22⋊C4—31no—
465C3×C22⋊C4—31no—
466C3×C22⋊C4—61no—
467C3×C22⋊C4—61no—
468C3×C22⋊C4—61no—
469C3×C22⋊C4—91no—
470C3×C22⋊C4—91no—
471C3×C22⋊C4—91no—
472C3×C22⋊C4—91no—
473C3×C22⋊C4—91no—
474C3×C22⋊C4—91no—
475C3×C22⋊C4—91no—
476C3×C42—31no—
477C3×C42—31no—
478C3×C42—31no—
479C3×C42—31no—
480C3×C42—31no—
481C3×C42—31no—
482C3×C42—31no—
483C3×C42—31no—
484C3×C42—61no—
485C3×C42—61no—
486C3×C42—61no—
487C3×C42—61no—
488C3×C42—91no—
489C3×C42—91no—
490C3×C42—91no—
491#217—31no—
492#217—31no—
493(C2×D3)⋊C4—31no—
494(C2×D3)⋊C4—31no—
495(C2×D3)⋊C4—31no—
496(C2×D3)⋊C4—31no—
497(C2×D3)⋊C4—31no—
498(C2×D3)⋊C4—31no—
499(C2×D3)⋊C4—31no—
500(C2×D3)⋊C4—31no—
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—31no—
503(C2×D3)⋊C4—31no—
504(C2×D3)⋊C4—31no—
505(C2×D3)⋊C4—61no—
506(C2×D3)⋊C4—61no—
507(C2×D3)⋊C4—61no—
508(C2×D3)⋊C4C2×C3×D311yescharacteristic
509(C2×D3)⋊C4C2×C3×D311yescharacteristic
510(C2×D3)⋊C4C2×C3×D311yescharacteristic
511C4⋊Dic3—31no—
512C4⋊Dic3—31no—
513C4⋊Dic3—31no—
514C4⋊Dic3—31no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—61no—
518C4⋊Dic3C2×C3×D311yescharacteristic
519Dic3⋊C4—31no—
520Dic3⋊C4—31no—
521Dic3⋊C4—31no—
522Dic3⋊C4—31no—
523Dic3⋊C4—31no—
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—61no—
528Dic3⋊C4C2×C3×D311yescharacteristic
529Dic3⋊C4C2×C3×D311yescharacteristic
530Dic3⋊C4C2×C3×D311yescharacteristic
531C4×Dic3—31no—
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—61no—
538C4×Dic3C2×C3×D311yescharacteristic
539C4×Dic3C2×C3×D311yescharacteristic
540C4×Dic3C2×C3×D311yescharacteristic
541C4×Dic3C2×C3×D311yescharacteristic
542C22×C32—21no—
543C22×C32—21no—
544C22×C32—21no—
545C22×C32—41no—
546C22×C32—61no—
547C22×C32—61no—
548C22×C32—61no—
549C22×C32C23×D311yescharacteristic
550C22×C32C23×D311yescharacteristic
551C22×C32C24×C311yescharacteristic
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3—21no—
555C2×C3×D3—21no—
556C2×C3×D3—21no—
557C2×C3×D3—21no—
558C2×C3×D3—21no—
559C2×C3×D3—21no—
560C2×C3×D3—21no—
561C2×C3×D3—41no—
562C2×C3×D3—41no—
563C2×C3×D3—41no—
564C2×C3×D3—61no—
565C2×C3×D3—61no—
566C2×C3×D3—61no—
567C2×C3×D3—61no—
568C2×C3×D3—61no—
569C2×C3×D3—61no—
570C2×C3×D3—121no—
571C2×C3×D3—121no—
572C2×C3×D3—121no—
573C32×C4—21no—
574C32×C4—22no—
575C32×C4—21no—
576C32×C4—21no—
577C32×C4—21no—
578C32×C4—21no—
579C32×C4—21no—
580C32×C4—21no—
581C32×C4—21no—
582C32×C4—21no—
583C32×C4—32no—
584C32×C4—32no—
585C32×C4—41no—
586C32×C4—41no—
587C32×C4—42no—
588C32×C4—41no—
589C32×C4—41no—
590C32×C4—41no—
591C32×C4—41no—
592C32×C4—41no—
593C32×C4—41no—
594C32×C4—61no—
595C32×C4—61no—
596C32×C4—61no—
597C32×C4—61no—
598C32×C4—61no—
599C32×C4—81no—
600C32×C4—81no—
601C3⋊Dic3—21no—
602C3⋊Dic3—21no—
603C3⋊Dic3—21no—
604C3×Dic3—22no—
605C3×Dic3—21no—
606C3×Dic3—21no—
607C3×Dic3—21no—
608C3×Dic3—21no—
609C3×Dic3—21no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—22no—
616C3×Dic3—22no—
617C3×Dic3—41no—
618C3×Dic3—41no—
619C3×Dic3—41no—
620C3×Dic3—41no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—61no—
624C3×Dic3—61no—
625C3×Dic3—61no—
626C3×Dic3—61no—
627C3×Dic3—121no—
628C3×Dic3—121no—
629C3×Dic3—121no—
630C3×Dic3#23512yes—
631C3×Dic3#23912yes—
632C3×Dic3C3×#4112yes—
633C3×Dic3C3×#4112yes—
634C4⋊Q8—91no—
635#126—31no—
636#126—91no—
637#126—91no—
638#126—91no—
639#124—91no—
640#124—91no—
641C22⋊Q8—91no—
642C22⋊Q8—91no—
643C4×Q8—31no—
644C4×Q8—91no—
645C4×Q8—91no—
646C4×D4—91no—
647#117—91no—
648#117—91no—
649C33#55611yescharacteristic, complemented, Sylow
650C23×C3—31no—
651C23×C3—31no—
652C23×C3—61no—
653C23×C3—91no—
654C22×D3—31no—
655C22×D3—31no—
656C22×D3—61no—
657C22×D3C22×C3×D311yescharacteristic
658C3×Q8—62no—
659C3×Q8—62no—
660C3×Q8—64no—
661C3×Q8—182no—
662C3×Q8—182no—
663C3×D4—182no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—31no—
674C2×C3×C4—31no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—31no—
679C2×C3×C4—31no—
680C2×C3×C4—31no—
681C2×C3×C4—31no—
682C2×C3×C4—31no—
683C2×C3×C4—31no—
684C2×C3×C4—31no—
685C2×C3×C4—31no—
686C2×C3×C4—31no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4—91no—
698C2×C3×C4—91no—
699C2×C3×C4—91no—
700C2×C3×C4—182no—
701C2×C3×C4—182no—
702C2×C3×C4C2×D3211yescharacteristic
703C2×C3×C4C2×D3211yescharacteristic
704C2×C3×C4C2×D3211yescharacteristic
705C2×C3×C4C22×C3×D311yescharacteristic
706C2×C3×C4C22×C3×D311yescharacteristic
707C2×C3×C4C22×C3×D311yescharacteristic
708C2×C3×C4C22×C3×D311yescharacteristic
709C2×C3×C4C22×C3×D311yescharacteristic
710C2×C3×C4C22×C3×D311yescharacteristic
711#67—62no—
712C2×Dic3—31no—
713C2×Dic3—31no—
714C2×Dic3—31no—
715C2×Dic3—31no—
716C2×Dic3—31no—
717C2×Dic3—31no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—62no—
722C2×Dic3C22×C3×D311yescharacteristic
723C2×Dic3C22×C3×D311yescharacteristic
724C2×Dic3C22×C3×D311yescharacteristic
725C2×Dic3C22×C3×D311yescharacteristic
726C2×Dic3C22×C3×D311yescharacteristic
727C2×Dic3C22×C3×D311yescharacteristic
728C2×Dic3C22×C3×D311yescharacteristic
729D12—62no—
730C4×D3—62no—
731C4×D3—62no—
732C4×D3—62no—
733Dic6—22no—
734Dic6—62no—
735Dic6—62no—
736Dic6—62no—
737Dic6—62no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—41no—
748C2×C32—41no—
749C2×C32—41no—
750C2×C32—121no—
751C2×C32C2×#23511yescharacteristic
752C2×C32C2×#23911yescharacteristic
753C2×C32D3×#4111yescharacteristic
754C2×C32D3×#4111yescharacteristic
755C2×C32#101011yescharacteristic
756C2×C32#101011yescharacteristic
757C2×C32C2×C3×#4111yescharacteristic
758C2×C32C2×C3×#4111yescharacteristic
759C2×C32C3×2−1+411yescharacteristic
760C3⋊D3—41no—
761C3×D3—41no—
762C3×D3—41no—
763C3×D3—81no—
764C3×D3—121no—
765C3×D3—121no—
766C3×D3—241no—
767C2×Q8—31no—
768C2×Q8—91no—
769C2×Q8—91no—
770C2×D4—91no—
771C22×C4—91no—
772C22×C4—91no—
773C4⋊C4—31no—
774C4⋊C4—31no—
775C4⋊C4—31no—
776C4⋊C4—31no—
777C4⋊C4—91no—
778C4⋊C4—91no—
779C4⋊C4—91no—
780C4⋊C4—91no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—91no—
784C4⋊C4C3×D3211yescharacteristic
785C22⋊C4—31no—
786C22⋊C4—31no—
787C22⋊C4—31no—
788C22⋊C4—91no—
789C22⋊C4—91no—
790C22⋊C4—91no—
791C22⋊C4—91no—
792C22⋊C4—91no—
793C22⋊C4—91no—
794C22⋊C4—91no—
795C42—31no—
796C42—31no—
797C42—31no—
798C42—31no—
799C42—91no—
800C42—91no—
801C42—91no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—41no—
806C22×C3—61no—
807C22×C3—61no—
808C22×C3—61no—
809C22×C3—61no—
810C22×C3—61no—
811C22×C3—61no—
812C22×C3—121no—
813C22×C3—121no—
814C22×C3—121no—
815C22×C3—181no—
816C22×C3—181no—
817C22×C3—181no—
818C22×C3C22×D3211yescharacteristic
819C22×C3C23×C3×D311yescharacteristic
820C22×C3C23×C3×D311yescharacteristic
821C2×D3—21no—
822C2×D3—21no—
823C2×D3—21no—
824C2×D3—61no—
825C2×D3—61no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—121no—
833C3×C4—22no—
834C3×C4—21no—
835C3×C4—21no—
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—21no—
839C3×C4—21no—
840C3×C4—21no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—32no—
844C3×C4—32no—
845C3×C4—32no—
846C3×C4—32no—
847C3×C4—41no—
848C3×C4—41no—
849C3×C4—41no—
850C3×C4—41no—
851C3×C4—41no—
852C3×C4—41no—
853C3×C4—41no—
854C3×C4—41no—
855C3×C4—42no—
856C3×C4—62no—
857C3×C4—62no—
858C3×C4—62no—
859C3×C4—61no—
860C3×C4—61no—
861C3×C4—61no—
862C3×C4—61no—
863C3×C4—61no—
864C3×C4—61no—
865C3×C4—61no—
866C3×C4—61no—
867C3×C4—61no—
868C3×C4—61no—
869C3×C4—81no—
870C3×C4—81no—
871C3×C4—121no—
872C3×C4—121no—
873C3×C4—121no—
874C3×C4—121no—
875C3×C4—181no—
876C3×C4—181no—
877C3×C4—181no—
878Dic3—21no—
879Dic3—21no—
880Dic3—21no—
881Dic3—21no—
882Dic3—21no—
883Dic3—61no—
884Dic3—61no—
885Dic3—61no—
886Dic3—61no—
887Dic3—61no—
888Dic3—61no—
889Dic3—121no—
890Dic3—121no—
891Dic3—121no—
892Dic3C3×#23512yes—
893Dic3C3×#23912yes—
894C32—21no—
895C32—21no—
896C32—21no—
897C32—41no—
898C32#558411yescharacteristic, complemented
899C32#570211yescharacteristic, complemented
900C32C3×#55611yescharacteristic, complemented
901C23—31no—
902C23—91no—
903Q8—62no—
904Q8—182no—
905Q8—182no—
906D4—182no—
907C2×C4—31no—
908C2×C4—31no—
909C2×C4—31no—
910C2×C4—31no—
911C2×C4—31no—
912C2×C4—31no—
913C2×C4—31no—
914C2×C4—91no—
915C2×C4—91no—
916C2×C4—91no—
917C2×C4—182no—
918C2×C4—182no—
919C2×C4C2×C3×D3211yescharacteristic
920C2×C4C2×C3×D3211yescharacteristic
921C2×C4C2×C3×D3211yescharacteristic
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—41no—
932C2×C3—41no—
933C2×C3—41no—
934C2×C3—121no—
935C2×C3—121no—
936C2×C3—241no—
937C2×C3—361no—
938C2×C3D3×#23511yescharacteristic
939C2×C3#6430911yescharacteristic
940C2×C3D3×#23911yescharacteristic
941C2×C3C2×C3×#23511yescharacteristic
942C2×C3C2×C3×#23911yescharacteristic
943C2×C3C3×D3×#4111yescharacteristic
944C2×C3C3×D3×#4111yescharacteristic
945C2×C3C3×#101011yescharacteristic
946C2×C3C3×#101011yescharacteristic
947D3—41no—
948D3—121no—
949D3—121no—
950D3—241no—
951C22—61no—
952C22—61no—
953C22—61no—
954C22—181no—
955C22—181no—
956C22—181no—
957C22C22×C3×D3211yescharacteristic
958C4—21no—
959C4—21no—
960C4—21no—
961C4—32no—
962C4—32no—
963C4—61no—
964C4—61no—
965C4—61no—
966C4—61no—
967C4—61no—
968C4—181no—
969C4—181no—
970C4—181no—
971C3—21no—
972C3—21no—
973C3—21no—
974C3—41no—
975C3#1059442111yescharacteristic, direct product factor
976C3C3×#558411yescharacteristic, complemented
977C3C3×#570211yescharacteristic, complemented
978C2—121no—
979C2—361no—
980C2C3×D3×#23511yescharacteristic
981C2C3×#6430911yescharacteristic
982C2C3×D3×#23911yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC2×C3×#626C22
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#556
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×#64107C2semidirect
2. C32×#898C2semidirect
3. C32×#887C2semidirect
4. C3×#63918C2semidirect
5. C3×C4×#627C2semidirect
6. C3×#63888C2semidirect
7. C3×#63887C2semidirect
9. C3×#63878C2semidirect
10. C3×#63861C2semidirect
13. C3×#63848C2semidirect
14. C3×#63837C2semidirect
15. C3×#63836C2semidirect
18. #10594421C3direct (N × H)
56. #64107C2×C3semidirect
66. C3×#898D3semidirect
67. C3×#898C2×C3semidirect
74. C3×#887D3semidirect
75. C3×#887C2×C3semidirect
90. #63918C2×C3semidirect
91. C4×#627C2×C3semidirect
92. #63888C2×C3semidirect
93. #63887C2×C3semidirect
95. #63878C2×C3semidirect
96. #63861C2×C3semidirect
99. #63848C2×C3semidirect
100. #63837C2×C3semidirect
101. #63836C2×C3semidirect
300. #898C3×D3semidirect
306. #887C3×D3semidirect
649. C33#556semidirect
898. C32#5584semidirect
899. C32#5702semidirect
900. C32C3×#556semidirect
975. C3#10594421direct (N × H)
976. C3C3×#5584semidirect
977. C3C3×#5702semidirect

Maximal subgroups

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

subgroupindex
C3×#641072
C32×#8982
C32×#8872
C3×#639182
C3×C4×#6272
C3×#638882
C3×#638872
C3×#638802
C3×#638782
C3×#638612
C3×#638522
C3×#638482
C3×#638372
C3×#638362
C3×#57023
C3×#55843
#105944213