Finite Group Databasebeta

← C3×#10594554 #13173993

Subgroups — C3×#10594554 #13173993

Order 1728.

1078 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64096C211yesmaximal, characteristic, complemented
2C32×#898C211yesmaximal, characteristic, complemented
3C32×#896C211yesmaximal, characteristic, complemented
4C3×#63915C211yesmaximal, characteristic
5C3×#63913C211yesmaximal, characteristic
6C3×#63887C211yesmaximal, characteristic, complemented
7C3×#63879C211yesmaximal, characteristic
8C3×#63878C211yesmaximal, characteristic, complemented
9C3×#63862C211yesmaximal, characteristic, complemented
10C3×#63862C211yesmaximal, characteristic, complemented
11C3×#63858C211yesmaximal, characteristic, complemented
12C3×#63855C211yesmaximal, characteristic, complemented
13C3×#63843C211yesmaximal, characteristic, complemented
14C3×#63840C211yesmaximal, characteristic, complemented
15C3×#63837C211yesmaximal, characteristic, complemented
16C3×#5702—31nomaximal
17C3×#5641—31nomaximal
18#10594554C311yesmaximal, characteristic, direct product factor
19C2×C3×#634C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×C32×Dic6C2211yescharacteristic
22C2×C3×#627C2211yescharacteristic
23C2×C3×#625C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C33×C4⋊C4C2211yescharacteristic
26C3×#3750C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C3×C4×C3⋊Dic3C2211yescharacteristic
30C3×C4×C3⋊Dic3C2211yescharacteristic
31C32×(C2×D3)⋊C4C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×C4⋊Dic3C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic
40C32×C4×Dic3C2211yescharacteristic
41C3×Dic3⋊Dic3C2211yescharacteristic
42C3×Dic3⋊Dic3C2211yescharacteristic
43C3×Dic3⋊Dic3C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×(C2×D3)⋊Dic3C2211yescharacteristic
47C3×(C2×D3)⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×#126—31no—
55C32×C22⋊Q8—31no—
56#64096C2×C311yescharacteristic, complemented
57C3×#946—31no—
58C3×Q8×Dic3—31no—
59C3×C4×#67—31no—
60C3×#926—31no—
61C3×#898—21no—
62C3×#898—31no—
63C3×#898—31no—
64C3×#898—31no—
65C3×#898D311yescharacteristic, complemented
66C3×#898C2×C311yescharacteristic, complemented
67C3×#896—21no—
68C3×#896D311yescharacteristic, complemented
69C3×#896C2×C311yescharacteristic, complemented
70C3×#892—31no—
71C3×#888—31no—
72C3×#888—31no—
73C3×#887—31no—
74C3×#887—31no—
75C3×#887—31no—
76C3×#887—31no—
77C3×#887—61no—
78C3×#885—31no—
79C3×#885—31no—
80C3×#885—31no—
81C3×#885—31no—
82C3×#67⋊C4—31no—
83C3×#879—31no—
84C3×#879—31no—
85C3×#879—31no—
86C3×#878—31no—
87C3×#877—31no—
88C3×#872—31no—
89C3×C4×Dic6—31no—
90#63915C2×C311yescharacteristic
91#63913C2×C311yescharacteristic
92#63887C2×C311yescharacteristic, complemented
93#63879C2×C311yescharacteristic
94#63878C2×C311yescharacteristic, complemented
95#63862C2×C311yescharacteristic, complemented
96#63862C2×C311yescharacteristic, complemented
97#63858C2×C311yescharacteristic, complemented
98#63855C2×C311yescharacteristic, complemented
99#63843C2×C311yescharacteristic, complemented
100#63840C2×C311yescharacteristic, complemented
101#63837C2×C311yescharacteristic, complemented
102C22×C32×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×C3×C3⋊Dic3C2311yescharacteristic
111C3×#634—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×C4×D3—22no—
119C32×Dic6—22no—
120C3×#627—22no—
121C3×#625—22no—
122C3×D3×Dic3—22no—
123C3×#556—91no—
124#5702—31no—
125#5641—31no—
126C2×C32×Q8—31no—
127C22×C32×C4—31no—
128C2×#634C22×C311yescharacteristic
129C2×C3×#67—31no—
130C2×C3×#67—31no—
131C22×C3×Dic3—31no—
132C2×C3×C4×D3—21no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3C2×D311yescharacteristic
135C2×C3×C4×D3C22×C311yescharacteristic
136C2×C3×Dic6—21no—
137C2×C3×Dic6—31no—
138C2×C3×Dic6—31no—
139C2×C3×Dic6—31no—
140C2×C3×Dic6—31no—
141C2×C3×Dic6—61no—
142C2×C3×Dic6C2×D311yescharacteristic
143C2×C3×Dic6C22×C311yescharacteristic
144C2×#627C22×C311yescharacteristic
145C2×#625C22×C311yescharacteristic
146C2×D3×Dic3C22×C311yescharacteristic
147C32×C4⋊C4—21no—
148C32×C4⋊C4—21no—
149C32×C4⋊C4—21no—
150C32×C4⋊C4—31no—
151C32×C4⋊C4—31no—
152C32×C4⋊C4—31no—
153C32×C4⋊C4—31no—
154C32×C4⋊C4—41no—
155C32×C4⋊C4C2×D311yescharacteristic
156C32×C4⋊C4C2×D311yescharacteristic
157C32×C4⋊C4C22×C311yescharacteristic
158C32×C22⋊C4—31no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4—31no—
161C32×C22⋊C4—31no—
162C32×C22⋊C4—31no—
163C32×C42—31no—
164#3750C22×C311yescharacteristic
165#3750C22×C311yescharacteristic
166C4×C3⋊Dic3C22×C311yescharacteristic
167C4×C3⋊Dic3C22×C311yescharacteristic
168C4×C3⋊Dic3C22×C311yescharacteristic
169C3×#217—31no—
170C3×#217—31no—
171C3×#217—31no—
172C3×#217—31no—
173C3×#217—31no—
174C3×(C2×D3)⋊C4—21no—
175C3×(C2×D3)⋊C4—21no—
176C3×(C2×D3)⋊C4—21no—
177C3×(C2×D3)⋊C4—21no—
178C3×(C2×D3)⋊C4—21no—
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)⋊C4C2×D311yescharacteristic
185C3×(C2×D3)⋊C4C2×D311yescharacteristic
186C3×(C2×D3)⋊C4C2×D311yescharacteristic
187C3×(C2×D3)⋊C4C2×D311yescharacteristic
188C3×(C2×D3)⋊C4C2×D311yescharacteristic
189C3×(C2×D3)⋊C4C22×C311yescharacteristic
190C3×(C2×D3)⋊C4C22×C311yescharacteristic
191C3×(C2×D3)⋊C4C22×C311yescharacteristic
192C3×(C2×D3)⋊C4C22×C311yescharacteristic
193C3×(C2×D3)⋊C4C22×C311yescharacteristic
194C3×C4⋊Dic3—21no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—31no—
199C3×C4⋊Dic3—31no—
200C3×C4⋊Dic3C2×D311yescharacteristic
201C3×C4⋊Dic3C22×C311yescharacteristic
202C3×Dic3⋊C4—21no—
203C3×Dic3⋊C4—21no—
204C3×Dic3⋊C4—21no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
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—61no—
215C3×Dic3⋊C4—61no—
216C3×Dic3⋊C4C2×D311yescharacteristic
217C3×Dic3⋊C4C2×D311yescharacteristic
218C3×Dic3⋊C4C2×D311yescharacteristic
219C3×Dic3⋊C4C22×C311yescharacteristic
220C3×Dic3⋊C4C22×C311yescharacteristic
221C3×Dic3⋊C4C22×C311yescharacteristic
222C3×C4×Dic3—21no—
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—31no—
231C3×C4×Dic3—31no—
232C3×C4×Dic3—31no—
233C3×C4×Dic3—31no—
234C3×C4×Dic3—31no—
235C3×C4×Dic3—61no—
236C3×C4×Dic3—61no—
237C3×C4×Dic3—61no—
238C3×C4×Dic3C2×D311yescharacteristic
239C3×C4×Dic3C22×C311yescharacteristic
240Dic3⋊Dic3C22×C311yescharacteristic
241Dic3⋊Dic3C22×C311yescharacteristic
242Dic3⋊Dic3C22×C311yescharacteristic
243Dic3⋊Dic3C22×C311yescharacteristic
244Dic3⋊Dic3C22×C311yescharacteristic
245(C2×D3)⋊Dic3C22×C311yescharacteristic
246(C2×D3)⋊Dic3C22×C311yescharacteristic
247(C2×D3)⋊Dic3C22×C311yescharacteristic
248(C2×D3)⋊Dic3C22×C311yescharacteristic
249(C2×D3)⋊Dic3C22×C311yescharacteristic
250Dic32C22×C311yescharacteristic
251Dic32C22×C311yescharacteristic
252Dic32C22×C311yescharacteristic
253C22×C33C2411yescharacteristic
254C2×C32×D3—21no—
255C2×C32×D3—21no—
256C2×C32×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—
266C3×C3⋊Dic3#4112yes—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
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—31no—
283C3×C22⋊Q8—31no—
284C3×C22⋊Q8—61no—
285C3×C22⋊Q8—91no—
286C3×C4×Q8—91no—
287C3×C4×Q8—91no—
288C3×C4×Q8—91no—
289C3×C4×D4—91no—
290C3×#117—91no—
291C3×#117—91no—
292#946—31no—
293Q8×Dic3—31no—
294C4×#67—31no—
295#926—31no—
296#898—31no—
297#898—31no—
298#898—31no—
299#898C3×D311yescharacteristic, complemented
300#896C3×D311yescharacteristic, complemented
301#892—31no—
302#888—31no—
303#888—31no—
304#887—31no—
305#887—31no—
306#887—31no—
307#887—31no—
308#887—61no—
309#885—31no—
310#885—31no—
311#885—31no—
312#885—31no—
313#67⋊C4—31no—
314#879—31no—
315#879—31no—
316#879—31no—
317#878—31no—
318#877—31no—
319#872—31no—
320C4×Dic6—31no—
321C23×C32—31no—
322C23×C32—31no—
323C22×C3×D3—21no—
324C22×C3×D3—21no—
325C22×C3×D3C22×D311yescharacteristic
326C22×C3×D3C22×D311yescharacteristic
327C22×C3×D3C23×C311yescharacteristic
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—41no—
346C2×C32×C4—41no—
347C2×C32×C4—41no—
348C2×C32×C4—62no—
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
361C2×C3⋊Dic3C23×C311yescharacteristic
362#634—22no—
363C3×#67—62no—
364C3×#67—62no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—21no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—62no—
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C23×C311yescharacteristic
391C2×C3×Dic3C23×C311yescharacteristic
392C2×C3×Dic3C23×C311yescharacteristic
393C2×C3×Dic3C23×C311yescharacteristic
394C2×C3×Dic3C23×C311yescharacteristic
395C2×C3×Dic3C23×C311yescharacteristic
396C3×C4×D3—22no—
397C3×C4×D3—22no—
398C3×C4×D3—42no—
399C3×C4×D3—62no—
400C3×Dic6—22no—
401C3×Dic6—22no—
402C3×Dic6—42no—
403C3×Dic6—62no—
404C3×Dic6—62no—
405C3×Dic6—62no—
406C3×Dic6—62no—
407C3×Dic6—64no—
408#627—22no—
409#625—22no—
410D3×Dic3—22no—
411#556—91noSylow
412C2×C33C2×#4111yescharacteristic
413C2×C33C2×#4111yescharacteristic
414C2×C332−1+411yescharacteristic
415C32×D3—41no—
416C32×D3—41no—
417C2×C3×Q8—31no—
418C2×C3×Q8—31no—
419C2×C3×Q8—61no—
420C2×C3×Q8—91no—
421C2×C3×Q8—91no—
422C2×C3×D4—91no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—61no—
426C22×C3×C4—91no—
427C2×#67—31no—
428C2×#67—31no—
429C22×Dic3—31no—
430C2×C4×D3—31no—
431C2×C4×D3C2×C3×D311yescharacteristic
432C2×Dic6—31no—
433C2×Dic6—31no—
434C2×Dic6—31no—
435C2×Dic6—31no—
436C2×Dic6—61no—
437C2×Dic6C2×C3×D311yescharacteristic
438C3×C4⋊C4—21no—
439C3×C4⋊C4—21no—
440C3×C4⋊C4—21no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—31no—
447C3×C4⋊C4—31no—
448C3×C4⋊C4—31no—
449C3×C4⋊C4—41no—
450C3×C4⋊C4—61no—
451C3×C4⋊C4—61no—
452C3×C4⋊C4—61no—
453C3×C4⋊C4—61no—
454C3×C4⋊C4—91no—
455C3×C4⋊C4—91no—
456C3×C4⋊C4—91no—
457C3×C4⋊C4—91no—
458C3×C4⋊C4—91no—
459C3×C4⋊C4—91no—
460C3×C4⋊C4—91no—
461C3×C4⋊C4D3211yescharacteristic
462C3×C4⋊C4C2×C3×D311yescharacteristic
463C3×C4⋊C4C2×C3×D311yescharacteristic
464C3×C22⋊C4—31no—
465C3×C22⋊C4—31no—
466C3×C22⋊C4—31no—
467C3×C22⋊C4—31no—
468C3×C22⋊C4—31no—
469C3×C22⋊C4—31no—
470C3×C22⋊C4—31no—
471C3×C22⋊C4—31no—
472C3×C22⋊C4—31no—
473C3×C22⋊C4—31no—
474C3×C22⋊C4—61no—
475C3×C22⋊C4—61no—
476C3×C22⋊C4—61no—
477C3×C22⋊C4—61no—
478C3×C22⋊C4—61no—
479C3×C22⋊C4—91no—
480C3×C22⋊C4—91no—
481C3×C22⋊C4—91no—
482C3×C22⋊C4—91no—
483C3×C22⋊C4—91no—
484C3×C42—31no—
485C3×C42—31no—
486C3×C42—61no—
487C3×C42—91no—
488C3×C42—91no—
489C3×C42—91no—
490C3×C42—91no—
491C3×C42—91no—
492C3×C42—91no—
493#217—31no—
494#217—31no—
495#217—31no—
496#217—31no—
497#217—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)⋊C4C2×C3×D311yescharacteristic
504(C2×D3)⋊C4C2×C3×D311yescharacteristic
505(C2×D3)⋊C4C2×C3×D311yescharacteristic
506(C2×D3)⋊C4C2×C3×D311yescharacteristic
507(C2×D3)⋊C4C2×C3×D311yescharacteristic
508C4⋊Dic3—31no—
509C4⋊Dic3—31no—
510C4⋊Dic3—31no—
511C4⋊Dic3—31no—
512C4⋊Dic3—31no—
513C4⋊Dic3C2×C3×D311yescharacteristic
514Dic3⋊C4—31no—
515Dic3⋊C4—31no—
516Dic3⋊C4—31no—
517Dic3⋊C4—31no—
518Dic3⋊C4—31no—
519Dic3⋊C4—31no—
520Dic3⋊C4—31no—
521Dic3⋊C4—31no—
522Dic3⋊C4—31no—
523Dic3⋊C4—61no—
524Dic3⋊C4—61no—
525Dic3⋊C4C2×C3×D311yescharacteristic
526Dic3⋊C4C2×C3×D311yescharacteristic
527Dic3⋊C4C2×C3×D311yescharacteristic
528C4×Dic3—31no—
529C4×Dic3—31no—
530C4×Dic3—31no—
531C4×Dic3—31no—
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—31no—
540C4×Dic3—61no—
541C4×Dic3—61no—
542C4×Dic3—61no—
543C4×Dic3C2×C3×D311yescharacteristic
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—41no—
548C22×C32—61no—
549C22×C32—61no—
550C22×C32—61no—
551C22×C32—61no—
552C22×C32—61no—
553C22×C32—61no—
554C22×C32C23×D311yescharacteristic
555C22×C32C23×D311yescharacteristic
556C22×C32C24×C311yescharacteristic
557C2×C3×D3—22no—
558C2×C3×D3—21no—
559C2×C3×D3—21no—
560C2×C3×D3—21no—
561C2×C3×D3—21no—
562C2×C3×D3—21no—
563C2×C3×D3—21no—
564C2×C3×D3—21no—
565C2×C3×D3—21no—
566C2×C3×D3—21no—
567C2×C3×D3—21no—
568C2×C3×D3—21no—
569C2×C3×D3—21no—
570C2×C3×D3—41no—
571C2×C3×D3—41no—
572C2×C3×D3—41no—
573C2×C3×D3—41no—
574C2×C3×D3—41no—
575C32×C4—21no—
576C32×C4—22no—
577C32×C4—21no—
578C32×C4—21no—
579C32×C4—21no—
580C32×C4—21no—
581C32×C4—21no—
582C32×C4—21no—
583C32×C4—21no—
584C32×C4—21no—
585C32×C4—32no—
586C32×C4—41no—
587C32×C4—41no—
588C32×C4—42no—
589C32×C4—41no—
590C32×C4—41no—
591C32×C4—41no—
592C32×C4—41no—
593C32×C4—41no—
594C32×C4—41no—
595C32×C4—61no—
596C32×C4—61no—
597C32×C4—61no—
598C32×C4—61no—
599C32×C4—61no—
600C32×C4—81no—
601C32×C4—81no—
602C3⋊Dic3—21no—
603C3⋊Dic3—21no—
604C3⋊Dic3—21no—
605C3⋊Dic3C3×#4112yes—
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—21no—
616C3×Dic3—22no—
617C3×Dic3—32no—
618C3×Dic3—32no—
619C3×Dic3—41no—
620C3×Dic3—41no—
621C3×Dic3—41no—
622C3×Dic3—41no—
623C3×Dic3—41no—
624C3×Dic3—62no—
625C3×Dic3—62no—
626C3×Dic3—62no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—61no—
630C3×Dic3—61no—
631C3×Dic3—61no—
632C3×Dic3—61no—
633C3×Dic3—121no—
634C3×Dic3#23712yes—
635C3×Dic3C3×#4112yes—
636C4⋊Q8—91no—
637#126—31no—
638#126—91no—
639#126—91no—
640#126—91no—
641#124—91no—
642#124—91no—
643C22⋊Q8—31no—
644C22⋊Q8—91no—
645C4×Q8—91no—
646C4×Q8—91no—
647C4×Q8—91no—
648C4×D4—91no—
649#117—91no—
650#117—91no—
651C33#55611yescharacteristic, complemented, Sylow
652C23×C3—31no—
653C23×C3—31no—
654C23×C3—31no—
655C23×C3—31no—
656C23×C3—61no—
657C23×C3—61no—
658C22×D3C22×C3×D311yescharacteristic
659C22×D3C22×C3×D311yescharacteristic
660C3×Q8—62no—
661C3×Q8—62no—
662C3×Q8—122no—
663C3×Q8—182no—
664C3×Q8—182no—
665C3×D4—182no—
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—21no—
674C2×C3×C4—21no—
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—62no—
697C2×C3×C4—62no—
698C2×C3×C4—91no—
699C2×C3×C4—91no—
700C2×C3×C4—91no—
701C2×C3×C4—91no—
702C2×C3×C4—122no—
703C2×C3×C4—182no—
704C2×C3×C4C2×D3211yescharacteristic
705C2×C3×C4C2×D3211yescharacteristic
706C2×C3×C4C2×D3211yescharacteristic
707C2×C3×C4C22×C3×D311yescharacteristic
708C2×C3×C4C22×C3×D311yescharacteristic
709C2×C3×C4C22×C3×D311yescharacteristic
710C2×C3×C4C22×C3×D311yescharacteristic
711C2×C3×C4C22×C3×D311yescharacteristic
712C2×C3×C4C22×C3×D311yescharacteristic
713#67—62no—
714#67—62no—
715C2×Dic3—31no—
716C2×Dic3—31no—
717C2×Dic3—31no—
718C2×Dic3—31no—
719C2×Dic3—31no—
720C2×Dic3—31no—
721C2×Dic3—31no—
722C2×Dic3—31no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—61no—
727C2×Dic3—62no—
728C2×Dic3C22×C3×D311yescharacteristic
729C2×Dic3C22×C3×D311yescharacteristic
730C2×Dic3C22×C3×D311yescharacteristic
731C2×Dic3C22×C3×D311yescharacteristic
732C2×Dic3C22×C3×D311yescharacteristic
733C2×Dic3C22×C3×D311yescharacteristic
734C4×D3—22no—
735C4×D3—62no—
736Dic6—22no—
737Dic6—62no—
738Dic6—62no—
739Dic6—62no—
740Dic6—62no—
741Dic6—64no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—41no—
752C2×C32—41no—
753C2×C32—41no—
754C2×C32—121no—
755C2×C32—121no—
756C2×C32C2×#23711yescharacteristic
757C2×C32#100711yescharacteristic
758C2×C32D3×#4111yescharacteristic
759C2×C32D3×#4111yescharacteristic
760C2×C32D3×#4111yescharacteristic
761C2×C32#101011yescharacteristic
762C2×C32C2×C3×#4111yescharacteristic
763C2×C32C2×C3×#4111yescharacteristic
764C2×C32C3×2−1+411yescharacteristic
765C3×D3—42no—
766C3×D3—41no—
767C3×D3—41no—
768C3×D3—41no—
769C3×D3—41no—
770C3×D3—81no—
771C2×Q8—31no—
772C2×Q8—91no—
773C2×Q8—91no—
774C2×D4—91no—
775C22×C4—31no—
776C22×C4—91no—
777C4⋊C4—31no—
778C4⋊C4—31no—
779C4⋊C4—31no—
780C4⋊C4—31no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—91no—
784C4⋊C4—91no—
785C4⋊C4—91no—
786C4⋊C4—91no—
787C4⋊C4—91no—
788C4⋊C4C3×D3211yescharacteristic
789C22⋊C4—31no—
790C22⋊C4—31no—
791C22⋊C4—31no—
792C22⋊C4—31no—
793C22⋊C4—31no—
794C22⋊C4—91no—
795C22⋊C4—91no—
796C22⋊C4—91no—
797C22⋊C4—91no—
798C22⋊C4—91no—
799C42—31no—
800C42—91no—
801C42—91no—
802C42—91no—
803C42—91no—
804C42—91no—
805C42—91no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—41no—
810C22×C3—62no—
811C22×C3—61no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—61no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3—121no—
824C22×C3—121no—
825C22×C3—121no—
826C22×C3—121no—
827C22×C3—121no—
828C22×C3C22×D3211yescharacteristic
829C22×C3C23×C3×D311yescharacteristic
830C22×C3C23×C3×D311yescharacteristic
831C2×D3—21no—
832C2×D3—21no—
833C2×D3—21no—
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—21no—
837C3×C4—22no—
838C3×C4—21no—
839C3×C4—21no—
840C3×C4—21no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—32no—
848C3×C4—32no—
849C3×C4—41no—
850C3×C4—41no—
851C3×C4—41no—
852C3×C4—41no—
853C3×C4—41no—
854C3×C4—41no—
855C3×C4—41no—
856C3×C4—41no—
857C3×C4—42no—
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—92no—
872C3×C4—121no—
873C3×C4—121no—
874C3×C4—121no—
875C3×C4—121no—
876C3×C4—121no—
877C3×C4—181no—
878C3×C4—181no—
879C3×C4—181no—
880Dic3—21no—
881Dic3—21no—
882Dic3—21no—
883Dic3—21no—
884Dic3—21no—
885Dic3—32no—
886Dic3—32no—
887Dic3—62no—
888Dic3—62no—
889Dic3—62no—
890Dic3—61no—
891Dic3—61no—
892Dic3—61no—
893Dic3—61no—
894Dic3—61no—
895Dic3—61no—
896Dic3—121no—
897Dic3C3×#23712yes—
898C32—21no—
899C32—21no—
900C32—21no—
901C32—41no—
902C32#564111yescharacteristic, complemented
903C32#570211yescharacteristic, complemented
904C32C3×#55611yescharacteristic, complemented
905C23—31no—
906C23—31no—
907Q8—62no—
908Q8—182no—
909Q8—182no—
910D4—182no—
911C2×C4—31no—
912C2×C4—31no—
913C2×C4—31no—
914C2×C4—31no—
915C2×C4—31no—
916C2×C4—31no—
917C2×C4—62no—
918C2×C4—91no—
919C2×C4—91no—
920C2×C4—91no—
921C2×C4—91no—
922C2×C4—182no—
923C2×C4C2×C3×D3211yescharacteristic
924C2×C4C2×C3×D3211yescharacteristic
925C2×C4C2×C3×D3211yescharacteristic
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—41no—
936C2×C3—41no—
937C2×C3—41no—
938C2×C3—122no—
939C2×C3—121no—
940C2×C3—121no—
941C2×C3—121no—
942C2×C3—121no—
943C2×C3—241no—
944C2×C3#6430611yescharacteristic
945C2×C3D3×#23711yescharacteristic
946C2×C3#6431511yescharacteristic
947C2×C3C2×C3×#23711yescharacteristic
948C2×C3C3×#100711yescharacteristic
949C2×C3C3×D3×#4111yescharacteristic
950C2×C3C3×D3×#4111yescharacteristic
951C2×C3C3×D3×#4111yescharacteristic
952C2×C3C3×#101011yescharacteristic
953D3—41no—
954D3—41no—
955C22—61no—
956C22—61no—
957C22—61no—
958C22—61no—
959C22—61no—
960C22—61no—
961C22C22×C3×D3211yescharacteristic
962C4—21no—
963C4—21no—
964C4—21no—
965C4—32no—
966C4—61no—
967C4—61no—
968C4—61no—
969C4—61no—
970C4—61no—
971C4—92no—
972C4—181no—
973C4—181no—
974C4—181no—
975C3—21no—
976C3—21no—
977C3—21no—
978C3—41no—
979C3#1059455411yescharacteristic, direct product factor
980C3C3×#564111yescharacteristic, complemented
981C3C3×#570211yescharacteristic, complemented
982C2—121no—
983C2—121no—
984C2C3×#6430611yescharacteristic
985C2C3×D3×#23711yescharacteristic
986C2C3×#6431511yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC2×C3×#625C22
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×#64096C2semidirect
2. C32×#898C2semidirect
3. C32×#896C2semidirect
6. C3×#63887C2semidirect
8. C3×#63878C2semidirect
9. C3×#63862C2semidirect
10. C3×#63862C2semidirect
11. C3×#63858C2semidirect
12. C3×#63855C2semidirect
13. C3×#63843C2semidirect
14. C3×#63840C2semidirect
15. C3×#63837C2semidirect
18. #10594554C3direct (N × H)
56. #64096C2×C3semidirect
65. C3×#898D3semidirect
66. C3×#898C2×C3semidirect
68. C3×#896D3semidirect
69. C3×#896C2×C3semidirect
92. #63887C2×C3semidirect
94. #63878C2×C3semidirect
95. #63862C2×C3semidirect
96. #63862C2×C3semidirect
97. #63858C2×C3semidirect
98. #63855C2×C3semidirect
99. #63843C2×C3semidirect
100. #63840C2×C3semidirect
101. #63837C2×C3semidirect
299. #898C3×D3semidirect
300. #896C3×D3semidirect
651. C33#556semidirect
902. C32#5641semidirect
903. C32#5702semidirect
904. C32C3×#556semidirect
979. C3#10594554direct (N × H)
980. C3C3×#5641semidirect
981. C3C3×#5702semidirect

Maximal subgroups

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

subgroupindex
C3×#640962
C32×#8982
C32×#8962
C3×#639152
C3×#639132
C3×#638872
C3×#638792
C3×#638782
C3×#638622
C3×#638582
C3×#638552
C3×#638432
C3×#638402
C3×#638372
C3×#57023
C3×#56413
#105945543