Finite Group Databasebeta

← C3×#10595151 #13174713

Subgroups — C3×#10595151 #13174713

Order 1728.

1558 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic, complemented
2C2×C3×#3805C211yesmaximal, characteristic, complemented
3C3×#64144C211yesmaximal, characteristic, complemented
4C32×#939C211yesmaximal, characteristic, complemented
5C3×Dic3×#67C211yesmaximal, characteristic, complemented
6C3×Dic3×#67C211yesmaximal, characteristic, complemented
7C3×#63970C211yesmaximal, characteristic, complemented
8C3×#63969C211yesmaximal, characteristic, complemented
9C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
10C3×#63964C211yesmaximal, characteristic, complemented
11C3×#63961C211yesmaximal, characteristic, complemented
12C3×#63905C211yesmaximal, characteristic, complemented
13C3×#63887C211yesmaximal, characteristic, complemented
14C3×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C3×#63839C211yesmaximal, characteristic, complemented
16C3×#5824—31nomaximal
17C3×#5611—31nomaximal
18#10595151C311yesmaximal, characteristic, direct product factor
19C2×C33×D4C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic
27C22×C32×Dic3C2211yescharacteristic
28C32×#237—24no—
29C2×C32×C4×D3C2211yescharacteristic
30C2×C32×Dic6C2211yescharacteristic
31C2×C3×#627C2211yescharacteristic
32C2×C3×#625C2211yescharacteristic
33C3×#3805—24no—
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36C2×C3×D3×Dic3C2211yescharacteristic
37C3×#3757C2211yescharacteristic
38C3×#3757C2211yescharacteristic
39C3×#3757C2211yescharacteristic
40C3×#3750C2211yescharacteristic
41C3×#3750C2211yescharacteristic
42C32×#217C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×Dic32C2211yescharacteristic
56C2×C32×#41—31no—
57C2×C3×#237—21no—
58C2×C3×#237—31no—
59C2×C3×#237—31no—
60C2×C3×#237D311yescharacteristic, complemented
61C2×C3×#237C2×C311yescharacteristic, complemented
62C2×#3805C2×C311yescharacteristic, complemented
63C32×#121—31no—
64#64144C2×C311yescharacteristic, complemented
65C3×#946—31no—
66C3×#944—31no—
67C3×#939—21no—
68C3×#939—31no—
69C3×#939D311yescharacteristic, complemented
70C3×#939C2×C311yescharacteristic, complemented
71C3×#938—31no—
72C3×#935—31no—
73C3×#935—31no—
74C3×#935—31no—
75C3×#935—31no—
76C3×#935—61no—
77C3×D4×Dic3—31no—
78C3×D4×Dic3—31no—
79C3×#929—31no—
80C3×#929—31no—
81C3×C4×#67—31no—
82C3×C4×#67—31no—
83C2×C3×C4⋊Dic3—31no—
84C3×#924—31no—
85C2×C3×Dic3⋊C4—31no—
86C2×C3×Dic3⋊C4—31no—
87C3×D3×C4⋊C4—31no—
88C3×#888—31no—
89C3×#883—31no—
90C3×#883—31no—
91C3×#878—31no—
92C3×#878—31no—
93Dic3×#67C2×C311yescharacteristic, complemented
94Dic3×#67C2×C311yescharacteristic, complemented
95#63970C2×C311yescharacteristic, complemented
96#63969C2×C311yescharacteristic, complemented
97C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
98#63964C2×C311yescharacteristic, complemented
99#63961C2×C311yescharacteristic, complemented
100#63905C2×C311yescharacteristic, complemented
101#63887C2×C311yescharacteristic, complemented
102D3×Dic3⋊C4C2×C311yescharacteristic, complemented
103#63839C2×C311yescharacteristic, complemented
104C23×C33C2311yescharacteristic
105C23×C33C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C33×D4—22no—
109C2×C33×C4C2311yescharacteristic
110C2×C3×C3⋊Dic3—22no—
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C32×#67—22no—
116C32×#67—22no—
117C32×#67—22no—
118C32×#67D414yescomplemented
119C2×C32×Dic3—22no—
120C2×C32×Dic3—22no—
121C2×C32×Dic3—22no—
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C32×C4×D3—22no—
129C32×Dic6—22no—
130C3×#627—22no—
131C3×#625—22no—
132C3×D3×Dic3—22no—
133C3×D3×Dic3—22no—
134C3×D3×Dic3—22no—
135C3×#547—91no—
136#5824—31no—
137#5611—31no—
138C32×#41—64no—
139C2×C32×Q8—31no—
140C2×C32×D4—21no—
141C2×C32×D4—21no—
142C2×C32×D4—21no—
143C2×C32×D4—31no—
144C2×C32×D4—31no—
145C2×C32×D4—31no—
146C2×C32×D4—31no—
147C2×C32×D4—41no—
148C2×C32×D4C2×D311yescharacteristic
149C2×C32×D4C2×D311yescharacteristic
150C2×C32×D4C22×C311yescharacteristic
151C22×C32×C4—31no—
152C22×C32×C4—31no—
153C22×C32×C4—31no—
154C22×C32×C4—31no—
155C22×C3⋊Dic3C22×C311yescharacteristic
156C2×C3×#67—21no—
157C2×C3×#67—21no—
158C2×C3×#67—21no—
159C2×C3×#67—21no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67C2×D311yescharacteristic
163C2×C3×#67C2×D311yescharacteristic
164C2×C3×#67C2×D311yescharacteristic
165C2×C3×#67C2×D311yescharacteristic
166C2×C3×#67C22×C311yescharacteristic
167C2×C3×#67C22×C311yescharacteristic
168C2×C3×#67C22×C311yescharacteristic
169C2×C3×#67C22×C311yescharacteristic
170C22×C3×Dic3—21no—
171C22×C3×Dic3—21no—
172C22×C3×Dic3—21no—
173C22×C3×Dic3—31no—
174C22×C3×Dic3—31no—
175C22×C3×Dic3—31no—
176C22×C3×Dic3—31no—
177C22×C3×Dic3—31no—
178C22×C3×Dic3—61no—
179C22×C3×Dic3C2×D311yescharacteristic
180C22×C3×Dic3C2×D311yescharacteristic
181C22×C3×Dic3C2×D311yescharacteristic
182C22×C3×Dic3C22×C311yescharacteristic
183C22×C3×Dic3C22×C311yescharacteristic
184C22×C3×Dic3C22×C311yescharacteristic
185C3×#237—28no—
186C3×#237—24no—
187C3×#237—24no—
188C3×#237—64no—
189C3×#237—64no—
190C2×C3×C4×D3—21no—
191C2×C3×C4×D3—31no—
192C2×C3×C4×D3—31no—
193C2×C3×C4×D3—31no—
194C2×C3×C4×D3C2×D311yescharacteristic
195C2×C3×C4×D3C22×C311yescharacteristic
196C2×C3×Dic6—21no—
197C2×C3×Dic6—31no—
198C2×C3×Dic6—31no—
199C2×C3×Dic6C2×D311yescharacteristic
200C2×C3×Dic6C22×C311yescharacteristic
201C2×#627C22×C311yescharacteristic
202C2×#625C22×C311yescharacteristic
203#3805—24no—
204C2×D3×Dic3C22×C311yescharacteristic
205C2×D3×Dic3C22×C311yescharacteristic
206C2×D3×Dic3C22×C311yescharacteristic
207C32×C4⋊C4—31no—
208C32×C22⋊C4—31no—
209C32×C22⋊C4—31no—
210#3757C22×C311yescharacteristic
211#3757C22×C311yescharacteristic
212#3757C22×C311yescharacteristic
213#3750C22×C311yescharacteristic
214#3750C22×C311yescharacteristic
215C3×#217—21no—
216C3×#217—31no—
217C3×#217—31no—
218C3×#217—31no—
219C3×#217—31no—
220C3×#217—31no—
221C3×#217—31no—
222C3×#217—31no—
223C3×#217—31no—
224C3×#217—31no—
225C3×#217—61no—
226C3×#217—61no—
227C3×#217—61no—
228C3×#217C2×D311yescharacteristic
229C3×#217C22×C311yescharacteristic
230C3×(C2×D3)⋊C4—21no—
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4C2×D311yescharacteristic
235C3×(C2×D3)⋊C4C22×C311yescharacteristic
236C3×C4⋊Dic3—31no—
237C3×C4⋊Dic3—31no—
238C3×C4⋊Dic3—31no—
239C3×C4⋊Dic3—31no—
240C3×C4⋊Dic3—31no—
241C3×Dic3⋊C4—21no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—31no—
245C3×Dic3⋊C4—31no—
246C3×Dic3⋊C4—31no—
247C3×Dic3⋊C4—31no—
248C3×Dic3⋊C4—31no—
249C3×Dic3⋊C4—31no—
250C3×Dic3⋊C4—31no—
251C3×Dic3⋊C4—31no—
252C3×Dic3⋊C4—31no—
253C3×Dic3⋊C4—31no—
254C3×Dic3⋊C4—31no—
255C3×Dic3⋊C4—61no—
256C3×Dic3⋊C4—61no—
257C3×Dic3⋊C4C2×D311yescharacteristic
258C3×Dic3⋊C4C22×C311yescharacteristic
259C3×C4×Dic3—31no—
260C3×C4×Dic3—31no—
261#3724C22×C311yescharacteristic
262#3724C22×C311yescharacteristic
263Dic3⋊Dic3C22×C311yescharacteristic
264Dic3⋊Dic3C22×C311yescharacteristic
265Dic3⋊Dic3C22×C311yescharacteristic
266Dic3⋊Dic3C22×C311yescharacteristic
267Dic3⋊Dic3C22×C311yescharacteristic
268(C2×D3)⋊Dic3C22×C311yescharacteristic
269(C2×D3)⋊Dic3C22×C311yescharacteristic
270(C2×D3)⋊Dic3C22×C311yescharacteristic
271Dic32C22×C311yescharacteristic
272C22×C33—21no—
273C22×C33—21no—
274C22×C33—21no—
275C22×C33—21no—
276C22×C33—21no—
277C22×C33C2×D412yes—
278C22×C33C2411yescharacteristic
279C2×C32×D3—21no—
280C2×C32×D3—21no—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C2×C32×D3C2×D412yes—
285C33×C4—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3—21no—
290C32×Dic3—21no—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C32×Dic3C2×D412yes—
295C32×Dic3#4112yescomplemented
296C2×C3×#41—31no—
297C2×C3×#41—31no—
298C2×C3×#41—61no—
299C2×C3×#41—91no—
300C2×#237—31no—
301C2×#237—31no—
302C2×#237C3×D311yescharacteristic, complemented
303C3×C4⋊Q8—91no—
304C3×#123—91no—
305C3×#123—91no—
306C3×#123—91no—
307C3×#123—91no—
308C3×C22⋊Q8—91no—
309C3×C22⋊Q8—91no—
310C3×#121—31no—
311C3×#121—31no—
312C3×#121—61no—
313C3×#121—91no—
314C3×C4×D4—91no—
315C3×C4×D4—91no—
316C2×C3×C4⋊C4—91no—
317C2×C3×C4⋊C4—91no—
318#946—31no—
319#944—31no—
320#939—31no—
321#939C3×D311yescharacteristic, complemented
322#938—31no—
323#935—31no—
324#935—31no—
325#935—31no—
326#935—31no—
327#935—61no—
328D4×Dic3—31no—
329D4×Dic3—31no—
330#929—31no—
331#929—31no—
332C4×#67—31no—
333C4×#67—31no—
334C2×C4⋊Dic3—31no—
335#924—31no—
336C2×Dic3⋊C4—31no—
337C2×Dic3⋊C4—31no—
338D3×C4⋊C4—31no—
339#888—31no—
340#883—31no—
341#883—31no—
342#878—31no—
343#878—31no—
344C23×C32—21no—
345C23×C32—21no—
346C23×C32—21no—
347C23×C32—21no—
348C23×C32—21no—
349C23×C32—21no—
350C23×C32—31no—
351C23×C32—31no—
352C23×C32—41no—
353C23×C32—41no—
354C23×C32C22×D311yescharacteristic
355C23×C32C22×D311yescharacteristic
356C23×C32C22×D311yescharacteristic
357C23×C32C22×D311yescharacteristic
358C23×C32C23×C311yescharacteristic
359C23×C32C23×C311yescharacteristic
360C22×C3×D3—21no—
361C22×C3×D3—21no—
362C22×C3×D3C22×D311yescharacteristic
363C22×C3×D3C22×D311yescharacteristic
364C22×C3×D3C23×C311yescharacteristic
365C22×C3×D3C23×C311yescharacteristic
366C32×Q8—62no—
367C32×D4—22no—
368C32×D4—24no—
369C32×D4—22no—
370C32×D4—22no—
371C32×D4—34no—
372C32×D4—42no—
373C32×D4—42no—
374C32×D4—44no—
375C32×D4—62no—
376C32×D4—62no—
377C32×D4—62no—
378C2×C32×C4—21no—
379C2×C32×C4—21no—
380C2×C32×C4—21no—
381C2×C32×C4—31no—
382C2×C32×C4—31no—
383C2×C32×C4—31no—
384C2×C32×C4—31no—
385C2×C32×C4—31no—
386C2×C32×C4—31no—
387C2×C32×C4—41no—
388C2×C32×C4—62no—
389C2×C32×C4—62no—
390C2×C32×C4—62no—
391C2×C32×C4—62no—
392C2×C32×C4C22×D311yescharacteristic
393C2×C32×C4C22×D311yescharacteristic
394C2×C32×C4C23×C311yescharacteristic
395C2×C3⋊Dic3—22no—
396C2×C3⋊Dic3C23×C311yescharacteristic
397C2×C3⋊Dic3C23×C311yescharacteristic
398C2×C3⋊Dic3C23×C311yescharacteristic
399C2×C3⋊Dic3C23×C311yescharacteristic
400C3×#67—24no—
401C3×#67—22no—
402C3×#67—22no—
403C3×#67—22no—
404C3×#67—22no—
405C3×#67—22no—
406C3×#67—22no—
407C3×#67—24no—
408C3×#67—42no—
409C3×#67—42no—
410C3×#67—62no—
411C3×#67—62no—
412C3×#67#6714yescomplemented
413C3×#67C3×D414yescomplemented
414C2×C3×Dic3—24no—
415C2×C3×Dic3—24no—
416C2×C3×Dic3—22no—
417C2×C3×Dic3—22no—
418C2×C3×Dic3—22no—
419C2×C3×Dic3—22no—
420C2×C3×Dic3—22no—
421C2×C3×Dic3—22no—
422C2×C3×Dic3—21no—
423C2×C3×Dic3—21no—
424C2×C3×Dic3—21no—
425C2×C3×Dic3—21no—
426C2×C3×Dic3—21no—
427C2×C3×Dic3—21no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—31no—
433C2×C3×Dic3—31no—
434C2×C3×Dic3—31no—
435C2×C3×Dic3—31no—
436C2×C3×Dic3—42no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—61no—
439C2×C3×Dic3—61no—
440C2×C3×Dic3—61no—
441C2×C3×Dic3—62no—
442C2×C3×Dic3—62no—
443C2×C3×Dic3—62no—
444C2×C3×Dic3—62no—
445C2×C3×Dic3—62no—
446C2×C3×Dic3—122no—
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C2×C3×Dic3C22×D311yescharacteristic
451C2×C3×Dic3C22×D311yescharacteristic
452C2×C3×Dic3C22×D311yescharacteristic
453C2×C3×Dic3C23×C311yescharacteristic
454C2×C3×Dic3C23×C311yescharacteristic
455C2×C3×Dic3C23×C311yescharacteristic
456C2×C3×Dic3C23×C311yescharacteristic
457C2×C3×Dic3C23×C311yescharacteristic
458C2×C3×Dic3C23×C311yescharacteristic
459C3×C4×D3—24no—
460C3×C4×D3—22no—
461C3×C4×D3—22no—
462C3×C4×D3—62no—
463C3×C4×D3—62no—
464C3×C4×D3—62no—
465C3×Dic6—24no—
466C3×Dic6—22no—
467C3×Dic6—22no—
468C3×Dic6—62no—
469C3×Dic6—62no—
470#627—22no—
471#625—22no—
472D3×Dic3—22no—
473D3×Dic3—22no—
474D3×Dic3—22no—
475#547—91noSylow
476C2×C33—22no—
477C2×C33—41no—
478C2×C33C22×D411yescharacteristic
479C2×C33C2×#4111yescharacteristic
480C2×C332−1+411yescharacteristic
481C32×D3—22no—
482C32×D3—41no—
483C3×#41—64no—
484C3×#41—64no—
485C3×#41—68no—
486C3×#41—184no—
487C2×C3×Q8—31no—
488C2×C3×Q8—31no—
489C2×C3×Q8—61no—
490C2×C3×Q8—91no—
491C2×C3×D4—21no—
492C2×C3×D4—21no—
493C2×C3×D4—21no—
494C2×C3×D4—31no—
495C2×C3×D4—31no—
496C2×C3×D4—31no—
497C2×C3×D4—31no—
498C2×C3×D4—31no—
499C2×C3×D4—31no—
500C2×C3×D4—31no—
501C2×C3×D4—31no—
502C2×C3×D4—41no—
503C2×C3×D4—61no—
504C2×C3×D4—61no—
505C2×C3×D4—61no—
506C2×C3×D4—61no—
507C2×C3×D4—91no—
508C2×C3×D4D3211yescharacteristic
509C2×C3×D4C2×C3×D311yescharacteristic
510C2×C3×D4C2×C3×D311yescharacteristic
511C22×C3×C4—31no—
512C22×C3×C4—31no—
513C22×C3×C4—31no—
514C22×C3×C4—31no—
515C22×C3×C4—31no—
516C22×C3×C4—31no—
517C22×C3×C4—31no—
518C22×C3×C4—31no—
519C22×C3×C4—61no—
520C22×C3×C4—61no—
521C22×C3×C4—61no—
522C22×C3×C4—61no—
523C22×C3×C4—91no—
524C22×C3×C4—91no—
525C22×C3×C4—91no—
526C22×C3×C4—91no—
527C2×#67—31no—
528C2×#67—31no—
529C2×#67C2×C3×D311yescharacteristic
530C2×#67C2×C3×D311yescharacteristic
531C2×#67C2×C3×D311yescharacteristic
532C2×#67C2×C3×D311yescharacteristic
533C22×Dic3—31no—
534C22×Dic3—31no—
535C22×Dic3—31no—
536C22×Dic3—31no—
537C22×Dic3—31no—
538C22×Dic3—61no—
539C22×Dic3C2×C3×D311yescharacteristic
540C22×Dic3C2×C3×D311yescharacteristic
541C22×Dic3C2×C3×D311yescharacteristic
542#237—24no—
543#237—64no—
544#237—64no—
545C2×C4×D3—31no—
546C2×C4×D3—31no—
547C2×C4×D3—31no—
548C2×C4×D3C2×C3×D311yescharacteristic
549C2×Dic6—31no—
550C2×Dic6—31no—
551C2×Dic6C2×C3×D311yescharacteristic
552C3×C4⋊C4—31no—
553C3×C4⋊C4—31no—
554C3×C4⋊C4—61no—
555C3×C4⋊C4—91no—
556C3×C4⋊C4—91no—
557C3×C4⋊C4—91no—
558C3×C4⋊C4—91no—
559C3×C4⋊C4—91no—
560C3×C4⋊C4—91no—
561C3×C4⋊C4—91no—
562C3×C4⋊C4—91no—
563C3×C4⋊C4—91no—
564C3×C22⋊C4—31no—
565C3×C22⋊C4—31no—
566C3×C22⋊C4—31no—
567C3×C22⋊C4—31no—
568C3×C22⋊C4—61no—
569C3×C22⋊C4—61no—
570C3×C22⋊C4—91no—
571C3×C22⋊C4—91no—
572C3×C22⋊C4—91no—
573C3×C22⋊C4—91no—
574C3×C22⋊C4—91no—
575C3×C22⋊C4—91no—
576C3×C42—91no—
577#217—31no—
578#217—31no—
579#217—31no—
580#217—31no—
581#217—31no—
582#217—31no—
583#217—31no—
584#217—31no—
585#217—31no—
586#217—61no—
587#217—61no—
588#217—61no—
589#217C2×C3×D311yescharacteristic
590(C2×D3)⋊C4—31no—
591(C2×D3)⋊C4—31no—
592(C2×D3)⋊C4—31no—
593(C2×D3)⋊C4C2×C3×D311yescharacteristic
594C4⋊Dic3—31no—
595C4⋊Dic3—31no—
596C4⋊Dic3—31no—
597C4⋊Dic3—31no—
598C4⋊Dic3—31no—
599Dic3⋊C4—31no—
600Dic3⋊C4—31no—
601Dic3⋊C4—31no—
602Dic3⋊C4—31no—
603Dic3⋊C4—31no—
604Dic3⋊C4—31no—
605Dic3⋊C4—31no—
606Dic3⋊C4—31no—
607Dic3⋊C4—31no—
608Dic3⋊C4—31no—
609Dic3⋊C4—31no—
610Dic3⋊C4—31no—
611Dic3⋊C4—31no—
612Dic3⋊C4—61no—
613Dic3⋊C4—61no—
614Dic3⋊C4C2×C3×D311yescharacteristic
615C4×Dic3—31no—
616C4×Dic3—31no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32—22no—
625C22×C32—21no—
626C22×C32—21no—
627C22×C32—21no—
628C22×C32—21no—
629C22×C32—21no—
630C22×C32—21no—
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—22no—
637C22×C32—22no—
638C22×C32—22no—
639C22×C32—32no—
640C22×C32—41no—
641C22×C32—42no—
642C22×C32—41no—
643C22×C32—41no—
644C22×C32—42no—
645C22×C32—41no—
646C22×C32—41no—
647C22×C32—41no—
648C22×C32—41no—
649C22×C32—41no—
650C22×C32—41no—
651C22×C32—41no—
652C22×C32—41no—
653C22×C32—41no—
654C22×C32—41no—
655C22×C32—41no—
656C22×C32—41no—
657C22×C32—61no—
658C22×C32—61no—
659C22×C32—61no—
660C22×C32—61no—
661C22×C32—61no—
662C22×C32—81no—
663C22×C32—81no—
664C22×C32—81no—
665C22×C32—81no—
666C22×C32D3×D412yes—
667C22×C32C2×#6712yes—
668C22×C32C2×C3×D412yes—
669C22×C32C23×D311yescharacteristic
670C22×C32C23×D311yescharacteristic
671C22×C32C24×C311yescharacteristic
672C2×C3×D3—21no—
673C2×C3×D3—21no—
674C2×C3×D3—21no—
675C2×C3×D3—21no—
676C2×C3×D3—21no—
677C2×C3×D3—21no—
678C2×C3×D3—21no—
679C2×C3×D3—21no—
680C2×C3×D3—21no—
681C2×C3×D3—21no—
682C2×C3×D3—22no—
683C2×C3×D3—41no—
684C2×C3×D3—41no—
685C2×C3×D3—41no—
686C2×C3×D3—41no—
687C2×C3×D3—41no—
688C2×C3×D3C2×#6712yes—
689C2×C3×D3C2×C3×D412yes—
690C32×C4—21no—
691C32×C4—22no—
692C32×C4—21no—
693C32×C4—21no—
694C32×C4—32no—
695C32×C4—32no—
696C32×C4—41no—
697C32×C4—41no—
698C32×C4—42no—
699C32×C4—61no—
700C32×C4—61no—
701C32×C4—61no—
702C32×C4—61no—
703C3⋊Dic3—21no—
704C3⋊Dic3—21no—
705C3⋊Dic3—21no—
706C3⋊Dic3—21no—
707C3×Dic3—22no—
708C3×Dic3—22no—
709C3×Dic3—21no—
710C3×Dic3—21no—
711C3×Dic3—21no—
712C3×Dic3—21no—
713C3×Dic3—21no—
714C3×Dic3—21no—
715C3×Dic3—21no—
716C3×Dic3—21no—
717C3×Dic3—22no—
718C3×Dic3—22no—
719C3×Dic3—41no—
720C3×Dic3—41no—
721C3×Dic3—61no—
722C3×Dic3—61no—
723C3×Dic3—61no—
724C3×Dic3—61no—
725C3×Dic3—61no—
726C3×Dic3—61no—
727C3×Dic3—61no—
728C3×Dic3—61no—
729C3×Dic3—121no—
730C3×Dic3—121no—
731C3×Dic3—121no—
732C3×Dic3—121no—
733C3×Dic3#23712yescomplemented
734C3×Dic3C2×#6712yes—
735C3×Dic3C2×C3×D412yes—
736C3×Dic3C3×#4112yescomplemented
737C2×#41—31no—
738C2×#41—91no—
739C4⋊Q8—91no—
740#123—91no—
741#123—91no—
742#123—91no—
743#123—91no—
744C22⋊Q8—91no—
745C22⋊Q8—91no—
746#121—31no—
747#121—91no—
748C4×D4—91no—
749C4×D4—91no—
750C2×C4⋊C4—91no—
751C2×C4⋊C4—91no—
752C33#54711yescharacteristic, complemented, Sylow
753C23×C3—21no—
754C23×C3—21no—
755C23×C3—21no—
756C23×C3—21no—
757C23×C3—21no—
758C23×C3—21no—
759C23×C3—31no—
760C23×C3—31no—
761C23×C3—31no—
762C23×C3—31no—
763C23×C3—41no—
764C23×C3—41no—
765C23×C3—61no—
766C23×C3—61no—
767C23×C3C2×D3211yescharacteristic
768C23×C3C2×D3211yescharacteristic
769C23×C3C22×C3×D311yescharacteristic
770C23×C3C22×C3×D311yescharacteristic
771C23×C3C22×C3×D311yescharacteristic
772C23×C3C22×C3×D311yescharacteristic
773C22×D3C22×C3×D311yescharacteristic
774C22×D3C22×C3×D311yescharacteristic
775C3×Q8—62no—
776C3×Q8—62no—
777C3×Q8—64no—
778C3×Q8—182no—
779C3×D4—24no—
780C3×D4—22no—
781C3×D4—22no—
782C3×D4—22no—
783C3×D4—34no—
784C3×D4—34no—
785C3×D4—42no—
786C3×D4—42no—
787C3×D4—44no—
788C3×D4—64no—
789C3×D4—62no—
790C3×D4—62no—
791C3×D4—62no—
792C3×D4—62no—
793C3×D4—64no—
794C3×D4—62no—
795C3×D4—62no—
796C3×D4—122no—
797C3×D4—122no—
798C3×D4—182no—
799C2×C3×C4—21no—
800C2×C3×C4—21no—
801C2×C3×C4—21no—
802C2×C3×C4—31no—
803C2×C3×C4—31no—
804C2×C3×C4—31no—
805C2×C3×C4—31no—
806C2×C3×C4—31no—
807C2×C3×C4—31no—
808C2×C3×C4—31no—
809C2×C3×C4—31no—
810C2×C3×C4—31no—
811C2×C3×C4—31no—
812C2×C3×C4—31no—
813C2×C3×C4—31no—
814C2×C3×C4—41no—
815C2×C3×C4—61no—
816C2×C3×C4—61no—
817C2×C3×C4—61no—
818C2×C3×C4—61no—
819C2×C3×C4—61no—
820C2×C3×C4—61no—
821C2×C3×C4—62no—
822C2×C3×C4—62no—
823C2×C3×C4—64no—
824C2×C3×C4—62no—
825C2×C3×C4—62no—
826C2×C3×C4—62no—
827C2×C3×C4—62no—
828C2×C3×C4—64no—
829C2×C3×C4—64no—
830C2×C3×C4—62no—
831C2×C3×C4—62no—
832C2×C3×C4—91no—
833C2×C3×C4—91no—
834C2×C3×C4—91no—
835C2×C3×C4—91no—
836C2×C3×C4—122no—
837C2×C3×C4—182no—
838C2×C3×C4—182no—
839C2×C3×C4—182no—
840C2×C3×C4—182no—
841C2×C3×C4C2×D3211yescharacteristic
842C2×C3×C4C22×C3×D311yescharacteristic
843C2×C3×C4C22×C3×D311yescharacteristic
844#67—22no—
845#67—22no—
846#67—22no—
847#67—62no—
848#67—62no—
849#67C3×#6714yescomplemented
850C2×Dic3—22no—
851C2×Dic3—22no—
852C2×Dic3—22no—
853C2×Dic3—31no—
854C2×Dic3—31no—
855C2×Dic3—31no—
856C2×Dic3—31no—
857C2×Dic3—31no—
858C2×Dic3—31no—
859C2×Dic3—31no—
860C2×Dic3—31no—
861C2×Dic3—61no—
862C2×Dic3—61no—
863C2×Dic3—61no—
864C2×Dic3—61no—
865C2×Dic3—62no—
866C2×Dic3—62no—
867C2×Dic3—62no—
868C2×Dic3—62no—
869C2×Dic3—62no—
870C2×Dic3—122no—
871C2×Dic3C22×C3×D311yescharacteristic
872C2×Dic3C22×C3×D311yescharacteristic
873C2×Dic3C22×C3×D311yescharacteristic
874C2×Dic3C22×C3×D311yescharacteristic
875C2×Dic3C22×C3×D311yescharacteristic
876C2×Dic3C22×C3×D311yescharacteristic
877C4×D3—22no—
878C4×D3—62no—
879C4×D3—62no—
880C4×D3—62no—
881Dic6—22no—
882Dic6—62no—
883Dic6—62no—
884C2×C32—22no—
885C2×C32—22no—
886C2×C32—22no—
887C2×C32—21no—
888C2×C32—21no—
889C2×C32—21no—
890C2×C32—21no—
891C2×C32—21no—
892C2×C32—21no—
893C2×C32—21no—
894C2×C32—21no—
895C2×C32—21no—
896C2×C32—41no—
897C2×C32—41no—
898C2×C32—41no—
899C2×C32—42no—
900C2×C32—42no—
901C2×C32—42no—
902C2×C32—41no—
903C2×C32—42no—
904C2×C32—41no—
905C2×C32—41no—
906C2×C32—62no—
907C2×C32—82no—
908C2×C32—81no—
909C2×C32—81no—
910C2×C32—82no—
911C2×C32—121no—
912C2×C32C2×D3×D411yescharacteristic
913C2×C32C2×#23711yescharacteristic
914C2×C32D3×#4111yescharacteristic
915C2×C32#101011yescharacteristic
916C2×C32#101011yescharacteristic
917C2×C32C22×#6711yescharacteristic
918C2×C32C22×C3×D411yescharacteristic
919C2×C32C2×C3×#4111yescharacteristic
920C2×C32C3×2−1+411yescharacteristic
921C3×D3—22no—
922C3×D3—22no—
923C3×D3—42no—
924C3×D3—41no—
925C3×D3—41no—
926C3×D3—81no—
927#41—64no—
928#41—184no—
929C2×Q8—31no—
930C2×Q8—91no—
931C2×D4—31no—
932C2×D4—31no—
933C2×D4—31no—
934C2×D4—31no—
935C2×D4—91no—
936C2×D4C3×D3211yescharacteristic
937C22×C4—31no—
938C22×C4—31no—
939C22×C4—31no—
940C22×C4—31no—
941C22×C4—91no—
942C22×C4—91no—
943C22×C4—91no—
944C22×C4—91no—
945C4⋊C4—31no—
946C4⋊C4—91no—
947C4⋊C4—91no—
948C4⋊C4—91no—
949C4⋊C4—91no—
950C4⋊C4—91no—
951C4⋊C4—91no—
952C4⋊C4—91no—
953C4⋊C4—91no—
954C4⋊C4—91no—
955C22⋊C4—31no—
956C22⋊C4—31no—
957C22⋊C4—91no—
958C22⋊C4—91no—
959C22⋊C4—91no—
960C22⋊C4—91no—
961C22⋊C4—91no—
962C22⋊C4—91no—
963C42—91no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—21no—
970C22×C3—22no—
971C22×C3—21no—
972C22×C3—21no—
973C22×C3—21no—
974C22×C3—21no—
975C22×C3—21no—
976C22×C3—21no—
977C22×C3—21no—
978C22×C3—21no—
979C22×C3—21no—
980C22×C3—21no—
981C22×C3—21no—
982C22×C3—21no—
983C22×C3—22no—
984C22×C3—22no—
985C22×C3—22no—
986C22×C3—32no—
987C22×C3—32no—
988C22×C3—41no—
989C22×C3—41no—
990C22×C3—41no—
991C22×C3—41no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—41no—
999C22×C3—41no—
1000C22×C3—41no—
1001C22×C3—41no—
1002C22×C3—42no—
1003C22×C3—41no—
1004C22×C3—42no—
1005C22×C3—62no—
1006C22×C3—61no—
1007C22×C3—61no—
1008C22×C3—61no—
1009C22×C3—61no—
1010C22×C3—61no—
1011C22×C3—61no—
1012C22×C3—61no—
1013C22×C3—61no—
1014C22×C3—61no—
1015C22×C3—61no—
1016C22×C3—81no—
1017C22×C3—81no—
1018C22×C3—81no—
1019C22×C3—81no—
1020C22×C3—121no—
1021C22×C3—121no—
1022C22×C3—121no—
1023C22×C3—121no—
1024C22×C3—121no—
1025C22×C3D3×#6712yes—
1026C22×C3C3×D3×D412yes—
1027C22×C3C2×C3×#6712yes—
1028C22×C3C22×D3211yescharacteristic
1029C22×C3C23×C3×D311yescharacteristic
1030C22×C3C23×C3×D311yescharacteristic
1031C2×D3—21no—
1032C2×D3—21no—
1033C2×D3—21no—
1034C2×D3—21no—
1035C2×D3—21no—
1036C2×D3C2×C3×#6712yes—
1037C3×C4—22no—
1038C3×C4—21no—
1039C3×C4—21no—
1040C3×C4—21no—
1041C3×C4—32no—
1042C3×C4—32no—
1043C3×C4—32no—
1044C3×C4—32no—
1045C3×C4—41no—
1046C3×C4—41no—
1047C3×C4—42no—
1048C3×C4—62no—
1049C3×C4—62no—
1050C3×C4—62no—
1051C3×C4—62no—
1052C3×C4—61no—
1053C3×C4—61no—
1054C3×C4—61no—
1055C3×C4—61no—
1056C3×C4—61no—
1057C3×C4—61no—
1058C3×C4—61no—
1059C3×C4—61no—
1060C3×C4—121no—
1061C3×C4—121no—
1062C3×C4—181no—
1063C3×C4—181no—
1064C3×C4—181no—
1065C3×C4—181no—
1066Dic3—21no—
1067Dic3—21no—
1068Dic3—21no—
1069Dic3—21no—
1070Dic3—61no—
1071Dic3—61no—
1072Dic3—61no—
1073Dic3—61no—
1074Dic3—61no—
1075Dic3—61no—
1076Dic3—61no—
1077Dic3—61no—
1078Dic3—121no—
1079Dic3—121no—
1080Dic3—121no—
1081Dic3—121no—
1082Dic3C3×#23712yescomplemented
1083Dic3C2×C3×#6712yes—
1084C32—21no—
1085C32—21no—
1086C32—21no—
1087C32—41no—
1088C32#561111yescharacteristic, complemented
1089C32#582411yescharacteristic, complemented
1090C32C3×#54711yescharacteristic, complemented
1091C23—31no—
1092C23—31no—
1093C23C2×C3×D3211yescharacteristic
1094C23C2×C3×D3211yescharacteristic
1095Q8—62no—
1096Q8—182no—
1097D4—22no—
1098D4—34no—
1099D4—62no—
1100D4—62no—
1101D4—62no—
1102D4—182no—
1103C2×C4—31no—
1104C2×C4—31no—
1105C2×C4—31no—
1106C2×C4—31no—
1107C2×C4—31no—
1108C2×C4—31no—
1109C2×C4—62no—
1110C2×C4—62no—
1111C2×C4—62no—
1112C2×C4—62no—
1113C2×C4—91no—
1114C2×C4—91no—
1115C2×C4—91no—
1116C2×C4—91no—
1117C2×C4—182no—
1118C2×C4—182no—
1119C2×C4—182no—
1120C2×C4—182no—
1121C2×C4C2×C3×D3211yescharacteristic
1122C2×C3—22no—
1123C2×C3—22no—
1124C2×C3—22no—
1125C2×C3—21no—
1126C2×C3—21no—
1127C2×C3—21no—
1128C2×C3—21no—
1129C2×C3—21no—
1130C2×C3—21no—
1131C2×C3—21no—
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—42no—
1135C2×C3—42no—
1136C2×C3—42no—
1137C2×C3—42no—
1138C2×C3—41no—
1139C2×C3—41no—
1140C2×C3—41no—
1141C2×C3—41no—
1142C2×C3—41no—
1143C2×C3—41no—
1144C2×C3—62no—
1145C2×C3—62no—
1146C2×C3—82no—
1147C2×C3—81no—
1148C2×C3—81no—
1149C2×C3—82no—
1150C2×C3—122no—
1151C2×C3—121no—
1152C2×C3—121no—
1153C2×C3—241no—
1154C2×C3#6430911yescharacteristic
1155C2×C3D3×#23711yescharacteristic
1156C2×C3C2×D3×#6711yescharacteristic
1157C2×C3C2×C3×D3×D411yescharacteristic
1158C2×C3C2×C3×#23711yescharacteristic
1159C2×C3C3×D3×#4111yescharacteristic
1160C2×C3C3×#101011yescharacteristic
1161C2×C3C3×#101011yescharacteristic
1162C2×C3C22×C3×#6711yescharacteristic
1163D3—22no—
1164D3—41no—
1165C22—21no—
1166C22—21no—
1167C22—21no—
1168C22—21no—
1169C22—21no—
1170C22—32no—
1171C22—61no—
1172C22—61no—
1173C22—61no—
1174C22—61no—
1175C22—61no—
1176C22C3×D3×#6712yes—
1177C22C22×C3×D3211yescharacteristic
1178C4—21no—
1179C4—32no—
1180C4—32no—
1181C4—61no—
1182C4—61no—
1183C4—61no—
1184C4—61no—
1185C4—181no—
1186C4—181no—
1187C4—181no—
1188C4—181no—
1189C3—21no—
1190C3—21no—
1191C3—21no—
1192C3—41no—
1193C3#1059515111yescharacteristic, direct product factor
1194C3C3×#561111yescharacteristic, complemented
1195C3C3×#582411yescharacteristic, complemented
1196C2—22no—
1197C2—41no—
1198C2—62no—
1199C2—121no—
1200C2C3×#6430911yescharacteristic
1201C2C3×D3×#23711yescharacteristic
1202C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#237C2semidirect
2. C2×C3×#3805C2semidirect
3. C3×#64144C2semidirect
4. C32×#939C2semidirect
5. C3×Dic3×#67C2semidirect
6. C3×Dic3×#67C2semidirect
7. C3×#63970C2semidirect
8. C3×#63969C2semidirect
9. C2×C3×Dic3⋊Dic3C2semidirect
10. C3×#63964C2semidirect
11. C3×#63961C2semidirect
12. C3×#63905C2semidirect
13. C3×#63887C2semidirect
14. C3×D3×Dic3⋊C4C2semidirect
15. C3×#63839C2semidirect
18. #10595151C3direct (N × H)
60. C2×C3×#237D3semidirect
61. C2×C3×#237C2×C3semidirect
62. C2×#3805C2×C3semidirect
64. #64144C2×C3semidirect
69. C3×#939D3semidirect
70. C3×#939C2×C3semidirect
93. Dic3×#67C2×C3semidirect
94. Dic3×#67C2×C3semidirect
95. #63970C2×C3semidirect
96. #63969C2×C3semidirect
97. C2×Dic3⋊Dic3C2×C3semidirect
98. #63964C2×C3semidirect
99. #63961C2×C3semidirect
100. #63905C2×C3semidirect
101. #63887C2×C3semidirect
102. D3×Dic3⋊C4C2×C3semidirect
103. #63839C2×C3semidirect
118. C32×#67D4semidirect
295. C32×Dic3#41semidirect
302. C2×#237C3×D3semidirect
321. #939C3×D3semidirect
412. C3×#67#67semidirect
413. C3×#67C3×D4semidirect
733. C3×Dic3#237semidirect
736. C3×Dic3C3×#41semidirect
752. C33#547semidirect
849. #67C3×#67semidirect
1082. Dic3C3×#237semidirect
1088. C32#5611semidirect
1089. C32#5824semidirect
1090. C32C3×#547semidirect
1193. C3#10595151direct (N × H)
1194. C3C3×#5611semidirect
1195. C3C3×#5824semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C2×C3×#38052
C3×#641442
C32×#9392
C3×Dic3×#672
C3×#639702
C3×#639692
C2×C3×Dic3⋊Dic32
C3×#639642
C3×#639612
C3×#639052
C3×#638872
C3×D3×Dic3⋊C42
C3×#638392
C3×#58243
C3×#56113
#105951513