Finite Group Databasebeta

← C3×#10595156 #13174717

Subgroups — C3×#10595156 #13174717

Order 1728.

1582 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic, complemented
2C2×C3×#3804C211yesmaximal, characteristic, complemented
3C3×#64148C211yesmaximal, characteristic, complemented
4C32×#939C211yesmaximal, characteristic, complemented
5C3×#63980C211yesmaximal, characteristic, complemented
6C3×#63978C211yesmaximal, characteristic, complemented
7C3×#63978C211yesmaximal, characteristic, complemented
8C3×#63970C211yesmaximal, characteristic, complemented
9C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
10C3×#63964C211yesmaximal, characteristic, complemented
11C3×#63958C211yesmaximal, characteristic, complemented
12C3×#63906C211yesmaximal, characteristic, complemented
13C3×#63888C211yesmaximal, characteristic, complemented
14C3×#63887C211yesmaximal, characteristic, complemented
15C3×#63851C211yesmaximal, characteristic, complemented
16C3×#5833—31nomaximal
17C3×#5597—31nomaximal
18#10595156C311yesmaximal, characteristic, direct product factor
19C2×C33×D4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic
27C22×C32×Dic3C2211yescharacteristic
28C22×C32×Dic3C2211yescharacteristic
29C22×C32×Dic3C2211yescharacteristic
30C32×#237—24no—
31C2×C32×C4×D3C2211yescharacteristic
32C2×C32×Dic6C2211yescharacteristic
33C2×C3×#627C2211yescharacteristic
34C2×C3×#626C2211yescharacteristic
35C2×C3×#626C2211yescharacteristic
36C2×C3×#625C2211yescharacteristic
37C2×C3×#624C2211yescharacteristic
38C3×#3804—24no—
39C2×C3×D3×Dic3C2211yescharacteristic
40C3×#3757C2211yescharacteristic
41C3×#3752C2211yescharacteristic
42C3×#3750C2211yescharacteristic
43C32×#217C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×#3722C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×C32×#41—31no—
57C2×C3×#237—21no—
58C2×C3×#237—31no—
59C2×C3×#237D311yescharacteristic, complemented
60C2×C3×#237C2×C311yescharacteristic, complemented
61C2×C3×#235—31no—
62C2×#3804C2×C311yescharacteristic, complemented
63C32×#121—31no—
64#64148C2×C311yescharacteristic, complemented
65C3×#946—31no—
66C3×#946—31no—
67C3×#939—21no—
68C3×#939—31no—
69C3×#939—31no—
70C3×#939—31no—
71C3×#939—31no—
72C3×#939—31no—
73C3×#939—31no—
74C3×#939—31no—
75C3×#939—61no—
76C3×#939D311yescharacteristic, complemented
77C3×#939C2×C311yescharacteristic, complemented
78C3×#938—31no—
79C3×#938—31no—
80C3×#930—31no—
81C3×#930—31no—
82C3×#930—31no—
83C2×C3×C4⋊Dic3—31no—
84C3×#924—31no—
85C3×#924—31no—
86C2×C3×Dic3⋊C4—31no—
87C3×#896—31no—
88C3×#896—31no—
89C3×#884—31no—
90C3×#884—31no—
91C3×#878—31no—
92C3×#878—31no—
93#63980C2×C311yescharacteristic, complemented
94#63978C2×C311yescharacteristic, complemented
95#63978C2×C311yescharacteristic, complemented
96#63970C2×C311yescharacteristic, complemented
97C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
98#63964C2×C311yescharacteristic, complemented
99#63958C2×C311yescharacteristic, complemented
100#63906C2×C311yescharacteristic, complemented
101#63888C2×C311yescharacteristic, complemented
102#63887C2×C311yescharacteristic, complemented
103#63851C2×C311yescharacteristic, complemented
104C23×C33C2311yescharacteristic
105C23×C33C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C33×D4—22no—
110C2×C33×C4C2311yescharacteristic
111C3×#638—22no—
112C3×#638—41no—
113C2×C3×C3⋊Dic3—41no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C32×#67—22no—
118C32×#67—22no—
119C32×#67—22no—
120C32×#67—41no—
121C2×C32×Dic3—22no—
122C2×C32×Dic3—41no—
123C2×C32×Dic3D414yescomplemented
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C32×C4×D3—22no—
131C32×Dic6—22no—
132C3×#627—22no—
133C3×#626—22no—
134C3×#626—41no—
135C3×#625—41no—
136C3×#624—22no—
137C3×D3×Dic3—22no—
138C3×#537—91no—
139#5833—31no—
140#5597—31no—
141C32×#41—64no—
142C2×C32×Q8—31no—
143C2×C32×D4—21no—
144C2×C32×D4—21no—
145C2×C32×D4—21no—
146C2×C32×D4—31no—
147C2×C32×D4—31no—
148C2×C32×D4—31no—
149C2×C32×D4—31no—
150C2×C32×D4—41no—
151C2×C32×D4C2×D311yescharacteristic
152C2×C32×D4C2×D311yescharacteristic
153C2×C32×D4C22×C311yescharacteristic
154C22×C32×C4—31no—
155C22×C32×C4—31no—
156C22×C32×C4—31no—
157C22×C32×C4—31no—
158C2×#638C22×C311yescharacteristic
159C2×#638C22×C311yescharacteristic
160C22×C3⋊Dic3C22×C311yescharacteristic
161C2×C3×#67—21no—
162C2×C3×#67—21no—
163C2×C3×#67—21no—
164C2×C3×#67—21no—
165C2×C3×#67—31no—
166C2×C3×#67—31no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—61no—
174C2×C3×#67—61no—
175C2×C3×#67C2×D311yescharacteristic
176C2×C3×#67C2×D311yescharacteristic
177C2×C3×#67C2×D311yescharacteristic
178C2×C3×#67C2×D311yescharacteristic
179C2×C3×#67C22×C311yescharacteristic
180C2×C3×#67C22×C311yescharacteristic
181C2×C3×#67C22×C311yescharacteristic
182C2×C3×#67C22×C311yescharacteristic
183C22×C3×Dic3—21no—
184C22×C3×Dic3—21no—
185C22×C3×Dic3—21no—
186C22×C3×Dic3—31no—
187C22×C3×Dic3—31no—
188C22×C3×Dic3—31no—
189C22×C3×Dic3—61no—
190C22×C3×Dic3C2×D311yescharacteristic
191C22×C3×Dic3C2×D311yescharacteristic
192C22×C3×Dic3C2×D311yescharacteristic
193C22×C3×Dic3C22×C311yescharacteristic
194C22×C3×Dic3C22×C311yescharacteristic
195C22×C3×Dic3C22×C311yescharacteristic
196C3×#237—28no—
197C3×#237—24no—
198C3×#237—24no—
199C3×#237—64no—
200C3×#235—64no—
201C2×C3×D12—31no—
202C2×C3×D12—31no—
203C2×C3×C4×D3—21no—
204C2×C3×C4×D3—31no—
205C2×C3×C4×D3—31no—
206C2×C3×C4×D3—31no—
207C2×C3×C4×D3C2×D311yescharacteristic
208C2×C3×C4×D3C22×C311yescharacteristic
209C2×C3×Dic6—21no—
210C2×C3×Dic6—31no—
211C2×C3×Dic6—31no—
212C2×C3×Dic6C2×D311yescharacteristic
213C2×C3×Dic6C22×C311yescharacteristic
214C2×#627C22×C311yescharacteristic
215C2×#626C22×C311yescharacteristic
216C2×#626C22×C311yescharacteristic
217C2×#625C22×C311yescharacteristic
218C2×#624C22×C311yescharacteristic
219#3804—24no—
220C2×D3×Dic3C22×C311yescharacteristic
221C32×C4⋊C4—31no—
222C32×C22⋊C4—31no—
223C32×C22⋊C4—31no—
224#3757C22×C311yescharacteristic
225#3752C22×C311yescharacteristic
226#3750C22×C311yescharacteristic
227C3×#217—21no—
228C3×#217—31no—
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—61no—
234C3×#217C2×D311yescharacteristic
235C3×#217C22×C311yescharacteristic
236C3×(C2×D3)⋊C4—21no—
237C3×(C2×D3)⋊C4—31no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—31no—
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×(C2×D3)⋊C4—61no—
245C3×(C2×D3)⋊C4C2×D311yescharacteristic
246C3×(C2×D3)⋊C4C22×C311yescharacteristic
247C3×C4⋊Dic3—31no—
248C3×C4⋊Dic3—31no—
249C3×C4⋊Dic3—31no—
250C3×C4⋊Dic3—31no—
251C3×C4⋊Dic3—31no—
252C3×Dic3⋊C4—21no—
253C3×Dic3⋊C4—31no—
254C3×Dic3⋊C4—31no—
255C3×Dic3⋊C4—31no—
256C3×Dic3⋊C4—31no—
257C3×Dic3⋊C4—31no—
258C3×Dic3⋊C4—31no—
259C3×Dic3⋊C4—31no—
260C3×Dic3⋊C4—31no—
261C3×Dic3⋊C4—31no—
262C3×Dic3⋊C4—61no—
263C3×Dic3⋊C4C2×D311yescharacteristic
264C3×Dic3⋊C4C22×C311yescharacteristic
265#3724C22×C311yescharacteristic
266Dic3⋊Dic3C22×C311yescharacteristic
267Dic3⋊Dic3C22×C311yescharacteristic
268Dic3⋊Dic3C22×C311yescharacteristic
269Dic3⋊Dic3C22×C311yescharacteristic
270Dic3⋊Dic3C22×C311yescharacteristic
271#3722C22×C311yescharacteristic
272(C2×D3)⋊Dic3C22×C311yescharacteristic
273(C2×D3)⋊Dic3C22×C311yescharacteristic
274(C2×D3)⋊Dic3C22×C311yescharacteristic
275C22×C33—21no—
276C22×C33—21no—
277C22×C33—21no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33C2×D412yes—
281C22×C33C2411yescharacteristic
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3—21no—
285C2×C32×D3—21no—
286C2×C32×D3—21no—
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3—21no—
290C2×C32×D3—21no—
291C33×C4—21no—
292C3×C3⋊Dic3—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3—21no—
295C32×Dic3—21no—
296C32×Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3C2×D412yes—
300C32×Dic3C2×D412yes—
301C2×C3×#41—31no—
302C2×C3×#41—31no—
303C2×C3×#41—61no—
304C2×C3×#41—91no—
305C2×#237—31no—
306C2×#237C3×D311yescharacteristic, complemented
307C2×#235—31no—
308C3×C22⋊Q8—91no—
309C3×C22⋊Q8—91no—
310C3×C22⋊Q8—91no—
311C3×C22⋊Q8—91no—
312C3×#121—31no—
313C3×#121—31no—
314C3×#121—61no—
315C3×#121—91no—
316C3×#121—91no—
317C3×#121—91no—
318C3×#121—91no—
319C3×#121—91no—
320C3×#121—91no—
321C3×#121—91no—
322C2×C3×C4⋊C4—91no—
323#946—31no—
324#946—31no—
325#939—31no—
326#939—31no—
327#939—31no—
328#939—31no—
329#939—31no—
330#939—31no—
331#939—31no—
332#939—61no—
333#939C3×D311yescharacteristic, complemented
334#938—31no—
335#938—31no—
336#930—31no—
337#930—31no—
338#930—31no—
339C2×C4⋊Dic3—31no—
340#924—31no—
341#924—31no—
342C2×Dic3⋊C4—31no—
343#896—31no—
344#896—31no—
345#884—31no—
346#884—31no—
347#878—31no—
348#878—31no—
349C23×C32—21no—
350C23×C32—21no—
351C23×C32—21no—
352C23×C32—21no—
353C23×C32—21no—
354C23×C32—21no—
355C23×C32—31no—
356C23×C32—31no—
357C23×C32—41no—
358C23×C32—41no—
359C23×C32C22×D311yescharacteristic
360C23×C32C22×D311yescharacteristic
361C23×C32C22×D311yescharacteristic
362C23×C32C22×D311yescharacteristic
363C23×C32C23×C311yescharacteristic
364C23×C32C23×C311yescharacteristic
365C22×C3⋊D3C23×C311yescharacteristic
366C22×C3×D3—21no—
367C22×C3×D3—21no—
368C22×C3×D3—31no—
369C22×C3×D3—31no—
370C22×C3×D3—61no—
371C22×C3×D3C22×D311yescharacteristic
372C22×C3×D3C22×D311yescharacteristic
373C22×C3×D3C23×C311yescharacteristic
374C22×C3×D3C23×C311yescharacteristic
375C32×Q8—62no—
376C32×D4—22no—
377C32×D4—24no—
378C32×D4—22no—
379C32×D4—22no—
380C32×D4—42no—
381C32×D4—42no—
382C32×D4—44no—
383C32×D4—62no—
384C32×D4—62no—
385C32×D4—62no—
386C32×D4—121no—
387C2×C32×C4—21no—
388C2×C32×C4—21no—
389C2×C32×C4—21no—
390C2×C32×C4—34no—
391C2×C32×C4—31no—
392C2×C32×C4—31no—
393C2×C32×C4—31no—
394C2×C32×C4—31no—
395C2×C32×C4—31no—
396C2×C32×C4—31no—
397C2×C32×C4—41no—
398C2×C32×C4—62no—
399C2×C32×C4—62no—
400C2×C32×C4—121no—
401C2×C32×C4C22×D311yescharacteristic
402C2×C32×C4C22×D311yescharacteristic
403C2×C32×C4C23×C311yescharacteristic
404#638—22no—
405#638—41no—
406C2×C3⋊Dic3—41no—
407C2×C3⋊Dic3C23×C311yescharacteristic
408C2×C3⋊Dic3C23×C311yescharacteristic
409C2×C3⋊Dic3C23×C311yescharacteristic
410C3×#67—24no—
411C3×#67—24no—
412C3×#67—22no—
413C3×#67—22no—
414C3×#67—22no—
415C3×#67—22no—
416C3×#67—22no—
417C3×#67—22no—
418C3×#67—42no—
419C3×#67—41no—
420C3×#67—41no—
421C3×#67—42no—
422C3×#67—62no—
423C3×#67—62no—
424C3×#67—62no—
425C3×#67—122no—
426C3×#67—121no—
427C3×#67—121no—
428C3×#67—121no—
429C3×#67—121no—
430C3×#67—121no—
431C3×#67—122no—
432C2×C3×Dic3—24no—
433C2×C3×Dic3—22no—
434C2×C3×Dic3—22no—
435C2×C3×Dic3—24no—
436C2×C3×Dic3—21no—
437C2×C3×Dic3—21no—
438C2×C3×Dic3—21no—
439C2×C3×Dic3—21no—
440C2×C3×Dic3—21no—
441C2×C3×Dic3—21no—
442C2×C3×Dic3—31no—
443C2×C3×Dic3—31no—
444C2×C3×Dic3—31no—
445C2×C3×Dic3—31no—
446C2×C3×Dic3—31no—
447C2×C3×Dic3—31no—
448C2×C3×Dic3—41no—
449C2×C3×Dic3—41no—
450C2×C3×Dic3—42no—
451C2×C3×Dic3—61no—
452C2×C3×Dic3—61no—
453C2×C3×Dic3—61no—
454C2×C3×Dic3—62no—
455C2×C3×Dic3—121no—
456C2×C3×Dic3—121no—
457C2×C3×Dic3—122no—
458C2×C3×Dic3#6714yescomplemented
459C2×C3×Dic3C3×D414yescomplemented
460C2×C3×Dic3C22×D311yescharacteristic
461C2×C3×Dic3C22×D311yescharacteristic
462C2×C3×Dic3C22×D311yescharacteristic
463C2×C3×Dic3C22×D311yescharacteristic
464C2×C3×Dic3C22×D311yescharacteristic
465C2×C3×Dic3C22×D311yescharacteristic
466C2×C3×Dic3C23×C311yescharacteristic
467C2×C3×Dic3C23×C311yescharacteristic
468C2×C3×Dic3C23×C311yescharacteristic
469C2×C3×Dic3C23×C311yescharacteristic
470C2×C3×Dic3C23×C311yescharacteristic
471C2×C3×Dic3C23×C311yescharacteristic
472C3×D12—62no—
473C3×D12—121no—
474C3×C4×D3—24no—
475C3×C4×D3—22no—
476C3×C4×D3—22no—
477C3×C4×D3—62no—
478C3×C4×D3—62no—
479C3×C4×D3—62no—
480C3×Dic6—24no—
481C3×Dic6—22no—
482C3×Dic6—22no—
483C3×Dic6—62no—
484C3×Dic6—62no—
485#627—22no—
486#626—22no—
487#626—41no—
488#625—41no—
489#624—22no—
490D3×Dic3—22no—
491#537—91noSylow
492C2×C33—22no—
493C2×C33—41no—
494C2×C33C22×D411yescharacteristic
495C2×C33H(5,𝔽2)11yescharacteristic
496C2×C332−1+411yescharacteristic
497C3×C3⋊D3—41no—
498C32×D3—41no—
499C32×D3—41no—
500C3×#41—64no—
501C3×#41—64no—
502C3×#41—68no—
503C3×#41—184no—
504C2×C3×Q8—31no—
505C2×C3×Q8—31no—
506C2×C3×Q8—61no—
507C2×C3×Q8—91no—
508C2×C3×D4—21no—
509C2×C3×D4—21no—
510C2×C3×D4—21no—
511C2×C3×D4—31no—
512C2×C3×D4—31no—
513C2×C3×D4—31no—
514C2×C3×D4—31no—
515C2×C3×D4—31no—
516C2×C3×D4—31no—
517C2×C3×D4—31no—
518C2×C3×D4—31no—
519C2×C3×D4—41no—
520C2×C3×D4—61no—
521C2×C3×D4—61no—
522C2×C3×D4—61no—
523C2×C3×D4—61no—
524C2×C3×D4—91no—
525C2×C3×D4—91no—
526C2×C3×D4—91no—
527C2×C3×D4—91no—
528C2×C3×D4—91no—
529C2×C3×D4D3211yescharacteristic
530C2×C3×D4C2×C3×D311yescharacteristic
531C2×C3×D4C2×C3×D311yescharacteristic
532C22×C3×C4—31no—
533C22×C3×C4—31no—
534C22×C3×C4—31no—
535C22×C3×C4—31no—
536C22×C3×C4—31no—
537C22×C3×C4—31no—
538C22×C3×C4—31no—
539C22×C3×C4—31no—
540C22×C3×C4—61no—
541C22×C3×C4—61no—
542C22×C3×C4—61no—
543C22×C3×C4—61no—
544C22×C3×C4—91no—
545C22×C3×C4—91no—
546C22×C3×C4—91no—
547C2×#67—31no—
548C2×#67—31no—
549C2×#67—31no—
550C2×#67—31no—
551C2×#67—31no—
552C2×#67—31no—
553C2×#67—31no—
554C2×#67—31no—
555C2×#67—61no—
556C2×#67—61no—
557C2×#67C2×C3×D311yescharacteristic
558C2×#67C2×C3×D311yescharacteristic
559C2×#67C2×C3×D311yescharacteristic
560C2×#67C2×C3×D311yescharacteristic
561C22×Dic3—31no—
562C22×Dic3—31no—
563C22×Dic3—31no—
564C22×Dic3—61no—
565C22×Dic3C2×C3×D311yescharacteristic
566C22×Dic3C2×C3×D311yescharacteristic
567C22×Dic3C2×C3×D311yescharacteristic
568#237—24no—
569#237—64no—
570#235—64no—
571C2×D12—31no—
572C2×D12—31no—
573C2×C4×D3—31no—
574C2×C4×D3—31no—
575C2×C4×D3—31no—
576C2×C4×D3C2×C3×D311yescharacteristic
577C2×Dic6—31no—
578C2×Dic6—31no—
579C2×Dic6C2×C3×D311yescharacteristic
580C3×C4⋊C4—31no—
581C3×C4⋊C4—31no—
582C3×C4⋊C4—61no—
583C3×C4⋊C4—91no—
584C3×C4⋊C4—91no—
585C3×C4⋊C4—91no—
586C3×C4⋊C4—91no—
587C3×C4⋊C4—91no—
588C3×C4⋊C4—91no—
589C3×C4⋊C4—91no—
590C3×C22⋊C4—31no—
591C3×C22⋊C4—31no—
592C3×C22⋊C4—31no—
593C3×C22⋊C4—31no—
594C3×C22⋊C4—61no—
595C3×C22⋊C4—61no—
596C3×C22⋊C4—91no—
597C3×C22⋊C4—91no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600C3×C22⋊C4—91no—
601C3×C22⋊C4—91no—
602#217—31no—
603#217—31no—
604#217—31no—
605#217—31no—
606#217—31no—
607#217—61no—
608#217C2×C3×D311yescharacteristic
609(C2×D3)⋊C4—31no—
610(C2×D3)⋊C4—31no—
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—31no—
613(C2×D3)⋊C4—31no—
614(C2×D3)⋊C4—31no—
615(C2×D3)⋊C4—31no—
616(C2×D3)⋊C4—61no—
617(C2×D3)⋊C4C2×C3×D311yescharacteristic
618C4⋊Dic3—31no—
619C4⋊Dic3—31no—
620C4⋊Dic3—31no—
621C4⋊Dic3—31no—
622C4⋊Dic3—31no—
623Dic3⋊C4—31no—
624Dic3⋊C4—31no—
625Dic3⋊C4—31no—
626Dic3⋊C4—31no—
627Dic3⋊C4—31no—
628Dic3⋊C4—31no—
629Dic3⋊C4—31no—
630Dic3⋊C4—31no—
631Dic3⋊C4—31no—
632Dic3⋊C4—61no—
633Dic3⋊C4C2×C3×D311yescharacteristic
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—21no—
637C22×C32—21no—
638C22×C32—21no—
639C22×C32—21no—
640C22×C32—21no—
641C22×C32—22no—
642C22×C32—21no—
643C22×C32—21no—
644C22×C32—21no—
645C22×C32—21no—
646C22×C32—21no—
647C22×C32—21no—
648C22×C32—21no—
649C22×C32—21no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—21no—
653C22×C32—22no—
654C22×C32—22no—
655C22×C32—22no—
656C22×C32—41no—
657C22×C32—42no—
658C22×C32—41no—
659C22×C32—41no—
660C22×C32—42no—
661C22×C32—41no—
662C22×C32—41no—
663C22×C32—41no—
664C22×C32—41no—
665C22×C32—41no—
666C22×C32—41no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—61no—
674C22×C32—61no—
675C22×C32—61no—
676C22×C32—61no—
677C22×C32—61no—
678C22×C32—61no—
679C22×C32—81no—
680C22×C32—81no—
681C22×C32—81no—
682C22×C32—81no—
683C22×C32D3×D412yes—
684C22×C32C2×#6712yes—
685C22×C32C2×C3×D412yes—
686C22×C32C23×D311yescharacteristic
687C22×C32C23×D311yescharacteristic
688C22×C32C24×C311yescharacteristic
689C2×C3⋊D3—21no—
690C2×C3⋊D3—21no—
691C2×C3⋊D3—21no—
692C2×C3×D3—22no—
693C2×C3×D3—21no—
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—21no—
697C2×C3×D3—21no—
698C2×C3×D3—21no—
699C2×C3×D3—21no—
700C2×C3×D3—21no—
701C2×C3×D3—21no—
702C2×C3×D3—21no—
703C2×C3×D3—21no—
704C2×C3×D3—21no—
705C2×C3×D3—41no—
706C2×C3×D3—41no—
707C2×C3×D3—41no—
708C2×C3×D3—41no—
709C2×C3×D3—41no—
710C2×C3×D3—61no—
711C2×C3×D3—61no—
712C2×C3×D3—61no—
713C2×C3×D3—61no—
714C2×C3×D3—61no—
715C2×C3×D3—61no—
716C2×C3×D3—121no—
717C2×C3×D3—121no—
718C2×C3×D3—121no—
719C32×C4—21no—
720C32×C4—22no—
721C32×C4—21no—
722C32×C4—21no—
723C32×C4—32no—
724C32×C4—32no—
725C32×C4—41no—
726C32×C4—41no—
727C32×C4—42no—
728C32×C4—61no—
729C32×C4—61no—
730C32×C4—61no—
731C32×C4—61no—
732C3⋊Dic3—21no—
733C3⋊Dic3—21no—
734C3⋊Dic3—21no—
735C3×Dic3—22no—
736C3×Dic3—22no—
737C3×Dic3—21no—
738C3×Dic3—21no—
739C3×Dic3—21no—
740C3×Dic3—21no—
741C3×Dic3—21no—
742C3×Dic3—21no—
743C3×Dic3—21no—
744C3×Dic3—21no—
745C3×Dic3—22no—
746C3×Dic3—22no—
747C3×Dic3—41no—
748C3×Dic3—41no—
749C3×Dic3—62no—
750C3×Dic3—61no—
751C3×Dic3—61no—
752C3×Dic3—61no—
753C3×Dic3—61no—
754C3×Dic3—61no—
755C3×Dic3—61no—
756C3×Dic3—121no—
757C3×Dic3—121no—
758C3×Dic3C2×#6712yes—
759C3×Dic3C2×#6712yes—
760C3×Dic3C2×C3×D412yes—
761C3×Dic3C2×C3×D412yes—
762C2×#41—31no—
763C2×#41—91no—
764C22⋊Q8—91no—
765C22⋊Q8—91no—
766C22⋊Q8—91no—
767C22⋊Q8—91no—
768#121—31no—
769#121—91no—
770#121—91no—
771#121—91no—
772#121—91no—
773#121—91no—
774#121—91no—
775#121—91no—
776C2×C4⋊C4—91no—
777C33#53711yescharacteristic, complemented, Sylow
778C23×C3—21no—
779C23×C3—21no—
780C23×C3—21no—
781C23×C3—21no—
782C23×C3—21no—
783C23×C3—21no—
784C23×C3—31no—
785C23×C3—31no—
786C23×C3—31no—
787C23×C3—31no—
788C23×C3—41no—
789C23×C3—41no—
790C23×C3—61no—
791C23×C3—61no—
792C23×C3—91no—
793C23×C3C2×D3211yescharacteristic
794C23×C3C2×D3211yescharacteristic
795C23×C3C22×C3×D311yescharacteristic
796C23×C3C22×C3×D311yescharacteristic
797C23×C3C22×C3×D311yescharacteristic
798C23×C3C22×C3×D311yescharacteristic
799C22×D3—31no—
800C22×D3—31no—
801C22×D3—61no—
802C22×D3C22×C3×D311yescharacteristic
803C22×D3C22×C3×D311yescharacteristic
804C3×Q8—62no—
805C3×Q8—62no—
806C3×Q8—64no—
807C3×Q8—182no—
808C3×D4—24no—
809C3×D4—22no—
810C3×D4—22no—
811C3×D4—22no—
812C3×D4—42no—
813C3×D4—42no—
814C3×D4—44no—
815C3×D4—62no—
816C3×D4—62no—
817C3×D4—64no—
818C3×D4—64no—
819C3×D4—62no—
820C3×D4—62no—
821C3×D4—62no—
822C3×D4—62no—
823C3×D4—122no—
824C3×D4—121no—
825C3×D4—121no—
826C3×D4—122no—
827C3×D4—182no—
828C3×D4—182no—
829C3×D4—361no—
830C3×D4—361no—
831C3×D4—361no—
832C2×C3×C4—21no—
833C2×C3×C4—21no—
834C2×C3×C4—21no—
835C2×C3×C4—31no—
836C2×C3×C4—31no—
837C2×C3×C4—31no—
838C2×C3×C4—31no—
839C2×C3×C4—34no—
840C2×C3×C4—34no—
841C2×C3×C4—31no—
842C2×C3×C4—31no—
843C2×C3×C4—31no—
844C2×C3×C4—31no—
845C2×C3×C4—31no—
846C2×C3×C4—31no—
847C2×C3×C4—31no—
848C2×C3×C4—31no—
849C2×C3×C4—41no—
850C2×C3×C4—61no—
851C2×C3×C4—61no—
852C2×C3×C4—61no—
853C2×C3×C4—61no—
854C2×C3×C4—64no—
855C2×C3×C4—61no—
856C2×C3×C4—61no—
857C2×C3×C4—62no—
858C2×C3×C4—62no—
859C2×C3×C4—64no—
860C2×C3×C4—62no—
861C2×C3×C4—62no—
862C2×C3×C4—64no—
863C2×C3×C4—91no—
864C2×C3×C4—91no—
865C2×C3×C4—91no—
866C2×C3×C4—121no—
867C2×C3×C4—121no—
868C2×C3×C4—122no—
869C2×C3×C4—182no—
870C2×C3×C4—182no—
871C2×C3×C4—361no—
872C2×C3×C4C2×D3211yescharacteristic
873C2×C3×C4C22×C3×D311yescharacteristic
874C2×C3×C4C22×C3×D311yescharacteristic
875#67—22no—
876#67—22no—
877#67—22no—
878#67—41no—
879#67—62no—
880#67—62no—
881#67—62no—
882#67—122no—
883#67—121no—
884#67—121no—
885#67—121no—
886#67—121no—
887#67—121no—
888#67—122no—
889C2×Dic3—22no—
890C2×Dic3—31no—
891C2×Dic3—31no—
892C2×Dic3—31no—
893C2×Dic3—31no—
894C2×Dic3—31no—
895C2×Dic3—31no—
896C2×Dic3—41no—
897C2×Dic3—61no—
898C2×Dic3—61no—
899C2×Dic3—61no—
900C2×Dic3—62no—
901C2×Dic3—121no—
902C2×Dic3—121no—
903C2×Dic3—122no—
904C2×Dic3C3×#6714yescomplemented
905C2×Dic3C22×C3×D311yescharacteristic
906C2×Dic3C22×C3×D311yescharacteristic
907C2×Dic3C22×C3×D311yescharacteristic
908C2×Dic3C22×C3×D311yescharacteristic
909C2×Dic3C22×C3×D311yescharacteristic
910C2×Dic3C22×C3×D311yescharacteristic
911D12—62no—
912D12—121no—
913C4×D3—22no—
914C4×D3—62no—
915C4×D3—62no—
916C4×D3—62no—
917Dic6—22no—
918Dic6—62no—
919Dic6—62no—
920C2×C32—22no—
921C2×C32—22no—
922C2×C32—22no—
923C2×C32—21no—
924C2×C32—21no—
925C2×C32—21no—
926C2×C32—21no—
927C2×C32—21no—
928C2×C32—21no—
929C2×C32—21no—
930C2×C32—21no—
931C2×C32—21no—
932C2×C32—41no—
933C2×C32—41no—
934C2×C32—41no—
935C2×C32—42no—
936C2×C32—42no—
937C2×C32—42no—
938C2×C32—41no—
939C2×C32—42no—
940C2×C32—41no—
941C2×C32—41no—
942C2×C32—82no—
943C2×C32—81no—
944C2×C32—81no—
945C2×C32—82no—
946C2×C32—121no—
947C2×C32—121no—
948C2×C32C2×D3×D411yescharacteristic
949C2×C32#100411yescharacteristic
950C2×C32#100911yescharacteristic
951C2×C32#101011yescharacteristic
952C2×C32#101011yescharacteristic
953C2×C32C22×#6711yescharacteristic
954C2×C32C22×C3×D411yescharacteristic
955C2×C32C3×H(5,𝔽2)11yescharacteristic
956C2×C32C3×2−1+411yescharacteristic
957C3⋊D3—41no—
958C3×D3—42no—
959C3×D3—41no—
960C3×D3—41no—
961C3×D3—41no—
962C3×D3—41no—
963C3×D3—81no—
964C3×D3—121no—
965C3×D3—121no—
966C3×D3—241no—
967#41—64no—
968#41—184no—
969C2×Q8—31no—
970C2×Q8—91no—
971C2×D4—31no—
972C2×D4—31no—
973C2×D4—31no—
974C2×D4—31no—
975C2×D4—91no—
976C2×D4—91no—
977C2×D4—91no—
978C2×D4—91no—
979C2×D4—91no—
980C2×D4C3×D3211yescharacteristic
981C22×C4—31no—
982C22×C4—31no—
983C22×C4—31no—
984C22×C4—31no—
985C22×C4—91no—
986C22×C4—91no—
987C22×C4—91no—
988C4⋊C4—31no—
989C4⋊C4—91no—
990C4⋊C4—91no—
991C4⋊C4—91no—
992C4⋊C4—91no—
993C4⋊C4—91no—
994C4⋊C4—91no—
995C4⋊C4—91no—
996C22⋊C4—31no—
997C22⋊C4—31no—
998C22⋊C4—91no—
999C22⋊C4—91no—
1000C22⋊C4—91no—
1001C22⋊C4—91no—
1002C22⋊C4—91no—
1003C22⋊C4—91no—
1004C22×C3—21no—
1005C22×C3—21no—
1006C22×C3—21no—
1007C22×C3—21no—
1008C22×C3—21no—
1009C22×C3—21no—
1010C22×C3—22no—
1011C22×C3—21no—
1012C22×C3—21no—
1013C22×C3—21no—
1014C22×C3—21no—
1015C22×C3—21no—
1016C22×C3—21no—
1017C22×C3—21no—
1018C22×C3—21no—
1019C22×C3—21no—
1020C22×C3—21no—
1021C22×C3—21no—
1022C22×C3—21no—
1023C22×C3—22no—
1024C22×C3—22no—
1025C22×C3—22no—
1026C22×C3—41no—
1027C22×C3—41no—
1028C22×C3—41no—
1029C22×C3—41no—
1030C22×C3—41no—
1031C22×C3—41no—
1032C22×C3—41no—
1033C22×C3—41no—
1034C22×C3—41no—
1035C22×C3—41no—
1036C22×C3—41no—
1037C22×C3—41no—
1038C22×C3—41no—
1039C22×C3—41no—
1040C22×C3—42no—
1041C22×C3—41no—
1042C22×C3—42no—
1043C22×C3—62no—
1044C22×C3—61no—
1045C22×C3—61no—
1046C22×C3—61no—
1047C22×C3—61no—
1048C22×C3—61no—
1049C22×C3—61no—
1050C22×C3—61no—
1051C22×C3—61no—
1052C22×C3—61no—
1053C22×C3—61no—
1054C22×C3—61no—
1055C22×C3—61no—
1056C22×C3—81no—
1057C22×C3—81no—
1058C22×C3—81no—
1059C22×C3—81no—
1060C22×C3—121no—
1061C22×C3—121no—
1062C22×C3—121no—
1063C22×C3—121no—
1064C22×C3—121no—
1065C22×C3—181no—
1066C22×C3—181no—
1067C22×C3—181no—
1068C22×C3D3×#6712yes—
1069C22×C3C3×D3×D412yes—
1070C22×C3C2×C3×#6712yes—
1071C22×C3C22×D3211yescharacteristic
1072C22×C3C23×C3×D311yescharacteristic
1073C22×C3C23×C3×D311yescharacteristic
1074C2×D3—21no—
1075C2×D3—21no—
1076C2×D3—21no—
1077C2×D3—21no—
1078C2×D3—21no—
1079C2×D3—21no—
1080C2×D3—61no—
1081C2×D3—61no—
1082C2×D3—61no—
1083C2×D3—61no—
1084C2×D3—61no—
1085C2×D3—61no—
1086C2×D3—121no—
1087C2×D3—121no—
1088C2×D3—121no—
1089C3×C4—22no—
1090C3×C4—21no—
1091C3×C4—21no—
1092C3×C4—21no—
1093C3×C4—32no—
1094C3×C4—32no—
1095C3×C4—32no—
1096C3×C4—32no—
1097C3×C4—41no—
1098C3×C4—41no—
1099C3×C4—42no—
1100C3×C4—62no—
1101C3×C4—62no—
1102C3×C4—62no—
1103C3×C4—62no—
1104C3×C4—61no—
1105C3×C4—61no—
1106C3×C4—61no—
1107C3×C4—61no—
1108C3×C4—61no—
1109C3×C4—61no—
1110C3×C4—61no—
1111C3×C4—61no—
1112C3×C4—121no—
1113C3×C4—121no—
1114C3×C4—181no—
1115C3×C4—181no—
1116C3×C4—181no—
1117Dic3—21no—
1118Dic3—21no—
1119Dic3—21no—
1120Dic3—21no—
1121Dic3—62no—
1122Dic3—61no—
1123Dic3—61no—
1124Dic3—61no—
1125Dic3—61no—
1126Dic3—61no—
1127Dic3—61no—
1128Dic3—121no—
1129Dic3—121no—
1130Dic3C2×C3×#6712yes—
1131Dic3C2×C3×#6712yes—
1132C32—21no—
1133C32—21no—
1134C32—21no—
1135C32—41no—
1136C32#559711yescharacteristic, complemented
1137C32#583311yescharacteristic, complemented
1138C32C3×#53711yescharacteristic, complemented
1139C23—31no—
1140C23—31no—
1141C23—91no—
1142C23C2×C3×D3211yescharacteristic
1143C23C2×C3×D3211yescharacteristic
1144Q8—62no—
1145Q8—182no—
1146D4—22no—
1147D4—62no—
1148D4—62no—
1149D4—62no—
1150D4—121no—
1151D4—182no—
1152D4—182no—
1153D4—361no—
1154D4—361no—
1155D4—361no—
1156C2×C4—31no—
1157C2×C4—31no—
1158C2×C4—34no—
1159C2×C4—31no—
1160C2×C4—31no—
1161C2×C4—31no—
1162C2×C4—31no—
1163C2×C4—62no—
1164C2×C4—62no—
1165C2×C4—91no—
1166C2×C4—91no—
1167C2×C4—91no—
1168C2×C4—121no—
1169C2×C4—182no—
1170C2×C4—182no—
1171C2×C4—361no—
1172C2×C4C2×C3×D3211yescharacteristic
1173C2×C3—22no—
1174C2×C3—22no—
1175C2×C3—22no—
1176C2×C3—21no—
1177C2×C3—21no—
1178C2×C3—21no—
1179C2×C3—21no—
1180C2×C3—21no—
1181C2×C3—21no—
1182C2×C3—21no—
1183C2×C3—21no—
1184C2×C3—21no—
1185C2×C3—42no—
1186C2×C3—42no—
1187C2×C3—42no—
1188C2×C3—42no—
1189C2×C3—41no—
1190C2×C3—41no—
1191C2×C3—41no—
1192C2×C3—41no—
1193C2×C3—41no—
1194C2×C3—41no—
1195C2×C3—82no—
1196C2×C3—81no—
1197C2×C3—81no—
1198C2×C3—82no—
1199C2×C3—122no—
1200C2×C3—121no—
1201C2×C3—121no—
1202C2×C3—121no—
1203C2×C3—121no—
1204C2×C3—241no—
1205C2×C3—361no—
1206C2×C3#6430911yescharacteristic
1207C2×C3#6431411yescharacteristic
1208C2×C3C2×D3×#6711yescharacteristic
1209C2×C3C2×C3×D3×D411yescharacteristic
1210C2×C3C3×#100411yescharacteristic
1211C2×C3C3×#100911yescharacteristic
1212C2×C3C3×#101011yescharacteristic
1213C2×C3C3×#101011yescharacteristic
1214C2×C3C22×C3×#6711yescharacteristic
1215D3—41no—
1216D3—41no—
1217D3—121no—
1218D3—121no—
1219D3—241no—
1220C22—21no—
1221C22—21no—
1222C22—21no—
1223C22—21no—
1224C22—21no—
1225C22—61no—
1226C22—61no—
1227C22—61no—
1228C22—61no—
1229C22—61no—
1230C22—61no—
1231C22—181no—
1232C22—181no—
1233C22—181no—
1234C22C3×D3×#6712yes—
1235C22C22×C3×D3211yescharacteristic
1236C4—21no—
1237C4—32no—
1238C4—32no—
1239C4—61no—
1240C4—61no—
1241C4—61no—
1242C4—61no—
1243C4—181no—
1244C4—181no—
1245C4—181no—
1246C3—21no—
1247C3—21no—
1248C3—21no—
1249C3—41no—
1250C3#1059515611yescharacteristic, direct product factor
1251C3C3×#559711yescharacteristic, complemented
1252C3C3×#583311yescharacteristic, complemented
1253C2—22no—
1254C2—41no—
1255C2—121no—
1256C2—121no—
1257C2—361no—
1258C2C3×#6430911yescharacteristic
1259C2C3×#6431411yescharacteristic
1260C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#537
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×#3804C2semidirect
3. C3×#64148C2semidirect
4. C32×#939C2semidirect
5. C3×#63980C2semidirect
6. C3×#63978C2semidirect
7. C3×#63978C2semidirect
8. C3×#63970C2semidirect
9. C2×C3×Dic3⋊Dic3C2semidirect
10. C3×#63964C2semidirect
11. C3×#63958C2semidirect
12. C3×#63906C2semidirect
13. C3×#63888C2semidirect
14. C3×#63887C2semidirect
15. C3×#63851C2semidirect
18. #10595156C3direct (N × H)
59. C2×C3×#237D3semidirect
60. C2×C3×#237C2×C3semidirect
62. C2×#3804C2×C3semidirect
64. #64148C2×C3semidirect
76. C3×#939D3semidirect
77. C3×#939C2×C3semidirect
93. #63980C2×C3semidirect
94. #63978C2×C3semidirect
95. #63978C2×C3semidirect
96. #63970C2×C3semidirect
97. C2×Dic3⋊Dic3C2×C3semidirect
98. #63964C2×C3semidirect
99. #63958C2×C3semidirect
100. #63906C2×C3semidirect
101. #63888C2×C3semidirect
102. #63887C2×C3semidirect
103. #63851C2×C3semidirect
123. C2×C32×Dic3D4semidirect
306. C2×#237C3×D3semidirect
333. #939C3×D3semidirect
458. C2×C3×Dic3#67semidirect
459. C2×C3×Dic3C3×D4semidirect
777. C33#537semidirect
904. C2×Dic3C3×#67semidirect
1136. C32#5597semidirect
1137. C32#5833semidirect
1138. C32C3×#537semidirect
1250. C3#10595156direct (N × H)
1251. C3C3×#5597semidirect
1252. C3C3×#5833semidirect

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×#38042
C3×#641482
C32×#9392
C3×#639802
C3×#639782
C3×#639702
C2×C3×Dic3⋊Dic32
C3×#639642
C3×#639582
C3×#639062
C3×#638882
C3×#638872
C3×#638512
C3×#58333
C3×#55973
#105951563