Finite Group Databasebeta

← C3×#10595043 #13174627

Subgroups — C3×#10595043 #13174627

Order 1728.

1650 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3828C211yesmaximal, characteristic, complemented
2C2×C32×#235C211yesmaximal, characteristic, complemented
3C2×C32×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#63978C214yesmaximal, complemented
5C3×#63916C212yesmaximal, complemented
6C3×#63909C212yesmaximal, complemented
7C3×#63871C212yesmaximal, complemented
8C3×#63857C212yesmaximal, complemented
9C3×#5833—31nomaximal
10C3×#5510—31nomaximal
11#10595043C311yesmaximal, characteristic, direct product factor
12C22×C33×C4C2211yescharacteristic
13C2×C3×#638C2212yes—
14C3×#3828—24no—
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2212yes—
17C2×C3×#634C2211yescharacteristic
18C2×C32×#67C2212yes—
19C22×C32×Dic3C2212yes—
20C32×#235—24no—
21C2×C32×D12C2211yescharacteristic
22C2×C32×C4×D3C2212yes—
23C2×C32×Dic6C2211yescharacteristic
24C2×C3×#626C2214yes—
25C32×C4⋊Dic3C2212yes—
26C32×C4⋊Dic3C2212yes—
27C3×Dic3⋊Dic3C2214yes—
28C3×#3722C2214yes—
29C3×(C2×D3)⋊Dic3C2214yes—
30C2×C32×#41—31no—
31C2×#3828C2×C311yescharacteristic, complemented
32C2×C3×#235—21no—
33C2×C3×#235—31no—
34C2×C3×#235—31no—
35C2×C3×#235—61no—
36C2×C3×#235D311yescharacteristic, complemented
37C2×C3×#235C2×C311yescharacteristic, complemented
38C2×C32×C4⋊C4—31no—
39C3×#946—32no—
40C3×#939—34no—
41C3×#938—32no—
42C3×#930—34no—
43C3×#930—32no—
44C2×C3×C4⋊Dic3—21no—
45C2×C3×C4⋊Dic3D311yescharacteristic, complemented
46C2×C3×C4⋊Dic3C2×C311yescharacteristic, complemented
47C3×#924—32no—
48C3×#897—32no—
49C3×#897—32no—
50C3×#895—32no—
51C3×#895—32no—
52#63978C2×C314yescomplemented
53#63916C2×C312yescomplemented
54#63909C2×C312yescomplemented
55#63871C2×C312yescomplemented
56#63857C2×C312yescomplemented
57C23×C33C2311yescharacteristic
58C22×C3×C3⋊D3C2312yes—
59C22×C32×D3C2312yes—
60C2×C33×C4D414yescomplemented
61C2×C33×C4C2311yescharacteristic
62C2×C33×C4C2311yescharacteristic
63C3×#638—24no—
64C2×C3×C3⋊Dic3C2312yes—
65C3×C4⋊(C3⋊D3)—22no—
66C3×C4×C3⋊D3—24no—
67C3×#634—22no—
68C32×#67—24no—
69C2×C32×Dic3—42no—
70C2×C32×Dic3C2314yes—
71C2×C32×Dic3C2312yes—
72C32×D12—22no—
73C32×C4×D3—24no—
74C32×Dic6—22no—
75C3×#626—44no—
76C3×#537—91no—
77#5833—31no—
78#5510—31no—
79C32×#41—64no—
80C2×C32×Q8—31no—
81C2×C32×D4—32no—
82C2×C32×D4—31no—
83C22×C32×C4—21no—
84C22×C32×C4—21no—
85C22×C32×C4—21no—
86C22×C32×C4—32no—
87C22×C32×C4—32no—
88C22×C32×C4—41no—
89C22×C32×C4C2×D311yescharacteristic
90C22×C32×C4C2×D311yescharacteristic
91C22×C32×C4C22×C311yescharacteristic
92C2×#638C22×C312yes—
93#3828—24no—
94C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
95C2×C4×C3⋊D3C22×C312yes—
96C2×#634C22×C311yescharacteristic
97C2×C3×#67—22no—
98C2×C3×#67—32no—
99C2×C3×#67—32no—
100C2×C3×#67—34no—
101C2×C3×#67—62no—
102C2×C3×#67C2×D312yes—
103C2×C3×#67C22×C312yes—
104C22×C3×Dic3—22no—
105C22×C3×Dic3C2×D312yes—
106C22×C3×Dic3C22×C312yes—
107C3×#235—28no—
108C3×#235—24no—
109C3×#235—24no—
110C3×#235—68no—
111C3×#235—64no—
112C3×#235—64no—
113C2×C3×D12—21no—
114C2×C3×D12—31no—
115C2×C3×D12—31no—
116C2×C3×D12—34no—
117C2×C3×D12—61no—
118C2×C3×D12C2×D311yescharacteristic
119C2×C3×D12C22×C311yescharacteristic
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—32no—
122C2×C3×C4×D3—32no—
123C2×C3×C4×D3—62no—
124C2×C3×C4×D3C2×D312yes—
125C2×C3×C4×D3C22×C312yes—
126C2×C3×Dic6—21no—
127C2×C3×Dic6—31no—
128C2×C3×Dic6—31no—
129C2×C3×Dic6—61no—
130C2×C3×Dic6C2×D311yescharacteristic
131C2×C3×Dic6C22×C311yescharacteristic
132C2×#626C22×C314yes—
133C32×C4⋊C4—32no—
134C32×C4⋊C4—32no—
135C3×#217—34no—
136C3×(C2×D3)⋊C4—34no—
137C3×(C2×D3)⋊C4—34no—
138C3×(C2×D3)⋊C4—34no—
139C3×C4⋊Dic3—22no—
140C3×C4⋊Dic3—22no—
141C3×C4⋊Dic3—34no—
142C3×C4⋊Dic3C2×D312yes—
143C3×C4⋊Dic3C2×D312yes—
144C3×C4⋊Dic3C22×C312yes—
145C3×C4⋊Dic3C22×C312yes—
146C3×Dic3⋊C4—34no—
147Dic3⋊Dic3C22×C314yes—
148#3722C22×C314yes—
149(C2×D3)⋊Dic3C22×C314yes—
150C22×C33—21no—
151C22×C33—21no—
152C22×C33C2×D412yes—
153C22×C33C2411yescharacteristic
154C2×C3×C3⋊D3—22no—
155C2×C3×C3⋊D3—22no—
156C2×C3×C3⋊D3—22no—
157C2×C32×D3—22no—
158C2×C32×D3—22no—
159C2×C32×D3—22no—
160C33×C4C2×D412yes—
161C33×C4C2×D412yes—
162C3×C3⋊Dic3—22no—
163C32×Dic3—22no—
164C32×Dic3—24no—
165C2×C3×#41—31no—
166C2×C3×#41—31no—
167C2×C3×#41—61no—
168C2×C3×#41—91no—
169C2×#235—31no—
170C2×#235—31no—
171C2×#235—61no—
172C2×#235C3×D311yescharacteristic, complemented
173C3×C22⋊Q8—92no—
174C3×C22⋊Q8—92no—
175C3×#121—92no—
176C3×#121—92no—
177C3×#121—94no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—61no—
181#946—32no—
182#939—34no—
183#938—32no—
184#930—34no—
185#930—32no—
186C2×C4⋊Dic3C3×D311yescharacteristic, complemented
187#924—32no—
188#897—32no—
189#897—32no—
190#895—32no—
191#895—32no—
192C23×C32—21no—
193C23×C32—21no—
194C23×C32—21no—
195C23×C32—32no—
196C23×C32—41no—
197C23×C32C22×D311yescharacteristic
198C23×C32C22×D311yescharacteristic
199C23×C32C23×C311yescharacteristic
200C22×C3⋊D3C23×C312yes—
201C22×C3×D3—22no—
202C22×C3×D3—32no—
203C22×C3×D3—32no—
204C22×C3×D3—62no—
205C22×C3×D3C22×D312yes—
206C22×C3×D3C23×C312yes—
207C32×Q8—62no—
208C32×D4—64no—
209C32×D4—62no—
210C2×C32×C4—24no—
211C2×C32×C4—24no—
212C2×C32×C4—24no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—32no—
220C2×C32×C4—34no—
221C2×C32×C4—44no—
222C2×C32×C4—41no—
223C2×C32×C4—41no—
224C2×C32×C4—64no—
225C2×C32×C4—122no—
226C2×C32×C4D1214yescomplemented
227C2×C32×C4#6714yescomplemented
228C2×C32×C4C3×D414yescomplemented
229C2×C32×C4C22×D311yescharacteristic
230C2×C32×C4C22×D311yescharacteristic
231C2×C32×C4C22×D311yescharacteristic
232C2×C32×C4C22×D311yescharacteristic
233C2×C32×C4C23×C311yescharacteristic
234C2×C32×C4C23×C311yescharacteristic
235#638—24no—
236C2×C3⋊Dic3C23×C312yes—
237C4⋊(C3⋊D3)—22no—
238C4×C3⋊D3—24no—
239#634—22no—
240C3×#67—28no—
241C3×#67—24no—
242C3×#67—24no—
243C3×#67—68no—
244C3×#67—64no—
245C3×#67—64no—
246C3×#67—124no—
247C2×C3×Dic3—22no—
248C2×C3×Dic3—24no—
249C2×C3×Dic3—32no—
250C2×C3×Dic3—32no—
251C2×C3×Dic3—42no—
252C2×C3×Dic3—42no—
253C2×C3×Dic3—44no—
254C2×C3×Dic3—62no—
255C2×C3×Dic3C22×D314yes—
256C2×C3×Dic3C22×D312yes—
257C2×C3×Dic3C23×C314yes—
258C2×C3×Dic3C23×C312yes—
259C3×D12—24no—
260C3×D12—22no—
261C3×D12—22no—
262C3×D12—64no—
263C3×D12—62no—
264C3×D12—62no—
265C3×D12—124no—
266C3×C4×D3—28no—
267C3×C4×D3—24no—
268C3×C4×D3—24no—
269C3×C4×D3—68no—
270C3×C4×D3—64no—
271C3×C4×D3—64no—
272C3×Dic6—24no—
273C3×Dic6—22no—
274C3×Dic6—22no—
275C3×Dic6—64no—
276C3×Dic6—62no—
277C3×Dic6—62no—
278#626—44no—
279#537—91noSylow
280C2×C33—22no—
281C2×C33C22×D411yescharacteristic
282C2×C33H(5,𝔽2)11yescharacteristic
283C2×C332−1+411yescharacteristic
284C3×C3⋊D3—42no—
285C32×D3—42no—
286C3×#41—68no—
287C3×#41—64no—
288C3×#41—64no—
289C3×#41—184no—
290C2×C3×Q8—31no—
291C2×C3×Q8—31no—
292C2×C3×Q8—61no—
293C2×C3×Q8—91no—
294C2×C3×D4—32no—
295C2×C3×D4—32no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—62no—
300C2×C3×D4—94no—
301C2×C3×D4—92no—
302C2×C3×D4—91no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—32no—
307C22×C3×C4—32no—
308C22×C3×C4—32no—
309C22×C3×C4—32no—
310C22×C3×C4—41no—
311C22×C3×C4—62no—
312C22×C3×C4—62no—
313C22×C3×C4—92no—
314C22×C3×C4D3211yescharacteristic
315C22×C3×C4C2×C3×D311yescharacteristic
316C22×C3×C4C2×C3×D311yescharacteristic
317C2×#67—32no—
318C2×#67—32no—
319C2×#67—34no—
320C2×#67—62no—
321C2×#67C2×C3×D312yes—
322C22×Dic3C2×C3×D312yes—
323#235—24no—
324#235—68no—
325#235—64no—
326#235—64no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—34no—
330C2×D12—61no—
331C2×D12C2×C3×D311yescharacteristic
332C2×C4×D3—32no—
333C2×C4×D3—32no—
334C2×C4×D3—62no—
335C2×C4×D3C2×C3×D312yes—
336C2×Dic6—31no—
337C2×Dic6—31no—
338C2×Dic6—61no—
339C2×Dic6C2×C3×D311yescharacteristic
340C3×C4⋊C4—32no—
341C3×C4⋊C4—32no—
342C3×C4⋊C4—32no—
343C3×C4⋊C4—32no—
344C3×C4⋊C4—62no—
345C3×C4⋊C4—62no—
346C3×C4⋊C4—94no—
347C3×C22⋊C4—94no—
348C3×C22⋊C4—94no—
349#217—34no—
350(C2×D3)⋊C4—34no—
351(C2×D3)⋊C4—34no—
352(C2×D3)⋊C4—34no—
353C4⋊Dic3—34no—
354C4⋊Dic3C2×C3×D312yes—
355C4⋊Dic3C2×C3×D312yes—
356Dic3⋊C4—34no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—22no—
360C22×C32—22no—
361C22×C32—21no—
362C22×C32—21no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—21no—
366C22×C32—21no—
367C22×C32—21no—
368C22×C32—22no—
369C22×C32—22no—
370C22×C32—22no—
371C22×C32—42no—
372C22×C32—41no—
373C22×C32—41no—
374C22×C32—41no—
375C22×C32—41no—
376C22×C32—41no—
377C22×C32—42no—
378C22×C32—42no—
379C22×C32—62no—
380C22×C32—62no—
381C22×C32—62no—
382C22×C32C2×D1212yes—
383C22×C32C2×#6712yes—
384C22×C32C2×C3×D412yes—
385C22×C32C23×D311yescharacteristic
386C22×C32C23×D311yescharacteristic
387C22×C32C24×C311yescharacteristic
388C2×C3⋊D3—22no—
389C2×C3⋊D3—22no—
390C2×C3⋊D3—22no—
391C2×C3×D3—24no—
392C2×C3×D3—22no—
393C2×C3×D3—22no—
394C2×C3×D3—22no—
395C2×C3×D3—22no—
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3—42no—
399C2×C3×D3—42no—
400C2×C3×D3—64no—
401C2×C3×D3—62no—
402C2×C3×D3—62no—
403C2×C3×D3—62no—
404C2×C3×D3—62no—
405C2×C3×D3—62no—
406C2×C3×D3—62no—
407C2×C3×D3—122no—
408C2×C3×D3—122no—
409C32×C4—22no—
410C32×C4—22no—
411C32×C4—22no—
412C32×C4—22no—
413C32×C4—22no—
414C32×C4—22no—
415C32×C4—42no—
416C32×C4—42no—
417C32×C4—62no—
418C32×C4—64no—
419C32×C4C2×D1212yes—
420C32×C4C2×D1212yes—
421C32×C4C2×#6712yes—
422C32×C4C2×#6712yes—
423C32×C4C2×C3×D412yes—
424C32×C4C2×C3×D412yes—
425C3⋊Dic3—22no—
426C3×Dic3—24no—
427C3×Dic3—24no—
428C3×Dic3—22no—
429C3×Dic3—22no—
430C3×Dic3—24no—
431C3×Dic3—44no—
432C3×Dic3—64no—
433C3×Dic3—62no—
434C3×Dic3—62no—
435C2×#41—31no—
436C2×#41—91no—
437C22⋊Q8—92no—
438C22⋊Q8—92no—
439#121—92no—
440#121—92no—
441#121—94no—
442C2×C4⋊C4—31no—
443C33#53711yescharacteristic, complemented, Sylow
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—32no—
448C23×C3—32no—
449C23×C3—41no—
450C23×C3—62no—
451C23×C3—92no—
452C23×C3C2×D3211yescharacteristic
453C23×C3C22×C3×D311yescharacteristic
454C23×C3C22×C3×D311yescharacteristic
455C22×D3—32no—
456C22×D3—32no—
457C22×D3—62no—
458C22×D3C22×C3×D312yes—
459C3×Q8—64no—
460C3×Q8—62no—
461C3×Q8—62no—
462C3×Q8—182no—
463C3×D4—64no—
464C3×D4—68no—
465C3×D4—64no—
466C3×D4—64no—
467C3×D4—62no—
468C3×D4—62no—
469C3×D4—184no—
470C3×D4—182no—
471C3×D4—364no—
472C2×C3×C4—24no—
473C2×C3×C4—24no—
474C2×C3×C4—24no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—34no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—34no—
485C2×C3×C4—44no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—62no—
489C2×C3×C4—64no—
490C2×C3×C4—68no—
491C2×C3×C4—64no—
492C2×C3×C4—64no—
493C2×C3×C4—92no—
494C2×C3×C4—122no—
495C2×C3×C4—122no—
496C2×C3×C4—124no—
497C2×C3×C4—184no—
498C2×C3×C4#62614yescomplemented
499C2×C3×C4C3×D1214yescomplemented
500C2×C3×C4C3×#6714yescomplemented
501C2×C3×C4C2×D3211yescharacteristic
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C22×C3×D311yescharacteristic
504C2×C3×C4C22×C3×D311yescharacteristic
505C2×C3×C4C22×C3×D311yescharacteristic
506C2×C3×C4C22×C3×D311yescharacteristic
507#67—24no—
508#67—68no—
509#67—64no—
510#67—64no—
511#67—124no—
512C2×Dic3—32no—
513C2×Dic3—32no—
514C2×Dic3—42no—
515C2×Dic3—62no—
516C2×Dic3C22×C3×D314yes—
517C2×Dic3C22×C3×D312yes—
518D12—22no—
519D12—64no—
520D12—62no—
521D12—62no—
522D12—124no—
523C4×D3—24no—
524C4×D3—68no—
525C4×D3—64no—
526C4×D3—64no—
527Dic6—22no—
528Dic6—64no—
529Dic6—62no—
530Dic6—62no—
531C2×C32—22no—
532C2×C32—24no—
533C2×C32—22no—
534C2×C32—22no—
535C2×C32—21no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—21no—
539C2×C32—21no—
540C2×C32—21no—
541C2×C32—21no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—41no—
545C2×C32—41no—
546C2×C32—41no—
547C2×C32—42no—
548C2×C32—42no—
549C2×C32—44no—
550C2×C32—122no—
551C2×C32C22×D1211yescharacteristic
552C2×C32#100411yescharacteristic
553C2×C32#100711yescharacteristic
554C2×C32#100911yescharacteristic
555C2×C32#101011yescharacteristic
556C2×C32C22×#6711yescharacteristic
557C2×C32C22×C3×D411yescharacteristic
558C2×C32C3×H(5,𝔽2)11yescharacteristic
559C2×C32C3×2−1+411yescharacteristic
560C3⋊D3—42no—
561C3×D3—44no—
562C3×D3—42no—
563C3×D3—42no—
564C3×D3—124no—
565C3×D3—122no—
566C3×D3—122no—
567#41—64no—
568#41—184no—
569C2×Q8—31no—
570C2×Q8—91no—
571C2×D4—32no—
572C2×D4—31no—
573C2×D4—94no—
574C2×D4—92no—
575C2×D4—91no—
576C22×C4—32no—
577C22×C4—32no—
578C22×C4—92no—
579C22×C4C3×D3211yescharacteristic
580C4⋊C4—32no—
581C4⋊C4—32no—
582C4⋊C4—94no—
583C22⋊C4—94no—
584C22⋊C4—94no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—41no—
606C22×C3—42no—
607C22×C3—64no—
608C22×C3—62no—
609C22×C3—62no—
610C22×C3—62no—
611C22×C3—62no—
612C22×C3—62no—
613C22×C3—62no—
614C22×C3—122no—
615C22×C3—122no—
616C22×C3—182no—
617C22×C3—182no—
618C22×C3—182no—
619C22×C3C2×#62612yes—
620C22×C3C2×C3×D1212yes—
621C22×C3C2×C3×#6712yes—
622C22×C3C22×D3211yescharacteristic
623C22×C3C23×C3×D311yescharacteristic
624C22×C3C23×C3×D311yescharacteristic
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—64no—
629C2×D3—62no—
630C2×D3—62no—
631C2×D3—62no—
632C2×D3—62no—
633C2×D3—62no—
634C2×D3—62no—
635C2×D3—122no—
636C2×D3—122no—
637C3×C4—22no—
638C3×C4—22no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—64no—
646C3×C4—64no—
647C3×C4—62no—
648C3×C4—62no—
649C3×C4—64no—
650C3×C4—124no—
651C3×C4—182no—
652C3×C4C2×#62612yes—
653C3×C4C2×#62612yes—
654C3×C4C2×C3×D1212yes—
655C3×C4C2×C3×D1212yes—
656C3×C4C2×C3×#6712yes—
657C3×C4C2×C3×#6712yes—
658Dic3—24no—
659Dic3—22no—
660Dic3—64no—
661Dic3—62no—
662Dic3—62no—
663C32—21no—
664C32—21no—
665C32—21no—
666C32—41no—
667C32#551011yescharacteristic, complemented
668C32#583311yescharacteristic, complemented
669C32C3×#53711yescharacteristic, complemented
670C23—32no—
671C23—92no—
672C23C2×C3×D3211yescharacteristic
673Q8—62no—
674Q8—182no—
675D4—64no—
676D4—62no—
677D4—184no—
678D4—182no—
679D4—364no—
680C2×C4—34no—
681C2×C4—32no—
682C2×C4—64no—
683C2×C4—92no—
684C2×C4—122no—
685C2×C4—184no—
686C2×C4C3×#62614yescomplemented
687C2×C4C2×C3×D3211yescharacteristic
688C2×C4C2×C3×D3211yescharacteristic
689C2×C3—24no—
690C2×C3—22no—
691C2×C3—22no—
692C2×C3—22no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—42no—
703C2×C3—42no—
704C2×C3—44no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—41no—
708C2×C3—124no—
709C2×C3—122no—
710C2×C3—122no—
711C2×C3—362no—
712C2×C3#6429711yescharacteristic
713C2×C3#6430711yescharacteristic
714C2×C3C22×#62611yescharacteristic
715C2×C3C22×C3×D1211yescharacteristic
716C2×C3C3×#100411yescharacteristic
717C2×C3C3×#100711yescharacteristic
718C2×C3C3×#100911yescharacteristic
719C2×C3C3×#101011yescharacteristic
720C2×C3C22×C3×#6711yescharacteristic
721D3—42no—
722D3—124no—
723D3—122no—
724D3—122no—
725C22—21no—
726C22—21no—
727C22—62no—
728C22—62no—
729C22—62no—
730C22—182no—
731C22—182no—
732C22—182no—
733C22C2×C3×#62612yes—
734C22C22×C3×D3211yescharacteristic
735C4—62no—
736C4—64no—
737C4—182no—
738C4C2×C3×#62612yes—
739C4C2×C3×#62612yes—
740C3—21no—
741C3—21no—
742C3—21no—
743C3—41no—
744C3#1059504311yescharacteristic, direct product factor
745C3C3×#551011yescharacteristic, complemented
746C3C3×#583311yescharacteristic, complemented
747C2—22no—
748C2—122no—
749C2—362no—
750C2C3×#6429711yescharacteristic
751C2C3×#6430711yescharacteristic
752C2C22×C3×#62611yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3828C2semidirect
2. C2×C32×#235C2semidirect
3. C2×C32×C4⋊Dic3C2semidirect
4. C3×#63978C2semidirect
5. C3×#63916C2semidirect
6. C3×#63909C2semidirect
7. C3×#63871C2semidirect
8. C3×#63857C2semidirect
11. #10595043C3direct (N × H)
31. C2×#3828C2×C3semidirect
36. C2×C3×#235D3semidirect
37. C2×C3×#235C2×C3semidirect
45. C2×C3×C4⋊Dic3D3semidirect
46. C2×C3×C4⋊Dic3C2×C3semidirect
52. #63978C2×C3semidirect
53. #63916C2×C3semidirect
54. #63909C2×C3semidirect
55. #63871C2×C3semidirect
56. #63857C2×C3semidirect
60. C2×C33×C4D4semidirect
172. C2×#235C3×D3semidirect
186. C2×C4⋊Dic3C3×D3semidirect
226. C2×C32×C4D12semidirect
227. C2×C32×C4#67semidirect
228. C2×C32×C4C3×D4semidirect
443. C33#537semidirect
498. C2×C3×C4#626semidirect
499. C2×C3×C4C3×D12semidirect
500. C2×C3×C4C3×#67semidirect
667. C32#5510semidirect
668. C32#5833semidirect
669. C32C3×#537semidirect
686. C2×C4C3×#626semidirect
744. C3#10595043direct (N × H)
745. C3C3×#5510semidirect
746. C3C3×#5833semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C2×C32×#2352
C2×C32×C4⋊Dic32
C3×#639782
C3×#639162
C3×#639092
C3×#638712
C3×#638572
C3×#58333
C3×#55103
#105950433