Finite Group Databasebeta

← C3×#10595034 #13174610

Subgroups — C3×#10595034 #13174610

Order 1728.

1850 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C32×#235C211yesmaximal, characteristic, complemented
3C32×#926C211yesmaximal, characteristic, complemented
4C3×#63981C212yesmaximal, complemented
5C3×#63962C212yesmaximal, complemented
6C3×#63916C212yesmaximal, complemented
7C3×C4×#626C214yesmaximal, complemented
8C3×#63871C212yesmaximal, complemented
9C3×#5828—31nomaximal
10C3×#5524—31nomaximal
11#10595034C311yesmaximal, characteristic, direct product factor
12C23×C3×C3⋊D3C2211yescharacteristic
13C22×C33×C4C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4×C3⋊D3—24no—
16C2×C3×C4×C3⋊D3C2212yes—
17C2×C3×C4×C3⋊D3C2212yes—
18C2×C32×#67C2212yes—
19C32×#235—24no—
20C2×C32×D12C2211yescharacteristic, complemented
21C2×C32×C4×D3C2212yescomplemented
22C2×C32×Dic6C2211yescharacteristic, complemented
23C2×C3×#626C2214yes—
24C32×#217C2212yes—
25C32×C4⋊Dic3C2212yescomplemented
26C32×C4×Dic3C2212yescomplemented
27C3×Dic3⋊Dic3C2214yescomplemented
28C3×#3722C2214yes—
29C3×(C2×D3)⋊Dic3C2214yescomplemented
30C2×C32×#41—31no—
31C22×C4×C3⋊D3C2×C311yescharacteristic, complemented
32C2×C3×#235—21no—
33C2×C3×#235D311yescharacteristic, complemented
34C2×C3×#235C2×C311yescharacteristic, complemented
35C22×C3×C4×D3—31no—
36C22×C3×C4×D3—31no—
37C22×C3×C4×D3—61no—
38C32×#117—31no—
39C3×#946—32no—
40C3×#938—32no—
41C3×#937—32no—
42C3×#935—32no—
43C3×C4×#67—34no—
44C3×#926—21no—
45C3×#926D311yescharacteristic, complemented
46C3×#926C2×C311yescharacteristic, complemented
47C3×#897—32no—
48C3×#895—32no—
49C3×#886—32no—
50C3×#882—32no—
51C3×C4×D12—34no—
52#63981C2×C312yescomplemented
53#63962C2×C312yescomplemented
54#63916C2×C312yescomplemented
55C4×#626C2×C314yescomplemented
56#63871C2×C312yescomplemented
57C23×C33C2311yescharacteristic
58C22×C3×C3⋊D3—22no—
59C22×C3×C3⋊D3—24no—
60C22×C3×C3⋊D3C2312yes—
61C22×C32×D3C2312yes—
62C2×C33×C4D414yescomplemented
63C2×C33×C4C2311yescharacteristic
64C2×C33×C4C2311yescharacteristic
65C2×C3×C3⋊Dic3—22no—
66C2×C3×C3⋊Dic3C2312yes—
67C3×C4×C3⋊D3—24no—
68C3×C4×C3⋊D3—24no—
69C32×#67—24no—
70C2×C32×Dic3C2314yes—
71C2×C32×Dic3C2312yes—
72C32×D12—22no—
73C32×C4×D3—24no—
74C32×Dic6—22no—
75C3×#626—28no—
76C3×#525—91no—
77#5828—31no—
78#5524—31no—
79C23×C3⋊D3C22×C311yescharacteristic
80C23×C3×D3—31no—
81C23×C3×D3—31no—
82C23×C3×D3—61no—
83C32×#41—64no—
84C2×C32×Q8—31no—
85C2×C32×D4—32no—
86C2×C32×D4—31no—
87C22×C32×C4—21no—
88C22×C32×C4—21no—
89C22×C32×C4—21no—
90C22×C32×C4—32no—
91C22×C32×C4—41no—
92C22×C32×C4C2×D311yescharacteristic
93C22×C32×C4C2×D311yescharacteristic
94C22×C32×C4C22×C311yescharacteristic
95C22×C3⋊Dic3C22×C311yescharacteristic
96C2×C4×C3⋊D3—24no—
97C2×C4×C3⋊D3C22×C312yes—
98C2×C4×C3⋊D3C22×C312yes—
99C2×C3×#67—22no—
100C2×C3×#67—34no—
101C2×C3×#67C2×D312yes—
102C2×C3×#67C22×C312yes—
103C22×C3×Dic3—31no—
104C22×C3×Dic3—31no—
105C22×C3×Dic3—61no—
106C3×#235—28no—
107C3×#235—24no—
108C3×#235—24no—
109C2×C3×D12—21no—
110C2×C3×D12—34no—
111C2×C3×D12C2×D311yescharacteristic, complemented
112C2×C3×D12C22×C311yescharacteristic, complemented
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—32no—
115C2×C3×C4×D3—32no—
116C2×C3×C4×D3—32no—
117C2×C3×C4×D3—32no—
118C2×C3×C4×D3—62no—
119C2×C3×C4×D3—62no—
120C2×C3×C4×D3—68no—
121C2×C3×C4×D3—64no—
122C2×C3×C4×D3—64no—
123C2×C3×C4×D3C2×D312yescomplemented
124C2×C3×C4×D3C22×C312yescomplemented
125C2×C3×Dic6—21no—
126C2×C3×Dic6C2×D311yescharacteristic, complemented
127C2×C3×Dic6C22×C311yescharacteristic, complemented
128C2×#626C22×C314yes—
129C32×C4⋊C4—32no—
130C32×C22⋊C4—32no—
131C32×C42—32no—
132C3×#217—22no—
133C3×#217—34no—
134C3×#217C2×D312yes—
135C3×#217C22×C312yes—
136C3×(C2×D3)⋊C4—34no—
137C3×(C2×D3)⋊C4—34no—
138C3×(C2×D3)⋊C4—34no—
139C3×C4⋊Dic3—22no—
140C3×C4⋊Dic3—34no—
141C3×C4⋊Dic3C2×D312yescomplemented
142C3×C4⋊Dic3C22×C312yescomplemented
143C3×Dic3⋊C4—34no—
144C3×C4×Dic3—22no—
145C3×C4×Dic3C2×D312yescomplemented
146C3×C4×Dic3C22×C312yescomplemented
147Dic3⋊Dic3C22×C314yescomplemented
148#3722C22×C314yes—
149(C2×D3)⋊Dic3C22×C314yescomplemented
150C22×C33—22no—
151C22×C33C2×D412yes—
152C22×C33C2411yescharacteristic
153C2×C3×C3⋊D3—28no—
154C2×C3×C3⋊D3—22no—
155C2×C3×C3⋊D3—22no—
156C2×C3×C3⋊D3#4114yescomplemented
157C2×C32×D3—22no—
158C2×C32×D3—24no—
159C33×C4C2×D412yes—
160C33×C4C2×D412yes—
161C3×C3⋊Dic3—22no—
162C32×Dic3—22no—
163C32×Dic3—24no—
164C2×C3×#41—31no—
165C2×C3×#41—31no—
166C2×C3×#41—61no—
167C23×C3×C4—91no—
168C2×#235C3×D311yescharacteristic, complemented
169C22×C4×D3—31no—
170C22×C4×D3—31no—
171C22×C4×D3—61no—
172C3×#123—92no—
173C3×C22⋊Q8—92no—
174C3×#121—92no—
175C3×#120—92no—
176C3×C4×D4—94no—
177C3×#117—31no—
178C3×#117—31no—
179C3×#117—61no—
180#946—32no—
181#938—32no—
182#937—32no—
183#935—32no—
184C4×#67—34no—
185#926C3×D311yescharacteristic, complemented
186#897—32no—
187#895—32no—
188#886—32no—
189#882—32no—
190C4×D12—34no—
191C23×C32—21no—
192C23×C32—21no—
193C23×C32—21no—
194C23×C32—32no—
195C23×C32—41no—
196C23×C32C22×D311yescharacteristic
197C23×C32C22×D311yescharacteristic
198C23×C32C23×C311yescharacteristic
199C22×C3⋊D3—22no—
200C22×C3⋊D3—24no—
201C22×C3⋊D3C23×C312yes—
202C22×C3×D3—22no—
203C22×C3×D3—32no—
204C22×C3×D3—32no—
205C22×C3×D3—62no—
206C22×C3×D3—64no—
207C22×C3×D3—64no—
208C22×C3×D3—68no—
209C22×C3×D3—64no—
210C22×C3×D3—62no—
211C22×C3×D3—62no—
212C22×C3×D3C22×D312yes—
213C22×C3×D3C23×C312yes—
214C32×Q8—62no—
215C32×D4—64no—
216C32×D4—62no—
217C2×C32×C4—24no—
218C2×C32×C4—24no—
219C2×C32×C4—24no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—32no—
227C2×C32×C4—34no—
228C2×C32×C4—44no—
229C2×C32×C4—41no—
230C2×C32×C4—41no—
231C2×C32×C4—64no—
232C2×C32×C4D1214yescomplemented
233C2×C32×C4#6714yescomplemented
234C2×C32×C4C3×D414yescomplemented
235C2×C32×C4C22×D311yescharacteristic
236C2×C32×C4C22×D311yescharacteristic
237C2×C32×C4C22×D311yescharacteristic
238C2×C32×C4C22×D311yescharacteristic
239C2×C32×C4C23×C311yescharacteristic
240C2×C32×C4C23×C311yescharacteristic
241C2×C3⋊Dic3—22no—
242C2×C3⋊Dic3C23×C312yes—
243C4×C3⋊D3—24no—
244C4×C3⋊D3—24no—
245C3×#67—28no—
246C3×#67—24no—
247C3×#67—24no—
248C3×#67—68no—
249C2×C3×Dic3—22no—
250C2×C3×Dic3—24no—
251C2×C3×Dic3—32no—
252C2×C3×Dic3—32no—
253C2×C3×Dic3—62no—
254C2×C3×Dic3—64no—
255C2×C3×Dic3—62no—
256C2×C3×Dic3—62no—
257C2×C3×Dic3C22×D314yes—
258C2×C3×Dic3C22×D312yes—
259C2×C3×Dic3C23×C314yes—
260C2×C3×Dic3C23×C312yes—
261C3×D12—24no—
262C3×D12—22no—
263C3×D12—22no—
264C3×D12—68no—
265C3×C4×D3—28no—
266C3×C4×D3—24no—
267C3×C4×D3—24no—
268C3×C4×D3—68no—
269C3×C4×D3—68no—
270C3×C4×D3—64no—
271C3×C4×D3—64no—
272C3×C4×D3—64no—
273C3×C4×D3—64no—
274C3×Dic6—24no—
275C3×Dic6—22no—
276C3×Dic6—22no—
277#626—28no—
278#525—91noSylow
279C2×C33—22no—
280C2×C33C22×D411yescharacteristic
281C2×C33C2×#4112yes—
282C3×C3⋊D3—24no—
283C32×D3—42no—
284C24×C3—91no—
285C23×D3—31no—
286C23×D3—31no—
287C23×D3—61no—
288C3×#41—68no—
289C3×#41—64no—
290C3×#41—64no—
291C2×C3×Q8—31no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
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—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—32no—
305C22×C3×C4—32no—
306C22×C3×C4—41no—
307C22×C3×C4—62no—
308C22×C3×C4—91no—
309C22×C3×C4—92no—
310C22×C3×C4—92no—
311C22×C3×C4—184no—
312C22×C3×C4D3211yescharacteristic
313C22×C3×C4C2×C3×D311yescharacteristic
314C22×C3×C4C2×C3×D311yescharacteristic
315C2×#67—34no—
316C2×#67C2×C3×D312yes—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—61no—
320#235—24no—
321C2×D12—34no—
322C2×D12C2×C3×D311yescharacteristic, complemented
323C2×C4×D3—32no—
324C2×C4×D3—32no—
325C2×C4×D3—32no—
326C2×C4×D3—32no—
327C2×C4×D3—62no—
328C2×C4×D3—62no—
329C2×C4×D3—68no—
330C2×C4×D3—64no—
331C2×C4×D3—64no—
332C2×C4×D3C2×C3×D312yescomplemented
333C2×Dic6C2×C3×D311yescharacteristic, complemented
334C3×C4⋊C4—32no—
335C3×C4⋊C4—32no—
336C3×C4⋊C4—62no—
337C3×C4⋊C4—94no—
338C3×C22⋊C4—32no—
339C3×C22⋊C4—32no—
340C3×C22⋊C4—62no—
341C3×C22⋊C4—94no—
342C3×C22⋊C4—94no—
343C3×C42—32no—
344C3×C42—32no—
345C3×C42—62no—
346#217—34no—
347#217C2×C3×D312yes—
348(C2×D3)⋊C4—34no—
349(C2×D3)⋊C4—34no—
350(C2×D3)⋊C4—34no—
351C4⋊Dic3—34no—
352C4⋊Dic3C2×C3×D312yescomplemented
353Dic3⋊C4—34no—
354C4×Dic3C2×C3×D312yescomplemented
355C22×C32—22no—
356C22×C32—24no—
357C22×C32—22no—
358C22×C32—22no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—22no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—42no—
366C22×C32—41no—
367C22×C32—42no—
368C22×C32—42no—
369C22×C32—44no—
370C22×C32—62no—
371C22×C32—64no—
372C22×C32C2×D1212yes—
373C22×C32C2×#6712yes—
374C22×C32C2×C3×D412yes—
375C22×C32C23×D311yescharacteristic
376C22×C32C23×D311yescharacteristic
377C22×C32C24×C311yescharacteristic
378C2×C3⋊D3—28no—
379C2×C3⋊D3—22no—
380C2×C3⋊D3—22no—
381C2×C3⋊D3C3×#4114yescomplemented
382C2×C3×D3—24no—
383C2×C3×D3—24no—
384C2×C3×D3—22no—
385C2×C3×D3—22no—
386C2×C3×D3—24no—
387C2×C3×D3—34no—
388C2×C3×D3—34no—
389C2×C3×D3—44no—
390C2×C3×D3—64no—
391C2×C3×D3—64no—
392C2×C3×D3—616no—
393C2×C3×D3—68no—
394C2×C3×D3—68no—
395C2×C3×D3—64no—
396C2×C3×D3—62no—
397C2×C3×D3—62no—
398C2×C3×D3—62no—
399C2×C3×D3—62no—
400C32×C4—22no—
401C32×C4—22no—
402C32×C4—22no—
403C32×C4—22no—
404C32×C4—22no—
405C32×C4—22no—
406C32×C4—42no—
407C32×C4—42no—
408C32×C4—62no—
409C32×C4—64no—
410C32×C4C2×D1212yes—
411C32×C4C2×D1212yes—
412C32×C4C2×#6712yes—
413C32×C4C2×#6712yes—
414C32×C4C2×C3×D412yes—
415C32×C4C2×C3×D412yes—
416C3⋊Dic3—22no—
417C3×Dic3—24no—
418C3×Dic3—24no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—24no—
422C3×Dic3—44no—
423C3×Dic3—64no—
424C3×Dic3—62no—
425C3×Dic3—62no—
426C2×#41—31no—
427C23×C4—91no—
428#123—92no—
429C22⋊Q8—92no—
430#121—92no—
431#120—92no—
432C4×D4—94no—
433#117—31no—
434C33#52511yescharacteristic, complemented, Sylow
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—32no—
439C23×C3—32no—
440C23×C3—41no—
441C23×C3—62no—
442C23×C3—92no—
443C23×C3—184no—
444C23×C3—182no—
445C23×C3C2×D3211yescharacteristic
446C23×C3C22×C3×D311yescharacteristic
447C23×C3C22×C3×D311yescharacteristic
448C22×D3—32no—
449C22×D3—32no—
450C22×D3—62no—
451C22×D3—64no—
452C22×D3—64no—
453C22×D3—64no—
454C22×D3—68no—
455C22×D3—62no—
456C22×D3—62no—
457C22×D3C22×C3×D312yes—
458C3×Q8—64no—
459C3×Q8—62no—
460C3×Q8—62no—
461C3×D4—64no—
462C3×D4—68no—
463C3×D4—64no—
464C3×D4—64no—
465C3×D4—62no—
466C3×D4—62no—
467C3×D4—188no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—24no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—34no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—34no—
481C2×C3×C4—44no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—62no—
485C2×C3×C4—64no—
486C2×C3×C4—68no—
487C2×C3×C4—64no—
488C2×C3×C4—64no—
489C2×C3×C4—92no—
490C2×C3×C4—182no—
491C2×C3×C4—184no—
492C2×C3×C4—184no—
493C2×C3×C4#62614yescomplemented
494C2×C3×C4C3×D1214yescomplemented
495C2×C3×C4C3×#6714yescomplemented
496C2×C3×C4C2×D3211yescharacteristic
497C2×C3×C4C2×D3211yescharacteristic
498C2×C3×C4C22×C3×D311yescharacteristic
499C2×C3×C4C22×C3×D311yescharacteristic
500C2×C3×C4C22×C3×D311yescharacteristic
501C2×C3×C4C22×C3×D311yescharacteristic
502#67—24no—
503#67—68no—
504C2×Dic3—32no—
505C2×Dic3—32no—
506C2×Dic3—62no—
507C2×Dic3—64no—
508C2×Dic3—62no—
509C2×Dic3—62no—
510C2×Dic3C22×C3×D314yes—
511C2×Dic3C22×C3×D312yes—
512D12—22no—
513D12—68no—
514C4×D3—24no—
515C4×D3—68no—
516C4×D3—68no—
517C4×D3—64no—
518C4×D3—64no—
519C4×D3—64no—
520C4×D3—64no—
521Dic6—22no—
522C2×C32—22no—
523C2×C32—24no—
524C2×C32—22no—
525C2×C32—22no—
526C2×C32—22no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—22no—
530C2×C32—22no—
531C2×C32—21no—
532C2×C32—41no—
533C2×C32—42no—
534C2×C32—42no—
535C2×C32—42no—
536C2×C32—44no—
537C2×C32—122no—
538C2×C32C22×D1211yescharacteristic
539C2×C32D3×#4112yes—
540C2×C32D3×#4112yes—
541C2×C32C22×#6711yescharacteristic
542C2×C32C22×C3×D411yescharacteristic
543C2×C32C2×C3×#4112yes—
544C3⋊D3—24no—
545C3×D3—44no—
546C3×D3—42no—
547C3×D3—42no—
548C3×D3—68no—
549C3×D3—64no—
550C3×D3—64no—
551C24—91no—
552#41—64no—
553C2×Q8—31no—
554C2×D4—32no—
555C2×D4—31no—
556C2×D4—94no—
557C22×C4—32no—
558C22×C4—91no—
559C22×C4—92no—
560C22×C4—92no—
561C22×C4—184no—
562C22×C4C3×D3211yescharacteristic
563C4⋊C4—32no—
564C4⋊C4—94no—
565C22⋊C4—32no—
566C22⋊C4—94no—
567C22⋊C4—94no—
568C42—32no—
569C22×C3—24no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—44no—
582C22×C3—41no—
583C22×C3—42no—
584C22×C3—64no—
585C22×C3—64no—
586C22×C3—62no—
587C22×C3—62no—
588C22×C3—64no—
589C22×C3—94no—
590C22×C3—124no—
591C22×C3—188no—
592C22×C3—182no—
593C22×C3—182no—
594C22×C3C2×#62612yes—
595C22×C3C2×C3×D1212yes—
596C22×C3C2×C3×#6712yes—
597C22×C3C22×D3211yescharacteristic
598C22×C3C23×C3×D311yescharacteristic
599C22×C3C23×C3×D311yescharacteristic
600C2×D3—24no—
601C2×D3—22no—
602C2×D3—34no—
603C2×D3—34no—
604C2×D3—64no—
605C2×D3—64no—
606C2×D3—616no—
607C2×D3—68no—
608C2×D3—68no—
609C2×D3—64no—
610C2×D3—62no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—62no—
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4—64no—
623C3×C4—64no—
624C3×C4—62no—
625C3×C4—62no—
626C3×C4—64no—
627C3×C4—124no—
628C3×C4—182no—
629C3×C4C2×#62612yes—
630C3×C4C2×#62612yes—
631C3×C4C2×C3×D1212yes—
632C3×C4C2×C3×D1212yes—
633C3×C4C2×C3×#6712yes—
634C3×C4C2×C3×#6712yes—
635Dic3—24no—
636Dic3—22no—
637Dic3—64no—
638Dic3—62no—
639Dic3—62no—
640C32—21no—
641C32—21no—
642C32—21no—
643C32—41no—
644C32#552411yescharacteristic, complemented
645C32#582811yescharacteristic, complemented
646C32C3×#52511yescharacteristic, complemented
647C23—32no—
648C23—92no—
649C23—184no—
650C23—182no—
651C23C2×C3×D3211yescharacteristic
652Q8—62no—
653D4—64no—
654D4—62no—
655D4—188no—
656C2×C4—34no—
657C2×C4—32no—
658C2×C4—64no—
659C2×C4—92no—
660C2×C4—182no—
661C2×C4—184no—
662C2×C4—184no—
663C2×C4C3×#62614yescomplemented
664C2×C4C2×C3×D3211yescharacteristic
665C2×C4C2×C3×D3211yescharacteristic
666C2×C3—24no—
667C2×C3—22no—
668C2×C3—22no—
669C2×C3—22no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—22no—
674C2×C3—22no—
675C2×C3—22no—
676C2×C3—42no—
677C2×C3—42no—
678C2×C3—44no—
679C2×C3—41no—
680C2×C3—42no—
681C2×C3—124no—
682C2×C3—122no—
683C2×C3—122no—
684C2×C3—184no—
685C2×C3#6430612yes—
686C2×C3C22×#62611yescharacteristic
687C2×C3C22×C3×D1211yescharacteristic
688C2×C3C3×D3×#4112yes—
689C2×C3C3×D3×#4112yes—
690C2×C3C22×C3×#6711yescharacteristic
691D3—42no—
692D3—68no—
693D3—64no—
694D3—64no—
695C22—22no—
696C22—62no—
697C22—64no—
698C22—94no—
699C22—188no—
700C22—182no—
701C22—182no—
702C22C2×C3×#62612yes—
703C22C22×C3×D3211yescharacteristic
704C4—62no—
705C4—64no—
706C4—182no—
707C4C2×C3×#62612yes—
708C4C2×C3×#62612yes—
709C3—21no—
710C3—21no—
711C3—21no—
712C3—41no—
713C3#1059503411yescharacteristic, direct product factor
714C3C3×#552411yescharacteristic, complemented
715C3C3×#582811yescharacteristic, complemented
716C2—22no—
717C2—122no—
718C2—184no—
719C2C3×#6430612yes—
720C2C22×C3×#62611yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×C3⋊D3C2semidirect
2. C2×C32×#235C2semidirect
3. C32×#926C2semidirect
4. C3×#63981C2semidirect
5. C3×#63962C2semidirect
6. C3×#63916C2semidirect
7. C3×C4×#626C2semidirect
8. C3×#63871C2semidirect
11. #10595034C3direct (N × H)
20. C2×C32×D12C22semidirect
21. C2×C32×C4×D3C22semidirect
22. C2×C32×Dic6C22semidirect
25. C32×C4⋊Dic3C22semidirect
26. C32×C4×Dic3C22semidirect
27. C3×Dic3⋊Dic3C22semidirect
29. C3×(C2×D3)⋊Dic3C22semidirect
31. C22×C4×C3⋊D3C2×C3semidirect
33. C2×C3×#235D3semidirect
34. C2×C3×#235C2×C3semidirect
45. C3×#926D3semidirect
46. C3×#926C2×C3semidirect
52. #63981C2×C3semidirect
53. #63962C2×C3semidirect
54. #63916C2×C3semidirect
55. C4×#626C2×C3semidirect
56. #63871C2×C3semidirect
62. C2×C33×C4D4semidirect
111. C2×C3×D12C2×D3semidirect
112. C2×C3×D12C22×C3semidirect
123. C2×C3×C4×D3C2×D3semidirect
124. C2×C3×C4×D3C22×C3semidirect
126. C2×C3×Dic6C2×D3semidirect
127. C2×C3×Dic6C22×C3semidirect
141. C3×C4⋊Dic3C2×D3semidirect
142. C3×C4⋊Dic3C22×C3semidirect
145. C3×C4×Dic3C2×D3semidirect
146. C3×C4×Dic3C22×C3semidirect
147. Dic3⋊Dic3C22×C3semidirect
149. (C2×D3)⋊Dic3C22×C3semidirect
156. C2×C3×C3⋊D3#41semidirect
168. C2×#235C3×D3semidirect
185. #926C3×D3semidirect
232. C2×C32×C4D12semidirect
233. C2×C32×C4#67semidirect
234. C2×C32×C4C3×D4semidirect
322. C2×D12C2×C3×D3semidirect
332. C2×C4×D3C2×C3×D3semidirect
333. C2×Dic6C2×C3×D3semidirect
352. C4⋊Dic3C2×C3×D3semidirect
354. C4×Dic3C2×C3×D3semidirect
381. C2×C3⋊D3C3×#41semidirect
434. C33#525semidirect
493. C2×C3×C4#626semidirect
494. C2×C3×C4C3×D12semidirect
495. C2×C3×C4C3×#67semidirect
644. C32#5524semidirect
645. C32#5828semidirect
646. C32C3×#525semidirect
663. C2×C4C3×#626semidirect
713. C3#10595034direct (N × H)
714. C3C3×#5524semidirect
715. C3C3×#5828semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×C3⋊D32
C2×C32×#2352
C32×#9262
C3×#639812
C3×#639622
C3×#639162
C3×C4×#6262
C3×#638712
C3×#58283
C3×#55243
#105950343