Finite Group Databasebeta

← C3×#73580 #11808214

Subgroups — C3×#73580 #11808214

Order 1152.

2017 conjugacy classes of subgroups.

The subgroup lattice has 721 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic, complemented
3C2×C3×C4×D12C212yesmaximal, complemented
4C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#4961C212yesmaximal, complemented
6C3×#4960C212yesmaximal, complemented
7C3×C4×(C2×D3)⋊C4C212yesmaximal, complemented
8C3×#4673C211yesmaximal, characteristic, complemented
9C3×#4672C211yesmaximal, characteristic, complemented
10C3×#4671C211yesmaximal, characteristic, complemented
11C3×#4656C211yesmaximal, characteristic, complemented
12C3×#2388—31nomaximal
13#73580C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C22×C3×#67C2212yes—
17C2×C3×#235—24no—
18C2×C3×#235—28no—
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2212yes—
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2212yes—
23C22×C3×Dic6C2211yescharacteristic
24C2×C32×C22⋊C4C2212yes—
25C2×C32×C42C2212yes—
26C2×C3×#217C2211yescharacteristic
27C3×C4×#67—24no—
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×C4⋊Dic3C2212yes—
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C3×C4×D12—28no—
37C32×#95C2211yescharacteristic
38C32×#95C2211yescharacteristic
39C3×C3⋊#95C2212yes—
40C3×C3⋊#95C2212yes—
41C22×C3×#41—31no—
42C22×#235C2×C311yescharacteristic, complemented
43C2×C3×C4×D4—31no—
44C2×C3×C4×D4—32no—
45C2×C4×#67C2×C311yescharacteristic, complemented
46C2×C4×D12C2×C312yescomplemented
47C3×#395—31no—
48C3×#394—32no—
49C3×#394—31no—
50C3×#393—31no—
51C3×#392—32no—
52C3×#392—31no—
53C3×C4×C22⋊C4—21no—
54C3×C4×C22⋊C4—32no—
55C3×C4×C22⋊C4D311yescharacteristic, complemented
56C3×C4×C22⋊C4C2×C311yescharacteristic, complemented
57#4961C2×C312yescomplemented
58#4960C2×C312yescomplemented
59C4×(C2×D3)⋊C4C2×C312yescomplemented
60#4673C2×C311yescharacteristic, complemented
61#4672C2×C311yescharacteristic, complemented
62#4671C2×C311yescharacteristic, complemented
63#4656C2×C311yescharacteristic, complemented
64C24×C32C2311yescharacteristic
65C23×C3×D3C2312yes—
66C23×C3×D3C2311yescharacteristic
67C22×C32×C4—24no—
68C22×C32×C4D414yescomplemented
69C22×C32×C4C2312yes—
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67—22no—
74C2×C3×#67—24no—
75C2×C3×#67—24no—
76C2×C3×#67—22no—
77C2×C3×#67—24no—
78C2×C3×#67—22no—
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2311yescharacteristic
83C3×#235—232no—
84C2×C3×D12—24no—
85C2×C3×D12—24no—
86C2×C3×D12—24no—
87C2×C3×D12—22no—
88C2×C3×D12—24no—
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3—24no—
91C2×C3×C4×D3—22no—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3D418yescomplemented
94C2×C3×Dic6—22no—
95C2×C3×Dic6—24no—
96C32×C22⋊C4—24no—
97C32×C42—24no—
98C3×#217—22no—
99C3×(C2×D3)⋊C4—24no—
100C3×(C2×D3)⋊C4—22no—
101C3×(C2×D3)⋊C4—24no—
102C3×(C2×D3)⋊C4—24no—
103C3×(C2×D3)⋊C4—24no—
104C3×C4⋊Dic3—24no—
105C3×Dic3⋊C4—22no—
106C3×C4×Dic3—22no—
107#2388—31noSylow
108C2×C3×#41—68no—
109C2×C3×#41—64no—
110C22×C3×Q8—31no—
111C22×C3×D4—32no—
112C22×C3×D4—31no—
113C22×C3×D4—31no—
114C22×C3×D4—32no—
115C23×C3×C4—21no—
116C23×C3×C4—32no—
117C23×C3×C4—31no—
118C23×C3×C4C2×D311yescharacteristic
119C23×C3×C4C22×C311yescharacteristic
120C22×#67C22×C312yes—
121C22×#67C22×C311yescharacteristic
122C2×#235—24no—
123C2×#235—28no—
124C22×D12C22×C311yescharacteristic
125C22×D12C22×C312yes—
126C22×C4×D3C22×C311yescharacteristic
127C22×C4×D3C22×C312yes—
128C22×Dic6C22×C311yescharacteristic
129C3×C4×D4—68no—
130C3×C4×D4—64no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—32no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C22⋊C4—32no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4—32no—
140C2×C3×C22⋊C4C2×D312yes—
141C2×C3×C22⋊C4C22×C312yes—
142C2×C3×C42—22no—
143C2×C3×C42—31no—
144C2×C3×C42C2×D312yes—
145C2×C3×C42C22×C312yes—
146C2×#217C22×C311yescharacteristic
147C4×#67—24no—
148C2×(C2×D3)⋊C4C22×C311yescharacteristic
149C2×(C2×D3)⋊C4C22×C312yes—
150C2×(C2×D3)⋊C4C22×C312yes—
151C2×(C2×D3)⋊C4C22×C312yes—
152C2×(C2×D3)⋊C4C22×C312yes—
153C2×C4⋊Dic3C22×C312yes—
154C2×Dic3⋊C4C22×C311yescharacteristic
155C2×C4×Dic3C22×C311yescharacteristic
156C4×D12—28no—
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—32no—
160C3×#95—32no—
161C3×#95C2×D311yescharacteristic
162C3×#95C2×D311yescharacteristic
163C3×#95C22×C311yescharacteristic
164C3×#95C22×C311yescharacteristic
165C3⋊#95C22×C312yes—
166C3⋊#95C22×C312yes—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32C2×D412yes—
172C23×C32C2411yescharacteristic
173C22×C3×D3—22no—
174C22×C3×D3—21no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3—21no—
183C22×C3×D3C2×D414yes—
184C22×C3×D3#4112yescomplemented
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4—28no—
190C2×C32×C4—22no—
191C2×C32×C4—22no—
192C2×C32×C4C2×D412yes—
193C2×C32×C4C2×D412yes—
194C2×C32×C4C2×D414yes—
195C2×C32×C4#4114yescomplemented
196C3×#67—216no—
197C3×#67—28no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3C2×D414yes—
207C2×C3×Dic3#4112yescomplemented
208C3×D12—216no—
209C3×D12—28no—
210C3×C4×D3—216no—
211C3×C4×D3—44no—
212C3×Dic6—28no—
213C22×#41—31no—
214C2×C4×D4—31no—
215C2×C4×D4—32no—
216#395—31no—
217#394—32no—
218#394—31no—
219#393—31no—
220#392—32no—
221#392—31no—
222C4×C22⋊C4—32no—
223C4×C22⋊C4C3×D311yescharacteristic, complemented
224C24×C3—21no—
225C24×C3—32no—
226C24×C3—31no—
227C24×C3C22×D311yescharacteristic
228C24×C3C23×C311yescharacteristic
229C23×D3C23×C312yes—
230C23×D3C23×C311yescharacteristic
231C3×#41—632no—
232C2×C3×Q8—64no—
233C2×C3×Q8—62no—
234C2×C3×D4—64no—
235C2×C3×D4—64no—
236C2×C3×D4—64no—
237C2×C3×D4—62no—
238C2×C3×D4—64no—
239C2×C3×D4—62no—
240C2×C3×D4—64no—
241C2×C3×D4—62no—
242C2×C3×D4—64no—
243C2×C3×D4—62no—
244C2×C3×D4—64no—
245C22×C3×C4—24no—
246C22×C3×C4—24no—
247C22×C3×C4—24no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—31no—
253C22×C3×C4—32no—
254C22×C3×C4—38no—
255C22×C3×C4—31no—
256C22×C3×C4—31no—
257C22×C3×C4—44no—
258C22×C3×C4—64no—
259C22×C3×C4—64no—
260C22×C3×C4—62no—
261C22×C3×C4—64no—
262C22×C3×C4D1214yescomplemented
263C22×C3×C4C3×D414yescomplemented
264C22×C3×C4C22×D312yes—
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C22×D312yes—
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C23×C312yes—
269C22×C3×C4C23×C311yescharacteristic
270C22×C3×C4C23×C312yes—
271C22×C3×C4C23×C311yescharacteristic
272C2×#67—22no—
273C2×#67—24no—
274C2×#67—24no—
275C2×#67—22no—
276C2×#67—24no—
277C2×#67—22no—
278C22×Dic3C23×C311yescharacteristic
279C22×Dic3C23×C311yescharacteristic
280C22×Dic3C23×C312yes—
281C22×Dic3C23×C311yescharacteristic
282#235—232no—
283C2×D12—24no—
284C2×D12—24no—
285C2×D12—24no—
286C2×D12—22no—
287C2×D12—24no—
288C2×C4×D3—24no—
289C2×C4×D3—24no—
290C2×C4×D3—24no—
291C2×C4×D3—22no—
292C2×C4×D3C3×D418yescomplemented
293C2×Dic6—22no—
294C2×Dic6—24no—
295C3×C4⋊C4—64no—
296C3×C4⋊C4—62no—
297C3×C22⋊C4—28no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—64no—
301C3×C22⋊C4—64no—
302C3×C22⋊C4—64no—
303C3×C22⋊C4—62no—
304C3×C22⋊C4—62no—
305C3×C22⋊C4—64no—
306C3×C42—24no—
307C3×C42—24no—
308C3×C42—44no—
309C3×C42—62no—
310#217—22no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—22no—
313(C2×D3)⋊C4—24no—
314(C2×D3)⋊C4—24no—
315(C2×D3)⋊C4—24no—
316C4⋊Dic3—24no—
317Dic3⋊C4—22no—
318C4×Dic3—22no—
319C22×C32—22no—
320C22×C32—22no—
321C22×C32—22no—
322C22×C32—42no—
323C22×C32—42no—
324C22×C32C22×D411yescharacteristic
325C22×C32C22×D412yes—
326C22×C32C2×#4112yes—
327C22×C32C2×#4111yescharacteristic
328C22×C32C2×#4111yescharacteristic
329C2×C3×D3—24no—
330C2×C3×D3—24no—
331C2×C3×D3—24no—
332C2×C3×D3—22no—
333C2×C3×D3—24no—
334C2×C3×D3—41no—
335C2×C3×D3—42no—
336C2×C3×D3—42no—
337C2×C3×D3—41no—
338C2×C3×D3—42no—
339C2×C3×D3—42no—
340C2×C3×D3—42no—
341C32×C4—22no—
342C32×C4—24no—
343C32×C4—42no—
344C32×C4#12014yes—
345C3×Dic3—24no—
346C3×Dic3—22no—
347C3×Dic3—41no—
348C3×Dic3—41no—
349C2×#41—68no—
350C2×#41—64no—
351C22×Q8—31no—
352C22×D4—31no—
353C22×D4—32no—
354C22×D4—32no—
355C22×D4—31no—
356C23×C4—32no—
357C23×C4—31no—
358C23×C4C2×C3×D311yescharacteristic
359C4×D4—68no—
360C4×D4—64no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—32no—
363C2×C22⋊C4—31no—
364C2×C22⋊C4—32no—
365C2×C22⋊C4—31no—
366C2×C22⋊C4—32no—
367C2×C22⋊C4—32no—
368C2×C22⋊C4—32no—
369C2×C22⋊C4C2×C3×D312yes—
370C2×C42—31no—
371C2×C42C2×C3×D312yes—
372#95—32no—
373#95—32no—
374#95C2×C3×D311yescharacteristic
375#95C2×C3×D311yescharacteristic
376C23×C3—24no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—22no—
387C23×C3—34no—
388C23×C3—32no—
389C23×C3—42no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—61no—
393C23×C3—62no—
394C23×C3—62no—
395C23×C3—62no—
396C23×C3—62no—
397C23×C3—62no—
398C23×C3—62no—
399C23×C3—62no—
400C23×C3—61no—
401C23×C3—62no—
402C23×C3C2×D1212yes—
403C23×C3C2×C3×D412yes—
404C23×C3C23×D311yescharacteristic
405C23×C3C24×C311yescharacteristic
406C22×D3—22no—
407C22×D3—21no—
408C22×D3—22no—
409C22×D3—22no—
410C22×D3—22no—
411C22×D3—22no—
412C22×D3—22no—
413C22×D3—22no—
414C22×D3—22no—
415C22×D3—21no—
416C22×D3C2×C3×D414yes—
417C22×D3C3×#4112yescomplemented
418C3×Q8—68no—
419C3×D4—616no—
420C3×D4—68no—
421C3×D4—68no—
422C3×D4—616no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—28no—
430C2×C3×C4—28no—
431C2×C3×C4—24no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
442C2×C3×C4—34no—
443C2×C3×C4—32no—
444C2×C3×C4—48no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—61no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4—61no—
454C2×C3×C4—616no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—62no—
458C2×C3×C4—62no—
459C2×C3×C4—124no—
460C2×C3×C4C2×D1212yes—
461C2×C3×C4C2×D1212yes—
462C2×C3×C4#23514yescomplemented
463C2×C3×C4D3×D414yes—
464C2×C3×C4C2×C3×D412yes—
465C2×C3×C4C2×C3×D412yes—
466C2×C3×C4C2×C3×D414yes—
467C2×C3×C4C3×#4114yescomplemented
468#67—216no—
469#67—28no—
470C2×Dic3—21no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3C2×C3×D414yes—
479C2×Dic3C3×#4112yescomplemented
480D12—216no—
481D12—28no—
482C4×D3—216no—
483C4×D3—44no—
484Dic6—28no—
485C2×C32—42no—
486C2×C32C2×#12011yescharacteristic
487C2×C32#52511yescharacteristic
488C2×C32#52512yes—
489C2×C32#53211yescharacteristic
490C2×C32#53212yes—
491C3×D3—44no—
492C3×D3—42no—
493C24—32no—
494C24—31no—
495C24C22×C3×D311yescharacteristic
496#41—632no—
497C2×Q8—64no—
498C2×Q8—62no—
499C2×D4—64no—
500C2×D4—64no—
501C2×D4—64no—
502C2×D4—64no—
503C2×D4—62no—
504C2×D4—64no—
505C2×D4—62no—
506C2×D4—62no—
507C2×D4—64no—
508C2×D4—62no—
509C2×D4—64no—
510C22×C4—24no—
511C22×C4—31no—
512C22×C4—32no—
513C22×C4—38no—
514C22×C4—31no—
515C22×C4—31no—
516C22×C4—64no—
517C22×C4—64no—
518C22×C4—62no—
519C22×C4—64no—
520C22×C4C3×D1214yescomplemented
521C22×C4C22×C3×D312yes—
522C22×C4C22×C3×D311yescharacteristic
523C22×C4C22×C3×D312yes—
524C22×C4C22×C3×D311yescharacteristic
525C4⋊C4—64no—
526C4⋊C4—62no—
527C22⋊C4—24no—
528C22⋊C4—64no—
529C22⋊C4—64no—
530C22⋊C4—64no—
531C22⋊C4—62no—
532C22⋊C4—62no—
533C22⋊C4—64no—
534C42—24no—
535C42—62no—
536C22×C3—24no—
537C22×C3—22no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—21no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—42no—
549C22×C3—42no—
550C22×C3—44no—
551C22×C3—44no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—64no—
557C22×C3—62no—
558C22×C3—64no—
559C22×C3—64no—
560C22×C3—64no—
561C22×C3—121no—
562C22×C3—122no—
563C22×C3—121no—
564C22×C3—122no—
565C22×C3—122no—
566C22×C3—122no—
567C22×C3—122no—
568C22×C3C22×D1211yescharacteristic
569C22×C3C2×#23512yes—
570C22×C3C2×D3×D412yes—
571C22×C3D3×#4111yescharacteristic
572C22×C3D3×#4111yescharacteristic
573C22×C3C22×C3×D411yescharacteristic
574C22×C3C22×C3×D412yes—
575C22×C3C2×C3×#4112yes—
576C22×C3C2×C3×#4111yescharacteristic
577C22×C3C2×C3×#4111yescharacteristic
578C2×D3—24no—
579C2×D3—24no—
580C2×D3—24no—
581C2×D3—22no—
582C2×D3—24no—
583C2×D3—41no—
584C2×D3—42no—
585C2×D3—42no—
586C2×D3—42no—
587C2×D3—42no—
588C2×D3—41no—
589C2×D3—42no—
590C3×C4—22no—
591C3×C4—24no—
592C3×C4—22no—
593C3×C4—24no—
594C3×C4—24no—
595C3×C4—42no—
596C3×C4—44no—
597C3×C4—44no—
598C3×C4—42no—
599C3×C4—42no—
600C3×C4—64no—
601C3×C4—62no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4#88214yes—
605C3×C4C3×#12014yes—
606Dic3—24no—
607Dic3—22no—
608Dic3—41no—
609Dic3—41no—
610C32#238811yescharacteristic, complemented, Sylow
611C23—22no—
612C23—22no—
613C23—21no—
614C23—21no—
615C23—34no—
616C23—32no—
617C23—61no—
618C23—62no—
619C23—62no—
620C23—62no—
621C23—62no—
622C23—62no—
623C23—62no—
624C23—62no—
625C23—61no—
626C23—62no—
627C23C2×C3×D1212yes—
628C23C23×C3×D311yescharacteristic
629Q8—68no—
630D4—68no—
631D4—616no—
632D4—616no—
633D4—68no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—34no—
642C2×C4—32no—
643C2×C4—61no—
644C2×C4—62no—
645C2×C4—62no—
646C2×C4—61no—
647C2×C4—616no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—124no—
653C2×C4C2×C3×D1212yes—
654C2×C4C2×C3×D1212yes—
655C2×C4C3×#23514yescomplemented
656C2×C4C3×D3×D414yes—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—22no—
660C2×C3—22no—
661C2×C3—21no—
662C2×C3—44no—
663C2×C3—42no—
664C2×C3—42no—
665C2×C3—124no—
666C2×C3—122no—
667C2×C3#547711yescharacteristic
668C2×C3C2×#88211yescharacteristic
669C2×C3#552411yescharacteristic
670C2×C3#554712yes—
671C2×C3#554812yes—
672C2×C3C2×C3×#12011yescharacteristic
673C2×C3C3×#52511yescharacteristic
674C2×C3C3×#52512yes—
675C2×C3C3×#53212yes—
676C2×C3C3×#53211yescharacteristic
677D3—44no—
678D3—42no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—42no—
683C22—42no—
684C22—64no—
685C22—62no—
686C22—64no—
687C22—64no—
688C22—64no—
689C22—121no—
690C22—122no—
691C22—122no—
692C22—122no—
693C22—122no—
694C22—121no—
695C22—122no—
696C22C22×C3×D1211yescharacteristic
697C22C2×C3×#23512yes—
698C22C2×C3×D3×D412yes—
699C22C3×D3×#4111yescharacteristic
700C22C3×D3×#4111yescharacteristic
701C4—22no—
702C4—24no—
703C4—42no—
704C4—64no—
705C4—62no—
706C4—121no—
707C4—121no—
708C4C3×#88214yes—
709C3—21no—
710C3#7358011yescharacteristic, direct product factor
711C3C3×#238811yescharacteristic, complemented
712C2—42no—
713C2—124no—
714C2—122no—
715C2C3×#547711yescharacteristic
716C2C2×C3×#88211yescharacteristic
717C2C3×#552411yescharacteristic
718C2C3×#554712yes—
719C2C3×#554812yes—
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×C4×C22⋊C4C2
socleC23×C32C24
hypercenterC3×C4×C22⋊C4D3
hypocenterC3C3×#2388
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C2×C3×C4×#67C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C32×C4×C22⋊C4C2semidirect
5. C3×#4961C2semidirect
6. C3×#4960C2semidirect
7. C3×C4×(C2×D3)⋊C4C2semidirect
8. C3×#4673C2semidirect
9. C3×#4672C2semidirect
10. C3×#4671C2semidirect
11. C3×#4656C2semidirect
13. #73580C3direct (N × H)
42. C22×#235C2×C3semidirect
45. C2×C4×#67C2×C3semidirect
46. C2×C4×D12C2×C3semidirect
55. C3×C4×C22⋊C4D3semidirect
56. C3×C4×C22⋊C4C2×C3semidirect
57. #4961C2×C3semidirect
58. #4960C2×C3semidirect
59. C4×(C2×D3)⋊C4C2×C3semidirect
60. #4673C2×C3semidirect
61. #4672C2×C3semidirect
62. #4671C2×C3semidirect
63. #4656C2×C3semidirect
68. C22×C32×C4D4semidirect
93. C2×C3×C4×D3D4semidirect
184. C22×C3×D3#41semidirect
195. C2×C32×C4#41semidirect
207. C2×C3×Dic3#41semidirect
223. C4×C22⋊C4C3×D3semidirect
262. C22×C3×C4D12semidirect
263. C22×C3×C4C3×D4semidirect
292. C2×C4×D3C3×D4semidirect
417. C22×D3C3×#41semidirect
462. C2×C3×C4#235semidirect
467. C2×C3×C4C3×#41semidirect
479. C2×Dic3C3×#41semidirect
520. C22×C4C3×D12semidirect
610. C32#2388semidirect
655. C2×C4C3×#235semidirect
710. C3#73580direct (N × H)
711. C3C3×#2388semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×C3×C4×#672
C2×C3×C4×D122
C32×C4×C22⋊C42
C3×#49612
C3×#49602
C3×C4×(C2×D3)⋊C42
C3×#46732
C3×#46722
C3×#46712
C3×#46562
C3×#23883
#735803