Finite Group Databasebeta

← C3×#76889 #11808208

Subgroups — C3×#76889 #11808208

Order 1152.

2007 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C2×C3×#893C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C212yesmaximal, complemented
4C32×#394C211yesmaximal, characteristic, complemented
5C3×#5223C211yesmaximal, characteristic, complemented
6C3×#4979C211yesmaximal, characteristic, complemented
7C3×#4960C212yesmaximal, complemented
8C3×#4959C212yesmaximal, complemented
9C3×Dic3×C22⋊C4C212yesmaximal, complemented
10C3×#4673C211yesmaximal, characteristic, complemented
11C3×#4666C211yesmaximal, characteristic, complemented
12C3×#2388—31nomaximal
13#76889C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×#67C2212yes—
17C23×C3×Dic3C2212yes—
18C2×C3×#237—28no—
19C2×C3×#237—24no—
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2212yes—
26C2×C32×C22⋊C4C2212yes—
27C2×C3×#217C2212yes—
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×Dic3⋊C4C2212yes—
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2212yes—
35C3×#893—24no—
36C3×#67⋊C4—28no—
37C32×#95C2211yescharacteristic
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2212yes—
40C3×C3⋊#95C2212yes—
41C22×C3×#41—31no—
42C22×#237C2×C311yescharacteristic, complemented
43C2×C3×C4×D4—31no—
44C2×C3×C4×D4—32no—
45C2×#893C2×C311yescharacteristic, complemented
46C2×#67⋊C4C2×C312yescomplemented
47C3×#395—31no—
48C3×#394—21no—
49C3×#394—32no—
50C3×#394D311yescharacteristic, complemented
51C3×#394C2×C311yescharacteristic, complemented
52C3×#393—31no—
53C3×#392—31no—
54C3×#392—32no—
55C3×C4×C22⋊C4—32no—
56C3×C4×C22⋊C4—31no—
57#5223C2×C311yescharacteristic, complemented
58#4979C2×C311yescharacteristic, complemented
59#4960C2×C312yescomplemented
60#4959C2×C312yescomplemented
61Dic3×C22⋊C4C2×C312yescomplemented
62#4673C2×C311yescharacteristic, complemented
63#4666C2×C311yescharacteristic, complemented
64C24×C32C2312yes—
65C23×C3×D3C2311yescharacteristic
66C23×C3×D3C2311yescharacteristic
67C2×C32×D4—24no—
68C2×C32×D4—22no—
69C22×C32×C4C2312yes—
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67—24no—
74C2×C3×#67—24no—
75C2×C3×#67—24no—
76C2×C3×#67—24no—
77C2×C3×#67—24no—
78C2×C3×#67—24no—
79C22×C3×Dic3—24no—
80C22×C3×Dic3—24no—
81C22×C3×Dic3D418yescomplemented
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C3×#237—232no—
87C2×C3×D12—22no—
88C2×C3×D12—22no—
89C2×C3×D12—22no—
90C2×C3×C4×D3—24no—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3—22no—
93C2×C3×C4×D3D414yescomplemented
94C2×C3×Dic6—22no—
95C2×C3×Dic6—24no—
96C32×C4⋊C4—22no—
97C32×C22⋊C4—24no—
98C32×C22⋊C4—24no—
99C3×#217—24no—
100C3×(C2×D3)⋊C4—22no—
101C3×(C2×D3)⋊C4—22no—
102C3×(C2×D3)⋊C4—24no—
103C3×(C2×D3)⋊C4—24no—
104C3×Dic3⋊C4—24no—
105C3×C4×Dic3—24no—
106C3×C4×Dic3—22no—
107#2388—31noSylow
108C2×C3×#41—68no—
109C2×C3×#41—64no—
110C22×C3×Q8—31no—
111C22×C3×D4—21no—
112C22×C3×D4—32no—
113C22×C3×D4—32no—
114C22×C3×D4—31no—
115C22×C3×D4C2×D311yescharacteristic
116C22×C3×D4C22×C311yescharacteristic
117C23×C3×C4—32no—
118C23×C3×C4—31no—
119C23×C3×C4—31no—
120C22×#67C22×C312yes—
121C22×#67C22×C312yes—
122C23×Dic3C22×C312yes—
123C2×#237—28no—
124C2×#237—24no—
125C22×D12C22×C311yescharacteristic
126C22×C4×D3C22×C311yescharacteristic
127C22×C4×D3C22×C311yescharacteristic
128C22×Dic6C22×C311yescharacteristic
129C3×C4×D4—68no—
130C3×C4×D4—64no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—32no—
133C2×C3×C4⋊C4C2×D311yescharacteristic
134C2×C3×C4⋊C4C22×C311yescharacteristic
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C22⋊C4—32no—
139C2×C3×C22⋊C4—32no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4C2×D312yes—
143C2×C3×C22⋊C4C2×D312yes—
144C2×C3×C22⋊C4C22×C312yes—
145C2×C3×C22⋊C4C22×C312yes—
146C2×C3×C42—32no—
147C2×C3×C42—31no—
148C2×#217C22×C312yes—
149C2×(C2×D3)⋊C4C22×C312yes—
150C2×(C2×D3)⋊C4C22×C312yes—
151C2×(C2×D3)⋊C4C22×C311yescharacteristic
152C2×(C2×D3)⋊C4C22×C311yescharacteristic
153C2×Dic3⋊C4C22×C312yes—
154C2×C4×Dic3C22×C312yes—
155C2×C4×Dic3C22×C311yescharacteristic
156#893—24no—
157#67⋊C4—28no—
158C3×#95—21no—
159C3×#95—31no—
160C3×#95—32no—
161C3×#95—32no—
162C3×#95C2×D311yescharacteristic
163C3×#95C22×C311yescharacteristic
164C3⋊#95C22×C311yescharacteristic
165C3⋊#95C22×C312yes—
166C3⋊#95C22×C312yes—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32—22no—
173C23×C32C2×D414yes—
174C23×C32C2411yescharacteristic
175C22×C3×D3—21no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—21no—
180C22×C3×D3—21no—
181C22×C3×D3—21no—
182C22×C3×D3—22no—
183C22×C3×D3C2×D412yes—
184C22×C3×D3#4112yescomplemented
185C32×D4—28no—
186C2×C32×C4—21no—
187C2×C32×C4—22no—
188C2×C32×C4—21no—
189C2×C32×C4—22no—
190C2×C32×C4—22no—
191C2×C32×C4—21no—
192C2×C32×C4—22no—
193C2×C32×C4—22no—
194C2×C32×C4C2×D412yes—
195C2×C32×C4#4112yescomplemented
196C3×#67—216no—
197C3×#67—216no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—216no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3C2×D414yes—
206C2×C3×Dic3C2×D414yes—
207C2×C3×Dic3C2×D412yes—
208C2×C3×Dic3#4114yescomplemented
209C3×D12—28no—
210C3×C4×D3—28no—
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#394C3×D311yescharacteristic, complemented
219#393—31no—
220#392—31no—
221#392—32no—
222C4×C22⋊C4—32no—
223C4×C22⋊C4—31no—
224C24×C3—22no—
225C24×C3—31no—
226C24×C3—31no—
227C24×C3C22×D312yes—
228C24×C3C23×C312yes—
229C23×D3C23×C311yescharacteristic
230C23×D3C23×C311yescharacteristic
231C3×#41—632no—
232C2×C3×Q8—64no—
233C2×C3×Q8—62no—
234C2×C3×D4—24no—
235C2×C3×D4—24no—
236C2×C3×D4—22no—
237C2×C3×D4—22no—
238C2×C3×D4—42no—
239C2×C3×D4—44no—
240C2×C3×D4—62no—
241C2×C3×D4—62no—
242C2×C3×D4—64no—
243C2×C3×D4—64no—
244C2×C3×D4—64no—
245C2×C3×D4—64no—
246C2×C3×D4—64no—
247C2×C3×D4—64no—
248C2×C3×D4—62no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—22no—
252C22×C3×C4—21no—
253C22×C3×C4—31no—
254C22×C3×C4—38no—
255C22×C3×C4—32no—
256C22×C3×C4—32no—
257C22×C3×C4—34no—
258C22×C3×C4—31no—
259C22×C3×C4—64no—
260C22×C3×C4—64no—
261C22×C3×C4—62no—
262C22×C3×C4—64no—
263C22×C3×C4—64no—
264C22×C3×C4C22×D312yes—
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C22×D311yescharacteristic
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C23×C312yes—
269C22×C3×C4C23×C311yescharacteristic
270C22×C3×C4C23×C311yescharacteristic
271C22×C3×C4C23×C311yescharacteristic
272C2×#67—24no—
273C2×#67—24no—
274C2×#67—24no—
275C2×#67—24no—
276C2×#67—24no—
277C2×#67—24no—
278C22×Dic3—24no—
279C22×Dic3—24no—
280C22×Dic3C3×D418yescomplemented
281C22×Dic3C23×C311yescharacteristic
282C22×Dic3C23×C312yes—
283C22×Dic3C23×C312yes—
284C22×Dic3C23×C311yescharacteristic
285#237—232no—
286C2×D12—22no—
287C2×D12—22no—
288C2×D12—22no—
289C2×C4×D3—24no—
290C2×C4×D3—24no—
291C2×C4×D3—22no—
292C2×C4×D3C3×D414yescomplemented
293C2×Dic6—22no—
294C2×Dic6—24no—
295C3×C4⋊C4—22no—
296C3×C4⋊C4—22no—
297C3×C4⋊C4—42no—
298C3×C4⋊C4—64no—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—44no—
304C3×C22⋊C4—44no—
305C3×C22⋊C4—64no—
306C3×C22⋊C4—64no—
307C3×C22⋊C4—62no—
308C3×C22⋊C4—64no—
309C3×C22⋊C4—62no—
310C3×C42—62no—
311C3×C42—64no—
312#217—24no—
313(C2×D3)⋊C4—22no—
314(C2×D3)⋊C4—22no—
315(C2×D3)⋊C4—24no—
316(C2×D3)⋊C4—24no—
317Dic3⋊C4—24no—
318C4×Dic3—24no—
319C4×Dic3—22no—
320C22×C32—24no—
321C22×C32—24no—
322C22×C32—24no—
323C22×C32—42no—
324C22×C32—42no—
325C22×C32—42no—
326C22×C32—42no—
327C22×C32C22×D411yescharacteristic
328C22×C32C22×D412yes—
329C22×C32C2×#4111yescharacteristic
330C22×C32C2×#4111yescharacteristic
331C22×C32C2×#4112yes—
332C2×C3×D3—22no—
333C2×C3×D3—22no—
334C2×C3×D3—22no—
335C2×C3×D3—24no—
336C2×C3×D3—22no—
337C2×C3×D3—41no—
338C2×C3×D3—42no—
339C2×C3×D3—41no—
340C2×C3×D3—42no—
341C2×C3×D3—42no—
342C32×C4—22no—
343C32×C4—22no—
344C32×C4—41no—
345C32×C4—42no—
346C3×Dic3—24no—
347C3×Dic3—24no—
348C3×Dic3—41no—
349C3×Dic3#12014yes—
350C2×#41—68no—
351C2×#41—64no—
352C22×Q8—31no—
353C22×D4—32no—
354C22×D4—32no—
355C22×D4—31no—
356C22×D4C2×C3×D311yescharacteristic
357C23×C4—32no—
358C23×C4—31no—
359C23×C4—31no—
360C4×D4—68no—
361C4×D4—64no—
362C2×C4⋊C4—32no—
363C2×C4⋊C4C2×C3×D311yescharacteristic
364C2×C22⋊C4—32no—
365C2×C22⋊C4—32no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—32no—
369C2×C22⋊C4C2×C3×D312yes—
370C2×C22⋊C4C2×C3×D312yes—
371C2×C42—32no—
372C2×C42—31no—
373#95—31no—
374#95—32no—
375#95—32no—
376#95C2×C3×D311yescharacteristic
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—21no—
390C23×C3—24no—
391C23×C3—32no—
392C23×C3—32no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—62no—
400C23×C3—61no—
401C23×C3—62no—
402C23×C3—61no—
403C23×C3—61no—
404C23×C3—62no—
405C23×C3—62no—
406C23×C3—61no—
407C23×C3D3×D414yes—
408C23×C3C2×C3×D414yes—
409C23×C3C23×D311yescharacteristic
410C23×C3C24×C311yescharacteristic
411C22×D3—21no—
412C22×D3—22no—
413C22×D3—22no—
414C22×D3—22no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—22no—
419C22×D3C2×C3×D412yes—
420C22×D3C3×#4112yescomplemented
421C3×Q8—68no—
422C3×D4—28no—
423C3×D4—28no—
424C3×D4—48no—
425C3×D4—68no—
426C3×D4—616no—
427C3×D4—616no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—22no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—34no—
447C2×C3×C4—32no—
448C2×C3×C4—34no—
449C2×C3×C4—34no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—42no—
453C2×C3×C4—42no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—41no—
457C2×C3×C4—42no—
458C2×C3×C4—68no—
459C2×C3×C4—616no—
460C2×C3×C4—62no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4—62no—
464C2×C3×C4—61no—
465C2×C3×C4—62no—
466C2×C3×C4—124no—
467C2×C3×C4D3×D412yes—
468C2×C3×C4#23712yescomplemented
469C2×C3×C4C2×C3×D412yes—
470C2×C3×C4C3×#4112yescomplemented
471#67—216no—
472#67—216no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—216no—
478C2×Dic3—21no—
479C2×Dic3—22no—
480C2×Dic3C2×C3×D414yes—
481C2×Dic3C2×C3×D414yes—
482C2×Dic3C2×C3×D412yes—
483C2×Dic3C3×#4114yescomplemented
484D12—28no—
485C4×D3—28no—
486C4×D3—44no—
487Dic6—28no—
488C2×C32—44no—
489C2×C32C2×#12011yescharacteristic
490C2×C32#52512yes—
491C2×C32#52511yescharacteristic
492C2×C32#53211yescharacteristic
493C2×C32#53212yes—
494C3×D3—42no—
495C3×D3—42no—
496C24—31no—
497C24—31no—
498C24C22×C3×D312yes—
499#41—632no—
500C2×Q8—64no—
501C2×Q8—62no—
502C2×D4—24no—
503C2×D4—22no—
504C2×D4—62no—
505C2×D4—62no—
506C2×D4—64no—
507C2×D4—64no—
508C2×D4—64no—
509C2×D4—64no—
510C2×D4—64no—
511C2×D4—64no—
512C2×D4—62no—
513C22×C4—31no—
514C22×C4—32no—
515C22×C4—32no—
516C22×C4—38no—
517C22×C4—34no—
518C22×C4—31no—
519C22×C4—64no—
520C22×C4—64no—
521C22×C4—62no—
522C22×C4—64no—
523C22×C4—64no—
524C22×C4C22×C3×D312yes—
525C22×C4C22×C3×D311yescharacteristic
526C22×C4C22×C3×D311yescharacteristic
527C22×C4C22×C3×D311yescharacteristic
528C4⋊C4—22no—
529C4⋊C4—64no—
530C22⋊C4—24no—
531C22⋊C4—24no—
532C22⋊C4—64no—
533C22⋊C4—64no—
534C22⋊C4—62no—
535C22⋊C4—64no—
536C22⋊C4—62no—
537C42—62no—
538C42—64no—
539C22×C3—24no—
540C22×C3—24no—
541C22×C3—24no—
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3—21no—
546C22×C3—22no—
547C22×C3—21no—
548C22×C3—22no—
549C22×C3—21no—
550C22×C3—44no—
551C22×C3—44no—
552C22×C3—44no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—64no—
562C22×C3—62no—
563C22×C3—62no—
564C22×C3—62no—
565C22×C3—62no—
566C22×C3—82no—
567C22×C3—82no—
568C22×C3—82no—
569C22×C3—82no—
570C22×C3—122no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3—122no—
574C22×C3—122no—
575C22×C3C2×D3×D412yes—
576C22×C3C2×D3×D411yescharacteristic
577C22×C3C2×#23711yescharacteristic
578C22×C3D3×#4111yescharacteristic
579C22×C3D3×#4112yes—
580C22×C3C22×C3×D411yescharacteristic
581C22×C3C22×C3×D412yes—
582C22×C3C2×C3×#4111yescharacteristic
583C22×C3C2×C3×#4111yescharacteristic
584C22×C3C2×C3×#4112yes—
585C2×D3—22no—
586C2×D3—22no—
587C2×D3—22no—
588C2×D3—24no—
589C2×D3—22no—
590C2×D3—41no—
591C2×D3—42no—
592C2×D3—42no—
593C2×D3—42no—
594C2×D3—41no—
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—34no—
600C3×C4—42no—
601C3×C4—42no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—42no—
605C3×C4—42no—
606C3×C4—64no—
607C3×C4—64no—
608C3×C4—81no—
609C3×C4—82no—
610C3×C4—121no—
611Dic3—24no—
612Dic3—24no—
613Dic3—41no—
614Dic3C3×#12014yes—
615C32#238811yescharacteristic, complemented, Sylow
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—32no—
623C23—32no—
624C23—61no—
625C23—62no—
626C23—62no—
627C23—61no—
628C23—61no—
629C23—62no—
630C23—61no—
631C23—62no—
632C23C3×D3×D414yes—
633C23C23×C3×D311yescharacteristic
634Q8—68no—
635D4—28no—
636D4—68no—
637D4—616no—
638D4—616no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—34no—
648C2×C4—32no—
649C2×C4—34no—
650C2×C4—34no—
651C2×C4—68no—
652C2×C4—616no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—61no—
658C2×C4—62no—
659C2×C4—124no—
660C2×C4C3×D3×D412yes—
661C2×C4C3×#23712yescomplemented
662C2×C3—21no—
663C2×C3—22no—
664C2×C3—21no—
665C2×C3—22no—
666C2×C3—21no—
667C2×C3—44no—
668C2×C3—44no—
669C2×C3—84no—
670C2×C3—122no—
671C2×C3—122no—
672C2×C3D3×#12011yescharacteristic
673C2×C3#559612yes—
674C2×C3#560611yescharacteristic
675C2×C3#565612yes—
676C2×C3#566811yescharacteristic
677C2×C3C2×C3×#12011yescharacteristic
678C2×C3C3×#52511yescharacteristic
679C2×C3C3×#52512yes—
680C2×C3C3×#53212yes—
681C2×C3C3×#53211yescharacteristic
682D3—42no—
683D3—42no—
684C22—24no—
685C22—24no—
686C22—24no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—62no—
692C22—62no—
693C22—62no—
694C22—64no—
695C22—62no—
696C22—121no—
697C22—122no—
698C22—122no—
699C22—122no—
700C22—121no—
701C22C2×C3×D3×D412yes—
702C22C2×C3×D3×D411yescharacteristic
703C22C2×C3×#23711yescharacteristic
704C22C3×D3×#4112yes—
705C22C3×D3×#4111yescharacteristic
706C4—22no—
707C4—22no—
708C4—34no—
709C4—41no—
710C4—42no—
711C4—64no—
712C4—64no—
713C4—121no—
714C3—21no—
715C3#7688911yescharacteristic, direct product factor
716C3C3×#238811yescharacteristic, complemented
717C2—44no—
718C2—122no—
719C2—122no—
720C2C3×D3×#12011yescharacteristic
721C2C3×#559612yes—
722C2C3×#560611yescharacteristic
723C2C3×#565612yes—
724C2C3×#566811yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#394C2
socleC23×C32C24
hypercenterC3×#394D3
hypocenterC3C3×#2388
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#394

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C2×C3×#893C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C32×#394C2semidirect
5. C3×#5223C2semidirect
6. C3×#4979C2semidirect
7. C3×#4960C2semidirect
8. C3×#4959C2semidirect
9. C3×Dic3×C22⋊C4C2semidirect
10. C3×#4673C2semidirect
11. C3×#4666C2semidirect
13. #76889C3direct (N × H)
42. C22×#237C2×C3semidirect
45. C2×#893C2×C3semidirect
46. C2×#67⋊C4C2×C3semidirect
50. C3×#394D3semidirect
51. C3×#394C2×C3semidirect
57. #5223C2×C3semidirect
58. #4979C2×C3semidirect
59. #4960C2×C3semidirect
60. #4959C2×C3semidirect
61. Dic3×C22⋊C4C2×C3semidirect
62. #4673C2×C3semidirect
63. #4666C2×C3semidirect
81. C22×C3×Dic3D4semidirect
93. C2×C3×C4×D3D4semidirect
184. C22×C3×D3#41semidirect
195. C2×C32×C4#41semidirect
208. C2×C3×Dic3#41semidirect
218. #394C3×D3semidirect
280. C22×Dic3C3×D4semidirect
292. C2×C4×D3C3×D4semidirect
420. C22×D3C3×#41semidirect
468. C2×C3×C4#237semidirect
470. C2×C3×C4C3×#41semidirect
483. C2×Dic3C3×#41semidirect
615. C32#2388semidirect
661. C2×C4C3×#237semidirect
715. C3#76889direct (N × H)
716. C3C3×#2388semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×C3×#8932
C2×C3×#67⋊C42
C32×#3942
C3×#52232
C3×#49792
C3×#49602
C3×#49592
C3×Dic3×C22⋊C42
C3×#46732
C3×#46662
C3×#23883
#768893