Finite Group Databasebeta

← C3×#82400 #11808211

Subgroups — C3×#82400 #11808211

Order 1152.

2101 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C2×C32×C4×D4C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C212yesmaximal, complemented
4C3×#5223C212yesmaximal, complemented
5C3×C4×#217C211yesmaximal, characteristic, complemented
6C3×#4991C211yesmaximal, characteristic, complemented
7C3×#4979C211yesmaximal, characteristic, complemented
8C3×#4960C211yesmaximal, characteristic, complemented
9C3×#4959C212yesmaximal, complemented
10C3×#4947C211yesmaximal, characteristic, complemented
11C3×C4×(C2×D3)⋊C4C212yesmaximal, complemented
12C3×#2388—31nomaximal
13#82400C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yes—
19C2×C3×#235—24no—
20C2×C3×#235—28no—
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2212yes—
23C22×C3×Dic6C2211yescharacteristic
24C32×C4×D4—24no—
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C42C2211yescharacteristic
29C2×C3×#217C2212yes—
30C2×C3×#217C2212yes—
31C3×C4×#67—28no—
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×(C2×D3)⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×C4×Dic3C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C22×C3×#41—31no—
42C22×#235C2×C311yescharacteristic, complemented
43C2×C3×C4×D4—21no—
44C2×C3×C4×D4—32no—
45C2×C3×C4×D4D311yescharacteristic, complemented
46C2×C3×C4×D4C2×C311yescharacteristic, complemented
47C2×C4×#67C2×C312yescomplemented
48C3×#395—31no—
49C3×#394—31no—
50C3×#394—32no—
51C3×#393—31no—
52C3×#392—32no—
53C3×#392—31no—
54C3×C4×C22⋊C4—31no—
55C3×C4×C22⋊C4—32no—
56#5223C2×C312yescomplemented
57C4×#217C2×C311yescharacteristic, complemented
58#4991C2×C311yescharacteristic, complemented
59#4979C2×C311yescharacteristic, complemented
60#4960C2×C311yescharacteristic, complemented
61#4959C2×C312yescomplemented
62#4947C2×C311yescharacteristic, complemented
63C4×(C2×D3)⋊C4C2×C312yescomplemented
64C24×C32C2311yescharacteristic
65C24×C32C2311yescharacteristic
66C23×C3×D3C2312yes—
67C2×C32×D4—22no—
68C2×C32×D4—22no—
69C2×C32×D4—22no—
70C22×C32×C4—24no—
71C22×C32×C4—22no—
72C22×C32×C4—24no—
73C22×C32×C4D414yescomplemented
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C2×C3×#67—24no—
80C2×C3×#67—24no—
81C2×C3×#67—24no—
82C2×C3×#67—24no—
83C2×C3×#67—24no—
84C2×C3×#67—24no—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2312yes—
88C3×#235—232no—
89C2×C3×D12—24no—
90C2×C3×D12—22no—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3D418yescomplemented
94C2×C3×Dic6—22no—
95C2×C3×Dic6—24no—
96C32×C4⋊C4—22no—
97C32×C22⋊C4—22no—
98C32×C22⋊C4—22no—
99C32×C42—22no—
100C3×#217—24no—
101C3×#217—24no—
102C3×(C2×D3)⋊C4—24no—
103C3×(C2×D3)⋊C4—24no—
104C3×(C2×D3)⋊C4—24no—
105C3×Dic3⋊C4—24no—
106C3×C4×Dic3—24no—
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—21no—
118C23×C3×C4—21no—
119C23×C3×C4—32no—
120C23×C3×C4C2×D311yescharacteristic
121C23×C3×C4C2×D311yescharacteristic
122C23×C3×C4C22×C311yescharacteristic
123C23×C3×C4C22×C311yescharacteristic
124C22×#67C22×C312yes—
125C22×#67C22×C312yes—
126C2×#235—24no—
127C2×#235—28no—
128C22×D12C22×C311yescharacteristic
129C22×C4×D3C22×C312yes—
130C22×Dic6C22×C311yescharacteristic
131C3×C4×D4—28no—
132C3×C4×D4—24no—
133C3×C4×D4—24no—
134C3×C4×D4—68no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—32no—
137C2×C3×C4⋊C4C2×D311yescharacteristic
138C2×C3×C4⋊C4C22×C311yescharacteristic
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—32no—
142C2×C3×C22⋊C4—32no—
143C2×C3×C22⋊C4—32no—
144C2×C3×C22⋊C4—32no—
145C2×C3×C22⋊C4—32no—
146C2×C3×C22⋊C4C2×D311yescharacteristic
147C2×C3×C22⋊C4C2×D311yescharacteristic
148C2×C3×C22⋊C4C22×C311yescharacteristic
149C2×C3×C22⋊C4C22×C311yescharacteristic
150C2×C3×C42—21no—
151C2×C3×C42—32no—
152C2×C3×C42C2×D311yescharacteristic
153C2×C3×C42C22×C311yescharacteristic
154C2×#217C22×C312yes—
155C2×#217C22×C312yes—
156C4×#67—28no—
157C2×(C2×D3)⋊C4C22×C312yes—
158C2×(C2×D3)⋊C4C22×C312yes—
159C2×(C2×D3)⋊C4C22×C312yes—
160C2×Dic3⋊C4C22×C312yes—
161C2×C4×Dic3C22×C312yes—
162C3×#95—31no—
163C3×#95—32no—
164C3×#95—32no—
165C3×#95—31no—
166C3⋊#95C22×C312yes—
167C3⋊#95C22×C312yes—
168C3⋊#95C22×C311yescharacteristic
169C3⋊#95C22×C311yescharacteristic
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—21no—
174C23×C32—22no—
175C23×C32—22no—
176C23×C32—22no—
177C23×C32—22no—
178C23×C32C2×D412yes—
179C23×C32#4112yescomplemented
180C23×C32C2411yescharacteristic
181C22×C3×D3—22no—
182C22×C3×D3—22no—
183C22×C3×D3—22no—
184C22×C3×D3—22no—
185C22×C3×D3—22no—
186C22×C3×D3—22no—
187C22×C3×D3C2×D414yes—
188C32×D4—28no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4—21no—
193C2×C32×C4—22no—
194C2×C32×C4—28no—
195C2×C32×C4—22no—
196C2×C32×C4—22no—
197C2×C32×C4—44no—
198C2×C32×C4C2×D414yes—
199C2×C32×C4C2×D412yes—
200C2×C32×C4C2×D412yes—
201C2×C32×C4#4112yescomplemented
202C3×#67—216no—
203C3×#67—216no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3C2×D414yes—
212C2×C3×Dic3#4114yescomplemented
213C3×D12—28no—
214C3×C4×D3—216no—
215C3×Dic6—28no—
216C22×#41—31no—
217C2×C4×D4—32no—
218C2×C4×D4C3×D311yescharacteristic, complemented
219#395—31no—
220#394—31no—
221#394—32no—
222#393—31no—
223#392—32no—
224#392—31no—
225C4×C22⋊C4—31no—
226C4×C22⋊C4—32no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—32no—
230C24×C3C22×D311yescharacteristic
231C24×C3C22×D311yescharacteristic
232C24×C3C23×C311yescharacteristic
233C24×C3C23×C311yescharacteristic
234C23×D3C23×C312yes—
235C3×#41—632no—
236C2×C3×Q8—64no—
237C2×C3×Q8—62no—
238C2×C3×D4—24no—
239C2×C3×D4—24no—
240C2×C3×D4—24no—
241C2×C3×D4—22no—
242C2×C3×D4—22no—
243C2×C3×D4—22no—
244C2×C3×D4—22no—
245C2×C3×D4—22no—
246C2×C3×D4—22no—
247C2×C3×D4—64no—
248C2×C3×D4—64no—
249C2×C3×D4—64no—
250C2×C3×D4—64no—
251C2×C3×D4—64no—
252C2×C3×D4—64no—
253C2×C3×D4—64no—
254C2×C3×D4—62no—
255C22×C3×C4—24no—
256C22×C3×C4—24no—
257C22×C3×C4—24no—
258C22×C3×C4—24no—
259C22×C3×C4—22no—
260C22×C3×C4—24no—
261C22×C3×C4—22no—
262C22×C3×C4—24no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—32no—
269C22×C3×C4—32no—
270C22×C3×C4—38no—
271C22×C3×C4—32no—
272C22×C3×C4—44no—
273C22×C3×C4—44no—
274C22×C3×C4—64no—
275C22×C3×C4—64no—
276C22×C3×C4#6714yescomplemented
277C22×C3×C4C3×D414yescomplemented
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C23×C311yescharacteristic
284C22×C3×C4C23×C311yescharacteristic
285C22×C3×C4C23×C311yescharacteristic
286C22×C3×C4C23×C311yescharacteristic
287C22×C3×C4C23×C311yescharacteristic
288C2×#67—24no—
289C2×#67—24no—
290C2×#67—24no—
291C2×#67—24no—
292C2×#67—24no—
293C2×#67—24no—
294C22×Dic3C23×C312yes—
295C22×Dic3C23×C312yes—
296C22×Dic3C23×C312yes—
297#235—232no—
298C2×D12—24no—
299C2×D12—22no—
300C2×C4×D3—24no—
301C2×C4×D3—24no—
302C2×C4×D3C3×D418yescomplemented
303C2×Dic6—22no—
304C2×Dic6—24no—
305C3×C4⋊C4—24no—
306C3×C4⋊C4—22no—
307C3×C4⋊C4—22no—
308C3×C4⋊C4—64no—
309C3×C22⋊C4—24no—
310C3×C22⋊C4—24no—
311C3×C22⋊C4—22no—
312C3×C22⋊C4—22no—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—22no—
315C3×C22⋊C4—64no—
316C3×C22⋊C4—64no—
317C3×C22⋊C4—64no—
318C3×C22⋊C4—64no—
319C3×C22⋊C4—64no—
320C3×C42—24no—
321C3×C42—22no—
322C3×C42—22no—
323C3×C42—64no—
324#217—24no—
325#217—24no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—24no—
329Dic3⋊C4—24no—
330C4×Dic3—24no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—24no—
335C22×C32—22no—
336C22×C32—41no—
337C22×C32—42no—
338C22×C32—42no—
339C22×C32—42no—
340C22×C32—41no—
341C22×C32C22×D412yes—
342C22×C32C22×D411yescharacteristic
343C22×C32C2×#4111yescharacteristic
344C22×C32C2×#4111yescharacteristic
345C22×C32C2×#4112yes—
346C2×C3×D3—24no—
347C2×C3×D3—24no—
348C2×C3×D3—24no—
349C2×C3×D3—42no—
350C2×C3×D3—42no—
351C2×C3×D3—42no—
352C2×C3×D3—42no—
353C32×C4—22no—
354C32×C4—22no—
355C32×C4—41no—
356C32×C4—41no—
357C32×C4#12014yes—
358C3×Dic3—24no—
359C3×Dic3—24no—
360C3×Dic3—42no—
361C2×#41—68no—
362C2×#41—64no—
363C22×Q8—31no—
364C22×D4—32no—
365C22×D4—32no—
366C22×D4—31no—
367C22×D4C2×C3×D311yescharacteristic
368C23×C4—32no—
369C23×C4C2×C3×D311yescharacteristic
370C23×C4C2×C3×D311yescharacteristic
371C4×D4—24no—
372C4×D4—68no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4C2×C3×D311yescharacteristic
375C2×C22⋊C4—32no—
376C2×C22⋊C4—32no—
377C2×C22⋊C4—32no—
378C2×C22⋊C4—32no—
379C2×C22⋊C4—32no—
380C2×C22⋊C4C2×C3×D311yescharacteristic
381C2×C22⋊C4C2×C3×D311yescharacteristic
382C2×C42—32no—
383C2×C42C2×C3×D311yescharacteristic
384#95—31no—
385#95—32no—
386#95—32no—
387#95—31no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—21no—
400C23×C3—22no—
401C23×C3—21no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—34no—
412C23×C3—42no—
413C23×C3—42no—
414C23×C3—42no—
415C23×C3—42no—
416C23×C3—62no—
417C23×C3—62no—
418C23×C3—62no—
419C23×C3—62no—
420C23×C3—62no—
421C23×C3—62no—
422C23×C3#23512yescomplemented
423C23×C3C2×#6712yes—
424C23×C3C2×C3×D412yes—
425C23×C3C3×#4112yescomplemented
426C23×C3C23×D311yescharacteristic
427C23×C3C24×C311yescharacteristic
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3—22no—
433C22×D3—22no—
434C22×D3C2×C3×D414yes—
435C3×Q8—68no—
436C3×D4—216no—
437C3×D4—28no—
438C3×D4—28no—
439C3×D4—68no—
440C3×D4—616no—
441C3×D4—616no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—22no—
449C2×C3×C4—21no—
450C2×C3×C4—28no—
451C2×C3×C4—28no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—22no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—24no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—34no—
467C2×C3×C4—34no—
468C2×C3×C4—48no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—48no—
473C2×C3×C4—44no—
474C2×C3×C4—44no—
475C2×C3×C4—62no—
476C2×C3×C4—62no—
477C2×C3×C4—62no—
478C2×C3×C4—62no—
479C2×C3×C4—616no—
480C2×C3×C4—62no—
481C2×C3×C4—62no—
482C2×C3×C4—62no—
483C2×C3×C4#23512yescomplemented
484C2×C3×C4D3×D414yes—
485C2×C3×C4C2×#6712yes—
486C2×C3×C4C2×#6712yes—
487C2×C3×C4C2×C3×D414yes—
488C2×C3×C4C2×C3×D412yes—
489C2×C3×C4C2×C3×D412yes—
490C2×C3×C4C3×#4112yescomplemented
491#67—216no—
492#67—216no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3C2×C3×D414yes—
501C2×Dic3C3×#4114yescomplemented
502D12—28no—
503C4×D3—216no—
504Dic6—28no—
505C2×C32—42no—
506C2×C32—42no—
507C2×C32C2×#12011yescharacteristic
508C2×C32#52511yescharacteristic
509C2×C32#52512yes—
510C2×C32#53212yes—
511C2×C32#53211yescharacteristic
512C3×D3—44no—
513C24—32no—
514C24C22×C3×D311yescharacteristic
515C24C22×C3×D311yescharacteristic
516#41—632no—
517C2×Q8—64no—
518C2×Q8—62no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—64no—
523C2×D4—64no—
524C2×D4—64no—
525C2×D4—64no—
526C2×D4—64no—
527C2×D4—64no—
528C2×D4—64no—
529C2×D4—62no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—32no—
534C22×C4—32no—
535C22×C4—38no—
536C22×C4—32no—
537C22×C4—64no—
538C22×C4—64no—
539C22×C4C3×#6714yescomplemented
540C22×C4C22×C3×D311yescharacteristic
541C22×C4C22×C3×D311yescharacteristic
542C22×C4C22×C3×D311yescharacteristic
543C22×C4C22×C3×D311yescharacteristic
544C22×C4C22×C3×D311yescharacteristic
545C4⋊C4—22no—
546C4⋊C4—64no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—64no—
550C22⋊C4—64no—
551C22⋊C4—64no—
552C22⋊C4—64no—
553C22⋊C4—64no—
554C42—22no—
555C42—64no—
556C22×C3—24no—
557C22×C3—24no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—24no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—24no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—21no—
573C22×C3—42no—
574C22×C3—44no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—42no—
581C22×C3—41no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—42no—
588C22×C3—42no—
589C22×C3—42no—
590C22×C3—41no—
591C22×C3—64no—
592C22×C3—64no—
593C22×C3—64no—
594C22×C3—122no—
595C22×C3—122no—
596C22×C3—122no—
597C22×C3—122no—
598C22×C3C2×#23511yescharacteristic
599C22×C3C2×#23511yescharacteristic
600C22×C3C2×D3×D412yes—
601C22×C3D3×#4112yes—
602C22×C3C22×#6711yescharacteristic
603C22×C3C22×C3×D412yes—
604C22×C3C22×C3×D411yescharacteristic
605C22×C3C2×C3×#4111yescharacteristic
606C22×C3C2×C3×#4111yescharacteristic
607C22×C3C2×C3×#4112yes—
608C2×D3—24no—
609C2×D3—24no—
610C2×D3—24no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—42no—
615C3×C4—24no—
616C3×C4—22no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—24no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—64no—
629C3×C4—64no—
630C3×C4—122no—
631C3×C4#93714yes—
632C3×C4C3×#12014yes—
633Dic3—24no—
634Dic3—24no—
635Dic3—42no—
636C32#238811yescharacteristic, complemented, Sylow
637C23—21no—
638C23—21no—
639C23—21no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—21no—
645C23—34no—
646C23—62no—
647C23—62no—
648C23—62no—
649C23—62no—
650C23—62no—
651C23—62no—
652C23C3×#23512yescomplemented
653C23C2×C3×#6712yes—
654C23C23×C3×D311yescharacteristic
655Q8—68no—
656D4—28no—
657D4—68no—
658D4—616no—
659D4—616no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—28no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—34no—
669C2×C4—34no—
670C2×C4—44no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—616no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4C3×#23512yescomplemented
680C2×C4C3×D3×D414yes—
681C2×C4C2×C3×#6712yes—
682C2×C4C2×C3×#6712yes—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—22no—
686C2×C3—22no—
687C2×C3—21no—
688C2×C3—44no—
689C2×C3—44no—
690C2×C3—42no—
691C2×C3—42no—
692C2×C3—42no—
693C2×C3—42no—
694C2×C3—124no—
695C2×C3#554712yes—
696C2×C3#554812yes—
697C2×C3#579111yescharacteristic
698C2×C3C2×#93711yescharacteristic
699C2×C3#583211yescharacteristic
700C2×C3C2×C3×#12011yescharacteristic
701C2×C3C3×#52511yescharacteristic
702C2×C3C3×#52512yes—
703C2×C3C3×#53212yes—
704C2×C3C3×#53211yescharacteristic
705D3—44no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—24no—
710C22—22no—
711C22—41no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—41no—
716C22—64no—
717C22—64no—
718C22—64no—
719C22—122no—
720C22—122no—
721C22—122no—
722C22—122no—
723C22C2×C3×#23511yescharacteristic
724C22C2×C3×#23511yescharacteristic
725C22C2×C3×D3×D412yes—
726C22C3×D3×#4112yes—
727C22C22×C3×#6711yescharacteristic
728C4—22no—
729C4—22no—
730C4—41no—
731C4—41no—
732C4—64no—
733C4—64no—
734C4—122no—
735C4C3×#93714yes—
736C3—21no—
737C3#8240011yescharacteristic, direct product factor
738C3C3×#238811yescharacteristic, complemented
739C2—42no—
740C2—42no—
741C2—124no—
742C2C3×#554712yes—
743C2C3×#554812yes—
744C2C3×#579111yescharacteristic
745C2C2×C3×#93711yescharacteristic
746C2C3×#583211yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#2388
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C2×C32×C4×D4C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C3×#5223C2semidirect
5. C3×C4×#217C2semidirect
6. C3×#4991C2semidirect
7. C3×#4979C2semidirect
8. C3×#4960C2semidirect
9. C3×#4959C2semidirect
10. C3×#4947C2semidirect
11. C3×C4×(C2×D3)⋊C4C2semidirect
13. #82400C3direct (N × H)
42. C22×#235C2×C3semidirect
45. C2×C3×C4×D4D3semidirect
46. C2×C3×C4×D4C2×C3semidirect
47. C2×C4×#67C2×C3semidirect
56. #5223C2×C3semidirect
57. C4×#217C2×C3semidirect
58. #4991C2×C3semidirect
59. #4979C2×C3semidirect
60. #4960C2×C3semidirect
61. #4959C2×C3semidirect
62. #4947C2×C3semidirect
63. C4×(C2×D3)⋊C4C2×C3semidirect
73. C22×C32×C4D4semidirect
93. C2×C3×C4×D3D4semidirect
179. C23×C32#41semidirect
201. C2×C32×C4#41semidirect
212. C2×C3×Dic3#41semidirect
218. C2×C4×D4C3×D3semidirect
276. C22×C3×C4#67semidirect
277. C22×C3×C4C3×D4semidirect
302. C2×C4×D3C3×D4semidirect
422. C23×C3#235semidirect
425. C23×C3C3×#41semidirect
483. C2×C3×C4#235semidirect
490. C2×C3×C4C3×#41semidirect
501. C2×Dic3C3×#41semidirect
539. C22×C4C3×#67semidirect
636. C32#2388semidirect
652. C23C3×#235semidirect
679. C2×C4C3×#235semidirect
737. C3#82400direct (N × H)
738. 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×C32×C4×D42
C2×C3×C4×#672
C3×#52232
C3×C4×#2172
C3×#49912
C3×#49792
C3×#49602
C3×#49592
C3×#49472
C3×C4×(C2×D3)⋊C42
C3×#23883
#824003