Finite Group Databasebeta

← C2×C3×#2704 #10670732

Subgroups — C2×C3×#2704 #10670732

Order 768.

2614 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#125C211yesmaximal, characteristic, complemented
2C22×C3×C22⋊Q8C211yesmaximal, characteristic
3C3×#2704C2116yesmaximal, direct product factor
4C2×C3×#398C211yesmaximal, characteristic, complemented
5C2×C3×#398C211yesmaximal, characteristic, complemented
6C2×C3×#398C211yesmaximal, characteristic, complemented
7C2×C3×#396C211yesmaximal, characteristic
8C2×C3×#396C211yesmaximal, characteristic
9C2×C3×#395C211yesmaximal, characteristic, complemented
10C2×C3×#391C211yesmaximal, characteristic, complemented
11C2×C3×#389C211yesmaximal, characteristic, complemented
12C2×C3×#389C211yesmaximal, characteristic, complemented
13C2×C3×#388C211yesmaximal, characteristic
14C2×C3×#388C211yesmaximal, characteristic
15C2×C3×#385C211yesmaximal, characteristic
16C2×C3×#380C211yesmaximal, characteristic
17C2×#2704C311yesmaximal, characteristic, direct product factor, Sylow
18C23×C3×Q8C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C2×C3×#125—28no—
21C2×C3×#125C2218yescomplemented
22C2×C3×C22⋊Q8—28no—
23C2×C3×C22⋊Q8C2218yes—
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C22×C3×C4⋊C4C2211yescharacteristic
32C22×C3×C4⋊C4C2211yescharacteristic
33C22×C3×C4⋊C4C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C22×C3×C4⋊C4C2211yescharacteristic
36C22×C3×C4⋊C4C2211yescharacteristic
37C22×C3×C4⋊C4C2211yescharacteristic
38C22×C3×C4⋊C4C2211yescharacteristic
39C22×C3×C22⋊C4C2211yescharacteristic
40C22×C3×C22⋊C4C2211yescharacteristic
41C22×C3×C22⋊C4C2211yescharacteristic
42C22×C3×C22⋊C4C2211yescharacteristic
43C22×C3×C22⋊C4C2211yescharacteristic
44C22×C3×C22⋊C4C2211yescharacteristic
45C22×C3×C42C2211yescharacteristic
46C22×C3×C42C2211yescharacteristic
47C3×#398C2218yescomplemented
48C3×#398C2218yescomplemented
49C3×#398C2218yescomplemented
50C3×#396C2218yes—
51C3×#396C2218yes—
52C3×#395C2218yescomplemented
53C3×#391C2218yescomplemented
54C3×#389C2218yescomplemented
55C3×#389C2218yescomplemented
56C3×#388C2218yes—
57C3×#388C2218yes—
58C3×#385C2218yes—
59C3×#380C2218yes—
60C2×C3×#95C2211yescharacteristic
61C2×C3×#95C2211yescharacteristic
62C2×C3×#95C2211yescharacteristic
63C2×C3×#95C2211yescharacteristic
64C2×C3×#95C2211yescharacteristic
65C2×C3×#95C2211yescharacteristic
66C2×C3×#95C2211yescharacteristic
67C2×C3×#95C2211yescharacteristic
68C2×C3×#95C2211yescharacteristic
69C2×C3×#95C2211yescharacteristic
70C22×#125C2×C311yescharacteristic, complemented
71C22×C22⋊Q8C2×C311yescharacteristic
72#2704C2×C3116yesdirect product factor
73C2×#398C2×C311yescharacteristic, complemented
74C2×#398C2×C311yescharacteristic, complemented
75C2×#398C2×C311yescharacteristic, complemented
76C2×#396C2×C311yescharacteristic
77C2×#396C2×C311yescharacteristic
78C2×#395C2×C311yescharacteristic, complemented
79C2×#391C2×C311yescharacteristic, complemented
80C2×#389C2×C311yescharacteristic, complemented
81C2×#389C2×C311yescharacteristic, complemented
82C2×#388C2×C311yescharacteristic
83C2×#388C2×C311yescharacteristic
84C2×#385C2×C311yescharacteristic
85C2×#380C2×C311yescharacteristic
86C25×C3C2311yescharacteristic
87C22×C3×Q8—24no—
88C22×C3×Q8—24no—
89C22×C3×Q8—42no—
90C22×C3×Q8C2314yes—
91C23×C3×C4—24no—
92C23×C3×C4—24no—
93C23×C3×C4—42no—
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2314yes—
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C3×#125—232no—
110C3×C22⋊Q8—232no—
111C2×C3×C4⋊C4—24no—
112C2×C3×C4⋊C4—24no—
113C2×C3×C4⋊C4—24no—
114C2×C3×C4⋊C4—24no—
115C2×C3×C4⋊C4—24no—
116C2×C3×C4⋊C4—24no—
117C2×C3×C4⋊C4—24no—
118C2×C3×C4⋊C4—24no—
119C2×C3×C4⋊C4—42no—
120C2×C3×C4⋊C4—42no—
121C2×C3×C4⋊C4—42no—
122C2×C3×C4⋊C4—42no—
123C2×C3×C4⋊C4—42no—
124C2×C3×C4⋊C4—42no—
125C2×C3×C4⋊C4D418yes—
126C2×C3×C4⋊C4C2314yes—
127C2×C3×C4⋊C4C2314yes—
128C2×C3×C4⋊C4C2314yes—
129C2×C3×C4⋊C4C2314yes—
130C2×C3×C4⋊C4C2314yes—
131C2×C3×C4⋊C4C2314yes—
132C2×C3×C4⋊C4C2314yes—
133C2×C3×C4⋊C4C2314yes—
134C2×C3×C4⋊C4C2314yes—
135C2×C3×C4⋊C4C2314yes—
136C2×C3×C4⋊C4C2314yes—
137C2×C3×C4⋊C4C2314yes—
138C2×C3×C4⋊C4C2314yes—
139C2×C3×C4⋊C4C2314yes—
140C2×C3×C4⋊C4C2314yes—
141C2×C3×C22⋊C4—24no—
142C2×C3×C22⋊C4—24no—
143C2×C3×C22⋊C4—42no—
144C2×C3×C22⋊C4—42no—
145C2×C3×C22⋊C4—42no—
146C2×C3×C22⋊C4Q818yescomplemented
147C2×C3×C22⋊C4C2314yes—
148C2×C3×C22⋊C4C2314yes—
149C2×C3×C22⋊C4C2314yes—
150C2×C3×C22⋊C4C2314yes—
151C2×C3×C22⋊C4C2314yes—
152C2×C3×C22⋊C4C2314yes—
153C2×C3×C42—24no—
154C2×C3×C42—42no—
155C2×C3×C42C2314yes—
156C2×C3×C42C2314yes—
157C3×#95C2314yes—
158C3×#95C2314yes—
159C3×#95C2314yes—
160C3×#95C2314yes—
161C3×#95C2314yes—
162C3×#95C2314yes—
163C3×#95C2314yes—
164C3×#95C2314yes—
165C3×#95C2314yes—
166C3×#95C2314yes—
167C23×Q8C22×C311yescharacteristic
168C24×C4C22×C311yescharacteristic
169C2×#125—28no—
170C2×#125C22×C318yescomplemented
171C2×C22⋊Q8—28no—
172C2×C22⋊Q8C22×C318yes—
173C22×C4⋊C4C22×C311yescharacteristic
174C22×C4⋊C4C22×C311yescharacteristic
175C22×C4⋊C4C22×C311yescharacteristic
176C22×C4⋊C4C22×C311yescharacteristic
177C22×C4⋊C4C22×C311yescharacteristic
178C22×C4⋊C4C22×C311yescharacteristic
179C22×C4⋊C4C22×C311yescharacteristic
180C22×C4⋊C4C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182C22×C4⋊C4C22×C311yescharacteristic
183C22×C4⋊C4C22×C311yescharacteristic
184C22×C4⋊C4C22×C311yescharacteristic
185C22×C4⋊C4C22×C311yescharacteristic
186C22×C4⋊C4C22×C311yescharacteristic
187C22×C4⋊C4C22×C311yescharacteristic
188C22×C22⋊C4C22×C311yescharacteristic
189C22×C22⋊C4C22×C311yescharacteristic
190C22×C22⋊C4C22×C311yescharacteristic
191C22×C22⋊C4C22×C311yescharacteristic
192C22×C22⋊C4C22×C311yescharacteristic
193C22×C22⋊C4C22×C311yescharacteristic
194C22×C42C22×C311yescharacteristic
195C22×C42C22×C311yescharacteristic
196#398C22×C318yescomplemented
197#398C22×C318yescomplemented
198#398C22×C318yescomplemented
199#396C22×C318yes—
200#396C22×C318yes—
201#395C22×C318yescomplemented
202#391C22×C318yescomplemented
203#389C22×C318yescomplemented
204#389C22×C318yescomplemented
205#388C22×C318yes—
206#388C22×C318yes—
207#385C22×C318yes—
208#380C22×C318yes—
209C2×#95C22×C311yescharacteristic
210C2×#95C22×C311yescharacteristic
211C2×#95C22×C311yescharacteristic
212C2×#95C22×C311yescharacteristic
213C2×#95C22×C311yescharacteristic
214C2×#95C22×C311yescharacteristic
215C2×#95C22×C311yescharacteristic
216C2×#95C22×C311yescharacteristic
217C2×#95C22×C311yescharacteristic
218C2×#95C22×C311yescharacteristic
219C24×C3—22no—
220C24×C3—22no—
221C24×C3—22no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3—22no—
225C24×C3C2×Q814yes—
226C24×C3C2412yes—
227C24×C3C2411yescharacteristic
228C2×C3×Q8—28no—
229C2×C3×Q8—28no—
230C2×C3×Q8—44no—
231C2×C3×Q8—416no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—28no—
269C22×C3×C4—28no—
270C22×C3×C4—44no—
271C22×C3×C4—416no—
272C22×C3×C4C2×D414yes—
273C22×C3×C4C2×D414yes—
274C22×C3×C4C2×D414yes—
275C22×C3×C4C2×Q814yes—
276C22×C3×C4C2×Q814yes—
277C22×C3×C4#4114yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2412yes—
282C22×C3×C4C2412yes—
283C22×C3×C4C2412yes—
284C22×C3×C4C2412yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2412yes—
289C22×C3×C4C2412yes—
290C22×C3×C4C2412yes—
291C22×C3×C4C2412yes—
292C3×C4⋊C4—28no—
293C3×C4⋊C4—28no—
294C3×C4⋊C4—28no—
295C3×C4⋊C4—28no—
296C3×C4⋊C4—28no—
297C3×C4⋊C4—28no—
298C3×C4⋊C4—28no—
299C3×C4⋊C4—28no—
300C3×C4⋊C4—44no—
301C3×C4⋊C4—44no—
302C3×C4⋊C4—44no—
303C3×C4⋊C4—44no—
304C3×C4⋊C4—44no—
305C3×C4⋊C4—44no—
306C3×C4⋊C4C2×D4116yes—
307C3×C22⋊C4—28no—
308C3×C22⋊C4—28no—
309C3×C22⋊C4—44no—
310C3×C22⋊C4—44no—
311C3×C22⋊C4—44no—
312C3×C22⋊C4C2×Q8116yescomplemented
313C3×C42—28no—
314C3×C42—44no—
315C25C23×C311yescharacteristic
316C22×Q8—24no—
317C22×Q8—24no—
318C22×Q8—42no—
319C22×Q8C23×C314yes—
320C23×C4—24no—
321C23×C4—24no—
322C23×C4—42no—
323C23×C4C23×C311yescharacteristic
324C23×C4C23×C311yescharacteristic
325C23×C4C23×C311yescharacteristic
326C23×C4C23×C311yescharacteristic
327C23×C4C23×C311yescharacteristic
328C23×C4C23×C311yescharacteristic
329C23×C4C23×C311yescharacteristic
330C23×C4C23×C311yescharacteristic
331C23×C4C23×C314yes—
332C23×C4C23×C311yescharacteristic
333C23×C4C23×C311yescharacteristic
334C23×C4C23×C311yescharacteristic
335C23×C4C23×C311yescharacteristic
336C23×C4C23×C311yescharacteristic
337C23×C4C23×C311yescharacteristic
338#125—232no—
339C22⋊Q8—232no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4C3×D418yes—
355C2×C4⋊C4C23×C314yes—
356C2×C4⋊C4C23×C314yes—
357C2×C4⋊C4C23×C314yes—
358C2×C4⋊C4C23×C314yes—
359C2×C4⋊C4C23×C314yes—
360C2×C4⋊C4C23×C314yes—
361C2×C4⋊C4C23×C314yes—
362C2×C4⋊C4C23×C314yes—
363C2×C4⋊C4C23×C314yes—
364C2×C4⋊C4C23×C314yes—
365C2×C4⋊C4C23×C314yes—
366C2×C4⋊C4C23×C314yes—
367C2×C4⋊C4C23×C314yes—
368C2×C4⋊C4C23×C314yes—
369C2×C4⋊C4C23×C314yes—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4C3×Q818yescomplemented
376C2×C22⋊C4C23×C314yes—
377C2×C22⋊C4C23×C314yes—
378C2×C22⋊C4C23×C314yes—
379C2×C22⋊C4C23×C314yes—
380C2×C22⋊C4C23×C314yes—
381C2×C22⋊C4C23×C314yes—
382C2×C42—24no—
383C2×C42—42no—
384C2×C42C23×C314yes—
385C2×C42C23×C314yes—
386#95C23×C314yes—
387#95C23×C314yes—
388#95C23×C314yes—
389#95C23×C314yes—
390#95C23×C314yes—
391#95C23×C314yes—
392#95C23×C314yes—
393#95C23×C314yes—
394#95C23×C314yes—
395#95C23×C314yes—
396C23×C3—28no—
397C23×C3—28no—
398C23×C3—28no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—44no—
406C23×C3—44no—
407C23×C3—44no—
408C23×C3—44no—
409C23×C3C22×D412yes—
410C23×C3C22×Q814yes—
411C23×C3C22×Q812yes—
412C23×C3C2×#4112yes—
413C23×C3H(5,𝔽2)12yes—
414C23×C3H(5,𝔽2)12yes—
415C23×C32−1+412yes—
416C23×C32−1+412yes—
417C23×C3C2511yescharacteristic
418C3×Q8—416no—
419C2×C3×C4—28no—
420C2×C3×C4—28no—
421C2×C3×C4—28no—
422C2×C3×C4—28no—
423C2×C3×C4—28no—
424C2×C3×C4—28no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
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—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—416no—
462C2×C3×C4—44no—
463C2×C3×C4—44no—
464C2×C3×C4—44no—
465C2×C3×C4—44no—
466C2×C3×C4—44no—
467C2×C3×C4—44no—
468C2×C3×C4—44no—
469C2×C3×C4—44no—
470C2×C3×C4C22×D414yes—
471C2×C3×C4C22×D414yes—
472C2×C3×C4C22×D414yes—
473C2×C3×C4C22×Q814yes—
474C2×C3×C4C22×Q814yes—
475C2×C3×C4C2×#4114yes—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24C2×C3×Q814yes—
483C24C24×C312yes—
484C24C24×C311yescharacteristic
485C2×Q8—28no—
486C2×Q8—28no—
487C2×Q8—44no—
488C2×Q8—416no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—44no—
528C22×C4—416no—
529C22×C4C2×C3×D414yes—
530C22×C4C2×C3×D414yes—
531C22×C4C2×C3×D414yes—
532C22×C4C2×C3×Q814yes—
533C22×C4C2×C3×Q814yes—
534C22×C4C3×#4114yes—
535C22×C4C24×C312yes—
536C22×C4C24×C312yes—
537C22×C4C24×C312yes—
538C22×C4C24×C312yes—
539C22×C4C24×C312yes—
540C22×C4C24×C312yes—
541C22×C4C24×C312yes—
542C22×C4C24×C312yes—
543C22×C4C24×C312yes—
544C22×C4C24×C312yes—
545C22×C4C24×C312yes—
546C22×C4C24×C312yes—
547C22×C4C24×C312yes—
548C22×C4C24×C312yes—
549C4⋊C4—28no—
550C4⋊C4—28no—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—28no—
554C4⋊C4—28no—
555C4⋊C4—28no—
556C4⋊C4—28no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—44no—
562C4⋊C4—44no—
563C4⋊C4C2×C3×D4116yes—
564C22⋊C4—28no—
565C22⋊C4—28no—
566C22⋊C4—44no—
567C22⋊C4—44no—
568C22⋊C4—44no—
569C22⋊C4C2×C3×Q8116yescomplemented
570C42—28no—
571C42—44no—
572C22×C3—24no—
573C22×C3—24no—
574C22×C3—24no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—416no—
579C22×C3—42no—
580C22×C3#53714yes—
581C22×C3#54114yes—
582C22×C3#54414yes—
583C22×C3#54614yes—
584C22×C3D4×Q814yes—
585C22×C3#55414yes—
586C22×C3#56214yes—
587C22×C3C23×D411yescharacteristic
588C22×C3C23×Q811yescharacteristic
589C22×C3C22×#4111yescharacteristic
590C22×C3C2×H(5,𝔽2)11yescharacteristic
591C22×C3C2×H(5,𝔽2)11yescharacteristic
592C22×C3C2×2−1+411yescharacteristic
593C22×C3C2×2−1+411yescharacteristic
594C3×C4—24no—
595C3×C4—24no—
596C3×C4—24no—
597C3×C4—24no—
598C3×C4—24no—
599C3×C4—24no—
600C3×C4—42no—
601C3×C4—42no—
602C3×C4—42no—
603C3×C4—42no—
604C3×C4—42no—
605C3×C4—42no—
606C3×C4—42no—
607C3×C4—42no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—28no—
615C23—28no—
616C23—28no—
617C23—44no—
618C23—44no—
619C23—44no—
620C23—44no—
621C23C22×C3×D412yes—
622C23C22×C3×Q814yes—
623C23C22×C3×Q812yes—
624C23C2×C3×#4112yes—
625C23C3×H(5,𝔽2)12yes—
626C23C3×H(5,𝔽2)12yes—
627C23C3×2−1+412yes—
628C23C3×2−1+412yes—
629C23C25×C311yescharacteristic
630Q8—416no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—416no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4C22×C3×D414yes—
683C2×C4C22×C3×D414yes—
684C2×C4C22×C3×D414yes—
685C2×C4C22×C3×Q814yes—
686C2×C4C22×C3×Q814yes—
687C2×C4C2×C3×#4114yes—
688C2×C3—44no—
689C2×C3#270418yesdirect product factor
690C2×C3C2×#53711yescharacteristic
691C2×C3C2×#54111yescharacteristic
692C2×C3C2×#54411yescharacteristic
693C2×C3C2×#54611yescharacteristic
694C2×C3C2×D4×Q811yescharacteristic
695C2×C3C2×#55411yescharacteristic
696C2×C3C2×#56211yescharacteristic
697C22—24no—
698C22—24no—
699C22—24no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—416no—
704C22—42no—
705C22C3×#53714yes—
706C22C3×#54114yes—
707C22C3×#54414yes—
708C22C3×#54614yes—
709C22C3×D4×Q814yes—
710C22C3×#55414yes—
711C22C3×#56214yes—
712C22C23×C3×D411yescharacteristic
713C22C23×C3×Q811yescharacteristic
714C22C22×C3×#4111yescharacteristic
715C22C2×C3×H(5,𝔽2)11yescharacteristic
716C22C2×C3×H(5,𝔽2)11yescharacteristic
717C22C2×C3×2−1+411yescharacteristic
718C22C2×C3×2−1+411yescharacteristic
719C4—24no—
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—42no—
733C3C2×#270411yescharacteristic, direct product factor, Sylow
734C2—44no—
735C2C3×#270418yesdirect product factor
736C2C2×C3×#53711yescharacteristic
737C2C2×C3×#54111yescharacteristic
738C2C2×C3×#54411yescharacteristic
739C2C2×C3×#54611yescharacteristic
740C2C2×C3×D4×Q811yescharacteristic
741C2C2×C3×#55411yescharacteristic
742C2C2×C3×#56211yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC23C25×C3
prime radicalC25×C3C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#125C2semidirect
3. C3×#2704C2direct (N × H)
4. C2×C3×#398C2semidirect
5. C2×C3×#398C2semidirect
6. C2×C3×#398C2semidirect
9. C2×C3×#395C2semidirect
10. C2×C3×#391C2semidirect
11. C2×C3×#389C2semidirect
12. C2×C3×#389C2semidirect
17. C2×#2704C3direct (N × H)
21. C2×C3×#125C22semidirect
47. C3×#398C22semidirect
48. C3×#398C22semidirect
49. C3×#398C22semidirect
52. C3×#395C22semidirect
53. C3×#391C22semidirect
54. C3×#389C22semidirect
55. C3×#389C22semidirect
70. C22×#125C2×C3semidirect
72. #2704C2×C3direct (N × H)
73. C2×#398C2×C3semidirect
74. C2×#398C2×C3semidirect
75. C2×#398C2×C3semidirect
78. C2×#395C2×C3semidirect
79. C2×#391C2×C3semidirect
80. C2×#389C2×C3semidirect
81. C2×#389C2×C3semidirect
146. C2×C3×C22⋊C4Q8semidirect
170. C2×#125C22×C3semidirect
196. #398C22×C3semidirect
197. #398C22×C3semidirect
198. #398C22×C3semidirect
201. #395C22×C3semidirect
202. #391C22×C3semidirect
203. #389C22×C3semidirect
204. #389C22×C3semidirect
312. C3×C22⋊C4C2×Q8semidirect
375. C2×C22⋊C4C3×Q8semidirect
569. C22⋊C4C2×C3×Q8semidirect
689. C2×C3#2704direct (N × H)
733. C3C2×#2704direct (N × H)
735. C2C3×#2704direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1252
C22×C3×C22⋊Q82
C3×#27042
C2×C3×#3982
C2×C3×#3962
C2×C3×#3952
C2×C3×#3912
C2×C3×#3892
C2×C3×#3882
C2×C3×#3852
C2×C3×#3802
C2×#27043