Finite Group Databasebeta

← C2×C3×#2698 #10670726

Subgroups — C2×C3×#2698 #10670726

Order 768.

2526 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#126C211yesmaximal, characteristic
2C22×C3×C22⋊Q8C211yesmaximal, characteristic
3C3×#2698C2116yesmaximal, direct product factor
4C2×C3×#400C211yesmaximal, characteristic, complemented
5C2×C3×#398C211yesmaximal, characteristic, complemented
6C2×C3×#398C211yesmaximal, characteristic, complemented
7C2×C3×#397C211yesmaximal, characteristic
8C2×C3×#397C211yesmaximal, characteristic
9C2×C3×#395C211yesmaximal, characteristic, complemented
10C2×C3×#391C211yesmaximal, characteristic, complemented
11C2×C3×#389C211yesmaximal, characteristic, complemented
12C2×C3×#388C211yesmaximal, characteristic
13C2×C3×#387C211yesmaximal, characteristic, complemented
14C2×C3×#385C211yesmaximal, characteristic
15C2×C3×#382C211yesmaximal, characteristic, complemented
16C2×C3×#381C211yesmaximal, characteristic
17C2×#2698C311yesmaximal, characteristic, direct product factor, Sylow
18C23×C3×Q8C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C2×C3×#126—28no—
21C2×C3×#126C2218yes—
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×C22⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4C2211yescharacteristic
37C22×C3×C22⋊C4C2211yescharacteristic
38C22×C3×C22⋊C4C2211yescharacteristic
39C22×C3×C22⋊C4C2211yescharacteristic
40C22×C3×C22⋊C4C2211yescharacteristic
41C22×C3×C42C2211yescharacteristic
42C22×C3×C42C2211yescharacteristic
43C3×#400C2218yescomplemented
44C3×#398C2218yescomplemented
45C3×#398C2218yescomplemented
46C3×#397C2218yes—
47C3×#397C2218yes—
48C3×#395C2218yescomplemented
49C3×#391C2218yescomplemented
50C3×#389C2218yescomplemented
51C3×#388C2218yes—
52C3×#387C2218yescomplemented
53C3×#385C2218yes—
54C3×#382C2218yescomplemented
55C3×#381C2218yes—
56C2×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58C2×C3×#95C2211yescharacteristic
59C2×C3×#95C2211yescharacteristic
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×#126C2×C311yescharacteristic
71C22×C22⋊Q8C2×C311yescharacteristic
72#2698C2×C3116yesdirect product factor
73C2×#400C2×C311yescharacteristic, complemented
74C2×#398C2×C311yescharacteristic, complemented
75C2×#398C2×C311yescharacteristic, complemented
76C2×#397C2×C311yescharacteristic
77C2×#397C2×C311yescharacteristic
78C2×#395C2×C311yescharacteristic, complemented
79C2×#391C2×C311yescharacteristic, complemented
80C2×#389C2×C311yescharacteristic, complemented
81C2×#388C2×C311yescharacteristic
82C2×#387C2×C311yescharacteristic, complemented
83C2×#385C2×C311yescharacteristic
84C2×#382C2×C311yescharacteristic, complemented
85C2×#381C2×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×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2314yes—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C3×#126—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⋊C4C2314yes—
123C2×C3×C4⋊C4C2314yes—
124C2×C3×C4⋊C4C2314yes—
125C2×C3×C4⋊C4C2314yes—
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×C22⋊C4—24no—
134C2×C3×C22⋊C4—24no—
135C2×C3×C22⋊C4—24no—
136C2×C3×C22⋊C4—24no—
137C2×C3×C22⋊C4—42no—
138C2×C3×C22⋊C4D418yes—
139C2×C3×C22⋊C4C2314yes—
140C2×C3×C22⋊C4C2314yes—
141C2×C3×C22⋊C4C2314yes—
142C2×C3×C22⋊C4C2314yes—
143C2×C3×C22⋊C4C2314yes—
144C2×C3×C22⋊C4C2314yes—
145C2×C3×C42—24no—
146C2×C3×C42—24no—
147C2×C3×C42C2314yes—
148C2×C3×C42C2314yes—
149C3×#95C2314yes—
150C3×#95C2314yes—
151C3×#95C2314yes—
152C3×#95C2314yes—
153C3×#95C2314yes—
154C3×#95C2314yes—
155C3×#95C2314yes—
156C3×#95C2314yes—
157C3×#95C2314yes—
158C3×#95C2314yes—
159C3×#95C2314yes—
160C3×#95C2314yes—
161C3×#95C2314yes—
162C3×#95C2314yes—
163C23×Q8C22×C311yescharacteristic
164C24×C4C22×C311yescharacteristic
165C2×#126—28no—
166C2×#126C22×C318yes—
167C2×C22⋊Q8—28no—
168C2×C22⋊Q8C22×C318yes—
169C22×C4⋊C4C22×C311yescharacteristic
170C22×C4⋊C4C22×C311yescharacteristic
171C22×C4⋊C4C22×C311yescharacteristic
172C22×C4⋊C4C22×C311yescharacteristic
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×C22⋊C4C22×C311yescharacteristic
181C22×C22⋊C4C22×C311yescharacteristic
182C22×C22⋊C4C22×C311yescharacteristic
183C22×C22⋊C4C22×C311yescharacteristic
184C22×C22⋊C4C22×C311yescharacteristic
185C22×C22⋊C4C22×C311yescharacteristic
186C22×C42C22×C311yescharacteristic
187C22×C42C22×C311yescharacteristic
188#400C22×C318yescomplemented
189#398C22×C318yescomplemented
190#398C22×C318yescomplemented
191#397C22×C318yes—
192#397C22×C318yes—
193#395C22×C318yescomplemented
194#391C22×C318yescomplemented
195#389C22×C318yescomplemented
196#388C22×C318yes—
197#387C22×C318yescomplemented
198#385C22×C318yes—
199#382C22×C318yescomplemented
200#381C22×C318yes—
201C2×#95C22×C311yescharacteristic
202C2×#95C22×C311yescharacteristic
203C2×#95C22×C311yescharacteristic
204C2×#95C22×C311yescharacteristic
205C2×#95C22×C311yescharacteristic
206C2×#95C22×C311yescharacteristic
207C2×#95C22×C311yescharacteristic
208C2×#95C22×C311yescharacteristic
209C2×#95C22×C311yescharacteristic
210C2×#95C22×C311yescharacteristic
211C2×#95C22×C311yescharacteristic
212C2×#95C22×C311yescharacteristic
213C2×#95C22×C311yescharacteristic
214C2×#95C22×C311yescharacteristic
215C24×C3—22no—
216C24×C3—22no—
217C24×C3—22no—
218C24×C3—22no—
219C24×C3—22no—
220C24×C3—22no—
221C24×C3C2×D414yes—
222C24×C3C2412yes—
223C24×C3C2411yescharacteristic
224C2×C3×Q8—28no—
225C2×C3×Q8—28no—
226C2×C3×Q8—44no—
227C2×C3×Q8—416no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
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—28no—
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—28no—
268C22×C3×C4—44no—
269C22×C3×C4—416no—
270C22×C3×C4C2×D414yes—
271C22×C3×C4C2×D414yes—
272C22×C3×C4#4114yes—
273C22×C3×C4#4114yes—
274C22×C3×C4C2412yes—
275C22×C3×C4C2412yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2412yes—
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—
288C3×C4⋊C4—28no—
289C3×C4⋊C4—28no—
290C3×C4⋊C4—28no—
291C3×C4⋊C4—28no—
292C3×C4⋊C4—28no—
293C3×C4⋊C4—28no—
294C3×C4⋊C4—28no—
295C3×C4⋊C4—28no—
296C3×C4⋊C4—44no—
297C3×C4⋊C4—44no—
298C3×C4⋊C4—44no—
299C3×C22⋊C4—28no—
300C3×C22⋊C4—28no—
301C3×C22⋊C4—28no—
302C3×C22⋊C4—28no—
303C3×C22⋊C4—44no—
304C3×C22⋊C4C2×D4116yes—
305C3×C42—28no—
306C3×C42—28no—
307C25C23×C311yescharacteristic
308C22×Q8—24no—
309C22×Q8—24no—
310C22×Q8—42no—
311C22×Q8C23×C314yes—
312C23×C4—24no—
313C23×C4—24no—
314C23×C4—42no—
315C23×C4C23×C311yescharacteristic
316C23×C4C23×C311yescharacteristic
317C23×C4C23×C311yescharacteristic
318C23×C4C23×C311yescharacteristic
319C23×C4C23×C311yescharacteristic
320C23×C4C23×C311yescharacteristic
321C23×C4C23×C311yescharacteristic
322C23×C4C23×C311yescharacteristic
323C23×C4C23×C311yescharacteristic
324C23×C4C23×C311yescharacteristic
325C23×C4C23×C314yes—
326C23×C4C23×C311yescharacteristic
327C23×C4C23×C311yescharacteristic
328C23×C4C23×C311yescharacteristic
329C23×C4C23×C311yescharacteristic
330#126—232no—
331C22⋊Q8—232no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4C23×C314yes—
344C2×C4⋊C4C23×C314yes—
345C2×C4⋊C4C23×C314yes—
346C2×C4⋊C4C23×C314yes—
347C2×C4⋊C4C23×C314yes—
348C2×C4⋊C4C23×C314yes—
349C2×C4⋊C4C23×C314yes—
350C2×C4⋊C4C23×C314yes—
351C2×C4⋊C4C23×C314yes—
352C2×C4⋊C4C23×C314yes—
353C2×C4⋊C4C23×C314yes—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4C3×D418yes—
360C2×C22⋊C4C23×C314yes—
361C2×C22⋊C4C23×C314yes—
362C2×C22⋊C4C23×C314yes—
363C2×C22⋊C4C23×C314yes—
364C2×C22⋊C4C23×C314yes—
365C2×C22⋊C4C23×C314yes—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42C23×C314yes—
369C2×C42C23×C314yes—
370#95C23×C314yes—
371#95C23×C314yes—
372#95C23×C314yes—
373#95C23×C314yes—
374#95C23×C314yes—
375#95C23×C314yes—
376#95C23×C314yes—
377#95C23×C314yes—
378#95C23×C314yes—
379#95C23×C314yes—
380#95C23×C314yes—
381#95C23×C314yes—
382#95C23×C314yes—
383#95C23×C314yes—
384C23×C3—28no—
385C23×C3—28no—
386C23×C3—28no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—44no—
394C23×C3—44no—
395C23×C3—44no—
396C23×C3—44no—
397C23×C3C22×D414yes—
398C23×C3C22×D412yes—
399C23×C3C2×#4112yes—
400C23×C3C2×#4112yes—
401C23×C3H(5,𝔽2)12yes—
402C23×C32−1+412yes—
403C23×C32−1+412yes—
404C23×C32−1+412yes—
405C23×C3C2511yescharacteristic
406C3×Q8—416no—
407C2×C3×C4—28no—
408C2×C3×C4—28no—
409C2×C3×C4—28no—
410C2×C3×C4—28no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
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—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—416no—
450C2×C3×C4—44no—
451C2×C3×C4—44no—
452C2×C3×C4—44no—
453C2×C3×C4—44no—
454C2×C3×C4—44no—
455C2×C3×C4—44no—
456C2×C3×C4—44no—
457C2×C3×C4—44no—
458C2×C3×C4—44no—
459C2×C3×C4—44no—
460C2×C3×C4C22×D414yes—
461C2×C3×C4C22×D414yes—
462C2×C3×C4C2×#4114yes—
463C2×C3×C4C2×#4114yes—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C2×C3×D414yes—
471C24C24×C312yes—
472C24C24×C311yescharacteristic
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—44no—
476C2×Q8—416no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—28no—
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—28no—
517C22×C4—44no—
518C22×C4—416no—
519C22×C4C2×C3×D414yes—
520C22×C4C2×C3×D414yes—
521C22×C4C3×#4114yes—
522C22×C4C3×#4114yes—
523C22×C4C24×C312yes—
524C22×C4C24×C312yes—
525C22×C4C24×C312yes—
526C22×C4C24×C312yes—
527C22×C4C24×C312yes—
528C22×C4C24×C312yes—
529C22×C4C24×C312yes—
530C22×C4C24×C312yes—
531C22×C4C24×C312yes—
532C22×C4C24×C312yes—
533C22×C4C24×C312yes—
534C22×C4C24×C312yes—
535C22×C4C24×C312yes—
536C22×C4C24×C312yes—
537C4⋊C4—28no—
538C4⋊C4—28no—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—28no—
542C4⋊C4—28no—
543C4⋊C4—28no—
544C4⋊C4—28no—
545C4⋊C4—44no—
546C4⋊C4—44no—
547C4⋊C4—44no—
548C22⋊C4—28no—
549C22⋊C4—28no—
550C22⋊C4—28no—
551C22⋊C4—28no—
552C22⋊C4—44no—
553C22⋊C4C2×C3×D4116yes—
554C42—28no—
555C42—28no—
556C22×C3—24no—
557C22×C3—24no—
558C22×C3—24no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—416no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3#53614yes—
565C22×C3#54114yes—
566C22×C3#54214yes—
567C22×C3#54614yes—
568C22×C3#54714yes—
569C22×C3#55214yes—
570C22×C3#56314yes—
571C22×C3C23×D411yescharacteristic
572C22×C3C22×#4111yescharacteristic
573C22×C3C22×#4111yescharacteristic
574C22×C3C2×H(5,𝔽2)11yescharacteristic
575C22×C3C2×2−1+411yescharacteristic
576C22×C3C2×2−1+411yescharacteristic
577C22×C3C2×2−1+411yescharacteristic
578C3×C4—24no—
579C3×C4—24no—
580C3×C4—24no—
581C3×C4—24no—
582C3×C4—42no—
583C3×C4—42no—
584C3×C4—42no—
585C3×C4—42no—
586C3×C4—42no—
587C3×C4—42no—
588C3×C4—42no—
589C3×C4—42no—
590C3×C4—42no—
591C3×C4—42no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—28no—
599C23—28no—
600C23—28no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23—44no—
605C23C22×C3×D414yes—
606C23C22×C3×D412yes—
607C23C2×C3×#4112yes—
608C23C2×C3×#4112yes—
609C23C3×H(5,𝔽2)12yes—
610C23C3×2−1+412yes—
611C23C3×2−1+412yes—
612C23C3×2−1+412yes—
613C23C25×C311yescharacteristic
614Q8—416no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—28no—
626C2×C4—28no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
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—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
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—416no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4C22×C3×D414yes—
669C2×C4C22×C3×D414yes—
670C2×C4C2×C3×#4114yes—
671C2×C4C2×C3×#4114yes—
672C2×C3—44no—
673C2×C3#269818yesdirect product factor
674C2×C3C2×#53611yescharacteristic
675C2×C3C2×#54111yescharacteristic
676C2×C3C2×#54211yescharacteristic
677C2×C3C2×#54611yescharacteristic
678C2×C3C2×#54711yescharacteristic
679C2×C3C2×#55211yescharacteristic
680C2×C3C2×#56311yescharacteristic
681C22—24no—
682C22—24no—
683C22—24no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—416no—
688C22—42no—
689C22C3×#53614yes—
690C22C3×#54114yes—
691C22C3×#54214yes—
692C22C3×#54614yes—
693C22C3×#54714yes—
694C22C3×#55214yes—
695C22C3×#56314yes—
696C22C23×C3×D411yescharacteristic
697C22C22×C3×#4111yescharacteristic
698C22C22×C3×#4111yescharacteristic
699C22C2×C3×H(5,𝔽2)11yescharacteristic
700C22C2×C3×2−1+411yescharacteristic
701C22C2×C3×2−1+411yescharacteristic
702C22C2×C3×2−1+411yescharacteristic
703C4—24no—
704C4—24no—
705C4—24no—
706C4—24no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—42no—
717C3C2×#269811yescharacteristic, direct product factor, Sylow
718C2—44no—
719C2C3×#269818yesdirect product factor
720C2C2×C3×#53611yescharacteristic
721C2C2×C3×#54111yescharacteristic
722C2C2×C3×#54211yescharacteristic
723C2C2×C3×#54611yescharacteristic
724C2C2×C3×#54711yescharacteristic
725C2C2×C3×#55211yescharacteristic
726C2C2×C3×#56311yescharacteristic
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
3. C3×#2698C2direct (N × H)
4. C2×C3×#400C2semidirect
5. C2×C3×#398C2semidirect
6. C2×C3×#398C2semidirect
9. C2×C3×#395C2semidirect
10. C2×C3×#391C2semidirect
11. C2×C3×#389C2semidirect
13. C2×C3×#387C2semidirect
15. C2×C3×#382C2semidirect
17. C2×#2698C3direct (N × H)
43. C3×#400C22semidirect
44. C3×#398C22semidirect
45. C3×#398C22semidirect
48. C3×#395C22semidirect
49. C3×#391C22semidirect
50. C3×#389C22semidirect
52. C3×#387C22semidirect
54. C3×#382C22semidirect
72. #2698C2×C3direct (N × H)
73. C2×#400C2×C3semidirect
74. C2×#398C2×C3semidirect
75. C2×#398C2×C3semidirect
78. C2×#395C2×C3semidirect
79. C2×#391C2×C3semidirect
80. C2×#389C2×C3semidirect
82. C2×#387C2×C3semidirect
84. C2×#382C2×C3semidirect
188. #400C22×C3semidirect
189. #398C22×C3semidirect
190. #398C22×C3semidirect
193. #395C22×C3semidirect
194. #391C22×C3semidirect
195. #389C22×C3semidirect
197. #387C22×C3semidirect
199. #382C22×C3semidirect
673. C2×C3#2698direct (N × H)
717. C3C2×#2698direct (N × H)
719. C2C3×#2698direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1262
C22×C3×C22⋊Q82
C3×#26982
C2×C3×#4002
C2×C3×#3982
C2×C3×#3972
C2×C3×#3952
C2×C3×#3912
C2×C3×#3892
C2×C3×#3882
C2×C3×#3872
C2×C3×#3852
C2×C3×#3822
C2×C3×#3812
C2×#26983