Finite Group Databasebeta

← C2×C3×#2725 #10670756

Subgroups — C2×C3×#2725 #10670756

Order 768.

2354 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#126C211yesmaximal, characteristic
2C22×C3×#125C211yesmaximal, characteristic, complemented
3C3×#2725C2116yesmaximal, direct product factor
4C2×C3×#400C211yesmaximal, characteristic, complemented
5C2×C3×#398C211yesmaximal, characteristic, complemented
6C2×C3×#397C211yesmaximal, characteristic
7C2×C3×#396C211yesmaximal, characteristic
8C2×C3×#396C211yesmaximal, characteristic
9C2×C3×#396C211yesmaximal, characteristic
10C2×C3×#389C211yesmaximal, characteristic, complemented
11C2×C3×#389C211yesmaximal, characteristic, complemented
12C2×C3×#389C211yesmaximal, characteristic, complemented
13C2×C3×#389C211yesmaximal, characteristic, complemented
14C2×C3×#388C211yesmaximal, characteristic
15C2×C3×#388C211yesmaximal, characteristic
16C2×C3×#387C211yesmaximal, characteristic, complemented
17C2×#2725C311yesmaximal, characteristic, direct product factor, Sylow
18C2×C3×#126—28no—
19C2×C3×#126C2218yes—
20C2×C3×#125—28no—
21C2×C3×#125C2218yescomplemented
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
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×C22⋊C4C2211yescharacteristic
38C22×C3×C22⋊C4C2211yescharacteristic
39C22×C3×C22⋊C4C2211yescharacteristic
40C22×C3×C22⋊C4C2211yescharacteristic
41C22×C3×C22⋊C4C2211yescharacteristic
42C22×C3×C22⋊C4C2211yescharacteristic
43C22×C3×C22⋊C4C2211yescharacteristic
44C22×C3×C42C2211yescharacteristic
45C22×C3×C42C2211yescharacteristic
46C22×C3×C42C2211yescharacteristic
47C3×#400C2218yescomplemented
48C3×#398C2218yescomplemented
49C3×#397C2218yes—
50C3×#396C2218yes—
51C3×#396C2218yes—
52C3×#396C2218yes—
53C3×#389C2218yescomplemented
54C3×#389C2218yescomplemented
55C3×#389C2218yescomplemented
56C3×#389C2218yescomplemented
57C3×#388C2218yes—
58C3×#388C2218yes—
59C3×#387C2218yescomplemented
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×#125C2×C311yescharacteristic, complemented
72#2725C2×C3116yesdirect product factor
73C2×#400C2×C311yescharacteristic, complemented
74C2×#398C2×C311yescharacteristic, complemented
75C2×#397C2×C311yescharacteristic
76C2×#396C2×C311yescharacteristic
77C2×#396C2×C311yescharacteristic
78C2×#396C2×C311yescharacteristic
79C2×#389C2×C311yescharacteristic, complemented
80C2×#389C2×C311yescharacteristic, complemented
81C2×#389C2×C311yescharacteristic, complemented
82C2×#389C2×C311yescharacteristic, complemented
83C2×#388C2×C311yescharacteristic
84C2×#388C2×C311yescharacteristic
85C2×#387C2×C311yescharacteristic, complemented
86C25×C3C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C3×#126—232no—
102C3×#125—232no—
103C2×C3×C4⋊C4—24no—
104C2×C3×C4⋊C4—24no—
105C2×C3×C4⋊C4—24no—
106C2×C3×C4⋊C4—24no—
107C2×C3×C4⋊C4—24no—
108C2×C3×C4⋊C4—24no—
109C2×C3×C4⋊C4—24no—
110C2×C3×C4⋊C4—24no—
111C2×C3×C4⋊C4—24no—
112C2×C3×C4⋊C4—24no—
113C2×C3×C4⋊C4—24no—
114C2×C3×C4⋊C4—42no—
115C2×C3×C4⋊C4—42no—
116C2×C3×C4⋊C4—42no—
117C2×C3×C4⋊C4D418yes—
118C2×C3×C4⋊C4C2314yes—
119C2×C3×C4⋊C4C2314yes—
120C2×C3×C4⋊C4C2314yes—
121C2×C3×C4⋊C4C2314yes—
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—24no—
138C2×C3×C22⋊C4—42no—
139C2×C3×C22⋊C4—42no—
140C2×C3×C22⋊C4C2314yes—
141C2×C3×C22⋊C4C2314yes—
142C2×C3×C22⋊C4C2314yes—
143C2×C3×C22⋊C4C2314yes—
144C2×C3×C22⋊C4C2314yes—
145C2×C3×C22⋊C4C2314yes—
146C2×C3×C22⋊C4C2314yes—
147C2×C3×C42—24no—
148C2×C3×C42—24no—
149C2×C3×C42—42no—
150C2×C3×C42C2314yes—
151C2×C3×C42C2314yes—
152C2×C3×C42C2314yes—
153C3×#95C2314yes—
154C3×#95C2314yes—
155C3×#95C2314yes—
156C3×#95C2314yes—
157C3×#95C2314yes—
158C3×#95C2314yes—
159C3×#95C2314yes—
160C3×#95C2314yes—
161C3×#95C2314yes—
162C3×#95C2314yes—
163C2×#126—28no—
164C2×#126C22×C318yes—
165C2×#125—28no—
166C2×#125C22×C318yescomplemented
167C22×C4⋊C4C22×C311yescharacteristic
168C22×C4⋊C4C22×C311yescharacteristic
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×C4⋊C4C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182C22×C22⋊C4C22×C311yescharacteristic
183C22×C22⋊C4C22×C311yescharacteristic
184C22×C22⋊C4C22×C311yescharacteristic
185C22×C22⋊C4C22×C311yescharacteristic
186C22×C22⋊C4C22×C311yescharacteristic
187C22×C22⋊C4C22×C311yescharacteristic
188C22×C22⋊C4C22×C311yescharacteristic
189C22×C42C22×C311yescharacteristic
190C22×C42C22×C311yescharacteristic
191C22×C42C22×C311yescharacteristic
192#400C22×C318yescomplemented
193#398C22×C318yescomplemented
194#397C22×C318yes—
195#396C22×C318yes—
196#396C22×C318yes—
197#396C22×C318yes—
198#389C22×C318yescomplemented
199#389C22×C318yescomplemented
200#389C22×C318yescomplemented
201#389C22×C318yescomplemented
202#388C22×C318yes—
203#388C22×C318yes—
204#387C22×C318yescomplemented
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×C3—22no—
222C24×C3C2412yes—
223C24×C3C2411yescharacteristic
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
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—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×C4C2×D414yes—
262C22×C3×C4C2×D414yes—
263C22×C3×C4C2×D414yes—
264C22×C3×C4#4114yes—
265C22×C3×C4#4114yes—
266C22×C3×C4C2412yes—
267C22×C3×C4C2412yes—
268C22×C3×C4C2412yes—
269C22×C3×C4C2412yes—
270C22×C3×C4C2412yes—
271C22×C3×C4C2412yes—
272C22×C3×C4C2412yes—
273C22×C3×C4C2412yes—
274C22×C3×C4C2412yes—
275C22×C3×C4C2412yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C3×C4⋊C4—28no—
281C3×C4⋊C4—28no—
282C3×C4⋊C4—28no—
283C3×C4⋊C4—28no—
284C3×C4⋊C4—28no—
285C3×C4⋊C4—28no—
286C3×C4⋊C4—28no—
287C3×C4⋊C4—28no—
288C3×C4⋊C4—28no—
289C3×C4⋊C4—28no—
290C3×C4⋊C4—28no—
291C3×C4⋊C4—44no—
292C3×C4⋊C4—44no—
293C3×C4⋊C4—44no—
294C3×C4⋊C4C2×D4116yes—
295C3×C22⋊C4—28no—
296C3×C22⋊C4—28no—
297C3×C22⋊C4—28no—
298C3×C22⋊C4—28no—
299C3×C22⋊C4—28no—
300C3×C22⋊C4—44no—
301C3×C22⋊C4—44no—
302C3×C42—28no—
303C3×C42—28no—
304C3×C42—44no—
305C25C23×C311yescharacteristic
306C23×C4C23×C311yescharacteristic
307C23×C4C23×C311yescharacteristic
308C23×C4C23×C311yescharacteristic
309C23×C4C23×C311yescharacteristic
310C23×C4C23×C311yescharacteristic
311C23×C4C23×C311yescharacteristic
312C23×C4C23×C311yescharacteristic
313C23×C4C23×C311yescharacteristic
314C23×C4C23×C311yescharacteristic
315C23×C4C23×C311yescharacteristic
316C23×C4C23×C311yescharacteristic
317C23×C4C23×C311yescharacteristic
318C23×C4C23×C311yescharacteristic
319C23×C4C23×C311yescharacteristic
320#126—232no—
321#125—232no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4C3×D418yes—
337C2×C4⋊C4C23×C314yes—
338C2×C4⋊C4C23×C314yes—
339C2×C4⋊C4C23×C314yes—
340C2×C4⋊C4C23×C314yes—
341C2×C4⋊C4C23×C314yes—
342C2×C4⋊C4C23×C314yes—
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×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4C23×C314yes—
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×C42—42no—
369C2×C42C23×C314yes—
370C2×C42C23×C314yes—
371C2×C42C23×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—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—44no—
390C23×C3—44no—
391C23×C3—44no—
392C23×C3—44no—
393C23×C3—44no—
394C23×C3—44no—
395C23×C3—44no—
396C23×C3C22×D412yes—
397C23×C3C2×#4112yes—
398C23×C3C2×#4112yes—
399C23×C3H(5,𝔽2)12yes—
400C23×C32−1+412yes—
401C23×C32−1+412yes—
402C23×C32−1+412yes—
403C23×C3C2511yescharacteristic
404C2×C3×C4—28no—
405C2×C3×C4—28no—
406C2×C3×C4—28no—
407C2×C3×C4—28no—
408C2×C3×C4—28no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
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—44no—
447C2×C3×C4—44no—
448C2×C3×C4—44no—
449C2×C3×C4—44no—
450C2×C3×C4—44no—
451C2×C3×C4—44no—
452C2×C3×C4—44no—
453C2×C3×C4—44no—
454C2×C3×C4—44no—
455C2×C3×C4C22×D414yes—
456C2×C3×C4C22×D414yes—
457C2×C3×C4C22×D414yes—
458C2×C3×C4C2×#4114yes—
459C2×C3×C4C2×#4114yes—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24C24×C312yes—
468C24C24×C311yescharacteristic
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
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—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×C4C2×C3×D414yes—
507C22×C4C2×C3×D414yes—
508C22×C4C2×C3×D414yes—
509C22×C4C3×#4114yes—
510C22×C4C3×#4114yes—
511C22×C4C24×C312yes—
512C22×C4C24×C312yes—
513C22×C4C24×C312yes—
514C22×C4C24×C312yes—
515C22×C4C24×C312yes—
516C22×C4C24×C312yes—
517C22×C4C24×C312yes—
518C22×C4C24×C312yes—
519C22×C4C24×C312yes—
520C22×C4C24×C312yes—
521C22×C4C24×C312yes—
522C22×C4C24×C312yes—
523C22×C4C24×C312yes—
524C22×C4C24×C312yes—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—28no—
528C4⋊C4—28no—
529C4⋊C4—28no—
530C4⋊C4—28no—
531C4⋊C4—28no—
532C4⋊C4—28no—
533C4⋊C4—28no—
534C4⋊C4—28no—
535C4⋊C4—28no—
536C4⋊C4—44no—
537C4⋊C4—44no—
538C4⋊C4—44no—
539C4⋊C4C2×C3×D4116yes—
540C22⋊C4—28no—
541C22⋊C4—28no—
542C22⋊C4—28no—
543C22⋊C4—28no—
544C22⋊C4—28no—
545C22⋊C4—44no—
546C22⋊C4—44no—
547C42—28no—
548C42—28no—
549C42—44no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—88no—
558C22×C3#53714yes—
559C22×C3#54114yes—
560C22×C3#54114yes—
561C22×C3#54714yes—
562C22×C3#54814yes—
563C22×C3#55314yes—
564C22×C3#56314yes—
565C22×C3C23×D411yescharacteristic
566C22×C3C22×#4111yescharacteristic
567C22×C3C22×#4111yescharacteristic
568C22×C3C2×H(5,𝔽2)11yescharacteristic
569C22×C3C2×2−1+411yescharacteristic
570C22×C3C2×2−1+411yescharacteristic
571C22×C3C2×2−1+411yescharacteristic
572C3×C4—24no—
573C3×C4—24no—
574C3×C4—24no—
575C3×C4—24no—
576C3×C4—24no—
577C3×C4—42no—
578C3×C4—42no—
579C3×C4—42no—
580C3×C4—42no—
581C3×C4—42no—
582C3×C4—42no—
583C3×C4—42no—
584C3×C4—42no—
585C3×C4—42no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—44no—
594C23—44no—
595C23—44no—
596C23—44no—
597C23—44no—
598C23—44no—
599C23—44no—
600C23C22×C3×D412yes—
601C23C2×C3×#4112yes—
602C23C2×C3×#4112yes—
603C23C3×H(5,𝔽2)12yes—
604C23C3×2−1+412yes—
605C23C3×2−1+412yes—
606C23C3×2−1+412yes—
607C23C25×C311yescharacteristic
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
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—44no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—44no—
654C2×C4—44no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4C22×C3×D414yes—
660C2×C4C22×C3×D414yes—
661C2×C4C22×C3×D414yes—
662C2×C4C2×C3×#4114yes—
663C2×C4C2×C3×#4114yes—
664C2×C3—82no—
665C2×C3#272518yesdirect product factor
666C2×C3C2×#53711yescharacteristic
667C2×C3C2×#54111yescharacteristic
668C2×C3C2×#54111yescharacteristic
669C2×C3C2×#54711yescharacteristic
670C2×C3C2×#54811yescharacteristic
671C2×C3C2×#55311yescharacteristic
672C2×C3C2×#56311yescharacteristic
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—88no—
681C22C3×#53714yes—
682C22C3×#54114yes—
683C22C3×#54114yes—
684C22C3×#54714yes—
685C22C3×#54814yes—
686C22C3×#55314yes—
687C22C3×#56314yes—
688C22C23×C3×D411yescharacteristic
689C22C22×C3×#4111yescharacteristic
690C22C22×C3×#4111yescharacteristic
691C22C2×C3×H(5,𝔽2)11yescharacteristic
692C22C2×C3×2−1+411yescharacteristic
693C22C2×C3×2−1+411yescharacteristic
694C22C2×C3×2−1+411yescharacteristic
695C4—24no—
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—42no—
709C3C2×#272511yescharacteristic, direct product factor, Sylow
710C2—82no—
711C2C3×#272518yesdirect product factor
712C2C2×C3×#53711yescharacteristic
713C2C2×C3×#54111yescharacteristic
714C2C2×C3×#54111yescharacteristic
715C2C2×C3×#54711yescharacteristic
716C2C2×C3×#54811yescharacteristic
717C2C2×C3×#55311yescharacteristic
718C2C2×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
2. C22×C3×#125C2semidirect
3. C3×#2725C2direct (N × H)
4. C2×C3×#400C2semidirect
5. C2×C3×#398C2semidirect
10. C2×C3×#389C2semidirect
11. C2×C3×#389C2semidirect
12. C2×C3×#389C2semidirect
13. C2×C3×#389C2semidirect
16. C2×C3×#387C2semidirect
17. C2×#2725C3direct (N × H)
21. C2×C3×#125C22semidirect
47. C3×#400C22semidirect
48. C3×#398C22semidirect
53. C3×#389C22semidirect
54. C3×#389C22semidirect
55. C3×#389C22semidirect
56. C3×#389C22semidirect
59. C3×#387C22semidirect
71. C22×#125C2×C3semidirect
72. #2725C2×C3direct (N × H)
73. C2×#400C2×C3semidirect
74. C2×#398C2×C3semidirect
79. C2×#389C2×C3semidirect
80. C2×#389C2×C3semidirect
81. C2×#389C2×C3semidirect
82. C2×#389C2×C3semidirect
85. C2×#387C2×C3semidirect
166. C2×#125C22×C3semidirect
192. #400C22×C3semidirect
193. #398C22×C3semidirect
198. #389C22×C3semidirect
199. #389C22×C3semidirect
200. #389C22×C3semidirect
201. #389C22×C3semidirect
204. #387C22×C3semidirect
665. C2×C3#2725direct (N × H)
709. C3C2×#2725direct (N × H)
711. C2C3×#2725direct (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×#1252
C3×#27252
C2×C3×#4002
C2×C3×#3982
C2×C3×#3972
C2×C3×#3962
C2×C3×#3892
C2×C3×#3882
C2×C3×#3872
C2×#27253