Finite Group Databasebeta

← C2×C3×#2737 #10670779

Subgroups — C2×C3×#2737 #10670779

Order 768.

2394 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2737C2116yesmaximal, direct product factor
2C2×C3×#397C211yesmaximal, characteristic, complemented
3C2×C3×#397C211yesmaximal, characteristic, complemented
4C2×C3×#395C211yesmaximal, characteristic, complemented
5C2×C3×#394C211yesmaximal, characteristic
6C2×C3×#393C211yesmaximal, characteristic, complemented
7C2×C3×#393C211yesmaximal, characteristic, complemented
8C2×C3×#390C211yesmaximal, characteristic
9C2×C3×#388C211yesmaximal, characteristic, complemented
10C2×C3×#388C211yesmaximal, characteristic, complemented
11C2×C3×#387C211yesmaximal, characteristic, complemented
12C2×C3×#387C211yesmaximal, characteristic, complemented
13C2×C3×#386C211yesmaximal, characteristic
14C2×C3×#383C211yesmaximal, characteristic, complemented
15C2×C3×#381C211yesmaximal, characteristic, complemented
16C2×C3×#380C211yesmaximal, characteristic, complemented
17C2×#2737C311yesmaximal, characteristic, direct product factor, Sylow
18C23×C3×Q8C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C24×C3×C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C22×C3×C22⋊C4C2211yescharacteristic
33C22×C3×C22⋊C4C2211yescharacteristic
34C22×C3×C22⋊C4C2211yescharacteristic
35C22×C3×C22⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4C2211yescharacteristic
37C22×C3×C42C2211yescharacteristic
38C22×C3×C42C2211yescharacteristic
39C3×#397C2218yescomplemented
40C3×#397C2218yescomplemented
41C3×#395C2218yescomplemented
42C3×#394C2218yes—
43C3×#393C2218yescomplemented
44C3×#393C2218yescomplemented
45C3×#390C2218yes—
46C3×#388C2218yescomplemented
47C3×#388C2218yescomplemented
48C3×#387C2218yescomplemented
49C3×#387C2218yescomplemented
50C3×#386C2218yes—
51C3×#383C2218yescomplemented
52C3×#381C2218yescomplemented
53C3×#380C2218yescomplemented
54C2×C3×#95C2211yescharacteristic
55C2×C3×#95C2211yescharacteristic
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
68#2737C2×C3116yesdirect product factor
69C2×#397C2×C311yescharacteristic, complemented
70C2×#397C2×C311yescharacteristic, complemented
71C2×#395C2×C311yescharacteristic, complemented
72C2×#394C2×C311yescharacteristic
73C2×#393C2×C311yescharacteristic, complemented
74C2×#393C2×C311yescharacteristic, complemented
75C2×#390C2×C311yescharacteristic
76C2×#388C2×C311yescharacteristic, complemented
77C2×#388C2×C311yescharacteristic, complemented
78C2×#387C2×C311yescharacteristic, complemented
79C2×#387C2×C311yescharacteristic, complemented
80C2×#386C2×C311yescharacteristic
81C2×#383C2×C311yescharacteristic, complemented
82C2×#381C2×C311yescharacteristic, complemented
83C2×#380C2×C311yescharacteristic, complemented
84C25×C3C2311yescharacteristic
85C25×C3C2311yescharacteristic
86C22×C3×Q8—42no—
87C22×C3×Q8—42no—
88C22×C3×Q8—42no—
89C22×C3×Q8C2314yes—
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—42no—
93C22×C3×D4C2314yes—
94C23×C3×C4—24no—
95C23×C3×C4—24no—
96C23×C3×C4—42no—
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2314yes—
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C2×C3×C4⋊C4—24no—
112C2×C3×C4⋊C4—24no—
113C2×C3×C4⋊C4—42no—
114C2×C3×C4⋊C4—42no—
115C2×C3×C4⋊C4—42no—
116C2×C3×C4⋊C4C2314yes—
117C2×C3×C4⋊C4C2314yes—
118C2×C3×C4⋊C4C2314yes—
119C2×C3×C4⋊C4C2314yes—
120C2×C3×C4⋊C4C2314yes—
121C2×C3×C22⋊C4—24no—
122C2×C3×C22⋊C4—24no—
123C2×C3×C22⋊C4—42no—
124C2×C3×C22⋊C4—42no—
125C2×C3×C22⋊C4—42no—
126C2×C3×C22⋊C4—42no—
127C2×C3×C22⋊C4—42no—
128C2×C3×C22⋊C4—42no—
129C2×C3×C22⋊C4—42no—
130C2×C3×C22⋊C4—42no—
131C2×C3×C22⋊C4—42no—
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C22⋊C4C2314yes—
135C2×C3×C22⋊C4C2314yes—
136C2×C3×C22⋊C4C2314yes—
137C2×C3×C22⋊C4C2314yes—
138C2×C3×C22⋊C4C2314yes—
139C2×C3×C22⋊C4C2314yes—
140C2×C3×C22⋊C4C2314yes—
141C2×C3×C22⋊C4C2314yes—
142C2×C3×C22⋊C4C2314yes—
143C2×C3×C42—24no—
144C2×C3×C42—42no—
145C2×C3×C42C2314yes—
146C2×C3×C42C2314yes—
147C3×#95C2314yes—
148C3×#95C2314yes—
149C3×#95C2314yes—
150C3×#95C2314yes—
151C3×#95C2314yes—
152C3×#95C2314yes—
153C3×#95C2314yes—
154C3×#95C2314yes—
155C3×#95C2314yes—
156C3×#95C2314yes—
157C3×#95C2314yes—
158C3×#95C2314yes—
159C3×#95C2314yes—
160C3×#95C2314yes—
161C23×Q8C22×C311yescharacteristic
162C23×D4C22×C311yescharacteristic
163C24×C4C22×C311yescharacteristic
164C22×C4⋊C4C22×C311yescharacteristic
165C22×C4⋊C4C22×C311yescharacteristic
166C22×C4⋊C4C22×C311yescharacteristic
167C22×C4⋊C4C22×C311yescharacteristic
168C22×C4⋊C4C22×C311yescharacteristic
169C22×C22⋊C4C22×C311yescharacteristic
170C22×C22⋊C4C22×C311yescharacteristic
171C22×C22⋊C4C22×C311yescharacteristic
172C22×C22⋊C4C22×C311yescharacteristic
173C22×C22⋊C4C22×C311yescharacteristic
174C22×C22⋊C4C22×C311yescharacteristic
175C22×C22⋊C4C22×C311yescharacteristic
176C22×C22⋊C4C22×C311yescharacteristic
177C22×C22⋊C4C22×C311yescharacteristic
178C22×C22⋊C4C22×C311yescharacteristic
179C22×C22⋊C4C22×C311yescharacteristic
180C22×C42C22×C311yescharacteristic
181C22×C42C22×C311yescharacteristic
182#397C22×C318yescomplemented
183#397C22×C318yescomplemented
184#395C22×C318yescomplemented
185#394C22×C318yes—
186#393C22×C318yescomplemented
187#393C22×C318yescomplemented
188#390C22×C318yes—
189#388C22×C318yescomplemented
190#388C22×C318yescomplemented
191#387C22×C318yescomplemented
192#387C22×C318yescomplemented
193#386C22×C318yes—
194#383C22×C318yescomplemented
195#381C22×C318yescomplemented
196#380C22×C318yescomplemented
197C2×#95C22×C311yescharacteristic
198C2×#95C22×C311yescharacteristic
199C2×#95C22×C311yescharacteristic
200C2×#95C22×C311yescharacteristic
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
211C24×C3—22no—
212C24×C3—22no—
213C24×C3—22no—
214C24×C3—22no—
215C24×C3—22no—
216C24×C3—22no—
217C24×C3—22no—
218C24×C3—22no—
219C24×C3—22no—
220C24×C3—22no—
221C24×C3—22no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3#4114yes—
225C24×C3C2412yes—
226C24×C3C2412yes—
227C24×C3C2411yescharacteristic
228C2×C3×Q8—44no—
229C2×C3×Q8—44no—
230C2×C3×Q8—44no—
231C2×C3×Q8—416no—
232C2×C3×D4—28no—
233C2×C3×D4—28no—
234C2×C3×D4—44no—
235C2×C3×D4—416no—
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—28no—
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—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—28no—
275C22×C3×C4—44no—
276C22×C3×C4—416no—
277C22×C3×C4#4114yes—
278C22×C3×C4#4114yes—
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—44no—
295C3×C4⋊C4—44no—
296C3×C4⋊C4—44no—
297C3×C22⋊C4—28no—
298C3×C22⋊C4—28no—
299C3×C22⋊C4—44no—
300C3×C22⋊C4—44no—
301C3×C22⋊C4—44no—
302C3×C22⋊C4—44no—
303C3×C22⋊C4—44no—
304C3×C22⋊C4—44no—
305C3×C22⋊C4—44no—
306C3×C22⋊C4—44no—
307C3×C22⋊C4—44no—
308C3×C42—28no—
309C3×C42—44no—
310C25C23×C311yescharacteristic
311C25C23×C311yescharacteristic
312C22×Q8—42no—
313C22×Q8—42no—
314C22×Q8—42no—
315C22×Q8C23×C314yes—
316C22×D4—24no—
317C22×D4—24no—
318C22×D4—42no—
319C22×D4C23×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×C311yescharacteristic
332C23×C4C23×C311yescharacteristic
333C23×C4C23×C311yescharacteristic
334C23×C4C23×C314yes—
335C23×C4C23×C311yescharacteristic
336C23×C4C23×C311yescharacteristic
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4C23×C314yes—
343C2×C4⋊C4C23×C314yes—
344C2×C4⋊C4C23×C314yes—
345C2×C4⋊C4C23×C314yes—
346C2×C4⋊C4C23×C314yes—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4C23×C314yes—
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×C22⋊C4C23×C314yes—
367C2×C22⋊C4C23×C314yes—
368C2×C22⋊C4C23×C314yes—
369C2×C42—24no—
370C2×C42—42no—
371C2×C42C23×C314yes—
372C2×C42C23×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—
384#95C23×C314yes—
385#95C23×C314yes—
386#95C23×C314yes—
387C23×C3—28no—
388C23×C3—28no—
389C23×C3—28no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—44no—
404C23×C3—44no—
405C23×C3—44no—
406C23×C3—44no—
407C23×C3—44no—
408C23×C3—44no—
409C23×C3—44no—
410C23×C3—44no—
411C23×C3—44no—
412C23×C3—44no—
413C23×C3—44no—
414C23×C3C2×#4114yes—
415C23×C3C2×#4112yes—
416C23×C3C2×#4112yes—
417C23×C3C2×#4112yes—
418C23×C3H(5,𝔽2)12yes—
419C23×C3H(5,𝔽2)12yes—
420C23×C3H(5,𝔽2)12yes—
421C23×C32−1+412yes—
422C23×C3C2511yescharacteristic
423C3×Q8—416no—
424C3×D4—416no—
425C2×C3×C4—28no—
426C2×C3×C4—28no—
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—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—416no—
465C2×C3×C4—44no—
466C2×C3×C4—44no—
467C2×C3×C4—44no—
468C2×C3×C4—44no—
469C2×C3×C4—44no—
470C2×C3×C4—44no—
471C2×C3×C4—44no—
472C2×C3×C4—44no—
473C2×C3×C4—44no—
474C2×C3×C4—44no—
475C2×C3×C4—44no—
476C2×C3×C4C2×#4114yes—
477C2×C3×C4C2×#4114yes—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24C3×#4114yes—
492C24C24×C312yes—
493C24C24×C312yes—
494C24C24×C311yescharacteristic
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—416no—
499C2×D4—28no—
500C2×D4—28no—
501C2×D4—44no—
502C2×D4—416no—
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—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—28no—
542C22×C4—44no—
543C22×C4—416no—
544C22×C4C3×#4114yes—
545C22×C4C3×#4114yes—
546C22×C4C24×C312yes—
547C22×C4C24×C312yes—
548C22×C4C24×C312yes—
549C22×C4C24×C312yes—
550C22×C4C24×C312yes—
551C22×C4C24×C312yes—
552C22×C4C24×C312yes—
553C22×C4C24×C312yes—
554C22×C4C24×C312yes—
555C22×C4C24×C312yes—
556C22×C4C24×C312yes—
557C22×C4C24×C312yes—
558C22×C4C24×C312yes—
559C4⋊C4—28no—
560C4⋊C4—28no—
561C4⋊C4—44no—
562C4⋊C4—44no—
563C4⋊C4—44no—
564C22⋊C4—28no—
565C22⋊C4—28no—
566C22⋊C4—44no—
567C22⋊C4—44no—
568C22⋊C4—44no—
569C22⋊C4—44no—
570C22⋊C4—44no—
571C22⋊C4—44no—
572C22⋊C4—44no—
573C22⋊C4—44no—
574C22⋊C4—44no—
575C42—28no—
576C42—44no—
577C22×C3—24no—
578C22×C3—24no—
579C22×C3—24no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—416no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—42no—
589C22×C3—42no—
590C22×C3—42no—
591C22×C3—42no—
592C22×C3—88no—
593C22×C3#53914yes—
594C22×C3#54214yes—
595C22×C3#54214yes—
596C22×C3#55114yes—
597C22×C3#55114yes—
598C22×C3#55514yes—
599C22×C3#56014yes—
600C22×C3C22×#4111yescharacteristic
601C22×C3C22×#4111yescharacteristic
602C22×C3C22×#4111yescharacteristic
603C22×C3C2×H(5,𝔽2)11yescharacteristic
604C22×C3C2×H(5,𝔽2)11yescharacteristic
605C22×C3C2×H(5,𝔽2)11yescharacteristic
606C22×C3C2×2−1+411yescharacteristic
607C3×C4—24no—
608C3×C4—24no—
609C3×C4—42no—
610C3×C4—42no—
611C3×C4—42no—
612C3×C4—42no—
613C3×C4—42no—
614C3×C4—42no—
615C3×C4—42no—
616C3×C4—42no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—42no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23C2×C3×#4114yes—
648C23C2×C3×#4112yes—
649C23C2×C3×#4112yes—
650C23C2×C3×#4112yes—
651C23C3×H(5,𝔽2)12yes—
652C23C3×H(5,𝔽2)12yes—
653C23C3×H(5,𝔽2)12yes—
654C23C3×2−1+412yes—
655C23C25×C311yescharacteristic
656Q8—416no—
657D4—416no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—28no—
663C2×C4—28no—
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—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—416no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4C2×C3×#4114yes—
710C2×C4C2×C3×#4114yes—
711C2×C3—44no—
712C2×C3—82no—
713C2×C3#273718yesdirect product factor
714C2×C3C2×#53911yescharacteristic
715C2×C3C2×#54211yescharacteristic
716C2×C3C2×#54211yescharacteristic
717C2×C3C2×#55111yescharacteristic
718C2×C3C2×#55111yescharacteristic
719C2×C3C2×#55511yescharacteristic
720C2×C3C2×#56011yescharacteristic
721C22—24no—
722C22—24no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—416no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—88no—
737C22C3×#53914yes—
738C22C3×#54214yes—
739C22C3×#54214yes—
740C22C3×#55114yes—
741C22C3×#55114yes—
742C22C3×#55514yes—
743C22C3×#56014yes—
744C22C22×C3×#4111yescharacteristic
745C22C22×C3×#4111yescharacteristic
746C22C22×C3×#4111yescharacteristic
747C22C2×C3×H(5,𝔽2)11yescharacteristic
748C22C2×C3×H(5,𝔽2)11yescharacteristic
749C22C2×C3×H(5,𝔽2)11yescharacteristic
750C22C2×C3×2−1+411yescharacteristic
751C4—24no—
752C4—24no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—42no—
764C3C2×#273711yescharacteristic, direct product factor, Sylow
765C2—44no—
766C2—82no—
767C2C3×#273718yesdirect product factor
768C2C2×C3×#53911yescharacteristic
769C2C2×C3×#54211yescharacteristic
770C2C2×C3×#54211yescharacteristic
771C2C2×C3×#55111yescharacteristic
772C2C2×C3×#55111yescharacteristic
773C2C2×C3×#55511yescharacteristic
774C2C2×C3×#56011yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC23C25×C3
prime radicalC23×C3×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#2737C2direct (N × H)
2. C2×C3×#397C2semidirect
3. C2×C3×#397C2semidirect
4. C2×C3×#395C2semidirect
6. C2×C3×#393C2semidirect
7. C2×C3×#393C2semidirect
9. C2×C3×#388C2semidirect
10. C2×C3×#388C2semidirect
11. C2×C3×#387C2semidirect
12. C2×C3×#387C2semidirect
14. C2×C3×#383C2semidirect
15. C2×C3×#381C2semidirect
16. C2×C3×#380C2semidirect
17. C2×#2737C3direct (N × H)
39. C3×#397C22semidirect
40. C3×#397C22semidirect
41. C3×#395C22semidirect
43. C3×#393C22semidirect
44. C3×#393C22semidirect
46. C3×#388C22semidirect
47. C3×#388C22semidirect
48. C3×#387C22semidirect
49. C3×#387C22semidirect
51. C3×#383C22semidirect
52. C3×#381C22semidirect
53. C3×#380C22semidirect
68. #2737C2×C3direct (N × H)
69. C2×#397C2×C3semidirect
70. C2×#397C2×C3semidirect
71. C2×#395C2×C3semidirect
73. C2×#393C2×C3semidirect
74. C2×#393C2×C3semidirect
76. C2×#388C2×C3semidirect
77. C2×#388C2×C3semidirect
78. C2×#387C2×C3semidirect
79. C2×#387C2×C3semidirect
81. C2×#383C2×C3semidirect
82. C2×#381C2×C3semidirect
83. C2×#380C2×C3semidirect
182. #397C22×C3semidirect
183. #397C22×C3semidirect
184. #395C22×C3semidirect
186. #393C22×C3semidirect
187. #393C22×C3semidirect
189. #388C22×C3semidirect
190. #388C22×C3semidirect
191. #387C22×C3semidirect
192. #387C22×C3semidirect
194. #383C22×C3semidirect
195. #381C22×C3semidirect
196. #380C22×C3semidirect
713. C2×C3#2737direct (N × H)
764. C3C2×#2737direct (N × H)
767. C2C3×#2737direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#27372
C2×C3×#3972
C2×C3×#3952
C2×C3×#3942
C2×C3×#3932
C2×C3×#3902
C2×C3×#3882
C2×C3×#3872
C2×C3×#3862
C2×C3×#3832
C2×C3×#3812
C2×C3×#3802
C2×#27373