Finite Group Databasebeta

← C2×C3×#2705 #10670733

Subgroups — C2×C3×#2705 #10670733

Order 768.

3046 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#126C211yesmaximal, characteristic, complemented
2C22×C3×#123C211yesmaximal, characteristic, complemented
3C3×#2705C2116yesmaximal, direct product factor
4C2×C3×#399C211yesmaximal, characteristic, complemented
5C2×C3×#396C211yesmaximal, characteristic, complemented
6C2×C3×#396C211yesmaximal, characteristic, complemented
7C2×C3×#394C211yesmaximal, characteristic, complemented
8C2×C3×#394C211yesmaximal, characteristic, complemented
9C2×C3×#392C211yesmaximal, characteristic
10C2×C3×#390C211yesmaximal, characteristic, complemented
11C2×C3×#390C211yesmaximal, characteristic, complemented
12C2×C3×#389C211yesmaximal, characteristic, complemented
13C2×C3×#388C211yesmaximal, characteristic, complemented
14C2×C3×#387C211yesmaximal, characteristic, complemented
15C2×C3×#386C211yesmaximal, characteristic, complemented
16C2×C3×#380C211yesmaximal, characteristic, complemented
17C2×#2705C311yesmaximal, characteristic, direct product factor, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C24×C3×C4C2211yescharacteristic
22C2×C3×#126—28no—
23C2×C3×#126C2218yescomplemented
24C2×C3×#123—28no—
25C2×C3×#123C2218yescomplemented
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×C22⋊C4C2211yescharacteristic
42C22×C3×C22⋊C4C2211yescharacteristic
43C22×C3×C22⋊C4C2211yescharacteristic
44C22×C3×C22⋊C4C2211yescharacteristic
45C22×C3×C22⋊C4C2211yescharacteristic
46C22×C3×C22⋊C4C2211yescharacteristic
47C22×C3×C22⋊C4C2211yescharacteristic
48C22×C3×C22⋊C4C2211yescharacteristic
49C22×C3×C42C2211yescharacteristic
50C22×C3×C42C2211yescharacteristic
51C3×#399C2218yescomplemented
52C3×#396C2218yescomplemented
53C3×#396C2218yescomplemented
54C3×#394C2218yescomplemented
55C3×#394C2218yescomplemented
56C3×#392C2218yes—
57C3×#390C2218yescomplemented
58C3×#390C2218yescomplemented
59C3×#389C2218yescomplemented
60C3×#388C2218yescomplemented
61C3×#387C2218yescomplemented
62C3×#386C2218yescomplemented
63C3×#380C2218yescomplemented
64C2×C3×#95C2211yescharacteristic
65C2×C3×#95C2211yescharacteristic
66C2×C3×#95C2211yescharacteristic
67C2×C3×#95C2211yescharacteristic
68C2×C3×#95C2211yescharacteristic
69C2×C3×#95C2211yescharacteristic
70C22×#126C2×C311yescharacteristic, complemented
71C22×#123C2×C311yescharacteristic, complemented
72#2705C2×C3116yesdirect product factor
73C2×#399C2×C311yescharacteristic, complemented
74C2×#396C2×C311yescharacteristic, complemented
75C2×#396C2×C311yescharacteristic, complemented
76C2×#394C2×C311yescharacteristic, complemented
77C2×#394C2×C311yescharacteristic, complemented
78C2×#392C2×C311yescharacteristic
79C2×#390C2×C311yescharacteristic, complemented
80C2×#390C2×C311yescharacteristic, complemented
81C2×#389C2×C311yescharacteristic, complemented
82C2×#388C2×C311yescharacteristic, complemented
83C2×#387C2×C311yescharacteristic, complemented
84C2×#386C2×C311yescharacteristic, complemented
85C2×#380C2×C311yescharacteristic, complemented
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C25×C3C2311yescharacteristic
89C22×C3×D4—24no—
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—24no—
93C22×C3×D4—42no—
94C22×C3×D4—42no—
95C22×C3×D4—42no—
96C22×C3×D4—42no—
97C22×C3×D4—42no—
98C22×C3×D4C2314yes—
99C22×C3×D4C2314yes—
100C22×C3×D4C2314yes—
101C23×C3×C4—24no—
102C23×C3×C4—24no—
103C23×C3×C4—42no—
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C23×C3×C4C2314yes—
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2311yescharacteristic
115C23×C3×C4C2311yescharacteristic
116C23×C3×C4C2311yescharacteristic
117C3×#126—232no—
118C3×#123—232no—
119C2×C3×C4⋊C4—24no—
120C2×C3×C4⋊C4—24no—
121C2×C3×C4⋊C4—24no—
122C2×C3×C4⋊C4—24no—
123C2×C3×C4⋊C4—42no—
124C2×C3×C4⋊C4—42no—
125C2×C3×C4⋊C4—42no—
126C2×C3×C4⋊C4—42no—
127C2×C3×C4⋊C4D418yescomplemented
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×C22⋊C4—24no—
138C2×C3×C22⋊C4—24no—
139C2×C3×C22⋊C4—24no—
140C2×C3×C22⋊C4—24no—
141C2×C3×C22⋊C4—24no—
142C2×C3×C22⋊C4—24no—
143C2×C3×C22⋊C4—24no—
144C2×C3×C22⋊C4—42no—
145C2×C3×C22⋊C4—42no—
146C2×C3×C22⋊C4—42no—
147C2×C3×C22⋊C4—42no—
148C2×C3×C22⋊C4—42no—
149C2×C3×C22⋊C4—42no—
150C2×C3×C22⋊C4—42no—
151C2×C3×C22⋊C4C2314yes—
152C2×C3×C22⋊C4C2314yes—
153C2×C3×C22⋊C4C2314yes—
154C2×C3×C22⋊C4C2314yes—
155C2×C3×C22⋊C4C2314yes—
156C2×C3×C22⋊C4C2314yes—
157C2×C3×C22⋊C4C2314yes—
158C2×C3×C22⋊C4C2314yes—
159C2×C3×C22⋊C4C2314yes—
160C2×C3×C22⋊C4C2314yes—
161C2×C3×C22⋊C4C2314yes—
162C2×C3×C22⋊C4C2314yes—
163C2×C3×C22⋊C4C2314yes—
164C2×C3×C22⋊C4C2314yes—
165C2×C3×C42—24no—
166C2×C3×C42—42no—
167C2×C3×C42C2314yes—
168C2×C3×C42C2314yes—
169C3×#95C2314yes—
170C3×#95C2314yes—
171C3×#95C2314yes—
172C3×#95C2314yes—
173C3×#95C2314yes—
174C3×#95C2314yes—
175C23×D4C22×C311yescharacteristic
176C23×D4C22×C311yescharacteristic
177C23×D4C22×C311yescharacteristic
178C24×C4C22×C311yescharacteristic
179C2×#126—28no—
180C2×#126C22×C318yescomplemented
181C2×#123—28no—
182C2×#123C22×C318yescomplemented
183C22×C4⋊C4C22×C311yescharacteristic
184C22×C4⋊C4C22×C311yescharacteristic
185C22×C4⋊C4C22×C311yescharacteristic
186C22×C4⋊C4C22×C311yescharacteristic
187C22×C4⋊C4C22×C311yescharacteristic
188C22×C4⋊C4C22×C311yescharacteristic
189C22×C4⋊C4C22×C311yescharacteristic
190C22×C4⋊C4C22×C311yescharacteristic
191C22×C4⋊C4C22×C311yescharacteristic
192C22×C22⋊C4C22×C311yescharacteristic
193C22×C22⋊C4C22×C311yescharacteristic
194C22×C22⋊C4C22×C311yescharacteristic
195C22×C22⋊C4C22×C311yescharacteristic
196C22×C22⋊C4C22×C311yescharacteristic
197C22×C22⋊C4C22×C311yescharacteristic
198C22×C22⋊C4C22×C311yescharacteristic
199C22×C22⋊C4C22×C311yescharacteristic
200C22×C22⋊C4C22×C311yescharacteristic
201C22×C22⋊C4C22×C311yescharacteristic
202C22×C22⋊C4C22×C311yescharacteristic
203C22×C22⋊C4C22×C311yescharacteristic
204C22×C22⋊C4C22×C311yescharacteristic
205C22×C22⋊C4C22×C311yescharacteristic
206C22×C42C22×C311yescharacteristic
207C22×C42C22×C311yescharacteristic
208#399C22×C318yescomplemented
209#396C22×C318yescomplemented
210#396C22×C318yescomplemented
211#394C22×C318yescomplemented
212#394C22×C318yescomplemented
213#392C22×C318yes—
214#390C22×C318yescomplemented
215#390C22×C318yescomplemented
216#389C22×C318yescomplemented
217#388C22×C318yescomplemented
218#387C22×C318yescomplemented
219#386C22×C318yescomplemented
220#380C22×C318yescomplemented
221C2×#95C22×C311yescharacteristic
222C2×#95C22×C311yescharacteristic
223C2×#95C22×C311yescharacteristic
224C2×#95C22×C311yescharacteristic
225C2×#95C22×C311yescharacteristic
226C2×#95C22×C311yescharacteristic
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3—22no—
231C24×C3—22no—
232C24×C3—22no—
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3—22no—
240C24×C3—22no—
241C24×C3—22no—
242C24×C3—22no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3#4114yes—
248C24×C3C2412yes—
249C24×C3C2412yes—
250C24×C3C2412yes—
251C24×C3C2411yescharacteristic
252C2×C3×D4—28no—
253C2×C3×D4—28no—
254C2×C3×D4—28no—
255C2×C3×D4—28no—
256C2×C3×D4—44no—
257C2×C3×D4—44no—
258C2×C3×D4—44no—
259C2×C3×D4—44no—
260C2×C3×D4—44no—
261C2×C3×D4—416no—
262C2×C3×D4—416no—
263C2×C3×D4—416no—
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—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—28no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—22no—
297C22×C3×C4—28no—
298C22×C3×C4—44no—
299C22×C3×C4—416no—
300C22×C3×C4C2×D414yes—
301C22×C3×C4C2×D414yes—
302C22×C3×C4C2×D414yes—
303C22×C3×C4#4114yes—
304C22×C3×C4C2412yes—
305C22×C3×C4C2412yes—
306C22×C3×C4C2412yes—
307C22×C3×C4C2412yes—
308C22×C3×C4C2412yes—
309C22×C3×C4C2412yes—
310C22×C3×C4C2412yes—
311C22×C3×C4C2412yes—
312C22×C3×C4C2412yes—
313C22×C3×C4C2412yes—
314C22×C3×C4C2412yes—
315C22×C3×C4C2412yes—
316C3×C4⋊C4—28no—
317C3×C4⋊C4—28no—
318C3×C4⋊C4—28no—
319C3×C4⋊C4—28no—
320C3×C4⋊C4—44no—
321C3×C4⋊C4—44no—
322C3×C4⋊C4—44no—
323C3×C4⋊C4—44no—
324C3×C4⋊C4C2×D4116yescomplemented
325C3×C22⋊C4—28no—
326C3×C22⋊C4—28no—
327C3×C22⋊C4—28no—
328C3×C22⋊C4—28no—
329C3×C22⋊C4—28no—
330C3×C22⋊C4—28no—
331C3×C22⋊C4—28no—
332C3×C22⋊C4—44no—
333C3×C22⋊C4—44no—
334C3×C22⋊C4—44no—
335C3×C22⋊C4—44no—
336C3×C22⋊C4—44no—
337C3×C22⋊C4—44no—
338C3×C22⋊C4—44no—
339C3×C42—28no—
340C3×C42—44no—
341C25C23×C311yescharacteristic
342C25C23×C311yescharacteristic
343C25C23×C311yescharacteristic
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4C23×C314yes—
354C22×D4C23×C314yes—
355C22×D4C23×C314yes—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—42no—
359C23×C4C23×C311yescharacteristic
360C23×C4C23×C311yescharacteristic
361C23×C4C23×C311yescharacteristic
362C23×C4C23×C311yescharacteristic
363C23×C4C23×C311yescharacteristic
364C23×C4C23×C311yescharacteristic
365C23×C4C23×C311yescharacteristic
366C23×C4C23×C311yescharacteristic
367C23×C4C23×C314yes—
368C23×C4C23×C311yescharacteristic
369C23×C4C23×C311yescharacteristic
370C23×C4C23×C311yescharacteristic
371C23×C4C23×C311yescharacteristic
372#126—232no—
373#123—232no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4C3×D418yescomplemented
383C2×C4⋊C4C23×C314yes—
384C2×C4⋊C4C23×C314yes—
385C2×C4⋊C4C23×C314yes—
386C2×C4⋊C4C23×C314yes—
387C2×C4⋊C4C23×C314yes—
388C2×C4⋊C4C23×C314yes—
389C2×C4⋊C4C23×C314yes—
390C2×C4⋊C4C23×C314yes—
391C2×C4⋊C4C23×C314yes—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4C23×C314yes—
407C2×C22⋊C4C23×C314yes—
408C2×C22⋊C4C23×C314yes—
409C2×C22⋊C4C23×C314yes—
410C2×C22⋊C4C23×C314yes—
411C2×C22⋊C4C23×C314yes—
412C2×C22⋊C4C23×C314yes—
413C2×C22⋊C4C23×C314yes—
414C2×C22⋊C4C23×C314yes—
415C2×C22⋊C4C23×C314yes—
416C2×C22⋊C4C23×C314yes—
417C2×C22⋊C4C23×C314yes—
418C2×C22⋊C4C23×C314yes—
419C2×C22⋊C4C23×C314yes—
420C2×C42—24no—
421C2×C42—42no—
422C2×C42C23×C314yes—
423C2×C42C23×C314yes—
424#95C23×C314yes—
425#95C23×C314yes—
426#95C23×C314yes—
427#95C23×C314yes—
428#95C23×C314yes—
429#95C23×C314yes—
430C23×C3—28no—
431C23×C3—28no—
432C23×C3—28no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—44no—
454C23×C3—44no—
455C23×C3—44no—
456C23×C3—44no—
457C23×C3—44no—
458C23×C3—44no—
459C23×C3—44no—
460C23×C3—44no—
461C23×C3—44no—
462C23×C3—44no—
463C23×C3—44no—
464C23×C3—44no—
465C23×C3—44no—
466C23×C3—44no—
467C23×C3—44no—
468C23×C3—44no—
469C23×C3—44no—
470C23×C3—44no—
471C23×C3C22×D412yes—
472C23×C3C2×#4114yes—
473C23×C3C2×#4112yes—
474C23×C3C2×#4112yes—
475C23×C3H(5,𝔽2)12yes—
476C23×C3H(5,𝔽2)12yes—
477C23×C3H(5,𝔽2)12yes—
478C23×C32−1+412yes—
479C23×C3C2511yescharacteristic
480C3×D4—416no—
481C3×D4—416no—
482C3×D4—416no—
483C2×C3×C4—28no—
484C2×C3×C4—28no—
485C2×C3×C4—28no—
486C2×C3×C4—28no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—416no—
520C2×C3×C4—44no—
521C2×C3×C4—44no—
522C2×C3×C4—44no—
523C2×C3×C4—44no—
524C2×C3×C4—44no—
525C2×C3×C4—44no—
526C2×C3×C4—44no—
527C2×C3×C4—44no—
528C2×C3×C4C22×D414yes—
529C2×C3×C4C22×D414yes—
530C2×C3×C4C22×D414yes—
531C2×C3×C4C2×#4114yes—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24C3×#4114yes—
553C24C24×C312yes—
554C24C24×C312yes—
555C24C24×C312yes—
556C24C24×C311yescharacteristic
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4—44no—
566C2×D4—416no—
567C2×D4—416no—
568C2×D4—416no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—28no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—28no—
603C22×C4—44no—
604C22×C4—416no—
605C22×C4C2×C3×D414yes—
606C22×C4C2×C3×D414yes—
607C22×C4C2×C3×D414yes—
608C22×C4C3×#4114yes—
609C22×C4C24×C312yes—
610C22×C4C24×C312yes—
611C22×C4C24×C312yes—
612C22×C4C24×C312yes—
613C22×C4C24×C312yes—
614C22×C4C24×C312yes—
615C22×C4C24×C312yes—
616C22×C4C24×C312yes—
617C22×C4C24×C312yes—
618C22×C4C24×C312yes—
619C22×C4C24×C312yes—
620C22×C4C24×C312yes—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4C2×C3×D4116yescomplemented
630C22⋊C4—28no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—28no—
635C22⋊C4—28no—
636C22⋊C4—28no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C42—28no—
645C42—44no—
646C22×C3—24no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—416no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—88no—
669C22×C3—88no—
670C22×C3#53714yes—
671C22×C3#53914yes—
672C22×C3#54214yes—
673C22×C3#54614yes—
674C22×C3#55014yes—
675C22×C3#55114yes—
676C22×C3#56014yes—
677C22×C3C23×D411yescharacteristic
678C22×C3C22×#4111yescharacteristic
679C22×C3C22×#4111yescharacteristic
680C22×C3C2×H(5,𝔽2)11yescharacteristic
681C22×C3C2×H(5,𝔽2)11yescharacteristic
682C22×C3C2×H(5,𝔽2)11yescharacteristic
683C22×C3C2×2−1+411yescharacteristic
684C3×C4—24no—
685C3×C4—24no—
686C3×C4—24no—
687C3×C4—24no—
688C3×C4—42no—
689C3×C4—42no—
690C3×C4—42no—
691C3×C4—42no—
692C3×C4—42no—
693C3×C4—42no—
694C3×C4—42no—
695C3×C4—42no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—28no—
703C23—28no—
704C23—28no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23C22×C3×D412yes—
738C23C2×C3×#4114yes—
739C23C2×C3×#4112yes—
740C23C2×C3×#4112yes—
741C23C3×H(5,𝔽2)12yes—
742C23C3×H(5,𝔽2)12yes—
743C23C3×H(5,𝔽2)12yes—
744C23C3×2−1+412yes—
745C23C25×C311yescharacteristic
746D4—416no—
747D4—416no—
748D4—416no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—28no—
758C2×C4—28no—
759C2×C4—28no—
760C2×C4—28no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—416no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4C22×C3×D414yes—
795C2×C4C22×C3×D414yes—
796C2×C4C22×C3×D414yes—
797C2×C4C2×C3×#4114yes—
798C2×C3—44no—
799C2×C3—82no—
800C2×C3—82no—
801C2×C3#270518yesdirect product factor
802C2×C3C2×#53711yescharacteristic
803C2×C3C2×#53911yescharacteristic
804C2×C3C2×#54211yescharacteristic
805C2×C3C2×#54611yescharacteristic
806C2×C3C2×#55011yescharacteristic
807C2×C3C2×#55111yescharacteristic
808C2×C3C2×#56011yescharacteristic
809C22—24no—
810C22—24no—
811C22—24no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—416no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—88no—
832C22—88no—
833C22C3×#53714yes—
834C22C3×#53914yes—
835C22C3×#54214yes—
836C22C3×#54614yes—
837C22C3×#55014yes—
838C22C3×#55114yes—
839C22C3×#56014yes—
840C22C23×C3×D411yescharacteristic
841C22C22×C3×#4111yescharacteristic
842C22C22×C3×#4111yescharacteristic
843C22C2×C3×H(5,𝔽2)11yescharacteristic
844C22C2×C3×H(5,𝔽2)11yescharacteristic
845C22C2×C3×H(5,𝔽2)11yescharacteristic
846C22C2×C3×2−1+411yescharacteristic
847C4—24no—
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C3C2×#270511yescharacteristic, direct product factor, Sylow
860C2—44no—
861C2—82no—
862C2—82no—
863C2C3×#270518yesdirect product factor
864C2C2×C3×#53711yescharacteristic
865C2C2×C3×#53911yescharacteristic
866C2C2×C3×#54211yescharacteristic
867C2C2×C3×#54611yescharacteristic
868C2C2×C3×#55011yescharacteristic
869C2C2×C3×#55111yescharacteristic
870C2C2×C3×#56011yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC23C25×C3
prime radicalC2×C3×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#126C2semidirect
2. C22×C3×#123C2semidirect
3. C3×#2705C2direct (N × H)
4. C2×C3×#399C2semidirect
5. C2×C3×#396C2semidirect
6. C2×C3×#396C2semidirect
7. C2×C3×#394C2semidirect
8. C2×C3×#394C2semidirect
10. C2×C3×#390C2semidirect
11. C2×C3×#390C2semidirect
12. C2×C3×#389C2semidirect
13. C2×C3×#388C2semidirect
14. C2×C3×#387C2semidirect
15. C2×C3×#386C2semidirect
16. C2×C3×#380C2semidirect
17. C2×#2705C3direct (N × H)
23. C2×C3×#126C22semidirect
25. C2×C3×#123C22semidirect
51. C3×#399C22semidirect
52. C3×#396C22semidirect
53. C3×#396C22semidirect
54. C3×#394C22semidirect
55. C3×#394C22semidirect
57. C3×#390C22semidirect
58. C3×#390C22semidirect
59. C3×#389C22semidirect
60. C3×#388C22semidirect
61. C3×#387C22semidirect
62. C3×#386C22semidirect
63. C3×#380C22semidirect
70. C22×#126C2×C3semidirect
71. C22×#123C2×C3semidirect
72. #2705C2×C3direct (N × H)
73. C2×#399C2×C3semidirect
74. C2×#396C2×C3semidirect
75. C2×#396C2×C3semidirect
76. C2×#394C2×C3semidirect
77. C2×#394C2×C3semidirect
79. C2×#390C2×C3semidirect
80. C2×#390C2×C3semidirect
81. C2×#389C2×C3semidirect
82. C2×#388C2×C3semidirect
83. C2×#387C2×C3semidirect
84. C2×#386C2×C3semidirect
85. C2×#380C2×C3semidirect
127. C2×C3×C4⋊C4D4semidirect
180. C2×#126C22×C3semidirect
182. C2×#123C22×C3semidirect
208. #399C22×C3semidirect
209. #396C22×C3semidirect
210. #396C22×C3semidirect
211. #394C22×C3semidirect
212. #394C22×C3semidirect
214. #390C22×C3semidirect
215. #390C22×C3semidirect
216. #389C22×C3semidirect
217. #388C22×C3semidirect
218. #387C22×C3semidirect
219. #386C22×C3semidirect
220. #380C22×C3semidirect
324. C3×C4⋊C4C2×D4semidirect
382. C2×C4⋊C4C3×D4semidirect
629. C4⋊C4C2×C3×D4semidirect
801. C2×C3#2705direct (N × H)
859. C3C2×#2705direct (N × H)
863. C2C3×#2705direct (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×#1232
C3×#27052
C2×C3×#3992
C2×C3×#3962
C2×C3×#3942
C2×C3×#3922
C2×C3×#3902
C2×C3×#3892
C2×C3×#3882
C2×C3×#3872
C2×C3×#3862
C2×C3×#3802
C2×#27053