Finite Group Databasebeta

← C2×C3×#2703 #10670731

Subgroups — C2×C3×#2703 #10670731

Order 768.

3542 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic, complemented
2C22×C3×#121C211yesmaximal, characteristic, complemented
3C3×#2703C2116yesmaximal, direct product factor
4C2×C3×#400C211yesmaximal, characteristic, complemented
5C2×C3×#397C211yesmaximal, characteristic, complemented
6C2×C3×#394C211yesmaximal, characteristic, complemented
7C2×C3×#392C211yesmaximal, characteristic, complemented
8C2×C3×#392C211yesmaximal, characteristic, complemented
9C2×C3×#392C211yesmaximal, characteristic, complemented
10C2×C3×#390C211yesmaximal, characteristic, complemented
11C2×C3×#388C211yesmaximal, characteristic, complemented
12C2×C3×#388C211yesmaximal, characteristic, complemented
13C2×C3×#386C211yesmaximal, characteristic, complemented
14C2×C3×#386C211yesmaximal, characteristic, complemented
15C2×C3×#386C211yesmaximal, characteristic, complemented
16C2×C3×#380C211yesmaximal, characteristic, complemented
17C2×#2703C311yesmaximal, characteristic, direct product factor, Sylow
18C23×C3×D4C2211yescharacteristic
19C23×C3×D4C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C23×C3×D4C2211yescharacteristic
22C23×C3×D4C2211yescharacteristic
23C23×C3×D4C2211yescharacteristic
24C24×C3×C4C2211yescharacteristic
25C24×C3×C4C2211yescharacteristic
26C2×C3×#123—28no—
27C2×C3×#123C2218yescomplemented
28C2×C3×#121—28no—
29C2×C3×#121C2218yescomplemented
30C22×C3×C4⋊C4C2211yescharacteristic
31C22×C3×C4⋊C4C2211yescharacteristic
32C22×C3×C4⋊C4C2211yescharacteristic
33C22×C3×C4⋊C4C2211yescharacteristic
34C22×C3×C22⋊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×C42C2211yescharacteristic
49C3×#400C2218yescomplemented
50C3×#397C2218yescomplemented
51C3×#394C2218yescomplemented
52C3×#392C2218yescomplemented
53C3×#392C2218yescomplemented
54C3×#392C2218yescomplemented
55C3×#390C2218yescomplemented
56C3×#388C2218yescomplemented
57C3×#388C2218yescomplemented
58C3×#386C2218yescomplemented
59C3×#386C2218yescomplemented
60C3×#386C2218yescomplemented
61C3×#380C2218yescomplemented
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×#123C2×C311yescharacteristic, complemented
71C22×#121C2×C311yescharacteristic, complemented
72#2703C2×C3116yesdirect product factor
73C2×#400C2×C311yescharacteristic, complemented
74C2×#397C2×C311yescharacteristic, complemented
75C2×#394C2×C311yescharacteristic, complemented
76C2×#392C2×C311yescharacteristic, complemented
77C2×#392C2×C311yescharacteristic, complemented
78C2×#392C2×C311yescharacteristic, complemented
79C2×#390C2×C311yescharacteristic, complemented
80C2×#388C2×C311yescharacteristic, complemented
81C2×#388C2×C311yescharacteristic, complemented
82C2×#386C2×C311yescharacteristic, complemented
83C2×#386C2×C311yescharacteristic, complemented
84C2×#386C2×C311yescharacteristic, complemented
85C2×#380C2×C311yescharacteristic, complemented
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C25×C3C2311yescharacteristic
89C25×C3C2311yescharacteristic
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—24no—
93C22×C3×D4—24no—
94C22×C3×D4—24no—
95C22×C3×D4—24no—
96C22×C3×D4—24no—
97C22×C3×D4—24no—
98C22×C3×D4—42no—
99C22×C3×D4—42no—
100C22×C3×D4—42no—
101C22×C3×D4—42no—
102C22×C3×D4—42no—
103C22×C3×D4—42no—
104C22×C3×D4—42no—
105C22×C3×D4—42no—
106C22×C3×D4—42no—
107C22×C3×D4—42no—
108C22×C3×D4C2314yes—
109C22×C3×D4C2314yes—
110C22×C3×D4C2314yes—
111C22×C3×D4C2314yes—
112C22×C3×D4C2314yes—
113C22×C3×D4C2314yes—
114C23×C3×C4—24no—
115C23×C3×C4—24no—
116C23×C3×C4—24no—
117C23×C3×C4—42no—
118C23×C3×C4—42no—
119C23×C3×C4—42no—
120C23×C3×C4C2311yescharacteristic
121C23×C3×C4C2311yescharacteristic
122C23×C3×C4C2311yescharacteristic
123C23×C3×C4C2311yescharacteristic
124C23×C3×C4C2311yescharacteristic
125C23×C3×C4C2311yescharacteristic
126C23×C3×C4C2311yescharacteristic
127C23×C3×C4C2311yescharacteristic
128C23×C3×C4C2314yes—
129C23×C3×C4C2311yescharacteristic
130C23×C3×C4C2311yescharacteristic
131C23×C3×C4C2311yescharacteristic
132C23×C3×C4C2314yes—
133C3×#123—232no—
134C3×#121—232no—
135C2×C3×C4⋊C4—24no—
136C2×C3×C4⋊C4—24no—
137C2×C3×C4⋊C4—24no—
138C2×C3×C4⋊C4—42no—
139C2×C3×C4⋊C4C2314yes—
140C2×C3×C4⋊C4C2314yes—
141C2×C3×C4⋊C4C2314yes—
142C2×C3×C4⋊C4C2314yes—
143C2×C3×C22⋊C4—24no—
144C2×C3×C22⋊C4—24no—
145C2×C3×C22⋊C4—24no—
146C2×C3×C22⋊C4—24no—
147C2×C3×C22⋊C4—42no—
148C2×C3×C22⋊C4—42no—
149C2×C3×C22⋊C4—42no—
150C2×C3×C22⋊C4—42no—
151C2×C3×C22⋊C4—42no—
152C2×C3×C22⋊C4—42no—
153C2×C3×C22⋊C4—42no—
154C2×C3×C22⋊C4—42no—
155C2×C3×C22⋊C4—42no—
156C2×C3×C22⋊C4D418yescomplemented
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×C22⋊C4C2314yes—
166C2×C3×C22⋊C4C2314yes—
167C2×C3×C22⋊C4C2314yes—
168C2×C3×C22⋊C4C2314yes—
169C2×C3×C22⋊C4C2314yes—
170C2×C3×C22⋊C4C2314yes—
171C2×C3×C42—42no—
172C2×C3×C42C2314yes—
173C3×#95C2314yes—
174C3×#95C2314yes—
175C3×#95C2314yes—
176C3×#95C2314yes—
177C3×#95C2314yes—
178C3×#95C2314yes—
179C3×#95C2314yes—
180C3×#95C2314yes—
181C23×D4C22×C311yescharacteristic
182C23×D4C22×C311yescharacteristic
183C23×D4C22×C311yescharacteristic
184C23×D4C22×C311yescharacteristic
185C23×D4C22×C311yescharacteristic
186C23×D4C22×C311yescharacteristic
187C24×C4C22×C311yescharacteristic
188C24×C4C22×C311yescharacteristic
189C2×#123—28no—
190C2×#123C22×C318yescomplemented
191C2×#121—28no—
192C2×#121C22×C318yescomplemented
193C22×C4⋊C4C22×C311yescharacteristic
194C22×C4⋊C4C22×C311yescharacteristic
195C22×C4⋊C4C22×C311yescharacteristic
196C22×C4⋊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×C22⋊C4C22×C311yescharacteristic
207C22×C22⋊C4C22×C311yescharacteristic
208C22×C22⋊C4C22×C311yescharacteristic
209C22×C22⋊C4C22×C311yescharacteristic
210C22×C22⋊C4C22×C311yescharacteristic
211C22×C42C22×C311yescharacteristic
212#400C22×C318yescomplemented
213#397C22×C318yescomplemented
214#394C22×C318yescomplemented
215#392C22×C318yescomplemented
216#392C22×C318yescomplemented
217#392C22×C318yescomplemented
218#390C22×C318yescomplemented
219#388C22×C318yescomplemented
220#388C22×C318yescomplemented
221#386C22×C318yescomplemented
222#386C22×C318yescomplemented
223#386C22×C318yescomplemented
224#380C22×C318yescomplemented
225C2×#95C22×C311yescharacteristic
226C2×#95C22×C311yescharacteristic
227C2×#95C22×C311yescharacteristic
228C2×#95C22×C311yescharacteristic
229C2×#95C22×C311yescharacteristic
230C2×#95C22×C311yescharacteristic
231C2×#95C22×C311yescharacteristic
232C2×#95C22×C311yescharacteristic
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—22no—
248C24×C3—22no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—22no—
252C24×C3—22no—
253C24×C3—22no—
254C24×C3—22no—
255C24×C3—22no—
256C24×C3—22no—
257C24×C3—22no—
258C24×C3—22no—
259C24×C3C2×D414yes—
260C24×C3#4114yes—
261C24×C3C2412yes—
262C24×C3C2412yes—
263C24×C3C2412yes—
264C24×C3C2412yes—
265C24×C3C2411yescharacteristic
266C2×C3×D4—28no—
267C2×C3×D4—28no—
268C2×C3×D4—28no—
269C2×C3×D4—28no—
270C2×C3×D4—28no—
271C2×C3×D4—28no—
272C2×C3×D4—28no—
273C2×C3×D4—28no—
274C2×C3×D4—44no—
275C2×C3×D4—44no—
276C2×C3×D4—44no—
277C2×C3×D4—44no—
278C2×C3×D4—44no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—44no—
283C2×C3×D4—44no—
284C2×C3×D4—416no—
285C2×C3×D4—416no—
286C2×C3×D4—416no—
287C2×C3×D4—416no—
288C2×C3×D4—416no—
289C2×C3×D4—416no—
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—22no—
298C22×C3×C4—22no—
299C22×C3×C4—22no—
300C22×C3×C4—28no—
301C22×C3×C4—22no—
302C22×C3×C4—22no—
303C22×C3×C4—22no—
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—22no—
315C22×C3×C4—22no—
316C22×C3×C4—22no—
317C22×C3×C4—22no—
318C22×C3×C4—22no—
319C22×C3×C4—22no—
320C22×C3×C4—22no—
321C22×C3×C4—28no—
322C22×C3×C4—28no—
323C22×C3×C4—44no—
324C22×C3×C4—44no—
325C22×C3×C4—44no—
326C22×C3×C4—416no—
327C22×C3×C4—416no—
328C22×C3×C4C2×D414yes—
329C22×C3×C4C2×D414yes—
330C22×C3×C4#4114yes—
331C22×C3×C4C2412yes—
332C22×C3×C4C2412yes—
333C22×C3×C4C2412yes—
334C22×C3×C4C2412yes—
335C22×C3×C4C2412yes—
336C22×C3×C4C2412yes—
337C22×C3×C4C2412yes—
338C22×C3×C4C2412yes—
339C22×C3×C4C2412yes—
340C22×C3×C4C2412yes—
341C22×C3×C4C2412yes—
342C3×C4⋊C4—28no—
343C3×C4⋊C4—28no—
344C3×C4⋊C4—28no—
345C3×C4⋊C4—44no—
346C3×C22⋊C4—28no—
347C3×C22⋊C4—28no—
348C3×C22⋊C4—28no—
349C3×C22⋊C4—28no—
350C3×C22⋊C4—44no—
351C3×C22⋊C4—44no—
352C3×C22⋊C4—44no—
353C3×C22⋊C4—44no—
354C3×C22⋊C4—44no—
355C3×C22⋊C4—44no—
356C3×C22⋊C4—44no—
357C3×C22⋊C4—44no—
358C3×C22⋊C4—44no—
359C3×C22⋊C4C2×D4116yescomplemented
360C3×C42—44no—
361C25C23×C311yescharacteristic
362C25C23×C311yescharacteristic
363C25C23×C311yescharacteristic
364C25C23×C311yescharacteristic
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—24no—
369C22×D4—24no—
370C22×D4—24no—
371C22×D4—24no—
372C22×D4—24no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4C23×C314yes—
384C22×D4C23×C314yes—
385C22×D4C23×C314yes—
386C22×D4C23×C314yes—
387C22×D4C23×C314yes—
388C22×D4C23×C314yes—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4C23×C311yescharacteristic
396C23×C4C23×C311yescharacteristic
397C23×C4C23×C311yescharacteristic
398C23×C4C23×C311yescharacteristic
399C23×C4C23×C311yescharacteristic
400C23×C4C23×C311yescharacteristic
401C23×C4C23×C311yescharacteristic
402C23×C4C23×C311yescharacteristic
403C23×C4C23×C314yes—
404C23×C4C23×C311yescharacteristic
405C23×C4C23×C311yescharacteristic
406C23×C4C23×C311yescharacteristic
407C23×C4C23×C314yes—
408#123—232no—
409#121—232no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4C23×C314yes—
415C2×C4⋊C4C23×C314yes—
416C2×C4⋊C4C23×C314yes—
417C2×C4⋊C4C23×C314yes—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4C3×D418yescomplemented
432C2×C22⋊C4C23×C314yes—
433C2×C22⋊C4C23×C314yes—
434C2×C22⋊C4C23×C314yes—
435C2×C22⋊C4C23×C314yes—
436C2×C22⋊C4C23×C314yes—
437C2×C22⋊C4C23×C314yes—
438C2×C22⋊C4C23×C314yes—
439C2×C22⋊C4C23×C314yes—
440C2×C22⋊C4C23×C314yes—
441C2×C22⋊C4C23×C314yes—
442C2×C22⋊C4C23×C314yes—
443C2×C22⋊C4C23×C314yes—
444C2×C22⋊C4C23×C314yes—
445C2×C22⋊C4C23×C314yes—
446C2×C42—42no—
447C2×C42C23×C314yes—
448#95C23×C314yes—
449#95C23×C314yes—
450#95C23×C314yes—
451#95C23×C314yes—
452#95C23×C314yes—
453#95C23×C314yes—
454#95C23×C314yes—
455#95C23×C314yes—
456C23×C3—28no—
457C23×C3—28no—
458C23×C3—28no—
459C23×C3—28no—
460C23×C3—28no—
461C23×C3—28no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—44no—
489C23×C3—44no—
490C23×C3—44no—
491C23×C3—44no—
492C23×C3—44no—
493C23×C3—44no—
494C23×C3—44no—
495C23×C3—44no—
496C23×C3—44no—
497C23×C3—44no—
498C23×C3—44no—
499C23×C3—44no—
500C23×C3—44no—
501C23×C3—44no—
502C23×C3—44no—
503C23×C3—44no—
504C23×C3—44no—
505C23×C3—44no—
506C23×C3—44no—
507C23×C3—44no—
508C23×C3—44no—
509C23×C3—44no—
510C23×C3C22×D414yes—
511C23×C3C22×D412yes—
512C23×C3C2×#4114yes—
513C23×C3C2×#4112yes—
514C23×C3C2×#4112yes—
515C23×C3H(5,𝔽2)12yes—
516C23×C3H(5,𝔽2)12yes—
517C23×C3H(5,𝔽2)12yes—
518C23×C3H(5,𝔽2)12yes—
519C23×C3C2511yescharacteristic
520C3×D4—416no—
521C3×D4—416no—
522C3×D4—416no—
523C3×D4—416no—
524C3×D4—416no—
525C3×D4—416no—
526C2×C3×C4—28no—
527C2×C3×C4—28no—
528C2×C3×C4—28no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—416no—
560C2×C3×C4—416no—
561C2×C3×C4—44no—
562C2×C3×C4—44no—
563C2×C3×C4—44no—
564C2×C3×C4—44no—
565C2×C3×C4—44no—
566C2×C3×C4—44no—
567C2×C3×C4—44no—
568C2×C3×C4—44no—
569C2×C3×C4C22×D414yes—
570C2×C3×C4C22×D414yes—
571C2×C3×C4C2×#4114yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24C2×C3×D414yes—
599C24C3×#4114yes—
600C24C24×C312yes—
601C24C24×C312yes—
602C24C24×C312yes—
603C24C24×C312yes—
604C24C24×C311yescharacteristic
605C2×D4—28no—
606C2×D4—28no—
607C2×D4—28no—
608C2×D4—28no—
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—44no—
622C2×D4—44no—
623C2×D4—416no—
624C2×D4—416no—
625C2×D4—416no—
626C2×D4—416no—
627C2×D4—416no—
628C2×D4—416no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—28no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—28no—
661C22×C4—28no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—416no—
666C22×C4—416no—
667C22×C4C2×C3×D414yes—
668C22×C4C2×C3×D414yes—
669C22×C4C3×#4114yes—
670C22×C4C24×C312yes—
671C22×C4C24×C312yes—
672C22×C4C24×C312yes—
673C22×C4C24×C312yes—
674C22×C4C24×C312yes—
675C22×C4C24×C312yes—
676C22×C4C24×C312yes—
677C22×C4C24×C312yes—
678C22×C4C24×C312yes—
679C22×C4C24×C312yes—
680C22×C4C24×C312yes—
681C4⋊C4—28no—
682C4⋊C4—28no—
683C4⋊C4—28no—
684C4⋊C4—44no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—28no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4C2×C3×D4116yescomplemented
699C42—44no—
700C22×C3—24no—
701C22×C3—24no—
702C22×C3—24no—
703C22×C3—24no—
704C22×C3—24no—
705C22×C3—24no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—416no—
712C22×C3—416no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—42no—
724C22×C3—42no—
725C22×C3—42no—
726C22×C3—42no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—88no—
731C22×C3—88no—
732C22×C3#53514yes—
733C22×C3#53814yes—
734C22×C3#54014yes—
735C22×C3#54614yes—
736C22×C3#54614yes—
737C22×C3#55314yes—
738C22×C3#56014yes—
739C22×C3C23×D411yescharacteristic
740C22×C3C22×#4111yescharacteristic
741C22×C3C22×#4111yescharacteristic
742C22×C3C2×H(5,𝔽2)11yescharacteristic
743C22×C3C2×H(5,𝔽2)11yescharacteristic
744C22×C3C2×H(5,𝔽2)11yescharacteristic
745C22×C3C2×H(5,𝔽2)11yescharacteristic
746C3×C4—24no—
747C3×C4—24no—
748C3×C4—24no—
749C3×C4—42no—
750C3×C4—42no—
751C3×C4—42no—
752C3×C4—42no—
753C3×C4—42no—
754C3×C4—42no—
755C3×C4—42no—
756C3×C4—42no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—28no—
770C23—28no—
771C23—28no—
772C23—28no—
773C23—28no—
774C23—28no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—44no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—44no—
800C23—44no—
801C23—44no—
802C23—44no—
803C23—44no—
804C23—44no—
805C23—44no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23C22×C3×D414yes—
812C23C22×C3×D412yes—
813C23C2×C3×#4114yes—
814C23C2×C3×#4112yes—
815C23C2×C3×#4112yes—
816C23C3×H(5,𝔽2)12yes—
817C23C3×H(5,𝔽2)12yes—
818C23C3×H(5,𝔽2)12yes—
819C23C3×H(5,𝔽2)12yes—
820C23C25×C311yescharacteristic
821D4—416no—
822D4—416no—
823D4—416no—
824D4—416no—
825D4—416no—
826D4—416no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—416no—
861C2×C4—416no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4C22×C3×D414yes—
871C2×C4C22×C3×D414yes—
872C2×C4C2×C3×#4114yes—
873C2×C3—44no—
874C2×C3—44no—
875C2×C3—82no—
876C2×C3—82no—
877C2×C3#270318yesdirect product factor
878C2×C3C2×#53511yescharacteristic
879C2×C3C2×#53811yescharacteristic
880C2×C3C2×#54011yescharacteristic
881C2×C3C2×#54611yescharacteristic
882C2×C3C2×#54611yescharacteristic
883C2×C3C2×#55311yescharacteristic
884C2×C3C2×#56011yescharacteristic
885C22—24no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—416no—
898C22—416no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—88no—
916C22—88no—
917C22C3×#53514yes—
918C22C3×#53814yes—
919C22C3×#54014yes—
920C22C3×#54614yes—
921C22C3×#54614yes—
922C22C3×#55314yes—
923C22C3×#56014yes—
924C22C23×C3×D411yescharacteristic
925C22C22×C3×#4111yescharacteristic
926C22C22×C3×#4111yescharacteristic
927C22C2×C3×H(5,𝔽2)11yescharacteristic
928C22C2×C3×H(5,𝔽2)11yescharacteristic
929C22C2×C3×H(5,𝔽2)11yescharacteristic
930C22C2×C3×H(5,𝔽2)11yescharacteristic
931C4—24no—
932C4—24no—
933C4—24no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—42no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—42no—
942C3C2×#270311yescharacteristic, direct product factor, Sylow
943C2—44no—
944C2—44no—
945C2—82no—
946C2—82no—
947C2C3×#270318yesdirect product factor
948C2C2×C3×#53511yescharacteristic
949C2C2×C3×#53811yescharacteristic
950C2C2×C3×#54011yescharacteristic
951C2C2×C3×#54611yescharacteristic
952C2C2×C3×#54611yescharacteristic
953C2C2×C3×#55311yescharacteristic
954C2C2×C3×#56011yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC23C25×C3
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
2. C22×C3×#121C2semidirect
3. C3×#2703C2direct (N × H)
4. C2×C3×#400C2semidirect
5. C2×C3×#397C2semidirect
6. C2×C3×#394C2semidirect
7. C2×C3×#392C2semidirect
8. C2×C3×#392C2semidirect
9. C2×C3×#392C2semidirect
10. C2×C3×#390C2semidirect
11. C2×C3×#388C2semidirect
12. C2×C3×#388C2semidirect
13. C2×C3×#386C2semidirect
14. C2×C3×#386C2semidirect
15. C2×C3×#386C2semidirect
16. C2×C3×#380C2semidirect
17. C2×#2703C3direct (N × H)
27. C2×C3×#123C22semidirect
29. C2×C3×#121C22semidirect
49. C3×#400C22semidirect
50. C3×#397C22semidirect
51. C3×#394C22semidirect
52. C3×#392C22semidirect
53. C3×#392C22semidirect
54. C3×#392C22semidirect
55. C3×#390C22semidirect
56. C3×#388C22semidirect
57. C3×#388C22semidirect
58. C3×#386C22semidirect
59. C3×#386C22semidirect
60. C3×#386C22semidirect
61. C3×#380C22semidirect
70. C22×#123C2×C3semidirect
71. C22×#121C2×C3semidirect
72. #2703C2×C3direct (N × H)
73. C2×#400C2×C3semidirect
74. C2×#397C2×C3semidirect
75. C2×#394C2×C3semidirect
76. C2×#392C2×C3semidirect
77. C2×#392C2×C3semidirect
78. C2×#392C2×C3semidirect
79. C2×#390C2×C3semidirect
80. C2×#388C2×C3semidirect
81. C2×#388C2×C3semidirect
82. C2×#386C2×C3semidirect
83. C2×#386C2×C3semidirect
84. C2×#386C2×C3semidirect
85. C2×#380C2×C3semidirect
156. C2×C3×C22⋊C4D4semidirect
190. C2×#123C22×C3semidirect
192. C2×#121C22×C3semidirect
212. #400C22×C3semidirect
213. #397C22×C3semidirect
214. #394C22×C3semidirect
215. #392C22×C3semidirect
216. #392C22×C3semidirect
217. #392C22×C3semidirect
218. #390C22×C3semidirect
219. #388C22×C3semidirect
220. #388C22×C3semidirect
221. #386C22×C3semidirect
222. #386C22×C3semidirect
223. #386C22×C3semidirect
224. #380C22×C3semidirect
359. C3×C22⋊C4C2×D4semidirect
431. C2×C22⋊C4C3×D4semidirect
698. C22⋊C4C2×C3×D4semidirect
877. C2×C3#2703direct (N × H)
942. C3C2×#2703direct (N × H)
947. C2C3×#2703direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×C3×#1212
C3×#27032
C2×C3×#4002
C2×C3×#3972
C2×C3×#3942
C2×C3×#3922
C2×C3×#3902
C2×C3×#3882
C2×C3×#3862
C2×C3×#3802
C2×#27033