Finite Group Databasebeta

← C3×#21875 #10640482

Subgroups — C3×#21875 #10640482

Order 768.

1158 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic
2C3×#2285C211yesmaximal, characteristic, complemented
3C3×#2283C211yesmaximal, characteristic, complemented
4C3×#1996C212yesmaximal, complemented
5C3×#1964C212yesmaximal
6C3×#1899C214yesmaximal, complemented
7C3×#1799C214yesmaximal, complemented
8#21875C311yesmaximal, characteristic, direct product factor, Sylow
9C3×#529—21no—
10C3×#529—21no—
11C3×#529—21no—
12C3×#529—21no—
13C3×#529—21no—
14C3×#529—21no—
15C3×#529—21no—
16C3×#529—21no—
17C2×C3×#126C412yescomplemented
18C2×C3×#125C411yescharacteristic, complemented
19C2×C3×#124C411yescharacteristic, complemented
20C2×C3×#123C2212yes—
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×C4×Q8C411yescharacteristic, complemented
24C2×C3×C4×D4C411yescharacteristic, complemented
25C2×C3×C4×D4C2212yes—
26C2×C3×#117C412yescomplemented
27C2×C3×#117C2212yes—
28C22×C3×C42C2211yescharacteristic
29C2×C3×#99C2218yes—
30C3×#384—21no—
31C3×#383—21no—
32C3×#382—21no—
33C3×#382—21no—
34C3×#381C2212yes—
35C3×#380C2212yes—
36C3×#380C2212yes—
37C3×#380C2212yes—
38C3×C4×C4⋊C4—21no—
39C3×C4×C4⋊C4—21no—
40C3×C4×C4⋊C4—21no—
41C3×C4×C22⋊C4C2212yes—
42C3×#376—21no—
43C3×#342C2218yes—
44C2×#529C2×C311yescharacteristic
45#2285C2×C311yescharacteristic, complemented
46#2283C2×C311yescharacteristic, complemented
47#1996C2×C312yescomplemented
48#1964C2×C312yes—
49#1899C2×C314yescomplemented
50#1799C2×C314yescomplemented
51C22×C3×Q8C2×C411yescharacteristic
52C22×C3×D4C2×C411yescharacteristic
53C22×C3×D4C2312yes—
54C23×C3×C4C2×C412yes—
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C3×#126—22no—
59C3×#126—22no—
60C3×#126—22no—
61C3×#126—22no—
62C3×#125—21no—
63C3×#125—21no—
64C3×#125—21no—
65C3×#125—21no—
66C3×#124—21no—
67C3×#124—21no—
68C3×#124—21no—
69C3×#124—21no—
70C3×#123—22no—
71C3×#123—22no—
72C3×#123—22no—
73C3×#123—22no—
74C3×C22⋊Q8—21no—
75C3×C22⋊Q8—21no—
76C3×C22⋊Q8—21no—
77C3×C22⋊Q8—21no—
78C3×#121—21no—
79C3×#121—21no—
80C3×#121—21no—
81C3×#121—21no—
82C3×C4×Q8—21no—
83C3×C4×Q8—21no—
84C3×C4×Q8—21no—
85C3×C4×Q8—21no—
86C3×C4×D4—22no—
87C3×C4×D4—22no—
88C3×C4×D4—22no—
89C3×C4×D4—22no—
90C3×C4×D4—21no—
91C3×C4×D4—21no—
92C3×C4×D4—21no—
93C3×C4×D4—21no—
94C3×#117—22no—
95C3×#117—22no—
96C3×#117—22no—
97C3×#117—22no—
98C3×#117—44no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4C2×C412yes—
104C2×C3×C4⋊C4C2×C412yes—
105C2×C3×C4⋊C4C2×C411yescharacteristic
106C2×C3×C4⋊C4C2×C412yes—
107C2×C3×C4⋊C4C2×C411yescharacteristic
108C2×C3×C4⋊C4C2×C412yes—
109C2×C3×C22⋊C4C2×C412yes—
110C2×C3×C22⋊C4C2×C412yes—
111C2×C3×C22⋊C4C2×C412yes—
112C2×C3×C22⋊C4C2×C412yes—
113C2×C3×C22⋊C4C2314yes—
114C2×C3×C22⋊C4C2314yes—
115C2×C3×C22⋊C4C2312yes—
116C2×C3×C42—22no—
117C2×C3×C42—22no—
118C2×C3×C42C2×C412yes—
119C2×C3×C42C2×C411yescharacteristic
120C2×C3×C42C2×C411yescharacteristic
121C2×C3×C42C2×C411yescharacteristic
122C2×C3×C42C2×C411yescharacteristic
123C2×C3×C42D411yescharacteristic
124C2×C3×C42D411yescharacteristic
125C2×C3×C42D411yescharacteristic
126C2×C3×C42D411yescharacteristic
127C2×C3×C42D411yescharacteristic
128C2×C3×C42D411yescharacteristic
129C2×C3×C42D411yescharacteristic
130C2×C3×C42D411yescharacteristic
131C3×#99—48no—
132C3×#95—22no—
133C3×#95—22no—
134C3×#95—22no—
135C3×#95—22no—
136C3×#95—22no—
137C3×#95—22no—
138#529—21no—
139#529—21no—
140#529—21no—
141#529—21no—
142#529—21no—
143#529—21no—
144#529—21no—
145#529—21no—
146C2×#126C3×C412yescomplemented
147C2×#125C3×C411yescharacteristic, complemented
148C2×#124C3×C411yescharacteristic, complemented
149C2×#123C22×C312yes—
150C2×C22⋊Q8C22×C311yescharacteristic
151C2×#121C22×C311yescharacteristic
152C2×C4×Q8C3×C411yescharacteristic, complemented
153C2×C4×D4C3×C411yescharacteristic, complemented
154C2×C4×D4C22×C312yes—
155C2×#117C3×C412yescomplemented
156C2×#117C22×C312yes—
157C22×C42C22×C311yescharacteristic
158C2×#99C22×C318yes—
159#384—21no—
160#383—21no—
161#382—21no—
162#382—21no—
163#381C22×C312yes—
164#380C22×C312yes—
165#380C22×C312yes—
166#380C22×C312yes—
167C4×C4⋊C4—21no—
168C4×C4⋊C4—21no—
169C4×C4⋊C4—21no—
170C4×C22⋊C4C22×C312yes—
171#376—21no—
172#342C22×C318yes—
173C24×C3C22×C412yes—
174C24×C3C2411yescharacteristic
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—42no—
178C2×C3×D4—22no—
179C2×C3×D4—22no—
180C2×C3×D4—24no—
181C2×C3×D4—24no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—42no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—24no—
190C22×C3×C4—24no—
191C22×C3×C4—42no—
192C22×C3×C4—42no—
193C22×C3×C4—44no—
194C22×C3×C4C22×C412yes—
195C22×C3×C4C22×C411yescharacteristic
196C22×C3×C4C22×C411yescharacteristic
197C22×C3×C4C22×C411yescharacteristic
198C22×C3×C4C22×C411yescharacteristic
199C22×C3×C4C22×C412yes—
200C22×C3×C4C22×C412yes—
201C22×C3×C4C22×C411yescharacteristic
202C22×C3×C4C22×C411yescharacteristic
203C22×C3×C4C2×D411yescharacteristic
204C22×C3×C4C2×D411yescharacteristic
205C22×C3×C4C2×D411yescharacteristic
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2×D411yescharacteristic
208C22×C3×C4C2×D411yescharacteristic
209C22×C3×C4C2×D411yescharacteristic
210C22×C3×C4C2×D411yescharacteristic
211C22×C3×C4C2×D411yescharacteristic
212C22×C3×C4C2×D411yescharacteristic
213C22×C3×C4C2×D411yescharacteristic
214C22×C3×C4C2×D411yescharacteristic
215C3×C4⋊C4—22no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—44no—
228C3×C4⋊C4—44no—
229C3×C4⋊C4—44no—
230C3×C4⋊C4—44no—
231C3×C22⋊C4—22no—
232C3×C22⋊C4—22no—
233C3×C22⋊C4—22no—
234C3×C22⋊C4—22no—
235C3×C22⋊C4—22no—
236C3×C22⋊C4—22no—
237C3×C22⋊C4—22no—
238C3×C22⋊C4—22no—
239C3×C22⋊C4—22no—
240C3×C22⋊C4—22no—
241C3×C22⋊C4—24no—
242C3×C22⋊C4—28no—
243C3×C22⋊C4—24no—
244C3×C42—22no—
245C3×C42—22no—
246C3×C42—44no—
247C3×C42—44no—
248C3×C42C22⋊C411yescharacteristic
249C3×C42C22⋊C411yescharacteristic
250C3×C42C22⋊C411yescharacteristic
251C3×C42C22⋊C411yescharacteristic
252C3×C42C22⋊C411yescharacteristic
253C3×C42C22⋊C411yescharacteristic
254C3×C42C22⋊C411yescharacteristic
255C3×C42C22⋊C411yescharacteristic
256C3×C42C22⋊C411yescharacteristic
257C3×C42C22⋊C411yescharacteristic
258C3×C42C22⋊C411yescharacteristic
259C3×C42C22⋊C411yescharacteristic
260C3×C42C22⋊C411yescharacteristic
261C3×C42C22⋊C411yescharacteristic
262C3×C42C22⋊C411yescharacteristic
263C3×C42C22⋊C411yescharacteristic
264C22×Q8C2×C3×C411yescharacteristic
265C22×D4C2×C3×C411yescharacteristic
266C22×D4C23×C312yes—
267C23×C4C2×C3×C412yes—
268C23×C4C23×C311yescharacteristic
269C23×C4C23×C311yescharacteristic
270C23×C4C23×C311yescharacteristic
271#126—22no—
272#126—22no—
273#126—22no—
274#126—22no—
275#125—21no—
276#125—21no—
277#125—21no—
278#125—21no—
279#124—21no—
280#124—21no—
281#124—21no—
282#124—21no—
283#123—22no—
284#123—22no—
285#123—22no—
286#123—22no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291#121—21no—
292#121—21no—
293#121—21no—
294#121—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×D4—22no—
300C4×D4—22no—
301C4×D4—22no—
302C4×D4—22no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4—21no—
307#117—22no—
308#117—22no—
309#117—22no—
310#117—22no—
311#117—44no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4C2×C3×C412yes—
317C2×C4⋊C4C2×C3×C412yes—
318C2×C4⋊C4C2×C3×C411yescharacteristic
319C2×C4⋊C4C2×C3×C412yes—
320C2×C4⋊C4C2×C3×C411yescharacteristic
321C2×C4⋊C4C2×C3×C412yes—
322C2×C22⋊C4C2×C3×C412yes—
323C2×C22⋊C4C2×C3×C412yes—
324C2×C22⋊C4C2×C3×C412yes—
325C2×C22⋊C4C2×C3×C412yes—
326C2×C22⋊C4C23×C314yes—
327C2×C22⋊C4C23×C314yes—
328C2×C22⋊C4C23×C312yes—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42C2×C3×C412yes—
332C2×C42C2×C3×C411yescharacteristic
333C2×C42C2×C3×C411yescharacteristic
334C2×C42C2×C3×C411yescharacteristic
335C2×C42C2×C3×C411yescharacteristic
336C2×C42C3×D411yescharacteristic
337C2×C42C3×D411yescharacteristic
338C2×C42C3×D411yescharacteristic
339C2×C42C3×D411yescharacteristic
340C2×C42C3×D411yescharacteristic
341C2×C42C3×D411yescharacteristic
342C2×C42C3×D411yescharacteristic
343C2×C42C3×D411yescharacteristic
344#99—48no—
345#95—22no—
346#95—22no—
347#95—22no—
348#95—22no—
349#95—22no—
350#95—22no—
351C23×C3—22no—
352C23×C3—24no—
353C23×C3—41no—
354C23×C3—41no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3C23×C411yescharacteristic
358C23×C3C22×D411yescharacteristic
359C23×C3C22×D411yescharacteristic
360C23×C3H(5,𝔽2)12yes—
361C23×C32−1+412yes—
362C3×Q8—42no—
363C3×Q8—42no—
364C3×D4—42no—
365C3×D4—42no—
366C3×D4—42no—
367C3×D4—44no—
368C3×D4—42no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—24no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—44no—
394C2×C3×C4—44no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—44no—
398C2×C3×C4—44no—
399C2×C3×C4—44no—
400C2×C3×C4—44no—
401C2×C3×C4—44no—
402C2×C3×C4—44no—
403C2×C3×C4C2×C22⋊C411yescharacteristic
404C2×C3×C4C2×C22⋊C411yescharacteristic
405C2×C3×C4C2×C22⋊C411yescharacteristic
406C2×C3×C4C2×C22⋊C411yescharacteristic
407C2×C3×C4C2×C22⋊C411yescharacteristic
408C2×C3×C4C2×C22⋊C411yescharacteristic
409C2×C3×C4C2×C22⋊C411yescharacteristic
410C2×C3×C4C2×C22⋊C411yescharacteristic
411C2×C3×C4C2×C22⋊C411yescharacteristic
412C2×C3×C4C2×C22⋊C411yescharacteristic
413C2×C3×C4C2×C22⋊C411yescharacteristic
414C2×C3×C4C2×C22⋊C411yescharacteristic
415C24C22×C3×C412yes—
416C24C24×C311yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—42no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—24no—
423C2×D4—24no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—42no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—44no—
436C22×C4C22×C3×C412yes—
437C22×C4C22×C3×C411yescharacteristic
438C22×C4C22×C3×C411yescharacteristic
439C22×C4C22×C3×C411yescharacteristic
440C22×C4C22×C3×C411yescharacteristic
441C22×C4C22×C3×C412yes—
442C22×C4C22×C3×C412yes—
443C22×C4C22×C3×C411yescharacteristic
444C22×C4C22×C3×C411yescharacteristic
445C22×C4C2×C3×D411yescharacteristic
446C22×C4C2×C3×D411yescharacteristic
447C22×C4C2×C3×D411yescharacteristic
448C22×C4C2×C3×D411yescharacteristic
449C22×C4C2×C3×D411yescharacteristic
450C22×C4C2×C3×D411yescharacteristic
451C22×C4C2×C3×D411yescharacteristic
452C22×C4C2×C3×D411yescharacteristic
453C22×C4C2×C3×D411yescharacteristic
454C22×C4C2×C3×D411yescharacteristic
455C22×C4C2×C3×D411yescharacteristic
456C22×C4C2×C3×D411yescharacteristic
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—44no—
470C4⋊C4—44no—
471C4⋊C4—44no—
472C4⋊C4—44no—
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—24no—
484C22⋊C4—28no—
485C22⋊C4—24no—
486C42—22no—
487C42—22no—
488C42—44no—
489C42—44no—
490C42C3×C22⋊C411yescharacteristic
491C42C3×C22⋊C411yescharacteristic
492C42C3×C22⋊C411yescharacteristic
493C42C3×C22⋊C411yescharacteristic
494C42C3×C22⋊C411yescharacteristic
495C42C3×C22⋊C411yescharacteristic
496C42C3×C22⋊C411yescharacteristic
497C42C3×C22⋊C411yescharacteristic
498C42C3×C22⋊C411yescharacteristic
499C42C3×C22⋊C411yescharacteristic
500C42C3×C22⋊C411yescharacteristic
501C42C3×C22⋊C411yescharacteristic
502C42C3×C22⋊C411yescharacteristic
503C42C3×C22⋊C411yescharacteristic
504C42C3×C22⋊C411yescharacteristic
505C42C3×C22⋊C411yescharacteristic
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—84no—
518C22×C3C22×C22⋊C411yescharacteristic
519C22×C3#52012yes—
520C22×C3#53511yescharacteristic
521C22×C3#53611yescharacteristic
522C22×C3#53712yes—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—42no—
534C3×C4—42no—
535C3×C4—42no—
536C3×C4—84no—
537C3×C4—84no—
538C3×C4#41012yes—
539C3×C4#41012yes—
540C23—22no—
541C23—24no—
542C23—41no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23C23×C3×C411yescharacteristic
547C23C22×C3×D411yescharacteristic
548C23C22×C3×D411yescharacteristic
549C23C3×H(5,𝔽2)12yes—
550C23C3×2−1+412yes—
551Q8—42no—
552Q8—42no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—44no—
557D4—42no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—44no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4C2×C3×C22⋊C411yescharacteristic
593C2×C4C2×C3×C22⋊C411yescharacteristic
594C2×C4C2×C3×C22⋊C411yescharacteristic
595C2×C4C2×C3×C22⋊C411yescharacteristic
596C2×C4C2×C3×C22⋊C411yescharacteristic
597C2×C4C2×C3×C22⋊C411yescharacteristic
598C2×C4C2×C3×C22⋊C411yescharacteristic
599C2×C4C2×C3×C22⋊C411yescharacteristic
600C2×C4C2×C3×C22⋊C411yescharacteristic
601C2×C4C2×C3×C22⋊C411yescharacteristic
602C2×C4C2×C3×C22⋊C411yescharacteristic
603C2×C4C2×C3×C22⋊C411yescharacteristic
604C2×C3—21no—
605C2×C3—22no—
606C2×C3—22no—
607C2×C3—21no—
608C2×C3—82no—
609C2×C3#231111yescharacteristic
610C2×C3C2×#41011yescharacteristic
611C2×C3C2×#41011yescharacteristic
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—84no—
624C22C22×C3×C22⋊C411yescharacteristic
625C22C3×#52012yes—
626C22C3×#53511yescharacteristic
627C22C3×#53611yescharacteristic
628C22C3×#53712yes—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—21no—
638C4—21no—
639C4—42no—
640C4—42no—
641C4—42no—
642C4—84no—
643C4—84no—
644C4C3×#41012yes—
645C4C3×#41012yes—
646C3#2187511yescharacteristic, direct product factor, Sylow
647C2—21no—
648C2—22no—
649C2—22no—
650C2—21no—
651C2—82no—
652C2C3×#231111yescharacteristic
653C2C2×C3×#41011yescharacteristic
654C2C2×C3×#41011yescharacteristic
subgroupG/H
center, socleC22×C3C22×C22⋊C4
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC2×C3×#121C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#2285C2semidirect
3. C3×#2283C2semidirect
4. C3×#1996C2semidirect
6. C3×#1899C2semidirect
7. C3×#1799C2semidirect
8. #21875C3direct (N × H)
17. C2×C3×#126C4semidirect
18. C2×C3×#125C4semidirect
19. C2×C3×#124C4semidirect
23. C2×C3×C4×Q8C4semidirect
24. C2×C3×C4×D4C4semidirect
26. C2×C3×#117C4semidirect
45. #2285C2×C3semidirect
46. #2283C2×C3semidirect
47. #1996C2×C3semidirect
49. #1899C2×C3semidirect
50. #1799C2×C3semidirect
146. C2×#126C3×C4semidirect
147. C2×#125C3×C4semidirect
148. C2×#124C3×C4semidirect
152. C2×C4×Q8C3×C4semidirect
153. C2×C4×D4C3×C4semidirect
155. C2×#117C3×C4semidirect
646. C3#21875direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C3×#22852
C3×#22832
C3×#19962
C3×#19642
C3×#18992
C3×#17992
#218753