Finite Group Databasebeta

← C3×#60146 #10678753

Subgroups — C3×#60146 #10678753

Order 768.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#568C211yesmaximal, characteristic, complemented
2C22×C3×#131C211yesmaximal, characteristic, complemented
3C3×D4×#41C211yesmaximal, characteristic
4C3×#2935C213yesmaximal, complemented
5C3×D4×M16C213yesmaximal, complemented
6C3×#2933C213yesmaximal, complemented
7C3×#2933C213yesmaximal, complemented
8C3×#2932C213yesmaximal, complemented
9C3×#2930C213yesmaximal, complemented
10C3×#2929C213yesmaximal, complemented
11C2×C3×#435C213yesmaximal, complemented
12C3×#2906C211yesmaximal, characteristic, complemented
13C3×#2880C211yesmaximal, characteristic, complemented
14C3×#2880C211yesmaximal, characteristic, complemented
15C3×#2875C211yesmaximal, characteristic, complemented
16#60146C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×#41C2211yescharacteristic
19C3×#568—28no—
20C2×C3×#131—28no—
21C2×C3×#131C2211yescharacteristic
22C2×C3×#131C2211yescharacteristic
23C2×C3×#131C2211yescharacteristic
24C2×C3×#131C2211yescharacteristic
25C2×C3×#131C2213yescomplemented
26C2×C3×#131C2213yescomplemented
27C2×C3×#131C2213yescomplemented
28C2×C3×#131C2213yescomplemented
29C22×C3×M16C2213yescomplemented
30C22×C3×M16C2213yescomplemented
31C22×C3×M16C2213yescomplemented
32C23×C3×C8C2213yescomplemented
33C3×#550C411yescharacteristic
34C3×D4×Q8C411yescharacteristic
35C3×#548C411yescharacteristic
36C3×#548C411yescharacteristic
37C3×#547C413yes—
38C3×#546C413yes—
39C3×#546C413yes—
40C3×D42C413yes—
41C3×#532C2213yes—
42C3×#525C2213yes—
43C3×#525C2213yes—
44C3×C4×#41C2211yescharacteristic
45C2×C3×C4×D4C2213yes—
46C3×#436C2216yescomplemented
47C3×#436C2216yescomplemented
48C3×#435C2211yescharacteristic
49C3×#435C2213yes—
50C3×#435C2213yescomplemented
51C3×#435C2213yescomplemented
52C3×#435C2213yescomplemented
53C3×#435C2213yescomplemented
54C3×#435C2213yescomplemented
55C3×#435C2213yescomplemented
56C3×#435C2216yescomplemented
57C3×#435C2216yescomplemented
58C3×#435C2216yescomplemented
59C3×C8×D4C2216yescomplemented
60C3×C8×D4C2216yescomplemented
61C3×#424C2213yescomplemented
62C3×#424C2213yescomplemented
63C3×#423C2213yescomplemented
64C2×C3×C4⋊C8C2213yescomplemented
65C3×#408C2213yescomplemented
66C3×#408C2213yescomplemented
67C3×#408C2213yescomplemented
68C3×#408C2213yescomplemented
69C3×#407C2213yescomplemented
70C3×#407C2213yescomplemented
71C2×C3×C22⋊C8C2213yescomplemented
72C2×C3×C22⋊C8C2213yescomplemented
73C3×#405C2213yescomplemented
74C3×#405C2213yescomplemented
75C3×C4×M16C2213yescomplemented
76C2×C3×#97C2213yescomplemented
77C2×#568C2×C311yescharacteristic, complemented
78C22×#131C2×C311yescharacteristic, complemented
79D4×#41C2×C311yescharacteristic
80#2935C2×C313yescomplemented
81D4×M16C2×C313yescomplemented
82#2933C2×C313yescomplemented
83#2933C2×C313yescomplemented
84#2932C2×C313yescomplemented
85#2930C2×C313yescomplemented
86#2929C2×C313yescomplemented
87C2×#435C2×C313yescomplemented
88#2906C2×C311yescharacteristic, complemented
89#2880C2×C311yescharacteristic, complemented
90#2880C2×C311yescharacteristic, complemented
91#2875C2×C311yescharacteristic, complemented
92C2×C3×#41—24no—
93C2×C3×#41—24no—
94C2×C3×#41—24no—
95C2×C3×#41—24no—
96C2×C3×#41C2×C413yes—
97C2×C3×#41C2×C413yes—
98C2×C3×#41C2×C411yescharacteristic
99C2×C3×#41C2×C411yescharacteristic
100C2×C3×#41C2313yes—
101C2×C3×#41C2313yes—
102C2×C3×#41C2311yescharacteristic
103C22×C3×Q8C2×C411yescharacteristic
104C22×C3×Q8C2×C411yescharacteristic
105C22×C3×D4C2×C413yes—
106C22×C3×D4C2×C413yes—
107C22×C3×D4C2×C413yes—
108C23×C3×C4C2313yes—
109C23×C3×C4C2313yes—
110C3×#131—24no—
111C3×#131—24no—
112C3×#131—24no—
113C3×#131—212no—
114C3×#131—212no—
115C3×#131—212no—
116C3×#131—212no—
117C3×#131D418yescomplemented
118C2×C3×M16—212no—
119C2×C3×M16—212no—
120C2×C3×M16—212no—
121C2×C3×M16C2311yescharacteristic
122C2×C3×M16C2313yes—
123C2×C3×M16C2313yes—
124C2×C3×M16C2313yes—
125C2×C3×M16C2313yes—
126C2×C3×M16C2313yes—
127C2×C3×M16C2316yes—
128C2×C3×M16C2313yes—
129C2×C3×M16C2313yes—
130C22×C3×C8—212no—
131C22×C3×C8C2311yescharacteristic
132C22×C3×C8C2313yes—
133C22×C3×C8C2313yes—
134C22×C3×C8C2313yes—
135C22×C3×C8C2313yes—
136C22×C3×C8C2313yes—
137C22×C3×C8C2316yes—
138C22×C3×C8C2313yes—
139C22×C3×C8C2313yes—
140C3×C4⋊Q8C2×C413yes—
141C3×#127C2×C413yes—
142C3×#124C2×C413yes—
143C3×#124C2×C413yes—
144C3×#123C2×C416yes—
145C3×#123C2×C416yes—
146C3×C22⋊Q8C2×C413yes—
147C3×C22⋊Q8C2×C413yes—
148C3×C22⋊Q8C2×C413yes—
149C3×C22⋊Q8C2×C413yes—
150C3×#121C2×C413yes—
151C3×#121C2×C413yes—
152C3×#121C2×C413yes—
153C3×#121C2×C413yes—
154C3×#121C2×C416yes—
155C3×#121C2×C416yes—
156C3×#120C2×C416yes—
157C3×#120C2×C416yes—
158C3×C4×Q8C2×C411yescharacteristic
159C3×C4×Q8C2×C411yescharacteristic
160C3×C4×D4C2×C413yes—
161C3×C4×D4C2×C413yes—
162C3×C4×D4C2×C413yes—
163C3×C4×D4C2×C413yes—
164C3×C4×D4C2×C413yes—
165C3×C4×D4C2×C413yes—
166C3×C4×D4C2313yes—
167C3×C4×D4C2316yes—
168C3×C4×D4C2311yescharacteristic
169C3×C4×D4C2313yes—
170C3×C4×D4C2313yes—
171C3×#117C2313yes—
172C2×C3×C4⋊C4C2×C413yes—
173C2×C3×C22⋊C4C2×C413yes—
174C2×C3×C22⋊C4C2×C413yes—
175C2×C3×C42C2313yes—
176C3×C4⋊C8C2311yescharacteristic
177C3×C4⋊C8C2313yes—
178C3×C4⋊C8C2313yes—
179C3×C4⋊C8C2313yes—
180C3×C4⋊C8C2316yes—
181C3×C22⋊C8C2311yescharacteristic
182C3×C22⋊C8C2311yescharacteristic
183C3×C22⋊C8C2313yes—
184C3×C22⋊C8C2313yes—
185C3×C22⋊C8C2313yes—
186C3×C22⋊C8C2313yes—
187C3×C22⋊C8C2313yes—
188C3×C22⋊C8C2313yes—
189C3×C22⋊C8C2316yes—
190C3×C22⋊C8C2316yes—
191C3×#97C2311yescharacteristic
192C3×#97C2313yes—
193C3×#97C2313yes—
194C3×#97C2313yes—
195C3×C4×C8C2316yes—
196C22×#41C22×C311yescharacteristic
197C22×#41C22×C311yescharacteristic
198#568—28no—
199C2×#131—28no—
200C2×#131C22×C311yescharacteristic
201C2×#131C22×C311yescharacteristic
202C2×#131C22×C311yescharacteristic
203C2×#131C22×C311yescharacteristic
204C2×#131C22×C313yescomplemented
205C2×#131C22×C313yescomplemented
206C2×#131C22×C313yescomplemented
207C2×#131C22×C313yescomplemented
208C22×M16C22×C313yescomplemented
209C22×M16C22×C313yescomplemented
210C22×M16C22×C313yescomplemented
211C23×C8C22×C313yescomplemented
212#550C3×C411yescharacteristic
213D4×Q8C3×C411yescharacteristic
214#548C3×C411yescharacteristic
215#548C3×C411yescharacteristic
216#547C3×C413yes—
217#546C3×C413yes—
218#546C3×C413yes—
219D42C3×C413yes—
220#532C22×C313yes—
221#525C22×C313yes—
222#525C22×C313yes—
223C4×#41C22×C311yescharacteristic
224C2×C4×D4C22×C313yes—
225#436C22×C316yescomplemented
226#436C22×C316yescomplemented
227#435C22×C311yescharacteristic
228#435C22×C313yes—
229#435C22×C313yescomplemented
230#435C22×C313yescomplemented
231#435C22×C313yescomplemented
232#435C22×C313yescomplemented
233#435C22×C313yescomplemented
234#435C22×C313yescomplemented
235#435C22×C316yescomplemented
236#435C22×C316yescomplemented
237#435C22×C316yescomplemented
238C8×D4C22×C316yescomplemented
239C8×D4C22×C316yescomplemented
240#424C22×C313yescomplemented
241#424C22×C313yescomplemented
242#423C22×C313yescomplemented
243C2×C4⋊C8C22×C313yescomplemented
244#408C22×C313yescomplemented
245#408C22×C313yescomplemented
246#408C22×C313yescomplemented
247#408C22×C313yescomplemented
248#407C22×C313yescomplemented
249#407C22×C313yescomplemented
250C2×C22⋊C8C22×C313yescomplemented
251C2×C22⋊C8C22×C313yescomplemented
252#405C22×C313yescomplemented
253#405C22×C313yescomplemented
254C4×M16C22×C313yescomplemented
255C2×#97C22×C313yescomplemented
256C24×C3C22×C413yes—
257C24×C3C22×C413yes—
258C3×#41—24no—
259C3×#41—24no—
260C3×#41—212no—
261C3×#41—212no—
262C3×#41—26no—
263C3×#41—26no—
264C3×#41—26no—
265C3×#41—26no—
266C3×#41C2×D414yes—
267C3×#41#4114yes—
268C2×C3×Q8—24no—
269C2×C3×Q8—24no—
270C2×C3×Q8C22×C413yes—
271C2×C3×Q8C22×C413yes—
272C2×C3×Q8C22×C411yescharacteristic
273C2×C3×D4—212no—
274C2×C3×D4—212no—
275C2×C3×D4—46no—
276C2×C3×D4C22×C411yescharacteristic
277C2×C3×D4C22×C413yes—
278C2×C3×D4C22×C416yes—
279C2×C3×D4C22×C416yes—
280C2×C3×D4C22×C413yes—
281C2×C3×D4C22×C413yes—
282C2×C3×D4C22×C413yes—
283C2×C3×D4C22×C413yes—
284C2×C3×D4C22×C416yes—
285C2×C3×D4C22×C413yes—
286C22×C3×C4—26no—
287C22×C3×C4—26no—
288C22×C3×C4—26no—
289C22×C3×C4—26no—
290C22×C3×C4C22×C413yes—
291C22×C3×C4C22×C413yes—
292C22×C3×C4C22×C413yes—
293C22×C3×C4C22×C413yes—
294C22×C3×C4C22×C413yes—
295C22×C3×C4C22×C413yes—
296C22×C3×C4C22×C413yes—
297C22×C3×C4C22×C413yes—
298C22×C3×C4C2411yescharacteristic
299C22×C3×C4C2413yes—
300C22×C3×C4C2413yes—
301C22×C3×C4C2411yescharacteristic
302C22×C3×C4C2413yes—
303C3×M16—26no—
304C3×M16—26no—
305C3×M16—26no—
306C3×M16—22no—
307C3×M16—26no—
308C3×M16—26no—
309C3×M16—212no—
310C3×M16—26no—
311C3×M16C2×D4112yescomplemented
312C2×C3×C8—26no—
313C2×C3×C8—26no—
314C2×C3×C8—26no—
315C2×C3×C8—22no—
316C2×C3×C8—26no—
317C2×C3×C8—26no—
318C2×C3×C8—26no—
319C2×C3×C8—212no—
320C2×C3×C8C2×D4112yescomplemented
321C2×C3×C8C2413yes—
322C2×C3×C8C2411yescharacteristic
323C2×C3×C8C2411yescharacteristic
324C2×C3×C8C2411yescharacteristic
325C2×C3×C8C2413yes—
326C2×C3×C8C2413yes—
327C2×C3×C8C2413yes—
328C2×C3×C8C2411yescharacteristic
329C3×C4⋊C4C22×C411yescharacteristic
330C3×C4⋊C4C22×C413yes—
331C3×C4⋊C4C22×C413yes—
332C3×C4⋊C4C22×C413yes—
333C3×C4⋊C4C22×C413yes—
334C3×C4⋊C4C22×C413yes—
335C3×C4⋊C4C22×C416yes—
336C3×C22⋊C4C22×C411yescharacteristic
337C3×C22⋊C4C22×C411yescharacteristic
338C3×C22⋊C4C22×C413yes—
339C3×C22⋊C4C22×C413yes—
340C3×C22⋊C4C22×C413yes—
341C3×C22⋊C4C22×C413yes—
342C3×C22⋊C4C22×C413yes—
343C3×C22⋊C4C22×C413yes—
344C3×C22⋊C4C22×C416yes—
345C3×C22⋊C4C22×C416yes—
346C3×C22⋊C4C22×C416yes—
347C3×C42C22×C413yes—
348C3×C42C22×C413yes—
349C3×C42C2413yes—
350C3×C42C2411yescharacteristic
351C2×#41—24no—
352C2×#41—24no—
353C2×#41—24no—
354C2×#41—24no—
355C2×#41C2×C3×C413yes—
356C2×#41C2×C3×C413yes—
357C2×#41C2×C3×C411yescharacteristic
358C2×#41C2×C3×C411yescharacteristic
359C2×#41C23×C313yes—
360C2×#41C23×C313yes—
361C2×#41C23×C311yescharacteristic
362C22×Q8C2×C3×C411yescharacteristic
363C22×Q8C2×C3×C411yescharacteristic
364C22×D4C2×C3×C413yes—
365C22×D4C2×C3×C413yes—
366C22×D4C2×C3×C413yes—
367C23×C4C23×C313yes—
368C23×C4C23×C313yes—
369#131—24no—
370#131—24no—
371#131—24no—
372#131—212no—
373#131—212no—
374#131—212no—
375#131—212no—
376#131C3×D418yescomplemented
377C2×M16—212no—
378C2×M16—212no—
379C2×M16—212no—
380C2×M16C23×C311yescharacteristic
381C2×M16C23×C313yes—
382C2×M16C23×C313yes—
383C2×M16C23×C313yes—
384C2×M16C23×C313yes—
385C2×M16C23×C313yes—
386C2×M16C23×C316yes—
387C2×M16C23×C313yes—
388C2×M16C23×C313yes—
389C22×C8—212no—
390C22×C8C23×C311yescharacteristic
391C22×C8C23×C313yes—
392C22×C8C23×C313yes—
393C22×C8C23×C313yes—
394C22×C8C23×C313yes—
395C22×C8C23×C313yes—
396C22×C8C23×C316yes—
397C22×C8C23×C313yes—
398C22×C8C23×C313yes—
399C4⋊Q8C2×C3×C413yes—
400#127C2×C3×C413yes—
401#124C2×C3×C413yes—
402#124C2×C3×C413yes—
403#123C2×C3×C416yes—
404#123C2×C3×C416yes—
405C22⋊Q8C2×C3×C413yes—
406C22⋊Q8C2×C3×C413yes—
407C22⋊Q8C2×C3×C413yes—
408C22⋊Q8C2×C3×C413yes—
409#121C2×C3×C413yes—
410#121C2×C3×C413yes—
411#121C2×C3×C413yes—
412#121C2×C3×C413yes—
413#121C2×C3×C416yes—
414#121C2×C3×C416yes—
415#120C2×C3×C416yes—
416#120C2×C3×C416yes—
417C4×Q8C2×C3×C411yescharacteristic
418C4×Q8C2×C3×C411yescharacteristic
419C4×D4C2×C3×C413yes—
420C4×D4C2×C3×C413yes—
421C4×D4C2×C3×C413yes—
422C4×D4C2×C3×C413yes—
423C4×D4C2×C3×C413yes—
424C4×D4C2×C3×C413yes—
425C4×D4C23×C311yescharacteristic
426C4×D4C23×C313yes—
427C4×D4C23×C313yes—
428C4×D4C23×C313yes—
429C4×D4C23×C316yes—
430#117C23×C313yes—
431C2×C4⋊C4C2×C3×C413yes—
432C2×C22⋊C4C2×C3×C413yes—
433C2×C22⋊C4C2×C3×C413yes—
434C2×C42C23×C313yes—
435C4⋊C8C23×C311yescharacteristic
436C4⋊C8C23×C313yes—
437C4⋊C8C23×C313yes—
438C4⋊C8C23×C313yes—
439C4⋊C8C23×C316yes—
440C22⋊C8C23×C311yescharacteristic
441C22⋊C8C23×C311yescharacteristic
442C22⋊C8C23×C313yes—
443C22⋊C8C23×C313yes—
444C22⋊C8C23×C313yes—
445C22⋊C8C23×C313yes—
446C22⋊C8C23×C313yes—
447C22⋊C8C23×C313yes—
448C22⋊C8C23×C316yes—
449C22⋊C8C23×C316yes—
450#97C23×C311yescharacteristic
451#97C23×C313yes—
452#97C23×C313yes—
453#97C23×C313yes—
454C4×C8C23×C316yes—
455C23×C3—26no—
456C23×C3—26no—
457C23×C3—26no—
458C23×C3—43no—
459C23×C3—43no—
460C23×C3—43no—
461C23×C3C23×C411yescharacteristic
462C23×C3C23×C413yes—
463C23×C3C23×C413yes—
464C23×C3C23×C413yes—
465C23×C3C23×C411yescharacteristic
466C3×Q8—26no—
467C3×Q8—26no—
468C3×Q8C4×D414yes—
469C3×D4—212no—
470C3×D4—212no—
471C3×D4—22no—
472C3×D4—26no—
473C3×D4—26no—
474C3×D4—26no—
475C3×D4—43no—
476C3×D4—43no—
477C3×D4—46no—
478C3×D4C4×D4112yes—
479C2×C3×C4—26no—
480C2×C3×C4—26no—
481C2×C3×C4—26no—
482C2×C3×C4—26no—
483C2×C3×C4—26no—
484C2×C3×C4—26no—
485C2×C3×C4—21no—
486C2×C3×C4—23no—
487C2×C3×C4—23no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—23no—
492C2×C3×C4—23no—
493C2×C3×C4—43no—
494C2×C3×C4—43no—
495C2×C3×C4C23×C411yescharacteristic
496C2×C3×C4C23×C411yescharacteristic
497C2×C3×C4C23×C413yes—
498C2×C3×C4C23×C413yes—
499C2×C3×C4C23×C411yescharacteristic
500C2×C3×C4C23×C411yescharacteristic
501C2×C3×C4C23×C413yes—
502C2×C3×C4C23×C413yes—
503C2×C3×C4C23×C413yes—
504C2×C3×C4C22×D416yes—
505C2×C3×C4C2×#4116yes—
506C2×C3×C4C2511yescharacteristic
507C3×C8—21no—
508C3×C8—23no—
509C3×C8—21no—
510C3×C8—23no—
511C3×C8—21no—
512C3×C8—23no—
513C3×C8C22×D412yes—
514C3×C8C22×D416yes—
515C24C22×C3×C413yes—
516C24C22×C3×C413yes—
517#41—24no—
518#41—24no—
519#41—212no—
520#41—212no—
521#41—26no—
522#41—26no—
523#41—26no—
524#41—26no—
525#41C2×C3×D414yes—
526#41C3×#4114yes—
527C2×Q8—24no—
528C2×Q8—24no—
529C2×Q8C22×C3×C413yes—
530C2×Q8C22×C3×C413yes—
531C2×Q8C22×C3×C411yescharacteristic
532C2×D4—212no—
533C2×D4—212no—
534C2×D4—46no—
535C2×D4C22×C3×C411yescharacteristic
536C2×D4C22×C3×C413yes—
537C2×D4C22×C3×C416yes—
538C2×D4C22×C3×C416yes—
539C2×D4C22×C3×C413yes—
540C2×D4C22×C3×C413yes—
541C2×D4C22×C3×C413yes—
542C2×D4C22×C3×C413yes—
543C2×D4C22×C3×C416yes—
544C2×D4C22×C3×C413yes—
545C22×C4—26no—
546C22×C4—26no—
547C22×C4—26no—
548C22×C4—26no—
549C22×C4C22×C3×C413yes—
550C22×C4C22×C3×C413yes—
551C22×C4C22×C3×C413yes—
552C22×C4C22×C3×C413yes—
553C22×C4C22×C3×C413yes—
554C22×C4C22×C3×C413yes—
555C22×C4C22×C3×C413yes—
556C22×C4C22×C3×C413yes—
557C22×C4C24×C311yescharacteristic
558C22×C4C24×C313yes—
559C22×C4C24×C313yes—
560C22×C4C24×C311yescharacteristic
561C22×C4C24×C313yes—
562M16—26no—
563M16—26no—
564M16—26no—
565M16—22no—
566M16—26no—
567M16—26no—
568M16—212no—
569M16—26no—
570M16C2×C3×D4112yescomplemented
571C2×C8—26no—
572C2×C8—26no—
573C2×C8—26no—
574C2×C8—22no—
575C2×C8—26no—
576C2×C8—26no—
577C2×C8—26no—
578C2×C8—212no—
579C2×C8C2×C3×D4112yescomplemented
580C2×C8C24×C313yes—
581C2×C8C24×C311yescharacteristic
582C2×C8C24×C311yescharacteristic
583C2×C8C24×C311yescharacteristic
584C2×C8C24×C313yes—
585C2×C8C24×C313yes—
586C2×C8C24×C313yes—
587C2×C8C24×C311yescharacteristic
588C4⋊C4C22×C3×C411yescharacteristic
589C4⋊C4C22×C3×C413yes—
590C4⋊C4C22×C3×C413yes—
591C4⋊C4C22×C3×C413yes—
592C4⋊C4C22×C3×C413yes—
593C4⋊C4C22×C3×C413yes—
594C4⋊C4C22×C3×C416yes—
595C22⋊C4C22×C3×C411yescharacteristic
596C22⋊C4C22×C3×C411yescharacteristic
597C22⋊C4C22×C3×C413yes—
598C22⋊C4C22×C3×C413yes—
599C22⋊C4C22×C3×C413yes—
600C22⋊C4C22×C3×C413yes—
601C22⋊C4C22×C3×C413yes—
602C22⋊C4C22×C3×C413yes—
603C22⋊C4C22×C3×C416yes—
604C22⋊C4C22×C3×C416yes—
605C22⋊C4C22×C3×C416yes—
606C42C22×C3×C413yes—
607C42C22×C3×C413yes—
608C42C24×C313yes—
609C42C24×C311yescharacteristic
610C22×C3—21no—
611C22×C3—23no—
612C22×C3—23no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—23no—
616C22×C3—23no—
617C22×C3—21no—
618C22×C3—23no—
619C22×C3—23no—
620C22×C3—23no—
621C22×C3—23no—
622C22×C3—21no—
623C22×C3—412no—
624C22×C3—86no—
625C22×C3C2×C4×D416yes—
626C22×C3#56812yescomplemented
627C22×C3C24×C411yescharacteristic
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—23no—
631C3×C4—23no—
632C3×C4—21no—
633C3×C4—23no—
634C3×C4—21no—
635C3×C4—23no—
636C3×C4C2×C4×D416yes—
637C3×C4C23×D411yescharacteristic
638C3×C4C22×#4111yescharacteristic
639C23—26no—
640C23—26no—
641C23—26no—
642C23—43no—
643C23—43no—
644C23—43no—
645C23C23×C3×C411yescharacteristic
646C23C23×C3×C413yes—
647C23C23×C3×C413yes—
648C23C23×C3×C411yescharacteristic
649C23C23×C3×C413yes—
650Q8—26no—
651Q8—26no—
652Q8C3×C4×D414yes—
653D4—22no—
654D4—26no—
655D4—212no—
656D4—212no—
657D4—26no—
658D4—26no—
659D4—43no—
660D4—43no—
661D4—46no—
662D4C3×C4×D4112yes—
663C2×C4—26no—
664C2×C4—26no—
665C2×C4—21no—
666C2×C4—23no—
667C2×C4—23no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—23no—
672C2×C4—23no—
673C2×C4—26no—
674C2×C4—26no—
675C2×C4—26no—
676C2×C4—26no—
677C2×C4—43no—
678C2×C4—43no—
679C2×C4C23×C3×C411yescharacteristic
680C2×C4C23×C3×C411yescharacteristic
681C2×C4C23×C3×C413yes—
682C2×C4C23×C3×C413yes—
683C2×C4C23×C3×C411yescharacteristic
684C2×C4C23×C3×C411yescharacteristic
685C2×C4C23×C3×C413yes—
686C2×C4C23×C3×C413yes—
687C2×C4C23×C3×C413yes—
688C2×C4C22×C3×D416yes—
689C2×C4C2×C3×#4116yes—
690C2×C4C25×C311yescharacteristic
691C8—21no—
692C8—23no—
693C8—21no—
694C8—23no—
695C8—21no—
696C8—23no—
697C8C22×C3×D412yes—
698C8C22×C3×D416yes—
699C2×C3—22no—
700C2×C3—26no—
701C2×C3—43no—
702C2×C3—43no—
703C2×C3—41no—
704C2×C3C22×C4×D411yescharacteristic
705C2×C3C2×#56811yescharacteristic
706C2×C3#357311yescharacteristic
707C22—21no—
708C22—23no—
709C22—23no—
710C22—21no—
711C22—21no—
712C22—23no—
713C22—23no—
714C22—21no—
715C22—23no—
716C22—23no—
717C22—23no—
718C22—23no—
719C22—21no—
720C22—412no—
721C22—86no—
722C22C2×C3×C4×D416yes—
723C22C3×#56812yescomplemented
724C22C24×C3×C411yescharacteristic
725C4—21no—
726C4—21no—
727C4—23no—
728C4—23no—
729C4—21no—
730C4—23no—
731C4—21no—
732C4—23no—
733C4C2×C3×C4×D416yes—
734C4C23×C3×D411yescharacteristic
735C4C22×C3×#4111yescharacteristic
736C3#6014611yescharacteristic, direct product factor, Sylow
737C2—22no—
738C2—26no—
739C2—43no—
740C2—41no—
741C2—43no—
742C2C22×C3×C4×D411yescharacteristic
743C2C2×C3×#56811yescharacteristic
744C2C3×#357311yescharacteristic
subgroupG/H
centerC2×C3×C4C25
commutatorC22C24×C3×C4
Frattini, cosocleC2×C4C25×C3
socleC22×C3C24×C4
prime radicalC3×D4×#41C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#568C2semidirect
2. C22×C3×#131C2semidirect
4. C3×#2935C2semidirect
5. C3×D4×M16C2semidirect
6. C3×#2933C2semidirect
7. C3×#2933C2semidirect
8. C3×#2932C2semidirect
9. C3×#2930C2semidirect
10. C3×#2929C2semidirect
11. C2×C3×#435C2semidirect
12. C3×#2906C2semidirect
13. C3×#2880C2semidirect
14. C3×#2880C2semidirect
15. C3×#2875C2semidirect
16. #60146C3direct (N × H)
25. C2×C3×#131C22semidirect
26. C2×C3×#131C22semidirect
27. C2×C3×#131C22semidirect
28. C2×C3×#131C22semidirect
29. C22×C3×M16C22semidirect
30. C22×C3×M16C22semidirect
31. C22×C3×M16C22semidirect
32. C23×C3×C8C22semidirect
46. C3×#436C22semidirect
47. C3×#436C22semidirect
50. C3×#435C22semidirect
51. C3×#435C22semidirect
52. C3×#435C22semidirect
53. C3×#435C22semidirect
54. C3×#435C22semidirect
55. C3×#435C22semidirect
56. C3×#435C22semidirect
57. C3×#435C22semidirect
58. C3×#435C22semidirect
59. C3×C8×D4C22semidirect
60. C3×C8×D4C22semidirect
61. C3×#424C22semidirect
62. C3×#424C22semidirect
63. C3×#423C22semidirect
64. C2×C3×C4⋊C8C22semidirect
65. C3×#408C22semidirect
66. C3×#408C22semidirect
67. C3×#408C22semidirect
68. C3×#408C22semidirect
69. C3×#407C22semidirect
70. C3×#407C22semidirect
71. C2×C3×C22⋊C8C22semidirect
72. C2×C3×C22⋊C8C22semidirect
73. C3×#405C22semidirect
74. C3×#405C22semidirect
75. C3×C4×M16C22semidirect
76. C2×C3×#97C22semidirect
77. C2×#568C2×C3semidirect
78. C22×#131C2×C3semidirect
80. #2935C2×C3semidirect
81. D4×M16C2×C3semidirect
82. #2933C2×C3semidirect
83. #2933C2×C3semidirect
84. #2932C2×C3semidirect
85. #2930C2×C3semidirect
86. #2929C2×C3semidirect
87. C2×#435C2×C3semidirect
88. #2906C2×C3semidirect
89. #2880C2×C3semidirect
90. #2880C2×C3semidirect
91. #2875C2×C3semidirect
117. C3×#131D4semidirect
204. C2×#131C22×C3semidirect
205. C2×#131C22×C3semidirect
206. C2×#131C22×C3semidirect
207. C2×#131C22×C3semidirect
208. C22×M16C22×C3semidirect
209. C22×M16C22×C3semidirect
210. C22×M16C22×C3semidirect
211. C23×C8C22×C3semidirect
225. #436C22×C3semidirect
226. #436C22×C3semidirect
229. #435C22×C3semidirect
230. #435C22×C3semidirect
231. #435C22×C3semidirect
232. #435C22×C3semidirect
233. #435C22×C3semidirect
234. #435C22×C3semidirect
235. #435C22×C3semidirect
236. #435C22×C3semidirect
237. #435C22×C3semidirect
238. C8×D4C22×C3semidirect
239. C8×D4C22×C3semidirect
240. #424C22×C3semidirect
241. #424C22×C3semidirect
242. #423C22×C3semidirect
243. C2×C4⋊C8C22×C3semidirect
244. #408C22×C3semidirect
245. #408C22×C3semidirect
246. #408C22×C3semidirect
247. #408C22×C3semidirect
248. #407C22×C3semidirect
249. #407C22×C3semidirect
250. C2×C22⋊C8C22×C3semidirect
251. C2×C22⋊C8C22×C3semidirect
252. #405C22×C3semidirect
253. #405C22×C3semidirect
254. C4×M16C22×C3semidirect
255. C2×#97C22×C3semidirect
311. C3×M16C2×D4semidirect
320. C2×C3×C8C2×D4semidirect
376. #131C3×D4semidirect
570. M16C2×C3×D4semidirect
579. C2×C8C2×C3×D4semidirect
626. C22×C3#568semidirect
723. C22C3×#568semidirect
736. C3#60146direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5682
C22×C3×#1312
C3×D4×#412
C3×#29352
C3×D4×M162
C3×#29332
C3×#29322
C3×#29302
C3×#29292
C2×C3×#4352
C3×#29062
C3×#28802
C3×#28752
#601463