Finite Group Databasebeta

← C3×#25555 #10644162

Subgroups — C3×#25555 #10644162

Order 768.

1136 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
1C2×C3×#552C211yesmaximal, characteristic, complemented
2C2×C3×#481C211yesmaximal, characteristic, complemented
3C2×C3×#468C211yesmaximal, characteristic, complemented
4C3×#2414C211yesmaximal, characteristic
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2035C211yesmaximal, characteristic, complemented
7C3×#2025C211yesmaximal, characteristic, complemented
8C3×#2000C211yesmaximal, characteristic, complemented
9C3×#1880C211yesmaximal, characteristic, complemented
10C3×#1875C211yesmaximal, characteristic, complemented
11C3×#1873C211yesmaximal, characteristic, complemented
12C3×#1870C211yesmaximal, characteristic, complemented
13C3×#1865C211yesmaximal, characteristic, complemented
14C3×#1854C211yesmaximal, characteristic, complemented
15C3×#1736C211yesmaximal, characteristic, complemented
16#25555C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C3×#552—24no—
20C3×#552—24no—
21C2×C3×#126—21no—
22C2×C3×#125—21no—
23C2×C3×#125C2211yescharacteristic
24C2×C3×#123—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×#117—21no—
32C2×C3×#117C2211yescharacteristic
33C2×C3×#117C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C3×#481—24no—
36C3×#468—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#106C2211yescharacteristic
39C2×C3×#106C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C3×#394—21no—
50C3×#392—21no—
51C3×#390—21no—
52C3×#390C2211yescharacteristic
53C3×#389C2211yescharacteristic
54C3×#388—21no—
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#552C2×C311yescharacteristic, complemented
65C2×#481C2×C311yescharacteristic, complemented
66C2×#468C2×C311yescharacteristic, complemented
67#2414C2×C311yescharacteristic
68#2059C2×C311yescharacteristic, complemented
69#2035C2×C311yescharacteristic, complemented
70#2025C2×C311yescharacteristic, complemented
71#2000C2×C311yescharacteristic, complemented
72#1880C2×C311yescharacteristic, complemented
73#1875C2×C311yescharacteristic, complemented
74#1873C2×C311yescharacteristic, complemented
75#1870C2×C311yescharacteristic, complemented
76#1865C2×C311yescharacteristic, complemented
77#1854C2×C311yescharacteristic, complemented
78#1736C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4D411yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C2×C3×SD16—22no—
88C2×C3×SD16—22no—
89C2×C3×SD16—41no—
90C2×C3×M16—22no—
91C2×C3×M16—22no—
92C2×C3×M16—41no—
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C3×#126—28no—
98C3×#125—28no—
99C3×#125—22no—
100C3×#125—22no—
101C3×#123—28no—
102C3×C22⋊Q8—22no—
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8D414yescomplemented
106C3×#121—22no—
107C3×#121—22no—
108C3×#121—22no—
109C3×#121—41no—
110C3×C4×Q8—22no—
111C3×C4×Q8—22no—
112C3×C4×D4—22no—
113C3×C4×D4—22no—
114C3×#117—28no—
115C3×#117—22no—
116C3×#117—22no—
117C3×#117—22no—
118C3×#117—41no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4D411yescharacteristic
128C2×C3×C4⋊C4D414yescomplemented
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4D411yescharacteristic
145C2×C3×C22⋊C4D411yescharacteristic
146C2×C3×C42—21no—
147C2×C3×C42—21no—
148C2×C3×C42—21no—
149C2×C3×C42C2311yescharacteristic
150C3×#107—22no—
151C3×#106—22no—
152C3×#106—22no—
153C3×#103—22no—
154C3×#103—22no—
155C3×#103—41no—
156C3×#102—22no—
157C3×#102—22no—
158C3×#102—22no—
159C3×C22⋊C8—22no—
160C3×C22⋊C8—22no—
161C3×C22⋊C8—41no—
162C3×#95—21no—
163C3×#95—21no—
164C22×SD16C22×C311yescharacteristic
165C22×M16C22×C311yescharacteristic
166#552—24no—
167#552—24no—
168C2×#126—21no—
169C2×#125—21no—
170C2×#125C22×C311yescharacteristic
171C2×#123—21no—
172C2×C22⋊Q8C22×C311yescharacteristic
173C2×C22⋊Q8C22×C311yescharacteristic
174C2×#121C22×C311yescharacteristic
175C2×#121C22×C311yescharacteristic
176C2×C4×Q8C22×C311yescharacteristic
177C2×C4×D4C22×C311yescharacteristic
178C2×#117—21no—
179C2×#117C22×C311yescharacteristic
180C2×#117C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182#481—24no—
183#468—24no—
184C2×#107C22×C311yescharacteristic
185C2×#106C22×C311yescharacteristic
186C2×#106C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#102C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×C22⋊C8C22×C311yescharacteristic
194C2×C22⋊C8C22×C311yescharacteristic
195C2×C22⋊C8C22×C311yescharacteristic
196#394—21no—
197#392—21no—
198#390—21no—
199#390C22×C311yescharacteristic
200#389C22×C311yescharacteristic
201#388—21no—
202#380C22×C311yescharacteristic
203#340C22×C311yescharacteristic
204#340C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#340C22×C311yescharacteristic
209#336C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211C24×C3—21no—
212C24×C3C2×D411yescharacteristic
213C24×C3C2×D411yescharacteristic
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8C2×D412yes—
220C2×C3×D4—22no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—41no—
228C2×C3×D4—41no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—81no—
233C2×C3×D4—81no—
234C2×C3×D4—81no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—24no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—42no—
254C22×C3×C4—42no—
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D412yes—
260C22×C3×C4C2×D412yes—
261C22×C3×C4C2411yescharacteristic
262C3×SD16—44no—
263C3×M16—44no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8#4112yes—
276C3×C4⋊C4—24no—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—24no—
279C3×C4⋊C4—24no—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—22no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—81no—
292C3×C4⋊C4C2×D412yes—
293C3×C4⋊C4C2×D412yes—
294C3×C4⋊C4C2×D412yes—
295C3×C4⋊C4#4112yes—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—42no—
302C3×C22⋊C4—42no—
303C3×C22⋊C4—42no—
304C3×C22⋊C4—42no—
305C3×C22⋊C4—81no—
306C3×C22⋊C4—81no—
307C3×C42—24no—
308C3×C42—24no—
309C3×C42—21no—
310C3×C42—21no—
311C3×C42—42no—
312C22×Q8C23×C311yescharacteristic
313C22×D4—21no—
314C22×D4—21no—
315C22×D4C3×D411yescharacteristic
316C22×D4C23×C311yescharacteristic
317C23×C4—21no—
318C23×C4C23×C311yescharacteristic
319C23×C4C23×C311yescharacteristic
320C2×SD16—22no—
321C2×SD16—22no—
322C2×SD16—41no—
323C2×M16—22no—
324C2×M16—22no—
325C2×M16—41no—
326C22×C8C23×C311yescharacteristic
327C22×C8C23×C311yescharacteristic
328C22×C8C23×C311yescharacteristic
329C22×C8C23×C311yescharacteristic
330#126—28no—
331#125—28no—
332#125—22no—
333#125—22no—
334#123—28no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8C3×D414yescomplemented
339#121—22no—
340#121—22no—
341#121—22no—
342#121—41no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×D4—22no—
346C4×D4—22no—
347#117—28no—
348#117—22no—
349#117—22no—
350#117—22no—
351#117—41no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4C3×D411yescharacteristic
361C2×C4⋊C4C3×D414yescomplemented
362C2×C4⋊C4C23×C311yescharacteristic
363C2×C4⋊C4C23×C311yescharacteristic
364C2×C4⋊C4C23×C311yescharacteristic
365C2×C4⋊C4C23×C311yescharacteristic
366C2×C4⋊C4C23×C311yescharacteristic
367C2×C4⋊C4C23×C311yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4C3×D411yescharacteristic
378C2×C22⋊C4C3×D411yescharacteristic
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42C23×C311yescharacteristic
383#107—22no—
384#106—22no—
385#106—22no—
386#103—22no—
387#103—22no—
388#103—41no—
389#102—22no—
390#102—22no—
391#102—22no—
392C22⋊C8—22no—
393C22⋊C8—22no—
394C22⋊C8—41no—
395#95—21no—
396#95—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3#12012yes—
418C23×C3C22×D411yescharacteristic
419C3×Q8—22no—
420C3×Q8—22no—
421C3×Q8—41no—
422C3×Q8—41no—
423C3×D4—44no—
424C3×D4—41no—
425C3×D4—41no—
426C3×D4—41no—
427C3×D4—41no—
428C3×D4—84no—
429C3×D4—84no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—48no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4#12012yes—
472C2×C3×C4C22×D411yescharacteristic
473C2×C3×C4C22×D411yescharacteristic
474C2×C3×C4C2×#4111yescharacteristic
475C2×C3×C4C2×#4111yescharacteristic
476C2×C3×C4H(5,𝔽2)11yescharacteristic
477C2×C3×C42−1+411yescharacteristic
478C3×C8—22no—
479C3×C8—41no—
480C3×C8—41no—
481C3×C8—41no—
482C24—21no—
483C24C2×C3×D411yescharacteristic
484C24C2×C3×D411yescharacteristic
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8C2×C3×D412yes—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—81no—
504C2×D4—81no—
505C2×D4—81no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—24no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4C2×C3×D411yescharacteristic
527C22×C4C2×C3×D411yescharacteristic
528C22×C4C2×C3×D411yescharacteristic
529C22×C4C2×C3×D411yescharacteristic
530C22×C4C2×C3×D412yes—
531C22×C4C2×C3×D412yes—
532C22×C4C24×C311yescharacteristic
533SD16—44no—
534M16—44no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8C3×#4112yes—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—22no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—81no—
563C4⋊C4C2×C3×D412yes—
564C4⋊C4C2×C3×D412yes—
565C4⋊C4C2×C3×D412yes—
566C4⋊C4C3×#4112yes—
567C22⋊C4—24no—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C42—24no—
579C42—24no—
580C42—21no—
581C42—21no—
582C42—42no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3C2×#12011yescharacteristic
605C22×C3#54611yescharacteristic
606C22×C3#54711yescharacteristic
607C22×C3#57511yescharacteristic
608C22×C3#57511yescharacteristic
609C22×C3#57711yescharacteristic
610C22×C3#57711yescharacteristic
611C3×C4—22no—
612C3×C4—41no—
613C3×C4—42no—
614C3×C4—41no—
615C3×C4—42no—
616C3×C4—42no—
617C3×C4—41no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—81no—
621C3×C4—81no—
622C3×C4#53211yescharacteristic
623C3×C4#53711yescharacteristic
624C3×C4#54611yescharacteristic
625C3×C4#54711yescharacteristic
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23C3×#12012yes—
647C23C22×C3×D411yescharacteristic
648Q8—22no—
649Q8—22no—
650Q8—41no—
651Q8—41no—
652D4—44no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—84no—
658D4—84no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—48no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4C3×#12012yes—
701C2×C4C22×C3×D411yescharacteristic
702C2×C4C22×C3×D411yescharacteristic
703C2×C4C2×C3×#4111yescharacteristic
704C2×C4C2×C3×#4111yescharacteristic
705C2×C4C3×H(5,𝔽2)11yescharacteristic
706C2×C4C3×2−1+411yescharacteristic
707C8—22no—
708C8—41no—
709C8—41no—
710C8—41no—
711C2×C3—42no—
712C2×C3—81no—
713C2×C3—161no—
714C2×C3#243011yescharacteristic
715C2×C3#300511yescharacteristic
716C2×C3#301011yescharacteristic
717C2×C3#331711yescharacteristic
718C2×C3#332311yescharacteristic
719C2×C3#334811yescharacteristic
720C2×C3#335111yescharacteristic
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22C2×C3×#12011yescharacteristic
743C22C3×#54611yescharacteristic
744C22C3×#54711yescharacteristic
745C22C3×#57511yescharacteristic
746C22C3×#57511yescharacteristic
747C22C3×#57711yescharacteristic
748C22C3×#57711yescharacteristic
749C4—22no—
750C4—41no—
751C4—42no—
752C4—41no—
753C4—42no—
754C4—42no—
755C4—41no—
756C4—42no—
757C4—42no—
758C4—81no—
759C4—81no—
760C4C3×#53211yescharacteristic
761C4C3×#53711yescharacteristic
762C4C3×#54611yescharacteristic
763C4C3×#54711yescharacteristic
764C3#2555511yescharacteristic, direct product factor, Sylow
765C2—42no—
766C2—81no—
767C2—161no—
768C2C3×#243011yescharacteristic
769C2C3×#300511yescharacteristic
770C2C3×#301011yescharacteristic
771C2C3×#331711yescharacteristic
772C2C3×#332311yescharacteristic
773C2C3×#334811yescharacteristic
774C2C3×#335111yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2414C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#552C2semidirect
2. C2×C3×#481C2semidirect
3. C2×C3×#468C2semidirect
5. C3×#2059C2semidirect
6. C3×#2035C2semidirect
7. C3×#2025C2semidirect
8. C3×#2000C2semidirect
9. C3×#1880C2semidirect
10. C3×#1875C2semidirect
11. C3×#1873C2semidirect
12. C3×#1870C2semidirect
13. C3×#1865C2semidirect
14. C3×#1854C2semidirect
15. C3×#1736C2semidirect
16. #25555C3direct (N × H)
64. C2×#552C2×C3semidirect
65. C2×#481C2×C3semidirect
66. C2×#468C2×C3semidirect
68. #2059C2×C3semidirect
69. #2035C2×C3semidirect
70. #2025C2×C3semidirect
71. #2000C2×C3semidirect
72. #1880C2×C3semidirect
73. #1875C2×C3semidirect
74. #1873C2×C3semidirect
75. #1870C2×C3semidirect
76. #1865C2×C3semidirect
77. #1854C2×C3semidirect
78. #1736C2×C3semidirect
105. C3×C22⋊Q8D4semidirect
128. C2×C3×C4⋊C4D4semidirect
338. C22⋊Q8C3×D4semidirect
361. C2×C4⋊C4C3×D4semidirect
764. C3#25555direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5522
C2×C3×#4812
C2×C3×#4682
C3×#24142
C3×#20592
C3×#20352
C3×#20252
C3×#20002
C3×#18802
C3×#18752
C3×#18732
C3×#18702
C3×#18652
C3×#18542
C3×#17362
#255553