Finite Group Databasebeta

← C3×#26784 #10645391

Subgroups — C3×#26784 #10645391

Order 768.

966 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#480C211yesmaximal, characteristic, complemented
2C2×C3×#474C211yesmaximal, characteristic, complemented
3C3×#2491C211yesmaximal, characteristic, complemented
4C3×#2361C211yesmaximal, characteristic, complemented
5C3×#2067C211yesmaximal, characteristic, complemented
6C3×#2057C211yesmaximal, characteristic, complemented
7C3×#2033C211yesmaximal, characteristic, complemented
8C3×#1999C211yesmaximal, characteristic
9C3×#1970C211yesmaximal, characteristic, complemented
10C3×#1925C211yesmaximal, characteristic, complemented
11C3×#1925C211yesmaximal, characteristic, complemented
12C3×#1923C211yesmaximal, characteristic, complemented
13C3×#1879C211yesmaximal, characteristic, complemented
14C3×#1852C211yesmaximal, characteristic, complemented
15C3×C4×#107C211yesmaximal, characteristic, complemented
16#26784C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic
19C2×C3×#124—21no—
20C2×C3×#121C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×C4×D4—21no—
23C2×C3×C4×D4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C3×#480—24no—
26C3×#474—24no—
27C2×C3×#107C2211yescharacteristic
28C2×C3×#107C2211yescharacteristic
29C2×C3×#107C2211yescharacteristic
30C2×C3×#107C2211yescharacteristic
31C2×C3×#107C2211yescharacteristic
32C2×C3×C4⋊C8C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×C4×C8C2211yescharacteristic
42C3×#394—21no—
43C3×#393—21no—
44C3×#390C2211yescharacteristic
45C3×#390C2211yescharacteristic
46C3×#390C2211yescharacteristic
47C3×#389C2211yescharacteristic
48C3×#388—21no—
49C3×#388—21no—
50C3×#386—21no—
51C3×#385—21no—
52C3×#380C2211yescharacteristic
53C3×C4×C4⋊C4C2211yescharacteristic
54C3×C4×C4⋊C4C2211yescharacteristic
55C3×C4×C22⋊C4C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#480C2×C311yescharacteristic, complemented
63C2×#474C2×C311yescharacteristic, complemented
64#2491C2×C311yescharacteristic, complemented
65#2361C2×C311yescharacteristic, complemented
66#2067C2×C311yescharacteristic, complemented
67#2057C2×C311yescharacteristic, complemented
68#2033C2×C311yescharacteristic, complemented
69#1999C2×C311yescharacteristic
70#1970C2×C311yescharacteristic, complemented
71#1925C2×C311yescharacteristic, complemented
72#1925C2×C311yescharacteristic, complemented
73#1923C2×C311yescharacteristic, complemented
74#1879C2×C311yescharacteristic, complemented
75#1852C2×C311yescharacteristic, complemented
76C4×#107C2×C311yescharacteristic, complemented
77C22×C3×Q8—21no—
78C22×C3×D4—21no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4—21no—
84C23×C3×C4C2311yescharacteristic
85C2×C3×D8—22no—
86C2×C3×D8—22no—
87C2×C3×D8—41no—
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C4⋊Q8—22no—
93C3×C4⋊Q8—41no—
94C3×#124—44no—
95C3×#121—22no—
96C3×#121—22no—
97C3×#121—22no—
98C3×#121—41no—
99C3×C4×D4—22no—
100C3×C4×D4—41no—
101C3×C4×D4—44no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—41no—
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4D411yescharacteristic
124C2×C3×C22⋊C4D411yescharacteristic
125C2×C3×C42—21no—
126C2×C3×C42—21no—
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C3×#107—22no—
130C3×#107—22no—
131C3×#107—22no—
132C3×#107—41no—
133C3×#107D414yescomplemented
134C3×C4⋊C8—22no—
135C3×#102—22no—
136C3×#102—22no—
137C3×#102—22no—
138C3×#102—22no—
139C3×#102—22no—
140C3×#102—22no—
141C3×C22⋊C8—22no—
142C3×C22⋊C8—22no—
143C3×C4×C8—22no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95—21no—
148C3×#95D411yescharacteristic
149C3×#95D411yescharacteristic
150C22×D8C22×C311yescharacteristic
151C2×C4⋊Q8C22×C311yescharacteristic
152C2×#124—21no—
153C2×#121C22×C311yescharacteristic
154C2×#121C22×C311yescharacteristic
155C2×C4×D4—21no—
156C2×C4×D4C22×C311yescharacteristic
157C22×C4⋊C4C22×C311yescharacteristic
158#480—24no—
159#474—24no—
160C2×#107C22×C311yescharacteristic
161C2×#107C22×C311yescharacteristic
162C2×#107C22×C311yescharacteristic
163C2×#107C22×C311yescharacteristic
164C2×#107C22×C311yescharacteristic
165C2×C4⋊C8C22×C311yescharacteristic
166C2×#102C22×C311yescharacteristic
167C2×#102C22×C311yescharacteristic
168C2×#102C22×C311yescharacteristic
169C2×#102C22×C311yescharacteristic
170C2×#102C22×C311yescharacteristic
171C2×#102C22×C311yescharacteristic
172C2×C22⋊C8C22×C311yescharacteristic
173C2×C22⋊C8C22×C311yescharacteristic
174C2×C4×C8C22×C311yescharacteristic
175#394—21no—
176#393—21no—
177#390C22×C311yescharacteristic
178#390C22×C311yescharacteristic
179#390C22×C311yescharacteristic
180#389C22×C311yescharacteristic
181#388—21no—
182#388—21no—
183#386—21no—
184#385—21no—
185#380C22×C311yescharacteristic
186C4×C4⋊C4C22×C311yescharacteristic
187C4×C4⋊C4C22×C311yescharacteristic
188C4×C22⋊C4C22×C311yescharacteristic
189#340C22×C311yescharacteristic
190#340C22×C311yescharacteristic
191#340C22×C311yescharacteristic
192#340C22×C311yescharacteristic
193#336C22×C311yescharacteristic
194#336C22×C311yescharacteristic
195C24×C3—21no—
196C24×C3—21no—
197C24×C3C2×D411yescharacteristic
198C2×C3×Q8—42no—
199C2×C3×Q8—42no—
200C2×C3×Q8—81no—
201C2×C3×D4—24no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—42no—
214C2×C3×D4—42no—
215C2×C3×D4—42no—
216C2×C3×D4—42no—
217C2×C3×D4—81no—
218C2×C3×D4#4112yes—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—42no—
232C22×C3×C4—42no—
233C22×C3×C4—42no—
234C22×C3×C4—42no—
235C22×C3×C4—81no—
236C22×C3×C4—81no—
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C3×D8—44no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8—21no—
250C2×C3×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8C2×D412yes—
255C2×C3×C8#4112yes—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—42no—
266C3×C4⋊C4—42no—
267C3×C4⋊C4—42no—
268C3×C4⋊C4C2×D412yes—
269C3×C4⋊C4C2×D412yes—
270C3×C4⋊C4#4112yes—
271C3×C22⋊C4—24no—
272C3×C22⋊C4—41no—
273C3×C22⋊C4—42no—
274C3×C22⋊C4—42no—
275C3×C22⋊C4—42no—
276C3×C22⋊C4—42no—
277C3×C22⋊C4—42no—
278C3×C22⋊C4—42no—
279C3×C22⋊C4—42no—
280C3×C22⋊C4—81no—
281C3×C22⋊C4—81no—
282C3×C22⋊C4D814yescomplemented
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—21no—
286C3×C42—21no—
287C3×C42—42no—
288C3×C42—42no—
289C22×Q8—21no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4C23×C311yescharacteristic
293C22×D4C23×C311yescharacteristic
294C23×C4—21no—
295C23×C4—21no—
296C23×C4C23×C311yescharacteristic
297C2×D8—22no—
298C2×D8—22no—
299C2×D8—41no—
300C22×C8C23×C311yescharacteristic
301C22×C8C23×C311yescharacteristic
302C22×C8C23×C311yescharacteristic
303C22×C8C23×C311yescharacteristic
304C4⋊Q8—22no—
305C4⋊Q8—41no—
306#124—44no—
307#121—22no—
308#121—22no—
309#121—22no—
310#121—41no—
311C4×D4—22no—
312C4×D4—41no—
313C4×D4—44no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4C23×C311yescharacteristic
320C2×C4⋊C4C23×C311yescharacteristic
321C2×C4⋊C4C23×C311yescharacteristic
322C2×C4⋊C4C23×C311yescharacteristic
323C2×C4⋊C4C23×C311yescharacteristic
324C2×C4⋊C4C23×C311yescharacteristic
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4C3×D411yescharacteristic
336C2×C22⋊C4C3×D411yescharacteristic
337C2×C42—21no—
338C2×C42—21no—
339C2×C42C23×C311yescharacteristic
340C2×C42C23×C311yescharacteristic
341#107—22no—
342#107—22no—
343#107—22no—
344#107—41no—
345#107C3×D414yescomplemented
346C4⋊C8—22no—
347#102—22no—
348#102—22no—
349#102—22no—
350#102—22no—
351#102—22no—
352#102—22no—
353C22⋊C8—22no—
354C22⋊C8—22no—
355C4×C8—22no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95C3×D411yescharacteristic
361#95C3×D411yescharacteristic
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—22no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—41no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3C2×D812yes—
383C23×C3C22×D411yescharacteristic
384C3×Q8—84no—
385C3×D4—22no—
386C3×D4—22no—
387C3×D4—48no—
388C3×D4—41no—
389C3×D4—41no—
390C3×D4—41no—
391C3×D4—41no—
392C3×D4—41no—
393C3×D4—41no—
394C3×D4—84no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—84no—
431C2×C3×C4—84no—
432C2×C3×C4C2×D812yes—
433C2×C3×C4C2×D812yes—
434C2×C3×C4C22×D411yescharacteristic
435C2×C3×C4C2×#4111yescharacteristic
436C2×C3×C4C2×#4111yescharacteristic
437C2×C3×C4C2×#4111yescharacteristic
438C2×C3×C4H(5,𝔽2)11yescharacteristic
439C2×C3×C42−1+411yescharacteristic
440C3×C8—22no—
441C3×C8—22no—
442C3×C8—41no—
443C3×C8—41no—
444C24—21no—
445C24—21no—
446C24C2×C3×D411yescharacteristic
447C2×Q8—42no—
448C2×Q8—42no—
449C2×Q8—81no—
450C2×D4—24no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—81no—
467C2×D4C3×#4112yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4C2×C3×D411yescharacteristic
487C22×C4C2×C3×D411yescharacteristic
488C22×C4C2×C3×D411yescharacteristic
489C22×C4C2×C3×D411yescharacteristic
490C22×C4C2×C3×D411yescharacteristic
491C22×C4C24×C311yescharacteristic
492D8—44no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8C2×C3×D412yes—
504C2×C8C3×#4112yes—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—42no—
516C4⋊C4—42no—
517C4⋊C4C2×C3×D412yes—
518C4⋊C4C2×C3×D412yes—
519C4⋊C4C3×#4112yes—
520C22⋊C4—24no—
521C22⋊C4—41no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—81no—
530C22⋊C4—81no—
531C22⋊C4C3×D814yescomplemented
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—42no—
537C42—42no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3—81no—
549C22×C3—81no—
550C22×C3—81no—
551C22×C3—81no—
552C22×C3—81no—
553C22×C3—81no—
554C22×C3—81no—
555C22×C3—81no—
556C22×C3—81no—
557C22×C3—81no—
558C22×C3—81no—
559C22×C3#52511yescharacteristic
560C22×C3D4211yescharacteristic
561C22×C3#54711yescharacteristic
562C22×C3C22×D811yescharacteristic
563C22×C3#57511yescharacteristic
564C22×C3#57611yescharacteristic
565C22×C3#57811yescharacteristic
566C3×C4—22no—
567C3×C4—22no—
568C3×C4—41no—
569C3×C4—42no—
570C3×C4—41no—
571C3×C4—41no—
572C3×C4—42no—
573C3×C4—42no—
574C3×C4—81no—
575C3×C4—81no—
576C3×C4—81no—
577C3×C4#53211yescharacteristic
578C3×C4#54211yescharacteristic
579C3×C4#54811yescharacteristic
580C3×C4#55111yescharacteristic
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23C2×C3×D812yes—
602C23C22×C3×D411yescharacteristic
603Q8—84no—
604D4—22no—
605D4—22no—
606D4—48no—
607D4—41no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—84no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4C2×C3×D812yes—
652C2×C4C2×C3×D812yes—
653C2×C4C22×C3×D411yescharacteristic
654C2×C4C2×C3×#4111yescharacteristic
655C2×C4C2×C3×#4111yescharacteristic
656C2×C4C2×C3×#4111yescharacteristic
657C2×C4C3×H(5,𝔽2)11yescharacteristic
658C2×C4C3×2−1+411yescharacteristic
659C8—22no—
660C8—22no—
661C8—41no—
662C8—41no—
663C2×C3—42no—
664C2×C3—82no—
665C2×C3—161no—
666C2×C3#246111yescharacteristic
667C2×C3#310011yescharacteristic
668C2×C3#312411yescharacteristic
669C2×C3#327711yescharacteristic
670C2×C3D4×D811yescharacteristic
671C2×C3#333411yescharacteristic
672C2×C3#334711yescharacteristic
673C22—22no—
674C22—22no—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22C3×#52511yescharacteristic
695C22C3×D4211yescharacteristic
696C22C3×#54711yescharacteristic
697C22C22×C3×D811yescharacteristic
698C22C3×#57511yescharacteristic
699C22C3×#57611yescharacteristic
700C22C3×#57811yescharacteristic
701C4—22no—
702C4—22no—
703C4—41no—
704C4—41no—
705C4—42no—
706C4—42no—
707C4—41no—
708C4—42no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4C3×#53211yescharacteristic
713C4C3×#54211yescharacteristic
714C4C3×#54811yescharacteristic
715C4C3×#55111yescharacteristic
716C3#2678411yescharacteristic, direct product factor, Sylow
717C2—42no—
718C2—82no—
719C2—161no—
720C2C3×#246111yescharacteristic
721C2C3×#310011yescharacteristic
722C2C3×#312411yescharacteristic
723C2C3×#327711yescharacteristic
724C2C3×D4×D811yescharacteristic
725C2C3×#333411yescharacteristic
726C2C3×#334711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#480C2semidirect
2. C2×C3×#474C2semidirect
3. C3×#2491C2semidirect
4. C3×#2361C2semidirect
5. C3×#2067C2semidirect
6. C3×#2057C2semidirect
7. C3×#2033C2semidirect
9. C3×#1970C2semidirect
10. C3×#1925C2semidirect
11. C3×#1925C2semidirect
12. C3×#1923C2semidirect
13. C3×#1879C2semidirect
14. C3×#1852C2semidirect
15. C3×C4×#107C2semidirect
16. #26784C3direct (N × H)
62. C2×#480C2×C3semidirect
63. C2×#474C2×C3semidirect
64. #2491C2×C3semidirect
65. #2361C2×C3semidirect
66. #2067C2×C3semidirect
67. #2057C2×C3semidirect
68. #2033C2×C3semidirect
70. #1970C2×C3semidirect
71. #1925C2×C3semidirect
72. #1925C2×C3semidirect
73. #1923C2×C3semidirect
74. #1879C2×C3semidirect
75. #1852C2×C3semidirect
76. C4×#107C2×C3semidirect
133. C3×#107D4semidirect
282. C3×C22⋊C4D8semidirect
345. #107C3×D4semidirect
531. C22⋊C4C3×D8semidirect
716. C3#26784direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4802
C2×C3×#4742
C3×#24912
C3×#23612
C3×#20672
C3×#20572
C3×#20332
C3×#19992
C3×#19702
C3×#19252
C3×#19232
C3×#18792
C3×#18522
C3×C4×#1072
#267843