Finite Group Databasebeta

← C3×#26818 #10645425

Subgroups — C3×#26818 #10645425

Order 768.

972 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#486C211yesmaximal, characteristic, complemented
2C2×C3×C4×D8C211yesmaximal, characteristic, complemented
3C3×#2452C211yesmaximal, characteristic, complemented
4C3×#2445C211yesmaximal, characteristic, complemented
5C3×#2067C211yesmaximal, characteristic, complemented
6C3×#2057C211yesmaximal, characteristic, complemented
7C3×#2054C211yesmaximal, characteristic, complemented
8C3×#2011C211yesmaximal, characteristic
9C3×#1970C211yesmaximal, characteristic, complemented
10C3×#1934C211yesmaximal, characteristic, complemented
11C3×#1934C211yesmaximal, characteristic, complemented
12C3×#1934C211yesmaximal, characteristic, complemented
13C3×#1879C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic, complemented
15C3×C8×C4⋊C4C211yesmaximal, characteristic, complemented
16#26818C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×#127C2211yescharacteristic
21C2×C3×#123—21no—
22C2×C3×C22⋊Q8—21no—
23C2×C3×C4×D4C2211yescharacteristic
24C2×C3×C4×D4C2211yescharacteristic
25C3×#486—24no—
26C3×C4×D8—24no—
27C2×C3×#107C2211yescharacteristic
28C2×C3×#107C2211yescharacteristic
29C2×C3×C4⋊C8C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×C4×C8C2211yescharacteristic
39C2×C3×C4×C8C2211yescharacteristic
40C2×C3×C4×C8C2211yescharacteristic
41C3×#396—21no—
42C3×#394—21no—
43C3×#394—21no—
44C3×#393—21no—
45C3×#390C2211yescharacteristic
46C3×#390C2211yescharacteristic
47C3×#390C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#390C2211yescharacteristic
50C3×#389C2211yescharacteristic
51C3×#389C2211yescharacteristic
52C3×#389C2211yescharacteristic
53C3×#386—21no—
54C3×#385—21no—
55C3×C4×C4⋊C4C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#486C2×C311yescharacteristic, complemented
63C2×C4×D8C2×C311yescharacteristic, complemented
64#2452C2×C311yescharacteristic, complemented
65#2445C2×C311yescharacteristic, complemented
66#2067C2×C311yescharacteristic, complemented
67#2057C2×C311yescharacteristic, complemented
68#2054C2×C311yescharacteristic, complemented
69#2011C2×C311yescharacteristic
70#1970C2×C311yescharacteristic, complemented
71#1934C2×C311yescharacteristic, complemented
72#1934C2×C311yescharacteristic, complemented
73#1934C2×C311yescharacteristic, complemented
74#1879C2×C311yescharacteristic, complemented
75#1862C2×C311yescharacteristic, complemented
76C8×C4⋊C4C2×C311yescharacteristic, complemented
77C22×C3×Q8—21no—
78C22×C3×D4—21no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4—21no—
85C2×C3×D8—22no—
86C2×C3×D8—22no—
87C2×C3×D8—22no—
88C2×C3×D8—22no—
89C2×C3×D8—22no—
90C2×C3×D8—41no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×C4⋊Q8—22no—
96C3×C4⋊Q8—41no—
97C3×#127—22no—
98C3×#127—41no—
99C3×#123—44no—
100C3×C22⋊Q8—44no—
101C3×C4×D4—22no—
102C3×C4×D4—22no—
103C3×C4×D4—41no—
104C3×C4×D4—41no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4D411yescharacteristic
110C2×C3×C4⋊C4D411yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C42C2311yescharacteristic
129C2×C3×C42C2311yescharacteristic
130C2×C3×C42C2311yescharacteristic
131C3×#107—22no—
132C3×#107—41no—
133C3×C4⋊C8—22no—
134C3×#102—22no—
135C3×#102—22no—
136C3×#102—22no—
137C3×#102—22no—
138C3×#102—22no—
139C3×#102—22no—
140C3×#102—22no—
141C3×#102D414yes—
142C3×C4×C8—22no—
143C3×C4×C8—22no—
144C3×C4×C8—22no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95—21no—
148C3×#95D411yescharacteristic
149C3×#95D411yescharacteristic
150C22×D8C22×C311yescharacteristic
151C22×D8C22×C311yescharacteristic
152C2×C4⋊Q8C22×C311yescharacteristic
153C2×#127C22×C311yescharacteristic
154C2×#123—21no—
155C2×C22⋊Q8—21no—
156C2×C4×D4C22×C311yescharacteristic
157C2×C4×D4C22×C311yescharacteristic
158#486—24no—
159C4×D8—24no—
160C2×#107C22×C311yescharacteristic
161C2×#107C22×C311yescharacteristic
162C2×C4⋊C8C22×C311yescharacteristic
163C2×#102C22×C311yescharacteristic
164C2×#102C22×C311yescharacteristic
165C2×#102C22×C311yescharacteristic
166C2×#102C22×C311yescharacteristic
167C2×#102C22×C311yescharacteristic
168C2×#102C22×C311yescharacteristic
169C2×#102C22×C311yescharacteristic
170C2×#102C22×C311yescharacteristic
171C2×C4×C8C22×C311yescharacteristic
172C2×C4×C8C22×C311yescharacteristic
173C2×C4×C8C22×C311yescharacteristic
174#396—21no—
175#394—21no—
176#394—21no—
177#393—21no—
178#390C22×C311yescharacteristic
179#390C22×C311yescharacteristic
180#390C22×C311yescharacteristic
181#390C22×C311yescharacteristic
182#390C22×C311yescharacteristic
183#389C22×C311yescharacteristic
184#389C22×C311yescharacteristic
185#389C22×C311yescharacteristic
186#386—21no—
187#385—21no—
188C4×C4⋊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×C3—21no—
198C2×C3×Q8—42no—
199C2×C3×Q8—42no—
200C2×C3×Q8—81no—
201C2×C3×D4—21no—
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—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—42no—
218C2×C3×D4—42no—
219C2×C3×D4—42no—
220C2×C3×D4—42no—
221C2×C3×D4—81no—
222C2×C3×D4—81no—
223C2×C3×D4C2×D412yes—
224C2×C3×D4#4112yes—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—42no—
231C22×C3×C4—42no—
232C22×C3×C4—42no—
233C22×C3×C4—42no—
234C22×C3×C4—81no—
235C22×C3×C4—81no—
236C22×C3×C4C2×D411yescharacteristic
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—28no—
244C3×D8—44no—
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—
256C2×C3×C8#4112yes—
257C3×C4⋊C4—22no—
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—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—42no—
268C3×C4⋊C4—42no—
269C3×C4⋊C4—42no—
270C3×C4⋊C4—42no—
271C3×C4⋊C4D814yescomplemented
272C3×C4⋊C4C2×D412yes—
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—42no—
281C3×C22⋊C4—81no—
282C3×C22⋊C4—81no—
283C3×C22⋊C4—81no—
284C3×C22⋊C4—81no—
285C3×C42—21no—
286C3×C42—21no—
287C3×C42—21no—
288C3×C42—21no—
289C3×C42—21no—
290C3×C42—21no—
291C22×Q8—21no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4C23×C311yescharacteristic
295C22×D4C23×C311yescharacteristic
296C22×D4C23×C311yescharacteristic
297C23×C4—21no—
298C23×C4—21no—
299C2×D8—22no—
300C2×D8—22no—
301C2×D8—22no—
302C2×D8—22no—
303C2×D8—22no—
304C2×D8—41no—
305C22×C8C23×C311yescharacteristic
306C22×C8C23×C311yescharacteristic
307C22×C8C23×C311yescharacteristic
308C22×C8C23×C311yescharacteristic
309C4⋊Q8—22no—
310C4⋊Q8—41no—
311#127—22no—
312#127—41no—
313#123—44no—
314C22⋊Q8—44no—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—41no—
318C4×D4—41no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4C3×D411yescharacteristic
324C2×C4⋊C4C3×D411yescharacteristic
325C2×C4⋊C4C23×C311yescharacteristic
326C2×C4⋊C4C23×C311yescharacteristic
327C2×C4⋊C4C23×C311yescharacteristic
328C2×C4⋊C4C23×C311yescharacteristic
329C2×C4⋊C4C23×C311yescharacteristic
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C42C23×C311yescharacteristic
343C2×C42C23×C311yescharacteristic
344C2×C42C23×C311yescharacteristic
345#107—22no—
346#107—41no—
347C4⋊C8—22no—
348#102—22no—
349#102—22no—
350#102—22no—
351#102—22no—
352#102—22no—
353#102—22no—
354#102—22no—
355#102C3×D414yes—
356C4×C8—22no—
357C4×C8—22no—
358C4×C8—22no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95C3×D411yescharacteristic
363#95C3×D411yescharacteristic
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3—41no—
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×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3C22×D411yescharacteristic
386C3×Q8—84no—
387C3×D4—22no—
388C3×D4—22no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—41no—
392C3×D4—41no—
393C3×D4—41no—
394C3×D4—41no—
395C3×D4—41no—
396C3×D4—41no—
397C3×D4—41no—
398C3×D4—41no—
399C3×D4—84no—
400C3×D4—84no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
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—22no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
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×C4C2×D812yes—
435C2×C3×C4#13512yes—
436C2×C3×C4C22×D411yescharacteristic
437C2×C3×C4C2×#4111yescharacteristic
438C2×C3×C4C2×#4111yescharacteristic
439C2×C3×C4C2×#4111yescharacteristic
440C2×C3×C4H(5,𝔽2)11yescharacteristic
441C2×C3×C42−1+411yescharacteristic
442C3×C8—22no—
443C3×C8—22no—
444C3×C8—22no—
445C3×C8—41no—
446C24—21no—
447C24—21no—
448C24—21no—
449C2×Q8—42no—
450C2×Q8—42no—
451C2×Q8—81no—
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—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—81no—
473C2×D4—81no—
474C2×D4C2×C3×D412yes—
475C2×D4C3×#4112yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4C2×C3×D411yescharacteristic
488C22×C4C2×C3×D411yescharacteristic
489C22×C4C2×C3×D411yescharacteristic
490C22×C4C2×C3×D411yescharacteristic
491C22×C4C2×C3×D411yescharacteristic
492C22×C4C2×C3×D411yescharacteristic
493C22×C4C24×C311yescharacteristic
494D8—28no—
495D8—44no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8C2×C3×D412yes—
506C2×C8C3×#4112yes—
507C2×C8C3×#4112yes—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4C3×D814yescomplemented
523C4⋊C4C2×C3×D412yes—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—81no—
533C22⋊C4—81no—
534C22⋊C4—81no—
535C22⋊C4—81no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—42no—
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—81no—
560C22×C3—81no—
561C22×C3—81no—
562C22×C3—81no—
563C22×C3#53211yescharacteristic
564C22×C3D4211yescharacteristic
565C22×C3#54811yescharacteristic
566C22×C3C22×D811yescharacteristic
567C22×C3C2×#13511yescharacteristic
568C22×C3#57611yescharacteristic
569C22×C3#57711yescharacteristic
570C3×C4—22no—
571C3×C4—22no—
572C3×C4—22no—
573C3×C4—22no—
574C3×C4—41no—
575C3×C4—42no—
576C3×C4—41no—
577C3×C4—81no—
578C3×C4—81no—
579C3×C4—81no—
580C3×C4—81no—
581C3×C4#52511yescharacteristic
582C3×C4#54211yescharacteristic
583C3×C4#54711yescharacteristic
584C3×C4#55111yescharacteristic
585C23—22no—
586C23—22no—
587C23—41no—
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—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23C22×C3×D411yescharacteristic
607Q8—84no—
608D4—22no—
609D4—22no—
610D4—22no—
611D4—22no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—84no—
621D4—84no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
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—41no—
650C2×C4—41no—
651C2×C4—84no—
652C2×C4—84no—
653C2×C4C2×C3×D812yes—
654C2×C4C2×C3×D812yes—
655C2×C4C2×C3×D812yes—
656C2×C4C3×#13512yes—
657C2×C4C22×C3×D411yescharacteristic
658C2×C4C2×C3×#4111yescharacteristic
659C2×C4C2×C3×#4111yescharacteristic
660C2×C4C2×C3×#4111yescharacteristic
661C2×C4C3×H(5,𝔽2)11yescharacteristic
662C2×C4C3×2−1+411yescharacteristic
663C8—22no—
664C8—22no—
665C8—22no—
666C8—41no—
667C2×C3—82no—
668C2×C3—82no—
669C2×C3—161no—
670C2×C3#246111yescharacteristic
671C2×C3#316911yescharacteristic
672C2×C3#317911yescharacteristic
673C2×C3D4×D811yescharacteristic
674C2×C3#328211yescharacteristic
675C2×C3#335811yescharacteristic
676C2×C3#336111yescharacteristic
677C22—42no—
678C22—42no—
679C22—42no—
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—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22C3×#53211yescharacteristic
699C22C3×D4211yescharacteristic
700C22C3×#54811yescharacteristic
701C22C22×C3×D811yescharacteristic
702C22C2×C3×#13511yescharacteristic
703C22C3×#57611yescharacteristic
704C22C3×#57711yescharacteristic
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—41no—
710C4—42no—
711C4—41no—
712C4—81no—
713C4—81no—
714C4—81no—
715C4—81no—
716C4C3×#52511yescharacteristic
717C4C3×#54211yescharacteristic
718C4C3×#54711yescharacteristic
719C4C3×#55111yescharacteristic
720C3#2681811yescharacteristic, direct product factor, Sylow
721C2—82no—
722C2—82no—
723C2—161no—
724C2C3×#246111yescharacteristic
725C2C3×#316911yescharacteristic
726C2C3×#317911yescharacteristic
727C2C3×D4×D811yescharacteristic
728C2C3×#328211yescharacteristic
729C2C3×#335811yescharacteristic
730C2C3×#336111yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#486C2semidirect
2. C2×C3×C4×D8C2semidirect
3. C3×#2452C2semidirect
4. C3×#2445C2semidirect
5. C3×#2067C2semidirect
6. C3×#2057C2semidirect
7. C3×#2054C2semidirect
9. C3×#1970C2semidirect
10. C3×#1934C2semidirect
11. C3×#1934C2semidirect
12. C3×#1934C2semidirect
13. C3×#1879C2semidirect
14. C3×#1862C2semidirect
15. C3×C8×C4⋊C4C2semidirect
16. #26818C3direct (N × H)
62. C2×#486C2×C3semidirect
63. C2×C4×D8C2×C3semidirect
64. #2452C2×C3semidirect
65. #2445C2×C3semidirect
66. #2067C2×C3semidirect
67. #2057C2×C3semidirect
68. #2054C2×C3semidirect
70. #1970C2×C3semidirect
71. #1934C2×C3semidirect
72. #1934C2×C3semidirect
73. #1934C2×C3semidirect
74. #1879C2×C3semidirect
75. #1862C2×C3semidirect
76. C8×C4⋊C4C2×C3semidirect
271. C3×C4⋊C4D8semidirect
522. C4⋊C4C3×D8semidirect
720. C3#26818direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4862
C2×C3×C4×D82
C3×#24522
C3×#24452
C3×#20672
C3×#20572
C3×#20542
C3×#20112
C3×#19702
C3×#19342
C3×#18792
C3×#18622
C3×C8×C4⋊C42
#268183