Finite Group Databasebeta

← C3×#26737 #10645344

Subgroups — C3×#26737 #10645344

Order 768.

904 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2491C211yesmaximal, characteristic, complemented
2C3×#2361C211yesmaximal, characteristic, complemented
3C3×#2054C211yesmaximal, characteristic, complemented
4C3×#2033C211yesmaximal, characteristic, complemented
5C3×#2023C211yesmaximal, characteristic, complemented
6C3×#1999C211yesmaximal, characteristic
7C3×#1987C211yesmaximal, characteristic, complemented
8C3×#1936C211yesmaximal, characteristic, complemented
9C3×#1925C211yesmaximal, characteristic, complemented
10C3×#1924C211yesmaximal, characteristic, complemented
11C3×#1921C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic, complemented
13C3×#1874C211yesmaximal, characteristic, complemented
14C3×#1824C211yesmaximal, characteristic, complemented
15C3×#1762C211yesmaximal, characteristic, complemented
16#26737C311yesmaximal, 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
25C2×C3×#107C2211yescharacteristic
26C2×C3×C4⋊C8C2211yescharacteristic
27C2×C3×#102C2211yescharacteristic
28C2×C3×#102C2211yescharacteristic
29C2×C3×#102C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×C22⋊C8C2211yescharacteristic
34C2×C3×C22⋊C8C2211yescharacteristic
35C2×C3×#97C2211yescharacteristic
36C3×#394—21no—
37C3×#393—21no—
38C3×#390C2211yescharacteristic
39C3×#390C2211yescharacteristic
40C3×#390C2211yescharacteristic
41C3×#389C2211yescharacteristic
42C3×#388—21no—
43C3×#388—21no—
44C3×#386—21no—
45C3×#385—21no—
46C3×#380C2211yescharacteristic
47C3×C4×C4⋊C4C2211yescharacteristic
48C3×C4×C4⋊C4C2211yescharacteristic
49C3×C4×C22⋊C4C2211yescharacteristic
50C3×#340C2211yescharacteristic
51C3×#340C2211yescharacteristic
52C3×#340C2211yescharacteristic
53C3×#340C2211yescharacteristic
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#2491C2×C311yescharacteristic, complemented
61#2361C2×C311yescharacteristic, complemented
62#2054C2×C311yescharacteristic, complemented
63#2033C2×C311yescharacteristic, complemented
64#2023C2×C311yescharacteristic, complemented
65#1999C2×C311yescharacteristic
66#1987C2×C311yescharacteristic, complemented
67#1936C2×C311yescharacteristic, complemented
68#1925C2×C311yescharacteristic, complemented
69#1924C2×C311yescharacteristic, complemented
70#1921C2×C311yescharacteristic, complemented
71#1879C2×C311yescharacteristic, complemented
72#1874C2×C311yescharacteristic, complemented
73#1824C2×C311yescharacteristic, complemented
74#1762C2×C311yescharacteristic, complemented
75C22×C3×Q8—21no—
76C22×C3×D4—21no—
77C22×C3×D4—21no—
78C22×C3×D4C2311yescharacteristic
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C23×C3×C4—21no—
82C23×C3×C4C2311yescharacteristic
83C2×C3×D8—22no—
84C2×C3×D8—41no—
85C2×C3×D8—41no—
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×C4⋊Q8—22no—
91C3×C4⋊Q8—41no—
92C3×#124—44no—
93C3×#121—22no—
94C3×#121—22no—
95C3×#121—22no—
96C3×#121—41no—
97C3×C4×D4—22no—
98C3×C4×D4—41no—
99C3×C4×D4—44no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—41no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
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⋊C4D411yescharacteristic
122C2×C3×C22⋊C4D411yescharacteristic
123C2×C3×C42—21no—
124C2×C3×C42—21no—
125C2×C3×C42C2311yescharacteristic
126C2×C3×C42C2311yescharacteristic
127C3×#107—22no—
128C3×C4⋊C8—41no—
129C3×#102—22no—
130C3×#102—22no—
131C3×#102—22no—
132C3×#102—22no—
133C3×#102—41no—
134C3×#102—41no—
135C3×C22⋊C8—41no—
136C3×C22⋊C8—41no—
137C3×#97—41no—
138C3×#95—21no—
139C3×#95—21no—
140C3×#95—21no—
141C3×#95—21no—
142C3×#95D411yescharacteristic
143C3×#95D411yescharacteristic
144C22×D8C22×C311yescharacteristic
145C2×C4⋊Q8C22×C311yescharacteristic
146C2×#124—21no—
147C2×#121C22×C311yescharacteristic
148C2×#121C22×C311yescharacteristic
149C2×C4×D4—21no—
150C2×C4×D4C22×C311yescharacteristic
151C22×C4⋊C4C22×C311yescharacteristic
152C2×#107C22×C311yescharacteristic
153C2×C4⋊C8C22×C311yescharacteristic
154C2×#102C22×C311yescharacteristic
155C2×#102C22×C311yescharacteristic
156C2×#102C22×C311yescharacteristic
157C2×#102C22×C311yescharacteristic
158C2×#102C22×C311yescharacteristic
159C2×#102C22×C311yescharacteristic
160C2×C22⋊C8C22×C311yescharacteristic
161C2×C22⋊C8C22×C311yescharacteristic
162C2×#97C22×C311yescharacteristic
163#394—21no—
164#393—21no—
165#390C22×C311yescharacteristic
166#390C22×C311yescharacteristic
167#390C22×C311yescharacteristic
168#389C22×C311yescharacteristic
169#388—21no—
170#388—21no—
171#386—21no—
172#385—21no—
173#380C22×C311yescharacteristic
174C4×C4⋊C4C22×C311yescharacteristic
175C4×C4⋊C4C22×C311yescharacteristic
176C4×C22⋊C4C22×C311yescharacteristic
177#340C22×C311yescharacteristic
178#340C22×C311yescharacteristic
179#340C22×C311yescharacteristic
180#340C22×C311yescharacteristic
181#340C22×C311yescharacteristic
182#340C22×C311yescharacteristic
183#340C22×C311yescharacteristic
184#340C22×C311yescharacteristic
185#336C22×C311yescharacteristic
186#336C22×C311yescharacteristic
187C24×C3—21no—
188C24×C3—21no—
189C24×C3C2×D411yescharacteristic
190C2×C3×Q8—42no—
191C2×C3×Q8—42no—
192C2×C3×Q8—81no—
193C2×C3×D4—24no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—42no—
206C2×C3×D4—42no—
207C2×C3×D4—42no—
208C2×C3×D4—42no—
209C2×C3×D4—81no—
210C2×C3×D4#4112yes—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—42no—
224C22×C3×C4—42no—
225C22×C3×C4—42no—
226C22×C3×C4—42no—
227C22×C3×C4—81no—
228C22×C3×C4—81no—
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2411yescharacteristic
235C3×D8—44no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—42no—
258C3×C4⋊C4—42no—
259C3×C4⋊C4—42no—
260C3×C4⋊C4#4112yes—
261C3×C4⋊C4#4112yes—
262C3×C4⋊C4#4112yes—
263C3×C22⋊C4—24no—
264C3×C22⋊C4—22no—
265C3×C22⋊C4—22no—
266C3×C22⋊C4—42no—
267C3×C22⋊C4—42no—
268C3×C22⋊C4—42no—
269C3×C22⋊C4—42no—
270C3×C22⋊C4—42no—
271C3×C22⋊C4—42no—
272C3×C22⋊C4—42no—
273C3×C22⋊C4—81no—
274C3×C22⋊C4—81no—
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—21no—
278C3×C42—21no—
279C3×C42—42no—
280C3×C42—42no—
281C22×Q8—21no—
282C22×D4—21no—
283C22×D4—21no—
284C22×D4C23×C311yescharacteristic
285C22×D4C23×C311yescharacteristic
286C23×C4—21no—
287C23×C4—21no—
288C23×C4C23×C311yescharacteristic
289C2×D8—22no—
290C2×D8—41no—
291C2×D8—41no—
292C22×C8C23×C311yescharacteristic
293C22×C8C23×C311yescharacteristic
294C22×C8C23×C311yescharacteristic
295C22×C8C23×C311yescharacteristic
296C4⋊Q8—22no—
297C4⋊Q8—41no—
298#124—44no—
299#121—22no—
300#121—22no—
301#121—22no—
302#121—41no—
303C4×D4—22no—
304C4×D4—41no—
305C4×D4—44no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4C23×C311yescharacteristic
312C2×C4⋊C4C23×C311yescharacteristic
313C2×C4⋊C4C23×C311yescharacteristic
314C2×C4⋊C4C23×C311yescharacteristic
315C2×C4⋊C4C23×C311yescharacteristic
316C2×C4⋊C4C23×C311yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4C3×D411yescharacteristic
328C2×C22⋊C4C3×D411yescharacteristic
329C2×C42—21no—
330C2×C42—21no—
331C2×C42C23×C311yescharacteristic
332C2×C42C23×C311yescharacteristic
333#107—22no—
334C4⋊C8—41no—
335#102—22no—
336#102—22no—
337#102—22no—
338#102—22no—
339#102—41no—
340#102—41no—
341C22⋊C8—41no—
342C22⋊C8—41no—
343#97—41no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95C3×D411yescharacteristic
349#95C3×D411yescharacteristic
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—22no—
357C23×C3—41no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3AGL(1,ℤ/8)12yes—
371C23×C3C22×D411yescharacteristic
372C3×Q8—84no—
373C3×D4—22no—
374C3×D4—22no—
375C3×D4—48no—
376C3×D4—41no—
377C3×D4—41no—
378C3×D4—41no—
379C3×D4—41no—
380C3×D4—41no—
381C3×D4—41no—
382C3×D4—84no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
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—84no—
420C2×C3×C4—84no—
421C2×C3×C4AGL(1,ℤ/8)12yes—
422C2×C3×C4C2×#4111yescharacteristic
423C2×C3×C4C2×#4111yescharacteristic
424C2×C3×C4C2×#4111yescharacteristic
425C2×C3×C4C2×#4111yescharacteristic
426C2×C3×C4H(5,𝔽2)11yescharacteristic
427C2×C3×C4H(5,𝔽2)11yescharacteristic
428C3×C8—41no—
429C3×C8—41no—
430C3×C8—41no—
431C3×C8—41no—
432C24—21no—
433C24—21no—
434C24C2×C3×D411yescharacteristic
435C2×Q8—42no—
436C2×Q8—42no—
437C2×Q8—81no—
438C2×D4—24no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—81no—
455C2×D4C3×#4112yes—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4C2×C3×D411yescharacteristic
475C22×C4C2×C3×D411yescharacteristic
476C22×C4C2×C3×D411yescharacteristic
477C22×C4C2×C3×D411yescharacteristic
478C22×C4C2×C3×D411yescharacteristic
479C22×C4C24×C311yescharacteristic
480D8—44no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4C3×#4112yes—
506C4⋊C4C3×#4112yes—
507C4⋊C4C3×#4112yes—
508C22⋊C4—24no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—81no—
519C22⋊C4—81no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—42no—
525C42—42no—
526C22×C3—22no—
527C22×C3—22no—
528C22×C3—22no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—42no—
534C22×C3—42no—
535C22×C3—42no—
536C22×C3—81no—
537C22×C3—81no—
538C22×C3—81no—
539C22×C3—81no—
540C22×C3—81no—
541C22×C3—81no—
542C22×C3—81no—
543C22×C3—81no—
544C22×C3—81no—
545C22×C3—81no—
546C22×C3—81no—
547C22×C3#52511yescharacteristic
548C22×C3#54611yescharacteristic
549C22×C3#54611yescharacteristic
550C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
551C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
552C22×C3#57611yescharacteristic
553C22×C3#57811yescharacteristic
554C3×C4—22no—
555C3×C4—42no—
556C3×C4—41no—
557C3×C4—41no—
558C3×C4—41no—
559C3×C4—42no—
560C3×C4—41no—
561C3×C4—42no—
562C3×C4—81no—
563C3×C4—81no—
564C3×C4—81no—
565C3×C4#52911yescharacteristic
566C3×C4#53811yescharacteristic
567C3×C4#55511yescharacteristic
568C3×C4#55911yescharacteristic
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23C3×AGL(1,ℤ/8)12yes—
590C23C22×C3×D411yescharacteristic
591Q8—84no—
592D4—22no—
593D4—22no—
594D4—48no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—84no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
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—84no—
639C2×C4—84no—
640C2×C4C3×AGL(1,ℤ/8)12yes—
641C2×C4C2×C3×#4111yescharacteristic
642C2×C4C2×C3×#4111yescharacteristic
643C2×C4C2×C3×#4111yescharacteristic
644C2×C4C2×C3×#4111yescharacteristic
645C2×C4C3×H(5,𝔽2)11yescharacteristic
646C2×C4C3×H(5,𝔽2)11yescharacteristic
647C8—41no—
648C8—41no—
649C8—41no—
650C8—41no—
651C2×C3—42no—
652C2×C3—82no—
653C2×C3—161no—
654C2×C3#245911yescharacteristic
655C2×C3#310911yescharacteristic
656C2×C3#312411yescharacteristic
657C2×C3#330811yescharacteristic
658C2×C3#330811yescharacteristic
659C2×C3#331811yescharacteristic
660C2×C3#332511yescharacteristic
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22C3×#52511yescharacteristic
683C22C3×#54611yescharacteristic
684C22C3×#54611yescharacteristic
685C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
686C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
687C22C3×#57611yescharacteristic
688C22C3×#57811yescharacteristic
689C4—22no—
690C4—41no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—41no—
695C4—42no—
696C4—42no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4C3×#52911yescharacteristic
701C4C3×#53811yescharacteristic
702C4C3×#55511yescharacteristic
703C4C3×#55911yescharacteristic
704C3#2673711yescharacteristic, direct product factor, Sylow
705C2—42no—
706C2—82no—
707C2—161no—
708C2C3×#245911yescharacteristic
709C2C3×#310911yescharacteristic
710C2C3×#312411yescharacteristic
711C2C3×#330811yescharacteristic
712C2C3×#330811yescharacteristic
713C2C3×#331811yescharacteristic
714C2C3×#332511yescharacteristic
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. C3×#2491C2semidirect
2. C3×#2361C2semidirect
3. C3×#2054C2semidirect
4. C3×#2033C2semidirect
5. C3×#2023C2semidirect
7. C3×#1987C2semidirect
8. C3×#1936C2semidirect
9. C3×#1925C2semidirect
10. C3×#1924C2semidirect
11. C3×#1921C2semidirect
12. C3×#1879C2semidirect
13. C3×#1874C2semidirect
14. C3×#1824C2semidirect
15. C3×#1762C2semidirect
16. #26737C3direct (N × H)
60. #2491C2×C3semidirect
61. #2361C2×C3semidirect
62. #2054C2×C3semidirect
63. #2033C2×C3semidirect
64. #2023C2×C3semidirect
66. #1987C2×C3semidirect
67. #1936C2×C3semidirect
68. #1925C2×C3semidirect
69. #1924C2×C3semidirect
70. #1921C2×C3semidirect
71. #1879C2×C3semidirect
72. #1874C2×C3semidirect
73. #1824C2×C3semidirect
74. #1762C2×C3semidirect
704. C3#26737direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#24912
C3×#23612
C3×#20542
C3×#20332
C3×#20232
C3×#19992
C3×#19872
C3×#19362
C3×#19252
C3×#19242
C3×#19212
C3×#18792
C3×#18742
C3×#18242
C3×#17622
#267373