Finite Group Databasebeta

← C2×C3×#2694 #10670721

Subgroups — C2×C3×#2694 #10670721

Order 768.

2722 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#125C211yesmaximal, characteristic, complemented
2C22×C3×#123C211yesmaximal, characteristic
3C3×#2694C2116yesmaximal, direct product factor
4C2×C3×#399C211yesmaximal, characteristic, complemented
5C2×C3×#399C211yesmaximal, characteristic, complemented
6C2×C3×#398C211yesmaximal, characteristic, complemented
7C2×C3×#397C211yesmaximal, characteristic, complemented
8C2×C3×#396C211yesmaximal, characteristic, complemented
9C2×C3×#394C211yesmaximal, characteristic
10C2×C3×#390C211yesmaximal, characteristic
11C2×C3×#389C211yesmaximal, characteristic, complemented
12C2×C3×#388C211yesmaximal, characteristic, complemented
13C2×C3×#388C211yesmaximal, characteristic, complemented
14C2×C3×#387C211yesmaximal, characteristic, complemented
15C2×C3×#385C211yesmaximal, characteristic, complemented
16C2×C3×#380C211yesmaximal, characteristic, complemented
17C2×#2694C311yesmaximal, characteristic, direct product factor, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C2×C3×#125—28no—
21C2×C3×#125C2218yescomplemented
22C2×C3×#123—28no—
23C2×C3×#123C2218yes—
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C22×C3×C4⋊C4C2211yescharacteristic
32C22×C3×C4⋊C4C2211yescharacteristic
33C22×C3×C4⋊C4C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C22×C3×C4⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4C2211yescharacteristic
37C22×C3×C22⋊C4C2211yescharacteristic
38C22×C3×C22⋊C4C2211yescharacteristic
39C22×C3×C22⋊C4C2211yescharacteristic
40C22×C3×C22⋊C4C2211yescharacteristic
41C22×C3×C22⋊C4C2211yescharacteristic
42C22×C3×C22⋊C4C2211yescharacteristic
43C22×C3×C22⋊C4C2211yescharacteristic
44C22×C3×C22⋊C4C2211yescharacteristic
45C22×C3×C22⋊C4C2211yescharacteristic
46C22×C3×C22⋊C4C2211yescharacteristic
47C22×C3×C42C2211yescharacteristic
48C22×C3×C42C2211yescharacteristic
49C3×#399C2218yescomplemented
50C3×#399C2218yescomplemented
51C3×#398C2218yescomplemented
52C3×#397C2218yescomplemented
53C3×#396C2218yescomplemented
54C3×#394C2218yes—
55C3×#390C2218yes—
56C3×#389C2218yescomplemented
57C3×#388C2218yescomplemented
58C3×#388C2218yescomplemented
59C3×#387C2218yescomplemented
60C3×#385C2218yescomplemented
61C3×#380C2218yescomplemented
62C2×C3×#95C2211yescharacteristic
63C2×C3×#95C2211yescharacteristic
64C2×C3×#95C2211yescharacteristic
65C2×C3×#95C2211yescharacteristic
66C2×C3×#95C2211yescharacteristic
67C2×C3×#95C2211yescharacteristic
68C2×C3×#95C2211yescharacteristic
69C2×C3×#95C2211yescharacteristic
70C22×#125C2×C311yescharacteristic, complemented
71C22×#123C2×C311yescharacteristic
72#2694C2×C3116yesdirect product factor
73C2×#399C2×C311yescharacteristic, complemented
74C2×#399C2×C311yescharacteristic, complemented
75C2×#398C2×C311yescharacteristic, complemented
76C2×#397C2×C311yescharacteristic, complemented
77C2×#396C2×C311yescharacteristic, complemented
78C2×#394C2×C311yescharacteristic
79C2×#390C2×C311yescharacteristic
80C2×#389C2×C311yescharacteristic, complemented
81C2×#388C2×C311yescharacteristic, complemented
82C2×#388C2×C311yescharacteristic, complemented
83C2×#387C2×C311yescharacteristic, complemented
84C2×#385C2×C311yescharacteristic, complemented
85C2×#380C2×C311yescharacteristic, complemented
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C22×C3×D4—24no—
89C22×C3×D4—24no—
90C22×C3×D4—42no—
91C22×C3×D4C2314yes—
92C23×C3×C4—24no—
93C23×C3×C4—24no—
94C23×C3×C4—42no—
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2314yes—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C3×#125—232no—
110C3×#123—232no—
111C2×C3×C4⋊C4—24no—
112C2×C3×C4⋊C4—24no—
113C2×C3×C4⋊C4—24no—
114C2×C3×C4⋊C4—24no—
115C2×C3×C4⋊C4—24no—
116C2×C3×C4⋊C4—24no—
117C2×C3×C4⋊C4—24no—
118C2×C3×C4⋊C4—42no—
119C2×C3×C4⋊C4—42no—
120C2×C3×C4⋊C4—42no—
121C2×C3×C4⋊C4—42no—
122C2×C3×C4⋊C4D418yes—
123C2×C3×C4⋊C4C2314yes—
124C2×C3×C4⋊C4C2314yes—
125C2×C3×C4⋊C4C2314yes—
126C2×C3×C4⋊C4C2314yes—
127C2×C3×C4⋊C4C2314yes—
128C2×C3×C4⋊C4C2314yes—
129C2×C3×C4⋊C4C2314yes—
130C2×C3×C4⋊C4C2314yes—
131C2×C3×C4⋊C4C2314yes—
132C2×C3×C4⋊C4C2314yes—
133C2×C3×C4⋊C4C2314yes—
134C2×C3×C4⋊C4C2314yes—
135C2×C3×C22⋊C4—24no—
136C2×C3×C22⋊C4—24no—
137C2×C3×C22⋊C4—24no—
138C2×C3×C22⋊C4—24no—
139C2×C3×C22⋊C4—24no—
140C2×C3×C22⋊C4—24no—
141C2×C3×C22⋊C4—42no—
142C2×C3×C22⋊C4—42no—
143C2×C3×C22⋊C4—42no—
144C2×C3×C22⋊C4—42no—
145C2×C3×C22⋊C4—42no—
146C2×C3×C22⋊C4C2314yes—
147C2×C3×C22⋊C4C2314yes—
148C2×C3×C22⋊C4C2314yes—
149C2×C3×C22⋊C4C2314yes—
150C2×C3×C22⋊C4C2314yes—
151C2×C3×C22⋊C4C2314yes—
152C2×C3×C22⋊C4C2314yes—
153C2×C3×C22⋊C4C2314yes—
154C2×C3×C22⋊C4C2314yes—
155C2×C3×C22⋊C4C2314yes—
156C2×C3×C22⋊C4C2314yes—
157C2×C3×C42—24no—
158C2×C3×C42—42no—
159C2×C3×C42C2314yes—
160C2×C3×C42C2314yes—
161C3×#95C2314yes—
162C3×#95C2314yes—
163C3×#95C2314yes—
164C3×#95C2314yes—
165C3×#95C2314yes—
166C3×#95C2314yes—
167C3×#95C2314yes—
168C3×#95C2314yes—
169C23×D4C22×C311yescharacteristic
170C24×C4C22×C311yescharacteristic
171C2×#125—28no—
172C2×#125C22×C318yescomplemented
173C2×#123—28no—
174C2×#123C22×C318yes—
175C22×C4⋊C4C22×C311yescharacteristic
176C22×C4⋊C4C22×C311yescharacteristic
177C22×C4⋊C4C22×C311yescharacteristic
178C22×C4⋊C4C22×C311yescharacteristic
179C22×C4⋊C4C22×C311yescharacteristic
180C22×C4⋊C4C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182C22×C4⋊C4C22×C311yescharacteristic
183C22×C4⋊C4C22×C311yescharacteristic
184C22×C4⋊C4C22×C311yescharacteristic
185C22×C4⋊C4C22×C311yescharacteristic
186C22×C4⋊C4C22×C311yescharacteristic
187C22×C22⋊C4C22×C311yescharacteristic
188C22×C22⋊C4C22×C311yescharacteristic
189C22×C22⋊C4C22×C311yescharacteristic
190C22×C22⋊C4C22×C311yescharacteristic
191C22×C22⋊C4C22×C311yescharacteristic
192C22×C22⋊C4C22×C311yescharacteristic
193C22×C22⋊C4C22×C311yescharacteristic
194C22×C22⋊C4C22×C311yescharacteristic
195C22×C22⋊C4C22×C311yescharacteristic
196C22×C22⋊C4C22×C311yescharacteristic
197C22×C22⋊C4C22×C311yescharacteristic
198C22×C42C22×C311yescharacteristic
199C22×C42C22×C311yescharacteristic
200#399C22×C318yescomplemented
201#399C22×C318yescomplemented
202#398C22×C318yescomplemented
203#397C22×C318yescomplemented
204#396C22×C318yescomplemented
205#394C22×C318yes—
206#390C22×C318yes—
207#389C22×C318yescomplemented
208#388C22×C318yescomplemented
209#388C22×C318yescomplemented
210#387C22×C318yescomplemented
211#385C22×C318yescomplemented
212#380C22×C318yescomplemented
213C2×#95C22×C311yescharacteristic
214C2×#95C22×C311yescharacteristic
215C2×#95C22×C311yescharacteristic
216C2×#95C22×C311yescharacteristic
217C2×#95C22×C311yescharacteristic
218C2×#95C22×C311yescharacteristic
219C2×#95C22×C311yescharacteristic
220C2×#95C22×C311yescharacteristic
221C24×C3—22no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—22no—
226C24×C3—22no—
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3—22no—
231C24×C3—22no—
232C24×C3—22no—
233C24×C3—22no—
234C24×C3#4114yes—
235C24×C3C2412yes—
236C24×C3C2412yes—
237C24×C3C2411yescharacteristic
238C2×C3×D4—28no—
239C2×C3×D4—28no—
240C2×C3×D4—44no—
241C2×C3×D4—416no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—28no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—28no—
279C22×C3×C4—44no—
280C22×C3×C4—416no—
281C22×C3×C4C2×D414yes—
282C22×C3×C4C2×D414yes—
283C22×C3×C4C2×D414yes—
284C22×C3×C4#4114yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2412yes—
289C22×C3×C4C2412yes—
290C22×C3×C4C2412yes—
291C22×C3×C4C2412yes—
292C22×C3×C4C2412yes—
293C22×C3×C4C2412yes—
294C22×C3×C4C2412yes—
295C22×C3×C4C2412yes—
296C22×C3×C4C2412yes—
297C22×C3×C4C2412yes—
298C3×C4⋊C4—28no—
299C3×C4⋊C4—28no—
300C3×C4⋊C4—28no—
301C3×C4⋊C4—28no—
302C3×C4⋊C4—28no—
303C3×C4⋊C4—28no—
304C3×C4⋊C4—28no—
305C3×C4⋊C4—44no—
306C3×C4⋊C4—44no—
307C3×C4⋊C4—44no—
308C3×C4⋊C4—44no—
309C3×C4⋊C4C2×D4116yes—
310C3×C22⋊C4—28no—
311C3×C22⋊C4—28no—
312C3×C22⋊C4—28no—
313C3×C22⋊C4—28no—
314C3×C22⋊C4—28no—
315C3×C22⋊C4—28no—
316C3×C22⋊C4—44no—
317C3×C22⋊C4—44no—
318C3×C22⋊C4—44no—
319C3×C22⋊C4—44no—
320C3×C22⋊C4—44no—
321C3×C42—28no—
322C3×C42—44no—
323C25C23×C311yescharacteristic
324C25C23×C311yescharacteristic
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—42no—
328C22×D4C23×C314yes—
329C23×C4—24no—
330C23×C4—24no—
331C23×C4—42no—
332C23×C4C23×C311yescharacteristic
333C23×C4C23×C311yescharacteristic
334C23×C4C23×C311yescharacteristic
335C23×C4C23×C311yescharacteristic
336C23×C4C23×C311yescharacteristic
337C23×C4C23×C311yescharacteristic
338C23×C4C23×C311yescharacteristic
339C23×C4C23×C311yescharacteristic
340C23×C4C23×C311yescharacteristic
341C23×C4C23×C314yes—
342C23×C4C23×C311yescharacteristic
343C23×C4C23×C311yescharacteristic
344C23×C4C23×C311yescharacteristic
345C23×C4C23×C311yescharacteristic
346#125—232no—
347#123—232no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4C3×D418yes—
360C2×C4⋊C4C23×C314yes—
361C2×C4⋊C4C23×C314yes—
362C2×C4⋊C4C23×C314yes—
363C2×C4⋊C4C23×C314yes—
364C2×C4⋊C4C23×C314yes—
365C2×C4⋊C4C23×C314yes—
366C2×C4⋊C4C23×C314yes—
367C2×C4⋊C4C23×C314yes—
368C2×C4⋊C4C23×C314yes—
369C2×C4⋊C4C23×C314yes—
370C2×C4⋊C4C23×C314yes—
371C2×C4⋊C4C23×C314yes—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4C23×C314yes—
384C2×C22⋊C4C23×C314yes—
385C2×C22⋊C4C23×C314yes—
386C2×C22⋊C4C23×C314yes—
387C2×C22⋊C4C23×C314yes—
388C2×C22⋊C4C23×C314yes—
389C2×C22⋊C4C23×C314yes—
390C2×C22⋊C4C23×C314yes—
391C2×C22⋊C4C23×C314yes—
392C2×C22⋊C4C23×C314yes—
393C2×C22⋊C4C23×C314yes—
394C2×C42—24no—
395C2×C42—42no—
396C2×C42C23×C314yes—
397C2×C42C23×C314yes—
398#95C23×C314yes—
399#95C23×C314yes—
400#95C23×C314yes—
401#95C23×C314yes—
402#95C23×C314yes—
403#95C23×C314yes—
404#95C23×C314yes—
405#95C23×C314yes—
406C23×C3—28no—
407C23×C3—28no—
408C23×C3—28no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—44no—
423C23×C3—44no—
424C23×C3—44no—
425C23×C3—44no—
426C23×C3—44no—
427C23×C3—44no—
428C23×C3—44no—
429C23×C3—44no—
430C23×C3—44no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3C22×D412yes—
434C23×C3C2×#4114yes—
435C23×C3C2×#4112yes—
436C23×C3C2×#4112yes—
437C23×C3H(5,𝔽2)12yes—
438C23×C3H(5,𝔽2)12yes—
439C23×C32−1+412yes—
440C23×C32−1+412yes—
441C23×C3C2511yescharacteristic
442C3×D4—416no—
443C2×C3×C4—28no—
444C2×C3×C4—28no—
445C2×C3×C4—28no—
446C2×C3×C4—28no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—416no—
483C2×C3×C4—44no—
484C2×C3×C4—44no—
485C2×C3×C4—44no—
486C2×C3×C4—44no—
487C2×C3×C4—44no—
488C2×C3×C4—44no—
489C2×C3×C4—44no—
490C2×C3×C4—44no—
491C2×C3×C4—44no—
492C2×C3×C4C22×D414yes—
493C2×C3×C4C22×D414yes—
494C2×C3×C4C22×D414yes—
495C2×C3×C4C2×#4114yes—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24C3×#4114yes—
510C24C24×C312yes—
511C24C24×C312yes—
512C24C24×C311yescharacteristic
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—44no—
516C2×D4—416no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—28no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—44no—
555C22×C4—416no—
556C22×C4C2×C3×D414yes—
557C22×C4C2×C3×D414yes—
558C22×C4C2×C3×D414yes—
559C22×C4C3×#4114yes—
560C22×C4C24×C312yes—
561C22×C4C24×C312yes—
562C22×C4C24×C312yes—
563C22×C4C24×C312yes—
564C22×C4C24×C312yes—
565C22×C4C24×C312yes—
566C22×C4C24×C312yes—
567C22×C4C24×C312yes—
568C22×C4C24×C312yes—
569C22×C4C24×C312yes—
570C22×C4C24×C312yes—
571C22×C4C24×C312yes—
572C22×C4C24×C312yes—
573C4⋊C4—28no—
574C4⋊C4—28no—
575C4⋊C4—28no—
576C4⋊C4—28no—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—28no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4C2×C3×D4116yes—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—28no—
588C22⋊C4—28no—
589C22⋊C4—28no—
590C22⋊C4—28no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C42—28no—
597C42—44no—
598C22×C3—24no—
599C22×C3—24no—
600C22×C3—24no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—416no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—88no—
614C22×C3#53614yes—
615C22×C3#53914yes—
616C22×C3#53914yes—
617C22×C3#54614yes—
618C22×C3#55014yes—
619C22×C3#55214yes—
620C22×C3#56214yes—
621C22×C3C23×D411yescharacteristic
622C22×C3C22×#4111yescharacteristic
623C22×C3C22×#4111yescharacteristic
624C22×C3C2×H(5,𝔽2)11yescharacteristic
625C22×C3C2×H(5,𝔽2)11yescharacteristic
626C22×C3C2×2−1+411yescharacteristic
627C22×C3C2×2−1+411yescharacteristic
628C3×C4—24no—
629C3×C4—24no—
630C3×C4—24no—
631C3×C4—24no—
632C3×C4—42no—
633C3×C4—42no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—42no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4—42no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—28no—
648C23—28no—
649C23—28no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23C22×C3×D412yes—
669C23C2×C3×#4114yes—
670C23C2×C3×#4112yes—
671C23C2×C3×#4112yes—
672C23C3×H(5,𝔽2)12yes—
673C23C3×H(5,𝔽2)12yes—
674C23C3×2−1+412yes—
675C23C3×2−1+412yes—
676C23C25×C311yescharacteristic
677D4—416no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—416no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4C22×C3×D414yes—
728C2×C4C22×C3×D414yes—
729C2×C4C22×C3×D414yes—
730C2×C4C2×C3×#4114yes—
731C2×C3—44no—
732C2×C3—82no—
733C2×C3#269418yesdirect product factor
734C2×C3C2×#53611yescharacteristic
735C2×C3C2×#53911yescharacteristic
736C2×C3C2×#53911yescharacteristic
737C2×C3C2×#54611yescharacteristic
738C2×C3C2×#55011yescharacteristic
739C2×C3C2×#55211yescharacteristic
740C2×C3C2×#56211yescharacteristic
741C22—24no—
742C22—24no—
743C22—24no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—416no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—88no—
757C22C3×#53614yes—
758C22C3×#53914yes—
759C22C3×#53914yes—
760C22C3×#54614yes—
761C22C3×#55014yes—
762C22C3×#55214yes—
763C22C3×#56214yes—
764C22C23×C3×D411yescharacteristic
765C22C22×C3×#4111yescharacteristic
766C22C22×C3×#4111yescharacteristic
767C22C2×C3×H(5,𝔽2)11yescharacteristic
768C22C2×C3×H(5,𝔽2)11yescharacteristic
769C22C2×C3×2−1+411yescharacteristic
770C22C2×C3×2−1+411yescharacteristic
771C4—24no—
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—42no—
784C3C2×#269411yescharacteristic, direct product factor, Sylow
785C2—44no—
786C2—82no—
787C2C3×#269418yesdirect product factor
788C2C2×C3×#53611yescharacteristic
789C2C2×C3×#53911yescharacteristic
790C2C2×C3×#53911yescharacteristic
791C2C2×C3×#54611yescharacteristic
792C2C2×C3×#55011yescharacteristic
793C2C2×C3×#55211yescharacteristic
794C2C2×C3×#56211yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC23C25×C3
prime radicalC23×C3×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#125C2semidirect
3. C3×#2694C2direct (N × H)
4. C2×C3×#399C2semidirect
5. C2×C3×#399C2semidirect
6. C2×C3×#398C2semidirect
7. C2×C3×#397C2semidirect
8. C2×C3×#396C2semidirect
11. C2×C3×#389C2semidirect
12. C2×C3×#388C2semidirect
13. C2×C3×#388C2semidirect
14. C2×C3×#387C2semidirect
15. C2×C3×#385C2semidirect
16. C2×C3×#380C2semidirect
17. C2×#2694C3direct (N × H)
21. C2×C3×#125C22semidirect
49. C3×#399C22semidirect
50. C3×#399C22semidirect
51. C3×#398C22semidirect
52. C3×#397C22semidirect
53. C3×#396C22semidirect
56. C3×#389C22semidirect
57. C3×#388C22semidirect
58. C3×#388C22semidirect
59. C3×#387C22semidirect
60. C3×#385C22semidirect
61. C3×#380C22semidirect
70. C22×#125C2×C3semidirect
72. #2694C2×C3direct (N × H)
73. C2×#399C2×C3semidirect
74. C2×#399C2×C3semidirect
75. C2×#398C2×C3semidirect
76. C2×#397C2×C3semidirect
77. C2×#396C2×C3semidirect
80. C2×#389C2×C3semidirect
81. C2×#388C2×C3semidirect
82. C2×#388C2×C3semidirect
83. C2×#387C2×C3semidirect
84. C2×#385C2×C3semidirect
85. C2×#380C2×C3semidirect
172. C2×#125C22×C3semidirect
200. #399C22×C3semidirect
201. #399C22×C3semidirect
202. #398C22×C3semidirect
203. #397C22×C3semidirect
204. #396C22×C3semidirect
207. #389C22×C3semidirect
208. #388C22×C3semidirect
209. #388C22×C3semidirect
210. #387C22×C3semidirect
211. #385C22×C3semidirect
212. #380C22×C3semidirect
733. C2×C3#2694direct (N × H)
784. C3C2×#2694direct (N × H)
787. C2C3×#2694direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1252
C22×C3×#1232
C3×#26942
C2×C3×#3992
C2×C3×#3982
C2×C3×#3972
C2×C3×#3962
C2×C3×#3942
C2×C3×#3902
C2×C3×#3892
C2×C3×#3882
C2×C3×#3872
C2×C3×#3852
C2×C3×#3802
C2×#26943