Finite Group Databasebeta

← C4×#17989464 #34008297

Subgroups — C4×#17989464 #34008297

Order 18688.

1482 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊#64408C211yesmaximal, characteristic
2C2×C4×C22⋊#64408C211yesmaximal, characteristic
3C2×#17989464C214yesmaximal
4C4×C22⋊C4×D73C211yesmaximal, characteristic
5C22×C22⋊#64408C2212yes—
6C22×C22⋊#64408C2212yes—
7C22×C4×#64408—21no—
8C22×C4×#64408C412yescomplemented
9C4×C22⋊#64408—21no—
10C4×C22⋊#64408—21no—
11C4×C22⋊#64408—21no—
12C4×C22⋊#64408—21no—
13C4×C22⋊#64408—21no—
14C4×C22⋊#64408—21no—
15C4×C22⋊#64408C412yescomplemented
16C4×C22⋊#64408C412yescomplemented
17C2×(C2×#64408)⋊C4—21no—
18C2×(C2×#64408)⋊C4C412yescomplemented
19#17989464C4116yesdirect product factor
20C23×C4×D73C2211yescharacteristic
21C2×C22⋊C4×D73C2212yes—
22C2×C42×D73—21no—
23C22⋊C4×Dic73C412yescomplemented
24C4×#11924005—21no—
25C4×C22⋊Dic73C411yescharacteristic, complemented
26#17988434—21no—
27#95×D73—21no—
28C4×C22⋊C4×C73C411yescharacteristic, complemented
29C23×#64408—22no—
30C23×#64408C2×C414yes—
31C2×C22⋊#64408—22no—
32C2×C22⋊#64408—22no—
33C2×C22⋊#64408—22no—
34C2×C22⋊#64408—24no—
35C2×C22⋊#64408—24no—
36C2×C22⋊#64408C2×C418yes—
37C2×C22⋊#64408C2×C418yes—
38C2×C22⋊#64408C2×C414yes—
39C2×C4×#64408—22no—
40C2×C4×#64408—22no—
41C2×C4×#64408—22no—
42C2×C4×#64408—22no—
43C2×C4×#64408—44no—
44C2×C4×#64408—44no—
45(C2×#64408)⋊C4—22no—
46(C2×#64408)⋊C4—22no—
47(C2×#64408)⋊C4—22no—
48(C2×#64408)⋊C4—22no—
49C24×D73C2311yescharacteristic
50C23×Dic73C2×C411yescharacteristic
51C22×C4×D73—22no—
52C22×C4×D73—44no—
53C22×C4×D73C2×C411yescharacteristic
54C22×C4×D73C2×C411yescharacteristic
55C22×C4×D73C2×C411yescharacteristic
56C22×C4×D73C2×C411yescharacteristic
57C22×C4×D73D411yescharacteristic
58C22×C4×D73D411yescharacteristic
59C22×C4×D73D411yescharacteristic
60C22×C4×D73D411yescharacteristic
61C22×C4×D73D411yescharacteristic
62C22×C4×D73D411yescharacteristic
63C22×C4×D73Q811yescharacteristic
64C22×C4×D73Q811yescharacteristic
65C2×C22⋊Dic73C2×C412yes—
66C2×#11924005—22no—
67C22⋊C4×D73—24no—
68C22⋊C4×D73C2×C418yes—
69C2×C4×Dic73—22no—
70C2×C4×Dic73—21no—
71C42×D73—44no—
72#14556498—22no—
73#14556498—21no—
74C23×C4×C73C2×C411yescharacteristic
75C2×C22⋊C4×C73C2×C412yes—
76C2×C42×C73—21no—
77#95×C73—21no—
78C22×#64408—24no—
79C22×#64408—24no—
80C22×#64408—24no—
81C22×#64408—28no—
82C22×#64408—44no—
83C22×#64408—44no—
84C22×#64408—44no—
85C22×#64408—44no—
86C22×#64408C4218yescomplemented
87C22⋊#64408—24no—
88C22⋊#64408—28no—
89C22⋊#64408—28no—
90C22⋊#64408—28no—
91C22⋊#64408C4218yescomplemented
92C4×#64408—44no—
93C4×#64408—44no—
94C4×#64408—44no—
95C4×#64408—44no—
96C23×D73—42no—
97C23×D73—42no—
98C23×D73C22×C411yescharacteristic
99C23×D73C22×C411yescharacteristic
100C23×D73C22×C414yes—
101C23×D73C2×D411yescharacteristic
102C23×D73C2×D411yescharacteristic
103C23×D73C2×D411yescharacteristic
104C23×D73C2×Q811yescharacteristic
105C23×D73#4114yes—
106C22×Dic73—22no—
107C22×Dic73—42no—
108C22×Dic73C4211yescharacteristic
109C22×Dic73C4211yescharacteristic
110C22×Dic73C22⋊C411yescharacteristic
111C22×Dic73C22⋊C411yescharacteristic
112C22×Dic73C4⋊C411yescharacteristic
113C22×Dic73C4⋊C411yescharacteristic
114C2×C4×D73—24no—
115C2×C4×D73—24no—
116C2×C4×D73—24no—
117C2×C4×D73—28no—
118C2×C4×D73—42no—
119C2×C4×D73—42no—
120C2×C4×D73—42no—
121C2×C4×D73—42no—
122C2×C4×D73—42no—
123C2×C4×D73—42no—
124C2×C4×D73—42no—
125C2×C4×D73—42no—
126C2×C4×D73—42no—
127C2×C4×D73—44no—
128C2×C4×D73—44no—
129C2×C4×D73C22⋊C411yescharacteristic
130C2×C4×D73C22⋊C411yescharacteristic
131C2×C4×D73C22⋊C411yescharacteristic
132C2×C4×D73C22⋊C411yescharacteristic
133C2×C4×D73C22⋊C411yescharacteristic
134C2×C4×D73C22⋊C411yescharacteristic
135C2×C4×D73C22⋊C411yescharacteristic
136C2×C4×D73C22⋊C411yescharacteristic
137C2×C4×D73C4⋊C411yescharacteristic
138C2×C4×D73C4⋊C411yescharacteristic
139C2×C4×D73C4⋊C411yescharacteristic
140C2×C4×D73C4⋊C411yescharacteristic
141C2×C4×D73C4⋊C411yescharacteristic
142C2×C4×D73C4⋊C411yescharacteristic
143C2×C4×D73C4⋊C411yescharacteristic
144C2×C4×D73C4⋊C411yescharacteristic
145C22⋊Dic73—22no—
146C22⋊Dic73C4214yescomplemented
147#11924005—28no—
148C4×Dic73—44no—
149C4×Dic73—42no—
150C24×C73C22×C411yescharacteristic
151C22×C4×C73—22no—
152C22×C4×C73—42no—
153C22×C4×C73C4211yescharacteristic
154C22×C4×C73C4211yescharacteristic
155C22×C4×C73C22⋊C411yescharacteristic
156C22×C4×C73C22⋊C411yescharacteristic
157C22×C4×C73C4⋊C411yescharacteristic
158C22×C4×C73C4⋊C411yescharacteristic
159C22⋊C4×C73—22no—
160C22⋊C4×C73C4214yescomplemented
161C42×C73—42no—
162C23×C73—41no—
163C23×C73—41no—
164C23×C73C2×C4211yescharacteristic
165C23×C73C2×C4212yes—
166C23×C73C2×C22⋊C411yescharacteristic
167C23×C73C2×C4⋊C411yescharacteristic
168C23×C73#11712yes—
169C22×D73—22no—
170C22×D73—22no—
171C22×D73—22no—
172C22×D73—22no—
173C22×D73—22no—
174C22×D73—22no—
175C22×D73—48no—
176C22×D73—48no—
177C22×D73—41no—
178C22×D73—41no—
179C22×D73—41no—
180C22×D73—41no—
181C22×D73—41no—
182C22×D73—41no—
183C22×D73C2×C4212yes—
184C22×D73C2×C4212yes—
185C22×D73C2×C22⋊C411yescharacteristic
186C22×D73C2×C22⋊C411yescharacteristic
187C22×D73C2×C4⋊C411yescharacteristic
188C22×D73C2×C4⋊C411yescharacteristic
189C22×D73#11712yes—
190C22×D73#11712yes—
191C22×D73C4×D414yes—
192C22×D73C4×D414yes—
193C22×D73C4×D414yes—
194C22×D73C4×Q814yes—
195C2×#64408—28no—
196C2×#64408—28no—
197C2×#64408—44no—
198C2×#64408—44no—
199C2×#64408—416no—
200C2×#64408—48no—
201C2×#64408—44no—
202C2×#64408—44no—
203C2×#64408—48no—
204C2×C4×C73—22no—
205C2×C4×C73—22no—
206C2×C4×C73—22no—
207C2×C4×C73—24no—
208C2×C4×C73—41no—
209C2×C4×C73—41no—
210C2×C4×C73—41no—
211C2×C4×C73—42no—
212C2×C4×C73—42no—
213C2×C4×C73#9511yescharacteristic
214C2×C4×C73#9511yescharacteristic
215C2×C4×C73#9511yescharacteristic
216C2×C4×C73#9511yescharacteristic
217C2×Dic73—22no—
218C2×Dic73—22no—
219C2×Dic73—22no—
220C2×Dic73—24no—
221C2×Dic73—41no—
222C2×Dic73—41no—
223C2×Dic73—41no—
224C2×Dic73—42no—
225C2×Dic73—42no—
226C2×Dic73#9511yescharacteristic
227C2×Dic73#9511yescharacteristic
228C2×Dic73#9511yescharacteristic
229C2×Dic73#9511yescharacteristic
230C4×D73—22no—
231C4×D73—22no—
232C4×D73—22no—
233C4×D73—22no—
234C4×D73—22no—
235C4×D73—22no—
236C4×D73—22no—
237C4×D73—22no—
238C4×D73—22no—
239C4×D73—41no—
240C4×D73—41no—
241C4×D73—41no—
242C4×D73—41no—
243C4×D73—41no—
244C4×D73—41no—
245C4×D73—416no—
246C4×D73#9914yes—
247C22×C73—21no—
248C22×C73—21no—
249C22×C73—21no—
250C22×C73—21no—
251C22×C73—21no—
252C22×C73—21no—
253C22×C73—42no—
254C22×C73—42no—
255C22×C73C4311yescharacteristic
256C22×C73C2×#9511yescharacteristic
257C22×C73#37611yescharacteristic
258C22×C73C4×C22⋊C412yes—
259C22×C73C4×C4⋊C412yes—
260C2×D73—21no—
261C2×D73—21no—
262C2×D73—21no—
263C2×D73—21no—
264C2×D73—21no—
265C2×D73—21no—
266C2×D73—28no—
267C2×D73—24no—
268C2×D73—24no—
269C2×D73—28no—
270C2×D73—42no—
271C2×D73—42no—
272C2×D73—44no—
273C2×D73—44no—
274C2×D73C4×C22⋊C412yes—
275C2×D73C4×C22⋊C412yes—
276C2×D73C4×C4⋊C412yes—
277C2×D73C4×C4⋊C412yes—
278C2×D73C2×#9912yes—
279C2×D73#41012yes—
280#64408—48no—
281#64408—48no—
282C4×C73—21no—
283C4×C73—21no—
284C4×C73—21no—
285C4×C73—44no—
286C4×C73#34212yescomplemented
287Dic73—21no—
288Dic73—21no—
289Dic73—21no—
290Dic73—44no—
291Dic73#34212yescomplemented
292C4×#342—731nomaximal, Sylow
293C2×C73—22no—
294C2×C73—21no—
295C2×C73—21no—
296C2×C73—22no—
297C2×C73C4×#9511yescharacteristic
298C2×C73C2×#34211yescharacteristic
299C2×C73#174011yescharacteristic
300D73—22no—
301D73—22no—
302D73—22no—
303D73C4×#9914yes—
304C2×C4×C22⋊C4—731no—
305C2×C4×C22⋊C4—731no—
306C2×C4×C22⋊C4—731no—
307C2×#342—734no—
308C73C4×#34211yescharacteristic, complemented, Sylow
309C24×C4—731no—
310C22×C22⋊C4—732no—
311C22×C22⋊C4—732no—
312C22×C22⋊C4—732no—
313C22×C42—732no—
314C22×C42—1461no—
315C22×C42—1461no—
316C4×C22⋊C4—732no—
317C4×C22⋊C4—732no—
318C4×C22⋊C4—731no—
319C4×C22⋊C4—732no—
320C4×C22⋊C4—1461no—
321C4×C22⋊C4—1461no—
322C4×C22⋊C4—1461no—
323C4×C22⋊C4—1461no—
324C4×C22⋊C4—1461no—
325C4×C22⋊C4—1461no—
326C4×C22⋊C4—1461no—
327C4×C22⋊C4—1461no—
328C4×C22⋊C4#6440811yescharacteristic, complemented
329C2×#95—732no—
330C2×#95—1461no—
331C2×#95—1461no—
332#342—7316no—
333C25—731no—
334C23×C4—2924no—
335C23×C4—731no—
336C23×C4—731no—
337C23×C4—731no—
338C23×C4—731no—
339C23×C4—731no—
340C23×C4—731no—
341C23×C4—731no—
342C23×C4—731no—
343C23×C4—731no—
344C23×C4—731no—
345C23×C4—734no—
346C23×C4—731no—
347C23×C4—731no—
348C23×C4—731no—
349C23×C4—1462no—
350C23×C4—1462no—
351C23×C4C2×#6440811yescharacteristic
352C2×C22⋊C4—738no—
353C2×C22⋊C4—734no—
354C2×C22⋊C4—732no—
355C2×C22⋊C4—738no—
356C2×C22⋊C4—738no—
357C2×C22⋊C4—1464no—
358C2×C22⋊C4—1462no—
359C2×C22⋊C4—1462no—
360C2×C22⋊C4—1462no—
361C2×C22⋊C4—1462no—
362C2×C22⋊C4—1464no—
363C2×C22⋊C4—1464no—
364C2×C22⋊C4C2×#6440812yes—
365C2×C42—21no—
366C2×C42—2924no—
367C2×C42—2924no—
368C2×C42—2924no—
369C2×C42—1462no—
370C2×C42—1462no—
371C2×C42—1462no—
372C2×C42—1462no—
373C2×C42—1462no—
374C2×C42—1461no—
375#95—21no—
376#95—1462no—
377#95—1462no—
378#95—1462no—
379#95—1462no—
380#95—1462no—
381#95—1461no—
382C24—2922no—
383C24—2922no—
384C24—734no—
385C24—731no—
386C24—731no—
387C24—731no—
388C24—734no—
389C24—731no—
390C24—731no—
391C24—731no—
392C24C22×#6440811yescharacteristic
393C22×C4—22no—
394C22×C4—42no—
395C22×C4—2922no—
396C22×C4—2922no—
397C22×C4—2922no—
398C22×C4—2924no—
399C22×C4—2924no—
400C22×C4—2922no—
401C22×C4—2922no—
402C22×C4—2922no—
403C22×C4—2922no—
404C22×C4—2922no—
405C22×C4—2922no—
406C22×C4—2924no—
407C22×C4—2924no—
408C22×C4—2924no—
409C22×C4—2924no—
410C22×C4—2922no—
411C22×C4—731no—
412C22×C4—731no—
413C22×C4—731no—
414C22×C4—731no—
415C22×C4—731no—
416C22×C4—731no—
417C22×C4—731no—
418C22×C4—731no—
419C22×C4—731no—
420C22×C4—738no—
421C22×C4—731no—
422C22×C4—731no—
423C22×C4—731no—
424C22×C4—731no—
425C22×C4—731no—
426C22×C4—731no—
427C22×C4—731no—
428C22×C4—731no—
429C22×C4—731no—
430C22×C4—731no—
431C22×C4—731no—
432C22×C4—731no—
433C22×C4—731no—
434C22×C4—1468no—
435C22×C4—1464no—
436C22×C4—1464no—
437C22×C4—1464no—
438C22×C4—1464no—
439C22×C4—1464no—
440C22×C4—1468no—
441C22×C4—1464no—
442C22×C4—1462no—
443C22×C4C4×#6440811yescharacteristic
444C22×C4C4×#6440811yescharacteristic
445C22×C4C22⋊#6440811yescharacteristic
446C22×C4C22⋊#6440811yescharacteristic
447C22×C4C4⋊#6440811yescharacteristic
448C22×C4C4⋊#6440811yescharacteristic
449C22⋊C4—22no—
450C22⋊C4—738no—
451C22⋊C4—734no—
452C22⋊C4—1468no—
453C22⋊C4—1464no—
454C22⋊C4—1468no—
455C22⋊C4—1468no—
456C22⋊C4—1468no—
457C22⋊C4—1462no—
458C22⋊C4C4×#6440814yescomplemented
459C42—42no—
460C42—2922no—
461C42—2924no—
462C42—2924no—
463C42—2924no—
464C42—2924no—
465C42—2924no—
466C23—41no—
467C23—41no—
468C23—2921no—
469C23—2921no—
470C23—2921no—
471C23—2921no—
472C23—2921no—
473C23—2921no—
474C23—2928no—
475C23—2928no—
476C23—732no—
477C23—732no—
478C23—734no—
479C23—734no—
480C23—731no—
481C23—732no—
482C23—731no—
483C23—731no—
484C23—731no—
485C23—732no—
486C23—734no—
487C23—734no—
488C23—1462no—
489C23—1462no—
490C23—1462no—
491C23—1462no—
492C23—1462no—
493C23—1462no—
494C23C2×C4×#6440811yescharacteristic
495C23C2×C4×#6440812yes—
496C23C2×C22⋊#6440811yescharacteristic
497C23C2×C4⋊#6440811yescharacteristic
498C23#1455667012yes—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—2921no—
509C2×C4—2921no—
510C2×C4—2921no—
511C2×C4—2921no—
512C2×C4—2921no—
513C2×C4—2921no—
514C2×C4—29216no—
515C2×C4—2922no—
516C2×C4—2922no—
517C2×C4—2924no—
518C2×C4—2924no—
519C2×C4—2924no—
520C2×C4—2928no—
521C2×C4—29216no—
522C2×C4—2924no—
523C2×C4—2928no—
524C2×C4—2921no—
525C2×C4—2921no—
526C2×C4—2921no—
527C2×C4—731no—
528C2×C4—734no—
529C2×C4—731no—
530C2×C4—731no—
531C2×C4—731no—
532C2×C4—1462no—
533C2×C4—1462no—
534C2×C4—1462no—
535C2×C4—1462no—
536C2×C4—1462no—
537C2×C4—1462no—
538C2×C4—1468no—
539C2×C4—1468no—
540C2×C4—1464no—
541C2×C4—1462no—
542C2×C4—1462no—
543C2×C4—1462no—
544C2×C4—1462no—
545C2×C4—1462no—
546C2×C4—1462no—
547C2×C4(C2×#64408)⋊C411yescharacteristic
548C2×C4(C2×#64408)⋊C411yescharacteristic
549C2×C4(C2×#64408)⋊C411yescharacteristic
550C2×C4(C2×#64408)⋊C411yescharacteristic
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—42no—
558C22—42no—
559C22—2924no—
560C22—2922no—
561C22—2922no—
562C22—2924no—
563C22—732no—
564C22—732no—
565C22—732no—
566C22—732no—
567C22—732no—
568C22—732no—
569C22—1468no—
570C22—1464no—
571C22—1464no—
572C22—1468no—
573C22—1461no—
574C22—1461no—
575C22—1461no—
576C22—1461no—
577C22—1461no—
578C22—1461no—
579C22C42×#6440811yescharacteristic
580C22C2×(C2×#64408)⋊C411yescharacteristic
581C22#1798952311yescharacteristic
582C22C4×C22⋊#6440812yes—
583C22C4×C4⋊#6440812yes—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—44no—
588C4—2924no—
589C4—2928no—
590C4—2928no—
591C4—732no—
592C4—1461no—
593C4—1461no—
594C4—1461no—
595C4#1798946412yesdirect product factor
596C2—22no—
597C2—21no—
598C2—21no—
599C2—22no—
600C2—734no—
601C2—1462no—
602C2—1462no—
603C2—1462no—
604C2C4×(C2×#64408)⋊C411yescharacteristic
605C2C2×#1798946411yescharacteristic
606C2#2262562911yescharacteristic
subgroupG/H
centerC2×C4(C2×#64408)⋊C4
commutatorC22×C73C43
FrattiniC24C22×#64408
FittingC4×C22⋊C4×C73C4
socleC22×C73C2×#95
prime radical, cosocleC24×D73C23
hypercenterC4×C22⋊C4#64408
hypocenterC73C4×#342
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C22×C4×#64408C4semidirect
15. C4×C22⋊#64408C4semidirect
16. C4×C22⋊#64408C4semidirect
18. C2×(C2×#64408)⋊C4C4semidirect
19. #17989464C4direct (N × H)
23. C22⋊C4×Dic73C4semidirect
25. C4×C22⋊Dic73C4semidirect
28. C4×C22⋊C4×C73C4semidirect
86. C22×#64408C42semidirect
91. C22⋊#64408C42semidirect
146. C22⋊Dic73C42semidirect
160. C22⋊C4×C73C42semidirect
286. C4×C73#342semidirect
291. Dic73#342semidirect
308. C73C4×#342semidirect
328. C4×C22⋊C4#64408semidirect
458. C22⋊C4C4×#64408semidirect
595. C4#17989464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊#644082
C2×#179894642
C4×C22⋊C4×D732
C4×#34273