Finite Group Databasebeta

← C22⋊C4×#11924007 #33007402

Subgroups — C22⋊C4×#11924007 #33007402

Order 18688.

2574 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
1C23×#11924007C211yesmaximal, characteristic
2C2×#17988445C211yesmaximal, characteristic
3C2×C4×#11924007C212yesmaximal, complemented
4C2×C22⋊C4×Dic73C211yesmaximal, characteristic
5C2×C22⋊C4×Dic73C211yesmaximal, characteristic
6#22608164C212yesmaximal, complemented
7#22608162C212yesmaximal, complemented
8#22608159C212yesmaximal, complemented
9#22608154C211yesmaximal, characteristic
10#22608153C211yesmaximal, characteristic
11C2×C4×C22⋊C4×C73C211yesmaximal, characteristic
12C24×Dic73C2211yescharacteristic
13C24×Dic73C2211yescharacteristic
14C22×#11924007—28no—
15C22×#11924007C418yescomplemented
16C22×#11924007C2211yescharacteristic
17C22×#11924007C2211yescharacteristic
18C22×#11924007C2211yescharacteristic
19C22×#11924007C2212yes—
20C22×#11924007C2211yescharacteristic
21C22×C22⋊Dic73C2211yescharacteristic
22C22×C22⋊Dic73C2211yescharacteristic
23C22×C4×Dic73C2212yes—
24C22×C4×Dic73C2212yes—
25#17988445C418yescomplemented
26C4×#11924007—28no—
27C22⋊C4×Dic73—24no—
28C22⋊C4×Dic73C418yescomplemented
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C2×#14556498C2212yes—
35C2×#14556498C2212yes—
36C24×C4×C73C2211yescharacteristic
37C22×C22⋊C4×C73C2211yescharacteristic
38C22×C22⋊C4×C73C2211yescharacteristic
39C22×C42×C73C2212yes—
40C4×C22⋊C4×C73—24no—
41C2×#95×C73C2212yes—
42C23×Dic73—24no—
43C23×Dic73—24no—
44C23×Dic73—24no—
45C23×Dic73—22no—
46C23×Dic73—22no—
47C23×Dic73—42no—
48C23×Dic73C2×C414yes—
49C23×Dic73C2×C414yes—
50C23×Dic73C2×C414yes—
51C23×Dic73C2×C414yes—
52C23×Dic73C2311yescharacteristic
53C23×Dic73C2312yes—
54C23×Dic73C2312yes—
55C23×Dic73C2311yescharacteristic
56C23×Dic73C2311yescharacteristic
57C23×Dic73C2311yescharacteristic
58C2×#11924007—24no—
59C2×#11924007—24no—
60C2×#11924007—24no—
61C2×#11924007—24no—
62C2×#11924007—232no—
63C2×#11924007—24no—
64C2×#11924007C2×C414yes—
65C2×#11924007C2×C414yes—
66C2×#11924007C2×C414yes—
67C2×#11924007C2×C414yes—
68C2×#11924007C2×C418yescomplemented
69C2×#11924007D418yes—
70C2×C22⋊Dic73—22no—
71C2×C22⋊Dic73—22no—
72C2×C22⋊Dic73—22no—
73C2×C22⋊Dic73—22no—
74C2×C22⋊Dic73C2×C414yes—
75C2×C22⋊Dic73C2×C414yes—
76C2×C4×Dic73—24no—
77C2×C4×Dic73—24no—
78C2×C4×Dic73—24no—
79C2×C4×Dic73—24no—
80C2×C4×Dic73—42no—
81C2×C4×Dic73C2×C418yescomplemented
82#14556498—24no—
83#14556498—24no—
84#14556498—24no—
85#14556498—42no—
86#14556498—42no—
87#14556498C2×C418yescomplemented
88#14556498C2×C418yescomplemented
89C25×C73C2311yescharacteristic
90C23×C4×C73—22no—
91C23×C4×C73—22no—
92C23×C4×C73—24no—
93C23×C4×C73—42no—
94C23×C4×C73C2×C414yes—
95C23×C4×C73C2312yes—
96C23×C4×C73C2311yescharacteristic
97C23×C4×C73C2311yescharacteristic
98C23×C4×C73C2312yes—
99C2×C22⋊C4×C73—22no—
100C2×C22⋊C4×C73—22no—
101C2×C22⋊C4×C73C2×C414yes—
102C2×C22⋊C4×C73C2×C414yes—
103C2×C22⋊C4×C73D414yes—
104C2×C22⋊C4×C73Q814yes—
105C2×C42×C73—24no—
106C2×C42×C73—24no—
107C2×C42×C73—42no—
108#95×C73—24no—
109C22×Dic73—21no—
110C22×Dic73—22no—
111C22×Dic73—22no—
112C22×Dic73—21no—
113C22×Dic73—22no—
114C22×Dic73—28no—
115C22×Dic73—28no—
116C22×Dic73—216no—
117C22×Dic73—216no—
118C22×Dic73—28no—
119C22×Dic73—22no—
120C22×Dic73—21no—
121C22×Dic73—22no—
122C22×Dic73—22no—
123C22×Dic73—22no—
124C22×Dic73—22no—
125C22×Dic73—22no—
126C22×Dic73—22no—
127C22×Dic73—22no—
128C22×Dic73—22no—
129C22×Dic73—21no—
130C22×Dic73—22no—
131C22×Dic73—22no—
132C22×Dic73—22no—
133C22×Dic73—22no—
134C22×Dic73—22no—
135C22×Dic73—28no—
136C22×Dic73—44no—
137C22×Dic73—48no—
138C22×Dic73—48no—
139C22×Dic73C42116yescomplemented
140C22×Dic73C22×C414yes—
141C22×Dic73C22×C414yes—
142C22×Dic73C22×C412yes—
143C22×Dic73C22×C412yes—
144C22×Dic73C22×C412yes—
145C22×Dic73C22×C412yes—
146C22×Dic73C22×C412yes—
147C22×Dic73C22×C412yes—
148C22×Dic73C22×C412yes—
149C22×Dic73C22×C412yes—
150C22×Dic73C2×D414yes—
151C22×Dic73C2×D414yes—
152C22×Dic73#4114yes—
153#11924007—28no—
154#11924007—28no—
155#11924007—28no—
156#11924007—216no—
157#11924007C22⋊C4116yesdirect product factor
158C22⋊Dic73—28no—
159C22⋊Dic73—28no—
160C4×Dic73—216no—
161C4×Dic73—48no—
162C24×C73—22no—
163C24×C73—22no—
164C24×C73—22no—
165C24×C73—22no—
166C24×C73C22×C412yes—
167C24×C73C22×C412yes—
168C24×C73C22×C412yes—
169C24×C73C2×D412yes—
170C24×C73C2×Q812yes—
171C24×C73#4112yes—
172C24×C73#4112yes—
173C24×C73C2411yescharacteristic
174C22×C4×C73—21no—
175C22×C4×C73—22no—
176C22×C4×C73—21no—
177C22×C4×C73—22no—
178C22×C4×C73—22no—
179C22×C4×C73—22no—
180C22×C4×C73—22no—
181C22×C4×C73—28no—
182C22×C4×C73—21no—
183C22×C4×C73—22no—
184C22×C4×C73—22no—
185C22×C4×C73—22no—
186C22×C4×C73—22no—
187C22×C4×C73—21no—
188C22×C4×C73—22no—
189C22×C4×C73—22no—
190C22×C4×C73—22no—
191C22×C4×C73—22no—
192C22×C4×C73—28no—
193C22×C4×C73—44no—
194C22×C4×C73—48no—
195C22×C4×C73—48no—
196C22×C4×C73C22×C414yes—
197C22×C4×C73C22×C412yes—
198C22×C4×C73C22×C412yes—
199C22×C4×C73C22×C414yes—
200C22×C4×C73C2×D414yes—
201C22×C4×C73C2×D414yes—
202C22×C4×C73C2×Q814yes—
203C22⋊C4×C73—28no—
204C22⋊C4×C73C4⋊C4116yescomplemented
205C42×C73—48no—
206C23×C73—22no—
207C23×C73—22no—
208C23×C73—24no—
209C23×C73—24no—
210C23×C73—22no—
211C23×C73—22no—
212C23×C73—24no—
213C23×C73—24no—
214C23×C73—24no—
215C23×C73—24no—
216C23×C73—24no—
217C23×C73—24no—
218C23×C73—24no—
219C23×C73—24no—
220C23×C73—24no—
221C23×C73—24no—
222C23×C73C2×C4214yes—
223C23×C73C2×C4⋊C414yes—
224C23×C73#11714yes—
225C23×C73C4×D414yes—
226C23×C73C4×D414yes—
227C23×C73C4×Q814yes—
228C23×C73C4×Q814yes—
229C23×C73C23×C411yescharacteristic
230C23×C73C23×C411yescharacteristic
231C23×C73C23×C411yescharacteristic
232C23×C73C22×D412yes—
233C23×C73C22×D411yescharacteristic
234C23×C73C22×Q811yescharacteristic
235C23×C73C2×#4112yes—
236C23×C73C2×#4111yescharacteristic
237C23×C73C2×#4111yescharacteristic
238C23×C73H(5,𝔽2)12yes—
239C23×C732−1+412yes—
240C2×C4×C73—22no—
241C2×C4×C73—24no—
242C2×C4×C73—22no—
243C2×C4×C73—24no—
244C2×C4×C73—24no—
245C2×C4×C73—24no—
246C2×C4×C73—24no—
247C2×C4×C73—24no—
248C2×C4×C73—24no—
249C2×C4×C73—24no—
250C2×C4×C73—22no—
251C2×C4×C73—24no—
252C2×C4×C73—22no—
253C2×C4×C73—24no—
254C2×C4×C73—22no—
255C2×C4×C73—24no—
256C2×C4×C73—416no—
257C2×C4×C73—42no—
258C2×C4×C73—42no—
259C2×C4×C73—42no—
260C2×C4×C73—42no—
261C2×C4×C73—42no—
262C2×C4×C73—42no—
263C2×C4×C73C2×C22⋊C414yes—
264C2×C4×C73C2×C4⋊C418yescomplemented
265C2×Dic73—22no—
266C2×Dic73—22no—
267C2×Dic73—24no—
268C2×Dic73—24no—
269C2×Dic73—22no—
270C2×Dic73—22no—
271C2×Dic73—24no—
272C2×Dic73—24no—
273C2×Dic73—232no—
274C2×Dic73—22no—
275C2×Dic73—24no—
276C2×Dic73—24no—
277C2×Dic73—24no—
278C2×Dic73—24no—
279C2×Dic73—22no—
280C2×Dic73—22no—
281C2×Dic73—24no—
282C2×Dic73—24no—
283C2×Dic73—416no—
284C2×Dic73—42no—
285C2×Dic73—42no—
286C2×Dic73—42no—
287C2×Dic73—42no—
288C2×Dic73—42no—
289C2×Dic73—42no—
290C2×Dic73—42no—
291C2×Dic73—42no—
292C2×Dic73—42no—
293C2×Dic73—42no—
294C2×Dic73C2×C4214yes—
295C2×Dic73C2×C4214yes—
296C2×Dic73C2×C22⋊C414yes—
297C2×Dic73C2×C22⋊C414yes—
298C2×Dic73#11714yes—
299C2×Dic73C4×D418yes—
300C2×Dic73C4×D418yes—
301C22×C73—24no—
302C22×C73—24no—
303C22×C73—24no—
304C22×C73—24no—
305C22×C73—28no—
306C22×C73—28no—
307C22×C73—28no—
308C22×C73—28no—
309C22×C73—24no—
310C22×C73—24no—
311C22×C73C4×C4⋊C418yescomplemented
312C22×C73C22×C4211yescharacteristic
313C22×C73C22×C22⋊C411yescharacteristic
314C22×C73C22×C4⋊C411yescharacteristic
315C22×C73C2×#11711yescharacteristic
316C22×C73C2×#11711yescharacteristic
317C22×C73C2×C4×D412yes—
318C22×C73C2×C4×D412yes—
319C22×C73C2×C4×D411yescharacteristic
320C22×C73C2×C4×D411yescharacteristic
321C22×C73C2×C4×Q811yescharacteristic
322C22×C73C2×C4×Q811yescharacteristic
323C22×C73#51811yescharacteristic
324C22×C73#51911yescharacteristic
325C22×C73#52012yes—
326C22×C73#52012yes—
327C22×C73D4212yes—
328C22×C73#54612yes—
329C22×C73#54712yes—
330C22×C73#54812yes—
331C22×C73D4×Q812yes—
332C22×C73#55212yes—
333C22×C73#55312yes—
334C22×C73#55412yes—
335C4×C73—24no—
336C4×C73—28no—
337C4×C73—42no—
338C4×C73—44no—
339Dic73—24no—
340Dic73—24no—
341Dic73—42no—
342Dic73—44no—
343Dic73—44no—
344Dic73C4×C22⋊C418yescomplemented
345C22⋊C4×C4⋊C4—731nomaximal, Sylow
346C2×C73—28no—
347C2×C73C2×C4×C22⋊C411yescharacteristic
348C2×C73C2×C4×C4⋊C411yescharacteristic
349C2×C73#227411yescharacteristic
350C2×C73D4×C22⋊C411yescharacteristic
351C2×C73Q8×C22⋊C411yescharacteristic
352C2×C73#234411yescharacteristic
353C2×C73#234511yescharacteristic
354C2×C73D4×C4⋊C412yes—
355C2×C73#235212yes—
356C2×C73#236012yes—
357C2×C73#236112yes—
358C23×C4⋊C4—731no—
359C2×#380—731no—
360C2×C4×C4⋊C4—732no—
361C2×C4×C22⋊C4—731no—
362C2×C4×C22⋊C4—731no—
363C2×C4×C22⋊C4D7311yescharacteristic
364#1436—732no—
365#1436—732no—
366C4⋊#95—732no—
367C22⋊#95—731no—
368C22⋊#95—731no—
369C73C22⋊C4×C4⋊C411yescharacteristic, complemented, Sylow
370C24×C4—731no—
371C24×C4—731no—
372C24×C4C2×D7311yescharacteristic
373C22×C4⋊C4—731no—
374C22×C4⋊C4—738no—
375C22×C4⋊C4—731no—
376C22×C4⋊C4—731no—
377C22×C4⋊C4—731no—
378C22×C4⋊C4—732no—
379C22×C4⋊C4—1468no—
380C22×C22⋊C4—731no—
381C22×C22⋊C4—731no—
382C22×C22⋊C4C2×D7311yescharacteristic
383C22×C22⋊C4C2×D7311yescharacteristic
384C22×C42—732no—
385C22×C42—732no—
386C22×C42C2×D7312yes—
387#380—738no—
388C4×C4⋊C4—1468no—
389C4×C22⋊C4—24no—
390C4×C22⋊C4—738no—
391C4×C22⋊C4—1464no—
392C2×#95—732no—
393C2×#95—732no—
394C2×#95—732no—
395C2×#95—732no—
396C2×#95—732no—
397C2×#95—732no—
398C2×#95—732no—
399C2×#95C2×D7312yes—
400C25C22×D7311yescharacteristic
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—24no—
404C23×C4—42no—
405C23×C4—2922no—
406C23×C4—734no—
407C23×C4—731no—
408C23×C4—734no—
409C23×C4—734no—
410C23×C4—734no—
411C23×C4—731no—
412C23×C4—731no—
413C23×C4—732no—
414C23×C4—732no—
415C23×C4—731no—
416C23×C4—1464no—
417C23×C4—1462no—
418C23×C4—1462no—
419C23×C4—1464no—
420C23×C4—1464no—
421C23×C4C4×D7314yes—
422C23×C4C22×D7312yes—
423C23×C4C22×D7311yescharacteristic
424C23×C4C22×D7311yescharacteristic
425C23×C4C22×D7312yes—
426C2×C4⋊C4—734no—
427C2×C4⋊C4—738no—
428C2×C4⋊C4—734no—
429C2×C4⋊C4—734no—
430C2×C4⋊C4—734no—
431C2×C4⋊C4—738no—
432C2×C4⋊C4—14632no—
433C2×C4⋊C4—1464no—
434C2×C4⋊C4—1464no—
435C2×C4⋊C4—1464no—
436C2×C4⋊C4—1464no—
437C2×C4⋊C4—1464no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—734no—
441C2×C22⋊C4—734no—
442C2×C22⋊C4—1462no—
443C2×C22⋊C4—1462no—
444C2×C22⋊C4—1462no—
445C2×C22⋊C4—1462no—
446C2×C22⋊C4Dic14614yes—
447C2×C22⋊C4C4×D7314yes—
448C2×C22⋊C4C4×D7314yes—
449C2×C22⋊C4C22⋊D7314yes—
450C2×C42—24no—
451C2×C42—24no—
452C2×C42—42no—
453C2×C42—2922no—
454C2×C42—738no—
455C2×C42—1464no—
456C2×C42—1464no—
457C2×C42—1464no—
458C2×C42—1464no—
459#95—24no—
460#95—2922no—
461#95—2922no—
462#95—738no—
463#95—738no—
464#95—1464no—
465#95—1464no—
466#95—1464no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24C2×C4×D7312yes—
472C24C2×C4×D7312yes—
473C24C2×C4×D7312yes—
474C24C2×C22⋊D7312yes—
475C24C2×Dic14612yes—
476C24#1192402812yes—
477C24#1192402812yes—
478C24C23×D7311yescharacteristic
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—28no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—28no—
498C22×C4—44no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—2928no—
502C22×C4—2928no—
503C22×C4—2924no—
504C22×C4—732no—
505C22×C4—732no—
506C22×C4—732no—
507C22×C4—734no—
508C22×C4—734no—
509C22×C4—7316no—
510C22×C4—732no—
511C22×C4—732no—
512C22×C4—732no—
513C22×C4—732no—
514C22×C4—734no—
515C22×C4—734no—
516C22×C4—734no—
517C22×C4—732no—
518C22×C4—1468no—
519C22×C4—1468no—
520C22×C4—1462no—
521C22×C4—1462no—
522C22×C4—1462no—
523C22×C4—1461no—
524C22×C4—1462no—
525C22×C4—1462no—
526C22×C4—1462no—
527C22×C4—1462no—
528C22×C4—1462no—
529C22×C4—1462no—
530C22×C4—1461no—
531C22×C4—1462no—
532C22×C4—1462no—
533C22×C4—1462no—
534C22×C4—1462no—
535C22×C4—1462no—
536C22×C4—1468no—
537C22×C4—1468no—
538C22×C4—14616no—
539C22×C4—14616no—
540C22×C4—1462no—
541C22×C4—1461no—
542C22×C4—1462no—
543C22×C4—1461no—
544C22×C4—1462no—
545C22×C4C2×C4×D7314yes—
546C22×C4C2×C4×D7312yes—
547C22×C4C2×C4×D7312yes—
548C22×C4C2×C4×D7314yes—
549C22×C4D4×D7314yes—
550C22×C4C2×C22⋊D7314yes—
551C22×C4C2×Dic14614yes—
552C4⋊C4—7316no—
553C4⋊C4—14616no—
554C4⋊C4—1468no—
555C4⋊C4—1468no—
556C4⋊C4—1468no—
557C22⋊C4—28no—
558C22⋊C4—1468no—
559C22⋊C4—1468no—
560C22⋊C4#11924007116yesdirect product factor
561C42—48no—
562C42—2928no—
563C42—14616no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—22no—
572C23—22no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—22no—
577C23—22no—
578C23—24no—
579C23—24no—
580C23C42×D7314yes—
581C23C2×#1192400714yes—
582C23#1455654814yes—
583C23C4×C22⋊D7314yes—
584C23C4×C22⋊D7314yes—
585C23C4×Dic14614yes—
586C23C4×Dic14614yes—
587C23C22×C4×D7311yescharacteristic
588C23C22×C4×D7311yescharacteristic
589C23C22×C4×D7311yescharacteristic
590C23C2×D4×D7312yes—
591C23C22×C22⋊D7311yescharacteristic
592C23C22×Dic14611yescharacteristic
593C23#41×D7312yes—
594C23C2×#1192402811yescharacteristic
595C23C2×#1192402811yescharacteristic
596C23#1455663612yes—
597C23#1455663812yes—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—416no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—2922no—
622C2×C4—2922no—
623C2×C4—2922no—
624C2×C4—2922no—
625C2×C4—2922no—
626C2×C4—2922no—
627C2×C4—2922no—
628C2×C4—2922no—
629C2×C4—2922no—
630C2×C4—2922no—
631C2×C4—29216no—
632C2×C4—734no—
633C2×C4—734no—
634C2×C4—734no—
635C2×C4—738no—
636C2×C4—738no—
637C2×C4—734no—
638C2×C4—734no—
639C2×C4—1462no—
640C2×C4—1464no—
641C2×C4—1464no—
642C2×C4—1464no—
643C2×C4—1464no—
644C2×C4—1462no—
645C2×C4—1462no—
646C2×C4—1464no—
647C2×C4—1464no—
648C2×C4—14632no—
649C2×C4—1464no—
650C2×C4—1464no—
651C2×C4—1462no—
652C2×C4—1462no—
653C2×C4—1464no—
654C2×C4—1464no—
655C2×C4—1462no—
656C2×C4—1462no—
657C2×C4C22⋊C4×D7314yes—
658C2×C4C2×#1192400718yescomplemented
659C22—24no—
660C22—24no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—24no—
665C22—28no—
666C22—28no—
667C22—28no—
668C22—28no—
669C22C4×#1192400718yescomplemented
670C22C2×C42×D7311yescharacteristic
671C22C2×C22⋊C4×D7311yescharacteristic
672C22C22×#1192400711yescharacteristic
673C22#117×D7311yescharacteristic
674C22C2×#1455654811yescharacteristic
675C22C4×D4×D7312yes—
676C22C4×D4×D7312yes—
677C22C2×C4×C22⋊D7311yescharacteristic
678C22C2×C4×C22⋊D7311yescharacteristic
679C22C2×C4×Dic14611yescharacteristic
680C22C2×C4×Dic14611yescharacteristic
681C22#1798906011yescharacteristic
682C22#1798906411yescharacteristic
683C22#1798906612yes—
684C22#1798906612yes—
685C22D4×C22⋊D7312yes—
686C22#1798922712yes—
687C22#1798923612yes—
688C22#1798924612yes—
689C22D4×Dic14612yes—
690C22#1798927012yes—
691C22#1798928612yes—
692C22#1798929612yes—
693C4—24no—
694C4—28no—
695C4—42no—
696C4—44no—
697C4—2922no—
698C4—2924no—
699C4—2924no—
700C4—738no—
701C4—1464no—
702C4—1464no—
703C2—28no—
704C2C4×C22⋊C4×D7311yescharacteristic
705C2C2×C4×#1192400711yescharacteristic
706C2#2261228611yescharacteristic
707C2C22⋊C4×C22⋊D7311yescharacteristic
708C2C22⋊C4×Dic14611yescharacteristic
709C2#2261280111yescharacteristic
710C2#2261280911yescharacteristic
711C2D4×#1192400712yes—
712C2#2261285412yes—
713C2#2261293712yes—
714C2#2261294812yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC22×C73C22×C42
FittingC2×C4×C22⋊C4×C73C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×C4×C22⋊C4D73
hypocenterC73C22⋊C4×C4⋊C4
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11924007C2semidirect
6. #22608164C2semidirect
7. #22608162C2semidirect
8. #22608159C2semidirect
15. C22×#11924007C4semidirect
25. #17988445C4semidirect
28. C22⋊C4×Dic73C4semidirect
68. C2×#11924007C2×C4semidirect
81. C2×C4×Dic73C2×C4semidirect
87. #14556498C2×C4semidirect
88. #14556498C2×C4semidirect
139. C22×Dic73C42semidirect
157. #11924007C22⋊C4direct (N × H)
204. C22⋊C4×C73C4⋊C4semidirect
264. C2×C4×C73C2×C4⋊C4semidirect
311. C22×C73C4×C4⋊C4semidirect
344. Dic73C4×C22⋊C4semidirect
369. C73C22⋊C4×C4⋊C4semidirect
560. C22⋊C4#11924007direct (N × H)
658. C2×C4C2×#11924007semidirect
669. C22C4×#11924007semidirect

Maximal subgroups

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

subgroupindex
C23×#119240072
C2×#179884452
C2×C4×#119240072
C2×C22⋊C4×Dic732
#226081642
#226081622
#226081592
#226081542
#226081532
C2×C4×C22⋊C4×C732
C22⋊C4×C4⋊C473