Finite Group Databasebeta

← C2×#22615386 #33256281

Subgroups — C2×#22615386 #33256281

Order 18688.

2334 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22615386C2116yesmaximal, direct product factor
2C2×#17988527C211yesmaximal, characteristic, complemented
3C2×#17988524C211yesmaximal, characteristic
4C2×#17988520C211yesmaximal, characteristic, complemented
5C2×#17988498C211yesmaximal, characteristic
6C2×#17988494C211yesmaximal, characteristic, complemented
7C2×#17988484C211yesmaximal, characteristic, complemented
8C2×#17988478C211yesmaximal, characteristic
9C2×#17988476C211yesmaximal, characteristic
10C2×#17988474C211yesmaximal, characteristic, complemented
11C2×#17988470C211yesmaximal, characteristic, complemented
12C2×#17988461C211yesmaximal, characteristic
13C2×#17988458C211yesmaximal, characteristic
14C2×C4×C4⋊Dic73C211yesmaximal, characteristic, complemented
15C2×#17988434C211yesmaximal, characteristic
16C2×#391×C73C211yesmaximal, characteristic, complemented
17C23×C4×D73C2211yescharacteristic
18C22×C4⋊Dic73C2211yescharacteristic
19C22×C4⋊Dic73C2211yescharacteristic
20C22×C4⋊Dic73C2211yescharacteristic
21C22×C4⋊Dic73C2211yescharacteristic
22C22×#11924007C2211yescharacteristic
23C22×#11924007C2211yescharacteristic
24C22×#11924007C2211yescharacteristic
25C22×#11924007C2211yescharacteristic
26C22×#11924005C2211yescharacteristic
27C22×#11924005C2211yescharacteristic
28C22×#11924005C2211yescharacteristic
29C22×#11924005C2211yescharacteristic
30C22×#11924005C2211yescharacteristic
31C22×#11924005C2211yescharacteristic
32C22×C4×Dic73C2211yescharacteristic
33C22×C4×Dic73C2211yescharacteristic
34C22×C4×Dic73C2211yescharacteristic
35#17988527C2218yescomplemented
36#17988524C2218yes—
37#17988520C2218yescomplemented
38#17988498C2218yes—
39#17988494C2218yescomplemented
40#17988484C2218yescomplemented
41#17988478C2218yes—
42#17988476C2218yes—
43#17988474C2218yescomplemented
44#17988470C2218yescomplemented
45#17988461C2218yes—
46#17988458C2218yes—
47C4×C4⋊Dic73C2218yescomplemented
48#17988434C2218yes—
49C2×#14556498C2211yescharacteristic
50C2×#14556498C2211yescharacteristic
51C2×#14556498C2211yescharacteristic
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C23×Q8×C73C2211yescharacteristic
60C22×C4⋊C4×C73C2211yescharacteristic
61C22×C42×C73C2211yescharacteristic
62#391×C73C2218yescomplemented
63C2×#95×C73C2211yescharacteristic
64C2×#95×C73C2211yescharacteristic
65C2×#95×C73C2211yescharacteristic
66C2×#95×C73C2211yescharacteristic
67C24×D73C2311yescharacteristic
68C23×Dic73C2311yescharacteristic
69C23×Dic73C2311yescharacteristic
70C23×Dic73C2311yescharacteristic
71C23×Dic73C2311yescharacteristic
72C23×Dic73C2311yescharacteristic
73C23×Dic73C2311yescharacteristic
74C23×Dic73C2311yescharacteristic
75C22×C4×D73—24no—
76C22×C4×D73—42no—
77C22×C4×D73—42no—
78C22×C4×D73C2314yes—
79C2×C4⋊Dic73—24no—
80C2×C4⋊Dic73—24no—
81C2×C4⋊Dic73—24no—
82C2×C4⋊Dic73—42no—
83C2×C4⋊Dic73C2314yes—
84C2×C4⋊Dic73C2314yes—
85C2×C4⋊Dic73C2314yes—
86C2×C4⋊Dic73C2314yes—
87C2×#11924007—24no—
88C2×#11924007—24no—
89C2×#11924007—42no—
90C2×#11924007—42no—
91C2×#11924007C2314yes—
92C2×#11924007C2314yes—
93C2×#11924007C2314yes—
94C2×#11924007C2314yes—
95C2×#11924005—24no—
96C2×#11924005—24no—
97C2×#11924005—24no—
98C2×#11924005—42no—
99C2×#11924005—42no—
100C2×#11924005Q818yescomplemented
101C2×#11924005C2314yes—
102C2×#11924005C2314yes—
103C2×#11924005C2314yes—
104C2×#11924005C2314yes—
105C2×#11924005C2314yes—
106C2×#11924005C2314yes—
107C2×C4×Dic73—42no—
108C2×C4×Dic73—42no—
109C2×C4×Dic73—42no—
110C2×C4×Dic73C2314yes—
111C2×C4×Dic73C2314yes—
112C2×C4×Dic73C2314yes—
113#14556498C2314yes—
114#14556498C2314yes—
115#14556498C2314yes—
116#14556498C2314yes—
117#14556498C2314yes—
118#14556498C2314yes—
119#14556498C2314yes—
120#14556498C2314yes—
121#14556498C2314yes—
122#14556498C2314yes—
123C22×Q8×C73—24no—
124C22×Q8×C73—24no—
125C22×Q8×C73—42no—
126C22×Q8×C73C2314yes—
127C23×C4×C73C2311yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C2×C4⋊C4×C73—42no—
135C2×C4⋊C4×C73C2314yes—
136C2×C42×C73—24no—
137C2×C42×C73C2314yes—
138#95×C73C2314yes—
139#95×C73C2314yes—
140#95×C73C2314yes—
141#95×C73C2314yes—
142C23×D73—22no—
143C23×D73—22no—
144C23×D73—22no—
145C23×D73—22no—
146C23×D73—22no—
147C23×D73—22no—
148C23×D73C2×Q814yes—
149C23×D73C2412yes—
150C22×Dic73—22no—
151C22×Dic73—22no—
152C22×Dic73—22no—
153C22×Dic73—22no—
154C22×Dic73—22no—
155C22×Dic73—22no—
156C22×Dic73—22no—
157C22×Dic73—22no—
158C22×Dic73—22no—
159C22×Dic73—22no—
160C22×Dic73—22no—
161C22×Dic73—22no—
162C22×Dic73—22no—
163C22×Dic73—22no—
164C22×Dic73—22no—
165C22×Dic73—22no—
166C22×Dic73—22no—
167C22×Dic73—22no—
168C22×Dic73—22no—
169C22×Dic73C2×Q814yes—
170C22×Dic73#4114yes—
171C22×Dic73C2412yes—
172C22×Dic73C2412yes—
173C22×Dic73C2412yes—
174C22×Dic73C2412yes—
175C22×Dic73C2412yes—
176C22×Dic73C2412yes—
177C22×Dic73C2412yes—
178C2×C4×D73—28no—
179C2×C4×D73—44no—
180C2×C4×D73—44no—
181C2×C4×D73—416no—
182C4⋊Dic73—28no—
183C4⋊Dic73—28no—
184C4⋊Dic73—28no—
185C4⋊Dic73—44no—
186#11924007—28no—
187#11924007—28no—
188#11924007—44no—
189#11924007—44no—
190#11924005—28no—
191#11924005—28no—
192#11924005—28no—
193#11924005—44no—
194#11924005—44no—
195#11924005C2×Q8116yescomplemented
196C4×Dic73—44no—
197C4×Dic73—44no—
198C4×Dic73—44no—
199C24×C73C2411yescharacteristic
200C2×Q8×C73—28no—
201C2×Q8×C73—28no—
202C2×Q8×C73—44no—
203C2×Q8×C73—416no—
204C22×C4×C73—22no—
205C22×C4×C73—22no—
206C22×C4×C73—22no—
207C22×C4×C73—22no—
208C22×C4×C73—22no—
209C22×C4×C73—22no—
210C22×C4×C73—22no—
211C22×C4×C73—22no—
212C22×C4×C73—22no—
213C22×C4×C73—22no—
214C22×C4×C73—22no—
215C22×C4×C73—22no—
216C22×C4×C73—22no—
217C22×C4×C73—22no—
218C22×C4×C73—22no—
219C22×C4×C73—22no—
220C22×C4×C73—22no—
221C22×C4×C73C2×Q814yes—
222C22×C4×C73#4114yes—
223C22×C4×C73#4114yes—
224C22×C4×C73#4114yes—
225C22×C4×C73C2412yes—
226C22×C4×C73C2412yes—
227C22×C4×C73C2412yes—
228C22×C4×C73C2412yes—
229C22×C4×C73C2412yes—
230C22×C4×C73C2412yes—
231C22×C4×C73C2412yes—
232C4⋊C4×C73—44no—
233C42×C73—28no—
234C23×C73C22×Q812yes—
235C23×C73C2×#4112yes—
236C23×C73C2×#4112yes—
237C23×C73C2×#4112yes—
238C23×C73C2×#4112yes—
239C23×C73H(5,𝔽2)12yes—
240C23×C73H(5,𝔽2)12yes—
241C23×C73C2511yescharacteristic
242C22×D73—28no—
243C22×D73—28no—
244C22×D73—28no—
245C22×D73—22no—
246C22×D73—22no—
247C22×D73—22no—
248C22×D73—22no—
249C22×D73—22no—
250C22×D73—22no—
251C22×D73—44no—
252C22×D73—44no—
253C22×D73—44no—
254C22×D73—44no—
255C22×D73C22×Q814yes—
256Q8×C73—416no—
257C2×C4×C73—28no—
258C2×C4×C73—28no—
259C2×C4×C73—28no—
260C2×C4×C73—28no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—44no—
279C2×C4×C73—44no—
280C2×C4×C73—44no—
281C2×C4×C73C22×Q814yes—
282C2×C4×C73C2×#4114yes—
283C2×C4×C73C2×#4114yes—
284C2×C4×C73C2×#4114yes—
285C2×Dic73—28no—
286C2×Dic73—28no—
287C2×Dic73—22no—
288C2×Dic73—22no—
289C2×Dic73—22no—
290C2×Dic73—22no—
291C2×Dic73—22no—
292C2×Dic73—22no—
293C2×Dic73—22no—
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—44no—
307C2×Dic73—44no—
308C2×Dic73—44no—
309C2×Dic73—44no—
310C2×Dic73—44no—
311C2×Dic73C22×Q814yes—
312C2×Dic73C2×#4114yes—
313C4×D73—416no—
314C22×C73#52914yes—
315C22×C73#53314yes—
316C22×C73#53814yes—
317C22×C73#55114yes—
318C22×C73#55414yes—
319C22×C73#55414yes—
320C22×C73#55914yes—
321C22×C73C23×Q811yescharacteristic
322C22×C73C22×#4111yescharacteristic
323C22×C73C22×#4111yescharacteristic
324C22×C73C22×#4111yescharacteristic
325C22×C73C22×#4111yescharacteristic
326C22×C73C2×H(5,𝔽2)11yescharacteristic
327C22×C73C2×H(5,𝔽2)11yescharacteristic
328C2×D73—24no—
329C2×D73—24no—
330C2×D73—24no—
331C2×D73—416no—
332C2×D73—42no—
333C2×D73—42no—
334C2×D73—42no—
335C2×D73—42no—
336C4×C73—24no—
337C4×C73—24no—
338C4×C73—24no—
339C4×C73—24no—
340C4×C73—42no—
341C4×C73—42no—
342C4×C73—42no—
343Dic73—24no—
344Dic73—24no—
345Dic73—42no—
346Dic73—42no—
347Dic73—42no—
348Dic73—42no—
349Dic73—42no—
350C2×#2589—731nomaximal, Sylow
351C2×C73#258918yescomplemented
352C2×C73C2×#52911yescharacteristic
353C2×C73C2×#53311yescharacteristic
354C2×C73C2×#53811yescharacteristic
355C2×C73C2×#55111yescharacteristic
356C2×C73C2×#55411yescharacteristic
357C2×C73C2×#55411yescharacteristic
358C2×C73C2×#55911yescharacteristic
359D73—44no—
360#2589—7316no—
361C2×#400—731no—
362C2×#399—731no—
363C2×#398—731no—
364C2×#393—731no—
365C2×#391—731no—
366C2×#391D7311yescharacteristic, complemented
367C2×#389—731no—
368C2×#388—731no—
369C2×#388—731no—
370C2×#387—731no—
371C2×#387—731no—
372C2×#385—731no—
373C2×#385—731no—
374C2×C4×C4⋊C4—731no—
375C2×C4×C22⋊C4—731no—
376C73C2×#258911yescharacteristic, complemented, Sylow
377C23×Q8C2×D7311yescharacteristic
378C24×C4—731no—
379C22×C4⋊C4—731no—
380C22×C4⋊C4—731no—
381C22×C4⋊C4—731no—
382C22×C4⋊C4—731no—
383C22×C4⋊C4—731no—
384C22×C4⋊C4—731no—
385C22×C4⋊C4—731no—
386C22×C4⋊C4—731no—
387C22×C4⋊C4C2×D7311yescharacteristic
388C22×C22⋊C4—731no—
389C22×C22⋊C4—731no—
390C22×C22⋊C4—731no—
391C22×C22⋊C4—731no—
392C22×C22⋊C4—731no—
393C22×C22⋊C4—731no—
394C22×C42—731no—
395C22×C42—731no—
396C22×C42—731no—
397C22×C42C2×D7311yescharacteristic
398#400—738no—
399#399—738no—
400#398—738no—
401#393—738no—
402#391—738no—
403#391C2×D7318yescomplemented
404#389—738no—
405#388—738no—
406#388—738no—
407#387—738no—
408#387—738no—
409#385—738no—
410#385—738no—
411C4×C4⋊C4—738no—
412C4×C22⋊C4—738no—
413C2×#95—731no—
414C2×#95—731no—
415C2×#95—731no—
416C2×#95—731no—
417C2×#95—731no—
418C2×#95—731no—
419C2×#95—731no—
420C2×#95—731no—
421C2×#95—731no—
422C2×#95—731no—
423C2×#95C2×D7311yescharacteristic
424C2×#95C2×D7311yescharacteristic
425C2×#95C2×D7311yescharacteristic
426C2×#95C2×D7311yescharacteristic
427C25—731no—
428C22×Q8—24no—
429C22×Q8—24no—
430C22×Q8—42no—
431C22×Q8C22×D7314yes—
432C23×C4—2922no—
433C23×C4—2922no—
434C23×C4—734no—
435C23×C4—731no—
436C23×C4—731no—
437C23×C4—731no—
438C23×C4—731no—
439C23×C4—731no—
440C23×C4—731no—
441C23×C4—731no—
442C23×C4—1464no—
443C23×C4C22×D7311yescharacteristic
444C23×C4C22×D7311yescharacteristic
445C23×C4C22×D7311yescharacteristic
446C23×C4C22×D7311yescharacteristic
447C23×C4C22×D7311yescharacteristic
448C23×C4C22×D7311yescharacteristic
449C23×C4C22×D7311yescharacteristic
450C2×C4⋊C4—42no—
451C2×C4⋊C4—2922no—
452C2×C4⋊C4—2922no—
453C2×C4⋊C4—2922no—
454C2×C4⋊C4—734no—
455C2×C4⋊C4—734no—
456C2×C4⋊C4—734no—
457C2×C4⋊C4—734no—
458C2×C4⋊C4—734no—
459C2×C4⋊C4—734no—
460C2×C4⋊C4—734no—
461C2×C4⋊C4—734no—
462C2×C4⋊C4—1464no—
463C2×C4⋊C4—1464no—
464C2×C4⋊C4—1464no—
465C2×C4⋊C4—1464no—
466C2×C4⋊C4—1464no—
467C2×C4⋊C4C22×D7314yes—
468C2×C22⋊C4—2922no—
469C2×C22⋊C4—2922no—
470C2×C22⋊C4—734no—
471C2×C22⋊C4—734no—
472C2×C22⋊C4—738no—
473C2×C22⋊C4—734no—
474C2×C22⋊C4—734no—
475C2×C22⋊C4—734no—
476C2×C22⋊C4—734no—
477C2×C22⋊C4—1464no—
478C2×C22⋊C4—1464no—
479C2×C22⋊C4—1464no—
480C2×C42—24no—
481C2×C42—2922no—
482C2×C42—2922no—
483C2×C42—2922no—
484C2×C42—734no—
485C2×C42—734no—
486C2×C42—734no—
487C2×C42C22×D7314yes—
488#95—734no—
489#95—734no—
490#95—734no—
491#95—734no—
492#95—734no—
493#95—734no—
494#95—734no—
495#95—734no—
496#95—734no—
497#95—734no—
498#95C22×D7314yes—
499#95C22×D7314yes—
500#95C22×D7314yes—
501#95C22×D7314yes—
502C24—734no—
503C24—732no—
504C24—1462no—
505C24—1462no—
506C24—1462no—
507C24—1462no—
508C24—1462no—
509C24—1462no—
510C24C23×D7311yescharacteristic
511C2×Q8—28no—
512C2×Q8—28no—
513C2×Q8—44no—
514C2×Q8—416no—
515C22×C4—22no—
516C22×C4—22no—
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—2924no—
533C22×C4—2924no—
534C22×C4—29216no—
535C22×C4—734no—
536C22×C4—734no—
537C22×C4—732no—
538C22×C4—732no—
539C22×C4—732no—
540C22×C4—732no—
541C22×C4—732no—
542C22×C4—732no—
543C22×C4—732no—
544C22×C4—1468no—
545C22×C4—1462no—
546C22×C4—1462no—
547C22×C4—1462no—
548C22×C4—1462no—
549C22×C4—1462no—
550C22×C4—1462no—
551C22×C4—1462no—
552C22×C4—1462no—
553C22×C4—1462no—
554C22×C4—1462no—
555C22×C4—1462no—
556C22×C4—1462no—
557C22×C4—1462no—
558C22×C4—1462no—
559C22×C4—1462no—
560C22×C4—1462no—
561C22×C4—1462no—
562C22×C4—1462no—
563C22×C4—1462no—
564C22×C4Q8×D7314yes—
565C22×C4#1192402714yes—
566C22×C4#1192402814yes—
567C22×C4#1192402914yes—
568C22×C4C23×D7312yes—
569C22×C4C23×D7312yes—
570C22×C4C23×D7312yes—
571C22×C4C23×D7312yes—
572C22×C4C23×D7312yes—
573C22×C4C23×D7312yes—
574C22×C4C23×D7312yes—
575C4⋊C4—44no—
576C4⋊C4—2924no—
577C4⋊C4—2924no—
578C4⋊C4—2924no—
579C4⋊C4—1468no—
580C4⋊C4—1468no—
581C4⋊C4—1468no—
582C4⋊C4—1468no—
583C4⋊C4—1468no—
584C22⋊C4—2924no—
585C22⋊C4—2924no—
586C22⋊C4—7316no—
587C22⋊C4—1468no—
588C22⋊C4—1468no—
589C22⋊C4—1468no—
590C42—28no—
591C42—2924no—
592C42—2924no—
593C42—2924no—
594C23—2924no—
595C23—2924no—
596C23—2924no—
597C23—2924no—
598C23—734no—
599C23—1468no—
600C23—1462no—
601C23—1462no—
602C23—1462no—
603C23—1462no—
604C23—1462no—
605C23—1462no—
606C23—1468no—
607C23—1468no—
608C23C2×Q8×D7312yes—
609C23#41×D7312yes—
610C23C2×#1192402712yes—
611C23C2×#1192402812yes—
612C23C2×#1192402912yes—
613C23#1455663612yes—
614C23#1455663712yes—
615C23C24×D7311yescharacteristic
616Q8—416no—
617C2×C4—28no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—28no—
627C2×C4—28no—
628C2×C4—28no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—29216no—
642C2×C4—2924no—
643C2×C4—2924no—
644C2×C4—2924no—
645C2×C4—2924no—
646C2×C4—2924no—
647C2×C4—734no—
648C2×C4—734no—
649C2×C4—1462no—
650C2×C4—1462no—
651C2×C4—1462no—
652C2×C4—1462no—
653C2×C4—1462no—
654C2×C4—1462no—
655C2×C4—1462no—
656C2×C4—1462no—
657C2×C4—1462no—
658C2×C4—1462no—
659C2×C4—1462no—
660C2×C4—1462no—
661C2×C4—1462no—
662C2×C4—1462no—
663C2×C4—1462no—
664C2×C4—1462no—
665C2×C4—1462no—
666C2×C4—1462no—
667C2×C4—1462no—
668C2×C4—1468no—
669C2×C4—1468no—
670C2×C4C2×Q8×D7314yes—
671C2×C4C2×#1192402714yes—
672C2×C4C2×#1192402814yes—
673C2×C4C2×#1192402914yes—
674C22—2922no—
675C22—2922no—
676C22—29216no—
677C22—2922no—
678C22—2922no—
679C22—1464no—
680C22—1464no—
681C22—1464no—
682C22#1798912314yes—
683C22#1798914114yes—
684C22#1798917114yes—
685C22#1798926314yes—
686C22#1798929514yes—
687C22#1798929814yes—
688C22#1798932214yes—
689C22C22×Q8×D7311yescharacteristic
690C22C2×#41×D7311yescharacteristic
691C22C22×#1192402711yescharacteristic
692C22C22×#1192402811yescharacteristic
693C22C22×#1192402911yescharacteristic
694C22C2×#1455663611yescharacteristic
695C22C2×#1455663711yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—2922no—
704C4—2922no—
705C4—2922no—
706C4—2922no—
707C4—2922no—
708C4—1464no—
709C4—1464no—
710C2—2924no—
711C2#2261538618yesdirect product factor
712C2C2×#1798912311yescharacteristic
713C2C2×#1798914111yescharacteristic
714C2C2×#1798917111yescharacteristic
715C2C2×#1798926311yescharacteristic
716C2C2×#1798929511yescharacteristic
717C2C2×#1798929811yescharacteristic
718C2C2×#1798932211yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#391×C73C2
socleC24×C73C24
prime radicalC24×D73C23
hypercenterC2×#391D73
hypocenterC73C2×#2589
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. #22615386C2direct (N × H)
2. C2×#17988527C2semidirect
4. C2×#17988520C2semidirect
6. C2×#17988494C2semidirect
7. C2×#17988484C2semidirect
10. C2×#17988474C2semidirect
11. C2×#17988470C2semidirect
14. C2×C4×C4⋊Dic73C2semidirect
16. C2×#391×C73C2semidirect
35. #17988527C22semidirect
37. #17988520C22semidirect
39. #17988494C22semidirect
40. #17988484C22semidirect
43. #17988474C22semidirect
44. #17988470C22semidirect
47. C4×C4⋊Dic73C22semidirect
62. #391×C73C22semidirect
100. C2×#11924005Q8semidirect
195. #11924005C2×Q8semidirect
351. C2×C73#2589semidirect
366. C2×#391D73semidirect
376. C73C2×#2589semidirect
403. #391C2×D73semidirect
711. C2#22615386direct (N × H)

Maximal subgroups

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

subgroupindex
#226153862
C2×#179885272
C2×#179885242
C2×#179885202
C2×#179884982
C2×#179884942
C2×#179884842
C2×#179884782
C2×#179884762
C2×#179884742
C2×#179884702
C2×#179884612
C2×#179884582
C2×C4×C4⋊Dic732
C2×#179884342
C2×#391×C732
C2×#258973