Finite Group Databasebeta

← #33007682

Subgroups — #33007682

Order 18688.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×Dic73C211yesmaximal, characteristic
3C2×C22⋊C4×Dic73C211yesmaximal, characteristic
4C2×C22⋊C4×Dic73C211yesmaximal, characteristic
5C2×#17988432C211yesmaximal, characteristic, complemented
6#22608192C211yesmaximal, characteristic, complemented
7#22608191C211yesmaximal, characteristic, complemented
8#22608190C211yesmaximal, characteristic, complemented
9#22608187C211yesmaximal, characteristic, complemented
10#22608178C211yesmaximal, characteristic
11#22608178C211yesmaximal, characteristic
12#22608176C211yesmaximal, characteristic
13#95×Dic73C211yesmaximal, characteristic, complemented
14#95×Dic73C211yesmaximal, characteristic, complemented
15C73×#1439C211yesmaximal, characteristic
16C24×Dic73C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C22×C22⋊Dic73C2211yescharacteristic
19C22×C22⋊Dic73C2211yescharacteristic
20C22×C22⋊Dic73C2211yescharacteristic
21C22×C4×Dic73C2211yescharacteristic
22C22×C4×Dic73C2211yescharacteristic
23C22×C4×Dic73C2211yescharacteristic
24C22×C4×Dic73C2211yescharacteristic
25C22×C4×Dic73C2211yescharacteristic
26C22×C4×Dic73C2211yescharacteristic
27C4⋊C4×Dic73—24no—
28C22⋊C4×Dic73—24no—
29C22⋊C4×Dic73—24no—
30C22⋊C4×Dic73C418yescomplemented
31#17988432—24no—
32C2×#14556498C2211yescharacteristic
33C2×#14556498C2211yescharacteristic
34C2×#14556498C2211yescharacteristic
35C2×#14556498C2211yescharacteristic
36C2×#14556498C2211yescharacteristic
37C2×#14556498C2211yescharacteristic
38C2×#14556498C2211yescharacteristic
39C2×#14556498C2211yescharacteristic
40C2×#14556498C2211yescharacteristic
41C2×#14556498C2211yescharacteristic
42C2×#14556498C2211yescharacteristic
43C2×#14556498C2211yescharacteristic
44C2×#14556498C2211yescharacteristic
45C2×#14556498C2211yescharacteristic
46C2×#14556498C2211yescharacteristic
47C2×#14556498C2211yescharacteristic
48C2×#14556498C2211yescharacteristic
49C22×C4⋊C4×C73C2211yescharacteristic
50C22×C22⋊C4×C73C2211yescharacteristic
51C22×C22⋊C4×C73C2211yescharacteristic
52C22×C22⋊C4×C73C2211yescharacteristic
53C2×#95×C73C2211yescharacteristic
54C2×#95×C73C2211yescharacteristic
55C2×#95×C73C2211yescharacteristic
56C23×Dic73—22no—
57C23×Dic73—22no—
58C23×Dic73—22no—
59C23×Dic73—22no—
60C23×Dic73—22no—
61C23×Dic73—22no—
62C23×Dic73C2×C414yes—
63C23×Dic73C2311yescharacteristic
64C23×Dic73C2311yescharacteristic
65C23×Dic73C2311yescharacteristic
66C23×Dic73C2311yescharacteristic
67C23×Dic73C2311yescharacteristic
68C23×Dic73C2311yescharacteristic
69C23×Dic73C2311yescharacteristic
70C23×Dic73C2311yescharacteristic
71C2×C4⋊Dic73—22no—
72C2×C4⋊Dic73—22no—
73C2×C4⋊Dic73—22no—
74C2×C22⋊Dic73—22no—
75C2×C22⋊Dic73—22no—
76C2×C22⋊Dic73—22no—
77C2×C22⋊Dic73—22no—
78C2×C22⋊Dic73—22no—
79C2×C22⋊Dic73—22no—
80C2×C22⋊Dic73—22no—
81C2×C22⋊Dic73—22no—
82C2×C22⋊Dic73C2×C414yes—
83C2×C4×Dic73—22no—
84C2×C4×Dic73—22no—
85C2×C4×Dic73—22no—
86C2×C4×Dic73—22no—
87C2×C4×Dic73—22no—
88C2×C4×Dic73—22no—
89C2×C4×Dic73—22no—
90C2×C4×Dic73—22no—
91C2×C4×Dic73—22no—
92C2×C4×Dic73—22no—
93C2×C4×Dic73—22no—
94C2×C4×Dic73—22no—
95C2×C4×Dic73—22no—
96C2×C4×Dic73—22no—
97C2×C4×Dic73C2×C414yes—
98C2×C4×Dic73C2×C414yes—
99C2×C4×Dic73D414yes—
100C2×C4×Dic73D414yes—
101#14556498—22no—
102#14556498—22no—
103#14556498—22no—
104#14556498—22no—
105#14556498—22no—
106#14556498—22no—
107#14556498—22no—
108#14556498—22no—
109#14556498—22no—
110#14556498—22no—
111#14556498—22no—
112#14556498—22no—
113#14556498—22no—
114#14556498—22no—
115#14556498—22no—
116#14556498C2×C414yes—
117#14556498C2×C414yes—
118C25×C73C2311yescharacteristic
119C23×C4×C73C2311yescharacteristic
120C23×C4×C73C2311yescharacteristic
121C23×C4×C73C2311yescharacteristic
122C23×C4×C73C2311yescharacteristic
123C23×C4×C73C2311yescharacteristic
124C23×C4×C73C2311yescharacteristic
125C2×C4⋊C4×C73—22no—
126C2×C4⋊C4×C73—22no—
127C2×C4⋊C4×C73—22no—
128C2×C22⋊C4×C73—22no—
129C2×C22⋊C4×C73—22no—
130C2×C22⋊C4×C73—22no—
131C2×C22⋊C4×C73—22no—
132C2×C22⋊C4×C73—22no—
133C2×C22⋊C4×C73—22no—
134C2×C22⋊C4×C73—22no—
135C2×C22⋊C4×C73—22no—
136C2×C22⋊C4×C73C2×C414yes—
137#95×C73—22no—
138#95×C73—22no—
139#95×C73—22no—
140C22×Dic73—21no—
141C22×Dic73—21no—
142C22×Dic73—21no—
143C22×Dic73—21no—
144C22×Dic73—21no—
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73—21no—
148C22×Dic73—21no—
149C22×Dic73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154C22×Dic73—21no—
155C22×Dic73—21no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C22×Dic73—21no—
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73—21no—
172C22×Dic73—21no—
173C22×Dic73—21no—
174C22×Dic73—21no—
175C22×Dic73—21no—
176C22×Dic73—21no—
177C22×Dic73—21no—
178C22×Dic73—21no—
179C22×Dic73—21no—
180C22×Dic73—21no—
181C22×Dic73—21no—
182C22×Dic73—28no—
183C22×Dic73—28no—
184C22×Dic73—28no—
185C22×Dic73—44no—
186C22×Dic73—44no—
187C22×Dic73—44no—
188C22×Dic73—44no—
189C22×Dic73C22×C412yes—
190C22×Dic73C22×C412yes—
191C22×Dic73C22×C412yes—
192C22×Dic73C22×C412yes—
193C22×Dic73C2×D412yes—
194C22×Dic73C2×D412yes—
195C22×Dic73C2×D412yes—
196C22×Dic73C2×D412yes—
197C22×Dic73#4112yes—
198C22×Dic73#4112yes—
199C22×Dic73#4112yes—
200C22×Dic73#4112yes—
201C22×Dic73#4112yes—
202C22×Dic73#4112yes—
203C4⋊Dic73—28no—
204C22⋊Dic73—28no—
205C22⋊Dic73—28no—
206C22⋊Dic73—28no—
207C4×Dic73—28no—
208C4×Dic73—28no—
209C4×Dic73—28no—
210C4×Dic73—28no—
211C4×Dic73—44no—
212C4×Dic73—44no—
213C24×C73—21no—
214C24×C73—21no—
215C24×C73—21no—
216C24×C73—21no—
217C24×C73—21no—
218C24×C73—21no—
219C24×C73—21no—
220C24×C73—21no—
221C24×C73—21no—
222C24×C73—21no—
223C24×C73—21no—
224C24×C73—21no—
225C24×C73C22×C412yes—
226C24×C73#4112yes—
227C24×C73#4112yes—
228C24×C73C2411yescharacteristic
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73C22×C412yes—
264C22×C4×C73C22×C412yes—
265C22×C4×C73C2×D412yes—
266C22×C4×C73C2×D412yes—
267C22×C4×C73#4112yes—
268C22×C4×C73#4112yes—
269C22×C4×C73#4112yes—
270C22×C4×C73#4112yes—
271C4⋊C4×C73—28no—
272C22⋊C4×C73—28no—
273C22⋊C4×C73—28no—
274C22⋊C4×C73—28no—
275C23×C73—22no—
276C23×C73—22no—
277C23×C73—22no—
278C23×C73—22no—
279C23×C73—22no—
280C23×C73—22no—
281C23×C73—22no—
282C23×C73—22no—
283C23×C73—22no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73—22no—
287C23×C73—22no—
288C23×C73—22no—
289C23×C73—22no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73—41no—
294C23×C73—41no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—41no—
298C23×C73—41no—
299C23×C73—41no—
300C23×C73—41no—
301C23×C73—41no—
302C23×C73—41no—
303C23×C73—41no—
304C23×C73—41no—
305C23×C73—41no—
306C23×C73—41no—
307C23×C73—41no—
308C23×C73—41no—
309C23×C73#11714yes—
310C23×C73C23×C411yescharacteristic
311C23×C73C22×D411yescharacteristic
312C23×C73C22×D411yescharacteristic
313C23×C73C2×#4111yescharacteristic
314C23×C73C2×#4111yescharacteristic
315C23×C73C2×#4111yescharacteristic
316C23×C73C2×#4111yescharacteristic
317C23×C73C2×#4111yescharacteristic
318C23×C73C2×#4111yescharacteristic
319C23×C73C2×#4111yescharacteristic
320C23×C73C2×#4111yescharacteristic
321C23×C73C2×#4111yescharacteristic
322C23×C73C2×#4111yescharacteristic
323C23×C73C2×#4111yescharacteristic
324C23×C73C2×#4111yescharacteristic
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—22no—
335C2×C4×C73—22no—
336C2×C4×C73—22no—
337C2×C4×C73—22no—
338C2×C4×C73—22no—
339C2×C4×C73—22no—
340C2×C4×C73—22no—
341C2×C4×C73—22no—
342C2×C4×C73—22no—
343C2×C4×C73—22no—
344C2×C4×C73—22no—
345C2×C4×C73—22no—
346C2×C4×C73—41no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
349C2×C4×C73—41no—
350C2×C4×C73—41no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73—41no—
355C2×C4×C73—41no—
356C2×C4×C73—41no—
357C2×C4×C73—41no—
358C2×C4×C73—41no—
359C2×C4×C73—41no—
360C2×C4×C73—41no—
361C2×C4×C73—41no—
362C2×C4×C73—41no—
363C2×C4×C73—41no—
364C2×C4×C73—41no—
365C2×C4×C73—41no—
366C2×C4×C73#11714yes—
367C2×Dic73—22no—
368C2×Dic73—22no—
369C2×Dic73—22no—
370C2×Dic73—22no—
371C2×Dic73—22no—
372C2×Dic73—22no—
373C2×Dic73—22no—
374C2×Dic73—22no—
375C2×Dic73—22no—
376C2×Dic73—22no—
377C2×Dic73—22no—
378C2×Dic73—22no—
379C2×Dic73—22no—
380C2×Dic73—22no—
381C2×Dic73—22no—
382C2×Dic73—22no—
383C2×Dic73—22no—
384C2×Dic73—22no—
385C2×Dic73—22no—
386C2×Dic73—22no—
387C2×Dic73—22no—
388C2×Dic73—41no—
389C2×Dic73—41no—
390C2×Dic73—41no—
391C2×Dic73—41no—
392C2×Dic73—41no—
393C2×Dic73—41no—
394C2×Dic73—41no—
395C2×Dic73—41no—
396C2×Dic73—41no—
397C2×Dic73—41no—
398C2×Dic73—41no—
399C2×Dic73—41no—
400C2×Dic73—41no—
401C2×Dic73—41no—
402C2×Dic73—41no—
403C2×Dic73—41no—
404C2×Dic73—41no—
405C2×Dic73—41no—
406C2×Dic73—41no—
407C2×Dic73—41no—
408C2×Dic73—41no—
409C2×Dic73—41no—
410C2×Dic73—41no—
411C2×Dic73—41no—
412C2×Dic73—41no—
413C2×Dic73—41no—
414C2×Dic73—41no—
415C2×Dic73—41no—
416C2×Dic73—416no—
417C2×Dic73#11714yes—
418C2×Dic73C4×D414yes—
419C2×Dic73C4×D414yes—
420C2×Dic73#12114yes—
421C2×Dic73#12314yes—
422C2×Dic73#12414yes—
423C2×Dic73#12614yes—
424C22×C73—24no—
425C22×C73—24no—
426C22×C73—24no—
427C22×C73—42no—
428C22×C73—42no—
429C22×C73—42no—
430C22×C73—42no—
431C22×C73—42no—
432C22×C73—42no—
433C22×C73—42no—
434C22×C73—42no—
435C22×C73—42no—
436C22×C73—42no—
437C22×C73—42no—
438C22×C73—42no—
439C22×C73C2×#11711yescharacteristic
440C22×C73C2×#11711yescharacteristic
441C22×C73C2×#11711yescharacteristic
442C22×C73C2×C4×D411yescharacteristic
443C22×C73C2×C4×D411yescharacteristic
444C22×C73C4×#4111yescharacteristic
445C22×C73C4×#4111yescharacteristic
446C22×C73C2×#12111yescharacteristic
447C22×C73C2×#12311yescharacteristic
448C22×C73#52511yescharacteristic
449C22×C73#52511yescharacteristic
450C22×C73#52511yescharacteristic
451C22×C73#52511yescharacteristic
452C22×C73#52511yescharacteristic
453C22×C73#52511yescharacteristic
454C22×C73C2×#12411yescharacteristic
455C22×C73C2×#12611yescharacteristic
456C22×C73#52911yescharacteristic
457C22×C73#52911yescharacteristic
458C22×C73#52911yescharacteristic
459C22×C73#52911yescharacteristic
460C22×C73#52911yescharacteristic
461C22×C73#52911yescharacteristic
462C22×C73#52911yescharacteristic
463C22×C73#52911yescharacteristic
464C22×C73#52911yescharacteristic
465C22×C73#52911yescharacteristic
466C22×C73#52911yescharacteristic
467C22×C73#52911yescharacteristic
468C22×C73#52911yescharacteristic
469C22×C73#52911yescharacteristic
470C22×C73#52911yescharacteristic
471C22×C73#52911yescharacteristic
472C22×C73#53211yescharacteristic
473C22×C73#53211yescharacteristic
474C4×C73—24no—
475C4×C73—42no—
476C4×C73—42no—
477C4×C73—42no—
478C4×C73—42no—
479C4×C73—42no—
480Dic73—42no—
481Dic73—42no—
482Dic73—42no—
483Dic73—42no—
484Dic73—42no—
485Dic73—42no—
486Dic73—42no—
487Dic73#38818yes—
488#13842—731nomaximal, Sylow
489C2×C73—44no—
490C2×C73#228311yescharacteristic
491C2×C73C2×#38811yescharacteristic
492C2×C73#229011yescharacteristic
493C2×C73#229011yescharacteristic
494C2×C73#229011yescharacteristic
495C2×C73#229311yescharacteristic
496C2×C73#229811yescharacteristic
497C2×C73#239211yescharacteristic
498C2×C73#239211yescharacteristic
499C2×C73#239511yescharacteristic
500C2×C73#239511yescharacteristic
501C2×C73#239811yescharacteristic
502C2×C73#239811yescharacteristic
503C2×C73#240111yescharacteristic
504C2×C73#240111yescharacteristic
505C2×C4×C4⋊C4—731no—
506C2×C4×C22⋊C4—731no—
507C2×C4×C22⋊C4—731no—
508C2×C4×C22⋊C4—731no—
509C2×#376—731no—
510#1443—731no—
511#1443—731no—
512#1442—731no—
513#1442—731no—
514#1440—731no—
515#1440—731no—
516#1439—731no—
517#1439D7311yescharacteristic
518C4×#95—731no—
519C4×#95—731no—
520C73#1384211yescharacteristic, complemented, Sylow
521C24×C4—731no—
522C22×C4⋊C4—731no—
523C22×C4⋊C4C2×D7311yescharacteristic
524C22×C22⋊C4—731no—
525C22×C22⋊C4—731no—
526C22×C22⋊C4—731no—
527C22×C22⋊C4C2×D7311yescharacteristic
528C22×C22⋊C4C2×D7311yescharacteristic
529C22×C22⋊C4C2×D7311yescharacteristic
530C22×C42—731no—
531C22×C42—731no—
532C22×C42—731no—
533C22×C42—731no—
534C22×C42—731no—
535C22×C42—731no—
536C4×C4⋊C4—1464no—
537C4×C22⋊C4—738no—
538C4×C22⋊C4—1464no—
539C4×C22⋊C4—1464no—
540#376—1464no—
541C2×#95—731no—
542C2×#95—731no—
543C2×#95—731no—
544C2×#95—731no—
545C2×#95—731no—
546C2×#95—731no—
547C2×#95—731no—
548C2×#95—731no—
549C2×#95—731no—
550C2×#95—731no—
551C2×#95—731no—
552C2×#95—731no—
553C2×#95—731no—
554C2×#95—731no—
555C2×#95—731no—
556C2×#95—731no—
557C2×#95—731no—
558C2×#95C2×D7311yescharacteristic
559C2×#95C2×D7311yescharacteristic
560C2×#95C2×D7311yescharacteristic
561C25C22×D7311yescharacteristic
562C23×C4—731no—
563C23×C4—734no—
564C23×C4—731no—
565C23×C4—731no—
566C23×C4—731no—
567C23×C4—731no—
568C23×C4—731no—
569C23×C4—731no—
570C23×C4—731no—
571C23×C4—1462no—
572C23×C4—1462no—
573C23×C4—1462no—
574C23×C4—1462no—
575C23×C4—1462no—
576C23×C4—1462no—
577C23×C4C22×D7311yescharacteristic
578C23×C4C22×D7311yescharacteristic
579C23×C4C22×D7311yescharacteristic
580C23×C4C22×D7311yescharacteristic
581C23×C4C22×D7311yescharacteristic
582C23×C4C22×D7311yescharacteristic
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—1462no—
587C2×C4⋊C4—1462no—
588C2×C4⋊C4—1462no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—734no—
598C2×C22⋊C4—1462no—
599C2×C22⋊C4—1462no—
600C2×C22⋊C4—1462no—
601C2×C22⋊C4—1462no—
602C2×C22⋊C4—1462no—
603C2×C22⋊C4—1462no—
604C2×C22⋊C4—1462no—
605C2×C22⋊C4—1462no—
606C2×C22⋊C4C4×D7314yes—
607C2×C42—734no—
608C2×C42—734no—
609C2×C42—734no—
610C2×C42—734no—
611C2×C42—1462no—
612C2×C42—1462no—
613C2×C42—1462no—
614C2×C42—1462no—
615C2×C42—1462no—
616C2×C42—1462no—
617C2×C42—1462no—
618C2×C42—1462no—
619C2×C42—1462no—
620C2×C42—1462no—
621C2×C42—1462no—
622C2×C42—1462no—
623C2×C42—1462no—
624C2×C42—1462no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—734no—
629#95—734no—
630#95—1462no—
631#95—1462no—
632#95—1462no—
633#95—1462no—
634#95—1462no—
635#95—1462no—
636#95—1462no—
637#95—1462no—
638#95—1462no—
639#95—1462no—
640#95—1462no—
641#95—1462no—
642#95—1462no—
643#95—1462no—
644#95—1462no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24C2×C4×D7312yes—
658C24#1192402712yes—
659C24#1192402912yes—
660C24C23×D7311yescharacteristic
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—2924no—
696C22×C4—2924no—
697C22×C4—2924no—
698C22×C4—2924no—
699C22×C4—732no—
700C22×C4—732no—
701C22×C4—732no—
702C22×C4—732no—
703C22×C4—732no—
704C22×C4—732no—
705C22×C4—732no—
706C22×C4—732no—
707C22×C4—732no—
708C22×C4—732no—
709C22×C4—732no—
710C22×C4—732no—
711C22×C4—732no—
712C22×C4—732no—
713C22×C4—1468no—
714C22×C4—1468no—
715C22×C4—1468no—
716C22×C4—1461no—
717C22×C4—1461no—
718C22×C4—1461no—
719C22×C4—1461no—
720C22×C4—1461no—
721C22×C4—1461no—
722C22×C4—1461no—
723C22×C4—1461no—
724C22×C4—1461no—
725C22×C4—1461no—
726C22×C4—1461no—
727C22×C4—1461no—
728C22×C4—1461no—
729C22×C4—1461no—
730C22×C4—1461no—
731C22×C4—1461no—
732C22×C4—1461no—
733C22×C4—1461no—
734C22×C4—1461no—
735C22×C4—1461no—
736C22×C4—1461no—
737C22×C4—1461no—
738C22×C4—1461no—
739C22×C4—1461no—
740C22×C4—1461no—
741C22×C4—1461no—
742C22×C4—1461no—
743C22×C4—1461no—
744C22×C4—1461no—
745C22×C4—1461no—
746C22×C4—1461no—
747C22×C4—1461no—
748C22×C4—1461no—
749C22×C4—1461no—
750C22×C4—1461no—
751C22×C4—1461no—
752C22×C4—1461no—
753C22×C4—1461no—
754C22×C4—1461no—
755C22×C4—1461no—
756C22×C4—1461no—
757C22×C4—1461no—
758C22×C4C2×C4×D7312yes—
759C22×C4C2×C4×D7312yes—
760C22×C4D4×D7312yes—
761C22×C4D4×D7312yes—
762C22×C4#1192402712yes—
763C22×C4#1192402712yes—
764C22×C4#1192402712yes—
765C22×C4#1192402712yes—
766C4⋊C4—28no—
767C4⋊C4—1468no—
768C22⋊C4—28no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—1468no—
772C22⋊C4—1468no—
773C22⋊C4—1468no—
774C42—2924no—
775C42—2924no—
776C42—1468no—
777C42—1468no—
778C42—1468no—
779C42—1468no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23#1455654914yes—
815C23C22×C4×D7311yescharacteristic
816C23C2×D4×D7311yescharacteristic
817C23C2×D4×D7311yescharacteristic
818C23#41×D7311yescharacteristic
819C23#41×D7311yescharacteristic
820C23#41×D7311yescharacteristic
821C23#41×D7311yescharacteristic
822C23#41×D7311yescharacteristic
823C23#41×D7311yescharacteristic
824C23C2×#1192402711yescharacteristic
825C23C2×#1192402711yescharacteristic
826C23C2×#1192402711yescharacteristic
827C23C2×#1192402711yescharacteristic
828C23C2×#1192402711yescharacteristic
829C23C2×#1192402911yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—2921no—
872C2×C4—2921no—
873C2×C4—2921no—
874C2×C4—2921no—
875C2×C4—2921no—
876C2×C4—2921no—
877C2×C4—2921no—
878C2×C4—2921no—
879C2×C4—2921no—
880C2×C4—2921no—
881C2×C4—2921no—
882C2×C4—2921no—
883C2×C4—2921no—
884C2×C4—2921no—
885C2×C4—2921no—
886C2×C4—2921no—
887C2×C4—2921no—
888C2×C4—2921no—
889C2×C4—2921no—
890C2×C4—2921no—
891C2×C4—2921no—
892C2×C4—2921no—
893C2×C4—2921no—
894C2×C4—2921no—
895C2×C4—2921no—
896C2×C4—2921no—
897C2×C4—2921no—
898C2×C4—2921no—
899C2×C4—29216no—
900C2×C4—734no—
901C2×C4—734no—
902C2×C4—734no—
903C2×C4—734no—
904C2×C4—734no—
905C2×C4—734no—
906C2×C4—734no—
907C2×C4—1462no—
908C2×C4—1462no—
909C2×C4—1462no—
910C2×C4—1462no—
911C2×C4—1462no—
912C2×C4—1462no—
913C2×C4—1462no—
914C2×C4—1462no—
915C2×C4—1462no—
916C2×C4—1462no—
917C2×C4—1462no—
918C2×C4—1462no—
919C2×C4—1462no—
920C2×C4—1462no—
921C2×C4—1462no—
922C2×C4—1462no—
923C2×C4—1462no—
924C2×C4—1462no—
925C2×C4—1462no—
926C2×C4—1462no—
927C2×C4—1462no—
928C2×C4#1455654714yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22#117×D7311yescharacteristic
945C22C2×#1455654711yescharacteristic
946C22C2×#1455654911yescharacteristic
947C22C4×D4×D7311yescharacteristic
948C22C4×D4×D7311yescharacteristic
949C22C4×#1192402711yescharacteristic
950C22C4×#1192402711yescharacteristic
951C22#121×D7311yescharacteristic
952C22#123×D7311yescharacteristic
953C22#1798909311yescharacteristic
954C22#1798909311yescharacteristic
955C22#1798909311yescharacteristic
956C22#1798909711yescharacteristic
957C22#1798910011yescharacteristic
958C22#1798910011yescharacteristic
959C22#124×D7311yescharacteristic
960C22#126×D7311yescharacteristic
961C22#1798911411yescharacteristic
962C22#1798911411yescharacteristic
963C22#1798911411yescharacteristic
964C22#1798911411yescharacteristic
965C22#1798911611yescharacteristic
966C22#1798911611yescharacteristic
967C22#1798911811yescharacteristic
968C22#1798911811yescharacteristic
969C22#1798911811yescharacteristic
970C22#1798911811yescharacteristic
971C22#1798911811yescharacteristic
972C22#1798912011yescharacteristic
973C22#1798912311yescharacteristic
974C22#1798912311yescharacteristic
975C22#1798912311yescharacteristic
976C22#1798912311yescharacteristic
977C22#1798913211yescharacteristic
978C22#1798913511yescharacteristic
979C4—24no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—2922no—
986C4—2922no—
987C4—2922no—
988C4—2922no—
989C4—2922no—
990C4—2922no—
991C4—2922no—
992C4—738no—
993C2—44no—
994C2#2261232611yescharacteristic
995C2#388×D7311yescharacteristic
996C2#2261236711yescharacteristic
997C2#2261236711yescharacteristic
998C2#2261237111yescharacteristic
999C2#2261239311yescharacteristic
1000C2#2261242511yescharacteristic
1001C2#2261316611yescharacteristic
1002C2#2261317611yescharacteristic
1003C2#2261318711yescharacteristic
1004C2#2261319611yescharacteristic
1005C2#2261321311yescharacteristic
1006C2#2261321911yescharacteristic
1007C2#2261322811yescharacteristic
1008C2#2261323311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC73×#1439C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenter#1439D73
hypocenterC73#13842
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×Dic73C2semidirect
5. C2×#17988432C2semidirect
6. #22608192C2semidirect
7. #22608191C2semidirect
8. #22608190C2semidirect
9. #22608187C2semidirect
13. #95×Dic73C2semidirect
14. #95×Dic73C2semidirect
30. C22⋊C4×Dic73C4semidirect
520. C73#13842semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic732
C2×C22⋊C4×Dic732
C2×#179884322
#226081922
#226081912
#226081902
#226081872
#226081782
#226081762
#95×Dic732
C73×#14392
#1384273