Finite Group Databasebeta

← C73×#22062 #32931466

Subgroups — C73×#22062 #32931466

Order 18688.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3002C211yesmaximal, characteristic
2C73×#2930C211yesmaximal, characteristic, complemented
3C73×#2879C211yesmaximal, characteristic, complemented
4C73×#1975C211yesmaximal, characteristic, complemented
5C73×#1974C211yesmaximal, characteristic, complemented
6C73×#1938C211yesmaximal, characteristic, complemented
7C73×#1937C211yesmaximal, characteristic, complemented
8C73×#1929C211yesmaximal, characteristic, complemented
9C73×#1929C211yesmaximal, characteristic, complemented
10C73×#1876C211yesmaximal, characteristic, complemented
11C73×#1876C211yesmaximal, characteristic, complemented
12C73×#1871C211yesmaximal, characteristic, complemented
13C73×#1855C211yesmaximal, characteristic, complemented
14C73×#1789C211yesmaximal, characteristic, complemented
15C73×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C2×#135×C73C2211yescharacteristic
18C2×#135×C73C2211yescharacteristic
19C2×#131×C73C2211yescharacteristic, complemented
20C22×M16×C73C2211yescharacteristic
21C22×M16×C73C2211yescharacteristic
22#525×C73C2211yescharacteristic
23#452×C73C411yescharacteristic, complemented
24#452×C73C411yescharacteristic, complemented
25#451×C73C411yescharacteristic, complemented
26#450×C73C411yescharacteristic, complemented
27#449×C73C411yescharacteristic, complemented
28#449×C73C411yescharacteristic, complemented
29#448×C73C411yescharacteristic, complemented
30#447×C73C411yescharacteristic, complemented
31#436×C73—21no—
32#436×C73—21no—
33#435×C73—21no—
34#435×C73—21no—
35C2×#108×C73C2211yescharacteristic, complemented
36C2×#108×C73C2211yescharacteristic, complemented
37#424×C73C2211yescharacteristic, complemented
38C2×#104×C73C2211yescharacteristic
39C2×#104×C73C2211yescharacteristic
40C2×#104×C73C2211yescharacteristic
41C2×#104×C73C2211yescharacteristic
42C2×#104×C73C2211yescharacteristic, complemented
43C2×#104×C73C2211yescharacteristic, complemented
44#416×C73C2211yescharacteristic
45#416×C73C2211yescharacteristic
46#408×C73—21no—
47#408×C73—21no—
48#408×C73C2211yescharacteristic
49#408×C73C2211yescharacteristic
50#408×C73C2211yescharacteristic
51#408×C73C2211yescharacteristic
52#408×C73C2211yescharacteristic, complemented
53#407×C73—21no—
54#407×C73—21no—
55#407×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57#405×C73C2211yescharacteristic, complemented
58C2×#97×C73C2211yescharacteristic, complemented
59C2×C4×C8×C73C2211yescharacteristic, complemented
60C4×C22⋊C4×C73C2211yescharacteristic
61#341×C73C2211yescharacteristic, complemented
62#341×C73C2211yescharacteristic, complemented
63#339×C73C2211yescharacteristic, complemented
64#339×C73C2211yescharacteristic, complemented
65#336×C73C2211yescharacteristic, complemented
66#336×C73C2211yescharacteristic, complemented
67C2×#41×C73—21no—
68C2×#41×C73—21no—
69C2×#41×C73—41no—
70C2×#41×C73—41no—
71C2×#41×C73—41no—
72C2×#41×C73—41no—
73C2×#41×C73C2×C411yescharacteristic
74C2×#41×C73C2×C411yescharacteristic
75C2×#41×C73C2311yescharacteristic
76C2×#41×C73C2311yescharacteristic
77C2×#41×C73C2311yescharacteristic
78C22×Q8×C73C2×C411yescharacteristic
79C22×D4×C73—21no—
80C22×D4×C73C2×C411yescharacteristic
81C23×C4×C73—21no—
82C23×C4×C73C2311yescharacteristic
83#135×C73—41no—
84#135×C73—41no—
85#135×C73—41no—
86#135×C73—41no—
87C2×Q16×C73C2×C411yescharacteristic
88C2×Q16×C73C2×C411yescharacteristic
89C2×SD16×C73C2×C411yescharacteristic
90C2×SD16×C73C2×C411yescharacteristic
91C2×SD16×C73C2×C411yescharacteristic
92C2×SD16×C73C2×C411yescharacteristic
93C2×D8×C73C2×C411yescharacteristic
94C2×D8×C73C2×C411yescharacteristic
95#131×C73—41no—
96#131×C73—41no—
97C2×M16×C73—21no—
98C2×M16×C73—21no—
99C2×M16×C73—41no—
100C2×M16×C73—41no—
101C2×M16×C73—41no—
102C2×M16×C73—41no—
103C2×M16×C73D411yescharacteristic
104C2×M16×C73D411yescharacteristic
105C2×M16×C73D411yescharacteristic
106C2×M16×C73D411yescharacteristic
107C2×M16×C73C2311yescharacteristic
108C2×M16×C73C2311yescharacteristic
109C2×M16×C73C2311yescharacteristic
110C2×M16×C73C2311yescharacteristic
111C22×C8×C73—21no—
112C22×C8×C73—21no—
113C22×C8×C73C2311yescharacteristic
114C22×C8×C73C2311yescharacteristic
115C22×C8×C73C2311yescharacteristic
116C22×C8×C73C2311yescharacteristic
117#123×C73—21no—
118C22⋊Q8×C73C2×C411yescharacteristic
119C22⋊Q8×C73C2×C411yescharacteristic
120#121×C73C2×C411yescharacteristic
121#121×C73C2×C411yescharacteristic
122#120×C73—21no—
123C4×D4×C73—21no—
124C4×D4×C73—21no—
125#117×C73C2311yescharacteristic
126C2×C22⋊C4×C73—21no—
127C2×C42×C73C2311yescharacteristic
128C2×C42×C73C2311yescharacteristic
129#108×C73—41no—
130#108×C73—41no—
131C4⋊C8×C73—21no—
132C4⋊C8×C73—21no—
133#104×C73—41no—
134#104×C73—41no—
135#104×C73—41no—
136#104×C73—41no—
137#104×C73—41no—
138#104×C73—41no—
139#103×C73C2×C411yescharacteristic
140#103×C73C2×C411yescharacteristic
141#103×C73C2×C411yescharacteristic
142#103×C73C2×C411yescharacteristic
143#102×C73C2×C411yescharacteristic
144#102×C73C2×C411yescharacteristic
145#102×C73C2×C411yescharacteristic
146#102×C73C2×C411yescharacteristic
147C22⋊C8×C73—21no—
148C22⋊C8×C73—21no—
149C22⋊C8×C73—21no—
150C22⋊C8×C73—21no—
151C22⋊C8×C73—21no—
152C22⋊C8×C73—21no—
153C22⋊C8×C73—21no—
154C22⋊C8×C73—21no—
155C22⋊C8×C73—21no—
156C22⋊C8×C73—21no—
157C22⋊C8×C73—21no—
158C22⋊C8×C73—21no—
159C22⋊C8×C73C2×C411yescharacteristic
160C22⋊C8×C73C2×C411yescharacteristic
161C22⋊C8×C73C2×C411yescharacteristic
162C22⋊C8×C73C2×C411yescharacteristic
163#97×C73—21no—
164#97×C73—41no—
165C4×C8×C73—21no—
166C4×C8×C73—41no—
167#95×C73—21no—
168C24×C73—21no—
169C24×C73#4111yescharacteristic
170#41×C73—21no—
171#41×C73—21no—
172#41×C73—21no—
173#41×C73—21no—
174#41×C73—21no—
175#41×C73—21no—
176#41×C73—21no—
177#41×C73—21no—
178#41×C73—21no—
179#41×C73—21no—
180#41×C73—21no—
181#41×C73—21no—
182#41×C73—41no—
183#41×C73—41no—
184#41×C73—41no—
185#41×C73—41no—
186#41×C73—42no—
187#41×C73—42no—
188#41×C73—42no—
189#41×C73—42no—
190C2×Q8×C73—21no—
191C2×Q8×C73—41no—
192C2×Q8×C73—41no—
193C2×Q8×C73C22×C411yescharacteristic
194C2×Q8×C73C22×C411yescharacteristic
195C2×Q8×C73C22×C411yescharacteristic
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—21no—
202C2×D4×C73—21no—
203C2×D4×C73—21no—
204C2×D4×C73—41no—
205C2×D4×C73—41no—
206C2×D4×C73—42no—
207C2×D4×C73—42no—
208C2×D4×C73C22×C411yescharacteristic
209C2×D4×C73C22×C411yescharacteristic
210C2×D4×C73C22×C411yescharacteristic
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—42no—
224C22×C4×C73—42no—
225C22×C4×C73C22×C411yescharacteristic
226C22×C4×C73C22×C411yescharacteristic
227C22×C4×C73C2×D411yescharacteristic
228C22×C4×C73C2×D411yescharacteristic
229C22×C4×C73#4111yescharacteristic
230C22×C4×C73C2411yescharacteristic
231Q16×C73—41no—
232Q16×C73—41no—
233SD16×C73—41no—
234SD16×C73—41no—
235SD16×C73—41no—
236SD16×C73—41no—
237D8×C73—41no—
238D8×C73—41no—
239M16×C73—21no—
240M16×C73—21no—
241M16×C73—21no—
242M16×C73—21no—
243M16×C73—21no—
244M16×C73—21no—
245M16×C73—21no—
246M16×C73—21no—
247M16×C73—41no—
248M16×C73—41no—
249M16×C73—41no—
250M16×C73—41no—
251M16×C73—42no—
252M16×C73—42no—
253C2×C8×C73—21no—
254C2×C8×C73—21no—
255C2×C8×C73—21no—
256C2×C8×C73—21no—
257C2×C8×C73—21no—
258C2×C8×C73—21no—
259C2×C8×C73—21no—
260C2×C8×C73—21no—
261C2×C8×C73—21no—
262C2×C8×C73—21no—
263C2×C8×C73—21no—
264C2×C8×C73—21no—
265C2×C8×C73—42no—
266C2×C8×C73—42no—
267C2×C8×C73C22×C411yescharacteristic
268C2×C8×C73C22×C411yescharacteristic
269C2×C8×C73C22×C411yescharacteristic
270C2×C8×C73C22×C411yescharacteristic
271C2×C8×C73C2×D411yescharacteristic
272C2×C8×C73C2×D411yescharacteristic
273C2×C8×C73C2×D411yescharacteristic
274C2×C8×C73C2×D411yescharacteristic
275C4⋊C4×C73—21no—
276C4⋊C4×C73—21no—
277C4⋊C4×C73C22×C411yescharacteristic
278C4⋊C4×C73C22×C411yescharacteristic
279C22⋊C4×C73—21no—
280C22⋊C4×C73—21no—
281C22⋊C4×C73—21no—
282C22⋊C4×C73—21no—
283C22⋊C4×C73—21no—
284C22⋊C4×C73—42no—
285C42×C73—21no—
286C42×C73—21no—
287C42×C73—21no—
288C42×C73—21no—
289C42×C73—21no—
290C23×C73—21no—
291C23×C73—21no—
292C23×C73—21no—
293C23×C73—21no—
294C23×C73—21no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—42no—
298C23×C73—81no—
299C23×C73—81no—
300C23×C73C4×D411yescharacteristic
301C23×C73C4×D411yescharacteristic
302C23×C73C2×#4111yescharacteristic
303Q8×C73—21no—
304Q8×C73—21no—
305Q8×C73—21no—
306Q8×C73—21no—
307Q8×C73—21no—
308Q8×C73—21no—
309Q8×C73—42no—
310D4×C73—21no—
311D4×C73—21no—
312D4×C73—21no—
313D4×C73—21no—
314D4×C73—21no—
315D4×C73—21no—
316D4×C73—42no—
317D4×C73—42no—
318D4×C73—42no—
319D4×C73—41no—
320D4×C73—41no—
321D4×C73—41no—
322D4×C73—41no—
323D4×C73—41no—
324D4×C73—41no—
325D4×C73—81no—
326D4×C73—81no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—21no—
332C2×C4×C73—21no—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—21no—
337C2×C4×C73—22no—
338C2×C4×C73—21no—
339C2×C4×C73—21no—
340C2×C4×C73—21no—
341C2×C4×C73—21no—
342C2×C4×C73—21no—
343C2×C4×C73—42no—
344C2×C4×C73—42no—
345C2×C4×C73—41no—
346C2×C4×C73—42no—
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×C73C4×D411yescharacteristic
358C2×C4×C73C4×D411yescharacteristic
359C2×C4×C73C23×C411yescharacteristic
360C2×C4×C73C22×D411yescharacteristic
361C2×C4×C73H(5,𝔽2)11yescharacteristic
362C2×C4×C73H(5,𝔽2)11yescharacteristic
363C2×C4×C73H(5,𝔽2)11yescharacteristic
364C2×C4×C73H(5,𝔽2)11yescharacteristic
365C8×C73—21no—
366C8×C73—21no—
367C8×C73—21no—
368C8×C73—21no—
369C8×C73—21no—
370C8×C73—21no—
371C8×C73—21no—
372C8×C73—21no—
373C8×C73—41no—
374C8×C73—41no—
375C8×C73—41no—
376C8×C73—41no—
377C22×C73—21no—
378C22×C73—21no—
379C22×C73—21no—
380C22×C73—21no—
381C22×C73—21no—
382C22×C73—21no—
383C22×C73—21no—
384C22×C73—21no—
385C22×C73—41no—
386C22×C73—41no—
387C22×C73—41no—
388C22×C73—41no—
389C22×C73—41no—
390C22×C73—41no—
391C22×C73—41no—
392C22×C73—41no—
393C22×C73—41no—
394C22×C73—81no—
395C22×C73—81no—
396C22×C73—84no—
397C22×C73C2×C4×D411yescharacteristic
398C22×C73#53811yescharacteristic
399C22×C73#53811yescharacteristic
400C4×C73—21no—
401C4×C73—21no—
402C4×C73—42no—
403C4×C73—41no—
404C4×C73—41no—
405C4×C73—41no—
406C4×C73—41no—
407C4×C73—41no—
408C4×C73—81no—
409C4×C73#51811yescharacteristic
410C4×C73#51811yescharacteristic
411C4×C73#53411yescharacteristic
412C4×C73#53511yescharacteristic
413#22062C7311yesmaximal, characteristic, direct product factor, Sylow
414C2×C73—21no—
415C2×C73—21no—
416C2×C73—41no—
417C2×C73—41no—
418C2×C73—81no—
419C2×C73—81no—
420C2×C73—81no—
421C2×C73#232111yescharacteristic
422C2×C73#295611yescharacteristic
423C2×C73#295711yescharacteristic
424#3002C2×C7311yescharacteristic
425#2930C2×C7311yescharacteristic, complemented
426#2879C2×C7311yescharacteristic, complemented
427#1975C2×C7311yescharacteristic, complemented
428#1974C2×C7311yescharacteristic, complemented
429#1938C2×C7311yescharacteristic, complemented
430#1937C2×C7311yescharacteristic, complemented
431#1929C2×C7311yescharacteristic, complemented
432#1929C2×C7311yescharacteristic, complemented
433#1876C2×C7311yescharacteristic, complemented
434#1876C2×C7311yescharacteristic, complemented
435#1871C2×C7311yescharacteristic, complemented
436#1855C2×C7311yescharacteristic, complemented
437#1789C2×C7311yescharacteristic, complemented
438#1753C2×C7311yescharacteristic, complemented
439C73#2206211yescharacteristic, direct product factor, Sylow
440C22×#41C22×C7311yescharacteristic
441C2×#135C22×C7311yescharacteristic
442C2×#135C22×C7311yescharacteristic
443C2×#131C22×C7311yescharacteristic, complemented
444C22×M16C22×C7311yescharacteristic
445C22×M16C22×C7311yescharacteristic
446#525C22×C7311yescharacteristic
447#452C4×C7311yescharacteristic, complemented
448#452C4×C7311yescharacteristic, complemented
449#451C4×C7311yescharacteristic, complemented
450#450C4×C7311yescharacteristic, complemented
451#449C4×C7311yescharacteristic, complemented
452#449C4×C7311yescharacteristic, complemented
453#448C4×C7311yescharacteristic, complemented
454#447C4×C7311yescharacteristic, complemented
455#436—21no—
456#436—21no—
457#435—21no—
458#435—21no—
459C2×#108C22×C7311yescharacteristic, complemented
460C2×#108C22×C7311yescharacteristic, complemented
461#424C22×C7311yescharacteristic, complemented
462C2×#104C22×C7311yescharacteristic
463C2×#104C22×C7311yescharacteristic
464C2×#104C22×C7311yescharacteristic
465C2×#104C22×C7311yescharacteristic
466C2×#104C22×C7311yescharacteristic, complemented
467C2×#104C22×C7311yescharacteristic, complemented
468#416C22×C7311yescharacteristic
469#416C22×C7311yescharacteristic
470#408—21no—
471#408—21no—
472#408C22×C7311yescharacteristic
473#408C22×C7311yescharacteristic
474#408C22×C7311yescharacteristic
475#408C22×C7311yescharacteristic
476#408C22×C7311yescharacteristic, complemented
477#407—21no—
478#407—21no—
479#407C22×C7311yescharacteristic
480C2×C22⋊C8C22×C7311yescharacteristic
481#405C22×C7311yescharacteristic, complemented
482C2×#97C22×C7311yescharacteristic, complemented
483C2×C4×C8C22×C7311yescharacteristic, complemented
484C4×C22⋊C4C22×C7311yescharacteristic
485#341C22×C7311yescharacteristic, complemented
486#341C22×C7311yescharacteristic, complemented
487#339C22×C7311yescharacteristic, complemented
488#339C22×C7311yescharacteristic, complemented
489#336C22×C7311yescharacteristic, complemented
490#336C22×C7311yescharacteristic, complemented
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41C2×C4×C7311yescharacteristic
498C2×#41C2×C4×C7311yescharacteristic
499C2×#41C23×C7311yescharacteristic
500C2×#41C23×C7311yescharacteristic
501C2×#41C23×C7311yescharacteristic
502C22×Q8C2×C4×C7311yescharacteristic
503C22×D4—21no—
504C22×D4C2×C4×C7311yescharacteristic
505C23×C4—21no—
506C23×C4C23×C7311yescharacteristic
507#135—41no—
508#135—41no—
509#135—41no—
510#135—41no—
511C2×Q16C2×C4×C7311yescharacteristic
512C2×Q16C2×C4×C7311yescharacteristic
513C2×SD16C2×C4×C7311yescharacteristic
514C2×SD16C2×C4×C7311yescharacteristic
515C2×SD16C2×C4×C7311yescharacteristic
516C2×SD16C2×C4×C7311yescharacteristic
517C2×D8C2×C4×C7311yescharacteristic
518C2×D8C2×C4×C7311yescharacteristic
519#131—41no—
520#131—41no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16D4×C7311yescharacteristic
528C2×M16D4×C7311yescharacteristic
529C2×M16D4×C7311yescharacteristic
530C2×M16D4×C7311yescharacteristic
531C2×M16C23×C7311yescharacteristic
532C2×M16C23×C7311yescharacteristic
533C2×M16C23×C7311yescharacteristic
534C2×M16C23×C7311yescharacteristic
535C22×C8—21no—
536C22×C8—21no—
537C22×C8C23×C7311yescharacteristic
538C22×C8C23×C7311yescharacteristic
539C22×C8C23×C7311yescharacteristic
540C22×C8C23×C7311yescharacteristic
541#123—21no—
542C22⋊Q8C2×C4×C7311yescharacteristic
543C22⋊Q8C2×C4×C7311yescharacteristic
544#121C2×C4×C7311yescharacteristic
545#121C2×C4×C7311yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C23×C7311yescharacteristic
550C2×C22⋊C4—21no—
551C2×C42C23×C7311yescharacteristic
552C2×C42C23×C7311yescharacteristic
553#108—41no—
554#108—41no—
555C4⋊C8—21no—
556C4⋊C8—21no—
557#104—41no—
558#104—41no—
559#104—41no—
560#104—41no—
561#104—41no—
562#104—41no—
563#103C2×C4×C7311yescharacteristic
564#103C2×C4×C7311yescharacteristic
565#103C2×C4×C7311yescharacteristic
566#103C2×C4×C7311yescharacteristic
567#102C2×C4×C7311yescharacteristic
568#102C2×C4×C7311yescharacteristic
569#102C2×C4×C7311yescharacteristic
570#102C2×C4×C7311yescharacteristic
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8—21no—
583C22⋊C8C2×C4×C7311yescharacteristic
584C22⋊C8C2×C4×C7311yescharacteristic
585C22⋊C8C2×C4×C7311yescharacteristic
586C22⋊C8C2×C4×C7311yescharacteristic
587#97—21no—
588#97—41no—
589C4×C8—21no—
590C4×C8—41no—
591#95—21no—
592C24—21no—
593C24#41×C7311yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×C4×C7311yescharacteristic
618C2×Q8C22×C4×C7311yescharacteristic
619C2×Q8C22×C4×C7311yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×C4×C7311yescharacteristic
633C2×D4C22×C4×C7311yescharacteristic
634C2×D4C22×C4×C7311yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4C22×C4×C7311yescharacteristic
650C22×C4C22×C4×C7311yescharacteristic
651C22×C4C2×D4×C7311yescharacteristic
652C22×C4C2×D4×C7311yescharacteristic
653C22×C4#41×C7311yescharacteristic
654C22×C4C24×C7311yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—41no—
672M16—41no—
673M16—41no—
674M16—41no—
675M16—42no—
676M16—42no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8C22×C4×C7311yescharacteristic
692C2×C8C22×C4×C7311yescharacteristic
693C2×C8C22×C4×C7311yescharacteristic
694C2×C8C22×C4×C7311yescharacteristic
695C2×C8C2×D4×C7311yescharacteristic
696C2×C8C2×D4×C7311yescharacteristic
697C2×C8C2×D4×C7311yescharacteristic
698C2×C8C2×D4×C7311yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×C4×C7311yescharacteristic
702C4⋊C4C22×C4×C7311yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—42no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23C4×D4×C7311yescharacteristic
725C23C4×D4×C7311yescharacteristic
726C23C2×#41×C7311yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4C4×D4×C7311yescharacteristic
782C2×C4C4×D4×C7311yescharacteristic
783C2×C4C23×C4×C7311yescharacteristic
784C2×C4C22×D4×C7311yescharacteristic
785C2×C4H(5,𝔽2)×C7311yescharacteristic
786C2×C4H(5,𝔽2)×C7311yescharacteristic
787C2×C4H(5,𝔽2)×C7311yescharacteristic
788C2×C4H(5,𝔽2)×C7311yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—41no—
798C8—41no—
799C8—41no—
800C8—41no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×C4×D4×C7311yescharacteristic
822C22#538×C7311yescharacteristic
823C22#538×C7311yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—81no—
833C4#518×C7311yescharacteristic
834C4#518×C7311yescharacteristic
835C4#534×C7311yescharacteristic
836C4#535×C7311yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2C73×#232111yescharacteristic
845C2C73×#295611yescharacteristic
846C2C73×#295711yescharacteristic
subgroupG/H
centerC2×C4×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
socleC22×C73C2×C4×D4
prime radicalC73×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C73 ◁ C22×M16×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#2930C2semidirect
3. C73×#2879C2semidirect
4. C73×#1975C2semidirect
5. C73×#1974C2semidirect
6. C73×#1938C2semidirect
7. C73×#1937C2semidirect
8. C73×#1929C2semidirect
9. C73×#1929C2semidirect
10. C73×#1876C2semidirect
11. C73×#1876C2semidirect
12. C73×#1871C2semidirect
13. C73×#1855C2semidirect
14. C73×#1789C2semidirect
15. C73×#1753C2semidirect
19. C2×#131×C73C22semidirect
23. #452×C73C4semidirect
24. #452×C73C4semidirect
25. #451×C73C4semidirect
26. #450×C73C4semidirect
27. #449×C73C4semidirect
28. #449×C73C4semidirect
29. #448×C73C4semidirect
30. #447×C73C4semidirect
35. C2×#108×C73C22semidirect
36. C2×#108×C73C22semidirect
37. #424×C73C22semidirect
42. C2×#104×C73C22semidirect
43. C2×#104×C73C22semidirect
52. #408×C73C22semidirect
57. #405×C73C22semidirect
58. C2×#97×C73C22semidirect
59. C2×C4×C8×C73C22semidirect
61. #341×C73C22semidirect
62. #341×C73C22semidirect
63. #339×C73C22semidirect
64. #339×C73C22semidirect
65. #336×C73C22semidirect
66. #336×C73C22semidirect
413. #22062C73direct (N × H)
425. #2930C2×C73semidirect
426. #2879C2×C73semidirect
427. #1975C2×C73semidirect
428. #1974C2×C73semidirect
429. #1938C2×C73semidirect
430. #1937C2×C73semidirect
431. #1929C2×C73semidirect
432. #1929C2×C73semidirect
433. #1876C2×C73semidirect
434. #1876C2×C73semidirect
435. #1871C2×C73semidirect
436. #1855C2×C73semidirect
437. #1789C2×C73semidirect
438. #1753C2×C73semidirect
439. C73#22062direct (N × H)
443. C2×#131C22×C73semidirect
447. #452C4×C73semidirect
448. #452C4×C73semidirect
449. #451C4×C73semidirect
450. #450C4×C73semidirect
451. #449C4×C73semidirect
452. #449C4×C73semidirect
453. #448C4×C73semidirect
454. #447C4×C73semidirect
459. C2×#108C22×C73semidirect
460. C2×#108C22×C73semidirect
461. #424C22×C73semidirect
466. C2×#104C22×C73semidirect
467. C2×#104C22×C73semidirect
476. #408C22×C73semidirect
481. #405C22×C73semidirect
482. C2×#97C22×C73semidirect
483. C2×C4×C8C22×C73semidirect
485. #341C22×C73semidirect
486. #341C22×C73semidirect
487. #339C22×C73semidirect
488. #339C22×C73semidirect
489. #336C22×C73semidirect
490. #336C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#30022
C73×#29302
C73×#28792
C73×#19752
C73×#19742
C73×#19382
C73×#19372
C73×#19292
C73×#18762
C73×#18712
C73×#18552
C73×#17892
C73×#17532
#2206273